Advances in
Cryogenic Engineering
VOLUME 211
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A Cryogenic Engineering Conference Publication
Advances in
Cryogenic Engineering
VOLUME 25
Edlted by
K. D. Tlmmerhaus
Engineering Research Center
University of Colorado
Boulder, Colorado
and
H. A. Snyder
Department of Aerospace Engineering Seiences
University of Colorado
Boulder, Colorado
SPRINGER SCIENCE+BUSINESS MEDIA, LLC
The Library of Congress cataloged the first volume of this title as follows:
Advances in cryogenic engineering. v. 1New York, Cryogenic Engineering Conference; distributed
by Plenum Press, 1960v. illus., diagrs. 26 cm.
are reprints of the Proceedings of the Cryogenic Engineering
Vols. 1Conference, 1954K. O. Timmerhaus.
Editor: 19601. Low temperature engineering-Congresses.
ed. 11. Cryogenic Engineering Conference.
1. Timmerhaus, K. 0.,
660.29368
TP490.A3
57-35598
Proceedings of the 1979 Cryogenic Engineering Conference,
held at the University of Wisconsin, Madison, Wisconsin,
August 21-24, 1979.
Library of Congress Catalog Card Number 57-33598
ISBN 978-1-4613-9858-5
ISBN 978-1-4613-9856-1 (eBook)
DOI 10.1007/978-1-4613-9856-1
© 1980 Springer Science+Business Media New York
Originally published by Plenum Press, New York in 1980
Softcover re print of the hardcover 1st edition 1980
Ali rights reserved
No part of this book may be reproduced, stored in a retrieval system, or transmittild,
in any form or by any means, electronic, mechanical, photocopying, microfilming,
recording, or otherwise, without written permission from the Publisher
CONTENTS
Foreward ........................................................ .
Russen B. Scott Memorial Award ................................... .
Samuel C. Collins Award .......................................... .
1979 Cryogenic Engineering Conference Board ....................... .
Awards Committees ............................................... .
Acknowledgments ................................................ .
xii
xiii
xiv
XV
XV
XVI
Superconductivity Applications-MHD and Fusion Magnets
A-1
A-2
A-3
A-4
A-5
A-6
Superconducting MHD Magnet Engineering Program, P. G.
MARSTON, A. M. DAwsoN, D. B. MoNTGOMERY, and J. E. C.
WILLIAMS, Francis Bitter National Magnet Labaratory . . . . . . . . . . .
Impact of High-Current Operation on the Cost of
Superconducting Magnet Systems for Large-Scale MHD
Applications, R. J. THOME, R. D. PILLSBURY, H. R. SEGAL, and
B. 0. PEDERSON, Magnetic Corporation of America . . . . . . . . . . . . .
Final Design of a Superconducting MHD Magnet for the CoalFired Flow Facility at the University of Tennessee Space
Institute, S.-T. WANG, L. R. TuRNER, L. GENENS, W.
PELCZARSKI, J. HoFFMAN, J. GoNCZY, H. Luowm, R. C.
NIEMANN, K. F. MATAYA, and E. KRAFT, Argonne National
Laboratory, and W. YouNG, University of Wisconsin . . . . . . . . . . . .
Cryogenic Aspects of the UTSI-CFFF Superconducting Dipole
Magnet for MHD Research, R. C. NIEMANN, S.-T. WANG, J. W.
DAWSON, L. GENENS, R. P. SMITH, L. R. TURNER, J. D.
GoNCZY, J. HOFFMAN, and K. F. MATAYA, Argonne National
Laboratory, P. SMELSER, Independent Consultant, and P. C.
VANDER AREND and S. STOY, Cryogenic Consultants, Inc. . . . . . .
Safety Analysis of the UTSI-CFFF Superconducting Magnet, L.
R. TuRNER, S.-T. WANG, and R. P. SMITH, Argonne National
Laboratory, P. C. VANDER AREND, Cryogenic Consultants,
Inc., and Y.-H. Hsu, General Atomic Company . . . . . . . . . . . . . . . .
Engineering Aspects of Cryogenic Laser-Fusion Targets, D. L.
MusiNSKI, T. M. HENDERSON, R. J. SIMMS, and T. R.
PATTINSON, KMS Fusion, Inc., and R. B. JAcoas, R. B. Jacobs
Associates, Inc. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
12
19
30
39
49
Superconductivity Applications-Energy Transfer and Storage
B-1
Energy Transfer in a System of Superconductive Magnets, M.
MASUDA, T. SHINTOMI, and K. AsAJI, National Labaratory for High
Energy Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
V
61
vi
B-2
B-3
B--4
B-5
B-6
B-7
B-8
Contents
Thermal Cycle Tests of a Modeted Superconducting Transmission
Line, C. F. SINDT and P. R. LuoTKE, NBS Thermophysical
Properties Division . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Design of a 400-kJ Pulsed Energy Storage Coil, S. K. SINGH, C. J.
HEYNE, D. T. HACKWORTH, M. A. JANOCKO, P. W. EcKELS, and
J. H. MURPHY, Westinghouse Electric Corporation . . . . . . . . . . . . . .
Operating Characteristics of a 1.5-MJ Pulsed Superconducting
Coil, S. H. KIM, S.-T. WANG, and M. LIEBERG, Argonne
National Labaratory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-MJ Magnet for Superconductive Energy Storage, T.
SHINTOMI, M. MAsUDA, H. SATO, and K. AsAn, National
Labaratory for High Energy Physics . . . . . . . . . . . . . . . . . . . . . . . . . . .
Conceptual Design of a 20-MJ Superconducting Forced-Cooled
Ohmic-Heating Coil, S. K. SINGH, J. H. MURPHY, M. A.
JANOCKO, H. E. HALLER, D. C. LITz, and P. W. ·EcKELS,
Westinghouse Electric Corporation, and J. D. RoGERS and P.
TRULLEN, Los Alamos Scientific Labaratory . . . . . . . . . . . . . . . . . . . .
Shape Optimization Study for a Three-Tunnel Superconductive
.Iinergy Storage Magnet, M. N. EL-DERINI, University of
Petroleum and Minerals, and R. W. BooM, University of
Wisconsin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20-kA Power Supply for Large Superconductive Coils, M.
MASUDA, T. SHINTOMI, and K. AsAn, National Labaratory for
High Energy Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
69
81
90
98
105
114
120
Superconductivity Applications-Rotating Machinery
C-1
C-2
C-3
C--4
Superconducting Generator Design for Airborne Applications, B.
B. GAMBLE and T. A. KEIM, General Electric Company.........
Superconducting Field Winding for a 10-MVA Generator, K. A.
TEPPER, J. V. MINERVINI, and J. L. SMITH, Jr., Massachusetts
Institute of Technology............. ..........................
Conductive Armature Shielding Design Concepts for Slow-Speed
Superconducting Generators in the 40- to 400-MVA Range, S.
KuzNETSOV, Imperial College of Science and Technology.........
Optimization of Superconducting Cryoturbogenerator FieldWinding Parameters, B. I. VERKIN, I. S. ZHITOMIRSKII, and R.
V. GAVRILOV, Academy of Seiences of the Ukrainian SSR . . . . . .
127
137
145
156
Superconductivity Applications-Magnet Technology
D-1
D-2
D-3
Superconducting Compensating Solenoids for the CELLO Detector
Experiment at PETRA, W. BARTH, N. FESSLER-WILHELMI, W.
LEHMANN, and P. TUROWSKI, Kernforschungszentrum Karlsruhe
Construction and Test of the CELLO Thin-Wall Solenoid, H.
DESPORTES, J. LE BARS, and G. MAYAUX, Centre d'Etudes
Nuc/eaires de Sac/ay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Quenches in the Superconducting Magnet CELLO, W. V.
HASSENZAHL, Los Alamos Scientific Labaratory . . . . . . . . . . . . . . . .
163
175
185
Contents
D-4
D-5
D-6
D-7
D-8
Construction and Testing of the Two-Meter-Diameter TPC Thin
Superconducting Solenoid, M. A. GREEN, P. H. EBERHARD, R.
R. Ross, and J. D. TAYLOR, Lawrence Berkeley Laboratory . . . . .
Superconducting Magnet System for the Spirit Cosmic Ray Space
Telescope, M. A. GREEN and J. M. DEÜLIVARES, Lawrence
Berkeley Laboratory, and G. TARLE, P. B. PRICE, and E. K.
SHIRK, University of Ca/ifornia, Berkeley . . . . . . . . . . . . . . . . . . . . . .
A Maintainable Superconducting Magnet System for Tokamak
Fusion Reactors, S. Y. HsiEH, G. DANBY, J. R. PowELL, P.
BEZLER, D. GARDNER, and C. LAVERICK, Brookhaven National
Laboratory, and M. FINKELMAN, T. BROWN, J. BuNDY, T.
BALDERES, I. ZATZ, R. VERZERA, and R. HERBERMAN,
Grumman Aerospace Corporation . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Prototype Low-Current Superconducting Quadrupole Magnet for
Fermilab's High-Intensity Laboratory, W. CRADDOCK, R. W.
FAST, P. GARBINCIUS, and L. MAPALO, Fermi National
Accelerator Laboratory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Superconducting Magnets of the Biomedical Facility at SIN, J.
ZELLWEGER, G. VECSEY, and I. HoRVATH, SIN Swiss Institute
for Nuclear Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
vü
194
200
207
222
232
Superconductivity Applications-Cryogenic Techniques
E-1
E-2
E-3
E-4
A Novel Thermometer Sensor for the mK Region Using the
Proximity Effect, H. NAGANO, Y. ÜDA, and G. Fum, Tokyo
University . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A Superconducting RF Notch Filter, C. S. PANG, C. M. FALCO,
R. T. KAMPWIRTH, and I. K. ScHULLER, Argonne National
Laboratory, and J. J. HuoAK and T. A. ANASTASIO, Department
of Defense . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Experimental Evaluation of a 1-Meter-Scale D-Shaped Test Coil
Fabricated from a 23-Meter Length of Internally Cooled, Cabled
Superconductor, M. 0. HoENIG, A. G. MONTGOMERY, and S. J.
W ALDMAN, Francis Bitter National Magnet Laboratory . . . . . . . . . .
Performance of Gas-Filled Thermal Switches, J. YAMAMOTO,
Osaka University. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
239
244
251
261
Cooling Superconducting Systems
F-1
F-2
F-3
F-4
Transient Cooling of a Faultworthy Superconducting Electric
Generator, J. A. ScHWOERER and J. L. SMITH, Jr., Massachusetts
Institute of Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Experimental Simulation of a Cryogenic System for a Large
Superconducting Rotor, L. SOBEL, J. L. SMITH, Jr., and F.
RuMORE, Massachusetts Institute of Technology . . . . . . . . . . . . . . . .
Rotor Cooling System for a 10-MVA Superconducting
Generator, M. T. BROWN, M. E. CRAWFORD, and J. L. SMITH,
JR., Massachusetts Institute of Technology . . . . . . . . . . . . . . . . . . . . . .
Safety Leads, M. KucHNIR and T. H. NICOL, Fermi National
Accelerator Laboratory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
266
275
285
294
Coateats
F-5
Magnet Leads for the First-Cell, D. P. ßROWN and W. J.
ScHNEIDER, Brookhaven National Labaratory . . . . . . . . . . . . . . . . . .
F-6 Thermal Control for the MFfF Magnet, J. H. VANSANT and R.
M. Russ, Lawrence Livermore Labaratory . . . . . . . . . . . . . . . . . . . . . .
F-7 Forced-Circulation Cooling System for the Argonne
Superconducting Heavy-Ion Linac, J. M. NIXON and L. M.
BoLLINGER, Argonne National Labaratory . . . . . . . . . . . . . . . . . . . . .
F-8 Energy Doubler Satellite Refrigerator Magnet Cooling System, C.
RODE, P. ßRINDZA, and D. RICHIED, Fermi National Accelerator
Laboratory, and S. STOY, Cryogenic Consultants, Inc. . . . . . . . . . . . .
F-9 Cryogenic Support System for Airborne Superconducting
Generators, P. J. KERNEY and P. A. LESSARD, CTI-Cryogenics . .
F-10 Economics of Cryogenic Systems for Superconducting Magnets,
G. Y. RoBINSON, JR., Massachusetts Institute of Technology . 0...
F-11 Minimization of Refrigeration Power for Large Cryogenic
Systems, M. A. HILAL, Michigan Technological University, and Y.
M. EYSSA, University of Wisconsin-Madison . . . . . . . . . . . . . . . . . .
Heat Transfer in Helium
G-1 Two-Dimensional Heat Transfer to Superfluid Helium, M. A.
HILAL, Michigan Technological University ..........
G-2 Heat Transfer to Helium-li in Cylindrical Geometries, S. W.
V AN SeiVER and R. L. LEE, University of Wisconsin-Madison
G-3 Maximum and Minimum Heat Flux and Temperature Fluctuation
in Film-Boiling States in Superfluid Helium, H. KoBAYASHI and K.
YASUKÖCHI, Nihon University ................. 0..............
G--4 Transient Heat Transfer in Boiling Helium-! and Subcooled
Helium-li, P. SEYFERT, G. CLAUDET, and M. J. McCALL, Centre
d'Etudes Nucleaires de Grenoble, and R. AYMAR, Centre d'Etudes
Nucleaires de Fontenay aux Roses . . . . . . . . . . . . . . . . . . . . . . . . . . . .
G-5 Heat Transfer Measurement With a Small Superconducting Coil
Subjected to Transient and Quasistatic Heating at Temperatures
between 1.8 and 4.2 K, D. GENTILE, Centre d'Etudes Nucleaires
de Saclay, and W. V. HASSENZAHL, Los Alamos Scientific
Labaratory ..............................................
G-6 Heat Transfer of Helium in a Pipe With Suction, L. L. VAsiLIEV,
G. I. BosROVA, and L. A. STASEVICH, The Luikov Heat and
Mass Transfer Institute . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
G-7 Heat Transfer and Helium Replenishment in Cabled Conductor
Cooling Channels, P. F. MICHAELSON, R. QuA Y, and R. F.
KOENIG, General Electric Company, and P. L. WALSTROM and J.
S. GoooARD, Oak Ridge National Labaratory . . . . . . . . . . . . . . . . .
G-8 Measurements of Heat Transfer and Helium Replenishment in
Long Narrow Channels, R. E. ScHWALL, F. J. RELES, and J. P.
HEINRICH, Intermagnetics General Corporation . . . . . . . . . . . . . . . . .
G-9 Vapor Locking and Heat Transfer under Transient and SteadyState Conditions, C.-J. CHEN, S.-T. WANG, and J. W. DAWSON,
Argonne National Labaratory.................................
G-10 Forced Two-Phase Helium Cooling of Large Superconducting
Magnets, M. A. GREEN, W. A. BuRNS, and J. D. TAYLOR,
Lawrence Berkeley Labaratory .
0
•••••
0
0
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0
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•
•
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300
308
317
326
335
342
350
358
363
372
378
385
393
398
406
412
420
Contents
Heat Transfer
H-1
H-2
H-3
H-4
H-5
H-6
H-7
H-8
Contact Heat Transfer in Solid Cryogens, B. I. VERKIN, R. S.
MIKHALCHENKO, V. F. GETMANETS, and L. G. GoNCHARENKO,
Academy of Seiences of the Ukrainian SSR . . . . . . . . . . . . . . . . . . . .
Digital Computer Simulation of Voidage in a Regenerator, J. B.
HARNESSand P. E. L. NEUMANN, University of Bradford........
Simulation of Cooldown Underneath Large Cryogenic Storage
Tanks, M. H. SEELAND and K. D. TIMMERHAUS, University of
Colorado . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Transient Pool Boiling of Liquid Helium Using a TemperatureControlled Heater Surface, P. J. GIARRATANO and N. V.
FREDERICK, NBS Thermophysical Properlies Division . . . . . . . . . . .
Heat Transfer during Subcooled Hydrogen Boiling, B. I. VERKIN,
Yu. A. KIRICHENKO, and N. M. LEVCHENKO, Academy of
Seiences of the Ukrainian SSR................................
Observation of Bubble Formation Mechanism of Liquid Nitrogen
Subjected to Transient Heating, 0. TsuKAMOTO and T.
UYEMURA, Yokohama National University, and T. UYEMURA,
Tokyo University . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Natural Convection Heat Leak in Supercritical Hydrogen Tanks,
A. J. BARRETT, Beech Aircraft Corporation . . . . . . . . . . . . . . . . . . . .
Techniques for Reducing Radiation Heat Transfer between 77
and 4.2 K, E. M. W. LEUNG, R. W. FAST, H. L. HART, and J. R.
HEIM, Fermi National Accelerator Laboratory . . . . . . . . . . . . . . . . . .
431
438
446
455
467
476
483
489
Flow Phenomena
J-1
J-2
J-3
J-4
J-5
K-1
K-2
Experience with an Orifice Flow Meter lnstalled in a Helium
Refrigerator, J. W. DEAN and W. F. STEWART, Los Alamos
Scientific Laboratory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Some Observations of a Free Jet Phenomenon in a 90° SharpEdge lnlet Geometry, R. C. HENDRICKS, NASA, Lewis Research
Center.....................................................
Experimental Study of Flow Instabilities in Forced Helium
Cooling Channels, Y. MATSUBARA, A. SuGAWARA, and K.
YASUKÖCHI, Nihon University................................
Acoustic Oscillation Phenomena in Low-Velocity Steady Flow
with Heating, J. A. LIBURDY, Clemson University, and J. L.
WoFFORD, Arkansas Power and Light Co. . . . . . . . . . . . . . . . . . . . . .
Control of Pressurized Superfluid Helium-li: Application to Loss
Analysis, M. X. FRAN(:OIS, Laboratoire d'Aerodynamique, and J. C.
LoTTIN and J. PLANCOULAINE, Centre d'Etudes Nucleaires de
Saclay.....................................................
Liquefaction and Refrigeration
Thermodynamic Optimization of Helium Liquefaction Cycles, R.
H. HUBBELL, Arthur D. Little, Inc., and W. M. ToscANO, FosterMiller Associates............................................
A 50-Liters/hr Helium Liquefier for a Superconducting Magnetic
Energy Storage System, P. J. KERNEY and D. A. McWILLIAMS,
CTI-Cryogenics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
500
506
521
528
541
551
563
X
K-3
K--4
K-5
Contents
A Closed-Cycle Thermally Activated Regenerative
Cryogenerator, J. B. HARNESSand P. E. L. NEUMANN, University
of Bradford . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A Study of Refrigeration for Liquid-Nitrogen-Cooled Power
Transmission Cables, R. C. LoNGSWORTH, Air Products and
Chemicals, Inc., and K. F. ScHOCH, General Electric Company . . .
The Effect of Temperature on lmpurity Adsorption from
Hydrogen on Activated Carbon and Silica Gel, W. C. KRATZ,
Air Products and Chemicals, Inc. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
574
585
597
Solid and Fluid Properties
L-1
Effect of Nitrogen Presence on Solid Solubility of Normal
Paraffins in Liquid Ethane, J. D. HorroVY, W. L. CHEN, J. P.
KoHN, and K. D. LUKS, University of Notre Dame..............
L-2 Solubility of Solid tert-Butyl Mercaptan in Liquid Methane and
an LNG Mixture, G. P. KuEBLER and C. McKINLEY, Air
Products and Chemicals, Inc. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
L-3 Prediction of C02 Solubility in Light Hydrocarbon Mixtures at
Low Temperatures, R. J. J. CHEN, V. W. LIAW, and D. G.
ELLIOT, DM International, Inc. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
L--4 Melting Point Data for Freeze Protection in Natural Gas Liquids
(NGL) Plants Using Methanol Dehydration, R. L. HoRTON and
G. C. DYSINGER, Phillips Petroleum Company..................
L-5 Measurement of Isochoric P-V-T Behavior of a Nominal95mol.%-Methane-5-mol.%-Propane Mixture from Near-Ambient
to Cryogenic Temperatures, K. ARAI and R. KoBAYASHI, Rice
University . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
L-6 Phase Behavior of Three Hydrogen-Containing Ternary Systems,
M. YoRIZANE, S. YoSHIMURA, and H. MAsuoKA, University of
Hiroshima, I. FUNADA: Kobe Steel Ltd., and C.-T. Fu and B.
C.-Y. Lu, University of Ottawa . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
L-7 Vapor Pressure and Heats of Vaporization and Sublimation of
Liquids and Solids of Ioterest in Cryogenics Below 1-atm
Pressure, G. N. BROWN, JR. and W. T. ZIEGLER, Georgia
Institute of Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
L-8 Simple and Generalized Equation of State for Vapor-Liquid
Equilibrium Calculations, T. ISHIKAWA, W. K. CHUNG, and B.
C.-Y. Lu, University of Ottawa...............................
L-9 Reduced Volumetrie Expansion and Isothermal Compressibility
Factor Plots, R. C. HENDRICKS, NASA, Lewis Research Center . . .
L-10 The Construction and Use of Exergy Diagrams, W. 0. DALY and
J. B. IIARNEss, University of Bradford . . . . . . . . . . . . . . . . . . . . . . . .
L-11 Densities and Dielectric Constants of LPG Components and
Mixtures at Cryogenic Storage Conditions, R. T. THoMPSON, JR.
and R. C. MILLER, University of Wyoming . . . . . . . . . . . . . . . . . . . . .
L-12 Dielectric Properlies of Liquid Hydrogen, V. V. PASHKOV and
M. P. LoBKO, Ukrainian Academy of Seiences . . . . . . . . . . . . . . . . .
609
616
620
629
640
654
662
671
682
693
698
709
Contents
xi
Cryogenic Applications-LNG
M-1
M-2
M-3
M-4
M-5
World Market for LNG Trade-Present and Future, B. M.
GIBSON, Air Products and Chemicals, Inc. . . . . . . . . . . . . . . . . . . . . .
LNG Project Development: Shipping and Terminal
Considerations, V. V. STAFFA and D. K. JHAVERI, Tennessee
Gas Transmission Company..................................
Marine Transportation of LNG at Intermediate Temperature, C.
P. ßENNETT, University of Manitoba . . . . . . . . . . . . . . . . . . . . . . . . . .
Explosion Hazards of LNG and LPG Carriers during Transport,
M. M. KAMEL and A. KHALIL, Cairo University................
Purification and Cryogenic Separation of SNG Produced from
Coal, A. A. CASSANO, T. C. LI, J. C. TAo, and T. R. TsAO, Air
Products and Chemica/s, Inc. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
715
730
751
757
763
Cryogenic Applications-Space Technology
N-1
N-2
N-3
N-4
A Portable 3 He Cryostat for Studies in Astrophysics, A.
SHERMAN and 0. FIGUEROA, Goddard Space Flight Center......
Mechanism of an Active Phase Separator for Space Applications,
H. D. DENNER, G. KLIPPING, I. KLIPPING, K. LÜDERS, J.
MENZEL, and U. RuPPERT, Freie Universität Berlin . . . . . . . . . . . . .
Progress on the Development of a 3- to 5-Year Lifetime Stirling
Cycle Refrigerator for Space, A. SHERMAN and M. GASSER,
Goddard Space Flight Center, M. GoLDOWSKY, North American
Phi/Ups Corporation, G. ßENSON, Energy Research and
Generation, Inc., and J. McCoRMICK, Mechanica/ Techno/ogy,
Inc. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Superfluid Helium Experiment for Spacelab 2, P. MASON, D.
COLLINS, P. COWGILL, D. ELLEMAN, D. PETRAC, M. SAFFREN,
and T. WANG, Jet Propulsion Labaratory.......................
775
783
791
801
Cryogenic Applications-Resource Utilization
0-1
0-2
0-3
Helium: lts Past, Present, and Future, E. F. HAMMEL, Los
Alamos Scientific Labaratory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Liquid Hydrogenas an Automotive Fuel, W. F. STEWART, Los
Alamos Scientific Labaratory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Liquid Nitrogenas an Energy Source for an Automotive Vehicle,
M. V. SussMAN, Tufts University . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
810
822
831
Indexes
Author Index
Subject Index
839
843
FOREWORD
The Cryogenic Engineering Conference celebrated its Silver Anniversary at the
1979 Conference held at Madison, Wisconsin. For many it provided an opportunity
to reminisce about the first Cryogenic Engineering Conference convened at the
National Bureau of Standards in Boulder, Colorado and also about the many
following conferences and advances that had been reported at these conferences.
It is difficult to realize that the first Cryogenic Engineering Conference was
held before the advent of multilayer insulation, the space age, large-scale LNG
Operations and superconductivity applications. The evolution of these activities has
been carefully recorded in past volumes of the Advances in Cryogenic Engineering.
· Once again, the Cryogenic Engineering Conference is happy to have had the
International Cryogenic Materials Conference cohost this meeting at the University
of Wisconsin. Collaboration between these two conferences has proven to be
mutually beneficial by providing the cryogenic engineer with an in-depth exposure to
materials properties, selection, and utilization to complement the exposure to new
applications and design concepts. The papers presented at this joint conference as
part of the International Cryogenic Materials Conference will be published as
Volume 26 of the Advances in Cryogenic Engineering.
Many have contributed to the success of the 1979 Cryogenic Engineering
Conference in Madison. The Cryogenic Engineering Conference Board is extremely
grateful to R. W. Boom and his staff at the University of Wisconsin for their excellent
handling of all the local arrangements and to the University of Wisconsin for serving
as hosts for this Silver Anniversary meeting of cryogenic specialists from all over the
world. The assistance of the many dedicated workers in the cryogenic field who have
once again contributed to the reviewing of the final manuscripts for this volume is
also gratefully acknowledged by the Cryogenic Engineering Conference Board and
the editor. The list of all those individuals who have assisted in the many important
tasks involved in completing the manuscripts for publication continues to grow
Ionger with each volume in this series, and any attempt to acknowledge individual
contributions in this limited space would not do justice to them. However, Special
recognition, as in past years, must be given to Mrs. Elva R. Dillman from the
University of Colorado for her continued assistance to the editor and her attention to
all the details involVed in the preparation of the final manuscripts for this and past
volumes. Her devotion to this activity has been exemplary.
This series has traditionally recognized individuals who in some way have
contributed significantly in extending the frontiers of cryÖgenic engineering or have
provided noteworthy assistance to the Cryogenic Engineering Conference. In the
spirit of this tradition this series recognizes another individual who has been an active
and eftective leader in the application of cryogenic engineering to a wide variety of
engineering problems and has ably supported the Cryogenic Engineering Conference. Accordingly, Volume 25 of the Advances in Cryogenic Engineering is
dedicated to H. 0. McMahon, retired director of Artbur D. Little and recipient of the
fourth Samuel C. Collins Award presented on August 23, 1979.
:di
RUSSELL B. SCOTT MEMORIAL AWARD
The objectives of this award are to provide increased recognition for the
recipients in the scientific community and to provide an incentive for high er quality in
both oral and written presentations at future Cryogenic Engineering Conferences.
The winners of the Russell B. Scott Memorial Award for the outstanding papers
presented at the 1977 Cryogenic Engineering Conference, as announced by the
Awards Committee, are as follows: In the cryogenic engineering research category,
T. R. Dali and J. C. Chato of the University of lllinois are recognized for their paper
"Effects of Natural Convection on Heat Transfer in Porous Cryogenic Insulations."
In the application of cryogenic engineering category, C. J. Mole, P. W. Eckels, H. E.
Haller, III, M. A. Janocko, S. A. Karpathy, D. C. Litz, E. Mullan, P. Reichner, and Z.
N. San j ana of the Westinghouse Research and Development Center, and D. W. Deis
of the Lawrence Livermore Laboratory, and M. S. Walker of Intermagnetics
General Corporation are acknowledged for their paper "A Superconducting
0.54-MJ Pulsed Energy Storage Coil."
The Cryogenic Engineering Conference extends its congratulations to all of
these award-winning authors.
xiii
SAMUEL C. COLLINS AWARD
The Samuel C. Collins Award for outstanding contributions to cryogenic
technology was presented to Howard 0. McMahon at the 1979 Cryogenic
Engineering Conference held at the University of Wisconsin. McMahon is a retired
president of Artbur D. Little, Inc., and a member (and form er chairman) of the board
of Cryogenic Technology, Inc., now Helix Technology Corporation.
The Collins Award was established in 1965 by the Cryogenic Engineering
Conference to honor Samuel C. Collins, professor of mechanical engineering at
Massachusetts Institute of Technology, who in 1946 invented the first practical
helium liquefier. Dr. Collins, retired from MIT in 1964, received the Award in 1965
and is now associated with the U. S. Naval Research Laboratory, where he is active in
the development of a helium Iiquefier for shipboard use. The Collins Award was
presented to Professor Klaus D. Timmerhaus, University of Colorado, Boulder, in
1967 and to Dr. Edward F. Hammel, Los Alamos Scientific Laboratory in 1973.
Howard 0. McMahon, a native of Killman, Alberta, Canada, received bis B.A.
and M.A. degrees from the University of British Columbia and bis Ph.D. from MIT.
He joined Artbur D. Little, Inc. in 1943 and worked with Dr. Collins on the
development of the first helium liquefier. His contributions to cryogenic technology
included the McMahon rectifying column packing, air separation heat exchangers,
and the coinvention of the Gifford-McMahon cryogenic refrigerator. The latter
made possible the development of efficient, highly reliable closed-cycle cryogenic
refrigerators for temperatures below 20 K, which are now used in a variety of
industrial and research applica~ions. He has received the Edward Longstreth Medal
of the Franklin Institute and the Frank Forrest Award of the American Ceramic
Society. Dr. McMahon is the author of many technical papers and holds 22 patents
on a wide variety of inventions, many in the field of cryogenic engineering.
Howard 0. McMahon, recipient of the Samuel C. Collins
Award, August 21, 1979.
xiv
1979 CRYOGENIC ENGINEERING
CONFERENCE BOARD
R. W. Fast, Chairman . . . . . . . . . . . . . .
R. F. Barron . . . . . . . . . . . . . . . . . . . . . .
R. W. Boom . . . . . . . . . . . . . . . . . . . . . .
M. B. Clapp . . . . . . . . . . . . . . . . . . . . . . .
D. B. Crawford, Vice-Chairman . . . . .
T. M. Flynn, Program Chairman . . . . .
C. D. Henning . . . . . . . . . . . . . . . . . . . . .
M. J. Hiza, Jr. . . . . . . . . . . . . . . . . . . . . .
J. E. Jensen· . . . . . . . . . . . . . . . . . . . . . . .
E. R. Lady . . . . . . . . . . . . . . . . . . . . . . . .
R. C. Longsworth . . . . . . . . . . . . . . . . . .
Fermi National Accelerator Labaratory
Louisiana Tech University
University of Wisconsin, Madison
Chicago Bridge and Iron Company
Puliman Keliogg
National Bureau of Standards
University of California, Lawrence
Livermore Labaratory
National Bureau of Standards
Brookhaven National Labaratory
University of Michigan
Air Products and Chemicals, Inc.
ex officio
B. W. Birmingham . . . . . . . . . . . . . . . . .
R. P. Reed . . . . . . . . . . . . . . . . . . . . . . . .
K. D. Timmerhaus, Editor,
Advances in Cryogenic Engineering .
D. A. Belsher, Administrator . . . . . . . .
National Bureau of Standards
National Bureau of Standards
University of Colorado
National Bureau of Standards
A WARDS COMMI'ITEES
RUSSELL B. SCOTI MEMORIAL A WARD COMMITIEE
M. J. Hiza, Jr., Chairman . . . . . . . . . . .
R. F. Barron . . . . . . . . . . . . . . . . . . . . . .
E. R. Lady . . . . . . . . . . . . . . . . . . . . . . . .
K. D. Timmerhaus . . . . . . . . . . . . . . . . .
National Bureau of Standards
Louisiana Tech University
University of Michigan
University of Colorado
S. C. COLLINS AWARD COMMITIEE
R. W. Fast, Chairman . . . . . . . . . . . . . .
D. B. Crawford . . . . . . . . . . . . . . . . . . . .
T. M. Flynn . . . . . . . . . . . . . . . . . . . . . . .
K. D. Timmerhaus . . . . . . . . . . . . . . . . .
Fermi National Accelerator Labaratory
Puliman Kellogg
National Bureau of Standards
University of Colorado
ACKNOWLEDGMENTS
The Cryogenic Engineering Conference Board is deeply grateful for the support
which the following organizations have given to the 1979 Cryogenic Engineering
Conference.
The Aerospace Corporation
AIRCO, Inc.
Air Products and Chemicals, Inc.
Ball Corporation
Chicago Bridge and Iron Company
General Electric Company
Helix Technical Corporation,
CTI-Cryogenics
Helix Process Systems Division
National Bureau of Standards,
Boulder Laboratories
Puliman Kellogg
Silbrico Corporation
Union Carbide Corporation,
Linde Division
University of Colorado
University of Wisconsin,
Madison
A-1
SUPERCONDUCfiNG MUD MAGNET
ENGINEERING PROGRAM
P. G. Marston, A. M. Dawson, D. 8. Montgomery, and
J. E. C. Williams
Francis Bitter National Magnet Laboratory
Massachusetts Institute of Technology
Cambridge, Massachusetts
INTRODUCfiON
MHD has the potential to become the first large-scale commercial application of
superconductivity. Recent accomplishments of the DOE/MHD development program have shown this fossil-fueled power generation technique to be capable of
higher efliciencies and lower-per-kilowatt-hour cost than any other near-term
technology.
A significant scale demonstration of all critical items is scheduled to begin in late
1979 at the DOE Component Development and Integration Facility (CDIF)
presently under construction in Butte, Montana. A sequence of progressively more
complex ftow train configurations will be demonstrated through 1986. Commercial
scale system and optimization studies have already identified component requirements. The next step will be operation, during the next decade, of a system large
enough to be conservatively scaled to commercial size.
These systems will require large, complex, and costly superconducting magnets
operating at fields of at least 6 T. The MIT Francis Bitter National Magnet Labaratory has been designated as the DOE magnet program field oflice to assist with the
creation and management of a national program of superconducting MHD magnet
technology development. This activity includes conceptual design and subsequent
contract management for a nurober of large magnets destined for use in a variety of
MHD experimental facilities.
Figure 1 shows the relative size and weight of superconducting magnets
presently under consideration. The smallest of these is the U-25 Bypassmagnet now
in use at the Soviet High Temperature Institute MHD pilot facility near Moscow.
The next larger unit represents the superconducting magnet under construction for
CDIF. The two largest magnets represent sizes identified for small commercial and
base-load power generation plants. The intermediate-sized unit is that presently
proposed for the Engineering Test Facility (ETF).
A five-year program of technological and industrial development willlead to the
selection of a design for the ETF magnet by late 1983 and construction by the late
1980's. This willlead ultimately to the construction of a commercial scale magnet for
a coal-burning MHD/steam power plant operating in a utility environment.
1
P. G. Manton, A. M. Dawson, D. B. M011tcomery, IUid J. E. C. Williams
MAGNET
APPLICATION
MAGNET
FIELD
STRENGTH
(T)
ELEVATION VIEW
STORED
MAGNETIC
ENERGV
( ALL VIEWS DRAWN
TO SAME SCALE l
MJ
WARM
BORE
SIZE
CRYOSTAT
SIZE
MAX. 00/LENGTH
MAGNET
WEIGHT
INLET/EXIT
( metersl
(lonnes)
( metersl
BASELOAD
1000 MWe
MHD
6
16000
------------
2 9/6 5
16/37
-7500
12 5/24
3000
SQ
*
250 MWe
MHD
ETF
(AVCOl
6
6000
2 1/3 9
SQ
6
1500
I 5/2 2 8
10 5/14 9
0.710 9
4 3/63
150
2 3/44
28
SO.
1500
CDIF
iGEl
U25 BYPASS
(ANLl
6
IBO
SQ
5
32
0
5
10
0.4/0 67
DIA
'---.J..._J
SCALE-METERS
Fig. 1. MHD magnet comparison.
The technology development program is dynamically integrated with the
magnet construction management in order to achieve the following: identify design
and manufacturing techniques for commercial scale units; identify failurc modes,
safety and risk considerations; define evaluation and success criteria; predict costs;
provide the fundamental engineering data base and design tools; and perform
verification testing and modeling.
Overall program network analyses have been developed. These show parallel
paths pursued in high-risk areas and component development on a progressively
increasing scale. Analytical tools are being refined and documented. A high degree
of expertise has been achieved via the use of industrial, university, and national
laboratory subcontractors, and by periodic reviews, conferences, seminars, workshops, and summer teaching courses.
MHD MAGNETS
Of the many configurations capable of providing suitable magnetic field distributions, the two basic concepts of most interest are the circular and the reetangular
saddle configurations. Figure 2 provides an artist's conception of a base..Joad size
MHD magnet, and Fig. 3 shows the CDIF size magnet system. Figure 4 presents
comparative cross sections of the two designs. The major components ar4 given in
the following sections.
Willding Substracture. Each superconducting wire in the winding rn\ISt be in
intimate contact with liquid helium for cooling, must be weH insulated to withstand
transient voltages during emergency discharge, and must be weH supported against
Superconducting MHD Magnet Engineering Program
3
Fig. 2. Base-load magnet using circular saddle design.
the !arge electromagnetic Lorentz forces. Most of the Iarge-scale magnet designs
identified today accomplish at least the mechanical support function via some form of
mechanical substructure which subdivides the winding into a number of mechanical
regions and thus Iimits cumulative Ioads on conductors and insulation.
Superstructure. This is the outer force-containment structure which supports
the cumulative electromagnetic load. The total bursting force (y direction, Fig. 4) for
a base-load size magnet is approximately 5000 ton/m of axiallength.
Fig. 3. CDIF superconducting magnet using reetangular saddle design.
4
P. G. Marston, A. M. Dawson, D. B. Montgomery, and J. E. C. Williams
z
types ol
section can be used)
WINDING AREA
V
ELEMENT IN BENDING
TENSION MEMBERS
Fig. 4. Comparative cross sections of reetangular and circular saddle designs.
HeUum Vessel. The containment vessel for the liquid helium coolant may be
external to the superstructure and therefore self-supporting. But in the larger units,
cost considerations willlikely require the use of the superstructure to support the
internal pressure Ioads of the helium vessel. This and the above elements constitute
the "cold mass."
Cold·Mass Supports. A very strong support system must minimize thermal
conduction to the cold rnass and also permit thermal contraction of the cold mass
relative to the room temperature support structure. A technique suitable for the
smaller magnets can be seen Fig. 3 and consists of eight glass-epoxy links which are
angled and capable of rotating in such a way that thermal motion is accommodated
without relaxing link tension. Support schemes for larger magnets are being studied
and willlikely incorporate pivoting support posts.
5
Superconducting MHD Magnet Engineering Program
Vacuum Vessel. Radiation heat loads to the helium temperature cold mass are
limited by vacuum insulation with an intermediate radiation shield maintained near
liquid nitrogen temperature. Multilayer insulation is incorporated on either side of
the radiation shield.
Ancillary Systems. Operation of the magnet requires a large helium refrigerator/liquefier to cool down, fill, and automatically maintain the liquid helium level in
the cryostat for long periods of time. A block diagram of the cryogenic system is
shown in Fig. 5.
The energizing, instrument, and protection systems must allow a 1-hr
discharge-charge cycle for fast channel replacement and must also provide a means
for removing most of the stored energy in the magnetic field in the event of system
failure. This is normally accomplished by use of a dump resistor permanently
connected across the magnet current leads. When the energizing circuit is opened,
the magnet current decays according to the Lmagnet! Rdumpres. time constant; nearly
all the stored energy is dissipated into the resistor.
UTILITY
VACUUM
PUMP
N2
VENT
COOLDOWN
EXCHANGE
He
GAS
STORAGE
COMPRESSOR
[
~r--
_-;>_
_-;>.
F~LL
LN2
STORAGE
N2
VENT
WCONNECTOR
-
VENT
He
REFRIGERATOR
COLDBOX
..9-
_-;>_
~~
t
~
n
LEADS
FILL
cON~
~
N2L
LHe
STORAGE
MAGNET
-··
Fig. 5. Cryogenic system block diagram.
6
P. G. Marstoa, A. M. Dawma, D. B. Moatxo~~~ery, ud J. E. C. WDams
TECHNOLOGY DEVELOPMENT
Superconductors and structures have received the greatest amount of attention
to date, in part because these inftuence most strongly the design of immediate (CDIF,
CFFF, Stanford) and intermediate (ETF, CDP) magnet systems.
Supercondudor Study. Superconductor studies have been conducted both by
this laboratory and industry. This laboratory has developed the minimum propagating zone (MPZ) theory. With this theory it is possible to calculate the length of a
conductor which will "quench" from a given thermal energy perturbation and
determine whether or not that quench normalzonewill recover to a superconducting
state or whether the quench will propagate throughout the entire magnet [ 1]. This
work has been extended by lwasa and Apgar
to a study of the transient heat
transfer to the liquid helium layer under film boiling conditions. An equation was
derived in that study for the transient heat transfer rate given by
eJ
d(}
q,((}) = q.((}) + a((}) dt
(1)
where a(8) is the effective heat capacity of the vapor layer. The term containing a(8)
is strongly dependent on surface conditions. Because of this term, transient heat
transfer in the film boiling region is much higher in the heating of a conductor, and
lower in the cooling than steady-state heat transfer; thus, heat transfer is hysteretic
with temperature cycling. This function determines quantitatively the vapor-layer
thickness as a function of temperature and thereby provides a guideline for sizing
cooling channels irr a superconducting winding. Sindair and Iwasa [3 ] have also
studied the time response of a superconductor to a thermal perturbation. The
duration of a perturbation was shown both analytically and experimentally to have a
large inftuence on quench energy. Brief, high-energy perturbation can be dissipated
without quench while a significantly lower energy perturbation over a Ionger time
period might Iead to quench. This work is now being extended to consider the
spatially dependent case. The MPZ theory outlined above has been applied in the
design of both the Stanford and CDIF superconducting magnets, and will be applied
in the ETF, CDP, and base-load designs.
Frictional heating is a potential source of quench-producing energy input in a
superconducting magnet winding. Energy input from the movement between
conductor and insulator or conductor and substructure is being studied in this
laboratory to identify the most suitable materials pairs for future magnet construction. This work, when complete, will provide another means of predicting a
potential perturbation.
Study contracts have been awarded to industry to evaluate stability and costs for
high-current superconductors of 25-250 kA. Several conductor configurations being
considered are shown in Fig. 6. The cost analyses have indicated a slight advantage
for a 100-kA conductor but the cost minimum is broad; more detailed studies could
push the optimum current as low as 25 kA. Present CDP studies use a 50-kA
conductor as a baseline.
The stability analyses considered three different effects: eddy current heating
due to ftux diffusion, reduction of recovery current due to transverse thermal
gradients, and reduction of recovery current due to transverse electrical currents.
These are particularly important when the operaring current exceeds the Maddock
et al. equal area criterion Iimit [4 ]. Each of these effects reduces the MPZ energy.
7
Superconducting MHD Magnet Engineering Program
,-/
y
~-
'
/-
~
Cable
superconduc tor
I
Fill er 1
rmm
~ ~~
Wl15 .42
I
'--
Superconducting
cable
Copper
submale
Supercond uctor
strand
Copper ~ -=-=r
strand~ ~
Co~per
5.42 mm
substratc
Separated substrate-Multiple
cables, single channel
1.45mm
lntegrated substrate conductor 12.5 kA modules
~1mm
~
Coppersubstrate
Superconducting cable
sol dered 10 Substra te
Fig. 6. Suggested high-current conductor
configurations.
Single integrated substrate conductor
Preliminary information has been developed regarding the effect of superconducting-to-normal transition time, stabilizer and solder properties which give rise to
transverse thermal gradients, and the effect of stabilizer thickness. Experimental
verification of these predictions and related analyses is scheduled during fiscal year
1980.
ICCS. Recent studies of the behavior of internally cooled cabled superconductors (ICCS) have demonstrated two important characteristics. The first is the
demonstration that frictional heat generated by Lorentz force compaction of the
cable is small and does little to degrade performance. The second is that even small
thermal perturbations generate high turbulence and local heat transfer so that very
little pumping or forced cooling is required.* Parameters affecting performance are
being studied analytically by Arp at the National Bureau of Standardsand experimentally by Hoenig, Iwasa, and Becker at FBNML.
* Hence the change in terminology from
"force cooled" to "internally cooled."
8
P. G. Manton, A. M. Dawson, D. 8. Montgomery, and J. E. C. Williams
Struetures. The electromagnetic force COntainment structure has two elements:
a substructure which is interposed with the conductors in such a way that the winding
is divided into a number of mechanical regions within which cumulative Ioads of
conductor and insulation can be limited to safe values; and a superstructure which
surrounds the winding/s,bstructure composite and contains overall magnetic forces.
Many conductor--substructure--superstructure combinations are possible and
their impact on final iQstalled cost creates a complex matrix of options to be
evaluated. Of particular importance is the impact of shipping size and weight
limitations on the need for on-site construction and test. The CDIF, CFFF, and
Stanford magnets represent three quite different structural design concepts. Relative
costs, fabricability, reliability in a utility environment, and scalability will be
compared during their design, construction, and test.
MAGNET PROCUREMENT
CDIF Superc:ondu~g Magnet. The CDIF magnet, shown in Fig. 3, uses a
glass-reinforced epoxy (NEMA G-10) substructure consisting of grooved subplates
wherein each conductor is supported in its own groove. This approach reduces
cumulative Ioads and frictional heating to an absolute minimum. It virtually eliminates any need for mechJlnical strengthin the conductor and might permit the use of
a flexible cable which could be wound on-site very easily. The design eliminates the
need for conductor insuhttion and provides a winding subunit which is handled and
assembled easily and has good mechanical integrity, strength, and precision. Preliminary tests suggest tbat the helium coolant channels may be eliminated. This
simplification will be verified in the test facility magnet now under construction.
An extensive study of the low-temperature mechanical properties of commercially available G-1 0 has shown the material to be satisfactory but requires
careful quality assurance monitaring of the manufacturer's process. Manufacturing
studies indicate that a comparable composite could be molded, giving superior
mechanical properties for the intended use and costing about one-quarter that of
machined G-10.
The CDIF superstructure is a straighttorward system of crossbeams and tension
members. The componeots are of 304LN type stainless steel weldments. Submerged
arc welding appears to be adequate but this has yet to be verified.
Sealeup. A scaling and cost study to ETF and CDP size is included in the CDIF
work statement [5]. A comparable study by A VCO-Everett Research Labaratory
considers a magnet havbig similar winding configuration but quite different substructure and superstructure of stainless steel and aluminum, respectively. The
AERL concept incorpotrates individual helium vessels for each winding half, thus
enabling the first order of modularization to deal with shipping size Iimits. Several
other reetangular saddle eonfigurations have been proposed which will be the subject
of study co~tracts during fiscal year 1980.
StaDlord Mapet. The Stanford magnet design concept uses semicylindrical
aluminum subplates in which the number of conductors per groove is limited to that
giving safe cumulative compressive Ioad on the turn-to-turn insulation. The superstructure consists of circular aluminum ring girders. The highly conductive and
closely coupled substructure will modify quench behavior to the degree that such a
design could be inherently fail-safe without the need for a dynamic energy-dumping
system.
Superconducting MHD Magnet Ellgineering Program
9
Certain problems of scaling are being addressed by General Dynamics/Convair
Division who have proposed that the cylindrical substructure be fabricated from a
series of longitudinal staves. This concept has thus been dubbed "cask." As in the
case of the rectangular-saddle configuration, additional circular-saddle studies are
anticipated.
CFFF Coai-Fired Flow Facility Magnet. This magnet is being designed and built
by Argonne National Laboratory. lt incorporates important similarities but also
important differences from the Argonne-built U-25 Bypass magnet presently
operating at the Soviet High Temperature Institute.
Both magnets have individually banded circular-saddle winding layers with
micarta filler material in the winding bore. In the U-25B, the banding is of very
tightly wound stainless steel. The radial forces are supported by a strong, thick
stainless steel bore tube. Loads are transmitted through the micarta fillers and bands.
In the CFFF magnet, the banding is of aluminum and is used solely as a
manufacturing aid to secure individuallayers as the winding is "built up." The radial
forces are supported by external curved beams cast from stainless steel and connected through aluminum tension links.
Support of the axial force components is also quite different. In the U-25B, a
very large portion of this Ioad is communicated to flanges on each end of the bore
tube via transfer structure tightly fitted at assembly between the saddles and flanges.
In the CFFF magnet, these Ioads are taken directly by the conductors.
It is anticipated that Argonne will perform scaleup studies for the CFFF
concept. Characteristics of the three magnets presently under construction are listed
in Table I.
Table I. Characteristics of the CFFF, CDIF, and Stanford
Snpercondncting Magnets
Design characteristics
CFFF
CDIF/SM
Stanford SM
SC
SC
SC
Peak on-axis field,* T
Inlet bore dimensions, m
Outlet bore dimensions, m
Active field length, m
Overall dimensions, m
Overalllength, m
Total weight, tons
Stored energy, J
Dipole moment, A-m 2
6
0.8diam.
1.0
3
4.9 X 4.1
6.4
172
168 X 106
6
0.98 X 0.78
0.98sq.
3
4.3 X 4.3
6.9
180
184 X 106
1 X 108
7.3
0.55 diam.
0.55 diam.
1.5
3.8 X 3.8
4.5
70
79 X 106
1.2 X 108
Conductor JA, A/m2
Heat tlux, W /cm 2
Operating current, A
Operating power, MW
2.0 X 107
0.135
4,000
1.65 X 107
0.4
6,000
2.08 X 107
0.7
5,000
ANLt
8
GE:t:
5.4
GD§
Type
Estimated cost, $106
Contractor
* Field horizontal in all cases.
t Argonne National Laboratory.
:j: General Electric Company Energy Systems Programs Division.
§ General Dynamics Corporation, Convair Division.
10
P. G. Ma-ston, A. M. Dlnnon, D. B. Moatpmery,lllld J. E. C. W&.ms
ANCILLARY STUDIES
Cryogenic Support Systems. A preliminary design and cost study by Cryogenic
Consultants, Inc. has identified helium refrigerator/liquefier systems in the range of
100-200 liters/hr of liquid-generating capacity and 400~800 W of refrigeration as
the range of interest for 50-kA commercial scale systems.
Power and Protection. A preliminary design and cost study for energizing,
energy dumping, control, and protection systems is in process by A. Kusko, Inc.
Shipping Study. Belding Corporation, the firm that transported the U-25B
magnet from Argonne to Moscow, has completed preliminary study of the overall
problern of shipping size and weight limitations. This information will help establish
the degree of modularity required and the relative amount of factory vs. on-site
construction required as a function of MHD generator size.
Isotensoidal Force Containment Concept. An advanced concept intended to
give a minimum cost baseline is being studied by Batteile Columbus Laboratories. In
this design, an internally cooled cabled conductor is used in such a way that its
stainless steel jacket is a major structural element. The saddle configuration is
isotensoidal and the axial Ioads are taken by the individual conductors (jackets). The
transverse forces on the straight sections of the windings are contained by banding,
which also has an isotensoidal configuration.
Cost Studies. Preliminary cost estimates have been made for several magnets.
Credible scaling factors have been determined, but considerable additional effort
and design refinement are required to achieve a reasonable degree of cost credibility.
Properfies of Materials. When one considers the long-term operation in a utility
environment of thousands of tons of exotic alloys operating highly stressed at near
absolute zero temperature, the inadequacy of existing data on properties of materials
becomes apparent. The degree of conservatism which must therefore be imposed on
allowable stress Ievels is also very costly. Several contracts with the National Bureau
of Standards (Boulder, Colorado) have been initiated to investigate both structural
and conductor materials and composites.
Facility. The existing facilities at FBNML are being upgraded to permit a variety
of significant-scale structural tests intended to simulate the actual operating conditions of proposed designs and to determine their eiementaland composite behavior.
One such test scheduled for fiscal year 1980 will examine the structural behavior of
internally cooled cabled superconductors. The experimental configuration shown in
Fig. 7 will permit a magnetically induced tension in the conductor jacket of up to
100,000 psi in a configuration simulating actual operating conditions. The dimensions and support are configured suchthat the ratio of the stress intensity (tension) in
the large radius region to the stress intensity (compressive) in the small radius region
is approximately unity. This test will simulate conditions for the isotensoidal design
and will also give valuable information for high-field fusion Tokamak coils using
niobium-tin (Nb3 Sn). By controlling the cable pitch and thus the relative strain of the
conductor and jacket, the stainless steel jacket can be operated at its stress limit
rather than the strain Iimit of the Nb 3 Sn conductor. This could reduce the amount of
structural material required in such systems by a significant factor.
Superconducting MHD Magnet Engineering Program
11
·~
\ I'
~)
"'
\
I
Fig. 7. Test facility magnet.
Development of lower-cost and superior GRP composites is also anticipated to
begin in fiscal year 1980. Scale modeling and verification testing of critical system
elements is scheduled to begin in mid-fiscal-year 1980.
Computer Codes. Existing computer codes for field, force, and stress are being
refined and put into easily usable and self-consistent format. These will be fully
documented and ultimately available for general use. Subroutines for cost analysis
will be developed.
CONCLUSIONS
The synergism of the parallel procurement and technology development activities permits a dynamic interaction which is a vital part of the national program. The
success of the program to date is best illustrated by the fact that only a few years ago
large superconducting magnets were considered the pacing technology for MHD
power generation. Today there is virtually total confidence in their ultimate success
and also in the fact that by the mid-1980's the technology and industrial basewill be
adequately in place to move smoothly into what seems certain to be an important
new international energy market.
REFERENCES
1.
2.
3.
4.
5.
M. N. Wilson and Y. lwasa, Cryogenics 18(1):17 (1978).
Y. lwasa and B. A. Apgar, Cryogenics 18(5):267 (1978).
M. L. Sindair and Y. lwasa, IEEE Trans. Magn. Mag-15(1):347 (1979).
B. J. Maddock, G. B. James, and W. T. Norris, Cryogenics 9:261 (1969).
J. L. Zar, "A Modular Design for a Superconducting Magnet for the ETF and larger MHD
generators," presented at 18th Symposium Engineering Aspects of Magnetohydrodynamics, Butte,
Montana, June 1979.
A-2
IMPACf OF IDGH-CURRENT OPERATION
ON THE COST OF SUPERCONDUCfiNG
MAGNET SYSTEMS FOR LARGE-SCALE
MHD APPLICATIONS*
R. J. Thome,t R. D. PUisbury,t H. R. Segal, and B. 0. Pederson
Magnetic Corporation of America
Waltham, Massachusetts
INTRODUCfiON
Reference designs for superconducting magnets for base Ioad magnetohydrodynamic (MHD) plan~s have indicated that they will be substantially larger and
more complex in geometry than the largest superconducting magnets now in
operation. The cost of many of the components and of some of the steps in
fabrication of these magnets may be expected tobe dependent on the current Ievel. A
question naturally arises, therefore, as to whether an optimum current Ievel may be
found from a cost standpoint. The purpose of this study was to perform a preliminary
investigation into this area.
The reference design concept C· 2] selected as a baseline is a 26-m-long magnet
system with an outside diameter of 9.6 m and an estimated weight of about 1200
tons. Conductor, structure, and dewar represent 14%,69%, and 17% of the total
weight, respectively. The magnet consists of an assembly of two reetangular saddle
and six racetrack coils nested so as to provide a field variation from 6 to 3.5 T along
the 16-m active-field length. Present estimates indicate that a magnet of this size
would be suitable for producing roughly 150 MWe from the MHD portion of a
combined MHD/conventional plant.
The method in this study involved development of a set of cost factors in the
general areas of system components, fabrication, and assembly. Components with
features expected to be strongly dependent on the current Ievel were studied in
sufticient detail to allow their characteristics to be determined for cost-estimating
purposes. These included conductor, substructure, the power supply subsystem, and
refrigerator/liquefier subsystem. The characteristics (and cost) of components of the
superstructure and dewar would not be expected to be a strong function of the
current Ievel and were, therefore, assumed to be the same for all cases. Cost
estimates for magnet fabrication and system assembly were developed by generating
• Study supported by the U. S. Department of Energy, MHD Division through M.I.T. Francis Bitter
National Magnet Laboratory's Superconducting MHD Magnet Development Program, DOE Contract
No. EX77-A-01-2295.
t Present address: Massachusetts Institute of Technology, Francis Bitter National Magnet Laboratory,
Cambridge, Massachusetts.
12
Impact of High-Current Operation on the Cost of Superconducting Magnet Systems
13
hypotheticäl manufacturing fiow diagrams, assigning cost elements to the individual
steps, and integrating these elements into cost factors dependent on current Ievel
(e.g., fabrication of winding and substructure) and cost factors assumed to be
independent of current Ievel (e.g., assembly to superstructure, dewar, and support
systems). For the purposes of discussion, consider the systemtobe composed of three
major subsystems: (1) magnet/dewar, (2) power supply, and (3) cryogenic.
MAGNET/OEWAR SUBSYSTEM
Conductor
The total amp-meterrequirementforthe reference design [2 ]was 1.73 x 109 Am. This may, as a first approximation, be assumed tobe independent of current Ievel.
It then determines the total conductor length required once the current Ievel is
selected.
A baseline configuration for the conductor cross section was chosen and is
illustrated in Fig. 1. It consists of a separate, fully transposed cable which is soldered
into the substrate during the winding fabrication process. The copper stabilizer is
grooved along the wide faces to provide extended heat transfer surfaces. Dimensions
for the conductor were based on an operating current at 90% of the short sample
current, a simple stability criteria on using an allowable surface heat ftux of 0.6
W I cm2 , and a local surface bearing pressure Iimitation of 10 ksi for the copper. Three
conductors were determined for each current Ievel in order to include an allowance
for grading of the conductor in a magnet of this scale. This was done by assuming that
30% of the conductor would be sized for 8 T, 45% for 6 T, and 25% for 4.2 T. The
weight of the stabilizer was then determined, estimated at a cost of $2/lb and added
to the cost of the cabled superconductor with the result that the cost for conductor
ranged from $8.2 x 106 at the 10-kA Ievel to $9.4 x 106 at the 250-kA Ievel with the
primary variation rising from the stabilizer since the total ampere-meters required
was assumed constant.
Substructure
The internal or substructure concept which was assumed provides a means for
cumulative electromagnetic Ioad transmittat around each conductor. Each conductor is inserted in a stainless steel channel which is then closed by a backing strip. The
walls and legs of the stainless steel substructure were sized to carry the maximum
cumulative Ioad out to the superstructure or to a plane of symmetry where it would
be equilibrated. The turn-to-turn insulation consists of a spiral wrap applied to the
conductor before insertion in the stainless steel substructural element.
Fig. 1. Baseline conductor configuration featuring a
separate fully transposed cable of NbTi/Cu composite
conductors which is inserted into the copper stabilizer during the winding fabrication process.
R. J. Thome, R. D. Pillsbory, H. R. Segal, and 8. 0. Pederson
14
At the lower current levels (i.e., I < 50 kA) the thickness requirements for the
channels were such that they could be roll formed. Fabrication of large quantities in
this manner was estimated to cost $1.40/lb. At the high current levels (250 kA) the
thickness requirements are large fractions of an inch, hence roll forming is probably
not feasible. The channel components would most likely be individually rolled then
positioned and welded at the corners. The unit price for fabrication in this manner
was estimated at $4.05/lb. At intermediate current levels the thicknesses vary
between the two extremes, hence a linear variation in unit cost was assumed. Length
requirements were based on those generated for the conductor. Total substructural
cost estimates ranged from $4 x 105 at the 10-kA level to $4.1 x 106 at the 250-kA
level.
Superstructure
As mentioned earlier, the total amp-meter requirement and, in turn, the overall
size of the winding was assumed to be independent of current level. The size of the
superstructure, then, also remains constant. The cost for the smaller lighter
components was estimated at $4.05/lb as in the case of the heaviest substructure.
The drawings of the basic stainless steel structural concept were reviewed with a
potential vendor who provided rough estimates of the total cost of the larger
components using an equivalent $8.43/lb, which was considered conservative. As a
result, the cost of the baseline design superstructure weight of 1.1 x 106 kg was
estimated at ($4.05 + $8.43)/2 or $6.24/lb foratotal of $15.2 x 106 .
Dewar
Since the winding and superstructure envelope were independent of current
level, the dewar size also remained constant. The dewar material in the reference
was primarily aluminum with a total weight of 3.84 X 105 kg. This was
design
combined with an estimated unit cost of $2.75/lb to yield adewar cost of $2.51 x
106 independent of current level.
eJ
POWER SUPPLY SUBSYSTEM
This subsystemwas assumed to consist of (1) the basicpower supply, (2) the
protective circuits, controls, and interlocks, (3) the bus work, and (4) the vaporcooled leads. The characteristics of each were considered, cost estimates developed,
and a single cost factor generated for the subsystem as a function of current level.
The peak power required to charge the magnet is directly proportional to the
energy stored and inversely proportional to the charge time. The baseline system
stores about 6.7 x 109 J, hence the peakpower required would be approximately 1
MW for charge times in the 4-16 hr range. Information from manufacturers
indicated that 50-kA, 5-V solid state units bad been built for about $80 x 103 and
that a 250-kA unit would cost an estimated $200 x 103 • Other units, with current
ratings between 50 and 250 kA, were expected to scale roughly linearly with current.
At these high current levels it was indicated that cost rose slowly with voltage; for
example, a 2-V, 250-kA supply was estimated at only 10% more than a 1-V supply at
the same current. To allow some ftexibility in voltage and power level selection, the
estimated cost rangewas increased by 15% at the low end and 50% at the high end
for the purposes of this study.
The primary protection for a superconducting magnet system of this type is a
discharge circuit consisting of a resistor across the coil terminals or a set of resistors
Impact of High-Current Operation on tbe Cost of Soperconduding Magnet Systems
15
across magnet sections. Because of the high degree of stability, the only likely
manner for a normal region to propagate is if a section of the magnet is not immersed
in liquid helium as would be the case if there were an interruption in liquid helium
supply to the main cryostat with a subsequent decrease in liquid Ievel.
Voltage and temperature transients during quench were performed for selected
cases at several current Ievels with imposed Iimits on the fraction of winding allowed
to go normal. Terminal voltages for discharge were limited to 2 kV and, in all cases,
the internal voltage and temperature Ievels were reasonable; hence, it was concluded
that standard methods of coil protection involving use of single or multiple resistors
across coil sections would be adequate.
In addition, estimates were made for the size of bus work and vapor cooled Ieads
(note that the latter will represent a significant current-level-dependent heat Ioad on
the cryogenic system). These were sized at a current density Ievel which would allow
operation without water cooling in the bus work or vapor cooling in the power Ieads
for the duration of a discharge. Neither component, however, appeared tobe a major
contributor to the cost of the system.
When totaled, the estimated cost for the components of this subsystem ranged
from about $2.1 x 105 at 10 kA to about $5.9 x 105 at 250 kA.
CRYOGENIC SUBSYSTEM
The refrigerator /liquefier requirements were estimated on the basis of heat
Ioads attributed to dewar losses, vapor-cooled Iead requirements, and Iosses due to
joule heating in joints between superconductors. The latter component is a major
contribution with a high Ievel of uncertainty owing to the Iack of data on large-scale
conductors. The required refrigeration and input power required were then estimated and are sumrnarized in Table I. The cost for the system was found using a
and updated with a cost escalation
cost/power relationship given by Strobridge
factor correspondin} to 8% per year. Results ranged from $4.64 x 105 at the 10-kA
Ievel to $1.53 x 10 at the 250-kA Ievel.
e1
Table I. Requirements for BaseUne System*
kA
Lead
requirement,
liters/hr
Number
of
joints
Joint
losses,t
liters/hr
Total
helium,
liters/hr
RefrigeratorI
liquefier
efficiency,
% ofCarnot
Electrical
power
input,:t:
10
25
50
100
150
200
250
30
75
150
300
450
600
750
189
189
189
114
94
95
113
19
33
82
176
313
548
1004
152
211
335
579
866
1256
1856
14
15
17
18
19
19
20
231
292
376
579
772
1024
1264
Operating
current,
* Dewar Iosses for the baseline were 103 liters/hr.
kW
t Assumes superconductor joint resistance = 10-lO n.
:t: Input power is based on assuming that the refrigerator /liquefier operates as liquefier for dewar and Iead
Iosses (enthalpy of boil-ofl gasnot available to refrigerator) and as a refrigerator for joint losses.
16
R. J. Thome, R. D. Plllsbury, H. R. Sepl, lllld 8. 0. Pedenon
FABRICATION AND ASSEMBLY
The fabrication cost elements which are sensitive to current Ievel are those
Operations associated with winding component preparation, winding, and assembly
to the substructure. The cost elements which are relatively insensitive to current Ievel
are those associated with assembly to superstructure, dewar, and the support
systems.
A simplified manufacturing blockdiagram is shown in Fig. 2. The operations up
through "Oamp turn in Place" are current-level dependent and were divided into 12
fabrication tasks. Foreach task, a Iabor and tooling cost were generatedas a function
of current Ievel based on (1) number of lengths of stabilizer received at the
fabrication facility (= number of stabilizer joints), (2) number of lengths of stainless
steel channel, (3) length of stabilizer, (4) lengths of stainless steel channels, (5)
number of turns in saddle coils/racetrack coils, (6) number of lengths of superconductor received at fabrication facility, and (7) length of superconductor. Labor
hours were estimated for each of the 12 tasks, engineering supervision assumed as
equivalent to 15% of the technician Iabor total. lt was then assumed that technician
Iabor would be billed at a rate of $15 per hour and that engineering Iabor would be
billed at $35 per hour. The costs for these operations decreased from $19.5 x 106 to
$7.32 x 106 from the 10-kA to the 250-kA Ievel with the greatest variation at the
low current Ievels.
The remaining Operations in Fig. 2 are independent of current Ievel. Labor
estimates were generated and priced at $15 or $20 per hour depending on the task
involved. Supervision was again assumed at 15% of the totallabor requirement and
priced at $35 per hour. The total cost for these operations was estimated at
$5.91 X 106 •
INGOMING INSPEGTION
OF STABILIZER,
GHANNEL
OTHER
GOIL MATERIALS
INGOMING
INSPEGTION
OF
SUPERGONOUGTOR
a
ASSEMBLE
STABILIZER
SS
GHANNEL
PREFORM
TURN SEGMENT;
OR MAGHINE,
THEN ASSEMBLE
PLAGE TURN
SEGMENT IN
POSITION a BRAZE
STABILIZER
GROUNO WRAP a
GURE INSULATION
GLAMP TURN
IN PLAGE
a
a
ASSEMBLE
SUPERGONOUGTOR
TURN SEGMENT;
SOLDER
a
a
a
APPLY SS STRIP
SPIRAL WRAP
TURN SEGMENT
WITH INSULATION
ASSEMBLE TO
SUPPORT SYSTEMS
Fig. 2. Manufacturing blockdiagram for coil assembly using separate substrate conductor.
Impact of High-Corrent Operation on the Cost of Soperc:ondocting Magnet Systems
17
COST INTEGRATION AND CONCLUSIONS
A total cost would have to be viewed with extreme caution since costs were
estimated primarily on past experience and general discussion with selected potential
vendors. Quotation drawings and specifications were not prepared and Submitted for
vendor evaluation since this was beyond the scope of this effort. Furthermore, no
allowance was made for design, quality assurance, facility preparation, or administrative expenses. However, the relative costs indicate trends and the exercise shows
which factors are current-level dependent.
The relative total cost is shown in Fig. 3 and the relationship between cost
components is shown in Fig. 4. The results indicate that (1) the component costs for
conductor, substructure, power supply subsystem, and refrigerator/liquefier
subsystem, generally increase with current level; (2) the cost for fabrication of
windings and substructure generally decreases with current level; (3) the combined
effects of items (1) and (2) is to yield a relatively flat minimum in the total system cost
in the vicinity of 100 kA. Alternate cases were also considered in which the allowable
heat flux from the conductor surface was varied between 0.3 and 0.9 W /cm 2 • The net
change in the bottom line total cost was a few percent.
There are several factors inherent in the study which tend to favor the higher
current levels. For example, the design assumes each conductor to be surrounded by
a substructural channel. Although this is necessary at the high current levels to satisfy
the local bearing pressure constraint assumed for the conductor, it is not necessary at
the lower levels where several conductors might be housed in each substructural
module. This approach would tend to make winding fabrication less costly at lower
current levels.
The study also assumed that the amp-meter requirement and winding envelope
remained independent of current level. In fact, the overall current density would
probably decrease somewhat as current level increased, therefore leading to a
greater conductor requirement and a larger winding with a need for an increase in
superstructure and dewar size.
1.2
1--
<n
0
u
0.8
..J
""0
1--
1--
"'>
>=
""..J
"'
Q:
Fig. 3. Relative total system cost vs. Operating current Ievel.
0.4
0
100
CURRENT, kA
200
18
R. J. Thome, R. D. Pilllbary, H. R. Sept, IIDd 8. 0. Pedenon
10°
Tolal Cosl
$
,_"'
z
w
z
0
a.
c
A
~
H
I
G
10 - 1
::e
B
0
<.>
...0
0
,_
F
"'<.>0
w
>
;::::
*
E
10-2
_,
~
w
a:
8 • Substruclure
C • Superstructure
0 " Oewar
E • Power Su pply
Subsystem
0
F • CryoQenic Subsystem
G " Mlsceltoneous Componenls
and Shlpptn-.,
H • Windl n9 ond Subtlructure
Assembly
I " Assombly to Superstructure,
Oewar ond Support
S ystems
100
200
CURRENT, kA
Fig. 4. Variation of component costs; total cost for a given
current Ievel is 1.0 (exclusive of design, quality assurance,
facility preparation, or administrative costs).
In addition, the lifetime cost of power to operate the cryogenic and power supply
subsystems would tend to shift the minimum to lower Ievels if this operating cost
were added to the capital cost of the magnet system.
As a result of the above, the relative total cost curve would be expected to show
somewhat less variation at the low-current end and more variation at the high current
end with a slight shift of the minimum to lower Ievels. Though the effects must be
evaluated in more detail and are dependent on the scale of the magnet, the
implication is that future reference designs for large-scale MHD magnets should
consider Operating current Ievels somewhat higher than the 10 to 20 kA typically
used to date.
REFERENCES
1. R. J. Thome, J. W. Ayers, T. M. Hrycaj, and R. D . Pillsbury, "Design of Superconducting Magnets for
Magnetohydrodynamic (MHD) Applications," Final Report ERDA Contract No. E (45-18)-2217,
June 1977.
2. R. J. Thome, R. D . Pillsbury, J. W. Ayers, and T. M. Hrycaj, IEEE Trans. Magn. MaJ-15(1) : 306
(1979).
3. T. R. Strobridge, NBS Tech. Note 655 (June 1974).
A-3
FINAL DESIGN OF A SUPERCONDUCTING
MHD MAGNE TFORmE COAL-FIRED
FLOW FACILITY AT THE UNIVERSITY OF
TENNESSEE SPACE INSTITUTE*
S.-T. Wang, L. R. Turner, L. Genens, W. Pelczarski, J. Hoffman, J. Gonczy,
H. Ludwig, R. C. Niemann, K. F. Mataya, and E. Kraft
Argonne National Labaratory
Argonne, Illinois
and
W. Young
University of Wisconsin, Madison, Wisconsin
INTRODUCf iON
The superconducting magnet system (SCMS) consists of a superconducting
magnet, magnet cryostat, a helium refrigerator/liquefier facility, a helium gashandling system, apparatus for cryogenic transfer and storage, a magnet power
supply, an integrated instrumentation and control system including a computer for
magnet operation, data acquisition, system status and diagnosis, and magnet protection. The complete systemwill be tested at Argonne and installed at the Coal-Fired
Flow Facility (CFFF) at the University of TennesseeSpac e Institute (UTSI) in 1981.
The cryogenic aspects and magnet safety are described and analyzed elsewhere C' 2 ].
The MHD warm bore, the magnet cryostat Iayout, and the axial field profile, are
shown in Fig. 1. Significant magnet system parameters are listed in Table I.
It is recognized that the UTSI SCMS must serve as a model with the design
scalable to future large MHD magnets as the Engineering Test Facility (ETF) andin
the full-size base Ioad systems. The successful experiences gained in designing and
fabricating the UTSI SCMS will definitely advance the state-of-the-art of large
MHD magnets and will provide a significant technological data base for future large
MHD superconducting magnets.
For a given conductor design, cooling provisions, and given coil structure, one
can compute the minimum propagating energy and perform verification experiments. Nevertheless, because of the complex mechanical nature of a given coil and
lacking acceptable criteria for the size of the disturbance against which the conductor
should be stable, the UTSI SCMS conductor is designed to be absolutely or
unconditionally cryostable. Despite the absolute stability, an achieved average
* Work supported by the U. S. Department of Energy.
19
20
1
r--
S.-T. Wang etal.
~00
cm
6~HCTIVE
FIELO
~
6
FIELD
TESLA
4.8 T
4.8 1
IN
3
AX I AL
POSITION ,
cm
-WARM B<JIE
108.8
- - t -- -300 cm HF. FIELD
80cm
DI A.
cm
- aA.
•~"--- ---'--
1-- - -- - -- - -
1
640 cm
- - - - -- - - -- --
-
-l
Fig. 1. MHD warm bore, cryostat Iayout, and field profile.
current density of about 2000 A/cm 2 over the coil cross section is adequate so that
the economy of the total ampere-turns needed is quite good.
The coil configuration is the U . S. SCMS type circular saddle eJ. The coil will be
assembled on the magnet bore tube with spiral banding. The bore tube will be about
6.3 cm thick (in the thickest section) and the banding will be strong enough for coil
assembly but too weak to transmit the 30,180-kgr/cm maximum burst force to the
bore tube. Fifteen ring girders will be used as the superstructure to contain the force.
The decentering force of about 0.2177 x 106 kgt will be taken up by end ftanges and
bore tube.
COIL CONFIGURATION S
As shown in Fig. 2, the magnet is circular saddle wound, with 14 layers. The
outer 13 layers are each 4.88 m long; the inner layer consists of two subcoils: 1A,
2.04 m long; and 1B, 2.87 m long. This coil spacing provides the required field
Final Design of a Superconducting MHD Magnet
21
Table I. Magnet System Parameters for CFFF SCMS
MHD warm working bore size
MHD on-axis field
MHD etfective magnetic length
Field ripple, uniformity and field tapper
Ripple along field taper
Cross-sectional field uniformity
Field taper
Magnetic coil characteristics
Coil winding bore (minimum)
Bore tube thickness (maximum)
Winding type
Operation current
Peak field
Winding build
Average current density
Cryostability
Stored energy
lnductance
Max. Iransverse force
Coil force support
Support against external forces during operating
and shipping
Cryostat
4.2 K cold-mass weight
4.2 K cold-mass dimensions
Liquid helium inventory
Heat leak to LHe 4
Vacuum vessel, support and LN 2 shield weight
Vacuum vessel dimension
Total magnet weight
Refrigerator /liquefier facility
lnlet 80 cm, end of etfective field 100 cm
Inlet at 4.8 T, peak at 6 T, outlet at 4.8 T
3.0m
±2.5% of on axis field
±5% of on axis field
0.2T/m
119cm
-6.3cm
Circular saddle with intermediate crossovers
3675 A
6.9T
0.53m
-2890 A/cm 2 in copper;
-2000 A/cm 2 in winding
0.142 W/cm 2
-168MJ
21H
30,180 kgdcm
Partial support from bore tube and major support
from external ring girders
3 g vertically down, 1 g vertically up, ±2 g axial, and
±1 g lateral
1.32 X 10 5 kg
-3.16-m diam x 5.05 m long
8962liters
14.0 watts (=20 liters/hr)
-4.06 X 104 kg
-3.6-m diam x 6.4 m long
-1.73X10 5 kg
Closed-cycle refrigeration capable of system cooldown in 4 weeks and liquid helium production
of 50 liters/hr. Other components are liquid
helium storage dewars, helium gas recovery.
profile. This coil cross section is chosen so that it is efficient in producing magnetic
field and keeps the azimuthal force buildup in each layer to an acceptable Ievel.
Layers two through nine all subtend an angle of 53°, ensuring that the radial force
from each layer is supported by the next.
CONDUCTOR DESIGN
To reduce conductor costs, three grades of conductor, A, B, and C, designed for
fields up to 7 .5, 6.5, and 4.5 T, respectively, will be used. The critical current is
4500 A at 4.2 K.
Grade A will be used at fields up to the peak field; grade B, up to 6.0 T; and
grade C, up to 4.0 T. Layer 1, containing only 42 turns, will consist of grade A
conductor. Layers 2-4 will have both grade A and B conductors. Layers 5-8 will have
all three grades; and the remaining six layers will have both grade B and C conductors. For the inner layers, the field where the layer begins to turn over at the
high-field end determines the turn at which grades must be changed; for the outer
layers, it is the field at the high-field end.
.Z2
S.-T. Wang et al.
SECTHll>l
A-A
SADDLE
COILS
BORE
TUBE
LOW
FIELD
END
HIGH
FIELD
END
TOP
VIEW
_ ::l,
f---- - - - - 4 . 8 8 1 1 -- -- -----t
Jlm 1_~~
RAD. .S91m
lA
RAD. _I.B - - - - -
t
j
.
SECTION B-B
Fig. 2. Coil configuration of circular saddle coil.
As shown in Fig. 3, the selected conductor will be 3.10 cm high with conductor
thickness varying according to the field grades. Present design plans call for the
superconducting insert to be a soldered cable of multiple wires of Nb-48% Ti
superconducting composites transposed around a copper strip. The stabilizer will be
an integrated piece with a longitudinal groove. The superconducting cable is to be
bonded by 50-50 noncorrosive soft solder to the longitudinal groove of OFHC
copper stabilizer. The depth of the longitudinal groove is such that the surface of the
superconducting cable strips will be 0.76 mm below the front face of the copper
stabilizer.
COIL STRUCI'URE
The turn-to-turn and layer-to-layer winding detail are shown in Fig. 4. The
turn-to-turn insulation will be provided by a pultruded fiberglass strip with keystoned cross section. The keystoned feature eliminates the tedious Iabor of inserting
angle-correcting wedges during coil winding. The pultruded fiberglass strip will be
fashioned in a fishbone-like pattern so that vapor-locking will be avoided and that
about 30% of the broad face will be cooled. The conductor designed with this face
cooling and 50% edge cooling will be cryostable with a steady-state heat transfer of
23
Final Design of a Superconducting MHD Magnet
TWENTY 1.02 mm
TWENTY 0.89 mm DIA.
SC WIRES-TWIST
DIA.
SC WIRES-TWIST
FllliiENT Oll . '
PITCH '
STR lND
DIA. a 10»...
FILAMENT
STR lND PITCH ' 0.2 TURN/tM
10 ...
0.2 TURM/tM
lMNEALED
COPPER
AHNEllED
COP PE A
SEVENTEEN 0.79 mm DIA,
SC WIRES-TWIST
FllliiENT Oll,' 60..._
STRAND PITCH ' 0.2 TURN/tll
AMM Ell ED
COPPER
Fig. 3. CFFF SCMS conductor.
PARTIAL VIEW OF SADDLE COI L
{ NOT TO SCALE)
PULTRUDED FISERGL ASS
BANOING- SPIRAL WO UNO
SUPERCONDUCTOR
KEYSTONE·SHAPED
PULTRUDED FISERGLASS
SUPERCONOUCTOR
( 4.7 mm • 31 mm )
END TURN REGION
STRAIGHT REGION
TURN·TO·TURN STRUCTURE
LAYE R· TO·LAYER STRUCTURE
Fig. 4. Coil structure of turn-to-turn and layer-to-layer.
24
S.-T. Wang etal.
about 0.14 W /cm 2 to the liquid helium. This low heat ftux assures the unconditional
stability for the conductor.
The CFFF SCMS is to consist of 14 coillayers. Except for coils in layer 1 which
will be banded to the bore tube by 321 stainless steel, each coillayer, having two
circular saddle coils, will be assembled onto the bore tube by pultruded fiberglass
banding of 1.85-cm width by 0.71-cm thickness. The pitch length is 3.7 cm for the
straight coil region and 2. 78 cm at the coil end regions. The pitch length is reduced at
the coil end region because the conductors in the coil end are nearly parallel to the
spiral banding at various locations. Thus about 50% of the conductor edges will be
cooled in the straight coil region while about 30% of the conductor edges will be
cooled in the coil end region.
A micarta coil form, similar to the one used in the U. S. SCMS, will be employed
to wind the CFFF SCMS saddle coil. The coil form will be fabricated from
3.084-cm-thick linen base phenolic Iaminate. The form is tobe slotted to allow it to
conform to the cylindrical saddle shape. The slots will be filled with glass fillers and
shell828-Versamid 140 epoxy to sustain the curved shape.
It is planned to insulate the bore tube with insulating sleeves which are
constructed of a wet-wound fiberglass cylinder of about 0.635-cm thickness. The
cylinder will be machined with cooling grooves 1.428 cm wide by 0.476 cm in depth.
A layer of 0.635-cm-thick G-10 coil blanket is tobe placed over the insulating
sleeve cylinder to provide both 50% edge cooling and coil support at the coil end
region. Similar coil blankets of 0.655-cm thickness are used to insulate the stainless
steel banding by placing the coil blankets ahove and beneath the stainless steel
banding of coillayer 1.
CRYOSTABILITY
Calculated recovery currents for the three grades of conductor are 3780 A at 7 T
for grade A, 3860 A at 6 T for grade B, and 4300 A at 4 T for grade C. The design
calculation is based on a heat transfer of 0.15 W /cm 2 • All such recovery currents are
above the design operating current of 3675 A. Specialattention must be paid to the
cryostability of the end regions, for three reasons: (1) Peak fields in Band C grade
(not A) conductors occur at these regions; (2) there is less edge cooling, because the
banding pitch is tighter; and (3) there may he lengths of conductor, up to 33 cm
(13 in.) long, covered by the handing in a region where the handing and conductor
run parallel.
ELECTROMAGNETIC FORCES AND PRESSURE
The conductor in the high-field (6.0 T) cross section A-A of Fig. 2 exerts a hurst
force of 30,180 kg,/cm outward on the girders; a clamping force of 24,287 kg,/cm
pushes the two halves of the magnet together.
Figure 5 shows the radial magnetic pressure due to the radial and azimuthal
components of force for each 5° azimuthal increment, totaled over all 14 layers to
give the net pressure and also totaled to the layer which gives the peak pressure. The
radial pressure shown in Fig. 5 includes the radial pressure due to the azimuthal
forces; the comhined pressure gives the hurst force of 30,180 kgt/cm. Figure 5 also
shows the accumulated pressure for each layer, calculated in the high-field cross
section. The nurober of turns per layer were chosen to Iimit this average pressure to
prevent yielding in the copper stahilizer of the conductor. The coil ends contrihute
axial forces as weil as hurst and clamping force.
Final Design of a Superconducting MHD Magnet
15
40
..,.
30
PEAK RADIAL PRESSURE
AMONG ALL LAYERS
( BOTTOM SC ALE)
:::.J!
w
a::
=>
"'"'
w
a::
20
<>.
RAOIAL
PRESSURE
LAYER 14
( BOTTOM
10
SCALE )
0
10
20
30
40
50
55'
DEGREES
GAP .
Fig. 5. Magnetic forces and pressure .
The decentering forces on each coil are especially bothersome for a dipole
magnet with a tapered field. These forces result from the asymmetric field distribution. Each layer experiences a different field at the two ends, and consequently
different and noncancelling forces. The 219,500 k&r is distributed nearly uniformly
over the outer 13 layers.
26
S.-T. Wang etal.
STRUCfURAL SUPPORT AND STRESS ANALYSIS
The bore tube provides some structural support for the cold mass and magnetic
forces. The assembly of two end ftanges and a cylindrical section will weigh
13,152 kg. The bore tube details and dimensions are shown in Fig. 6.
The derentering magnetic force is supported by the ftange at the high-field end
and by a step in the tube. In addition to the magnet forces, the bore tube assembly is
designed for a 3.4-atm (50-psi) pressure in the helium vessel.
The end ftanges are annular plates of 2.34-m diameter supported at the inner
boundary by the bore tube. The outer boundary attaches to the outer helium shell.
Bending moments transferred by the end ftanges to the bore tube are supported by
gussets on the tube section outboard to the ftanges. A total of 32 gussets (including
four supportlink gussets) are provided on the high-field ftange and 16 (including four
support link gussets) are provided on the low-field ftange. All gussets have a
minimum thickness of 2.54 cm except the 10.16cm thick gussets at the cold-mass
support link locations. The ftanges will be cast from ASTM A 351-7 5 grade CF8M
modified stainless steel. This material contains a maximum of 0.04% carbon and is
the cast alloy of wrought 316-L. Cast stainless properlies and soundness are
enhanced with an increase of ferrite. Since the increased permeability associated
with ferriteisnot detrimental to the design, ferritein the range of 5-15% has been
specified. The yield stress of the ftange material will be at least 517 MNI m2 (7 5 kpsi)
at 4.2 K. The maximum calculated stress 339 MN/m 2 occurs at the inner corner
SUPPORT LINK
LOAD UNE
A
G
8
I
D
II
K
II
-
339 •250
88
1~0
33
1~7
29,&
I~
6Z
IIAGNETIC
PLUS IIEUUII
LOAOING
PRESSURE
~
90"~
Fig. 6. Bore tube, end ftange, and stresses.
Final Design of a Superconducting MHD Magnet
27
where the high-field end ftange joins the cylindrical tube. To minimize the ftange
momentstransferred to the bore tube, a 22.86-cm (9-in.) stub of tubewill be cast as
an integral part of the ftange. This positions the weld in a location where the moments
have essentially died out.
Fabrication of the tubular section of the assembly will be from rolled and welded
annealed, and pickled, corrosion-resisting chromium nickel steel plate type 316-L,
as per ASTM A240-75. The 4.547-m-long tubewill be fabricated from four rolled
sections, solution annealed prior to welding. This method of fabrication results in one
longitudinal and five circumferential welds. The stress value at various high-stress
points are indicated in Fig. 6.
The 11 main girder rings are 30.48 cm wide, spaced 2.54 cm apart, and
symmetrically located over the 300-cm effective field region. Each ring consists of
two 130° cast stainless steel segments pinned to six (three per side) aluminum tie
plates as shown in Fig. 7. The cross section of the main girder segments is an 1-beam
with a solid center portion. Thesesegments will be cast fromASTM A 351-75 grade
CF8M (type 316 stainless steel).
Selection of aluminum tie bars in the main girder rings was made to minimize the
weight and to assure that the girders will be tight against the fiberglass bands after
cooldown. Three 5.08 x 20.32 x 165.6-cm-long plates per side fabricated from
2219-T87 aluminum have been specified to meet the need of good ductility and high
yield strength.
The pin selected for the finger arrangement shown in Fig. 7 is 6.67 cm in
diameter and is solution treated and aged A-286 stainless steel with an estimated
yield of 896 MN/m 2 (130,000 psi) at 4.2 K.
The conductors at each coil end will be supported by two end ring girders made
of 90° segments of 2219 T87 aluminum alloy. The girder located closest to the
high-field plane will have a radial thickness of 30.48 cm whereas the outer girder will
be 20.32 cm thick. The segmentswill be cut from a 5.08-cm-thick plate stock. The
maximum tensile stress in the body of the 20.48-cm ring girder is 193 MN/m2 • The
maximum tensile stress in the girder at the pin holes is 234.4 MN/m 2 •
POWER SUPPLY, INSTRUMENTATION, AND MAGNET PROTECTION
The power supply will have an output characteristic of 200 V and 5000 A. A
0.05-0 dump resistor ~submerged in a water tank, will be used to safelydischarge the
magnet in the event of an emergency. Design considerations indicate that the magnet
can be energized in 70 min and discharged in 7 min. The maximum discharge
terminal voltage will be 100 V with respect to the groundin-g center tap of the dump
resistor.
A total of 95 strain gauges are distributed among high-stress points. Thermocouples fabricated of copper-constantan, silicone diode, and Au-Fe are used within
the coil winding, helium vessel, bore tube, ring girder, cold-mass support and
nitrogen shield system. Potential taps will be needed for monitoring charging
voltages and the normal transition of the conductor. Motion of the conductor will be
monitored by an accelerometer and microphones in addition to the potential taps.
Hall probes will be used to measure the MHD channel field and the peak field in the
winding. Finally, the liquid helium Ievel and the liquid nitrogen Ievel will be
measured by a NbTi probe and oxygen bellow assembly, respectively.
MAIN RING GI RDER
UNDERSIDE VIEW
) - -- ({!) -
EJ1]
..
END
TOP \/ l EW
2219 - T87
ALUMINUM
PLATE
6.67-cm- DIA. PIN
E$cJ
PLATE
2219·187 ALUMINUM
~5-cm-THK.
~,., _,,._ '"
Fig. 7. Main ring girder and end ring girder.
2219-187 ALUMINUM
TIE-PLATE
6.67-cm- DIA . PI N
CAST SS
RING GIRDER
l
fGRDOIIE PATTERN
2219-T87 ALUMINUM
TIE- PLATE
6.67-cm- DIA. PI N
Final Design of a Superconduding MHD Magnet
29
1. R. C. Niemann, S.-T. Wang, J. W. Dawson, L. Genens, R. P. Smith, L. R. Turner, J. D. Gonczy, J.
Hoffman, K. F. Mataya, P. Smelser, P. C. Vander Arend, and S. Stoy, in Advances in Cryogenic
Engineering, Val. 25, Plenum Press, New York (1980), p. 30.
2. L. R. Turner, S.-T. Wang, R. P. Smith, P. C. Vander Arend, and Y.-H. Hsu, in Advances in Cryogenic
Engineering, Val. 25, Plenum Press, New York (1980), p. 39.
3. S.-T. Wang, R. C. Niemann, R. L. Kustom, P. Smelser, W. J. Pelczarski, L. R. Turner, E. W. Johanson,
E. F. Kraft, S. H. Kim, J. D. Gonczy, H. F. Ludwig, K. F. Mataya, W. E. LaFave, F. J. Lawrentz, and F.
P. Catania, in Advances in Cryogenic Engineering, Val. 23, Plenum Press, New York (1978), p. 17.
DISCUSSION
Question by E. Mullan, Westinghouse R & D Center: What is the expected power output from the
MHD facility?
Answer by author: The maximum power output from the MHD facility will be about 80 MW
(thermal).
Comment by T. Hrycaj, Magnetic Corporation of America: I do not understand how the fishboneIike turn-to-turn structure helps avoid vapor locking. In Fig. 4, the fishbone-like pattern appears to cut off
any radial ventilation of gaseous helium between layers. Furthermore, the lower half of the fishbone-like
pattern Iooks like it would actually trap rising helium bubbles.
Answer by author: Vapor locking is avoided because the longitudinal groove of the conductor is
recessed below the broad face of the conductor and also because the punched slots of the turn-to-turn
insulator do expose the slots to the longitudinal groove of the conductor.
A-4
CRYOGENIC ASPECfS OF THE UTSI-CFFF
SUPERCONDUCfiNG DIPOLE MAGNET
FOR MHD RESEARCH*
R. C. Niemann, S.-T. Wang, J. W. Dawson, L. Genens, R. P. Smith,
L. R. Turner, J. D. Gonczy, J. Hoftman, and K. F. Mataya
Argonne National Laboratory
Argonne, Illinois
P. Smelser
Independent Consultant
Jefferson, Missouri
and
P. C. Vander Arend and S. Stoy
Cryogenic Consultants, Inc.
Allentown, Pennsylvania
INTRODUCI'ION
The Argonne National Laboratory, under the sponsorship of the Fossil Energy
Division of the U. S. Department of Energy, has designed and is constructing a 6-T,
0.8-m minimum warm bore superconducting dipole magnet system for magnetohydrodynamic (MHD) research. The system will be installed and operated at the
University of TennesseeSpace Institute (UTSI) Coal Fired Fuel Facility (CFFF). The
systemwill consist of a coil assembly contained in a liquid helium cryostat, a helium
refrigerator/liquefier slstem, and controls and instrumentation for cooldown and
steady-state operation L1-4].
MAGNET CRYOSTAT
The cryostat consists of a helium vessel surrounded by a liquid-nitrogen-cooled
thermal shield contained in a vacuum vessel. The cryostat geometry is shown in
Fig. 1.
Steady-state heat fluxes to the helium vessel and the thermal shield have been
minimized by the use of multilayer insulation along with low-heat-leak support
* Work supported by the U. S. Department of Energy.
30
Cryogenic Aspects of the UTSI-CFFF Superconducting Dipole Magnet
31
Fig. 1. UTSI-CFFF MHD magnet geometry.
structures. Instrumentation Ieads are sized to reduce the heat leak with intercepts
employed to reduce conduction heat flux. Bafftes will be employed to reduce the
radiation heat flux in penetrations. The steady-state heat flux to the helium vessel is
14.0 W or 19.6 liters/hr. The steady-state heat flux to the thermal shield is 179.6 W
equivalent to 4.3 liters/hr boil-off. The cryostat design parameters are given in Table
I with internal details shown in Fig. 2.
WEIGHT SUPPORT RING
SUPPORT TUBE
LHe VESSEL
VACUUII VESSEL
ALUMINUM
RING
GIROERS
COLO MASS SUPPORT
WARM BORE
PEOESTAL
FLOOR PAO
Fig. 2. UTSI- CFFF MHD magnet cryostat internal details.
31
R. C. Niemann et al.
Table I. UTSI CFFF SCMS Cryostat Design ~arameters
He4 Vessel
Designpressures (gauge)
lotemal 3.45 x 105 Pa (SO psi)
Extemal1.03 x 105 Pa (15 psi)
Weight
Bore tube and end ftanges
Coil assembly
Ring girders
Outer shell
Total
Uquid inventory
Loads
Radiation
He4 vessel supports
Leads (c:ontribution with excess cooling)
12R loss in conductor joints
Penetrations, instrumentation Ieads,
standoffs, etc.
Total
Tempersture
Boil-off rate
Material
Thermal radiation shield
Type
Loads
Radiation
He 4 vessel support heat intercepts
He4 vessel neck intercepts
Standoffs, piping, etc.
Total
Tempersture
Boil-off rate
Weight
Material
Vacuum vessel
Design pressures (gauge)
Internal1.38 x 105 Pa (20 psi)
Extemall.03 x 105 Pa (15 psi)
Weight
Shell
Support structure
Total
Material: 304 ss
17,230kg
57,6SOkg
47,620 kg
7,070kg
129,570 kg (142.8 tons)
8,9601
94.1 m2 at 0.043 W/m 2
8 supports at 0.125 W /support
61 joints at 0.04 WI joint
4.5K
19.6liters/hr
316 ss (cast and wrought)
= 4.17W
= l.OOW
= 1.48W
= 2.44W
= 4.89W
13.98 w
Conduction cooled with Ioad into liquid nitrogen
reservoir. Aluminized Mylar on both sides.
97.1 m2 at 0.645 W/m 2
8 supports at 3.02 W /support
"'62.63W
=24.16W
61.46W
31.41 w
180.00W
80K
4.3 liters/hr
2,180 kg (2.4 tons)
304 ss with copper tube liquid nitrogen tracing
17,510kg
20,950kg
38,460 kg (42.2 tons)
The helium vessel, fabricated from 316 ss, is designed for the stresses of
cooldown, steady-state operation, and fault conditions. Cooldown will be by forced
convection of helium gas. Manifolding will provide uniform cooling of coil, ring
girders, and helium vessel. Initial filling of the helium vessel will be through a tube to
the bottom of the helium vessel. Refilling of the helium vessel will be through a tube
which terminates in the upper regions of the helium vessel. The connections between
300- and 4.5-K environmentswill consist of two vertical penetrations at the end of
the vessel. Two ports will provide redundant pressure relief.
The helium vessel is suspended by a low-heat-leak support system employing
tension-member-type supports. Epoxy fiberglass support members will be heat
Cryogenic Aspects of tbe UfSI-CFFF Superconducting Dipole Magnet
33
intercepted at an intermediate point by connection to the thermal shield. The
support system has four pairs of hangers affixed to each end of the helium vessel. The
tension members will be preloaded to 50% of their maximum design Ioad to protect
against possible impact loading.
The helium vessel will be surrounded by a shield consisting of a liquid-nitrogencooled metallic envelope to intercept thermal radiation from 300 K. The shield has
an average temperature of 80 K with a maximum temperature difference of 3 K.
Considerations were made for eddy-current-induced forces in the shield associated
with rapid discharge of the magnet. The shield incorporates a 304 ss sheet cooled by
liquid nitrogen flowing in copper tubing. An externalliquid nitrogen supply reservoir
sized to permit refilling a minimum of once every 48 hr will be employed.
The space between the helium vessel and the thermal shield will contain ten
layers of multilayer .insulation. The space between the thermal shield and the vacuum
vessel will contain 50 layers of multilayer insulation. The shield will be instrumented
with thermocouples to monitor performance and to provide for diagnostics during
the cooldown and steady-state operation of the magnet.
The assembly of the magnet cryostat will be completed by the installation of the
vacuum vessel, designed as both a pressure vessel and a support structure. The 304 ss
vessel will withstand the stresses of initial evacuation and purging, cooldown,
steady-state operation, and fault conditions. Closure of the vacuum vessel will be at
the helium vessel 300-4.5 K penetrations. Bellows will be employed to allow for
differential thermal contraction without development of large stresses.
THE CRYOGENIC SYSTEM
The cryogenic system includes all elements for pumpdown and purge of the
magnet cryostat, cooldown and filling from 300 K, and steady-state operation. The
cryogenic system has been designed with emphasis on redundancy, high reliability,
and safety. A schematic of the closed-loop helium flow system is shown in Fig. 3.
A detailed arrangement of the cryogenic equipment is shown in Fig. 4.
A helium refrigerator /liquefier will be employed to cool down the magnet from
300 to 20 K, to initially fill the helium vessel, and to provide liquid for steady-state
operation. The refrigeration capacity is as required by the stipulated magnet
cooldown time. The liquefaction capacity of 50 liters/hr will allow a redundancy
factor of approximately 2.5 relative to the predicted liquid helium boil-off. Liquid
nitrogen precooling will be used to aceeierate the early phases of cooldown. The cold
box will employ turboexpanders.
A helium compressor system provides process gas for the refrigerator/liquefier.
The system can operate at approximately 50% rated capacity. The compressor
system will be used to pump boil-off gas to storage.
A 7500-liter liquid-nitrogen-shielded liquid helium storage dewar will be
employed for filling the magnet, as a liquid reserve for times of equipment outages,
and for storage of helium during magnet shutdown periods. Provisions will exist for
the filling of the storage dewar for a liquid helium tanker which will be the primary
source of liquid helium for the initial filling.
Helium gas storage will consist of a single large storage tank having a capacity
of 113,600 Iiters (30,000 gal) at a maximum storage pressure of 1.72 x 106 Pa
(250 psig), i.e., approximately 2500 Iiters of equivalent liquid.
A cryogenic console will contain control and diagnostic equipment for the
operation of the cryogenic system. The console will be located at the refrigeration
~1.721106 Pa
II g/ooc
COMPRESSOR
No. I
u.__
..."'"'
!
0
.."'
w• Yn .. n
i1.72x10 6 Pa
18 9/IOC
No.2
COMPRESSOR
~vn
!0
l
LHo
(7500 L )
DEWAR
II
200W.4l 4.5 K
50 L/HR
REFRIGERATOR/LIQUEFIER
YVI"'Irn
,\.'r.
~-}
He GAS RETURN
5'.
COOLDOWN
RET RN
LHo
MAGNET
SUPERCONDUCTING-
FILL LINE
DEWAR
SUPPL V
f _?_
I
fj'~
HEADER
Fig. 3. UTSI-CFFF SCMS cryogenic schematic.
~
COOLDOWN
'
I
(
I
I
~
I
r-
8960 L
LHo
t
400L
Jj
t
t
I
f
FLOWMETE RS
[][ ]!]
~ ..L..,
•••
RESERVOIR
( '"•
HEATER
{p-
1-
ro
1-
SUPPLV
Ho GAS
HIGH•
000~'""'
1
~
t
• t •
-·
"r-W-
1900 L
~
r-
'\..'r.
LN 1 FLASH TANK
r--1
1-
@ 1.72 aiO' Po
113,600 L
Ho GAS STORAGE
MEDIUM- PRESSURE
PRESSURIZATION
22,700 L
U.T.S.I. LN 1 DEWAR
WARM
9
1
LN 1 TO REFRIGERATOR
f Tg
-.::<2.
I--
Cryogenic Aspec:ts of the UTSI-CFFF Superconducting Dipole Magnet
LIQUEFIER/REFRIGERATOR
1 _ _,/V' '-I
,.- CRYOGENIC RELAY PANELS
\
I
1\!IJj
~
\
l
I
\ SCMS CONTROL EQUIPMENT
WITH CCIIPUTER
-----.
\ La '
coNTRoL
LHe OEWAR
35
8
I
I
I
BUILOING
I
I
I
I
I ____ j
HELIUM
TRANSFER
'I LINES
L-
PIPING RACK
~*=t---rfl
~i
TEST BUILOIN.G
NORTH
(
SCALE IN METERS
------'=-""""'""'=::----PO-WE_R_,SUPPLY, ETC.
t
10
LsuPERCONDUCTING
MAGNET
Fig. 4. UTSI-CFFF SCMS cryogenic equipment arrangement.
equipment for adjustments during cooldown and operation. Critical parameters
required for steady-state operation will be remotely monitared and controlled from
the CFFF control room.
Liquidnitrogen will be supplied from the 22,700-liter (6000-gal) UTSI storage
dewar and will be transferred to the magnet area in insulated lines. To assure the
required liquid quality for operation of the refrigeration equipment, a 1900-liter
(500-gal) flashtank will be installed in the cryogenics area and will serve as a centrat
distribution point for liquid nitrogen to the cryostat and the refrigerator/liquefier.
A utility vacuum systemwill be provided for the initial pumpdown and purge of
the magnet cryostat, evacuation of transfer lines, refrigeration equipment, and other
elements of the cryogenic system as required.
A detailed listing of the major components of the cryogenic system is given in
Table II.
INSTRUMENTATION
Instrumentation will be provided for the Operation of the magnet system which
includes cryostat pumpdown and purge, cooldown, steady-state Operation, system
diagnostics, and safety.
The cryostat is monitared for lead gas flow, cold mass support forces, helium
level, nitrogen Ievel, helium vessel pressure, insulating vacuum, and temperatures
within the coil, the force containment structure, and the thermal radiation shield.
The cryogenic system has been designed to permit remote monitaring of certain
parameters. A remote instrument panel will be provided to monitor the critical
operating conditions of the system. The panel includes readout of pressures,
expander speeds, temperatures, and alarm signals for key components. Signals will
be provided to the magnet system control computer for automated monitoring,
analysis, and control. Remote control will be provided for J-T valve settings,
cooldown bypass valve settings, compressor shutdown, emergency shutdown, etc.
R. C. NieJaua et 111.
36
Table 0. UTSI CFFF SCMS Cryopnic Syste• Major Co•ponents
Component
Quantity
Capacity
1
2
6.0-T field with 0.8-m minimum
warm bore
50 liters/hr or 200 W at 4.5 K
0.04 kg/total (minimum)
Magnet cryostat
Refrigerator/liquefier cold box
He4 oompressor
liquid helium transfer lines
Liquid helium storage dewar
Helium gas storage tank
Cryogenic oonsole
Cryogenic rack
liquid nitrogen storage dewar
Liquid nitrogen flash tank
Liquid nitrogen transfer lines
Utility vacuum system
Cold box to LHe4 dewar
(ooaxial). liquid helium
dewar to magnet cryostat
cold box to magnet cryostat-2
1
1
1
1
1
1
From liquid nitrogen dewar to
flash tank, to cold box, and to
magnet cryostat
1
7500liters
113,600 Iiters (30,000 gal) at
1.72 x 106 Pa (250 psig)
N/A
N/A
22,700 Iiters (6000 gal)
1900 Iiters (500 gal)
N/A
OPERATION
The cryostat will be cooled down with helium gas from the refrigerator/
1\quefier. A full-ftow liquid nitrogen precooler will be included in the cold box. Flow
to the cryostat is through a vacuum jacketed transfer line. The helium distribution
piping is shown in Fig. 5. Gas is distributed to the bore tube and the ring girder areas
through internal gas headers. Flow to the bore tube is through four ftow channels
machined axially on the bore tube. Flow to the ring girders is through multiple
headers located between the girders. Distribution of ftow between the bore tube and
ring girders is accomplished with a valve located in the supply to the ring girder
headers. The results of the cooldown calculations are shown in Fig. 6. This figure
indicates the temperature vs. the relationship for the centrat cold bore tube, the
middle layer coil (i.e., coil No. 7), the outer shell of the helium vessel, and a
composite for the integrated magnet cold mass. The calculated cooldown time from
300 to 20 K is 24.9 days with a ftow of 0.04 kg/s of helium gas through the precooler.
To evaluate potential thermal stress problems associated with temperature
difterentials within the cold mass, a detailed cooldown analysiswas made. Because of
the large size of the coil and the generally porous characteristics of the final assembly,
laminar ftow exists with the resulting film coefficient for heat transfer being as low as
24 W /m2 K. However, the large surface area for heat transfer results in the cold
helium gas quickly warming up to structure temperatures. By evaluating the energy
balance and heat transfer relationships for each sector of the magnet, the temperature of each component vs. time was calculated.
Once the cold mass reaches 20 K, cooldown will consist of liquid transfer from
the storage dewar. The time from 20 to 4.5 K and filling with liquid helium has been
calculated to be 53.6 hr, the total amount of liquid helium employed for this
Operation being 12,366 Iiters.
Cryogenic Aspects of the UTSI-CFFF Superconducting Dipole Magnet
37
BORE TUBE
COOLING
HEAOERS
FILLE R WITH HO LES
Fig. 5. UTSI-CFFF MHD magnet cryostat helium piping.
Once filled, the Ievel will be maintained by periodic filling from the storage
dewar. Because of the large liquid inventory above the coil assembly, i.e., 1550
Iiters, it will be possible to batch fill the magnet with intervals as long as 24 hr
between transfers.
During non-MHD Operating periods, the magnetcold mass will be kept at a
temperature below 20 K to eliminate possible differential thermal motion which
could require careful subsequent energization.
300
280
260
240
220
100
"'~~
...
~
....
"'0..
....::11
~
180
1~0
140
120
100
80
60
40
20
COOL DOWN TIME . OAYS
Fig. 6. UTSI-CFFF SCMS cold mass temperature vs. time.
38
R. C. Niemann et al.
FAULT CONDmONS AND RESPONSES
The cryostat will be equipped with a vent system to handle major faults of the
system leading to a massive heat flux to the liquid. The following two faults were
considered:
1. The coil goes normal and the normal zone propagates.
2. Massive vacuum insulation failure occurs and the helium vessel becomes a
huge cryopanel. Calculations are based on a case where the connection between the
environment and the vacuum space are large enough so that heat transfer to the
helium vessel becomes a limiting factor. Once the liquid outside the coil is warmed,
fluid flow will start and the warmer liquid will enter the coil volume. This will initiate
quenching of the magnet and additional fluid needs to be vented to maintain cryostat
pressure at a safe Ievel.
A vent system for the liquid helium cryostat has been designed for a maximum
flowrateof 15.0 kg/s,amaximumpressurein the cryostatof 2.3 x 105 Pa (19.1 psig)
and the temperature of the fluid in the vent line of 16 K. The vent system consists of a
nominal 0.15-m(6-in.)-diameter pipe at both the 300- to 4.5-K penetrations.
Cryogenic-system-related fault conditions have been considered with those
factors having the ability to affect magnet system operation being pressure variations
resulting from liquid transfer and refrigerator/liquefier malfunction. The effect of
pressure variations is minimal owing to the large thermal mass afforded by the large
liquid inventory of the cryostat. Refrigerator /liquefier malfunction should not
directly affect the operation of the magnet since filling is from the storage dewar.
Operations of the magnet with MHD channels should provide minimal
perturbing influences. The warmborewill not be loaded by the channel so that direct
vibrational coupling should not exist. The warm bore will be provided with an
insulating Iiner capable of withstanding 10,000 V to ground.
ACKNOWLEDGMENTS
The authors wish to acknowledge the contributions of the following individuals to the design effort:
J. Kotora, D. Gacek, E. Kraft, W. Sajdak of Argonne National Laboratory; R. Waiting, independent
consultant; D. Krajcinovicof University of Dlinois Circle Campus; M. Hila! of the Michigan Technological
University; and W. Young of the University of Wisconsin.
HEFERENCES
1. S.-T. Wang, L. R. Turner, R. C. Niemann, L. Genens, and M. S. Srinivasan, "A Superconducting
Dipole Magnet System for the MHD Facility at University of TennesseeSpace Institute," presented at
13th lntersociety Energy Conversion Engineering Conference, San Diego, California, August 20-25,
1978.
2. S.-T. Wang, R. C. Niemann, L. R. Turner, L. Genens, W. Pelczarski, J. Gonczy, J. Hoffman, Y.-C.
Huang, N. Modjeski, and E. Kraft, IEEE 'li'ans. Magn. Mag-15(1):302 (1974).
3. S.-T. Wang, R. C. Niemann, L. R. Turner, L. Genens, W. Pelczarski, J. Gonczy, J. Hoffman, Y.-C.
Huang, N. Modjeski, E. Kraft, K. Mataya, H. Ludwig, B. Phillips, J. Dawson, J. R. Purcell, W. Young,
S. Stoy, and P. C. Vander Arend, "A Superconducting Dipole Magnet for the UTSI MHD Facility,"
presented at Superconducting MHD Magnet Design Conference, Cambridge, Massachusetts, October
18-19, 1978.
4. S.-T. Wang, L. Turner, R. Niemann, L. Genens, W. Pelczarski, J. Dawson, S. Kim, R. Smith, N. Kim,
J. Gonczy, J. Purcell, J. Stekly, W. Young, J. Zar, P. Vander Arend, S. Stoy, and P. Smelser, "A
Superconducting Dipole Magnet System for the CFFF MHD Facility at the University of Tennessee
Space Institute," presented at 18th Symp. on Engineering Aspects of MHD, Butte, Montana, June
18-20, 1979.
A-5
SAFETY ANALYSIS OF THE UTSI-CFFF
SUPERCONDUCTING MAGNET*
L. R. Turner, S.-T. Wang, and R. P. Smith
Argonne National Laboratory
Argonne, Illinois
P. C. Vander Arend
Cryogenic Consultants, Inc.
Allentown, Pennsylvania
and
Y.-H. Hsu
General Atomic Company
San Diego, Califomia
INTRODUCI10N
Argonne National Labaratory is building a large superconducting dipole
magnet [ 1] for MHD research at the University of TennesseeSpace Institute-coal
Fired Flow Facility (UTSI-cFFF). In designing such a large (170-MJ stored energy)
magnet, great attention must be devoted to the safety of the magnet and personnel.
The conductor for the UTSI-cFFF magnet incorporates significant copper
and contributes to the magnet
stabilizer' which both insures its cryostability
safety. This paper first presents the quench analysis, followed by the cryostat fault
condition analysis. Two analyses of exposed turns follow: The first shows that gas
cooling protects uncovered turns, and the second that the cryostat pressure relief
system protects them. Finally the failure mode and safety analysis is presented.
el
MAGNET QUENCH ANALYSIS
The behavior of the magnet in the event of a quench is modeled using the quench
analysis program OUENCH [3]. The code calculates the longitudinal quench velocity
for a conductor not in contact with helium coolant. For cases involving liquid helium,
this velocity can be provided as a starting parameter. The transverse quench
velocities can be provided from a calculation based on appropriate thermal properties. The quench volume of the coil grows in time as an ellipse whose axes are the
* Work supported by tbe U. S. Department of Energy.
39
6
7
8
9
10
11
12
13
14
15
16
5
1
2
3
4
Case
108
109
105
99
112
118
118
125
156
224
242
246
266
302
325
236
Decay time
constant,
s
54
63
51
67
71
115
146
124
173
145
241
276
243
55
59
61
Peak
temp.,
K
600
584
619
643
673
517
545
526
640
286
252
248
219
180
200
538
Peak inductive
voltage,
V
0.303
0.294
0.309
0.319
0.404
0.263
0.278
0.268
0.396
0.158
0.138
0.134
0.116
0.083
0.071
0.327
n
Final
resistance,
3.50
2.00
15.00
31.00
7.50
15.00
1.00
0.75
0.32
0.55
0.55
0.32
0.32
15.00
0.05
0.32
Longitudinal
quench velocity,
m/s
-5%
-5%
-5%
-5%
-5%
-5%
-5%
-5%
-5%
-1%
-1%
-1%
-1%
-0%
-5%
-1%
Ratio of transverse
quench velocity
to longitudinal
0.73
0.71
0.75
0.76
1.00
0.69
0.68
0.65
1.00
0.40
0.37
0.35
0.31
0.24
0.19
1.00
Fraction
energy
in coil
0
0
0
0
0
20
0
0
0
0
24
0
24
0
0
0
%Helium
Table I. Calculated Quench Results for Various Choices of Quench Velocity, Coil Protection, and Helium Cooling
r
I
;z:
:<
E.
J.
~
I..
il
J:1;1'.1
:-
PI'
I
~
~
II
PI'
r
~
41
Safety Alllllysis of the UTSI-CFFF Supercouducting Mapet
300
...a:"
::>
!C 200
...
...
a:
0..
:Ii
1-
...J
ö
c.J
..."
100
c(
0..
Fig. 1. Calculated coil peai( temperature for
various quench conditions as a function of
calculated current decay time. The numbers
refer to the various cases listed in Table I.
L-----~~----~L___--~~~
100
200
300
TIME-CURRENT DECAY. s
respective velocities multiplied by the elapsed time. The ohrnie heating generated in
the winding structure as the stored energy of the field is dissipated can be calculated
by the program, along with the time constant of the decay, the energy extracted by
the protection resistor, the peak coil temperature, and relevant voltages.
The conductor immersed in liquid helium is unconditionally stable, i.e., any
normal zone in the conductor collapses. But, when there is no liquid helium in the
winding voids, the normal zone will spread with a velocity of =750 cm/s. The
cryostat fault condition analysis in the following section is based on this "no helium"
calculation.
Table I shows the peak temperature and peak inductive voltage for several sets
of quench parameters. Without the protection circuitry described elsewhere, [ 1] the
fraction of the stored energy deposited in the coil is 1.00. The vaporization of local
liquid helium is not included explicitly in the OUENCH program. It can be modeled by
increasing the enthalpy of the conductor. The last column of TableI refers to this
additional enthalpy.
Since the code makes no heat transfer calculations, the presence of liquid helium
in the winding is modeled by a lower quench velocity. To see how important
turn-to-turn and layer-to-layer heat transfer is, the program was rerun with the
parameters which specify heat transfer reduced to values corresponding to a
configuration with longitudinal propagation only. The table shows the peak coil
temperature, peak inductive voltage, and decay time constant for each of the cases.
Figure 1 shows the coil peak temperature, i.e., the temperature of the region where
the quench initiated, as a function of the current decay time constant.
CRYOSTAT FAULT CONDmON ANALYSIS
The cryostat must be equipped with a vent system to handle major faults of the
system which provide a massive heat ftux to the liquid helium in the cryostat. The
following two conditions are considered.
Magnet Quench
The normal zone grows at a velocity of =750 cm/s for a coil in a helium gas
atmosphere. In calculating the required rate of venting, it is assumed that there is
42
L. R. Turner, S.-T. Wang, R. P. Smith, P. C. Vander Arend, and Y.-H. Hsu
liquid in the coil void fraction. This case appears to be very conservative because it is
not real. Ha coil really quenches at this rate, liquid helium is not present and does not
require to be expelled from the coil. But, if liquid helium were present, the normal
zone would grow very slowly if at all.
To be conservative, velocity along the conductor is set at 15 m/s (twice the value
obtained above) with turn-to-tum and layer-to-layer velocities about 16 times lower.
The cryostat contains a large amount of liquid helium in poor thermal contact with
the coil itself, which does not participate directly in the transfer of heat from the coil.
After the quench is initiated, boiling occurs inside the magnet structure, and the
vapor generated displaces liquid helium out of the coil. The displaced liquid rises
in the stack of the cryostat [4 ] and forces gas into the vapor retum line to the
refrigerator; but the vapor line capacity is limited and pressure rises in the cryostat.
The quench relief valve is set at 2.3 atm (19.1 psig), and approximately 0.5 s is
required to expel enough liquid from the coil to compress the gas in the vapor volume
of the stack to 2.3 atm. At that pressure there is no more boiling in the coil and
heating of a single-phase fluid occurs, starting circulation of fluid through the coil. To
maintain a constant pressure in the cryostat, the rate of venting must equal the
increase in volume from the heating in the coil. If the fluid vented is at 2.3 atm and
15 K, the vent line required consists of a 6-in. (0.015-m) IPS pipe equipped with a
relief valve capable of handling 9000 g/ s of helium vapor. To reduce pressure drop in
the line, it is important that the entrance should be shaped to avoid the effects of a
sharp-edged orifice.
Massive Failure of Vacuum Insolation
Consider the situation where the system experiences a massive vacuum failure
to air. Boiling occurs on the inside of the cylindrical cryostat wall and the vapor
generated displaces liquid into the stack [4 ]. Gas in the stack is compressed until the
pressure reaches 2.3 atm. This takes a very short time because of the extremely high
heat flux into the liquid. The quench relief valve [4 ] opens and maintains cryostat
pressure at 2.3 atm. Boiling stops and the cryostat contains single-phase fluid. Fluid
circulates in the space between cylindrical shell and girder rings Cl due to density
differences, with velocities of the order of 40 cm/s. The outside wall of the cryostat is
at approximately 70-7 5 K, in order for air to liquefy. Free access of air to the cryostat
has been assumed. Heat flux through the cylindrical wall is of the order of 1.25-1.5
W I cm 2 • The temperature of the liquid rises, and the volume increases as determined
by the temperature rise and mass flow rate along the wall. This increase in volume
needs to be vented to maintain constant cryostat pressure.
The required rate of venting is approximately 7200 g/s. The fluid temperature
initially is approximately 16 K. Practically all of the heat added to the cryostat passes
through the cylindrical shell. Rate of heat input to the vessel is on the order of 525
kW. The minimumrate of condensation of air (with free access to the ~ostat) is
1100 g/s. Even for air at sonic velocity, a minimumhole area of 60 cm2 (such as a
3-in. pipe) is needed to supply air at that rate.
It appears that a massive vacuum break to airwill automatically be followed by a
quench of the magnet, but the rate of mass expulsion of the warm fluid in contact with
the normal coil is not as fast as for a quench without vacuum failure. The mass
expulsion from the cryostat may be as high as double the rate calculated for quench
alone.
Finally, a vacuum failure of the liquid helium cryostat is much less serious than a
vacuum failure to air because the helium gas transfers heat to the cryostat at a much
Safety Analysis of the UTSI-CFFF Superconducting Magnet
43
60
"
50
....
<I
40
"'0::=>
0::
"'...
:Ii
"'....
"
"'...
<I
30
20
TI ME, s
Fig. 2. Recovery of uncovered length following 1-kJ perturbation.
lower rate than liquefying air. In fact, rupture of the helium vessel into a vacuum
space open to airwill immediately reduce the rate of heat transfer from condensation
because of a significant lowering of the partial pressure of air.
ANALYSIS OF EXPOSED LENGm: EFFECf OF He GAS COOLING
The analysis of an uncooled length of conductor, as might occur from the liquid
Ievel falling below the top of the coils, is carried out with the BACKSAFE program
using the back difference method, which permits the time increment to be changed
during computation without mathematical instability. A heat balance is applied to
each conductor element; the temperature changes under the combined effect of
perturbing heat input, Joule heating, heat transfer to the coolant, conduction along
the conductor, and turn-ta-turn conduction between conductors. The curve for
convective vapor cooling of the uneavered length of conductor was obtained
from the heat transfer coefficients calculated for the Rayleigh number, using the
temperature-dependent properties of 1-atm helium vapor.
Figure 2 shows the recovery of the conductor carrying 3675 A from a perturbation with a 1-kJ energy addition. The figure shows that recovery is identical
whether the 1 kJ was initially distributed among 0.20 m of conductor at 72 K or
0.40 m at 57 K. If the conductor is cooled by liquid, it recovers in about 6 s. Fora 6-m
one-half turn uneavered length, the temperature drops to 20-25 K in about 60s;
subsequently, if the magnet is being dumped with a time constant of 420 s,
temperature recovery is complete in 409 s. Whether or not the dump circuit acts, the
magnet is not harmed by a 1-kJ heat input, even assuming the conservative cooling
curve of 1-atm helium gas.
ANALYSIS OF EXPOSED LENGm: EFFECf OF PRESSURE
RELIEF SYSTEM
This section shows that the CFFF magnet is self-protecting even if the dump
resistor circuit fails while the helium level is low and a normal zone appears.
44
L. R. Turner, S.-T. Wang, R. P. Smith, P. C. Vander Arend, and Y.-H. Hsu
The magnet has good thermal conductivity along the conductor (x direction),
and poor thermal conductivities along the turn-to-turn direction (z direction) and
the layer-to-layer direction (y direction); the latter two are about 2 x 10- 3 times the
former. The conductor is unconditionally stable; consequently, any normal zone
beginning above the liquid Ievel will not propagate below. For heat transport in a
layer (x-z plane) parallel to the liquid helium surface, the contribution in the y
direction is considered as a step function; a layer is counted as soon as a section of
that layer emerges from the liquid. The temperature distribution along the y and z
directions are assumed to be the same. Thus, the problern is that of a twodimensional heat transport with liquid helium cooling just below the liquid Ievel. The
cooling by helium vapor is ignored.
Throughout the analysis [5 ], the steady-state boiling liquid helium heat transfer
is used. The latent heat of helium is adjusted to include the enthalpy needed for
raising the localliquid helium from 4.2 K to the boiling temperature. The average
temperature of gaseous helium is chosen as 5 K to obtain the pressure as a function of
time.
In the calculation [5 ], the normal region spreads out in the x, y, z directions and
the dump resistor circuitry is inactive. The temperature distribution of the top layer,
the heat generation rate, the pressure in the cryostat, and the liquid helium Ievel are
all calculated.
The results shown in Figs. 3 and 4 are for the CFFF conductor with an initial
current of 3.675 kA and an initial vapor volume of 1200 Iiters at a pressure of 1 atm.
The peak temperature is about the same for different initialliquid Ievels; typically, it
rises up to 71 Kin 70s.
Figure 3 shows the pressure and liquid Ievel as functions of time for different
initialliquid Ievels. The buildup of pressure and the lowering of liquid Ievel are faster
2.5
2 .3
0 .10
E
...J
0
<..>
...._
2 .1
0
...0
Cl.
E 1. 9
"
"'~
"'"'
"'
"'
0..
~
CAS E 2 ,
LIQ UID LEVEL
0
...J
"'
CD
"'<..>z
1.7
<t
t-
1.5
CASE I'
PRESSURE
"'ä
...J
"'>
"'
...J
0
5
0
:::;
1.1
T I ME, s
Fig. 3. Calculated liquid helium Ievel and pressure vs. time.
Safety Analysis of tbe UTSI-CFFF Sopercondocting Mapet
45
3.6
PEAK TEMPERATURE
3.2
2.8
""
"'a::::>
2.4
.....
<(
CURRENT
a:
"':I!
"'.....
""
"'
2.0
0..
<(
50
1.6
<(
""
.....
z
"'a:a:
:::>
<>
40
1.2
0..
30
20
10
0
60
70
80
90
100
110
120
TIME, s
Fig. 4. Peak temperature and current vs. time after all helium is removed.
for the lower initial liquid Ievel because a larger amount of conductor rapidly
generates and dissipates more heat into the liquid. Since the average temperature of
the vapor will probably be higher than 5 K, the calculated pressure is somewhat
underestimated. Also, the turn-to-turn cooling is neglected so the calculated
conductor temperature is slightly higher than the actual temperature.
For the worst case in which initially only part of the top layer is involved, it takes
about 70s to build up pressure to 2.05 atm with the vapor temperature at 5 K and the
peak temperature at 71 K. If all the helium is expelled, and there is no cooling at all
afterward, the peak temperature and current as functions of time are as shown in Fig.
4. The peak temperature is only 89 K, and the current decreases to 2% of the initial
operating current in 135 s. If the pressure relief valve is set at 3.0 atm, the peak
temperature is about 110 K, still a safe value.
FAlLURE MODE AND SAFETY ANALYSIS
The possible failure modes, with their probabilities, associated hazards, and
recommended actions are listed in Table II. Since the UTSI-CFFF magnet has an
unconditionally stable coil, a trouble-free cryostat, a conservative power supply, and
a carefully planned alarm, protection and diagnostic system, failure events associated
with these items are estimated in a low probability category. On the other band, less
critical item failures such as cryogenic piping rupture are estimated in a medium
category, while a facility power failure is a likely event.
The CFFF is in Seismic Zone No. 1, which means that earthquakes may cause
minor darnage to structures with periods greater than 1 s and intensities that fall in
the V and VI range on the M.M. scale. The probability of earthquake occurrence at
UTSI is low. Nevertheless, the CFFF magnet and its associated equipment are
designed so that they will remain in place and be functional following a major
earthquake in Zone No. 1.
Conductor going
normal
Loss of insulating
vacuum
Magnet coil open
circuit
Magnet/ cryostat
Magnet/ cryostat
Magnet/ cryostat
Magnet/ cryostat
Magnet/ cryostat
Magnet/ cryostat
Magnet/ cryostat
2
3
4
5
6
7
Over current or over
field
Current Iead too hot
and open circuit
Helium vessel relief
valve fails to open
during quench
Liquid nitrogen fill
valve fails to close
Failure
mode
Items
Systems
components
Low
Low
Low
Low
Low
Low
Low
Estimated
probability
Arcing in coil, Ieads,
power supply, dump
switch
Ring girder break
Liquid nitrogen
overflow
Dump resistor dumps
magnet energy
Dump magnet energy;
pressure relief valve
open; helium vent to
atmosphere (outside
building); air may be
liquefied
Arcing in coil, Ieads,
power supply, dump
switch
Burst disk will open
Failure
effects
Electrocution if in
contact with these
systems
Winding break apart
Freeze 0-ring or flesh
on contact
Electrocution if in
contact with these
systems
Explosion due to liquid
oxygen
Explosion due to liquid
oxygen
None
Hazard
description
Table II. CFFF SCMS Fallure Mode and Safety Analysis
Avoid 0-ring
freeze/personnel
contact
Personnel must be
isolated from these
systems
Provide escape
measures
Personnel must be
isolated from these
systems
Provide escape
measures
Provide escape
measures
None
Recommended
action
f
;:c
~
I
r::r.
=
J.
~
i~
<
~
~
J
~
!I'
\G
=
~
!"I
5"
I
I
!I'
r
*
Explosion or
uncontrolled
attraction by magnet
Fallure to open
during energy dump
Not enough water in
the tank during
normal operation
High-pressure gas
bottle (He or N2)
Dump resistor
Dump resistor
Power cables to
magnet
Facility power
11
12
13
14
15
Broken cable
between dump
resistor and power
supply
Power fails
Rupture
Cryogenic piping
10
High
Low
Low
Low
Low
Medium
Low
Loss of insulating
vacuum
Liquid nitrogen ftash
9
Low
Loss of insulating
vacuum
Liquid He storage
dewar
8
Injury to personnel or
magnet cryostat
Release high-pressure
gas or high-velocity
impact
Coil temperature will
rise to 100K
May open circuit unless
dump switch is closed
Freewheeling
May arc in coil, Ieads,
power supply, dump
switch
None
May have some hazard
as coil opens circuit
unless dump switch is
closed in time
Electrocution if in
contact with these
systems
None
Injury to personnel
Flying debris or
released liquid
Emergency relief valve
open
Explosion possible if
liquid oxygen
produced
Explosion possible if
liquid oxygen produced
Emergency relief valve
open
Provide battery
operated magnet
current readout
Personnel must be
isolated from these
systems
Interlock dump switch
operation to dump
resistor water Ievel
None
Locate dewar in
secured area and
provide escape route
Locate tank in secured
area and provide
escape routes
Secure this piping and
identify these lines with
warning signs
Secure and locate to
remote area
•
i
~
II
Ia
Ig.
..
f...
~
h
~
II
Er
s.
~
t'll
48
L. R. TIII'IIU, S.-T. WIIJII, R. P. Slllitla, P. C. Vander Arnd, and Y.-H. Hsu
REFERENCES
1. S.-T. Wang, L. R. Turner, L. Genens, W. Pelczarski, J. Hoffman, J. Gonczy, H. Ludwig, R. C.
2.
3.
4.
5.
Niemann, K. Mataya, E. Kraft, and W. Young, in Advances in Cryogenic Engineering, Vol. 25, Plenum
Press, New York (1980), p. 19.
L. R. Turner, S.-T. Wang, and J. Harrang, IEEE Trans. Magn. Mag-15:371 (1979).
M. N. Wilson, "Computer Simulation of the Quenching of a Superconducting Magnet," Rutherford
Laboratory, RHEL/M/151 (1969).
R. C. Niemann, S.-T. Wang, J. W. Dawson, L. Genens, R. P. Smith, L. R. Turner, J. D. Gonczy, J.
Hoflman, K. F. Mataya, P. Smelser, P. C. Vander Arend, and S. Stoy, in Advances in Cryogenic
Engineering, Vol. 25, Plenum Press, New York (1980), p. 30.
Argonne National Laboratory Superconducting Magnet Group, "Final Design of a Superconducting
MHD Magnet for the CFFF-UTSI," Argonne National Laboratory, ANL-MHD-79-12, Vol. II
(1979).
A--6
ENGINEERING ASPECfS OF CRYOGENIC
LASER-FUSION TARGETS
D. L. Musinski, T. M. Henderson, R. J. Simms, and T. R. Pattinson
KMS Fusion, Inc., Ann Arbor, Michigan
and
R. B. Jacobs
R. B. Jacobs Associates, Inc.
Boulder, Colorado
INTRODUCI'ION
For efficient burn of the deuterium-tritium fuel contained within a hollow,
sphericallaser fusion target the fuel core must first be driven to a high density and
then subsequently be elevated in temperature to initiate the reaction. To achieve
high final fuel densities the internal pressure within the target must be overcome
during the implosion. A cryogenic target, one in which the fuel is condensed as a
liquid or solid layer on the inner surface of the spherical shell, may overcome the
mechanisms [ 1] which can Iimit the final density. Fuel initially confined to the wall of
the target cannot respond quickly enough upon absorption of energy to fill the
interior volume of the target before the target implodes. At a given Ievel of Iaser
power, a cryogenic liquid or solid layer target should compress to a higher fuel
density and produce a higher yield than a target containing the same mass of fuel in
the gaseous state [2 ].
The expected advantage of cryogenic targets can be illustrated by considering
the specific example of a target filled with fuel at 100 atm. If irradiated at room
temperature, the entire amount of fuel is available to absorb energy and impede the
target implosion. However, if irradiated as a liquid-layer target at 21 K (approximately 1 K above the point where the fuel starts to solidify) only a small fraction of
the fuel is in the gaseous state, contained within the inner boundary of the liquid
layer. Raoult's law applied to a specific fuel fill of 8.4% HD, 9.3% HT, 19.7% 0 2 ,
46.2% DT and 17.0% T 2 [ 3 ] indicates that the pressure within the interior volume of
this liquid-layer target is 293 torr. At room temperature, the pressure of this
amount of gaseous fuel would be 5.5 atm. Thus, only 5.5% ofthe total amount of fuel
is available to absorb energy and impede the implosion if the target is irradiated as a
liquid layer target.
If the same target is irradiated at 15 K as a solid-fuel-layer target, the
pressure within the interior of the target is only 11 torr. This corresponds to less than
0.02% of the total amount of fuel. Further lowering of the target temperature
49
50
D. L. Musillski. T. M. Heodenoo, R. J. Simms, T. R. Pattiosoo, md R. B. Jacobs
Iikewise lowers the vapor pressure and hence lowers the amount of fuel remaining in
the gaseous phase. A solid-fuel-layer target irradiated at the minimum temperature
attainable should, therefore, yield optimum results. An extensive program has been
undertaken to test these expectations experimentally. This paper discusses an
essential element of the program-the engineering technology developed to
integrate cryogenic systems into actual fusion target chambers.
LIQUID-LAYER AND NONUNIFORM SOLID-LAYER TARGETS
From an engineering point of view, the most direct way to produce a cryogenic
target is by use of the technique referred to as point-contact conduction cooling [4 ]
(as illustrated in Fig. 1). The target is bonded to the end of a 17-JLm-diameter copper
fiber which is one element of a direct conduction path from the target to a source of
refrigeration at Iiquid-helium temperatures. This technique is chiefly applicable to
liquid-layer targets, i.e., targets in which the fuel is condensed as a liquid layer that
completely covers the inside surface of the containing shell. Once the liquid layer has
been established and stabilized by setting and stabilizing the temperature of the
cryostat, target manipulation and alignment within the experimental target chamber
proceed in the same manner as for a gaseous target at room temperature. Thus, this
7 ] to be conducted with minimum distechnique allows cryogenic experiments
ruption of the normal routine of the target chamber.
During the experimental sturlies on liquid-layer targets it became apparent that
absorption of room temperature radiation dominates the dynamics [8 ] of the fuel
layer. The liquid-layer configuration observed is the system's response to the
absorbed radiative energy. The most direct engineering way to reduce this energy
and its subsequent effect on the fuel is by the use of a radiation shield.
Figure 2 shows, in schematic form, the integration of a simple cryogenic shield
(or shroud) in the experimental chamber. A modular increase in the system's
e-
r·
t5cm
8.5cm
1 l ~COLD
;t:-rr
~ENSK)N
TIP
2cm
INDIUM
CRUSH
WUHER
Fig. 1. Point-contact conduction cooling cryostat.
Engineering Aspects of Cryogenic Laser-Fusion Targets
51
StiROUO
PISTOM
Fig. 2. Integration of simple cryogenic radiation shield in target chamber.
complexity, this shield allows a nonuniform solid fuellayer tobe formed within the
target. A solid layer of DT fuel that completely covers the inside surface of the target
(Fig. 3) can be formed by starting with a liquid layer that is protected under the
radiation shield [4 ] and quickly lowering the temperature of the shell/fiber interface .
The thermal gradient imposed across the interior surface of the liquid layer by this
procedure causes evaporation from the surface of the liquid layer. Since the heat of
vaporization for the hydrogen isotopes is large compared with the heat of fusion (a
factor of 6.6 for 0 2 ) , forced boiling of about 15% of the liquid causes the remaining
liquid to freeze on the inner surface of the glass shell.
Fig. 3. Solid-fuel Iayer on inside surface of
target.
D. L. Muslnsld, T. M. Hendenon, R. J. Simms, T. R. Pattinson, and R. B. Jacobs
52
7.0 r - - - - - - - - - - - . . . . . ,
6.0
al 70 ·J~m dia. 30 atm
bl 100jlm dia . 30 at m
cl SO·)Im dia. 100 atm
dl100·)1m dia. 100 atm
5.0
E
~ 4.0
TARGETJ
LEVEL
..J
w
~ 3.0
a:
1- 2.0
d
1.0
100
0
10
20
30
40
50
60
70
80
90
x 10- 3 sec
Fig. 4. Piston retraction of radiation shield.
150
190
EXPOSURE TIME x10·3...,
Fig. 5. Solid-fuellayer vs. exposure time. Initial fuel
approximately 85% of available fuel.
Once frozen, the temperature of the fuellayer is held below the melting point of
the fuel by conduction throu~h the copper fiber. As a result, the solid layer of Fig. 3
sublimes instead of melting [ ] when the radiation shield is retracted and the target
is exposed to room temperature radiation. A fuel layer that must sublime rather
than melt has a substantiallifetime, i.e., time during which solid fuel remains as a
continuous layer on the inner wall of the target. The amount of solid fuel remaining
on the inner surface of this target at the moment the Iaser is fired is determined by the
duration of the exposure to room temperature radiation. This exposure time is
determined by the retraction speed of the heat shield (Fig. 4). This exposure time also
sets some bounds on the range of target size and fuel fill that can be used with this
system. Figure 5 shows the amount of fuel remaining as a continuous layer on the
inner surface of a target as a function of exposure time, for various size targets and
fuel fills. The approximately 30-ms exposure time of the retraction device shown in
Fig. 4 allows a targetassmall as 70 J.l.ffi in diameter with a fill pressure of 30 atm tobe
irradiated with an appreciable amount of fuel remaining as a continuous layer on the
inner surface of the target.
Although this technique allows the formation and irradiation of solid-fuel-layer
targets, these layers are inherently nonuniform. The liquid (about 15% of the fuel)
that vaporizes during formation of the solid layer freezes as a small spheroidal
volume localized over the shell/fiber interface. Also, the amount of fuel that
sublimes during the exposure time is added to this localized spheroidal mass.
Because of this inherent asymmetry these targets are not considered optimal for Iaser
experiments. However, integration of the more complex system into the experimental target chamber afforded the opportunity to clearly identify and specify the
problern areas involved with timing an active system (the retracting shield) to the
Iaser firing sequence. The key requirements or problern areas were then addressed
when designing the system for uniform solid fuellayer targets.
PRODUCDON OF UNIFORM SOLID-FUEL-LAYER TARGETS
There are two separate aspects of producing a uniform solid fuellayer target for
Iaser irradiation. First, the system and procedure must provide a source of refrigeration to form the fuellayer in a manner that maximizes uniformity. Second, the
system must be amenable to integration of the apparatus and procedures with the
experimental target chamber. The constraints imposed by existing systems dictate, to
a great extent, the options available.
Engineering Aspects of Cryogenic Laser-Fusion Targets
35
53
HFUEL • 2.9a10 6 J
HGLASS' 4 .9110 8 J
"30
a"'
t3 25
0
PELLET DIA !00
~ 20
300K FILL PRESSUREIPl
• IOOATM
..;
)• 100~11
~
...~
LIQUID+ VAPOR
SOLID +LIQUID
SOLID
Fig. 6. Lifetime of a fuel layer exposed to room temperature
radiation.
100
150
200
T I ME , MSEC
Achieving uniformity in a solid fuel layer requires that two conditions [8 ] be
satisfied. First, any temperature gradient on a given radial surface within the target
shell or fuellayer must be small during the condensation and freezing of the fuel. Any
temperature gradient within the target is relieved by a redistribution of fuel,
evaporation from the warm region and subsequent condensation at the cold region.
This redistribution of fuel mass per unit time becomes negligible only below 10 K.
Therefore, while the fuel is condensing and freezing (35 to 18 K for the nominal
100 atm, 100-JLm-diameter target), temperature gradients are intolerable. The
second condition for achieving uniformity requires that the time for condensation
and freezing be minimized. Under the inftuence of gravity the liquid and/or liquid
and solid mixture can sag within the target. Minimizing the time minimizes the sag. A
condensing and freezing time of 20 ms permits a theoretical nonuniformity of less
than 5%. Cooling with gaseous helium can in principle satisfy both of the conditions.
The most practical method of minimizing the condensation and freezing time is
to heat the fuel in a previously frozen target, vaporize it, and allow it to refreeze
rapidly within a cold environment. In a series of well-controlled bench experiments
using an isothermal static helium environment, Miller [9 ] has demonstrated the
degree of uniformity that is possible with this method. He was able to produce targets
that met the criterion of 20% WNU. * In addition, he showed that a CW Iaser is an
efficient means of coupling heat to the target. Subsequently, Woerner [ 10] confirmed
this result in a similar system. However, integration of a static isothermal environment with the experimental target chamber is a formidable task requiring several
Ievels of complexity [ 11 ]. For the existing experimental chamber a static isothermal
environment is not required.
The primary constraints imposed by the existing experimental chamber are that
the main illuminating beams must not be blocked or degraded nor may any of the
diagnostic equipment be precluded from Operation. These constraints make it
unavoidable that the target be exposed to room temperature radiation for at least a
short time prior to the shot. The degradation of the uniformity of the fuellayer when
exposed to room temperature radiation is limited for any particular target by both
the amount and the physical properties of the fuel. Figure 6 illustrates the point. It
shows the calculated lifetime of the various phases of deuterium in a typical isolated
target, initially at 10 K, that is exposed to 300-K radiation. (The target is assumed to
have an absorptivity of unity for room temperature radiation.) After 10 ms, the
* WNU =
(maximum thickness minus minimum thickness)/(minimum thickness).
54
D. L. Musinskl, T. M. Henderson, R. J. Simms, T. R. Pattinson, and R. 8 . Jacobs
temperature of the fuel has reached the melting point where the uniformity of the
fuellayer degrades as melting commences. Thus, forauniform solid-fuel-layer target
which is thermally isolated, the maximum exposure time is limited to less than 10 ms.
To minimize the amount of vaporized fuel an exposure time significantly less than
10 ms is also desirable.
EQUIPMENT REQUIRED FOR UNIFORM SOLID FUEL LA VERS
The system that has been designed and constructed to meet the requirements of
uniformity and compatibility with the target chamber uses a gaseous-helium shroud
and is shown in schematic form, integrated with the target chamber, in Fig. 7. Much
like the heat shield, it is lowered from the top of the experimental chamber to
envelop the prealigned target and form the fuellayer. Just prior to the target shot the
shroud is retracted, uneavering the frozen target.
The details of the gaseous-helium shroud are shown schematically in Fig. 8.
Simplicity of design is achieved by using a commercially available cryostat and
allowing the shroud to continually supply gaseous helium at a constant rate through a
pinhole orifice to the region around the target. Four windows are provided at the
target Ievel, two for observation and two for a heating Iaser (the CW alignment Iaser
of the target chamber) used to vaporize the fuel in situ prior to the rapid refreeze [9 ].
Alignment of the target at the focus of the Iaser system is critical (±5-~tm
permissible displacement). One must either attempt to prevent any displacement of a
prealigned target while the fuel layer is being formed or provide for repositioning
afterward. To avoid the complexity of alignment while the target is under the shroud,
the system was designed to minimize target displacement during fuel-layer formation. The target is mounted on a copper post which fits into a collet joint in the
extension of the lower cryostat. Before target alignment and formation of the fuel
layer, the temperature of the lower cryostat is set at a value less than 10 K to avoid
subsequent thermal displacement of the target under the shroud. Although the target
is mounted on a copper post as in previous cryogenic experiments (Fig. 1) with
CRYOGENIC
SHROUD
LASER
BEAM
CRYOSTAT
EXTENSION
Fig. 7. Gaseous-helium shroud integrated in target chamber.
55
Engineering Aspects of Cryogenic Laser-Fusion Targets
COMMERICAL
CRYOSTAT
GAS
FLOW
FILTER
TARGET
LOWER
CRYOSTAT
EXTENSION
Fig. 8. Schematic of gaseous-helium shroud.
liquid-layer targets, the target itself is thermally isolated from the post by a 200- to
400-ILm length of 10-ILm-diameter glass fiber. This mounting arrangement prevents
target motion due to cooling under the shroud, yet assures that the cold gaseous
helium is the dominant source of refrigeration for layer formation. Nonuniformities
due to asymmetrical cooling by the fiber are thus avoided.
To prevent mechanical displacement of the target, the shroud does not touch the
lower cryostat extension. The annular gap between the two acts as a variable
impedance to the ftow of gaseous helium from the target region inside the shroud to
the rest of the target chamber. For maximum fuel-layer uniformity, the pressure near
the target needs to be maximized in order to minimize the condensation and freezing
time. This pressure is determined by both the throughput of the pinhole and the size
of the annular gap. The throughput into the target chamber is set by the size of the
pinhole, which must be chosen so that the pressure throughout the target chamber is
no higher than approximately 3 mtorr. At higher pressures, the conductivity of the
gas in the target chamber is sufficient to overload the cryostats and prevent operation
below 10 K. For this throughput, the pressure near the target is maximized by
decreasing the gap to a minimum. Condensing and freezing of typical targets in this
system occurs in :::;30 ms.
The physical dimensions of the shroud plus the overlap of shroud and targetpost
are dictated by considerations of shroud retraction. Exposure of the target to room
temperature radiation may be considered to start when the bottom of the shroud
reaches the level of the target. From this position the shroud must be lifted clear of
the path of the converging laser beams within 10 ms. The acceleration needed to
accomplish this can be minimized by maximizing the shroud overlap, i.e., the
distance over which the shroud accelerates before exposing the target. The actual
overlap chosen (4 cm) is a compromise between maximizing the overlap and assuring
that the clearance (1.6 mm) between the inside of the shroud and the target-post
56
D. L. MuiDsld, T. M. Henderson, R. J. Simms, T. R. Pattinson, and R. B. Jacobs
CEILING
TARGET
CHAMBER FLANGE
Fig. 9. Schematic of shroud retraction device.
extension can be maintained during both initial alignment of the system and shroud
retraction.
The retraction system is shown in schematic form in Fig. 9. A primary design
consideration (recognized when using the piston retraction system of the radiation
shield) is the minimization of target motion due to vibration. Since any impulse
applied to the target chamber could displace the target, the retraction system is
mounted on the ceiling and not on the target chamber. The only mechanical coupling
between the retraction device to the target chamber is through a 2-in.-diameter
bellows, the minimum size that will permit x, y alignment of the shroud through the
vacuum seal (see Fig. 7).
The force for retraction is provided by two evacuated 5-in.-diameter bellows.
This force is initially counterbalanced by flat-faced electromagnets. Retraction is
triggered during the laser-firing sequence by dumping the current in the magneticfield coils. Since the holding force of the magnets is very sensitive to gap, free
acceleration of the shroud is achieved quickly and the release time is highly
reproducible. Figure 10 shows the position of the shroud as a function of time during
retraction. Time zero on the figure is the time when the magnet dumping circuit is
triggered. The data shown were taken from multiple exposures on high-speed
Polaroid film of an indicator flag attached to the system. The two data points at each
time point are the worst-case data for a series of 25 runs conducted over a two-day
interval. Total travel is 10.8 cm and occurs in 60 ms. Laserirradiation of the target is
timed to occur at the point indicated on the figure before deceleration (provided by
two commercial shock absorbers) begins. This timing precludes target vibration due
to deceleration shock. With Iaser irradiation occurring at this point, the exposure of
the target to room temperature radiation is kept to 4.0 ± 0.35 ms.
EVALUATION OF SOLID-FUEL LAYERS
To evaluate the quality of the fuel layers produced with this apparatus the
interferometer 2 ], shown schematically in Fig. 11, was constructed and used in the
e
57
Engineering Aspects of Cryogenic Laser-Fusion Targets
,,
10
9
8
E
7
_,"-
6
>
5
w
<(
...
er:
4
~TARGET
3
2
LEVEL
1
0
~t = :!::350,._
0
10
20
30
40
50
60
70
TIME x10-3tee
Fig. 10. Retraction of gaseous-helium shroud.
off-line simulation chamber as weil as in the target chamber. The major feature of
this interferometer is the shearing cube C3 ]. With it both high contrast and stability
are assured as weil as the ability to continuously vary both the background phase and
phase gradient. The illuminating lens is adjusted to focus the Iaser behind the target,
producing a diverging beam a few target diameters wide at the plane of the target.
The imaging lens is set to focus the crossover of the Iaser beam on the back side of the
shearing cube while focusing an image of the target on the image plane. By limiting
the focus point on the shearing cube, extraneous phase shifts due to variations in the
surface of the cube are eliminated. Phase shift and shearing are controlled by sliding
and rotating one-half of the shearing cube relative to the other.
so•J.
REFLECTIV ITY
ARGONION
LASER
SHEAR ING CUBE
Fig. 11. Sheari ng cube interferometer system.
58
D. L. Musinski, T. M. Henderson, R. J. Simms, T. R. Pattinson, and R. B. Jacobs
The quality of targets that this system is capable of producing is shown in Fig. 12.
Figure 12a is the interferometric image of a DT-filled target when the fuel is in the
gas phase. Figure 12b is an interferometric image of the same target when the fuel
condensed in the solid phase. Using a criterion based on computermodefing for these
interferometric images [9 ] the target shown in Fig. 12b meets the criterion of around
20% WNU.
At the present time the ability repeatedly to obtain acceptable uniformity in a
solid layer is not entirely satisfactory. A remelt of the target shown in Fig. 12b may
produce the target of Fig. 12c as often as it reproduces the image of Fig. 12b.
High-speed movie films (500 fps) taken of the vaporize/refreeze cycle clearly show
that during condensation, while the fuel is in the liquid state, the fuellayer is very
uniform. The nonuniformities observed in the final stable solid layer occur either
Fig. 12. (a) Interferometric image of a DT-filled
target, fuel in gas phase; (b) interferometric image
of a DT-filled target, fuel in uniform solid layer;
and (c) interferometric image of a DT-filled target,
fuel in a nonuniform solid layer.
Engineering Aspects of Cryogenic Laser-Fusion Targets
59
during or after freezing of the liquid. At present not all the factors responsible for the
uniformity or nonuniformities are understood. Further study is required to identify
and understand these factors so that uniformity of the fuellayer can be controlled
and repeated.
LASER IRRADIATION OF UNIFORM SOLID-FUEL-LAYER TARGETS
The additional operational procedures required for these solid-layer targets
have been integrated into the normal routine of the experimental program. The
target is installed in the experimental chamber and aligned with the main Iaser,
following the same sequence as that used in the liquid-layer experiments [6 ]. First,
the gaseous-helium shroud is lowered over the target to freeze the fuel. Next, the CW
alignment Iaser, which is coaxial with the main Iaser system, is used to vaporize the
fuel within the target. Because of the large angular coverage of the target by the
ellipsoidal-mirror illuminating system (see Fig. 12), beam reducers are inserted into
t}!e path of the alignment Iaser. These allow the ellipsoidal-mirror illuminating
system to focus all the power of the alignment Iaser onto the target through two of the
four windows in the shroud. The power of the alignment Iaser is increased until the
fuel within the target evaporates. An operator watehing the interference pattern of
the target regulates the freezing of the fuel by shuttering the CW alignment Iaser until
the uniformity of the solid-fuellayer appears satisfactory. The interference pattern is
then photographed and the beam reducers are retracted from the path of the main
beam. The final preparatory step is to charge the shroud-retraction device by
energizing the holding magnets and evacuating the 5-in.-diameter bellows. Triggering of the retraction device is controlled automatically by appropriate timing
circuits locked into the normal automated laser-firing sequence.
MIRROR- LENS ILLUMINATION SYSTEM
REDUCED BEAM
NORMALBEAM
BEAM REDUCER
'-'·
REDUCED BEAM
>
<
NORMAL BEAM
Fig. 13. Laser-heating a shrouded target in the target chamber.
60
D. L MuiDIId, T. M. Headenoa, R. J. Süa.s, T. R. Patdaloa,lllld R. 8. Jacobs
SUMMARY
Experiments with cryogenic liquid-layer targets, using point-contact conduction
cooling, have opened the way to experiments with solid-layer targets. The engineering and integration of successively more complex systems identified the critical
design features and procedures needed to achieve uniformity of the fuellayer. The
technology has been refined and extended in several iterative steps to eliminate the
major causes of nonuniformity and to provide an interferometric viewing system that
enables an operator to observe and evaluate the layer formation. The gaseoushelium shroud and retraction system were shown to be capable of producing and
presenting to the laser a satisfactorily uniform (:520% WNU) solid-fuel-layer target.
Successfullaser irradiation of such targets demonstrates that this system now oflers
the opportunity to experimentally study in a systematic way a new class of laser
fusion targets-uniform solid-fuel-layer targets.
ACKNOWLEDGMENTS
'Ibis work was supported in part by the United States Department of Energy under Contracts
EY-76-C-02-2709, ES-17-C-02-4149, ED-78-C-08-1598, and DE-AC08-78DP40030.
The successes achieved in this cryogenic work are very much a consequence of outstanding teamwork
within the Division of Material Seiences at KMS Fusion. The authors owe particular thanks to D. L.
Melmoth whose close attention to details avoided many pitfalls and to E. J. Calabro who, despite a long Iist
of restrictions and constraints, succeeded in converting a few general concepts into a practical, remarkable, trouble-free design for the shroud-retraction mechanism. Special thanks must also be extended to
R. D. Sigler who suggested the use of the shearing cube interferometer and who guided the authors in its
use. J. A. Tarvin contributed both valuable discussions and laboratory expertise during the final testing
stage of the gaseous-helium shroud.
REFERENCES
1. G. S. Fraley and R. J. Mason, Phys. Rev. Len. 35:520 (1975).
2. R. J. Mason, Nucl. Fusion 15:1031 (1975).
3. R. G. Schneggenburger, W. S. Updegrove, and R. L. Nolen, Jr., Rev. Sei. Instrum. 49(11):1543
(1978).
4. T. M. Henderson, R. B. Jacobs, D. L. Musinski, R. J. Simms, and G. H. Wuttke, in Advances in
Cryogenic Engineering, Vol. 23, Plenum Press, New York (1978), p. 690.
5. T. M. Henderson and R. R. Johnson, Appl. Phys. Len. 31:18 (1917).
6. T. M. Henderson, D. L. Musinski, R. B. Jacobs, and R. J. Simms, in Chem. Eng. Progr. Symp. Series, to
be published.
7. R. L. Berger et aL, in Proc. 7th Intern. Conference on Plasma Physics and Controlled Nuclear Fusion
Research, VoL 3, IAEA, Innsbruck, Austria (1979).
8. T. M. Henderson, R. J. Simms, and R. B. Jacobs, in Advances in Cryogenic Engineering, Vol. 23,
Plenum Press, New York (1978), p. 682.
9. J. R. Miller, in Advances in Cryogenic Engineering, Vol. 23, Plenum Press, New York (1978), p. 669.
10. R. L. Woemer and C. D. Hendricks, Technical Digest-Topical Meeting on Inertial Confinement
Fusion, 'JbE1, San Diego, California, February 7-9, 1978.
11. J. R. Miller, R. D. Day, E. H. Farnum, W. G. Hansen, H. E. Tucker, and W. A. Teasdale, Technical
Digest-Topical Meeting on lnertial Confinement Fusion, 'JbE10, San Diego, California, February
7-9, 1978.
12. J. A. Tarvin, D. L. Musinski, T. R. Pattinson, R. D. Siglerand G. E. Busch, in Proc. 23rd Intern.
Symposium and Instrument Display of the Society of Photo-Optical Instrumentation Engineers, San
Diego, California, to be published.
13. B. J. Sanders, Appl. Opt. 6:1 (1967).
B-1
ENERGY TRANSFER IN A SYSTEM OF
SUPERCONDUCTIVE MAGNETS
M. Masuda, T. Shintomi, and K. Asaji
National Labaratory for High Energy Physics
Ibaraki, Japan
INTRODUCTION
Magnetic fusion reactors, equilibrium coils, and ohrnie heating coils require
large pulses of energy which are repeated over relatively short periods of time.
Accelerator magnets fabricated with normal conductors or superconductors have
similar operating conditions, the same pulse time, and require almost the same
amount of energy, namely, hundreds to thousands of MJ. These large pulsed energies
can a:ffect apower grid adversely.
Many schemes have been proposed for accelerator magnets; some have been
constructed and operated successfully. One scheme entails reactive power control by
thyristors C] for a proton synchrotron; however, no matter how precisely the reactive
power has been controlled by the thyristor device, the active power has never been
properly controlled.
In fusion reactors, energy storage devices are needed not only to suppress
adverse effect to the power grid but also to improve efficiency by saving energy losses
over an operation cycle. Schemes also have been proposed for fusion reactors, such
as homopolar generators, flywheel motor generators, and superconductive energy
storage.
The flywheel motor generator was employed in older accelerators; but for the
past decade, it has not been employed in modern accelerators due to mechanical
failure of the generator pole. Now the static rather than the rotating machine has
become conventional. Minimizing the amount of energy from the power grid is a
problern common to both fusion reactors and large accelerators. Pulsed superconductive energy storage is one of the solutions to this problem.
Numerous energy transfer methods have been proposed; the most promising
The method proposed by the Wisconsin group
ones have already been reviewed
is one of the most useful methods to transfer a large amount of energy between
coils. The purpose of this paper is to describe a technique useful for superconductive
energy storage, namely, the energy transfer between two superconducting coils,
assuming that one is the storage coil and the other the accelerator magnet or the
poloidal coil in a tokamak, for example.
eJ
eJ.
61
62
M. Masuda, T. Shintomi, and K. Asaji
Fig. 1. Placement of two 100-kJ superconducting coils.
EXPERIMENTAL PROCEDURE
Two superconducting coils, each storing 100 kJ, were placed in the same Dewar.
A similar experiment has been already carried out by Argonne group [4 ] where one
shot energy transfer has been attempted. In the present experiment it has been
demonstrated that not only is it possible to transfer pulsed energy from one coil to the
other but also to allow a surge of energy to flow back and forth between the two
superconducting coils. Figure 1 shows the assembly of the two 100-kJ superconducting coils. The specifi.cations for the coil are given in Table I. The circuit and the
specifi.cations for the experiment are shown in Fig. 2 and Table II, respectively.
Table I. Specifications of the 100-kJ Coil
Dimension of coil
Inner diameter, m
Outer diameter, m
Length, m
Number of turns
lnductance, H
Dimension of wire, mm 2
Diameter of filament, p.m
Number of filaments
Composition of filament
Cu ratio
Twisted pitch, mm
Critical current, A
0.2
0.25
0.2
1284
0.22
2.4 X 1.53
55.6
271
Nb-Ti
4.16
29.1
900 at 5 T
63
Energy Transfer in a System of Superconductive Magnets
CO I L 1
BRIDGE 1
COMM UTATION
CAPACITORS
BRIDGE 2
COIL 2
Fig. 2. Schematic diagram of test arrangement.
Control of the energy transfer rate was accomplished by controlling the phase
delay from one bridge to the other. The circuit was completely symmetrical, and the
reverse of the phase delay inverted the transfer. The phase angle control circuit is
shown in Fig. 3. The high frequency signal (up to 1 MHz) from the voltage-tofrequency converter (VFC) was fed to two dividers and to the data distribution
circuits for the thyristor bridges. The phase diflerence between the two bridgeswas
controlled by input fed to a digital comparator by means of an analog-to-digital
converter (ADC). The sign for the input data depended upon whether there was a
phase advance or delay from one bridge to the other. The transferrate and direction
could be controlled by the input signal.
The signal from the VFC was changed by input which was proportional to the
current ftowing in the commutation capacitors. The output from the clock determines the frequency of the ac voltage between the capacitors and then the control
voltage of the capacitor terminals for all conditions.
Figure 4 shows the waveforms of the ac voltage and dc output voltage for various
phase angles of the bridges. The experimental procedure for each runwas as follows.
A dc power source (50 A and 100 V) was used to drive thyristor bridge 1 and this
generated an ac voltage of 400-500 Hz between the terminals of the commutating
capacitors. The generated ac voltage was rectified and then coil 2 was charged up to
its maximum by thyristor bridge 2. After this charging cycle the system was isolated
Table II. Specifications for the Power
Supply
Input dc power supply
Voltage, V
Current, A
Thyristor for the bridges
Reverse voltage, V
Rated on-state current, A
Commutation capacitors
Capacitance/arm, pF x 5
Rated voltage, V
Connection
100
50
1200
1000
500
200
star
64
M. Muuda, T. Shintomi, and K. Asaji
DATA
INPUT
f
DATA
INPUT 9
Fig. 3. Control circuit for the phase angle of the bridges.
from the dc power source by a switch and the stored ener gy in coil 2 was transferred
immediately to coil1 by the inverse Operation of bridges 1 and 2. Afterall the energy
had been transferred to coil 1 by the thyristor bridges, the process was reversed and
the energy was transferred back to coil 2 by the inverse operation of the thyristor
bridges.
The main feature of this experiment was the possibility of obtaining a continuous back and forth ftow of energy between the two coils. However, the dissipation of
energy particularly in the thyristors limited the process to about five to seven cycles.
Figures 5a and 5b show the recorder traces for the one-shot energy transfer and the
continuous oscillation of energy between the two coils, respectively.
ESTIMATION OF LOSSES
Estimation of losses, one of the most important factors in evaluating energy
transfer, has been attempted for the one-shot scheme. Schematic diagrams of the
circuit and the current waveforms of the two coils for this calculation are shown in
(A)
(8)
Fig. 4. Waveforrns of ac voltages and dc voltages for various phase angles. Legend: (A) 0°; and
(B) 90°.
65
Energy Transfer in a System of Superconductive Magnets
500
(A)
400
<{
1-
z
300
IIJ
""""
::>
u
...J
200
8
100
00
10
5
15
TIME , SEC
500
400
<{
1-
zIIJ
""""
::>
u
...J
300
200
8
100
0
0
15
10
5
TIME , SEC
Fig. 5. Current waveforms for energy transfer. Legend: (A) one-shot energy
transfer; and (B) energy transfer using two coils.
Figs. 6a and 6b, respectively. The energy in this analysis is transferred from IP to I. in
a period of time T. Since the two supercondueting coils were identical, their nominal
rated currents were the same. In practice the actual current was about 10-30%
smaller than the transmitted current because of losses. These losses were mainly
caused by the thyristor forward voltage drops, the protection resistors and the circuit
cables. The energy loss per one-shot energy transfer can be estimated as follows:
Ä
r[
W= nip-;Ä V+ r( Ip-;) + ni.-;Ä V+ r( I.-;) dt
=~LI; -~LI;
The current ratio, I./ IP
=
2
2
]
(1a)
(1b)
a, is obtained by solving equation (1). In the present case,
M. Masuda, T. Shintomi, and K. Asaji
66
~T~
Fig. 6. Schematic diagram of circuit and current waveforms of
the two coils.
L
1.0
lp : 300 A
~
~
0. 5
T'
1. 0
SEC
IL
p -- 500 A
0.5
'T ,
SEC
L
lp : 700 A
Fig. 7. Calculated efficiencies for the one-shot
energy transfer with three different amounts
of current. Legend: - - , without resistors;
-- -, with resistors.
? 0.5
T, SEC
Energy TrlliiSfer in a System of Supercondnctive Magmets
67
L, r, and a V were assumed tobe 0.22 H, 10 mfi, and 2.0 V, respectively. Substitution of these values into the above relations yields
( 0.11
+ -10- T)
2
3
a
2
2
1
( 0.11- 2T-1 10+ 3T-a- T) = 0
Ip
Ip
3
(2)
Solving for a results in
T
(3)
a = 1-231- 0.03T
p
On the other band, IP and I. are shared by the coils and the protection resistors
as shown in Fig. 4. The sharing ratio, ß, is given as
L
ß = Ip/ I P
=
1
1 + To/ T
( 4)
r
Thus, the total efficiency of energy transfer, Tl = (I~'/ I!' )2 , is obtained from
"' =
[ß
2
(
1 _ 23T
I;ß _
0.03T)
(5)
The calculations have been performed for three different coil currents and operating
with or without the protection resistors. The results are summarized in Fig. 7.
EXPERIMENTAL RESULTS AND DISCUSSIONS
More than 30 experimental runs have been carried out. Transfer efficiencies, "''
have been calculated and good agreement with the calculated results has been
obtained as shown in Fig. 8. Since the coupling between the two coils is less than 5%,
the efficiencies were only slightly affected. The shorter the transfer time, the better
"
WITHOUT RESISTCRS
o
WITH RESISTCRS
CALCULATION
t;
i5
u
u:
0.5
lL
UJ
o~----~-----L----~L-----~-----L-
0
2
3
4
5
TRANSFER TIME , SEC
Fig. 8. Experimental results for the efficiencies of one-shot energy
transfer with and without protection resistors.
68
M. Muada, T. Sldatoaü. lllld K. Auji
the transfer efficiency becomes when the protection resistors are removed. When the
protection resistors werein the circuit, quick transfer of energy became difficult. One
of the main reasons for a low transfer efficiency could be the protection resistors.
Even if varistorsbad been employed for protective purpose, they might also have bad
an adverse eflect on the quick transfer of energy.
The decay of the total energy in the system is caused by the Iosses of the
thyristor, Iead wires, and the commutation capacitors except for the protection
resistor loss. The fact that the thyristor loss is dominant is explained by the diflerence
of the decay time constants in Fig. 5 as follows: only one bridge is related to the decay
in Fig. Sa. On the other band, two bridges are related to the faster decay in Fig. Sb.
The diflerence of the decay was also confirmed by an estimation of the losses. The
thyristor loss results from the forward voltage drop which is a constant value for any
type and size of thyristor. Therefore, the thyristor loss is linearly proportional to the
current. On the other band, the stored energy is always proportional to the square of
the current. Thus, the thyristor loss for a larger system, such as 100 MJ or more for
example, will play a minor role in the Iosses of a superconductive energy storage
system.
NOTATION
Ip = primary current flowing into the commutation capacitors
I} = primary coil current
I, = secondary current flowing into the commutation capacitors
L = inductance of the coil
n = number of thyristors
R = resistance of the cable
r = resistance of the resistor
t = time during the energy transfer
T0 =time constant between the superconducting coil and the protection resistor, L/ R
4 V = forward voltage drop
4 W = energy loss per one-shot energy transfer
a = current ratio, Ij IP
ß = sharing ratio of the currents, IJ It;
TJ = transfer efficiency
T = transfer time
REFERENCES
1. M. Masuda, S. Matsumoto, and T. Shintomi, IEEE Trans. Nucl. Sei. NS-24:1306 (1977).
2. R. S. Ramshaw and E. P. Dick, in Advances in Cryogenic Engineering, Vol. 21, Plenum Press, New
York (1976), p. 149.
3. H. A. Peterson, N. Mohan, W. C. Young, and R. W. Boom, in Proc. Intern. Conference on Energy
Storage, Compression and Switching, Plenum Press, New York (1974), p. 309.
4. R. E. Fuja, R. L. Kustom, and R. P. Smith, in Advances in Cryogenic Engineering, Vol. 23, Plenum
Press, New York (1978), p. 97.
B-2
THERMAL CYCLE TESTS OF A MODELED
SUPERCONDUCTING TRANSMISSION LINE
C. F. Sindt and P. R. Ludtke
NBS Thermophysical Properfies Division
Boulder, Colorado
INTRODUCTION
Superconducting power transmission lines (SPTL) will be enclosed in an
insulated conduit which typically is a vacuum insulated, double-walled vessel. The
outer wall is rigid and the inner cold wall has provisions for thermal contraction and
expansion. Three cable assernblies (one for each phase) are used in the alternating
current systems. In the system designed by Brookhaven National Laboratories
(BNL), high-pressure cold helium gas at 6 K ftows down the hollow core of each
cable. This gas is recooled to 6 K from 8 K by expansion at the cable end and ftows
back around the outside of the cables. In the Brookhaven installation, the ends of the
SPTL cable will be fixed (i.e., the length of the cable held constant) so that a
significant thermally induced axial stress will develop in the cable as it is cooled. The
goal of the testswas to investigate the thermoelastic behavior of a 3.5-m section of a
model of a SPTL cable constrained to constant length while the cable section was
subjected to repeated thermal cycles between ambient and operating temperature.
The cable, which was constructed according to BNL specification number PTP
# 76-22, was built up from a number of helically wrapped layers (bronze core,
superconductor, dielectric); one of the outer layers is a Iead sheath which provides a
hermetic seal (see Fig. 1). The cooldown tensile Ioad produces an elastic deformation
in the helically wound elements which act as coil springs. If friction between these
elements is neglected, this spring Ioad is small compared to the Ioad on the Iead
sheath which is stressed beyond its elastic Iimit during cooldown. Likewise, the Iead
sheath will be compressed beyond the elastic Iimit during warmup. Although
repeated thermal cycling of an operating SPTL is not expected, it is nevertheless
necessary to provide for this contingency. Thm~ the cable must remain functional
throughout a number of thermal cycles.
The primary test objective was to observe if physical darnage to the cable would
occur as a result of thermal cycling. Additional objectives were: to determine the
cable tensile and compressive Ioads during thermal cycling; to test the ability of the
end clamps to withstand thermal and assembly cycles; and to determine if the cable
or end clamps developed leaks at operating temperature and pressure. To accomplish these objectives, two different 3.5-m lengths of cable were subjected to a
number of thermal cycles while maintaining the cable length constant.
69
Bronze Co re, 2 He 1 i c e s
5 Strips
Alumi num Sta bilizer,
2 Hel ic e s , 5 strips
Coppe r Supe r cond uctor,
2 Helic es
5 St rips
Inne r Die 1ec t ri c Screen
( in tercalate d) , 2 Tapes
Me t al l i zed Po l y i mide
Oi e l e c tr ic , Polye thyle ne
93 Laye r s
Oute r Oie lect r ic Scree n
(i nt e rca l a t ed), 2 Tapes
Coppe r Superco nductor,
2 Hel ic es
Al umi nu m St abilizer,
2 Helic e s
Outer Conductor Jnsulatio n
( kap t on), 4 layers
St ai n less Steel Comp r ession
layer
Taped Fiber9lass Thermal
lnsu l ation, 2 layers
Lead Gas Jacket
Armer, Myl ar- Brgnze la~...ent
l ay Angle of 80 to 85
Dimensions in Millimeters
Fig. 1. Cut back view of cable.
0 D
l L
Di rect ion
Thi ckness
A
21. II
120
RH
1.02
8
23.11
133
LH
1.02
c
23.88
89
RH
. 38
D
24 . 64
36
LH
.38
24.84
112
RH
. 10
F
25 . 04
112
LH
. 10
G
25.15
H
40.38
RH
. 20
7.62
I
40.48
LH
.05
J
40.69
185
RH
. 10
K
40 . 89
185
LH
.10
L
41.65
! 57
RH
. 38
!57
LH
. . 38
RH
.51
M
42.41
N
43 . 43
0
44.45
p
45.46
. 51
Q
49.79
2 .16
R
50 . 14
. 178
50.50
. 178
s
229
RH
.51
Thermal Cycle Tests of a Modeted Superconducting Transmission Line
71
EXPERIMENTAL APPARATUS
The test fixture, Fig. 2, must meet several requirements in these constant-length
thermal cycling tests. The test requires (1) a mechanism for maintaining the cable
length constant with varying Ioad; (2) aDewar and cryogenic fluid system for cooling
the cable to liquid nitrogen temperature; and (3) a gripper and seal arrangement to
transmit Ioad from the cable to the test fixture while maintaining a hermetic seal with
the lead sheath.
The test fixture, which accommodates a 3.5-m cable segment, has a reetangular
steel framework built up from two 100-mm-square tubes, 5.4-m long, that are
bridged at each end by 75 x 127 mm H beams, 0.5 m long. A screw mechanism at
each end may be manually adjusted so as to maintain the cable length constant in the
face of variable loads. The cable is enclosed in a polyurethane-foam-insulated spool
piece and the end clamps are enclosed in the vacuum-insulated housings attached to
each end of the spool piece. The cable, spool piece, and end housings are all
supported at either end by rails with linear ball bearings (see Fig. 2). The cable
assembly is isolated from forces in the support structure by means of internal and
external bellows in the end housings, as weil as by means of 0-ring slip joints at the
end housings.
The lead seal and terminal clamp assembly for attaching the end of the cable to
the test fixture and the assembly procedure were provided by Brookhaven National
Laboratory. An enclosure cap was added to the clamp assembly, which is shown in
Fig. 3, to facilitate pressurization of the inner line and to provide the structurallink
between the cable and the test fixture.
INSTRUMENTATION
The length of the cable is monitored with 30 power microscopes which are
aligned with view ports 86 mm from each end of the spool piece. These microscopes
are supported from the concrete ftoor by heavy duty tripods, so their position is
independent of the Ioad on the cable and test fixture. The cable length reference
points are scribe marks on Invar rods which are attached to the end fixtures. The
cable length was held constant to within ±0.12 mm using this system of microscopes
and adjusting screws.
Cable temperatures were determined with type-T thermocouples referenced to
a boiling liquid nitrogen bath. The cable was cooled from one end rather than
uniformly along its length; the purpose of the temperature measurements was to
determine when the entire cable segmentbad cooled to the desired temperature. The
measurements were not intended to represent the temperature of the cable
composite since the sensor could not be placed in the body of the cable without
destroying the integrity of the Iead sheath.
The axial tensile or compressive Ioad on the cable was determined with a Ioad
cell [2000-lb (9000-N) capacity]. A purely axialload at the cell is assured by the
guide mechanism for the cable extension tube shown in Fig. 2. The calibration
accuracy of the Ioad cell is 0.25% of full scale. The precision of the load cell was
checked with dass S weights; the measurement uncertainty was 0.1%.
The axialload on the cable differs from the force on the Ioad cell and is given by
the expression
(1)
where Fe is the force on the cable, Fd is the force measured by the Ioad cell, FP is the
0
Fig. 2. Test apparatus. Legend: A, Liquid fill and pressure port for i.d. of cable; B, cable length adjusting nut; C, subassembly end guide and supports; D, liquid fill for o.d.
of cable; E, auxiliary supports (used only when necessary to remove vacuum dewars on ends); F, observation port; G, base axis of symmetry; H, vent for o.d. of cable; I,
Observation port; J, subassembly end guides and supports; K, Ioad cell; L, vent for i.d. of cable; M, cable length adjusting nut.
0
0 - --
@
I
1
·---·---·---·---·--·--·--·-- --:-·--·--
5384.8 ± 3 mm (212 t 1/8 in. = 17.66 ft) - - - - - - - - - - - - -------,
r--- - - - - - 3048 .0 ± 1 mm (120 ± 5/ 128 in .= 10ft)- - - - - --
Vscuum
Invar Spscer
Fig. 3. E nd clamp.
Indium Ses/
Sleeve
~
~
i
I
f
IICI
I
I
•
ia.
0..
!)
i
..
~
74
C. F. Slndt and P. R. Ludtke
Fig. 4 . End assembly schematic.
pressure force due to the differential pressure across the end fixtures, Fcp is the axial
force on the cable resulting from internal pressurization, and F1 is the friction force
on the cable and cable extensions. The friction force from the supports and 0-ring
seal is estimated to be less than ±45 N (± 10 lb )-small compared to the other forces .
The pressure force, Fm is due to the differential pressure across the inner bellows
assembly. A tensile force of 151 N (34 lb) results.
In considering the effect of internal pressurization of the cable, it has been
observed that the behavior of a composite cable can be much less predictable and
reproducible than the behavior of a noncomposite cable. Referring to Fig. 4, the axial
force on the composite cable due to internal pressurization is
Fcp
= P[A.- (A. -
Ac)(l- a)C]
(2)
where Pis the differential internal pressure, A. is the inside area of the Iead sheath,
Ac is the inside area of the bronze core, a is the void fraction of cross-sectional area
of the composite inside the Iead sheath, and C is the degree of coupling between the
inner composite and the Iead sheath and clamp assembly. For an internal cable
differential pressureof 1.5 MPa, Fcp mayvaryfrom 2470 N (555lb) to 340 N (77lb),
depending on the voids in the cross-sectional area of the inner composite and the
degree of coupling between the Iead sheath and the inner composite.
Another important consideration is the effect internal pressurization has on the
spring constant of the various metal helices in the cable. The bronze core and other
metal helices may exert axial forces as a result of temperature change, and these
forces may change as the result of internal pressurization. This is because the various
helices behave as springs in the absence of friction , but could tend to behave as rigid
tubes if there is friction between them. Such friction could decrease if the Iead sheath
were pushed radially away by pressure, or increase if the sheath contracted more
than the rest of the cable during cooldown.
TEST PROCEDURES
Two cable samples were tested, each by a different procedure. Cable No. 1 was
cooled and then pressurized, whereas cable No. 2 was cooled with the core
pressurized. The latter procedure simulates the expected operating conditions more
closely.
Cable No. 1 was first leak checked by pressurizing the cable interior with helium
gas to 1.5 MPa and measuring the rate of pressure decay in the valved-off system over
a 15-min period. The sensitivity of the pressure measurement was 3.4 kPa. All
Thermal Cycle Tests of a Modeled Superconducting Transmission Line
75
pressurization and depressurization cycles were made in 345-kPa increments, so that
the cable could be maintained at a fixed length by means of the adjusting screws.
After the leak check, the pressure was bled down to ambient pressure and the
cable was cooled to liquid nitrogen temperature by ftowing liquid nitrogen through
the core and around the outside of the cable. The liquid nitrogen ftow rate was
adjusted so as to achieve cooldown in about 90 min. The cable was then again leak
checked by measurement of the pressure decay using helium gas prechilled to about
80 K. Following the leak check, the cable interior was bled down to ambient pressure
(again in 345-kPa increments to allow for cable adjustment) and the cable was
warmed by ftowing 350 K nitrogen gas through and around it. The cable warmed to
200 K in about 3 hr. The remainder of the warmup was achieved unattended in the
following 12 hr using a low ftow rate of ambient temperature nitrogen gas.
The procedure for cable No. 2 was the same except that it was cooled down by
ftowing liquid nitrogen around the outside of the cable while the interior was
pressurized to 1.5 MPa with helium gas. Cable No. 1 was cycled twenty times and
then removed for inspection. Cable No. 2 was cycled five times, removed for
inspection, then reassembled and cycled an additional fifteen times.
Both cables were preloaded with 590-N (134-Ib) tension [440-N (100-lb) Ioad
cell and 150-N (34-lb) bellows force] before the firstthermal cycle. The cable length
was then referenced by fixing the microscope cross hairs on the scribe marks of the
Invar rods, and this length was maintained throughout the test series.
RESULTS AND DISCUSSION
Cable No.l
Figure 5 presents Ioad cell vs. time for four typical thermal cycles of the 20 cycles
to which cable No. 1 was subjected. The test data are constrained to definite time
intervals, i.e., actual cooldown time may have varied slightly (± 10 min) from the 1! hr
indicated. Following the first thermal cycle, the preload on the cable changed from
the initiai440-N (100-lb) tension (Ioad cell reading) to 1330-N (299-lb) compression
and remained near this value for the remaining 19 tests. This shift in the initial cable
(Ioad cell) Ioad occurred with both cables and is attributed to the yielding of the Iead
sheath which occurs during the first thermal cycle. As the cable is cooled the Ioad
passes through a maximum and then decreases slightly as the cable comes to
equilibrium at 7 6 K. This behavior may be due to creeping of the spirally wo und core
with respect to the Iead sheath.
As the cable is pressurized, the Ioad cell force is reduced by approximately 4000
N (900 lb) compared to the maximum of 2470 N (555lb) that is calculated for the
pressure times area term. Fora solid cable the two forces must be equal. In this case,
however, it is likely that pressurizing the Iead sheath releases the grip of the sheath on
the inner composite sufficiently that the composite relaxes even though its length is
held constant. A recovery of 800 N (180 lb) in the tension Ioad occurs as the cable
core is depressurized. This is within the range of 428 N (961b) to 2466 N (554lb)
which may be attributed to the pressure times area term, but differs appreciably from
the average change of 1600 N (360 lb) which occurred when the cable was pressurized for leak checks at ambient temperature. The hysteresis in these ambient
temperature pressure cycles was small. The Ioad decreased by 1646 N (370 lb) with
pressurization and increased by 1557 N (350 lb) with depressurization.
After test number 20, the cable was removed from the test fixture. The
enclosure cap and split-end cap were removed from the clamp assembly, revealing
""
0
800
1000
0
~-800
0
E
"'~"' -600
.~ -400
0
- 200 '--
olJ
200
~ 400
!:.
~ 7 600
w
-'
-'
u
0
"'
"-
u
I-
1400 I-
1600
1800
2000
2200 I-
t
2400 I-
J
t
0
V
I V
l .b
I o
I I
I I
I I
I I
I I
I
I
I
I D
l cf>
8lf
20 min PressureLoss Leak Check
a t 76 K
to
""(1>
JD
"'00
v.-,
0
a>
vo
~
~
~~~~
'\JO
VdJ
Coo l to 76 K
2
I
I
I
I
I
f
1
CR
l "~o
D
"'
V
öl
A 0
"'o
0
0
l> D
0
01\.
~larmup Period,
0
~ CXl
TIME, hrs
oR ov
A OV
V
4
v
o o0
"
v
Circulate Warm N2 Gas
Thru & Around Cab le
v
Do oo
v
~.
Fig. 5. Force vs. time for cable No. 1.
t.O
"dl~
oB
( Oepress uriz e
II
II
I
..
Unattended Overni te
•
~
~
I
•I
I I
0
~
Cl>
"
oo
~
D
I I
- -24
"bo
'SO
0
ij
~0
~
I
I
I I
I I
Oepressuri
1\I~I
1 1
1
I I
J/ I
~
Pressure
ss Leak Check
Ambient Temp .
20 - min
Pressur i ze
I nside of Cable
to 15 atm
o - Test M20
o - Test #13
Test Ml2
v - Test #3
l> -
-2000
0
2000
4000
6000
8000
10,000
..J
0
0
u
w
..
-'
..J
0
u
""
"'
"-
"'c0
...
.,"'
z:
.
Thermal Cycle Tests of a Modeted Superrondoding Transmission Line
77
Fig. 6. End view of cable No. 1.
tbe end of tbe cable inside tbe stainless steel strands. This examination sbowed tbat
tbe dielectric and outer dielectric screen bad unraveled sligbtly as sbown in Fig. 6.
This was probably due to tbe relative movement between tbe cable layers near tbe
severed end of tbe cable.
After removing tbe cable from tbe center spool piece, it was noted tbat tbe Iead
sbeatb bad extruded radially outward between tbe inner bronze wrap and bad
crossed tbe outer bronze wrap, as sbown in Fig. 7. This radial bulge or spiral annulism
occurred at tbe end opposite to wbere liquid nitrogen coolant was introduced. In
spite of tbe spiral annulism, tbe Iead sbeatb remained intact, and tbere was no
leakage in tbis area.
Fig. 7. Annulism in cable No. 1.
78
C. F. Sindt and P. R. Ludtke
Cable No. 2
In view of the problern with cable No. 1, the test procedure was reviewed and it
was decided that cable No. 2 should be cooledunder pressure since this is the manner
in which the cable will be cooled in practice. lt was also decided to thermal cycle the
cable five times and then remove it for inspection before completing the full 20-cycle
test.
Inspection after five thermal cycles showed that the lead sheath of cable No. 2
bad expanded outward slightly at the "windows," where the Iead sheath was covered
only with Mylar. Otherwise the cable bad the same appearance as when it was
installed in the test fixture. This same "window" expansionwas observed with cable
No.l.
The cable was reinstalled in the test fixture and testing continued for another
fifteen cycles. Again, no perceptible darnage was observed other than the slight
expansion at the "windows," which was noted after the first five cycles, and a
waviness in the surface which became noticeable when sighting along the cable.
The outside diameter of the cable was measured at random locations along its
length in order to determine the magnitude of the surface irregularities. From 18
different measured diameters in the two planes, the maximum difference was 1.55
mm (0.061 in.). Cable No. 2 showed much less evidence of the dielectric and outer
dielectric screen unraveling or fraying as shown in Fig. 6.
Load cell vs. time measurements for five of the last fifteen cycles is shown in Fig.
8. During a typical test on cable No. 2, pressurization of the inner line (ambient
temperature) resulted in a decrease in the load cell force of 2220-2670 N (500600 lb) as shown in Fig. 8. During cooldown the Ioad cell force changed from
approximately 2670 N (600 lb) in compression to 7120 N (1600 lb) or 7560 N
(1700 lb) in tension.
Cable No. 2 was then warmed in the same manner as cable No. 1 (no internal
pressure). The resulting Ioad cell force the next morning, with no internal pressure,
averaged 670-N (150-lb) compression for the first five cycles and approximately
1330 N (300 lb) for the following fifteen cycles.
Both cables were installed with a tensile force of 440 N (100 lb) (no internal
pressure) but after the first cooldown cycle, this changed to 1110-N (250-lb)
compression for cable No. 1 as shown in Fig. 5 and a Ioad cell force of 2670-3110-N
(600-700-lb) compression for cable No. 2 as shown in Fig. 8. The Ioad cell forces on
cable No. 1 given in Fig. 5 are considerably higher than those on cable No. 2 in Fig. 8
because the latter was internally pressurized.
GENERAL DISCUSSION
There was no measurable leakage across the Iead sheath or the Iead seal clamp
assembly during any of the 40 tests. The cause of the annulism in the Iead sheath of
cable No. 1 is not clear. lt could be the result of buckling due to the compressive
forces that occur on warmup. If some yielding due to pressure forces bad already
occurred at that "window" site then it would be more susceptible to buckling.
Whether or not the change in the operating procedure prevented cable No. 2 from
developing an annulism is problematical, since the mechanism of failure for cable
No. 1 is unclear. lt could be fortuitous that cable No. 1 buckled and cable No. 2 did
not. On the other band, it is possible that cooling the cable under pressure prevented
the annulism by either (1) maintaining tight contact between the Iead sheath and the
outer Mylar-bronze wrapping, thus preventing relative movement and random
"'
0
""--'
0
u
--'
_.
..,
~
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0
0..
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::r:
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z
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e
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z
,_
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.0
2000
c
X
1
Cold Pres sure- \
Loss Leak Checkl
Cooldown t o 76K
~"
ttJ9
t.~
9
~
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.p
o.
t.
o
.·~'11
t. o'B
zel
01
I'
0
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9
6
9
~20
c #18
•
9
9t.
0
•
"v
9
0
•
t.~9
•
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l owing t-tornln
Fo 1
1 pr essure
(no interna
0
Una ttended
Ove rn i te
Warmup
fl
~
•
I
'
~
I
~
Cable Stress a~
Warmup Period ,
Ci r cu l a t e Warm N2 Gas Thru
And Ar ound Cab 1e
T I ME , hrs
0
•
6
t8
0
t. 113
16
•
Coo 1down Test
Fig. 8. Force vs. time fo r cable No. 2.
0
•
• 9 .,;:.
t t. :..
Oepress uri
Inner Line
-2000
6000
.."
""
u
0
0
""--'
u
""
--'
....
0
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u...
z
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80
C. F. Siadt aacl P. R. Ltultke
Table I. Etled of Cable Pressure on Load CeU Reading
Change in Ioad cell force, N(lb)
Wann
Pressurize to 1.5 MPa
Depressurize to 0.1 MPa
Cold
Pressurize to 1.5 MPa
Depressurize to 0.1 MPa
Cable No. 1
Cable No. 2
-1650 (-370)
+1560 (+350)
-2220 to -2570 (-500 to -600)
-4000 (-900)
+800(+180)
+440(+100)
enlargement of the window, or (2) allowing freer movement of the composite with
respect to the sheath, and thus reducing the compressive Ioad that the composite
exerts on the sheath during warmup.
The thermoelastic behavior of the cable is quite complex as evidenced by Figs. 5
and 8. In particular, note the change in Ioad cell force as the cable is pressure cycled
between 0.1 and 1.5 MPa as summarized in Table I. Without a detailed stress analysis
of the complex cable structure, one can do little more than speculate on the cause for
such differences in the change in the Ioad cell force. lt would seem clear, however,
that the thermal-pressure history, and how this history affects the coupling between
the shield and the core, has a large effect on the force transmitted from the cable to
the fixtures.
B-3
DESIGN OF A 400-kJ PULSED ENERGY
STORAGE COIL*
S. K. Singh, C. J. Heyne, D. T. Hackworth,
M. A. Janocko, P. W. Eckels, and J. H. Murphy
Westinghouse Electric Corporation
Pittsburgh, Pennsylvania
INTRODUCfiON
The design of the conductor for the 400-kJ, 25-kA pulsed energy storage coil
Cl, being built by Westinghouse for the Los Alamos Scientific Laboratory, differs
n
significantly from the conductor fabricated previously for a 300-kJ coil because of
the low-loss requirements and fast pulse rate. As a consequence of the short
discharge interval and low-loss requirements, the conductor in this application has a
low copper-to-superconductor ratio.
DESIGN CONSIDERATIONS
The superconducting energy storage coil specification under discussion required
an energy storage of 400 kJ at an operating current of 25 kA with a discharge time of
0.7 ms. In addition, the coil structure is required to withstand the forces resulting
from a current of 35 kA, and the loading conditions associated with a ten-coil stacked
assembly. The required coil inductance is 1.28 mH resulting in a design terminal
voltage of 60 kV for the 0.7-ms discharge. The superconductor current density
should exceed two-thirds of the short sample value measured along the Ioad line with
cooling provided by immersion in a liquid helium bath. The combined energy Iosses
during a full charge-discharge cycle from all sources including eddy currents,
self-field, hysteresis, and mechanical motion must be less than 0.3% of the 400-kJ
stored energy when the coil is treated as a centrally located coil in a solenoidal stack
of ten such coils.
Because of the inductance and size constraints and the desire for a fully
ventilated coil, it was decided to adopt a multilayer, helically wound coil design. The
resulting design utilizes a stranded and cabled conductor in a three-layer configuration, with an open structure and pool boiling. The loss requirement necessitated a
nonconducting structure for conductor support. The major coil parameters are
shown in Table I.
* Work supported by the Los Alamos Scientific Laboratory, University of California, under Contract No.
X67-6665.
81
82
S. K. Siap, C. J. Heyne, D. T. Hackworth, M. A. JIIIOdto, P. W. Eckels, and J. H. Murphy
Table I. Parameters for 400-kJ Energy Storage Coil
Inductance, mH
Stored energy at 25 kA, kJ
Length, cm
Diameter, maximum, cm
Number of layers
Centtal field at 25 kA, T
Matrix
Superconductor
Current, kA
Current, fault mode 0.1 s duration, kA
Voltage across coil, kV
Operating point of superconductor
Discharge period, s
Charge period, s
Holding time, s
Cycle time, s
Energy Iosses full cbarge--discharge cycle, %
Cooling mode
e1
1.2s
400 ± 12
-71
67.47
Odd, 3 preferred
2.2 to 2.5 [4 ]
Cu-CuNi
NbTi
25
35
60
>~ along Ioad line
0.0007 to 1.0
30 to 300
30 to 300
300 to 900
< 0.3%
Pool boiling, 4.5 K
CONDUCTOR DESCRIPTION
The cross section of the superconducting cable is shown in Fig. 1. It consists of 12
primary cables cabled around an elliptical mandrei made from fiberglass, stainless
steel, and Kapton insulation. The winding pitch for these cables is approximately
28 cm. Each primary cable consists of seven subcables which are wound around a
fiberglass mandrel. The winding pitch for the primary cables is 2.54 cm.
PHOSPHOR
BRONZE
DUMMY
COO DUCTOR
I>Ti
Cu
Fig. 1. Cross section of 400-kJ coil conductor.
Design of a 400-kJ Pulsed Energy Storage Coil
83
Table II. Cable Characteristics
Superconductor characteristics
Peakoperating current density, iscop• A/m 2
Finished strand diameter, 2R 0 , mm
Outside radins of superconducting bundle, R 1, mm
NbTi filament diameter, d, p.m
Diameter of copper sheath, d 2 , p.m (across hexagonal flats)
Diameter of cupro-nickel sheath, d 3 , p.m
Filaments per strand
Filament twist pitch, mm
Overall Cu 0 .9 Ni0 . 1 : Cu: NbTi ratios
Interior Cu 0 .9 Ni 0 . 1 : Cu: Nb Ti ratios
Omega insulation thickness, p.m
Number of strands per cable
Volume per cable, cm 3
3.175
1: 1.5: 1
0.36: 1.5: 1
25.4
504
6722
Dummy conductor characteristics
Finished strand diaml:ter, 2R 0 , mm
Composition
Number of strands per cable
Volume per cable, cm 3
0.381
Phosphor-bronze
84
1120
Mandrei characteristics
Width, 2a, cm
Thickness, 2b, mm
Composition
Volume per cable, cm 3
1.54
3.81
304L
6850
1.52 X 109
0.381
0.172
14.4
21.7
23.2
199
The subcable is fabricated from six insulated mixed-matrix superconductor
strands cabled around a phosphor-bronze dummy conductor. The winding pitch for
the subcables is approxirnately 3.18 crn.
The superconducting strands are cornposed of 199NbTi filarnents approxirnately 14.4 J.l.ffi in diarneter, enclosed by a copper sheath approxirnately 3.67 J.l.ffi
thick and ernbedded in a Cu0 .9 Ni 0 . 1 rnatrix. The ratio of the constituents in the
conductor interior is to be 0.36 parts Cu0 .9 Ni0 . 1 to 1.5 parts Cu to 1.0 parts NbTi. The
filarnents are uniforrnly dispersed in this interior region of the conductor. In forrning
the conductor, a CuNi sheath is used to hold this rnixed rnatrix together. The
resulting overall ratios of Cu0 .9 Ni 0 . 1 : Cu: NbTi therefore becorne 1: 1.5: 1. To
reduce the ac loss, the conductor filarnents are twisted approxirnately one turn per
3.18 rnrn.
The superconducting strands are insulated frorn each other by an approxirnately 25.4-J.~.rn-thick coating of polyarnide-imide (Westinghouse Omega®)
insulation. Table II presents a detailed surnrnary of the conductor characteristics.
AC LOSS CALCULATIONS
The 400-kJ energy storage coil was designed to have a loss of less than 0.3% of
the stored energy for a central coil in a ten-coil stack during a 30-s charge and an
0. 7 -rns discharge. This section presents the loss calculations perforrned to deterrnine
the coil performance.
The calculation of the ac lasses have been rnade using what are generally
regarded as the rnost accurate forrnulas available at present CJ. Table III presents the
surnrnary of the loss calculations.
84
S. K. SiJiah, C. J. Heyne, D. T. Hackwortb, M. A. JIUIOCko, P. W. Eckels, and J. H. Mnrphy
Table lU. Summary of Loss Calcolations (Losses in Joules)
Central coil of
10-coil stack
Isolated coil
Superconducting
Normal
Superconducting
Normal
0
70.0
462.4
436.7
0
70.0
462.4
0
77.5
381.1
463.7
0
77.5
381.1
Dummy strands
Eddy current--charging
Eddy current--discharge
0
0.3
0
0.3
0
0.3
0
0.3
Mandrei
Eddy current--charging
Eddy current--discharge
0
99.8
0
99.8
0
129.5
0
129.5
1069.2
450K
0.238
952.2
450K
0.212
1052.1
400K
0.263
Type of discharge
Superconducting strands
Eddy current--charging
Hysteresis--charging
Eddy current--discharge
Hysteresis-discharge
J2 R --discharge
Totallosses
Stored energy
% Loss of stored energy
319.7
319.7
908.1
400K
0.227
MECHANICAL DESIGN
The structure design is based upon the 300-kJ coil [2 ] that has been successfully
tested at LASL when subjected to an ohmic-heating cycle eJ. The structural design
of the coil was governed by the following design criteria:
1. The entire structure was to be nonconducting.
2. Liquid helium coolant was to be in direct contact with all superconducting
strands throughout the coil and Iead area.
3. Combined primary stress intensity should not exceed two-thirds of the
material yield stress, or 40% of the ultimate, at operating temperature.
4. The structure must withstand the loading conditions associated with a
10-coil stacked assembly.
The main coil structure consists of an inner fiberglass composite tube. This tube
also acts as the first-layer coil former and establishes the concentricity of the
remaining layers. The superconducting wire is wound into a helical groove in the coil
former. Theseturnsare separated by teeth that provide the necessary spacing of the
turns and provide structural restraint at axial forces generated in the turns. Cooling
ducts are machined in the coil former axially below the turns to provide helium
coolant to the first layer. The cooling ducts also provide a channel for helium gas,
generated during the pulse cycle, the escape ftom the layer to the gas collection
chamber at the top of the assembly.
Each wound layer was over-wrapped with resin-coated fiberglass fibers and then
cured, in order to contain the turns and to restrain the superconductor against radial
forces developed when the coil is energized. To provide adequate layer-to-layer
insulation, 11layers of 0.127-mm-thick Kapton polymide film were applied to the
outside surface.
The remaining two layers of the coil are essentially the same as the first layer,
with the exception that insulation was not required on the outside surface of the coil
Design of a 400-kJ Pulsed Energy Storage Coil
85
assembly. However, an additionallayer of Mylar was wrapped on the outside of the
structure to provide a protective coating for the assembly. The whole coil assembly is
then heated for 16 hr at 150°C. This treatmenteures the resin-coated fiberglass wrap
on the outside of each former.
The material selected for the cylindrical formerswas G-10 Micarta® filament
wound material [ 2 ]. The matrix system used for this grade was selected for its crack
resistance when subjected to a sudden immersion in liquid nitrogen.
The maximum stresses in the former conductor core at operating temperature
are -31.3 and 211.4 MPa, respectively. This is weil within the design maximum
values for the former and conductor core. The pressure between the conductor and
former, based on thesetangential stresses, was calculated tobe 5.71 MPa.
Energizing the coil results in radial and axial electromagnetic forces. The
resulting hoop stress in the conductor core and the glass tape was calculated as
follows. The loading of the system is based on the Ioad sharing between the cured
glass tape and the conductor core as a function of the areas and elastic modulus of
each. The calculations are based on the assumption that both, glass tape and
conductor core, deftect an equal amount due to the radial force. Therefore,
81
=
P1L1
A1E1'
P2L2
82 = A 2E2
( 1)
(2)
8 = 81 = 82
L
= L1 = L2
(3)
Therefore,
A1E1
(4)
A2E2
(5)
P = P1 +P2
Using (1) and the fraction of Ioad sharing, the stresses on the conductor core and
glass tape can be calculated. Table IV presents the corresponding stresses on the
stainless steel conductor core and the cured glass tape.
The axial forces are a maximum at the ends of the coil and are directed inward.
The 0.508-cm-thick tooth between conductor winding slots must be capable of
supporting this Ioad without excessive stresses. Since each former cylinder has 100
0.635-cm-wide axial slots cut along its length, the slot tooth must support an
increased Ioad over the magnetic forces. Axialloading will be assumed applied along
Table IV. Conductor Core and Cured Glass Tape Stresses Due to Radial Field
Forces (Stresses in MPa)
Layer No. 1
Layer No. 2
Layer No. 3
Load condition
Core
Tape
Core
Tape
Core
Tape
Single coil, 25 kA
Single coil, 35 kA
Ten-coil stack, 25 kA
Ten-coil stack, 35 kA
Thermal interference stress
148.6
291.3
173.4
339.8
211.4
28.7
24.5
56.2
48.1
81.4
159.4
112.2
220.0
102.1
18.4
13.4
36.3
26.3
15.7
30.7
37.6
30.7
102.1
6.2
2.6
5.1
5.1
86
S. K. Singh, C. J. Heyne, D. T. Hackwortb, M. A. JIIIIOCko, P. W. Eckels, and J. H. Murphy
Table V. Maximum Conductor Loading and Peak Bending and Shear Stress on Slot
Teeth Resulting from Axial Loading for Layer No. 1
Loading
Stress, MPA
Load condition
Maximum
cond.load,
N/cm
Total coil
Ioad,
kN
Peak
bending
stress
Maximum
shear
stress
Single coil, 25 kA
Single coil, 35 kA
Ten-coil stack, 25 kA
Ten-coil stack, 35 kA
333
652
350
686
744
1458
851
1669
28.9
56.6
30.4
59.6
10.9
21.5
11.5
22.6
the centerline of the conductor. The large fillet radii of 0.953 cm is used to strengthen
the teeth, but if beam theory is applied, the bending stress will be
Mc
ub
=
1
(Px)(h/2)
=
bh 3 112
6px
=
(6)
h2
Location of the peak bending stress can be determined by plotting the value of x/ h 2
along the length. These values of peak stress are tabulated in Table V at 40% along
the tooth length.
Designstrengthof the former is 38.6 MPa (0.4uultimate) in the direction transverse to the filaments. Comparison of this value to the values in Table V indicates
that at the standard operating condition of 25 kA the tooth is adequately designed
with a 0.953-cm fillet. At the extended operating condition of 35 kA the tooth is still
within the Iimits if it is assumed that the design strength can be increased to ~ of
Uu)timate or 64.7 MPa.
The axialload will be less on the teeth toward the central region of the coil, but
the Ioad will accumulate in the coil formers to a peak Ioad as shown in Table V.
Calculation of the cylinder stress values at 25-kA single-coil Operation gives the
stress as 12.4 MPa. For the single-coil extended operation of 35 kA the axial
compressive stress on the former is 24.4 MPa. Both of these stress values are weil
within the design strength of the former material.
THERMOHYDRAULIC ANALYSIS
The 400-kJ coil is intended to demoostrate feasibility of a lower-loss, advanceddesign conductor using proven cooling techniques of the 300-kJ coil
In
appearance, the 400-kJ coillooks very much like its predecessor, the 300-kJ coil, but
there is one major difference in the thermal design parameters. The 400-kJ coil
thermal stability is reduced from that of the 300-kJ coil. The reasons for the reduced
thermal stability are mandated by low-loss requirement and existing conductor
manufacturing technology limitations.
The cooling channels and interconnecting ducts are designed to be of such
dimensions and inclinations that the vapor escapes completely from the coil in the
minimum operation cycle time. With escape of vapor assured, cooling during the
cycle is accomplished by the evaporation of liquid helium.
The operational cycle Iimits of the coil are summarized in Table VI. Note that
the coil may become resistive during discharge but must retum to the superconducting state during the rest interval for recharge. Table 111 summarizes the Iosses or
e].
87
Design of a 400-kJ Pulsed Energy Storage CoU
Table VI. 400-kJ Coil Cyde Summary
Process operation
line
0-1
1-2
2-3
3-0
Charge to 25 kA
Hold at 25 kA
Discharge to 0 A
Rest
Total period
Conductor
state
SC*
SC
SC/resistive
SC/resistive
Minimum
interval,
s
Maximum
interval,
s
30
3
7 X 10-4
267
300
300
300
1
299
900
* Superconducting.
internal heat generated in the conductor during each process. The values given are
peak values but are presumed spatially and temporarily constant and enter the
thermodynamic states trajectory equations as average values.
During coil charging (process 0-1), a hysteresis loss of 10.4 mJI cm3 of conductor
is generated in the NbTi filaments, producing a maximum steady-state temperature
rise in the filament of approximately 10-8 K, a rise in the conductor strand
of 6 x 10-7 K, and a heliumfilm rise of 2 x 10-5 K. In the stainless steel mandrei the
Iosses and temperature rise during charging are also negligible. Thus the process 0-1
is essentially an isothermal process.
During the hold period (process 1-2), the ripple in the power supply is the only
source of loss. The loss due to the ripple in the power supply is 0.2 m W I cm3 averaged
over 3-s hold periods. This can also be considered an isothermal process.
During discharge, heat is generated within the conductor which is sufficient to
induce a transition to the resistive state. Figure 2 shows the computed temperature
rise culminating in a final temperature of 16.8 K. In this computation the mode of
heat transfer is presumed to be nucleate boiling with a maximum surface fiux at
16.8 K of 0.6 W lcm2 • Some question could exist as to whether nucleate boiling can
be sustained within the conductor, but the final average volume fraction of vapor
within the conductor not including the helium contained in the risers is 20% and the
vapor quality is 3.3%. In the short discharge transient, nucleate boiling is expected to
exist.
r---------------------------------------,
DISCHARGE INTERVAL
~
18
16
14
"". 12
4
0
L-~~--~~~--~~~--~~~--~~~~
0
678
TIME, MSEC
101112131415
Fig. 2. Thermal cycle of 400-kJ coil.
88
S. K.
smp, C. J. Heyae, D. T.llaebrortll, M. A. JMOCko, P. W. Eckels, ud J. H. Marphy
Entering the rest period of 265 s (process 3-0), the conductor contains 20%
volume fraction of vapor and is at 16.8 K. No heat generation continues, but the
conductor must recover to the superconducting state. During process 3-0, reduced
heat exchange is expected to occur within the cable confines. Nucleate boiling is
expected to continue in the relatively large open regions of the bubble riser channels.
Thus heat will be conducted axially along the conductor to the boiling patch. For a
riser channel pitch of 1.6 cm the effective length is 1.0 mm. The axial Biot number of
0.026 indicates that axial thermal impedance can be neglected. Figure 2 shows the
recovery transient and predicts recovery of the superconducting state in about 12 ms.
Thus the temperature of thermodynamic state point 0 is achieved in 20 ms after
discharge, but the coil has not fully returned to its original thermodynamic state
because of the 20% vapor quality remaining in the conductor. It must be shown,
then, that vapor bubbles can escape from the most distant points in the coil during the
rest interval.
The bubble velocity is computed for a constant area channel with the expectation that the technique closely approximates the actual rise velocity. In a fluid such
as water with relatively high surface tension a variable area riser such as exists in the
400-kJ coilleads to an uneven bubble motion that can significantly slow the vertical
rise. In helium, the low-surface tension Ieads to bubble breakup and suppresses the
uneven motion regime. The characteristic channel dimension used in the computation is the minimum that exists (6.1 cm) even though bubble velocity correlates best
with maximum channel dimension. The time for bubble escape is approximately 14 s,
and the initial thermodynamic state is recovered in 34 s after initiation of the
discharge.
ACKNOWLEDGMENTS
The authors gratefully acknowledge the contributions and helpful suggestions of J. D. Rogers and
P. Thullen of the Los Alamos Scientific Laboratory.
NOTATION
A 1 = area of conductor core, 0.204
A 2 =total area of glass tape, 0.88 cm 2
b = tooth width
c = extreme fiber distance from neutral axis
E 1 = elastic modulus of conductor core, 200 GPa
E 2 = elastic modulus of glass tape, 33 GPa
h = thickness of tooth (variable)
I = cross-section moment of inertia
L = length of components
M = bending moment
P = applied Ioad
p = PI b = applied Ioad per unit width
n = distance from point of loading to location of stressed action
8 = deßection due to radial force
cm 2
REFERENCES
1. C. J. Heyne, D. T. Hackworth, S. K. Singh, M. A. Janocko, P. W. Eckels, and J. H. Murphy, "Design
and Fabrication of 400-kJ Superconducting Pulsed Energy Storage Coil," Final Report, Westinghouse
Electric Corporation, LASL Contract No. X67-6665 (1979).
Design of a 400-kJ Pulsed Energy Storage Coil
89
2. E. Mullan, D. W. Deis, P. W. Eckels, H. E. Haller, 111, M. A. Janocko, S. A. Karpathy, D. C. Litz, C. J.
Mole, P. Reichner, Z. N. Sanjana, and M. S. Walker, "Design and Fabrication of 300-kJ Superconducting Energy Storage Coil," Westinghouse Final Report E. M. 5077, LASL Contract No. XN4-32767 -3
(July 1977).
3. F. W. Grover, Inductance Calculations, Dover, New York (1946).
4. T. F. Yang, in Proc. 5th Intern. Conference on Magnet Technology, MT-5 Frascati, Italy ( 197 5), p. 203.
5. P. Thullen, J. D. G. Lindsay, D. M. Weldon, and H. F. Vogel, IEEE Trans. Magn. Mag-15(1):538
(1979).
B-4
OPERATING CHARACTERISTICS OF A 1.5-MJ
PULSED SUPERCONDUCTING COIL*
S. H. Kim, S.-T. Wang, and M. Lieberg
Argonne National Laboratory
Argonne, Illinois
INTRODUCfiON
The ohrnie heating coils of tokamak fusion reaetors require a stored energy on
the order of 1 GJ, a ramping rate of -9 T/s, and a peak operation eurrent of 50 to
approximately 100 kA. Owing to power balanee requirements of the reaetors at
these sizes, only supercondueting eoils are expeeted to be economieal. For the
development of the ohrnie heating eoils, a eryostable pulsed supereondueting coil has
been eonstrueted and tested at Argonne National Laboratory. The eoil has a stored
energy of 1.5 MJ and a peak field of 4.5 T with a peak operation eurrent of 11.2 kA.
The eoil was tested with both de and pulsed eurrents.
FABRICATION OF THE CABLE
The design of the cable for the 1.5-MJ coil is based on detailed cryostability
The cable was fabricated by
studies of basie cables and 5-kJ model coils
Supercon, lne., to Argonne National Laboratory specifieations by twisting 24 basie
eables around an insulated stainless steel strip with a twist piteh of 22.5 cm. A
close-up of the eable eross-seetion is shown in Fig. 1. The basie cable is made by
twisting three seven-strand conductors (triplex cable) with a twist piteh of 2.2 cm.
The seven-strand conduetors are made of six OFHC copper wires twisted around a
superconducting center conductor and soldered with Staybrite. Since the requirements of low ae Iosses and cryostability confiict with eaeh other, the basie principle
chosen is to achieve cryostability within the basic cable. To restriet ac coupling
among the 24 triplex cables in the final cable, only limited current sharing among the
triplex is allowed by coating a thin insulating film around the seven-strand conductors. The critical current of a short sample of the basic cable is 405 A at 5 T. Each
superconducting strand has a diameter of 0.051 cm and contains 2041 6-JLm
filaments with a twist pitch of 1.27 cm. The copper-to-superconductor ratio for each
strand is 1.8.
The final cable is compressed during the cabling by heavy rolls from four sides.
This is required to minimize mechanical perturbations of the basic conductors during
pulsing of the 1.5-MJ coil. The compression did not darnage the insulation between
eJ
* Work supported by the U. S. Department of Energy.
90
Operating Characteristics of a 1.5-MJ Pulsed Superconducting Coil
91
Fig. 1. Cross section of ac cable.
the stainless steel strip and the 24 triplex cables. However, owing to the deformation
of the soft soldering in the seven-strand conductor, about 5% degradation of the
recovery current in the triplex has been observed. The finished cable has a width of
3.78 cm and a thickness of 0.74 cm. The first 25-m-long cable was produced as a test
of the cabling technique. The total cable length fabricated for the coil was about
590 m long.
1.5-MJ COIL FABRICATION
Coil winding with a spongy cable is a rather interesting experience. The coil is
composed of 18 helicallayers with an average of 14.3 turns in each layer. Turn-toturn insulations are provided by two layers of 0.02-cm-thick glass-cioth tape and two
layers of 0.01-cm-thick Mylar tape. The winding layers for the first to tenth layers are
separated by 0.48-cm-thick and 0.64-cm-wide G-10 strips. In the low-field region of
the eleventh to eighteenth layer, the thickness of the strips is reduced to 0.32 cm.
Characteristics of the coil are listed in Table I.
Figure 2 provides a close inspection of the coil winding in the thirteenth layer.
Spaces between the strips provide 0.64-cm-wide cooling channels in the vertical
direction. The G-10 bobbin has cooling channels in the radial direction. During the
winding, the tension in the cable was increased gradually from 225 to 450 kg to
provide a constant radial pressure in the coil. Totallength of the cable used for the
coil is about 510 m. Nine potential taps have been installed in the coil to study
possible conductor motion and six thermocouples to monitor temperature variation
during the test of the coil. When the coil is charged, the average hoop stress in the
cable is about 310 MN/m 2 • Part of the stress can be sustained by the stainless steel
strip in the cable itself. To support the excess stress, 16 bands are placed outside the
coil. Each band is fabricated of 30 layers of 0.025-cm-thick by 3.2-cm-wide
fiberglass cloth.
EXPERIMENTAL ARRANGEMENT FOR TUE COIL TESTS
The 1.5-MJ coil is assembled for tests as shown in Fig. 3. Details of the plastic
Most of the
cryostat developed for the coil have been reported elsewhere
materials used for the arrangement are nonmetallic to avoid eddy current Iosses
during the pulsing of the coil. The topflange is constructed of 5.7-cm-thick Micarta
plate. The coil is suspended to the top flange using eight 0.64-cm-diameter stainless
e].
92
S. H. Kim, S.-T. Wang, and M. Lieberg
Table I. Characteristics of Pulsed Superconducting Coil
Central field, T
Peak field, T
Operation current, kA
Inductance, mH
CoiiiD, cm
Coil OD, cm
Axiallength, cm
Number of layers
Total number of turns
Cryostable recovery heat flux, WI cm 2
Layer-to-layer spacing, cm
Average current density, Alcm 2
Cable cross section, cm
Cable length, m
Total ampere-meters, A-m
Maximum radial magnetic pressure, MPa
Maximum axial magnetic pressure, MPa
Maximum dBidT, Tls
Maximum dll dT, kAis
Charging voltage, V
Hysteresis loss in the filaments, kJ I cycle
Eddy current loss in the matrix at 9 Tls, kJicycle
AC losseslstored energy at 9 T ls, %
Eddy current loss in the stainless steel
at 9 Tls, Jlcycle
Heat flux due to ac Iosses at 9 Tls, mW lcm 2
4.2
4.5
11
24
41.6
81.0
58.1
18
258
0.35
0.48 (1st-10th layer)
0.32 (11th-18th layer)
2290 (1st-10th layer)
2685 (11th-18th layer)
3.78 X 0.74
510
5.8 X 106
83
28
11
27
650
-0.1
2.65
-0.1
60
-10
steel rods. The bottom of the coil is further supported by a 2.54-cm-thick Micarta
plate. Thermalradiation shields consisting of a 10-cm-thick piece of Styrofoam and
eight layers of aluminum foil are attached to the bottom of the top ftange. The two
coil terminals are brought to the top of the coil by gradually changing the winding
angles. After removing the thin insulation in the basic cable, each terminal is soft
soldered to eight copper-stabilized monolithic superconductors, 1 cm wide and 0.2
cm thick. This design allows a change in the directions of the terminals and makes the
terminals mechanically solid. The terminals are connected to the bottom tips of the
vapor-cooled current Ieads.
The Ieads purchased from American Magnetics Inc., have a current capacity of
up to 15 kA dc. Heat leaks of the Ieads are about 22 W without current and 30 W with
12 kA dc. During the test of the coil the liquid helium Ievel should be maintained
between the bottom tips of the Ieads and the top of the coil. The distance between
them is about 23 cm; this corresponds to a helium boil-off energy of about 380 kJ.
With this energy the coil can be pulsed about 140 times with a pulsing rate of 9 T /s.
DC SHARING
The 1.5-MJ coil was fi.rst charged to the critical current of the short sample cable
(11.2 kA) by a 5-V, 12-kA dc power supply. During the fi.rst charge of the coil no
major conductor motion or mechanical perturbation was observed. Figure 4 shows
the critical current and the Ioad line of the coil. The critical current of the cable was
determined from measurements of the critical current of short sample triplex cable.
Operating Characteristics of a 1.5-MJ Pulsed Superconducting Coil
Fig. 2. Thirteenth layer of 1.5-MJ coil winding.
Fig. 3. Experimentalarrangement for the 1.5-MJ coil.
93
94
S. H. Kim, S.-T. Wang, and M. Lieberg
>-
"'
I, kA
Fig. 4. Critical current of short sample cable and Ioad line of
the 1.5-MJ coil.
To demoostrate the cryostability of the coil, it was charged beyond the critical
current up to 11.75 kA (from point A to pointBin Fig. 4). A bridge circuit was used
to detect when parts of the coil in the high-field region became normal. Beyond the
critical current, unbalanced valtage of the bridge increased gradually; this indicated a
stable current sharing between the superconducting strands and the copper stabilizer. The current-sharing section, with a resistive valtage of 2 mV, was estimated to
be about 1.5 m lang. Charging the coil to point A without developing a resistive
valtage is a significant result. This means that the cable is fully transposed and the
current-carrying capacity of each of the 24 basic cables is equal without any
degradation.
PULSED-CURRENT TESTS
Single Pulsing. After the current-sharing test, the coil was pulsed with a 7 -MW
(650 V at 10.9 kA) power supply. A summary of the pulsed-current characteristics is
shown in Table I. The coil was charged to a 4.4-T peak field in 0.4 sec and discharged
to zero in 0.6 s with a maximum ramping rate of 11 T /s. The off-time between pulses
was 10 s. The terminal valtage of the coil, V ooih can be written as
(1)
where L is the inductance of the coil and V1oss is the valtage associated with the
energy Iosses in the coil during pulsing. Figure 5 is a set of recordings for a typical
pulsing test. In this figure the peak current is 10 kA with a pulsing time of 1 s. The left
side of the figure is an expansion of the recording, and the right side shows a
continuous pulsing between off-time of 10 s. The current variation dl/ dt is close to a
triangular waveform (Fig. Sa) with a maximum rate of 27 kA/s. This rate is not
limited by the coil performance but by the power supply used. The terminal valtage
of the coil, V ooii (Fig. Sb), is balanced with an inductive valtage taken from a mutual
Operating Characteristics of a 1.5-MJ Pulsed Superconducting Coil
95
Fig. 5. Recording of a single-pulsing test. Legend: (a) current waveform; (b) coil terminal voltage; (c) loss
voltage; and (d) integrated loss voltage.
inductor placed outside of the coil. The resulting loss voltage, V coih is shown in Fig.
Sc.
Double Pulsing. After more than 3000 single pulses the coil was tested with
double triangular waveform pulses as shown in Fig. 6. The double-pulsing modewas
used to simulate the full ftux swing of ohmic-heating coils. The peak current during
the pulsing was 10.6 kA with a central field of 4.0 T. The current waveform is shown
in Fig. 6a. The full period of the double pulsing was 9.5 s with an off-time of 6.9 s. The
charging and discharging times were about 0.64 s, respectively, in each pulse. The
double pulse at the left side of the figure is an expansion of the pulses at the right side
of the figure. Potentialleads are taped to several layers of the coil. The potentials
between layers 2 and 4 and between layers 12 and 14 are shown in Figs. 6b and 6d,
respectively. After 570 double-pulsing cycles no visible differences between the two
voltage waveforms have been observed.
AC LOSSES
The ac Iosses of the coil were determined from helium boil-off during the pulsing
and by the electronic integrator method 3 ]. Alternating current Iosses as a function
e·
96
S. H. Kim, S.-T. Wang, and M. Lieberg
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coil (2 V /div.); (c) loss voltage of coil (0.2 V /div.); and (d) voltage of 12th-14th layer (5 V /div.).
of (dB/ dt) 2 are shown in Fig. 7. Data points shown as circles and triangles are
obtained from the tests with single pulses, and data points shown as solid rectangles
are obtained from the double-pulsing test. Eddy current Iosses in the copper
stabilizer can be expressed as (4 ]
(2)
where Veu is the volume of copper, lp is the twist pitch length, R is the radius of
superconducting wire, p 1 is the effective transverse resistivity, and R, is the conductor radius including copper stabilizer. The linear variation of the ac Iosses as a
function of .8 2 in Fig. 7 indicates that most of the Iosses are a result of the eddy
current in the copper.
The insulation on the surface of the six-strand wireisthin enough to have limited
This allows a certain degree of ac
current sharing among the triplex cable
coupling among the 24 triplex cable of the 15-MJ coil. If the coupling is assumed to
be limited within the six-strand wire, from the experimental data of Fig. 7 and (2) the
effective resistivity is found to be about 2 x 10- 10 0-m, which is somewhat lower
than expected. This is an indication that some portion of the ac Iosses come from the
ac coupling among the triplex cables and the six-strand wires. From the above results
one can conclude that the thin insulation of the 1.5-MJ coil cable has an Optimum
thickness to compromise the current sharing and low ac lasses.
eJ.
Operating Charac:teristics of a 1.5-MJ Pulsed Supercouducting Coil
2.5
I
lo/
/
2.01-
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oo /
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--'
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/
y
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/
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-
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-
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~%
Q:)Cö
0
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6
~o/ 6
1.51-
0.5 1-
-
oo/
o':/
r
10
97
0
I
20
30
40
I
I
I
50
60
70
80
(d8tdt) 2 , ( Ttd
Fig. 7. Ac Iosses vs. (dB/dt) 2 . Data points of circles and
triangles represent single-pulsing tests while solid rectangles
.represent double-pulsing tests.
PULSING EFFECf ON THE CRYOSTABILITY
After the pulsing tests of the coil, another dc current test has been conducted
using a 50-kA, 5-V dc power supply. This testwas designed to investigate the pulsing
effect on the cryostability of the coil. The coil was charged with a charging valtage of
0. 7 V. No significant change in the critical current was observed. The coil remained in
a current-sharing state up to 1 kA above the critical current, and recovered to the
superconducting state by reducing the current. The coil was quenched when the
current was further increased. The amount of the energy released in the quench
estimated from the blow out of the helium was approximately 0.5 MJ. In the
subsequent charging, discharging, and quench, no significant changes in the characteristics of the coil have been observed.
SUMMARY
1t has been demonstrated for the first time that a relatively large cryostable
superconducting coil can be pulsed with relatively low ac Iosses at high ramping rates.
The low ac Iosses with limited current sharing have been achieved by insulating the
surface of the basic cable with a thin organic film. The ac Iosses at 9 T/s are about
0.1% of the stored energy in the coil. After more than 4000 pulsing cycles, no
changes in the pulsing characteristics and cryostability of the coil have been
observed. The quench current of the coil was approximately 1 kA higher than the
critical current of the coil.
REFERENCES
1. S.-T. Wang,S. H. Kim, L. R. Turner,K. M. Thompson, W.F. Praeg,C.I. Krieger,and R.L. Kustom,in
Advances in Cryogenic Engineering, Vol. 23, Plenum Press, New York (1978), p. 255.
2. S. H. Kim, S.-T. Wang, W. F. Praeg, C.l. Krieger, and M. Lieberg, IEEE Trans. Magn. Mag-15:840
(1979).
3. S. H. Kim and S.-T. Wang, "Fusion Power Program Quarterly Progress Report," Argonne National
Laboratory, ANL/FPP-78-4 (1978).
4. W. J. Carr, Jr., J. Appl. Phys. 45:929 (1974).
B-5
3-MJ MAGNET FOR SUPERCONDUCI1VE
ENERGY STORAGE
T. Shintomi, M. Masuda, H. Sato, and K. Asaji
National Labaratory for High Energy Physics
Ibaraki, Japan
INTRODUCfiON
Superconductive energy storage requires different kinds of magnets depending
on its applications. Load leveling of electric power requires a cryogenically stabilized
magnet, similar to the dc magnets used for bubble chambers. The stored energy for
such magnets is 10 12 to approximately 10 13 J which is larger than the stored energy of
magnets for other uses. One of the most important problems is how to reduce Iosses
at the interface between the superconductive coil and the power grid.
Another type of magnet utilizing pulsed superconductive energy storage is that
used for accelerators and fusion reactors. This magnet should be also cryostable since
it is required to transfer a huge amount of energy in a short period of time, frequently
on the order of 1 sec. lt is necessary, however, for this application to use a
nonstabilized superconductor in order to suppress ac Iosses which result from the
pulsed operation.
The dewar vessel for a pulsed magnet requires more stringent specifications
because the eddy current which results from a fast change in the magnetic field
significantly increases the heat Ioad at liquid helium temperature. A plastic dewar
must be used to prevent eddy currents even if it is prone to helium leaks through the
plastic wall.
Aseries of investigations C-3 ] by the present authors that uses 100-kJ coils has
demonstrated that energy storage for an extended period of time does not require a
superconductive switch to maintain the persistent current and energy transfer using a
thyristor inverter with capacitors is one of the best methods for pulsed power Ioads,
especially for large amounts of pulsed energy storage. A practical evaluation of such
energy storage, however, requires data using coils much larger than 100 kJ. A 3-MJ
energy storage magnet is thus the next step toward a full scale magnet.
The 3-MJ coil was constructed to ascertain the following information:
1.
2.
The efficiency of the coil when used as an energy storage device for Ioad leveling
of an electric power system measured by energy transfer to apower line utilizing
thyristor bridges.
The energy transfer between the 3-MJ coil and two 100-kJ coils using the
thyristor bridges proposed by the group at the University of Wisconsin [4 ]. (This
will provide the design concepts for the pulsed energy storage associated with
fusion reactors, accelerators and other pulsed power Ioads.)
98
99
3-MJ Magnet for Superconductive Energy Storage
Table I. Design Parameters
Coil specification
Stored energy, MJ
lnductance, H
Mean radius, cm
Length, cm
Winding thickness, cm
Number of turns
Nominal current, A
Central field, T
Maximum field at wire, T
Weight of wire, kg
Weight of bobbin, kg
3
5.4
60
29.2
8.0
1773
1050
1.9
5.0
280
310
Wire specification
Size, mm
Matrix ratio (Cu: Nb Ti)
Filament diameter, J.Lmrp
Number of filaments per wire
Wire twist pitch, mm
Critical current at 5 T, A
B
A
1.5 X 3.0
3.0
24.5
2257
30
1500
1.5 X 3.0
3.0
61.5
361
40
1600
3. The self-protection of the coil upon intentionally quenching one section of the
divided coil.
The design and construction of the 3-MJ superconductive energy storage system and
also the preliminary experimental operation are reported in this paper.
COIL
Specifications
To obtain high efficiency as an energy storage magnet, the coil must have a large
inductance, particularly for load-leveling applications. Judging from previous studies
with the 100-kJ unit, the efficiency of the 3-MJ unit was estimated to be approximately 70% for repetition times on the order of 10 min exclusive of cryogenic and
mechanicallosses. The efficiency is given by [5 ]
71
= 1 - ~ aRPT- 2n Ll
v(;J
1/2
T
(1)
where the factor, a, is inversely proportional to the inductance of the coil. This
implies that with a larger inductance, a larger system efficiency should be possible.
The rated current in this study was fixed at 1050 A to obtain the above target
efficiency. The coil thickness was designed so that the field at the coil end did not
exceed that at the inner surface of the coil in the medium plane. Designparameters of
the coil are listed in Table I. Superconductors A and B were fabricated by Kobe Steel
and Hitachi, respectively.
Structure
The salient points of the design are that the coil is divided axially into three
sections and that the superconductors are reinforced by stainless steel tapes as shown
in Figs. 1 and 2, respectively. The segmentation functions not only to Iimit the
pressure exerted on the windings caused by axially compressive forces but also to
100
T. Sbintomi, M. Masuda, H. Sato, and K. Asaji
IO.Scm
120cm'l>
Fig. 1. Cross section of the 3-MJ coil.
Fig. 2. Schematic view of the winding.
protect the coil. When one of the coil sections quenches, its energy is partly
transferred to adjacent sections in a superconducting state through mutual coupling
and partly to a power line by means of inverter operation of thyristor bridges as
shown in Fig. 3. This mode enables the quenched section to discharge its energy
faster than by the usual protection modes.
To achieve such a large inductance the coil was fabricated with a large number of
turns of a relatively fine wire, in contrast with other fast-pulsed magnets [6 ' 7 ]. At the
same time, the coil bad to have such characteristics as high strength against magnetic
forces and excellent cooling for pulsed operation. The superconductors were
supported against the radial expansion force by stainless steel tapes which were
wound together with the superconductors in a bifilar winding. Good cooling was
obtained by winding B-stage epoxy impregnated tapes spirally around the superconductors. The wire was covered about 40% with this tape with a thickness of 0.53
mm.
Construction
The superconductor was coated with a 40-50-~tm thickness of polyimid to
provide adequate insulation protection against the test voltage of 4 kV before
applying the B-stage epoxy tapes. This extra insulation protects the coil against the
high voltages encountered in pulsed operation. Breakdown voltage of the coil was
determined tobe over 2 kV. The coil was wound under a tension of 100 N and cured
at a temperature of l20°C for 7 hr. The superconductors were reinforced by stainless
steel tapes and secured by the epoxy-impregnated tapes. The stainless steel tapes
acted not only as reinforcing members but also as a surface for reliable bonding with
the epoxy impregnated tapes. The bobbin was constructed of stainless steel and
segmented to reduce eddy currents induced by fiux change encountered in pulsed
operation.
FundaiTIIItltal cct
Superconducting state
Normal state of one segiTIIItlt
Fig. 3. Schematic circuits developed for coil protection.
101
3-MJ Magnet for Superconductive Energy Storage
120cm95
q
1-'
I
o - lloHI-+IJ""'"""'
I~
I
Fig. 4. Schematic of the cryostat.
CRYOSTAT
The cryostat for the 3-MJ systemwas constructed of stainless steel although a
plastic Dewar is more suitable for pulsed operation. The cryostat was designed as a
scaled-down model of what might be used in a practical superconductive energy
storage system, i.e., the coil has a small aspect ratio and a small heat leak. Even so, it
is short in height as shown in Fig. 4. In order to reduce the heat leak, the walls of the
helium vessel were fabricated of thin stainless steel and reinforced by thick stainless
steel members.
Cooldown tests were performed on the assembled cryostat. The estimated
volume of helium required for cooldown is shown in Table II. During actual
cooldown a total of 450 Iiters of liquid helium was transferred into the vessel with a
resultant boil-off of 170 Iiters. Heat leak was measured by monitaring the liquid
helium Ievel with a superconductive Ievel sensor. The measured heat leak was 3. 7 W.
PRELIMINARY TEST OF COIL
Excitation of Coil
The assembled coil before placement in the cryostat is shown in Fig. 5. The coil
was excited by using two thyristor converters in series. Each section of the coil was
tested before the entire coil was excited. While one section was under excitation, the
others were short circuited with 8-0 resistors. The middle section was excited first
and attained a current of 480 A after six quenches. The lower section was then tested
and attained a current of 500 A after five quenches. The upper section did not show
any quenching characteristics up to a current of 500 A.
Table II. Estimate of Liquid Helium Consumption during Initial Cooldown
Liquid helium, Iiters
Components
Bobbin and structure
Cooling channel
Cooling channel
Wire
He vessel
Materials
ss 304
Phenolic resin
B-stage epoxy tape
Cu+NbTi
SS 304L
Total
Weight, kg
max.
min.
294
16
7
273
130
720
429
48
21
549
190
1237
32
5
2
41
14
94
101
T. Shintomi, M. Masuda, H. Sato, and K. Asaji
Fig. 5. Assembled coil before placement in the cryostat.
The entire coil was finally excited, and after six quenches attained a current of
685 A . The coil returned to its superconductive state after some of the quenches
when the current was decreased below the quenching current (see Table 111). In some
quenches the coil did not recover and about 100 liters of helium were evaporated.
Queuehing
The quenching which was observed during training may be classified into two
modes. The first mode is associated with the generation of a localized normal state in
the superconductors characterized by a low propagation speed. As shown in entry
# 2 of Table 111, the propagation velocity of the normalzonewas estimated as 0.63
m/s using the derivative of the unbalanced coil voltage of 15mV/sand the substrate
resistance per unit length (38 #LÜ/m at 4.2 K). When the normal region appeared, the
current decreased because the control function of the thyristor was changed to an
inverter operation. The superconductive state recovered at a current of 528 A within
about 10 s after quench without excessive evaporation of helium. This suggests that a
few turns of the coil went normal but recovered because of the low normal state
Table ßl. Observed Propagation Veloeides and Recovery Currents at
the Quenches
Quench
No.
Quench current,
A
#1
#2
#3
#4
625
635
635
655
Propagation velocity,
m/ s
Recovery current,
A
1.1
517
528
460
540
0.63
1.2
1.1
103
3-MJ Magnet for Snperconductive Energy Storage
propagation velocity and the rapid initiation of the inversion operation of the
thyristor bridges.
The second mode of quench was followed by considerable evaporation of
helium at a current of 678 A. Later, the coil deformationwas carefully checked and it
was found that the upper section bad moved toward the middle section incurring a
maximum deformation of 3.3 mm. Judging from the deformation of the flange and
the calculated electromagnetic force equation, the axial compressive force was
estimated at 170 tons. lt can be shown that when a coil is moved adiabatically over a
distance of 1 mm on the average, the entire superconductor could easily increase its
temperature sufficiently to exceed the critical temperature in a short time.
The time, Tv, needed for the current of the quenched coil to decrease to zero is
given by the following equation, assuming the entire coil is in the normal state:
L ( 1 +-RJo)
Tv =-In
Re
VI
(2)
This time for the test coil is calculated to be 22 s assuming the temperature of the
entire coil is below 20 K. When the temperature of part of the coil is above 20 K, the
calculated value of time is in good agreement with the measured one of 17.0 s.
Propagation Velocity of aNormal Zone
The propagation velocities of anormal zone were measured for several currents
and the results are listed in Table III. They range from 0.63 to 1.2 m/s. Dresner [8 ]
has calculated the velocity for the case of constant thermophysical properties,
including the effect of current sharing. Stekly's parameter, a, is estimated to lie
between 10 and 40; however, there are uncertainties owing to incomplete knowledge
of the heat transfer coefficient and the effect of the spirally wound tapes on the
superconductor. The data for low propagation velocity of about 1 m/s and the
measured recovery currents are consistent with the value of a calculated by Dresner.
The currents reported for quenches in the first mode are the critical values at which
the normal zones propagate or recover.
Operating Efficiency
Measurements were made to estimate the operating efficiency of the system.
The efficiencies obtained are shown in Fig. 6 for a stored energy Ievel of 0.85 MJ.
1.0
STORED ENERGY
O.B5 MJ
>
u
0
~ .5
ü
Li:
"w
Fig. 6. Operating efficiency vs. discharging time for the
coil.
%~--------~5~0----------7,100~-­
DISCHARGING TIME , sec
104
The data can be represented by the following relation:
71
= 1 - 0.0050T
(3)
The slope of this line is determined by the Iosses in the power supply and Iead wires.
The circuit resistance is calculated to be 18 mß if this relation is utilized. This value
agreed with the eflective resistances of the power supply and the Iead wires.
SUMMARY
The 3-MJ superconducting solenoid, which is intended not only for the power
leveling but also for the pulsed storage, was constructed by using monolithic
multifilament superconductors. The coil was reinforced to withstand the radial
expansion force by the stainless steel tapes wound in the bifilar winding. On the other
band, the axial segmentation of the coillimited the pressure exerted on the windings
caused by the axial compressive force.
Measurements of the propagation velocity and the recovery current were
performed in a preliminary test. The values obtained are consistent with previous
measurements made by Dresner. The coil experienced quenches because of wire
movement which immediately followed deformation of the structure. To minimize
this movement, the coil structure will be reinforced in the axial direction.
ACKNOWLEDGMENTS
The authors gratefully acknowledge the contributions of Y. Oda, N. Sato, M. Nakano, Y. Hayashi,
and their collaborators of the Tokyo Institute of Technology.
NOTATION
E, = maximum stored energy of the coil
10 = coil current at quench
L = inductance of the coil
n = number of thyristors of the power supply in series
Re = resistance of the coil at quench
RP = effective resistance of the power supply and Iead wires
T = time for charging or discharging coil
T0 = discharging time at quench
V1 = inverter input voltage of the power supply at quench
~V = forward voltage drop of the thyristor
a = 2/L
71 = efficiency of energy storage without cryogenic and mechanicallosses
REFERENCES
1. M. Masuda, T. Shintomi, S. Matsumoto, H. Sato, and A. Kabe, in Proc. 6th Intern. Conference on
Magnet Technology, ALFA, Bratislava, Czechoslovakia (1977), p. 254.
2. M. Masuda, T. Shintomi, H. Sato, and A. Kabe, IEEE Trans. Magn. Mq-15:318 (1979).
3. M. Masuda, T. Shintomi and K. Asaji, in Advances in Ctyogenic Engineering, Vol 25, Plenum Press,
New York (1980), p. 61.
4. H. A. Peterson, N. Mohan, W. C. Young, and R. W. Boom, in Energy Storage, Compression, and
Switl:hing, Plenum Press, New York (1976), p. 309.
5. M. Masuda and T. Shintomi, Ctyogenics 17:607 (1977).
6. C. J. Mole, D. W. Deis, P. W. Eckels, H. E. Haller, M. A. Janocko, S. A. Karpathy, D. C. Litz, E.
Mullan, P. Reichner, Z. N. Sanjana, and M. S. Walker, in Advances in Ctyogenic Engineering, Vol 23,
Plenum Press, New York (1978), p. 57.
7. S.-H. Kim, S.-T. Wang, W. F. Praeg, C. I. Krieger, and M. Lieberg, IEEE lrans. Magn. Mac-15:840
(1979).
8. L. Dresner, IEEE lrans. Magn. Mq-15:328 (1979).
B-6
CONCEPTUAL DESIGN OF A 20-MJ
SUPERCONDUCTING FORCED-COOLED
OHMIC-HEATING COIL*
S. K. Singh, J. H. Murphy, M. A. Janocko,
H. E. Haller, D. C. Litz, and P. W. Eckeis
Westinghouse Electric Corporation
Pittsburgh, Pennsylvania
and
J. D. Rogers and P. Thullen
Los Alamos Scientific Laboratory
Los Alamos, New Mexico
INTRODUCfiON
Conceptual design of a 20-MJ superconducting coil is described which was
developed to demoostrate the feasibility of an ohmic-heating system. The superconductor material was Nb 3 Sn for a 9-T maximum field. Cabled and braided
conductors were investigated and the braided conductors were identified as the best
alternates because of their high operating current densities and their high porosity
C]. The coil was designed to be cryostable for bipolar operation from a +9- to -9-T
maximum field within 1 s. The forced-cooled design described in this paper utilizes
crossftow cooling. The coil was designed to generate the ftux swing while simultaneously meeting the limitations imposed by cooling, insulation, current density,
and stresses in the materials.
DESIGN CONSIDERATIONS
The superconducting ohmic-heating coil described in this study required an
energy store of 20 MJ at a current of 50 kA. The coil structure was to withstand the
forces resulting from 60 kA carried by the coil. The required coil inductance was
16 mH, resulting in a terminal voltage of 1600 V for a resistive discharge and 2500 V
for a capacitive discharge. The coil was designed for bipolar operation from +9to -9-T maximum field on the conductor, and bipolar half-cycle sinusoidal
* Work
supported by University of California, Los Alamos Scientific Laboratory, Contract No. L488407C-1.
lOS
106
S. K. Siqla et tll.
Table I. Coil Design Parameters
Energy storage rating at 50 kA, MJ
Peak field, T
lnductance, mH
Insulating rating, k V
Type of cooling
Type of conductor
Superconductor material
Coillength, cm
Coil diameter, cm
Coil bore, cm
Number of turns
Number of layers
20
9
16
10
Forced
Braid
Nb3 Sn
139.7
149.4
33.0
240
10
operation from full positive field to full negative field within 1 s. The hold time
between field reversal was to range from 10 to 100 sec at full field. The coil wastobe
cryostable and not go normal durlog bipolar operation. The superconductor material
was Nb3Sn for a peak field of 9 T.
A multilayer helically wound coil design was selected because of the stored
energy requirement, high operating current density, and the desire for a fully
ventilated coil. The resulting design utilized a lattice braided conductor in a ten-layer
configuration. The major design parameters are shown in Table I.
eJ
CONDUCI'OR DESIGN
Several
conductors were designed for potential application in a forcedcooled ohmic-heating coil. The superconducting material considered was a Nb 3Sn
braid. All conductors were designed to be cryostable, i.e., the heat generation rate
when all of the current is in the stabilization material is less than the heat removal
rate. The copper-to-noncopper ratio and the strand diameter were selected to give
an operating current density to critical current density ratio approximately equal to
50%.
AC LOSSES
The ac Iosses in the ohmic-heating coil conductors have been calculated
assuming a nonoptimized superconductor configuration. Table II summarizes these
calculations and the reference conductor characteristics. The predominant ac loss, in
all cases, is eddy current loss in the copper stabilizer. This loss can be lowered by
incorporating resistive webbing. However, because the surface heat ßux during the
field pulses is between 2 and 14 times smaller than the surface heat ßux required for
cryostability, this loss reduction has been ignored at this time.
MECHANICAL DESIGN
The structural design and analysis were based on the 300-kJ coil [3] that has
been successfully tested at LASL when subjected to an ohmic-heating cycle [4 ]. The
pulsed operaring cycle requires minimization of electrically conducting structures to
minimize eddy current Iosses during the operating cycle. For this reason fiberreinforced composites were used wherever possible in the coil structure. The
structural designwas developed using the following design codes:
1. The maximum strain in the Nb3Sn superconductor should be limited to
0.1%.
Conceptual Design of a Superconducting Ohmic-Heating Coil
107
Table II. Reference 50-kA Conductor Characteristics
Peak field, T
Type of cooling
Type of conductor
Material
Number of strands
Bare strand diameter, cm
Insulated strand diameter, cm
Number of filaments
Filament outside diameter, J.Lm
Filamentinside diameter, J.Lm
Filament twist length, cm
1 to Je ratio
Cu-to-non-Cu ratio
Packing factor
Conductor width, cm
Conductor thickness, cm
Conductor current density, kA/cm 2
Matrix conductivity, um, mho/m
Transverse conductivity, u .L • mho/m
Sheath conductivity, u, mho/m
Peak ac loss per pulse, J/cm 3
Peak field pulse heat ftux, mW /cm 2
Cryostability recovery heat ftux, mW/cm 2
9
Forced
Braid
Nb3 Sn
503
0.0965
0.102
6,328
3.5
1.5
1.0
0.500
3.069
0.41
3.50
2.86
5.00
5.9 X 108
1.2 X 109
1.7 X 109
1.66
58.0
448
2. The primary stress intensity in the structure should be less than two-thirds
material yield stress or 40% of ultimate, whichever is less.
3. The maximum stress theory will be used for composite structures.
The design concept for the coil is shown in Fig. 1. The concept uses teeth to
support axial forces and stainless steel bands for radial support. The axial and radial
forces vary within the coil cross section.
FilAMENT WOJNO KEYS
C()IJOUCTOR SUPPORT
GROOVE
AXIAL STRUCTURE
HELIUM COOlANT
CHANNEL
Fig. 1. Cross section of a layered wound coil.
108
S. K. Slngb et al.
The structural design considers three areas, the tooth thickness, the banding
thickness, and the former thickness. The tooth thickness calculations are based on a
cantilever beam with uniform loading in the axial direction. The tooth width can be
decreased from its maximum value at the coil ends toward the center as the axial
force decreases.
The banding concept uses an overwind of metal band on the conductor outside
surface. The thickness of the band is varied to Iimit the strain in the conductor to
prevent degradation of its current-carrying capacity. The band is fastened at each
end on each layer. This will enable tension to be developed within the band.
The former thickness is sized to achieve the required prestress during cooldown
to minimize conductor motion. When the coil is energized, the compression is
relieved as the magnetic force in the conductor increases. This results in a relatively
constant tension in the banding until the magnetic forces exceed the preload forces.
This concept was used successfully in the 300-kJ coil [2 ]. The prestress in both the
band and former are dependent upon the physical and mechanical properties of the
two subassemblies. The technique assumes an infinitely rigid conductor. The concept
also assumes that each layer acts independently. The former thickness can be
structurally graded for each layer; however, for the conceptual design, a constant
thickness was chosen for every layer.
The materials selected for the structural component include G-10 Cl for the
axial structure and spacers, KEVLAR for the former and 304L [3 ] stainless steel for
the banding.
Using a maximum bending stress of 38.6 MPa (40% of 96.5 MPa), assuming an
axial alignment of fibers, the tooth thickness was calculated at 1.96 cm. The shear
stress was calculated to be 5.8 MPa, which is 12% of the allowable value of
48.2MPa.
The radial strain was limited to 0.1% for Nb 3 Sn superconductors. This resulted
in band hoop stress of 201 MPa. The variation of banding thickness with radiuswas
calculated and the results are shown in Fig. 2. Using these banding thicknesses and a
former thickness of 1.07 cm, the banding prestress due to cooldown was calculated
and the results are shown in Fig. 2.
The axial structures are bonded to the formers using polyurethane adhesion.
Polyurethane adhesives are the most appropriate for use at cryogenic temperature
This is because they share the least embrittlement at very low temperatures compared to other classes of adhesives. They can be cured at room temperatures and do not need much pressure during eure.
e].
Thennohydraulie Analysis and Design
The forced-cooled design is very similar to the pool-cooled 300-kJ coil design [2 ]
except that there are no bypass channels around the conductor and the conductor is
cooled by crossflowing helium. Crossflow was selected instead of parallel flow for this
coil on the following basis:
1. A sheathed cable could not be reliably bent around the small radii.
2. Headering of the coil would be difficult because of its compactness.
3. In parallel flow the pressure drop is inversely proportional to temperature,
so a minimum additional flow over the basic stabilization value is required to
maintain adequate flow to a normalized, elevated temperature section.
4. Heat transfer coefficients are high for small strands of conductor in
crossflow.
Coneeptual Design of a Snperconductinc Obmic-Heatinc CoU
109
l75r-------------------------------------------------------,
.500
~........
..,e
vi
...z
~
(
l25
I
I
I
I D _;i
I
lDD
u
,_ o. 75
:;:
"'l!:
0
BANDING
I
~;rHICKNESS I
\
fVOD
\
,<
I I
.350 ii
I
.275:;;
\.I I
0.25
I
~c- ..-c'\_BANDING\ I
0.00
I
:i 0.50
""
/
I
0
.425
\
PRE-STRESS
25
50
I
~
.,.~
""
.200
sJo
COIL RADIUS. cm
Fig. 2. Variation of banding thickness and stress with radius.
5. The helium expansion effect occurring during a normalization has a minimal
effect on the ftow field in crossftow cooling.
The Ieads from the coil to room temperature are conduction heat transfer
dominated and cooled by supercritical helium ftow which is controlled by a critical
orifice at room temperature. The high ftow rate of the 50-kA Iead precludes any
significant rise in pressure in the expansion of the coolant owing to absorption of
energy during a quench. A pressure of 6 atm and a temperature of 4.2 K were
selected as the Operating thermodynamic state of the coolant, based on adequate
thermodynamic-ftuid dynamic stability of the coolant channels and adequate dewar
strength.
A supercritical ftow circuit is shown in Fig. 3. The heliumpump and downstream
heat exchangers are located in a dewar filled with helium by the refrigerator. The
refrigerator capacity is matched tothedewar Ioad by the increase in heat leak as pool
depth is increased. By applying this method of forced circulation, the refrigerator is
decoupled from the coil, coil dewar, and Iead Ioad. Figure 3 also shows a cold
Pressurlzer Une
Regulator
,--------------0<1- From Relrigerator
Cold Return to Relrigeralor
J-T Vahe
Dewar
Warm Return
Fram Leads
Fig. 3. Forced-cooled coil ftow schematic.
S. K. Singh et al.
110
Return
~
~
Coil
(
(
V
~
I
Room Te mperature
Critical Nozzle
_,_....,-150gph
~alm
b..
u::J
~
Dewar
.. Sh 1elds
Radlaiion
Return
Leads
4.2K
~
Lead Casing
Fig. 4. Forced-cooled Iead and coil flow schematic.
pressurized line used to make up the Iead ftow and to control the pressure in the
forced-cooled circuit.
The conductors are transverse to the axial ftow of coolant in the coil. Flow enters
the coil on the centerline and ftows to a distribution header on the opposite end as
shown in Fig. 4. The ftow proceeds to the opposite end where an insulating shroud
returns the ftow over the coil surface eliminating any possibility of heat leak to the
conductor from a stratified dewar. The ftow then turns to ftow upward along the
dewar walls to carry away any heat leak from ambient and returns to the pump. This
system prevents dewar stratification and the recirculation of any temperature spikes
introduced into the coolant by pulsed operation.
Stability Analysis
In the initial design phase it was determined that for the conductors and
geometries that are practical for this coil, a forced convection coefficient of
0.07 W I cm 2 - K is appropriate. Because a strand-to-strand insulation has not been
identified for Nb 3 Sn, a representative value of k/ 8 = 1.0 W / cm 2 - K was used in
conjunction with the critical temperature for I/ lc = 0.50 to determine that a heat
transfer coefficient of 0.2 W /cm 2 -K is required. An insulation having a k/ 8 of unity
could be a polyamide, polyethylene, or epoxy of 0.01-mm thickness or glass 0.1 mm
thick.
The peak Iosses in the forced-cooled design result in a surface heat ftux of
0.058 W /cm 2 or a local peak temperature of the conductor of 6.0 K. This is weil
below the current-sharing temperature of 6.9 K. The average heat generation per
cycle will not exceed 0.83 J/cm 3 of conductor or 0.577 J/cm 3 of helium in the
conductor. lf the heat generated in a full bipolar swing is stored locally in static
coolant the temperature will rise to 5.3 K. In a 1-s cycle the helium within the
conductor volume will be replenished 50% from the coil channels so that satisfactory
performance is assured. The residence time of helium in the coil is approximately
26 s which will not produce an excessive temperature rise in the shortest bipolar cycle
of 11 s. Depending on the exact space-time averaging of the ac losses, the ftow
velocity could be increased by 10-15% for safety margin, but the need for additional
margin is not demonstrated by this analysis.
The forced-cooled conductor stability is described in terms of a steady and
transient criteria. Whereas the steady-state minimum propagating zone criteria for
pool cooling is satisfied by a simple choice of conservative surface heat ftux, the
forced-cooled conductor average surface heat ftux is lower, leading to a design
minimum propagating zone that specifies the cooling system pumping power.
Conceptual Design of a Superconducting Ohmic-Heating Coil
111
The transient stability of the conductor is described in terms of recovery from an
instantaneous, adiabatic, 20-K conductor temperature rise with the surrounding
helium at 4.2 K. The half-turn criterion is of sufficient length that axial conduction
can be neglected. Cooldown is then given by simultaneous solution of (1) and (2):
(T-t-q"'Acu/Up)/(To-t-q"'Acu/Up)=exp[-
Up (-r--r0 )]
CvPAc
(1)
This simplistic method of solution is adequate because the temperature rise of the
helium is less than 2 K. The temperature of the conductor is found by marehing
forward in small time steps and is conservative because the conductor-ftuid
temperature difference is written in terms of the fluid temperature at the end of the
time step, not the average as is customary. The transient heat transfer coefficient,
allowing for surface renewal by turbulent eddies during the thermal boundary layer
development process, is given as
1/2
k
]
h = 2 [ pcP
(3)
7T(T- To
which decays to the steady value given by
jh
=
0.91 Re- 0 . 51 1/1,
Re:::; 54.6
(4)
jh
=
0.61 Re- 0 . 4 1/1,
Re
54.6
(5)
h
. -
lh- CpGo (Pr
2::
)2/3
(6)
"'= 0.91
(7)
The overall U is determined as a series impedance of the Kapitza resistance (taken
here as 2.5 cm 2 -K/W), insulation resistance (8/k = 1.0 cm 2 -K/W) and convection
impedance (liters/hr). Application of the simple series impedance formulation can
be verified by the heat transmissiontime constants for the conductor, insulation, and
helium which are approximately 1,_"s, 0.1 ms, and 0.2 s, respectively.
Solving (1) and (2) yields a recoverytime of 2.4 ms and the information that the
required steady-state heat transfer coefficient is much less than that required by the
minimum propagating zone (MPZ) value. In this case the transient stability criterion
does not set the minimum ftow rate. The forced convection cooled coil is designed so
that the Stekly energy balance criterion is exceeded in the conductor volume swept
by the cooling channels and the steady-state minimum propagating zone for a
crossftow cooled conductor given by (8) exceeds the width of the conductor support
pad:
kA)
(:::; 2 ( Up
112
tanh - 1 (
1
)
------.,.
2- - - - - - - -
[pef Acu/ Up(Tc - t)]- 1
(8)
For the values in Table III the minimum propagating zone is 1. 79 cm, which is larger
than the repeat length of the structure.
From (5), the mass velocity required to obtain the space-averaged heat transfer
coefficient of 0.032 W/cm 2 -K is 0.782 g/cm 2 -s. The total ftow area of the coil is
S. K. SiDP et t1L
112
Table
m.
Parameten Used to Detennine the
Minimum Propagating Zone
Value
Parameter
U =(~X 0.003 +~X 0.09),* W/cm 2 -K
Aeu,cmz
A."cm 2
3
p 2
PeJ, W/cm
Pe at 9 T, 0-cm
Tc-t,K
keuat9T, W/cm-K
0.0320
2.775
3.69
144.9
24.59
7.575 X 10-8
6.4
1.3
*Average over the swept conductor volume and still (supported) volume.
2.835 x 103 cm 2 foratotal ftow rate of 2.217 kg/s. The pressure drop is given by the
Burke-Plummer relation, equation (9), for a Reynolds number of 8000:
äpi
=
L 'f
1-
e
3.5 _!_(G~)
e3
Dp 2 p
9)
(
The expansion and contraction Iosses per meter are
äPi
L
[(1 - e )2 + (1.0/ e na~/2p
L
X
(10)
Fora coillength of 1.57 m the total pressure drop is 0.947 kPA. Pump work is given
by the relation
Wp
= (rh/ p )M
(11)
'71th
For a pump thermal efficiency of 50% the cold refrigeration Ioad due to pumping is
29.9W.
The quench analysis of a coil is solely concerned with survivability of the coil and
dewar. A conventional quench of the coil with the protection circuit and dump
resistor Operation results in 0.03 J/cm 3 heat addition to the conductor. This is less
than a conventional bipolar swing.
CONCLUSION
The design has demonstrated the feasibility of the ohmic-heating coil. The
thermal analysis indicates that the cooling of the coil is adequate for the coil to
remain superconducting during a full bipolar swing from +9 to -9 T. The structural
analysis shows that enough structure is provided to withstand the Lorentz forces. In
brief, the overall coil design meets or exceeds all the performance requirements.
NOTATION
Ac = area of conductor
Aeu = area of copper
CP = specific heat at constant pressure
Cv = specific heat at constant volume
Dw = diameter wire
Conceptual Design of a Superconducting Ohmic-Heating Coil
113
G = mass velocity
G 0 = superficial mass velocity
h = heat transfer coefficient
ih = Colburnj-factor
J = current density .
k = thermal conductivity
L = length .
M' = mass helium per unit length of conductor
m = mass flow rate
p = perimeter, pressure
Pr = Prandtl nurober
q"' = heat generated per unit volume
Re = Reynolds nurober
t, T = temperature of coolant, metal
U = unit thermal surface conductance
wp = pump work
Greek Symbols
8 = insulation thickness
e = void fraction
= thermal efficiency
= density
p, = resistivity
T =time
( = minimum propagating zone
11th
p
Subscripts
c = critical
o = outlet, outside
s = surface
REFERENCES
L M. A Janocko, IEEE Trans. Magn. Mag-15(1):794 (1979).
2. S. K. Singh, J. H. Murphy, M. A. Janocko, H. E. Haller, H. Riemersma, T. L. Vota, D. C. Litz, R.
Gromada, P. W. Eckels, Z. N. Sanjana, and F. N. Domeisen, "Prototype Tokamak Ohmic-Heating
20 MJ Superconducting Coil Study," Part I I -Technical Report, Contract No. L-48-8407C-1 (April
1978).
3. E. Mullan, D. W. Deis, P. W. Eckels, H. E. Haller, 111, M. A Janocko, S. A Karpathy, D. C. Litz, C. J.
Mole, P. Reichner, Z. N. Sanjana, and M. S. Walker, "Design and Fabrication of 300 kJ-Superconducting Energy Storage Coil," E. M. 5077, Subcontract No. XN4-32767-3 (July 1977).
4. P. Thullen, J. D. G. Lindsay, D. M. Weldon and H. F. Vogel, "Superconducting Ohmic-Heating Coil
Simulation," presented at Applied Superconductivity Conference, Pittsburgh, Pennsylvania, 1978.
B-7
SHAPE OPTIMIZADON STUDY FOR A
THREE-TUNNEL SUPERCONDUCfiVE
ENERGY STORAGE MAGNET
M. N. EI-Derini
University of Petroleum and Minerals
Dhahran, Saudi Arabia
and
R. W.Boom
University of Wisconsin
Madison, Wisconsin
INTRODUCfiON
lt has been shown CJ with the aid of the virial theorem that, regardless of
configuration, an energy storage magnet would be prohibitively expensive if all
structural supports were built with known fabricated materials. Accordingly, it has
been proposed that the magnet be buried in tunnels in bedrock, a less expensive
structure.
For an underground solenoid it is relatively easy to carry radial pressure out to
the bedrock. Struts connect the conductor to footpads on a rock wall so that radial
forces are transmitted directly to the rock. Axial forces present greater difficulties
because in a straight solenoid they are parallel to the walls. The compression Ioad
produces a severe s}lear stress in the rock if this Ioad is carried directly to the wall.
One would need a virial theorem mass if this Ioad is carried intemally in the
fabricated structure. The concept of a segmented solenoid was introduced to help
alleviate this problem. Cold structures may be used to carry axial Ioads in the upper
segment of an hourglass segmented solenoid to the bottom of the segment. Similarly,
cold structures carry forces to the ceiling of the lower segment. Axial forces are
carried a short distance and transferred to a rock ftoor or ceiling through insulated
struts instead of transmitting them from one end of the magnet to another by an
expensive cold structure.
There is still a substantial structure required to carry the forces along the
conductor before they are transferred to the tunnelend or across the midplane of the
centrat section. The mass of the structure can be reduced still further by increasing
the number of segments. Unfortunately there must be a substantial rock wall
separating each segment from its neighbors, otherwise there would be a danger of
114
Shape Optimization Study for a Supercondudive Energy Storage Mapet
115
Fig. 1. C-shaped solenoid of radii R 1 , R 2 and lengths h 1
and h 2 •
collapse in the tunnel structure. Also, as the number of tunnels and the number of
separate dewars increase, the size of a machine increases for a given energy.
Constant-field magnets reduce the axial forces and the shear stresses on the
walls. Thus, constant field segmented magnets will have both the advantage of
constant field magnets and segmented magnets. An hourglass constant-field segmented solenoid is better than a straight constant-field segmented solenoid. Hourglass solenoids for energy storage use reduce the maximum stress of straight
segmented solenoids from 6000 to 3200 psi for a 10,000-MW-hr magnet.
A broad study for a three-tunnel solenoid has been performed to ascertain the
best shape of a segmented solenoid which minimizes the axial forces and shear
stresses. A new cross-sectional configuration in the form of a C, as shown in Fig. 1,
seems tobe optimum. The length and radius of the central section are h 1 and Rh
while the length and radius of the horizontal end sections are h 2 and R 2 , respectively.
The distribution of the turns is not uniform but is distributed in a manner to obtain
constant field along the inner surface of the solenoid. The ampere-turn per unit
length which is proportional to the distribution of turns is shown in Figs. 2 and 3 for
the vertical and horizontal sections.
3000.------,------,-------.-----.
..
·;;;
CL
CL
Ul
Ul
1&.1
Ul
Ul
1&.1
a::
a::
I-
I-
U)
U)
-1000
-3ooo~----L---~L---~L---Jo
0.0
2.0
4.0
6.0
7.5
AXIAL DISTANCE , m
Fig. 2. Ampere-turns per unit length, normal and
shear stresses in the central section of C-shaped
solenoid.
4
- 200 <>&e
10
12
74
75.5
HORIZONTAL DISTANCE , m
Fig. 3. Ampere-turns per unit length, normal
and shear Stresses in the end sections of the
C-shaped solenoid.
116
M. N. EI-Dedlll _. R. W. Boom
Fig. 4. A general three-segmented solenoid. The hourglass is
for 8 = 90" and the C-shape is for 8 = o•.
PROCEDURE
The current distribution per unit length, J(z/ 1), is represented by Legendre
polynomials as
J(z/ I) = aopo(z/ I)+ azpz(z/ I) + a4p4(zj I)
(1)
where a 0 , a 2 , and a4 are evaluated using the Ieast-squares method to obtain a
constant magnetic field along the inner surface of the solenoid. This procedure has
been described in previous publications 4 ].
In addition to developing an optimum configuration for the constant field
solenoid, a broad study of the three-tunnel solenoid (see Fig. 4) has been performed.
In this study the hourglass and the C-shaped magnet are obtained when fJ = 90° and
fJ = 0°, respectively. Results are presented for different fJ's, the same radii R 1 and
R 2 , the same length of the centrat tunnel h 1 and the same maximum magnetic field,
BM = 5.5 T. The length of the end tunnel, h 2 , is adjusted so that the stored energy, E,
is the same in all solenoids. The axial force quality factor, the maximum shear and
normal stresses vs. the angle, fJ, and the length h 2 are plotted in Figs. 5, 6, and 7 for
e·
Fig. 5. Axialforce quality factor for dillerent shapes from two dillerent views.
Sbape Optimization Study for a Supercondudive Energy Storage Magnet
117
Fig. 6. Maximum shear stresses from two different views.
constant energy with R 1 = R 2 = 70 m, h 1 = 7.5 m, and z 2 = 14m. lt may be shown
that more length of the end tunnel is required for constant energy conditions if the
angle 8 decreases from 90° to 0°. This means that more magnet area and more
conductor are required for the C-shaped solenoid than for the hourglass solenoid.
However, the C-shaped solenoid has smaller axial forces and smaller shear stress in
the walls than the hourglass solenoid. The shear stress of the C-shaped solenoid is
22% less than that for a constant field hourglass solenoid. Another important point is
that the structure of the C-shaped solenoid is a small fraction of the virial theorem
mass, Oe. The latter factor is a compelling reason for selecting a constant-field
C-shaped solenoid similar to that shown in Fig. 8.
The quality factors of the C-shaped solenoids are calculated for different aspect
ratios, ß. The radial, vector forces and mass factors ( 0 1,, 0 1", and Qc) increase for
higher ß. The axial force factor, 0 1•• and the maximum shear stress on the other band,
decrease for higher ß. The maximum normal stress has a local minimum between
Fig. 7. Maximum normal stresses from two different views.
118
M. N. El-Derbli IUld R. W. Boolll
Fig. 8. Mass quality factor for different shapes from two different views.
aspect ratios of 0.19 and 0.30. The maximum shear stress occurs on the horizontal
tunnels, while the maximum normal stress occurs on the vertical central tunnel. The
dimensions of the tunnels and their relative positions affect the maximumnormal and
shear stresses. To decrease the shear stresses, the outer tunnels should be close to the
central tunnel and take into consideration the minimum distance between tunnels to
prevent collapsing.
CONCLUSIONS
To make a large energy storage unit economical, the compressive forces must be
reduced. lt is important to reduce the axial forces or the fractional virial theorem
mass, Oe. This is achieved by using a constant-field C-shaped magnet as shown in
Figs. 5 and 8 because the C-shaped magnet has the minimum 0 1• and a low Oe. lt is
also important to reduce the shear stress to increase the design feasibility of the
tunnels and reduce their cost. The C-shaped magnet has a minimum shear stress as
shown in Fig. 6. The conclusion derived from these results is that the constant-field
C-shaped magnet is a good solution for the shear stress and axial force problems. In
addition, the constant field C-shaped magnet has the advantages of the constant
magnetic field solenoid, i.e., it utilizes the superconductor more effectively and does
not have the end field problem. A final important advantage of the constant-field
C-shaped magnet is that tunnel excavation is relatively simpler.
As noted earlier, the principal disadvantage of the C-shaped magnet is that it
requires more conductor and larger surface area.
ACKNOWLEDGMENTS
This work has been supported by the National Science Foundation, Department of Energy, and the
Wisconsin Electric Utilities Foundation.
NOTATION
a0 , a 2 , and a4
= Legendre polynomial coeflicients
= maximum magnetic field
E = stored energy
h 1 = height of the central section of the C-sbaped solenoid
h 2 = length of the horizontal end sections of the C-sbaped solenoid
BM
Shape Optbnizadon Stndy for a Snperc:ondnctive Energy Storage Magnet
119
J = current per unit length
I = length of the magnet
n = number of turns
Oe= fractional virial theorem mass
Q1, = radial force factor
Q1• = total vector force factor
Q1z = axial force factor
R 1 = radius of the central section of the C-shaped solenoid
R 2 = inner radius of the horizontal end sections of the C-shaped solenoid
Z = axial distance from the median plane
ß = aspect ratio = Iengtb/average diameter
fJ = angle of the end sections on the horizontal plane
REFERENCES
1. R. W. Boom, "Wisconsin Superconductive Energy Storage Project, Feasibility Study Report," Vol. I,
University of Wisconsin,.Madison, Wisconsin (July 1974).
2. M. N. EI-Derini, R. W. Boom, and M. A. Hila!, in Advances in Cryogenic Engineering, Vol. 23, Plenum
Press, New York (1978), p. 88.
3. R. L. Willig and R. W. Moses, Jr., IEEE Trans. Magn. Mag-13(5):1122 (1977).
4. M. N. EI-Derini, Doctoral Dissertation, University of Wisconsin, Madison, Wisconsin (1978).
B--8
20-kA POWER SUPPLY FOR LARGE
SUPERCONDUCDVE COILS
M. Masuda, T. Shintomi, and K. Asaji
National Laboratory for High Energy Physics
Ibaraki, Japan
INTRODUCfiON
There are no comQlercial power supplies designed exclusively for use with
superconductors. Instead, conventional power supplies are slightly modified, taking
into consideration the Ioad impedance of the superconductors.
The recent trend has been that superconducting magnets carry large currents;
for example, 20 kA in fusion reactors and more than 100 kA in energy storage coils.
lt is doubtful whether conventional power supplies will be able to handle such
large-current magnets. The purpose of the power supply for superconductors is
twofold. One is for exciting superconducting magnets and the other is for supplying a
current to short-length test samples of superconductors.
Some typical component configurations of power supplies include: (1) a
large-current transformer, a rectifier, and an array of transistors for current
stabilization; (2) a large-current transformer, rectifier diodes, and thyristors connected to the primary winding of the transform er for current stabilization;
(3) a large-current transformer and thyristors connected to the secondary winding
of the transformer for current stabilization (the most conventional type); and
(4) a large current transformer with a mechanical voltage adjuster connected
to the primary winding of the transform er. Other variations can be considered
including the motor generator.
All of the conventional power supplies have problems when considered for use
with large-current superconducting coils. The most serious problern is the use of a
large-current transformer for impedance conversion. The secondary winding of a
transformer carrying more than 20 kA is no Ionger fabricated of wires but of bus
bars. The wide and thick conductors make its winding too difficult to be economical.
Thus, the power supply for more than 20-kA output should be based on other design
criteria. A new principle is introduced in the proposed power supply. Even so, a small
current transformer is still employed to generate the dc source. The direct current is
converted to ac by thyristor switching.
The idea of dc conversion is not new. lt is commercially available as a so-called
switching regulator, which is now used in place of a transistor-dropper method. The
method introduced here uses switching but is quite different from the switching
regulators.
120
121
20-kA Power Sapply for Luge Sapereoadaetive Coils
I.
2~ 2~
L~ L~
Fig. 1. Elementary circuit for dc-dc conversion.
BRIDGE
62
~
++ +
CAPACITOR
{~
0
i~
l
BRIDGE
63
PRINCIPLE OF OPERATION
The basic principle of switching involved here is an ac-dc-ac-dc conversion. The
commercial ac line is converted to a large direct current through successive processes
of rectification, inversion, and rectification. The significant part of the process is the
dc-ac-dc conversion through specially designed thyristor units [ 1].
The conventional dc-ac inverter using thyristors is commercially available and is
designated as a voltage-controlled inverter. The waveform of the output voltage is
rectangular. On the other hand, the current-controlled inverter is a device commonly
used to control the speed of induction motors. The device introduced hereisdifferent
from both types. Since commutation is performed by capacitors charged by the
constant current, this is a current-controlled inverter. The significant characteristic of
this circuit is current amplification, which makes it effective as a high-current dc
power supply.
The principle of the current amplification is given below but a detailed analysis
of the circuits is beyond the scope of the present paper. In Fig. 1, 10 is the constant
input dc current. The current ftows in the thyristor bridge, B2 as in a conventional,
three-phase Graetz bridge. The ac voltage is generated on terminals of capacitors
which cause thyristor commutation. The waveforms of the voltages generated for
delta and star capacitor connections are shown in Figs. 2a and 2b. The ac voltage is
rectified to supply the dc current to the Ioad. The firing of bridge B3 is in the same
sequence as in B2 but at different angles. The output voltage is controlled by the
firing angle of B3.
By rough estimation, the peak voltage at the capacitor, Vc, is given as
Vc = kloi/C
(1)
where f is the inverter frequency in Hertz, C is the capacitance in farads, 10 is the
input current in amperes, and k is a constant. At no Ioad, Vc is controlled by 10 • At
full Ioad, the input and the Ioad currents ftow together into the capacitor and Vc
increases. When the states for no Ioad and full Ioad are defined as 0 and 100,
respectively, and the ac voltages are given by
Vc(O)
Vc(100)
= klo/f(O)C
(2)
= kiJf(100)C
(3)
where h is full-load current. It is assumed that IL » / 0 • From (2) and (3), the
following equation is obtained:
IJio
= [/(100)//(0)][Vc(lOO)/Vc(O)]
(4)
When 10 is held constant, Vc(O) is generated essentially from the forward voltage
drop of the thyristors and is approximately equal to the input dc voltage. The voltage,
121
M. Masuda, T. Shintomi, and K. Asaji
VcJ
~
""-'-/
(a)
(b)
Fig. 2. (a) Calculated waveform of voltage generated on capacitors which are connected in a
star configuration. (b) Calculated waveform of voltage generated on capacitors which are
connected in a delta configuration.
Vc, increases with load current to a maximum value of Vc(100). The required output
power, P, is given as
(5)
where K varies slowly with h. The input voltage changes with the load while the
input current is kept constant.
Equation (4) shows the current amplification. For example, if the load current is
20 kA and the output voltage is 20 V, then the outputpower of 400 kW could be
supplied from a 200 A and 2 kV input. The current amplification, h/ Io, is 100 and
this is achieved by a voltage ratio Vc(100)/ Vc(O) of 20 and a frequency ratio
/(100)//(0) of 5. The frequency ratio of five implies f(O) = 100Hz and /(100) =
500Hz, for example. In the present inverter, as shown in Fig. 2, the thyristors
employed do not require fast switching characteristics because the commutation is
performed by the slowly charged voltages on the capacitors. The maximum
frequency possible with conventional power thyristors is about 1 kHz.
MODEL POWER SUPPLY
A 1000-A modelpower supply was constructed and excited with a 100-kJ
superconducting magnet [2 ]. The approximate specifications of the model unit are
given in Table I. The schematic diagram of the control unit is shown in Fig. 3. The
master oscillator supplies a high-frequency clock whose frequency is divided by
frequency dividers. Their outputs are fed to distribution circuits com~sed of shift
registers and power amplifiers. The thyristors of bridge B2 are fired sequentially with
phase differences of 60°. Bridge B3 is fired in the same mode as B2 but with a phase
difference from B2 that is determined by counting a preset number of cycles of the
123
20-kA Power Supply for Large Superconductive Coils
Table I. Specifications of Test Arrangement
Input dc power supply
Thyristor of bridge 2 and 3
Commutation capacitor/arm
Connection of capacitance
Dummy Ioad magnet
Superconductive Ioad coil
100V,50A
1200 V, 1000 A
200 V, 500 f.LF X 5
Star
5 mH, 10mn
1000 A, 0.2 H, Nb-Ti
master oscillator frequency. The phase difference between B2 and B3 is independent
of the frequency of the master oscillator which enables the Operation of the inverter
to be very flexible.
As shown in (4), to obtain the highest current amplification, the lowest possible
valtage Vc(O) must be employed. In that case, thyristors tend to miss the commutations because of low anode voltages. The low valtage is compensated for by
decreasing the master oscillator frequency with the variable frequency controller
VFC.
There are two methods to control the output current. One is with the phase
angle and the other is with the frequency. Figure 4 shows the waveform of the ac
valtage and the current in the capacitor in the delta connection. Figure 5 shows the
output current vs. the phase angles.
In the present work, the electromagnet constructed of a normal conductor was
used as a preliminary Ioad. Aftertuning the model unit, the 100-kJ superconductive
magnet was connected and excited to 1000 A. The specifications for the test are
shown in Table I.
The efficiency of the model unit is about 7 5%. Since the lass by the thyristor
forwardvaltage drop is dominant, the efficiency can be improved more than 90% by
improved design of the power supply, which has a sufficiently higher outputvaltage
than the forward voltage.
DATA
I-~-
INPUT(f)
DATA
INPUT(8)
Fig. 3. Schematic diagram of the control circuit.
SCR'S
TRIGGER
CIRCUIT
124
M. Masuda, T. Shintomi, and K. Asaji
Fig. 4. Measured waveform of generated voltage and current on andin the
capacitors.
CONCEPTUAL DESIGN OF A 20-kA POWER SUPPLY
The conceptual design of a 20-kA power supply has been carried out. No special
parts have been used and no technical difficulties were encountered. The connection
diagram is shown in Fig. 6 and the specifications are given in Table II.
The advantages of the proposed power supply are as follows:
1.
2.
3.
4.
lt is easy to generate a large dc current.
The system does not need a large current transformer.
Only a small section of busbar is needed.
By employing frequency changes, the thyristors can operate without commutation failures because of sufficient anode voltage.
5. The control unit may be digital and thus noise resistant.
6. The unit is essentially a constant-current source, providing safety from overcurrent caused by commutation failures and Ioad short circuits.
INPUT
CURRENT
20 A
200
10 A
...
~
!5
u
100
SA
~
30
90
60
FI RING />NGLE ,
0
Fig. 5. Load current vs. the firing angle of the thyristors in the bridges.
20-kA Power Supply for Large Superconductive Coils
l
V.
AC INPUT
3LOAD
I
ill
BRIDGE
81
BRIDGE
82
CAPACITOR
125
BRIDGE
83
Fig. 6. Eleroentary circuit of the 20-kA power supply.
7.
8.
The operation frequency can be high even with conventional thyristors providing means for reducing ripples present in the output current even with small
filters.
The harmonic current generated from the thyristor instruments has frequencies
of (n ± 1)/ where n is the pulse number of the rectifier; therefore, there will be
little pollution of the commercial ac line.
There are two conventional types of power supply for superconductors on the
market. One is the large current transformer with gate-controlled thyristor bridges
for current regulation. This type is valuable for large power but not for the large
currents that are required for a superconductive energy storage unit for diurnal
energy storage on a utility network nor for the huge coils of fusion reactors.
The multiphase power supply has a ripple current with characteristic
fundamental frequencies of nf, 300Hz, or 600Hz in a 50-Hz utility system where n
is the pulse number of a thyristor bridge and 6 or 12 in general. However, a slight
unbalance between voltage and phase of the three phases or an unbalance between
firing circuits will give noncharacteristic ripple frequencies such as 100, 150, 200Hz,
etc. in the output current. For the characteristic frequencies, the maximum ripple, for
example at 300Hz, is about 5% when thyristors are fired with the maximum angle.
Decreasing the ripple to 0.1%, requires an attenuation in the filter of around 34 dB.
When the attenuation rate of 6 dB/oct of the conventional ripple filter composed of
inductors and capacitors are employed for ripple reduction, the resonance frequency
Table II. Appro:ximate Specifications for 20-kA Power Supply
Input transforroer
Thyristor in bridge 1 and 2
Cororoutation capacitor
Thyristor in bridge 3
Output
Priroary
Secondary
Power rating
Voltage
Current
Nurober
Voltage
Capacity
Nurober
Voltage
Current
Nurober
Voltage
Current
6.6kV
660V
400kVA
2.0kV
200A
12
800 V dc 330 V ac
14roF
3
2.0kV
2500 A (3 phase)
18
15V
20kA
126
M. Masuda, T. Sbintomi, and K. Asaji
of the filter must be lower than 10Hz. For the worst case, that is, for noncharacteristic frequencies, the size of the filter is not economically acceptable.
The other power supply, which also has a large-current transformer, the rectifier
with parallel-connected transistors for current regulation and for ripple reduction is
also not acceptable because employment of a number of transistors makes it less
reliable. The proposed power supply can use an operational frequency higher than
500 Hz without expensive high-power thyristors specifically designed for fast
switching, and a small filter can adequately reduce the ripple current.
HEFERENCES
1. H. A. Peterson, M. A. Hilal, W. C. Young, and R. W. Boom, in Energy Storage, Compression, and
Switching, Plenum Press, New York (1974), p. 309.
2. M. Masuda, T. Shintomi, S. Matsumoto, H. Sato, and A. Kabe, in Proc. 6th Intern. Conference on
Magnet Techno/ogy, ALFA, Bratislava, Czechoslovakia (1978), p. 254.
C-1
SUPERCONDUCTING GENERATOR DESIGN FOR
AIRBORNE APPLICATIONS*
8. 8. Gamble and T. A. Keim
General Electric Company
Corporate Research and Development
Schenectady, New York
PROGRAM OBJECfiVE
During the past eight years, the United States Air Force has actively pursued the
development of lightweight, superconducting generators in the multimegawatt
power range for airborne applications [ 1 ' 2 ]. This development work coupled with that
of university and industrial laboratories for utility applications has pointed to the
technical feasibility of these machines. Extrapolation of this technology to higher
power densities requires the combination of advanced component concepts and
materials in a single machine. The objective of the design presented here is to
consolidate advanced concepts and advanced materials developed for superconducting generators to attain specific design goals and to advance the state-of-the-art for
superconducting generators for airborne applications.
DESIGN GOALS AND CONSTRAINTS
The airborne high-power system is depicted schematically in Fig. 1. The
generator is to be designed to provide 20-MW of dc power at a voltage of 20-40 kV
from the rectifier. A nominal speed of 6000 rpm was selected from the limited speed
range of the proposed drive turbine. The inertia is required tobe 13.6 kg-m (10
slug-fe) or Iess, and the specific weight goal is 0.045 kg/kW (0.1 lb/kW). These
ambitious goals aretobe met in a design capable of 1-s field ramping and 1-s spin-up
FUEL -
Fig. 1. Airborne high-power system.
* Work supported by Air Force Aero Propulsion Laboratory, Wright-Patterson Air Force Base, Ohio,
under U. S. Air Force Contract No. F33615-76-C-2167.
127
1ll
B. B. c..111e ud T. A. Keim
Table I. Selected Design
Cbaracteristics
20MW
4pole
6000rpm
200Hz
29.6 kV line-to-line (nns)
Parameters
Field current density, A/cm2
Field current, A
Field inductance, H
Armature current density (annulus), A/cm 2
Copper volume fraction (armature)
Synchronaus reactance, pu
Transient reactance, pu
Subtransient reactance, pu
Equivalent power factor
Efficiency
15,000
867
0.69
1760
0.39
0.56
0.50
0.26
0.86
0.93
to design conditions. The generator is to be capable of both continuous operation
with run times of up to 5 min and pulsed operation.
OVERALL DESIGN
These goals were used as design constraints in a machine sizing study to consider
the most appropriate machine configuration for this application. The result of this
study was the selection of a four-pole, conductively shielded machine with a direct
water-cooled, involute end-turn armature. The generat characteristics of the selected design are presented in Table I.
A cross-section of the overall design is presented in Fig. 2, and the corresponding critical dimensions are given in Table II. To achieve this compact, lightweight
Table U. Selected Design
Weight*
lb
kg
Rotor
Field-winding outer radius
Shield outer radius
Thickness
Length
Bearing to span
870
395
Stator
Armature thickness
Outer radius
Shield inside radius
Thickness
Straight length
Total
870
395
1740
790
* Dry weight, without auxiliaries.
Dimensions
in.
m
9.0
10.5
0.75
21.0
32.0
0.229
0.267
0.019
0.533
0.813
1.0
12.0
19.7
0.75
6.0
0.025
0.305
0.500
0.019
0.152
Fig. 2. Design (cross section).
TOROUE TUBE EXTENSION
COOLANT HEADERS
ENVIRON MENT AL
SHIELO
ELECTROMAGNETIC SH IELD
=
DRIVE
FLANGE
BE.ARING
FILAMENT WRAP
~
....
Sl
t
f
J
Ii
J·
t
111
1
i{'
130
8. 8. Gamble and T. A. Keim
design, the following significant design features have been included:
1. Field winding composed of four racetrack-shaped, epoxy-impregnated
modules manufactured with multifilamentary Nb 3 Sn superconductor in a cabled
configuration.
2. Nonconducting composite support structure shrunk between the bore tube
and the torque tube.
3. Torque tube cantilevered from the undriven end of the machine.
4. Outer aluminum electromagnetic shield with a high natural frequency in the
ovalizing mode.
5. High current density, direct water-cooled armature.
6. Conducting (aluminum) environmental shield to Iimit the fields external to
the generator.
7. Integral water tank.
ROTOR DESIGN
The rotor design is most strongly influenced by the combined requirements of a
1-s start-up and a 0.1-lb/kW specific weight. The initial phase of this program
included a sizing study which encompassed the selection of the superconductor, the
principal rotor details, and the generator configuration.
Superoonduc:ting Field Winding
The field winding is the most critical rotor component. The field-winding
configuration dictates the support structure design and much of the remaining rotor
design. The field winding was designed on the basis that the superconductor must be
constrained to prohibit wire-sliding motion in response to sudden field ramping and
torsional spin-up. Therefore, a fully impregnated winding was selected. The potential Iimitation to the use of fully impregnated modules in fast-ramping applications is
the temperature rise within the module, owing to heating of the transient conductor.
Early in this program, it was decided to Iook to Nb 3 Sn with its high critical
temperature as the means to achieve fast-ramping capability in a fully impregnated
winding.
The selected superconductor is shown in Fig. 3. This Nb 3 Sn cable is being
developed under a United States Air Force contract at the Intermagnetics General
Corporation. As discussed above, this conductor was selected primarily for its
temperature capability. A completely fair comparison between the types of superconductors is difficult, but the generat magnitude of the difference can be indicated
by a simple comparison. For the 6.8-T peak field and the 15,000-A/cm2 module
current density of the selected field-winding configuration, Nb 3 Sn is capable of
operating at about 8 K while NbTi would be capable of operating at temperatures
less than 6 K. For an epoxy-impregnated field winding in a 4-K helium pool, this
corresponds to a fourfold increase in enthalpy margin.
The characteristics of the selected superconductor have been the subject of
substantial investigation including both critical current optimization and loss
measurements [3 ]. A cable is preferred for this application because it has a low-loss
and high-current configuration. High current is desirable to Iimit the voltage
required for rapid field ramping.
Even with the superior performance of Nb 3 Sn, the large forces to be
experienced by the field winding in this application dictate the selection of a winding
design which Iimits local wire-sliding motion, frictional heating, and subsequent
Superconducting Generator Design for Airborne Appliations
131
0.0008 in.
BRONZE and Nb3Sn CORE
Ta (7.2%) (44.4%)
0.039 in.
/--...
_....\.
\
/~
\ (?
)
'-----
/
/-......
\
MOLYBOENUM
CENTAAL STRAND
(
\(
....__/
"l
/
\
)
\ ......__...,- )
=
0.211
BRONZE AND Nb3Sn MODULE PACKING FACTOR
OVERALL CURRENT DENSITY = 15,000 Alcm2
BRONZE AND Nb:JSn CORE CURRENT DENSITY = 7.11 x 104 Alcm2
8.4K (at 6.8 tesla)
T0
9K (at 6 tesla)
0. 23
Cu FAACTION OF THE MODULE
864.6 amperes
CABLE CURRENT
=
=
=
=
Fig. 3. Preferred superconductor.
quenching of the winding. It is the objective of the winding development portion of
this program to combine the advanced Nb 3 Sn-cabled superconductor with the
epoxy-impregnation techniques which have been successfuily applied to NbTi
windings [4 ].
A racetrack shape with a reetangular cross-section was selected for a fieldwinding module configuration (Fig. 4). This configuration has been selected for its
simplicity, which permits a more readily controilable manufacturing process than
would be possible with a more complex shape. A module bore of 7.62 cm was
selected to Iimit the conductor strain in bending to approximately 1%.
The selected operating current density of 15,000 A/cm 2 , based on the crosssectional area of the winding module, results in the field distribution plotted in Fig. 4
for the midplane of the module at the start of the circular end-turn. The peak field
seen by the superconductor is 6 .8 Ton the winding bore. This field quickly tapers
towards zero near the module center. The peak field region is weil cooled, since it
occurs on the module surface. The critical temperature distribution and the calculated temperature distribution foilowing a 1-s ramp to design current are also
plotted in Fig. 4. As would be expected, the temperature distribution peaks weil
away from the peak field location. Similar calculations indicate that a steady-state
uniform heat rate up to 4 mW/cm 3 can be accommodated without exceeding the
local critical temperatures.
Aspart of the present program, verification of winding performance by testing a
cylindrical winding module prior to manufacturing the racetrack modules is planned.
The cross section and the bore of the test module are the same asthat of the racetrack
modules. Testing will include rapid field ramping to verify transient performance.
131
B. B. G81Dble and T. A. Keim
13
12
11
"'·
w
cc
::>
10
9
1--
<{
cc
w
8
~
w
1--
7
0..
K
~
1.6 x 10""' w/ cm• K
p cp = 6.06 x lO''T'·"Jicc • K
@1
-4 1-- 7.62 cm(3 in. I
ITB(
37.3cm
(14.7 in.l
~"!tl
(8.7 in. I
10
9
8
7
6
B(TI
5
4
6
3
5
2
4
0 L-~--~2---3~~4L_~5--~6---7L-~8--~9~
0
X,cm
0
Fig. 4. Winding module field and temperature distributions following
a 1-s ramp.
Support System
The function of the support system is to support the field winding in response to
centrifugal and electromagnetic forces. The support system is depicted in Fig. 5.
The racetrack-shaped modules are contained in a support structure constructed
from G-11 CR epoxy-glass Iaminate. This grade specification was selected for this
application because at 4.2 K it has a high modulus, 3.9 x 104 MPa (5.7 x 106 psi, in
the warp direction) [ 5 ], and a high compressive strength, 724 MPa (1 05,000 psi, in the
warp direction)
and because it is nonconducting, it is lossless in an ac magnetic
field.
This structure is assembled around an Inconel-718 bore tube (23.7-cm OD,
19.13-cm ID). The function of the bore tube is to serve as an inner vacuum barrier
and to provide radial stiffness for the assembly. The bore tube, the support structure,
and the winding modules will be cooled to liquid nitrogen temperature and assembled inside the Inconel-718 torque tube. Inconel-718 is selected because it isahigh
strength (uy = 1405.8 MPa, 203.9 ksi at 4 K), weldable, nonmagnetic material
available in tubular forgings.
The torque tube is to be prestressed to a tensile stress of approximately 60,000
psi to limit the relative sliding motion of the support structure with respect to the
winding modules with spin-up and application of Ioad. An additional benefit of
prestressing is to limit the magnitude of the cyclic stress seen by the torque tube. With
the application of centrifugal and electromagnetic load, the torque tube experiences
an overall hoop stress of approximately 620.5 MPa (90,000 psi) with a superimposed
bending stress resulting in an outer fiber peak stress of 758 MPa (110,000 psi).
Considering the entire cycle of spin-up, excitation, and shutdown, the torque tube
will experience cyclic stress with a magnitude of 172 MPa (25,000 psi) on a base
eJ.
Superconducting Generator Design for Airborne Applications
SUPPORT STRUCTURE
133
TORQUE TUBE
FIELD WINDING MODULE
Fig. 5. Field-winding and support system.
stress of 386 MPa (85,000 psi) for a maximum of 72,000 cycles in 100 hr of
operation.
lt should be noted that there are no torque transmitting keys in the torque tube
to cause stress concentrations. The torque is transmitted by friction between the
support structure and the torque tube. A coefficient of friction of 0.045 is sufficient to
carry the fault torque.
The low-temperature region of the rotor is vacuum supported from the undriven
shaft ftange by a single torque tube extension. The cantilevered design was selected
to separate the axial thermal contraction and torsional deftections of the torque tube
from those of the electromagnetic shield. In addition, this design reduces the heat
input to the low-temperature region and greatly simplifies the assembly. The short
length of the rotor allows this designtobe considered. The first rotor bending critical
speed occurs at 1.5 times the speed of rotation.
Electromagnetic Shielding
The rotor shielding is designed as a two-component system. An ambient
temperature electromagnetic shield excludes the majority of the nonsynchronaus
fields from the inner colder members. In this application, an ac generator feeding a
rectifier Ioad, the dominant source of the nonsynchronaus magnetic field, is expected
to be the nonsinusoidal nature of the armature currents, resulting in a 1200-H
frequency fieldas seen by the electromagnetic shield. A second actively cooled shield
at approximately 100 K intercepts thermal radiation and provides additional electromagnetic shielding.
The selected electromagnetic shield design is a 707 5-T6 aluminum, rolled-ring
forging with a 53.6-cm OD, a 49.8-cm ID, and a 53.3-cm unsupported length. The
shield thickness, 1.91 cm, presents 5.5 skin depths at 1200 H and was selected
primarily from considerations of fault crushing forces and natural frequency in the
ovalizing mode. The shield thickness results in a natural frequency of 1350 Hin the
134
B. B. Glllllble and T. A. Keim
Table lU. Fault Conditions Associated witb Field Design
Fault shear stress (4 pu)
Fault peak bending stress
Hoop stress in response to uniform fault compressive force
Centrifugal hoop stress
MPa
psi
15.1
330.3
-62.2
78.4
2,189
47,907
-9,017
11,375
four-pole ovalizing mode, assuming fixed ends and neglecting electromagnetic
stiffening effects. The fault conditions on the shield are summarized in Table
111.
Shield heating is a particularly important consideration in this application.
Prolonged single-phase faults cannot be tolerated, and it has been proposed to
short-circuit all three phases of the armature in the event of a single-phase fault. A
second area of particular concern is shield heating in response to nonsynchronaus
armature currents associated with the rectifier Ioad. Shield heating computations are
somewhat inexact, but it appears that in the absence of fittering or active shield
cooling continuous operation may be permitted for 2 min. Analysis indicates this can
be extended by blowing airdown the gap, by including cooling tubes on the armature
bore, or by including a modest filter (mass 45 kg) in the system.
Helium Flow Circuit
The function of the helium ftow circuit is to remove ramping and other winding
Iosses and to intercept heat conducted and radiated to the low-temperature region of
the rotor. The winding modules are cooled by helium in the slots and channels in the
support structure. A liquid-vapor interface occurs near the radially innermost
winding module surfaces. Therefore, the majority of the winding is in contact with
subcooled and supercritical liquid. In the high centrifugal field, large convective
heat-transfer coefficients can be expected, and the thermal impedance to the transfer
of heat to the liquid is dominantly in the impregnated winding module.
The majority of the helium ftow circuit is located in the removable subassembly
in the undriven end of the rotor. The ftow circuit components are depicted in Fig. 6.
Liquid is fed into the rotor through the relative motion bayonet in the radial tubes
feeding the winding region. This radial tube desigt! follows that developed for an
earlier 20-MVA superconducting generator rotor [6 ].
The hydrostatic head of the liquid in the winding pool covering the ends of the
radial supply tubes is balanced by that of the vapor column in these supply tubes to
provide a ftow or Ievel control. The vapor generated at the winding pool surface at
point 8 is compressed as it ftows radially to state point 10. The gas is heated as it ftows
to state point 11 while cooling the torque-tube-extension heat exchanger. The
ambient temperature gas ftows radially inward to point 12 before exiting out the
helium transfer coupling. The compression from state points 9 to 10 is only partially
offset by the expansion from points 11 to 12. The selected dimensions result in a
pressure at the liquid-vapor interface of 0.42 atm and a temperature of 3.4 K.
The winding-pool temperature distribution in this application is approximately
isentropic in that the support structure and winding assembly have a low radial
thermal conductance. The winding-pool temperature distribution varies from 3.4 K
at the Iiquid-vapor interface to 4.4 Kat the outer surface. The steady-state mass flow
is 0.6 g/s.
Superoonduding Generator Design for Airborne Applicadons
135
ELECTROMAGNETIC SHIELD
RETURN
HELIUM
LIQUID
HELIUM
®
Fig. 6. Flow circuit schematic.
During transient operation, 1-s ramping Iosses (510 J}, sudden loading Iosses
(30 J), and viscous Iosses (120 J) are introduced to the low-temperature region
components. This serves to slightly pressurize the winding pool containing 4.5 Iiters
of liquid. If the generator is operated in a continuous mode, this is relieved by an
increase in ftow through the torque-tube-extension heat exchanger. If the rotor
speed is reduced, the vapor evolved is vented out the exhaust tubes. These exhaust
tubes are also intended to carry cooldown ftow.
1t should be noted that the torque-tube-extension heat exchanger is conical in
shape to prevent axial heat transfer via secondary ftows in the cooling stream. The
vapor-cooled, field-winding current Ieads slant radially inward for the same reason.
ARMATURE DESIGN CONSIDERATIONS
To date, the major thrust of the program has been in the areas of generator
overall design and rotor detailed design, but the achievement of the goals of this
program will also require significant advances in armature design. The most
important armature design considerations are the requirements for 29.6-kV line-toline rms and the annulus current density of 1760 A/ cm 2 • The required voltage will be
achieved in part by virtue of the short required life at voltage, 100 hr. The iron-free
designwill utilize voltage grading to reduce the insulation requirement. The required
current density will be achieved by constructing the armature conductor from
hollow-copper which will be cooled by high-velocity, high-pressure, subcooled
water.
FUTURE WORK
The achievement of the goals of this program requires the combination of
advanced design concepts and advanced materials. The design presented here
addresses these goals and will be developed as part of the present program through
136
B. B. GluOie Md T. A. Keim
static testing of the rotor and initialarmatme component development. This includes
the following:
1. Manufacturing a cylindrical module of a representative cross section to
verify the pedormance of an epoxy-impregnated Nb 3 Sn cable winding for fast field
ramping applications.
2. Individual pedormance testing of the winding modules before assembly
into the rotor support system.
3. Static (nonrotating) testing of the rotor ftow circuit and the field winding
while the rotor is suspended from the undriven end. The one torque-tube-extension
heat exchanger design allows operation of the ftow circuit in this position.
4. Building armature bars and testing thermal pedormance and voltage
capability.
The selected design concepts will be verified with these tests. This verification will
demoostrate that superconducting generator technology is extrapolatable to higher
power densities than have been demonstrated to date.
ACKNOWLEDGMENT
The assistance of H. L. Soulhall of the Air Force Aero Propulsion Laboratory at Wright-Patterson
Air Force Base, Ohio, is gratefully acknowledged.
REFERENCES
1. H. L. Southall and C. E. Oberly, IEEE Trans. Magn. Mag-15:711 (1979).
2. R. D. Blaugher, J. H. Parker, and J. L. McCabria, IEEE Trans. Magn. Mag-13:755 (1977).
3. G. R. Wagner, S. S. Shen, R. E. Schwall, A. Petrovich, and M. S. Walker, IEEE Trans. Magn.
Mag-15:228 (1979).
4. M. J. Jefteries and E. T. Laskaris, "Rotor Winding Development for a 20-MVA Superconductive AC
Generator," paper presented at Conference on Technical Applications of Superconductivity, Alushta,
USSR, 1975.
5. J. R. Benzinger, "Manufacturing capabilities of CR Grade Laminates," paper presented at NBS-DOE
Workshop, Vail, Colorado, October 24-26, 1978.
6. E. T. Laskaris, IEEE Trans. Magn. Mag-13:759 (1977).
C-2
SUPERCONDUCTING FJELD WINDING FOR A
10-MVA GENERATOR*
K. A. Tepper, J. V. Minervini, and J. L. Smith, Jr.
Massachusetts Institute of Technology
Cambridge, Massachusetts
INTRODUCTION
A research program funded by the U. S. Department of Energy has been
underway since 197 6 to develop advanced concepts for superconducting generators
to be used in large central power stations. The background and scope of the program
have been reported previously [ 1]. A prototype 10-MVA machine is being constructed and will be tested under fullload while connected to a power system. The
first part of the present program has concentrated on the analysis of advanced
concepts to solve key problems identified through earlier experiments and analyses
e·3].
One major new feature selected for demonstration in the 10-MVA generator is
a dual shielding system to protect the superconducting field winding from ac
magnetic fields while still providing adequate damping. The generator Iayout is
shown in Fig. 1. Both the outer wound damper shield and the inner solid conducting
shield are positioned on the rotor and maintained at liquid helium temperature. The
compact cryogenic structure for the shields minimizes the distance between the field
winding and armature winding and thus maximizes magnetic coupling.
FIELD-WINDING DESCRIPTION
The support structure for the superconductors in the winding space is a
multiplicity of yokes (see Figs. 2 and 3), each with a boss and a pin for support at the
top and bottom. The side walls of the yokes are tapered, increasing in width toward
the top, and the top and bottom walls are deeper than the side walls.
The superconductors are wound into modules which are surrounded by the
yokes. The modules are fitted into the rotor such that the yokes mesh (see Fig. 4),
filling as much of the space between the inner and outer support cylinders with
superconductor or structure as possible. The bosses at the top and bottom of each
yoke contact the inner and outer support tubes. The yokes are supported against
azimuthal and axial motion by pins inserted between the inner support tube and the
yoke bottom, and the outer support tube and the yoke top.
Once the yokes are filled with the superconductors, the yoke tops are welded
onto the side walls. The weid is made to penetrate to the stress-relieving holes, which
* Work supported by U. S. D.O.E. under Contract No. EX-76-A-01-2295 Task Order No. 11.
137
ROTOR
SHAFT
INNER
SUPPORT
TUBE
OUT ER
SUPPORT
TUBE
DAMPER
Fig. I. Cross section of 10-MYA rotor.
YOKE
LHE
RESERVOIR
SUPERCONOUCTOR
MODULE
CENO TURNl
WINDING SPACE
....
~
1'1.>
J
r
i!""
I
~
!""
~
i
p::
?"
~
Superconducting Field Windlogfora 10-MVA Generator
139
.0 15 R. TYP.
(8) PLC S.
MODULE
I
2
3
4
5
6
7
G
1.711
1.817
1.688
1.634
1.450
1.412
1. 268
H
I
1.1 93 .259
1.193 .312
1.049 .320
1.04ll .293
.905 .273
.905 .254
.761 . 254
J
K
.743
.714
.743
.714
599
568
568 599
.484 .455
.4 24 .455
.279 .3 11
L
.892
.985
.887
.911
.781
.805
.66 1
Fig. 2. Shop drawing of yokes.
puts a radius at the end of the parting-line crack. The weid is made with the aid of a
water-cooled chill to control thermal darnage to the superconductors. During a test
weid, copper strips covered with epoxy were clamped to the yoke wall to simulate the
superconductors. The weid was carried out successfully without any thermal
degradation of the epoxy.
The individual modules of superconductors are wound into radial layers with
adjacent radiallayers separated by parting strips to form slip planes. The slipplanes
Fig. 3. Photograph of yoke.
K. A. Tepper, J. V. Minervini, and J. L. Smith, Jr.
140
/
/
/
/
/
-----
- --
OUTER
SUPPORT
- -/
/~
I
I
r---?--~~~
I
SUPERCONDU CTOR
MODULES
Fig. 4. View of straight section of winding space.
are necessary in order to ensure that the epoxy superconductor interface shear stress
is maintained below the failure stress of the bond.
The two saddle coils have seven modules each, with the size of the modules
varying with angle. The largest modules are at the junction of two saddle coils, and
the smallest are closest to the pole faces. This shaping serves three purposes. First, it
puts the maximum concentration of superconductors where they contribute the
maximum to the dipole field; second, it puts the maximum concentration of
superconductors where the azimuthal-directed self-forces are smallest; and finally
this distribution minimizes the field concentration near the pole faces and in the
end-turns.
CONDUCfOR
The conductor selected for the field winding of the 10-MVA generator is a
monolithic multifilamentary composite conductor, 2.72 x 1.49 mm, with a copper
matrix and niobium-titanium superconducting filaments. Two superconductors with
these specifications are being considered. The copper-to-superconductor ratios are
1.65: 1 with 2100 filaments of 30 #Lm diameter and 2: 1 with 817 filaments of 46 #J-m.
The 1.65 : 1 wire has a higher critical current and a lower hysteresis loss than the 2: 1
wire, which has a slightly higher thermal margin. Two test solenoids are being
fabricated to evaluate the conductor performance under simulated operating conditions. Other important conductor and winding-module characteristics are listed in
Superconducting Field Winding for a 10-MVA Generator
141
Table I. Field-Winding and Conductor Characteristics
Conductor
1.65: 1
Dimensions, mm
Copper: Nb-Ti ratio
Filament diameter, 10-6 m
Number of filaments
Twist length, mm
Operating current, A
Conductor current density, A/m 2
Overall current density, A/m 2
Winding
Ampere-turns
Peak field, T
Inductance, H
Modules
Dimensions, mm
Number of modules
Turns per module
Maximum
Minimum
Total number of turns
2.72 X 1.49
1.65
30
2160
12.7
939
2.32 X 108
1.28 X 108
2:1
2.72
1.49
2
46
817
12.7
939
2.32 X 10 8
1.28 X 10 8
X
1.74 X 10 6
4.8
2.1
40.72
X
15.21
7
140
56
1456
Table I. This type of conductor was selected for the characteristics of low ac loss, ease
of winding into the module structure, and mechanical and electrical stability.
STRUCI'URAL ANALYSIS
The major motivation for developing the yoke concept for the superconductor
support system was to isolate the superconductors from the high shear stresses
present in the inner and outer support tubes during the high-torque phase of an
electrical fault. The stress and the deformation of the rotor were found by modeling
the rotor as a circular cylinder carrying torque. The stress in the outer and inner
supports are well within their shear strengths. In an early design the field-winding
region between the inner and outer support was filled with alternating layers of
epoxy-bonded double-pancake windings and epoxy fiberglass bands, a design very
similar to the MIT 3-MVA rotor [4 ]. This design was unsatisfactory because the
deformations of the center and outer supports are imposed on the superconductors in
the winding space as an axial gradient of circumferential motion. All the superconductors are continuously epoxied together so they deform as a circular cylinder.
The imposed deformation causes a shear stress at the epoxy interfaces between
superconductors which exceeds the shear strength of epoxy. Note that the stresses in
the epoxy are not because the composite winding carries a large percentage of the
torque, but because the deformations of the inner and outer supports are imposed on
the winding.
The yoke-module configuration solves this problern since the circumferentially
independent design of the structure isolates the superconductors from stresses
developed during the high-torque phase of a fault. An added advantage of the yoke
design is that no hoop stresses are developed in the windings because all modules are
circumferentially independent.
The analysis of the winding space for all but the torsionalloads is carried out in
two steps. The first step is to analyze a single yoke and the superconductor inside of it.
142
K. A. Tepper, J. V. Miaerviai, 1111d J. L. Smith, Jr.
Table U. Bending Stress in Yokes
Locations*
A
8
c
D
E
F
Bending stress,
MPa
300
11
350
110
25
26
* See Fig. 2 for Iocations.
The second is to model the winding space containing the superconductor filled yokes
and the other rotor components. The analysis of the individual yokes will be given
followed by the overall rotor analysis.
One yoke and the superconductors inside the yoke are modeled as a frame filled
with radial running strips of copper. The dimensions of the yokes are shown in Fig. 2.
The copper strips, representing the superconductors, are the full height of the yoke
by the width of one superconductor, approximately 0.15 cm.
The rentrifugal and radial Lorentz forces push the superconductors against the
yoke tops; however, since the yoke bottom and the bottoms of the superconductors
are not bonded together the superconductors are in a state of compression. The
maximum value of these stresses in the superconductor during the most severe
operating conditions is u = -18 MPa.
The azimuthat Lorentz forces are transmitted through adjacent layers of
superconductors to the side walls of the yokes. Again, since the yoke side walls and
the layers of superconductor are not bonded together there are no tensile stresses
in the azimuthat direction. The compressive stress in the superconductor resulting
from the accumulation of Ioad has a maximum value in the seventh module and is
u = -20 MPa. The side walls of the yokes bendunder the azimuthat Lorentz force.
The superconductors are bent into the shape taken by the side wall. The maximum
values of the shear stress, r, and the normal stress, u, in the superconductors are
u = 37 MPa and r = 3.9 MPa.
In the second step of the stress analysis of the winding space, the yokes are
modeled as frames in order to evaluate the stresses in the yokes resulting from the
interaction of the winding space and the rest of the rotor. Since the superconductors
are not potted into the yokes they do not contribute to the radial sti:ffness of the
frames. This model has been coded into a multiple cylinder and truss program
The peak stress Ievel is in the yokes closest to the junction of the two saddle coils and
occurs during an armature short circuit when the radial Lorentz forces on the damper
reach a peak. The results of this analysis are given in Table II.
Two tests of the strength of the yokes have been made. The firstwas a test of the
compressive strength of the yokes between the top and bottom bosses. The second
testwas of the strength of the yoke 's side wall and top and bottom pin configurations.
The results of the tests are in agreement with the predicted behavior.
eJ.
THERMAL ANALYSIS
The yoke-module winding configuration is attractive for conductor cooling
because it exposes a large fraction of conductor surface to the liquid helium while
providing reserve helium capacity surrounding the modules. This gives good steady-
Supereouductiog F1eld Winding for a 10-MVA Geuerator
143
state convective cooling and also allows for transient cooling by means of the large
heat capacity of the liquid helium.
The large power density of this generator requires a high-field winding-current
density and this precludes the use of a completely cryostable conductor. The
superconductor must always be maintained below the critical temperature. Any
normal zone will quickly propagate throughout the winding in a rapid quench and
thus local normal transitions must be avoided.
A heat transferanalysiswas performed to determine the thermal response of the
conductor modules to heat inputs into the winding space. The sources of these heat
inputs are: conduction into the winding space from surrounding components (i.e.,
structural shells and electromagnetic shields), internal heat generation within the
conductors, and frictional heating due to relative conductor motion. The internal
heat generation is a result of eddy current and hysteresis Iosses in the composite
superconductors when they are exposed to local alternating magnetic fields or during
field current ramping. The values of the Iosses are calculated by a computerprogram
that performs a dynamic simulation of fault transients on the generator including
three-dimensional field effects [6 ]. The dual shielding arrangement of the generator
provides excellent electromagnetic shielding of the field winding resulting in a peak
ac Ioss rate of 1 mW/cm 3 • This Ioss rate was the peak average Ioss rate during a
three-phase terminal fault from rated Ioad with the fault being cleared followed by
reclosing to the bus. The total global winding loss rate for this condition was 8 W of
which 6.5 W is from hysteresis and 1.5 W is from eddy currents. Although this is the
peak Ioss rate, this value was used as a steady-state rate of heat generation to give a
conservative estimate for the maximum conductor temperature.
The frictional heating occurs at the interface of the slip planes as the azimuthal
Lorentz forces increase during field current ramping. The mechanism is as follows.
The increasing azimuthalload causes the side wall of the yokes to bend. The radial
layers of superconductors bend to the same shape as the side wall. Since the interface
shear is limited by friction, the layers deform as discrete beams, not as one thick
beam. This results in relative motion across the slip planes. A worst-case analysis
yields a peak heating rate of 0.6 mW/cm 3 if the field is charged in 30 sec.
The heat transfer analysis consists of three thermal models: a two-dimensional
steady-state model in a transverseplane (r-6}, a two-dimensional steady-state model
in a radial plane (8--z ), and a transient adiabatic heating model. The two-dimensional
model in the transverse plane assumes a uniform internal heat generation with no
axial conduction. The two-dimensional model in the 8--z plane assumes uniform
internal heat generation with no radial conduction. Both models utilize the effective
conductivities of the conductor-insulation composite cross section with surface heat
flux through convective heat transfer coefficients. The maximum conductor
temperature rise for an internal energy generation of 1 mW/cm3 is 0.01 K.
The transient adiabatic temperature rise resulting from a uniform heat input to
the winding space was estimated by considering the heat capacity of the helium. This
temperature rise during a fault is 0.3 K. The winding will remain superconducting
under all operating conditions because the maximum temperature will not exceed
the critical temperature (approximately 5 K) foranominal operating temperature of
4.2K.
CONCLUSIONS
A prototype electrical generator of 10-MVA rating with a superconducting field
winding is being constructed. A unique yoke-module type of support system is being
144
K. A. Tepper, J. V. Milleniai, .... J. L s.ltll, Jr.
employed in the field winding. Structural and thermal analyses of this configuration
indicate that this system will provide stable mechanical, thermal, and electrical
operation under both steady-state and transient conditions.
REFERENCES
1. J. L. Smith, Jr., G. L. Wilson, and J. L. Kirtley, Jr., IEEE Trans. Magn. Mac-15(1):727 (1979).
2. J. L. Smith, Jr., G. L. Wilson, J. L. Kirtley, Jr., and T. A. Keim, IEEE Trans. Magn. Mq-13(1):751
(1979).
3. "Demonstration of an Advanced Superoonducting Generator," Interim Rept. 7, MIT Cryogenic
Engineering Labaratory and Electric Power Systems Engineering Labaratory, E(49-18)-2295-7 .Oll,
IR 7, pp. 3-5.
4. J. L. Smith, Jr ., J. L. Kirtley, Jr ., P. Thullen, and H. H. Woodson, Proc. 1972 Applied Superconducßvity
Conference, IEEE Pub. No. 72, CH0652-5-TABS (1972) p. 145.
5. "Demonstration of an Advanced Superoonducting Generator," Interim Rept. 7, MIT Cryogenic
Engineering Labaratory and Electric Power Systems Engineering Labaratory, E(49-18)-2295-7 .Oll,
IR 7, pp. 232-238.
6. S. D. Umans, P. B. Roemer, J. A. Mallick, and J. L. Wilson, "Three Dimensional Transient Analysis of
Superconducting Generators," presented at IEEE Power Engineering Society, 1979 Winter Meeting.
C-3
CONDUCTIVE ARMATURE SIDELDING
DESIGN CONCEPTS FOR SLOW-SPEED
SUPERCONDUCTING GENERATORS IN
THE 40- TO 400-MVA RANGE
S. Kuznetsov
Imperial College of Science and Technology
London, England
INTRODUCfiON
This study is concerned with the electrical dimensioning of passive, electromagnetic shields surrounding air gap armature windings for slow-speed multipolar superconducting-field generators which make exclusive use of conductive
rather than integrated conductive and ferromagnetic shields. Special reference is
made to the problern of screening the composite stator winding and superconducting
field for environmental and improved short-circuit protection rather than being
applied to damp transient rotor oscillations. The conceptual machines used to
illustrate the limitations on exclusive conductive shielding are 6-48 pole units with a
corresponding stator rating rauging from 40 to 400 MVA at 60-Hz output. The
specific cryogenic rotor circuit incorporates a Nb-Ti superconductor cable with
design details included to calculate winding inductances and intermagnet forces. A
high-voltage multilayer stator winding is dimensioned for numerically determining
the Maxwell stress vector in the vicinity of the stator shield and reducing the
load-dependent, radial magnetic forces on the superconductor.
The motivation for proposing the construction of !arge slow-speed superconducting generators as peaking units for electric utility applications and as central
drives for ac ship propulsion is based on the following.
1. The basic geometry of the slow-speed generator coupled with the use of
conductive shielding indicates that the machine is fundamentally much stifler than an
equivalently sized generator with ferromagnetic stator shielding. The increased
no-load eddy current Iosses in the conductive shield are partially oflset by the
substantial reduction in reactive kV A attributable to stator leakage reactance, while
the rotor-to-stator mutual coupling remains virtually unchanged.
2. The conductive shielding concept reduces the armature reaction eflect of
the outermost winding layers compared with alternative screening methods allowing
better voltage regulation and armature conductor mechanical protection.
3. The conductor stator shield is clearly superior over a ferromagnetic shield in
limiting transient forces on the superconducting rotor during stator short circuit for
slow-speed machines where the synchronous and transient reactance are typically
under 10%.
145
146
S. Kuznetsov
Apart from the greatly increased liquid helium refrigeration requirements
encountered with multipolar machines over high-speed machines with an equivalent
field MMF rating, the major constraint on the use of high-field type II superconductors on the rotor is the steady-state azimuthalload torques and radial magnetic push
which exceed those experienced in superconducting turbogenerator designs. A
practical upper Iimit on the realization of slow-speed superconducting generators
(SSSG) using Nb-Ti field coils was depicted by the design of a 400-MV A-size,
150 rpm hydrogenerator based on an equivalent rotor peripheral speed, active
height, and pole pitch as a conventional615-MVA hydrogenerator [ 1]. The range of
design considered in this analysis all retain the same rotor peripheral speed of 70 m/s
)
l!llildjll ,11111111 P
@)
Qll!llulll!jdj! dll
ffil!llll ill!illll' b
ii!HHHHHiffllllll
ill!ll!!lll'llllllllll
lllllllilil!ll lllilb
cllllillllllllllllllll
IIIIIIIIIIIIIIIIIIIIP
illllilll!,jjjii!IIIP
cllllililillllllllllll
llliilllllilllllllllb
qll!lllilillllllllill
jll!!lillll!l!lll!tll
llll!lllilll!Jl!!I!!D
llilllllll!iilll'lllb
lillllilll!l!ijj,II!P
al!rtll!!llllllll!lll
llllilljljliljllilllb
~llllillllllllllll
lllllllllllllllll~
qllllll!llllllllll
lllllllillllll l!l~
Airgap
0
Fig. 1. One-half-pole segment radial-azimuthat view of conceptual SSSG machine.
Legend: (0) aluminum armature shield; (1) EHV stator Roebel conductors; (2) stainless
steel rotor damper shields; (3) copper ambient temperature damper; (4) compression
spacers; (5) vacuum; (6) 80-K heat radiation shield; (7) 4.2-K liquid helium COntainment
vessel; (8) rotor torque transfer banding; (9) Nb-Ti superconductor field winding; (10)
liquid helium cooling ducts; (11) field winding COntainment block; and (12) rotor torque
axial transfer coupling.
Conductive Armature Shielding for Slow-Speed Supereonducting Generators
147
Table I. Comparative Dimensions and Performance of
Representative Slow-Speed Superconducting Generators
6-Pole unit
48-Pole unit
Rotor
Diameter, m
Active height, m
Weight w/o shaft, kg
Peripheral speed, m/s
WR2 , kg-m 2
Inertia constant (w /o shaft)
Mass of superconducting cable, kg
Cost of field winding conductor, 1979 $
Nominal ac loss in superconductor, kW
Field array Iead refrigeration, kW
Torque transfer refrigeration, kW
1.11
3.45
7.7 X 103
70
2.12 X 10 3
0.419
1.54 X 103
3.3 X 105
2
3
190
8.92
3.45
5.4 X 104
70
9.6 X 105
0.30
1.08 X 104
2.3 X 106
16
3
1700
Stator
Diameter, m
Mass, kg*
Rating, 60°C rise, MVA
Terminal voltage, kV
Air-gap, mechanical, mm
Acti_ve height, m
Current loading, A/m periphery
Short circuit ratio
Load 1 2 R loss, kW
No-load eddy current loss, kW
Efficiency at 0.90 PF
Specific power density, kVA/kg
1.47
4.1 X 10 3
40
20
19
3.88
34,000
>11
188
235
96.6
2.55
9.3
3.56 X 104
400
230
19
4.02
36,000
>15
1140
1520
98.8
3.12
* Winding and shield only.
and rated rotor Ioad torque of 480 kN-m/pole acting on a pole area of 1.83 m2 • A
segment of the 400-MVA machine taken in the radial-azimuthat plane is shown in
Fig. 1; note that the radial curvature is very small. The dimensions and performance
specifications are included in Table I.
The major areas of concern are: (1) the critical thickness of the conductive
shield in a solid-shell form [2 ] that depicts the transition from inductance-limited
screening to resistance-limited screening; (2) matehing the reftected surface
impedance of the conductive screen to the combined reaction wave of the field and
stator MMF's and establishing the optimum degree of inductance-limited screening
as a function of rotor Ioad angle; (3) maintaining the external magnetic field to less
than 0.5 mT at a distance of 2m from the stator shell so that these machines are
adequately screened for ship propulsion applications; (4) examining the confticting
electromagnetic requirements demanded by the dual use of a single conductive
shield for both steady-state and transient operation; and (5) the relative performance of the stationary conductor stator shield against experimental evidence on
rotating warm damper shields (excluding inertial free shields) in limiting the specific
transient radial magnetic stress applied to the superconducting cables under terminal
short circuit. Although the rotor heat radiation and warm shields are shown in Fig. 1,
their effect is not included in the foregoing magnetic field plots so as to isolate the
singular effect of the stationary-shield concept.
148
S. Kuznetsov
ROTOR FJELD STRUCTURE
In contrast to conventional superconducting turbogenerator rotor designs
whereby all of the rotor structure from the cold radiation shield inwards is maintained at a cryogenic temperature eJ, the cryogenic portion of the described
slow-speed superconducting rotor is constrained to a relatively narrow band of about
0.14 m in radial thickness and mounted on an ambient temperature rotor spider to
connect with the central shaft. Most important, the high-torque SSSG is only
practical when the field coils are abnormally sieoder in comparison with turbogenerator field coils. For the reference design, all of the superconducting coils have a
width to pole pitch aspect ratio of 6.46 : 1. This shape is avoided in single isolated
high-field, air-core coils as the Lorentz forces tend to ovalize any quasireetangular
shapes. However, when a series of long "racetrack"-shaped superconducting coils
are situated in a tightly packed band along the rotor spider periphery, a uniformly
stressed array can be obtained for the SSSG at a rotor radius of curvature ranging
from 0.55 to 4.46 m. Fundamentally, high-aspect magnets are only permissible in
rotating machines when their shortest transverse dimension is aligned in the same
direction as the rotating magnetic field in order to avoid any large differences in
tangential torque applied to the leading and trailing conductor portions of the coils.
The advantage gained by going to a large multipolar SSSG design is brought out
by the apparent enhancement of the superconductor's criucal current capability
simply by the reduction in internal magnetic field for a given air-gap induction
density. For example6 at rated Ioad, the field MMF of the 400-MVA machine
amounts to 0.54 x 10 A-turns/pole. If this value of excitation is applied to a single
isolated magnet, the Nb-Ti critical current density would be based on a peak
llcm
__I____ _
''
'
\
\
\
I
\
I
I
I
I
I
I
I
I
I
I
I
I
I
/
...
-
......
\
\
\
I
I
I
I
I
\
I
I
I
I
/
/
I
I
I
to rotor shar'
I
I
Fig. 2. Contour lines of constant radial magnetic flux density (in mT) of
an axial-radial segment, 16.7° from the direct axis.
Conductive Armsture Shielding for Slow-Speed Superconducting Generators
149
magnetic field of 3.3 T. With similar magnets arranged immediately adjacent (and
oppositely polarized) in an array, the peak internal field is 5.3 T. Specifically, at a
pole pitch of 0.57 m, the use of a !arge radius, multiple magnet system results in an
18% reduction in critical internal field intensity per ampere of excitation.
ROTOR FIELD REPRESENTATION
The magnetic field and Maxwell stress vectors (Fig. 2) are calculated by
performing a discrete conductor, three-dimensional integration over all of the
conductors contained in both the rotor and stator assernblies using a variation of the
Biot-Savart law in a closed-form solution. The crucial numerical technique isthat all
coil shapes must be discretized into exclusively orthogonal components since there is
no mutual coupling between components in different planes. The orthogonal
components of the model are made sufficiently smaller than the cable cross section;
both the axial and radial curvature of the superconducting coils including the end
regions are represented in the discretization with an error not exceeding 1 part in 103
for the total field to stator mutual coupling. A flux plot of the axial component of
magnetic field density for the 400-MVA machine at a radial distance of 0.13 m from
the field pole planar center line is shown in Fig. 3. In this one specific case, the
armature conductor active length is only marginally Ionger than the superconducting
field coil. This gives instant visual representation of the undesirable radial magnetic
forces acting on the first layer of armature winding.
Fig. 3. Contour lines of constant axial magnetic ftux density (in mT) in an axialazimuthat segment, 13-cm radial from the field pole face at the first stator winding
layer. (Shortened axial active length of 0.80 m, pole pitch of 0.57 m, and field
excitation = 540 kA-turns/pole).
150
S. Kuznetsov
STATOR ELECTRICAL DESIGN
To appreciate the most general effect of stator conductive shielding, a nonhelical, nonspiral concentric wave winding with straight conductors has been used in
the conductor discretization. The stator pole pitch progressively increases as a
function of radial distance and an azimuthat offset in individual conductor spacing
amounting to a 4° shift/layer has been employed for the primary purpose of reducing
peak electric field potentials and for valtage harmonic control. In this most basic
stator structure, the end region connections are nearly free of axial magnetic stresses
by having the active length of the stator exceed the active rotor field length by 0.55 m
per side (or 16% oversizing). This increase in axiallength yields a 2.7% increase in
fundamental rotor-stator coupling and reduces the second harmonic component of
axial force on the stator layer nearest the air gap from 7.9 to 0.6% using the rated
tangential force on the SSSG as a base.
CONDUCTIVE SHIELD SELECTION
Ideally an electromagnetic shield surrounding the stator winding should be a
composite, Iaminated ferromagnetic and conductive structure to fully satisfy the
differing steady-state and transient requirements [4 ]. However, a single solid aluminum shell clearly identifies its potential inftuence on limiting field and stator coil
mechanical stresses. If stray eddy current Iosses were of no concern, then it would be
desirable to individually shield each concentric layer of stator winding. As a
compromise between minimizing capital investment and short circuit rotor forces vs.
minimizing stray eddy lasses, an upper bound on the maximum shield dissipated
power at no Ioad has been established at 100% of the stator rated Ioad 1 2 R lass
(based on a stator current density of 3 A/mm 2 ). The inductive coupling between each
armature layer and the shield is shown in Fig. 4.
To ensure that the inclusion of the stator shield can be accurately represented in
the magnetic field analysis of the entire machine, it has been necessary to discretize
the solid conductive shield into finite conductor sections with judicious care taken to
define the shape of the eddy current paths as would occur on the real machine. The
ratio of the axial current density to the azimuthat component of current density in the
shield is shown in Fig. 5. The bulk of the experimental work carried out on air-gap
winding machines of this type has been directed towards plotting the exact eddy
current distribution in continuous shells as a function of transient time constants,
reftected impedances, and axial overhang lengths. These tests have concluded that in
the recommended inductance-limited shells for the range of 40- to 400-MVA
machines, all shields have nearly perfect one-dimensional axial current ftow in the
portion covering the rotor pole face. This experimental evidence has obviated the
need to slit the conductive shield axially at regular intervals to ensure unidirectional
ftow under the transients originally envisioned.
All of the computational results have assumed that the conductive shell is
composed of standard 2219-T81 aluminum ofresistivity 3.7 x 10-8 0-m. In general,
the shell thickness of 0.014 m is near optimum based on the universal, 60-Hz shield
power transfer curves of Fig. 6. The radial attenuation of the shield reaction field in
Fig. 3 is approximately 160 mT /m; at the first or bare winding layer, the leakage
reactance is only changed from 2.55 H/m(axial)/m (periphery) to 2.23 H/m/m. The
effect of the single stator shield has changed the machine synchronaus reactance
Conductive Armature Shielding for Slow-Speed Superconducting Generators
151
40~~--~----~---,----,---~----~--~----,-~
6
_;
0
~
E
i
30
"'-
.,
6
400 MVA Design
0
10 0 MVA
6
0
6
V
c:
0
:!
V
:>
6
0
."
-"
."
c:
~20
0
u
6
0
6
0
"'c:
·~
c:
~
~
u;"'
0
;; 10
-.;
·~
"'
0 ~~12~--~--~16----~--~20~--~--~
24~--~--~2~8~
Rodiol Seporat ion belween Shoeld and Stator Wond•ng Layers,cm
Fig. 4. Shield to stator winding coupling inductance for 0.014-m-thick shield
and two-conductors/pole/phase stator with end region conductors included.
from 0.078 to 0.066 pu. For these machines, the total stator current loading is
36,000 A rms/m periphery while the equivalent shield current loading is 7000 A/m
for a magnetic density at the shield inner surface of 870 mT.
In terms of the shield's direct effect on the rotor torque, an additionalloading of
1.51 kN-m perpole is incurred at rated Ioad in the 400-MVA design and approaches
2.0 kN-m/pole in the 40-MV A type. The balanced-phase, centered-rotor radial
magnetic pull on the superconductor integrates to 4.8 x 104 N/pole at rated Ioad and
0.90 power factor leading owing to the stator winding alone; this increases to
5.7 x 104 N/pole with the addition of the shield. These two criteria of rotor torque
and radial magnetic pull are used exclusively to evaluate the performance of the
shield because they independently express the energy stored in the direct and
quadrature axes of the generator. For example, if the SSSG is Operated in the lagging
power factor mode (absorbing reactive power) at about 20% of rated stator loading,
then it is possible to effectively neutralize the radial magnetic force on the superconducting field magnets for the particular inductance-limited shell recommended;
this effect has been repeatedly demonstrated in laboratory machines.
152
S. Kumetsov
I0 2r------,-------r------,-------,-------1, -- -- - - ,
...
.t:
:;
.....E
..,
10°
..
..
.~
M
..,
.':!
0::
1Ö1
d=0.01' m
60 Hz
1>= 3.7x 10·8
o.s
1.0
Xar ia l
1.5
per uni t
Fig. 5. Mean ratio of axial current density to azimuthat current density in stator
shield as a function of axial distance from the machine centerline per unit of stator
conductor active length per side.
LABORATORY INDUCTION SIMULATOR
A full-scale conductive shield of the type described and applicable for an
80-MVA SSSG is currently undergoing laboratory tests in the form of a 2.2-mdiameter rotating disk annulus with a high-field, 80,000-A/m air gap, axial ftux
stationary excitation winding to simulate the predicted magnetic field density at the
shielding interface experienced in the superconducting machines. The experimental
facility is shown in Fig. 7 with the Maxwell stress instrumentation in the air gap and
telemetry of the rotor disk current ftow distribution. Aluminum, Dural, and solid
steel disks of up to 30-mm thickness have been evaluated up to tip speeds of 140 m/s.
The time-transient diffusion effects in shields as !arge as those proposed for the
400-MVA unit have been simulated by the use of an azimuthal-propagating space
Conductive Armature Shielding for Slow-Speed Superconducting Generaton
153
2 ' 1 C 'r+-~-------.-------.--------.-----,
N
E
~
...c,..
..
..
104
0
.3
~
~
0
0..
..,
-.;
&.
V'l
V
..
V
a.
"'
5 110 3~......__ _ _ _ __.__ __ _ ____._ _ __
5
10
Shield Thickness, m m
_ _.___....J
20
15
Fig. 6. Specific shield power loss density for positive sequence fields at 60Hz and
constant field current of 500 kA-turns.
edge effect produced by a discontinuous, step-function-excitation winding arc of
180° acting on a continuous rotor. Under the condition that the shield is to be
operated in the inductance-limited mode, which is valid for general line-induced
transients in the generator, the eddy current loss in the full-scale shield may be
directly calculated from measurements made from only the azimuthat component
of the magnetic field intensity at the model shield inner periphery. Furthermore,
when the induction simulator is operated at synchronous speed, the azimuthat
buildup of the air-gap magnetic ftux density traveling wave actingintime quadrature
with the excitation current may be expressed [5 ], without recourse to numerical
solution as
_ #Lo
~ T;lsi(l
bq (t) - L.. 1T i~l g;
-
e -X?r/T·wT.)
· · cos ( wt -
X )
-7r
T;
(1)
where
2
T; = T~#J-0
1T
pg;
( 2)
and x is the azimuthat distance under the constant 1. excitation winding that an
eiemental rotor segment has moved since entry at hq = 0. The magnitude of bq(x) at a
154
S. Kuznetsov
Fig. 7. High-speed Iaboratory induction simulator. Axialftux, air ~tan winding of 180° arc excitation to simulate
transient shield operation by use of azimuthal magnetic
diffusion edge effect.
point x obtained from (1) is related to the instantaneous value of bd(t') in the
full-scale salient pole generator at a time t' from the initiation of the actual time
transient at t0 as
TW
x = - ( t ' - t0 )
(3)
1T
In the laboratory induction simulator, with a 2.2-m aluminum annulus, 9.5 mm thick,
and resistivity of 3.25 x 10- 8 0-m, a shield magnetization time constant, T, of 89 ms
has been attained for a pole pitch of 0.253 m. The advantage of this experimental
apparatus is that with this particular disk, shields for a 60-Hz superconducting
generator up to 19.4 mm thick may be evaluated by frequency scaling to 250 Hz in
tests, in addition to using a continuously occurring space transient to simulate rapid,
time-rlependent eddy current diffusion effects.
CONCLUSIONS
The advantage of the passive, conductive armature shield is its capability of
reducing steady-state magnetic forces on air gap armature windings, and in contrast
Conductive Armsture Sbielding for Slow-Speed Superconducting Generators
ISS
to saturable ferromagnetic shields, the conductive shield provides better protection
of transient forces on the field superconductor and rotor damper shield during
symmetrical and negative-sequence faults. lts disadvantages are increased steadystate power dissipation, larger balanced rotor torques, and lower values of synchronous and subtransient generator reactances. Additionally, the stator conductive
shield reduces the radial magnetic forces on the field superconductors in steady-state
operation when the generator absorbs reactive power. The multipolar superconducting machine is thus practical either as a utility peaking unit or as a ship propulsion
motor where the power-to-weight criterion takes precedence over absolute
efficiency.
ACKNOWLEDGMENTS
The author would like to express bis gratitude to E. R. Laithwaite of the Heavy Electrical
Engineering Department at Imperial College for his technical advice, and to the National Research
Development Corporation of England for the use of their laboratory machinery.
NOTATION
b = instantaneous magnetic flux density
g, = airgap between ith stator winding and shield inner periphery
J., = stator winding current loading of ith layer
t =time
T = stator shield magnetization time constant
x = azimuthal distance from entry edge of excitation winding
X = reactance at 60Hz
z = total nurober of stator winding layers
Greek Symbols
p. 0 = free-space permeability
w = electrical radian frequency
p = resistivity
T = pole pitch
Subscripts
d = direct axis
i = stator winding ith layer
q = time quadrature component
s = stator
REFERENCES
1. S. Kuznetsov, IEEE Trans. Magn. Mag-1S:719 (1979).
2. G. G. Lessmann, W. A. Logsdon, R. Kossowsky, M. P. Mathur, and J. M. Wells, "Structural Materials
for Cryogenic Applications," Rept. 74-904-CRYMT-2, National Bureau of Standards Contract No.
CST-9304, Westinghouse Electrical Corporation, Pittsburgh, Pennsylvania (1974).
3. P. Thullen, T. A. Keim, and J. V. Minervini, IEEE Trans. Magn. Mag-11:653 (1975).
4. C. J. Carpenter and M. Djurovic, Proc. IEEE 122:681 (1975).
5. E. R. Laithwaite, Induction Machines for Special Purposes, Chemical Publishing Company, New York
(1966), p. 76.
C-4
OPTIMIZATION OF SUPERCONDUCTI NG
CRYOTURBOGEN ERATOR
FJELD-WINDING PARAMETERS
B. I. Verkin, I. S. Zhitomirskü, and R. V. Gavrilov
Physico- Technical Institute of Low Temperatures
Academy of Seiences of the Ukrainian SSR
Kharkov, USSR
INTRODUCTION
A mathematical formulation and algorithm is proposed for the design of
superconducting cryoturbogenerator field windings, e.g., saddle-shaped windings.
The choice of the particular set of component dimensions in a cross-sectional plane of
a rotor can be optimized in combination with the dimensions of the supporting
elements for the winding and cooling channels as weil as the percentage of superconducting material in a cable cross section. This set of variable parameters is
considered to be optimum for a given external diameter of a winding if it results in a
maximum ftux in the armature-winding region (corresponding to the unit length of an
active part of the winding) and it meets the constraints of cryostatic stability and
strength.
Examples of computer utilization of the proposed algorithm are given. Results
show that the algorithm is very effective.
PROBLEM AND METROD OF SOLUI10N
The objective function that is normally chosen in the optimal design of superconducting cryoturbogenerator field windings is the magnetic ftux <I> averaged over
the radius of an armature winding for unit length of active winding. Providing the
maximum <I> makes it possible to attain the maximum specific power by means of only
n parameters which define the superconducting field-winding configuration in a
rotor cross section. Substitution of Z for this n-dimensional vector and the superconducting current density by j gives the relation
<I> = <I>(Z, j) = <I>(Z, 1}j
(1)
In order to obtain the optimum configuration Z and current density j we must
consider the following basic requirements:
1.
2.
j ::5 ß min ico with the minimum being taken over the values n at different points
in the winding.
The mechanical stresses resulting from the centrifugal and electrodynamical
forces in the superconducting field winding and its supporting elements must not
156
Optimization of Superconducting Cryoturbogenerator Field-Winding Parameters
3.
157
exceed the values permissible for a given material at a specified loading and
temperature range.
The requirements as to shape of the magnetic field generated by the superconducting field winding in the armature-winding region must be satisfied.
Using the constraints of 1 and 2 above tagether with the inequality (1) makes it
possible to eliminate the variable j from the adjustable parameters. Restrietion 3 is
best considered by means of a penalty function Cl The problern then reduces to a
search for an absolute extremum.
To solve the problern posed above the method of configurations has been used
[ 2 ]. The calculation of the magnetic field and electrodynamic forces was made with a
method which takes account of the discrete winding distribution
eJ.
EXAMPLE: WINDING IN PARALLEL SLOTS
An application of this method is the optimal design of the winding for the
cross-sectional scheme presented in Figs. 1 and 2. Here the winding is embedded in
parallel slots of the monolithic rotor. The centrifugal and electrodynamic forces
affecting the superconducting field winding are transferred to the teeth (1) and
wedges (2); these must satisfy the strength requirements described previously. In
addition, the strength requirements of the compounded winding must also be
satisfied.
At a given external rotor radius r, the geometry of the winding cross section is
uniquely defined by the parameters y;, a;, b;, (i = 1, 2, ... , v). These parameters
form the vector Z and are also the unknowns in the design.
1
3
X
Fig. 1. Schematic view of cryoturbogenerator cross section. Legend: 1,
superconducting field winding; 2, armature winding; and 3, ferromagnetic shield.
158
B.I. Vedda, I. S. Zldtominldi, md R. V. Gavrilov
y
4
X
Fig. 2. Schematic of rotor cross section. Legend: 1, framework; 2,
superconducting field winding; 3, framework teeth; and 4, wedges.
I.
+---
Fig. 3. Optimized geometry of rotor cross section (dashed line)
compared with geometry estimated before optimization (solid line).
Optimization of Snpercondneting Cryotarbogenerator Field·W"mding Pu81Deters
159
Table I. Winding Parameters
Magnetic
llux,
Wb/m
S/Cu fieldwinding
area, m 2
Numberof
turns
perpole
Permissihle
current, A
1.07
1.18
0.0294
0.0275
1820
1700
1000
980
Zo
Z*
Figure 3 shows a comparison of the calculated optimum vector Z* obtained
from the above-mentioned method (dashed line) and the geometry corresponding to
the initial vector Z 0 derived from preliminary considerations (solid line). lt follows
from Table I (where some parameters of the above windings are given) that witp this
optimization scheme the magnetic fl.ux was increased by 10% and the superconductor requirement was reduced by 7%.
Note that among the constraints given, only the first and the second turned out
to be operational ones since for these equality is attained. With respect to constraint
(3), it was satisfied over the entire range investigated.
OPTIMIZATION OF TUE CRYOSTABILIZATION PARAMETERS
In the large cryoturbogenerators currently projected for utility networks, the
stabilization problern of superconducting field windings assumes ever greater
importance particularly since reliability is so critical. Load asymmetry and its time
variations, vibrations and hunting oscillations of the rotor, and helium fl.ow rate
variations Iead to disturbances of the magnetic field, exciting current, and temperature. These disturbances can be sufliciently large to result in quenching. Shutting off a
generator in an emergency when the quenching takes place is unacceptable because
it causes surges in a utility network. The only acceptable solution to the problern is
the attainment of cryostatic stabilization which permits the winding to return to the
superconducting state from a full or partial quenching. In view of these design
considerations, a scheme which uses transverse cooling (i.e., one with the helium
channels normal to the winding conductors) and where each conductor appears tobe
subjected to alternating cooled and noncooled regions is more useful for the large
cryoturbogenerators (Fig. 4).
Let us first consider that part of the conductor between the cooled and
noncooled regions. lf the lengths of the cooled and noncooled regions, 211 and 21,
1
I
2
~~
"
1
\
)
II
I
I
I
'
I
X
0
Fig. 4. Scheme for cooling of winding. Legend: 1, monolithic layer of superconducting field
. winding; and 2, helium channels.
160
8. L Veftm, L S. ZW...UIIIdi, IUid R. V. Gamlov
respectively, are much greater than the characteristic dimensions of the conductor
cross section, then the conductor temperature field may be considered as one
dimensional; i.e., T = T(x). This temperature field can be described by a nonlinear
heat-conduction equation T; the nonlinearity is a result of the temperature dependence of the heat capacity C.., heat conduction A.., and electrical resistivity Pe· To
simplify this procedure the equation may be linearized so that the solution f to the
linell! pro_blem would be a "worst-case" solution of the original nonlinear problem,
i.e., T s T throughout the range of interest. The worst-case conditions are obtained,
for example, by substituting the maximum value PM for Pe in the temperature range
considered and by substituting the minimum value AM for Ae.
For a stationary normal zone, assumed to be in a conductor and occupying the
region 0 s x s x 0 , there is some value for the helium heat-transfer coeffi.cient a 0
where a > a 0 that permits the problern with the above boundary conditions to
reduce to
0 <X< I+ l1
dT =O
dx
'
X=
0,
X
=
I+
l1
(2)
where
[ 2
QM= { PMA2'
0:5 X :5 Xo
0,
0,
{
OHe = a(To- T)P
A
'
and has a solution
I$ X$ I+ 11
f satisfying the condition
T(x 0 ) < Tc(I/ {A, B)
(3)
This means that the critical nonlinear problern has a stationary solution in the normal
zone which is less than that expected from (3).
Now Iet the values of a 0 , corresponding to different x 0 , be limited and a * =
maxosxosl+h a 0 • Then if a > a*, a normal zone of any size will return to the
superconducting state and the coil will be completely stable.
As an analysis of (2) shows, the condition of complete stabilization may be
represented as follows:
(4)
where s must be less than unity.
lt may be shown for given values of B and T0 which satisfy (4) that the maximum
value of the average current density I/ A may be obtained when the fraction of
superconductor in a cable cross section is given byt
= [o.5 + (0.25 + K-1/2>1/2r1
(5)
r
t Results similar to these have been obtained by Wipf [4 ).
Opdmization of Sapercondnc:ting Cryotarbogenentor Field-Winding Pllftllleters
161
where
K
=
aPI1
ic(To, B)(iJic/iJT)PcuA(l + lt)
The maximum avaiJable current density which meets the stabilization requirements
is obtainable from the relations
isc =(*je
(6a)
I/A = (* 2jc
(6b)
Considering that, as a rule, K « 1 we may write that
r* = K112,
(I/A)
!>
=K112. = [
max
]c
aPltic(To, B) ] 112
A(l + lt)PculiJic/ iJTI
Satisfying the requirements for cryostabilization at a current density which is not too
small appears to be possible if one takes care of the following:
1.
The field winding should be fabricated of a material having a ratio of
ic/liJic/iJTI as large as possible (for example, Nb 3 Sn).
2. The structural design should be made to provide suffi.ciently effective heat
exchange between the helium and the winding conductors. As evaluations have
shown, there exists a real possibility of obtaining a value of more than 106 W /m 3 K
for the complex aPld A(l + 11 ).
To account for the effect of induction and helium temperature changes, B and
T0 , respectively, over the winding thickness it is necessary to solve a much more
complex problem.
For such a design scheme of a superconducting field winding and outer rotor
radius we must determine the superconducting field winding current density, the
distribution of the winding throughout the rotor cross section, the dimensions of the
channels through which the helium is circulated, the fraction of superconductor in
the cross section of the superconducting cable, and the dimensions of the supporting
elements at which the magnetic flux of an exciting field is maximum with respect to
the active portion of the cryoturbogenerator. In addition to requirements (1), (2),
and (3), noted earlier, we must take into account the requirement of cryostatic
stabilization for the superconducting field winding.
NOTATION
A = cross-sectional area of conductor
a; = thickness of ith tooth
b;
=
width of ith modulus
B = magnetic induction
I = transport current
j = current density
critical current density
current density in superconductor
P = perimeter of cooled surface
T0 = helium temperature
Tc(j, B) = critical temperature of superconductor carrying current of density j at a ftux B
Y; = height of ith modulus
ß = safety factor allowing for the possible degradation, ß < 1
( = superconductor fraction of a cable cross section
211 = number of moduli forapole
Pcu = resistivity of copper matrix at 20 K
cl» = magnetic ftux
ic =
isc =
162
B. I. Verkin, I. S. Zhitominkii, and R. V. Gavrilov
REFERENCES
1. E. Polak, Computational Metlwds in Optimization, Academic Press, New York (1971).
2. D. J. Wilde, Optimum Seeking Metlwds, Prentice-Hall, Inc., Englewood Qiffs, New Jersey (1964).
3. I. S. Zhitomirskii and R. V. Gavrilov, Magnitnoje pole i elektrodinamicheskije usiliya v ekranirovannoy elektricheskoy machine s nemagnitnym serdechnikom, Izvestiya AN USSR, Energetika i transport
(5):122 (1977).
4. S. L. Wipf, "Stability and Degradation of Superconducting Current-Carrying Devices," Los Alamos
Scientific Laboratory Rept. LA-7275 (December 1978).
D-1
SUPERCONDUCTING COMPENSATING
SOLENOIDS FOR THE CELLO DETECTOR
EXPERIMENT AT PETRA
W. Barth, N. Fessler-Wilhelmi, W. Lehmann, and P. Turowski
Kernforschungszentrum Karlsruhe
Institut für Technische Physik
Karlsruhe, Federal Republic of Germany
INTRODUCTION
One of the main components of the detector experiment CELLO in the e + estorage ring PETRA at DESY /Hamburg is the superconducting magnet system. The
magnets have been developed as a joint project by CEN/Saclay and Kernforschungszentrum Karlsruhe. CEN has built the thin-walled main solenoid with a length
of 3.5 m and a winding diameter of 1.7 m creating a magnetic field of 1.5 Tin the
center CJ. Two magnetically identical solenoids, located symmetrical to the main
coil, must be positioned with a magnetic field opposite to the central field to cancel
the integral field effect on the orbiting particle beams. This compensating solenoid
system, including its supporting cryogenic system, has been designed and constructed
by the Kernforschungszentrum Karlsruhe. The main coil was constructed with a wall
thickness of :s.A/2 (equivalent to 45 mm of aluminum); this requirement was
imposed by the radiation length A of the generated particles. The compensating coils,
on the other band, were designed and built by conventional techniques for superconducting magnets. The solenoids within their cryostats are to be mounted in
movable iron yoke doors surrounded by muon chambers and a liquid argon end cap
calorimeter as shown in Fig. 1. The outer geometry and the required warm bare
parameters determine the dimensions of the cryostats, i.e., a length of 1.10 m and an
outer and inner diameter of the horizontal part of 0.8 and 0.4 m, respectively.
The compensating coils are parts of a 4.2-K helium circuit which includes the
main solenoid (cooled by forced-flow helium), a complex helium transfer line system
and a refrigerator, and have been built by CEN/Saclay. The compensating coils are
cooled by a liquid helium bath and the cryostats have shields cooled by the return gas.
Each cryostat is connected in parallel to the refrigerator over a length of 13 and 18 m,
respectively.
The design of the magnets and cryostats along with their peripheral equipment
and the cooling flow scheme is reported here. Results of the tests on the completed
equipment including magnet performance, thermal insulation, safety aspects, and
the status of the final installation at DESYare also presented.
163
1
2
J
4
5
6
7
8
9
10
11
12
13
Vacuum Beam Pipe
Superconduding Coil of Oetector
fron Yoke
Compensation Coils
Movmg Devices
Feed Llnes lor liquid Helium
MPI,Nünchtn
101. brlwht
OESY. Hllllburg
Unin nity IiD ol Pari•
S.ctoy
Orur
ParticiP.anls :
Fig. 1. Schematic view of the detector experiment CELLO (DESY).
Centrat Orilt ·and Proportional Chambers
Endcap Proportional thambers
Endcap Shower Counters Iliquid Argon 1
Cylinlfric Shower CountersUiquid Argon]
Proportional Chambers for MuOn Detecfion
Drift Chambers tur Forward Detedor
Shower Counler for Forward Detector
<~1:1-1-<»
Total Weight : ~ 1400 I
Magnet Aeld ' 15 kr
DETECTOR
I
:-=
!
~
i
~
l
~
~
?'!
j
~
:'""
Superconducting Compensating Solenoids for the CELLO Detector Experiment
165
Table I. Solenoid and Superconductor Parameters
Solenoid
Length of coil, m
Inner winding diameter, m
Outer winding diameter, m
Centrat field, T
Maximum field at conductor, T
Nominal current, A
Overall current density, kA/cm 2
Max. stored energy with iron yoke, MJ
Max. stored energy as air coil, MJ
Superconductor
Cross section without insulation, mm
Filaments, ,_.m <P
Twist, mm
Cu/SC ratio
Critical current at Bmax of 3.8 T, A
Residual resistivity ratio of Cu
Insulation
0.86
0.5
0.54
3.5
3.8
1050
15
-1.4
1
3.1 X 1.9
460 X 50
50
5: 1
2380
-280
Wrapped Capton foil with a
thickness of 50 ,_.m
COIL DESIGN AND CONSTRUCTION
The important parameters of the two identical solenoids mounted within the
iron yoke are given in Table I. The superconductor consists of a multifilamentary
NbTi wire of reetangular cross section manufactured by Vacuumschmelze Hanau.
The parameters of this conductor are also listed in Table I. Short sample measurements with this superconductor were performed by the transformer method [2 ]. The
results are shown in Fig. 2 together with the Ioad line of the magnet.
A stainless steel tube forms the inner part of the liquid helium cryostat and also
acts as the coil mandrel. The mandrei was supported within the bore during winding
by a holding fixture to take the reaction forces from winding the conductor estimated
at 180 N. The conductor has been wound in ten layers with interlayers of glass
rows. Each layer was impregnated during winding with epoxy resin Araldit CY
221 and hardener HY 979 supplied by CIBA. The flanges of the coil former were
prepared with a nonadhesive Teflon foil to prevent the release of crack energy
between the winding and the flanges during the magnetic field rise. The superconductor was fabricated in two lengths for each coil. The ends of the conductors
were connected by an uHrasonie welding technique where the contact resistance is
lower than 10- 8 n.
eJ
CURRENT LEADSFORmE SOLENOIDS
Current to the compensating solenoids is supplied by gas-cooled Ieads. The
CELLO experiment requires that there should not be any atmospheric condensation
on the helium return gas lines and no mist formation on the head of the Ieads.
Accordingly, the return gas lines are guided within the vacuum jacket of the liquid
helium transfer lines while the room temperature ends of the Ieads are warmed by
heater elements. The inner part of the current Ieads consists of an OFHC-copper
braid whose Jength and cross section were optimized by using the calculations of
Lock [4 ]. Measured Iosses in the self-sufficient mode at a nominal current of 1050 A
required design values of about 1.8 W per pole, i.e., 1.7 mWI A-pole.
166
W. Barth, N. Fessler-Wilhelmi, W. Lehmann, and P. Turowski
,A
\
•r
des1gn volue
w•th
~
IV
I>
.voo;
/
~y.~Q
"'<:'
~
I
"'
V!_)-___j__-------1
test volue fwtthoul
i
ony quench)
I
i
0
3
5
I
6
7 B, T
Fig. 2. Characteristic values of conductor and compensating solenoids as air coils.
Voltage tests have shown that these current leads can be operated up to a
voltage of about 1.3 kV above ground. However, in the magnet tests a breakdown to
ground occurred at a voltage of only 180 V. In this incident the 1-MJ stored energy of
the magnet burned out parts of the current leads while the helium plasma beam
burned a hole into the cryostat wall. The magnet coil itself showed no damage. This
accident was obviously caused by a small undetected helium gas leak at the top of the
current leads. The leak allowed the small space between the top and electrical ground
to fall with helium gas. Since helium gas has a low breakdown voltage, the accident
was inevitable. To avoid such accidents, metallic structural parts have been replaced
by insulating glass fiber elements and additional selenium surge absorbers have been
installed across the current leads as overvoltage protection.
PERFORMANCE TEST OF THE SOLENOIDS
At PETRA the two compensating solenoids will be operated in movable iron
yoke doors. Before delivery and final mounting the two coils were pretested in a
horizontal test cryostat as air coils at Karlsruhe. The characteristics of the solenoids
under test conditions are shown in Fig. 2. Both magnets have been operated without
any quench, i.e., without any training, up to an operating current limit of 1150 A with
Superconducting Compensating Solenoids for the CELLO Detector Experiment
167
600
Fig. 3. Field decay and internal voltage characteristic of coils at 1150 A. Lower curve shows
magnetic field decay from 3.8 T to zero; upper curve
shows internal voltage curve of coil with a maximum
value of 525 V.
a central field of 3.7 T and a maximum field at the conductor of 4 T, i.e., 72% of the
short sample value on the Ioad line of the coils.
The discharge behavior of the magnet into an external resistor of 0.5 0, was
studied at different currents. The data include field decay and valtage characteristics.
Typical curves are shown in Fig. 3 for a maximum operating current of 1150 A .
During discharge the coils partially reverted to the normal conducting state owing to
the eddy current heating in the superconductor. About 70% of the stored energy was
dissipated into the externalload. This is equivalent to a real temperature rise in the
coil of only 30 K.
The coils and the safety circuit were also testedunder real quench conditions. A
Helmholtz coil pair was placed in such a manner that the windings of the magnet coil
were located between this coil pair. A field pulse of about 200 T /s with a change in
magnetic field of 0.3 T drove the magnet coil at 1150 A into a quench along the Ioad
line. The result was an immediate appearance of coil resistance. The field decay
initiated by the quench is similar in behavior to that noted after quick switchoff.
These procedures have been repeated several times to test the reliability of the
magnets. After these pretests the magnets were mounted in their permanent
cryostats. The mounting arrangement of one of these magnets is shown in Fig. 4.
Final tests of the magnets in the permanent assembly in Karlsruhe provided the same
results as found in the pretests.
CONDITIONS AND SPECIFICATIONS FOR CRYOGENIC SYSTEM
The special character of the cryotechnical requirements lies in the restricted
space available in the detector block and the limited access to the cryostats (see Fig.
1). These requirements for a very compact design of the cryostats and components
resulted in helium lines, vacuum lines, and safety lines that are lang and complex.
Figure 5 shows the basic arrangement of the helium cooling circuit; the cryogenic
specifications are also indicated. The cooling concept selected provides foraparallel
helium supply to the three superconducting magnets. 1t is necessary that the
compensating coil cryostats can be moved axially while at the operating temperature.
This requirement is satisfied by the installation of flexible line sections within the
liquid helium supply lines between the "L-lines" and the "mainline" and within the
168
W. Bll'th, N. Fessler-WUhelmi, W. Lehmama, ud P. Turowski
Fig. 4. Compensating solenoid during mounting into cryostat.
warm return gas line (not indicated). This enables experimenters access to various
measurement locations, such as spark chambers and liquid argon counters, without
warming up the compensating coil system.
CRYOGENIC DESIGN OF COMPENSATING COIL SYSTEMS
The design of the cryostats for the compensating coils is shown in Fig. 6. The
ring-shaped helium tank, with a liquid helium volume of approximately 25liters, was
welded at the fronts and surrounded by an exit gas-cooled shield on all sides. The
mechanical design has been basedonaxial forces of 15,000 N and radial forces of
5000 N; these specifications are predicated on a positioning accuracy for the coil of
±2 mm in the axial and ±0.5 mm in the radial direction relative to the iron yoke. Heat
conduction to the liquid helium bath is kept small by use of special radial supporting
elements between the cold shield and the helium tank. These consist of tubes and
bolts arranged concentrically and in series to realize small cross-section areas and
long distances for the heat ftow. The design is difficult because there is only
approximately a 50-mm radial distance between the heliumtank and the cold shield.
The heliumtank has been designed for a maximum pressure of 10 bar.
Figure 7 shows the process ftow sheet for a compensating coil system. The
helium is fed from the distribution box of the refrigerator through the transfer line
system to the cryostat. The exit gas leaves the cryostat in four separate pathways,
namely, through the two current Ieads (EL), through the cold shield of the inlet line,
and through the cold shield of the cryostat. Part of the gas also passes in thermal
contact with the safety line (SL). Alliinesare located within the same vacuum jacket
(see section A-A, Fig. 6). The exit gas lines are heated to room temperature in
separate ftows in a common electrical heater (690). After having passed through
control valves and ftow measurement sections, the warmed return gas is fed to the
compressor suction side of the refrigerator.
The present design, i.e., heating all the return gas, allows individual cooling
operation of the coils, shortens the overalllengths of the transfer lines, and obviates
v -1
-·--·--·~ --- ·--
Compensating1__ .
salenoi d A --
-
· -
· -
Fig. 5. Basicarrangement of helium cooling circuit.
Main solenoid
0.45 gls lor eurrent Iead
0.42 g LH•ts
L-tine
E
-
Lim it ol del ivery
------1
,.
KfK
•
-- •
beam axis
-·-
: . -, CompensaFj
·Jng
l~. Solenoid 8
2, 8 m
M
...
"'
E
1
$
i·
ä
ii
§
l""
n
i
f
".
I
f
f;
".
g.
ft
170
W. Barth, N. Fessler-WUhelmi, W. Lehmann, and P. Turowski
Fig. 6. Compensating coil cryostat.
the need for additional cold flexible line parts. The higher operational reliability of
such a cryogenic system is rated against a lower overall efficiency of the system.
Decreased efficiency results from a decreased use of the enthalpy of the cold return
gas ftow from the compensating coil cryostats.
The cryostat is protected against faults by means of a safety line integrated into
the vacuum jacket of the L-line. Helium blow down is not permitted because of
danger to the electronic equipment located within the detector block. In case of a
pressure rise in a compensating coil cryostat the neighboring cryostats are protected
by a nonreturn valve (NF 632) and by a corresponding valve control in the helium
ftow to the cryostat (LCV 315) and a valve in the helium return ftow to the
compressor of the refrigerator (FV 624).
PERFORMANCE TESTS OF mE CRYOGENIC SYSTEMS
Prior to delivery, cryostats and L-lines were tested together for tightness,
function, and thermal Iosses at the manufacturer's site (Leybold-Heraeus/Köln).
These tests were performed with a dummy cylinder welded in place of the solenoids
and with liquid helium filling. After delivery the dummy helium tanks were replaced
by the superconducting coils and the systems were completed with respect to the ftow
Superconducting Compensating Solenoids for the CELLO Detector Experiment
171
Col dbox
FV624
;
9
Ef!J~ -X
LCV 316
HCV 623
NF62!i
to Comptessor
L-----<-
+--....J
Air
'
to second
Compensating
-- ---- --------,
Solenoid ( 8 )
-- ---,
I
I
I
I'
'
L----- - -------l - -------- -- -------
Fig. 7. Flow diagram of compensating coil systems. Legend: CSA, compensating coil A; CDL, cooldown
line; SL, safety line ; TSL, transfer line (section J6-J8); EL, return gas cooled electricalleads; PS, phase
separator; S, superconducting probe; Q , quenchdetector; and DR, discharge resistor.
sheet. They were subjected to extensive cryotests at the Kernforschungszentrum
Karlsruhe.
The complete systems including the magnets (approximately 500 kg) were
cooled down individually within 30 hr. The average coolant flow was 1 g/s at a
maximum pressure of 1.2 bar abs with an enthalpy recovery of about 50% of the cold
return gas. Since the complete finalliquid helium supply systemwas not available at
either test location, it was only possible to measure the cryostat Iosses in a discontinuous mode via the helium evaporation rate while the supply was closed.
Because of the restricted liquid helium volume (max. 16.5-liter reservoir capacity
171
W. Barth, N. Fessler-WUhelmi, W. Lehmann, and P. Turowski
within the dome) there was only a limited period of stabilization. This resulted in
higher loss values than expected for high liquid helium Ievels and a more pronounced
dependence of the Iosses on the liquid helium Ievel (even at zero current) than can be
explained by variations in the heat exchange surfaces and lengths of heat conduction,
especially of the current Iead. Therefore, the results (see Fig. 8) of loss measurements
performed on the compensating coil system B under different operating conditions
represent maximum values. Under continuous ftow conditions at DESY, the dotted
extensions of curves 3, 4, and 5 of Fig. 8 is the expected maximum Iosses at high
Ievels.
The increased evaporation Iosses which occur at 1050 A for liquid helium Ievels
between approximately 30 and 45% inside the dome are a result of screw connections for the junctions between the normal conducting and superconducting parts of
the current Ieads having a relatively !arge heat exchange area with the helium. The
emersion of these two elements, located at different Ievels in the liquid helium bath,
Ieads to a reduction in the evaporation of liquid helium. This effect becomes
noticeable at the high current Ievel of 1050 A and a constant mass ftow through the
lnsulal ion vacuum
ä ,w
s
10 ·6 mbar
Temperature al lhe oullel of
the cryostat shield 30- 60K
9
Specif icat ion value
e
design value
6
5
5
4
---- - ...----".,----"'"-3
LHe- leve l ,'!.
~--~-+--+-~--------~~~~-80
70
nom ina'l Ievel
60
so
40
30
20
10
0
empt'y dome
1 - - - - - litt:O(J+) =110min - - - - - l
Fig. 8. Evaporation Iosses of cryostat vs. liquid helium Ievel inside dome.
Legend: Curve 1, · with dummy cylinder but without magnet and current Ieads;
Curve 2, 0 with dummy cylinder and additional 5-W electrical heat Ioad inside
liquid helium bath, simulating improved shield cooling; Curve 3, + with magnet
and current Iead (I= 0, ni1e ad = 2 x 0.1 g/s) ; Curve 4, l;, with magnet and
current Iead (I = 870 A (normal current), ni 1ead = 2 x 0.1 g/s) ; and Curve 5, 'l
with magnet and current Iead (I= 1050 A (nominal current), 1e ad = 2 x 0.1
g/s).
m
Superconductlng Compensating Solenoids for the CELLO Detector Experiment
173
current leads of 2 x 0.1 g/s, the same value as for the nominal current of 870 A. In
other words, the dashed line for curve 5 in Fig. 8 is approached with an increased rate
of helium ftow through the current leads at the 1050-A level. In the continuous ftow
mode at DESY, this increased ftow of heliumgaswill be available owing to the losses
in the transfer line and the resulting supply of two-phase helium to the compensating
coil system, as indicated in Fig. 5.
The measured cryostat losses of the compensating coil system A were within
approximately 10% of the losses for system B. As mentioned previously, a discharge
of the magnet at 1050 A initiated a voltage ftashover at the current lead causing
noticeable darnage which led to a breakdown of the insulation vacuum. Within a time
period of 2 s, the pressure inside the helium tank and the insulation vacuum tank
increased to the blowdown pressure of the firststage of the safety line (4 bar abs).
This incident apparently caused a slight change in the insulating capability of the
cryostat; the darnage could not be located and remedied with certainty without
dismantling the welded components before delivery to DESY. Hence, after repair
and reinstallation of the new current lead, the measured losses were higher by about
2 to 3 W for currents of zero and 1050 A.
In spite of the higher losses of cryostat A, the sum of the losses (maximum
values) stilllies within the values specified for the compensating coil systems. This is
because of the lower values obtained for cryostat Band the two supply lines (L-lines)
of 1.5 W each, including the loss of the couplings.
Figure 9 shows the pressure rise inside the cryostats after discharge of the
magnets. The curves indicate that for normal discharge and for flashover situations
P abs
•
bar
t [ l O S O A , Syst.A'''
llOOA'
i:- lOSOA "
870 A, Syst_ A
600A, Syst. B
LH~
• 'Yolurnt' b4ol01t' sw•!cl\ ott
10 20 JJ '0 50 60
17 • 21 I
t i me , s
Fig. 9. Pressure rise inside cryostat and blowdown time
after discharge of magnets. * Voltage ftashover incident in
system A, destruction of current Iead inside vacuum tank,
breakdown of insulation vacuum; **Voltage ftashover
incident in system B, destruction of current Iead outside
vacuum tank, breakdown of insulation vacuum; ***normal
discharge of magnet with removal of 70% of the stored field
energy and with the first safety valve closed.
174
W. Barth, N. Fessler-Wilhelmi, W. Lehmann, and P. Turowski
encountered with the venting of the insulation vacuum by helium, the first blowdown
stage of the safety line is sufficient protection for the system. The second relief valve
to be opened at 6.5 bar abs, in addition to the first stage, can cope with the dynamic
Ioads encountered when the insulation vacuum is vented with atmospheric air [5 ] and
a simultaneous magnet quench without energy decoupling occurs. Functioning of the
second valve was assured in one of the tests shown in Fig. 9.
CONCLUSION
The results of the pretests have shown that all requirements for the compensating coil systems can be fulfilled. The coils can be operated safely up to the design
value without quench and the performance of the cryogenic system with regard to
function, tightness, and Iosses matches the specifications.
The compensating coil systems have been transferred to DESY, integrated
within the CELLO detector block and the helium circuit. At the end of July 1979 the
compensating coil systems were cooled down to 4.3 K for the first time in parallel
with the main solenoid by the L'Air Liquide refrigerator in DESY. These tests
confirmed that the overalllosses of the cryostats and transfer lines were within the
specifications of Fig. 5 and that the increased loss noted previously within the
compensating cryostat A was due to a contact between the heliumtank and the shield
within the dome. This problern has now been eliminated. The initial Operation of the
system at the installed CELLOexperiment has just started. Full rated current was
attained without any problems. Further tests are in progress.
ACKNOWLEDGMENTS
The work reported is a joint eflort of mechanical, cryogenic, and electronic engineering groups of
Kernforschungszentrum Karlsruhe, Institut für Technische Physik. The authors express their gratitude for
the work done and cooperation experienced in the teams. The authors also thank the magnet group of
CEN-Saclay/France for the fruitful collaboration, as weil as the assistance of Dr. Horlitz of DESY and Dr
Oberlack of MPI München.
REFERENCES
1. H. Desportes, in Proc. 6th Intern. Conference on Magnet Technology, ALFA, Bratislava,
Czechoslovakia (1978), p. 474.
2. P. Turowski, M. Scherer, and W. Go II, in Proc. 5th Intern. Conference on Magnet Technology, Rome,
Italy (1976), p. 541.
3. N. Fessler-Wilhelmi and K. P. Jüngst, "Ultrasonic Welded Multifilament Superconductors" Kernforschungszentrum Karlsruhe unpublished report.
4. J. M. Lock, Cryogenics 9(6):438 (1969).
5. W. Lebmann and G. Zahn, in Proc. 7th Intern. Cryogenic Engineering Conference, lPC Science &
Technology Press, Guildford, England (1979), p. 569.
D-2
CONSTRUCTION AND TEST OF TUE CELLO
THIN-WALL SOLENOID
H. Desportes, J. Le Bars, and G. Mayaux
Centre d'Etudes Nucleaires de Saclay
Saclay, France
INTRODUCTION
A large thin-wall superconducting solenoid has been constructed at Saclay and
mounted on a large detector CELLO. This is one of the experiments installed on the
e + e- colliding beam facility PETRA at DESY (Hamburg).
The complete magnet system, in addition to this main solenoid, includes two
compensating solenoids symmetrically located on each side of the main one, a thick
1000-ton iron shielding intended as a hadron filter, and a 300-W closed-cycle helium
refrigerator supplying the three magnets. The two superconducting compensating
coils have been designed and constructed at the ITP of Karlsruhe and are described
elsewhere
The major requirement for the main solenoidwas that it be very light weight or
"transparent" to radiation. The amount of material allowed for the radial thickness
of the complete magnet (including thermal shields and vacuum walls) was not
permitted to exceed half a radiation length or 45 mm of aluminum.
The design of the solenoid was prepared in close collaboration with the ITP
in 1976. It was designed to
Karlsruhe at the time of the CELLO physics proposal
meet stringent requirements with the best available experience in superconducting
magnet technology. The basic concepts of the design which were selected at that time
These concepts were closely followed
have already been reported elsewhere
during the construction and have proved to be fully valid in view of the performance
tests. The tests have demonstrated that such a design enables a minimum wall
thickness to be achieved together with simple, reliable, and safe operational procedures.
e].
eJ
eJ.
MAGNET DESIGN
The two most significant points of the design are (1) the use of a high-purity
stabilized aluminum, high-current conductor and {2) cooling by conduction from an
external pipe in which a force fiow of two-phase helium is circulated.
Stabilization of the conductor was considered essential to smooth out thermal
effects of mechanical disturbances or of other instabilities and to provide sufficient
heat capacity to the conductor so that it is intrinsically protected when a quench
develops in the coil. High-purity aluminum is advantageous in the present application because its radiation length is six times higher than that of copper and its
175
176
H. Delportes, J. Le Ibn,_. G. May.u
electrical and thermal conductivities are an order of magnitude higher than copper at
low temperature. This last characteristic is particularly helpful for diflusing heat
which may be produced locally. In case of a quench, it slows down the temperature
rise due to the Joule eflect and speeds up the quench propagation through the entire
magnet.
Force-fiow cooling was preferred to bath cooling, mainly to reduce the amount
of material involved in surrounding the coil with a helium container. Such a container
would have required thick walls to withstand the large intemal pressures resulting
from an aceidentat fiash vaporization such as could occur in the case of a vacuum
break. Another advantage of force-fiow cooling is that it enables the magnet to be
cooled down smoothly and uniformally without incurring thermal stresses due to
large temperature gradients. Also, even though the cooling efficiency using exterior
cooling may be sufficient for maintaining the magnet at the required temperature in
normal operation, it becomes inadequate when large heat fiuxes are produced in the
magnet; thus, it does not prevent quench propagation, which is essential for safety
reasons.
Other features of the design include a single continuous layer of conductors for
the winding, a complete epoxy impregnation of all the elements of the coil package
(bore tube, conductor, bandage, and cooling tube), the use ofthin aluminum-alloy
shells for all the structural elements (bore tube, thermal shields, and vacuum tank),
and an array of fiberglass struts distributed symmetrically at both ends of the solenoid
as a support structure.
MAGNET CONSTRUCfiON
The first item needing special study was finding a conductor able to fulfill the
above requirements. The conductor configuration selected is shown in Fig. 1. It
consists of a reetangular 2.2 x 1.6-mm superconducting composite with the smallest
possible ratio of Cu/Nb-Ti (1: 1), soft soldered onto a high-purity aluminum strip of
2.2 x 9 mm. The development and the entire fabrication of the aluminum stabilization were carried out at Saclay; the basic superconductor was ordered from Airco.
Full details covering the fabrication and tests of this conductor have been reported
elsewhere 4 ].
The total length of conductor used in the solenoid is 6700 m, which, in view of
the limited lengths of the superconductor available, required four splices along the
winding. Splices were made by cutring up part of the aluminum strip, overlapping the
two ends of the composite over a length of 30 cm, and soft-soldering the three
elements together in such a way that the cross section of the spliced partwas the same
as that of the individual conductor; this method of fabrication will not disturb the
winding regulari~. The electrical resistance of such a joint has been measured to be
less than 2 x 10-9 n. A schematic cross-section of the magnet is shown in Fig. 1
where the various components are given with their respective dimensions.
The actual winding procedure called for a carefully controlled process requiring
special equipment. The winding line is shown in Fig. 2. The conductor was initially
stored on a spirally wound spool (not visible in the photograph), with its axis in a
vertical position. From this spool the conductor was driven through a tension device,
a wrapping machine (for insulation), two epoxy wetting devices on each side of the
wrapper, and was finally laid around the winding bore tube. The winding bore tube
was driven by a horizontallathe and was fitted with a pressing device made of a ring
clamped on the bore tube itseH. A series of jacks, assisted by means of sector pads,
e·
177
Construdion and Test of the CELLO Thin-WaU Solenoid
,-----------------------------------------------Ou te r vac u um tan k
,
Ii II J
,--------------------------------------------------- 0 u ter sh iel d
r------------------------------------------- Coo Iing tubes
,--------------------------- Mechanical bandage
I
Conductor
Inner shield
Inner vacuum tank
-T-----------------------------------------------------+----------------------------------~--8
j; ~
n;r--[~~~~--""'DJ~ ~
L!'l
~
~-------------------------------~20
N
"
(0
'
~
______________________________~
~------------------------------------- 3560 --------------------------------------,
~---------------------------------------------- 4020 ---------------------------------------------~
Mechanical bandage
Conductor _____________.....,._
Alum inum support
Bore tube ---------·~>...l...lt-H..u..~
Fig. 1. (Top) Longitudinalcross section schematic of
the CELLO solenoid and (bottom) detail of the coil
package. Dimensions in millimeters.
maintained a constant axial pressure on the edge-wound conductor as the winding
progressed. This ensured a tight packing of the turns and prevented any tipping of the
conductor. The conductor was insulated by double-wrapping it with silk tape of
80-#1-m thickness. (Silk was found mechanically stronger than glass when it was wetted
and wrapped around the sharp cornered conductor.) The epoxy used was Ciba x
193/2594 C grade ; this epoxy remained liquid for weeks at room temperature.
Progress of the winding is shown in Fig. 3 where the action of the pressing pads can be
observed.
178
H. Desportes, J. Le Bars, and G. Mayaux
Fig. 2. Winding line.
After completion of the conductor layer, the surface was given extra insulation
and an aluminum alloy stripwas wound over the insulation. This winding consisted of
a continuous layer using the same winding line but without insulation and with the
pressing device removed.
At this stage, a thermally insulated shroud was mounted around the coil while it
was still on the lathe. Curing of the epoxy, with infrared heaters placed inside the
Fig. 3. Winding in progress.
Construction and Test of the CELLO Thin-Wall Solenoid
179
Fig. 4. Finished coil with cooling pipe laid on its surface.
shroud, was achieved at 150°C in 5 h; during this period the coil was continuously
rotated on the lathe.
After curing, the whole coil package was bonded tagether and formed a rigid
structure. The next operation involved machining the inner bare of the bare tube to
reduce its wall thickness to 3 mm from an initial thickness of 30 mm. The preformed
cooling pipe was then glued and clamped on the surface of the solenoid using Stycast
2850 MT, a strong compound with good thermal conductivity. The pipe was
constructed of a single piece of aluminum alloy tubing and laid along 16 straight runs,
as shown in Fig. 4. This kept the length of the cooling loop to a minimum of 60 m
resulting in a low pressure drop for the helium ftow, and also providing the same
cooling path for each turn of the winding.
The assembly of the coil in its cryostat required care, but the procedure was
straightforward. The four cylindrical shells, consisting of the thermal shields and the
vacuum tank, were positioned concentrically both inside and outside of the solenoid
and were closed by end ftanges after the support system bad been securely tied to the
ends of the solenoid. Multilayer insulation was applied to the entire surface between
the shield and the vacuum tank. The complete assembly was carried out in a vertical
position.
The thermal shields are cooled with helium gas supplied from the refrigerator at
60 K. This cold gas is circulated in pipes and follows the same pattern as for the
solenoid.
The support system consists of two sets of fiberglass struts, one for centering and
holding the weight of the coil and eventual asymmetric lateral forces, and the other
for axial support. The arrangement of the struts is shown in Fig. 5. The thermal shield
is suspended separately in a similar way.
The last stage of the assembly required connecting all electrical and cryogenic
circuits to the external transfer elements. This was done through a horizontal pipe (at
one end of the solenoid) connected to a vertical chimney in which all the circuits were
180
H. Desportes, J. Le Bars, and G. Mayaux
- -_·-:--:.: ===-=-=: _=;jt_=_=_ :_ =-=-=-~.-.
lt
'
1/
/1
·ft
#
i'
/I
end v i ew without cap_
back
external vi ew with a cut i n the
outer
vacuum tank
front
Fig. 5. Arrangement of support struts.
Fig. 6. Arrangement of equipment inside chimney.
. _FRONT
Construction and Test of the CELLO Thin-Wall Solenoid
181
Fig. 7. CELLO solenoid assembled inside the argon
calorimeter and iron shield.
collected according to the scheme discussed in the next section. The inside arrangement of the chimney is shown in Fig. 6. Figure 7 shows the completed magnet
installed inside the large argon calorimeter used in the experiment at PETRA
surrounded by the thick iron shield.
CRYOGENIC CIRCUIT
The three magnets installed in the experiment are supplied with cooling from
the same refrigerator, but in different modes; the compensating solenoids are cooled
in a pool boiling mode while the main solenoid is cooled in forced flow.
The diagram of Fig. 8 shows only the cryogenic circuits for the main solenoid
operation. A fraction of the helium flow is diverted at the last stage of the refrigerator
and is subcooled and liquefied through a heat exchanger and a J-T valve. The
two-phase flow is then circulated through the solenoid cooling pipe. From here it
returns to an auxiliary reservoir situated in the chimney of the magnet. In the
reservoir, part of the liquid is separated and part of the gas is extracted for cooling the
current Ieads, which are connected to the terminals of the solenoids through
leak-tight feedthroughs at the bottom of the reservoir. The remaining fraction of the
two-phase flow is returned to the refrigerator cold box where the liquid is ultimately
separated and mixed with the liquid directly produced by the second J-T valve from
the main flow of the refrigerator. The reservoir in the refrigerator is used for
transferring liquid to the compensating coils.
181
H. Desportes, J. Le Bars, and G. Mayaux
. f!EFBIGEBATOR
COLD
WARM RETURN LIN...L_
LI NE
44 K
r- · - - ·
PSV
...
>
...w
c
PSV
(I)
L .,
TA
- Fig. 8. Cryogenic circuits for the solenoid Operation.
Construction and Test of the CELLO Thin-Wall Solenoid
183
The entire system is operated by automatic control devices. The regulated
parameters include the two-phase helium ftow in the solenoid cooling loop, both
ftows of helium gas in the current Ieads, the liquid Ievels in the liquid helium
reservoirs, the pressure of the cold helium return ftow, and the temperatures at the
warm end of the current Ieads.
The refrigerator itself, manufactured by Air Liquide, is a two-turbine type. 1t
does not require liquid nitrogen and is also automatically controlled; accordingly, it
requires a minimum of supervision and is designed for long periods of continuous
Operation (-4000 hr).
TESTS OF TUE SOLENOID
Two series of tests have been performed on the completed solenoid, the first at
Saclay without the iron shield and the second at PETRA with the entire system
assembled for the experiment. The tests at Saclay were carried out without the
refrigerator. Special cryogenic circuits were used which transferred helium from one
dewar through the solenoid cooling loop and back to a second dewar. All the
control and safety equipment was operated as in the final installation.
The first test showed evidence of a fault in the solenoid. A permanent resistive
spot was detected at all currents which caused the coil to quench repeatedly at a
current of 1900 A (expected nominal current was 3400 A). The normal region had a
resistance of 2 x 10-7 n, corresponding to about 10 cm of aluminum strip. The
power dissipated in this resistance at the quench current was 0.7 W; this gives an
upper Iimit to the heat which can be removed locally by the cooling scheme. After
dismounting the solenoid, the defect was identified by X-ray techniques as an open
break of the superconductor. Careful examination of the break revealed the
presence of a metallump inclusion in the superconductor which clearly initiated the
rupture. The break must have occurred during the winding but was not observed at
that time since the two ends of the superconductor were still bonded to the aluminum
strip and the entire conductor was wrapped with insulation.
Since the broken conductor was located on the sixth turn from the end of the
solenoid, the last six turns were removed from the winding and no other repair was
attempted. This only shortened the solenoid by less than 0.5%.
After reassembly, the magnetwas tested again and was charged to its maximum
current. No training was experienced and no instability or jump could be observed
during the current charging. Also, there was no temperature change nor mechanical
deformation as noted by strain gauges measurements.
The magnetwas quenched several times at a current of 3200 A, independent of
the charging rate. This quench value is weil below the specified rated current of the
conductor. In view of the above observations, the quench can only be explained by a
degraded characteristic of the superconducting material in the area of the quench.
The problern was located this time in the central region of the solenoid.
This last assumption was further confirmed during the final test of fhe magnet
installed on its experimental site at PETRA. This testwas carried out in July 1979.
The two compensating solenoids, the huge iron shielding, and the refrigerator were
also installed for the test. The complete system was cooled down from room
temperature and filled with helium at 4.4 K in approximately 3 days. lt has been
running continuously since then with remarkable stability and reliability. In this new
environment the main solenoid could by charged up to 3000 A in less than 10 min,
again with very stable behavior, but it was quenched at a current of 3025 A. This new
114
H. Desportes, J. Le Ibn, mtd G. Maya11X
degradation can be attributed to two factors whose inßuence is only eflective when
the current is limited by the H-1 characteristic of the superconductor. Theseare the
magnetic field increase due to the iron and the operaring temperature of the solenoid.
The first eflect is small, as the peak field is only increased by -5% in .the centrat
region of the solenoid, but the temperature was effectively higher by as much as 0.2
to 0.3 K than during the test at Saclay. Such a temperature diflerence is responsible
for a decrease in the current capacity of the superconductor by about 4 to 6%; this
corresponds to the diflerence in the quench values. Further tests will confirm these
conclusions.
In view of these results, the practical field available for physics w~th CELLO is
1.3 T. An important result of the tests is the assurance gained on the complete safety
of the magnet. Careful analysis of the quench behavior bad been carried out
theoretically and was experimentally checked at three values of quench current
during the tests. This analysis is presented elsewhere [5 ]. The results exceeded the
most optimistic predictions; with respect to both longitudinal and transverse velocilies of quench propagation. During a quench at 3200 A, the normal resistance of the
winding increased within a few seconds to a value four times higher than the external
discharge resistor provided for protection and the temperature of the coil remained
below 60 K; this shows that even without external protection the magnet would be
intrinsically safe.
lt is worth considering the role played by the conductor aluminum stabilization
on the performance. Because of its very low resistivity, the diffusiontime constant for
the current to transfer to the aluminum is large (of the order of 100 ms). Accordingly,
at the front of the quench propagation all the current is in the small amount of copper
and heats up the conductor rapidly, which, with the high thermal conductivity of the
aluminum, helps to speed up the propagation. After this initial stage, the current
transfers to the aluminum; the Joule effect is very much reduced and the temperature
rise is slowed down. This permits a reasonably long time for the discharge of the
magnet.
CONCLUSION
The concepts used in the design of the CELLO magnet have been justified. A
better knowledge of the quench behavior has been gained. Technological experience
on this rather new type of magnet construction will be useful in future designs.
The operating current Iimitation experienced during the tests is a result of local
degradation of the superconductor properties. The reason for this eflect is not known
but it raises again the crucial need for complete quality control in superconducting
material production.
RE FE RENCES
1. W. Barth, N. Fessler-Wilhelmi, W. Lehman, and P. Turowski, in Advances in Cryogenic Engineering,
Vol. 25, Plenum Press, New York (1980), p. 163.
2. "Proposal for a 411" Magnetic Detector for PETRA," prepared by Desy, Karlsruhe, München, Orsay,
Paris, and Saclay (July 1976).
3. H. Desportes, in Proc. 6th Intern. Conference on Magnet Technology, ALFA, Bratislava Czechoslovakia (1977), p. 474.
4. P. Genevey and J. Le Bars, in Proc. 6th Intern. Conference on Magnet Technology, ALFA Bratislava
Czechoslovakia (1977), p. 1093.
5. W. V. Hassenzahl, in Advances in Cryogenic Engineering, Vol. 25, Plenum Press, New York (1980), p.
185.
D-3
QUENCHES IN THE SUPERCONDUCTING
MAGNET CELLO
W. V. Hassenzahl
Los Alamos Scientific Laboratory, University of California
Los Alamos, New Mexico
INTRODUCTION
The superconducting magnetCELLOwas tested with currents up to 3200 A at
Saclay and has been installed at DESY in Harnburg where it will be used for particle
physics experiments requiring colliding beams of electrons and positrons. The testing
of this unique, large, one-layer solenoid provides an excellent opportunity to
evaluate the theory of quench propagation under adiabatic conditions, that is, in a
coil in which the conductors are not in direct contact with helium. In an early test of
this coil, quenches occurred as a result of a broken conductor. This report describes
the quenchesthat occurred, gives the details of the damaged conductor, and includes
an analysis of the quenches. Observed axial quench velocities are compared to the
calculated values based on both measurements and calculations of the thermal
conductivity of the fabricated coil. The coil and conductor dimensions and characteristics are given in Table I. The coil and conductor are shown in Fig. 1, and a
complete description can be found elsewhere CJ.
Table I. CELLO Coil and Conductor Characteristics
Interna) diameter, mm
External diameter, mm
Length, mm
Thickness, mm
Number of turns
Design current, A
Guaranteed current, A
Operating current, A
Short-sample critical current, A
Protection resistance, 0
Inductance, H
Cu to NbTi ratio
Cu+ NbTi section, mm 2
High-purity Al section, mm 2
Residual-resistivity ratio of Al
Thermal conductivity of high-purity Al at 4.2 K, W /cm-K
185
1656
1705
3414
24.5
1276
3400
2800
3100
-4000
0.16
1.06
1: 1
1.6 X 2.22
2.24 X 9
2=700
=60
186
W. V. Hassenzahl
COOUNG TUBE
MANOREL- WINOING TUBE
Fig. 1. Layout and detailed cross section of the superconducting magnet CELLO.
QUENCHES IN CELLO COIL
Theoretical Background
Superconducting coils are known to undergo transitions from the superconducting to the normal state. These transitions or quenches, which may begin at one or
more places in the coil, propagate both along and perpendicular to the conductor. In
the single-layer CELLO coil there is only one effective direction in which the quench
can propagate perpendicular to the conductor.
Quench Velocity Along a Conductor. The propagation velocity of quenches
has been studied extensively [2-6]. The calculation by Broom and Rhoderick [2 ] gives
the velocity of propagation, Vc, as a function of various conductor parameters and of
the maximum temperature in the normal region by
Ve =
)
kp
f(Om-20c)(
OeOm(Om - Oe)
C
112
J(k)
=- -
C Oe
1/ 2
G(O)
(1)
where C is the specific heat, k is the thermal conductivity, p is the resistivity, I is the
current, Oe is the difference between the critical temperature and the operating
temperature, and Om is the difference between the maximum temperature in the
normal region and the operating temperature.
Stekly and Hoag made the approximation that G(O) = 1, which is valid only
after the centrat temperature of the normal region of a Nb Ti conductor reaches about
25 or 30 K [6 ' 7 ].
The velocities calculated with the actual conductor characteristics and G(O) =
1 are the dashed curves in Fig. 2. For comparison, the results of several measurements by Scherer and Turowski [8 ] are the solid curves in Fig. 2. The calculated
velocities are typically higher than those measured. As the length of the conductor
eJ
Quenches in the Superconducting Magnet CELLO
60
I
THEORY - - - EXPERIMENT--8 • 2T
....."'
I
I
GORREGTION FOR
SHORT SAMPLE
E
u
g 40
/
B~tT
w
/
>
I
z
f/ //
0
\
1<[
(!)
<[
a..
a:
I
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OBSERVED
VELOCITY IN THE COIL
I-
0
I
PROPAGATION~~
~
187
20
/
//
/
/
a..
COMPOSITE
ONLY
I
u
z
w
/
:::>
0
0
0
1000
2000
3000
4000
CURRENT,A
Fig. 2. Ouench-propagation velocities for the CELLO superconductor-copper
composite and the complete conductor with high-purity aluminum. Both
theoretical and experimental values are shown.
used by Scherer and Turowski is weil known, one can calculate the evolution of
temperature within the sample and thus the propagation velocity as a function of
time. The corrected velocity, which agrees better with the experiments, is marked
with an asterisk in Fig. 2. This simple example demonstrates the need for a complete
analysis of measurements made on small samples under laboratory conditions before
applying the results to the performance of large coils.
Quench Velocity Perpendicular to a Conductor. A quench propagatesnot only
along but also perpendicular to a conductor. The perpendicular velocity depends
strongly on the transverse thermal conductivity k l.. Wilson [9 ] shows that v l. =
vc(kl.jkc) 112 • The question is: What is the magnitude of k1.? Of course, one can
calculate k 1. and hope that the result is acceptable. One is reasonably confident in this
calculation for a coil such as CELLO, but not for coils with round or cabled
conductors nor for those cooled directly by helium.
Table II gives the value of the axial thermal conductivity, kaxiah calculated from
the known thermal conductivities of epoxy fiberglass and aluminum at 4.2 K. The
thermal conductivities of copper and NbTi are also given in Table II, even though
they contribute little to kaxiai because they are very small relative to that of aluminum.
The averagethermal conductivity for a layered structure can be calculated from
(2)
where Ii is the length of a section of material, ki is the thermal conductivity of that
section, and Rii is the contact resistance between materials. For CELLO, one can use
188
W. V. lbaeDDhl
Table D. 'lbennal Conductivity of Materials in the
CELLO CoU at 4 K
Thermal conductivity,
W/cm-K
Material or configuration
=60
=0.06
-0.05
1 X 10- 3
1.3 X 10- 3
1.0 X 10- 3
1.1 X 10- 3
Pure aluminum*
Structural aluminum*
Coppert:J:
Superconductor:J:
Epoxy fiberglass insulation:J:
Conductor insulation*
As-wound axial conductivity*
* Measured value.
t Calculated value.
:J: Literature value.
the values in Table II and a contact resistance, R, of approximately 5 cm 2 K/W C0 ] to
calculate
2.24
0.278
kaxial=2.518 ( 60+1. 3 Xl0
3
+2x5
)-l =O.OllW/cm-K
(3)
To determine if this calculation was correct for the CELLO coil, a sample of ten
insulated conductors was assembled in ablockthat simulated the actual coil. Table II
gives the measured thermal conductivity of this sample.
It is believed that the order of magnitude difference between the measured and
calculated values of kaxiah is quite large because the test sample was not under
compression; consequently the calculated value is closer to the characteristic of the
assembled coil. One possible reason for this difference is the very poor cohesion
between the epoxy and the thin layer of solder that forms the conductor surface.
Quench Volume. The quench volume in two- and three-dimensional coils, Vz
and V3 , respectively, can be characterized by
(4)
and
(5)
where t is the time, k" and ky are the thermal conductivities in the x and y directions,
v" and Vy are the velocities in the x and y directions, and h is the thickness of a
two-dimensional coil [ 11 ].
These equations are valid only until the quench reaches a boundary of the coil.
In CELLO, for example, if an entire turn is normal before the quench reaches one
end of the coil, the quench front will then propa~te only along the axis of the coil,
and its speedwill be v" = vc(kd kc) 112, i.e., about 1lx, as fast as in the conductor. Here
the normal volume increases linearly with time [dV/ dt oc Vc(kd kc) 112] until one end
of the coil is reached.
189
Qoenches in the Sopercondoctiog Magnet CELLO
Fig. 3. Voltages observed across the CELLO coil
during a quench at 1900 A.
Another possibility isthat at some time t 1 the quench reaches one end of the coil
before a complete turn is normal. If this occurs, the volume is
V=
k
22(X)
kc
Vcf
1/ 2
2
+ Vcf'
f1
k )
(X
kc
1/ 2
(6)
'
until the quench completely encircles the coil.
Quenches in the CELLO Coil
Figure 3 shows the resistive voltages observed across the CELLO coil. These
voltages indicate that the quenches started near one end of the coil. Of the three
regions apparent in this figure, the first two appear to be quadratic, but the third is
almost linear. These three regions are characterized in Table III.
The linear slope during region 3, after t = 0.2 s, indicates that the quench is
propagating in only one direction. The very low values of axial thermal conductivity
in the coil and the slow increase in resistance indicate that this propagation is along
the axis of the coil. As the quench was known to start near one end of the coil, the
velocity can be calculated by assuming the quench front is moving axially along the
coil in one direction. The velocity is given by
il.R sA
v =---=0.34m/s
(7)
ilt 27Tpr
where il.R is the change in resistivity during the time ilt, s is the axiallength of a turn,
A is the area of the aluminum, p is the resistivity of the aluminum at 4 K, and r is the
radius of the coil.
The slope during region 3 appears to deviate a bit from linearity in the last 0.3 s.
This fact indicates that the maximum temperature is probably less than about 20 K,
which is consistent with direct temperature measurements taken during the test and
with computations made using the program OUENCH.
Table 111. Voltages Observed Across the CELLO Coil During a Quench
Quench region
End time,*
s
Change in
voltage,
V
1
2
3
0.035
0.105
1.1
0.9
0.85
2.75
Change in
resistance,
n
4.9
4.4
1.5
X 10~ 4
X 10~ 4
X 10~ 3
Voltageltime
characteristic
Quadratic
Quadratic
Linear
* Because the voltage changes very slowly at the beginning of a quench it is difficult to estimate
exactly when it starts. Thus, the times may be low by as much as 0.007 s.
190
W. V. Hassenzahl
From tbe calculated axial velocity of 0.34 m/s, tbe quencb sbould bave traveled
about 1.2 cm or five turns during tbe first 0.035 s in region 1. The fact tbat tbe quencb
actually started in tbe sixtb turn, as discussed later, supports tbis calculation and gives
an axial velocity of about 0.40 m/s. Thus, at tbe end of -0.035 s, tbe quencb bad
reacbed one end of tbe coil.
For region 2, tbe quencb propagates along tbe axis of tbe coil in only one
direction and continues propagating along tbe conductor, circumferentially around
tbe coil. Finally, after 0.105 s, tbe quencb bad completely encircled tbe coil, traveting
2.64 m, to give a quencb velocity of 24 m/s along tbe conductor. This value, wbicb is
plotted in Fig. 2, is considerably bigher tban eitber tbe calculated value or tbe value
measured by Scherer and Turowski. As discussed above, tbe time at wbicb tbe
quencb begins is not weH defined, but a cbange of 0.007 s will not reduce the velocity
significantly. On tbe otber band, for the quench to meet itself on the opposite side of
the coil it must transfer to the adjacent turns and then propagate along them. Thus
the quench that begins in the broken section actually travels more than halfway
around the coil before meeting itself in the fifth and seventh turns. Correcting
for this effect would give a slightly higher velocity. The error bar on the point at
1900 A in Fig. 2 indicates these two effects. During subsequent tests of the
CELLO coil a quench was initiated at 2550 A. It took 0.07 to 0.08 s for the quench
to circle the coil, giving a propagation velocity of 33 to 38 m/s, which is also
plotted in Fig. 2.
If the above sequence were reversed, that is, if the quench bad encircled the coil
after 0.035 s, then, instead of being quadratic, the voltage characteristic in region 2
would be linear.
There remains a slight discrepancy between the axial quench velocity determined from the slope of the voltage in region 3 and the velocity found simply from
the duration of the first region and the known position of the origin of the quench.
This difference may be due to one or a combination of several factors.
1. The temperatures of the adjacent turns were elevated by Joule heating in
the broken section before the quench began. This effect would reduce the heat
required to achieve a given propagation velocity. Equivalently, (Jm and Oe of (1)
would be reduced and Vc would be higher.
2. The actual duration of region 1 could have been 0.042 s, because the
voltage increases slowly at the beginning of a quench.
3. The resistivity of the aluminum used to calculate the velocity may be too
great.
The third item deserves extra attention because an unrepresentative sample
may have been used to measure the 4-K resistivity, which was found tobe about
4.5-5 nfi-cm. This value may be high by as much as a factor of 2 owing to excessive
handling of tbe sample. The d V/ dt during the quench gives dR/ dt, which, in quench
region 3, is proportional to the product pv. There is thus an ambiguity and neither p
nor v can be found directly from region 3. However, as tbe velocity, 34 cm/s, is in
error by at most 20%, the measured resistance can be off by at most 20%, neglecting
magnetoresistance [ 12 ' 13 ], which is quite small in aluminum at fields below 1 T.
The voltage of region 1 corresponds to almost 40 turns normal, even tbough it is
certain that only 12 turns have portions that arenormal and that tbe total normal
length must be between 10 and 12m. This difference is very puzzling. There is,
however, a long delay between the time when tbe current transfers from the
superconductor into the copper and when most of it bas transferred to the aluminum.
191
Quenches in the Superconducting Magnet CELLO
I = 1900 A ORIGIN -1Lmm FROM ONE END
DIFFU SION TIME FOR HIGH PURITY
ALUMINIUM 1 =0.1 s
--- ------
2.0
>.
---
IJJ
~
OBSERVED VOLTAGE
1.5
0
>
10
0.5
0
0
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
,sec
TI ME
Fig. 4. A comparison of observed and calculated voltages across the CELLO coil during a
quench originating in the broken conductor, six turns from one end of the coil. The
measured resistances of the high-purity aluminum and copper are used. The only variable is
the diffusion time for current into the high-purity aluminum.
This process of current transfer is described by the well-known diffusion equation
d 2J
dx 2
=
1 dJ
D dt
(S)
which gives an exponential solution for the penetration of current into a conducting
slab. The characteristic time constant, T m • is given by
'Tm=
16L2
1097Tp
(9)
where L is the thickness of a slab conductor in cm and p is its resistance in !l-ern. The
current penetrates 1 mm of aluminum having p = 5 n!l-cm in about 0.011 s. But 1 s
is required for current to fully penetrate a 9-mm-thick aluminum slab.
Though the diffusion of current into the aluminum conductor CELLO is more
complicated than a simple exponential function, the program QUENCH was modified
to give an exponential characteristic for the resistivity of the high-purity aluminum.
The diffusion time Tm and the aluminum resistance were varied in the program.
One of the closest approximations to the observed quench voltage is given in Fig. 4
along with an expanded version of the observed curve of Fig. 3.
REPAIR OF CELLO COIL
During these tests of CELLO a resistive section was observed at all currents.
The voltage between turn 1059 and the end of the coil corresponds to a resistance of
2 J.'Ü or to a normal region about 12 cm long.
192
W. V. Hassenzahl
Fig. 5. Enlargement of the in situ x-ray of the damaged section of
the CELLO conductor. There is a gap of about 2 mm between the
broken conductor ends.
It was originally believed that this normal region was probably produced by
overheating the conductor during the fabrication process when the copper superconductor composite was being soldered to the aluminum stabilizer. But it was
possible that the conductor was broken so the coil was x-rayed. In CELLO, because
there is only a thin layer of material that is relatively opaque to x-rays, =1.6 mm of
copper superconductor composite, it is possible to detect a mechanical defect in the
composite with this technique. Figure 5, a magnified copy of the original x-ray, shows
a bad section of conductor, found in the sixth turn from one end of the coil. The
broken conductor contained an inclusion of NbTi with a high oxide content.
Inspection of the broken region clearly indicated that the break occurred before
the epoxy in the coil was cured as there was some penetration of epoxy into the space
between the composite and the aluminum near the break. Certainly the conductor
was not broken before the soldering operation when the composite and the superconductor were joined. The last seven turns of the coil were removed and the void
filled with an aluminum spacer and epoxy.
FINAL TEST OF CELLO COIL AND CONCLUSIONS
During the final test of CELLO a heater produced quenches at 2550 A and
there were unprovoked quenches at 3200 A. The resistance of a section of conductor
glued to the outside of the coil was used to monitor these quenches and to determine
the final temperature after the quench. A temperature of 60 K was reached in less
than 20 s after a 3200-A quench, indicating good thermal contact between all coil
Quenches in the Superconducting Magnet CELLO
193
components. That the current is limited to 3200 A probably is because of a defect in
the conductor similar to that which caused the break. This explanation is supported
by the fact that the composite was ordered in a single length, =7000 m, but broke
several times during fabrication, probably because of other inclusions.
The analysis of this rather complex quench lends support to the use of existing
theories to calculate quench propagation velocities and to predict the behavior of
coils subjected to quenches.
REFERENCES
1. H. Desportes, J. Leßars, and G. Mayaux, in Advances in Cryogenic Engineering, Vol. 25, Plenum
Press, New York (1980), p. 175.
2. R. F. Broom and E. H. Rhoderick, Brit. J. Appl. Phys. 2:292 (1960).
3. z. J. J. Stekly and E. Hoag, J. Appl. Phys. 34:1376 (1961).
4. W. H. Cherry and J. I. Gittleman, Solid-State Electron. 1:287 (1960).
5. L. Dresner, IEEE Trans. Magn. Mag-13(1):1328 (1979).
6. C. Meuris, "Protection d'une Bobine ou d'un Ensemble de Bobines Supraconductrices Lors d'un
Passage a !'Etat Resistif," Saclay Rept. STIPE/76-80 (October 1976).
7. W. V. Hassenzahl, "Quench-Modifications and Documentation," Saclay Rept. SUPRA/78-61
(October 1978).
8. M. Schererand P. Turowski, Cryogenics 18:515 (1978).
9. M. N. Wilson, "Computer Simulation of the Quenching of a Superconducting Magnet," Rutherford
High Energy Laboratory, Rept. RHEL/M 151 (1968).
10. M. Van de Voorde, "Results of Physical Tests on Polymers at Cryogenic Temperatures," CERN
Rept. ISR-MA/75-38 (1975).
11. P. H. Eberhard, M. Alston-Garnjost, M. A. Green, P. Lecomte, R. G. Smits, J. D. Taylor, and V.
Vuillemin, "Quenches in Large Superconducting Magnets," presented at 6th Intern. Conf. on
Magnet Technology, Bratislava, Czechoslovakia, 1977.
12. F. Fickett, Phys. Rev. 83:1941 (1971).
13. V. I. Gostishchev and A. A. Drozd, Phys. Met. Metallurgy 39(6):168 (1975).
D--4
CONSTRUCDON AND TESTING OF THE
TWO-METER-DIAMETER TPC
THIN SUPERCONDUCTING SOLENOID
M. A. Green, P. H. Eberhard,
R. R. Ross, and J. D. Taylor
Lawrence Berkeley Laboratory
Berkeley, Califomia
INTRODUCTION
The TPC experiment at PEP is one of several colliding beam experiments which
use thin superconducting solenoid magnets. The CELLO experiment at PETRA in
Hamburg, Germany and a detector for the ISR at CERN in Geneva, Switzerland use
superconductors with an aluminum matrix 3 ]. The TPC magnet and a magnettobe
used at Cornell University use the concept of a shorted secondary circuit to protect a
high-current-density copper-based superconductor (4 ].
The Lawrence Berkeley Labaratory (LBL) has developed and tested the
concept of proteering a large high-current-density solenoid magnet with shorted
secondary windings [5 ]. This development work has been reported earlier (6 ]. The
construction and testing of three test coils, two of which have a diameter of 1 m and
one which has a diameter of 2 m have led to the construction of the TPC detector
magnet.
The TPC magnet is described elsewhere 8 ] as weil as in this report. This report
presents the basic parameters of the TPC magnet, describes the steps of construction
(and presents the results of the first tests of some of the magnet system subassemblies).
c-
e'
TPC MAGNET BASIC PRINCIPLES
The TPC magnet is different from almost all other large superconducting
magnets which have been built to date. The data gathered on photons by the TPC
detector will be enhanced by a magnet which is as transparent as possible to photons.
As a result, the thin solenoid design concept evolved. The features which make the
TPC magriet unique among large superconducting magnets are as follows:
1. The superconductor operates at matrix current densities which are much larger
than conventionallarge superconducting magnets.
2. The TPC magnet is designed so that its quench is protected by a system of
shorted secondary windings. These windings control the quench process and
prevent bot spot formation.
194
195
Construction and Testlog of the TPC Thin Superconducting Solenoid
lnsu lotor
Squoshed
3 / 4" 0 0
Alum inum Tub ing
1100 Aluminum
0
I
10
I
I
20
I
I
30
I
I
Mill imeiers
Fig. 1. Cross-sectional view of TPC superconducting coil package.
3. The TPC magnet is cooled by forced two-phase helium cooling instead of helium
bath cooling.
4. The TPC magnet has an integrated coil and inner cryostat which is cast in epoxy
resin (see Fig. 1).
The TPC magnet has a warm inside diameter of 2.04 m. The outside diameter is
2.36 m in the center and 2.44 m at the ends. The length of the cryostat, which
encloses the coil, electricalleads, and coil cryogenic system, is 3.84 m. Access to the
coil, the electrical services, liquid helium, signal wires, and vacuum is restricted to a
small portion of the outside corner of one end of the cryostat vacuum vessel. The
TPC magnet refrigeration system (refrigerator cold box and control dewar) is
connected to the magnet by about 18m of transfer line running under a wall of
radiation shielding. The magnet is monitored by a small computer.
Table I shows the basic parameters of the TPC magnet as it operates at design
current in its iron return yoke. When the TPC magnet is operated in its iron yoke, it
behaves like an infinite solenoid which has a peak induction in the coil which is
scarcely different from the uniform induction within the magnet bore. The TPC
magnet is designed to produce a field near the center, uniform to better than 1 part in
1000. High field uniformity is required in order that the time projection chamber
detector functions properly. The design current density, J, in the superconductor is
ver~ high for a magnet which operates at a stored energy, E, of 11 MJ. As a result,
EJ product is over fifty times that of conventional large superconducting magnets
[9].
Table I. Basic Parameters of TPC Magnet in Its Iron Return Yoke
Coil diameter, m
Coillength, m
Number of turns
Design central induction, T
Design current, A
Magnet coil inductance, H
Current density J in superconductor matrix at design current, A/m 2
Magnetic energy stored at design current, J
EJ2 productat design current, JA 2fm 4
Maximum charge voltage, V
Minimum charge time to design current, s
2.172
3.295
1772
1.5
2225
4.41
6.87 X 108
10.91 X 106
5.15 X 10 24
5
2000
196
M. A. Green, P. H. Eberhard, R. R. Ross, and J. D. Taylor
Fig. 2. Winding of superconducting coil onto epoxy-cast ultrapure aluminum layer.
CONSTRUCTION OF THE TPC MAGNET
Construction of the TPC magnet began during the summer of 1978 with the
fabrication of a 9.55-mm-thick 1100-0 aluminum bore tube, which is one of the
shorted secondary circuits used for quench protection (see Fig. 1). A layer of 600
turns of ultrapure aluminum, insulated turn to turn with dacron cord, was wound on
the bore tube. The ultrapure aluminum, which is in the form of a 3-mm-diameter
wire, has a residual resistance ratio at 4.2 K of at least 1500. A great deal of care bad
to be used while winding the ultrapure aluminum because this material deforms at
almost no stress, resulting in increased resistivity of the aluminum at low temperature. Once the ultrapure aluminum layer was wound, it was vacuum impregnated in
epoxy resin.
The cast ultrapure aluminum layer provided a firm platform on which to wind
the 1.0 x 3.7-mm Formvar insulated superconductor. The superconductor, which
has a copper to superconductor ratio of 1.8, has over 2000 25-t.tm-diameter Nb-Ti
filaments, which are twisted one twist every 50 mm. This conductor will carry at least
3200 A at 4.2 K and 2.0 T. Figure 2 shows the superconductor being wound onto the
cast ultrapure aluminum layer.
The 1772 turns of superconductor was wound in two layers under tension of
690 N (155 1b). This prestrains the superconductor to allow it to match the thermal
contraction of the surrounding aluminum. The superconducting coil has an electrical
center tap between the two layers. (See Fig. 1 for the location of the superconductor.)
A layer of ftattened 19.1-mm 00, 3002 aluminum tube with 2-mm-thick walls is
wound over superconducting coil. The aluminum tube serves a dual function.
One-third of the turns carry two-phase liquid helium to cool the magnet, and the
layer of aluminum tube serves as an elastic support for the coil system. The latter
function Iimits the total strain of the coil package when magnetic forces are applied.
The superconductor and ftattened cooling tube were vacuum cast with epoxy resin to
form a rigid integrated structure.
CONSTRUCTION OF THE CRYOSTAT
The TPC magnet aluminum cryostat vacuum vessel has an ID of 2.04 m and an
OD at the ends of 2.44 m. The centrat section of the outer cylinder is recessed for
some drift chambers which are about 3 m long. The overalllength of the cryostat is
3.84 m. The TPC cryostat vacuum vessel not only provides vacuum for the superin-
Construction and Testing of the TPC Thin Superconducting Solenoid
197
Support Pod
Outer Vocuum
Vessel
Superconducting Coil
Pockoge
T PC Pressure Vessel
Fig. 3. Cross-sectional view of coil package within its cryostat (note support rod).
sulation but the inner wall is also an 11-atm pressure vessel which holds the
argon-methane mixture needed for the time projection chamber. A cross section
showing the coil package within the cryostat is shown in Fig. 3. This figure also shows
one of the compression support rods.
The TPC magnet coil package is insulated with multilayer insulation and has a
liquid nitrogen shield. The insulation and the shield are not shown in Fig. 3. The
superconducting coil package is connected to the outer cryostat vessel with a
bicycle-type support system of 25-mm-diameter fiberglass epoxy rods. The support
systemwill cary a Ioad of 2 x 105 N (20 tons) in any direction. The cold mass of the
coil package is about 1500 kg. The total refrigeration needed to cool the TPC magnet
coil package is estimated tobe between 10 and 15 W at 4.4 K (not including the gas
used to cool the 2500-A electricalleads).
CONSTRUCTION AND TESTING OF THE TPC CRYOGENIC SYSTEM
The TPC magnet is cooled with two-phase helium carried in the tubes around
the coil (see Fig. 1). The principle behind the cryogenic system is described in detail
elsewhere C0 ] . The TPC magnet cryogenic system consists of a 200-liter control
dewar, a conditioner dewar, and 85 m of liquid nitrogen shielded transfer lines which
carry both liquid nitrogen and two-phase helium to the TPC magnet and two
1.8-m-long compensating solenoids. The control dewar contains the helium pump
described by Green et al. [10] and a copper tube heat exchanger. The control dewar
reduces the inlet quality of the two-phase heliumentering the cryogenic distribution
system and the control dewar is a controlled buffer volume of liquid helium between
the refrigerator and the Ioad. The TPC magnet control dewar with its heliumpump is
shown in Fig. 4.
The control dewar, helium pump, and the primary transfer lines were tested
before final connection to the magnet. The measured control dewar heat leak varied
from 2 to about 6 W depending on the liquid Ievel in the control dewar. Initialtests
of the transfer line performance showed a heat leak of about 0.3 to 0.4 W /m. This
heat leak is high and there are expectations to reduce it through the elimination of
198
M. A. Green, P. H. Eberhard, R. R. Ross, and J, D. Taylor
Fig. 4. TPC magnet control dewar and helium pump.
oscillations and improved insulation. The helium pump was operated at mass ftow
rates from 8 to 40 g/s circulating through the control dewar and transfer line system.
Helium pump adiabatic efficiencies of about 50% were measured.
MAGNET POWER SUPPLY, QUENCH PROTECTION SYSTEM AND
ELECTRONIC DATA LOGGERS
The TPC magnet power supply can provide the TPC magnet with up to 3000 A
at 10 V. The power supply can charge the TPC magnetto full design field in about
40 min. The TPC power supply is a six-phase supply which is regulated on the
primary side of the transformer. The power supply has been successfully tested at full
current.
The quench protection system consists of four distinct elements: (1) the
9.5-mm-thick 1100 aluminum bore tube, (2) the layer of ultrapure aluminum, (3) a
SCR "circuit breaker" with a varistor across the Ieads, and (4) a capacitor bank which
discharges into the center tap between the two layers of the coil. The first two quench
protection systems are passive, the latter two elements are dynamic quench protection systems which require the quench tobe detected quickly. Bothof the dynamic
quench protection methods have been tested on a 2-MJ thin solenoid [ 12 ].
A microprocessor data Iogger is used to monitor twelve channels of data
simultaneously every millisecond. The data Iogger is programmed to take data in a
Construction and Testlog of tbe TPC Tbin Superconducting Solenoid
199
set sequence for 10 s after a quench has been detected. The magnet coil package has
the following instrumentation built into it: (1) ten small coils, which can be used to
initiate a quench and measure the velocity of normal region propagation, (2) five
silicon diode temperature sensors, (3) five coils closely coupled to the superconducting coil which measure the change of magnetic flux during a quench, and (4) three
voltage taps at the coil ends and at the center tap. The data from the instrumentation
built into the coil package is transmitted to the data logger. The data stored in the
data logger are then processed by the TPC experiment computer.
CONCLUSIONS
Tests on the completed TPC magnetwerein preparation in mid-1979 and the
extent of passive quench protection afforded by the design was not known. Tests of
the TPC magnet without iron are scheduled during the fall of 1979. Tests of the TPC
magnet with iron at SLAC are scheduled to occur in the spring of 1980.
ACKNOWLEDGMENTS
The authors wish to acknowledge the efforts of A. Barone, D. Coyle, and W. Wenzel of the LBL
assembly shop. They wish to acknowledge the engineering effort of P. Miller, W. Burns, and B.Garfinkel
of the LBL Mechanical Engineering Department. They thank C. Covey and H. Van Slyke for continuous
effort expended building the magnet cryogenic distribution system. G. Gibson and R. Smits are
acknowledged for their rote in the development of the TPC Magnet electronics systems. This work was
performed under auspices of the United States Department of Energy.
REFERENCES
1. "Proposal for a 4'71" Magnetic Detector for PETRA (CELLO)," DESY, IEKP Karlsruhe, MPI
München, Orsay, Paris University, Saclay (August 1976).
2. M. Morpurgo, Cryogenics 17(2):89 (1977).
3. M. Morpurgo and G. Posso, Cryogenics 17(2):87 (1977).
4. M. A. Green, in Proc. 6th Intern. Conference on Magnet Technology, ALFA, Bratislava,
Czechoslovakia (1978), p. 429.
5. R. C. Wolgast, H. P. Hernandez, P. R. Aron, H. C. Hitchcock, and K. A. Solomon, in Advances in
Cryogenic Engineering, Vol. 8, Plenum Press, New York (1963), p. 601.
6. M. A. Green, Doctoral Dissertation, University of California, Berkeley, California (1977).
7. M. A. Green, W. A. Burns, P. H. Eberhard, G. M. Gibson, P. B. Miller, R. R. Ross,R. G. Smits,andJ.
D. Taylor, in Proc. 7th Intern. Cryogenic Engineering Conference, IPC Science and Technology Press,
Guildford, England (1979), p. 86.
8. M.A.Green,P.H.Eberhard,J.D. Taylor, W.A. Burns,B. Garfinkei,G.H. Gibson,P. B. Miller,R.
R. Ross, R. G. Smits, and H. W. Van Slyke, IEEE Trans. Magn. Mag-15(1):128 (1979).
9. P. H. Eberhard, M. Alston-Garnjost, M. A. Green, P. Lecomte, R. G. Smits, J. D. Taylor, and V.
Vuillemin, in Proc. 6th Intern. Conference on Magnet Technology, ALFA Bratislava, Czechoslovakia
(1978), p. 654.
10. M. A. Green, W. A. Burns and J. D. Taylor, in Advances in Cryogenic Engineering Vol. 25, Plenum
Press, New York (1980), p. 420.
11. J. D. Taylor, M. Alston-Garnjost, P. H. Gibson, M. A. Green, B. Pardoe, M. Pripstein, R. R. Ross,
and R. G. Smits, IEEE Trans. Magn. Mag-15(1): 855 (1979).
D-5
SUPERCONDUCI1 NG MAGNET SYSTEM
FOR TUE SPIRIT COSMIC RAY
SPACE TELESCOPE
M. A. Green and J. M. DeOiivares
Lawrence Berkeley Laboratory
Berkeley, Califomia
and
G. Tarle, P. 8. Price, and E. K. Shirk
University of Califomia
Berkeley, Califomia
INTRODUCfiON
The identity of the source of the cosmic radiation is one of the oldest and most
interesting unanswered questions of 20th-century physics. While it has become
increasingly clear that these energetic particles owe their existence to some of the
most violent processes that occur in our galaxy (e.g., supemovae), a detailed
understanding of the cosmic ray source and the conditions of galactic propagation
has not been achieved. Of particular interest in this regard is the isotopic composition
of the cosmic radiation since nuclear abundance anomalies would provide the most
exciting clues as to their nuclear origin. The iron isotopes provide the most fruitful
candidates for such a study since they are both abundant and are least modified by
galactic transport. To date the most accurate isotopic studies of the iron group cosmic
rays CJ have ruled out large deviations from solar system source composition. In
order to achieve a convincing separation of the isotopes of iron it is necessary to
design an instrument which can collect over 104 iron nuclei and achieve a mass
resolution of u :5 0.15 amu.
Three important developments have made the design of such an instrument
possible: (1) With considerable impetus from the new generation of accelerators,
magnet and cryogenic technology has reached the stage where very large volumes
can be filled with uniform fields in excess of 2 T; (2) A track recordingplasticdetector
made of CR-39 has been developed
that is sensitive to minimum-ionizing
particles of the so-called very heavy group (20 :S Z :S 30) has very good charge
resolution, yields etched tracks of very high optical quality, and can be made in films
thin enough that multiple Coulomb scattering can be negJ.ected; and (3) the advent of
the space shuttle will make it possible to lift payloads weighing many tons into orbit
for periods of several weeks.
eJ
200
Supercoadudin1 Mapet System for tbe SPIRIT Coamic Ray Space Telescope
201
One of the authors (GT) has conceived of an instrument (SPIRIT) which
capitalizes on these recent developments and can achieve the required collecting
power and resolution in a 10-day shuttle ßight using only passive components. A
three-tiered passive hodoscope consisting of track-recording plastic with a thin
(60-"m) centrallayer will record the trajectories of cosmic ray particles through a
magnetic field with an average strength of 2 T. These particles will be traced to their
end of range in a stack of CR-39 where their charge will be determined by
measurements of etched cone length. The measurement of magnetic rigidity in
combination with the measurement of range will b"e used to determine particle mass.
THE SUPERCONDUCfiNG MAGNET
In order to achieve the resolution and collecting power necessary to meet the
experimental objectives of SPIRIT, a superconducting magnet with an average field
of 2 T over a control volume of 1 m 3 is needed. The control volume must be clearly
accessible to cosmic radiation entering from a polar angle from 0 to about 45° (see
Fig. 1). Spatial gradients need to be kept below 4 T/m, so that shifts in detector
orientation expected during flight will not result in a degradation of resolution. The
entire apparatus must be contained in the space shuttle orbiter cargo bay which has a
dynamic envelope diameter of 4.57 m.
The proposed magnet consists of six coils. The four inner coils generate a
uniform high field over the control volume. The two outer coils will generate a
smaller field over a larger volume so that the entire assembly will have a zero net
dipole moment, which results in a negligible distant field.
The design of the SPIRIT magnet system is similar in concept to the highcurrent-density type of magnet which has been under development for the last four
years 5 ]. This development work has come to fruition with the construction of the
2-m-diameter, 3.3 m long, 1.5-T thin solenoid which is designed to operate at a
currentdensityof7 x 108 A/m 2 andatastoredenergyofgreaterthan 10 MJ[5 ]. This
design concept, which is used in the TPC solenoid [5], is particularly applicable for
use in space.
The SPIRITmagnet has the following characteristics: (1) Intrinsically stable
high-current-density superconductor is used, (2) quench protection is based on the
use of LBL shorted secondary concept, (3) cooling of the superconducting magnet is
e-
1~
Fig. 1. Cross-sectional view of SPIRITexperiment showing the
six-coil superconducting magnet system.
202
M. A. Green, J. M. DeOiivares, G. Tarle, P. B. Price, and E. K. Sbirk
done with pumped two-phase helium, and (4) the magnet coil, the shorted secondary,
and the cooling system are integrated into a single package which is contained within
a single cryostat vacuum vessel.
Large currents are required in the four inner coils in order to generate the 2-T
induction over the volume of the experiment and meet the requirement for clearly
accessible solid angle. As a result, peak inductions within the superconductor will
approach 8 T. Therefore, it is proposed that the four inner coils be wound with
prereacted multifilamentary Nb 3 Sn. The two outer coils, which carry lower currents
would use multifilamentary Nb-Ti conductor. Electrically, the six coils are connected
in series; the loop is closed by a persistent switch. The SPIRITmagnet would operate
in the persistent mode for the entire 10 days of the shuttle ßight.
Table I shows the basic parameters of the six coils. The placement of the coils in
the magnet is shown in Fig. 1. There are three types of coils (there are two coils of
each type). The four inner coils carry over 11 x 106 A in order to generate 2 Tover
the experimental volume of 1 m 3. As a result, the use of Nb 3Sn conductor is
proposed. If one reduces the average induction in the experimental region from 2 to
1.5 T, the current in the inner coils is reduced to 8.2 x 106 A. The peak induction in
the coil is reduced to 6.0 T which permits Nb-Ti conductor to be used instead of
Nb3Sn.
Table II presents the electrical parameters of the six coil magnet system shown
in Fig. 1. The proposed SPIRITmagnet has an inductance of 85.1 H. When the
central induction is 2 T, the magnetic energy stored in the coil system is just over
34 MJ. It is proposed that the coil superconductor be operated at a current density of
3 x 108 A/ m 2 • The proposed conductor current density is about six tim es higher than
the conductor current density normally used in a magnet with a 34-MJ stored energy.
(Typical superconducting magnets with a stored energy of 34 MJ use cryostable
conductors with a matrix current density of less than 5 x 107 A/m 2 .) The high
conductor current density is necessary in order to reduce the mass of the magnet
system. Table 111 presents the parameters for the superconductor proposed for use in
the SPIRIT magnet.
The proposed operating current density and high stored energy result in a high
EJ 2 product, where E is stored energy and J is superconductor matrix current
density. Thus, it is proposed that a well-coupled secondary circuit made from very
pure aluminum be used for quench protection. The shorted secondary quench
Table I. Basic Parameters of tbe Three Types of Coils Proposed for the SPIRIT
Superconducting Magnet System
Parameter
Inside diameter, m
Outside diameter, m
Distance from center, m
Coil package length, m
Coil package total current, A
Number of turns
Current per turn, A
Peak induction in the coil package, T
Superconductor type
Coils
1Aand lB*
Coils
2A and 2B*
Coils
3A and 3Bt
0.800
1.100
0.600
0.400
2.484 X 106
2760
900
-8.2
Nb 3Sn
1.100
1.400
0.750
0.250
3.096 X 106
3440
900
-7.2
Nb3 Sn
1.892
2.292
1.250
0.200
-1.620 X 106
1800
-900
-4.0
Nb-Ti
* Inner coils which produce the 2-T field within the experimental volume.
t Outer coils which cancel the dipole moment generated by the inner coils.
Superconducting Magnet System for the SPIRIT Cosmic Ray Space Telescope
203
Table II. Electrical Parameters for the SPIRIT Superconducting Magnet System
(Six Coils Hooked in Series)
Integrated average induction within the experiment, T
Experimental volume, m3
Magnet system design current, A
Magnetsystem self-inductance, H
Magnet system stored energy at its design current E, J
Current density in the superconductor matrix J, A/m 2
El 2 productat the design current, JA 2 /m 4
2.0
-1.0
900
86.2
34.3 X 106
3 X 108
3.1 X 1024
protection system is used on the 2-m-diameter TPC solenoid which has an EJ 2
product of 5.4 x 10 24 JA 2 /m 4 • The shorted secondary concept affects the quench
process in the following ways:
1. The shorted secondary causes the coil current to shift from the coil to the
secondary circuit. As a result, there is less current in the coil to contribute to the
conductor bot spot.
2. The shorted secondary circuit absorbs a substantial amount of the magnet
stored energy. In the proposed magnet system, the shorted secondaries are expected
to absorb about 70% of the magnetic energy (this energy will be shared by all of the
coils, not just the one that went normal).
3. The shorted secondary will cause "quench back" in the other coils when one
of the six coils turnsnormal through ordinary quench propagation. ("Quench back"
is the process by which superconducting magnet coils are driven fully normal by the
shortened secondary winding [4 ].) Quench back is a key element in the protection of
thin high-current-density solenoids which have been built at LBL.
The shorted secondary circuit would be insulated from the superconductor. It is
desirable that inductive coupling between the coil and the secondary circuit be
maximized. It is proposed that the shorted secondary circuit be made from ultrapure
aluminum (0.99999 pure or better) which has a residual resistance ratio at 4.2 K and
0 T of about 2000. Aluminum has a much lower magnetoresistance at 8 T than
Table III. Properties of Superconductor Proposed for SPIRIT Superconducting
Magnet System
Nb-Tit
Uninsulated matrix dimensions, mm
Insulated matrix dimensions, mm
Insolation type
Copper-to-superconductor ratio
Bronze-to-unreacted-Nb ratio
Number of filaments
Filament diameter, m
Twist pitch, mm
Averagematrix resistivity at 4.2 K (!1-m)
Current capacity at 4.2 K, A
at ST
at lOT
3X1
3.1 X 1.1
epoxy
-1 to 1
-2.8 to 1
>30,000
-4
-so
-10-9
3900
1100
* Multifilamentary Nb 3 Sn is proposed for the four inner coils
3X1
3.1 X 1.1
Formvar
-1.8 X 1
NA
-2000
-2S
-2
-so
X
10- 10
1600
1A, 1B, 2A, and 2B. This conductor has
some copper in the matrix.
t Multifilamentary Nb-Ti is proposed for the two outer coils 3A and 3B.
M. A. Green, J. M. DeOUvares, G. Tarle, P. 8. Price, and E. K. Shirk
204
Aluminum shorted secondory
circuil
·®
Nb1 Sn supe rconduct ing
coils
Eleclri col insulotion •
\
®
CJ
1\1\r
®
®
\ Helium cooling tubes
®
\
\
\
\
\
SC ALE
10
\
\
15
\
20 CM
\
!.\\
Fig. 2. Cross section of proposed inner coils (coils 1
and 2) for the SPIRIT magnet.
copper. lt also has one-third the density. At full field, one can expect the shorted
secondary circuit to have a residual resistivity ratio greater than 300. As a result, the
shorted secondary circuit is expected to have a time constant in excess of 30 s. If the
coupling between the coil and the shorted secondary circuits meets expectations,
effective shifting of the coil current will occur.
The proposed coils will have the superconductor, shorted secondary, and a
forced-ftow tubular cooling system combined into an integrated package. The
proposed superconducting coils are designed to be weil insulated with insulation to
ground adequate to 10 kV or more. Therefore, the superconductor, shorted secondary, and cooling system aretobe cast in epoxy resin. This technique has been used
successfully in the TPC solenoid and three 1- and 2-m-diameter test coils [6 ] . Figure 2
shows a proposed arrangement of superconductor, shorted secondary circuit, cooling
tube, and mechanical support inside of the two inner coils.
The shield coils not only effectively eliminate magnet moment, but also greatly
reduce stray magnetic field in the shuttle bay. lt is proposed that the superconducting
magnet be located at the rear of the space shuttle bay. The expected stray magnetic
induction in a region normally housing astronauts is expected to be around 10-4 T.
1t is proposed that coil 1 and 2 (in each half) be attached directly (see Fig. 2). A
compressive force of 7. 7 x 105 N (77 metric tons) is expected between the two halves
(between coils lA, 2A, 3A and coils lB, 2B, 3B). This forcewill be carried with the
cold column struts between coil lA, 2A and coil lB and 2B. The columns are
arranged so that there is full access of the cosmic rays to the experiment. A tensile
force of 5.8 x 106 N (580 tons) is expected between each of the two outer coils and
their companion inner coils. This force will be supported with a continuous web of
metal between the outer and inner coils. The six coils are expected to act as a rigid
frame which will have a cold mass of about 4000 kg (the helium tanks and the coil
cryogenics will attach directly to this frame).
THE CRYOSTAT AND CRYOGENIC COOLING SYSTEM
The proposed superconducting magnet coils will be cooled using two-phase
helium pumped through tubes in the coil package (see Fig. 3). The two-phase helium
will be circulated from a separate helium storage tank located at the end of the
experiment (see Fig. 1). Forced tubular cooling offers a number of advantages over
the more conventional bath cooled systems CJ:
1. Tubular cooled systems can be cooled easily from room temperature by a
refrigerator which is external to the cryostat system.
Superconduding Magnet System for the SPIRIT Cosmic Ray Space Telescope
105
----1------_:• •=·~ --'
Gas cooled rod1at1on sh1elds
r
·------
-----,I
I
I
I
I
I
I
I
I
I
I
____________ j
Fig. 3. Simplified schematic diagram of SPIRIT
magnet helium tank and distribution system.
L
~~0 ~e; h~u: ~e~t :c;:n~r- "fc~o-:;a~
storage tank
\ vocuum
boundary
I
I
--I
2. Only a small fraction of the liquid helium is in direct thermal contact with
the superconductor at any one time during a quench. The tubular cooling system can
contain the pressure rise owing to this small amount of helium. Helium boil-off
during a quench is orderly and weil controlled.
3. In conventional systems, diamagnetic repulsion of the helium in a weightless environment would result in a loss of liquid cooling capacity [8 ]. Tubular cooled
coils would contain two-phase helium which is in direct contact with the coil at all
times.
4. The design of the cryostat is simplified. Many of the cryogenic safety
problems found in conventional bath systems are eliminated.
The forced two-phase tubular cooling system requires a helium pump to
circulate the helium from the helium storage tank located at the end of the magnet.
The entry to the pump is located near the zero field point in the tank. As a result,
diamagnetic repulsion insures that liquid heliumwill always be delivered to the pump
entry [9 ]. The pump proposed is similar to a reciprocating bellows-type pump which
The pump will be designed to pump 1.0 g/s across a
has been under development
pressure rise of 2 x 104 Pa (0.2 bar). lt is expected that such a pump will require
about 1 to 1.5 W of refrigeration. (This is equivalent to 1.4-2 liters/hr of liquid
helium from the tank.)
A 2500-liter helium tank can be built into the end of the coil as shown in Fig. 1.
The coils and tank would be thermally isolated with fiberglass epoxy spacers. The
coils and tank would be insulated with a combination of superinsulation and shields
which use the helium boil-off from the tank. A total heat leak of 2 to 3 W is expected
into the 4-K region producing a helium boil-off rate of about 5 to 6 liters/hr. The
total helium inventory in the tank should be enough for about 20 days.
n.
CONCLUSIONS
The proposed SPIRIT superconducting magnet system appears to be within the
state of the art. A coil system which uses multifilamentary Nb 3 Sn and Nb-Ti is similar
to the proposed fusion magnets. Forced two-phase cooling and quench protection
using shorted secondary circuits has been demonstrated. Forced-cooled high-current-density superconducting coils are weil suited to space application. The
development of this technology and the space shuttle make possible the study of
some of the fundamental physics which occurs in deep space.
206
M. A. Green, J. M. DeOiivares, G. Tarle, P. 8. Price, and E. K. Sbirk
ACKNOWLEDGMENTS
The authors acknowledge work done by P. H. Eberhard and others of the Lawrence Berkeley
Laboratory. Much of the research which has led to this report was performed under the auspices of the
United States Department of Energy and the Space Seiences Laboratory of the University of California at
Berkeley.
REFERENCES
1.
2.
3.
4.
5.
6.
7.
8.
9.
G. Tarle, S. P. Ahen, and B. G. Cartwright, Phys. Rev. Lett. 41:771 (1978).
B. G. Cartwright, E. K. Shirk, and P. B. Price, Nucl. Instrum. Meth. 153:457 (1978).
M. A. Green, in Advances in Cryogenic Engineering, Vol. 21, Plenum Press, New York (1975), p. 24.
M. A. Green, Doctoral Dissertation, University of California, Berkeley, California (1977).
M. A. Green, P. H. Eberhard, J. D. Taylor, W. A. Burns, B. Garfinkel, G. H. Gibson, P. B. Miller, R. R.
Ross, R. G. Smits, and H. W. Van Slyke, IEEE Trans. Magn. Mag-15(1):128 (1979).
M. A. Green, P. 8. Miller, and W. F. Wenzel, in Nonmetallic Materials and Composites at Low
Temperatures, Plenum Press, New York (1979).
M. A. Green, W. A. Burns, and J. D. Taylor, in Advances in Cryogenic Engineering, Vol. 25, Plenum
Press, New York (1980), p. 420.
W. L. Pope, G. F. Smoot, L. H. Smith, and C. E. Taylor, in Advances in Cryogenic Engineering, Vol. 20,
Plenum Press, New York (1974), p. 47.
W. L. Pope, L. H. Smith, and G. F. Srnoot, U. S. Patent 4027494 (1977).
D-6
A MAINTAINABLE SUPERCONDUCTING
MAGNET SYSTEM FOR TOKAMAK
FUSION REACTORS*
S. Y. Hsieh, G. Danby, J. R. Powell, P. Bezler,
D. Gardner, and C. Laverickt
Brookhaven National Laboratory
Upton, New York
and
M. Finkelman, T. Brown, J. Bundy, T. Balderes,
I. Zatz, R. Verzera, and R. Herberman
Grumman Aerospace Corporation
Bethpage, New York
INTRODUCTION
In the search for inexhaustible energy sources, nuclear fusion energy has
received much attention in the past decades. Of the various confinement approaches,
the Tokamak is by far the most developed fusion concept. The recent achievements
in plasma research at major U. S. fusion laboratories promise demonstration of the
scientific feasibility of magnetic fusion within the next few years.
In the authors' view, the present route towards the design and construction of
superconducting magnets for tokamak reactors, although probably satisfactory for
experimental devices, will not be acceptable for commercial fusion power plants.
One may accept a certain risk of malfunction for a one of a kind, short lifetime, fusion
device, but extremely reliable, maintainable systemswill be required for commercial
plants.
The DEALSmagnetapproach Cl has been proposedas a way to increase the
reliability and ease of maintainance of magnetic fusion reactors. The DEALS
[demountable externally anchored low stress] magnet system uses demountable
superconducting joints, so that if any portion of the magnet fails, it can be replaced
relatively quickly. In addition, the conductor / support structure assembly is arranged
so that the conductors transfer the magnetic forces on them to an external reinforcement structure. The load transfer device and demountable joints are designed
so that the reinforcement structure operates at relatively high tensile stress/strain
levels, while the conductors operate at relatively low compressive strain levels. This
concept has been investigated during the past two years by a joint Brookhaven
National Laboratory /Grumman Aerospace Corporation study team. A design study
* Work performed under the auspices of the Department of Energy.
t Consultant to Brookhaven National Laboratory.
207
208
S. Y. Hsieh et al.
of a high field ignition test reactor (HFITR) has been carried out, with preliminary
experiments on small-scale demountable joints. The conclusion isthat demountable
superconducting magnet systems appear feasible for Tokamak fusion reactors.
Extensive development work is required, however, before practical large magnet
systems can be designed and constructed. The most important need appears to be for
further experiments on the mechanical and electrical properties of relatively large
scale, prototype, superconducting, demountable joints to establish a data base for
design and construction. The balance of this paper describes the latest design
approach for the DEALS magnet involving movable pressure-contact, superconducting joints and experiments on such joints. It should be pointed out that these
latest design efforts, although they represent improvements over earlier concepts,
should not be regarded as the final optimum approach for a demountable magnet.
[ 2]
CONCEPT OF A MAINTAINABLE, DEMOUNTABLE,
SUPERCONDUCfiNG MAGNET SYSTEM
The tokamak fusion reactor is a very complex system consisting of a TF magnet,
poloidal coils, plasma chamber, etc., all interlocked together. If any component of
this system fails, it will be almost impossible to service or to repair the component
without making a major disassembly of the highly radioactive reactor. At a minimum, there will be a prolonged plant shutdown of many months, and it may not be
feasible at all. In this event the capital investment in the reactor will be lost.
In the DEALS magnet concept, TF magnet coils are formed from removable
coil segments. These segments can be mass produced at a central facility and then
shipped to power plant construction sites for joining.
Figure 1 shows a cross-sectional view of a typical DEALS conductor assembly
inside a coil case. The conductors are wide (83 cm), thin (0.8 cm) plates of copper
MAIN JOOLANT CHANNEl
0.8cm VOIO
CERAMIC SIOE INSUL.
ClEARANCE GAPS
0.3 cm CERAMIC INSUl. (491 TYP
0.8 cm CONDUCTOR (501 TYP
T
Fig. 1. Coil case design.
Maintainable Superconducting Magnet System for Tokamak Fusion Reactors
209
/'... ENGAGE EITHER THE
l r WAY AS SHOWN OR
-====7!
f-
HORIZONTALLY
DEPENDI NG ON
DESIGN
PRETINNED
SURFACES
Fig. 2. Schematic of idealized demountable joint.
Not drawn to scale.
with a transposed superconducting braid at the midplane. The conductor is formed
by soldering the superconducting braid between two copper plates. Coolant grooves
are arranged on the conductor surfaces for heat transfer to a liquid helium bath. The
conductors are cryostable with maximum heat ftuxes in the range of 0.3 to 0.4 W /cm2
when all the current ftows into the copper stabilizer. The conductors in each coil
segment are typically several meters long. At the ends, one-half of the copper
stabilizer is milled away to form a region where the demountable jointwill be made
when the coil segments are put together to form the complete coil. The current passes
from a given conductor to the next by transfer through the overlapping joint area,
which is on the order of 3 to 4 x 103 cm 2 in area. The conductors are arranged so that
the completed assembly forms a multiturn coil with the turns in series. Conductors
are insulated from each other and from the coil case by ceramic or epoxy-fiberglass
plates (see Fig. 1). A schematic diagram illustrating the configuration of the multiple
turn joints is shown in Fig. 2 and described in detail elsewhere [ 1•2 ].
The segmented coil approach is a key feature oftheDEALS magnet design and
has important benefits in terms of accessibility and maintainability for tokamak
reactors. Figure 3 illustrates how all parts of the TF magnet and associated reactor
system can be accessed and maintained.
Sequence 1
The center tension post is first lowered into place and embedded in the concrete
foundation. The tension post can be Iowered into place as one section or each of its 16
components can be separately lowered into place if it is necessary to reduce the
maximum Ioad on the overhead crane. The lower collar and the insulator ring are
then lowered into a temporary location in the basement and the Iower poloidal field
.. \ •
\y: .
EF/OH COIL RING ASSY
~ : · , lf' •
:·~~~~·.
~ING
INSULATOR
t
. .i
._I
I
I
•,
• -
. - . "l .•
)
2
\IN80 LWR TOROUE
SUPPORT STRUCTURE
MAGNET LEG " "
VEATICAL INBO
INBD VERTICAL TOROUE
_-I/SUPPORT STRUCTURE
;j i -I
Iu__~
II
.I
·
·..
BUCKING COLUMN/INNER
'OROUE RING ASSY
•
INSULATO~
LOWER TOAOUE PLATE/
BLOCKS
POLOIOAL FIELD COILS
' I,
•I
'
~
... •
t. ,
POST
ASSEMBLY
SEOUENCE- 1
CENTE~
uPR
TO~OUE
'LATE
4
UPR OUTBO TOROUE
SUPPO~T STRUCTURE
UPR OUTBD MAGNET LEG
5
OUTBD VERT ICAL MAGNET LEG
OUTBO VERTICAL
TOROUESUPPOATSTRUCTURE
VACUUM VESSEL SHIELDING
:""'
"Q
1:1"
r...
~
:<
s
I
I
1
~
(
-'--------
(
~·
~
____,... .
~
.
< _j .,
.> - \
\
Fig. 3. Total assembly sequence 1 to 6.
lWR OUT80 MAGNE T lE G
FINGER JOINT AAEA
VESSEl iLWR IN PLACIEI
3
P'REASSEMBlED VA.CUUM
I
OUTBO STRUCTURAL
SUPPORT ASSV
6
I-I~ INSUlATOA BLOCKS
I
UPR INSULATOR RING
UPA AlETA lHING AING
N
....
....
I
~
:::1
f
111"
ä
=-
~
!!
i
fi
i
a
8'
;
i
~
ii'
J
::
212
S. Y. Hsieb et al.
coils and lower torque plate/insulator blocks are seated above the lower collar. This
entire assernbly is later repositioned during the third step in the assernbly sequence.
Sequence 2
The bucking colurnn and inner torque ring assernbly next is lowered into its final
position. The equilibriurn field and ohrnie heating coil ring assernbly is then placed
between the bucking colurnn and the tension post.
The inboard vertical, and lower torque support structures are assernbled and
each of the 16 vertical inboard rnagnet legs is then inserted into its channel and
locked into place as shown above.
Sequence 3
Each of the 16 lower inboard rnagnet legs is insulated in place and the rnating
finger joints of the rnagnet segrnents are connected. The heliurn and vacuurn Dewars
are then connected. At this point the lower outboard poloidal field coils are installed
followed by the lower outboard torque support structure. Each of the 16 lower
outboard rnagnet legs is then positioned and the rnating finger joints connected. The
lower collar assernbly is now raised frorn its ternporary position to its final position
and locked into place by the lower retaining ring followed by the vacuurn vessel,
which can be preassernbled and tested off-line if desired.
Sequence 4
At this stage the vacuurn vessel shielding is installed and the outboard vertical
rnagnet legs can now be placed in position and the rnating finger joints connected.
Sequence 5
The fifth stage in the assernbly procedure involves the installation of the upper
outboard and upper inboard torque support structure. Each of the 16 upper
outboard rnagnet legs is put in place and the rnating finger joints are connected. This
sequence is followed by lowering of the 16 upper inboard rnagnet legs into place.
Since these are the last of the rnagnet legs to be installed, rnating finger joint
connections are required at both ends of the rnagnet leg. The last step in sequence 5 is
then to place the upper torque plate and insulator blocks in the assernbly.
Sequence 6
The upper poloidal field coils, upper insulator ring and upper collar are now
lowered into position. The upper collar assernbly is then locked into place by the
upper retaining ring. This sequence rnirrors the lower collar assernbly in sequence 3.
The outboard insulator blocks are installed at this point and each of the 16
outboard structural support assernblies is wheeled into place along tracks. After each
of these assernblies is properly aligned, the assernbly sequence is finally cornpleted by
inserting the upper and lower pins as shown above.
LOW-TEMPERATURE MOVABLE JOINT APPROACH
Various types of conductor joints have been used in rnagnet coil applications,
including both soldered and pressure contact joints. Both types have been successfully used for roorn ternperature copper and low-ternperature superconducting coils.
However, these joints are usually held rigidly together by bolts, reinforcernent, and
structure supports. Low-ternperature rnovable joints have been investigated at
LASL
and MIT [4 ].
e1
Maintainable SuperconductinK Mapet System for Tokamak Fusion Reac:tors
213
A soldered type of demountable, superconducting, movable jointwas proposed
in the first DEALS studies C]; while feasible in principle, soldered jointswill require
an actively controlled type (e.g., hydraulic pistons) of Ioad transfer device between
the coil segments and the external reinforcement structure. A movable pressure
contact type joint is now favored as the best approach and forms the basis for the
HFITR DEALS design eJ and the assembly sequence shown in Fig. 2. The
overlapping regions at the ends of adjacent conductor plates are pressed together
with a modest clamping pressure to establish good electrical contact, but are free to
move slightly (-1 cm) relative to each other. This eliminates the need for actively
controlled Ioad transfer devices between conductors and the external reinforcement
structure. lnstead, simple, passive, low thermal conductivity, blocks can be used; the
movable joints then permit the conductors to move to accommodate differential
thermal and mechanical movements between conductors and the reinforcement
structure. The heat leak through the passive support blocks is quite low and permits
the use of an external warm reinforcement structure. Such a structure should be
substantially eheaper than a cold reinforcement structure.
Current transfers from one conductor to the next across the ftat overlapping
joint regions. The joint surfaces must provide adequately low electrical resistance
and permit small, slow motions without degrading either mechanical or electrical
properties.
Experiments on properties of movable pressure contact joints are described in
the following section. Two design approaches have been developed for applying
pressure on movable pressure contact type joints and these are described in the
remainder of this section. lt should be remernbered that no tensile Ioads are carried
by conductors (other than those resulting from frictional forces associated with joint
surfaces, which are small), and that magnetic forces aretransferred to the external
reinforcement structure. Relative joint movement is allowed during the following
conditions: (1) during cooldown or warmup while clamping pressure is not required;
(2) under controlled clamping pressure to achieve tolerable contact resistance when
the magnet is energized or discharged in normal operation; and (3) during a quench
or emergency shutdown situation that requires quick release of the clamping
pressure.
The design approach shown in Fig. 4 is a self-activating clamping and/or
declamping mechanism which takes advantage of both the Lorentz force which
pushes the magnet coil segmentoutward and the support structure element acting as
an elastic constraint which confines the magnet coil and pushes it inward. The ramp
mechanism (which might be curved for a desirable controlled clamping pressure) is
designed to utilize both the outward Lorentz force for clamping the joint and the
inward hoop force from the structure for declamping the joint. This will satisfy the
requirements mentioned above in (2) and (3). The movable part of the ramp
mechanism is designed to develop the initially required joint pressure. This can be
adjusted on each individual joint aftercooldown but before the magnet is energized.
A second design approach acts in a similar way to the first design except that it is
sensor activated. The activator cylinders will operate in the direction (based on the
signal) that either exerts or releases pressure on the joint. This is a simple screw
thread mechanism.
In the magnet start-up sequence, an initial preloading of the joints is applied
through the adjustable movable ramp mechanism to ensure sufficient contact area
and a low-enough resistance to permit the magnettobe energized. The current is then
built up to operationallevel and the 12 R Iosses are monitored to ensure that they are
S. Y. Hsieh et al.
214
MOVABLE RAMP
MECHANISM
(a)
n...;;;_----,~
MOVABLE RAMP
MECHANISM
PRESSURE PLA TE
SUPPORT HOUSING
PRESSURE----~~---1/
PLATE
T/F COIL FINGER
JOINT AREA
SECTION AA
(b)
Fig. 4. (a) Conceptual joint design (baseline). (b) Conceptual joint design (baseline).
Maintainable Superconducting Magnet System for Tokamak Fusion Reactors
215
within bounds. As the current increases, the electromagnetic forces on the conductors and joints increase and the conductors are permitted to move slightly in the
contact region to allow the conductor and joint stresstobe transferred to the external
support system. This is accomplished automatically by the ramp design which will
exert increasing clamping pressure on the joint when the coil moves radially outward,
taking into account the requirement of the tolerable contact resistance and degree of
joint movement at every stage of the charging process. During discharge of the coil
under normal or emergency conditions, the joint clamping pressure will be released
in the first design by the hoop force in the structure when the coils are pushed inward
or in the second design by the sensor-activated screw mechanism.
PRELIMINARY EXPERIMENTAL RESULTS
Since a movable joint is very desirable for demountable superconducting
magnets, it is important to demoostrate the feasibility of this joint concept. A small
experimental test rig, shown schematically in Fig. 5, was set up to obtain information
on some fundamental parameters concerning this type of joint. The various
components designed for these test purposes can be identified in the actual equipment shown in Fig. 6. Experimental measurements were made on a set of small
sample movable joints (4.74-cm 2 contact area), shown at the bottom of Fig. 6, to
determine electrical resistivity as a· function of surface type and contact pressure,
friction coefficient as a function of surface type and contact pressure, and effects of
surface motion on joint electrical and mechanical properties.
Fig. 5. Test rig for simulating movable
contacts.
l16
S. Y. llsieh et al.
Fig. 6. Experimental setup and sample movable joint.
A simple experimental setup (Fig. 6) permits testing the joint at various
pressures and current densities using small areas of contact surface which can be
changed as desired, either by changing the contact size or material type. Surface
conditions between the contacting surfaces can also be changed.
During a given contact test, electrical resistivity and friction coefficient were
measured both statically and dynamically (i.e., when the upper and lower contact
surfaces moved relative to each other), as a function of contact pressure. First,
contact pressure was monotonically increased from the low end of the range to the
upper, with measurements taken at a number of intermediate loading conditions.
Measurements were then taken as a function of monotonically decreasing contact
pressure; this was followed by another set of measurements under increasing
pressure conditions.
Several additional Observations can be derived from these experiments. First,
the resistance of the joint is essentially the same whether or not the joint surfaces are
moving relative to each other. This indicates that the DEALSjoints should be able to
move during Operation without adversely affecting performance, particularly since
the rates of relative motion for the DEALS application will be very small compared
to the rates in the experiments.
Second, although joint resistance decreases with increasing contact pressure, it
remains relatively low at low contact pressures, i.e., several hundred psi (-2-3 MPa),
particularly for the indium coated joints. This indicates that although moderate
clamping pressures [e.g., -600 psi (40 MPa)] may be desirable during the steady
state, fully energized period to keep joint resistance low, reduced clamping pressures
Maintainable Superconducting Magnet System for Tokamak Fusion Reactors
217
[e.g., -300 psi (20 MPa)] during the period of magnet energization or discharge
should not result in any significant heating problems.
Third, the joint resistance is much greater (one to two orders of magnitude,
depending on pressure and surface type) than the resistance of a perfect joint with no
interfacial resistance. The reason for this is not certain and needs further study. It
may relate to imperfect contact between surfaces or to some thin poorly conducting
film on the surfaces. lt is clear that the softer surfaces at the joints, i.e., those with
indium coatings, have lower resistances than those with hard surfaces. The thickness
of gold on the gold-plated copper surfaces is too small to affect their mechanical
conformity. No galling was observed on the thin indium- and gold-coated surfaces,
even when high contact pressures [i.e., -1000 psi (70 MPa)] were applied. It appears
likely that softer surfaces, or a combination of a soft and hard surface will be more
desirable for joints than hard surfaces.
Joint resistances were derived from current and voltage measurements on the
joint. The voltage measurement was compared with the voltage across a calibrated
standard resistance at the same temperature. A calibrated Ioad cell was used to
measure contact pressure on the joint. The friction coefficient was then derived from
the contact pressure and the applied torque as the joint was moved. The maximum
rates of movement between the joint surfaces was estimated tobe -1 cm/s, but no
precise measurements were taken. There was no change in joint resistance during
movement for the range of 0 to -1 cm/s. For service in aDEALS magnet, rates of
joint movement will be very small, on the order of 10- 5 cm/s during normal charge or
discharge of the magnet.
Four types of contact surfaces were tested: (1) thick indium(-20 mil)-coated
copper surfaces; (2) thin indium(- 3 mil)-coated copper surfaces; (3) thin gold-plated
copper surfaces; and (4) bare copper surfaces. Figure 7a shows the measured
resistances for the two indium surfaces, and Fig. 7b shows the measured joint
resistances for the gold-plated copper surfaces. Results for the bare copper surfaces
arenot shown; typically, resistances for the bare copper joint were a factor of 2 to 3
higher than those for gold-plated copper joints.
The thin indium surfaces give the lowest joint resistance. If the measured value
for this surface is used to calculate / 2 R joint heating fortheDEALS HFITR magnet
system, the total heating is approximately ten times greater than the value projected
in the study. The study value was estimated to be 1 kW at 4 K, which with a
refrigeration factor of 326 kWe/kW (4 K), required a refrigerationinputpower of
0.32 MW. Using the experimental electrical resistance values found forthin indiumcoated copper surfaces, total joint heating for the complete TF system would be 10
kW at 4 Kor 3.2 MW for the refrigerationpower input. Adding in the additional
refrigeration for the other thermal inputs (current Ieads, passive support blocks, eddy
current heating, etc.) the totalrefrigerationpower input is 4.4 MW. This appears to
be quite acceptable. Considering that a 1000 MW fusionpower plant will not be
much larger than the HFITR, the refrigerationpower input for aDEALS magnet
system represents less than 0.1% of the plant output. However, in a better controlled
experiment, it is likely that joint resistance can be substantially reduced by further
optimization of joint surfaces.
The measurements of friction coefficient for indium (Fig. 8a) and gold-plated
copper (Fig. 8b) surfaces indicate that the friction coefficient is relatively uniform
with contact pressure, and that the barder surface exhibits somewhat lower friction
coefficients than the softer one (-0.4 vs. 0.5). The friction coefficient for the indium
surface is quite acceptable, however, in terms of aDEALS joint.
S. Y. Hsieh et al.
118
• STt.TIC
0 OYNAMIC
3.7
t
CXlNTIICT AREA • 474 al0' 4 m1
fXP I IIIIITIAL INCREASIIIIG
PRESSURE CYCLE
V>
::1:
r
03
0
0
u
i
.
w
u
z
0------
02
"'
>-
V>
;;;
!I!
THICI< INDIUM 13·2.3 ·78)
-~
a::
o--------<:l
0 .1
• STATIC
V>
:::<
r
086
0 DYNAMIC
f
0
0
a::
u
CXlNTIICT AREA • 4 74 al0' 4 m1
:i'
w~
02
~
~ THIIII 1NDIUMI4· 20 ·78)
:!
V>
;;;
~
01
1000
4000
3000
20CIO
APPL IED LOAD, NEWTOIII
(a)
176
t
RUIIII
RUN 2
RUIII3
"':::<r
INITIAL INCRE ASING
PRESSURE CYCLE
DECREASING PRESSURE
CYCLE
INCREASING PRESSURE
CYCLE
• STATIC
0 DYNAM IC
05
CXlNTIICT AR(A• 474 a10' 4 m1
0
0 04
a::
u
i
~
t:l
z
:!
03
"' 02
~
a::
Dl
1000
2000
3000
APPLI[D LOAD, NEWTON
4000
(b)
Fig. 7. (a) Contact resistance as a function of applied clamping pressure
(indium-plated surfaces). (b) Contact resistance as a function of applied
clamping pressure (gold-plated surfaces).
Maintainable Snperconducting Magnet System for Tokamak Fusion Reactors
219
I
~
1
z
8
INDIUM ON INDIUM (4·20·18)
0
f=
u
er
...0...
0
0
llt CYCLE·UP
2 n4l CYCLE ·DOWN
1-
z
w
Q
......
w
0
u
.2
.I
0
1000
2000
4000
3000
APPLIEO LOAD , NEWTON
(a)
CONTACT AREA = 4 74
x I0" 4 m1
z
0
i=
!::!
......0
0:
.4
1-
z
....
u
o I st CYCLE • UP
.3
0
ii:
....0
(.)
2nd CYCLE- DOWN
0 3 rd CYCLE ·UP
1&.
.2
.I
0
1000
2000
3000
4000
APPLIEO LOAD, NEWTON
(b)
Fig. 8. (a) Coefficient of friction as a function of applied clamping pressure (indium-plated
surfaces). (b) Coefficient of friction as a function of applied clamping pressure (gold-plated
surfaces).
ZlO
S. Y. llliell et al.
Tbe eflect of joint size on electrical and mechanical properties was not investigated. DEALSjoints will have approximately 103 greater contact area than the
small-scale tests described here, and a future development program should examine
the eflect of scale. It is likely that if there is any eflect, it will be related to the ability to
manufacture large ftat joint surfaces and maintain uniform pressure over this large
area. Tbe eflect of magnetic field on joint properties was not investigated either and
would have to be examined in any development program.
Tbe results of the movable joint tests give strong indication that large-scale
movable joints can probably be developed. Tbe next step toward the development of
the DEALSmagnet concept is to build a small prototype coil containing several turns
of about 1-m length with movable joints. Operation of such a prototype coil would
demoostrate the practicality oftheDEALS system on a sufficiently large scale that it
could be considered as a viable alternate to the mainline wound coil approach.
SUMMARY AND CONCLUSIONS
Tbe DEALS magnet concept has significant implications and potentially
important benefits for magnetic fusion reactors. DEALS magnets are expected tobe
readily maintainable if failures occur, they can be demounted to improve accessibility to other reactor systems (blankets, beam lines, etc.). Tbeir capability to
operate at low conductor stress should improve reliability. Magnet components can
be made, produced, and assembled at the construction site with minimum field
work-elimination of winding stress allows the use of brittle superconductors and
insulators. High-current conductors can be employed for rapid energy extraction
capability. Pulsed field losses are low, even for heavily stabilized conductors.
Design studies indicate that adequate structural support should be readily
achieved, practical conductors appear fabricable, cryostable Operation is feasible,
and estimated refrigeration requirements are reasonable. Tbe primary technical
issue for the DEALS concept appears tobe the electrical and mechanical feasibility
of the demountable superconducting joint. Design studies of an attractive joint
option, the movable pressure contact type, have been carried out along with
experimental measurements of the electrical and mechanical properties of smallscale movable joints. Tbis type of joint allows current tobe carried while overlapping
joint surfaces move slightly to accommodate differential thermal and mechanical
movements in the conductor/support structure assembly. Mechanisms for applying
moderate, adjustable clamping pressures to multiturn joints have been devised.
Experiments indicate that the electrical resistivity of such joints is not aflected by
relative motion of the surfaces, that joint / 2 R heating is sufficiently low to yield
practical refrigeration requiremeqts, that frictional coefficients are reassurably low,
and that joint surfaces are not adversely aflected by the applied clamping pressures
and relative motion.
On the basis of the studies and experiments, it is concluded that the DEALS
concept appears feasible. More work should be carried out, including tests of larger
joints to develop the engineering base for the design and construction of large-scale
systems.
ACKNOWLEDGMENTS
The authors would üke to thank the foUowing people for their contribution to this paper: J. Jackson,
J. Allinger, and J. Weisenbloom for their designing of the test rig and making of the experimental
measurements on a series of sample joints, S. Majeski for the drawings, and P. Walton for the typing.
Maintainable Superconducting Magnet System for Tokamak Fusion Reactors
221
REFERENCES
1. J. Powell, S. Y. Hsieh, and J. Lehner, "DEALS: A Demountable Externally Anchored Low Stress
Superconducting Magnet System for Fusion Reactors," BNL Rept. 50616 (1977).
2. J. Powell, S. Y. Hsieh, P. Bezler, D. Gardner, M. Reich, C. Laverick, M. Finkelman, T. Brown, J.
Bundy, R. Herberman, and C. H. von Keszycki, "A Niobium-Tim DEALS Toroidal Magnet System
foraHigh Field Ignition Test Reactor," BNL Rept. 50802 (1977).
3. J. Lindsay and D. H. Whitaker, Los Alamos Scientific Laboratory, private communication.
4. Y. Iwasa, Massachusetts Institute of Technology, private communication.
D-7
PROTOTYPE LOW-CURRENT
SUPERCONDUCDNGQUADRUPOLE
MAGNET FOR FERMILAB'S
HIGH-INTENSITY LABORATORY*
W. Craddock, R. W. Fast, P. Garbindus, and L. Mapalo
Fermi National Accelerator Laboratory
Batavia, Illinois
INTRODUCDON
A low-current saddle-type quadrupole magnet using very similar cable and
design criteria as its companion dipole Cl has been built and tested in a vertical
cryostat. The low current is achieved by taking the 15 film-insulated strands of a
cable and connecting them in series. With currents of approximately 250 to 350 A, it
becomes economically possible to use a separate power supply for each of the
magnets in the beamline. Magnetparametersare given in Table I.
COIL FABRICATION
Because electrical insulation must be maintained between the individual strands
of the cable rather than just between turns, extreme care must be used in the
manufacturing of these coils. These coils have, therefore, been built so that they are
wound as tightly as possible without damaging the insulation. They must be
eventually compressed with moderate preload or thermal pressures in all directions.
The quadrupole field was obtained using the ~ rule [2 ]. However, each of the four
layers consist of two coils wound from two separate spools of wire. In order to make
the transition between layers, adjacent layers have their coils wound around poles
which are 90° apart. Thus the coils of layers one and three and the coils of layers two
and four are directly above one another. Figure 1 shows layers three and four. The
end turns of layer three are just barely visible under the Kevlar banding. This
technique minimizes the number of wire splices. It also reduces the magnetic field in
the coil ends by separating the end turns and distributing the fJ component of current
in opposing directions.
Bach of the coils was wound with 60 lb of tension directly on the bore tube
around G-10 fiberglass-epoxy poles. As each half-turn was laid down, it was
clamped along its length subjected to a pressure of 30 psi. With both half-turns down,
the pressure was increased momentarily to 300 psi. This procedure produced tight
* Work sponsored by the U. S. Department of Energy.
212
Prototype Low-Current Superconducting Quadrupole Magnet
Table I. Magnet Parameters
Cable
Spiral cable wrapping
Cable dimensions
Bare strand diameter
Conductor
Cu/NbTi ratio
Effective coil length
Total magnet length
ColdboreID
Inductance
Short-sample current
Peak field on conductor
Cable current density
Maximum current achieved
Maximum stored energy
Design gradient without iron
Design gradient with iron
Bore tube
Outer support pipe
Number of layers
Inner coil radius
Outer coil radius
15 polyester polyamide-imide insulated strands
0.1-mm(0.004-in.)-thick B-staged fiberglass epoxy tape
2.21 x 8.87 mm (0.0863 x 0.349 in.)
1.02 mm (18AWG)
206 filaments of Nb45 wt.% Ti with a ~-in. pitch
2.9
88.4 cm (34.8 in.)
116.5 cm (45.88 in.)
13.3 cm (5.25 in.)
2.8H
343 A at 4.4 K
4.5T
2.10 x 104 A/cm 2
First run: 323 A (48.4 T/m)
Second run: 343 A (51.4 T/m)
165 kJ
53.5 T/m (13.6 kG/ in.)
56.3 T/ m (14.3 kG/in.)
8.76-mm(0.345-in.)-thick 2024-T4 aluminum
17.5 mm (0.688 in.)
6061-T6 aluminum
4
7.56 cm (2.975 in.)
11.30 cm (4.45 in.)
.040THK GIO INSULATION .,,.,,.. ,. __
.022 x 3fe KEVLAR WEAVE BAND
(1800 LB BREAKING STRENGTH)
SHEET
Fig. 1. Cutaway view of magnet. Third and fourth layers are shown.
223
124
W. Cnddock. R. W. Fast, P. Garbindus, ud L. Mapalo
Fig. 2. Coil winding setup. Hydraulic cylinders clamp on the top brackets.
end turns. Figure 2 shows the tooling. Upon winding an entire layer, two pairs of split
G-1 0 islands are placed in the vacant 30° between the coils, and the winding fixture is
removed. The hydraulic compressing fixture, shown in Fig. 3, is then pinned into the
holes of the split islands. Each hydraulic cylinder pulls on every other steel ~and
which in turn separates the split island and rompresses the wire on the opposite side.
The bottom of the conductor slides on a Teflon-sprayed 0.006-in. G-10 sheet which
permanently isolates each layer, while a 0.014-in. Teflon-coated fiberglass cloth
protects the top of the conductor from abrasion against the bands during compression. The conductor is compressed, neglecting friction, with 2700 psi in the azimuthat
direction and 500 psi in the radial direction. At this point the magnet is baked at
380 K for 2 hr. The heating step was initially included to eure the B-staged epoxy
tape to insure a morerigid coil package. Thetapethat was used bad very little epoxy,
but it was found that the heating procedure compressed each quadrant of conductor
by an additional 0.150 in. on the average, probably from a change in the coefficient of
friction. During heating, anodized aluminum end saddles are driven against the
conductor, preloading the end turns with approximately 500 lb. After the magnet has
cooled, shims are tapped into the gap of the split islands. Conductor placementwas
within -0.050 in. One at a time, each 6-in. section of compression bands and
hydraulics are removed as the magnet is banded with a 1-in. pitch of Kevlar-49t
braid. The 0.022 x 0.375-in. braid has a nominal breaking strength of 1750 lb and
provides an averageradial pressure of 150 psi. The Kevlar is subsequently relaxed
during the preloading of the outer support pipe. Its function is to provide an overall
tight conductor package, maintain radial tolerances during winding, and to provide
the helium cooling channels during operation. The last fabrication step is to apply the
final preload with countersunk stainless steel bolts in the outer support pipe. A radial
preload of 700 psi was chosen for the first run and 1000 psi for the second. In
addition, four large aluminum reinforcing rings were added outside the aluminum
support pipe to reduce the bending moment in the bolts for the second run.
t Aramid fiber produced by duPont.
Prototype Low-Cnrrent Superconducting Quadrupole Magnet
225
Fig. 3. Compression fixture . Legend: (1, 2) steel bands; (3, 4) 6-in.-long steel blocks; (7) bronze bushing;
(8) hardened steel shaft to resist bending moment; and (10) hollow core hydraulic cylinder.
STRUCTURA L ANALYSIS
Under a biaxialload of 1500 psi, the conductor was measured to have a Young's
modulus of 1.5 x 106 psi. When the conductor was subjected to a constant pressure
of 2160 psi, the estimated thermal strain from liquid nitrogen to liquid helium
temperature was measured as 0.0038. These two values were used in all subsequent
analysis.
Stresses in the conductor from preloading, thermal contraction, and electromagnetic loading must be considered. The principal preloading mechanism is the
bolts in the outer aluminum support pipe. If the conductor has not been wound
tightly up to this point, the radial pressure cannot preload the conductor in the
azimuthal direction. For calculations, it is assumed that the conductor tends to
116
W. Craddock, R. W. Fast, P. Garbindus, and L. Mapalo
behave as a fluid and nearly all the radial pressure from the support pipe is
transmitted through to the bore tube.
Thermal stresses arise from the difference in thermal contraction between the
G-1 0 island/conductor combination and aluminum. The estimated thermal strain of
the island/conductor package at 4.2 K is 0.0037. By choosing an aluminum rather
than a stainless steel bore tube which the dipole COunterpart uses, radial preload
pressure is sacrificed for azimuthat pressure. The conductor can be thought of as
being wedged between the islands when cooled to 4.2 K. On cooldown an additional
200 psi radial loading should be gained, although strain gages on the outer pipe
indicate a smallloss of preload for the first run. The strain gages were unusable for
the second cooldown, but the thermal strain of the conductor is smaller when cooled
under greater pressures.
The electromagnetic force calculations were provided by Snowdon CJ. When
considering the first octant, the radial component of force and the x component of
the (J component of force of each conductor are distributed on the outer support
pipe. Equations (1) and (2) give the internal bending moments and tensile Ioads in a
pipe subjected to uniformly distributed Ioads shown in Fig. 4 as derived from
integrating point Ioads [4 ].
M = -wR 2 [(480 /7r + cos 80 - sin 80 ) cos (J- 1]- wR 2 [1 - cos(O- 80 )](8- 80 ) 0
(1)
T
= -wR[(cos Oo- sin 80 ) cos 8- 1]- wR[l - cos(O- 80 )](8- 80 ) 0
(2)
where M is the bending moment, T is the tensile Ioad in lb/in., w is the distributed
Ioad in lb/in., and the brackets ( )0 indicate unity for (J ~ 80 and zero for (J < 80 •
Fig. 4. Definition of symbols used in (1) and (2).
Prototype Low-Current Superconducting Quadrupole Magnet
227
in
0..
-2000
~
ii:
~
:::1
"'1500
0::
IIJ
1:::l
0
z
0
IIJ
!3 1000
~
IIJ
0::
0..
Fig. 5. Radialand total electromagnetic loading
of outer support pipe at 340 A.
300
0
A superposition of these uniformly distributed loads at various angles approximates the electromagnetic loading on the outer support pipe. The y component of
the 8 component is assumed tobe carried by the conductor and bore tube. Figure 5 is
the distribution of electromagnetic loads on the outer support pipe. The maximum
stress in the aluminum support pipe is 10,000 psi at 323 A. In addition to the
redistribution of radial forces, approximately 1700 psi of the tangential preload at
the G-10 island is lost on the conductor as it is pinched towards its midplane. The
pinch force is 2500 psi at the conductor midplane. Table II is a summary of conductor
stresses for the second run.
Table II. Estimated Stresses on Conductor (343 A)*
u"(r = 3 in.)
u"(r = 4.5 in.)
u 99 (r = 3 in.)
at island boundary
at conductor midplane
u 99 (r = 4.5 in.)
at island boundary
at conductor midplane
* All units in psi.
Preload
Cooldown
357 A
Total
-950
-1000
0
-200
+400
-700
-550
-1900
-1150
-1150
-700
-700
+2300
-20
-2000
-1100
-1100
-600
-600
+2200
-450
-2150
-o
-o
221
W. Craddock, R. W. Fut, P. GarWncill8, ud L. ~
ELECfRICAL
Figure 6 shows the electrical connections. The dump resistors are center tap
grounded with a 100-0 resistor. This reduces the possible valtage to ground in half,
but still Iimits the current in case a fault to ground develops during magnet discharge.
Furthermore, the magnet was wired in such a manner as to keep sections with the
greatest valtage differences as far apart as physically possible. The cable was wired in
series with each strand lying next to its two closest electrical neighbors. Each half of
the magnet on either side of ground is completely isolated from the other half by
islands and a 0.006-in.-thick G-10 sheet between layers. Three out of the 15 strands
could not be used. Two pairs of strands developed electrical shorts at the crossover
between layers and bad to be wired in parallel. The third wire is a plain copper wire
which was used to propagate the quench by shunting current through it. At no time
were the two copper wires connected tagether or to ground. When a valtage
imbalance is detected, the SCR disconnects the power supply, and simultaneously an
auxiliary power supply can energize stainless steel heaters sandwiched between the
conductor and the G-10 islands. Three modes of energy extraction were tried and are
shown in Fig. 6. At least one of the two copper wires was always left open or
connected to the data acquisition system. The safety Ieads were always connected
and provide an alternate path for current to bypass the quenching section.
COLD~---!--- -3> AMBIENT
B
I
----,----+1- - - - - - - - V
I
VOLTAGE TAP
TYP
V
COIL rElTER TYP
A
I
I
------~~----~------.--V
COPPER
COIL B
SCR
Q~NCH
SWITCH
V
Fig. 6. Electrical connections. Oose switch A for inductive hot wire
technique; close switch B for directly coupled hot wire. The copper coils
are actually one strand out of 15 in the cable.
Prototype Low-Current Superconducting Quadrupole Magnet
229
TEST RESULTS
Figure 7 is tbe quadrupole training curve. Witb tbe firstcooldown 94% of sbort
sample was reacbed before it was decided to increase tbe preload and add four
reinforcing rings. Before tbe preloading was cbanged, all tbe bolts in tbe outer
support pipe were totally relaxed. From previous experience witb low-current dipole
racetrack coils and from tbe Energy Doubler program [5 ] , it is expected tbat little if
any training from tbe first run can be retained after a preload relaxation. On tbe
second cooldown, tbe sbort-sample Iimit was reacbed witbin tbree quencbes. Thus
tbe 1000 psiradial preload gives good training bebavior witb minimum conductor
stresses.
The original design gradient was not quite reacbed. Had tbe two sborted pairs
been available, it is probable tbat 56 T /m witbout iron could bave been reacbed.
It is especially desi'rable witb tbis style of low-current magnet to minimize tbe
voltages during a quencb by selecting tbe smallest value energy dumping resistor
wbicb is consistent witb avoiding a wire burnout. Stainless steel strip beaters along
tbe islands, and an inductive and direct coupled bot wire tecbniques were all tested to
measure tbeir effects on quencb propagation. If botb copper circuits are open, ac
Iosses in tbe wire are ignored, and quencbing does not occur; tbe square root of tbe
joule beat dissipated in tbe external resistors must be proportional to tbe magnet
current prior to firing tbe SCR. This is curve A in Fig. 8. Curve B, called coasting
witbout beaters, refers to tripping tbe SCR prior to a spontaneous quencb. Above tbe
100-A Ievel some of tbe energy is released in tbe 4.2-K environment. Near tbe sbort
sample Iimit, 35% of tbe energy is dissipated internally. The effectiveness of tbe
beaters is tbe difference between curves B and C. The stainless steel beaters bave a
typical surface beat ftux of 18 W/cm 2 witb an average beat input of 3500 J and a
maximum temperature of 120 K as measured witb cbromel-constantan tbermocouples. Curve Eis tbe inductive bot wire tecbnique. This circuit was found tobe not
400
-
350
U)
0..
::!'
<{
...z
w 250
a:
a:
CRYOSTAT PRESSURE
• -3 PSIG
x -0 PS IG
::>
u
...w
200
z
C>
<{
::!'
150
100
50
Fig. 7. Quadrupole training curve. Curve A , 700 psi
preload ; Curve B, 1000 psi preload.
5
10
15
OUENCH NUMBER
20
130
W. Craddock, R. W. Fast, P. Garbincius, and L. Mapalo
-~ 13
~
:>
~ 12
"'
· II
-~
"'a:
~
i3"'
a:
.J
"'z
ffi
I-
10
9
a
7
X
"' 6
~
ß
0.
5
B
4
:I;
,...
~ 3
"'z
"' 2
0
100
200
300
400
MAGNET CURRENT . AMPS
Fig. 8. Energy extraction at room temperature vs.
magnet current. (A) Theoretical 100% efficiency; (B)
coast witbout beaters; (C) coast witb beaters; (D)
quencb witb beaters; (E) inductive bot wire tecbnique
witb beaters; (F) directly coupled bot wire tecbnique
witb beaters. Letter "0" denotes a spontaneaus quencb.
nearly as etfective as the directly coupled copper wire, curve F, where roughly half
the total energy is absorbed by the coil at 250 A. Changing the polarity of this copper
loop made little ditference in the quench propagation at all current Ievels. From 40 to
60% of the energy which is removed at room temperature is dissipated in the 1.43-0
current limiting resistor of the copper loop which is to be expected from
the ratio of the resistances. Obviously, if both copper loops were used, quench
propagation would have been further improved.
Basedon adiabatic conditions, the integral JI 2 dt can be equated to a maximum
bot spot temperature in the superconducting windings [6 ' 7 ]. A measured value of
RRR = 70 was used in these calculations. Under normal conditions a 337-A coast
without heaters bad the highest theoretical bot spot temperature of 250 K. A 200-K
hot spot was the worst case for any of the current driven hot wire runs. The Iow
external resistance of 0.83 0 of this circuit caused this comparatively high temperature but reduced the peak voltage to ground by 60%. At 273 A with both copper
loops open, the SCR and stainless steel heaters failed to trip during a quench. The
magnetwas self-protecting and experienced a 275-K bot spot in the quenching loop.
The safety Ieads probably saved the magnet from a burnout.
The thermal stability of the magnet was investigated by powering the stainless
steel heaters and one of the copper loops. For one of the stainless steel heater tests,
the magnet current was set at 308 A. With a surface heat ftux of 0.03 WI cm of cable,
0.057 J I cm induced a quench. Next the current was adjusted to 333 A, 97% of short
sample. This corresponds to a thermal temperature reserve of only 0.15 K [8 ].
Fifty-three watts of heat were dissipated in one-half the magnet by one of the copper
wires for 6i min before quenching occurred. In the highest field region of the magnet,
the power density was 0.0027 Wlcm. The relatively porous nature of this conductor
allows this stable performance even with currents very close to the short-sample
Iimit.
Prototype Low-Current Superconduding Quadrupole Magnet
231
FUTURE
Twenty-six full-length, 10-ft quadrupoles are eventually required. To reduce
the costs, the full-size quads will be two-layer, 4i-in. clear bore magnets using a
copper to superconductor ratio wire of 1.8 : 1 or smaller. There is no plan to place this
prototype in the High Intensity Lab. Beam quenching sensitivity will be tested with
one of the low current dipoles.
ACKNOWLEDGMENTS
The authors wish to thank J. Satti, P. Mazur, B. Cox, S. Snowdon, J. Heim, and P. Mantsch for their
suggestions. A special thanks goes to S. Anderson who was in charge of magnet construction and who
helped perfect the many special techniques. They also wish to acknowledge R. DeNeen, J. Guerra, D.
Garcia, S. Dochwat, S. Tonkin, and L. Sawicki, who helped with the construction and test setup.
HEFERENCES
1. B. Cox, T. Dilman, P. H. Garbincius, L. Kula, P. 0. Mazur, J. A. Satti, A. Skrabaly, and E. Tilles, IEEE
Trans. Magn. Mag-15(1):126 (1979).
2. A. Asner, Proc. 1968 Summer Study on Superconducting Devices and Accelerators, Part III Brookhaven National Labaratory Rept. 50155 (C-55), Upton, New York (1968), p. 866.
3. S. C. Snowdon, private communication # 102577-0930.
4. R. Roark and W. Young, Formulas for Stress and Strain, McGraw-Hill Book Company, New York
(1975), Table 17.
5. W. B. Fowler, P. V. Livdahl, A. V. Tollestrup, B. P. Strauss, R. E. Peters, M. Kuchnir, R. H. Flora, P.
Limon, C. Rode, H. Hinterberger, G. Biallas, K. Koepke, W. Hanson, and R. Brocker, IEEE Trans.
Magn. Mag-13(1):280 (1977).
6. P. Eberhard, M. Alston-Garnjost, M. A. Green, P. Lecomte, R. G. Smits, J. D. Taylor, and V.
Vuillemin, "A Burnout Safety Condition for Superconducting Magnetsand Some of Its Applications,"
Lawrence Berkeley Labaratory Rept. LBL-7272 (September 1977).
7. B. J. Maddock and G. B. James, Proc. IEE 115(4):543 (1968).
8. J. Allinger, G. Danby, H. Foelsche, J. Jackson, D. Lowenstein, A. Prodell, and W. Weng, IEEE Trans.
Magn. Mag-15(1):119 (1979).
·
D-8
SUPERCONDUCfiNG MAGNETS OF TUE
BIOMEDICAL FACILITY AT SIN
J. ZeUweger, G. Vecsey, and I. Hoi'Vath
SIN Swiss Institute for Nuclear Research
Villigen, Switzerland
INTRODUCfiON
Negative 1r-meson therapy has gained more and more interest in the past few
years because of the unique absorption characteristics and depth dose behavior of
these particles with a high linear energy transfer (LET) near the desired region. The
technique could be superior to conventional X-rays, and may constitute major
progress in tumor therapy. Furthermore, three-dimensional tumortreatmentwill be
possible.
A test facility for tumor irradiation therapy with negative 1T mesons is under
construction at SIN [ 1]. Superconducting ac magnets for tumor scanning [2 -4] are
necessary and represent a major part of such a facility. Similar to the Stanford double
torus spectrometer CJ, the facility uses 60 identical beams, with 60 pancake coils and
60 slits. A design ftux of up to 2 x 109 1r/s will be concentrated on the tumor tissue.
More design details are given elsewhere [4 '6--8].
Two prototype coils were tested. The first torus with its 60 pancake coils is
presently under test. Results are presented in this report.
THE PION APPLICATOR
The applicator (Fig. 1) essentially consists of two toroidal magnets on a common
axis defined by the primary proton beam. The toroidal field is generated by
superconducting pancakes (60 per torus), subdividing the pion ftux into 60 individual
beams of common central momentum. The momentum width and intensity of each
beam is controlled individually by a variable slit in the dispersion plane. The magnets
are suspended in a common vacuum chamber; optical alignment can be established
in the cold state. Forwardneutronsand protons are shielded from the patient by a
large cylindrical steel block (140 Mp) inside the chamber. Thermalradiation shields
at 90 K cover the inner walls of the tank and a proton collimator should protect the
entrance coils from radiation darnage and excessive nuclear radiation heating. The
pion beams leave the vacuum through 60 stainless steel windows and enter the
patient after crossing a monitor chamber assembly. The position of the patient, the
pion momentum (i.e., magnet current) and the slit position are controßed by a
microprocessor according to a previously calculated treatment plan.
Z3Z
Superconduding Magnets of tbe Biomedical Facillty at SIN
slit system
vacuum chilmber
p;~t ient
233
tank
Fig. 1. Cross-sectional view of the pion applicator.
SUPERCONDUCI1NG MAGNETS
Patient size, treatment volume, maximum treatment time, available beam
intensity, pion physics, and the beam optics formed the basis of the magnet design.
The overall size of the vacuum chamber including the magnets is based on the
following requirements:
1. The patient tank bad to be large enough to allow adequate scanning
movements of the patient in three dimensions and to incorporate additional equipment.
2. The proton and neutron shield bad to be thick enough to absorb the spent
600-MeV proton beam.
3. With the design primary proton current of 20 p,A, an acceptance angle of 1
steradian at 60° pion production was necessary to stay within the desired treatment
time for a treatment volume of 1liter.
4. An average pion lifetime of 26 ns at rest limited the overall path length.
5. A dispersion-free optical system with a magnification of approximately 1: 1
was desired.
First-order calculations fixed the main dimensions of the coils and the important
beam parameters such as "curvature x radius." Second-order calculations introduced concave curvatures and slight rotations of the entry and exit regions of the coil
relative to the centrat beam trajectory (see Figs. 1 and 2). Results of the calculations
are summarized elsewhere [6 ' 7 ]. For convenience in treatmentplan development, the
irradiationangle at the target image (tumor) in the patienttank was chosentobe 90°.
Patient size, the beam parameter "curvature x radius," and the penetration depth of
pions defined the required B field. The desired treatmenttime necessary to scan the
J. Zellweger, G. Vecsey, and I. Horvath
234
\
TORUS
2
\
TORU 5 1
Fig. 2. Pancake coils of torus 1 and torus 2.
treatment valume defined the scan frequency and amplitude (:fo Hz and 10% af
Bmu).
The superconducting cable was fabricated af Nb-Ti with a copper stabilizer. The
design current selected was 2500 A and was a campramise between small ac lasses,
small current transfer lasses, law quench discharge valtage, and convenient size for
winding pu~ases. Elaborate conductor design resulted in a high current density af
220 A/mm with a low average ac loss of 1.5 mW/m (or 15 W/torus) at 5.5 K and
2.8 T. Summarized data are given in Table I.
The coil frame was constructed of glass-reinforced epoxy material mainly to
minimize ac lasses. The frame was designed to withstand the magnetic pressure on
the winding (120 kp/cm). In the energized state, a resulting force of 2600 kp
(3200 kp for torus 2) acts on each coil. Rivets were needed for reinforcement of the
two-piece frame and to ensure an acceptable displacement of the patted winding
during operation.
The pancake coils in each torus are electrically connected in series. The valtage
of each coil is continuously monitared by two detectors (for safety purposes) and
Table I. Cable Data
Electrical data
l c. A/mm2 220 (at 5.5 K and 2.8 T)
Im.., A2500
P 80, W /torus 15 (at fo Hz and 0.1 Imaxl
Dimensions
4.15 mrn x 2.9 rnrn
Cable
Copper area, A eu. rnm2
NbTi area, ANbTi> rnm 2
Aeu : ANbTi
Filamentdiameter, ~rn
Nurober of filarnents
7.5
1.05
7:1
::530
1400
Superconducting Magnets of the Biomedical Facility at SIN
_
235
·--1-"'F-rivet
I·-
FU11.ltJ
y-
p
I
copper
cooling
~
tu~s
IA'III!III-+-+-T-IIIIi• ·
fiilll=t=t=t:::1\Mf-11'!11r-t--t--t--lllliJ
-
Nb-Ti- copper
w inding
· - -1-
ili
1-+-+-+-!IU:,l"_,
m-+-+-+-m'·
I
IJIIII--t---r-t-__,11111 I ,
-
COOling ITleSh
IIIU-+-+-+-m·tll
I,
Fig. 3. Cross-sectional view of the superconductor winding.
compared to the voltage of the neighboring coil. The difference in the two voltages is
sensed and used as a signal for quench detection. Bachtorus can be deenergized in 2 s
following a quench and the energy dissipated in a parallel shunt resistor. The
discharge voltage rises to 1.5 kV, when the torus is fully energized.
The coils and their support rings are indirectly cooled-two separate copper
cooling tubes are used (see Fig. 3)-by forced ftow of supercritical helium at an inlet
pressure of 10 atm. Efficient heat removal in the winding is maintained by aseparate
cooling mesh. The coils are cooled in series. An additional heat exchanger in the
helium bath guarantees that a temperature of 4.5 K is maintained in the cooling
circuit after each group of five coils. The helium is circulated by a multipurpose
helium refrigerator, which considers each torus to be a separate Ioad. Details are
given in a separate report [8 ]. Specific data for the coils and the magnets are
summarized in Table II.
COIL TEST
Two pancake coils of torus 1 were chosen for this test. The short sample current
for this cable was determined tobe 2800 A at 5.5 K and 2.8 T, 12% above the design
current. A 7 -Mp iron double mirror was used to simulate the toroidal magnetic field
(see Fig. 4 ). The supportring configuration was simulated using appropriate supports
and one bearing.
J. Zellweger, G. Vecsey, and I. Horvath
236
Table II. Magnet Data*
Coil data
Bmax at the winding, T
Current, A
Turns
Ampere turns, A-turns
Enclosed flux per turn, V-s
Average length, m
Magnetdata
Magnetic energy, MJ
lnductance, H
B field x radius, T-m
Totalturns
Totallength, m
Torus 1
Torus 2
2.84
2408
60
144,480
0.707
2.8
2.7
2412
48
115,820
0.99
3.5
3.0
1.0
1.73
3600
10,800
3.5
1.2
1.4
2880
10,800
*Operating temperature, 4.5- 5.5K; pion momentum, 220MeV/c,
where c is the velocity of light.
-
~ I
i
iron
double
I
mirror
I
I
! I
\
II
I
coi ls
--
. I
r- \
I!
. I .i
'l '------------
I
l
I
I
I
I
support
> cool ing
tube s
bearing
_j
Fig. 4. Test assembly for two pancake coils.
Superconducting Magnets of the Biomedical Facility at SIN
237
Prior to the test, the coils, the iron mirror, the supports, and the bearing were
cooled down to the circulating helium temperature of 4.5 K. The test results are as
follows:
1. The cooldown time of the test assembly, having approximately the same
weight as the torus, was about 3 days.
2. Five quenches were observed before the design current of 2500 A was
reached: one quench for coill; four quenches for coil2. After an additional quench,
2650 A was attained. The "worst-case" cable temperature was 5 K during an
energizing cycle. Training steps are shown in Fig. 5. For coil 2 the current increase
per step was constant and showed no statistical distribution, a behavior which has not
been explained.
3. Owing to the mechanicallimitations of the coil, the critical current of the
cable at 5.5 K could not be determined.
4. Although the ac loss of 4 W per coil was too high, the coil could be swept and
ramped at the specified frequency and amplitude. An electrical short circuit in the
cooling structure owing to inadequate glass insulation was found to cause this·
excessive ac loss.
5. Coil performance remained unchanged even after numerous thermal
cycles, energizing cycles, or quenches. The coils withstood the magnetic and thermal
stresses without any visible darnage or loss of performance.
The performance of the two prototype coils of torus 1 met the design requirements except for the excess ac loss, which was eliminated by a thicker insulation
:;{
C>
C>
"'
N
-;:
C>
C>
90
80
70+---;----r---+----~--+----r---+-+-5
4
2
COIL 1
COIL 2
number ol trAining steps
Fig. 5. Training steps for the two pancake coils of torus L
J. Zellweaer, G. Veaey, anc1 1. Homath
layer. With this minor design change, important for future coil production, and with
the encouragement of these results it was decided to advance immediately to the full
torus test.
TORUS TEST
Torus 1 with its 60 pancake coils is presendy under test. The short sample
currents of the cables used range from 2650 to 3400 A at 5.5 K and 2.8 T.
Preliminary results are as follows:
1. The cooldown time of torus 1 was 4.5 days.
2. 2410 A was attained after 56 quenches. The first quench occurred at
1530 A and the 19th at 2000 A. During each energizing cycle, the "worst-case"
cable temperature was 4.9 K. After a quench, the average temperature of the
quenched coil increased to 20 K. No otber coil except the quench-initiating coil was
observed to quench, although the discharge time was 2 s. Twenty-seven coils did not
quench during the tests. The plot of the training steps shows an exponential
characteristic with a slight curvature. The current changes per training step show
statistical behavior as expected. There is no correlation between the coil or the
amount of quenches per coil and the short sample current; this supports the theory
that training is induced by the mecbanical energy release associated with cracks or
conductor displacements since all coils were exposed to identical boundary conditions and were operated weil below the critical short sample current.
3. Alt~rnating current loss of the torus at the specified amplitude and
frequency (Bmax = 0.06 T/s) is 10 W, wbich is below the calculated value. The cable
maintained its superconducting state even after a fast discbarge with Bmax = 1.4 T / s
following a quench, verifying its excellent ac performance.
The results presently obtained with torus 1 already fulfill the requirements for
patient treatment. However, final results will be reported when available.
REFERENCES
1.
2.
3.
4.
5.
6.
G. Vecsey, SIN Rept. TM-62-01 (1976).
H. Blattmann, Rad. Environmental Biophysics 16:205 (1979).
J. Zellweger, SIN Rept. TM-62-02 (1978).
J. Zellweger, SIN Rept. TM-65-01 (1978).
D. Boyd, H. A. Schwettman, and J. Simpson, NucL Instrum. Meth. 111:315 (1973).
R. Frosch and J. McCulloch, SIN Rept. TM-37-003/004/005 (1973).
1. J. Crawford, SIN Rept. TM-37-008-009 (1977).
8. J. Zellweger, in Proc. 6th Intern. Magnet Technology Conference, ALFA, Bratislava, Czechoslovakia
(1977), p. 361.
E-1
A NOVEL THERMOMETER SENSOR FOR TUE
mK REGION USING THE PROXIMITY EFFECT
H. Nagano, Y. Oda, and G. Fujü
Tokyo University, Tokyo, Japan
INTRODUCTION
A normal metal which is in good electrical contact with a superconductor shows
superconducting properlies because of the proximity effect C· 2 ]. This effect in
Cu-clad Nb and Cu-clad Nb-Ti wires has been measured and is thought to be
applicable as a new type of thermometer sensor below 1 K [ 3 ' 4 ].
When the temperature of such a wire is decreased, the Nb part of the wire
transforms to the superconducting state at Tc, the critical temperature of Nb. If the
temperature is decreased further, the Cooper pairs in the Nb leak into the Cu. The
leakage distance of these Cooper pairs depends on the temperature and the electron
mean free path IN in the Cu. The leakage distance increases as the temperature
decreases and as the electron mean free path is increased. Thus, in a weak magnetic
field, a Meissner effect is seen in the Cu, caused by the leakage of the Cooper pairs
into the Cu. The region of this Meissner effect increases with a decrease in
temperature. Resistance of the Cu perpendicular to the Nb wire is expected to
decrease as the temperature is lowered because of an increase in the leakage
distance. Since the leakage length of the Cooper pairs depends on some function of
the temperature, it is possible to use the effect as a thermometer below 1 K.
MAGNETIC SUSCEPTIBILITY
The magnetic susceptibility of Cu-clad Nb wire has been measured by an ac
mutual inductance bridge. In practice, the mutual inductance is proportional to the
susceptibility. Thus, the size of the Meissner region can be calculated from the
mutual inductance of the Cu-clad Nb wire. Forthis purpose the specimen is attached
to the mixing chamber of a dilution refrigerator and the temperature is measured by
both germanium and carbon thermometers. At the critical temperature of Nb the
change in the mutual inductance is expressed as !l.M0 (Tc), while the !l.M(T)
represents the change of the mutual inductance after the transition. The latter change
is caused by an increase of the Meissner region in the Cu. The size of the Meissner
region is expressed as
!l.M(T)
{[
(1)
p = r 1 + !l.Mo(Tc)
- 1
]t/2 }
In this relation p is the distance of the Meissner region extending into the Cu from the
boundary of the Nb/Cu interface and r represents the radius of the Nb core wire. The
2.39
H. N...-. Y. Oda, ud G. Fejli
.·
1.0
.
30
E
·'
"-
... 20
..
10
..
..
~0
.~
00
/
2
3 _LI.
·t5
6
8
T2. K
Fig. 1. Temperature dependence of the Meissner region, p,
for Cu-clad Nb wire (0.35 mm Cu OD and 0.25 mm Nb 10).
Residual resistance ratio of material in upper curve is 90
while for the lower curve it is 55.
cylinder of radius (r + p) is the Meissner region. From the experimental evaluation of
äM0 (Tc) and äM(T), p can be calculated by use of (1) [4 ].
The temperature dependence of p is shown in Fig. 1. The horizontal axis is
plotted as a function of r-t/2. This figure indicates that p is a linear function of T- 112
below about 1 K. The Meissner region, p, becomes larger when the resistance ratio of
the Cu is larger. Above 1 K, pisalinear funtion of T- 1 instead of T- 112 •
In the region where the electron mean free path IN is shorter than the
coherence length ~N in the Cu, p has been calculated theoretically by Deutscher and
de Gennes [ 1]. From their calculation, p is expressedas
p
= ~N [log ~Nf A (0) - 0.116]
(2)
where A(O) represents the penetration depth at the Nb/Cu interface. The function
inside the parenthesis is only minimally affected by the temperature. Thus, the
temperature dependence of p is determined mainly by ~N· In the approximate Iimit
the relation between ~N and the temperature is expressedas ~N = (hv,.IN/6'7Tk8 T) 112 •
This signifies that p is a linear function of T- 112 • In this relation, v,. is the Fermi
velocity of Cu. When IN is larger than ~N. the relation between ~N and the
temperature is expressed as ~N = hv,./2'7Tk8 T; thus, above 1 K, IN is larger in
magnitude than ~N and p shows a T- 1 dependence.
The thickness of the Cu cladding is expressedas d, and x represents the distance
from the Nb/Cu interface. In the region where x < p, Cu shows perfect diamagnetism. In the region where d > x > p, Cu is in the normal state, and the magnetic
ßux can be assumed to penetrate freely. In this case, the magnetic susceptibility of Cu
in the region of x < p is -!",, and the susceptibility of Cu in the region d > x > p is
essentially zero. Thus, the average magnetic susceptibility of Cu, expressed as Xav•
can be given as
1 Vp
Xav = - 4'7T Veu
(3)
A Novel Thermometer Sensor for the mK Region Using the Pro:dmity Eßed
241
20 .-------.-------.-------~----·
0
15
0
0
0
5
0
3
Magnetic Field • Oe
Fig. 2. Magnetic field dependence of p at 99.5 mK.
The average susceptibility of a specimen whose resistance ratio is 90 can be
determined from Fig. 1 as Xav = 10- 2 T- 112 • This value should be compared with the
magnetic susceptibility of CMN, which is generally used as a thermometer below 1 K,
of 8.5 X 10-4 T- 1• Thus, at 1 K the Xav is about twelve times larger than the
susceptibility of CMN. Since the temperature dependence of Xav and XCMN is
markedly different, XcMN > Xav at very low temperatures. However, from 1 K to
about 10 mK, Xav is larger than XCMN· If Cu-clad Nb wire is used as a thermometer
sensor below 1 K, its sensitivity is stilllarger than that of the CMN above 10 mK.
Moreover, the thermal contact with the metal is quite good. Because of these
characteristics the Cu-clad Nb wire appears as a good temperature sensor for the mK
region.
MAGNETIC FJELD DEPENDENCE
The magnetic field dependence of p is shown in Fig. 2. This plot shows that p is
very sensitive to magnetic fields. lt decreases significantly even in a magnetic field of
less than 1 Oe. At lower temperatures, p is very sensitive to the field strength andin
the presence of a field the temperature dependence of p is not a linear function of
T - 172. If shielding from a magnetic field is less than 10 mOe, the effect from the field
can be neglected.
Usually, the magnetic field in a laboratory, which is mainly the earth field, is
about 500 mOe; so, if the IL-metal shield is doubled or tripled, it is not too difficult to
reduce the residual field to less than 10 mOe. Such types of shielding are quite
common in experiments involving Squids.
ELECfK.ICAL CONDUCTIVITY
The preliminary measurement of the electrical resistance of Cu-clad Nb is shown
in Fig. 3. The preparation of the specimen was as follows. First, Cu-clad Nb-Ti
multifilament wire of reetangular cross section was rolled into a thin tape. Then it was
cut alternately from both sides at right angles to the direction of the filaments (see
Fig. 4). The resistance was measured using the four-probe method. The resistance of
such a specimen changed suddenly at the Tc of Nb-Ti similar to the mutual
inductance change observed in Fig. 1 at Tc. As the temperature was decreased below
Tc, the resistance also gradually decreased. It is thought that this part of the decrease
was caused by the proximity effect. The decrease in the resistance does not show the
H. Nagano, Y. Oda, and G. Fujii
242
2.0
c:
E
."
1.0
.~
~·
·:. ~· .···t
0 ~0------~
5--------.~0------~.5
T, K
Fig. 3. Typical behavior of the electrical resistance, R,
of Cu surrounding many Nb-Ti fine wires. Measuring
current is 10 mA dc.
T- 112 dependence. There are two possible reasons for this nondependence. First,
the distance between each Nb-Ti fine wire varies throughout the sample. When the
temperature is slightly below T" some of the Cu is in the normal state surrounding
each Nb-Ti wire. Because of the proximity effect, the superconducting region
progressively increases in the Cu and the change in the resistance becomes large.
With further decrease in temperature, the superconducting region in the Cu
continues to increase and finally overlaps with other similar regions. The rate of
resistance change with respect to temperature decreases. When the Nb-Ti fine wires
arenot uniformly distributed in the Cu specimen, the temperature dependence of the
resistance is somewhat difficult to evaluate. The other reason that it does not show
the T- 112 dependence isthat the magnitude of the dc current affects the measurement. In the case of Fig. 3 a dc current of 10 mA was used. In this case the
superconducting region in the Cu may have been decreased by the magnetic field of
the dc current. Usually, with the conventional dc method it becomes difficult to attain
sufficient sensitivity. The temperature dependence of the resistance for the same type
of specimen measured by an ac bridge using the Squid as a null detector is shown in
Fig. 5. In this case a current of 10- b A was used. The temrerature dependence is
different from that of Fig. 3, but there is still neither a T- 1 / or a T - 1 dependence;
this is probably because of the random distribution of the Nb-Ti fine wires.
Fig. 4. Schematic diagram of specimen prepared for the resistance measurement.
A Novel Thermometer Sensor for tbe mK Region Using tbe Proximity Etlec:t
243
90 r-------~--------.---------.-------~-----.
0
c:
'='~.
0
80
UJ
u
0
0
z
,_
<{
0
"'~ 70
0
a:
0
60
cP
0
0
TE MPERATU RE ,
I<
Fig. 5. Temperature dependence of the resistance due to the proximity effect. Measuring current is 10- 6 A.
CONCLUSION
The magnetic susceptibility change of Cu-clad Nb (or Nb-Ti) wire, caused by
the proximity effect, shows a T- 11 2 dependence as an approximate limit, and is
thought tobe applicable as a new thermometer sensor. The temperature dependence
of the electrical resistance for such a specimen has been studied. In order to ascertain
an accurate temperature dependence it is necessary to utilize a specimen in which the
superconductor wires are uniformly distributed. However, even a nonuniform
randomly Cu-clad superconductor could be used as a secondary temperature sensor
if the resistance and the temperature dependence is known.
REFERENCES
1. G. Deutscherand P. G. de Gennes, Superconductivity, Vol. 2, R. D. Parks, ed., Marcel Dekker, lnc.
New York (1969), p. 1005.
2. Orsay Group, Phys. Condensed Matter 6:307 (1967).
3. Y. Oda and H. Nagano, J. Phys. Soc. (Japan) 44:2007 (1978).
4. Y. Oda, G. Fujii, and H. Nagano, Jpn. J. Appl. Phys. 18:1411 {1979).
DISCUSSION
Question by S. W. Van Sciver, University of Wisconsin: Have you accounted for the Kondo effect in
the copper? This should have a temperature dependence that is similar to the susceptibility, i.e.,
xcc 1/TI/ 2.
Answer by author: The impurities in Cu of our specimen, Cu-clad Nb, are thought tobe about 10 ppm
on a weight ratio. The magnetic susceptibility attributed to the Kondo effect is paramagnetic and its
magnitude is about 10- 7 emu at 1 K. In the case of the proximity effect, the magnetic susceptibility is
diamagnetic and its magnitude is 10- 2 I T 112 • This magnitude is fairly !arge in comparison with that
expected from the Kondo effect.
E-2
A SUPERCONDUCTING RF NOTCH FILTER*
C. S. Pang, C. M. Falco, R. T. Kampwirth, and I. K. Schuller
Argonne National Laboratory
Argonne, Illinois
and
J. J. Hudak and T. A. Anastasio
Department of Defense
Fort Meade, Maryland
INTRODUCfiON
Over the past several years major improvements have been made in the quality
of high Tc A-15 superconductors. In particular, high-quality thin films of Nb 3 Sn and
Nb 3 Ge have been fabricated using chemical vapordeposition C], coevaporation, [2 ]
and magnetrOD sputtering
techniques. Aside from the potential applications of
these materials to ac power transmission, high-field magnets, and particle accelerators, their high transition temperatures might be exploited for use in devices cooled
by closed-cycle refrigeration.
Most superconducting devices such as the various forms of Josephson junction
devices, super-Schottky diodes, cavity and helical resonators, and thin-film
bolometers generally require operation at liquid helium temperatures. Low operating temperatures are often necessary to reduce device noise, provide lower resistive
losses, or obtain the specific superconducting properties offered by low Tc materials.
The inherent disadvantage of low operating temperature is that refrigeration is
typically provided by liquid helium baths which must be replenished frequently. In
addition, the transfer of liquid heliuni from storage dewars is awkward and unacceptable to a nontechnical user. Small Joule-Thomson expansion liquefier stages
added to closed-cycle refrigerators can be used in some applications, but are not
readily available.
Applications that would allow use of high-quality, high Tc thin-film materials
and allow operating temperatures between 9 and 15 K could take advantage of the
reliable refrigeration systems which are now commercially available. A preliminary
investigation is presented of a radio frequency superconducting notch filter employing thin-film technolo~ which could be used for interference reduction in a
communication system [ ].
eJ
* Work supported by DOD under MIPR-H98230.
244
A Superconducting RF Notch Filter
245
Fig. 1. Model circuit of notch filter.
CIRCUIT DESIGN
The circuit used in this investigation is shown in Fig. 1. The filter consists of
an inductively coupled superconducting tank circuit which is placed in parallel with
the Ioad of the receiver, RL. The mutual inductance between L 1 and L 2 is controlled
by the coupling constant, k. The circuit is tuned by varying the capacitor C 2 and the
resistive Iosses of the tank circuit are modeled by the series resistance R 2 • For a
narrow band of frequencies the filter impedance becomes very small with respect to
the Ioad, thereby reducing the strength of the interfering signal at the receiver. The
maximum value of the notch depth, D, the 3-dB bandwidth of the notch, tl.f, and the
center frequency, / 0 , at which maximum attenuation occurs, are given by [5 ]
D(dB)
= -20 log (1 + B)
1
Re
[
2
1 ] 112
tl.f = 27T L 1(1- k 2 ) 1 + B- B 2
fo =
__!_ [L2C2(1
27T
- e)]- 112
(1)
(2)
(3)
where B = ReL 2 /R 2 Lt and R = R.Rd(R. + RL).
Equation (1) shows that reducing R 2 leads to a deeper notch if the other circuit
parameters are kept constant. lt is also clear that the circuit has the property that the
bandwidth and notch depth are independent of the center frequency. In the intended
application this is a desirable feature which allows for a very large tuning range.
Knowledge of L~. L 2 , D, and tl.f allows one to solve for the value of R2. Thus, the
circuit can also be used to study the nature of the superconducting losses.
CIRCUIT REALIZA TION
The filter circuit was implemented using the planar geometry shown in Fig. 2.
The coupling constant, k, between L 1 and L 2 was controlled by the separation
distance between plates A and B, and the capacitance, C2 , was controlled by the
separation between plates B and C. The present design allows the superconducting
tank circuit to be built without the need for any plate to plate connections, thus
eliminating contact resistance as a potential source of problems.
The planar geometry was chosen so that spottered films of high Tc Nb 3 Sn or
Nb 3 Ge could be used. However, for these initial experiments niobium films were
used for convenience. Films, about 0.5 #Lm in thickness, were deposited using
electron beam and spottering techniques on S-em-diameter single-crystal-sapphire
(Ah0 3 ) and fused-quartz (Si0 2 ) substrates. In order to obtain better adhesion
between the niobium film and substrate, the latter was held at a temperature of about
300 to 400°C during the deposition process. Scanning electron microscopy showed
the film surface tobe smooth on the scale of 0.1 #Lm.
246
C. S. Pang et al.
L,
A
L2
B
c
c~'
c~'
FILTER CONFIGURATION
Fig. 2. Geometry of circuit elements and their relative position.
(Notice the plate-to-plate connections are not required in this
design.)
The circuit elements were etcbed into tbe films using pbotolitbograpbic tecbniques. The circuit patterns for tbe masks were computer generated and plotted on a .
Gerber plotter; emulsion masks were made by pbotoreduction with a x 10 reduction
camera. Shipley AZ-1350J photoresist was spun onto tbe films and exposed by a
mercury arc lamp using direct contact printing. The etchant used for tbe final
development of tbe coil and plate patterns consisted of one part H 2S04 , two parts
HF, one part HN0 3 , and four parts H20 by volume. Tbis etcbant was found to work
weil on Nb 3 Sn as weil as on niobium [6 ].
The primary and secondary inductors were made witb 50-~J.m-wide lines on
75 IJ.ID centers and bad 25 and 58 turns, respectively. Eacb inductor bad an inside
diameter of 3.00 cm and an outside diameter of 3.86 cm. The values of L 1 and L 2
were calculated CJ to be 40 and 210 IJ.H. The superconducting properties of tbe
circuit elements made from the sputtered niobium films were obtained by standard
dc measurements. The transition temperature was found to be 9.3 K and tbe dc
critical current of tbe coils was about 90 mA. The typical resistivity ratio between
room temperature and a temperature just above tbe transition temperature was
about five .
RESULTS AND DISCUSSION
Measurements were carried out at 4.2 K witb tbe circuit assembly sbown in Fig.
2, immersed directly in liquid belium. Signals were transmitted into and out of tbe
cryostat with tbe help of 50-0 semirigid coaxiallines. The signal source used was an
HP 606-A signal generator, and tbe input and output voltages were measured on an
oscilloscope witb a 50-0 termination. The overall-frequency response of the filter
was obtained by performing point by point measurements. For illustration purposes,
a typical curve of tbe output to source signal ratio vs. frequency over the entire
frequency range is sbown in Fig. 3. Tbis was taken witb tbe input signal Ievel at
A Superconducting RF Notch Filter
247
0.75 .------,-----,---l ----,---;l-----,-- - , - - - - -- , - - r - --TI
I
,;'
..~050 -r
..
z
C>
v;
"-'
~ 0.25
-'
"-'
a::
I
1
0 o~-~--~
4 --~-~~-~,o~-,,~
2 -~1~
4 --t~6--~
~s~
FREQUENCY. MHz
Fig. 3. Overall frequency response of filter.
40 mV. Anode exists in the low-frequency range, the output signal rises rapidly with
frequency and Ievels oft at higher frequencies when the impedance of the filter circuit
becomes greater than the 50-n Ioad resistance. As the frequency increases further,
the voltage ratio remains at about 0.5. The notch of the filter appears as a sharp dip of
the output voltage. The detailed shape of a notch on an enlarged frequency scale is
shown in Fig. 4.
From a series of measurements, a plot of the reciprocal of the square of the notch
frequency vs. the tuning capacitance was obtained, as shown in Fig. 5. The linear
dependence of 1/f~ with C 2 is in accordance with the relation in (3). From this plot
the stray capacitance of L 2 and the associated capacitor plates is found to be about
3.2 pF from a straight-line extrapolation. The existence of this capacitance imposes
an upper Iimit of 11 .7 MHz on the tuning range. Furthermore, the same results allow
the calculation of the actual inductance of the secondary coil, which is found to be
53 J.LH. It should be noted that this value is about four times smaller than the nominal
inductance calculated from the geometry. In addition, from an independent
experiment, by measuring the resonant frequencies of the tank circuits of a capacitor
connected in series with the coils, the ratio of inductance between L 1 and L2 was
obtained to be 0.75, and the above observed value of L 2 was confirmed. The
0
~ -2
~ -4
~
...,_~ · 6
!ii -8
- 10
-12
Fig. 4. Detailed shape of a typical notch.
5.90
5.92
FREQUENCY , 11Hz
5.94
C. S. Pang et td.
0.03
':'~ 0.02
:z:
"'
0
4
CAPACITANCE . pf
8
12
Fig. 5. Dependence of notch frequency on tank
circuit capacitance.
reduction of inductance in L 2 appears to be the result of magnetic field screening
produced by the superconducting plates which are located in proximity to the coil.
As shown in (1), the depth is sensitive to the resistance R2 and the coupling
coefficient k. By increasing the coupling, the maximum notch depth observed was
about 17 dB for the nominal 50-0 loading conditions. Values of k and R2 can be
calculated from the measured depth and bandwidth of the notch from (1) and (2).
The values of k obtained in this fashion are smaller than theoretically predicted
based upon the inductance of L 1 and L 2 , and the separation of the coils.
values
This result indicates that the presence of superconducting materials near the coils
reduces the ftux coupling, and that magnetic shielding has to be taken into account in
a realistic calculation of the coupling coefficient. The resistance of the tank circuit
obtained in this fashion is given in Fig. 6 as a function of frequency. From this graph,
the resistance is found to be proportional to w n with n approximately equal to 1.6
over the entire frequency range .
n
...
0
z
~
(/)
Cii
~ 5
...
0
~
"'::>(/)
R
er f 1. 57
3
1. 5 L--L..---'--........L.........L.---l......L..L...I....L..J....L..J'--__J
3
5
10
15
20
F REQ UENCY ,
M Hz
Fig. 6. Resistance of secondary coil as a function
of frequency at 4.2 K.
A Supercondudinc RF Noteh Filter
Z49
The maximum power handling capability of the filter is about 4 mW, which
corresponds to about 50 mA and 200 V of current and voltage being developed in
the tank circuit. This is in reasonable agreement with critical current measurements.
In the frequency range of 2 to 12 MHz, the output to source signal ratio is
independent of the signal strength within the 4-mW maximum just discussed, which
indicates that the resistance does not vary with the current in contrast with the results
of Blair et al. [8 ], who find that the rf loss increases with signallevels. Finally, the
quality factor Q of the present filter is about 2000 with 50-.0 source and output
impedance while the circuit is fully loaded.
Theoretical calculations indicate that at temperatures below Tc/2 and frequencies lower than the pair-breakin;, frequency, the intrinsic resistance is proportional to the square of the frequency [ ]. For real materials, however, the resistance is
also determined by other material properties [ 1 0-- 16], such as (1) surface roughness
and the oxide layer on the superconductor, (2) trapped magnetic vortices and normal
domains in the material, (3) magnetic hysteresis effects of the ftux motion, (4) Iosses
by magnetic coupling to normal metals, and (5) dielectric loading. Recently, Judish et
al. 7 ] measured the surface resistance of a helically loaded Iead cavity at frequencies
from 136 to 472 MHz. Extrapolation of their data to 10 MHz and 4.2 K yields a
value of the surface resistance of about 10-9 .0, which is within a factor of 20 of the
measurements obtained in this study on the niobium film (normalized to the same
low-temperature resistivity).
Although the dominant loss has not been identified in this case, the strong
frequency dependence of the observed resistance rules out the possibility of dielectric loss in the substrate materials. Such a loss depends on the dielectric loss tangent
which is only a weak function of frequency in the range of the present
measurements 8 ]. Hysteresis loss can also be ruled out since this loss should depend
linearly on frequency and a dependence of the loss on signal strengths has not been
observed.
e
e
SUMMARY
A preliminary investigation has been conducted of a superconducting notch
filter for possible application in the 2 to 30 MHz high-frequency (HF) communication band. The circuit was successfully implemented using planar geometry so that
closed-cycle refrigeration could be used to cool circuits fabricated from high Tc
Nb3Sn or Nb3Ge thin films. In the present design, circuit Q's of about 2000 were
obtained with a 50-.0 source and output impedance. Circuit Q's of about 1000 to
2000 are required in ordertoperform fittering of signals in the HF band; the high Q's
available with superconducting technology coupled with the possibility of implementing a wide tuning range outperforms conventional tunable notch filters. Conventional HF notch filters have typical circuit Q's of about 75 to 100 at 10 MHz and
are typically limited to an octave tuning range. The maximum input power to the
filter was found to be about 6 dBm, which enables the superconducting filter to be
used to protect receiver front ends from strong HF intederence signals. Measurements indicate the rf critical current is comparable to the dc critical current, thus
providing a means for estimating the maximum power handling capability. The
undesirable effects of magnetic ftux shielding on L2 has led to an improved design
utilizing rutile (Ti0 2 ), a low-loss and high-dielectric-constant material, to reduce the
capacitor plate area. Knowledge of the resistance and its frequency dependence can
be used to predict the performance of resonators at other frequencies. In this
250
C. S. P11111 et al.
preliminary investigation the dominant source of loss has not been uniquely
identified, although the results indicate that dielectric or hysteresis Iosses are not
dominant.
ACKNOWLEDGMENTS
The authors would like to thank K. E. Gray for useful conversations and T. R. Werner for
experimental assistance.
RE FERENCES
1. A. I. Braginski, J. R. Gavaler. G. W. Roland, M. R. Daniel, M. A. Janocko, and A. T. Santhanam,
IEEE Trans. Magn. Mag-13:300 (1977).
2. R. E. Howard, C. N. King, R. H. Norton, R. B. Zubeck, T. W. Barbee, and R. H. Hammond, in
Advances in Cryogenic Engineering, Vol. 22, Plenum Press, New York (1975), p. 332.
3. R. T. Kampwirth, J. W. Hafstrom, and C. T. Wu, IEEE Trans. Magn. Mag-13:315 (1977); and R. T.
Kampwirth, C. T. Wu, and J. W. Hafstrom, in Advances in Cryogenic Engineering, Vol. 24, Plenum
Press, New York (1978). p. 465.
4. Cutter/Hammer, Airborne Instrument Lab., Final Report, Contract DA ll-119AMC-02530(4)
(Dec. 1966).
5. DOD Tech. Memorandum, Rept. No. S-2111. 633 (July 1977).
6. R. T. Kampwirth, I. Schuller, and C. M. Falco, patent pending (1978).
7. F. W. Grover, Inductance Calculations, Dover Publishing Company, New York (1962).
8. D. G. Blair and W. 0. Hamilton, Rev. Sei. Instrum. 50:279 (1979).
9. D. C. Mattis and J. Bardeen, Phys. Rev. 111:412 (1958).
10. T. A. Buchhold, Cryogenics J:141 (1963).
11. J. L. Zar, J. Appl. Phys. 35:1610 (1964).
12. C. R. Radden and W. H. Hartwig, Phys. Rev. 148:313 (1966).
13. J. M. Pierce, J. Appl. Phys. 44:1342 (1973).
14. S. Giordano, H. Hahn, H. J. Halama, C. Varmazis, and L. Rinderer, J. Appl. Phys. 44:4185 (1973).
15. J. M. Victor and W. H. Hartwig, J. Appl. Phys. 39:2539 (1968).
16. P. Kneisel, 0. Stoltz, and J. Halbritter, IEEE Trans. Magn. Mag-15:21 (1979).
17. J. P. Judish, C. M. Jones, F. K. McGown, and W. T. Milner, Phys. Rev. B 15:4412 (1977).
18. Reference Data for Radio Engineers, ITT, Howard W. Samf Company, New York (1973).
DISCUSSION
Question by D. Petrac, Jet Propulsion Laboratory: How many turns does the inductor have and what
are its inductance values?
Answer by author: There are 25 and 58 turns in the primary and secondary coil, respectively, with a
mean diameter of about 3.4 cm. The calculated values of inductance are 40 and 210 ~-tH.
Question by C. H. Morgan, Brookhaven National Laboratory: Did you consider geometrics other
than flat spirals, e.g., coaxial coils?
Answer by author: Yes, besides the planar configuration presented here, we have also considered a
geometry in which the inductors were fabricated by etching thin-film coating on a hollow dielectric
cylinder.
Question by R. C. Longsworth, Air Products and Chemicals, Inc.: How was the device cooled during
the experimental work?
Answer by author: In this measurement the filter assembly was immersed directly into a liquid helium
bath.
Question by R. C. Longsworth, Air Products and Chemicals, Inc.: What will the closed-cycle
refrigerator requirement be in terms of temperature, temperature stability, capacity, vibration, etc.?
Answer by author: It should be kept in mind that we are only in the preliminary stages of a feasibility
study period. All of the details of filter performance, operation, and construction depend on the results of
the study. These have not all been worked out. The goal of the first part of the study is to establish the
limitations of filter performance. Wehave not yet measured the performance as a function of temperature.
So far, the study suggested that the operating temperature of a Nb3 Sn filter should be kept below about 12
to 13 K and it is expected that performance will be insensitive to temperatures below this point.
E-3
EXPERIMENTAL EVALUATION OF A 1-METERSCALE D-SHAPED TEST COIL FABRICATED
FROM A 23-METER LENGTH OF INTERNALL Y
COOLED, CABLED SUPERCONDUCTOR*
M. 0. Hoenig, A. G. Montgomery, and S. J. Waldman
Francis Bitter National Magnet Laboratoryt
Massachusetts Institute of Technology
Cambridge, Massachusetts
INTRODUCTION
Superconducting magnets have generally been cooled by means of pool-boiling
helium within a cryostat vessel. The internally cooled, cabled superconductor ICCS,
on the other hand, requires only the circulation of helium through its passages.
In the 1-m-scale cryogenic facility the test coil is suspended in a thermally
shielded vacuum where it is exposed to a background magnetic field, provided by a
pair of split solenoids, clamped across its central, straight section (see Fig. 1).
Refrigeration and helium ftow are su,pplied by a Model 1400, CTI refrigerator.
In past work 3 ] various internally cooled, cabled conductors were subjected to
stability tests. Such coils bad the shape of a tightly wound cable, protected from
Lorentz forces by tensile winding restraint. The primary objective of the 1-m-scale
test facility is its ability to expose straight lengths of unsupported conductor, such as
the side of a D-shaped coil, to Lorentz force.
e-
TEST COIL
Figure 2 shows the test coil installed. The coil itself was wound in a single-layer
pancake 152 cm talland 71 cm wide using six turns of conductor. The aluminumsheathed conductor was placed in an anodized aluminum extrusion (see Fig. 3) and
was cowound, with the extrusion into the coil shape. Five turns of the conductor, one
electrical termination, and one hydraulic connection are shown in Fig. 4.
CONDUCTOR
Figure 5 shows a section of the conductor, which consists of 19 sets of triplets.
Each triplet is a twisted set of three strands, each 1.05 mm in diameter. The coil was
formed by twisting first 6, then 12 triplets around a central triplet, with each layer
* Work supported by the U. S. Department of Energy.
t Supported by the National Science Foundation.
251
151
M. 0. Hoenlg, A. G. Montgomery, and S. J. Waldman
Fig. 1. D-shaped test coil shown with split-pair
solenoid.
Fig. 2. D coil, split-pair solenoid and helium canister,
supported by 15-K top plate.
Experimental Evaluation of a D-Shaped Test Coil
253
Fig. 3. Aluminum-sheathed cable and
anodized
aluminum
extrusion.
Legend: 1, Coil space; 2, aluminum
tube (12-mm diameter); 3, aluminum
extrusion (anodized); 4, fiberglass
insulation (epoxy impregnated); 5,
insulation overwrap (epoxy impregnated); 6, epoxy filled space.
individually transposed. The cable is contained in an aluminum tube with a 0.9-mmthick wall. The helium cross section inside the tube represents 40% of the total
cross-sectional area.
SUPERCONDUCfOR
The superconducting wire was fabricated by MCA. * Each strand has a diameter
of 1.05 mm and consists of 83% copper and 17% NBTi in the form of 671 filaments
of approximately 8-IJ.m diameter. The same cable and superconductor have been
tested previously [ 1] in the form of a 15-cm-diameter test coil.
BACKGROUND FIELD COILS
A 7-T background field was provided for the test coil by means of a pair of
iron-filled split solenoids, fabricated by MCA, and illustrated in Figs. 1 and 2. The
solenoids were attached to the test coil in the manner shown in Fig. 6. A plan view of
the assembly is shown in Fig. 7.
* Magnetic Corporation of America.
254
M. 0. Hoenig, A. G. Montgomery, and S. J. Waldman
Fig. 4. Section of coil shown with electrical and hydraulic
terminations.
Fig. 5. Magnified cross section of conductor, showing
aluminum sheath and cabled conductor with NbTi
filaments (hexagonal shape).
FORCED·FLOW COOLING AND REFRIGERATION
A simplified schematic of the forced-flow helium cooling system is shown in Fig.
8. Coldhelium ftow to the test coil is obtained from the cold, high-pressure side of the
refrigerator. The gas at 3 to 4 atm pressure is cooled down to coil-operating
temperature (4.7 to 5.3 K) by means of heat exhange to 1 atm liquid helium within a
canister reservoir shown in Fig. 2.
2SS
Experimental Evaluation of a D-Shaped Test Coil
Fig. 6. Adapterblock and coil with pulse coil,
ready for bolting between split-pair
solenoids.
0
AOAPTER _
BLOCK
0
0
0
45" 01A , 15K THERM AL
SH ROUO
18"
39"
Fig. 7. Plan view of assembly, showing cross section of test coil.
Helium enters and leaves the test coil as a single-phase fluid. Mixed with
additional bypass coolant, it passes through the thermal shroud, maintaining its
temperature close to 15 K. Downstream of the shroud the helium is expanded to
1.2 atm for return to the refrigerator.
The refrigerator, with its two standard compressors, has a nominal capacity of
7 5 W. Since this is not adequate to satisfy the total requirements, additional helium is
supplied during steady-state operation to maintain liquid Ievel in the helium canister.
TEST FACILITY
The integrally tubulated stainless steel shroud assembly is illustrated in Fig. 9.1t
is cooled to about 15 K by the refrigerator. The shroud provides a 172-cm-tall,
M. 0. Hoenig, A. G. Montgomery, and S. J. Waldman
256
WARM RETURN
TO COMPRESSOR
COLD
300A LEADS
:12777d7777ZZZ;6ZZZ7~
1
[~
VACUU M SPACE
~==)VACUUM
CHAMB ER
= --=--"' h
Figo SoSimplified schematic of forced-flow helium cooling systemo
ROOM TEMP. TOP PLATE
78 K o LNz COOLED PL ATE
15 K o HELIUM COOLED PLA TE
45°0 0 D SUPPORT RING _____...
TEST
68"
VOLUME
44"0 D COI L SUPPORT RING
15K
WALL
HELIUM COOLE D
CY LI NDER - - - -- HELIUM COOLED
BOTTOM PLATE
Fig. 9. Elevation view of 15-K, evacuated test volumeo
Elqteriolental Evaluation of a D-Shaped Test CoD
157
114-cm-diameter, 1. 75-m3 working volume within its optically tight enclosure. The
shroud is brought up vertically into position, is bolted to its 15 K top plate, and thus
surrounds the test coil and its apparatus. The 15-K structure is suspended from a
liquid-nitrogen-cooled stainless steel plate and support ring, itself suspended from
the top, room temperature support plate of the vacuum chamber.
INSTRUMENTATION
The dewar and D coil were instrumented with 20 carbon resistors to indicate
steady-state temperatures. Calibrated carbon glass resistors were attached to the
liquid helium inlet and outlet of the D coil, as weil as the orifice meter. Static helium
pressures in the system were measured with room temperature transducers connected by means of capillary tubes. Helium pressure transients were measured with a
cryogenic strain gage pressure transducer. This 0-150 psig transducer was placed
upstream of the D coil as shown in Fig. 8.
A voltage-tap pair was connected to each of six turns of the D coil. On each
conductor turn, pair connections were placed on opposite sides of the high magnetic
field region and one of the Iead wires was brought through the high-field region to
meet the other in order to minimize inductive pickup in the voltage tap pairs.
A two-layer pulse coil was wound onto the D coil. This pulse winding is
represented in Fig. 6. A capacitor bank charged from 80 to 500 V could be
discharged into the coil to produce a 0.3- to 2.2-T pulse with a 12-ms width.
Although a significant fraction of the field may be screened out by the 0.9-mm-thick
aluminum sheath, the penetrating magnetic field pulse induces currents within the
cable itself within the conduit. A pulse coil calibration was performed on a separate
length of the conductor in zero field, allowing for the correlation between a capacitor
discharge voltage and the deposition of heat energy in the cable. A capacitor
discharge voltage of 300 V was tentatively correlated to the deposition of
270 mJ I cm3 of cable metal. A cryogenic pressure transducer was used to examine
the thermodynamic state of the pressurized helium, approximately 5 ms, after pulse
discharge. The capacitor voltage discharge was thus related to the indicated internal
energy change in helium. Initial helium temperature and pressure within the cable
space were 4.2 K and 3 atm, respectively.
Helium ftow through the D coil was measured by means of a cryogenic orifice
plate ftow meter. The ftow meterwas located downstream of the D coil as shown in
Fig. 8. The ftow meter was calibrated by passing helium through the cryogenic ftow
meter and a room temperature volumetric gas meter at a constant-mass ftow rate.
TEST COIL OPERATION
The test coil has a critical current rating of 6800 A at 5.0 K and 7 T. lt can be
subjected to pulsed eddy-current heating. The following procedures were used in its
operation.
Pumpdown and Cooldown
The 4-ft-diameter by 8-ft-tall vacuum chamber was evacuated by means of a
6-in diffusionpump to about 2 X 10-5 torr within about 6 hr. The heliumsystemwas
purged and connected to the refrigerator, with both systems at room temperature.
Initial cooldown to 100 K took about 24 hr and was carried out by the
refrigeration system using its liquid-nitrogen-cooled heat exchanger. Subsequent
cooldown to 10 K took another 12 hr using the full output of the two expansion
258
M. 0. Hoe.U., A. G. MHf~GmerY, IUid S. J. Waldaum
engine Model1400 CTI refrigerator. As noted from the schematic (Fig. 8), helium
ftow can be regulated to cool down the cabled conductor and thermal shroud in
series, followed by the D coil's current Ieads and the split-pair solenoid with its Ieads,
in parallel. Gas ftow is then returned to the refrigerator, partly through the warm
output of the Ieads.
The capacity of the refrigerator is adequate to bring the D coil temperature to
approximately 10 K and the split pair solenoid and thermal shroud temperature to
20K.
Preparadon for Test Operadon
Final cooldown of the system can be carried out in less than 1 hr. Liquidhelium
is transferred to the canister, located within the thermal shroud, and connected to
feed the split pair solenoids by gravity.
The system is ready for test Operation once the following requirements have
been satisfied:
1. Split-pair solenoids must be fully ftooded with liquid helium from the
canister. Once the 300-A Ieads to the solenoids are adequately cooled, the solenoids
can be charged up to the current Ievel corresponding to the desired field.
2. The D coil 7000-A current Ieads must be adequately cooled.
3. The D coil inlet and outlet temperatures must be at or below 5 K and steady.
4. Helium pressure and ftow rate through the test coil must be established.
Test Operadons
Steady State. Steady-state operations were performed at 6 and 7 T for extensive
periods of time with a dc current of 6000 A. No quench of the test coil was observed.
Critical Cu"ent Tests. The coil was brought up to its critical current in a
background field of 7 T and a helium temperature of 5.0 Kin the cable. Quench
occurred at 6720 A corresponding to a current density of 817 A/mm 2 (NbTi),
matehing the short sample current density of the superconductor at 5 K and 7 T.
As observed in the schematic (Fig. 8), helium can only expand out of the coil
through its downstream connection. This was arranged in this manner to measure
pressure buildup (on the upstream end of the conductor) as the result of a quench.
Starting with an initial pressure of 2.65 atm, a peak pressure of 6.6 atm was noted 1 s
after the appearance of voltage, indicating a normality.
Cu"ent Sweep and Reversal Tests. Several current sweep tests were performed
to see if wire motion in the cabled conductor in its straight section would generate
sufficient heat to cause a quench. With the background field at 6 T, the current, I, was
ramped up to 5500 A in 25() ms. Peak dl/ dt was 40,000 A/s at zero time. Though
the temperature of efB.uent helium was slightly elevated, no quench occurred.
Steady-state conditions were established at 5500 A. In a similar test the conductor
quenched in an attempt to reach 6000 A in 250 ms. Peak dl/ dt, in this case, was
44,000A/s.
The direction of the current was reversed several times in order to see the effect
of possible bunching of cable strands. No effect was observed.
Pulse-Heating Tests. Table I shows the results of numerous pulse-heating tests.
With a given current, field, helium ftow rate, and helium pressure established, the
conductor was heated with a pulse coil. The data showing maximum stability have
been plotted in Fig. 10, in terms of approximate thermal energy input (mJ/cm3 ) per
unit volume of wire vs. 1/10 , the normalized current.
Experimental Evaluation of a D-Shaped Test CoD
...E
.
u
~
"'...J
<[
u
259
0
v
N
0
0
N
(/)
>(!)
Q:
"'z
"'
1"'
0
!!!
0
~
<[
:::0
x
0
Q:
ll.
ll.
<[
0
CD
...
0
Fig. 10. Stability curve; pulsed energy vs. normalized
current.
02
04
06
08
10
NORMALIZED CURRENT, 1/lo
CONCLUSIONS AND DISCUSSION
Steady-state Operations of the D coil were performed at 89% of its quench
current of 6702 A (7 T) at a temperature of 5 K. The critical current of the coil was
found to match its short sample quench current at 7 T and 5 K. Rapid (250-ms)
current sweep tests demonstrated that the conductor current could be brought up
from 0 to 5500 A without quench, with a peak, dl/ dt, of 40,000 A/s. This ramp
stability is viewed as evidence that Lorentz force generated wire movement, if any,
produced insignificant conductor heating at this operating Ievel. Pulse heating tests
indicated recovery from a range of heating pulses at both 6 and 7 T. These results are
plotted in Fig. 10. The coil was Operated at a reduced helium velocity (Table I) with
no change in stability e]. While normal Operations took place at a helium pressure of
3 atm, a test run was made at 4 atm in order to determine the effect of increased
pressure on performance. No effect was found. In no instance were extreme
pressures observed upon nonrecovery. It is believed that because the high magnetic
field is confined to about 4% of the conductor under test, the normalcy does not
propagate into the low field (96%) of the D coil.
Table I. Stability Test Data
Field,
T
Temperature,*
K
Pressure,*
atm
7
7
7
6
6
6
6
5
5
5
5
5
5
5
3
3
3
3
3
3
* Helium properties.
3
Velocity,*
cm/s
18
18
6.6
18
18
18
18
A
Normalized
current
Pulse
time,
ms
Pulse
voltage,
V
2900
4700
4700
5600
6500
6000
2000
0.43
0.70
0.70
0.83
0.97
0.89
0.30
12
12
12
12
12
12
12
180
80
80
125
80
105
280
Current,
M. 0. Hoenig, A. G. Moatgomery, lllld S. J. Waldman
Testoperations were performed at conductor temperatures of 4.7 to 5.3 K.
Since the NbTi critical temperature Tc at 7 T is only 6.1 K, the thermal margin was
very limited. Relatively high stable energy inputs (Fig. 10) would thus tend to
indicate rapid recovery and very short normal and current-sharing periods.
REFERENCES
1. M. 0. Hoenig and A. G. Montgomery, in Proc. 7th Symp. Engineering Problems of Fusion Research,
Vol. I, IEEE Science Center, Piscataway, New Jersey, (1977), p. 780.
2. Y. lwasa, M. 0. Hoenig, and D. B. Montgomery, IEEE Trans. Magn. Mag-13:678 (1977).
3. M. 0. Hoenig, J. W. Lue, and D. B. Montgomery, in Proc. 6th Intern. Conference on Magnet
Technology, ALFA, Bratislava, Czechoslavakia (1978), p. 1021.
E-4
PERFORMANCE OF GAS-FILLED
THERMAL SWITCHES
J. Yamamoto
Osaka University
Suita, Osaka, Japan
INTRODUCTION
A thermal switch has been developed for precooling a superconducting magnet
with a cryocooler C· 2 ]. The switch is essentially a heat pipe [3 ], which provides a high
heat transfer rate when the working gas is being liquefied and acts as an insulator
when the dewar for the magnet is filled with liquid helium. Configuration and
performance of the switch are described herein.
CONSTRUCTION
The thermal switch consists of a gas-filled stainless steel tube (262 mm lang,
15 mm in diameter and 0.3 mm in thickness), with cone-shaped copper ends as
illustrated in Fig. 1. The encapsulated gas begins to liquefy when the temperature at
the upper end reaches the condensation temperature of the gas. As the gas condenses
on the upper cone, droplets form and fall off the apex onto the lower cone, where
they evaporate. This process of condensation and evaporation in the tube transfers
heat from the lower end of the tube to the upper end. While this process is occurring,
the switch is said to be in the "on" condition.
The temperature range or band during the "on" state of operation is wider when
the charging pressure of the gas is increased. During a typical operation the thermal
switch is filled with either nitrogen or hydrogen at 1.3 MPa (13 atm) at room
temperature. When either end of the thermal switch is below the triple point of the
gas (13.9 K for hydrogen and 63.2 K for nitrogen), the switch automatically reverts
to the "off" condition owing to the solidification of the fluid.
PERFORMANCE
Figure 2 shows the relation between the gas pressure in the tube and the
temperature of the upper end (Tu) and the lower end (T1) for the nitrogen-filled
switch when a small copper piece (about 50 g) is attached on the lower end, and the
upper end is cooled by a cryocooler. The saturated vapor pressure curve for nitrogen
is also shown in the figure as a dotted line. A dashed line shows the change of the
inside pressure.
As the temperature of the upper end is lowered, the inside pressure decreases
and T 1 slowly decreases, because the switch is "off". When Tu matches the saturation
261
J. Yamamoto
262
gas inlet tube
..J...i-- - - - - -
-
copper cone
- - - - - stainless steel tube
(15 mm od, 0.3 mm
thicknessl
E
E
N
!El
copper cone
Fig. 1. Configuration of thermal switch. Stainless
steel tube is capped by copper end pieces. After
filling with working gas at 1.3 MPa, the inlet tube is
sealed off.
1.
'
I
l
II!
0..
o. i
::i';
N2
>' :
a.
1.0
""' I!
.'"I.
-·
I
~i
0 .5
T.K
Fig. 2. Pressure vs. temperature curve for a
nitrogen-filled switch during the precooling stage.
Dashed line shows an isothermal change.
Performance of Gas-Filled Thermal Switches
263
o. a .---~--.----..----.--.------.
CO 0.6
Q.
::E
0.4
0.2
Fig. 3. Pressure vs. temperature curve for a
H 2 -filled switch during the precooling stage.
T. K
temperature of the enclosed gas, the nitrogen gas starts to liquefy, thereby activating
the thermal switch. Tu follows along the saturated vapor-liquid line of Fig. 2 when
the switch is in the "on" state. Finally T1 is coincident with Tu on the saturated
vapor-liquid line.
The same situation is observed for the hydrogen switch as shown in Fig. 3;
however, the saturated vapor pressure line corresponds to lower temperatures. The
thermal switches which were used to provide the data in Figs. 2 and 3 were not sealed
off but bad an extension tube for measuring pressures. The volume of the extension
tube is about 5% of the total volume of the switch itself.
The measured heat transfer rates of the switches as a function of Tu are shown in
Fig. 4. To obtain these heat transfer rates, a small electrical heater was mounted on
the lower end of the switch. The heat transfer rate was determined by dividing the
applied electrical heat at the lower end by the temperature difference of the two ends.
Hz swltch
100
r",
i
I
I
I
'
I
I
r
I
I
\
lI N2 switch
.
I
'I
+
I
I
I
I
I
\
Fig. 4. Heat transfer rate of the nitrogen and hydrogen
gas-filled switches. Abscissa depicts temperature of the
upper end of switch.
....
0'~-~-~~----,~~-~-.h,;
len"4)llrtllure , K
J. Yamamoto
15
3:1.0
i
~
2
~
05
0
2
6T. K
3
4
Fig. 5. Heat transfer performance of the hydrogen switch in the "on" condition. Abscissa
represents the temperature difference, T1 - Tw.
The heat transfer rate was measured under conditions of low applied heat so that it
would be independent of the temperature diflerence. This provides a close approach
to the isothermal conditions noted in Figs. 2 and 3.
The nitrogen switch provided a heat transferrate of 3 x 10- 1 W /K during the
"on" condition (T.. range of 63 to 88 K). The hydrogen switch showed a very similar
heat transferrate although the T.. in the "on" condition moves to a lower temperature (16 to 20 K). The heat transfer rates shown in the figure include the contribution
of the stainless steel tube. This is estimated as 3.6 x 10-4 W /K and 4.3 x 10-s W /K
at 60 K and 10 K, respectively.
With T.. lower than the triple point of the filling gas and temperatures below the
"on" condition, the heat transfer rate is about 5 x 10-4 W /K; when compared to
that estimated for the stainless tube alone, one can see that the heat transfer is
primarily determined by the tube conduction. At temperatures above the "on"
condition, the heat transferrate shown in the figure (about 5 x 10-3 W /K) is a result
of the natural convection of the filled gas.
Figure 4 shows the heat ftow of the hydrogen switch during the "on" condition.
The heat ftow is proportional to the temperature diflerence between the two end
cones up to 1.1 W. When additional electrical heat is applied at the lower end of the
switch, a saturation phenomenon occurs which may be caused by a limited condensation rate at the surface of the upper cone.
CONCLUSION
Application of the thermal switch to a real cryostat with a cryocooler results in
an eflective "on" region which is wider than that shown in Fig. 4 because a large
temperature diflerence is caused in the precooling stage (see Figs. 2 and 3). The "on"
temperature range can be incremented up or down and its duration increased or
decreased by changing gas composition and pressure.
The perfonnance of the switch is very attractive for many applications in
cryogenics. The application. of the switch for grecooling a superconducting
magnet has been successfully examined elsewhere [ ].
ACKNOWLEDGMENTS
The author wishes to acknowledge the services of M. Yanai of Osaka Oxygen Industries, Ltd. for
designing the thermal switch and the helpful discussions ofT. Shigi and Y. Inuishi during this work.
Performance of Gu-Filled Thermal Switdles
265
RE FE RENCES
1. J. Y amamoto and T. Shigi, in Proc. 7th Intern. Cryogenic Engineering Conference, IPC Press, Guildford,
England (1978), p. 593.
2. J. Yamamoto and M. Yanai, Rev. Sei. Instrum. 50:1382 (1979).
3. R. P. Bywaters and R. A. Griffin, Cryogenics 13:344 (1973).
DISCUSSION
Question by E. Lady, University of Michigan: Is the heat transfer of the thermal switch limited to the
vertical direction?
Answer by the author: Yes, the droplet of the liquefied gas transports heat in the thermal switch.
F-1
TRANSIENT COOLING OF A FAULTWORTHY
SUPERCONDUCDNG ELECTRIC GENERATOR*
J. A. Schwoerer and J. L. Smith, Jr.
Massachusetts Institute of Technology
Cambridge, Massachusetts
INTRODUCDON
In order for superconducting generatorstobe of use in power stations, they must
be made faultworthy, or able to withstand the effects of a short circuit on the power
lines. The work described herein is part of an MIT-DOE program to design a
2000-MVA generator, the size of commercial interest, and to build and test a
10-MVA prototype. Designs of faultworthy superconducting generators to date
have stationary, normally conducting armatures, rotating superconducting field
windings, and several rotating electromagnetic shields between the field winding and
the armature [ 1- 3 ]. The MITdesign has two electromagnetic shields and is unique in
that these are structurally part of the rotor and operate in the steady state at
temparatures in the range of 4 to 6 K. A system of cold shields, as opposed to having
at least the outermost shield self-supporting and at room temperature, simplifies the
structural problern and has other advantages, but it makes the cooling problern much
more difficult [ 1]. Fora representative 2000-MVA design, subjected to a severe fault
used for design purposes, the time-averaged total losses in the shields are 4 MW
during the first 0.1 s and thereafter drop by an order of magnitude and decay
exponentially. The transient cooling scheme must prevent this heat input from
increasing the temperature of the superconductor to the level where it will go normal.
The principal feature of this transient cooling scheme is a self-pumping helium
ßow system for removing the heat input to the shields. This works in combination
with thermal isolation layers which protect the superconductor during the short time
that the temperature of the shields is high. The transient cooling scheme is described
and analyze<\ below. This analysis has been used to show that the cooling concept is
viable for both 10- and 2000-MVA sizes.
COOLING SCHEME DESCRIPTION
Figure 1 is a preliminary design layout of the 10-MVA generator. The outer of
the two electromagnetic shields is the damper. It is a copper winding connected to an
extemal resistor and is designed both to damp out rotor swings and to shield the
superconductor from unsteady fields. The inner of the electromagnetic shields is the
* Work supported by U. S. DOE under Contract No. EX-76-A-01-2295, Task Order No. 11.
266
SUPPORT TUB E
I
He COUPL I NGS
VACUU M AI R G A P
T0
10 C M
STA T OR BOR E SEAL
O UT ER
I
Fig. 1. MIT 10-MVA preliminary design Iayout.
HOOP SUPPO RT
STAND - OFF R ~GS
S O L I D SHIEL D
TO POWER COUPLI N<";
T HERMAL
~
i
ftl
;
"~
:1.
~
ii'
l"l
!
Ii
s=
1
~
a-~
ri
.,2.
Jf
2.
~
a
~·
~
J. A. Schwoerer and J. L. Smith, Jr.
SH I ELO
HE LI UM
RESERVOIR
FLOOOEO
SHI ELO
CHECK
VALVE
Fig. 2. Schematic of shield cooling system.
solid shield. It is a solid copper cylinder designed to intercept the unsteady magnetic
fields that leak through the damper. During a fault, approximately 95% of the
rotor heat input occurs in the damper in the form of 12 R losses, approximately 5%
occurs in the solid shield as 1 2 R losses, and « 1% occurs in the field winding as
magnetic hysteresis Iosses in the superconductor and 12 R Iosses in the copper
matrix Cl.
The self-pumping helium ftow systems for cooling the solid shield and damper are
separate and identical in the generalized design analyzed here. The system for either
shield is diagrammed in Fig. 2. It consists of a reservoir near the end of the rotor,
helium passages in the shield connected to the reservoir by a line containing a check
valve, and a vent line leading from the end of the shield opposite the reservoir to the
rotor centerline and then out to the atmosphere. The ftow is throttled by a nozzle at
the end of the vent line. Recently, consideration has been given to a modified design
in which the helium cooling systems for the damper and solid shield are interconnected and there is a single check valve that is near the centerline between the
field-winding reservoir and one of the shield reservoirs [ 1].
The other parts of the transient cooling system are the thermal isolation layers and
the cooling system for the field winding. The 10-MVA design, shown in Fig. 1, has
stainless-steel-epoxy thermal standoft rings between the damper and the solid shield.
The stainless steel outer support tube doubles as a thermal isolation layer between
the solid shield and the field winding. The field winding is ftooded with helium and
connected to the field-winding reservoir by radial passages containing copper
isothermalizing bars.
The operation of the cooling system is as follows. Because of the centrifugal
acceleration, the pressure of the helium in the shields and the field winding is always
above the critical pressure ; thus, boiling does not occur. In each shield the transient
heat input causes the pressure to rise, closing the check valve and producing ftow out
the vent line. The resultant expansion produces a cooling effect and counteracts the
pressure rise. When the pressure in the shield again becomes equal to the pressure at
the bottom of the shield reservoir, the check valve opens. This first period of the
operation is termed the "blowdown phase." The cold helium that enters the shield
from the reservoir partly mixes with and partly displaces the helium in the shield and
produces further cooling. The ftow is driven by the thermosiphon effect: the fluid in
the vent line is less dense than that in the reservoir. Thus the second period of
operation is designated as the "chimney phase." Oscillations in the shield pressure
similar to those observed in filling a helium dewar may occur.
The resulting shield temperature history is, roughly speaking, a sharp rise
followed by an exponential return to the steady-state Ievel. The thermal isolation
layers are designed so that the time it takes for the thermal wave to propagate across
the layers is long compared to the time it takes for the self-pumping systems to recool
the shields.
Transient Cooling of a Fanltwortby Snperoondncting Electric Generator
269
ANALYSIS
The analysis described here deals primarily with the self-pumping shield cooling
system shown in Fig. 2. It has been assumed that the heat capacity of the solid parts of
the shield is negligible such that the electrical heat generation is nearly instantaneously transferred to the helium. For cooling channel geometries that have been
considered, there is significant enhancement of the heat transfer by the secondary
flow driven by natural convection, and the convective heat transfer coefficient has
been calculated tobe approximately 0.5 W /cm 2 K [4 ]. While the configuration of the
helium passages in the shields has not been finalized, one can conceive of designs,
with conductors and helium in direct contact and a large amount of surface area,
where the assumption is accurate.
In designs to date, the heat transfer between the shields and the adjacent
thermal isolation layers has been neglected in the analysis of the self-pumping shield
cooling system. This has led to conservative results since either the heat transfer with
the thermal isolation layers has been small compared to the electrical heat generation
in the shields, or, at a given time, the net heat transfer has been out of the shields. This
might not be true for the solid shield in some designs. In such a case, an iterative
procedure would be followed in which the heat input to the shield would be adjusted
according to the calculated heat transfer with adjacent thermal isolation layers.
The design is such that changes in state at the entrance and exit of the shield may
be neglected. This is reasonable since the cross-sectional area of the line between the
reservoir and the shield and that of the vent line are approximately the same as the
combined cross-sectional area of the cooling passages in the shields. Finally, it has
been verified by calculation that the kinetic energy resulting from the fluid velocity in
the direction of ftow can be neglected, except at the vent line exit nozzle, throughout
the transient.
For the blowdown phase, when the check valve is closed, it is assumed that the
state of the helium in the shield is uniform. This is accurate because heating is
uniform, the pressure drops due to viscous and inertial effects are very small, and the
axial thermal conductivity of the shield is high. Applying conservation of mass and
conservation of energy to an annular control volume around the shield, one obtains
dp.
dt
and
V
_1_( () _m/•)
Ps
du, =
Vp,
dt
(1)
(2)
For the chimney phase, when the check valve is open, two limiting-case models
are considered: an "instant-mixing" model and a "no-mixing" model. In the
instant-mixing model the state of the helium in the shield is assumed to be uniform.
The high axial thermal conductivity of the shield and the fact that the natural
convection flows tend to be very strong are factors which breakdown axial variations
of the states in the shield. In the no-mixing model it is assumed that the helium that
enters the shield from the reservoir does not mix or undergo heat transfer with the
helium already in the shield. In both models the reservoir is assumed to be infinite
and the shield pressure to be uniform and constant throughout the chimney phase.
Recent work has studied the effects of depleting the reservoir [ 1 ]. Also, it
270
J. A. Schwoerer and J. L. Smith, Jr.
appears that mixing effects may cause pressure oscillations under some circumstances. For certain combinations of helium states in the shield and reservoir, the
instant-mixing model produces a negative ftow into the shield which violates the
equations of mixing. This appears to be associated with the fact that when helium of
the two states in question mix at constant volume, the pressure drops. However, this
problern has not been encountered in recent designs. lt is possible that pressure
oscillations will occur only for those cases where the instant-mixing model gives this
negative ftow at the inlet.
For the instant-mixing model, the conservation of mass and conservation of
energy are again applied to an annular control volume around the shield. Changes in
u. and p. are related by the constant pressure assumption according to the thermodynamic property (aujap)p,. Combining these results gives
6- mv(h. -
du.
dt
V{p.
+ [(u.-
h,)
h,)j(aujap)pJ}
(3)
and
.
m,
=
.
mv
V
+ (aujap)p,
du.
dt
(4)
For the no-mixing model, the helium in the shield is divided into a number of
control mass elements. Applying conservation of energy to an arbitrary control mass
results in
dhCM
6
dt
VpcM
(5)
The history of mass ftow rate in the vent line determines the time span for which a
given control mass element is in the shield.
The analysis of the helium ftow circuit is completed by relating mv to the state at
the shield exit. In designs to date it has been reasonable to assume that the ftow in the
vent line is quasisteady. lt has also been assumed that the ftow is isentropic
throughout the vent line and that the helium in the nozzle behaves like an ideal gas.
The model is approximate since the ftow may be two phase in the nozzle and helium
departs from the ideal gas model for the range of states of interest. For designs to
date, the ftow in the nozzle is choked during most of the transient.
The equations that describe the self-pumping shield cooling system were solved
by computer. For the blowdown phase and for the instant-mixing model of the
chimney phase, an Adams-method subroutine developed by Shampine and Gordon
was used [5 ]. For the no-mixing model the Runge-Kutta method was simpler for
keeping track of the different control mass elements. The data for helium properties
needed to integrate the equations were supplied by a subroutine package from the
National Bureau of Standards ft
The heat transfer across the thermal isolation layers is an unsteady conduction
problern with variable-temperature boundary conditions. The problern is nonlinear
because the thermal conductivity and heat capacity of stainless steel are strong
functions of temperature. The problern was solved by computer using the explicit
Euter method.
The factor that determines whether the transient cooling system is effective is
clearly whether the temperature rise of the superconductor is acceptable. There is
electromagnetic heating in the field winding in addition to the conduction across the
Transient Cooling of a Faultworthy Superconducting Eledric Generator
271
inner thermal isolation layer. A conservative estimate of the temperature rise of the
field winding is that which results if all of the heat input in excess of the steady-state
Ievel is stored in the heat capacity of the helium contained in the winding.
RESULTS
The operation of the self-pumping shield cooling system is demonstrated by the
results for the damper of a representative 2000-MVA design. One of the design
considerations is matehing the volume of helium in the shield and the minimum area
of the nozzle in the vent line to the heat input and shield radius so that performance is
optimized. In the present case the damper radius is 82 cm, the helium volume in the
damper is 7.9 x 104 cm3 , and the nozzle area is 10 cm 2 . The helium state in the
reservoir near the rotor centerline is 1atm saturated liquid. The heat generation
during a three-phase fault on the generator terminals Iasting 0.1 s is a constant rate of
3.9 MW for 0.1 s followed by a decayinr, exponential starting at a Ievel fö that of the
initial rate with a time constant of 2 s [ ]. This is nearly the warst possible fault that
could occur.
During the first 0.1 s of the transient, the calculated state of the helium in the
shield moves from state A to state Bon Fig. 3. When the rate of heating decreases,
the state at first follows path BC on Fig. 3. After the check valve opens, the states in
the shield fall on curve AD. Point D corresponds to the maximum temperature at the
shield exit predicted by the no-mixing model. The calculated pressure, temperature,
and density of the helium in the shield during the blowdown phase are plotted vs.
time in Fig. 4. The shield temperature predictions of the two chimney phase models
are plotted in Fig. 5. Both the exit temperature and the mixed mean temperature
calculated by the no-mixing model are given. The results for density of helium in the
shield during the chimney phase are plotted in Fig. 6. The total use of helium from the
reservoir is calculated to be 60 kg by the no-mixing model and 80 kg by the
instant-mixing model.
The results for the operation of the other components of the transient cooling
system for the 2000-MVA design are briefty given below. For the solid shield, the
Fig. 3. Locus of transient helium states-2000-MVA
damper.
4 .0
s, J/gm/K
6 .0
6 .0
J. A. Schwoerer and J. L. Smitb, Jr.
0 .20
100
....""
E 18
"'0.
E
"
0
0..
8
90
0 .16
0 .05
0 .10
t ,
sec
0.15
Fig. 4. Shield properties during blowdown phase-2000-MVA
damper.
radius is 68 cm, the helium volume is 4.4 x 104 cm3 , and the nozzle area is again
10 cm2 • The history of heat generation is of the same form as for the damper and has
an initiallevel of 0.14 MW. The temperature reached by isentropic compression
from the state at the reservoir centerline is 5.3 K. The maximum temperature occurs
during the chimney phase and is 6.5 Kat 2 s according to the instant-mixing model
and 7.2 K at 4 s according to the no-mixing model for the state at the shield exit. The
length of the transient is 16 s according to the instant-mixing model and 8 s by the
no-mixing model. The estimates of total helium used for cooling the solid shield are
14 kg (instant mixing) and 10 kg (no mixing).
The distance between the solid shield and the damper is set by electrical rather
than thermal considerations, and the solid shield is almost 100% isolated from the
heat input to the damper. The heat transfer to the field winding has a steady-state
level of 350 W if one assumes that the steady-state temperature of the solid shield is
reached by isentropic compression from the centerline state in the reservoir while the
field winding, cooled by copper bars, is at the same temperature as the reservoir
centerline. The peak transient heat transfer rate to the field winding is 700 W at 7 s.
18
30
t,
StC
40
Fig. 5. Shield temperature predictions during
chimney phase-2000-MVA damper.
Transient Cooling of a Faultworthy Superconducting Eledric Generator
273
0 . 18
u
....u
~
<>..
0 .16
0 . 14 ..__,__..___"L__"L__ _.__
20
10
0
_.__~---'----='
30
40
t, 'ec
Fig. 6. Shield helium density predictions during chimney
phase-2000-MVA damper.
The total heat input in excess of the steady-state Ievel is 4500 J and occurs over a
period of about 50s. This heat input is large compared to the anticipated electrical
heat generation in the field winding. If all of the heat were stored in the heat capacity
of the field winding, the temperature rise would be about 0.1 K, which is acceptable.
More detailed results for the 2000-MVA design and results for the 10-MVA
design are given elsewhere [1 ' 7 ]. The cooling system concept has been found to be
viable for both generator sizes.
SUMMARY
A transient cooling system has been described and analysed for a fault-worthy
superconducting generator having two electromagnetic shields mounted on the rotor
and operating at cryogenic temperature. The results of applying the analysis to a
representative 2000-MVA generator design have been briefly described. Detailed
results given elsewhere show that the design concept is viable for both 10- and
2000-MVA sizes. A refined version of the cooling system design presented here will
be used in the MIT 10-MVA superconducting generator.
NOTATION
h = specific enthalpy
m, = mass ftow rate from reservoir to shield
m. = mass ftow rate in vent line
P = pressure
(} = total rate of heat generation in the shield
t = time since start of transient
u = specific internal energy
V = shield void volume
p = density
Subscripts
s = shield state (assumed uniform)
r = state at bottom of reservoir
CM = state of control mass
174
J. A. Schwoerer and J. L. Smith, Jr.
REFERENCES
1. Cryogenic Engineering Labaratory and Electric Power Systems Engineering Laboratory,
2.
3.
4.
5.
6.
7.
Massachusetts Institute of Technology, "Demonstration of an Advanced Superconducting Generator," U. S. DOE InterimReportE(49-18)-2295, Task Order No. 11, IR 1, Sec. I.B.1; IR4,Sec. II.A.3;
IR 7, Sec. I.D, Sec. IV.D; IR 8 Sec. IV.D.2.
J. H. Parkerand R. A. Towne, "Superconducting Generator Design," EPRI Final Report EL-557
(1977).
M. J. Jefferies and P. A. Rios, "Superconducting Generator Design," EPRI Final Report EL-663
(1978).
R. G. Scurlock and G. K. Thornton, Intern. J. Heat Mass Transfer 20:31 (1977).
L. F. Shampine and M. K. Gordon, Computer Solution of Ordinary Differential Equations, W. H.
Freeman, San Francisco (1975).
R. D. McCarty, NBS Tech. Note 631 (1972).
J. A. Schwoerer, M.S. thesis, Dept. of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts (1978).
F-2
EXPERIMENTAL SIMULATION OF A
CRYOGENIC SYSTEM FOR A LARGE
SUPERCONDUCTING ROTOR*
L. Sobel, J. L. Smith, Jr., and F. Rumore
Massachusetts Institute of Technology
Cambridge, Massachusetts
INTRODUCTION
The high-tip speed experiment described in this study involves a cryogenic rotor
designed to test an advanced cooling system for the rotor of a superconducting
generator. The experiment does not include an actual superconductor field winding
but does include a helium chamber typical of the winding space in an actual
superconducting rotor.
The cooling system performance of the small diameter experimental rotor
simulates that of a large-diameter synchronaus rotor by operating at a proportionately higher rotational speed. The experimental rotor has a diameter of about
0.20 m and is designed to operate at 15,000 rpm. This gives a tip velocity of 157 m/s
corresponding to that of a 3600 rpm synchronaus rotor with a diameter of 0.84 m.
However, all experimentation thus far has been at rotor speeds not exceeding
8000 rpm (tip speed of 83.0 m/s).
The major aspects of the rotor's mechanical design have been developed and
presented by Tepper [ 1]. A cross section of the rotor is shown in Fig. 1. The design of
the cooling system is based upon recommendations presented in a study by Bejan [2 ].
A description of the cooling system giving details of its operation and design has been
presented by Tepper [3 ]. A schematic of the complete rotor test system excluding the
data acquisition system is shown in Fig. 2.
The technical and theoretical achievements of the experimental program are as
follows: (1) The thermal and ftow performance of the torque tube has been measured
at 8000 rpm; (2) the reliability of the internal instrumentation and the data acquisition hardware and software systems have been established; and (3) the theoretical
analysis of boil-off in the rotating frame has been verified experimentally. The
cryogenic experiments and analysis are discussed in this paper. The digital data
acquisition system with electro-optical coupling to the rotor and all aspects of
instrumentation are discussed in other publications [4-6].
Two major problems with regard to rotor operation have also emerged from
experimentation. A significant heat leak axially down the centerline of the rotor
creates ftow instabilities under certain conditions of rotor operation. The ftow
* Work supported by U. S. DOE under Contract No. EX-76-A-01-2295, Task Order No. 11.
275
276
L. Sobel, J. L. Smith, Jr., and F. Rumore
(.p\_ TEMPERATURE
~
TRANSOUCER
®--
PR ESSURE
TRANSOUCER
TOROUE TUBE
®-HEATER
'J _;
RADIATION
SHIELDS
Fig. 1. Cross section of high tip speed rotor.
instabilities and some practical steps to avoid instabilities are also discussed herein.
Transient "dryout" testing indicates that the geometry of the winding spacereseryoir in this rotor may be inhibiting centrifugal convection of heat from the rotor
periphery to the centerline. This aspect of rotor operation is discussed in more detail
elsewhere
n.
Experimental Simulation of a Cryogenic System for a Superconducting Rotor
277
Iranster tube
(!) ollen-brodley
(!) t hermocouple
0 pressure oooe
0
pressure tronsducer
~moss flowmeter
-(-check volve
[K]moss flow regulotor
Ct:] pressure
0
heot exchonger
-
ttwotlle
J
..!...
rotometer
rel1ef volve
regulotor
Fig. 2. Flow diagram of high tip speed experiment.
TORQUE TUBE
The torque tube is the critical component of the thermal isolation system of a
superconducting synchronous generator. The torque tube thermally separates the
cryospaces of the rotor from the room temperature environment and transmits
generator torque to the cold windings on the rotor.
Figure 3 shows the torque tube design used in this rotor. The torque tube is
composed of a Micarta tube sandwiched between two thin-wall tubes of 304 stainless
steel. The inner and outer tubes carry the structuralloads and the Micarta tube has a
series of axial passages and circumferential grooves which serve as passages for the
flow of helium vapor which cools the torque tube and thus reduces the conduction
heat leak into the cold spaces of the rotor.
The thermal performance of the torque tube under various operating conditions
is evaluated from the following experimental results: (1) the boil-off rate of liquid
helium, (2) the torque tube temperature profile, and (3) the ternperature gradient at
the cold end of the torque tube. The flow performance is determined by measuring
the torque tube pressure drop as a function of mass flow rate .
Torque tube temperature profiles for varying torque tube mass flow rates at a
rotational speed of 8000 rpm are shown in Fig. 4. These profiles were made during
"dryout" tests discussed later. Thesetests were run with constant torque tube mass
ALL EN- BRAOLEY
RADIATION
THE Rt.IOCOUPLE
STAINLESS
o,__.____,
.5 1 cm
Fig. 3. Partial torque tube cross section showing placement
of cold end Allen-Bradley resistors. Dimensions: a =
0.81 cm; b = 5.71 cm; c = 0.605 cm; d = 0.203 cm.
278
L. Sobel, J. L. Smith, Jr., and F. Rumore
0
0
"'
,..
0
N
Wo
0::"'
=>-
I-
a:O
a::~
w
Q_o
::t:N
w-
o-
0
"'
0
<D
0
"'
Fig. 4. Torque tube temperature profiles. Data points are connected for visual aid only.
flows and Iasted from 20 to 60 min each. At low mass flows the torque tube time
constant was greater than the duration of the test. However, a reasonable
identification of the steady-state torque tubeprofileswas possible. The points plotted
in Fig. 4 are the temperature indications from the three thermocouples and the two
Allen-Bradley resistors mounted in the torque tube. These graphs clearly show the
dependency of the cold end heat leak on mass flow rate. Also, as the mass flow rate
increases, the temperature profiles at 8000 rpm begin to resemble the curve at
1000 rpm. Hence it is possible to conclude that the torque tube performance is not
rotationally dependent and that the torque tube temperature profile is only a
function of mass flow rate.
The cold end heat leak for the torque tubewas calculated from the temperature
profiles of Fig. 4 and the associated mass flow rate . The one-dimensional coupled
convection-conduction equation of the form
(1)
was solved for the temperature distribution between the known temperatures of the
two Allen-Bradley resistors shown in Fig. 3. The conductance of the torque tube,
including the stainless steel and Micarta, is essentially linear in T from 10 to 50 K,
which allows for a closed-form solution of (1).
Table I shows the calculated heat leak based on the cold end temperatures for
each curve of Fig. 4. Also shown is the heat leak associated with the measured flow
rate in the torque tube. The rhhrs product is corrected for the varying liquid Ievel in
the rotor which in the presence of a centrifugal field creates a nonuniform distribution of thermodynamic states in the liquid system
When the gradient heat leak and mass ftow rate heat leaks are equal, the torque
tube flow is self-sufficient. This occurs at a mass ftow rate between 20 and 23 mg/s
with an associated heat leak of 0.4 to 0.5 W. The magnitude of this heat leak is
approximately as predicted by Tepper [ 1], and the associated temperature profile is
nearly linear over most of the torque tube as predicted by Bejan
eJ.
eJ.
Experimental Simnladon of a Cryogenie System for a Supereondueting Rotor
179
Table I. Beat Leak vs. Torque Tube Mass-F1ow Rate
qL, W
riJ,mg/s
T1
T2
0.0
8.0
15.0
20.5
22.5
27.5
16.5
16.6
15.3
13.0
8.2
8.0
57.0
49.8
44.9
38.0
17.0
14.0
37.0
43.0
9.9
9.3
10.5
10.1
(1.1
= 8000rpm
10.0
6.5
4.6
2.8
0.27
0.11
w
= 1000rpm
0.005
0.005
±%
mh1J0.95*, w
18%
18%
19%
20%
28%
35%
0.0
0.2
0.37
0.51
0.56
0.67
55%
58%
0.87
1.01
* Correction for work output of device.
TableI also shows the value of vapor self-cooling. Self-sufficient flow reduces
the cold end heat leak by at least a factor of 22 over the zero-flow torque tube heat
leak. (In the zero-flow run the torque tube was colder than for the thermal steady
state so the calculated heat leak is too low for this run.)
To facilitate the self-pumping capability of the rotor eJ, the torque tube flow
resistance should be small so that the pressure drop due to flow is small compared to
the self-pumping pressure rise. The torque tube pressure drop has been recorded at
1000 rpm for mass flow rates ranging from 30 to 110 mg/s. The experimental
relationship has the form
In !l.P
= 2.05 In m- 12.08
(2)
which indicates a pressure drop of only 0.004 atm at self-sufficient flow. The pressure
drop is a factor of 2 less than predicted C]. The slope of about 2 indicates that the
pressure drop is associated with entrance and exit Iosses in the channels of the torque
tube and in the rotating face seal [3 ]. At 8000 rpm the eflect of vapor compression
prevents the accurate measurement of torque tube pressure drop. However,
experience indicates that similar pressure drops are encountered at thesehigh speeds
as weil.
DRYOUT TESTS
Experiments have been run to study the boil-ofl rate of liquid helium in the
rotating frame. The experiments are necessary to provide a means of relating the
mass flow rate of exiting vapor from the rotor to the heat leak into the reservoir.
Estimation of heat leak based on the loss of latent heat in the fluid reservoir alone will
be in error by as much as 25% at high tip speeds because the rotating reservoir is, in
fact, an engine, converting some of the heat input into work as liquid vaporizes.
Appropriate heat leak calculations during boil-ofl must take into account the loss of
angular momentum within the rotor, the geometry of the liquid-filled spaces, as weil
as the changing internal and kinetic energies of the helium in the rotor.
A practical analysis of boil-ofl in a rotating frame requires making certain
assumptions about the state of the fluid within the rotor. As liquid boils away, the
vapor-liquid interface moves radially outward. The saturated vapor at the interface
condenses as it migrates from a high pressure at the interface to a low, presumably
fixed pressure at the centerline of the rotor. The radial pressure gradient in this
-
L Sollel, J. L s.ldl, Jr., _.. F. a-n
"rainstonn" is established by the centrifugal compression of the vapor. The liquid
droplets are thrown up against the radial baftles in the reservoir (not shown in Fig. 1)
and form a slow-moving thin film. At each radins the centrifugal forces on the liquid
are assumed to be balanced by the radial pressure gradient established by the vapor
and the viscons shear between the liquid film and the baffte walls. The goveming
equation of state in the two-phase region is therefore
p., = J
Jdp
liJ
2
(3)
rdr
A single-phase region extends from the vapor-liquid interface to the outer radius
of the winding space. In the absence of any heat leak, the fluid is compressed
isentropically under the inftuence of centrifugal acceleration. A radial temperature
gradient is established that is in convectively neutral equilibrium. However, heat
conducted into the reservoir at the outer radins produces an additional radial
temperature gradient which gives rise to gross convection currents transporting
warm and less dense helium to the vapor-liquid interface where it is cooled by
vaporization. The bulk fluid motion is assumed to be adiabatic though highly
irreversible. With this assumption, the goveming equation of state in the singlephase region is (after Thullen [8 ])
r2
J'2
1
,,
j, dht- 2 =
liJ
2
ds1-2 = 0
rdr,
(4)
With the previous assumptions, the first law equation written for a control
volume encompassing the fluid reservoir and winding space and cutting through the
torque tube of the rotor is
.
Q
a
+-J.
at c.v.
(liJ
r)pdV = mh
2 2
0
a
+at
(1),~
(u
+2 - pdV
c.v.
J.
2
(5)
where m = -(ajat) Jc.v. pdVfromcontinuity. Thesecond termon theleft-handside
of (5) accounts for the work produced by the control volume as a result of the torque
from the loss of angular momentum due to boiling.
This equation is integrated numerically using the NBS Helium Properlies
Program. In order to evaluate the integral over the control volume, the states at
incremental radü within the rotor are determined using (3) and (4). The rotor heat
leak rate is assumed to be independent of time.
Dryout tests were run, simply, by filling the rotor with liquid at 8000 rpm,
shutting oft the inlet ftow, and then monitorlog the ensuing boil-o:ff history as the
liquid Ievel in the rotor dropped. Each experimental run bad a different torque tube
outlet flow rate which was held constant for the duration of a run. This insured a
constant torque tube heat leak. The bulk of the exiting vapor left through the
emergency discharge line.
Figure 5 shows the mass flow time history of one such run. Superimposed on the
experimental curve is the numerical solution of (5) for a (} roughly equal to that
measured at the cold end of the torque tube. Tbe results of several tests were equally
favorable and are described fully in other references [5 ' 7 ].
Tbe e:ffect of geometry on the thermodynamics of boil-o:ff in the rotating frame
can also be seen in Fig. 5. Tbe step change drop and rise in mass ftow rate occurs as
the vapor-liquid interface moves through the narrow radial channels which join the
reservoir to the winding space.
Experimental Simulation of a Cryogenic System for a Superoondncting Rotor
0
0
N
..
"'- THE CIR ETICA L
• -EXPERIME NT
(fl~
-....-
281
•
<..:>
::i:O
"'
w."
1-- N
er.-
a:
0
:J::O
o....J
LL..IIl
,...
(/)
(/)
cr_O
:r::"'
"'"'
0
0
6
9
12
15
18
TI ME, MIN
21
24
27
30
Fig. 5. Theoretical and experimental mass ftow rate histories
for constant heat leak at rotor outer radius.
FLOW INSTABILIDES
A ftow instability occurs at 7000 to 8000 rpm when the transfer tube inlet valve
is shut and the torque tube and emergency discharge lines are unthrottled. The
torque tube mass ftow will cycle from 0 to 40 mg/s over a period of 30 s. While the
torque tube ftow is increasing, the emergency discharge ftow is zero. It was further
noted that the centerline temperature cycles nearly in phase with the mass ftow out of
the torque tube. Shortly after the centerline temperature reaches a maximum, the
torque tube ftow drops to zero and gas begins to exit from the emergency discharge
line.
A probable explanation for this instability is as follows. When the torque tube
outlet pressure is atmospheric, the isentropic compression of cold vapor in the torque
tube inlet creates a vacuum at the centerline of the rotor. This centerline vacuum
prohibits the ftow of vapor out of the emergency discharge or bayonet bleed lines.
However, if the vapor at the torque tube inlet is heated, for example, by heat leaking
down the external connections to the centerline of the rotor, there will be a
progressive decrease in vapor density and a concomitant decrease in torque tube
inlet vapor compression. Since the torque tube has a finite pressure drop, this slowly
Ieads to a loss of centerline vacuum and of torque tube mass ftow. The loss of torque
tube mass ftow results in an increased heat leak through the torque tube and into the
fluid reservoir. The ensuing boil-off pressurizes the rotor until the centerline is
slightly above atmospheric pressure. Then the boil-off gas can escape the rotor
through the bayonet bleed and emergency discharge lines. This cools the centerline
and the torque tube inlet in the process. Within seconds the density of the vapor
column in the torque tube inlet has increased sufficiently to restore the centerline
vacuum and the ftow through the emergency discharge line stops.
This instability has significant implications. In the "self-pumping mode," that is,
when one is relying on cold vapor compression in the torque tube inlet to lower the
centerline pressure and draw in liquid from the dewar, the presence of a centerline
heat leak may cause a loss of centerline vacuum. In essence, centerline heating could
282
L. Sobel, J. L. Smith, Jr., and F. Rumore
cause a cessation of ftow at a time when greater ftow in needed. Similarly, a surge in
boil-off could draw in too much liquid, causing liquid to spill into the torque tube
inlets causing overpressurization in the torque tube and structural damage.
A very significant source of heat leak into the reservoir comes from the transfer
tube itself. An experiment was performed to est~tblish the magnitude of the heat
absorbed by liquid helium as it travels from the dewar through the transfer tube and
into the centerline of the rotor.
The transfer tube was put into a partially filled liquid helium dewar so that the
inlet of the tube remained suspended in the vapor phase above the liquid. The outlet
of the transfer tube was connected to a liquid nitrogen shielded dewar which was
connected at the outlet port to a mass ftow meter. The temperatures at the inlet and
outlet of the transfer tube were measured by means of Allen-Bradley resistors
mounted inside. The pressures at the transfer tube inlet and outlet were also
measured.
The heat leak in the transfer tube is calculated from the mass ftow and the
measured temperatures and pressures at the inlet and exit. (The NBS Helium
Properties Program was used to calculate the inlet and exit enthalpies.) The results
are shown plotted in Fig. 6. The wide discrepancy in heat leak at the low mass ftows
results from the inaccuracy in mass ftow measurement.
The graph shows that the magnitude of the transfer tube heat leak is about
1.5 W. An error analysis establishes an uncertainty Iimit of ±6%, or ±0.1 W. For
purposes of comparison this heat leak is nearly a factor of 3 higher than the
self-sufficient coolant requirement of the torque tube. Thus a total ftow of approximately 70 mg/s is required to transfer any liquid into the rotor at all. The calculated
heat leak is also much higher than the predicted heat leak for the transfer tube.
However, some fraction of the calculated heat leak is attributable to end effects
which arenot present when the transfer tube outlet is inserted into the rotor.
To impede the convection of warm gas along the centerline from the warm parts
of the transfer coupling to the helium reservoir, a set of baffies was inserted in the
centerline helium inlet tube. The baffies consist ofthin paper disks cut to match the
diameter of the centerline tube. The disks were skewered on a thin stainless steel
welding rod and separated by spacers made of plastic tubing. The baffie assembly is
removable. The edges of the paper disks are snipped around the circumference to
allow a space for liquid to enter during fill-up and for cold gas to exit as weH. The
additional pressure drop associated with these baffies is insignificant when the fluid is
(.(')~,-------------------,~
34.7 moJs •l. Iiter/ti' of l He , 4.2 K
<!>~
a:
3:
"'
a:.n
W-'
..J
....
a:
w
:r:
10
20
70
60
so
~0
MRSS FLClH • MG/S
30
80
90
Fig. 6. Results of transfer tube heat Ieak test.
100
Experimental Simulation of a Cryogenic System for a Superconducting Rotor
283
very cold. The bafftes act as a one way valve. They facilitate the flow of cold gas in or
out at the periphery of the centerline tube but blockwarm gas from coming down the
center.
To further insure that the centerline heat leak did not seriously affect the
"dryout tests," a mass flow regulator was installed on the torque tube outlet. In
essence, flow stability was achieved by placing a large flow resistance on the torque
tube outlet. The dryout tests, however, are run with the inlet valve shut. Because of
the centerline heat leak, it may not even be advisable to run the system in the steady
state with a significant centerline vacuum when the inlet valve is open.
CONCLUSION
"Dryout" testing has established a frame of reference for studying the steadystate behavior of the cooling system. Future tests will determine two heat transfer
coefficients. The first relates surface heater power to heater surface temperature and
local winding space fluid temperature. The second is a gross convection heat transfer
coefficient. This coefficient will relate heater power to heater temperature and
reservoirfluid temperature minus the a T of isentropic compression. Furthermore, a
model has been proposed describing complex cellular flow patterns convecting heat
from the outer radius to the liquid-vapor interface. Verification of the theory
depends on experimentally determining the thermal time constants of the fluid
system.
Finally, a major scope of testing will determine how best to control the effects of
the centerline heat leak. The degree of torque tube and transfer tube throttling
required to insure stability in the steady state will also be determined.
NOTATION
A =
Jc.v.=
cP =
h =
h18 =
h0 =
k(T) =
m=
P =
6=
qL =
·, =
s=
T =
T1 =
T2 =
u =
W=
x=
conduction area
control volume intergral
helium specific heat
enthalpy
latent heat
centerline enthalpy
thermal conductivity
helium mass flow rate
pressure
heat input
cold end heat leak
radius
enthropy
temperature
temperature indicated by coldest Allen-Bradley in torque tube
temperature indicated by next coldest Allen-Bradley in torque tube
internal energy
work output
conduction length
Greek Symbols
w = rotational speed
p = fluid density
Pv = saturated vapor density
o/ot =time derivative
L. Sobel, J. L. Slllith, Jr., IUitl F. Rumore
REFERENCES
1. K. A. Tepper, S.M. thesis, Massachusetts Institute of Technology, Cambridge, Massachusetts (1976).
2. A. Bejan, Ph.D. dissertation, Massachusetts. Institute of Technology, Cambridge, Massachusetts
(1974).
3. K. A. Tepper, J. L. Smith, Jr., and F. C. Rumore, in Advances in Cryogenic Engineering, Vol. 23,
Plenum Press, New York (1978), p. 118.
4. D. Otten, "Demonstration of an Advanced Superconducting Generator," ERDA Contract No.
E(49-18)-2295, Task Order No. 11-IR4, Interim Report (January 1978), p. 123.
5. L. Sobel, S.M. thesis (unpublished), Massachusetts Institute ofTechnology, Cambridge, Massachusetts
(1979).
6. R. A. Bukovich, S.M. thesis, Massachusetts Institute of Technology, Cambridge, Massachusetts
(1978).
7. L. Sobel and J. L. Smith, Jr., "Analysis of Boiloft of Helium in a Centrifugal Field," paper submitted to
Cryogenics.
8. P. Thullen, Ph.D. dissertation, Massachusetts Institute of Technology, Cambridge, Massachusetts
(1969).
F-3
ROTOR COOLING SYSTEM FOR A 10-MVA
SUPERCONDUCTING GENERATOR*
M. T. Brown, M. E. Crawford, and J. L. Smith, Jr.
Massachusetts Institute of Techno/ogy
Cambridge, Massachusetts
INTRODUcriON
The Cryogenics Laboratory and the Electric Power Systems Laboratory at MIT
are currently involved in an effort funded by the U. S. Department of Energy to
develop a 10-MVA superconducting generator. This machine incorporates the most
advanced concepts available in order to demoostrate the greatest possible growth in
the state of the art. A rotor and stator comprise the generator. Within the rotor are
the superconducting field winding and two electromagnetic shields. The winding and
shields are kept at liquid helium temperature by the rotor cooling system. The rotor is
supported between thin-walled, vapor-cooled torque tubes for thermal isolation,
and further isolation is obtained by using an evacuated stator bore containing a
stationary thermal radiation shield.
The rotor composition is depicted in Fig. 1. The superconducting field winding is
contained between two torque-carrying support tubes, and the winding is immersed
in liquid helium supplied from the field-winding reservoir. The first electromagnetic
shield, a highly conductive copper can shield, is mounted on the outside of the outer
support tube. Grooves in the tube form liquid helium cooling channels for the can
shield. The second shield is a damper winding of finely stranded and transposed wire.
lt is separated from the can shield by a sheath of low thermal diffusivity material, and
the winding is cooled by three layers of liquid-helium-filled tubes. The shield channel
and damper cooling tube network are connected to a reservoir and separator to form
a cooling system that operates independently of the field-winding cooling process.
In steady-state operation the magnetic field is constant in rotor coordinates,
except for space harmonics and phase unbalance of the armature-winding reaction
field. These ac fields are screened from the superconducting field winding by currents
induced in the damper shield winding and by eddy currents induced in the conducting
can shield. The resulting power dissipation in the shields is the principal thermal Ioad
that must be removed by the rotor shield cooling system. The system also serves to
remove the transient heat dissipation within the shields during a generator powergrid fault. In this paper an analysis and performance predictions are carried out for
the 10-MVA rotor shield cooling system during steady-state operation.
* Work supported by U. S. DOE under Contract No. EX-76-A-01-2295, Task Order No. 11.
285
286
M. T. Brown, M. E. Crawford, and J. L. Smith, Jr.
WOUNO OAMPER
--~
STATOR CORE
CONOUCTIVE
CAN SHIELO
ARMATURE
TOR BORE TUBE
F IELO WI NO I NG
THERMAL RAD I ATION
SHIELO
Fig. 1. 10-MVA rotor and stator assembly.
COOLING SYSTEM PROCESS
The proposed damper shield and can shield cooling loop are shown in Fig. 2.
Helium is fed into the field-winding reservoir. From there, it spills into the damper
and shield reservoir, then cycles through the wound damper, into the separator, and
back through the can shield. The boil-off gas generated in the cooling process is used
to cool the rotor torque tubes. In the design there is a simple check valve located
Fig. 2. Rotor cooling system and helium flow circuit. Legend: 1.
emergency discharge, 2. field-winding current Ieads, 3. helium
inlet, 4. field-winding reservoir, 5. field winding, 6. reservoir fill
tube, 7. check valve, 8. separator, 9. conductive can shield,
10. shield and damper reservoir, 11. gas vent, 12. torque tube,
13. wound damper.
Rotor Cooting System for a 10-MVA Supereonducting Generator
287
between the cooling cycle and field-winding reservoir to prevent the latter from
pressurizing during a generator fault.
In the steady state, fluid ftows from the reservoir to the damper where it absorbs
heat and expands. Thus, on its radial return to the separator, it has a lower density
than in the damper and shield reservoir, and this difference in density provides a
pressure differential for ftow through the damper tubes. The separator will accumulate liquid by this process until the liquid pressure head in the separator exceeds that
of the reservoir, at the shield radius, inducing liquid ftow from the separator to the
reservoir via the shield, thus completing the cooling loop.
During a generator electrical fault the increased heat dissipation in the wound
damper and can shield will cause a rapid expansion of the helium. This will effectively
stop the steady-state ftow loop, and cause blowdown whereby the helium in the
damper and shield blow out into the reservoir and separator. In this pressurized state
the check valve will seal oft the damper and shield reservoir, and the continually
expanding heliumwill begin venting through the emergency discharge. The reservoir
and separator will be sized to handle the transient cooling requirements. Refilling
will take place after recooling of the shield and damper.
ANALYSIS
The objectives of the analysis were to determine the mass ftow rate of helium in
the loop, temperature rises across the damper and shield, and the boil-off vapor rates
which provide coolant to the torque tubes. Parameters in the analysis included the
helium centerline condition, geometry of the cooling loop, and the power dissipation
in the damper and can shield.
The loop for steady-state cooling consists of a reservoir, damper cooling tubes,
separator, and can shield cooling channels. The loop is modeledas a closed circuit,
ignoring the slight changes in mass ftow through the circuit due to boil-off in the
reservoir and separator. In fact, the boil-off rate is about three orders of magnitude
less than the loop ftow rate, and the slight differences in mass ftow rate through the
loop are insignificant. The model for this analysis is shown in Fig. 3.
m
• Vs-;11
.
-
~EPARATOR
5 ..
~
-
""
__j_
La
R1•4.76 CM
~SATURATED
.,
-
APOR
~~V
TO TOfiOUE
QRESERVOIR
""
•
TU BEmyR
lq
~
LIQUID
SEPARATOR
RESERVOIR
I-CIR CUIT
MAss FLO w
.
~
.
3
'-1.2 ATM
SAT. LI Q.
1---
~AN,HIELD
R6 • 17 CM
-~
6
7
"'
Rz• 20 CM
__1
2
OoAMPER
Fig. 3. Steady-state heating model of the damper/shield cooling circuit.
-
M. T........ M. 1:. c..wror., _. J. L s.ldt, Jr.
Determination of the helium mass ftow rate involves linking it to the pressure
drops in the system. In the analysis it is assumed that frictional pressure drops occur
between states 6 and 7 in the can shield and states 2 and 3 in the damper. All other
frictionallosses are neglected.
The pressure drops in the loop are modeled using a conventional head-loss
formulation written in terms of the mass ftow rate:
llP =
L) ·2)
·2
L(I[J,. ( 2 ~ 2 + L K{ 2;A 2)
(1)
In the above equation, I is the friction factor for smooth-walled turbulent ftow
and centrifugal and Coriolis eflects on I are ignored. For the Reynolds number
regime applicable to the cooling loop, it is assumed that
I=
0.184[:"r
0 2
·
(2)
The L/ D,. term represents channel ftow length divided by hydraulic diameter, or the
L/ D equivalent for the elbows and headers. The K coefficient accounts for entrance
and exit Iosses and abrupt expansion and contraction losses.
The analysis assumes that ftow in all radially directed pipes is one dimensional
and isentropic. In the generator, radial ftows would be assured by judicious use of
bafftes and tubes. This is necessary to keep any tangential shear forces to a minimum.
By conservation of angular momentum a free ftow of high mass ftows would be overly
dissipative. The change in enthalpy for isentropic ftow is
2
llh
= -w2( r2
0
2
- r-)
I
(3)
where w is the rotorangular speed and r; and ro are the inner and outer radü of the
ftow loop geometry.
Heat rejection from the helium to the reservoir or separator is modeled as a
condensing process whereby the incoming fluid is returned to its saturated liquid
state. This is assumed to occur at the radius of the liquid Ievel in the reservoir or
separator. The heat rejection is given by
tlout = m(h2." - h ..,)
(4)
Note that the vapor mass ftow for each torque tube can be approximated by
equating the heat rejection to the product of the boil-ofl vapor rate, m.,, and the heat
of vaporization, h18• Thus the boil-ofl vapor rate becomes
•
• h2<1>-
m.,=m
h
hsat
(5)
fg
Heat input to the ftow loop is from electrical power dissipation in the damper or
can shield. lt is modeled as a first law heat addition
tlin = m(hout- hin)
(6)
Figure 4 shows a typical set of eight thermodynamic states for the cooling loop.
The equations described in the preceding paragraphs were used to connect these
states. State 1 is fixedas saturated liquid at radius r 1 • State 2 follows from (3) and a
fixed r2 with s1 = s2. State 3 is determined by assuming mand using (1) and (6). State
Rotor Cooling System for a 10-MVA Superconducting Generator
•
289
AHoAMPER
•
2
liH= F(AR)
H
SATURATED
LIQUID LINE
AHSEPARATOR
t
s
Fig. 4. Enthalpy--entropy diagram of fluid ftow states.
4 follows by assuming r4 in (3) and s3 = S4. State 5 is saturated liquid at T 4 • State 6
follows from (3) and a fixed r6 with s5 = s6 • State 7 is determined using (1) and (6).
Finally, state 8 follows from (3) and a fixed r7 with s7 = s8 • At this point the saturated
liquid condition corresponding to T 8 is compared with state 1. lf there is no
agreement, a new set of rit and r4 must be assumed, and the solution is iterated to
convergence.
COMPUTATIONAL METHOD
A unique computational procedure was developed to determine the mass ftow
rate for a given set of parameters. Equations connecting the eight thermodynami c
states were written using (1) through (6). An additional set of algebraic equations
for the thermodynamic properties of helium were obtained by curve-fitting the
The resulting set of 14 nonlinear coupled equations is given in
NBS helium data
Table I.
These equations were algebraically combined using MACSYMA [ 2 ], a computer
system for symbolic manipulation. The resulting equation is of the form
eJ.
r!
+ /2 (rit)r~ + [I(rit) = 0
(7)
M. T. Browa, M. E. Cnwford, aad J. L. Smitla, Jr.
290
Table I. System of Equations Goveming Cooling
Loop in Steady-State Mode
Defining
Equation
qd = m(h3 - hz)
Pz- P 3 = d'm ~.s +
e'm 2
= a'h 3 + b's 3 + c'
h 3 - h 4 = w 2 /2(r~- r~)
h4 = fT 2 + T(g' + SJ) + i'
h 5 = j'T+ k'
P3
s
=
l'T+ o'
~- h 5 = w 2 /2(r~- r:)
State 3
Property
State 4
Property
State 5/Property
q",. = m(h7 - h 6 )
State 6
Property
State 7
h 1 - h 8 = w 2 /2(r~- ri)
h 8 = aa's 1 + bb'
Property
State 8
State 8/Property
P6
=
u'h6 + v's 5 + w'
p6- p1 = r'mL8 + t'm2
P1 = u'h 1 + v's 7 + w'
Note: Defined system parameters
h1, st> PI
hz, Sz, Pz
qcs, qd
rb Tz, r6
where / 1 and / 2 are algebraic functions. This equation can be factored and rearranged
to obtain
(8)
Examination of (8) shows that for real values, the minimum mass flow will occur
when
(9)
Equation (9) was solved for musing a Newton-Raphson iteration method, and
the corresponding r4 was obtained from (8). Additional values of m that Slltisfy (8)
were determined by incrementally changing the mass ftow. The upper limit on mis
the condition when either h 8 = h 1 or h4 = h 5 , corresponding to zero heat rejoction in
either the reservoir or separator. Note that the quadratic nature of the tolution
implies that there will be two values of r4 for a given m.
RESULTS AND DISCUSSION
Sampie calculations have been carried out for the geometry given in Fig. 3,
based on the current 10-MVA design parameters eJ. State 1 was fixed at 1.2 atm
saturated liquid at r 1 = 4.76 cm from the centerline. The heat inputs to the damper
and can shield were qd = 9.2 W and 4cs = 1.6 W. The damper coolin& circuit
consisted of 624 tubes, each with 0.284-cm2 ftow area, and the can shield cooling
circuit consisted of 72 channels, each with 0.227-cm2 ßow area. Four sets of
perforations through the support structures connected the separator/reservQj.r to the
can/damper, and were a significant factor controlling the circuit mass ßow rate. In
the sample calculation 12 ßow channels oomprised a set of perforations (i.e., 12
291
Rotor Cooling System for a 10-MVA Superc:ondncting Generator
1.180
1.178
1.176
1.174
P,
atm
1.112
1.170
1.188
--RESERVOIR CENTERLINE _ _ __.,__
PRESSURE
1.168
138.1
1584
1585
138.2
1385
138.8
138.7
138.8
ril . g/s
Fig. 5. Pressure at the centerline in the separator vs. circuit mass flow.
channels connecting the reservoir to the damper). On the reservoir end the total
perforation cross-sectional flow area was set at 50% of the total can and damper
cross-sectional area. On the separatorend the perforation area was 100%.
Figure 5 shows a graph of the centerline pressure of the separator vs. mass ftow
rate for a given reservoir centerline pressure. Note that the minimum mass flow is
138.7 g/s and that there are two values of possible balancing pressures (i.e., two r4
values) in the separator for each mass ftow. Figure 6 shows the heat rejected from the
reservoir and separator for each of these two values and the end points are defined by
•
8
QREJECTION~
Watts
/
/
8
/
./'
--
_........---'- -
- - =-
""'---SEPARATOR
~~-(
4
3
2
\.
"
RESERVOIR
..........
............
..............
......_
138.6
138.8
ril, g/s
Fig. 6. Heat rejection in the separator or reservoir vs. circuit mass flow.
M. T. Bnnra, M. E. Cnwfonl, ad J. L Smltll. Jr.
either zero heat rejection or total heat rejection in the separator (or reservoir). By
using (5), the variation of vapor mass ftows into each torque tube can be calculated.
lt should be noted that for actual operation of the generator it would require
control of both the reservoir and the separator centerline pressures to achieve the
desired Operating state. (This would be by either torque tube pressure controls or
controls of the boil-ofl-vapor mass ftow rates.) Calculations with variations of the
reservoir centerline pressure on the order of ±0.5 atm (at R 1 = 4.76 cm) produced
no significant changes in the nature of the operating curve in terms of shape or mass
ftow rates. Thus the reservoir centerline pressure may be made to vary with the
understanding that only the magnitude of the separator pressure (referred to the
reservoir) would vary on the depicted curves but they still would relate the generat
variance of the second input, separator pressure (or vapor-mass ftow rate), for the
system Operation.
The sample calculations indicate that the natural-convection-driven helium
mass ftow induced by the heat input is large, resulting in small temperature increases
across the can and damper. For the range of mass ftow rates in Fig. 5, the average
temperaturein the can is about 4.75 K andin the damper it is about 4.88 K, and the
temperature rise is about 0.05 K. A calculation was also performed for the situation
involving a doubling of the heat inputs. For this case, the damper temperature rises
are about 0.10 K.
SUMMARY
A rotating closed-loop liquid helium cooling system has been designed that
derives its pumping action from a natural convection or thermosyphon effect. The
loop is comprised of two axially oriented warm reservoirs which receive heat from
the electromagnetic shields, and annular cold reservoirs at either end of the warm
reservoirs which dissipate the heat by boiling. The major driving mechanism is the
centrifugally created pressure diflerence across the outermost warm reservoir, with a
warmer radial column of helium at one end compared to the other end. The loop
pumping capacity is quite high. For the sample calculation the self-pumping rate is
about 139 g/s for a 10.8-W heat input to the warm reservoirs. By changing the
annular reservoir geometry the helium mass ftow rate can be adjusted to accommodate frictional pressure drops associated with various proposed header designs
that connect the warm and cold reservoirs.
NOTATION
A = cross-sectional area
D,. = hydraulic diameter
f = friction factor in head-loss equation
h = enthalpy
h,8 = heat of vaporization
K = coefticient in head-loss equation
L = length
m = mass ftow rate
P = pressure
q = heat ftow rate
r = radii from centerline
s = entropy
T = temperature
a', b', c', etc. = all primed letters are coefficients for either curve fits or parametric relations
Rotor Cooling System for a 10-MVA Superconduding Generator
293
Greek Symbols
p = density
w = rotor rotational speed
REFERENCES
1. R. D. McCarty, NBS Tech. Note 631 (1972).
2. MACSYMA Reference Manual, Math. Lab. Group, Project MAC, Massachusetts Institute of Technology, Version 9, December 1977.
3. "Demonstration of an Advanced Superconducting Generator," Interim Rept. 7, Massachusetts
Institute of Technology, Cryogenic Engineering Laboratory and Electric Power Systems Engineering
Laboratory, E(49-18)-2295, Task Order No. 11, IR 7 (1979).
F-4
SAFETY LEADS*
M. Kuclmir and T. H. Nicol
Fermi National Accelerator Labaratory
Batavia, Illinois
INTRODUCDON
The current plan for the Fermilab superconducting synchrotron (energy
doubler) calls for the installation of approximately 1000 superconducting magnets in
the 6-km tunnel of the main ring accelerator.lts 3 x 108 -J emergency energy dump
system CJ is based on "safety Ieads" between 4 and 300 K situated after every fifth
magnet. With this system, when a quench is detected the power supply is turned off
and a 0.5-!l air-cooled "energy fountain" resistor is switched into the coil buss at
each of six energy transfer stations. This causes the magnet current to decay with a
time constant of 10 s. This decaying current has to be diverted from the developing
quench, and this is done by shunting the current out from the group of five magnets
containing the quench by means of the "safety Ieads." Protection for these magnets is
achieved by firing their internal heaters which spread the normal zone to a safe size.
The magnetic energy: of these five magnets is transferred to the helium and
mechanically vented
eJ.
DESIGN CONSIDERATIONS
The above-described particular use for these current Ieads and the large number
required justify an optimized design. Considerable capital savings in room temperature plumbing is achieved by dry (instead of vapor cooled [3 ]) Ieads. Advantage can
be taken from the infrequent nature of their use to minimize their inactive state heat
leak Ioad. The Iead itself can be allowed to become bot when carrying current, but its
junction to the magnets must remain superconducting otherwise the quench will
propagate out of the confined five-magnet cell. To satisfy this condition the coldest
part of the Iead (the "quench stopper") has a large contact area to liquid helium.
High valtage to ground (several kilovolts) might develop between the Iead and
the cryostat, requiring good electrical isolation and making heat sinking to 78 K
impractical. The Iead will conduct heat directly from 300 to 4 K through the thermal
insulation vacuum space. Several materials were considered for the bot section of the
Iead. Numerical calculations for the expected temperature rise of a small segment of
Iead as a function of time were carried out for these materials under an adiabatic
approximation. In this approximation, the rate of temperature increase, dT/ dt, of an
element of cross section s and unit length of the Iead is determined only by the
* Work sponsored by the U. S. Department of Energy.
194
295
Safety Leads
electric power, / 2 p/ s, dissipated in the lead and its heat capacity
IJ.CS
(1)
where p(T), c(T), and IL are the resistivity, specific heat, and density of the material,
respectively. In this approximation cooling effects are neglected. The maximum
expected current of 4.6e -t/lD kA (where t is in seconds) will cause the element to
reach a maximum final temperature, T max• which depends on its initial temperature,
Tinit• and the quench load as given by
(2)
A new material property, the quench load capability f, can be defined as
- F-
f-
2 - 1L
S
f
Tmax
Tm&t
c(T)
P
(3)
(T) dT
For maximum quench load per heat leak, one should maximize the ratio
F
6
s 2f
s/ I J~ 00 k(T) dT
=
(4)
slz
where k(T) is the thermal conductivity and z = f!U:oo k(T) dT] is an index-of-merit
of the material. Table I presents calculated values for fand z of selected materials for
a conservative 1init of 300 K and a practical T max of 514 K.
Constantan was selected instead of stainless for its electrical characteristics as
weH as for its availability as a well-characterized material. The value of f in equations
(2) and (3) specifies a value for s of 2.5 cm 2 • This cross section, the specification of an
allowable heat leak of 0.5 W and the thermal conductivity integral of Constantan
(516 W /cm from 4 to 300 K) determine a value for I of 258 cm. The known resistivity
of Constantan (3.6 x 10-5 n cm) permits an easy estimate of the maximum voltage
drop (4.6 x 103 x 258 x 3.6 x 10-5 /2.5 = 17 V) across the lead, a value needed for
electrical considerations.
Table I. Load Capability and Index-of-Merit of
Selected Materials for a Heat Excursion from
300 to 514K
f,
Material
MJ/Ocm
Copper
Nickel
Constantan
Stainless
Niobium
Titanium
314
56
17.2
10.4
22
8.4
4
Z,
s/~-tficm 3
0.20
0.26 or 0.09
0.33
0.34
0.14
0.08
M. "--lllir Md T. H. Nicol
QUENCH STOPPER DESIGN CONSIDERADONS
The liquid-helium-immersed part of the Iead cannot be treated in the same
adiabatic approximation; rather, a term expressing the heat transferred to the liquid
is essential. This is provided by
dT
p(T)
2
p,sc(T)-d = I ( t ) - - hp(T- TL)
t
s
(5)
where h is the heat transfer coefficient, p is the perimeter of the quench stopper cross
section, and TL the temperature of the liquid.
Numerical solutions of this differential equation for several materials using heat
exchange coefficients found in the Iiterature [4 ] indicated that a copper conductor/radiator 25.4 cm long with an 8-cm2 cross section and a surface area of 5000 cm 2
was suitable. These calculations were based on copper properlies that will probably
be different for the copper actually used. To overcome this difficulty an actual test of
the performance of such a quench stopper was carried out and is described after the
construction details.
CONSTRUCDON DETAILS
A five-magnet unit is composed of four dipole magnets and one quadrupole
magnet. The quadrupole magnet cryostat contains a service volume to house various
components necessary for the operation and protection of the system. Relief lines for
the helium and nitrogen shield, instrumentation, correction coil power Ieads, vacuum
relief and pumpouts, beam sensors, and transition piping are among those services
contained therein. The available space for these components is approximately 36 cm
high, 46 cm wide, and 51 cm long. The safety Iead is also incorporated in this area. Its
drypartwas formed from a cable of Constantan wire to a shape compatible with the
available space. Cable was chosen over solid stock for ease of forming and availability. Nineteen strands of 0.411-cm-diameter wire were needed to satisfy the required
cross section. This cable was then formed to the shape shown in Fig. 1. Electrical
insulation is provided by one layer of Kapton followed by one layer of glass cloth
tape. Connection at both ends, one to the quench stopper, the other to an extended
cable, is via ceramic vacuum feedthroughs. Internat support and standoff is by G-lO
saddle pieces.
As previously indicated the quench stopper is a copper conductor with large
heat exchange area. To comply with the low profile required by space limitations, this
device was made of readily available copper strips 25.4 cm long, 1.27 cm high, and
0.079 cm thick. These were assembled as shown in the insert of Fig. 2, stacked 80
across and fumace brazed to form the assembly shown in Fig. 2. The resulting unit is
25.4 cm long, 1.27 cm high, and 12.7 cm wide.
Unlike the safety Iead .cable which lies in the insulating vacuum space, the
quench stopper is in a space ftooded with single-phase liquid helium (see Fig. 1).
During a quench, potentials as high as 5 kV could develop between this assembly and
ground (the single-phase box). lnsulation must be provided which will not only
withstand this potential difference but will allow the free ftow of helium across the
"fins" of the quench stopper.
Safety Leads
297
.162" Dia Constontan
19 Ploce5
SINGLE PHASE
HELIUM SPACE
OUENCH
STOPPER
LEAD CABLE
Fig. 1. Safety Iead shape and location in the service volume of the quadrupole
cryostat.
NEMA G-10 pieces surround the finished assembly at all points where it is in
close proximity to the walls of the single-phase box, as shown in Fig. 1. The
placement of the quench stopper is in an active cooling region, i.e., directly over the
relief line opening. Relief valves are activated at the time of quench detection to
prevent overpressure. Helium ftowing past the quench stopper fins maintains the
splice end of the assembly below the superconducting transition temperature.
-• -
CORNER DETAIL
SHOWING ALTERNATING
1/32" STRIP 1/32" SPACE
I
Fig. 2. Quench stopper section of the safety Iead.
M. Kuchnir and T. H. Nicol
298
SUPERCON
CABLE
Fig. 3. Quench stopper test setup.
QUENCH STOPPER TEST
The first prototype was instrumented with precalibrated carbon resistor thermometers: T 2 near the Constantan junction and T3 near the superconducting cable
splice. This prototypewas installed after a vacuum-encapsulated 76-cm-long section
of Constantan cable. Care was taken to get a reasonably good simulation at the
junction between the Constantan and the quench stopper. To insure that T 2 and T3
measured the temperature of the copper, the thermometers and some immediate
length of their CuNi alloy Ieads were varnished in a hole drilled in the copper and
covered with epoxy to isolate them from the liquid. Another carbon thermometer,
18
17
FINAL T1 > 460 K
l>T3 <50 mK
T
l~rouq~ou l
~~~I
(Q.,I
~ 2
!3
U
I
(Q
(Q3)
I
0
10
20
30
40
50
TIME , sec
I
I
I
60
70
80
l
Fig. 4. Temperature excursions for three current
pulses in the quench stopper test.
Safety Leads
299
Tt. monitored the temperature of a specific location in the Constantan. A superconducting cable completed the circuit. Figure 3 shows this arrangement. Seven
pulses of current simulating quenches, 01 through 07, were fired. Figure 4 shows
events 03, 06, and 07 with the resultant temperature excursions of T 2 (top of
quench stopper) and T3 (bottom of quench stopper). 06 corresponds to a typical
maximum quench and 03 to common weaker quenches. 07 was a finallong-held
pulse, which also bad minimal effect in raising the temperature of the bottom of the
quench stopper.
ACKNOWLEDGMENTS
The authors would like to acknowledge the supportof G. Kalbfteisch, G. Biallas, N. H. Engler, and H.
Fulton in the development, and W. A. Wojak, H. Warren, W. Habrylewicz, C. Hess, and J. Tague in the
testing.
NOTATION
c = specific heat
F = quench Ioad [see equation (2)]
f = quench capability [see equation (3)]
h = heat transfer coefficient
I = electrical current
k = thermal conductivity
I = length of conductor
p = perimeter of cross section
() = heat leak
Q1-Q7 = events simulating quenches
s = cross section of conductor
t =time
T = temperature
1init = initial temperature of a Iead section
TL = temperature of liquid helium
T max = maximum temperature of Iead
T 1 - T 3 = thermometers used in the test or their temperatures
z = index of merit
Greek Symbols
p.
p
= density
= resistivity
REFERENCES
1.
2.
3.
4.
R. Stiening, R. Flora, R. Lauckner, and G. Tool, IEEE Trans. Magn. Mag-15:670 (1979).
M. Kuchnir and K. Koepke, IEEE Trans. Nucl. Sei. NS-26:4045 (1979).
M. C. Jones, V. M. Yeroshenko, A. Starostin, and L. A. Yaskin, Cryogenics 18(6):337 (1978).
P. J. Giarratano and R. V. Smith, in Advances in Cryogenic Engineering, Vo/. 11, Plenum Press, New
York (1966), p. 492.
DISCUSSION
Question by M. A. Green, Lawrence Berkeley Laboratory: Did you consider 304 stainless steel as a Iead
material? How did it compare with the Constantan material?
Answer by author: Yes, we did.ltwouldresultin a thicker andshorter Iead, quite acceptable. Butforthis
prototype, we decided on Constantan for its smaller temperature coefficient that obviated some transient
analysis on the voltage drop calculation.
F-5
MAGNET LEADS FOR THE
FIRST-CELL*
D. P. Brown and W. J. Sdmeider
Brookhaven National Laboratory
Upton, New York
INTRODUCDON
The ISABELLE refrigeration system utilizes compressed liquid helium to supply
refrigeration to nearly 1100 superconducting bending and focusing magnets. These
magnets steer the proton orbits of the accelerator and are arranged into two
interlocking rings. The magnet Ieads used to power, correct, and trim these superconducting magnets make up a substantial portion (25%) of the total heat Ioad that
the refrigerator must be capable of supplying. These magnet Ieads have been
designed to minimize the heat input into the refrigeration system. The design and
preliminary test results of four different types of Ieads in use on the ISABELLE
prototype, the first-cell, are described.
DISCUSSION
c-
Magnet Ieads are designed to minimize 3 ] the heat input into the refrigeration
system. This is accomplished by optimizing the cross-sectional area of the conductor
and intercepting with some gaseous helium ßow, a portion of the resistive heat
generated, and the heat conducted from the room temperature end into the coolant.
The total refrigeration [4 ] cooling Ioad, Q" is the sum of the heat ßux, Q", from
the cold end of the Iead into the coolant and the mass ßow, m, up the Iead times some
factor, f, characterizing the refrigerator cycle. Thus
Q,
= Q" + mf
(1)
where f is a factor which characterizes the refrigerator in a refrigerator/liquefier
mixed-duty operation. For a theoretical Carnot cycle plantat 4.4 K this factor would
have a value of 80 W-s/ g and, for actual refrigerators, values in the range of 50 to
95 W-s/ g have been reported [4 ]. The actual value depends on the relative efficiency
of the plant when operated as a refrigerator vs. operation as a liquefier. For the
particular refrigeration cycle that will be used for ISABELLE, in mixed-duty operation
approximately 630 W of room temperature input power is required to produce and
deliver 1 W of magnet refrigeration below 3.8 K and 33,700 W are required to
* Work performed under the auspic:es of the U. S. Department of Energy.
300
301
Magnet Leads for the First-Cell
ELECTRICAL FEEDTHROUGH FOR
VOLTAGE TAPa TEMPERATURE
SENSORS
GAS FEEDTHROUGH
ELECTR I CAL
FEEDTHROUGH
ME TAL SEAL F L ANGE
-
I
--1
TEMPER AT URE SENSORS
OFHC COPPER
CONDUCTOR
MAGNET LEAD VESSE L ~ '
~
SEE FIG. 5
1_
- " ' t -:nu_
STA I N LESS STEE L
SUPPORT TUBE
SUPERCONDUCTOR
BUSS
Fig. 1. 4250-A main power Ieads.
produce 1 g/ s of ftow for lead cooling. The value of f used to optimize the leads is the
ratio of these two values, 53.4 W-s/g.
CONSTRUCI10N DETAILS
There are four different classes of leads for varying current ratings designed for
the first-cell and ISABELLE. These are delineated in Table I. The current rating and
301
D. P. Brown and W. J. Schneider
Table I. Classes of Leads for Varying Current Ratings Designed for tbe First-CeU
and ISABELLE
Oass
Lead type
Current
rating,
A
II
I
Mainpower
Sextupole quad trim Rohinsbypass
±4250
±300
III
Octopole decupole duodecupole
±50 X 12
IV
Steering
Steering
±50
± 100
X
X
12*
12
Number
required
for
first-cell
Calculated
conduction
heat Ioad,
Calculated
total
heat Ioad,
2
4
4
1
4
4
4
4
0
6.1
0.7
19.1
1.8
0.8
2.6
0.7
1.6
1.7
5.2
w
w
*Not fully used.
reason for the various Ieads required for ISABELLE have been discussed previously
[s].
The 4250-A (Figs. 1 and 2) and 300-A Ieads are similar in design except that the
main power Iead is made of OFHC (oxygen-free high-conductivity) copper, while the
300-A Iead is manufactured of brass. A helix (acme thread) is cut into the conductor
(brass or OFHC) outer diameter. The conductor is then shrunk into a stainless steel
support tube. Helium gas flows up the helix, and, as a result of the design, a steep
temperature gradient exists in the conductor at the warm end from 50 to 300 K. At
the outlet, the gaseous helium flows through an insulator which isolates the Iead from
ground and returns the gas to the helium refrigerator compressor suction.
The 50-A (Figs. 3 and 4) and 100-A Iead designs are similar to each other except
for the size of the twelve conductors. A Teflon core has a helix (acme thread)
machined into its outer diameter. Twelve OFHC copper wires are equally space<i
Fig. 2. Actual 4250-A main power Iead.
Magnet Leads for the First-Cell
12CONOUCTOR 50A LEAD
ELECTRICAL FEEOTHROUGH
GAS OUTLET-300 K
ELECTRICAL LEA OT HROUGH
FOR TEMPERATURE SENSORS
METAL SEAL
FL ANGE
TEFLON SHEATH
12 INDIVIDUAL OFHC
COPPER GONDUCTORS
TEMPERATURE SENSORS
TEFLON CORE Wl TH
GAS HELIX
HELIX GAS PASSAGE
.
__.-MAGNET LEAD VESSEL
SEE FIG. 5
!"'-·----~
}
__ __J
GAS INLET
4 K
Fig. 3. Twelve-conductor 50-A correction or steering Iead.
303
304
D. P. Brown aad W. J. Seimelder
Fig. 4. Actual twelve-conductor 50-A correction or steering Iead.
TEMPERATURE SENSORS
TOTAL OF 6 EA . MAGNET
LEADS PER VESSEL
I
I .
'
I
3"0D MAIN
COOLANT TUBE
INDIUM SEALS
Fig. 5. Magnet Iead vessel.
16" (40.6 cm) LONG x
I" (2.54 cm) 0 0
TO HOLD LEADS
TUBES
Magnet Leads for the First-CeU
305
around the periphery of the Teflon core intercepting the helix. A Teflon jacket is then
shrunk around the diameter of the Teflon core holding the wires in place. Heliumgas
traveling around the helix intercepts heat in each of the twelve wires. Owing to this
configuration, a steep 50- to 300-K temperature gradient results at the warm end in
the copper wires. The gaseous helium then flows through an insulator and returns to
the helium refrigerator compressor suction. Because of the relatively modest current
rating (50 or 100 A), these single Ieads are capable of handling twelve separate
circuits. Consequently, the 50-A lead has a total capability of 600 A and the 100-A
Iead is capable of 1200 A.lt is not desirable to parallel any of these circuits because
the current flow is not self-regulating. However, if a parallel scheme is used, it is
essential that a control system be employed to insure that the current flow divides
evenly.
FIRST-CELL
The nurober of Ieads as shown in Table I are required to meet the power
requirement of the first-cell. The magnet lead vessel shown in Figs. 5 and 6 is
designed to accommodate six Ieads. Therefore, two magnet Iead vessels are required
for the first-cell. By way of comparison, ISABELLE will require upwards of 100
magnet Iead vessels. The heat leak to the 4-K stream on these vessels is expected to
be5W.
Fig. 6. Actual magnet Iead vessel under construction.
306
D. P. Brown and W. J. Schneider
The two-magnet lead vessels provide the transition between the 4-K environment of the magnets and ambient temperature. Each of the first-cell leads is
equipped with a temperature sensor which modulates an electric control valve or
solenoid valve and maintains some preset temperature at one point along the length
of the lead. The design of the control systein is described elsewhere [6 ].
Voltage taps are provided at the top and bottom of the leads. The differential
voltage measured is a function of the integrated resistance of the lead and, for a given
current, is an indicator of the temperature protUe of the lead. The differential voltage
is incorporated into a safety circuit which will shut down the power supply in the
event a preset voltage drop is exceeded. The steering dipoles (QF and QD) are
powered from the tunnel end in a vessel that is integral with the magnet interconnector. One class 111 50-A lead is employed. However, it is not fully used.
HEAT TRANSFER
Numerical calculations of lead performance have been made with a computer
program developed at CERN [ 4 ] and modified for the conditions at ISABELLE. These
results were used to optimize the various class leads. Figure 7 shows a plot of the mass
ftow and differential voltage vs. the current level for minimum refrigeration
requirements on the 4250-A lead.
z'
0 . 30
~
1<l
D::
0 . 25
loJ
~
>
D::
LI..
loJ
0 . 20
10 0
D::
0
D::
0
~
::> -
::l; l
- u 0 . 15
~ lo.l
80
LI..
...J
0 .1
60
>
loJ
0 .05
40
~
0
...J
LI..
0
0
<l
loJ
1<l
D::
loJ
\!)
<l
1-
~V)
0::::=;
ol!>
E
Q..
0
20
1000
LEAD
2000
3000
4000
50 0 0
CURRENT, A M PE RES
Fig. 7. 4250-A Iead performance at minimum refrigeration.
...J
Magnet Leads for the Fmt-Cell
307
The CERN design used on the main power and the trim Ieads provides an
enhanced heat transfer area and a stabilizing thermal mass which inhibits aceidentat
Iead burnout. The multibundle-type Iead used for corrections and steering is a new
concept in Iead design. The multiplicity of these Ieads necessitates bundling to reduce
the complexity of the control system and reduce space requirements. The heat
transfer area for the 50- and 100-A Ieads appears tobe adequate.
FABRICATION AND TESTING
Leads from each dass have been fabricated and are presently being assembled
into a magnet Iead vessel. ISABELLEdipolemagnet 005 is also being assembled for a
force ftow test scheduled for late summer of 1979. Preliminary tests of Ieads similar
The referenced 7-ft bubble chamber Ieads were
to these have been excellent
designed for and operated with hydrogen as a coolant. In addition, prototype
CERN-type Ieads have been built and tested on earlier ISABELLE magnets using both
helium pool boiling and forced-ftow cooling. Results for these Ieads have been
consistently good and compared favorably to the predicted values although they
operated somewhat cooler than anticipated.
eJ.
ACKNOWLEDGMENTS
The authors wish to acknowledge the assistance of many members of the ISABELLEstaffin designing,
fabricating, and testing these Ieads, and A. Walsh for graciously typing the paper.
REFERENCES
1. R. K. Thomas, J. R. Purcell, and R. W. Boom, in Advances in Cryogenic Engineering, Vol. 23, Plenum
Press, New York (1978), p. 219.
2. C. L. Goodzeit, "Optimization of Gas Cooled Superconducting Magnet Leads-A Method for
General Materials," BNL Report, BNL # 17233, (September 1972).
3. W. J. Schneider, Brookhaven National Laboratory, private communication.
4. D. Güsewell and E. V. Haebel, in Proc. 3rd Intern. Cryogenic Engineering Conference, IPC Science and
Technology Press, Guildford, England (1971), p. 187.
5. G. Parzen, IEEE Trans. Nucl. Sei. N26(3):3995 (1979).
6. M. Afrashteh, Brookhaven National Laboratory, private communication.
DISCUSSION
Question by M. A. Green, Lawrence Berkeley Laboratory: In the final figure of the paper, are the values
of valtage drop and mass ftow given for a single Iead or are they given for a Iead pair? Are the Ieads designed
specifically for your refrigerator, which appears to have a much lower value of refrigeration to liquefaction
coefficient than most refrigerators?
Answer by author: In the final figure of the paper, the valuesof valtage drop and mass ftow are for a single
Iead. Yes, the mass ftow that the Ieads have been optimized for are specifically for the ISABELLE
refrigerator. However, use of the Ieads on a different refrigerator only necessitates that the mass ftow be
adjusted to produce minimum refrigeration. lt would be necessary to know [, the factor which characterizes the refrigerator/liquefier mixed-duty cycle to obtain that optimization.
F--6
THERMAL CONTROL FOR THE
MFTF MAGNET*
J. H. VanSant and R. M. Ross
Lawrence Livermore Laboratory, University of Califomia
Livermore, Califomia
INTRODUCDON
The Mirror Fusion Test Facility (MFTF) will have the world's largest magnet.
Externat dimensions of the assembled Yin-Yang magnetwill be 7.8 by 8.5 by 8.5 m,
and it will weigh approximately 300 tons. More than 8000 Iiters of circulating liquid
helium will be required to maintain the nearly 50 km of superconductor at below
5.0 K while the latter carries almost 6000 A in a magnetic field up to nearly 7.7 T.
Such formidable conditions have necessitated extensive planning to achieve the
required thermal control.
This paper describes four features of these thermal control plans. First, it
outlines the proposed cooldown and warmup schedules for the MFTF and the
procedure for regenerating extemal cooling surfaces. Then it discusses the design of
an extemal quench resistor, based on an estimate of the superconductor's maximum
temperature. Last, it explains how a computer model of liquid helium circulation was
used to aid in choosing pipe size for the liquid helium lines.
To minimize heat Ioads on the magnet system, all liquid helium temperature
surfaces will be in a 1.3-l.f.Pa (10-nTorr) vacuum and shielded by liquid nitrogen. In
fact, the entire magnet, which will be maintained at less than 4.5 K, will be installed in
a 12-m-diameter, 18-m-long vacuum vessel that also will be the mirror fusion
chamber. The vessel will support the magnet by means of seven liquid-nitrogencooled banger and stabilizer rods. Externat surfaces of the magnetwill be shielded by
311 m 2 of liquid-nitrogen-cooled panels. In regions where plasma and neutral beam
impingements will occur, 100m2 of water-cooled panels will shield the liqwd
nitrogen panels.
A sectional view of one magnet coil in its major radius region is shown in Fig. 1
and illustrates typical MFI'F construction. Tables I and II describe the magnet
materials and conditions. A unique feature of the magnet design is the guard vacuum
space, which serves two principal purposes. It protects the fusion chamber from
developed helium leaks through the support structure and provides an additional
ftow channel to circulate gas for more eftective cooldown or warmup of the structural
case. Moreover, the vacuum space and the urethane shim help to insulate the magnet
coil.
• Work pcrformed under the auspices of the U. S. Department of Energy by Lawrence Uvermore
Laboratory under Contract No. W-7405-Eng-48.
308
309
Thermal Control for tbe MFfF Magnet
pla sma shield
Neutra l beam shield
Fig. 1. A section view of one MFTF magnet coil,
showing construction details for both the magnet and
for the cooling system that surrounds it. The section is
along Iine AA in the small drawing.
Table I. Properties of tbe MFfF Magnet
Design current, A
Maximum magnetic ftux density, T
Conductor size, cm
Copper-to-superconductor ratio
Effective copper area for current, cm 2
Conductor surface area for heat transfer, cm 2 /cm
Transition temperature at maximum current and field, K
Maximum liquid helium temperature, K
Number turns per coil
Conductor length per coil, m
Coil porosity
Stored magnetic energy, MJ
5775
7.68
1.24 X 1.24
6.7/1
1.25
8.17
5.0
4.52
1392
24,785
0.32
440
310
J.H.V..s.tudR.M.R. .
Table D. Materials aad Conesponding Weigbt for
the MFI'F Mapet
Materials
Magnet
Conductor (copper, superconductor)
Insulation (G-11)
lacket (316 stainless)
Sbim (uretbane)
Bladder (copper)
Case (304 LKN stainless)
Intercoil supports
Gas baflle
Total
Accessories
Liquid uitrogen shields (316 stainless)
Water shields (316 stainless, copper)
Liquidhelium ducts (316 stainless)
Current Ieads (copper)
Hanger rods (316 stainless)
Miscellaneous hardware
Total
Weight,
kg
52,820
5,730
16,180
3,370
1,130
178,370
36,360
6,180
300,140
10,650
3,430
2,730
500
12,730
1,100
31,140
COOLDOWN AND WARMUP
The magnet cooldown schedule will be programmed to prevent unacceptable
structural thermal stresses. Cooling gases circulated through the coil and guard
vacuum spaces will be supplied at temperatures decreasing from 225 to 100 K during
a minimum 50-hr period. During this period, approximately 20 g/s of helium and
400 g/s of nitrogenwill be circulated through the coil and guard vacuum spaces,
respectively. Afterwards, the helium ftow will be increased to 100 g/s, and the guard
vacuum will be pumped down to approximately 13 Pa. An additional 50 hr are
estimated for complete cooldown to 4.5 K. The total energy extraction is approximately 29 GJ. Severe ftow asymmetry between the two coils (e.g., 30%) is not
expected to cause unacceptable thermal stresses, but ftow control will be employed.
During warmup of the magnet, the gas temperature schedules will be nearly
reversed from cooldown. That is, the helium supply temperature will increase from
approximately 75 to 150 K during a 50-hr period at a ftow of 100 g/s through only
the conductor pack. Then nitrogen and helium will be circulated through the guard
vacuum and coil spaces at supply temperatures increasing from 150 to 300 K during
the next 70 hr.
The design stress Iimit for the structural case is 550 MPa (80,000 psi) which
provides a 1.5 factor of safety based on tensile yield strength. Calculated stresses
during cooldown and warmup range from approximately 55 MPa (8000 psi)
compression to 90 MPa (13,000 psi) tension resulting in a factor of safety greater
than 9.
A numerical analysis of the magnet cooldown and warmup cycles performed by
General Dynamics Convair Division [ 1] yielded the foregoing thermal schedules.
They are intended to prevent thermal stresses from exceeding design Iimits.
However, strain and temperature at many locations will be. monitared during
thermal cycles.
Thermal Control for the MFI'F Magnet
311
EXTERNAL SURFACE REGENERATION
Cryopumping panels in the MFfF vessel will periodically be thermally cycled to
regenerate the surfaces. Tbe magnet's external surfaces must be warmed to approximately 15 K at the same time to prevent released gases from recondensing. To
accomplish this, the magnet liquid nitrogen shields are to be drained and warm
nitrogen gas (300 K) circulated through them to radiate heat to the magnet surface.
The shield temperature will be controlled so as to minimize cumulative heat transfer
to the magnet.
Prior to the regeneration cycle, the magnet must be deenergized to prevent a
quench. Subsequently, the liquid helium must be pumped out so that transfer lines
inside the vacuum vessel can also be regenerated. However, by proper thermal
control of external surfaces, the time required for recooling the magnetto 4.5 K and
reenergizing it should be minimized.
MAGNET DISCHARGE
If any detectable portion of the magnet coil should become normally conducting
and not recover to superconducting, the contained energy will be dissipated in an
external discharge resistor. This resistor is sized to Iimit both voltage and maximum
conductor temperature.
A conservative method for estimating the maximum conductor temperature is
to compute an adiabatic temperature rise using
0
[''
J,
0
1 2 R dT
= ~ Lm;
f
Tmax
To
•
c; dT
(1)
Instantaneous thermal communication between the conductor and adjoining
materials is assumed. The participating materials are the superconductor, copper,
interlayer and interturn insulation, and helium gas.
Tbe current history is defined as
{Io,
I_
- 10 exp(-T/ To),
(2)
Since R can be expressedas pL/ A, (1) can be restated in the following form of
f~To (
A
Td
To
1) =tm; f
+2
Tmax
To
(c;/p)dT
(3)
Solution of (3) yields the maximum temperature as a function of delay until a
discharge is initiated. Figure 2 shows this curve for a current decay time constant of
69 s. This decay constant corresponds to a peak voltage of 1000 V across a 0.17-.0
quench resistor, with 12 H inductance in the magnet (i.e., To = Hl0 / V max). Copper
properties assumed in (3) are those of OFHC copper having a residual resistivity
ratio equal to 150 and a 7.76-T magnetic field [2 ].
Figure 2 shows that a maximum temperature of 200 K is reached if a 10-s delay
in initiating discharge is allowed. Longer decay time constants (i.e., lower quench
voltages) result in higher temperatures. This temperature is considered permissible
since it is a conservative estimate and is limited to a small region of the coil where
both initial transition to normal conduction and peak field could occur. A 200-K
temperature rise from 5 K should result in less than 0.1% thermal expansion of the
J. H. V..s..t ud R. M.
312
a-
X
"'E
t-.
z
Q)
~
Q)
a.
E
J!l
E
E
::J
X
"'
~
0
10
20
40
30
50
Discharge delay time,rd, s
Fig. 2. Maximum conductor temperaturein MFIF as a function of delay time. The decay
time constant To = 69 s.
conductor. Also, 10 s is adequate time to inititate a discharge with an automatic
quench detecting system.
Magnet structural materials can also develop resistive heating during a fast
discharge by a transformer coupfing eflect between the magnet coil and surrounding
structure. Because of its properties, the copper guard-vacuum bladder will show the
greatest temperature increase from this source. Assuming adiabatic conditions,
resistive and sensible heating of the copper can be equated by the relation
f.
00
V 2 /R dT
0
= L.,m
f
Tmax
cdT
(4)
To
Fora 1392 : 1 turn ratio, 1000-V peak coil voltage, and a 69-s current decay time
constant, this equation becomes
0.26~0 = ( Tmax pc dT
YL.,
(5)
JTo
Solution of this equation yields a maximum temperature of 70 K for the copper
bladder, which is an acceptable temperature increase.
A similar analysis of the stainless steel case yields a temperature of 13 K. Total
energy dissipation in the case, bladder, and coil jacket is approximately 7 MJ, or less
than 1.5% of the energy contained by the magnet before discharge.
HELIUM CIRCULADON
Important to the thermal control of the magnet is an adequate circulation of
liquid helium. Forced pumping is not practical, so natural circulation was chosen
because it has been satisfactory in smaller magnet systems. A computer model of the
liquid helium natural circulation was developed to estimate steady-state mass ßow
313
Thermal Control for the MFI'F Mqnet
Return valve
27m~
I
9m
Heliumtransfer lines
Fig. 3. Schematic diagram of the liquid helium
circulation. The helium transfer Iines are
15-cm schedule 10 pipes.
rate and vapor quality. Also, a sensitivity study was made to determine which
parameters have the greatest inßuence and to estimate the range of uncertainty for
the liquid helium ßow rate.
The principal requirement of the liquid helium system is to maintain quality with
less than 10 vol.% vapor in the magnet. Heat transfer analyses indicate that
significantly higher vapor qualities would probably inhibit cryostability.
A schematic of the liquid helium system, shown in Fig. 3, illustrates the lengths,
bends, and altitudes of the pipes, the dewar, and the magnet. Note that the magnet
inlet and outlet are approximately 16 and 9 m, respectively, below the liquid helium
dewar.
The conductor pack and magnet shape do not immediately lend themselves
to an obvious ßow-modeling approach. Therefore, in modeling the magnet
three approaches were considered: the Blasius friction equation, Darcy's porous
media equation, and a three-dimensional orifice model
In selecting an
appropriate method, estimates of hydraulic diameter, ßow tortuosity, porosity,
permeability, friction factor, and effective orifice dimensions were made, and the
three approaches were compared by means of their respective pressure drops. The
porous media approach resulted in the smallest pressure drop, the Blasius approach
yielded a pressure drop ten times greater, and the orifice approach gave a pressure
drop that was a thousand times greater. The orifice assumption was rejected as
unrealistic. The Blasius iriction method was chosen over the porous media approach
because the former was more conservative. Thus, the magnet pressure loss was
estimated with a modified Blasius friction equation in the following form:
e].
4P = (/LmTld,.M 2 /2-yA;q, 2 )
(6)
Flow in the magnet is expected to be laminar by the Reynolds number
definition, so that the friction factor is given as
f = 64JJ.Apt!J/ 71Md,.
(7)
314
I. H. VaaSaat aad R. M. Rllll8
Pressure Iosses in the piping system were simply modeled using loss coefficients
for bends, valves, entrance-exit regions, and other effects. These were calculated
as functions of the friction factor f. The effect of two-phase ßow was also included by
using the Lockhart and Martinelli correlation [5 ]. Flow in the piping system was
assumed turbulent.
Helium ßow rates were estimated by an iterative computing method. Using an
assigned heat Ioad for selected ßow model elements and an assumed ßow rate,
helium properlies were determined for each element node using NBS data [6 ]. The
resulting pressure imbalance in the ßow circuit owing to cumulative contributions of
friction, momentum, and gravity was computed. The ßow rate was readjusted and
the calculations repeated until the pressure imbalance was acceptably small. This
procedure provided a means for determining the effect of heat Ioad on ßow rate (Fig.
4a). Also, vapor quality was determined and appears as a function of heat Ioad in Fig.
4b.
[ 4]
--- ----
(b)
200
--300
700
Fig. 4. Computed helium tlow rate (a) and vapor quality (b) as a function of the system
heat Ioad. The dashed curves above and below the graphs show the extent of
uncertainty in each calculation. (Assumed liquid helium head in the supply dewar is
1m.)
Thermal Control for the MFfF Magnet
315
Table 111. Uncertainty Range of Flow Parameters
Parameter
Range
Friction factor, f
Tortuosity factor, 1J
Porosity, 4J
Liquid helium dewar head, m
Hydraulic diameter, dh, cm
Piping heat leakage, W
Length of piping, m
0.014 to 0.018
1.5 to 2.0
0.30 to 0.35
0.5 to 1.0
0.15 to 0.35
30 to 80
80 to 100
Table IV. Liquid Helium System Heat Sources
Heat input,
w
Source
Liquid nitrogen shield radiation
Liquid nitrogen shield conduction
~agnethangerrods
Conductor joints
Instrumentation Ieads
Helium ducts
Total
160
45
60
45
70
80
460
Because the modeling procedure entails some uncertainties, it was of interest to
determine how sensitive the results were to changes in certain variables. Table 111
shows the maximum expected range in these flow parameters, and Table IV shows an
estimate for the totalliquid helium system heat input. The results of the sensitivity
study are reflected in Figs. 4a and 4b by the uncertainty range curves.
The effects of two-phase flow are significant for helium at mass qualities as low
as only 1% and flows near 300 g/s. Surprisingly, the static head inside the liquid
helium dewar is the most significant parameter affecting mass flow rate because of
the relatively low fluid ftow resistance of liquid helium. The pipe friction is far more
influential on flow than either magnet friction or heat input.
On the basis of this calculation a pipe with a 15-cm ID was selected for the liquid
helium supply and return lines. This pipe size and the estimated system heat Ioad of
460 W yield an equilibrium mass flow rate of approximately 700 g/s. Vapor quality
at the top of the magnet is less than 4 vol.% (0. 7% by mass), and is less than 20 vol.%
at the top of the return line. These results imply that an adequate safety margin has
been provided in the thermal control of the magnet.
NOTATION
A = conductor area
AP = area for conductor pack
c = specific heat
dh = hydraulic diameter
f = friction factor
H = inductance
I= current
10 = initial current
i = material index
J. H. V..S..t ud R. M. a..
316
L = oonductor length
Le = eflective length
L". = 8ow path length througb the magnet
m = IIUIIII per unit length
M = IIUIIII ftow rate
R=resistance
T = temperature
V= voltage
Greek Symbols
'Y = density
." = tortuosity factor
,.,. = viscosity
p
= resistivity
-r" = delay time
-r0 = current decay time oonstant
t/J
= porosity
REFERENCES
1. R. F. O'Neill and D. H. Riemer, "Thermodynamic Analysis of the Magnet System for Mirror Fusion
2.
3.
4.
5.
6.
Test Facility," General Dynamics Convair Division, San Diego, Califomia, CASD-LLL-78-002
(October 1978).
Handbook on Materials for Superconducting Machinery, Metals and Ceramies Information Center,
Sattelle Memorial Institute, Columbus, Ohio (1974).
R. B. Jacobs, "Helium Circulation in the MFTF Magnet.System," Lawrence Livermore Laboratory,
Livermore, California, internal oommunication (November 8, 1977).
Standard Handbook for Mechanical Engineers, 8th ed. McGraw-Hill Book Company, New York
(1978).
Fluid Flow Data Book, General Electric Co., Schenectady, New York (1977).
R. D. McCarty, NBS Tech. Note 631 (1972).
DISCUSSION
Question by P. W. Eckels, Westinghouse ElectricCorporation: Have anyofyourexperimentsindicated
a maximum permissible vapor fraction in the conductor?
Answer by author: No, they have not. However, we believe thatour 10vol.% vapor Iimit isconservative
on the basis of allowable heat transfer area decrease without loss of cryostability for the MFTF
superconductor.
F-7
FORCED-CIRCULATION COOLING
SYSTEM FOR THE ARGONNE
SUPERCONDUCTING HEAVY-ION LINAC*
J. M. Nixon and L. M. BoUinger
Argonne National Laboratory
Argonne, Il/inois
INTRODUCTION
The Argonne superconducting heavy-ion linac is a prototype heavy-ion
accelerator used to increase the energy of an ion beam from a tandem electrostatic
accelerator C· 2 ]. The accelerating elements are split-ring-type resonators with
hollow niobium drift tubes mounted in cylindrical housings. The housings are made
of explosively bonded niobium clad copper [3 ' 4 ]. The resonators, along with superconducting solenoid focusing magnets are positioned axially in cryostats on support
structures which also serve as helium supply andreturn manifolds, as shown in Fig. 1.
The resonators and magnets are cooled by a continuous forced-ftow circulation of
liquid helium directly from a refrigerator.
The cooling system consists of the refrigerator, a 1000-liter dewar with built-in
heat exchanger coil, a 46-m3 helium gas storage tank, three distribution boxes with
valves, heat exchangers, and transfer line ports, connected by a 20-m-long, liquidnitrogen-shielded, coaxial distribution line. A plan view of the linac cryostats, a
buncher cryostat, and the cooling system components is shown in Fig. 2.
DESIGN REQUIREMENTS
The principal requirement for the cooling system is that it provide continuous
refrigeration of the superconducting resonators and magnets at temperatures of
s4.9 K, for long periods of time. The unique shape of the split-ringresonator, and its
mounting base-down on the support structure, requires continuous forced-ftow
circulation of helium through its drift tubes for adequate cooling.
Because the resonators and magnets are connected in parallel, ftow must be
divided reliably. For simplicity, fixed restrictors are used to divide the ftow, but this
requires that the quality of the entering helium be kept constant regardless of the
upstream heat load, otherwise the downstream units could receive variable cooling.
Uniform ftow division is accomplished by having the helium enter each cryostat as
saturated, or slightly subcooled liquid. This is achieved by heat exchange with the
return ftow, as described below.
* Work performed under the auspices of the U. S. Department of Energy.
317
318
J. M. Nixon and L. M. BoUinger
HELIUM
LIQUID
MITliDGEN
AND
LIN!
0
10
SCAU . .
Fig. 1. End view of beam-line cryostat. The magnet is behind the resonator.
A second required feature is the capability of installing or removing any cryostat
without interrupting the operation of the remainder. This is accomplished by
providing a pair of transfer lines between the distribution boxes and the adjacent
cryostats, together with supply, return, and bypass valves for each cryostat.
As the third requirement, the system has to supply liquid helium, allow its
withdrawal for use in cooling a separate cryostat for testing resonators before they
are installed in the linac, and provide for closed-circuit recovery of the boil-off gas
during operation of the linac.
319
Forced-Circulation Cooling System for Linac
~
I
TANDEM
VAULT
0
2
I
3
4
SCALE (meters)
5
HELIUM
REFRIGERATOR
BUNCHER
L INAC ASSEMBLY AREA
: ··:
3 COMPRESSORS i... .. j
ON FLOOR ABOVE
r··,
;__j
. ., . . : .; .•. ..0:
. ..
'·.
O
,_ .. ,
L.. j
RESONATOR
TEST CRYOSTAT
·. ·.
•
•
...
••• •
• •
0
.
'
.. .
~
Fig. 2. Plan view of superconducting linac cryostats and helium-distribution system.
CRYOGENIC SYSTEM DESCRIPTION
The helium circuit is shown with some typical heat Ioads in the ftow diagram of
Fig. 3. Approximate helium conditions at correspondingpoints araund the circuit are
given in the pressure-enthalpy diagram of Fig. 4.
The scheme used to control the quality of the outgoing stream in this system is
similar in some respects to that used in cooling the magnets of the Fermilab Energy
Doubler [5 ]. The outgoing stream is held at higher pressure and temperature than the
return stream. Pressure is dropped through a J-T expansion at the far end, and
the returning, cooler, two-phase stream picks up heat from the outgoing stream.
In the energy doubler, the outgoing stream is not allowed to vaporize, whereas in the
present system the outgoing stream vaporizes in each cryostat, and is then condensed
and subcooled in heat exchangers before entering the next cryostat. The use of
two-phase ftow directly from a refrigerator, and improvement of the quality by heat
exchange in a dewar that receives the return ftow, are also features found in the
cooling system for the large superconducting solenoid for the MINIMAG
[6'7] .
.
expenment
The principal component of the cooling system is a CTI Model1400 refrigerator/liquefier, rated at 95 W at 4.6 K with three compressors and liquid nitrogen
precooling. The machine has a variable-speed engine and dual charcoal adsorbers
with valves and heaters for regeneration while operating. The approximate mass ftow
is 6.7 g/s with three compressors. The refrigerator module is located adjacent to the
linac and is connected by bayonets to the end of the distribution line. The compressors are located about 50 m away on a thick concrete ftoor above the tandem. In this
J. M. Nixon and L. M. BoWn&er
3%0
2
J- T.
MOOEL 1400
REFRIG
-BEAM
-
A
BUNCHER
HEAT LEAKS
LINAC CRYOSTATS
Fig. 3. Cooling system helium flow diagram. Assumed heat Ioads are shown.
remote location, vibrations from the compressors are isolated from the sensitive
resonators.
The static heat leaks of the components are constant, but the rf power to the
resonators is variable. The heat Ioad of each resonator is usually in the range of 2 to
4 W. An average of 3 W is assumed for this example. In operation of the linac, the
resonators are separately phased, and power to the various resonators can be
optimized to give maximum acceleration for the available refrigeration capacity.
15.40
10
30
12
H, EN T HALPY,
32
J/g
Fig. 4. Pressure-enthalpy diagram for the circuit and heat Ioads of Fig. 3 (m = 6.7 g/s).
Forced-Cireulation Cooling System for Linac
321
As shown in Figs. 3 and 4, helium leaves the refrigerator at point 2 and enters
heat exchanger HX 1 in the 1000-liter dewar. The quality, or gas fraction, of the fluid
at point 2 depends upon its enthalpy at point 1, before the refrigerator J-T
expansion, and the pressure of the outgoing stream in the distribution line. With
three compressors, m = 6.7 g/s, and if P 2 = 185 kPa, then the quality, x 2 = 0.06,
and the heat removed in HX 1 to condense and subcool the ftow to 4. 7 K is 17.6 W.
Helium then ftows through cryostat D, absorbs 30 W total heat input, resulting
in an X4 of 0.22. HX2 in distributionbox D removes 30 W so that conditions at point
5 are almost the same as at point 3, except that the pressure is Iower. Similarly heat is
added in cryostat C and removed in HX3 bringing the ftow to point 7. The heat Ioads
of cryostat A and the buncher, being much smaller than the previous ones, are taken
together in series. The J-T expansion, 9-10, drops the return stream to a pressure
slightly above that of the 1000-liter dewar, and Iowers its temperature to give a
reasonable temperature difference in the three heat exchangers. The return stream
passes through the shell sides of HX2 and HX3, absorbing heat from the outgoing
stream. The quality increases at each heat exchanger, until it enters the dewar with
x 12 = 0.73. Part of the returning liquid is evaporated by the heat load from HX1,
making the final quality, x 13 = 0.88, leaving 12% of the ftow to accumulate as liquid
for this case.lf the total heat load of the system is less than the refrigeration capacity,
the liquid Ievel in the dewar rises. If the Ioad exceeds the capacity, the liquid Ievel
drops and the excess gas is transferred to the storage tank. The 88% of the ftow that is
gas returns to the refrigerator as saturated vapor at the temperature and pressure of
the dewar, as at point 1311•
MECHANICAL DESIGN AND FABRICATION
Main Helium Distribution Line
The main helium line connects the refrigerator with the 1000-liter dewar, the
D, C, and A distribution boxes, and on through the taodem shielding wall to
the buncher for a total Iength of about 20m. The center of the line is 2.44 m
above the ftoor. A typical cross section is shown in Fig. 5. The innermost tube carries
the higher pressure outgoing ftow, while the annulus between it and the next tube
carries the reduced pressure return ftow. The helium lines are surrounded by an
RETURNING HELIUM
G-10 INSULATOR
VACUUM
012345
SCALE .cm
Fig. 5. Typical cross section of helium distribution line.
3ZZ
J. M. Nlxon and L. M. BolliDger
annular radiation shield made up of two larger pipes through which liquid nitrogen is
fed continuously. About 5liters/hr of liquid nitrogen is supplied at the refrigerator
end and exhausts as gas at the buncher end.
The sections of line were preassembled in the shop, and field welded with the
distribution boxes and dewar. The entire line is welded except for one joint at the
corner near the dewar. 'Ibis joint, which has 0-ring seals for the vacuum jacket,
double indium seals on the coaxial helium line, and a nickel-gasketed coupling for
the liquid nitrogen line, allows the section of line that connects the refrigerator and
dewar to be removed if necessary for maintenance of these components.
Dewar and Dewar Neck Insert
The 1000-liter dewar is a commercial gas-shielded design modified with a
larger neck to accept a 150-mrn-diameter insert. A heat exchanger coil consisting of
18.3 m of 15.8-mm-OD x 0.9-mm-wall copper tubing was installed in the bottom of
the helium vessel before it was welded shut.
The dewar neck insert extends 0.6 m below the top ftange and contains four
helium tubes: high pressure to and from the heat exchanger coil, and low pressure
into and out ofthedewar. The high-pressure lines are connected to the coil by means
of a pair of nickel-gasketed couplings. The heat leak of the neck insert is minimized
by bleeding a small ftow of gas up past heat-intercepting copper disks brazed at
intervals to the stainless tubes.
Distribution Boxes
The distribution boxes are liquid-nitrogen-shielded vacuum vessels located
adjacent to the heads of the linac cryostats. They contain two transfer line bayonet
ports and manual supply, return, and bypass valves in the outgoing stream. The C and
D boxes also contain heat exchangers, HX2 and HX3, which have helical coils of the
same length and tube size as the dewar coil, mounted in vertical tanks.
The A box contains six manual helium valves, an air-operated J-T valve, a
cooldown line with a cold check valve, but no heat exchanger. The helium piping is
surrounded by annular liquid nitrogen tanks which are connected in series with the
liquid nitrogen shields of the line. All of the boxes and the entire line have a common
insulating vacuum.
The vessels were assembled, welded, and leak tested in the shop, then erected on
site and welded to the sections of line. Figure 6 is a photograph showing the three
boxes and the partially completed line during construction. All of the TIG welds
were made with an argon purge and helium mass spectrometer leak tested when
completed. The system has been thermally cycled a number of times since the initial
cooldown and there has never been a leak.
IDstrumentation
The most useful diagnostic parameters are the dewar liquid Ievel and dewar
pressure. Outputs from a superconducting Ievel sensor and a pressure transducer are
recorded continuously on a strip chart, and are also used to actuate an alarm when
high or low Iimits are exceeded. A differential pressure gage with a ± 125-Pa (±0.5 in.
of water) range is connected on one side to the dewar, and on the other side to the
dewar through a valve in series with a small reference pressure tank. When the valve
is closed, the instantaneous dewar pressure is trapped in the reference tank, and the
gage then gives an extremely sensitive indication of the rate of dewar pressure
Forced-Circulation Cooling System for Linac
323
Fig. 6. View showing distribution boxes and partially
completed line during construction.
change. This has proven to be indispensable in adjusting the refrigerator and in
making heat Ioad measurements.
Other gages indicate pressures in the outgoing stream as it enters the distribution boxes, J-T valve, and the low-pressure return sides of HX2 and HX3.
Temperatures are determined by germanium resistance thermometers on the
helium lines entering and leaving cryostats C and D, entering cryostat A, and leaving
the buncher. Copper-Constantan thermocouples are also attached at the same
locations to monitor cooldown. Additional thermocouples give temperatures of the
liquid nitrogen shields in the distribution boxes and the temperature of the nitrogen
exhaust from the shield circuit.
Current to a 250-W heater in the dewar is monitored with a digital voltmeter.
Liquid helium Ievels in the shell sides of HX2 and HX3 are determined by
superconducting Ievel sensors.
OPERATING EXPERIENCE
The system has been in operation almost continuously since June 1978, with
only a few shutdowns for maintenance and for warmups to clear blockages caused by
helium contamination. Linac beam acceleration runs of up to three weeks' duration
have been completed with no interruptions caused by the cooling system [8 ]. The
extreme flexibility of the system has been demonstrated by its ability to operate with
the dewar and the distribution line, or with any combination of the linac cryostats.
Figure 7 shows schematically the multiplicity of functions it performs. Experiments
to determine the best ways to optimize performance under these varying conditions
are continuing tobe made.
ReHability of the system has been reasonably good. After the usual learning
period, there have been only a few unscheduled stoppages. These were caused by
324
J. M. Nixon and L. M. Bollinaer
LINAC
PORTABLE
DEWAR
Fig. 7. Schematic of helium-refrigeration and distribution
system, which performs the following functions: (1) cools
linac; (2) makes liquid; (3) provides liquid inventory; (4)
saves gas from precooling linac; and (5) saves gas from
miscellaneous use.
several instances of helium contamination, and the premature failure of bearings and
an 0-ring on the expansion engine.
The source of the most serious helium contamination was found tobe a hairline
fatigue crack that developed in a copper elbow in a compressor suction line after
about 2300 hr Operation.
One of the most demanding functions of the refrigeration system is the
cooldown of an accelerator section, in which the elementstobe cooled have a mass of
about 1100 kg. Initial efforts to accomplish the cooldown by means of the refrigerator alone were not very successful because the ftow rates of warm gas are severely
limited and the coaxial design of the distribution line maximizes this problem.
Consequently a procedure has been adopted that depends heavily on the use of liquid
helium from the 1000-liter dewar. In essence, the procedure is as follows: The
resonators are cooled to approximately 80 K by ftowing liquid nitrogen through
precooling lines not shown in Fig. 3. Then, helium from the main distribution line is
allowed to ftow through the cryostat, and the outgoing warm gas is returned to the
refrigerator by means of the warm-gas recovery line shown in Fig. 3. Simultaneously,
liquid helium from a portable dewar is transferred through the previously mentioned
precooling lines in the cryostat, and the outgoing gas is also fed into the warm-gas
recovery line. Finally, when the resonator temperatures have been lowered to
:515 K, the outgoing helium can be returned to the 1000-liter dewar through the
normal coaxial path.
The complete cooldown cycle requires about 24 hr, of which about 18 hr are
used for nitrogen precooling and the remaining 6 hr are required to decrease the
temperature from 80 to 4.6 K. Since the helium-induced cooling rate considerably
exceeds the capacity of the refrigerator, some excess helium gas is generated and this
is pumped by the refrigerator compressors into the storage tank. The net usage of
liquid during cooldown is typically 400 Iiters.
The heat Iosses of various components of the distribution system have been
measured with some care by two methods. One approach is to measure the rate of
boil-off of helium gas. The second approach is a heat-balance method in which the
unknown heat input associated with some Ioad is balanced by means of the known
heat input from the heater in the 1000-liter dewar under the condition that the
Forced-Cireulation CooUng System for Linac
325
pressure in the dewar (and hence the refrigeration capacity of the system) is
constant. The sensitivity and response time of the system are such that it is feasible to
measure a change of load of a small fraction of a watt in an hour.
CONCLUSIONS
All of the design objectives of the cooling system have been accomplished.
Forced circulation of liquid helium directly from a refrigerator through a complex
circuit to an extended array of superconducting devices has been demonstrated
successfully.
ACKNOWLEDGMENTS
The success of the system is the result of the efforts of many people. In particular, much of the design
of the heat exchangers and distribution system is due toP. C. Vander Arend, Cryogenic Consultants,
lncorporated, Allentown, Pennsylvania. An exceptional job of fabrication, welding, assembly, and testing
of the system was performed by personnel of the Argonne Centtal Shops and Quality Assurance
Divisions.
REFERENCES
1. L. M. Bollinger, R. Benaroya, B. E. Qiflt, A. H. Jaffey, K. W. Johnson, T. K. Khoe, C. H. Scheibelhut,
K. W. Shepard, and T. P. Wangler, in Proc. 1976 Prown Linear Accelerawr Conference, AECL-5677
(1976), p. 95.
2. L. M. Bollinger, IEEE Trans. Nucl. Sei. NS-24:1076 (1977).
3. R. Benaroya, L. M. Bollinger, A. H. Jafley, T. K. Khoe, M. C. Olesen, C. H. Scheibelhut, K. W.
Shepard, and W. A. Wesolowski, IEEE Trans. Magn. Mag-13:516 (1977).
4. K. W. Shepard, C. H. Scheibelhut, R. Benaroya, and L. M. Bollinger, IEEE Trans. Nucl. Sei.
NS-24:1147 (1977).
5. P. C. Vander Arend, in Advances in Cryogenic Engineering, Vol. 23, Plenum Press, New York (1978),
p.420.
6. M. A. Green, "MINIMAG Experiment, Large Superconducting Solenoid Magnet, The Cryogenic
System," Lawrence Berkeley Labaratory Eng. Note M4834, UCID 3754 (June 1975).
7. M. A. Green, in Advances in CryogenicEngineering, Vol. 21, Plenum Press, New York (1975), p. 24.
8. K. W. Shepard, IEEE 'li"ans. Nucl. Sei. NS-16:3659 (1979).
DISCUSSION
Question by G. H. Morgan, Brookhaven National Laboratory: You mentioned you were concerned
about the parallel ftow arrangement. Was this because of the possibility of oscillations?
Answer by author: The concern was that if helium entered the parallel ftow-dividing restrictors
(lengths of small-diameter tubing) as a two-phase mixture of varying vapor fraction, then the mass ftow
metered to each resonator would vary widely, possibly resulting in insufficient cooling. To prevent this, the
aim was to cool the stream so that it always entered the restrictors as liquid, making the ftow supplied to
each resonator fairly constant.
F-8
ENERGY DOUBLER SATELLITE
REFRIGERATOR MAGNET
COOLING SYSTEM
C. Rode, P. Brindza, and D. Ridüed
Fermi National Accelerator Laboratory
Batavia, Illinois
and
S. Stoy
Cryogenic Consultants, Inc.
Allentown, Pennsylvania
INTRODUCI'ION
The Fermi National Accelerator Laboratory superconducting accelerator
(energy doubler) is a 6-km-long magnetring consisting of 1000 magnets ultimately to
be cooled by 24 "satellite" refrigerators. At present there are three operating
refrigerators and several strings of magnets, the Iongest being 0.15 km, through
which a proton beam of 1.25 x 10 13 protonsperpulse has been transported.
MAGNET COOLING
To coollong superconducting magnet strings a forced-feed system is required.
Whether one uses a pump, JT valve, or wet expander is immaterial; what matters is
the pressure drops, temperature increases, and heat transfer coefticients to the coils.
Subcooled liquid helium (as opposed to two-phase or supercritical gas) has been
chosen with two-phase counterftow heat exchange. Subcooled liquid, i.e., liquid
0.3 K below the boiling point, has the highest heat capacity per unit volume as well as
the highest heat transfer coefticients.
The temperature and pressure distribution for fs of the doubler ring, based on
prior magnet test data and calculations, is shown in Fig. 1. The liquid helium is
subcooled by a small heat exchanger located in the supply container. lt then reaches
equilibrium after the first magnet, point 3. There is a small increase in temperature,
0.05 K, from point 3 to point 4, owing to the two-phase pressure drop in the return
stream from point 5 to point 6. The heat generated by the coil located in the
single-phase (subcooled liquid) chamber is removed by heat exchange, vaporizing
the liquid in the two-phase chamber. The :ftow is controlled by the J-T valve to
326
Energy Doubler SateUite Refrigerator Magnet Cooling System
POINT
T(K)
I
4.90
4.50
4.55
4 .60
4.47
4.42
4.42
4 52
2
3
4
5
6
7
8
~
1.8
1.8
1.8
1.8
1.25
1.2
1.2
12
~
%LIQUJD
14.22
11 .2 0
11.47
II. 75
11.75
27.49
27.99
31.01
100.
100.
100.
100.
96.
13.
10.
0.1 K Super Heat
327
Fig. 1. Details of cooling loop for a string of cryogenic magnets (is of
the total ring).
maintain point 8 at 0.1 K of superheat. The shield is cooled with two-phase nitrogen
with the discharge as 85 K gas.
REFRIGERATION SYSTEM
A hybrid system which consists of a 4000 to 5000 liters/hr central helium
liquefier (CHL) coupled with a small-diameter liquid feedline to 24 satellite refrigerators has been chosen to cool the doubler (Fig. 2). The feedline supplies liquid
helium for both the satellite refrigerators and the magnet Iead ftow as weil as liquid
nitrogen for the magnet shields. In addition, there are three gas headers; the highand low-pressure helium headers interconnect the six compressor buildings with the
24 refrigerators, while the nitrogen header serves as the gas return to the central
nitrogen plant. There is also a helium interconnection gas line between the compressor building and the central helium plant.
The satellites act as amplifiers with a gain of 12 by using the enthalpy of the
helium supplied by the centralliquefier as liquid, converting it to 4.5-K refrigeration,
and returning it as 278.5-K gas. This arrangement combines advantages of a single
central facility with those of individual stand-alone units stationed around the ring.
The centralliquefiers have the high efficiency associated with large components, but
requirements for distribution of cryogenic liquids and electric power to the service
buildings are reduced. The likelihood of continued operation in the event of
equipment failure is also significantly improved. Table I gives a summary of the total
system requirements, consumption, and production specifications, together with
power requirements. Table II gives a summary of the magnet heat Ioads.
CENTRAL HELIUM LIQUEFIER
The central helium liquefier system consists of three large compressors, a helium
liquefier, nitrogen liquefier, purification equipment, and storage tanks. The
compressors are surplus compressors from an air separation plant. Two of the three
have been modified for helium service, while the third will operate on nitrogen. The
nitrogen plant will provide precooling for the helium plant as weil as shield cooling
328
C. Rode, P. Brindza, D. Ricbiecl, aad S. Stoy
CENTR AL HELIUM
LIOUEFIER
SATELLITE REFRIGERATORS AT
- SERVICE BUILDINGS
( 4 PER SEC TOR)
Fig. 2. Layout of refrigeration system.
for transfer line and magnets, the nitrogen production being rated at 2550 liters/hr,
which will be supplemented by purchased liquid nitrogen.
Both the helium and nitrogen plants will produce subcooled fluids at 3 atm for
introduction into the feedline at 4.65 and 80.0 K, respectively. The returns from the
feedline will then transfer any excess liquid into two storage dewars. These two
dewars, which are the only two in the entire system, serve a dual function. They
provide system stability and liquid for a few hours of operation if the central
liquefiers have to be shut down for minor repair.
SATELLIT E REFRIGER ATOR
The unit consists of a 35-ft-long heat exchanger column (Fig. 3) a liquid
expansion engine, two flow-splitting subcoolers, and a standby gas expansion engine.
The unit has four modes of operation. The primary mode, which is used for the
energy doubler, is the "satellite mode." In this mode the unit is continuously supplied
Table I. Summary of Refrigeration Requirements and Producaion Figures
Refrigeration Requirements
1000 Ge V, 35-s cycle
1000 Ge V, dc
w
Helium
Magnet system helium, 4.6 K
satellite consumption
Total
liters/hr
350
=1,548
=1,898
7,480
7,480
w
Nitrogen
Equivalent
liters/hr
480
100
21,600
4,500
Magnet system nitrogen, 80 K
Helium transfer line
Central He liquefier for 3446 liters/hr of LHe
Total for 3446 liters/hr of LHe
Total at max. operation
w
19,918
19,918
w
liters/hr
350
3,096
3,446
Equivalent
liters/hr
480
100
2,068
2,648
3,580
21,600
4,500
kW
6,270
2,552
2,540
Input power requirement
24 Satellites
Central helium liquefier
Nitrogen reliquefier
11,362
Total
Production Figures
w
Helium
Satellite refrigerators
Central helium liquefier
Nitrogen
Liquefier
liters/hr
23,184
::=::4,000
2,550
Table II. 4.6-K Refrigeration Loadsand 80-K Nitrogen Requirements for
Highest Heat Load Building
1000 Ge V, dc
Each
w
liters/hr
w
liters/hr
1000 Ge V, 35-s cycle
w
liters/hr
Refrigeration Loads
34 Dipole magnets
34 Dipole ac losses*
11 Quad magnets
11 Quad ac losses*
1 Pair 5000-A leadst
Set end boxes
238.0
7.0
13.0
7.0
11.0
10.0
20.0
Totals
1.05
77.0
11.55
14.0
10.0
20.0
14.0
345.0
25.55
Nitrogen Requirements
34 Dipole magnets
11 Quadrupole magnets
Totals
* 35-s cycle time.
t Seven out of 24 buildings.
w
22.4
13.5
w
238.0
442.0
77.0
121.0
10.0
20.0
11.55
14.0
25.55
908.0
w
762
138
762
138
900
900
330
C. Rode, P. Briadza, D. Ridüed, ud S. Stoy
- - 45FT
cold
box
-
-40
-35
berm
~-- -
'!t high
P"tnure
He heoder ~
0;
/
--25
-
-20
---15
---10
Fig. 3. Cross section of satellite refrigerator and cryogenic feed to the superoonducting magnets in the
tunnel.
331
Energy Doubler Satellite Refrigentor Mapet Cooling System
Table 111. Satellite Refrigerator Parameters
Mode
Consumption
Satellite
Refrigerator
Liquefier
Energy doubler standby
1291iters/hr He (4.48 g/s)
52 liters/hr N 2
84 liters/hr N 2
59 liters/hr N 2
Production
Compressor
Pin = 1.05 atm
Pout = 20 atm
Flow = 57.54 g/s
966W
623W
126 liters/hr LHe
490 W plus 26.6 liters/hr LHe
(0.92 g/s)
with 4.48 g/s liquid helium (plus 0.5 g/s power Iead ftow) from the centralliquefier.
This causes an imbalance in the heat exchanger ftow (53.06-g/s supply vs. 57 .54-g/s
return) giving a double pinch at 25 and 5 K. The liquid engine expands from 20 atm
to 1.8 atm, producing slightly subcooled liquid. The cold end refrigeration comes
from three sources: 44% from the heat exchangers ftow imbalance, 48% from the
liquid expander, and 8% from the centralliquefier ftow.
In the other three modes, liquid nitrogen is used instead of liquid helium. The
standby gas engine is now operated at 30 K for these modes, while the liquid engine
produces a two-phase Iiquid-gas mixture. The cold box and expanders have been
tested, as described in Table 111 and shown schematically in Fig. 4, in the first three
modes and have exceeded design in both the liquefier and refrigerator modes and
3 atm
LIQUID
FEED
LI NE
16 atm
lWf1 GAS RElUlN TO
CENTAAL tELllll UQIEF I ER
4.48g/sec
(
( VAL VE LOCATED AT B-0)
COMPRESSOR BUILDING
VALVE LOCATED AT
)
REFRIGERATOR COLD BOX
4 .48g/sec
20atm
300K
!.05atm
278. 5K
•
•
l
L---~
SATELLITE MODE
LIQUID
NITROGEN
4.2g/sec
20atm
LIQUID
ENG INE
53.34g/sec
300K
81. OK
EXCHANGER
57. 54g/sec
282. 5K
#2
79.0K
18.0K
6.0K
EXCHANGER
EXCHANGER
EXCHANGER
1!3
#4A
#48
26.60K
17.25K
REFRIGERATOR. LIQUEFIER & E.D. STANDBY MODE
(refrigerator values illustrated)
Fig. 4. Satellite refrigerator modes.
LOAD
1.2atm
4.52K
C. Rode, P. BriDdza, D. Ridlled, aad S. Stoy
332
90% of design in the first attempt in the satellite mode. The energy doubler standby
mode is a mixture of refrigeration and liquefaction modes with a trade-off ratio of
5.0 W to 1.0 liters/hr. This mode is designed to cool strings of magnets without the
aid of the CHL both durlog initial construction and later durlog failures of the CHL.
This modewas used for both the 10- and 25-magnet Al runs. There are many
additional mixtures of satellite and refrigeration modes that can be used if the central
liquefier is operating at reduced efficiency.
FEEDUNE
The liquid helium and nitrogen will be fed to the doubler by a 25-section,
6-km-long vacuum-jacketed loop (see Figs. 2 and 5). The loop runs from the central
helium liquefier to A4, around the ring to A3, and then back to the centralliquefier.
The nitrogen which is used to cool the shield of the magnets also provides the shield
for the feedline. The sections are coupled by two rigid, vacuum-jacketed U-tubes,
each with a branch tee to feed the local refrigerator. This will permit installation,
testing, and cooldown of one section at a time without interfering with the Operation
of the restof the system. With the connection of the last service building, A3, back to
the central helium liquefier, any section can be taken out of service for repair, if
needed, by feeding the return line in reverse. A maximum 4.5-K heat Ioad of 150 W
and a maximum 80-K Ioad of 4500 W for the entire line is anticipated.
20 ATM He HE ADER
"u" TUBE
CONNECTIONS
AND DRAW POINTS
3ATM
3ATM
LEGEND
HELIUM
NITROGEN
20 T023
MAGNET STRING
.. ""------A------.......,
Fig. 5. Satellite refrigerator interconnections.
--
Energy Doubler Satellite Refrigentor Mapet Cooliog System
333
GAS LINES
The satellite gas piping consists of three gas header loops. A 22-cm-diameter
low-pressure helium pipe and a 9-cm-diameter low-pressure nitrogen pipe are
located on the wall of the tunnel behind the magnet. The helium pipe is the suction
line for the compressors as weil as the main magnet relief and manifold for Iead and
cooldown ftow. The nitrogen pipe is the collection header for all shield ftow,
precooler ftow, and also nitrogen reliefs. The third header is a high-pressure helium
pipe which is located on the main-ring-road side of the berm.
Two 9-cm gas headers which connect to the centralliquefier are located at A4.
The first is a 5 to 16 atm bidirectional helium gas line. Normally it is used as the gas
return for the liquid supplied by the centrat liquefier, transmitting gas into the
discharge of the centrat liquefier compressors (13 atm). During startup and ED
standby mode the line can also supply gas to the 22-cm header. The second header is
teed into the 9-cm hitrogen loop and is the main nitrogen return for the nitrogen
liquefier.
The compressor system is located in the six "zero" buildings with four compressors per building for maximum capacity. The compressors are connected across the
two helium headers with all 24 in parallel. The grouping of compressors into a header
system totally decouples cold boxes from compressor operation; e.g., all four
compressors at BO can be shut down without shutting down any cold boxes. This, of
course, involves the loss of ~ of the total capacity.
COOLDOWN AND WARMUP
If one attempts to cool down long strings of doubler magnets in the normal
operating mode it would take several months or might be altogether impossible. The
reason for this is that the magnets are heat exchangers and therefore most of the
refrigeration that is supplied is heat exchanged with the return line and then vented.
Therefore a single-pass cooling of the single phase is used rather than loop ftow, with
the two-phase deadheaded. The wave front is very steep and travels through the
magnet string much like a step function through a transmission line; i.e., the
discharge remains at room temperature during almost the entire cooldown cycle.
Cooldown with the central helium liquefier operational is very straightforward.
The satellite is adjusted to the liquefier mode producing 126 liters/hr, which is added
to the 200 liters/hr from the centrat liquefier (if one is cooling only one service
building this might be as high as 2000 liters/hr, stress, pressure drops, and thermoacoustic oscillations permitting). The cooling fluid is run through the single phase of
the magnets, returning to the compressor suction by way of the cooldown lines (see
Figs. 1 and 5) where it is recompressed to 20 atm. The excess gas is then returned to
the discharge of the centralliquefier compressor (13 atm) where it is reliquefied. The
wave front is shut off when it reaches one of the cooldown lines and the magnet J-T
valve is opened. When it reaches the second cooldown line, the same procedure is
repeated, 1000 Iiters of liquid helium aretransferred from the centralliquefier to fill
the magnets, the dry engine is turned off, and the satellite is tuned for the satellite
mode.
If the centrat liquefier is not operational, it is slightly more complicated. The
satellite is programmed to produce 20 K gas and run in this mode for about 44 hr with
a ftow rate of about 200 liters/hr; it is then reprogrammed to produce 10 K gas for
about 8 hr. Owing to the nonlinearities in the heat capacities of metals the 10-K wave
will catch up with the 20-K wave at the cooldown line. When the discharge
334
C. Rode, P. Briudza, D. Ridded, IUid S. Stoy
temperature reaches 25 K the cooldown lines are closed and the magnet J-T valves
are opened. The satellite is reprogrammed to the ED standby mode, and cools the
magnet string to 5 K in a few hours; this is known as a transition. After the transition
there is a choice of operation; if cooldown is urgent, 1000 Iiters of liquid is obtained
from extemal sources. Otherwise the satellite can be used to fill the magnet. The fill
time is inversely proportional to the excess refrigeration available, i.e., the excess
expander capacity at the service building and the excess compressor capacity in the
whole ring. Therefore, fil1 time can vary from 10 hr to a week. This is the mode that
was used in the 25-magnet runs. During the filling time, the magnets were energized
and the proton beam is tuned to injection energies.
F-9
CRYOGENIC SUPPORT SYSTEM FOR
AIRBORNE SUPERCONDUCTING GENERATORS
P. J. Kerney and P. A. Lessard
CTI-Cryogenics
Waltham, Massachusetts
INTRODUCTION
The U. S. Air Force is currently developing electrical generators for a variety of
airborne applications requiring high-power and high-voltage capability Cl The
airborne environment imposes severe constraints on volume and weight which make
a superconducting generator an attractive approach owing to its small size and high
power-to-volume ratio. Since superconducting generators are in direct competition
with other energy production schemes for these applications, the design of the
cryogenic support subsystem strongly influences system potential. A study*, therefore, has been underway to evaluate techniques and system designs for providing the
cryogenic cooling to support an airborne superconducting generator system. This
paper describes the system constraints, airborne applications, and the resulting
cryogenic cooling requirements. The design methodology and trade-off considerations are discussed for the airborne support system, the ground support system,
and the cryogenic transport system. Primary emphasis was placed on minimizing the
weight of the airborne system and providing the most cost-effective approach for
supplying the cryogenic cooling from the wellhead source to the aircraft.
SYSTEM CONSTRAINTS
A superconducting generator system is considered attractive for airborne
applications employing generator configurations with outputs above 10 MW. A
summary of these hypothetical applications is included in Table I. Superconducting
generator designs are still in their infancy, and the U. S. Air Force is presently
sponsoring several exploratory research and development programs in airborne
superconducting generators e-'4].
The present generator configuration imposes two important interface constraints on the airborne cryogenic cooling system. First, owing to the generator flow
control system, the helium inlet pressure to the generator cannot be less than 1 atm
absolute. Second, because the return gas from the generator is utilized to intercept
heat leaks in the torque tube and the power Ieads, the gas exiting the generator is
essentially at ambient conditions. The specific airborne cryogenic subsystem weight
and cooling requirements for the three applications are listed in Table I.
*Air Force Flight Dynamics Labaratory Contract No. F33615-78-C-3413.
335
P. J. Kenaey aad P. A. Leisud
336
Table I. Spedfication and Design Goals
Application
Airborne
Cryogenic
On-board LHe cooling system weight
generator,
capacity,
target,
MW
liters/hr
lb
Airborne
operational
time,
hr
1
10
10
100
10
2
20
20
200
10
3
50
40
500
6
Operational
conditions
Continuous operation for 20
years
Ground cold ready 30-day
ftight Operation
Ground cold ready 24-hr ftight
operation
The ground support subsystem also is subject to important constraints. The
subsystem must be capable of delivery, storage, and transfer of all necessary cryogens
from point of origin to the airborne system with maximum reliability and minimum
cost. Specifically, the support system must (1) maintain the generator at a steadystate standby temperature :580 K, (2) be capable of cooling the generator from the
standby steady-state temperature to the 4.2 K operational temperaturein a specified
time, and (3) provide adequate base storage to satisfy the cryogenic cooling
requirements for a specified length of service. Additionallogistics associated with the
ground support subsystem typically include a periodic maintenance cycle for each
aircraft requiring the system to be warmed to 300 K and subsequently cooled to the
standby temperature.
SYSTEM COOLING REQUIREMENTS
The ground cryogenic cooling requirements are strongly dependent on the
thermal characteristics of the particular generator configuration. The cryogenic
subsystem must be capable of supplying sufficient refrigeration for transient as weil
as steady-state cooling applications. The steady-state requirement is that the
generator be maintained in a cold ready condition on the ground at some specified
temperature TR, which is less than 80 K. Two types of generator cooldowns are
required: a "partial cooldown" from TR to the 4.2-K operational temperature and a
"full cooldown" from ambient to TR following normal maintenance of the system.
To establish TR and the resultant cooling requirements and the corresponding
cryogenic support equipment, it was necessary to model the thermal characteristics
of the generator.
A simplified analysis was performed to determine the mass ftow rate of gaseous
helium at 4.5 K required to maintain the generator at a specified steady-state
temperature. An energy balance on the generator yields
mHe
hin + QL
+ Or + QR
= mrhr
+ mLhL
(1)
The continuity equation yields
eJ
(2)
Assuming that QR is constant at 0.125 w
and that the ftow split between mL and
mr is the same for all Operating points, (1) and (2) can be combined to estimate
generator temperatures as a function of helium ftow. The results, plotted in Fig. 1, are
based on estimates of the thermal characteristics of a 20-MW generator design with a
77 -K winding temperature [5 ].
Cryogenic Support System for Airborne Superconduding Generators
337
60
50
0:
"'~
40
C>
z
ö
z
..."'
....
;::
"'>-
0
"'
30
20
~
"'
10
.2
.3
.4
.5
.6
FLOW TO GENERATO R, 9/s
Fig. 1. Generator winding temperature vs. 4.5 K helium gas
maintenance ftow.
To obtain the helium mass ftow requirements during the cooldown operation,
the generator, as a first approximation, was modeled utilizing a lumped-parameter
analysis. The transient energy equation for the generator is
(3)
Assuming the generator is all copper and that the ratio of specific heats (Cg/Cp) is
constant at one-half its initial value (i.e., at TR) and assuming that the cooldown to
10 K requires 15 min, at which time liquid helium is added, yields
@final
--= e
E>initial
-C /C rizHe
p
·--tc
mg
(4)
The results of this analysis are plotted in Fig. 2. The mass of the generator was
assumed to scale as the square root of the power generated, thus producing the
cooldown curves for the 10- and 50-MW generators.
The total ground cooling requirements were calculated for each application and
are tabulated in Table II. A standby temperature lower than the originally specified
80 K was used because of the large decrease in required cooldown ftow at lower
temperatures.
HELIUM DELIVERY CONCEPTS
Delivery of helium from its source of supply to the base can be accomplished in
three general ways: entirely in liquid form, entirely in gaseous form, or some
combination of the two. On the basis of cost comparison alone, it can be demonstrated that shipment in liquid form is preferable to shipment in gaseous form.
338
P. J. Kerney and P. A. Lessard
150
2"'
8
50 MW
125
-'
0
0
'-'
8
... 100
0
20 MW
0:
5
ß
0:
~
X
...
75
-'
10 MW
0
10
20
70
INIT I AL WI NOING TEMP , K
Fig. 2. Transient generator winding cooldown vs. initial winding
temperature.
Cost data obtained from helium suppliers [6 ] indicate that the transportation
costs and capital equipment costs associated with liquid cryogen transport are factors
of 5.5 and 3.5 less than the corresponding costs for gaseous cryogen transport,
respectively. On the basis of this comparison, it was determined that all transportation of the cryogen be in liquid form.
GROUND SUPPORT SUBSYSTEM CONCEPTS
The primary objectives of the ground support system are to maintain the
superconducting generator at a steady standby temperature and to efficiently handle
the liquid helium required for the flight operational conditions indicated in Table I.
The principal design constraint for the ground support system concepts was cost. A
number of system alternatives were studied and compared on the basis of minimum
20-year life cycle cost.
The simplest and most direct approach to meeting the ground support cryogenic
requirements would be a no-recovery system in which the required helium is
transported to the base in liquid form and stored in large dewars. As indicated in
Table II, considerable quantities of helium are required to satisfy the airborne and
Table II. Airborne and Ground Cooling Requirements
Application
Airborne
operational hrs
LHe required for
airborne cooling
Annual helium req'd
for ground cooling
(equivalent Iiters)
1
2
3
219,000 hr/yr
8640 hr/30 days
36 hr/day
2,409,000 liters/year
190,000 liters/30 days
1600 liters/1 day
2,500,000 Iiters
1,450,000 Iiters
278,000 Iiters
Cryogenic Support System for Airborne Superconducting Generators
339
ground cooling requirements. In this nonrecovery approach, all the helium is vented
to the atmosphere and lost. Owing to the uncertainty of the helium supply ['·8 ] and
the subsequent impact on the price of helium, this approachwas ascertained to have a
prohibitively high life cycle cost.
The most cost-effective approach was determined to be a centrat base liquefier
with adequate base storage. In this concept, liquid helium is transported to the base,
and all helium utilized for ground cooling is recovered and subsequently reliquefied
into suitable dewars. Replenishment helium is only required to accommodate the
airharne cooling requirements.
The main components of the ground support subsystem are the liquefier module
with appropriate transfer lines, base storage dewar(s), purifier, recover compressor, and high-pressure gas storage. The boil-off gas from the storage dewar bank is
utilized to maintain the generator at the standby temperature. The return gas from
the generator is then used for gas shielding of the transfer lines to minimize lasses. In
applications where usage is high, the transportation vehicles also act as the dewar
bank.
An additional cost trade-off in this approach is to consider reducing the base
storage requirements for the independent operational capability by supplying a back
up generator for the base liquefier. The cooling requirements and base storage
system would then be supplemented by the operating base liquefier.
AIRBORNE SUBSYSTEM CONCEPTS
The most critical portion of the overall cryogenic system for the superconducting generator is the airharne cooling system. Severe constraints on system weight
(Table I) and generator interface requirements preclude a variety of approaches that
might otherwise be very attractive. For example, on board reclamation of helium
boil-off in application #1 would req\}ire a compressor and gas storage bottlesthat
would exceed the 100-lb weight goal by approximately an order of magnitude.
The requirement of positive pressure helium gas ftow to the generator eliminates any techniques that would take advantage of the decreased pressure and
temperature with altitude. The return gas temperature of 300 K precludes any
concept that would utilize the available refrigeration in a cold return stream to
minimize the airharne systems size and weight. Methods for on board helium
reclamation, via a recovery compressor with high-pressure gas storage, or a
completely closed-cycle cooler design were likewise discarded owing to the stringent
airharne weight specifications.
The only viable approach that meets all of the airharne requirements is an
open-cycle dewar with provisions for venting the gaseaus helium to the atmosphere.
Figure 3 is a graphical representation of weight vs. capacity for commercially
available dewars. The data indicate that commercially available dewars would be
heavy and that a specially designed spherical aluminum dewar would better satisfy
airharne weight restrictions.
The supply dewar is a spherical aluminum configuration with appropriate
plumbing, valving, and instrumentation. The design will allow initial purging and
cooldown of the system to 4.2 K and recovery of all ftash and boil-off gas associated
with this process. Filling of the generator/dewar and supply dewar can be accomplished individually or simultaneously in series or parallel. The system is equipped
with adequate safeties and controls for in-ftight venting and pressure relief of either
dewar.
P. J. Keney ud P. A. Lellard
•
1200
•
DESIGN WEIGHT GOAL
SPHERICAL ALUMINUM (REF. 91
COMMERCIAL GAS SHIELDED
(MVE, CVI, LINDE)
1000
"'
__..
CD
800
....
~ 600
------ ----
400
200
100
200
.
300 400
500 600
CAPACITY, LITERS
SPHERICAL ALUMINUM
700
800
Fig. 3. Liquid helium dewar weight (empty) vs. capacity.
SUMMARY
The basic cryogenic support system design to satisfy the cooling requirements
for an airborne superconducting generator includes liquid helium delivery to the
base, a central base liquefier, and a spherical aluminum airborne dewar. Table 111
summarizes the basic component sizes for the hypothetical applications. Also
included in the table is the annual helium consumption for each application with and
without the base helium reclamation. Table 111 also summarizes the 20-year life
cycle cost for each application for various base support options. As the tabulation
indicates for all system options in every application, the no-helium-recovery concept
is less cost effective than helium reclamation. This conclusion was reached even
though the cost analysis assumes the price of helium will rise at a rate less than the
gross national product. This is considered a conservative assumption since a number
of studies C·8 ] indicate that the helium gas available in proven helium-rieb reserves
will approach projected demand in the 1990-2000 time frame with a probable
subsequent rise in helium costs. Table 111 also shows that providing a backup
generator for the base liquefier is more cost effective in all applications.
Table m. Component Sizing Snmmary
On-board
dewarsize,
Application
Iiters
1
2
3
125
250
300
Base
Jiquefier
size,
litersihr
A* Bt
C:f:
100 100
200 200
NA 25
* A, no recovery.
t B, standby generator for liquefier included.
:f: C, totally independent storage.
20-year
life cycle cost,
106 1978$
(discounted)
Net helium
usage per
base,
106 scf/yr
Liquid
storage,
1000 gal
A
B
c
A
B
c
A
130
168
3.5
27.5
45.0
NA
120
93
3.5
165
60
0.26
NA
60
0.26
0.06
43
15
3.0
44
8.2
B
c
26 28
5.8 6.9
NA 2.2
Cryogenic Support System for Airborue Supercouducting Geuerators
341
CONCLUSIONS
A total cryogenic support system to provide cooling for airborne superconducting generators has been analyzed. The most cost-effective system is one providing
for liquid cryogen transport to the base, a central base liquefier with a backup
generator for ground cooling and reliquefaction, and a lightweight spherical aluminum open-cycle liquid helium dewar system for airborne operational cooling.
On-ground helium reclamation is recommended for all applications.
ACKNOWLEDGMENTS
The work reported in this paperwas sponsored by the U. S. Air Force, Wright-Patterson Airforce
Base, Dayton, Ohio, under Contract No. F33615-78-C-3413; Lt. G. Rondash, Program Manager. The
support and guidance provided by Maj. G. Puhl of the Flight Dynamics Laboratory and C. Oberly of the
Aero Propulsion Laboratory are gratefully acknowledged. J. L. Smith, Jr. of Massachusetts Institute of
Technology has served as the superconducting generator consultant for this study. His assistance in
defining the generator interface requirements and the generatorcooldown characteristics was invaluable
to the program.
NOTATION
c. = specific heat of generator, Jlg-K
CP = specific heat of helium, Jlg-K
h;n = enthalpy of gas entering generator, J I g
hL = enthalpy of gas exiting through power Ieads, J I g
hT = enthalpy of gas exiting through torque tube, Jlg
m. = mass of generator, g
mHe = mass ftow of 4.5 K gas to generator, gls
mL = mass ftow of gas exiting through power Ieads, gls
mT = mass ftow of gas exiting through the torque tube, gls
QL = totalleak to generator through power Ieads, W
QR =total radiation heat leak to generator, W
QT = total heat leak to generator through torque tube, W
t =time, s
tc = cooldown time, s
T = temperature, K
TR = generator standby steady-state temperature, K
(J = T generator - T heliwm K
Blina! = 10.0 K- 4.2 K = 5.8 K
B;n;t;al = TR- 4.2 K
REFERENCES
1.
2.
3.
4.
5.
6.
7.
8.
9.
H. Southall and C. Oberly, IEEE Trans. Magn. Mag-15(1):711 (1979).
C. E. Oberly, IEEE Trans. Magn. Mag-13:260 (1977).
R. D. Blaugher, J. L. McCabria, and J. H. Parker, Jr., IEEE Trans. Magn. Mag-13:755 (1977).
B. B. Gamble, T. Keim, and P. A. Rios, "Superconducting Rotor Research," AFAPL-TR-77-68
General Electric Company (November 1977).
B. B. Gamble, private communication.
P. Hickey, private communication.
"Helium, A Public Policy Problem," report by the Helium Study Committee, Board on Mineral and
Energy Resources Commission on Natural Resources, National Research Council, National Academy
of Sciences, Washington, D.C. (1978).
"The Energy Related Applications of Helium and Recommendations Concerning the Management of
the Federal Helium Programs," ERDA-13 (April 1975).
H. E. Simpkins and R. L. Reed, in Advances in Cryogenic Engineering, Vol. 12, Plenum Press, New
York (1967), p. 640.
F-10
ECONOMICS OF CRYOGENIC SYSTEMS
FOR SUPERCONDUCTING MAGNETS*
G. Y. Robinson, Jr.
Massachusetts Institute of Technology
Cambridge, Massachusetts
INTRODUCTION
The majority of the cryogenic systems installed for cooling superconducting
magnet systems over the past ten years have been aimed at providing a reliable
experimental facility for proving the viability of superconductor systems and for
advancing the state of the art of superconducting magnets. As a result, the criteria for
cryogenic system selection has been that of lowest initial cost and maximum
reliability. Systemsnow being installed and those being designed for future installation will be operated on a continuous basis giving impetus to an economic analysis
in which the overall operating cost of the cryogenic facility becomes an increasingly
important parameter in the design and selection of the system. In addition, conservation of energy through increased efficiency and conservation of heliumwill become
significant design criteria.
Economics should be considered early in the design phase to permit evaluation
of the "trade-offs" and options available in selection of the system and in the
preparation of specifications. This study describes some of the options which should
be considered and gives insight as to their impact on operating cost. The first section
deals with component equipment costs and presents data which can be used by the
designer in making a cost trade-off analysis. In the second section, methodology for
an operating cost is presented and, finally, examples of typical trade-offs and their
effect on Operating costs are reviewed.
The major components of the cryogenic system are indicated in Fig. 1 and
include, in addition to the superconducting magnet dewar, the refrigerator /liquefier
cold box and compressor, helium transfer lines, liquid helium storage, liquid nitrogen
storage, gaseaus helium storage, and helium purification equipment.
COSTS
Costs for the major components of the cryogenic system are presented in this
section. The curves shown are the average cost obtained from three suppliers or the
actual costs of equipment purchased within the last year and updated to reftect prices
in effect for the second quarter of 1979.
* Supported in part by the U. S. Department of Energy.
341
343
Economics of Cryogenic Systems for Superconducting Magnets
Fig. 1. Cryogenic system.
Refrigerat ors
The present-da y cost of helium refrigerato r-liquefier s is shown in Fig. 2 and
in 1969 and
does not differ widely from costs initially reported by Strobridge
of the
portion
upper
the
in
units
for
here
reported
Costs
updated by him in 1974.
in the
Costs
inflation.
to
owing
er
high
somewhat
e
range-ar
W
10-k
to
1e
curve-th
lower portion (100 to 1000 W) have been affected by both inflation and lower
thermodyn amic efficiency. However, these increases have been counterac ted by
economies owing to standardiz ation and productio n of multiple units. As a result the
eJ
106
<f1
...
a:
..J
..J
0
0
,:
<f1
0
u
105
I04 L--,--,-,.,rn.r~-.-~~rrrn~--.-r-r
103
102
10
REFRIGERATOR CAPACITY
1../ATTS AT 4 SK
Fig. 2. Helium refrigerator cost.
G.Y.R....... k.
344
costs are only slightly higher than they were ten years ago. As the requirement for
greater numbers of large refrigeraton increases, a reduction in cost can be expected.
Over the past ten years, the emphasis on refrigerator development and procurement has been directed towards holding equipment costs to a minimum and
increasing reliability. The trend has shifted to oil-lubricated screw compressors and
turbo expanden and away from reciprocating equipment mainly to tak:e advantage
of the higher reliability experience with rotary equipment. This trend has led to a
general decrease in Carnot efficiency rather than an increase as might be anticipated
with advancing development. Refrigerator/liquefien produced in the late 1960s
were approachlog 20% of Carnot, whereas units presently available are closer to
10%. lt is clear that there is a need for further development to increase efficiency and
still maintain the achieved reliability.
The costs of equipment shown in Fig. 2 are based on units using liquid nitrogen
precooling. The cost of refrigeraton which do not use liquid nitrogen precooling will
be approximately 10% higher in the upper range and up to as much as 50% higher in
the low range.
Transfer Lines
Costs of various sizes of helium transfer lines is shown in Fig. 3. The lower curve
indicates cost of "off the shelf" or catalog standard vacuum-insulated transfer line
sections suitable for small installations. Installations which require the long length of
lines with numerous elbows and joints are approximately twice the cost as shown in
10
800
a:
.....
"'
:z:
"'
~
~600
....1
....1
0
0
~
0
u
400
ZOO
~ARD
SECTIONS
100
lf.!
2
3
4
TRANSFER LINE SIZE,
INCHES
Fig. 3. Heliumtransfer line cost.
5
Eeonomia of Cryopaic Systems for Supercooductiug Magoets
345
o-'
V>
0
u
103
STORAGE DEWARS,
LITERS
Fig. 4. Liquid storage Dewar cost.
the field-erected curve. The cost of liquid-nitrogen-traced lines or concentric helium
lines is on the order of 1t to 2 times that of unshielded lines.
Liquid Storage
Cost of liquid helium and nitrogen storage dewars is shown in Fig. 4. dewars in
the range shown are standard sizes which are produced in moderate quantity. The
cost of helium dewars increases with capacity to the 0.6 power, as might be expected.
Costs have escalated in line with the general cost index over the past few years and
can be expected to continue to increase.
Gas Storage
Cost of helium storage at 1 atm in gas bags and at 18 atm in cylindrical vessels
are shown in Fig. 5. The cylindrical vessels are standard ASME coded 250-psi
propane storage tanks which have proven adequate and economical because of
quantity of production. Their cost ranges from 35t to 50t per pound of steel.
Specially designed tanks of nonstandard dimensionswill cost between $0.75 and
$1.00 per pound.
Helium Purifiers
In the larger sizes, helium purifiers are built on a custom basis. Costs are shown
in Fig. 6. As the demand for helium recovery purifiers increases it is expected that
costs will be reduced slightly. The costs shown are for separate purifier units. Purifiers
which are built in as an integral part of the liquefier refrigerator will cost approximately one-third of that shown.
OPERATING COSTS
Cryogenic system Operating costs include in addition to the direct charges for
power, water, and liquid nitrogen, the cost of Iabor and maintenance and a capital
G. Y. Robüuoo, Jr.
346
104
o/)
a:
<(
-'
-'
0
0
>-'
o/)
0
u
10 3
10 2
L----,-,-,-,"<T~---,-,-,-,"<T~---,-,-,3
102
10
10
HELIUM GAS STORAGE,
EQUIVALENT LIQUID LITERS
Fig. 5. Heliumgasstorage cost.
:Q
<(
-'
-'
0
0
,_.
o/)
0
u
10
.I
HELIUM PURIFIERS,
CUBIC METERS/MIN
Fig. 6. Helium purifier cost.
Eeonomics of Cryogenic Systems for Superconducting Magnets
347
Table I. Operating Cost Basis
Schedule operation
Power
Water
Liquid nitrogen
Helium
Labor
Maintenance
Capital charge
Installed cost
7700 hr per year
$0.035 per kW hr
$0.04 per 1000 gal
$0.07 per Iiter
$0.035 per
$7.00 per operating hr
3% of equipment cost
15% of installed cost
2 times equipment cost
re
Table II. Refrigerator Operating Cost
Power
Water
Liquid nitrogen
Labor
Maintenance
Capital
Annual operating cost
$53,900
740
32,340
53,900
7,500
74,000
$222,380
charge which is a percentage of the installed equipment cost. In the cost analysis,
presented here, the installed cost is assumed to be twice the equipment cost and
includes cost of foundations, piping, etc., but not site and building. The basis for the
operating cost analysis is shown in Table I.
Actual costs will vary depending on location of the facility. However, the model
is a reasonable average and provides a basis from which sensitivity of the various
factors can be determined.
A typical refrigerator producing 200 W of refrigeration at 4.5 K costs $250,000
and requires 200 kW of power and liquid nitrogen precooling at the rate of 60
liters/hr. The annual operating cost of this unit calculated on the basis of TableI is
shown in Table II.
COST TRADE-OFFS
In this section several cases are cited as examples of operating cost analysis with
the aim of indicating areas where overall costs can be reduced.
Case 1-Refrigerator Location
Refrigerators are sometimes regarded as service equipment and located
remotely from the superconducting magnet without forethought as to the impact of
transfer line heat leak and pressure drop, which often exceeds the refrigeration
requirement for the equipment being cooled and sometimes doubles the cost of the
refrigerator.
Some magnet installations, because of fringe fields, make it necessary to locate
the refrigerator a distance of 30 to 50 m from the magnet. In this case, liquidnitrogen-traced transfer lines should be considered. A typical vacuum-insulated
untraced transfer line has a heat leak of 0.65 W /m. If the length of transfer line is a
total of 100m, then the heat lass will be 65 W, which is much higher than the lass
in the magnet dewar, which might be in the 20- to 30-W range. If we assume that a
G. Y.
a--.., Jr.
200-W refrigerator is required, it will cost $250,000. The cost of unshielded transfer
lines will be $40,000 and the annual operating cost is $235,000. Liquid-nitrogentraced transfer lines will cost $80,000 but the heat loss will be only 0.065 W /m or a
total of 6.5 W. The refrigerator capacity can be reduced to 140 W at a cost of
$200,000 and an annual operating cost of $214,000. The result is an initial
investment reduction of $10,000 and an annual savings of $21,000.
Case D-He6um and Refrigeradon Recovery
Most magnet systems are designed to permit retum of cold gas to the refrigerator with significant savings in investment and operating cost. In this example,
consider a cryopump system which requires 45 liters/hr liquid boil-off and the
following alternatives: (A) purchase liquid helium and vent boil-off; (B) purchase
helium gas, liquefy and vent boil-off; (C) liquefy andrecoverwarm helium; and (D)
operate as closed loop with cold gas retum to the refrigerator.
At a cost of $2.25 per Iiter of helium the annual cost of case Ais $780,000. The
liquefierfor case B costs $150,000 and requires 100 kW ofpower and 45 liters/hrof
liquid nitrogen. The annual operating cost is $155,000 and the cost of makeup
helium at $3.50 per 100 is $322,000 foratotal of $477,000. For case C the same
liquefier is used with an added recovery system and purifier, making the annual
operating cost a total of $170,000.
A closed-loop cold gas return system will require a refrigerator of 30- to 40-W
capacity requiring only one-fourth the power and liquid nitrogen and will have an
annual operating cost which is less than $100,000. In summary, the Operating costs
would be (A) $780,000, (B) $477,000, (C) $170,000, and (D) $100,000. In addition
to the significant cost saving in cases C and D there is also the valuable saving of
helium gas.
te
Case 111-Refrigerator Ef&ciency Improvement
As indicated above, the demand for increased reliability in refrigerators has led
to the production of equipment which have Carnot efficiencies which are considerably lower than those indicated by Strobridge. This case will show the effect of this
lower efficiency on operating cost. Consider the case of the 200-W refrigerator in
Table II which costs $250,000. This unit has a Camot efficiency of 6.6%. A
refrigerator of similar capacity purchased in 1967 has a Carnot efficiency of 18.3%. If
the same equipment cost were assumed, then the annual operating cost of the more
efficient unit would be $195,260 with an annual power cost saving of $28,000.
Alternatively, for the same annual operating cost, the initial cost could be $343,000.
It appears that added investment is warranted in order to reduce power requirements.
There are a number of ways in which Carnot efficiency can be increased from the
10% to the 20% range at a moderate increase in equipment cost. These include
increase in the number of compressor stages, use of larger or more efficient heat
exchangers, increase in the number of expander stages, and introduction of cold
recompression. Bach of these steps reduces the loss due to thermodynamic irreversibility in the cycle and has been employed to improve efficiency in a number of cases.
For example, the installation of a third expansionstage or "wet" expander in the
MIT liquefier in 1969 resulted in an increased capacity of 33%. This in turn,
increased the Carnot efficiency from 13.8 to 19.1 %. This marked increase in
efficiency was recognized by commercial operators and resulted in subsequent
liquefaction plants being retrofitted with an additional expander.
Economics of Cryogenic Systems for Superconducting Maguets
349
In other cases it has been shown that by taking the steps indicated above,
efficiency can be increased from 11 to 24%. The payoff for development in this area
is not only realized in the dollar saving but also in a substantial saving in energy for a
given system.
ACKNOWLEDGMENTS
The author acknowledges with thanks, the support of J. L. Smith, Jr. and the assistance of numerous
suppliers of cryogenic equipment in providing cost information, including Intermagnetics General,
Cryogenic Technology, Inc., CVI Inc., MVE, Eaton Meta! Products, and Flexiliner Corporation.
REFERENCES
1. T. R. Strobridge, NBS Tech. Note 655 (June 1974).
2. F. J. Kadi and R. C. Longsworth, "Assessment and Study of Concepts and Methods of Cryogenic
Refrigeration for Superconducting Transmission Cables," Rept. C00-2552-6, U. S. ERDA Contract
No. E(11-1)-2552 (February 1976).
3. T. R. Strobridge and R. 0. Voth, IEEE Trans. Nucl. Sei. NS-24(3):1222 (1977).
4. M. A. Green, H. S. Pines, and P. A. Doyle, Cryogenics 19(2):81 (1979).
5. H. Quack and Ch. Trepp, Sulzer Tech. Rev. 60(4):157 (1978).
6. R. W. Johnson, S. C. Collins, and J. L. Smith, Jr., in Advances in Cryogenic Engineering, Vol. 16,
Plenum Press, New York (1971), p. 171.
DISCUSSION
Question by G. H. Morgan, Brookhaven National Laboratory: I am surprised to hear that people are
accepting a factor-of-2 increase in refrigerator power consumption in turn for increased reliability. Could
you comment on this?
Answer by author: First Iet me say that this increase in power required is not entirely owing to
reliability requirements. The desire to produce a unitat the lowest possible initial cost is also a factor. With
regard to reliability, I believe the approachwas entirely justifiable and that a goal has been reached. I think
what is required now is an emphasis on the part of the refrigerator manufacturers toward improving
efficiency and a recognition on the part of the users that increased initial cost is warranted in order to
reduce power requirements.
F-11
MINIMIZATION OF REFRIGERATION POWER
FOR LARGE CRYOGENIC SYSTEMS
M. A. Hilal
Michigan Technological University
Houghton, Michigan
and
Y. M. Eyssa
University of Wisconsin-Madison
Madison, Wisconsin
INTRODUCTION
Some cryogenic systems, such as superconducting magnetic energy storage and
superconducting generators, require Ioad-hearing supports to transfer forces to a
room temperature (warm) structure. lt is necessary to minimize the refrigeration
power required to overcome heat leaks through the supports in order to improve
system efficiency.
In previous studies of heat flow optimization of mechanical supports [ 1-4], it was
shown that absolute minimum refrigeration power can be achieved with an infinite
series of infinitesimally small refrigerators intercepting the heat leak as it flows from
the bot end to the cold end. It was also shown that the absolute minimum can be
approached by intercepting the heat leak at a finite number of locations. Bejan and
Smith
showed that coollog a mechanical SUpport by a variable mass flow rate of
helium gas generates the same amount of entropy as an optimized infinite number of
refrigerators. They also concluded that the optimum can be approached very closely
by cooling with one stream of helium gas, and that continuous cooling of mechanical
supports by helium gas is better than discrete coollog by a finite number of
independent refrigerators. This conclusion is only true if the gas stream is optimally
refrigerated back to the low-end temperature, an arrangement that also requires an
infinite series of infinitesimally small refrigerators or an equivalent system to cool the
gas stream back to the low-end temperature.
In this paper a simple system is considered where the refrigeration power
required is mainly due to heat leak through the supports. In this case the cold gas can
either be used to cool the supports, thus reducing the heat leak at the ends, or can be
retumed to the refrigerator heat exchangers to improve the coeffi.cient of performance. The goal here is to optimize the supports and the refrigerators simultaneously, which, in turn, minimizes the required refrigeration power rather than
improving the coeffi.cient of performance of the refrigerator. Optimization results
eJ
350
351
Mioimizadon of Refrigeradon Power for Large Cryogenic Systems
~
0.003-
~
u
Fig. 1. Coefficient of performance for a two-engine
1.8-K refrigerator vs. high pressure.
0.002-
I
""'
0.0010~~5-_"",:,.---:':-1--.:17-~·=---=I~
10
15
20
25
30
35
PRESSURE , atm
reported in this paper are for cryogenic systems operating at 1.8 or 4.2 K. Only
optimization of large-size systems is considered since high-efficiency expansion
engines, compressors, and heat exchangers are absolutely necessary in those systems.
The supportsarealso optimized using discrete cooling and thus require separate
refrigerators operating at different temperatures. In this case the refrigerators are
optimized at different temperatures independent of the supports. The optimized
refrigerators are used to intercept heat at finite locations on the supports.
Supports with variable cross-sectional areas are also considered in this paper.
This is done to reduce the refrigerator power if the allowable stress varies with
temperature.
REFRIGERATOR OPTIMIZATION
The Claude cycle with multiple expansion engines and an expansion valve at the
cold end is the basis for the present optimization study. Engine arrangements, the
T-S diagram, optimization details, and optimization results for 4.2-K refrigerators
are published elsewhere [5 ]. That study showed that the cycle is optimized by
changing the high pressure and the inlet temperature of each engine.
The computerprogram developed in the prior study for 4.2-K refrigerators has
been modified and used in the present study to optimize cryogenic systems using
superfluid helium. The optimization results for 1.8-K cryogenic systems are reported
here. Figure 1 shows the coefficient of performance vs. high pressure for two
expansion engine refrigerators operating at 1.8 K. The superfluid helium properties
used in the refrigerator program were based on the tabulated values reported by
Brooks and Donnelly [6 ]. The optimum inlet temperatures and the optimum mass
flow rates through the engines are also given in Table I. In this optimization
calculation the compressor efficiency was assumed tobe 85%. The low-temperature
Table I. Optimum Parametersfora 1.8-K
Two-Engine Refrigerator
First engine
Second engine
Inlet
temp., K
Exit
temp., K
Fraction
ftow rate
291.959
36.959
62.901
7.896
0.04293
0.12967
M. A.IIIW _. Y. M. E,.a
35%
and the high-temperature engine were also assumed to be 85% efficient. The
temperature diflerences across the first, second,and third heat exchangers were 10,
0.5, and 0.5 K, respectively. The low pressurewas set equal to the helium vapor
pressure at 1.8 K.
OPTIMIZATION OF REFRIGERATORS FOR CRYOGENIC SUPPORTS
In large superconducting systems such as energy storage magnets and electric
generators, most of the need for refrigerationpower is owing to the heat leak through
supports. lt was reported [2 ' 3 ] previously that for systems where the heat leak
through the mechanical supports dominates the heat Ioad in a cryogenic vessel, it is
advantageous to use the evaporating gas to cool the supports. This section of the
paper will show that the system is optimized if a fraction of the vapor is used to
continuously cool the supports while the rest is retumed to the refrigerator heat
exchanger to improve the coefficient of performance. This case is also compared to
that of intercepting the heat Ioad at a finite number of locations using separate
refrigerators. In both cases, only large refrigerator systems are considered.
Supports Coutinuously Cooled by Evaporating Gases
Consider the refrigerator system shown in Fig. 2, where a fraction I of the
refrigerant is used to cool a mechanical support and the remaining part is retumed to
the heat exchangers. The refrigerator is designed to remove an amount of heat, Oe,
conducted to the cold end through a mechanical support. This is represented by
Oe=
Axm
(1)
where A is the latent heat, x is the liquefied fraction, and m is the total mass ftow rate.
Given a mass ftow rate, Im, to cool the support and a heat leak Oe. the length to the
cross-sectional area, L/ A, of the support can be determined (see the Appendix). By
changing the value of I the required value of L/ A can be determined. For a given
fraction f, the refrigerator system is optimized for best coefficient of performance,
independent of the support, as reported previously [5 ]. H we change the total mass
ftow rate m it is possible to calculate the total refrigeration power as a function of the
Support mass ftow rate me =Im. Results of these calculations are shown in Figs. 3
and 4 for epoxy-fiberglass supports with a cold end at 1.8 K and 304 stainless steel
support with the cold end at 4.2 K, respectively. It is also shown that the coefficient of
performance decreases significantly as more ftow is diverted to cool the support.
1
FIRST
ENGINE
J
SECOND
ENGINE
xm
Fig. 2. Refrigerator-support system in which a fraction
of the ftow rate is used to cool the support.
353
Minimization of Refrigeration Power for Luge Cryogenic Systems
3
...u
z
<(
'I
a:
0
....
<(
...
...J
...a:
Q.
a:
w
Q.
...0
...z
;t
0
Q.
...
~
.........
0
...J
<(
....
u
~
mCp , WATT/K
Fig. 3. Total refrigeration power and coefficient of performance vs. heat capacity associated with a mass ftow rate
to epoxy-fiberglass supports with a cold-end temperature
of 1.8 K.
Supports Cooled by a Finite Number of Refrigerated Shields
The heat leak to the cold end is intercepted at a finite number of locations using
separate refrigerated shields. An optimization procedure reported in a previous
publication Cl was used to minimize the total refrigeration power. Using the
coefficient of performance optimized for large refrigeration systems, the optimum
temperatures, locations, and refrigeration power are calculated for different
numbers of shields. The total refrigeration power using any number of shields is less
than the refrigeration power required by vapor-cooled supports. Table II shows the
optimization results for a 304 stainless steel support with a cold end at 4.2 K and an
epoxy-fiberglass support with a cold end at 1.8 K.
':"
Q
"
w
u
z
~
<l:
~
a:
u
~
0
~
...J
6
n.
u..
a:
w
n.
0 .3
mCp. WATT/K
Fig. 4. Total refrigerator power and coefficient of performance vs. heat
capacity associated with a mass ftow rate to 304 ss supports with a
cold-end temperature 4.2 K.
354
M. A. Hllal and Y. M. Eyssa
Table II. Optimum Temperatures, Locations, and Refrigeration Power for Finite
Number of Shields Compared to Continuous C~oling
Number
of
shields
T2,K
T~>K
T3,K
AXdL
AX2/L
AX3/L
AX4/L
304 Stainless steel at Tc = 4. 2 K
0
1
2
3
CC*
39.7
21.6
13.7
81.7
40.7
108.8
0.338
0.189
0.110
0.662
0.334
0.201
0.477
0.295
0.394
Epoxy-fiberglass uniaxial, S-954/E787, in plane Tc = 1.8 K
0
1
2
3
30.8
12.4
7.78
cc
67 .6
30.8
102.5
0.463
0.299
0.223
0.537
0.314
0.232
0.387
0.252
0.293
PL/A,
W/cm
5345.0
1060.0
758.4
664.8
4895.0
512.4
112.9
78.6
68.8
406.0
* Continuous cooling.
REFRIGERATION POWER FOR VARIABLE-CROSS-SECTION
SUPPORTS
In many cases the allowable stress on cryogenic supports is a strong fupction of
the temperature. The refrigeration power can be reduced using a varial}Je crosssectional area support to take advantage of high stresses at low temperat'ures.
Consider the variable-cross-section support shown in Fig. 5. Let th~re be N
shields, which intercept heat flowing from the bot end TH = TN+2 to the cold end at
T1 = Tc. The cross-sectional area between the two shields is determined by the
mechanicalload and the lowest allowable stress in the temperature range of the two
shields. At each shield a refrigerator with inputpower Pi will remove heat at the rate
llQ = Qi - Qi+ Using calculus of variation, it can be proven that the absolute
minimum refrigeration power (N = oo) is
Pmin
= ~oT1f~H[k(T)/~(T)r /2 dTr
(2)
where A 0 is the cross-sectional area at TH• L is the support length, k is the local
thermal conductivity, and u" is the local design stress normalized to its valut at room
temperature.
TN+2: TH:
300 K
/ / / / / / / ' C ! ! f / / / / / / /1/
•o
r,., --~ ~ ~ ..~- ~· --:
T1
T;.,
--
_ _
o.c ~•-L ~
_ _ _ _o !:!.-_a,.:!~
7777777777))77777/7777
T; • Tc
L
l
Fig. 5. Variable cross-sectional area support model.
JSS
Minimization of Refrigeration Power for Large Cryogenic Systems
Table 111. Absolute Minimum Refrigeration Power for
Epoxy-Fiberglass Uniaxial, S-994/E787, in Plane C1
300 K)
(TH
=
Absolute minimum refrigeration power
Lower-end
Temp.,
Tc
PL/A,
constant cross section
W/cm,
variable cross section
1.4
1.8
4.2
25.8
24.0
18.3
18.7
17.5
13.5
Results for a variable-cross-section support are shown in Table III. The results
are compared to that öf the constant-area cross section reported by Hilal and
Boom C]. For fiberglass-epoxy the refrigeration power using variable crosssectional area supports is reduced by 26% if the cold end temperature is 4.2 K. The
shield temperature and location forafinite number of shields can be calculated using
equations (16), (17), (18), and (20) in the paper by Hilaland Boom Cl
To take into consideration that the allowable stress is a function of temperature,
D;
CJ.
1
D; = un(T; + 1)
[
e;( T~-1)- C;+l(T;~l -1)] t;•+l kdT
T
T
T
(3)
where un(T; + 1) is the normalized allowable stress at the shield temperature Ti+l·
Optimized calculations for epoxy-fiberglass uniaxial, S-994/E787, in plane CJ at Tc
of 1.8 K, and 4.2 K for a constant cross-sectional area and a variable cross-sectional
area, are shown in Table IV. The coefficients of performance used in these calculations are those optimized for a large refrigeration system.
Table IV. Optimum Temperatures, Locations, and Refrigeration Power for Finite
Number of Shields (Epoxy-Fiberglass Uniaxial, S-994/E787, in Plane) C1
Nurober
of
shields
T~>K
Tz,K
T 3 ,K
ll.XdL
fl.Xz/L
ll.X3 /L
ll.X4/L
PL/A,
W/cm
0.293
0.294
112.9
94.08
78.67
61.99
68.85
53.16
Tc= 1.8 K
1
1
2
2
3
3
C*
Vt
c
V
c
V
30.8
36.16
'12.4
14.23
7.78
8.38
67.6
80.62
30.8
36.3
102.5
116.6
0.463
0.466
0.299
0.303
0.223
0.220
0.537
0.534
0.314
0.316
0.232
0.238
0.387
0.381
0.252
0.248
Tc= 4.2K
1
1
2
2
3
3
c
V
c
c
V
V
43.6
51.0
21.13
23.65
14.20
15.49
* Constant cross section.
t Variable cross section.
85.2
98.4
43.3
51.6
121.5
134.5
0.456
0.463
0.298
0.230
0.219
0.221
0.544
0.537
0.317
0.319
0.228
0.238
0.385
0.381
0.263
0.249
0.290
0.292
72.24
60.55
55.29
44.016
50.016
39.048
356
M. A. Hilalud Y. M. Eyssa
DISCUSSION OF RESULTS AND CONCLUSION
The present study shows that in certain applications refrigerators should not be
optimized independent of the cryogenic system. For a mechanical support system in
particular, optimum operating conditions exist where a fraction of the helium vapor
is used to cool the support and the remaining part is returned to the refrigerator.
The present study also shows that discrete cooling using any number of
refrigerated stations requires less refrigeration power than continuous cooling. For
discrete cooling the refrigerators can be optimized independently for the best
coefficient of performance. In the case of continuous cooling, some of the ftow is used
to cool the support and thus affects the performance of the refrigerator.
Further reduction in refrigeration power is possible by varying the crosssectional area between shields, taking advantage of the fact that allowable stresses
are strong functions of temperature. It can also be concluded that high coefficients of
performance for large systems can be obtained. In this case more efficient compressors, heat exchangers and expansion engines can be used.
NOTATION
= strut cross-sectional area
= strut cross-sectional area at room temperature
= efficiency constant
= mathematical expressiontobe used with equation (18) of reference
= force
= strut length
= temperature
=cold-end temperature
= hot-end temperature
Oe = heat conducted to cold end
CP = helium specific heat
k = thermal conductivity
m = total helium mass ftow rate
rilc = helium mass ftow rate to the support
s = length variable
x = liquefied fraction
Un = normalized stress to room temperature value
u 0 = allowable stress at room temperature
A = heat of vaporization
A
A0
C
D,
F
L
T
Tc
TH
eJ.
REFERENCES
1. M. Hila! and R. W. Boom, in Advances in Cryogenic Engineering, Vol. 22, Plenum Press, New York
(1977), p. 224.
2. A. Bejan and J. L. Smith, Jr., Cryogenics 14(3):158 (1974).
3. A. Bejan and J. L. Smith, Jr., in Advances in Cryogenic Engineering, Vol. 21, Plenum Press, New York
(1976), p. 247.
4. A. Bejan, Cryogenics 15(5):290 (1975).
5. M. Hila!, Cryogenics 19(7):415 (1979).
6. J. Brooks and R. Donnelly, "The Calculated Properties of Helium II," Tech. Report, The Institute of
Theoretical Science, University of Oregon, Eugene, Oregon (1973).
7. M. D. Campbell, "Thermophysical Properties of Plastic Materialsand Composites to Liquid Hydrogen
Temp. (-423°F)," ML-TDR-64-33, Part III, Air Force Material Laboratory, Wright-Patterson Air
Force Base, Ohio (August 1965).
Minimizadon of Refrigeradon Power for Luge Cryogenic Systems
357
APPENDIX
Consider the support shown in Fig. 3. Assurne perfect heat exchange between
the helium gas and the support. For such conditions,
d
dT
dT
ds kA ds = rhcCp ds
(A-1)
Integrating this expression yields
dT
= Oe
ds
kA-
.
+ mccp(T - Tc)
(A-2)
For the support system then
F
1 F
A=--=-u(T) Uo Un
(A-3)
Substituting (A-3) into (A-2) and integrating results in
L
F/uo =
I
TH
Tc
--=---k'--10"-:-"=---=:-:Oe+ rhcCp(T- Tc)
(A-4)
For a fixed L, F, and u 0 there is a relation between Oe and rhccp. For constant
cross-sectional area struts, (A-4) reduces to
(A-5)
DISCUSSION
Question by G. H. Morgan, Brookhaven National Laboratory: Since the cross section is determined
by mechanical stress requirements, how can the cross section be allowed to vary?
Answer by author: The cross section is determined by both the magnetic Ioad and the mechanical
design strength. Since the mechanical design strength varies with temperature, it is possible to have
different cross sections between shields as shown in Fig. 5.
G-1
TWO-DIMENSIONAL HEAT TRANSFER
TO SUPERFLUID HELIUM*
M. A. Hilal
Michigan Technological University
Houghton, Michigan
INTRODUCTION
Steady-state boiling heat transfer to superfluid helium has been studied by many
investigators 3 ]. In previous experiments a metalblock was attached to the end of a
tube filled with superfluid helium. When the block is heated, internal convection
currents take place which result in one-dimensional flow inside the tube. Matthews
and Leonard ["] studied boiling heat transfer from reetangular surfaces in a saturated
superfluid helium bath. They measured the critical heat flux as a function of
orientation, temperature, and depth.
In the present experiment the heat transfer from a cylindrical surface immersed
in superfluid has been studied attemperatures of 1.9, 1.95, 2.05, and 2.1 K. The flow
of both the superfluid helium and normal helium components in this study can be
considered as a two-dimensional flow; the critical and the recovery heat flux, two
important parameters in the äesign of cryogenic systems are expected to be different
from values measured previously 3 ]. The purpose of the present study was to
measure both the critical and the recovery heat flux as a function of helium Ievel
above the surface. The results of these measurements were then compared with the
results of Matthews and Leonard [4 ].
The flow of normal helium leaving the surface can be considered similar to the
flow of conventional fluidsernerging from a circular cross section. No attempt in this
study has been made to extend the model to cover Kapitza resistance under
two-dimensional flow conditions. Rather, the model is used to explain the large
increase in the critical heat flux in this two-dimensional flow.
c-
c-
EXPERIMENTAL APPARATUS
The various parts of the experiment are shown in Fig. 1. An insulated OFHC
copper cylinder, 1. 91 cm in diameter, was suspended in a superfluid helium bath
contained in a 11.3-cm-diameter dewar. The helium Ievel inside the dewar was
measured using a superconducting liquid Ievel indicator and the helium bath
temperature was measured using a high-precision vacuum gauge.
The copper cylinder was 1.25 cm high and was surrounded by a nylon block for
insulation (Fig. 2). Evanohm wire was wound around the cylinder as a heater. A
thermocouple junction, gold-0.07-at.%-iron vs. chromel, was soldered to the
* Work conducted at the University of Wisconsin as part of the energy storage project and supported by
the U. S. Department of Energy.
358
Two-Dimensional Heat Transfer to Superfluid Helium
359
CU ELEMENT
--- --------7'"---~ --==
SUPERFLUID
HELIUM
=
Fig. 1. Experimental apparatus.
copper cylinder near the surface exposed to the superfluid helium and the reference
junction was immersed in the helium bath. Both facing-up and facing-down orientations were used. The power input to the heater was determined by measuring the
voltage and the current independently. The calibration tables published by Sparkset
al. [5 ] were used to calculate the temperature difference.
Fig. 2. Test cylinder.
360
M.A.Hßal
,
I
•
lo---+
0 2.05 K -
3
25 cm MI.." lovel
• 2.<Y.> K - 20cm ".,.." lovol
c, 2.05 K - 24 .6 cm helium Ievei
9 L9 K - 26.7cm nel;um IOYtl
N
E
~
..
ö
:I:
I
.5
Fig. 3. Boiling curve for different liquid Ievels and different temperatures.
RESULTS
The heat ftux vs. temperature difference is shown in Fig. 3 for different
temperatures and different helium Ievels. The critical (maximum) heat ftux depends
both on the bath temperature and the liquid Ievel. A limited number of data points
was taken in the film boiling region. In this region a long time was required to reach
steady state and the liquid helium Ievel could have changed appreciably.
Figure 4 shows the maximum heat ftux as a function of the helium Ievel at
different temperatures. Figure 5 shows the recovery heat ftux also as a function of
liquid Ievel at different temperatures and orientations.
DISCUSSION OF RESULTS
As can be seen from Fig. 3, the critical heat ftux in superfluid helium occurs at
large temperature differences. At a temperature of 2.05 K and for 20 cm of liquid
Ievel, the temperature difference is 3.4 K. The helium pressure at the surface of the
experiment is 3.93 KPa, which is lower than the Iambda pressure. At these large
temperature differences the surface can be exposed to either superfluid helium or
helium vapor.
The critical heat ftux is plotted vs. the liquid head above the surface as shown in
Fig. 4. For liquid Ievels up to 25 cm the critical heat ftux does not have a strong
dependence on the depth. Also, since large temperature differences occur at the
critical heat ftux, the results for 1.95, 2.05, and 2.1 K do not differ appreciably.
361
Two-Dimensional Heat Transfer to Superfluid Helium
~
~~~
3
N
E
u
'3=
"
;;::"
I
2
•
I
I
/
I
/
/
/
/
/
/
/
/
/
•
,/
0
.
• •
0
•
•
0
• 1.95 K- orientation 11 down
• 2.05 K- orientotion is up
• 2.05 K- or~entaflon is down
o 2.10 K- onentot1on is up
- 2.05 K- onalyhcol
--- Matthews ond Leunord doto
ö
•
I
1 o~----L-----I~0----~----~20~--~----~30~----L---~40
Liquid Level , cm
Fig. 4. Critical heat flux vs. depth for different temperatures.
Todetermine the critical heat flux analytically as a function of depth we assume
that the normal helium velocity leaving the surface is given by
1
(1)
Vn CX::--a +bz
where Vn is the velocity of the normal helium component, z is the variable height, and
a and b are constants.
Equation (1) represents the velocity distribution for a flow ernerging from a
circular cross section jet [6 ] and is valid for both laminar and turbulent flow. It is
necessary to mention that (1) is modified to take into account the finite cross sectional
area of the surface. Similar velocity distributions for the superfluid helium
component are assumed where the surface is considered a sink. Using the GorterMellink coefficient of friction it was possible to determine the critical heat flux as a
function of depth. The analytical results are shown in Fig. 4. The critical heat flux
obtained analytically is smaller than the experimental value at low liquid Ievels. The
deviation between the analytical and the experimental results can be reduced if it is
assumed that superheating takes place near the surface. The analytical modelwill be
reported in a future publication.
The surface orientation, as observed by previous investigators [4 ], did not have a
significant eflect on the critical heat flux results. The recovery heat flux at 2.05 and
1.95 K is shown in Fig. 5. The values shown in these figures are average values since
the liquid Ievel changed appreciably in this region. It has been noted that the
transition to the film boiling region, as reported in previous studies, is associated with
a loud noise and that the noise disappears following transition to the Kapitza
conductance region. The data of Matthews and Leonard are shown on Fig. 4 for
comparison.
CONCLUSIONS
High critical heat flux is achieved in two-dimensional flow systems in
comparison with one-dimensional flow systems. In two-dimensional systems, the
M.A.Hßal
362
3
N
E
u
......
31:
,
u::"
V ot;,.o
2
V
0
i
o 1.95 K- orientcmon is down
" 2.05 K- O<ientotion io up
" 2.05 K - O<ientalion io down
::r::
V
20
10
Loquid
30
40
Level , cm
Fig. 5. Recovery heat ftux vs. depth for different temperatures.
ftow resistance is concentrated near the surface, independent of liquid Ievel. The
liquid Ievel increase therefore results in more superheat at the surface but does not
change the ftow resistance. This should be considered in the design of large cryogenic
systems using superfluid helium as a coolant such as superconducting energy storage
magnets. A preliminary analytical study indicates that the critical heat ftux from the
surface of a cylinder can be predicted using a conventional velocity distribution for
ftow ernerging from circular cross section jets.
ACKNOWLEDGMENTS
The author wishes to thank M. Steinhoff for his assistance during several phases of this project.
Thanks arealso expressed toS. W. V an Seiver for bis very helpful discussions and comments.
REFERENCES
1. S. W. Van Sciver, in Advances in Cryogenic Engineering, Vol. 23, Plenum Press, New York (1978),
p. 340.
2. B. W. Clement and T. H. K. Frederking, in Liquid Helium Technology, Pergarnon Press, Oxford,
England (1967), p. 49.
3. G. BonMardion, G. Claudet, andP. Seyfert, inProc. 7thlntem. Cryogenic EngineeringConference, IPC
Science & Technology Press, Guildford, England (1979), p. 214.
4. D. W. B. Matthews and A. C. Leonard, in Advances in Cryogenic Engineering, Vol. 19, Plenum Press,
New York (1974), p. 417.
5. L. L. Sparksand W. J. Hall, NBS Rept. 9712 (1969).
6. H. Schlichting, Boundary-Layer Theory, McGraw-Hill Book Company, New York (1960), Chaps. IX,
XXIV.
DISCUSSION
Question by R. C. Hendricks, NASA Lewis Research Center: From your ftow model it appears as an
axisymmetric jet; could you provide additional information relative to your source term?
Answer by author: The ftow model considered is applicable for axisymmetric jets. Equation (1) is
valid for both laminarandturbulent jets and the constants a and b can be adjusted to fit the experimental
results.
G-2
HEAT TRANSFER TO HELIUM-li
IN CYLINDRICAL GEOMETRIES
S. W. Van Seiver and R. L. Lee
University of Wisconsin-Madison
Madison, Wisconsin
INTRODUCTION
Renewed interest in the properties of helium-11 has been inspired by numerous
new engineering applications for the fluid 3 ]. Of particular concern is the heat
transfer behavior and its effect on the design of stable superconducting magnets.
Sturlies of heat transfer to helium-11 in linear systems have investigated such
phenomena as peak heat transport, including superfluidity breakdown [4 - 7 ], effects
of normal fluid turbulence [8 - 9 ], and time-rlependent heat transfer
In general,
experiments with cylindrical geometries have been limited to measurements of the
peak heat flux from a cylindrical heater or wire in an open bath. On the basis of
experience with the linear system, it appears clear that to characterize cylindrical
heat transfer, a careful accounting of the heat flow in the adjacent helium is
necessary.
Ioterest in understanding radial heat transfer to helium-11 is related to work on
the Wisconsin Superconductive Energy Storage project, which proposes to use a
round cross-section conductor cooled in a bath of helium-11 Cl. The present study is
aimed at characterizing the radial heat transfer problem, much as has been achieved
for linear systems.
e-
co-n ].
THEORETICAL BACKGROUND
The solution to the problern of heat flow in helium-11 has traditionally been cast
in the form of the two fluid hydrodynamic equations with an additional term which
takes into account the mutual friction between the two interpenetrating fluids,
normal and superfluid. The equations which must be solved are C2 ]
1
I
13
-av.
at = --p Vp + SVT- pn A V s - Vn
(1)
and
Ps
I -vn 13 +Tin- [ V2Vn +-V(V·vn)
1
]
(2)
--SVT+p.Av.
Pn
Pn
3
where v. and vn are the superandnormal fluid velocities and A is the Gorter-MeHink
mutual friction parameter.
aV=
n --Vp
1
-
at
P
363
364
S. W. Vu SdYer aad R. L. Lee
The steady-state (iJv/iJt = 0) solution to heat ftow through a slit has been
published [1 2•13]. Experimentally, it has been demonstrated to be a relatively
accurate representation of most one-dimensional heat ftow data C4 ]. For largediameter tubes (d > 1 mm), the solution to (1) and (2) simplifies to an expression for
the temperature gradient
(_!]_)
dT = Ap,.
dx
S p.ST
3
(3)
where Q is the heat ftux density through the helium.
A simple method of showing the origin of (3) is to reduce (1) to steady-state
conditions (iJv8 / iJt = 0) and assume no temperature-induced pressure gradients,
Vp = 0. The latter assumption is equivalent to neglecting normal fluid interactions
with boundaries, a mechanism that has been shown to be negligible in large systems
(d > 1 mm). Using the expression for the conservation of momentum
(psVs
+ p,.v,.) = 0
(4)
and assuming that the heat flow is carried by the normal fluid only
Q =pSTv,.
(5)
an identical expression to (3) results. Furthermore, the expression is not limited to
linear heat flow, being applicable to all geometries provided the position dependence
of the heat flux is taken into account.
Consider a cylindrical heating element of radius r 0 with an applied surface heat
ftux,
The heat flux density as a function of position coordinate r can be written as
Oo.
Q(r)
= Oo(~)
(6)
The radial coordinate temperature gradient becomes
aT = Ap,. (~) 3
ar
S p.ST
(rr
0) 3
(7)
By analogy with linear experiments, the peak heat ftux density in a cylindrical
heat. ftow experiment can be determined by integrating (7). With the boundary
conditions on the temperature at infinity set to be that of the bath, the resulting
expression
Q~
= ( -2
ro
JT Ps
2
T1
3S4T3
Ap,.
)1/3
dT
(8)
should predict the peak surface heat ftux, Q~, where T1 is the bath temperature and
T2 is the maximum allowable temperature of the helium near the heater surface
(2.17 K for p > 5 KPa and determined by the hydrostatic head for pressures below
5 KPa). The goal in the present experiments is to test this expression.
EXPERIMENT
A schematic. of the experimental apparatus is shown in Fig. 1. A cylindrical
heater sample machined from OFHC copper is placed between two insulating disks
of fiberglass-reinforced polyester, 140 mm OD and 12.7 mm thick. The copper
Heat Transfer to Helium-li in Cylindrical Geometries
TO
ELECTRONICS
t
365
TO
HIGH PRESSURE GAS
HEAT
EXCHANGER
HED:
P=Ps•r
Tii.SK
NEEDLE
VALVE
OEWAR'---....
PRESSURE
CYLINOER
HEAT
TRANSFER
SAMPLE
Fig. 1. Schematic of experimental apparatus.
sample is 13.26 mm OD and has 4.76 mm of its length exposed to the helium, giving a
total heat transfer surface area of 198 mm 2 • Spacing between the insulating disks is
held constant at 4.76 mm to ensure purely radial heat flow.
Temperatures are measured by means of six 1/8-W Allen Bradley resistors,
nominal value 75 .n, calibrated against a germanium standard resistor. One of the
carbon resistors and the germanium resistor are located inside the copper heater
sample. The remaining five resistors are ground to a thickness of 1 mm and placed
between the insulatingplates at 7.6, 9.7, 12.7, 25.9, and 66.0 mm from the center of
the heater. Each resistor is oriented on a different equally spaced radialline.
The present apparatus is designed to allow measurements to be made at
saturated vapor pressure as weil as subcpoled conditions. For the pressurized results,
a separate cylinder surrounds the experiment and is filled through the needle valve.
Data near saturated vapor pressure are acquired by removing the pressure cylinder.
In this case, the hydrostatic head of helium is determined using a superconducting
Ievel indicator. Heat is applied by passing a current through a wire-wound resistor
(room temperature resistance of 180 0) inside the sample. Both step function and
continuous heating were studied. The resistance thermometers are measured using a
potentiometric conductance bridge for the steady-state values and a chart recorder
with a constant current supply for the transient measurements.
S. W. Van Sdver and R. L. Lee
RESULTS AND DISCUSSION
Steady-State Measurements
Surface heat transfer data for the present experiment are shown in Fig. 2, which
is a plot of heat ftux density vs. temperature difference between the heater and
adjacent liquid helium. For comparison, the data have been displayed at both 4.2 and
2.1 K to show differences between normal and superfluid helium for the cylindrical
geometry.
In general, the two sets of results are qualitatively similar. For both cases, there
is a small ä T region associated with nucleate boiling for the normal helium and
Kapitza resistance phenomena C5 ] for superfluid helium. Heat transfer coefficients,
h, in this region are typically araund 1 W I cm 2 K for both sets of data.
Critical heat ftux results are substantially different for the two sets of data. At
2.1 K, with a hydrostatic head of 40 cm, the peak heat ftux occurs at 2.1 W I cm 2 and
recovery at 1.9 W lcm 2 , roughly 90% of the peak. The normal helium heat transfer
has lower values, with a peak at 0.63 Wlcm2 and recovery at 0.26 W lcm 2 of 40% of
the peak. These rather low normal helium peak heat fluxes are most probably caused
by the confined geometry of the heat transfer surface.
A summary of the experimentally determined steady-state peak heat fluxes in
superfluid helium are plotted in Fig. 3 as a function of bath temperature.
Unfortunately, the apparatus was not equipped to regulate the hydrostatic head, so
there is a slight variation in the helium depth with time. This variation is also shown in
the figure by the lower dashed line. The observed peak heat flux data have the
characteristic behavior seen in this type of experiment near saturated vapor pressure
6 - 18]. A maximum in the peak heat flux occurs near 1.9 K, with a rapid decrease in
value at higher temperatures. For linear heat flow experiments, this behavior can be
quantitatively understood in terms of the bulkfluid properties. The goal here was to
e
2
0
•
2.1 K
4.2 K
6/:l
0
N
1::.~----~-~~~::.::::.~-=~
0
00
0
0
0
E
,----------------------0
?I:'u
. 0.5
0
0
0
0
.
•
0.2
0
0.1
0.05L-___ L_ _ _ _J__J--~_LLLWL----L--L~~~~~--~
0.05
0.1
0.2
0.5
I
2
5
10
20
liT. K
Fig. 2. Heat transfer and boiling curves for current experiment in He II and He I.
Heat Transfer to He6um-ß in Cylindrical Geometries
5
4
N
E
~ 3
0
-·
•
. ..
•
.•
-- --- --
367
50
E
()
•
- --/
10
Fig. 3. Experimentally determined peak heat ftuxes in superfluid
helium. Solid curve is predicted values for indicated hydrostatic
heads using (8).
apply the analysis discussed in the previous section to the present case de"lling with a
cylindrical geometry.
The expression for the peak heat ftux density in superfluid helium confined to a
cylindrical geometry is given by (8). Evaluating this expression for the conditions in
the current experiment, the predicted peak heat ftux is somewhat higher than the
experimental values. The solid curve in Fig. 3 shows these predicted values for the
given hydrostatic head. The ratio of the theoretical peak heat ftux, Q~h, to the
experimental value O!x is nearly constant, i.e., 0~/ O!x = 1.24 ± 0.07 for all
temperatures. It should be noted that similar data [ 16] on cylindrical heaters have
been analyzed and these also give experimental peak heat ftuxes below the
theoretically predicted value, although the ratio is higher.
Several possible explanations for the above behavior can be tested in the present
experiment. For example, the Gorter-Mellink parameter, determined from linear
experimental data [ 7 ' 13 ], has been used in (7) to determine whether it is independent
of geometry by evaluating the data for the temperature distribution in the helium.
Figures 4 and 5 show the difference in temperature between the bath and the two
resistors nearest the heater surface, at 7.6 mm radius and 9.7 mm, vs. the heat ftux.
Within the scatter in the data, these results correlate with a straight line on a log-log
plot. Furthermore, both fits appear to have slopes very nearly equal to 3, which
agrees with the cubic dependence observed in linear experiments. By using (7), the
Gorter-Mellink parameter can be calculated to give values of 120 cm-s/g at 1.95 K,
220 cm-s/g at 2.05 K and 310 cm-s/g at 2.1 K. This is within the range of values
measured in linear systems C4 J.
At this point, there is no clear explanation for the discrepancy between the
predicted and experimental peak heat ftuxes. As noted above, the temperature
gradients and Gorter-Mellink parameters are in agreement with values measured in
linear systems. However, a few possibilities as to the origin of these results are worthy
of mention.
The most promising explanation lies in the behavior of the helium near the
surface. In the cylindrical geometry, the heat ftux density near the sample is
s. w. v. SciY• _.. R. L
Lee
2.1 K
..
3.5
4
4.5
5
Fig. 4. Temperature difference between thermometer located
nearest the heater (r = 7.6 mm) and that in the bath.
amplified, inducing the major temperature excursions to occur there. Therefore, any
deviations from the normal mutual friction behavior would occur in a region that is
not accessible to bulk fluid measurements. This eflect would be amplified for small
diameters, which appears to be in agreement with experiment [16].
Alternately, there may be a fundamental error in the assumptions leading to
(8). That the form of (8) is correct within a proportionality factor makes this
explanation less probable. Further work will be required in this area to formulate a
complete understanding of the results.
Fig. 5. Temperature difference between thermometer located
second nearest the heater (r = 9.7 mm) and that in the bath.
Beat TraDSfer to Helium-D in Cylindrical Geometries
'I
'I
-
2
0
~
•
•
•
'·...
1.5f-
369
1.9 K
2.0 K
2.1 K
.
•
0
'lo
o.
"'
.,
...
0
.-
10.1
At. sec
10
100
Fig. 6. Increase in peak heat ftux during short-time transient
heating.
Transient Measurements
Two types of transient measurements have been conducted in the present study.
The first involves applying a step function heat pulse to the cylindrical sample and
measuring the length of time to the onset of film boiling. Similar work has been
previously reported for a long linear system [11 ]. The results of the present study are
plotted in Fig. 6 as the ratio of the transient to the steady-state heat flux, Q/ Q*. This
method of displaying the data shows a temperature-independent form for the effect.
As can be seen from the data, there is an observed enhancement of a factor of 2 in
peak heat flux for times of the order 250 ms.
The understanding of short-time high heat transfer rate experiments has been
shown to involve an enthalpy balance within the helium adjacent to the heater. For
the long linear system, the rate of enthalpy rise has been shown to correlate with the
heat flux. A critical ingredient of this type of analysis is a measure of the transient
temperature distribution in the bulk fluid, the second type of transient measurement
carried out in the present experiment.
Two temperature rise distributions are plotted in Fig. 7 just at the onset of film
boiling. As before, the approach to understanding these data is to calculate the extra
enthalpy associated with these distributions and compare that with the enhanced
heating rate during the transient experiment. The two exponential fits in Fig. 7 are
the type used to calculate the enthalpy. As an example, consider the 9.4-W I cm2 data.
The total calculated enthalpy rise in the helium is 0.032 J/cm2 • This value is only a
few percent of what must be absorbed during the 390 ms of transient heating. Similar
results are encountered for the lower heat flux data. Consequently, it appears that the
bulk fluid outside the experimental region is participating in the absorption of
enthalpy. Only a small temperature rise in the surrounding helium bath would be
necessary to account for the energy deposited during transient heating. A problern
which remains is how the heat is transmitted from the heater to the bath under no
measurable temperature differences.
S. W. Vu Seiver aad R. L. Lee
370
Q
• 5.9
• 9.4
r-r0
,
'\",2
.,.c:J
Fig. 7. Temperature rise of thermometers in the
heliwn at the onset of film boiling. At 5.9 W/cm2 ,
flt = 1.4 s and at 9.4 W/cm2 , llt = 0.39 s. Bath
temperature is 1.9 K.
mm
ACKNOWLEDGMENTS
The authors would like to thank W. Leake for help in reducing the data. The work was supported by
the Department of Energy.
NOTATION
A = Gorter-Mellink mutual friction parameter
p = pressure
q = heat flux density
r = radial position coordinate
Q = heat flux
Q* = steady-state peak heat flux
Q 0 = surface heat flux
S = entropy
T = temperature
t =time
v,. = normal fluid velocity
v. = superfluid velocity
x = one-dimensional position coordinate
p,. = normal fluid density
p. = superfluid density
REFERENCES
1. R. W. Boomet al., "Wisconsin Superconductive Energy Storage Project, Vol. II," University of
Wisconsin (January 1976).
2. S. 0. Hong. P. F. Michaelson, I. N. Sviatoslavsky, W. C. Young, and R. W. Boom, IEEE Trans. Magn.
Mq-15:756 (1979).
Heat Transfer to HeUum-11 in CyUudrical Geometries
371
3. R. Aymar, G. Claudet, C. Deck, R. Duthil, P. Genevey, C. Leloup, J. C. Lottin, J. Parain, P. Seyfert,
A. Torossiam, and B. Turck, IEEE Trans. Magn. Mag-15:542 (1979).
4. C. Linnet and T. H. K. Frederking, J. Low Temp. Phys. 21:447 (1975).
5. G. Bon Mardion, G. aaudet, and P. Seyfert, in Proc. 7th Intern. Cryogenic Engineering Conference,
IPC Science and Technology Press, Guildford, England (1979), p. 214.
6. G. Kraflt, J. Low Temp. Phys. 31:441 (1978).
7. S. W. Van Sciver, Cryogenics 18:521 (1978).
8. W. W. Johnson and M. C. Jones, in Advances in Cryogenic Engineering, Vol 23, Plenum Press, New
York (1978), p. 363.
9. S. C. Soloski and T. H. K. Frederking, in Proc. 7th Intern. Cryogenic Engineering Conference, IPC
Science and Technology Press, Guildford, England (1978), p. 222.
10. H. Kobayashi, K. Yasukochi, and K. Tokuyama, in Proc. 6th Intern. Cryogenic Engineering Conference, IPC Science and Technology Press, Guildford, England (1976), p. 307.
11. S. W. Van Sciver, Cryogenics 19:385 (1979).
12. C. J. Gorter and J. H. Mellink, Physica 15:285 (1949).
13. W. F. Vinen, Proc. R. Soc. (London) A240:114 (1954).
14. V. D. Arp, Cryogenics 10:96 (1970).
15. N. S. Snyder, NBS Tech. Note 385 (1969).
16. T. H. K. Frederking and R. L. Haben, Cryogenics 8:32 (1968).
17. A. C. Leonard and M. A. Clermont, in Proc. 4th Intern. Cryogenic Engineering Conference, IPC
Science and Technology Press, Guildford, England (1973), p. 301.
18. D. W. B. Mathews and A. C. Leonard, in Advances in Cryogenic Engineering, Vol. 19, Plenum Press,
New York (1974), p. 417.
DISCUSSION
Question by P. Seyfert, Centre d'Etudes Nucleaires de Saclay, France: Were the transient heat
transfer experiments performed with the pressure vessel in place?
Answer by author: Both the steady-state and transient heat transfer experiments were performed at
"near saturated vapor pressure" conditions. These are achieved by removing the pressure vessel and
measuring the hydrostatic head of helium.
Question by S. Caspi, Lawrence Berkeley Laboratory: How does the liquid Ievel enter into the
Gorter-Mellink equation?
Answer by author: The liquid Ievel enters equation (8) for the peak heat ftux density, Q~, through the
upper Iimit to the integral, T2 • The maximum allowable temperature in the helium is therefore
T2 = T1 +
I
pdT
0
-dp
dp
where dT/ dp is the slope of the vapor pressure curve of liquid helium.
G-3
MAXIMUM AND MINIMUM HEAT FLUX
AND TEMPERATURE FLUCTUATION
IN FILM-BOILING STATES
IN SUPERFLUID HELIUM
H. Kobayashi and K. Yasuköchi
Nihon University, Tokyo, Japan
INTRODUCTION
Superfluid liquid helium (helium-11), especially the subcooled helium-II, is said
to have special advantages as a coolant of superconducting devices, particularly
where there is a possibility ofthermal hazard. First of all, helium-II has better coolinß,
characteristics than boiling normal helium, that is, a large peak heat flux Omax C· ]
(At Omax• film boiling begins and at Omin.
and also a large recovery heat flux Omin
the liquid near the heated metal surface reenters the stable non-film-boiling.) For the
stabilization of superconducting magnets, it is important that the mechanism of heat
transfer to helium-II is understood. Investigations have been made into the
behavior of transitions between the non-film-boiling state and the film-boiling state
at critical heat fluxes (Omax. Omin) both in the saturated and in the subcooled
helium-II, as weil as the cooling stability in the film-boiling state. The mechanism of
noisy film boiling which emits an audible high-frequency sound in the saturated
helium-II [4 ], also was studied. So far, several investigators have observed the noisy
film-boiling process by means of high-speed motion picture techniques [5 ] and
microphone techniques [6 ]. In the present research, the frequency of the temperature
change was measured with the help of a microthermometer and a clear correlation
was determined between the cooling condition and the temperature fluctuation of
the metal surface.
eJ.
EXPERIMENT
The experiments were performed with a Niebrome foil element (10 #tm thick)
with an exposed area of 6.4 mm 2 • This elementwas attached to a resin substrate into
which a carbon resistor bad been embedded as a temperature sensor (see Fig. la).
The element was heated by supplying a dc current directly through the foil. This
element was in direct contact with about 5 Iiters of liquid helium-II. The bath
temperature Tb maintained relatively constant because of the large amount of liquid
present. The temperature was measured and controlled with the help of a germanium
thermometer. The immersion deptb H was regulated manually by Iifting or pushing
the support rod through the vacuum-tight seal with the help of a superconducting
continuous Ievel indicator. In order to observe the temperature change of the foil
372
Maximum and Minimum Heat Flux and Tempersture Fluctuation in Superfluid Helium
liqui d Su rface
T
373
5011
H
lnsulator
Aquadag Carbon
Si deV iew
NiCr Foil
Top Vlew
Mic ro-Thermom"l "r
(a)
( b)
Fig. 1. Schematic drawing of the test element. Legend: (a) side and top view of the Nichrome
foil element ; (b) structure of the microthermometer.
surface in the film-boiling state, a microthermometer was fabricated of colloidal
Aquadag carbon, about 50 1-'m in length and a few microns in thickness, as shown in
Fig. lb. The microthermometer responded tothermal oscillations of up to several
kilohertz. For some of the experimental work, the heater element was placed at the
innermost part of the reetangular channel. The channel bad an open end with
dimensions of 50 x 25 x d mm, where d is the variable channel height. In
measurements of the temperature ftuctuation, frequencies were determined after a
wait of a few minutes to achieve steady state in the film boiling at each heat ftux.
Subcooled helium-II (from TA. to 1.62 K) was produced in adewar vessel similar to
that used by Bon Mardion et al. C].
RESULTS AND DISCUSSION
Qmax&Dd Qmin
The general behavior of the heat transfer in the saturated helium-II must be
divided into three regimes depending on the immersion depth H. The position of the
boundaries for the regimes depends on Tb [4 ]. The following detailed discussion is
applicable for a Tb of 1.91 K, as shown in Fig. 2 although the phenomena were
observed at other temperatures as weil. Researchers have already established
experimentally and theoretically [8 - 12 ] that Omax of saturated helium-II increases
with depth in a manner unlike that of subcooled helium-II. Values of Omax seem tobe
comparable with the data of the references if the size effect C0 J and the different
sample configurations are taken into account. For H < 8 cm (region I), Omin
increases and the hysteresis in the Q vs. a T characteristic becomes smaller as H
increases. Here, the film boiling is silent, i.e., produces no audible sound. For
8 < H < 22 cm (region II), Omin becomes successively larger and the hysteresis
almost disappears at 22 cm, i.e., Omin coincides with Omax· However, the silent
boiling can be made noisy by thermal or mechanical shock. If there has been a
transition into noisy film boiling from the silent film-boiling state, the hysteresis is
fairly large. For H > 22 cm (region III), film botling always is spontaneously
accompanied by sound and the hysteresis becomes undesirably large. Consequently
Omin must be subdivided into o:nin for silent film boiling and o::,in for noisy film
374
H. Kobayasbi and K. Yasuköcbi
8
6
N
E
u
3:4
0
0
2
00
10
H
.
cm
Fig. 2. Critical heat ftuxes as a function of the immersion depth at
Tb = 1.91 K in saturated helium-11. Solid points represent data
obtained on the thin frost-covered surface.
boiling. Noisy film boiling reduces the heat transfer and shifts the second rise of Q vs.
ll.T towards higher temperatures. On the other band, in subcooled helium-11 the
peak heat ftux is fairly large and it is to be noted that there is almost no hysteresis at
least for the thin foil element that was used. The general nature of this hysteresis-free
behavior was confirmed with the help of foil samples of stainless steel with larger
exposed areas. This observation is different from the hysteresis characteristics
obtained in earlier work by Van Seiverfora bulk specimen of aluminum C3 ] . The
dependence of the critical heat ftuxes on the bath temperature was measured for both
saturated and subcooled helium-11. The results at a liquid height of 20 cm are shown
in Fig. 3.
15
0
5
Omax 4.2 K
0 ~~~--~--~--~--~--~__J
1.5
1.6
1.7
1.8
Tb
1.9
2.0
K
2.1
T,
Fig. 3. Critical heat ftuxes as a function of the bath
temperaturein saturated (dashed line) and subcooled (solid line) helium-11 (H = 20 cm).
Maximum and Minimum Heat Flux and Tempersture Fluctuation in Superfluid Helium
375
Temperature Fluctuation
In subcooled helium-11, within the temperature range of these experiments,
there was no noise in the film-boiling state, and thus, the results below all refer to
saturated helium-11. Figures 4a-4c show typical traces of the changes in resistivity of
the microthermometer due to temperature ftuctuations in the noisy-film-boiling
state for d of oo (without a channel), 2 and 4 mm, respectively. The frequency of the
thermal oscillation f as a function of H, with d as parameter, at Tb = 1.91 K and
Q = 4.5 W I cm 2 , is shown in Fig. 5. In this case only the frequencies of the
fundamental modes were evaluated, although the oscillations have several
harmonics. The frequency increases steadily with H . Obviously, there are two basic
types of oscillation modes; one for no channel (d = oo, Fig. 4a) and the other for
fairly narrow channels (d < 3 mm, Fig. 4b). The modes gradually merge with one
another at d = 4 mm, Fig. 4c. In the narrower channel, the thermal oscillation seems
tobe related not only to the filmlike Iifting off of liquid helium from the metal surface
but also to the blow-off of helium-11 along the channel due to the destruction of
superftuidity. Thermal noise observed in a long tube C4 ] also might have some
relationship with these results.
When the metal surface was covered with a thin film of frost, the frequency
increased significantly for a d of infinity tagether with Omax and Omin as shown in
Figs. 2 and 5. So far, it has not been possible to find a satisfactory explanation for this
observation; also, the results themselves might be somewhat ambiguous. However,
the fact that the frequency varies in a manner similar tothat of the critical heat ftuxes
has been verified. Similar experiments for d not equal to infinity have not yet been
performed.
For constant values of H, Tb, and d, f decreases with increasing Q; above a certain
value, the sound fades out altogether although oscillations continue up to higher Q
·,,·:i'/\\\vwr~'A'V\\\\\,~,\: 1
.
... ..
.
(a)
(b)
Fig. 4. Timevariation of the resistance of the microthermometer at Tb= 1.91 K, and Q = 4.5 W /cm2 •
Legend: (a) d = oo, H = 12 cm, (b) d = 2 mm, H =
12 cm, (c) d = 4 mm, H = 17 cm. (2 mV/div,
20msec/div, 0.11-'A.) At d=oo the element is
exposed to the helium-II without channel.
(c)
376
H. Kobayasbi ud K. Yuukkbi
Tb:1 .9 1 K
Q:4.5W/cm2
400
.;
300
N
J:
200
100
H ,
Fig. 5. Frequency ofthermal noise vs. immersion
depth.
cm
(Fig. 6). At a heat ftux of Q:;,in• that is, durlog the transition from film boiling to
non-film-boiling, the frequency of the noise becomes inaudibly high. The characteristics of the oscillations do not change with the orientation of the heated surface
within the liquid nor do Q~in• o:;.in• and Omax· The amplitude of the temperature
ftuctuations seems tobe of the order of 1 K. However, it is difficult to measure the
absolute value of the amplitude accurately as the sensitivity of the microthermometer depends on temperature.
Tb:l.91K
H :12cm
400
0
d
=00
300
N
J:
200
100
4
s
6
Q
,
7
6
W/cm2
9
10
Fig. 6. Frequency vs. heat-ftux density.
Muimum and MiDbnam Heat F1u and Temperatue F1actutloa Ia Saperbid He6um
377
CONCLUSION
In helium-11 the effective cooling stability is larger than that in boiling normal
helium. In saturated helium-11, however, the noise of film boiling reduces the cooling
effect and results in a lowering of the recovery heat ftux. The high frequency of
thermal oscillations in the region of film boiling implies good coollog conditions for
the case of saturated helium-11. However, as these present experiments have shown,
from a practical point of view, that subcooled helium-11 under atmospheric pressure
is to be preferred as the coolant of a superconducting magnet. Also, stabilization of
metals by subcooled helium-11 provides safeguards relative tothermal hazards since
the cooling effect extends to higher peak heat-ftux densities than in any other
coolant. The metals will not exhibit an hysteresis in the heat transfer characteristics
and will be stable without ftuctuating noisily in the film boiling region.
ACKNOWLEDGMENTS
The authors wish to thank T. Ogasawara, L. Boesten, and K. Enomoto for their informative
comments and assistance.
NOTATION
d = channel height
f = frequency of temperature fluctuation
= immersion depth
= heat flux density per unit heated surface area
Omas = maximum non-film-boiling heat flux (peak heat flux)
H
Q
Qmin = minimum film-boiling heat flux (recovery heat flux)
= recovery heat flux from silent film boiling
Q::W, = recovery heat flux from noisy film boiling
T = temperature of heated element sudace
Tb = bath temperature
llT = T- Tb
Q~
REFERENCES
1. H. Kobayashi, K. Yasuköchi, and K. Tokuyarna, Proc. 6th Intern. Cryogenic Engineering Conference,
IPC Science & Technology Press, Guildford, England (1976), p. 307.
2. B. W. Clement and T. H. K. Frederking, in Pure and Applied Cryogenics, Vol. 6, Pergarnon Press,
London (1966), p. 49.
3. G. P. Lemieux and A. C. Leonard, in Advances in Cryogenic Engineering, Vol. 13, Plenum Press, New
York (1968), p. 624.
4. A. C. Leonard, Proc. 3rd Intern. Cryogenic Engineering Conference, IPC Science & Technology Press,
Guildford, England (1970), p. 109.
5. F. L. Ebright and R. K. lrey, in Advances in Cryogenic Engineering, Vol. 16, Plenum Press, New York
(1971), p. 386.
6. P. Bussieres and A. C. Leonard, in Pure and Applied Cryogenics, Vol. 6, Pergarnon Press, London
(1966), p. 61.
7. G. Bon Mardion, G. Claudet, P. Seyfert, and J. Verdier, in Advances in Cryogenic Engineering, Vol.
23, Plenum Press, New York (1978), p. 358.
8. A. C. Leonard and E. R. Lady, in Advances in Cryogenic Engineering, Vol. 16, Plenum Press, New
York (1971), p. 378.
9. J. S. Goodling and R. K. lrey, in Advances in Cryogenic Engineering, Vol. 14, Plenum Press, New
York (1969), p. 159.
10. R. L. Haben, R. A. Madsen, A. C. Leonard, and T. H. K. Frederking, in Advances in Cryogenic
Engineering, Vol. 17, Plenum Press, New York (1912), p. 323.
11. T. H. K. Frederking and R. L. Haben, Cryogenics 8::J2 (1968).
12. D. W. B. Mathews and A. C. Leonard, in Advances in Cryogenic Engineering, Vol. 19, Plenum Press,
New York (1974), p. 417.
13. S. W. Van Sciver, Cryogenics 18:521 (1978).
14. S. W. Van Seiver and 0. Christianson, Proc. 7th Intern. Cryogenic Engineering Conference, IPC
Science & Technology Press, Guildford, England (1978), p. 228.
TRANSIENT HEAT TRANSFER IN
BOILING HELIUM-I AND
SUBCOOLED HELlUM-B
P. Seyfert, G. Claudet, and M. J. McCall
Centre d'Etudes Nucleaires de Grenoble
Grenoble, France
and
R. Aymar
Centre d'Etudes Nucleaires de Fontenay aux Roses
Fontenay aux Roses, France
INTRODUCfiON
One of the problems still remaining in the design of reliable superconducting
magnets is the accommodation of unavoidable heat inputs to the system. Resin
fracture and conductor movement cause localized Iosses while time-varying
magnetic fields affect generallosses throughout the coil system.
In the initial stages, the thermal balance between these heat inputs and the heat
absorbed by the coolant govems the temperature response of the concemed
conductor elements. If the Ievel is reached where current sharing appears, an
additional temperature-dependent heat source is switched on. The occurrence of
recovery depends on the heat transfer properties of the coolant. The contribution of
transient effects on heat transfer may be decisive in this respect and merits careful
investigation.
Normal boiling helium has already been investigated in this regard [1- 5 ]. A few
authors have reported on technologically interesting transient heat transfer characteristics of superfluid helium [6-8]. This paper presents a first account of experimental
results obtained in the course of a still ongoing program. A similar investigation but
using a different experimental technique will be published elsewhere r].
EXPERIMENTAL TECHNIQUE
Several test cells were fabricated using a common design of two straight
concentric 0.1-mm-thick stainless steel tubes with helium being maintained in the
annular space between the two tubes. A 1-mm-thick copper tube carrying a
thermocouple and heater coil replaced the centrat section of the outer tube and
served as the heated surface. Alltest cells bad an OD of 10 mm and the same heated
surface element. Figure 1 shows a cross-sectional view of the compound heating
element and the central part of a test cell.
378
Transient Heat Transfer in BoUing HeUnm-1 and Sabcooled HeUnm-D
379
Fig. 1. Cross-sectional view of central part of a test cell.
In each of the three versions of electrical heater used, the electrical insulation
was achieved by a thin (6-~m) coating of alumina. The coating was obtained by
anodizing a 12-~m-thick aluminum layer deposited with an electroplating technique
on the copper surface. The processing was carried out by an industriallaboratory*.
During experiments it turned out that test cells equipped with all three heater
versions gave about the same temperature response, namely, an exponential-like rise
of 4 to 5 ms duration.
The temperature of the heated surface was sensed by a Au/Fe Chromel
thermocouple. A relatively remote position (see detail on Fig. 1) was chosen for the
thermocouple junction so as not to disturb the uniformity of the heat flux entering the
liquid helium. The thermocouple signal was used as a detector for the transient
quasiequilibrium states rather than as an absolute thermometer.
Based on the construction principle described above, four different geometries
of test cells were devised with the aim of simulating specific situations actually
occurring in superconducting magnet windings. Figure 2 shows a schematic drawing
of all test cells used.
Test cells of type 1 are representative of events giving rise to a disturbance which
concerns a large conductor volume. Initially heat released in any conductor segment
can only be transferred to the fluid adjacent tothat part of the conductor. On the
other band, test cell 4 is representative of a situation initiated by a localized
disturbance. All the fluid contained in the affected cooling channel and bath is
potentially available for heat transfer. The test cells of type 2 and 3 represent
intermediate cases which could contribute to the understanding of the present
transfer mechanisms.
Fig. 2. Test cells used in study. Types 1, 2, and 3
are virtually closed. Both ends of type 4 are
connected to the bath via intermediate constrictions.
*Siemens AG, Erlangen, Germany.
2 hole~ 0 3ITvn
310
P. Seyfert, G. Clndet, M. J. McCall, ud R. Ayawo
For experiment the test cells were placed in a vacuum container immersed in a
bathofliquid helium at atmo5pheric pressure which could be operated either at 4.2 K
or in the range of 1.6 to 2.16 K C'1. The closed cells, types 1 to 3, were connected to
the bath by fine capillaries which ensured their initial filling and a recovery time of
some minutes after the discharge of a pulse.
PROCEDURE
Initially, the behavior of all test cells subjected to simple reetangular heat pulse
disturbances was investigated. In the case of the closed cells any significant excursion
in the film boiling regime was avoided because of the dsk of damage due to the
resulting overpressure. Since vapor formationwas not expected to cause any harm to
the open cell, recovery from transient film boiling was studied exclusively with this
cell by applying dual-heat pulses composed of an initial intense reetangular pulse
simulating a disturbance, followed by a second pulse of reduced amplitude (designated as postheating) representing the joule heating within a conductor element.
Trace records of a typical monopulse experiment are shown in Fig. 3. Heater
current traces are Iabeted A, B and corresponding temperature traces are Iabeted a,
b. Upon onset of heater power the temperature is seen to reach, in a few milliseconds,
a plateau in the range of 0.3 to 2 K above the initial value.
If a certain duration of the heat pulse is exceeded (trace B, b) a runaway of the
temperature occurs. At this point a limiting energy can be defined as the amount of
heat that the liquid has absorbed prior tothermal runaway. lt is believed that the
limiting energy is an interesting property of transient heat transfer when applications
are concemed. The purpose of the monopulse experiments therefore was to measure
this property as a function of heat ftux amplitude.
When the dual heat pulses were applied to the open test cell (type 4), trace
records as shown in Fig. 4 were obtained. Three temperature traces, Iabeted a, b, c
are shown. For better clarity of presentation the corresponding heater current traces
are omitted. Thermal runaway is initiated almost immediately by the fi.rst pulse, but a
more or less pronounced transient recovery is attained with power reduction to the
postheating Ievel.
Trace a exhibits a recovery to a temperature difference of the order of 1 K, stays
at this Ievel for a while, then rises rapidly to a second Ievel of about 4.2 K and finally
rises to values weil above 4.2 K. Increasing the duration of the fi.rst heat pulse reduces
tbe duration of the lower recovery Ievel. Trace c always remains above it. Trace b
barely reaches this Ievel and corresponds to a limiting situation for recovery. The
purpose of the dual-pulseexperimentswas to determine tbe limiting values for initial
pulse energy as a function of the postheating power.
Fig. 3. Trace records of a typical monopulse experiment.
Heater current traces are labeled A. B and c:orresponding
temperature response trac:es a, b. Vertical scale for temperature is 1.70 K/div; time scale is 6 ms/div.
Transient Heat Transfer in Bolling Helium· I and Subcooled Helium· II
381
o
'
I
c
Fig. 4. Trace record of a typical dual-pulse experiment.
Temperature response traces are Iabeted a, b, c. Vertical
scale is 3.4 K/div; time scale is 600 ms/div. The initial
peaks of traces b, c are off the chart and are at 20 and
23 K, respectively.
'
I
DISCUSSION OF EXPERIMENTAL RESULTS
The mono pulse results are shown in two diagrams which present the previously
defined limiting energy vs. heat flux amplitude with both quantities being referred to
the unit area of heated surface. Figure 5 shows the results obtained with pressurized
superfluid helium contained in test cells of type 1 (1 mm and 2 mm) and with normal
helium in the type-4 test cell. Each of the straight lines passing through the origin is
associated with a particular pulse duration which is indicated as a parameter.
The experimental values have been compared to the enthalpy increase [11 ] of
the helium mass for the limiting case of a uniform heating up toT>.. = 2.163 K. The
calculated values are indicated as dash-dotted horizontal lines along the ordinate.
Up to a flux density of 4 W /cm 2 , the experimental values are between 5 to 8% below
this theoreticallimit. Even at 8 W /cm 2 , the experimental values show a negative
deviation less than 20% from this Iimit.
The first important conclusion that can be drawn from these results is that as
long as the propagation distance for heat in pressurized superfluid helium is in the
mm range, the fluid participates essentially as a whole for transient heat transfer. As a
practical consequence, subcooled helium-11 can act as a thermal bailast by adjusting
0
6
7
8
H.ot flux,W;cm2
Fig. 5. Monopulse experiments. Results obtained with
three type-1 test cells (• and x independent cells with
same nominal d = 2 mm, [:J d = 1 mm) containing subcooled superfluid helium and one type-4 test cell (V
d = 2 mm) containing normal boiling helium. Solid Iines
through the data points show trend of the data.
382
P. Seyfert, G. Claudet, M. J. McCall, and R. Aymar
the depth of the cooling channels to the estimated heat release of the generalized
pulsing disturbances.
The behavior of boiling helium-1, on the other hand, is quite different in this
respect. Figure 5 shows results obtained in this study together with data from similar
measurements published in the literature. Although exhibiting almost the same
shape, the curves differ from each other in absolute value by factors of 3 to 5. Part of
this discrepancy is probably due to the different sample geometries used.
Normalliquidhelium has an extremely low thermal conductivity (10 4 less than
copper) which Iimits the depth of the fluid layer that can actively participate in a
transient heat transfer event. lwasa Cl observed that increasing the channel gap of
his sample arrangement from 0.12 mm to higher values caused the limiting absorbed
energy to approach saturation at a gap width of 0.5 mm. Hence, one of the test cells
with a channel gap of 2 mm should have benefitted from the best possible values of
limiting energy available in normal helium. Considering the present experimental
results from this point of view, it is concluded that in normal helium at 4.2 K only a
fixed amount of energy (10 mJ/cm 2 ) can be absorbed with heat flux densities below
0.5 to 0.6 W /cm 2 •
Finally, monopulse experiments have been performed with the more extended
test cell types 2, 3, and 4. Figure 6 shows the results obtained in subcooled helium-11
at 1.8 K. The curves clearly demonstrate the influence of fluid volumes situated at
increasing distances from the heated surface as a function of the heat flux.
The results obtained with dual-pulse experiments performed in the locally
heated open test cell, type 4, are shown in Fig. 7. One should note that unique values
for the steady-state Iimit were found for helium-11 at all bath temperatures.
Hysteresis effects are apparently absent with this fluid for the test cell geometry used.
On the contrary, the well-known hysteresis effect in normal boiling helium-1 gave
rise to the two characteristic quantities qpb (occurrence of film boiling with slowly
increasing heat flux) and q, (recovery from film boiling with slowly decreasing heat
flux).
lt appears as a general result for helium-11 and helium-1 that, provided the
postheating amplitude does not exceed the steady-state Iimit (q, in the case of
helium-1), recovery is secured irrespective of the energy of the initial disturbance
~ 300
c"'
~>.. 200
~
~
w 100
10m~
Sm~
4
6
7
6
H.a t f lu x,W/cm2
Fig. 6. Monopulse experiments. Results obtained with test
cells of type 2( +), 3(~) . and 4( Y) containing unsaturated
superfluid helium.
Transient Heat Transfer in Boiling HeHum-1 and Subcooled HeHum-11
383
T. ::1.60K
1.0
'\5
Po~t-hoaling heol f1u",W/cm2
Fig. 7. Dual-pulse experiments. Results obtained with type-4 test
cell. Power ratio of initial pulse to postheating part shown as:
• = 10; x = 6; + = 3; 6 = 2; D = 1.5. Vertical straight lines
indicate steady-state Iimiting heat ftux values.
(this corresponds to full recovery current when referring to stability criteria). In
helium-11, recovery is still possible for postheating amplitudes above the steady-state
Iimit, if the energy of the disturbance is restricted (criterion of transient stability). As
an example, in the particular case of the test cell geometry used at 1.8 K and with a
postheating amplitude of 1.5 W /cm 2 (twice the steady-state Iimit) transient recovery
occurs despite disturbances as large as 35 mJ/cm 2 •
In boiling helium-I a new singular value of heat ftux density qtr appears midway
between q, and qpb· No recovery appeared possible above this value. Between q, and
q1., there is a zone of conditional recovery, indicated with a hatched stripe in Fig. 7. In
fact, the admissible energy values within this zone are those of the limiting energy
found in the monopulse experiments (Fig. 6) and consequently depend on the heat
ftux of the initial disturbance.
lt is evident from the data that considerable benefit is obtained from transient
effects in unsaturated helium-11 compared to boiling helium-1. The results of
conductor stability experiments [12 ] clearly confirm these findings. The results
obtained on pulsive heat transfer by Kobayashi and Yasuköchi [8 ] also indicate an
increased cooling capacity of helium-11 compared to helium-1. They show, however,
marked differences with the present data which are believed to stem from different
experimental conditions: The authors have investigated saturated helium-11,
whereas this work considered subcooled helium-11. In addition, their heater pulse
sequence is not equivalent to the dual pulse utilized in this study.
An additional point concerning subcooled helium-11 should be noted. This study
shows that a heat ftux above the steady-state Iimit together with a superimposed
energy of an initialpulse can be maintained for a specified time without impairing the
recovery capability. Apparently the fluid can remove more heat than the limiting
steady-state ftux would predict. A rough estimate supports the assumption that this
excess heat is responsible for the temperature profile in the channel.
384
P. Seyfert, G. Claudet, M. J. McC.U, ud R. Aymar
CONCLUSIONS
The present investigation of transient heat transfer properlies of subcooled
superfluid helium compared to those of normal boiling helium was carried out with
special attention to potential applications. Experimental conditions which are
directly related to problems of superconducting magnet technology have been
emphasized. The results of the monopulse experiments provide a means to cope with
large disturbances or ac losses.
Subcooled superfluid helium responds to heat pulses up to several watts per
square centimeter by an initial quasiequilibrium state during which the fluid within a
few millimeters from the heated surface absorbs nearly its total energy-carrying
capacity up to the Iambda temperature. The associated temperature rise of the
heated surface remains almost constant and is moderate in size. Actual values are
currently being measured for copper with surface quality similar to conductor matrix
material. With an initial bath temperature of 1.8 K for instance, every layer of fluid
can accommodate nearly 28 mJ per unit surface area and per millimeter thickness.
The corresponding phenomenon in normal boiling helium only gives access to fixed
amounts of energy (10 mJ/cm 2) if the heat flux remains below 0.6 W/cm 2 •
Accommodation of intense localized disturbances followed by an excursion into
the current-sharing state of the concerned conductor segment is simulated with the
dual-pulse experiments. When the transient quasiequilibrium state in the superfluid
helium is exceeded in a locally heated cooling channel the large momentary
temperature excursion is followed by a transient recovery even if the initial pulse is
continued with a postheating amplitude above the steady-state limiting flux. This
behavior which is not observed in normal boiling helium should allow considerable
improvement of stability in magnets cooled with superfluid helium. On the other
band, if a permanent heat flux is suddenly switched on in the normal boiling helium, a
new limiting heat flux value below the well-known peak nucleate boiling flux appears
which cannot be exceeded without jumping into the film boiling region.
Results already show that transient heat transfer in subcooled superfluid helium
considerably increases the overall heat transfer properties above the steady-state
performance. The corresponding contribution of normal boiling helium appears
quite small in this respect. The decisive advantage of subcooled superfluid helium is
based on its large exploitable enthalpy reservoir.
REFERENCES
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
Y. lwasa, M. J. Leupold, and J. E. C. Williams, IEEE Trans. Magn. Mag-13(1):20 (1977).
0. Tsukamoto and S. Kobayashi, J. Appl. Phys. 46(3):1359 (1975).
Y. Iwasa and B. A. Apgar, Cryogenics 18(5):267 (1978).
W. G. Steward, Intern. J. Heat Mass Transfer 21:863 (1978).
C. Schmidt, Appl. Phys. Lett. 3%(12):827 (1978).
H. Kobayashi, K. Yasuköchi, and K. Tokuyama, in Proc. 6th Intern. Cryogenic Engineering Conference, IPC Science & Technology Press, Guildford, England (1977), p. 301.
S. W. Van Seiver and 0. Christianson, in Proc. 7th Intern. Cryogenic Engineering Conference, IPC
Science & Technology Press, Guildford, England (1979), p. 228; also Cryogenics 18(9):521 (1978).
H. Kobayashi and K. Yasukochi, Cryogenics 19(2):93 (1979).
D. Gentile and W. V. Massenzahl, in Advances in Cryogenic Engineering, Vol. 25, Plenum Press,
New York (1980), p. 385.
G. Bon Mardion, G. Claudet, P. Seyfert, and J. Verdier, in Advances in Cryogenic Engineering, Vol.
23, Plenum Press, New York (1978), p. 358.
J. Maynard, Phys. Rev. B 14(9):3868 (1976).
G. Claudet, C. Meuris, J. Parain, and"B. Turck, IEEE Trans. Magn. Mag-15(1):340 (1979).
G-5
HEAT TRANSFER MEASUREMENT WITH
A SMALL SUPERCONDUCTING COIL
SUBJECTED TO TRANSIENT AND
QUASISTATIC HEATING AT TEMPERATURES
BETWEEN 1.8 AND 4.2 K
D. Gentile
Centre d'Etudes Nucleaires de Saclay
Saclay, France
and
W. V. Hassenzahl
Los Alamos Scientific Labaratory
Los Alamos, New Mexico
INTRODUCTION
This paper reports results of some heat transfer experiments with a small,
noninductively wound coil constructed of a monofilamentary, copper-stabilized,
NbTi superconductor. These experiments have been made in helium at different
temperatures, particularly at 1.8 and 4.2 K. The 1.8-K measurements were performed at the equilibrium vapor pressure and atmospheric pressure. The different
tests were in the quasistatic and transient heat transfer regimes. To determine the
surface temperature and calculate heat transfer coefficients in helium, it was necessary to measure certain physical characteristics of the conductor. These preliminary
tests are described briefty in the first section and references are given to publications
describing each experiment. The method of measuring temperatures using
monofilamentary conductor was described elsewhere [ 1- 3 ].
EXPERIMENTAL PROCEDURE
Apparatus
Two identical, noninductively wound coils of a monofilamentary, copperstabilized, NbTi conductor on a 10-mm-diameter, 14-mm-long stainless steel
mandrei were used for the measurements. The radial dimensions of the conductor
are superconductor, 36-#-1-m diameter, copper, 55-#-1-m diameter, and insulation,
65-#-1-m diameter. For the heat transfer tests the insulation was removed; but, to have
good insulation between turns, a 65-#-1-m-diameter nylon monofilamentary spacer
385
D. Geadle aad W. V.IIMieiiZÜI
was wound between turns of the superconductor. Each sample bad 101 turns wound
from 3.20 m of conductor. The conductor and insulation of one coil were glued to the
mandrel; the other bad only a thin insulating layer between the coil and mandrel.
Significant ditferences were detected between the heat transfer characteristics of the
two coils.
Before discussing the results, it is worth noting immediately that the surfaces of
these samples were quite irregular with an area of about 2.45 cm2 • If, instead of
considering all of the exposed surface, only the surface of the coil covered by the
conductor is considered, the area is reduced to about 1.56 cm2 • Heat transfer
between a surface and a fluid is normally ~ven as a function of the heated surface.
For these calculations a surface of 2.00 cm was used. For transient measurements,
the etfective surface is probably closer to 2.45 cm2 , andin the film boiling regime for
steady-state conditions it is certainly closer to 1.56 cm2 •
Measurement Method
The purpose of these experiments is to determine the heat transfer mechanism
between a solid and helium. This measurement is accomplished by generating a heat
ftux in the sample and obtaining a heat exchange coefficient based on the surface
temperature.
This method, which uses the superconductor as both sensor and heater, was
developed at Saclay by Schmidt [4 ]. It is based on the fact that current in a
superconductor decreases linearly with increasing temperature above Tc and that at
constant temperature the longitudinal electric field in the superconductor increases
exponentially with the transport current eJ. The physical constants of the conductor'
such as critical temperature, critical magnetic field, magnetoresistivity of copper and
current/voltage characteristics of the conductor must be determined precisely to
apply this method. These characteristics are described in a separate report [6 ].
A previous publication has indicated that the systematic error due to the
knowledge of the physical constants was about 0.1 K. Other errors in calculating
temperature are due to the inaccuracies in the method of measuring voltages across
the coil. The maximum error is estimated to be less than 0.5 K.
EXPERIMENTAL RESULTS
Qnasistatic Beat Transfer Regime
This section describes the steady-state heat transfer for three different conditions: 4.2 K, saturated bath; 1.6 K, saturated bath; and 1.8 K, atmospheric pressure.
An electric method is used to obtain the heat ftux, q, vs. the temperature ditference,
llT = Ts- TB, where Ts is the surface temperature and TB is the bath temperature.
From the voltage/current characteristic of the conductor in a constant background
magnetic field, one can deduce the heat transfer characteristic from the Joule heat
generated in the sample and dissipated in the bath, q = UI/ S, where U is the voltage
across the coil, I is the transport current, and S is the wetted surface (==2 cm2 ). The
surface temperature relation was developed earlier as C]
Tc- TB
(
E
E)
Ts = TB + Ia, + ß ln(E/ Eo) Ia, + ß In Eo -I + RN
(1)
where Ts is the surface temperature, TB is the bath temperature, Tc is the critical
temperature, Eis the longitudinal electric field in the conductor, Ico is the critical
Heat Transfer Measurement with a Small Superconducting Coil
387
1o r--------+--------~--------r-~
i
......... GOOOLN>An> I<EY,l : 1.8(12K,CO!'PER
- - - GOOOLN3An) IREY, T:1.55 K, COPPER
T:l8K - .../
I i ...
......_ B: 3l,T: 1,621(,c:a.c..tated witl>~ :a.3634AIK(oor~·
I
- ·-
T: , .ZK(our r051Jts)
T: 1.8K--i'------- -- + - - - -- --=ic-t?-if---i
X
~ 1)_, r--------+---------t;-:__,.;LfYL--ir"'"~
!;t
ILI
:r
2 3
l>T, K
Fig. 1. Steady-state heat transfer characteristics at three
different temperatures.
current corresponding to an electric field E 0 of 1 JL VI cm, ß is the change in current in
the conductor when the field changes by one decade (tll = 0.016A), I is the
transport current in the conductor, and RN is the normal resistance of the copper in
parallel with the superconductor.
Figure 1 shows the results of these measurements and also those of Goodling
and Irey CJ at 3 T. The curves are very similar; nevertheless, note that the curve for
the new data increases more quickly for q > 0.1 WI cm2 •
Supposing that the exchanged flux is q = h(tlT)", the data in Fig. 1 give
n = 1.06 and h = 0.3 W I cm2 K. During the current rise, a weak heating was noted in
the helium bath at 1.6 K. At the beginning, the bath temperature was 1.6 K,
corresponding to a transport current of 3 A and just before the transition to film
boiling, it was 1. 7 K for a current of 5 A.
The 4.2-K curve is nearlyidentical to the 1.6-K curve below a flux of 0.1 W lcm 2 ,
but there is a significant difference in the peak nucleate boiling maximum. At 4.2 K
the peak nucleate boiling maximum is about 0.8 W lcm 2 ; at 1.6 K it is about
4 Wlcm 2 •
Other measurements were made at T8 = 1.8 K under atmospheric pressure [8 ].
A maximum heat flux was found before the transition of about 9 WI cm2 , which is
much higher than the previously measured values for a temperature difference of
about 2.5 K. This curve gives a heat transfer coefficient of
h = lim qT· = 0.89Wicm2 -K
4T-O/l
(2)
388
D. GentUe and W. V. Hassenzahl
soo...w
so...w
I-
1'\.
V '-
u-
Fig. 2. Voltage across and current in the sample during a 40-ms
pulse.
Sms
Transient Heat Transfer in an Infinite Bath
In a transient heat transfer study, heat pulses of 10 f-'S to 10 ms were produced in
the sample and the voltage recorded across the sample and across a series shunt
resistor. These two voltages, which are shown in Fig. 2, determine Ieo and I for use in
(1). Figure 3 shows the conductor surface temperature calculated with (1) as a
function of time for various values of q. The temperature remains nearly constant for
heat ftuxes below the steady-state maximum ftux, about 10 W /cm 2 • Above this ftux
the temperature is constant for a time, ft. and then rises quickly and passes the critical
temperature, Tc, above which (1) is no Ionger valid.
25.7
7
21 .3W/cm1
W/cm2
6
•
5
3
.zs.lJ',
---•- -+-+-+r
Wfaril
2 o~.~--------~I.~
0 ----------10~--~
t ,m5
Fig. 3. Conductor surface temperature vs. time,
with heat ftux as a parameter. Bath temperature is
atl.SK.
389
Heat Transfer Measurement with a Small Superconduc:ting Coil
Table I. Coefficients for Heat Transfer in a 1.8-K, 1-Atm LiquidHelium Bath
q,
a,
W/cm 2
Ts,
K
W/cm 2 K 4
Ts-TB
TB
hKfh<].
hK
0.57
1.07
2.9
7.87
16
17.3
19
21.3
25.7
30
37
44
2.56
2.98
3.75
4.35
4.9
5
5.51
5.66
6.05
6.4
6.8
7
0.018
0.016
0.0155
0.023
0.028
0.0282
0.021
0.021
0.0194
0.018
0.0174
0.0185
0.422
0.656
1.083
1.417
1.722
1.778
2.061
2.144
2.361
2.556
2.778
2.889
1.83
2.485
4.115
5.845
7.825
8.233
10.53
11.28
13.41
15.54
18.24
19.71
0.75
0.91
1.48
3.08
5.16
5.4
5.12
5.52
6.04
6.52
7.4
8.46
The time constants of the coil and conductor, in particular for the heat transport
in the NbTi, are on the order of a few microseconds. The classicallaw that the heat
flux is proportional to the difference T1 - T~ has been verified. If Tn remains
constant and Ts is taken at about 1 ms on the curves of Fig. 3, q may be expressedas
q = a(T1-
T~)
(3)
Table I gives the values for a. This result and the Kapitza theory may be compared.
The Kapitza conductance, hK, is given by
!!..T 2
3 !!..T
[
.
hK=_!!_=4aT11+-(-)+(-)
Tn
2 Tn
!!..T
1 !!..T
+-(-)
4 Tn
3
]
(4)
where 4aT1 = hCJc = lim.1r-+o (q/ !!..T), and limH-+O (hK! hCJc) ~ 1. For Ts > TA,
hK/hCJc increases quickly, which is probably caused by a small helium-1 layer at the
solid surface. As heat ftux is increased, the He-1/He-11 interface is not weil defined,
and finally apart of the heat ftux, above a certain value qmax. vaporizes the He-l film.
Because gas is a good insulation, the removal of the heat from the surface is not very
good and the temperature difference increases quickly. This flux, qmax• referred to by
4
12 10 8.5 6.7
4.3
4W/crn 2
2.9W/cm 2
~:JJJL ~--·
'.s
Fig. 4. Conductor surface temperature vs. time, with heat
flux as a parameter. Bath temperature is at 4.2 K.
390
D. Gentile and W. V. Hassenzahl
/I
yJ
1.5
:.::_ 1.0
Cl>
0.5
v-
0
4
8
I
12
Q. w/cm 2
Pannetier et al. [ 11 ] is between 1 and 10 Wlcm 2 and is a function of temperature,
pressure, geometry, orientation, and immersion depth of the sample. For
comparison, similar results are presented at 4.2 K. Figure 4 shows the temperature
difference between the conductor and the helium bath vs. time. Note that the
temperature is nearly constant for a time and then rises very quickly to the critical
temperature. This rapid temperature increase is due to the onset of film boiling.
The initial stable value of Ts is given in Fig. 5 and is proportional to q. The heat
transfer can thus be described by a single heat transfer coefficient for all q values,
h = qiT; = 6 Wlcm 2 -K, which is in agreement with the Kapitza conductance.
The classical law of thermal conduction that the heat ftux, q, follows a t- 112
dependence has also been verified. The solution to the classical heat equation gives a
relation between q and t of q = TrLD 112 t- 112 , where L is the heat of vaporization
(2.4 Jlcm 3 ) and Dis the thermal diffusivity (5 x 10-4 cm 2 ls). This formula gives a q
that is a factor 2 above the present experimental results. This agreement is satisfactory because the theory corresponds to exchange on a ftat surface. The difference
is probably a result of geometric factors. To sum up, the total energy transferred
before onset of film boiling is q = TrLD 112 I t 112 - 0.2 J I cm 2 for t < 1 ms. The heat
transfer coefficient is about 6Wicm 2 -K for transient and 0.5Wicm2 -K for
steady-state conditions.
Transient Heat Transfer in Helium Channels
Similar experiments were made with the same coils cooled by He-Il in 1- and
2-mm-thick, concentric channels. To avoid damaging the coil or the helium
container, which could occur if the energy deposited were greater than the maximum
that could be evacuated, the power deposited in the sample was first fixed for a very
short pulse and then the pulse duration was increased until a transition occurred in
the sample. Figures 6a and 6b show the evolution of the conductor temperature vs.
time.
The voltage observed across the coil is nearly constant foratimethat depends on
the power, then it rises very quickly to another plateau that indicates the critical
temperature has been exceeded. After this plateau is reached, the dissipated power
still remains nearly constant because the current is automatically decreased as the
resistance and voltage increase. For power dissipation larger than about 9 W I cm2 ,
the plateaus in voltage and temperature are almost nonexistent and the temperature
rise comes very quickly after the beginning of the pulse.
The curves of Figs. 6a and 6b indicate that there may be two different heat
transfer mechanisms, depending on the value of the heat ftux. Below 9 W lcm 2 the
temperature is constant until the transition; above about 9 W lcm 2 the temperature
Heat Transfer Measurement with a Small Superconductina Coil
391
8
~ 6
...:
5
50
60
10
(a)
w---------~~
3 ~-------~=-------~
t . ms
(b)
Fig. 6. Evolution of the conductor temperature vs. time
for (a) 1-mm and (b) 2-mm channels. Bath temperature is
at 1.8 K and pressure is 1 atm.
of the helium near the conductor increases immediately to the critical temperature.
Also, the transfer is better with a larger channel.
One Iimit on the energy that can be accepted by the helium in the channel is fixed
by the total enthalpy available between the bath temperature and the transition
temperature. After this amount of energy has been deposited in the helium, the heat
transfer should decrease very quickly. This energy is
f
2 . 17K
Eo
= Vch
1.8 K
pCdT
(5)
where p is the density, Cis the specific heat, and Vch is the volume of the channel.
Figure 7 is a comparison of the Iimit, E 0 , and the amount of energy that was
2
deposited in the helium before a transition occurred. For fluxes above 9 W /cm the
product of the power and time before the break in the voltage curve of Fig. 2 was
taken as the deposited energy.
CONCLUSION S
The method of measurement used here has the advantage of a relatively fast
response time and makes possible the study of heat transfer with high fluxes with
392
D. Gentile and W. V. Hauenzahl
0
UJ
~0.5
5
10
0 .w/cm 2
Fig. 7. Normalized energy that can be absorbed in a channel
vs. generated power.
neither separate beater nor separate tbermometer. From tbe experimental results
using tbis metbod it appears tbat a quasistatic beat ftux of about 1 W/cm2 can be
maintained in 4.2 K liquid belium, wbereas 10 W/cm 2 can be sustained at 1.8 K
under a pressure of 1 atm. Experiments in a belium batb at 4.2 and 1.8 K sbow tbat a
ftux bigber tban tbe steady-state beat ftux can be maintained for a period tbat
decreases as tbe beat ftux increases. Tbe product of pulse lengtb and pulse power
decreases witb increasing power. A new pbenomenon bas been observed in tbe
experiments witb belium cbannels. Tbere is probably a cbange in tbe beat-transfer
mecbanism wben tbe beat ftux into tbe cbannel is bigber tban tbe static beat-ftux Iimit
in an infinite batb. To explain tbis pbenomenon, it will be necessary to investigate tbe
propagation of beat in He-II.
ACKNOWLEDGMENTS
The authors wish to thank G. Claudet and P. Seyfert of the CEN/Grenoble for their suggestions and
auistance during these experiments.
REFERENCES
1. W. Hauenzahl, D. Gentile, and M. Polak, "A Method of Determining Temperatures and Heat
Transfer Coefficients with a Superconductive Sample," tobe published in J. Appl. Phys.
2. D. Gentile, W. Hauenzahl, and M. Polak, "Heating of Monofilamentary NbTi Superconductors in
tbe Current Sbaring State," CEN/Saclay Rept. Supra 78-73 (1978).
3. D. Gentile, W. Hassenzabl, and M. Polak, Cryogenics 20(1):37 (1980).
4. C. Scbmidt, Appl. Phys. Len. 32(12):827 (1978).
5. M. Polak, I. Hlasnik, and L. Krempasky, Cryogenics 13(12):702 (1973).
6. D. Gentile, W. Hauenzahl, and M. Polak, "Cbaracteristiques d'un monofilament de NbTi a
temp6ratures inferieures a 4.2 K," CEN/Saclay Rept. Supra 79-15 (1979).
7. J. S. Goodling and R. K. lrey, in Advances in Cryogenic Engineering, Vol. 14, Plenum Press, New
York (1969), p. 159.
8. D. Gentile and W. Hassenzabl, "Exchanges tbermiques entre un echantillon supraconducteur et
l'belium superfluide sous pression atmospberique," CEN/Saclay Rept. Supra 79-02 (1979).
9. L. J. Cballis, private communication.
10. D. Gentile, "Etude du transfert thermique entre un echantillon supraconducteur et l'belium en
regime transitoire," CEN/Saclay Rept. Supra 78-43 (1978).
11. B. Pannetier, J. Phys. (Paris), supplement au No. 10, Colloque C4 (1972), p. C4.
12. 0. Tsukamoto and S. Kobayashi, Jpn . J. Appl. Phys. 46:1359 (1975).
G-6
HEAT TRANSFER OF HELIUM IN
A PIPE WITH SUCTION
L. L. Vasiliev, G. I. Bobrova, and L. A. Stasevieh
The Luikov Heat and Mass Transfer Institute
Minsk, BSSR, U.S.S.R.
The development of effective means of cooling helium is presently of great
significance. The enhancement of such heat transfer and, particularly that due to
suction of the fluid through a permeable channel wall has been the subject of many
publications.
The available Iiterature shows that such sturlies of heat transfer have involved
fluid flowing in different geometry channels to determine whether it is possible to
enhance this heat transfer process by permitting suction of some of the fluid through
the permeable channel wall. Most of these sturlies involve theoretical analyses of the
process. The emphasis has been on laminar flow. This is presumably because the
theoretical analysis of laminar flow is simpler and more tractable than turbulent flow.
The number of experimental studies, however, is limited.
Equations applicable for motion, continuity, and energy were used to analyze
the steady-state laminar heat transfer. It was shown C· 2 ] about thirty years ago that
the motion equation for fully developed laminar flow in tubes with suction or
injection through a permeable channel wall may be reduced to a nonlinear differential equation of the fourth order. These investigations were later extended, supplemented, and published 4 ].
Since suction enhances heat transfer in a porous channel flow, previous investigators have focused their attention not only on the solution of the fluid dynamics
problern but also on the effect of suction on the temperature distribution along the
porous pipe radius and length. Thus, Yuan et al. [3 ] have studied the effect of low
injection velocities of the fluid through the porous wall on the wall temperature
distribution. Temperature profiles have been calculated by Pederson et al. [5 ] for a
flow moving inside a porous pipe at a constant wall temperature. Baithby [6 ], on the
other band, studied the fluid dynamics and heat transfer for a constant wall
temperature and heat flux; an analysis was made of the effect of injection, suction,
and channel geometry on temperature and velocity profiles. It is readily apparent
that a comprehensive study of heat transfer of a fluid flowing in permeable pipes, i.e.,
with suction and injection, involves a great deal of difficulties; understanding of this
problern even for laminar flow is still incomplete at this time.
For turbulent heat transfer the problern is much more complicated. In this case
both suction and injection strongly affect fluid dynamics and heat transfer. The effect
of surface suction of heat and mass transfer characteristics for turbulent pipe flow in
pipes has been studied analytically by Kinney et al. Cl. These authors have shown
e·
393
394
L. L. Vuiliev, G. I. Bobrova, aad L. A. Sauevieh
Fig. 1. Experimental arrangement.
that suction exerts considerable influence on the Nusselt number, friction
coefficients, and velocity profiles.
At present, porous heat exchangers find wide use in electric and cryogenic
devices. Their design requires a knowledge of the heat transfer coefficient. Therefore, it is important to experimentally verify the analytical relationships that describe
turbulent heat transfer to rarefied gases in pipes subjected to suction and injection.
There are few studies that verify the theoretical predictions with experimental
results. The knowledge in this field also is insufficient to soggest some simple and
reliable methods for estimating heat transfer efficiency in porous heat exchangers.
This present study is designed to provide additional experimental data on the effect
of suction on the heat transfer of helium flowing inside a porous ceramic pipe.
Figure 1 shows the experimental equipment; it consists of a traditional horizontal cryostat described elsewhere [8 ] . This device consists of a 5-m-long cryostat (2),
pump (6), power supply (1), rotameter (7), gas meters (8), and recording unit (9). The
test volume consisted of a 650-mm-long thin-walled stainless pipe, 40 mm in
diameter (Fig. 2). The tubewas surrounded with a nitrogen screen (1). A vacuum
between the tube and screen served as insulation; the residual gas pressure in the
vacuum space was maintained at about 10-5 mm Hg.
The nitrogen screen and test volume were placed inside of a 120-mm-diameter
pipe (3), which was maintained at room temperature and thermally insulated from
the nitrogen bath by means of vacuum insulation. A porous electrically heated tube
(5) was located along the axis of the test volume. An adiabatic screen (4) placed 5 mm
from the external pipe surface was kept at a temperature between 1 and 2 K, the
same as the porous wall temperature. To compensate for temperature deformation,
all tubes were fitted with end bushings. Helium at moderate excess pressure, supplied
from a 40-liter dewar (3) (Fig. 1), was firsttransferred through a thermally insulated
region to achieve hydrodynamic stabilization of the flow before being transferred
through the porous tube. As the fluid moved down the porous tube, some of the fluid
entered the peripheral channel through the permeable wall. The flow in the centrat
and peripheral channels was regulated by valves (4) (see Fig. 1). Gas flow rates were
regulated by PC-5 rotameters (7) and then measured by PI-40 gas counters (8)
placed in series with the rotameters. From the gas counters the heliumwas returned
to the cooling system. The rotameters were used mainly to regulate the flow, i.e., a
deviation of the indicating float from the prescribed Ievel indicated a change in the
fluid discharge at the inlet of the porous tube. Preliminary measurements of the
pressure drop along the length of the porous tube indicated valuesrangingfrom 0.01
to 0.1 atm. Therefore, to simplify the experimental device and measuring system,
pressure was monitored in the centrat and peripheral channels using standard
MO-type manometers and having a scale division of 0.005 atm (Fig. 2).
Heat Transfer of Helium in a Pipe with Sudion
395
Fig. 2. Detail of porous tube.
The porous tubes were fabricated by sintering spherical bronze powder (0.2 to
0.315-mm-diameter particles). The porosity of the tube wall varied from 28% to
40% ; the permeability coefficient was equal to 7 x 10-8 cm 2 , the maximum pore size
was 190 ~m, while the mean pore size was 60 ~m. The tubewas 600 mm long with an
inner diameter of 12 mm and an outer diameter of 17 mm. Tobe passive section with
1/d = 300 was also 12 mm in diameter. Heat was supplied to the tube by direct
current from a BY 12/600-type rectifier.
The temperature was measured with copper-copper plus iron thermocouples
(6) (Fig. 2) utilizing 0.3-mm-thick electrodes. The thermocouples, spaced 100 mm
apart, were embedded ftush with the porous tube wall. Bach thermocouple junction
was located on the internal tube surface.
During the experiment, measurements were obtained for the porous wall
temperature, screen temperature, inlet and outlet ftow temperatures, ftow rates of
nitrogen and helium along the tube and for that drawn through the wall into the
peripheral channel, current intensity, and voltage to the heaters of the porous wall
and screen. The internal porous wall and screen temperatures were kept constant by
regulating the voltage supplied to the test tube and screen. Thus, there was no radial
temperature drop in the space around the porous tube. This arrangement permitted
easy estimation of the heat ftux.
The power input to the porous tube was removed partially by the helium ftow
along the tube axis and partially by the fluid drawn through the wall; the latter is
given by q = MsCp a r. where M. is the mass of the withdrawn gas, Cp is the heat
capacity, and ar. is the measured temperature difference of the gas withdrawn
before and after it enters the porous wall.
t'L
Tx T
'
~
6
Fig. 3. Temperature distribution along porous tube for different
rates of fluid withdrawal through the wall at Re; 0 = 2.4 x 104 •
Legend: 1, G = 0.3 g/s; 2, G = 0.25 g/s; 3, G = 0.2 g/s; and
4, G = 0.15 g/s.
2
0
I
I
V
/
v
V
~
V
-
_.....
V
1 /~ ....., Ir:::: '=100
200
500
400
~
I
L.mm
L. L. Vasillev, G. I. Bobrova, and L. A. Stasevieh
396
00
500
400
~00
200
100
/
0.10
/
V
0. 15
I
I
f/
0.20
I
I
0.25
C,g/s
Fig. 4. Average Nusselt nurober along tube length versus rate of
fluid withdrawal.
When .1 T, is zero, as in this study, the heat ftux density was determined as the
power per unit thermal surface of the porous tube. Figure 3 presents the experimental temperature distribution along the porous tube for different rates of fluid
withdrawal through the porous wall when the helium ftow rate at the porous tube
inlet was held constant at a Reynolds number of 2.4 x 104 • The Reynolds number in
this case was computed in terms of the velocity at the porous tube inlet. The velocity
was defined as V = V/ F, where V is the helium ftow rate at the inlet. The viscosity of
helium and other physical parameters were evaluated at a temperature of 10 K. The
inlet helium pressure was fixed at 1.1 atm while the outlet pressure was 1.05 atm.
The Nusselt number was calculated in the following manner. The average heat
transfer coefficient along the porous tubewas determined for each condition and the
heliumthermal conductivity was estimated at 10 K. This average Nusselt number
along the tube is presented in Fig. 4. With increasing suction through the wall, the
temperature along the tube decreased. This was valid over the range of Reynolds
numbers encountered (1.6 x 104 to 4.5 x 104 ). There was no marked effect of wall
porosity on the temperature profile within the temperature range investigated.
Temperature distributions along the tube and Nusselt numbers were compared
with similar relations obtained by Aggarwal and Hollingsnorth [9 ]. The latter
presented results for heat transfer in a porous tube with air and noted that at a fixed
Reynolds number for the inlet ftow, the Nusselt number increases with increased
suction. The temperature distribution along a porous tube and the Nusselt number as
a function of the suction obtained by those authors are similar to the data presented
in Figs. 3 and 4. In other words, the suction effect on the temperature distribution and
the heat transfer coefficients for air and helium appear to be the same.
NOTATION
G=
I=
M, =
Nu =
quantity of heliuro drawn through porous wall
porous tube length
roass of gas withdrawn
Nusseil nurober
q = heat ftux density
Re = Reynolds nurober
T = teroperature of internal porous tube surface
T0 = starting length teroperature
V = heliuro ftow rate at porous tube inlet
F = cross-sectional area of porous tube
Heat Transfer of Helium in a Pipe with Suction
397
REFERENCES
J. R. Sellars, J. App/. Phys. 26:489 (1955).
A. S. Berrnan, J. Appl. Phys. 24:9 (1953).
S. W. Yuan and A. B. Finkelstein, Trans. ASME 78:4 (1956).
R. Kinney, Intern. J. Heat Mass Transfer 11:9 (1969).
R. Y. Pederson and R. Kinney, Intern. J. Heat Mass Transfer 14:1 (1971).
G. Baithby, Intern. J. Heat Mass Transfer 14:1 (1971).
R. Kinney and E. Sparrow, Trans. ASME (Ser. C) (2):121 (1970).
G. I. Bobrova and V. A. Morgun, in Heat and Mass Transfer af Cryagenic Fluids in Paraus Heat
Exchangers, Izd. ITMO AN BSSR, Minsk, U.S.S.R. (1974), p. 63.
9. J. K. Aggarwal and M. A. Hollingsnorth, Intern. J. Heat Mass Transfer 16:591 (1973).
1.
2.
3.
4.
5.
6.
7.
8.
G-7
BEAT TRANSFER AND HELIUM
REPLENISHMENT IN CABLED
CONDUCTOR COOLING CHANNELS*
P. F. Michaelson, R. Quay, and R. F. Koenig
General Electric Company
Schenectady, New York
and
P. L. Walstrom and J. S. Goddard
Oak Ridge National Laboratory
Oak Ridge, Tennessee
In the design of the superconducting conductor for the Large Coil Program
(LCP) test coil, which is a large magnet cooled by pool boiling in liquid helium and
operated with its bore axis horizontal, it is necessary to know the heat transfer
capabilities of the conductor as a function of orientation (i.e., location along the coil
perimeter) in the hydrodynamic environment of the magnet winding. In addition to
conductor orientation, the conductor configuration and winding ventilation might be
expected to affect the rate of removal of Joule heat from the stabilizer. This rate is
important in the event of an incident which drives the conductor normal because the
rate must be high enough to permit the conductor to recover to its superconducting
condition. Early research by others [1-6] suggested that allowable heat ftuxes for
recovery from a normalcy in a horizontally oriented conductor surface region of the
magnet winding may be half or less of those of vertically oriented regions.
This test was pedormed to determine the effects of orientation on the steadystate recovery heat ftux, and on possible hysteresis in the helium boiling curve, for
two sample configurations, each configuration consisting of a set or array of Large
Coil Segment (LCS) test conductor bars, one set with and one set without holes
through its cores. The LCS conductor is a prototype of the GE-LCP conductor, with
cooling channels twice as wide as the LCP conductor's.
The LCP conductor and the existing LCS conductor have stlbelements cabled
and soldered about a copper core as shown in Fig. 1. The subelements are a
composite of a superconductor element Iaminated into a grooved copper stabilizer.
The LCS conductor was used for this test because it is similar to the LCP conductor
and was available.
* Work supported by the U. S. Department of Energy under contract No. W-7405-eng-26 with the Union
Carbide Corporation.
398
Heat Transfer and Helium Replenishment in Cabled Conductor Cooling Channels
399
Fig. 1. LCS conductor.
TEST PROCEDURE
The test sample was a three column by ten row array of 30.5-cm-long dummy
(nonsuperconducting) LCS conductor bars with insulating spacers between rows and
columns, simulating the GE-LCP test coil winding cross section (Fig. 2). The sample
is long compared to the important cooling channellength (13 cm); this is the distance
between intersections of the subelement grooves and the grooves in the insulating
spacers between columns (Fig. 3). The sample was prepared at GE, and sent to
ORNL where it was instrumented and tested. Heaters were installed in two of the
conductor bars. The heaters, magnesium oxide insulated Niebrome wires with an
outer sheath of Inconel, were soldered into the fulllength of the groove in ten of the
eleven subelements of each of the two heated bars.
In one of the two heated conductor bars, transverse holes approximately 2 mm
in diameter were drilled through the copper core between subelements to enhance
helium circulation. The turn-to-turn insulation and the LCS bars above and below
this conductor were also provided with transverse holes with a random spatial
relationship to the holes in the heated conductor bar.
Differential Au 0.07 at. %Fe vs. Cu thermocouples were then installed. The
reference junctions were located in the helium bath below the test assembly, to avoid
vapor from the heated bars. A total of twelve thermocouples were installed on each
of the two heated bars; in addition, a thermocouple was installed on each of the four
bars surrounding each of the two heated bars. The thermocouple locations on each of
the heated bars included the heated subelements, the unheated subelement, and the
core. After being instrumented, the bars were assembled into the steel support
fixture, as shown in Fig. 2.
The cover plate was bolted on using a torque such that the pressure on the test
bars during the test would be the same as that expected on the conductors in the LCP
400
P. F. Micbaelson, R. Quay, R. F. Koenig, P. L. Walstrom, and J. S. Goddard
t2 '" ·
HEATED SPECtMENS
LCP PAN GAKE - TO-PANCAKE
tNSULATION
~.._....-- GE
SLOT
OPPER CORE
I
HOLES ORILLED THROUGH CORE
( LOWER SPECIMEN ONL Y)
Fig. 2. Sampie geometry, simulating the LCP test coil winding cross section. Sampie bar orientation shown
is horizontal (angle= 0°).
test coil durlog operation. This was done so that the heat transfer from the heated
conductor to the adjacent unheated conductors in the test would simulate that in
service in the test coil.
The instrumented fixture was mounted on a pivot mechanism attached to the
dewar header (top ftange), which allowed the sample orientation tobe changed to
known angles from outside the dewar. The apparatus was precooled with liquid
nitrogen, then cooled with helium.
Data of the heat ftux vs. temperature difference between the various sample
locations and the helium bath were measured by applying power to the heaters while
monitorlog the thermocouple outputs. Power data and thermocouple voltages were
recorded by a fast multichannel digital system after amplification with differential
amplifiers (Fig. 4).
The heater current was programmed in either a square-wave shape or a
staircase-up, staircase-down waveform (Fig. 5). Each step in the heater power
staircase was three seconds in width. This duration was sufficiently long that
steady-state temperatures were reached by all thermocouples, with rare exceptions,
before a change to a new heater power level (Fig. 6). The measurements were taken
at both increasing and decreasing heater power steps in order to detect any hysteresis
in the liquid helium boiling curve.
The steady-state helium boiling curve for increasing and decreasing heater
powerlevelswas measured for one sample set at one orientation by this process. The
Heat Transfer and Helium Replenishment in Cabled Conductor Coollog Cbannels
Fig. 3. Majordetails oftheLarge Coil Programtest coil.
401
P. F. Mlchaelson, R. Quay, R. F. Koenig, P. L. Walstrom, and J. S. Goddard
401
16 THERMOCOUPLE
4 CHANNEL
BIOMATION
TRANSIE NT
RECORDER
X-Y
RECORDER
CHANNELS
....
0
<
...J
..,
~
Cu
>----"'+l ~
u
Au-Fe
TEST
SPECIMEN
POP 11/03
MICROCOMPUTER
FLOPPY
DISC
<t
cD
CURRENTSENSING
RESISTOR
MICROPROCESSORFUNCTION
GENERATOR
Fig. 4. Schematic of measurement apparatus.
Fig. 4. Schematic of measurement apparatus.
Fig. 5. Example of heater power Ievel vs. time ; power Ievel at maximum step
is 145 W for this run.
Heat Transfer and Helium Replenishment in Cabled Conductor Cooling Channels
403
Fig. 6. Example of thermocouple voltage vs. time; l:lT at maximum step is
8.5 K for this run.
process was repeated for both sample sets, with each heated separately, for each
angle of orientation. The recovery heat ftux was calculated by dividing the heater
power at the point of abrupt slope change ("knee") in the boiling curve by the
product of the length and cooled perimeter of the heated bar.
The LCS conductor has a cooled perimeter of 100 mm, located along the wetted
surfaces of the cooling channels. These channels are 3 mm wide by 3 mm high by
130 mm long. The entire boiling curve is required for any complete stability analysis
of a conductor, but the recovery heat ftux may be used for a quick comparison
between experimental results.
TEST RESULTS AND DISCUSSION
The steady-state helium boiiing curves obtained in this test are presented in
Figs. 7 and 8. Also given in each figure are the corresponding values for the recovery
heat ftux vs. angle of orientation of the conductors.
Very few of the heat steps displayed any hysteresis and the amount was small (a
few percent or less) when present at all. "Hysteresis" herein is defined as different
heat transfer rates at a given tl T between the sample surface and the coolant bath,
depending on whether the sample temperature was rising or falling with time.
Temperature gradients along the heated sample as weil as across the solder interfaces
between the subelements and the core were small (a few percent or so) compared to
the temperature difference between the sample and the helium bath, even though the
ends of the heated bar were not insulated from the helium bath. At high power Ievels
in the horizontal orientation, there was some heating (0.1 to 0.3 K) of the bars
immediately above the heated bar.
The magnitude of the experimental uncertainty in heater power vs. temperature
is approximated by the size of the open circles used for each data point shown in Figs.
7 and 8. The uncertainty in the heat ftux values is estimated as ± 10%, with
404
P. F. Mlthaelson, R. Quay, R. F. Koenlg, P. L. Walstrom, and J. S. Goddard
180
SAMPLE WITH NO TRANSVERSE HOLES
160
9
2
•
Omm (W/cm )
0 . 18
0 . 22
0 .24
0 . 25
140
~
5
~
120
100
0
0.
er:
80
w
f-
<I
w
60
I
40
20
0
2
0
3
7
6
5
4
9
8
1t
tO
6T , K
Fig. 7. Steady-state helium boiling curve; sample without transverse
holes.
approximately half of this arising from the uncertainty in the cooled perimeter of the
LCS conductor, and half arising from uncertainty in the amount of heat conducted to
the adjacent bars and off the ends of the bars.
A study of transient heat transfer effects may help in assessing the likelihood of
formation of a temporary normalcy. Such data are useful in general, but arenot
needed for the LCP test coil, so this test was not designed to systematically study
transient effects. However, some general or qualitative information may be extracted
180
SAMPLE WITH TRANSVERSE HOLES
160
140
~
t20
cr:
~ tOO
0
0.
er:
w
80
I-
<I
w
•
9
60
Om;n ( W/cm
o·
I
10•
0 .27
20
20°
45"
0 .30
0 . 33
0.33
90"
0
2
4
5
6
7
)
0.26
40
0
2
8
9
10
II
6T,K
Fig. 8. Steady-state helium boiling curve; sample with transverse holes.
Beat Trausfer and HeUum Replellishment in Cabled Conduetor CooUng Chaneis
405
from the data. For example, most of the heater Ievel steps produced thermocouple
signals with no visible transient content, and this is true of the example signal of Fig.
6. However, a few of the square wave traces, taken with a high data sampling rate, did
show transients for both of the samples (holes and no holes in the core), and for time
durations that were "hydrodynamic-like," i.e., large fractions of a second. Transitions from nucleate to film boiling heat transfer rates, on the order of 0.1 s, were
also observed.
In interpreting this (transient case) information, it is noted that mechanisms
involved in the transient heat transfer may include as parameters: (1) the enthalpy
of the copper and/or the helium, (2) the latent heat of the helium, (3) the establishment of a heat-induced ftow pattern in the helium channels, and (4) possible long
thermal time constants across solder interfaces of low thermal conductivity.
Mechanisms (1) and (2) appear unlikely, based on the long time duration of the
transients observed. Mechanism (4) appears unlikely, based upon the small thermal
gradients measured during steady-state heating. The data are suggestive of a
velocity-enhanced heat transferrate which occurs after a helium ftow pattern is set up
by vapor jetting from the heated region. Further study of transient heat transfer in
conductor bondies appears warranted.
CONCLUSIONS
Changing the orientation of a simulated LCP winding section (a sample of
"complex" geometry, with surfaces oriented in many directions) from vertical to
horizontal degrades the recovery heat ftux from 0.28 W /cm 2 for vertically oriented
conductor bondies to 0.18 W /cm 2 for horizontally oriented bundles. Also, the
addition of transverse holes in the insulation and conductor core enhances the heat
transfer.
Based in part on this data and results from a simple, long-channel-type heat
transfer experiment
a less conservative LCP design was adopted. (Previously an
80% degradationbad been assumed.) In another "complex-sample" experiment [8 ],
an angle-dependent degradation of 33% was reported for another design of a
conductor for the Large Coil Program.
The higher transient and steady-state heat transfer rates obtained using complex
samples, as compared to simple long channel or ftat plate data, may be due to coolant
ftow that is induced by the heating, as has been suggested for other restricted bath
geometry conductors [9 ' 10].
n,
REFERENCES
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
B. J. Maddock, G. B. James, and W. T. Norris, Cryogenics 9:261 (1969).
A. P. Butler, G. B. James, B. J. Maddock, and W. T. Norris, Intern. J. Heat Mass Transfer 13:105
D. N. Lyon, in Advances in Cryogenic Engineering, Vol. 10, Plenum Press, New York (1965), p. 371.
G. B. James, K. G. Lewis, and B. J. Maddock, Cryogenics 10:480 (1970).
M. N. Wilson, in Liquid Helium Technology, Pergarnon Press, Oxford, England (1966), p. 109.
D. N. Cornish, D. W. Deis, A. R. Harvey, D. G. Hirzel, J. E. Johnston, R. L. Leber, R. L. Nelson, and
J. P. Zbasnik, in Proc. 6th Intern. Conf on Magnet Technology, ALFA, Bratislava, Czechoslovakia
(1977), p. 76.
F. J. Reles, J. P. Heinrich, and R. E. Schwall, in Advances in Cryogenic Engineering, Vol. 25, Plenum
Press, New York (1980), p. 406.
R. P. Krause, E. H. Christensen, R. D. Bradshaw, and R. E. Tatro, IEEE Trans. Magn.
Mag-15:748 (1979).
J. W. Lue, J. R. Miller, and L. Dresner, in Advances in Cryogenic Engineering, Vol. 25, Plenum Press,
New York (1980), p. 251.
M. 0. Hoenig, A. G. Montgomery, and S. J. Waldman, IEEE Trans. Magn. Mag-15:793 (1979).
MEASUREMENTS OF BEAT TRANSFER
AND HELIUM REPLENISHMENT
IN LONG NARROW CHANNELS
R. E. Schwall, F. J. Reles,* and J. P. Heinriebt
Intermagnetics General Corporation
Guilderland, New York
INTRODUCTION
The use of large cabled conductors has proven to be a cost effective method of
fabricating high-current, superconducting composites with low normal state heat
flux. Such conductors are presently being manufactured for use on very large
superconducting coils. In the course of work on the design of severallarge coils, a
need was identified to expand the existing data base on boiling helium heat transfer in
long narrow channels. The work reported here was conducted to obtain the data
necessary for efficient conductor design.
Of the small amount of data available in the literature, perhaps the best-known
which presents critical heat ftux data
work isthat of James, Lewis, and Maddock
for channels up to 2 cm in length. Wilson [ ] measured channels up to 20 cm in
length, but the heated surface in his experimentwas stainless steel and there is some
question about the applicability of the results to copper channels. Sydoriak [3 ]
presented a hydrodynamic correlation of data on 72 different parallel plate evaporators with the plates vertical in all cases.
In the present experiment, the heat flux as a function of channel orientation has
been measured for a single channel size (13 x 0.11 x {).37 cm) which is typical of
those utilized in large cabled conductors. Partiewar attention was given to the
variation of the boiling characteristic for orientations near horizontal and to the
reversibility of the heat transfer curve. The effect of helium replenishment was
qualitatively evaluated by obtaining data with manifolds to restriet the flow of helium
into and out of the channels.
CJ.
EXPERIMENTAL APPARATUS AND PROCEDURE
The experimental apparatus (see Fig. 1) consisted of a copper plate with grooves
milled on one face. Ten grooves were cut with a center-to-center spacing of 0.49 cm.
The plate was mounted in a housing constructed of G-10 epoxy-fiberglass plates and
• Present address: Xciton Corporation, Latham, New York.
t Present address: General Elec:tric Company, Schenectady, New York.
406
Heat Transfer and Helium Replenisbment in Long Narrow Cbannels
407
all surfaces of the G-10 which contacted the copper plate were sealed with silicone
rubber. G-10 thickness was 1.59 cm on the ungrooved face and the edges and
0.635 cm on the grooved face. The helium manifolds have a totallength of 3.56 cm
and are angled at 45° such that those above the plate always opened upwards and
those below the plate always opened downwards. Heater strips were mounted on the
ungrooved face of the plate with current supplied via NbTi superconductive wire.
This arrangement eliminated vapor generation near the sample due to heating of the
Ieads. The heaters were powered by an IGC model 180M power supply with
adjustable ramp rate. The power was determined by measuring the current and the
valtage across the heater.
Temperature was measured by a combination of resistive thermometers and
Au-0.07 at.% Fe vs. Chrome I thermocouples. Two resistance thermometers were
mounted in holes drilled in the sides of the plate perpendicular to the grooves. The
sensors were located approximately 0.13 cm below the bottarn of the grooves and
were mounted with heat sink compound to ensure good thermal contact. Thermocouples were installed on each corner of the plate and at the center top of the
center tooth. In each case, the thermocouple junction was mounted on the copper
plate and covered with silicone rubber. The thermocouple and thermometer Ieads
were heat sinked to the side of the plate using cigarette paper and 7031 varnish. The
thermocouple reference junctions were placed on a copper block located weil below
the rest of the apparatus. Allleads were coated with silicone ruhher to reduce heat
transfer to the bath.
The angular orientation of the apparatus was varied by rotation about a simple
COPPER
BLOCK
MANIFOLD
·r;:: - -+---
MANIFOLD
1 2.29 cm X 0 .48 cm l
HEATER
STRIPS
Fig. 1. Heat transfer apparatus. Configuration illustrated is Case II channels-up.
G10
HOUSING
408
R. E. ScbwaU, F. J. Reles, and J. P. Heinrich
hinge at the base of the G-1 0 sheet. A threaded rod attached to the front of the G-1 0
housing and extending to the top of the dewar was used to lock the apparatus at any
given angle. With this arrangement, the sample orientation could be varied from
horizontal (6 = 0) to vertical (6 = 90°) without being removed from the dewar. To
change the orientation from "channels-up" to "channels-down" however, required
removal from the dewar.
The experimental procedure consisted of slowly ramping the input power to
some Ievel and then holding it constant to establish equilibrium. The readings of all
the temperature sensors were recorded and the process was repeated until a
temperature was reached that was weil into the film boiling regime. The power Ievel
was then reduced in steps, and data points were again recorded. One of the
thermocouple outputs was amplified and fed to an X- Y recorder along with the
heater current so that the behavior of the sample could be continuously observed.
EXPERIMENTAL RESULTS
Heat transfer data were taken with the copper plate vertical, horizontal, and at a
number of angles between these extremes. Particular emphasis was placed on
characterizing the heat transfer at small angles to the horizontal, where the behavior
was expected to change rapidly. Both orientations of the plate (channels-up and
-down) were studied. All data were obtained in free-boiling helium at 4.2 K and
1 atnt pressure. Data were obtained for three experimental configurations:
Case I: The grooved ends of the copper plate were exposed to the helium bath.
Case 11: The grooved ends were covered with a 0.16-cm-thick G-10 plate with
inlet and outlet manifolds in place. These manifolds, shown in Fig. 1, are intended to
simulate the passages which would be available for vapor removal and helium
replenishment in a large magnet.
Case III : All channels and holes were blocked with silicone rubber to obtain a
measurement of the background heat leak.
A typical curve of heat flux vs. temperature difference, corrected for background heat loss, is shown in Fig. 2. Individual data points within a run were
repeatable to ±2%, although, as discussed later, variations from run to run were
somewhat larger. Initially, the heat flux increased rapidly at small temperature
differences in the nucleate boiling regime. At a heat flux Ievel characteristic of the
sample orientation, film boiling began and the surface temperature rose by several
degrees. As the heat flux was increased further, the surface temperature increased
approximately linearly with heat flux. When the heat flux was decreased, the same
curve was retraced. This Iack of hysteresis, which is markedly different from typical
0 .4
i
~ 0 .3
;t
.rj 0.2
0 .1
0 .0-1'----+--+---+--+-----t--+---i-8
0
6
2
4
b.T , K
Fig. 2. Heat flux vs. temperature difference for
Case I, open ends. Channels-up 8 = 90•. Heat flux
is corrected for background Iosses through G-10.
Heat Transfer and Helium Replenishment in Long Narrow Channels
409
0 .5
45°
0.4
I
E
u
J: 0 .3
·Ö
0.1
0 . 0 +-----~--~r---~----~-----+-----+-----r-
0
2
4
8
6
10
12
14
AT, K
Fig. 3. Heat flux vs. temperature difference for Case II channels-up.
Parameter is orientation angle of channels.
pool boiling, is apparently characteristic of long, narrow channels and/ or complex
channel geometries. lt is qualitatively similar to that reported by Wilson [2 ] for
channels of similar lengths and widths and by Cornish et al. [4 ] for an assembly of
MFfF conductors from the MFTF magnet. The shape of the curves, even at the
low-temperature end, is virtually identical to that reported by Wilson.
In Fig. 3 the heat flux data are presented as a function of angle for Case II in the
channels-up orientation. The effect of increasing angle is seentobe an increase in the
breakaway heat flux and an increase in the heat flux attained for any given !1 T after
breakaway is achieved. Figure 4 presents the same data for the channels-down
orientation. The results are qualitatively similar with the exception of the fJ = 90°
0.5
30°
0 .4
jE 0 .3
u
J:
·Ö
0.2
0 .1
0.0
0
2
4
6
A T, K
8
10
12
14
Fig. 4. Heat flux vs. temperature difference for Case II channels-down.
Parameter is orientation angle of channels.
410
R. E. Schwall, F. J. Reles, and J. P. Heinrich
0.3
"I
E
u
~
·O
o Channels Up
• Channels Down
0 .1
0 . 0 +:-----.;fc::-----::t:-:---+-,---+--+---:t:-:00 15" 30• 45" so• 75• 90"
Hori zonta l
Orientation of Channels
Fig. 5. Breakaway heat flux as a function of channel
orientation for Case I, open ends. Heat flux is corrected
for background Iosses through G-10.
curve, which is depressed below the () = 30° and () = 45° results. Individual data
points have been omitted for clarity and the curves shown represent the best fit to a
minimum of eight data points.
Figures 5 and 6 show the breakaway heat ftux as a function of angle for two
different experimental conditions. In each case, data for channels-up and channelsdown orientation are presented. The curves are qualitatively similar and resemble
the data of James, Lewis, and Maddock CJ for short channels. There is a clear
minimum at () = 0, i.e., forahorizontal channel and a fairly smooth variation of heat
ftux with angle up to 90°. The minimum is most pronounced for Case II (Fig. 6) where
the manifolds were placed over the helium inlet and outletslots of the copper plate.
BACKGROUND LOSSES
The data presented have been corrected for the "background" heat loss by
conduction through the G-1 0 blocks, Ieads, and thermocouples. This contribution
was measured at the conclusion of the experiment by filling all helium passages with
silicone rubber (Case 111) and measuring in the channels-up configuration. The
background loss exhibits an angular dependence, being a minimum at () = 0 and a
maximum at () = 90°. At the breakaway transition, the background corresponds
to approximately 6 x 10- 3 W /cm2 at oo and araund 2.7 x 10- 2 W /cm2 at 90°. These
represent quite small corrections in an experiment of this type.
DISCUSSION
As noted in Figs. 5 and 6, the shape of the heat ftux vs. angle curves is similar for
faces-up and faces-down. There is, however, a difference of up to 12% in the heat
I
E
u
~
·0
• Channels Up
• Channels Down
0 .1
o.oo•
15•
Horizontal
30 •
45"
so•
75"
90"
Orientat ion of Channels
Fig. 6. Breakaway heat flux as a function of channel
orientation, Case li. Helium manifolds in place. Heat
flux is corrected for background Iosses through G-10.
Heat Tnnsfer and Helium RepleDisbment in Long Narrow Channels
411
ftux measured. This is true even at 90°, where the cases should be identical. This
discrepancy, although not large for a helium heat transfer measurement, is
considerably greater than the precision of the measurements and its source is not
understood. Also surprising is the fact that the breakaway heat ftux is generally larger
in the channels-down configuration than in the channels-up mode. The work of
Lyon [5 ] on ftat plates, for example, showed peak nucleate boiling heat ftux in an
upward-facing ftat plate to be four times that in a downward-facing plate. The
asymmetry in the thickness of the G-10 plates in the present apparatus could mean
that the background losses would be smaller in the channels-down position than in
the measured channels-up orientation. This would serve, however, to raise the
corrected channels-down data and does not explain the present results. It is possible,
however, that Lyon's data are not applicable in the present case. James et al. CJ
reference the work of Lyon but their data show breakaway heat ftuxes that are higher
in some cases with the heated foil facing downward.
CONCLUSIONS
The heat transfer to helium in narrow channels similar to those in large cabled
conductors lacks hysteresis and the breakaway heat ftux is below the peak typically
reported for pool boiling. The breakaway heat ftux and the heat ftux in the
film-boiling region is found to depend strongly on the angle between the channel and
the horizontal. The heat ftux obtained at any given angle is decreased and the heat
ftux minimum at () = 0 is accentuated when the entry and exit of fluid to the channels
is controlled by external manifolds.
ACKNOWLEDGMENTS
This work, performed at Intermagnetics General Corporation, was sponsored by the General Electric
Company, Schenectady, New York, under ESPD Subcontract No. F91-51164. The authors gratefully
acknowledge a nurober of helpful comments by one of the referees.
REFERENCES
1. G. B. James, K. G. Lewis, and B. J. Maddock, Cryogenics 10:480 (1970).
2. M. N. Wilson, in Liquid Helium Technology, Pergarnon Press, Oxford, England (1966), p. 109.
3. S. G. Sydoriak, in Proc. 13th Intern. Conf. on Low Temperature Physics-LT-13, Vol. 4, K. D.
Timmerhaus, W. J. O'Sullivan, and E. F. Hammel, eds., Plenum Press, New York (1974), p. 607.
4. D. N. Cornish, D. W. Deis, A. R. Harvey, D. G. Hirzel, J. E. Johnston, R. L. Leber, R. L. Nelson, and J.
P. Zbasnik, in Proc. 6th Intern. Conf. on Magnet Technology, Editorial Committee MT6, ALFA
Bratislava Publishers, Bratislava, Czechoslovakia (1978), p. 76.
5. D. N. Lyon, in Advances in Cryogenic Engineering, Vol. 10, Plenum Press, New York (1965), p. 371.
G-9
VAPOR LOCKING AND HEAT TRANSFER
UNDER TRANSIENT AND STEADY-STATE
CONDIDONS*
C.-J. Chen, S.-T. Wang, and J. W. Dawson
Argonne National Labaratory
Argonne, fllinois
INTRODUCTION
The technology of stable superconducting magnets has become synonymous
with the study and use of composite conductors. The composite conductor, a
superconductor paralleled with a normal metal, helps provide mag11et stability by
supplying alternate electrical and thermal paths for the superconductor when it
becomes normal. If these alternate paths of normal metal can carry the total
transport current continuously and still remain below the transition temperature of
the superconductor, the composite conductor is said tobe cryostable. The operational definition of cryostability requires sufficient cooling to dissipate Joule heating.
The degree of cryogenic stability depends on the heat transfer characteristics of
the liquid helium cooling channels. Normal zones created following mechanical
disturbances will either grow or collapse depending on the heat transfer rates from
the conductor to the adjacent cooling channels. It is important to design large
magnets with cooling channels sufficiently large so that vapor binding will not occur
under both steady-state and transient conditions.
Steady-state and transient heat transfer to liquid helium channels has been
studied by various investigators [1- 5 ]. This study was undertaken to determine the
vapor locking in the cooling channels of a cryostable superconducting magnet rJ, to
investigate the heat transfer characteristics under steady-state and transient conditions, and to study the effects of vapor accumulation of the multiple coillayers.
Heat ftux, energy density, temperature rise, and vapor fraction, are defined in
the following figures and paragraphs as electrical power to heaterI cooling surface
area of the conductor, electrical energy to heaterI conductor volume, temperature
difference between the sample and the liquid helium bath, and volume fraction of
vapor in the cooling channel, respectively.
APPARATUS AND MEASURING TECHNIQUES
To obtain the effects of transient and steady-state heat transfer and vapor
formation on cryostable conductors, samples were fabricated to simulate the real
• Work supported by the U. S. Department of Energy.
41Z
Vapor Locking and Heat Transfer under Transient and Steady-State Conditions
413
cryostable superconductor and the cooling channels to be used in the large MHD
superconducting magnet, designated as CFFF-SCMS [6 ], currently under construction at Argonne National Labaratory (ANL). The cross section of the conductor
is 3.1 by 0.47 cm and that of the cooling channel is 0.97 by 0.076 cm. Figure 1 shows
an assembly of a simulated single coillayer. Three conductors are sandwiched in
between insulation of 0.064-cm-thick pultruded fiberglass strip. A 0.0064-cm-thick
double-coated adhesive Mylar tapewas used to bond the conductor together. The
resulting assembly provided actual cooling channels. The assembly was covered
about 50% with 0.64-cm-thick Micarta strips to simulate identical cooling conditions
of the conductors within the CFFF -SCMS coil structures.
A 0.0025-cm-thick stainless steel heater was inserted in the middle conductor.
The insulation between the heater and the conductor was a 0.0075-cm-thick lens
paper impregnated with GE-7031 insulating varnish. Maximum power dissipated by
the heater was about 5 kW.
The temperature of the conductors was measured with a Chromel vs. gold-0.07
at.% iron thermocouple. Good thermal coupling of the thermocouple insulation was
provided by wrapping the indium solder tip of the thermocouple with a single layer of
0.0025-cm-thick lens paper impregnated with GE-7031 varnish.
Fig. 1. Assembly of simulated single coillayer for vapor-locking and heat transfer experiments.
Legend: A, simulated conductor with heater; B, simulated conductor without heater; C,
pultruded fiberglass insulation and front-cooling channel; D, pultruded fiberglass insulation and
rear-cooling channel; E, Micarta blocks; F, half-covering Micarta blocks; G, copper holders; H,
horiznntAI cooling channel; and I, vertical cooling channel.
414
c..J. Chen, S.-T. Wang, and J. W. Dawson
The vapor fraction in the channel was determined by measuring the change in
the capacitance of the channel. The capacitance change, aC, of the channel due to
the presence of vapor is given by
(1)
where a is the volume fraction of helium vapor inside the channel and CL is the
capacitance of the channel when it is filled completely with liquid helium. When the
channel is completely filled with helium gas, the vapor fraction, a, is equal to unity
and the capacitance change reaches a maximum value designated as aCmax· If the
temperature of the helium vapor remains constant, (1) can be simplified to
ac
a =--
aCmax
(2)
A capacitance bridge with a triaxial cable to compensate for any leakage current was
used to measure the capacitance change. The sensitivity of this bridge was about
3 V /pf capacitance change.
The maximum capacitance change for the cooling channel of the simulated
assembly was about 1.4 pf. The wetted area of the front side of the middle conductor
was 33.98 cm2 and that of the rear side was 16.16 cm 2 • The volume of the conductor
used was 28.53 cm 3 while the volume of each channel was 2.58 cm 3 •
RESULTS
The experimental study was conducted employing either a steady state or a
transient current to the heater. In either case, the temperature difference and the
capacitance changes were measured. The capacitance bridge was calibrated before
each run. Sufficient equilibration time was allowed after each energy pulse to ensure
escape of all vapor bubbles from the channels and cooldown of the conductors to
liquid helium temperature. The waiting duration is on the order of a minute and is
proportional to the injected energy.
Steady-State Results
The steady-state heat transfer characteristics for the channel are shown in Fig. 2.
This figure indicates that the critical heat ftux for the transition from nucleate boiling
to film boiling is about 0.4 W I cm 2 while the recovery heat ftux for the transition from
film boiling to nucleate boiling is about 0.25 W /cm 2 • The temperature rise changes
quite markedly from 0.2 K to about 7 K when the transition from nucleate boiling to
film boiling occurs. During the recovery process, the temperature decreases rapidly
from 1 to 0.1 K when the nucleate boiling regime is attained. This indicates that a
single-layer assembly can remove steady-state heat ftuxes up to 0.4 W /cm 2 , which is
equivalent to the conductor dissipating a steady-state Joule heating of 1.16 W /cm
length of conductor. The steady-state heat transfer coefficient, h, decreases shortly
after the peak nucleate heat ftux is reached. This results in a decreased heat ftux to the
channels.
Figure 3 shows the vapor fraction observed at the front and the rear channels as
a function of the applied heat ftux. The vapor fraction is about 0.44 for the front
channel and about 0.36 for the rear channel when the heat ftux is close to the peak
nucleate heat ftux. This is equivalent to about 0.1 cm 3 of liquid helium vaporized
within the channels per centimeter length of conductor.
_10_,
0
10 _,
10°
TE MPERATUR[ RISE. 6 T. K
-
-- .,.._
0
10'
.;
-_::_:;?
Fig. 2. Heat transfer characteristics under steady-state
conditions.
:r:
w-
<(0
o-•
"-
::>
-'
X
~
-.
u
w
w
,_
ci
uo
-.....3':
":::;0
~ r-----------------------------------.
0
~
"'c:i
0
~
c:i
"'
l>:;;
_ c:i
z
HEAT FLUX INJECTED, W/CM'
' ""'10_, , , """'10-· ' , """'10°
I
Fig. 3. Characteristics of vapor formation under steadysiate conditions.
=
Ul
~
....
i"
=
"'
SI
~
~
i
~I10 _, .<,
0
0
'1
i
:.
~·
a
~
~
Cl.
=
:::1
~
:::1
=.
~
ä=
Cl.
,
/
:.
IIQ
:::1
9:
0
t"'
~
i
c:i
0
~
~
c:i
~:;
o.,
"'
o. ....
Q;o
..._
<( "l
ug
;:::
f RONT
- ~RE A R
~ ,-----------------------------------------------~
0
416
C.-J. Chen, S.-T. Wang, and J. W. Dawson
Tnmsient Results
For the transient heat transfer sturlies the pulse duration and power Ievel of the
heater were varied as desired. The vapor fraction and temperature rise presented are
the maximum values observed for each pulse. The heat transfer characteristics are
presented below.
Figure 4 shows the energy density vs. temperature rise for different pulse
durations. These results indicate that the temperature rise is a function of the energy
density and is independent of the pulse duration. The critical energy density for
boiling transition is about 100 mJ/cm 3 • If the mechanical disturbance dissipates an
amount of energy less than the critical value, the peak temperature rise is less than
1 K. When the injected energy density was increased to about 1 J I cm3 , the temperature of the conductor rose to about 15 K peak value. The temperature recoveryrate
was about 0.02 K/ms.
Figure 5 shows the heat ftux under different pulse duration vs. temperature rise.
Observations showed that the shorter the pulse duration, the higher the critical value
for boiling transition. When the pulse duration was Ionger than 200 ms, the heat
transfer characteristics approached those observed under steady-state condition.
These data show that the critical heat ftux for a 10-ms pulse is about ten timesthat of
the critical heat ftux for a 200-ms pulse.
The vapor fractions observed for the front and rear channels vs. the heat ftuxes
under different pulse duration are plotted in Fig. 6. The vapor fraction of the front
channel is less than that of the rear channel at the lower heat ftux range, but this trend
reverses as the heat ftux is increased. However, the vapor fraction of the front
channel again is less than that of the rear channel when the heat ftux has been
increased sufficiently to induce the transition of nucleate boiling to film boiling. To
explain these phenomena, consider the following arguments:
1. At the low-heat ftux range, both channels are in the free convection regime
in which fluid moves under the inftuence of buoyant forces arising from changes in
density. The velocity is zero at the heated surface (no-slip boundary condition),
increases rapidly in a thin boundary layer adjacent to the surface, and becomes zero
again far from the surface. The wetted surface of the front side continues from
bottom to top, while the wetted surface of the rear side is blocked by turn-to-turn
insulation. This obstruction inhibits the free convection in the rear channel. With
these restrictions on convection, the vapor fraction in the rear channel would be
greater than that in the front channel.
2. When the heat ftux increases, both channels are in the nucleate boiling
regime. The vapor bubbles begin to appear at the heating surface and depart from the
surface. Since the wetted area of the front side is about twice that of the rear side, the
energy transferred into the front channel is more than that transferred into the rear
channel. A larger transfer of energy results in a greater vapor fraction.
3. In the high heat ftux range, the liquid helium of the front channel apparently
attains film boiling while the rear channel does not. Thus, the heat transfer into the
rear channel is more than that into the front channel resulting in a vapor fraction that
is greater for the rear channel than for the front channel.
Figures 7 and 8 show the vapor fraction of the front channel and the rear channel
vs. the energy density. The transition to film boiling occurred in the front channel in
the 100 mJ/cm 3 range, but did notoccurin the rearchannel up to 1 J/cm 3 . Thisresult
is consistent with the heat ftux data of Fig. 6.
:::; 0 -
"
10_,
10°
TEMPERA TURE RISE , AT. K
10'
+
~~~~~n;--,-,-rrnT~----~~~---r-r~
I
DURAliON
. - . DUR AliON
,.....,. DUR A!ION
Fig_ 4. Heat transfer characteristics under transient conditions for different pulse durations_
_10_,
0
w~
zo
w-
0::
<.;J
>-
0
w
z
iii
~
,_
E
.......
-,
u--
-c = 50 00 ms
-c : 100.0 ms
ot = 2000 ms
IO.OOOms
1: :
0-o DURATION
2 ~------------------------------------,
w
g
g 10I _,
ö
!
A;
"C=
ms
200.0 ms
1: = 100.0
TEMPERA TURE RISE, lH , K
I """'I
10_, I " '""'
10 _, I ii illlll
10' I"""''
10' I " "'"I
10 '
A
=20.00 ms
'( ::::: 50.00 I'I'IS
'C
1 ::::: 10.00 P'!'l l
Fig_ 5_ Temperature rise of conductor with respect to heat ftux
under transient conditions-
:X:
w
<(
....
LL.
...J
:::>
X
~-
--,0
u
wo
I--
0
~
:::;;
u
g
• ········• DURAl iON
• --- - DURATION
• - X DURA TION
- D URATION
cr---v OURATION
9r--------------------------------,
~
....
....
.....
a
~
t
(""l
i
~
lf
Cl..
=
!
[
~
..§~
~
~
;:
l
110
~
~
t"'
~
..
'Cl
418
C.-J. Chen, S.-T. Wang, and J. W. Dawson
0
~ ~--------------------------------------------,
<>-<> f RON T
1 = 5.0 00 I"I"'S
~
ci
$.000
.,..". REAR
_ rRON T
-:: = 10.000 ms
x- ·x REAR
1
<>--<> fRON T
(). -o RE AR
t
't:
ITI S
= 10.000ms
=100 .0
ms
t= 100.0
T!''
:i/!1
I
I
I
z
I
0
;::
r
/X
uo
< ~
ci
Cle
.....
A/
1
I
I
6
I
I
., I
• I
0
;(l
ci
10°
10'
HE AT FLU X IN JECTEO. W/ CM'
Fig. 6. Vapor fraction of cooling channels with respect to heat
flux under transient conditions.
0 .7
lOOm
0 .6
,_"'
~
0
·:~ ~·9)r.
5 ...
0 .4
0..
;! 0 . 3
0.2
0. 1
0
( OO••
20'" "'Y ~~.7 ~
0 .5
~
"'
....
"'0
1'\
501111
-~
.:Y
I
/l
ID
·-
[
f
100
1000
ENERGY DENSITY
10000
Fig. 7. Characteristics of vapor formation under transient conditions for
the front channel. Legend : A, 1 ms; T , 2 ms; e. 5 ms ; 0 , 10 ms ; x,
20 ms; \1, 50 ms ; 0 , 100 ms ; • · 200 ms.
Vapor Locking and Heat Transfer under Transient and Steady-State Conditions
0 .7
L
;t
0 .6
z
0
~0 . 5
«
a:
..._
a:
0.4
~0.
0 .2
0 .I
0
~
....,7
~
/"'
V
10
/
--
-
-
-
,j
100
419
-
'
1000
ENERGY OENSITY
10,000
OIJ /
/ tm'
Fig. 8. Characteristics of vapor formation under transient conditions for
the rear channel. Legend: &, 1 ms; ~ . 2 ms ; e, 5 ms ; 0 , 10 ms ; x,
20 ms ; 'V, 50 ms; 0, 100 ms ; • · 200 ms.
CONCLUSIONS
Based on the experimental results obtained, the following conclusions can be
made: (1) The critical steady-state heat flux for the transition from nucleate boiling to
film boiling is about 0.4 W I cm 2 ; (2) the critical transient energy density for the
boiling transition is about 100 mJ/cm 3 ; (3) the front channel attains film boiling
much easier than the rear channel; and (4) no temperature rise greater than 1 K is
possible if the heat flux does not exceed the critical heat flux under steady-state
conditions or the energy density does not exceed the critical energy density under
transient conditions.
REFERENCES
1. M. N. Wilson and Y. Iwasa, Cryogenics 18(1):17 (1978).
2. C. N. Whetstone and R. W. Boom, in Advances in Cryogenic Engineering, Vol. 13, Plenum Press, New
York (1968), p. 68.
3. 0. Tsukamoto and S. Kobayashi, J. Appl. Phys. 46:1359 (1975).
4. G. B. James, K. G. Lewis, and B. J. Maddock, Cryogenics 10:480 (1970).
5. M. A. Hilal, J. W. Dawson, J. D. Gonczy, L. R. Turner, and S.-T. Wang, IEEE Trans. Magn .
Mag-15:59 (1979).
6. S.-T. Wang, R. C. Niemann, L. R. Turner, L. Genens, W. Pelczarski, J. Gonczy, J. Hoffman, Y-C.
Huang, N. Modjeski, and E. Kraft, IEEE Trans. Magn. Mag-15:302 (1979).
G-10
FORCED TWO-PHASE HELIUM
COOLING OF LARGE
SUPERCONDUCTING MAGNETS
M. A. Green, W. A. Borns, and J. D. Taylor
Lawrence Berkeley Labaratory
Berkeley, California
INTRODUCTION
A major problern with alllarge superconducting magnets is the cryogenic and
refrigeration system. Almost all of the !arge magnets are cryogenically stabilized.
They are cooled in a bath of boiling helium. Nucleate boiling in liquid helium permits
heat ftuxes of 3000 W /m 2 to be transferred with a temperature drop of less than
0.5 K. The bath-cooled magnet is difficult to cool from room temperature to 4 K.
Helium, which is a difficult fluid to use as a coolant because of its low atomic weight,
must ftow into each region of the magnet; if the ftow in a section of the magnet is
restricted, stratification occurs and that magnet section remains warm.
Once the pool-boiled magnet is cold and the cryostat is filled with liquid helium,
the refrigeration problemsarenot over. Helium has a very low heat of vaporization
(20 JI g at 4.2 K) C]. As a result, the release of !arge quantities of magnet-stored
energy during a quench (even cryostable magnets quench on occasion) will result in
!arge quantities of helium gas being ftashed. For example, 1' MJ of energy will
vaporize 400 liquid Iiters of helium into 286m 3 (10,000 te) of helium gas at STP
conditions. The !arge amount of helium gas generated by a quench requires careful
design of the inner cryostat vessel and the relief valve system. The thickness of a !arge
diameter pressure vessel which is designed for at least 3 atm is not trivial.
·
Large superconducting magnets do not have to be bath cooled in many cases. lt
is often immaterial how an intrinsically stable superconductor is cooled as long as it is
kept below its critical temperature. Bath cooling, with liquid helium in direct contact
with the superconductor, is undesirable in any magnet which is designed so that it can
quench. The helium in direct contact with the superconductor restricts the growth of
the propagating normal region, which makes burnout of the coil more likely. The
helium cooling in an intrinsically stable coil should be away from the superconductor.
A forced-ftow helium tubular cooling system will provide all of the cooling that is
needed. This systemwill also avoid all of the major problems which are encountered
in any !arge cryogenic system. The advantages of the tubular cooling over an ordinary
bath-cooled system are as follows:
1. The cooldown of the magnet is weil controlled because the helium ftows in a
well-defined path.
420
Foreed Two-Phue Helium Cooling of Large Sapereondaetlng Magnets
421
2. The mass of the tubular cooling system is less than that of a helium bath
cryostat.
3. The amount of helium in direct contact with the magnet coil is minimized.
Helium boil-off during a quench is orderly and weil controlled. Cryogenic safety in
such a system is greatly enhanced.
4. Tubular cooling is unaffected by magnetic forces. A bath-cooled superconducting magnet in space is vulnerable to diamagnetic repulsion; a tubular cooled
system is not.
The tubular cooling system is not new; a number of superconducting magnets
use this system 5]. The Lawrence Berkeley Labaratory system is different because
it employs two-phase helium instead of supercritical helium (the critical pressure of
helium is 2.25 x 105 Pa; the critical temperature for helium is 5.19 K). The reasons
for choosing two-phase helium over supercritical helium are as follows:
e-
1. A two-phase "boiling" helium system will operate at lower temperatures
than a supercritical helium system. A lower Operating temperature allows the
superconductor to transmit more current.
2. The mass ftow required in the cooling circuit for a given amount of
refrigeration is lower for a two-phase system than for a supercritical system. In most
cases the pressure drop will be lower as weil.
3. Boiling two-phase helium can transfer large local heat ftuxes without
changing the temperature of the stream.
Two-phase helium forced cooling is, in most cases, superior to supercritical
cooling. There are instances when this is not true; they are when (1) the dielectric
strength of the helium must be uniform (for example, in superconducting transmission lines); (2) the pressure drops in the system must be above 5 x 104 Pa; (3) the
Operating temperature range includes temperatures above 5.2 K; and (4) when the
superconductor is supposed to have full cryogenic stability.
DESIGN OF A TWO-PHASE COOLING SYSTEM
The most important consideration in design of two-phase ftow systems (this
applies to other systems as weil) is the elimination of parallel paths. The most
desirable system is the simple series ftow system. A series ftow system has almost no
control problems; therefore, no additional refrigeration is expended to control the
ftow. When a parallel ftow system cannot be avoided, one should strive to minimize
the number of parallel ftow circuits. Each parallel circuit should have its own control
dewar system. The principle of the control dewar will be discussed later.
There are two other important considerations when one designs a two-phase
helium ftow system. Theseare low pressure drop and ftow stability. The former is
achieved by choosing an appropriate length-to-diameter ratio and the latter is
achieved by choosing an appropriate operating regime. The two, unfortunately, go
band in band. There is, however, wide latitude in choosing tube diameter and tube
length.
In general, one wants to operate on the liquid side of the two-phase liquid vapor
dome. One also wants to operate in the bubble and froth regime of the Baker [6 ]
diagram. (In general, one would like to operate the system and have mass ftows per
unit area of greater than 10 kg/ s-m 2 , which avoids the slug-and-plug ftow regime [1].)
Two-Phase Pressure Drop
A series of pressure drop calculations were performed using the MartinelliNelson Technique [8 ]. Although the calculations agreed with the experimental
422
M. A. Green, W. A. 81111111, ud J. D. Taylor
results, they were very time consuming. A much simpler equation, given below,
yielded almost the same results for round tubes (the reason for this isthat the density
change across the two-phase dome is less than a factor of 8):
!l.P =
_!_ m2 (1 +
Tr2
P
fz)
_!_
D D4
(1)
where f = 0.184 Re -o. 2 (turbulent ftow smooth pipes), Re = 4m/ TrD~J-, and where m
is the mass ftow, p is the average density of the exiting helium, z is the tube length, D
is the tube diameter, IL is the helium gas phase viscosity; and !l.P is the pressure drop
along the tube.
In order to achieve low pressure drop, one wants to maximize the density of
helium in the cooling tube. For that reason, the systems are designed to operate so
that liquid helium which circulates has the lowest quality X. (Quality, in this case, is
defined in the samesense as it is for steam.) Quality Xis defined as
(2)
where H, S, and V are the enthalpy, entropy, and specific volume, respectively; the
subscript I denotes saturated liquid, the subscript g denotes saturated vapor, while a
quantity without a subscript denotes the two-phase region. H, S, and V are bounded
by the liquid vapor dome so that the quality X is always between zero and unity
(0 :S x :S 1). Once V, the two-phase specific volume is known, the density of the
two-phase fluid can be determined by taking the reciprocal of V. Since a reduction in
the quality for the ftow system reduces the pressure drop, the operating temperature
is reduced and the temperature change across the system is minimized.
Helium Control Dewar and Cool Dewar Circuit
Two types of systems can be used to circulate low-quality helium through the
magnet cooling tube, namely, (1) a liquidheliumpump used as a circulator or (2) a
refrigerator compressor used as a circulator. Both systems use a heat exchanger to
ensure that the helium will enter the system at or near the saturated liquid line.
Figure 1 shows schematic diagrams for the two approaches.
The heliumpump loop system shown in Fig. 1a has the following advantages: (1)
The refrigerator is completely decoupled from the Ioad. In theory, one could
Substitute liquid helium from a storage dewar for the refrigerator. (2) The mass ftow
through the system is limited by the capacity of the pump, not the capacity of the
refrigerator. Key disadvantages associated with the use of a heliumpump system are
that the pump work is absorbed by the helium, requiring extra refrigeration, and the
simple pump loop system cannot be used to cool the magnet from room temperature;
in such a system one should connect the magnet cooling system directly to a
refrigerator.
The refrigerator compressor can be used as a circulator provided a heat
exchanger is used with an accumulator. The function of this heat exchanger is to
reduce the inlet quality to the magnet cooling tube. The quality change across the
magnet remains constant for a given mass ftow in the circuit. The circuit shown in Fig.
1b has two Joule-Thomson valves (J-T valves) which expand the gas in two stages.
The first J-T valve expands from 15-18 bar to 3 bar. The heat is transferred to the
boiling liquid helium in the accumulator tank as the gas ftows through the heat
exchanger. Expansion of the gas from 3 bar to the final inlet pressure to the magnet
Forced Two-Phase Helium Cooling of Large Superconduding Magnets
423
REFRIGERATION
MAGNET
(a)
LIQUID HELIUM CIRCULATION WITH PUMP
(b) LIQUID HELIUM CIRCULATION WITH REFRIG. COMPRESSOR
Fig. 1. Schematic of two types of two-phase helium circulation for
tubular cooled superconducting magnets.
coil will result in an inlet quality which approaches zero. If there were no heat
exchanger, the inlet quality to the magnet coil would be around 0.4; the pressure
drop in the tubular cooling system would be higher by a factor of 2 to 3.
The system shown in Fig. 1b is analyzed from a thermodynamical standpoint by
Green [9 ]. This system is capable of being operated at 40 to 60% over the capacity of
the refrigerator for short periods of time. (The amount of time is dependent on the
amount of excess liquid helium in the accumulator.) lt can be cooled by the
refrigerator directly, provided one bypasses the gasback to the compressors after it
has been circulated through the Ioad being cooled from room temperature. Figure 2
shows how the system shown in Fig. 1b can be inserted into a system to cool a magnet
down, operate the magnet assuming a certain pressure drop, and warm the magnet
back up to room temperature.
Figure 2 is highly schematic, but it shows the essence of the LBL control dewar
system which can be located remotely from the Ioad being cooled. A hybrid system
which uses both a helium pump and refrigerator compressors as circulators has been
built to cool the TPC magnet [1°]. Redundancy has been built into the system so that
the magnet can be operated whether or not the refrigerator operates. (The helium
pump circulates stored liquid while the refrigerator is inoperative.) If the helium
pump is inoperable but there is a refrigerator, the forced flow through the coil is
supplied by the refrigerator itself.
I
300 K to 80 K.
~
Open J- T valve.
11KJ
Closed full flow valve.
Lines not corrying flow.
Open full flow volve.
Closed J- T valve.
[:;o::J
.......
Llnes carrying flow.
CLEGEND>
cl Normal operation at temperotures below 10 K.
al Cooldown from
~--:;;~----+-4-
Control Dewar
*
I
iI
r--
1
Fig. 2. Cooldown, normal operation, and warmup of a superconducting magnet with forced two-phase helium cooling.
dl Wormup from 4 K to 300 K.
I...M/INVIIINM---
I
\ Control
I
I
bl Cooldown from 80 K to 10 K.
l
~
~
~
[
j
~
~
f
~
~
e
Forced Two-Phase HeUum CooUng of Luge Sapercondacting Magnets
425
Garden Hose Eflect
Large superconducting magnets, that are force-cooled with two-phase helium,
may face an additional problern which depends on the orientation of the cooling
circuit. If the magnet cooling circuit is oriented so that the two-phase ftow is
horizontal or near horizontal, the two-phase ftow should be stable and should result
in a pressure drop that is predictable using (1). If the two-phase ftow is vertical with
many up and down loops, the ftow is subject to the so-called "garden hose" pressure
drop and "garden hose" oscillation.
Such a pressure drop with associated oscillations is not ful!y understood, but it
has been observed experimentally. The pressure drop can be visualized by looking at
a garden hose which is half full of water and hangs in a coil on a peg. lt takes an
increase in pressure to force the water out of the hose due to the additive effect of the
various heads of water in each of the coils. A similar behavior has been noted in
helium systems even though the ftow is presumed to be in the bubble-and-froth
regime of the Baker diagram.
This type of pressure drop can be estimated approximately by using the
following expression for a coil of N round loops, of major diameter D, which have an
axis orientation angle of () from the horizontal:
M*
= 0.2 Nda (p 1 -
pg) cos 8
(3)
where P* is the pressure drop due to the above effect, p, is the density of the helium
liquid phase, pg is the density of the helium gas phase, and a is the acceleration of
gravity. The coefficient 0.2 is derived from experimental measurements ofthistype
of pressure drop and is probably related to the velocity of the coolant. At best, (3) can
only be regarded as an approximation. M* is added to the pressure drop calculated
in (1).
From (3) it appears that this type of pressure dropwill decrease as the system
approaches the critical pressure because the quantity (p,- pg) is reduced as one
approaches the critical pressure. The other obvious Iimitation is that !l.P* is less than
the difference between the critical pressure and the system exit pressure regardless of
the values of N and D. A reduction of the ND product will reduce the pressure drop.
Changing the axis of the hoops from horizontal (8 = 0) to vertical (8 = 90) will
eliminate !l.P* entirely.
This specific type of oscillation is probably caused by a change in ftow regime,
i.e., from bubble and froth to slug and plug. Starting and stopping the ftow requires
the ftow to cross over the slug-and-plug ftow regime. The oscillatory behavior of
slug-and-plug ftow, coupled with various spring constants of the system, which
includes the refrigerator or pump loop, probably contributes to the oscillation. The
amplitude of the pressurepulse due tothistype of oscillation appears tobe no greater
than the pressure drop M*.
Gas-Cooled Electrical Leads
Gas-cooled electricalleads present no problern on a forced-cooled two-phase
helium. First, one can take two-phase helium directly from the cooling system
without any ill effect to the magnet, the Ieads, or the cooling circuit. No additional
Iead pot is necessary. Second, the superconducting Ieads from the magnet do not
have to be in liquid helium. They only have to be in contact with the refrigeration
supplied by liquid helium.
426
M. A. Green, W. A. Bums, and J. D. Taylor
The implications of the two previous points permit one to design magnets that
have the electricalleads brought out into the vacuum space and attached to a pipe or
busbar cooled by liquid helium. The high-voltage arcing, which is a common fault in
large magnets, can be eliminated. Therefore, quench protection voltages up to 5 kV
are relatively easy to handle. A second implication is that installation and assembly
can be simplified.
The design of the electricallead itself is not changed by the fact that it operates
with a two-phase cooling system. However, one must remernher that Iead operation
on a refrigerator is different from operation in a bath of helium without a refrigerator. (This statement is true for bath-cooled magnets as weil as force-cooled magnets.)
The precautions one must take with gas-cooled Ieads which operate with a forcedftow system are (I) the Ieads should be oriented so that the warm end is above the
cold end, and (2) the ftow of gas through the Ieads must be controlled so that the Ieads
do not operate at a warm temperature. One may use a controller which measures
Iead temperature or one may measure the voltage drop across the electrical Iead.
EXPERIMENTAL MEASUREMENTS
The LBL group has operated three large test superconducting magnets using a
two-phase tubular cooling system. Most of the early work was undertaken using a
modified version of the circulation system shown in Fig. lb [ 11 ' 12 ]. Tests were
performed in the summer of 1979 using a helium pump.
Solenoid Tests on a Refrigerator
Two 1-m-diameter test solenoids and one 2-m-diameter test solenoid were
cooled by two-phase helium and were operated at or near critical current at
temperatures from 4.6 to 4.8 K. The two I-m-solenoids were operated in series. The
cooling circuit tubes are shown in Fig. 3. The circuit length was 235 m while the
cooling tubeIDwas 10.8 mm. There were a total of 72 turns of cooling tube Im in
diameter. The axis of the two coils in series was vertical (8 = 90 K). The 2-m test coil
contains 365m of 10.8-mm-ID tube wound in 55 turns which are 2m in diameter.
During the test the coil axis was vertical. The 2-m-diameter solenoid is shown in
Fig. 4.
The cooldown of both tests took a bit over one day when a CTi model 1400
refrigerator was used. Figure 5 shows the pressure drop in the cooling circuit as the
two I-m-diameter solenoids cooled down. The onset of two-phase ftow in the tube
was signaled by a sudden drop in the pressure drop across the circuit. Since the
cooling circuit axis was vertical, no "garden hose" pressure drop or oscillation was
observed. There was no oscillatory behavior observed in temperature or pressure.
Changes in pressure drop were gradual. Increasing the liquid in the accumulator
Fig. 3. Cross section of one of the LBL twophase cooled test coils.
Forced Two-Phase Helium Cooling of Large Superconducting Magnets
Fig. 4. Two-meter-diameter LBL test coil cooled with twophase helium.
0
0
0
0
10 5
')'
•
•
E
z
e
Q.
"0
~
:>
"'"'~
a.
10 4
ItTwo-phas•
~
f low ,egion
• Stngle-phase How
• Two-phose
trow
10 3 1~~~~~--~~~~~~~~~~~~2 3
5
10
20 30 50
100 200 400
Average
mog net tempe rolure • K
Fig. 5. Pressure drop through 235m of 10.8-mm-ID tube as a
function of average temperature (note dramatic change in
pressure drop when two-phase ftow is established).
427
428
M. A. Green, W. A. Bums, and J. D. Taylor
resulted in a decrease in the pressure drop. The temperature eorresponded to the
saturation temperature, whieh was eontrolled by the absolute pressure in the tube.
The 2-m test coil behaved similarly to the 1-m test eoils. There were pressure drops
during two-phase ftow of less than 104 Pa and no oseillatory behavior. At 4.6 K the
CTi 1400 refrigerator supplied two-phase helium to the experiment at the rate of
4g/s.
The gas-cooled eleetriealleads performed just as they would have in a bath of
helium. Liquid entering the bottom of the gas-cooled Ieads had no effeet on their
performanee. Gas ftow through the eleetriealleads was regulated with a needle valve
just upstream from a Rotometer-type gas ftow meter.
"Garden Hose" Tests
The garden hose effeet was tested with aseparate experiment. Detailed data are
given by Taylor et al. [13]. Subsequently, the test coil was mounted in series with the
2-m-diameter test coil, in order to test the effeet of pressure drop oseillations on a
supercondueting magnet.
The test coil was fabricated from 160 turns of 16.6-mm-ID tube. The diameter
of eaeh turn was 0.9 m. The tube was divided into two bundles of 80 turns eaeh.
Pressure taps and carbon resistor temperature sensors were installed at the ends of
the two eireuits and at a eenter tap between the two bundles. Pressure was measured
by room-temperature transducers. The test coil was run on the CTi 1400 refrigerator
with two-phase helium mass ftows as high as 4 to 5 g/s.
The measured pressure drop for this test eoil was about 2 x 104 Pa [2.4 x 104 Pa
is predicted using (3)]. In addition, a pressure oseillation with a period of about 30 s
was seen. (Short ehops of higher frequeney were seen, but the 30-s period was
eonsistently observed.) The peak-to-valley amplitude of this oseillation was around
2 x 104 Pa. Oscillations noted at one pressure tap did not eorrelate weil with
oseillations observed at other taps. Temperatures tended to eorrelate with absolute
pressure (except at the entry of the experiment).
Several Observations ean be made about the experimental data: (1) the pressure
drop and the oseillation amplitude deereased as the pressure inereased, the "garden
hose" effeet eeased at or near the eritieal point; (2) the oseillation frequency did not
vary a great deal with either pressure or mass ftow; (3) other mueh Ionger-period
oscillations (about 30 min) were observed when the eontrol dewar was empty and
the existence of two-phase ftow was in doubt.
HeUum Pump Loop Tests
A reciproeating double-aeting bellows-type helium pump was fabrieated and
tested at LBL. The pump is driven by a torque motor at room temperature; the
reeiproeating motion is transmitted to the pump at 4 K through a shaft whieh
operates between room temperature and 4 K. The helium pump is connected to a
copper tube heat exehanger whieh has an area of about 2m2 • This heat exehanger
removes most of the pump work from the pumped helium stream. The helium pump
and its heat exehanger are shown in Fig. 6. More data on the LBL heliumpump are
reported by Burns et al. rt 4 ].
The helium pump was first tested in its dewar without any external transfer
lines. The volumetrie eftieieney was measured as a funetion of torque motor speed,
stroke, and pressure aeross the pump. In general, the highest volumetrie efticiencies
were found at the highest speeds and lowest pressure rise across the pump. At a mass
ftow of 27 g/s and a pressure rise of about 4 x 104 Pa, volumetrie eftieieneies as high
Forced Two-Phase Helium Cooling of Large Superconducting Magnets
429
Fig. 6. LBL heliumpump with tubular heat exchanger.
as 80% were observed. At lower pressure rises, volumetric efficiencies of 90% or
more were observed. The pump is eapable of delivering about 50 g/s but volumetrie
efficiencies were not measured at mass ftows greater than 27 g/s. At low mass ftows
the volumetric efficiency dropped below 50%. lt is believed that late closing of one of
the popet inlet valves at the lower speeds is responsible for the deeline in volumetrie
efficiency.
The helium pump was tested in conjunction with the TPC magnet control dewar
and transfer lines. The pump was run at mass ftow rates of about 8 and 40 g/s. The
eontrol dewar was refrigerated by CTi model1400 refrigerator and the pump was
run when there was no refrigeration. At the highest mass ftow (40 g/s), the ealeulated
adiabatie efficieney was about 50% . At the lower mass ftow rate (8 g/s), the adiabatie
efficieney appeared to drop to about 30%. The measurements are eonsistent with the
decline in volumetric efficiency which occurs at low pump mass ftow.
CONCLUSIONS
The two-phase foree-cooled system is desirable for many kinds of supereondueting magnet systems to be used in aeeelerators, particle physics and in spaee.
Two-phase eooling systems are often lower eost than eonventional bath systems.
LBL has demonstrated that foreed two-phase eooling works very weil in largediameter thin solenoid magnets. Two-phase ftow systems ean be designed so that
they are a reliable way of cooling supereondueting magnets at temperatures
430
M. A. Green, W. A. Bums, and J. D. Taylor
approaching that of a bath cryostat. The two key elements in the design of two-phase
ftow systems is the elimination of parallel circuits and the minimization of the number
of up and down loops which can cause "garden hose" oscillation and pressure drop.
ACKNOWLEDGMENTS
The authors wish to thank P. Eberhard for his encouragement. They also thank R. R. Ross, H. Van
Slyke, and C. Covey for their work on the experiments. This work was performed under the auspices of the
U. S. Department of Energy.
REFERENCES
1. R. D. McCarty, NBS Tech. Note 631 (1972).
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
M. Morpurgo, CERN, private communication.
CERN Courier, "Villigen Superconducting Muon Channel Begins Operation," 15(2):36 (1975).
M. MacAshan, Stanford University, private communication.
M. A. G,reen, IEEE Trans. Nucl. Sei. NS-18:669 (1971).
0. Baker, Oil Gas J. 53(12):185 (1954).
M. A. Green, "Determination of the Safe Operating Point for Hydraulic Operation of the Magnets
and Transfer Lines for ESCAR," LBL Engineering Note M4956 (August 1976).
R. W. Lockhart and R. D. Marinelli, Chem. Eng. Progr. 45(1):39 (1949).
M. A. Green, "MINIMAG Experiment, Large Superconducting Solenoid Magnet, the Cryogenic
System." LBL Engineering Note M4834 (June 1975).
M. A. Green, in Proc. 7th Intern. Cryogenic Engineering Conference, IPC Science and Technology
Press, Guildford, England (1979), p. 86.
M. A. Green, "The Development of Large High Current Density Superconducting Solenoids for Use
in High Energy Physics Experiments," Doctoral Dissertation, University of California at Berkeley,
LBL-5350 (May 1977).
M. A. Green, Cryogenics 17(1):17 (1977).
J. D. Taylor and M. A. Green, "Garden Hose Test," LBL Physics Note 857 (November 1978).
W. A. Bums, "The Construction and Test of a Double Acting Bellows Liquid Helium Pump," tobe
published as a LBL report.
DISCUSSION
Comment by K. D. Timmerhaus, University of Colorado: This paper advocates the application of
forced convection boiling for the cooling of superconducting magnets and supports thi& position with
operational experience. However, much of the past Iiterature on this type of cooling is less optimistic than
the authors. Would the authors care to comment on this difterence in viewpoint?
Answer by author: This paper suggests that two-phase cooling is most applicable in devices which are
not cryogenically stable. The key to making two-phase cooling work is the control dewar. This reduces the
inlet quality of the helium to near zero (allliquid). The two-phase helium is circulated through the Ioad and
returned to the control dewar. The only instability we have observed is the so-called "garden hose"
instability. The second thing which is important is to make mass ftow per unit area high enough so that the
slug-plug ftow region of the Baker diagram is avoided. This requires mass ftows per unit area of greater
than 10 kg/m2 • We try to operate our systems at mass ftow rates per unit area of at least 40 kg/m.
The skepticism of many relative to this type of cooling is understandable, but I think there is ample
experimental evidence to suggest that such fears may be unfounded. The reason is that two-phase helium
behaves difterently from two-phase nitrogen or water-stream mixtures. The difterences are that helium is
a low-density fluid, the density ratio between the liquid and gas phases is much lower than for other ftuids,
and helium has a low critical pressure.
H-1
CONTACT HEAT TRANSFER IN
SOLID CRYOGENS
B. I. Verkin, R. S. Mikhalchenko,
V. F. Getmanets, and L. G. Goncharenko
Physico-Technical Institute of Low Temperatures
Academy of Seiences of The Ukrainian SSR
Kharkov, USSR
INTRODUCTION
Wide-spread use of contact cooling in cold sublimation accumulators employing
solid cryogens has necessitated experiments to investigate contact heat exchange
with such low-temperature refrigerants [1 ' 2 ]. The first results were not too accurate
or reliable and covered only a narrow range of parameters. A thorough analysis of
the contact heat transfer has, however, been extremely difficult because of the
particular conditions under which it occurs, namely, the relative motion of the
heat-exchange surfaces with continuously changing structure of the contact zone and
the vapor ftow from the subliming solid-cryogen surface. This work was undertaken,
therefore, to obtain more reliable experimental data for solid nitrogen, argon,
and methane. lt was also performed to provide a better insight into the contact
heat transfer mechanism which occurs during continuous motion of the in vacuo
subliming refrigerant.
METHOD
The apparatus and the technique used in this experimental work have been
described elsewhere C]. The advantage of this technique over that described by
(involving large systematic errors in the heat transfer coefficient
Voroshilov et al.
measurement because ofthelarge heat ftux from the outside to the contact zone) is
essentially adiabatic conditions achieved in the measuring cell. The latter was a
cylindrical vessel, 120 mm in diameter and 200 mm in length, fabricated of 0.3-mmthick stainless steel. The cryogenic liquid under study was solidified in the cell by
evacuation of the space above the solid-cryogen sample to a pressure below that of
the triple point. Heat was applied through the cell bottom and to the porous piston
resting upon the solid-cryogen sample. This piston could be loaded with a maximum
of five weights by means of a vacuum maniP-ulator. These weights provided contact
pressures of up to 10 kPa (about 0.1 k~/cm 2 ).
Based on previous experiments [ ], the experimental technique was further
improved so as to obtain more reliable results for the contact heat transfer
coefficient. As indicated previously [1], if the heat applied was no larger than
0.1 WI cm2 , the temperature remained uniform throughout the solid-cryogen sample
eJ
431
432
8.1. Verlda, R. S. Mikhalchenko, V. F. Getmanets, and L. G. Goncharenko
(except for a narrow contact zone, 1 or 2 mm in thickness) and was equal to the
saturation temperature associated with the equilibrium vapor pressure. This permitted temperature measurement in the solid cryogen to be made indirectly (by
monitorlog only the vapor pressure in the cryogenic refrigerant during the experiment) and thus eliminated the use of thermocouples in the contact zone. In the earlier
cell design, many thermocouples and control threads were located in the space near
the contact heat exchanger to monitor the motion of the heat transfer zone.
Preliminary experiments showed that this prevented good contact between the
subliming surface and the contact heat exchanger and thus caused underestimation
of the contact heat transfer coefficient [ 1] .
The new experiments were also used to further an understanding of the effect
that the specific thermal ftux (in the range of q = 10-3 to 10- 1 W /cm 2 ) , the
specific contact pressure on the sample (Pc = 0.5 to 10 kPa), the vapor pressure (P =
1 to 500 torr), the position of the heater with respect to the directional vapor ftow and
the cryogenic refrigerant temperature have on the contact heat transfer coefficient.
EXPERIMENTAL RESULTS
The experimental results indicate that the contact heat transfer coefficient is
independent of the vapor pressure and also the heater positionrelative to vapor ftow
(i.e., ftow from below the solid-cryogen block and through it, or from the top and
through the upper heater). The results of the other experiments are shown in Figs. 1
through 4.
An analysis of the results suggests that there are two different mechanisms of
heat transfer in the low-temperature zone and near the triple point. In order to
understand the heat transfer mechanism for solid-cryogen sublimation near the
triple point, the authors also studied contact heat transfer during the melting of solid
nitrogen and argon (see Fig. 4).
2
0
0
." .
••
~
! • B
~
~
0
0
0
0
0
~~
o- I
6 - J
0 - J
2
Fig. 1. Contact temperature difterence 4 T
during Sublimation in the low-temperature zone vs. specific thermal ftux q.
Conditions: (1),(2),(4), Pc = 0.5-5 kPa ;
(3) Pc = 2.5 Pa; (1) methane (T, = 67 K) ;
(2), (3) nitrogen (T, = 49--{;1 K) ; (4)
argon (T, = 77-82 K).
6
Fig. 2. Eftect of contact pressure on the
temperature difterence, 4 T, in the contact
zone during solid-argon Sublimation.
T, =
Conditions : (q = 1.39 W/cm 2 ,
78 K): (1) Pc = 5 kPa; (2) Pc = 0.5 kPa;
(3) Pc = 10 kPa.
Contact Heat Transfer in So6d Cryogens
433
~1171
'1,.•K
Fig. 3. Variation with time, -r, of the contact heat
transfer coefficient during solid-argon Sublimation
(T, = 78-82 K) for a variety of conditions:
(1) q = 1.39 X 10-2 W /cm2 , Pc = 0.5 kPa, P = 30 kPa;
(2) q = 1.39 x 10-2 W/cm 2 , Pc = 5 kPa, P =50 kPa;
(3) q = 1.08 x 10-2 W/cm2 , Pc = 5 kPa, P = 30 kPa;
(4) q = 0.60 x 10-2 W/cm 2 , Pc = 5 kPa, P = 30 kPa;
(5) q = 1.78 x 10-2 W /cm2 , Pc = 5 kPa, P = 30 kPa;
and (6) q = 1.39 X 10- 2 W /cm2 , Pc = 5 kPa, P =
30 kPa.
174
tll
o• c .
ooo
• 4o• g~•a•J ~
/14
0
"'
0
{
o- 2
IJ.P
IJ
. "- . . .
.• -
2
j
•
"'
0
0
0
0
4 - ~
•-s
0 - 6
6
'{h
Consider first the specific features and the mechanism of contact heat transfer in
the low-temperature zone. As is evident in Fig. 1, all coolants investigated are
characterized by a linear contact temperature drop increase which is dependent on
the specific thermal flux.
It was also shown by the experiments that the temperature drop in the contact
zone is constant for all the cryogenic refrigerants investigated as the contact pressure
is increased from 0.5 to 5 kPa. According to previous work C· 2 ], this concept is valid
for solid neon, nitrogen, argon and carbon dioxide for contact pressures from 0.5 to
100 kPa. However, additional experiments showed that for solid argon, rapid
decrease in the temperature drop (approximately by a factor of 2) occurs as the
contact pressure is increased from 5 to 10 kPa (see Fig. 2). This is evidently caused by
rapid changes in the contact zone structure as a result of plastic deformation owing to
a stress rise in the contact zone to above the solid-argon yield stress.
To further elucidate the contact heat transfer under conditions of low contact
pressure, the pistonwas replaced with the lightest possible heater, 1.25 g in weight
and 50 cm2 in area. The experiments using this modification revealed that a
reduction in contact pressure from 500 to 2.5 Pa caused only a relatively small
increase (by an order of 1.5 to 1.7) in the contact temperature drop. Even this minor
increase seems to stem from heater placement owing to rigidity of the thermocouple
and heater Ieads and not from changes in the structure and heat transfer mechanism
in the contact zone.
These results suggest the conclusion that as the contact pressure is varied from
zero to the solid-cryogen yield stress, the contact heat transfer coefficient is constant
to a first approximation, irrespective even of the thermal flux (see Fig. 3). The contact
heat transfer coefficients in the low-temperature zone for solid nitrogen, argon, and
methane are, 0.48 x 10-2 , 0.68 x 10-2 , and 0.75 x 10-2 W /cm2 K, respectively.
Fig. 4. Assumed pattern of changes for the contact heat
exchange temperature in the vicinity of the triple point
and experimental data for the contact temperature
difference during sublimation and melting of solid
nitrogen. Legend: (1) sublimation at T, = 61.2 K; (2)
sublimation at T, = T,; and (3) melting.
434
B.l. Verldu, R. S. Mikhalcheako, V. F. Gebuaets, ud L. G. Gondw'enko
DISCUSSION
Using these values and other experimental results, one can provide some
insights on the mechanism of contact heat transfer when some information on the
contact zone structure is known or possibly available from an analysis of experimental data.
Estimates show that the minimum contact pressures (2.5 Pa) are much higher
than the maximum possible increase in the vapor pressure (-0.01 Pa) acting on the
contact heat exchanger. Therefore, there may not be an uninterrupted gas cushion at
the solid surface and there must be a number of contact points at the subliming
surface.
The minimum relative contact area may be estimated from the equality condition that exists between the contact pressure and the sublimingmaterial yield stress, u,
i.e., Tim = Pc/u. Thus, for solid nitrogen, with Pc = 100 kPa [2 ] and u = 900 kPa,
Tim = 0.1, while for solid argon, Tim= 0.04 (Pc = 7.5 kPa and u = 200 kPa). The
remaining area may be occupied by a vapor cushion. As was determined by
experiments [1 ], the equivalent thickness of this gas layer may not exceed 1 or 2 mm.
The minimum equivalent gas layer thickness may also be estimated because the
contact heat exchange can only move in a plane-parallel fashion provided that the
sublimation rate and heat ftows are equal over the entire heat exchanger. Then
assuming that the heat transfer through the gas cushion is mere thermal conduction,
we obtain for the minimum thickness of the equivalent gas layer that ße = Äg/ a. For
solid nitrogen, in particular, ße = 0.1 mm. This is the same to a first approximation
for the other solid cryogens as weil.
Based on the above data for the contact zone structure, one may estimate the
contributions of various factors to the contact heat transfer. In the general case, heat
transfer across the contact zone may be realized by thermal conduction through the
contact points and through the gas cushion by radiation and free or forced convection. With regard to solid cryogens, radiation may be neglected because of the low
temperatures used. Free convection in the 0.1- to 1-mm gaps cannot occur because
of the low gas density and temperature gradients. To estimate the role of the
forced convection owing to gas ftow from the subliming surface and along the heat
transfer surface, we need to define the gas ftow behavior. lt is readily apparent that, at
pressures above 100 Pa, viscous gas ftow occurs in the gap. For the conditions under
consideration, the following relation is readily derived for the turbulent region of
forced convection:
Re
=
_g_ 2: 2300
TsJLH
(1)
where Q is the total heat ftux to the sublimation zone within the perimenter H. The
maximum value for the Reynolds number, as obtained by the present experiments
(with Q = 10 W, '• = 250 kJ/kg, JL = 6 x 10-7 kg/ms, H = 10 cm) was 100. Thus,
for the conditions of contact heat transfer investigated, the gas ftow cannot be
turbulent.
For effective gas thermal conductivity in the laminar ftow near the subliming
surface, Getmanets et al. [3 ] arrived at the relation Ae11 = ÄgNu where the Nusselt
number is determined by the following relation [3]:
Nu= 1
4TCp)
+0.156( 1 +---;;-
(2)
Contad Heat Transfer in So6d Cryogens
435
Using the experimental value of !l.T for the contact zone (less than 10 K), this gives a
Nusselt number value for nitrogen of less than 1.02. Therefore, the forced convection effect on the contact heat transfer may be neglected.
Since the longitudinal gas velocity along the heat exchanger is close to the
velocity of sound (about 200 m/s), it is desirable to estimate the thermal effects which
can arise in the ftow as its velocity is reduced. Proceeding from the law of energy
conservation for a ftow, the maximum variation of the specific enthalpy is simply
!:ii = V 2 /2 while the largest possible thermal ftux through a unit area is given by
!:i.l = !:iim = !:ii!I
F
F
r.
(3)
For the initial parameters mentioned above, !:i.T/F = 0.5 x 10-2 W/cm 2 , which is
5% of the applied thermal ftux (q = 0.1 W/cm 2 ). The actual effect of reducing the
velocity is stilllower because zero velocity and ideal heat transfer for the contact heat
exchange cannot be attained.
The absence of an effect of the forced gas ftow on contact heat transfer is
confirmed by the fact that the latter remained essentially unchanged as the vapor
pressure was varied from 0.1 to 50 kPa, proportional to variations in both the
transverse inlet velocity and the longitudinal gas velocity along the heat transfer
surface. Therefore, the analysis carried out Ieads to the unambiguous conclusion that
over the parameter range explored (q = 1 X 10-3 to 3 x 10-2 W/cm 2 , P = 0.1 to
50 kPa, Pc = 0.5 to 10 kPa), contact heat transfer is entirely dependent on the heat
transfer through the contact points and the thermal conductivity of the gas cushion.
One would expect that the number of contact points on the subliming surface is
close to the number of crystalline grains exposed on the surface. This number, as
calculated by formulas and using the experimental findings of Verkin et al. [4 ] is
20 cm - 2 for solid nitrogen. This enables one to consider the structure and heat
conduction in the contact zone in more detail.
Thermal resistance of the contact is determined by two factors: phononthermal
resistance and thermal resistance owing to thermal ftux contraction. Estimations
using relations developed by Little [5 ] showed that the temperature drop owing to
phononthermal resistance at nitrogen temperature is negligible (10-4 K).
The thermal resistance is more pronounced owing to contraction of the thermal
ftux to n isolated contact points. Under these conditions, according to Shlykov [6 ]
a
As
= 2 71
112 -
Jn/Tr
1.41 + 0.371
(4)
This relationship, using 71 = 0.1, provides an a value for solid nitrogen of
5.6 x 10-3 W /cm 2 which is very close to the measured value of 4.8 x 10-3 W /cm 2 •
With 71 of 0.04, the calculated value of a for solid argon is 2.5 x 10-3 W /cm 2 K
(assuming the same number of contact points as for solid nitrogen, n = 20 cm - 2 ) as
compared to the experimental value of 6.8 x 10-3 W /cm 2 K. From the relation
71 = nTra 2 we obtain the contact point radius a of 400 ~m for a grain size L of 2 mm.
The estimates given above suggest that the thermal resistance owing to thermal
ftux contraction is predominant in contact heat transfer. Accordingly, we may
approximate the contact heat transfer coefficient in the low-temperature zone from
aL; KJ 2AsL:J
=
(5)
436
B. I. Verldu, R. S. Mlkhalcheuko, V. F. Getmuets, md L. G. Goaeharenko
The above mechanism of contact heat transfer prevails at temperatures at least
several degrees below the triple point. However, as the operational temperature of
the solid coolant ina:,eases, or as the specific thermal ftux increases, the critical
condition given by ll.T = (T,- T&)a/q > 1 is no Ionger valid, and the contact heat
exchange temperature will rise above the triple point of the coolant. As a result, a
liquid layer will appear on the solid surface and the contact heat transfer coefficient
will change rapidly; the change is greatly inftuenced by either the boiling or melting
heat transfer coefficient. Therefore, this study first attempted to experimentally
investigate contact heat transfer near the triple point for both sublimation and
melting of the solid cryogen.
The experimental work reported here has shown that heat transfer in the contact
zone develops as depicted in Fig. 4. If the initial temperature of the solid cryogen is
equal to that of the triple point, then as the thermal ftux increases, the contact heat
exchange temperature can be represented by curve 9. Thus, just as was the case for
contact heat exchange in the low-temperature zone, there isalinear behavior of the
temperature drop with thermal ftux growth but with a higher value for the contact
heat transfer coefficient (a = 4 x 10-2 W /cm 2 K for nitrogen). The slope of the
curve depends on the process underway in the contact zone (melting or evaporation)
and the associated heat transfer coefficient. At lower temperatures of the solid
cryogen, the process first develops similar to the sublimation curve in lowtemperature zone 4. Thereupon, as the heat exchange reaches the triple point
temperature, the temperature drop evolves as one of curves 5 through 8 or parallel to
them, as dictated by the initial solid-cryogen temperature.
It should be emphasized that the contact heat transfer coefficient for melting is
10 to 15 times as high (4 x 10-2 and 0.1 W /cm 2 K for nitrogen and argon, respectively) as for low-temperature sublimation (4.8 x 10-3 and 6.8 x 10-3 W /cm 2 K,
respectively). Thus, the contact heat transfer coefficient for melting is close tothat for
Sublimation near the triple point.
The rise in contact heat transfer coefficient near the triple point is explained as
being due to the liquid layer that develops in the contact zone. The thermal
conductivity ofthisliquid layer is at least several times higher than that of the vapor.
Therefore, replacement of the vapor by the liquid in the gap near the contact heat
exchange Ieads to an enlargement of the effective contact area for each grain of the
solid. This effect, in turn, Ieads to a higher heat transfer coefficient.
CONCLUSIONS
In the course of this work, more accurate values for the coefficient of contact
heat transfer to nitrogen, argon, and methane have been obtained for a wide range of
conditions. Two distinct laws of heat transfer during solid-cryogen Sublimation in the
low-temperature zone and in the vicinity of the triple point have been determined.
lt has been shown that in the low-temperature zone there is a critical contact
pressure on the solid cryogen (equal to the solid-cryogen yield stress), whose increase
results in a sharp change in the heat transfer coefficient magnitude because of plastic
ftow at the contact points. The contact heat transfer coefficient for subcritical contact
pressure conditions at low temperatures is determined principally by the thermal
resistance of isolated contact points and therefore depends on the solid cryogenic
refrigerant thermal conductivity and crystalline grain size.
Pronounced increase in the contact heat transfer coefficient (by an order of
magnitude and more) has been revealed in the case of either sublimation or melting
Contact Heat Transfer in Solid Cryogens
437
in the vicinity of the triple point owing to the enlargement of the effective contact
area because of liquid layer development in the contact zone.
NOTATION
a = contact spot radius
cp
=
=
=
=
=
L =
m=
Nu=
n =
P =
Pc =
0 =
q =
Re =
r, =
Tc =
T, =
T, =
t. T =
V =
F
H
J
i
gas thermal capacity
area
perimeter
enthalpy
specific enthalpy
grain size
mass flow rate of gas
Nusselt number
number of contact points per unit area
vapor pressure
specific contact pressure
total heat flux
specific thermal flux
Reynolds number
sublimation heat
contact heat exchange temperature
solid coolant temperature
triple point temperature
temperature difference between gap walls, (Tc - T,)
gas velocity
Greek Symbols
a = contact heat transfer coefficient
8, = equivalent thickness of gas layer
11 = contact area
11m = minimum relative contact area
A.11 = effective gas thermal conductivity
Ag = gas thermal conductivity
A, = nonporous cryogen thermal conductivity
REFERENCES
1. R. S. Mikhalchenko, V. F. Getmanets, L. G. Goncharenko, and A. V. Polyakov, in Proceedings of6th
Intern. Cryogenic Engineering Conference, IPC Science & Technology Press, Guildford, England
(1976), p. 293.
2. B. S. Voroshilov, A. B. Grachev, and V. M. Brodyanski, Inzh.-Fiz. Zh. 33:238 (1977).
3. V. F. Getmanets and R. S. Mikhalchenko, in Gidrodinamika i teploobmen v kriogennykh sistemakh,
Naukova Dumka, Kiev, U.S.S.R. (1978), p. 24.
4. B. I. Verkin, V. F. Getmanets, and R. S. Mikhalchenko, Cryogenics 19:17 (1979).
5. W. H. Little, Can. J. Phys. 37:334 (1959).
6. Yu. P. Shlykov, E. A. Ganin, and S. N. Tsarevski, in Kontaktnoye termicheskoye soprotivleniye,
Moscow, U.S.S.R. (1977), p. 328.
H-2
DIGITAL COMPUTER SIMULATION OF
VOIDAGE IN A REGENERATOR*
J. 8. Harness and P. E. L. Neumannt
University of Bradford
Bradford, England
INTRODUCTION
A regenerator is a device which transfers energy between two ftuids by storing
that energy in a matrix. Normally the two ftuids are both gaseous and the matrix, in
small-scale versions, normally consists of small spheres. Regenerators work over
wide temperature ranges and have many applications from the preheaters for blast
furnaces down to very small devices found in refrigerators operatingdown to 12 K.
This study describes modifications to regenerator theory, developed for the largescale application, so that it may be applied to small-scale applications as weil.
REGENERATOR THEORY
Regenerator theory has been developed for applications such as Cowper stoves
and precooling stages of a tonnage liquefaction plant where the concern is with
long-period rapid ftow, and the mass of gas passing in one period is large compared
with the amount contained in the void space at any one instant. In order to produce a
mathematical model C] of the situation, one of the assumptions made is that at the
reversal of the gas stream no gas is left in the regenerator voids. This is not the case
with regenerators used in Stirling engines and refrigerators and similar cycles. Here,
the ftow alternates in very rapid cycles and only a small proportion of the gas passes
through the bed during the course of the cycle; it often happens that this is less than
the amount contained in the voids. This is expressed quantitatively by stating that the
"holdup," defined as the ratio of the mass of gas contained in the voids tothat passing
through in one unidirectional blow period, is greater than unity. If a plug ftow model
is adopted where the linear velocity of the gas is regarded as uniform throughout the
volume and there is no mixing, it is implied that a certain volume of gas remains
permanently resident in the regenerator as illustrated in Fig. 1. In some cycles the
holdup is large, while in a Stirling refrigerator values of 0.5 to 1.2% holdup are
usually encountered.
Another feature of regenerator operation in thermodynamic cycle applications
is that the gas ftow rate and inlet temperatures are not uniform throughout the blow
period and the physical properties gas and solid are temperature dependent. lt is
* Work sponsored by the Ministry of Defence, U.K.
t Present address: David Livingstone Consultants Ltd., Brighton, England.
438
Digital Computer Simulation of Voidage in a Regenerator
439
GAS
New
gas
OUT
New
gas
Fig. 1. Effect of voidage in regenerators with short
period times.
eJ
clear from experimental work [2 ] that the conventional regenerator theories
are
not capable of predicting the performance of regenerators operating in cyclic
machines.
ASSUMPTIONS FOR COMPUTER MODEL
Regenerators normally used are cylinders closely packed with spheres or wire.
The gas is channeled along numerous tortuous paths through the bed which are
interconnected but have branches at many places and can be regarded as independent of one another. There is no reason for favoring a path at one point in the bed
over another, so it is reasonable to adopt a plug ftow model with uniform velocity
across the bed. Although mixing on a small scale may occur, it is assumed that
longitudinal mixing over a distance large enough to affect the gas temperature profile
can be ignored.
As in many previous models it is assumed that the thermal conductivity is infinite
across the bed while it is zero along the bed. The temperature distribution within the
solid may be considered to be uniform. Calculations based on the Hausen [1 ] model
indicate that this is the case. Other nonconvective heat transfer processes which may
take place in the regenerator (in particular radiation) are neglected. Also initially
neglected are the physical property variation with temperature of the gas and solids,
although some suggestions are made later as to the development of a more exact
representation.
In the absence of an effective theoretical analysis of the process of convective
heat transfer in packed beds, the heat transfer coefficient must be derived from one of
the several empirical correlations available, each of which is intended for a certain
range of Reynolds numbers and particle size. The correlations most applicable to the
regenerators under consideration and used in this work are those developed by
Littman et al. CJ.
BASIC EQUATIONS
e].
The differential equations which describe the basic processes of heat transfer
A heat balance over a small
within the regenerator are those given by Hausen
element of the regenerator after simplification yields
_ m,C, dT,
HA, dt
= T. _ T. = pAxL,Cp dTg + GCpL, aTg
'
g
HA,
dt
HA, ax
(1)
It is convenient at this point to introduce a reference gas ftow rate Go so that
r = G/ Go and a reference heat transfer coefficient Ho so that (J = H/ Ho. Equation
J. B. a . - ud P. E. L Neuwut
440
(1) can be rewritten using the following dimensionless quantities:
= HoA,x/ GoCpL,.,
71 = HoA,J/ m,C,.,
q, = pAxL,Cp/ m,C,.,
Ao = HoA,/ GoC",
1T = HoA,T/ mrC,
lt should be noted that the dimensionless void fraction q, represents the ratio of
~
the heat capacity of the gas in the void to that of the solid matrix. The parameters Ao
and 1To are the Hausen reduced length and period applied to a regenerator Operating
under constant ftow rate G 0 • Under these conditions
Hu
Ao
= q,-
(2)
1To
Thus, equation (1) becomes
_ aT. = 8 r(T. _ T. ) = cf> aTg + raTg
a71
•
a71
g
where both 8 and rare functions of Go. For constant ftow rate conditions r
thus (2) becomes
_ aT. = T. _ T. = -~.. iJTg + iJTg
a71
•
g
o/
(3)
a~
a71
a~
=
8
=
1;
(4)
which is similar to that used by other workers [4 ' 5 ].
The boundary conditions are determined at the reversal and inlet conditions.
For each ftow period the initial values of both the solid and gas temperatures at all
points in the bed are required, but in counterftow operation at the beginning of a
period, these are placed equal to the values at the end of the previous period, i.e.,
T; (~. 71 = 0) = T~ (A- ~. 71 = 1T)
T~ (~, 71- O)
=
T~(A- ~. 71
= 1T)
(5a)
(Sb)
The gas inlet temperature is also a function of the condition
(6)
Equation (3) differs from the simpler theories [1 ' 6 ] only in the presence of the extra
term involving q, but a coordinate transformation can be used to eliminate this term,
namely, z = ~. y = 71 - q,~, or inversely ~ = z and 71 = y + cf>z. With this transformation equation (3) becomes
= T. _ Tg = iJTgl
_ aT.,
ay
az
z
(7)
y
The usual finite difference technique [6 ] may be used to solve these equations.
Certain modifications to this procedure are necessary at the boundaries of the mesh
created by the technique because of the change in the coordinate system; the
boundary conditions
have to be changed to
eJ
T; (z, y
T~ (z,
= -t/>z) =
y = -t/>z) =
T; (A- z, y
T~(A- z,
= 1T- t/>z)
(8a)
y = 1T- t/>z)
(Sb)
441
Digital Computer Simulation of Voidage in a Regenerator
t
t
z
z
A
.J-.
-VA
'~
...
"'
.J-~
.
TI-VA
~
0
~
0
TI
Y-
-VA
TI
TI-VA
Y-
(b)
(o)
Fig. 2. Effect of transformation on the finite difference grid. (a) Where the reversal coincides with the grid
points; (b) where the reversal does not coincide with the grid points.
The effect that these transformations have on the solution is illustrated in Fig. 2.
lt should be noted that the rectilinear coordinates y and z are those in which (7) is
defined; hence, in the finite difference technique [6 ] which is to be employed, a
rectilinear network must be superimposed. Figure 2 shows how this is achieved.
Commencing with the initial conditions specified on the left-hand sloping boundary,
it is possible to advance the solution, working in rows parallel to this edge, through
the entire network. There are problems, neglected by previous authors [4 ' 5 ], in this
method because of the Iack of freedom in closing the grid ratio, namely, that the
increments are related by the expression
Äy = <P Az
(9)
If batch Ay and Az are to be reasonably sized integral fractions of A and 7T,
respectively, it is necessary that the quantity Hu = <PA/ 7T be a rational number with
small numerator and denominator. If one does not adhere to this imposition,
reconciliation is best achieved by interpolating the conditions at the end of the period
from the calculated grid on either side. Here the variations in temperature are likely
to be at their smallest in the time abscissa y. Another expedient available when
Hu < 1, and particularly useful for small </J, is to change the time increment Ay over
part of the range. This permits economies in the number of time steps and hence
computer time.
lt is also possible when solving (7) to make use of a more rectilinear grid; hence
the two step sizes may be chosen independently, each satisfying its own error
condition, while the number of steps can be maintained at a reasonable Ievel. This
technique is basically unchanged from the previous method, but generates a parallelogram network of elements as in Fig. 2b. Any formula for interpolation which
makes use of the available information is acceptable but must be consistent with the
order of the truncation errors inherent in the trapezoidal formula for the differential
equations; a simple linear expression is normally adequate. The second of the above
systemswill be referred to as the interpolation method and contains a fault which has
been disregarded by previous workers.
TUE GAS-GAS INTERFACE
At the onset of ftow reversal, gas commences to enter the regenerator through
the previous exit port, pushing the gas contained in the voids through the bed at
reversal. At the boundary where these two bodies of gas meet there is a discontinuity
in temperature. In reality, diffusion and conduction processes would soon eliminate
this jump in temperature, but this mathematical model contains no terms to account
for these effects. These discontinuities create problems with the finite step deviation
442
J. B. Hamess and P. E. L. Newnann
approximations, which, dependent as they are on the absence of high-order deviations, break down under such circumstances. This would occur with any derivative
along a path which crosses the discontinuity. In fact, the gas temperature derivative
aTg/ax is taken along the constant y line, which represents a characteristic of the
ftow; in other words, it is taken along a path tracing the history of a gas particle as it
passes through the bed. Thus, it is proportional to the substantial or proper time
derivative DTn/ Dt. These characteristic lines include the path traveled by the
discontinuity; so the gas temperature derivatives run parallel to and do not cross it.
The solid temperature derivative does not cross the boundary, but here the
temperature discontinuity is only of the second order and much smaller than that of
the gas because of the higher heat capacity. The situation may be properly dealt with
if two gas temperatures are retained at all points on the interface, i.e., the line y = 0
in Fig. 2. The old gas temperature is used in all expressions relating to the old gas
region and the new gas temperature. The resulting boundary profile may be
calculated without any reference to the old gas region. This is possible with the
reetangular grid technique of Fig. 2a, but not the interpolation method of Fig. 2b
because of the necessity to perform an unacceptable interpolation across the
discontinuity. lt is found that the two boundary gas temperatures rapidly approach
one another, the differing values for the solid/gas temperature drops leading to
different rates of heat transfer which tend to achieve this effect. In many cases, by the
time the gas exit is reached, there is no perceptible jump in temperature. A
comparison of the results of computer programs using the two methods reveals that,
although in the body of the regenerator there are some discrepancies, the exit gas
curve and the effectiveness computed from this curve are the same. For the
interpolation method the ambiguous initial gas entrance temperature (at the point
x = 0, y = 0) is set to the mean of the two alternative values, namely, the final exit
temperature from the previous period and the initial inlet temperature for the
current period. This simulates some form of diffusion, although no attempt is made to
account for this in detail.
MODIFICATIONS FOR VARIABLE GAS FLOW
Variable gas ftow is introduced differently in the two methods. In the interpolation model each strip extending one step in the y direction and running parallel
with the sloping initial ordinate, represents a one-time interval in the action of the
complete regenerator. Successive strips can be regarded as a sequence of short,
individual cocurrent blow periods. To each of these may be assigned a different ftow
rate, set as the reference value Goforthat strip. The associated quantities fJ and rare
then introduced so that (7) can be solved with values appropriate tothat strip. Thus, a
continuously varying ftow rate is represented by discrete values; each value is the
average over a single time step. This is an approximation consistent with the
numerical procedure.
In the reetangular grid model the situation is complicated by the compulsory
connection between the step sizes with the constants involved varying with ftow. A
better technique is to use a different transform from above, devised directly from (3),
namely,
aT.
aT.
(lOa)
-• = !1(y, z)-•
a71
ay
..~.. aTg _ 1 (
)aTg
r-aTg+ ' 1
' - - y,za~
a71
2
az
(lOb)
Digital Computer Simulation of Voidage in a Regenerator
443
where ft and [2 are functions tobe defined later. This Ieads to the requirements
The inverse relationships can be derived and after lengthy calculations give the
results
( az)
a~
1J =
!2
(lla)
f(7J)
( az) = 0
a1J e
( ay)
<P/1
a~
1J =
(llb)
(11c)
f(7J)
( ay) = !1
a1J e
(lld)
The first two of the relationships in (11) imply that h = f(17 )/(~), while substitution
of (10) into (3) indicates that it is desirable to have / 1 = [2. The simplest choice is for
/1 = h = r, so that (11) becomes
(az)
=1
a~ 1J
(12a)
(12b)
(ay)
a~ 1J
= -<P
(12c)
(12d)
Integration then gives
(13a)
z=~
y
= L1J
f(17') d17'-
cP~
(13b)
Thus, equation (3) in the new Coordinates becomes
aTs fJ
aTg
--=-(T -T)=-
a1J
r
s
g
az
(14)
This is the same as (7) apart from the presence of the factor 8/f which enters the finite
difference scheme although it will not alter the distribution of the points on the grid.
As this factor is a function of time, it Ieads to varying values of the multipliers in the
numerical scheme as one calculates the grids. The definition of y, incorporating
the integration of the ftow term, gives precisely the transformed variable required
for the evaluation of the substantial derivatives of the solid and gas temperatures. lt
J. B. Raraeis ud P. E. L. Neuwm
444
may be regarded as an advancement coordinate, mapping intervals in the progression of the gas front regardless of any irregularity in the elapsed time coordinate.
VARIATIONS IN PHYSICAL PROPERTIES WITH
TEMPERATURE AND FLOW
Many of the physical properties of the gas and solid that appear in these
equations are temperature dependent; this renders the solution nonlinear and not
directly amenable to the methods discussed above. Willmott proposed an iterative/perturbation scheme which may be incorporated into the interpolation method
set forth above with the grid network in the latter maps properly applied onto
Willmott's grid as a whole. The reetangular grid transformation model cannot be
modified in such a manner. An attempt to introduce the necessary and unpredictable
variations in the dimensionless step lengths at each grid point Ieads to a complete
description of the transformation system. Under theseadditional requirements, only
one of the models is now available. A vastly increased amount of computation is
involved and the need to adopt an iterative technique destroys the essentially linear
nature of the solution.
n
CONCLUSIONS
The methods discussed above were programmed in FORTRAN for the ICL
1904S computer at the University of Bradford. From the results it is clear that if one
uses the simpler design method, such as those of Schalkwijk [8 ], one obtains an
answer for the effectiveness of the regeneratorthat is smaller than that attained from
the methods discussed above. This is illustrated in Fig. 3.
1.0
Iffi
0.9
Fig. 3. Variation of effcctiveness with reduced length.
Digital Computer Simulation of Voidage iu a Regenerator
445
NOMENCLATURE
A,
Ax
CP
C,
G
G0
H
H0
Hu
L,
m,
Tg
T.
t
x
y
z
= total surface area of packing for whole bed
= area of hydraulic x section
= heat capacity of gas
= heat capacity of regenerator packing
= gas ftow rate
= reference gas ftow rate
= heat transfer coefficient
= reference heat transfer coefficient
= holdup
= length of regenerator
= mass of packing of regenerator
= temperature of gas
= temperature of regenerator packing
=time
= distance along the regenerator
= dimensionless time, new transform
= dimensionless length, new transform
Greek Symbols
~ =
11 =
p =
T =
q, =
A=
1T =
dimensionless length
dimensionless time
density of gas
period time of regenerator
ratio of heat capacities of gas in voids and matrix
reduced length
reduced period
Superscripts
' = bot period
" = cold period
REFERENCES
1. H. Hausen, Wärmeübenragung in Gegenstrom, Gleichstrom, und Kreuzstrom, Springer-Verlag, Berlin,
West Germany (1950).
2. A. Bretherton, W. H. Granville, and J. B. Harness, in Advances in Cryogenic Engineering, Vol. 16,
Plenum Press, New York (1970), p. 333.
3. H. Littman, R. G. Barvile, and A. H. Pulsifer, IEC Fund. 7:554 (1968).
4. P. L. Heggs and K. J. Carpenter, Trans. Inst. Chem. Eng. 54:232 (1976).
5. A. J. Willmott and C. Hinchcliffe, lnt. J. Heat Mass Transfer 19:821 (1976).
6. A. J. Willmott, lnt. J. Heat Mass Transfer 7:1291 (1964).
7. A. J. Willmott, Int. J. Heat Mass Transfer 11:1105 (1968).
8. W. F. Schalkwijk, Trans. ASME Series A, J. Eng. Power 81:142 (1959).
B-3
SIMULATION OF COOLDOWN UNDERNEATH
LARGE CRYOGENIC STORAGE TANKS
M. H. Seeland* and K. D. Timmerhaus
University of Colorado
Boulder, Colorado
INTRODUCTION
With worldwide energy demand continuing to expand and corresponding
petroleum supplies questionable, natural gas demand is expanding rapidly. The
trend toward higher natural gas consumption is being observed throughout the
world.
As a result of the increasing demand and higher prices, gas reserves have
increased by development of existing gas fields and with new discoveries. According
to Hiwada C], confirmed reserves are currently about 2200 Tcf, but undiscovered
reserves are estimated at 7500 Tcf. Many years of gas production could be maintained by these confirmed and undiscovered reserves, even if the current 50Td/year production were to double to 100 Tcf/year, the energy equivalent of
current worldwide oil consumption.
Major energy-consuming countries, such as the Western European nations and
Japan, do not have abundant reserves and therefore depend on importing natural
gas. Transportation, therefore, has become one of the major problems in natural gas
expansion. Naturalgas is presently transported either by pipeline or by tanker in the
form of liquefied natural gas (LNG). Unfortunately, either transportation method
requires huge investments and long Iead times. Actual output has, therefore, lagged
appreciably in most gas-producing countries and predictions of future demand and
output are highly questionable particularly in view of the magnitude of the increases
(although most forecasts show major increases).
The mode of international trade in natural gas will be changing since projected
LNG imports are expected to account for 60% of the total natural gas imports. The
present situation has about 80% of the natural gas imports handled by pipeline. Even
though LNG trade is now fifteen years old, progress has fallen short of expectations
owing to the need for guarantees for the huge investments. Currently, however, the
increased demand and the improved prices have established a new era of cooperation
and progress in the LNG field. Various international projects are being planned now
for implementation in the early 1980's.
Storage is important in an LNG system for both base Ioad and peak shaving
plants. Above-ground double metal-wall tanks are the most common type of LNG
* Present address: IBM, Boulder, Colorado.
446
Simulation of Cooldown Undemeath Large Cryogenic Storage Tanks
447
storage tanks. The inner wall of such a storage tank is constructed of a steel alloy
(e.g., 9% nicket steel) exhibiting acceptable properties at cryogenic temperatures,
while the outer wall is generally constructed of mild carbon steel. Since such mild
carbon steels become brittle below -50 to -100°C and frost heaving can occur if the
soil below the tank freezes, a potential hazard to the tank is created if cold
temperatures progress too far from the inner tank. Therefore, the overall insulation
scheme and heater design below such tanks are extremely important. Failure of the
outer tankwallnot only reduces the generat tank support, but also results in methane
leakage since the insulated space between the walls, ftoor, and roof of the tank is
normally saturated with methane gas.
Design optimization of an above-ground double metal-wall storage tank
includes many factors. The more important factors are (1) insulation material and
thickness, (2) location and spacing of the heaters below the tank,. (3) heat input to the
heaters, (4) location of the heater temperature control points, (5) minimization of
heat leak to the tank, and (6) power failure backup energy systems. These factors
must be considered simultaneously to minimize material cost and heat leak to the
tank while preventing the possibility of failures owing to low-temperature embrittlement of the outer tank wall and frost heaving underneath the tank.
To aid in the analysis of these many design factors, a simplified computer
simulation of the transient two-dimensional heat transfer occurring underneath such
a tank was developed in this study. The program simulates temperature proflies
below and around the tank as a function of time. Generalization of the program was
undertaken in order to facilitate the theoretical analysis of numerous design options
in a relatively short time.
MATHEMATICAL MODEL
The development of a mathematical model useful for simulating the transient
two-dimensional heat transfer occurring underneath a cryogenic tank durlog cooldown must recognize numerous factors. For example, several different materials will
generally be involved; often with quite complicated geometries. Heat input sources
are involved and these are controlled and energized in a variety of ways. The
mathematical simulation model can have both insulated or constant temperature
boundaries depending upon the situation at band. For example, an insulated
boundary could be specified to provide an approximation for a boundary that is
considerably removed from areas of large heat ftux under the cryogenic tank, while a
constant temperature boundary could be the inner ftoor of the cryogenic tank once
liquid covered the ftoor.
The equations for such a transient two-dimensional conductive heat transfer
simulation can be developed from a generat energy balance equation presented by
Bird et al. e], namely,
a
ae (pCvT) = -(V·q)- P(V·v)- (1':Vv)
(1)
where q is the heat ftux vector, v is the velocity vector of the system, and 1' is the shear
stress tensor. For the specific case being considered, the velocity vector is zero and Cv
is equivalent to Cp. With the addition of a heat source term, the relation simplifies to
aT
c -ae
= -(V·q) + o
P
P
(2)
M. H. Seelud aad K. D. 'I1IIuaerlwls
448
Using Fourier's law of heat conduction (q = -kVT) and assuming that the
thermal conductivity of the material is constant, (2) can be expanded in terms of
reetangular coordinates to
a2 T
a2 T
ar
pC-=k-+k-+Q
2
2
p
ax
ae
(3)
ay
Equation (3) is the transient two-dimensional heat transfer equation that was
used to develop the numerical approximations for this simulation.
Although the steady-state form of (3) can be solved analytically, the transient
form realistically requires the use of a computer. In order toreformwate (3) into a
form suitable for computer analysis, either finite-element or finite-difference
numerical approximations could be used. Both methods establish a grid of points in
the area of solution.
The finite-element method integrates the equation over finite differential areas.
These areas are usually triangles in order to allow for improved curve-fitting
capabilities. The finite-element method is usually applied to microscopic or simple
system analysis owing to the large computer time requirements associated with the
integration routines.
The finite-difference method, on the other band, estimates the differential
equations with numerical approximations and, therefore, requires no integration.
The numerical approximations are based on changing the differential variables to
discrete variables. For example, the exact relation to calculate temperature 7f+ 1
located at x + Llx relative to temperature 1j located at x in a transient heat
conduction simulation is given by a Taylor series as
)(;Pr)
(a )(a-axzT) i+ (a__K_
+ ··· +
ax i
3!
3
2
2
( ar) + ~
Ti+I=1f+Llx2!
ax i
-3
(4)
Upon rearranging (4), the firstderivative takes the form
( aT)
ax i
= 7f+ 1 -
Llx
Tj _
(ax)(a 2 ~)
2!
ax
i
_
(ax 2)(a3 ~)
ax
3!
i
_ ••• _
(5)
The second derivative takes the form
(aaxT) i =
2
2
7f+l-
2Ti + 1f-1
(Llx) 2
_ (ax 2)(a4 ~)
12
ax
_ .•• _
i
(6)
In approximating equation (3J with the finite-difference method, similar equations
can be developed for (a 2 Tjay ) and (aTja8).
With the aid of these relationships, {3) becomes
pCp(T~t~; T~i) = k [Ti,j+l -(!;)~ + Ti,i-1] + k [Ti+l,i -(!~~~ + Ti-l,i] + Q
(7)
where the temperatures on the right-hand side of the resulting equation can be either
at the previous time interval n {explicit) or the new time interval n + 1 (implicit).
Upon rearranging the explicit form of the temperatures in (7), the new time interval
Simulation of Cooldown Underneath Large Cryogenic Storage Tanks
449
can be calculated from
rzt = (aäll) [ (aäli)TZj + .:l~2 (TZj-1 -
2TZi
+ TZi+d
+ .:l> (T7-1.i- 2TZi + T7+1,j) + ~]
(8)
where a = kj(pCp). Equation (8) is simple to formulate and easy to use, but,
unfortunately, explicit solutions have restrictions. In order to assume convergence to
the differential equation solution as Llx, äy, and Llll are decreased, the ratios Llll/ Llx 2
and Llll/ ä/ are limited in magnitude. The convergence criteria for (8) is [3 ]
1
Llll
(9)
~ 2 [(.:lx) 2 + (äy) 2]
Therefore, even though Llll could be increased as steady state is approached, the
convergence criteria prescribed by (9) may limit the size of Llll.
The implicit form of (7) results in an equation with five unknowns. lts use would
result in the need to solve a large matrix for the temperatures at all points for the new
time interval. In order to establish smaller matrices for solution, an implicit method,
the alternating-direction implicit (ADI) method 4 ], was finally chosen for the
simulation calculation. Since the ADI method is unconditionally stable, it requires
no convergence criteria.
The ADI method uses two different finite-difference solutions for each time
interval. An intermediate time interval of (ll + .:lll/2) is used to determine intermediate temperatures of T*. These intermediate temperatures are then used to solve
for temperatures at time (ll + Llll).
The first finite-difference equation is developed from (7) (explicitly in the x
direction and implicitly in the y direction) and involves only three unknowns. This
permits establishment of a tridiagonal matrix for each column of temperatures (i.e.,
for each j, a matrix is set up to solve for T* at all i's).
The second finite-difference equation of the ADI method is developed from (7)
explicitly in the direction (T*'s are known) and implicitly in the x direction. This
permits the establishment of another readily solvable tridiagonal matrix for each row
of temperatures (i.e., for each i, a matrix is set up to solve for Tatall j's).
The two basic equations for the ADI method upon simplification are as follows:
e·
y
-T1-1.i
+ 2(Ay + l)T[i-
.:ly2) [T;,j-1
= ( .:lx2
+ 2(Ax
-T;,j-1
T1+1.i
(lOa)
(0)
k
(lOb)
+ 2(Ax + l)T;,i- T;.i+1
äx 2) [T;-1.i
* + 2(Ay= ( .:ly
2
(Q)
k
+ T;.i+1] + Lly 2
- l)T;,i
*
l)T;.i
* ] + Llx 2
+ T;+1.i
where Ax = äx 2 /allll and Ay = Lly 2 /aä8. These relations, such as (lOa), can be
rewritten for computer use in a generat form as
(11)
M. H. Seeland and K. D. TimiDerbaus
450
where constants A, B, and C are functions of p, C"' k, and äy, and constant D is a
~unction of p, C"' k, äx, äy, Q, and T~i-1• T~i> and T~i+l·
As noted previously, a simulation generally involves many types of materials
with widely differing properties and geometric shapes. Thus, there can be points in
the established grid that do not conform to (1 Oa) and (1 Ob). Included in the grid could
be interfaces between materials, corners of material interfaces, additional heat
sources, insulated boundaries, and constant temperature boundaries. These special
cases require further modifications of (lOa) and (lOb) before they can be included in
the final computer program. Their development is rather lengthy but straighttorward
and will not be detailed herein.
The inclusion of natural convective boundaries in the Simulation model also
requires some reformulation of the basic equations before they can be used in the
simulation model. A heat balance along a boundary subjected to natural convection
can be expressed by
k(~~) = h(Ts- Tamb)
(12)
where T. and Tamb are the surface and ambient temperatures, respectively. The
convective boundary temperatures will change very gradually owing to the assumed
constant ambient conditions. Because of these small changes, (12) can be solved
explicitly for all points along the convective boundaries and these temperatures are
considered as constant for the AD I method solution. The resulting amplified relation
for convective heat transfer from horizontal surfaces developed for this simulation
model is as follows:
Tn+l
I,J
=
2aMJh) rn. + }:_ Tn
(t _I__
Ay
äyk
Ay
<,J
. + (2aä8h) T
amb
äyk
<+l,J
(l 3 )
A similar relation has been developed for the convective heat transfer from vertical
surfaces.
As noted earlier, convergence criteria must be satisfied with explicit formulation. For the convective heat transfer relations, the convergence criteria as
developed by Adams and Rogers [5 ] are
1
aä8
--<---äy2- 2 + häy/k
(14)
This sets the maximum ä8 as
(15)
In order to predict the temperature of the points on the convective boundary for
the ä8 interval of the implicit formulation, the explicit equation must be repeated for
many ä8max increments. The nurober of repetitions necessary is given by the ratio of
ä8/ä8max•
As discussed previously, the ADI method used in the program establishes a
matrix for each column of temperatures for the first set of calculations and each row
for the second set of calculations. Each column or row begins and ends with either a
constant temperature or insulated boundary. The resulting equations set up a
tridiagonal matrix of the form
Simulation of Cooldown Undemeath Large Cryogenic Storage Tanks
B1 C1
A2 B2
0
A3
0
D1
D2
D3
0
c2
B3
c3
0
A,
B,
c,
0
0
0
AR BR
D,
451
(16)
DR
The matrix coefficients (A, B, C), as developed from relationssuch as (10) and
(11), are calculated for allsolid materials, horizontal interfaces, vertical interfaces,
and corners. These coefficients are recalculated only when the time increment
changes. Since the D coefficients are functions of the previous temperatures, they are
recalculated for every time increment. Solution of the resulting matrix uses Gaussian
elimination (i.e., the Thomas algorithm).
A heat source can be simulated in the program either at a material interface or
imbedded in one of the materials. Such a heat source can be controlled as desired to
provide energy input to the transient heat transfer system under study. This is
accomplished by locating a control point for each source and monitaring the
temperature at this point after each time increment. If the temperature at the control
point falls below a specified temperature, the program energizes the heater system
and the designated energy is added to the appropriate ADI metbad equations for the
next time increment calculations. This energy input will continue to be added until
the control point temperature attains an upper specified temperature. The control
point location and desired temperature range for this control point can be input as
desired.
The final option for heat sources is that a time can be specified, whereupon the
energy input from the heat sources can be set equal to zero. This is essentially a
"shutdown" time for the heat source and represents apower failure forareal storage
tank.
Any number of time loops can be set in the program. Foreach time loop, !:18 and
the ending time for the loop are set. Since the program is unconditionally stable,
solution feasibility is independent of the choice of !:18. But, since error is a function of
!:18, trials have to be made to insure that !:18 is sufficiently small to provide consistent
results.
The error associated with the time increment approaches zero as steady state is
approached; therefore, time increments can usually be increased as time progresses.
However, when there are changes being made to the temperature distribution, the
time increment must be decreased until steady state again is being approached.
In order to calculate overall heat lass or gain at a boundary, the temperature
differential at the boundary is required. The option to have the program average
temperatures is available. Using the surface temperature averaging option, the
average temperature differential and, therefore, the average heat flux can be
determined at any boundary. Theseaverage surface temperatures arenot only an
average of all temperatures along the boundary, but also are an average over time
from time zero until the specified end of the program.
DISCUSSION OF RESULTS
The computerprogram that has been developed in this study was generalized to
provide substantial flexibility in evaluating time-temperature effects of design
M. H. Seeland and K. D. Timmerluaus
452
Power Off
30
20
u
0
10
,j
...
...."
.e
.
..."'
"'-
0
-10
'"""
-20
-30
3000
0
4000
Hours
Fig. 1. Temperature vs. time at three specific locations underneath a
well-insulated cryogenic tank supplied with heating coils. Legend: 1,
location near center of tank but at some distance from heating coil; 2,
location adjacent to heating coil; 3, Iocation near edge of tank but at
some distance from heating coil.
changes in specific cryogenic storage tanks. In addition, the generality of tht
equations allows the program to be useful in many other heat transfer applications.
Essentially any case that concerns heat conduction can be readily simulated with the
program. Minor modifications can be made to handle more detailed convection
calculations or boundaries other than the constant temperature and the insulated
boundary situation considered here. Owing to the input ftexibilities, essentially any
geometric shape can be simulated. The program currently requires 90° corners, but
could be modified to handle irregular boundaries. Heat sources and constant
temperature interfaces are already incorporated in the model and these options can
be used to simulate heating or refrigeration coils if needed.
The computer program was originally used to predict the time-temperature
relation at various specific locations underneath a well-insulated cryogenic tank
supplied with a heat coil controlled from one of these locations. Figure 1 presents a
time-temperature profile for three of these locations. One of the locations was near
the center of the tank at some distance from the heating coil. The second location was
adjacent to the heating coil and was used as the control point for the heater. The
heater was energized when the temperature at this location decreased to 5°C and was
programmed for shutoff when the temperature at the location reached l5°C. The
third location was near the edge of the tank but also at some distance from the
heating coil.
A study of the three selected time-temperature curves indicates that in the first
900 hr of cooldown the heater was not energized because the control point temperature was above soc during that time period. Once this specific temperature was
attained, the heater was energized for approximately 300 hr with a resultant increase
in temperature at this location to l5°C. The beater was then deenergized and the
cooling process repeated until the temperature bad again dropperl to 5°C, where-
Simulation of Cooldown Undemeath Large Cryogenic Storage Tanks
453
upon the entire process was repeated. The other two locations which were at some
distance from the heater did not show the large changes in temperature that were
characteristic of the control point. The effect of the periodic heater Operation at these
locations was observable but was also fairly weil damped out.
At the end of 3000 hr of operation, the heater was completely shut oft to
simulate apower failure. Since there was no periodic energy makeup by the heater,
the temperatures at all three locations showed continued decreases in temperature
for the next 1000 hr of monitoring. At the end ofthistime it was evident from the
time-temperature record of all three locations that steady state still bad not been
attained. This is not surprising since 1000 hr (-40 days) is still a relatively short time
in the cooldown history of many cryogenic storage tanks.
More recently the computer program has been utilized to follow the timetemperature history for a large LNG storage tank. In this task it has been quite
successful in matehing temperatures observed at numerous locations over extended
time periods and under varying heater inputs. Differences between observed and
predicted temperatures have been on the order of 1 to 2°C. The principal disadvantage to the program has been its rather rigid grid structure, which provides some
difficulty in establishing temperature profiles along each material interface encountered underneath a typical cryogenic storage tank. Present studies are attempting to
minimize this deficiency of the simulation model.
CONCLUSIONS
In general, the design of insulation and heater systems to protect cryogenic
storage tanks is complicated, but extremely important. A common pitfall is to design
these systems, analyzing each part separately, and then failing tobring these parts
together to establish the complete design. With so many interrelated parts, it is
important that these be carefully integrated into the overall system. Any simulation
program similar to the one developed in this study can be a great aid in making such
an analysis.
NOTATION
CP =
c. =
h =
k =
P =
q=
Q =
T =
T~ 1 =
T!':i =
v=
x=
y =
heat capacity at constant pressure
heat capacity at constant volume
heat transfer coefficient
thermal conductivity
pressure
heat input
heat input in heat transfer equations
temperature
temperature at point (i, j) at time n
intermediate time temperature at point (i, j)
velocity vector
distance in x direction
distance in y direction
Greek Symbols
p = density
a = thermal diffusivity
T = shear stress tensor
8 =time
454
M. H. Seeland and K. D. Tunmerhaus
REFERENCES
1. R. Hiwada, CEER 10 (11):9 (1978).
2. R. B. Bird, W. E. Stewart, and E. N. Lightfoot, Transport Phenomena, J. Wiley and Sons, Inc., New
York (1966) p. 314.
3. B. Carnahan, H. A. Luther,-and J. 0. Wilkes, Applied Numerical Methods, John Wiley and Sons, Inc.,
New York (1969), p. 429.
4. J. Douglas, Jr., J. Soc. Ind. Appl. Math. 3:42 (1955).
5. J. A. Adamsand D. F. Rogers, Computer-Aided Heat Transfer Analysis, McGraw-Hill Book Co., New
York (1973), p. 181.
H-4
TRANSIENT POOL BOILING OF
LIQUID HELIUM USING A
TEMPERATURE-CONTROLLED
HEATER SURFACE
P. J. Giarratano and N. V. Frederick
NBS Thermophysical Properlies Division
Boulder, Colorado
INTRODUCTION
Many superconducting devices are subject to transient heating. These transients
occur during normal Operation in pulsed magnet energy storage systems, or they may
occur in superconducting magnets because of ftux jumping or mechanical instabilities
in the magnet windings. The thermal stability of the superconductors under these
conditions depends upon the effectiveness of the coolant (helium) to absorb the heat
and cool the superconductor below its critical temperature so that anormalzonewill
not be propagated.
Because the time scale for the heating, resulting from the above types of
disturbances, is of the order of milliseconds, the recovery process depends on the
transient heat transfer rate. Therefore, efficient cryostability analysis relies on a
knowledge of the transient heat transfer characteristics of liquid helium since
steady-state values may lead to unnecessarily conservative designs.
For pool-boiling systems, cryostability analysis requires information on the
entire q vs. !l.T curve including the nucleate-boiling, transition-boiling, and filmboiling regimes. A Iiterature search indicates that the transition-boiling portion of
the curve has not been established for helium even under steady-state conditions.
This is owing primarily to the hysteretic effect in going from the nucleate- to
film-boiling regime and the fact that the controlled parameter in the experiments has
traditionally been the heat ftux rather than the temperature difference.
Transient helium heat transfer data have previously been reported by
Jackson [~, Tsukamoto and Kobayashi ~2 ], Bailey [3 ], Iwasa and Apgar [4 ],
Steward [ ], Schmidt [6 ], and Brodie et al. [ ]. In all these sturlies heat ftux was the
controlled parameter.
In this experiment, a specially designed electronic temperature conteoller has
been employed to linearly vary the temperature vs. time of a carbon film heater
surface submerged in a liquid helium bath. The entire boiling curve q vs. ll.T,
including transition boiling, is obtained for various values of dT/ dt ranging from 0
(steady state) to approximately 7500 K/s.
455
P. G. Giarnt.o ud N. V. Fredericl
456
Carbon Film Surface f 10.5 cm • 0.334 cm l
Carbon Film Surlace 2
lnsula1ion
1.3 cm
0.1cm
0.64cm
T
Ouar1z '-
~
~ Carbon film
(0.5pm lhickl
: : ILialion
Fig. 1. Description of test sample.
EXPERIMENTAL SYSTEM
Test Sampie
The heater surface, which also served as the thermometer for determining the
surface temperature, is a 0.5-JLm (5000-A) thick carbon film which was vapor
deposited on a 1-mm-thick quartz substrate (see Fig. 1). The estimated thermal
diffusion time across the film is of the order of nanoseconds. The surface area of
carbon film surface 1 is 0.167 cm 2 (0.5 x 0.334 cm). This particular sample was used
in a previous experiment which required adjacent heater surfaces and this is the
reason for the two carbon films. However, in this experiment only the smaller surface
was utilized and calculations have determined that lateral heat transfer was negligible.
In the earlier part of the transient heating, where molecular conduction predominates, the ratio of the heat flux going into the helium to that going into the
quartz substrate is approximately
(1)
For helium and a quartz substrate at 4 K this ratio is approximately 16.
In the steady state the heat flux ratio is
~.
~i
s
I
1)
q,/q. = h, ( -k + -k- + -hif
(2)
where h1 is the film coefficient between the carbon film and fluid, h;1 is the film
coefficient between the insulation and fluid, and ~.. ~; are the thickness of the
substrate and insulation, respectively. Using a range, 0.05 s h1 s 0.8, and ignoring
1I h;1 since it is small compared to ~;/ k;, one obtains 50 < q1/ q. < 800.
Therefore, in both the transient and steady state, the heat transfer is largely
unidirectional from the heated surface to the fluid as desired.
The sample is suspended in a vertical orientation in a 33-liter liquid helium
storage dewar which is vented to the Boulder, Colorado atmospheric pressure of
0.82 atm (8.3o9 x 104 Pa). Therefore, the data were obtained under saturated
conditions with bulkfluid temperature of 4.02 K.
Transient Pool Boiling of LHe Using a Temperature-Controlled Heater Surface
457
VR!ll 1
From Function
Generator
Rlest
RSTD
Dual
ChaMel
Digital
Record ing
Oscilloscope
Fig. 2. Schematic of electronic temperature
controller and data acquisition equipment.
Tempersture Controller
The essential feature of this experiment was sweeping the temperature of the
carbon film linearly with time. This was accomplished by an electronic feedback
control system, the basic components of which are shown in Fig. 2. The output of the
operational amplifier controls the power supply current through the test sample so
that the output of the analog voltage divider (which is proportional to the test film
resistance) matches that of the VR(T), drive signal. VR(T), was predetermined to
give the desired temperature vs. time characteristic. For the steady-state data, the
drive signal VR(t) was a steady-state voltagerather than a time-sweeping voltage.
Although not shown in the schematic of Fig. 2, it was also possible to control the
power (heat flux) rather than the resistance (temperature). The steady-state data
obtained were the same under both modes of operation.
Data Acquisition
The voltage drops across the carbon film and a standard resistor were recorded
at intervals as close as 0.5 JLS with a digital recording oscilloscope, 2048 points were
recorded on each sweep of the oscilloscope on each of two channels giving a total
sweep time of about 1 ms for the fastest rate.
These data provided the carbon film temperature rise and the corresponding
heat flux as a function of time. A minicomputer system processed the data and stored
the results on magnetic tape for a permanent record.
Accuracy of Results
The carbon thermometer was calibrated at room temperature and by nitrogen
and helium vapor pressure measurements. The maximum uncertainty in temperature measurement owing to calibration and recording instrument error is estimated
to be ± 1.5%. Each time the carbon film was cooled from room temperature to
helium temperature, the resistance of the carbon film was recorded. This resistance
was found to be 2.6% less than the calibration resistance for the worst case. This
offset, determined before each run, was assumed to be constant over the entire
temperature range (up to 90 K) and was included in the calculations. Because of the
offset and calibration error the total uncertainty in ~ T is estimated to be of the order
±5% .
The heat fl.ux uncertainty is of the order ±0.4% arising from instrumentation
error, error in surface area measurement, and accuracy of the standard resistor used
in the measurement circuit.
458
P. J. Glarratano and N. V. Frederick
TIME . s
4 .5
4 .0
3.5
N
NE
E 3.0
<.>
~
-..
3:
x:::>
...
.....
...es:
-'
2.5
3:
x
""'
:::>
.....
2.0
4
1.5
.....
...es:
:r;
:r;
1.0
0.5
TIME. s
Fig. 3. Sampies of time-rlependent heat flux and temperature-difference data.
PRESENTATION OF RESULTS
Typical plots of controlled a T vs. time and the resulting q vs. time are shown in
Fig. 3 for two different values of dT/ dt. Since a finite amount of power must be
dissipated in the sample for the temperature controller to function, it is not possible
to start control at a T = 0. As seen in Fig. 3 a T was generally of the order 0.6 K at
t = 0. Consequently, the mode of heat transfer at the outsetwas already nucleate
boiling. As the rate of change of temperature difference was increased, the various
modes of pool-boiling heat transfer were observed. That is, the heat flux increased up
to qmax (nucleate-boiling mode), decreased to a minimum, qmin (transition-boiling
mode), and finally increased again beyond qmin (film-boiling mode). It was also
determined that for rates of dT/ dt less than about 600 K/s the film-boiling regime
was characterized by noise in the heat flux. This is illustrated in Fig. 3 for the slowest
rate of heating.
Figure 4 is a plot of heat flux vs. temperature difference for values of dT/ dt
varying from 7500 K/s down to 0, i.e., steady state. As can be seen, the steady-state
boiling curve bad a positive slope for all values of a T, i.e., even during the transition
to film boiling the heat flux continued to increase. However, as dT/ dtwas increased,
the negative slope portion of the q vs. a T curve began to emerge, becoming quite
pronounced at dT/ dt = 7500 K/s. Under the transient condition, the peak nucleateboiling heat flux, qmax• the minimum film-boiling heat flux , qm;n, and the aT's at
which they occur all increased with increasing dT/ dt.
The most unexpected aspect of the data shown in Fig. 4 is the shape of the
steady-state curve. The explanation for the absence of a negative-slope portion of
the curve is not immediately obvious to the authors. It is planned to investigate heat
transfer characteristics for surfaces other than carbon film and larger size samples to
determine whether size or surface effect may account for this portion of the curve. It
was noted, however, that for the steady-state data, there was virtually no evidence of
Transient Pool Boiling of LHe Using a Temperature-Controlled Heater Surface
459
/
1.0
I
11
I
Kutateladze ....._
......_
Correlation
P=0.82 atm
I
I /:
I ,/0.[
I / " /1.:
0.1
I
I
I
I
I
I
(Zuber Correlationl
· ···---- 7500 K/s
4000 K/s
- ··-
-
· 2000 K/ s
•··•· ···•· · 1000 K/s
- - - 400 K/s
- ····- 200 K/s
- - 4 0 K/ s
ar. K
Fig. 4. Helium-boiling curve for various rates of heating.
hysteresis in heat flux during several heating and cooling cycles. This was true under
temperature control and heat flux control. As dTI dt was increased, hysteresis
became evident and increased with increasing dT/ dt. This will be discussed in more
detaillater in the paper.
For comparison, Fig. 4 shows the nucleate pool-boiling correlations of
Kutateladze [8 ] , the film-boiling correlation of Breen and Westwater [9 ], and the
minimumfilm boiling heat flux calculated from Zuber's C0 J correlation. The deviation of these data from Kutateladze's predicted values is not unusual if one compares
the other steady-state nucleate-boiling data in the literature with the same correlation, e.g., Brentari's [11 ] comparison of helium pool-boiling data with the Kutateladze correlation. The deviation of these data from the Breen and Westwater
correlation for film boiling is more substantial, but not surprising, in view of the
absence of a transition boiling regime for these steady-state data. At high fiT for the
steady-state condition, the data asymptotically approach the Breen and Westwater
predicted film-boiling values.
DISCUSSION
The concept of the existence of a thin macrolayer of liquid beneath an
agglomeration of vapor bubbles during nucleate boiling near the peak heat flux has
been suggested by many investigators. An excellent discussion of this view and a
summary of the literature reporting the existence of the macrolayer is given by Yu
P. J. Giarratano and N. V. Frederick
460
and Mesler [12]. Based on these observations, it has been assumed that a liquid layer
of thickness 81 has been formed prior to the transient.
A further assumption that has been made is that the thermodynamic and
transport properties of the layer can be evaluated at the temperature of the heater
surface, and that the time-dependent heat input, q(t), is partially dissipated into the
bulk liquid above the macrolayer at a rate equal to the steady-state value, q•••
corresponding to liT(t). The remaining heat input goes toward heating and vaporizing the liquid film, i.e.,
(3)
where the first term on the right-hand side of (3) represents the sensible heat
accumulated in the liquid layer while the second term involves the heat absorbed in
vaporization of the liquid layer.
As· can be seen from Fig. 4, this model is in qualitative agreement with the
experimental data obtained in this study in that the transient heat transfer is greater
than the steady-state value for a given 11 T, and the difference increases with
increased rate of heating.
It was concluded from the data that the total excess energy, I (q,- q••) dt, up to
the time where minimum film boiling was established, tqmtn' was approximately a
constant for all rates of heating (see Table I). This result lends further support to the
concept of the liquid macrolayer. The initial thickness, 80 , was estimated by ignoring
the sensible heat term of (3) and these values have an average value of 4 x 10-4 cm.
Yu and Mesler C2 ] have reported thicknesses of the liquid macrolayer ranging from
4.8 x 10-4 cm to 9 x 10-4 cm for their nucleate-boiling data for water near the peak
heat ftux.
Since I (q 1 - q..) dt was a constant, as the time scale for the transient decreased
with increased rate of heating, it follows that the difference between the transient and
steady-state heat transfer must increase. This was observed experimentally.
In spite of the highly simplified model described above, which does not take into
account convective effects, it does appear to qualitatively predict theseexperimental
results with the heat absorbed by the liquid layer accounting for the enhanced heat
transfer under the transient condition.
Iwasa and Apgar [4 ] found that their transient helium film-boiling data could be
described by an expression similar to (3). The difference between their transient and
Table I. Calculation of 8o
Heating rate,
K/s
7500
4000
2000
1000
400
200
100
40
J[q(t)- q,.] dt,
J/cm 2
13.3 X 10-4
13.9 x 10-4
12.8 x 10-4
14.6 X 10-4
11.3 X 10-4
11.1 X 10-4
7.0 X 10-4
10.5 x 10-4
4.8 X 10-4
5.0 X 10-4
4.6 X 10-4
5.3 X 10-4
4.1 x 10-4
4.0 X 10-4
2.5 X 10-4
3.8 X 10-4
Avg = 11.8 x 10-4
Avg = 4.3 x 10-4
Transient Pool Boiling of LHe Using a Temperature-Controlled Heater Surface
461
steady-state heat transfer data was accounted for by the heat absorbed (on heating)
by the vapor layer insulating the heater surface and the latent heat absorbed in
vaporizing the bulk liquid above the vapor layer. This is consistent with the
experimental transient film-boiling data presented here as is also evident from Fig. 4
where q(t) > q•• in the film-boiling region and where the difference q(t)- q••
increases with increasing heating rate.
COMPARISON WITH DATA OF STEWARD
An interesting comparison of this data during the heating cycle is made with
Steward's [5 ] data for helium pool boiling in Fig. 5. First, however, it must be noted
that Steward's data were obtained with a carbon film sample similar to the one used
in this study but under different transient conditions. His data were obtained for a
step input in heat ftux, and thus he recorded and presented temperature rise as a
function of time for various constant heat ftuxes. By plotting the linear AT vs. time
variations used in this experiment on Steward's plot and selecting the q's and AT's
along this line, the q vs. AT plots for various dT/ dt could be obtained for Steward's
data. The maximum upper bound on the error in q and AT owing to this plotting
procedure is approximately ±50% for both variables. However, since a fairly smooth
curve could be drawn through the data points so obtained, a more realistic estimate
of the error is ±25% for both variables.
There is a distinct similarity between the two sets of data which were obtained
under different transient conditions. The similarity suggests that the heat transfer
process is independent of the temperature history if the time to achieve the AT is the
same. This matter requires moreextensive experimental and analytical investigation,
but if substantiated, then a singleexperimental investigation using, e.g., a step in heat
ftux as the transient condition could be used to predict q vs. AT under transient
conditions where the temperature difference is the time-dependent variable.
The similarity between the cross plot of Steward's data (obtained during a step in
heat ftux) and the present data (obtained during temperature control) are also
interpreted as evidence in support of the existence of the liquid macrolayer. That is,
the energy required to vaporize the liquid layer (resulting in the transition to film
boiling) is a constant and is independent of how the energy is applied.
Analogaus to the model described earlier for a temperature-controlled transient, we may write for a heat-ftux-controlled experiment the heat balance as
(4)
That is, for heat ftuxes above the steady-state peak nucleate-boiling heat ftux, q•• m•x
(below this heat ftux there would be no transition to film boiling) we assume again
that the heat input, qin, is partially dissipated into the bulk fluid at a rate equal to
q••max' and the excess heat goes to heat and vaporize the liquid macrolayer resulting in
a transition to film boiling. Minimum film boiling occurs when sufficient excess
energy has been transferred to completely vaporize the liquid macrolayer.
The energy balance for the time to reach minimum film boiling is given by
(5)
where Oexcess represents the energy required to heat and vaporize the liquid
macrolayer. Using Steward's experimental data for heat ftuxes which exhibited
transition to film boiling [q ~ 1 W /cm 2 ], it was determined that qssmax = 0.95 W /cm 2
.,;.
--3:...
NE
3:
.,;.
~
NE
I
' I"'
Stewa rd 's dcua,
CIOSS plot of
Obtained lrom
I
0.011
01
I
1
I
!I
I
I0
II
I
I
K 1S
I
!!
II
LH . K
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I
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t
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I
100
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1
rl
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/~
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<:T
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10
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o o1 !
0 1f
10
t
· ~·
I
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td
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I
I
I
. . .. ..
I
I
I
I
l
I
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I
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. ....
I
I
I
__/
llT. K
Fig. 5. Comparison of helium-boiling curves obtained under two different transient heating conditions.
!
! /L
0.011
::"IC
Obtained IIom
1:·.~:.:~:
10
I
'"
J
!!I
I! I I
II
::J
j
. . .. ..
I
"10:"
:::!.
~
Cl.
~
'"'l
~
.
?'!
Cl.
"'=
Q
=
!
:::
;-
~
~
~
I
~
""
.".
Transient Pool Boiling of LHe Using a Temperature-Controlled Heater Surface
463
and Oexcess = 14 X 10-4 J/cm 2 • Oexcess determined from Steward's data thus is in
agreement with the values given in Table I for the temperature-controlled experiment.
HYSTERESIS
A limited series of experimental runs are available in which the hysteresis in heat
ftux during heating and cooling cycles was investigated. Hysteresis, is defined here as
the difference between q(t)heatinj and q(t)cooling at the same 6.T. Experimentally,
attempts were made to maintain dT/ dtlheating = ldT/ dtlcooling and for some runs the
Rare • 1490 Kl s
Dweil
Ralo · 2900 K/ s
-- 0 Ms
-
"'E
150 Ms
10°
<>
;:
qs1udv s1a1e 1'
x
........
...
I
::1
I
I
1<[
:
...
'
....
I
10 '
I
I
I
<[
:
I
I
I
I
I
I,
I
I
I
- - ... J
10 -2
0.2
10
10
LH . K
IH. K
- 290 K/s
N
....
E
-..<>
E
3:
<>
~
x
........
...
x
::1
......
.....
::1
1<[
....
:
<[
:
IH. K
LH . K
Fig. 6. Hysteresis data including the film-boiling region.
P. J. Giarrataoo aod N. V. Frederick
...E
<>
~
><
...
.....
::I
...
I-
et
::z::
IH. K
Fig. 7. Hysteresis data in the nucleate-boiling region.
dwell time between heating and cooling cycles was varied from 0 to a time period
sufficient to reach steady state.
As noted earlier, the reported steady-state data exhibited no hysteresis. As the
rate of heating increased, hysteresis began to emerge and increased with increasing
heating rate. The degree of hysteresis also increased with dwell time between heating
and cooling. The graphs shown in Fig. 6 show the experimental data exhibiting these
trends. The temperature excursion was up to approximately 13 K, weil into the
film-boiling regime for all values of dT/ dt noted. However, as shown in Fig. 7, for a
temperature excursion in the nucleate-boiling region, little or no hysteresis was
detected even at the relatively high rate of heating, 1780 K/s.
The observed hysteresis in Fig. 6 is qualitatively understood in the context of the
simple models discussed earlier. That is, q(t)- q.. = dT/dt > 0 on heating and
q(t) - q.. = dT/ dt < 0 on cooling. This suggests that the degree of hysteresis for the
fast transients is greater than that for the slower transients. At dT/ dt = 0 (steady
state) the models predict q(t) = q•• for both heating and cooling and thus agrees with
the present experimental observation of no hysteresis for the steady-state condition.
The effect of dwell time between heating and cooling cycles, and the absence of
hysteresis in the nucleate-boiling regime, even for a fast transient, Fig. 7, is not
readily understood in terms of the simple models. A more detailed experimental
investigation and careful analysis of hysteresis during heating and cooling is required.
SUMMARY OF RESULTS
The entire boiling curve, q vs. ~ T, was obtained for various values of dT/ dt. This
was made possible through the use of an electronic temperature controller which was
used to linearly vary in time the surface temperature of the carbon film heat transfer
surface.
Under steady-state conditions (dT/ dt = 0) there was no evidence of transition
boiling in the usual sense, i.e., a decrease in heat flux with increased temperature
difference. Surface effects or sample size may explain this result; however, further
experimental investigation is required.
Transient Pool Boiling of LHe Using a Tempenture-ControUed Heater Sudace
465
As dT/ dt was increased, the transition-boiling regime began to emerge, the
peak nucleate-boiling heat ftux, the minimum film-boiling heat ftux, and the !iT's at
which they occurred all increased with increasing dT/ dt (see Fig. 4 ). A simple model
shows that the difference between the transient and steady-state heat transfer for a
given !1 T is accounted for by the excess heat required to vaporize a liquid macrolayer
of thickness approximately 4 JLm adjacent to the heater surface. Calculations
showed that the energy required to completely vaporize the macrolayer (complete
establishment of film boiling) is a constant of approximately 12 x 10-4 J/cm 2 • This
was shown to be true for the present data obtained with temperature as the
controlled variable as well as Steward's [ 5 ] data with heat ftux as the controlled
variable.
Hysteresis in heat ftux during heating and cooling cycles which extend iQ.tO the
film-boiling region increased with increased dT/ dt with no hysteresis for the
steady-state condition. This experimental Observation was also qualitatively
explained by the model which predicts q(t)- q•• -= dT/ dt (greater than zero on
heating, less than zero on cooling, and equal to zero for steady state). No hysteresis
was observed in the nucleate-boiling region even for the higher heating rates. The
model does not completely account for this result.
ACKNOWLEDGMENTS
The funding for this work was granted by the Air Force Office of Seienlilie Research, Bolling Air
Force Base, Washington, D.C. with W. Dunnill, Program Manager. The authors also gratefully acknowledge the contributions of V. D. Arp, M. C. Jones, and W. G. Steward through many helpful discussions
regarding this work.
NOTATION
CP = specific heat at constant pressure, 1/g-K
dT/dt= rate of change of temperature, K/s
h = heat transfer coefficient, W /cm 2 -K
k =thermal conductivity,.W/cm-K
q = heat flux, W/cm 2
t =time, s
~ T = surface temperature minus bulk temperature, K
Greek Symbols
a = thermal diffusivity, cm 2 /s
8 = thickness, cm
A = latent heat of vaporization, J I g
p
= density, g/cm 3
Subscripts
f =fluid
i =
incip =
in=
I=
max =
min =
ss =
s =
insulation
incipient nucleate boiling
input
liquid
maximum nucleate boiling
minimum film boiling
steady state
substrate
466
P. J. Giarratmo and N. V. Freclerick
REFERENCES
1. J. Jackson, Cryogenics 9:103 (1969).
2. 0. Tsukamoto and S. Kobayashi, J. Appl. Phys. 46:1359 (1975).
3. R. L. Bailey, "Heat Transfer to Liquid Helium in Pulsed Heated Channels," Experiment Report
RL-73-089, Dept. of Engineering Science, Rutherford High Energy Laboratory, Chilton, Didcot,
Berkshire, England (1973).
4. Y. lwasa and B. A. Apgar, Cryogenics 18:267 (1978).
5. W. G. Steward, Intern. J. Heat Mass Transfer 21:863 (1978).
6. C. Schmidt, Appl. Phys. Lett. 32:827 (1978).
7. L. C. Brodie, D. N. Sinha, J. S. Semura, and C. E. Sanford, J. Appl. Phys. 48:2882 (1977).
8. S. S. Kutateladze, Fundamentals of Heat Transfer, Academic Press, Inc., New York (1963).
9. B. P. Breen and J. W. Westwater, Chem. Eng. Progr. 58(7):67 (1962).
10. N. Zuber, M. Tribus, and J. W. Westwater, "Hydrodynamic Aspects of Boiling Heat Transfer,"
AECU-4439 (1959).
11. E. G. Brentari, P. J. Giarratano, and R. V. Smith, NBS Tech. Note No. 317 (1965).
12. C.-L. Yu and R. B. Mesler, Intern. J. Heat Mass Transfer 20:827 (1977).
DISCUSSION
Question by J. W. Westwater, University of Illinois: The boiling heat flux at any ~ T is determined in
part by the fluid flow pattern set up at that ~ T. Most of the runs described in this paper were completed in
less than one second. This seems too short a time to allow for the establishment of any flow pattern
characteristic such as the peak heat flux. What rate of changing the heater temperatures do you think will
give an unsteady-state boiling curve which is equivalent to the steady-state boiling curve?
Answer by author: All of our experimental data show that for heating rates less than 40 K/s, the
unsteady-state boiling curve is essentially equivalent to the steady-state boiling curve.
Comment by P. Seyfert, Centre d'Etudes Nucleaires de Saclay, France: The model suggested in this
paper implies a macrolayer of fluid ad jacent to the surface with a heat flow independent of initial thickness.
The Observations presented by Tsukamoto et al. * suggest, on the other hand, a liquid layer with initial
thickness strongly dependent on heat flux. Even though, different fluids were investigated (helium and
nitrogen) could you comment on this contradiction?
Answer by author: We cannot presume to explain Tsukamoto's observed heat flux dependence of the
vapor film thickness which was formed at the onset of film boiling in his experiment. However, if we
assume that it is reasonable to compare their vapor film thickness with the nucleate-boiling liquid film
thickness of our study, then we pointout that the mass equivalent of liquid thickness which would produce
the vapor film thickness reported by Tsukamoto ranges from 1.4 x 10-4 to 2.9 x 10-4 cm as given by
[Bvapor(Tsukamoto) X (Psatliquid/Pvapor@ Tttansition)]. This is the same order of liquid thickness calculated
from the modeland helium data of our paper, namely, 4.3 x 10-4 cm.
Question by D. Petrac, Jet Propulsion Laboratory: A carbon film is used both as a heater and as a
thermometer in your measurements. Did you consider the effect of reflections from the carbon layer in the
determination of the ~T since the calibration was performed at different power inputs (current Ievels)
than during the measurements?
Answer by author: Since the presentation of this paper, we have conducted tests on carbon film
samples similar to the one used in this experiment to determine more conclusively the current dependence
of the resistance. This was achieved by installing an independent heat source between the lower surface of
the substrate and the insulation. The carbon film covered the entire top surface of the substrate. For
various values of power input to the independent heat source, the resistance of the carbon film was
recorded using a 2 x 10-6 -A current source. Then, with the independent heat source turned off, the power
input to the carbon film was varied and the corresponding resistance recorded. A plot of resistance vs.
power Ievel for the two cases was the same. We conclude that for these films the resistance is independent
of the current Ievel through the film and depends only on the temperature.
* 0. Tsukamoto, K. Uyemura, and T. Uyemura, in Advances in Cryogenic Engineering,
Press, New York (1980), p. 476.
Vol. 25, Plenum
H-5
HEAT TRANSFER DURING SUBCOOLED
HYDROGEN BOILING
B. I. Verkin, Yu. A. Kirichenko, and N. M. Levchenko
Academy of Seiences of the Ukrainian SSR
Kharkov, USSR
INTRODUCTION
Various applications of cryogenic liquids in engineering have created continuous interest in the heat transfer processes occurring during subcooled boiling.
Experimental studies of pool boiling of subcooled cryogenic liquids are few in
The
number. These include studies with hydrogen CJ. nitrogen [2 ], and helium
available data are insufficient to determine the subcooling effect upon the heat
transfer coefficients. The limited information which is available on the vapor bubble
dynamics in boiling nitrogen was obtained with very low subcooling, i.e., about
1 K [ 4 ].
In this work the vapor bubble dynamics and heat transfer during subcooled
hydrogen boiling were studied experimentally in the pressure range from 0.072 to
5 bar. A model is proposed to explain the heat transfer mechanism operating in
subcooled boiling. Based on the model and experimental data, a relationship has
been derived which adequately describes the heat transfer in boiling hydrogen with
maximum subcooling for p:::; 3 bar.
eJ.
EXPERIMENTAL CONDITIONS
Bubble growth and detachment were studied during subcooled hydrogen
boiling with the aid of high-speed photography at pressures ranging from 0.072 to
1 bar, and subcooling (Tsat- T1) ranging from 0 to 6.4 K. Heating was provided by a
dc current passing through the steel and copper-nickel horizontal tubes, 3 to 5 mm in
diameter. The temperature of the heater wall and the liquid was measured with
platinum resistance thermometers. Subcooling was provided by helium supercharging. The mean bulk temperature of the liquid was maintained constant and
equal to the triple point by keeping it in contact with solid hydrogen. Thus, the
experiments were carried out under maximum permissible subcooling for each
pressure.
GROWTH AND DESTRUCTION OF V APOR BUBBLES
The growth and destruction of vapor bubbles in subcooled boiling hydrogen are
These results are shown in Fig. 1, where
described by Daugherty-Rubin's theory
the relative subcooling and reduced pressures are CptJ/ L < 0.08 and pj Pc < 0.03,
eJ.
467
468
8.1. Verkin, Yu. A. Klrichenko, and N. M. Levchenko
respectively. The equation for bubble growth is given by
R = ß-r"
with n
= 0.5, and the growth modulus is
ß = cß"a
n
I
ßya
= cß
(1)
(A-~Tsat)"ß
,-va
Lpva
(2)
with n13 = 0.75 and C13 :::::: 2.
Observations made of hydrogen boiling under large subcooling conditions
(I} > 4.5 K), showed that individual bubbles became attached to the heater and their
size remained constant during the entire period of filming (0.2 s).
DETACHMENT CHARACTERISTICS
The pressure dependence of the vapor bubble detachment radii Rd is shown in
Fig. 2 along with data for saturated hydrogen boiling [6 ' 7 ]. For subcooled boiling at
0.072 to 0.2 bar Rd.ub :=:::: RtJ..,; but for p > 0.2 bar Rd.ub < RtJ.., (the indices "sub" and
"sat" refer to subcooling and saturation, respectively).
The data obtained in this study may be qualitatively (and for Rd even quantitatively) interpreted in terms of the dynamic and quasistatic conditions of vapor
bubble growth and detachment [8 ]. At low pressures the detachment characteristics
t
(( M•
0 ·1
!;
(0
Ql
• ·z
D-j
~
0~
t-.._ 0
\
llI
!lt.o.<_
(0
tl'!
ll6
~
"
\.
_,
lo
1--
).a,
......
1-o--,
1'---P.k.
9 6
Fig. 2. Departure radius of vapor bubble vs. pressure for
boiling hydrogen. Saturated liquid: 1 and 2, present results; 3,
Bewiloqua et al. ['], subcooled boiling.
469
Heat Transfer during Subcooled Hydrogen Boiling
a8
-*
• - z 00 _,
6 - " (Ö) - 6
Q- 1
~
0
-~
Fig. 3. Tmax/ Tc vs. reduced subcooling Cp t~/ L. Legend :
1, water, reference 10; 2, reference 10 (p = 1 bar) ; 3,
hydrogen, present results; 4, nitrogen, present results ; 5,
reference 9 (p = 1 bar); 6, unexplained results.
T
/
/~
_._
1\
_T_ . . .J-•
'?
~~
0
~
L
(}()}
{]Oll
Q(Jd
tXM
(J.f
tll2
are governed by dynamic forces , i.e., forces of the liquid inertial reaction [8 ] . Thus,
_ C2ß2; 3g-2; 3
R d _- c R ß4! 3g -1 / 3,
(3)
'Td T
At higher pressures the ftow changes to the quasistatic regime [8 ] and the Rd
value can be found from the buoyancy-surface-tension equilibrium relation given by
[3
J1/ 3 -
R cU
R _ _
d 2 g(pi - Pv)
_ [
3bU 2T.sat
]1/ 3
g(pt - Pv)flTsat
'
(4)
where Re = bR* is the radius of the microcavity from which the bubble departs, and
R* is the critical radius of the vapor nucleus.
Experimental data for Rd and 'Td with saturated and subcooled hydrogen boiling
(Cp-&1 L < 0.08) are generalized by (3) and (4) for CR : : : : 1, bsat::::::: 15, bsub::::::: 4, and the
growth moduli calculated by (2). Maximum errors are estimated tobe not more than
±30%.
Daugherty-Rubin's theory [5 ] is helpful in describing the time dependence of
the relative magnitudes of bubble radius (RI Rmax vs. Tl Tc, where Tc is the time
covering the period from bubble nucleation till its complete destruction), if the
parameter 'Tmaxi'Tc is known. In Fig. 3 'Tmaxi'Tc is shown vs. the relative subcooling
Cp-&I L along with data for boiling water [9 ' 10 ]. 'T maxi 'Tc is seen to vary from 0 to 0.5 as
CptJIL approaches 0.1. Note that 'Tmaxi'Tc = 0.5 is the limiting value in DaughertyThe curve in Fig. 3 can be employed to obtain a rough theoretical
Rubin's theory
estimate of the relative magnitude of bubble evolution. Absolutevalues of R(T) can
be derived if some technique for evaluating Rmax and 'Tmax is available. For the entire
range of the parameters studied Rmax ::::::: Rd; the error is estimated tobe no more than
±5% . The relation between 'Tmax and 'Td is shown in Fig. 4, where the data for water
arealso given. 'Tdi'Tmax increases for greater subcoolings. Once 'Td is known, 'Tmax can
be calculated from relation
eJ.
(5)
Fig. 4. Td/Tmax vs. reduced subcooling Cp{}/ L. Water: 1,
reference 10 (p = var); 2, reference 10 (p = 1 bar).
Hydrogen: 3, present results. Nitrogen: 4, present results.
aoz
470
8.1. Verkln, Yu. A. Klrlchenko, and N. M. Levchenko
BEAT TRANSFER MODEL
To develop a heat transfer model assume that the heat flux density q during
subcooled nucleate boiling consists of three components,
(6)
where q 1 is a fraction of the heat flux density consumed by vaporization atthe heater,
q 2 is the fraction expended on heating the cold liquid replacing the bubble that has
just departed (or condensed) from the heater, and q3 is the fraction of the total heat
flux density removed through natural convection. The latter is negligible for
developed nucleate boiling.
We can write
(7)
and
(8)
Here, Ii T 1 is the temperature gain in the "cold liquid" replacing the departed bubble.
In the first approximation
liT1
=
Tw -11
2
Tt
= O.S(Tw - Tt) = O.S(IiTsat + ~)
On substituting (7), (8), (9) into (6), provided that q3
qsub
(9)
= 0, one obtains
= ~7TR~fLpvz(1 + O.S.Ja + O.S.fasub)
(10)
where
di
_
"'a-
Pt Cp Ii Tsat
L Pv '
di
_
PtCp~
eTasub- L
Pv
Within the model considered, (10) suggests that during saturated liquid boiling
(~
= 0, .faaub = 0) and at sufficiently high pressures (.Ja < 2) the heat transferred
from the heater to the liquid is mainly consumed by liquid evaporation at the heater
{q1 > q 2 ). During saturated liquid boiling at low pressures (.Ja > 2) and boiling with
considerable subcooling (.Ja + .Jasub > 2) the energy from the heater is expended on
heatingthe liquid {q2 > q 1 ). This mechanism of "exchange" between the "bot" liquid
of the boundary layer at T1(Tw > T1 > 11) and the "cold" liquid of the core at Tt
accounts, as will be shown below, for the pressure dependence of the heat transfer
coefficients arising during subcooled boiling.
The model developed permits the heat flux fraction for evaporationtobe found.
From (7) and (10) it follows that
qsub
2 + .Ja
+ cfasub
(11)
For ,Ja + .fasub » 1 (Iow pressures and considerable subcooling at both high and low
pressures)
(11a)
Heat Transfer during Subcooled Hydrogen Boiling
471
As seen from (11) and (11a), the heat ftux fraction for vaporization increases as
pressure rises and the total temperature drop (Tw - T 1) decreases.
The model proposed is employed to relate the heat transfer coefficients for
saturated and subcooled liquid boiling. Equation (10) leads to the relation between
the heat ftux densities for subcooled and saturated liquid boiling
qsub = R~;ubfsubZsub(2 +Ja + Jasub)
2 +Ja
R d ••.fsatZsat
qsat
For similar temperature drops (d Tsub
(12)
= d Tsat)
(13)
The expression in the brackets is readily calculated for a given d Tsat· This can be
simplified for the limiting cases of very high or very low pressures as
PvCpiJ
1+
-2Lpv
(14)
for Ja « 1 and
{}
1+-
(15)
aT,
for Ja » 1.
To evaluate the factor in front of the brackets in (13) requires a knowledge of the
boiling molecular characteristics of saturated and subcooled liquids (Rd, ß, Z). If the
time dependence of the bubble radius obeys (1), the growth modulus is represented
by (2) [ 6 ], the frequency f being 1I T d, and the density of the vaporization centers Z is
found from
(16)
where Cz is a constant about 10-7 to 10-8 and nz
becomes
=
2 [11 ]. Equation (13) then
(17)
=
For similar q (qsub qsat), asub/ asat can be estimated to a first approximation, if
the assumption of q- aT;at is made. Then
( CXsub)
asat
q
=
(CXsub) 113
asat
(18)
.6.Tsat
Weshall calculate asub/ asat for boiling hydrogen using (13), (17), and published
data on boiling molecular characteristics.
According to Judd and Merte C2 ], the density of vaporization centers seems to
be weakly dependent on subcooling, and hence for all cases it is assumed that
Zsub = Zsat· Substituting (2) and ßsat = 4Ja 0 · 5 ~ [ 6 ] into (17) and taking into account
that
(19)
471
2
~7
tO
8
6
64ft)''
-
-
~ :;
*
2
8. I. Verldn, Yu. A. Kiricbenko, and N. M. Levcbenko
2
-.Q._
Fig. 5. Dependence a 1ub/a .., on pressure. Experiment: 1,
= 104 W/m 2 ; 2, q = 2 x 104 to 6 x 104 W/m2 • Calculation:
3, equation (21).
0
* 6 8f0'
P.la,
*
2
q
b8
which follows from Fig. 2 at p > 0.4 bar, one obtains
= (asub)
(q•ub)
qsat 4T..,
asat
= 0 _125"al/2(t +
4T..,
"a
"asub)
2+
(20)
Having taken equation (17) into account, the relation for the heat transfer
coefficients at constant q is now given by
fh
( asub)
asat q
"a
= 0.5"al/6(1 +~)
2+
1/3
(21)
Figure 5 plots equation (21) and presents appropriate mean experimental data.
To make the calculation more convincing we assume "a = 2"ao, where "ao is
calculated from the temperature drop corresponding to the onset of liquid boiling.
Figure 5 shows that the model that was developed adequately describes the
experimental data up to a pressure of 4 bar; the maximum deviation of the calculated
dependence, curve 3, from the experimental points is about ±20%. At a pressure of
5 bar the experimental and calculated values differ by a factor of 2.
The estimates obtained (Fig. 5) permit the conclusion that the model provides a
reasonable qualitative description of the relation between the heat transfer
coefficients for boiling subcooled and saturated liquids. In fact, the calculation using
(17) and (21) together with the experimental data give similar qualitative results:
aaub = aaat for p < 0.3 bar, asub < asat for p > 0.5 bar. The relation decreases with
increasing p. The quantitative agreement between the experimental data and the
model to within ±20% at p = 0.072 to 4 bar can be considered satisfactory for such a
rough estimate.
Experimental data showing the pressure dependence of the heat transfer
coefficients aaat and asub are plotted in Fig. 6, where the heat transfer coefficient
variations are presented in relative magnitudes a (p )/ a (p = 0.5 bar). Normalization
to a (p = 0.5 bar) was chosen because at p < 0.5 bar, asat = asub as the experimental
results suggest. As seen in Fig. 6, the difference between the heat transfer coefficients
aaat and aaub is quite pronounced under high pressures. At p = 5 bar they differ by a
factor of 2 to 4.
,f (P,
« (t~
I
• -1
0 -2
~
I(!
6
6
/ V
5
V -j
l> _,
2
~ vt
A
.6
F1'"
'i.
*6610'
0
V
P.kr
2
4
6611l'
2
*
b8
Fig. 6. Dependence of relative heat transfer coefficients on
pressure in boilin} hydrogen. Subcooled boiling: 1, q =
1 x 104 ; 2, 2 x 10 ; 3, 4 x 104 ; 4, 6 x 104 W/m2 • Saturated
hydrogen boiling: 5', q = 1 x 104 ; 5, (2 to 4) x 104 W/m2 ; 6,
calculation by equation (23).
473
Heat Transfer during Suboooled Hydrogen Boillng
HEAT TRANSFER COEFFICIENTS DURING HYDROGEN
BOILING AT IDGH PRESSURES
Tests reported above on the proposed model show that its mechanism of heat
removal from the heater is sufficient to account roughly for the dependence of the
heat transfer coefficient on pressure and subcooling. During subcooled hydrogen
boiling the heat transfer coefficients can be found using (8). Using (9) and (16) with
nz = 2, and/ = 1/Td = ß 2 /R~ into (8) Ieads to
_~ C
q -
37r R
C2C A(Lpv) 11 \Cppl) 312 (äTsat + "') äT!:f6
(3 z
4/3T5/3 [{p ) ]1/3
U
sat
I Pv g
(22)
Assuming a slight difference between the temperature drops for saturation and
subcooling and taking into account that asub = qsub/ ä Tsat. a less precise but more
compact and convenient relationship is obtained after some transformations neglecting the magnitudes of low powers as
asub
A
1/3
(
cp/)1) 1/2(
= B1[(PI _ Pv ) g ]1/9 -T.
U sat
äTsat
+"'
)1/3 2/3
(23)
q
Here B1 = B · F, where B = ~~7rCRC~Cz) 113 = 0.34 x 10-2 with Cz
B = 1.7 x 10-2 with Cz = 10- , and F defined by
F
= (LPv
äTsat)
=
10-8 and
1118
(24)
uTsat
can be considered a dimensional constant owing to its weak dependence on pressure.
Inserting the mean value of ä T sat for each pressure, F varies from 2.5 to 2.75 cm - 1118
in the range of pressures from 0.3 to 5 bar. Its maximum deviation from the mean
value is ±5% .
In the calculation using equation (13) äTsat was used to denote the temperature
drop during the saturated liquid boiling. In this case an error of about 5% is
permissible; the error results from factors F and (äT. + "'). A more accurate
calculation of heat transfer may be made using (22).
The experimental data on heat transfer in subcooled boiling hydrogen are
generalized (Fig. 7) using (23) in terms of the coordinates asub/ A, q, where asub is the
experimental heat transfer coefficient and A is the set of thermophysical properties
in (23), i.e., A = asub/ Bq 213 •
2
lJ
~
R
6
0-J
lf
t;,. - ~
2
Fig. 7. Generalized experimental results for subcooled
hydrogen boiling, equation (23). Legend: 1, p = 0.072 bar;
2, p = 0.14 bar; 3, p = 0.25 bar; 4, p = 0.54 bar; 5, p =
1 bar; 6, p = 21bar; 7, p = 3 bar; 8, p = 4 bar; and
9, p = 5 bar.
b'~
D- f
0-2
8
~
V~ ~
/a ~~
~ Vo'
r:s
~
2
.~
~
0-5
V -6
r-.~~"' ·y
6
·oo
D- '
0 -8
~IN'
0 -g
9 "IM'
10' 2
4 " 8 tJ'
2
4 "8 tJ'
2
474
8. I. Verkin, Yu. A. Kirlchenko, and N. M. Levchenko
As seen in Fig. 7, for q > 7 x 103 W /m 2 the maximum error in the generalization is ±25% for the pressure range of 0.072 to 3 bar. The experimental coefficientB
is about 0.5 x 10-2 • At p = 4 to 5 bar, the heat transfer coefficients depart from the
generalized dependence. The difference between experiment and the calculation
utilizing (23) for p > 3 bar is also illustrated in Fig. 6. At p :53 bar the calculated
dependence essentially coincides with the mean experimental results. This is in
agreement with the data in Fig. 5, which shows that for p > 4 bar the estimate by the
model differs sharply from experimental results.
The fair amount of discrepancy between experiment and theory at p > 3 bar
suggests that either some additional aspects of the process other than evaporation in
the bubble and "liquid exchange" between the boundary layer and the cold core
should be considered under relatively high pressures and subcooling, or that the
expression for the molecular characteristics of boiling at p :5 1 bar should not be
extrapolated to the pressures greater than 3 bar.
NOTATION
A = Olsub/ Bl
a = thermal diffusivity, m 2 /s
b = constant
CP = isobaric specific heat, J/kg-K
eR. c,., Cz = constants
g = gravitational acceleration, 9.81 m/s 2
L = latent vaporization heat, J /kg
nß, nz = powers
p = pressure, bar
q = heat flux density, W /m 2
R = bubble radius, m
Rmax = maximum bubble radius, m
T = temperature, K
~ T = temperature drop, K
Z = density of vaporization centers defined by equation (16)
13
clh
Greek Symbols
01 = heat transfer coefficient, W /m 2 K
ß = growth modulus
A =thermal conductivit~, W /m K
p = mass density, kg/m
fJ = subcooling, K
r =time, s
T max = time Of maximum growth, S
u = surface tension coefficient, N/m
Subseripts
C = critical value
d = detachment
I=
sat =
sub =
v =
w=
liquid
saturation
subcooled boiling
vapor
heater wall
REFERENCES
1. C. F. Sindt, in Advances in Cryogenic Engineering, Vol. 19, Plenum Press, New York (1974), p. 427.
2. B. Mazurek, R. Gruca, and J. Rutkowski, in Proc. 6th Intern. Cryogenic Engineering Conference, IPC
Science & Technology Press, Guildford, England (1977), p. 230.
Beat Transfer during Subc:ooled Hydrogen Boning
475
3. H. Tsuruga and K. Endoh, in Proc. 5th Intern. Cryogenic Engineering Conference, IPC Science &
Technology Press, Guildford, England (1975), p. 262.
4. H. C. Hewitt and J. D. Parker, Trudy AOIM Teploperedacha 90c::22 (1968).
5. D. E. Daugherty and H. H. Rubin, in Proc. 1963 Heat Transfer and Fluid Mechanics lnst., Stanford
University Press, Stanford, California (1964), p. 222.
6. Yu. A. Kirichenko and N. M. Levchenko, Zh. Prikl. Mekh. Tekh. Fiz. 1976(4):103 (1976).
7. L. Bewiloqua, W. Görner, R. Knöner, and H. Vinzelberg, Cryogenics 14:516 (1974).
8. Yu. A. Kirichenko, Inzh. Fiz. Zh. 25(1):5 (1973).
9. L. Leppert and K. Pitts, in Prob/emy teploobmena, Atomizdat, Moscow (1967), p. 142.
10. D. M. Kostanchuk, thesis for candidate of Technical Seiences degree, Kiev, ITTF AN Ukr. SSR
(1971).
11. K. A. Zhokhov, in Aerodinamika i teploobmen v rabochikh elementakh energooborudovania, TsKTI,
Leningrad (1969), p. 131.
12. R. I. Judd and H. Merte Jr., Int. J. Heat Mass Transfer 15(5):1075 (1972).
H-6
OBSERVATION OF RUBBLE FORMATION
MECHANISM OF LIQUID NITROGEN
SUBJECTED TO TRANSIENT HEATING
0. Tsukamoto and T. Uyemura
Yokohama National University
Yokohama, Japan
and
T. Uyemura
Tokyo University
Tokyo,Japan
INTRODUCDON
Several photographic observations of steady-state pool boiling of liquid
nitrogen have been published C-2 ]. However, there are few papers reporting the
Observation of transient-state boiling. Also, there is little information on bubble
formation mechanism or heat transfer characteristics of the transient-state boiling in
~
a cryogenic liquid.
This paper presents optical observation of bubble formation at the surface of a
thin wire, heated by a stepwise transient in liquid nitrogen. Bubble formation was
observed by a high-speed camera with a frame speed of 5000 frames/s. Interesting
phenomena, peculiar to transient heating, were observed.
Usually, it is assumed that when a wire is heated with a stepwise increase in the
current, the boiling at the wire surface is nucleate for a short while after the step
current has passed; eventually the boiling moves into film boiling, provided that the
heating power per unit surface area of the wire is above the steady-state bornout heat
flux. This follows because part of the Joule heating power is absorbed in changing the
enthalpy of the wire at the beginning of the heating. However, it was observed that
the boiling at the surface of a wire immersed in a saturated liquid nitrogen bath went
directly into the film-boiling state without passing through the nucleate-boiling state.
This phenomenon occurred even when the wire surface heat flux was below the
steady-state bornout heat flux. Recently, Shinha et al. [3 ] reported on experimental
results of transient heat transfer characteristics in liquid nitrogen, where they
referred to a "premature" transition to film boiling. They verified that this is the case
by measuring the heat transfer characteristics associated with the process. Highspeed photographs of such a premature transition to the film boiling have been made
in this study. In addition, the transient heat transfer characteristics associated with
476
Obse"ation of Rubble Formation Meehanism of Liquid Nitrogen
477
the process were measured. This paper discusses the bubble formation mechanism
for the transient heating and its relation to the heat transfer characteristics.
EXPERIMENTAL ARRANGEMENT
The experimental arrangement is shown in Fig. 1. A platinum wire was
immersed horizontally in a pool of liquid nitrogen (at atmospheric pressure)
contained in a 10-cm-ID glass dewar. The platinum wire was mounted under spring
tension. The length and diameter of the heating wire were 23.5 mm and 0.05 mm,
respectively. By applying a step voltage, a step current was fed to the wire through a
current-limiting resistor. The resistance of the current-limiting resistor was
considerably !arger than that of the wire so that the current could be regarded as
constant in the range where the wire temperature was below 200 K. Even though the
amount of Joule heating varied with the change in resistivity of the wire, the driving
step current was sufficient for the present experiment.
Current and voltage waveforms of the wire were recorded by digital transient
recorders. The bulk temperature of the wire was estimated from the value of the
resistance of the wire. The surface temperature of the wire was assumed to be equal
to its bulk temperature because the wire was so thin that its cross-sectional
quartz
tlmer
glass dewar
current
waveform
T. R. 2
valtage
waveform
500W mercury lamp
hlgh-speed
liquid N2
movle camera
platinum wire
C. R.
current limiting resistor
T. R.
digital transient recorder
Fig. 1. Schematic of experimental arrangement.
478
0. Tllllbmoto IUld T. UyeJHI'II
temperature distribution could be regarded as being uniform. The transient heat ftux
q(t) transferred from a unit of wire surface into the liquidnitrogenwas determined
from the following equation:
q(t)
= __!__ [v(t)i(t) _ pc(T).".{~) 2 d7l
'TI'd
L
2
dtJ
(1)
Differential values of the wire temperature were determined by a graphical differential method.
The photographs were taken with a 16-mm high-speed movie camera. In the
experiments, the movie camera was started 0.6 s before a step current was fed to the
wire initiating the transient heating event. The framespeedwas about 5000 frames/s
when the wire current began to build up. The starting times of the movie camera and
the transient heating event were controlled by a quartz timer. The precise frame
speed and event start time were determined from time marks on the film. Lighting
was provided from the rear by a 500-W mercury lamp diffused through a frosted
glass.
The Ievel of liquid nitrogen was kept several centimeters above the platinum
wire throughout the experiments. All data and photographs were taken at atmospheric pressure.
RESULTS AND DISCUSSIONS
The experimental steady-state bornout heat ftux was 17 W /cm 2 • For step
heating, direct transitions to film boiling occurred whenever the surface heat ftux was
more than 50% of the steady-state bornout heat ftux. A typical example of
experimental current and voltage waveforms which were obtained during one such
direct transition to film boiling is shown in Fig. 2. At t = 0, a step current was fed to
the wire. The critical current icr above which the direct transition to film boiling
occurred was 0.90 A and the corresponding Joule heating power per unit surface
area of the wire was 8.2 W I cm2 for a temperature difference of 25 K. Temperature
changes in the wire for various values of the step current are shown in Fig. 3. For the
case in which direct transition to film boiling occurred, the temperature rise of the
wire was small for a short time period after the step current bad been fed to the wire.
Then, the wire temperature began to rise rapidly [curves (a), (b), and (c) in Fig. 3]. At
a current near icr, the transition can be either sametime to film boiling or to nucleate
boiling. For the case where the transition to nucleate boiling occurred, the wire
temperature initially approached a steady-state convective value and then decreased
when the nucleate boiling began [curve (d) in Fig. 3]. (Usually, the transition to
nucleate boiling took more than several seconds after the initiation of heating, and
the temperature trace when nucleate boiling beganisnot shown in the figure.) Fora
smaller current, the wire temperature approached a steady-state convective value,
and no boiling occurred [curve (e) in Fig. 3].
High-speed photographs of the liquid-vapor interface for the voltage and
current waveforms of Fig. 2 are presented in Fig. 4. This is the case where a
premature transition to film boiling occurred. For a short time after a step current
bad been passed through the wire at t = 0, no change occurred around the wire.
However, at t = t4 , a propagating vapor sheath quickly surrounded the wire [photographs (a) through (c) of Fig. 4]. The entire wire was surrounded with a vapor
sheath in less than 3 ms after the first vapor appeared. After that, the surface of the
vapor sheath began to undulate with the vapor sheath becoming divided into several
Observation of Rubble Formation Mechanism of Liquid Nitrogen
479
2.0
>
.
........,"'
11>
~
1 .2
0
>
0 . ~
0
50\
td
100
150
200
150
200
time , ms
1.0
<.
..
11>
11>
0.
E
"'
0.5
0
50
100
time , ms
Fig. 2. Example of current and voltage waveforms during heating
of wire. Joule heating per unit surface area of the wire is
10.4 W /cm 2 at t = td.
parts [(d) through (f) in Fig. 4]. This process consumed about 5 ms. Each part of the
divided sheath then grew to a bubble. The bubbles kept growing until they separated
from the wire [(g) through (h) of Fig. 4]. Steady film boiling occurred thereafter. The
bubble formation process, as shown in Fig. 4, was generally observed, when a
premature transition to film boiling occurred. When the heat flux to the wire surface
increased above the steady-state burnout heat flux, many small bubbles appeared
almost simultaneously at t = td on the wire surface as shown in the photographs of
Fig. 5. These small bubbles coalesced and a thin vapor sheath with undulated surface
surrounded the wire. Then, the vapor sheath divided into larger bubbles and film
boiling commenced. The time td when the vapor sheath surrounded the wire
coincided with the time when the wire temperature began to rise abruptly. When the
wire surface is surrounded by the vapor sheath, the heat is transferred through the
vapor sheath and the heat transfer coefficient decreases abruptly. The value of td
depends on the heating power. Curves of td vs. the heating power per unit surface
area of the wire are shown in Fig. 6. Values of td varied considerably. Variations were
larger as the heating power was decreased. Average thicknesses of the vapor sheath
for various values of heating power per unit surface of the wire are listed in Table I.
The mechanism of the vapor sheath formation is believed to be as follows: When
a step current passes through the wire, liquid araund the wire is initially heated by the
0. Tsukamoto and T. Uyemun
480
(b)
(c)
50
40
.,
00
"". 30
~
(d)
20
(e)
10
100
50
150
200
t, ms
Fig. 3. Temperature changes of the wire for various values of wire current. (a) I = 1.05 A
(q = 10.5 W /cm 2); (b) I= 0.98 A (q = 9.6 W /cm 2 ) ; (c) I= 0.92 A (q = 8.5 W /cm 2 ); (d) I=
0.88 A (q = 7.2 W/cm 2 ); (e) I= 0.68 A (q = 4.1 W /cm 2 ) . (q in parenthesis is the value at t = td.)
heat conducted from the surface of the wire CJ. Convection of liquid around the wire
is not fully developed in a time as short as td. The liquid around the wire is
superheated until, at td, it vaporizes abruptly. If this is true, the latent energy required
to form the vapor e., which is contained in the vapor sheath, should agree with the
energy ec which is transferred through the wire surface until the vapor sheath forms,
provided that convection of the liquid is not completely developed (see Table I).
( a)
t=O msec
( b)
t= 54 . 6 msec
(c)
t= 55 . 8 ms e c
.
(e )
t=61. 3 msec
\ f) t =6j.2
rn~ ec
( d ) t=59.4 msec
-
(g ) t =68 . o mc;ec
(h) t= 73 . 8 ms e c
Fig. 4. High-speed photographs of the vapor-liquid interface at the wire surface. Photographs show the
case for the premature transition to film boiling (q = 10.4 W /cm 2 ).
Observation of Rubble Fonnation Mechanism of Liquid Nitrogen
-
I
(a)
481
t =O msec
(b) t =4 . 6 msec
t =4 .8 msec
(c)
(d)
t=5.2 msec
(h)
t =29.0 msec
•
(e)
t=7.0 msec
(f)
t=B. 6 msec
t=16.6 msec
(g)
Fig. 5. High-speed photographs for higher Joule heating power (td = 4.6 ms}. Heating power per unit
surface area of the wire is 35.1 W /cm 2 •
8oo
600
4oo
200
..
100
80
U}
8
'0
.j..)
..: ·.
60
•
::·
.
...,·
40
·''t
"'...1',
20
..
t
;.
10
8
I.
\
"·\
6
4
4
6
8 10
20
40
60 80
q , W/cm 2
Fig. 6. Time when vapor surrounds the wire, td, vs. the
heating power per unit surface area of the wire. (The value of
the heating power is the value at t = td.}
48l
0. Tsukamoto and T. Uyemura
Table I. Energy for Formation of Vapor Sheath
No.
q*, W/cm 2
td,ms
68 v,mm
1
2
3
4
8.3
10.4
10.9
18.4
27.2
35.1
124
55.8
36.1
14.1
7.6
4.8
0.60
0.69
0.68
0.45
0.43
0.33
5
6
q*
ec, 103 J/cm e., 103 J/cm
13.18
2.61
4.07
2.05
1.27
0.99
2.55
3.38
3.23
1.43
1.30
0.76
= Joule heating power per unit area of the wire.
Except for the case where the time td was exceptionally long, the agreement between
e, and ec is good.
Preliminary experiments have been performed with liquid helium. Very little
data are available at this time. Direct transitions or premature transitions to film
boiling in liquid helium have so far not been observed. This is probably due to the
much smaller surface tension of liquid helium where the latter detaches from the wire
surface more easily than nitrogen bubbles.
ACKNOWLEDGMENTS
The authors gratefully acknowledge the technical advice of Y. Yamamoto, and T. Tsuno for taking
high-speed photographs. The useful discussions with N. Inai are also appreciated.
NOTATION
C( T)
d
= specific heat of heater wire
= diameter of wire
e, = latent energy required to produce the vapor contained in a unit length of vapor sheath
ec = energy dissipated into the liquid from the surface of the wire per unit length until the vapor sheath
forms
i(t) = wire current
icr = critical current above which direct transition to film boiling occurs
L = length of the wire
q(t) = heat ftux dissipated into liquid per unit surface area of wire
T = bulk or surface temperature of the wire
.1 T = difterence between wire temperature and bulk temperature of liquid nitrogen
td = time when the vapor sheath surrounds the wire or time when the voltage across the wire begins to
rise abruptly
v(t) = voltage across the wire
Greek Symbols
6av = average thickness of the vapor sheath
p = density of wire
REFERENCES
1. R. J. Simoneau and K. J. Baumeister, in Advances in Cryogenic Engineering, Vol. 16, Plenum Press,
New York (1971), p. 416.
2. E. R. F. Vinter, A. K. Vong, and P. MacFadden, J. Heat Mass Transfer 9:301 (1968).
3. D. N. Shinha, L. C. Brodie, J. S. Semura, and F. M. Young, Cryogenics 19(4):225 (1979),
4. P. J. Berenson, J. Heat Transfer 83, Series C (3):351 (1961).
H-7
NATURAL CONVECTION HEAT LEAK
IN SUPERCRITICAL HYDROGEN TANKS
A. J. Barrett
Beech Aircraft Corporation, Boulder Division
Boulder, Colorado
INTRODUCTION
Information on natural convection, such as thermal pumping in large-diameter
cryogenic lines, is weil documented C· 2 ]. However, less information is available on
natural convection heat transfer in small-diameter tubes filled with supercritical
fluid. Natural convection occurs in cryogenic systems where the warm tube interface
(as shown in Fig. 1) is located below the cold tube tank connection. Natural
convection heat leak increases the boil-aff rate; therefore, it is of practical
importance to be able to predict its occurrence and to reduce the heat leak.
This study was initiated to develop a method of predicting natural convection for
variations in system geometry, fluid properties, and temperature gradients. The
natural convection heat leak was determined from test data and an empirical
correlation was obtained for the prediction of natural convection.
DISCUSSION
The natural convection considered here is similar to that described by
Trucks C]. Consider a column filled with fluid at different temperatures, opening at
the top into a tank filled with the same fluid at the colder temperature. The pressure
at the bottarn of the column is unequal because of the density difference existing in
the column. The pressure differential causes flow from the cold end to the warmer
end. Furthermore, flow continues as long as the temperature differential is present to
provide the driving force. Maintaining the temperature differential requires a
continual supply of cold liquid from the tank and a heat input to the warm column.
Steady-state recirculation flow rates and temperatures for natural convection
systems are established by balancing system frictional pressure Iosses against the
driving force caused by the density differential in the cohimn.
This paper is concerned with the occurrence of natural convection in smalldiameter tubes that are filled with supercritical hydrogen. The warm end of the tube
is at ambient temperature and is located below the cold reservoir. Free convection in
vertical tubes has been studied C-4 ]. However, these past studies did not include
supercritical cryogenic fluids.
483
484
A. J. Barrett
flll TUBE-3/8" 0 D
x
.022 WALL
X
.022 WALL
~
GIRTH RING • IIY
...,
/g.
I
j
I
~
OINIIIY
PRO I!
Fig. 1. Upright tank configuration.
TEST DATA
Aseries of testswas run in which natural convection heat leak occurred. The test
configuration consisted of a spherical hydrogen dewar with fill and vent lines going
from the top of the pressure vessel to an equatorial girth ring (see Fig. 1). In addition
to the upright configuration, the tank was turned upside down and the same tests
were repeated. In the inverted condition, natural convection did not occur. TableI
485
Natural Convection Heat Leak in Supercritical Hydrogen Tanks
Table I. Summary of Test Conditions*
Test
designation
Ambient
temperature, 0 R
Cold fluid
temperature, 0 R
Cold fluid
pressure, psia
1
2
3
4
5
6
7
8
9
10
570
570
570
570
570
570
515
515
515
515
48
66
48
66
48
66
48
66
48
66
280
280
280
278
280
283
257
262
250
260
Upright
Inverted
X
X
X
X
X
X
X
X
X
X
* Ambient pressurewas 12 psia.
presents a summary of the test conditions. The two cold fluid temperatures are 48°R
for the full condition and 66°R for the 34% full condition. Fluid pressures were
maintained between 250 and 280 psia.
A summary of heat leak values from the tests is shown in Table li. Total heat
leak values were computed from the measured flow and the specific heat quantity
which was determined from fluid temperature and pressure. Natural convection only
occurs with the tank in the upright position, and the maximum value is 11.9
Btu/hr/line for a full tank. When the fluid quantity was depleted to the 34% full
condition, natural convection heat leak was 3.3 Btu/hr/line. In order to determine
the natural convection heat leak, it was necessary to predict the heat leak without
convection and then subtract the prediction from actual test data. Heat leak
predictions were obtained using an analytical hydrogen tank model that was correlated with the fluid condition of Test No. 10. The analytical modelwas made to
Table II. Summary of Heat Leaks
Test
designation
Baseline
heat leak
design,
Btu/hr
Natural
convection
heat leak,
Btu/hr
4.9
23.8
(11.9 /line)
6.6
(3.3/line)
2
4.0
3
4
5
6
4.9
4.0
4.9
4.0
7
3.8
8
9
10
3.0
3.8
3.0
Pressure
oscillation
heat leak,
Btu/hr
Total,
Btu/hr
Tank
quantity,%
28.7
100
10.6
34
100
34
100
34
23.8
6.6
80.3
4.4
149
4.0
109
15
7.9/line
(10.8/line
prediction)
4.2
2.4
22
144.1
2.8
2.2
10
6.2
3.0
100
34
100
34
l
Ambient
temperature
= 570°R
Ambient
temperature
= 515°R
486
A. J. Barrett
agree exactly with Test No. 10. Also, by comparing test results (Nos. 7 and 9 for
example), it is possible to obtain the natural convection heat leak.
In a similar matter, it was possible to estimate the pressure oscillation heat leak
in the tests. With a full tank, the oscillation caused heat leak was in excess of
144 Btu/hr, and as tank quantity was depleted, oscillation heat leak dropped below
5 Btu/hr. In the 515°R environment tests, the test configuration had a smaller
diameter supply line outside the tank so that pressure oscillations were reduced.
RESULTS
Initially, heat leak data were correlated with a computer model similar tothat
described by Trucks CJ. However, probably owing to the relatively low total heat
leak encountered, satisfactory agreement was not obtained. Therefore, a dimensional analysisapproachwas used and the following expressionwas developed:
.
G
= DCf[gpD 3 (Pc- Pa)(ha- hc)]N
fik (Ta _ Tc}
convectlOn
(1)
where an overbar denotes a value taken at arithmetic mean temperature. Using the
above equation, a series of parametric curves was generated to show the sensitivity of
10°
.;
(.)
c
ü"'
:>
'0
c
10" 1
a:
u
.,
0
~
0
Cl
c V
·~ ~
u--
G>:l
> t-
§co
u
(;;
:;
:;;
z
10""'
X
T =560° R
A
T =660° R
Cold fluid temp . T =48° R
.50
.75
1.00
1.25
T ube diameter , inches
Fig. 2. Effect of tube diameter on natural convection heat leak at
48°R.
Natural Convection Heat Leak in Supercritical Hydrogen Tanks
487
10°
.,·u
c
10-'
~
u
;,
"ca:
u .,
0
"'
0c "~
·z-'=
u._
O>::J
> 1-
g!Il
u
~
::>
~
10_,
.50
.75
1.00
1.25
Tube diameter, inches
Fig. 3. Effect of tube diameter on natural convection heat leak at 66°R.
natural convection to tube diameter, temperature gradient, and fluid density. The
results are shown in Fig. 2 where the natural convection conductance is plotted
against tube diameter. This figure indicates that conductance varies as the fourth
power of the tube diameter. The effect of ambient temperature seems tobe small. In
Fig. 3, the same parameters are plotted. However, the cold fluid temperature was
raised to 66°R, which lowers the fluid density. A comparison between Figs. 2 and 3
shows a reduction in heat transfer as the fluid density is reduced.
The correlation between the empirical expression and test data is shown in
Table II. By comparing the total heat leaks in Tests Nos. 7 and 9, a natural convection
heat leak of 7.9 Btu/hr/line is obtained. The predicted value is 10.8 Btu/hr /line. In
this comparison, it was assumed that the pressure oscillation heat leak was the same
in each test.
CONCLUSION
An expression has been developed for the prediction of natural convection in
terms of system geometry, fluid properties, and temperature environment. The
correlation between test data and (1) is within 26% as shownon Table II, case 7. It
would have been beneficial if more test data bad been available to substantiate the
relationship. Equation (1) may be used during the design phase of supercritical fill
488
A. J. Barrett
and vent lines to select the proper tube diameter to reduce the natural convection
heat leak.
NOTATION
C = empirical constant (0.444 x 10-7 )
D = tube diameter, ft
g = acceleration Ievel, ft/hr 2
h =fluid enthalpy, Btu/lb
k = mean fluid thermal conductivity, Btu/hr-ft-•R
N = empirical constant (0.984)
T = fluid temperature, •R
Greek Symbols
p = mean fluid density, lb/fe
ii = mean fluid viscosity, lb/ft-hr
Subsaipts
a = ambient
c = cold fluid
REFERENCES
1. H. F. Trucksand W. D. Randolph, in Advances in Cryogenic Engineering, Vol. 10, Plenum Press, New
York (1965), p. 341.
2. S. K. Morgan and H. F. Brady, in Advances in Cryogenic Engineering, Vol. 7, Plenum Press, New York,
(1962), p. 206.
3. D. W. Murphy, in Advances in Cryogenic Engineering, Vol. 10, Plenum Press, New York (1964), p.
353.
4. E. R. G. Eckert and T. W. Jackson, "Analytical Investigation of Flow and Heat Transfer in Coolant
Passages of Free Convection Liquid Cooled Turbines," NASA TN 2207 (1950).
DISCUSSION
Question by B. A. Hands, University of Oxford, England: Did you examine the effect of a net mass
flow through the tube?
Answer by author: No.
H-8
TECHNIQUES FOR REDUCING
RADIATION HEAT TRANSFER
BETWEEN 77 AND 4.2 K*
E. M. W. Leung, R. W. Fast, H. L. Hart, and J. R. Heim
Fermi National Accelerator Laboratory
Batavia, Illinois
INTRODUC'fiON
The present-day applied superconductivity is a liquid-helium-based technology.
The efficiency of a cryogenic or superconducting device is determined by its rate of
consumption of the cryogen. Liquidhelium has an extremely small heat of vaporization; thus, its storage almost always requires a state-of-the-art insulating method.
Radiation heat leak becomes significantly more important as larger superconducting
devices are built, such as huge high-energy physics analysis magnets, fusion reactor
systems, and energy Storage facilities. For large superconducting magnets, 3 ] it is
common practice to surround the liquid helium vessel with a nitrogen shield (at 77 K)
and wrap multilayer insulation around both the liquid helium vessel and the nitrogen
shield in an attempt to further reduce the heat leaks (Fig. la). Multilayer insulation is
inexpensive and generally effective; yet, it is a rather difficult material to apply
because its performance depends on a few hard-to-control parameters such as the
layer density, the compressive loading, and the lateral heat transfer effect. The
effective insulation capability obtained in practice is at least a factor of 2 worse than
carefully measured laboratory values (or those claimed by manufacturers). Careless
and/ or inexperienced application can easily generate heat leak values a few times
higher than the predicted value, especially when dealing with peculiarly shaped
cryostats.
Extensive study and test programs [4-6] have been carried out in an attempt to
better understand the thermal performance of multilayer insulation but a Iack of
experimental data still exists for temperatures below 60 K. In fact, the only experimental heat transfer data that appear to be available is a value of 14.3 mWym 2
(1.33 mW /fe) for a 60 layers/in. Linde system (Al foil + glass paper) [']. A commonly used design parameter taking penetrations and other imperfections into
account is 43.0 mW /m 2 (4.0 mW /ft2) for NRC-2 insulation,t which is both the
cheapest and easiest to apply of the multilayer insulations. In this paper, the 77- to
4.2-K performance of NRC-2 insulation as a function of the number of layers is
presented. Results indicate that a much smaller number of layers is required to
c-
* Work sponsored by the U. S. Department of Energy.
t Manufactured by King Seeley Company, Winchester, Massachusetts.
489
490
E. M. W. Leung, R. W. Fast, H. L. Hart, and J. R. Heim
'".• """'" .",1I
Wal ls of LN2 Vesse I
($ometimes Reploced by o
Nitrogen Shield)
Woll of the
Vocuum Bo•
Vocuum
(a)
L He Vessel wall ot 4 2K
Hi<J> contoct resistonce,
- - -...1
low thermal conductivity
conn ecti ans
(b)
Fig. 1. (a) Typical arrangement of insulation system in !arge superconducting devices. (b) Floating-shield concept.
obtain optimum performance, compared to the large number of layers (40 for
minimum kp or 120 for minimum k) between 300 and 77 K. Pushing this concept of
complete elimination of solid conduction to the Iimit would Iead directly to the
classical calculation of Scott [8 ], who indicated an achievable heat transferrate of the
order of 21.5 mW/m 2 (2 mW;te) between surfaces at 77 and 4.2 K, provided that
both surfaces have sufficiently low emissivities (e = 0.01 to 0.03). Recent work of
Chaussy et a/.[9 ] showed that a value of 18.7mW/m2 (1.74mW/fe) could be
otained by covering both the 77-K and 4.2-K surfaces with a commercial aluminum
adhesive tape, Eccoshield PST.* Substituting the emissivity values confirmed by
Chaussy for aluminum (e77 = 0.03 and e4.2 = 0.011) into the parallel plate formula
(for diffuse reftection) given by Scott [8 ]
6
A
u(T~- T1)
(1/ Et) + (1/ E2 - 1)
(1)
results in a heat transferrate of 16.5 mW /m 2 (1.53 mW /ft2 ).
This paper describes a test program set up to further verify low radiation heat
loss via this "reftective coating" method and to study the problern of degradation and
contamination associated with such low emittance surfaces. The heat transfer from
* Manufactured by Emerson Cuming, Inc., Canton, Massachusetts.
Techniques for Reducing Radiation Heat Transfer between 77 and 4.2 K
491
77 to 4.2 K has been measured for cleaned copper to cleaned copper, Eccoshield Al
tape to Eccoshield Al tape, 3M (Industrial tape # 425) Al tape to 3M Al tape. In
addition, other ideas and experiments are also presented leading to a practical
scheme for use in the Chicago Cyclotron Magnet (CCM), a large superconducting
split solenoid, currently under construction at Fermilab.
RADIATION HEAT TRANSFER AND EMISSIVITIES
Success in reducing radiation heat transfer depends on achieving surfaces of low
emissivities. Metals approximate gray bodies rather weil in the infrared region,
consequently, one can take the spectral emissivity values tobe the same as the total
emissivities without any appreciable error. The knowledge of low-temperature
emissivity and absorptivity values is limited C0- 12]. Note that the emissivity value for
a given material is also a function of the wavelength (Fig. 2) of the incoming thermal
radiation (in other words, the temperature of the heat source). The emissivity of a
practical surface may be quite different from the value predicted for the given
material under ideal conditions since it is a strong function of chemical purity and
surface roughness, contamination, and method of preparation. Engineering testing
of practical reflective surfaces is therefore justified. Good electrical conductors such
as silver, gold, copper, and aluminum have low infrared absorptivity. Gold is too
expensive for practical use, while silver and copper tend to tarnish easily in air.
Aluminum, with its natural protective layer of aluminum oxide (transparent to
infrared radiation of temperature <100 K), is often used. Electropolished copper
protected by a transparent benzotriozollayer, a few molecular layers thick, is also a
good choice because the nitrogen shields in superconducting devices are typically
made of copper whose high thermal conductivity helps to maintain a uniform
temperature.
The "floating-shield" concept is to insert a second reflective shield between the
helium vessel surface and the nitrogen shield (see Fig. 1b). Theoretically, it can
reduce the heat leak by a factor of 2. In practice, by attaching this secondary shield
through high-contact resistance connections, one can reduce the heat leak by 35 to
40%. Radiation heat Ioad from 77 to 4.2 K of less than 10 mW /m 2 is achievable
using this method. If one selects to cool this secondary shield with excess helium
boil-off, one can easily reduce the temperature of the shield to around 50 K, in which
case the heat Ioad to 4.2 K would be approximately 5 mW/m 2 •
It has been suggested that a superconductor be used as a reflector. The
emissivity should approach zero as the electrical resistivity vanishes. The Bardeen,
~
~
Fig. 2. Dependence of the emittance of a surface
on its temperature and the average wavelength of
the incoming thermal radiation.
1.0
-~
Tz
I
T,
' - Temperoture of
emilfing sur face
Average wovelengtn of the incoming
thermal rodiotion , ), AVG
492
E. M. W. Leung, R. W. Fast, H. L. Hart, and J. R. Heim
Cooper, and Schrieffer (BCS) theory [u] suggests that foramaterial in the superconducting state there is an energy gap for electron states such that a threshold
excitation is required before energy can be absorbed. This relationship takes the
form of
(2)
Eg = hv = 3.5 kTc
In other words, a superconductor of a critical temperature Tc would not absorb
thermal radiation of the wavelength A > hc/3.5 kTc. The average wavelength of the
thermal radiation from a surface at a temperature T is governed by the Wien
displacement law
(3)
(AT)avg = 4107 ~m-K
Simple arithmetic shows that Nb 3 Sn (Tc = 18.3 K, He = 1.85 x 104 kA/m), a
superconductor considered having a rather high Tc by present-day standards, can
only be a perfect reflector for thermal radiation from a surface of temperature less
than 15 K. Hence, a superconductor is of limited value as an infrared reflector for
most helium systems.
TEST APPARATUS
A drawing of the test setup is shown in Fig. 3. The 4.2-K surface A is a flat
copper plate completely surrounded by a reetangular copper box B at 77 K. The
sample to be tested is either attached (e.g., multilayer insulation), taped (e.g., Al
3.0 METE RS
A
SECTION
A-A
Fig. 3. Thermalradiationtest setup. Legend: A, 4.2-K fin; B,
reetangular 77-K box ; C, inner helium vessel; D, outer
helium vessel; E, nitrogen vessel; F, vent tube.
Techniques for Reducing Radiation Heat Transfer between 77 and 4.2 K
493
tape), or coated onto both A and B. A capped-off 12.7-mm-ID copper tubesoldered
to A is connected to the inner helium vessel C through a coupling. Any heat absorbed
by the 4.2-K fin A rnanifests itself as liquid helium boil-off from C because all other
sources of heat are intercepted by the outer helium vessel D and the radiation bafftes
which almost enclose the inner helium vessel. The outermost concentric liquid
nitrogen vessel E shields the outer helium vessel D from room temperature. The
reetangular copper box B, which constitutes the warm temperature boundary, is
cooled by liquid nitrogen from this outermost vessel E and is insulated with
multilayer insulation from the outside. The whole apparatus is placed inside a
vacuum vessel. A vacuum of at least 2 x 10-7 torr is maintained when measurements
are made. The surface area of the 4.2-K fin is approximately 2.26 m2 (24.375 te) .
The total heat absorbed by the 4.2-K fin is divided by this area to give the
experimental heat transferrate per unit area between the 77- and 4.2-K surfaces.
Large storage volumes are provided for both liquid helium and liquid nitrogen so as
to facilitate prolonged testing (15 to 20 days), which is essential for degradation and
contamination studies. The pressure in the liquid nitrogen vessel can be reduced to
produce a lower warm boundary temperature.
Fig. 4. Exterior view of the thermal radiation test apparatus (without
the insulation shroud and one side wall of the nitrogen box) with the
large-diameter vacuum chamber in the background.
494
E. M. W. Leung, R. W. Fast, H. L. Hart, and J. R. Heim
EXPERIMENTAL TECHNIQUE
Instrumentation
The temperature of B is monitored using several copper-Constantan thermocouples and that of A with calibrated carbon resistors. Variation of the temperature across both A and B is calculated and measured to be negligible.
The boil-off rate of the liquid helium in Cis measured with a calibrated wet test
meter (accuracy ±0.2% ). An electrical signal is sent to a running strip chart recorder
upon completion of each revolution of the meter indicator suchthat continuous (and
therefore average) readings can be taken. The temperature of the evolving gas is read
directly on the wet-meter and the liquid helium boil-off rate at 273.16 K and
760 mm Hg can then be calculated. It is important to note that the ratio of the
saturated liquid density to the helium vapor density at 4.2 K is only 7.5:1 at 1 atm;
therefore, the actual heliumevaporationrate should be 1.154 times the boil-off rate
measured with the wet-meter.
A typical experimental run produces results similar tothat shown in Fig. 5. The
loss rate measurement is influenced by the variation of atmospheric pressure, which
is therefore monitored continuously. A correction C4 ] for the rate of vaporization
resulting from small atmospheric pressure changes can be approximated by the
general formula
dmr = !Vdp
(4)
dt
dt
and in the case of liquid helium,
ER= 7.9 x 10- 3 V
(dt)
(4')
40.0
30.0
e
~ 20.0
E
.5
~
·0
10.0
Ist
2nd
3rd
4th
5th
6th
7th
81h
9 th
IO ih
lllh
nme . Days
Fig. 5. Typical data obtained from a run. Run No. 10: Eight layers of NRC-2 on
blackened 4.2-K surface, Eccoshield Al tape on 77-K surface. Average heat Ioad into
the 4.2-K surface per unit area Q/ A = 13.45 ± 0.5 mW /m 2 •
Teebniques for Redudug Radiatiou Heat Trausfer betweeu 77 aud 4.2 K
495
This explains the ±5 to 10% variation in the boil-off rate data. Forthis reason, each
run is generally conducted over a period of a week or more to average out the effect
of pressure variations and to insure the achievement of equilibrium conditions.
Callbration
The only major heat source into Cis heat conduction down the vent tube F. This
was calculated tobe 8.3 mW using the method described in Scott [16]. Background
runs of the apparatus without both A and B were performed. In the beginning,
thermal acoustic oscillation was encountered and a background heat leak value five
times higher than calculated was observed. The thermal acoustic oscillation was
removed by filling the vent tube with cotton plugs which separated the gas ftow into
small ftow channels C7 ]. The background run then yielded a result of 10.7 mW. The
Iiterature on thermal acoustic oscillations C8 - 20 ] revealed that the system was nearly
stable against oscillation and at the expected boil-off rates the background heat leak
down the vent tube would only be about 0.3 mW. A sample run with the Eccoshield
aluminum tape on both the 4.2- and 77-K surface gives a heat transferrate per unit
area of 1.40 ± 0.05 mW /fe, which compares weil with the value obtained by
Chaussy [9 ]. Six months later, after six other experimental runs, this configuration
was tested again. A result of 1.38 ± 0.05 mW /fe was obtained, showing good
reproducibility. lt is estimated that the overall accuracy of the measurements are
±10%.
RESULTS AND DISCUSSION
Aseries of six runs were performed using NRC-2 on a 4.2-K surface painted
with 3M black Velvet paint [1 5 ] to simulate a dirty stainless steel helium vessel.
Eccoshield tapewas applied to the 77-K surface. The results are shown in Fig. 6.
Other data are given in Table I. By comparing the results of runs Nos. 1, 3, and 4,
it can be seen that if in the NRC-2 series, one had used bare ETP copper at 77 K, the
heat ftux would have been higher and vice versa for the 3M Al tape.
18
17
17.1 mW/m 2
16
NE
~
E
.!:
15
~
·0
14
13
12 L---~~o----'zo----~-----~r---~5o.---·ro--~ro~--~aro
No. of Layers of NRC -2
Fig. 6. Radiation heat ftux vs. number of layers of NRC-2 in a 50.8-mm
gap from 77 to 4.2 K.
E. M. W. Le-., R. W. Fut. H. L.a.rt. ud J. R. Heilll
496
Table I. Heat Transfer from 77.4 to 4.2 K
System
Run
No.
4.2-K surface
77-K surface
1.
Eccoshield Al tape
Eccoshield Al tape
2.
Eccoshield Al tape
Eccoshield Al tape
3.
Electrolytic Tough Pitch
Cu (rinsed with Bright
Dip and cleaned with
Oakite)
Tough
Electrolytic
Pitch Cu (rinsed with
and
Dip
Bright
cleaned with Oakite)
4.
3M Al tape
3M Al tape
5.
Blackened with black 3M
Velvet paint; then 8
Jayers of NRC-2 wrapped
around the black surface
6.
Blackened with black 3M
Velvet paint; then 8
Jayers of NRC-2 wrapped
around the black surface
Blackened with black 3M
Velvet paint; then 8
Jayers of NRC-2 wrapped
around the black surface
1 layer of double-side
Mylar
aluminized
epoxied to 77-K CU
surface using Crest
# 7344 epoxy*
6 layers of NRC-2
attached by nylon
screws and polyester
threads.
ftoating
Aluminum
shield
7.
Heat transfer
rate
unit area,
mW/m2
(mW/ft2 )
Remarks
Calculated value is 16.5
mW/m2 using emissivities
values deduced from data
of Chaussy et al.
14.9 ± 0.5
Same surfaces after being
(1.38 ± 0.05) left in Iab and in apparatus
for 6 months. No degradation observed. Repeatibility
of data checked.
15.6 ± 0.8
Experiment was run for 11
(1.45 ± 0.075) days continuously. No sign
of degradation observed.
Typical method used on
Jarge magnets previously
constructed at Fermilab.
# 425
lndustrial Tape
12.4 ± 0.5
(1.15 ± 0.05)
seems to have better
adhesive property at 77-K
than Eccoshield Tape.
Aluminized Mylar, mea28.8 ± 0.5
sured to have a 500 A alu(2.00 ± 0.05)
minum Jayer on each side. t
Outgassing of epoxy detected.
17.3±0.5
77-K surface has 2 inter(1.60 ± 0.05)
weaving areas carefully
prepared.
15.1 ± 0.5
(1.40 ± 0.05)
18.1 ± 0.5
Nylon screws with stainless
(<1.68 ± 0.05) steel nuts were used as the
standoffs. Floating shield
made from 0.127-mm-thick
aluminum sheets.
* Crest Products Company, Santa Ana, California.
t King-Seeley Company, same supplier as NRC-2.
The measured value from run No. 1 (15.1 mW/m 2 ) is well approximated by (1),
assuming e 77 = 0.03 and E4.2 = 0.011 (16.5 mW/m 2 ). However, the geometry of the
apparatus, a ftat plate inside a reetangular box, may not be adequately represented by
(1). A detailed anal~is using configuration factors gives a heat transferrate per unit
area of 17.2mW/m2 , using the emissivities above. This indicates that geometrical
effects account for 4 to 5% of the difference.
Residual resistivity ratio (RRR) measurements of a few samples were made and
are included in Table II. This gives a relative indication of how good the sample is as
an infrared re