Development of a Model to Predict
Flow Oscillations in Low-Flow Sodium Boiling
by
Alan E. Levin
Peter Griffith
Energy Laboratory Report No. MIT-EL-80-006
April 1980
Room 14-0551
77 Massachusetts Avenue
Cambridge, MA 02139
Ph: 617.253.5668 Fax: 617.253.1690
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i77
REPORTS IN REACTOR THERMAL HYDARULICS RELATED TO THE
MIT ENERGY LABORATORY ELECTRIC POWER PROGRAM
A.
Topical Reports
(For availability check Energy Laboratory
Headquarters, Room E19-439, MIT, Cambridge,
Massachusetts, 02139)
A.1
A.2
A.3
A.4
General Applications
PWR Applications
BWR Applications
LMFBR Applications
A.1
M. Massoud, "A Condensed Review of Nuclear Reactor ThermalHydraulic Computer Codes for Two-Phase Flow Analysis," MIT
Energy Laboratory Report MIT-EL-79-018, February 1979.
J.E. Kelly and M.S. Kazimi, "Development and Testing of the
Three Dimensional, Two-Fluid Code THERMIT for LWR Core and
Subchannel Applications," MIT Energy Laboratory Report
MIT-EL-79-046, December 1979.
A.2
P. Moreno, C. Chiu, R. Bowring, E. Khan, J. Liu, N. Todreas,
"Methods for Steady-State Thermal/Hydraulic Analysis of PWR
Cores," MIT Energy Laboratory Report MIT-EL-76-006, Rev. 1,
July 1977 (Orig. 3/77).
J.E. Kelly, J. Loomis, L. Wolf, "LWR Core Thermal-Hydraulic
Analysis--Assessment and Comparison of the Range of Applicability of the Codes COBRA-IIIC/MIT and COBRA IV-l," MIT
Energy Laboratory Report MIT-EL-78-026, September 1978.
J. Liu, N. Todreas, "Transient Thermal Analysis of PWR's by
a Single Pass Procedure Using a Simplified Model Layout," MIT
Energy Laboratory Report MIT-EL-77-008, Final, February 1979,
(Draft, June 1977).
J. Liu, N. Todreas, "The Comparison of Available Data on PWR
Assembly Thermal Behavior with Analytic Predictions," MIT
Energy Laboratory Report MIT-EL-77-009, Final, February 1979,
(Draft, June 1977).
A.3
L. Guillebaud, A. Levin, W. Boyd, A. Faya, L. Wolf, "WOSUBA Subchannel Code for Steady-State and Transient ThermalHydraulic Analysis of Boiling Water Reactor Fuel Bundles,"
Vol. II, Users Manual, MIT-EL-78-024. July 1977.
ii
L. Wolf, A Faya, A. Levin, W. Boyd, L. Guillebaud, "WOSUBA Subchannel Code for Steady-State and Transient ThermalHydraulic Analysis of Boiling Water Reactor Fuel Pin Bundles,"
Vol. III, Assessment and Comparison, MIT-EL-78-025, October 1977-.
L. Wolf, A. Faya, A. Levin, L. Guillebaud, "WOSUB-A Subchannel
Code for Steady-State Reactor Fuel Pin Bundles," Vol. I, Model
Description, MIT-EL-78-023, September 1978.
A. Faya, L. Wolf and N. Todreas, "Development of a Method for
BWR Subchannel Analysis," MIT-EL-79-027, November 1979.
A. Faya, L. Wolf and N. Todreas, "CANAL User's Manual," MITEL-79-028, November 1979.
A.4
W.D. Hinkle, "Water Tests for Determining Post-Voiding Behavior
in the LMFBR," MIT Energy Laboratory Report MIT-EL-76-005,
June 1976.
W.D. Hinkle, Ed., "LMFBR Safety and Sodium Boiling - A State
of the Art Reprot," Draft DOE Report, June 1978.
M.R. Granziera, P. Griffith, W.D. Hinkle, M.S. Kazimi, A. Levin,
M. Manahan, A. Schor, N. Todreas, G. Wilson, "Development of
Computer Code for Multi-dimensional Analysis of Sodium Voiding
in the LMFBR," Preliminary Draft Report, July 1979.
M. Granziera, P. Griffith, W. Hinkle (ed.), M. Kazimi, A. Levin,
M. Manahan, A. Schor, N. Todreas, R. Vilim, G. Wilson, "Development of Computer Code Models for Analysis of Subassembly Voiding
in the LMFBR," Interim Report of the MIT Sodium Boiling Project
Covering Work Through September 30, 1979, MIT-EL-80-005.
A. Levin and P. Griffith, "Development of a Model to Predict
Flow Oscillations in Low-Flow Sodium Boiling," MIT-EL-80-006,
April 1980.
M.R. Granziera and M. Kazimi, "A Two Dimensional, Two Fluid
Model for Sodium Boiling in LMFBR Assemblies," MIT-EL-80-011,
May 1980.
G. Wilson and M. Kazimi, "Development of Models for the Sodium
Version of the Two-Phase Three Dimensional Thermal Hydraulics
Code THERMIT," MIT-EL-80-010, May 1980.
iii
B.
Papers
B.1
B.2
B.3
B.4
B.1
General Applications
PWR Applications
BWR Applications
LMFBR Applications
J.E. Kelly and M.S. Kazimi, "Development of the Two-Fluid
Multi-Dimensional Code THERMIT for LWR Analysis," accepted
for presentation 19th National Heat Transfer Conference,
Orlando, Florida, August 1980.
J.E. Kelly and M.S. Kazimi, "THERMIT, A Three-Dimensional,
Two-Fluid Code for LWR Transient Analysis," accepted for
presentation at Summer Annual American Nuclear Society
Meeting, Las Vegas, Nevada, June 1980.
B.2
P. Moreno, J. Kiu, E. Khan, N. Todreas, "Steady State Thermal
Analysis of PWR's by a Single Pass Procddure Using a Simplified Method," American Nuclear Society Transactions, Vol. 26
P. Moreno, J. Liu, E. Khan, N. Todreas, "Steady-State Thermal
Analysis of PWR's by a Single Pass Procedure Using a Simplified
Nodal Layout," Nuclear Engineering and Design, Vol. 47, 1978,
pp. 35-48.
C. Chiu, P. Moreno, R. Bowring, N. Todreas, "Enthalpy Transfer
Between PWR Fuel Assemblies in Analysis by the Lumped Subchannel Model," Nuclear Engineering and Design, Vol. 53, 1979,
165-186.
B.3
L. Wolf and A. Faya, "A BWR Subchannel Code with Drift Flux
and Vapor Diffusion Transport," American Nuclear Society
Transactions, Vol. 28, 1978, p. 553.
B.4
W.D. Hinkle, (MIT), P.M Tschamper (GE), M.H. Fontana, (ORNL),
R.E. Henry (ANL), and A. Padilla, (HEDL), for U.S. Department
of Energy, "LMFBR Safety & Sodium Boiling," paper presented at
the ENS/ANS International Topical Meeting on Nuclear Reactor
Safety, October 16-19, 1978, Brussels, Belgium.
M.I. Autruffe, G.J. Wilson, B. Stewart and M. Kazimi, "A Proposed Momentum Exchange Coefficient for Two-Phase Modeling of
Sodium Boiling," Proc. Int. Meeting Fast Reactor Safety Technology, Vol. 4, 2512-2521, Seattle, Washington, August 1979.
M.R. Granziera and M.S. Kazimi, "NATOF-2D: A Two Dimensional
Two-Fluid Model for Sodium Flow Transient Analysis," Trans. ANS,
33, 515, November 1979.
NOTICE
This report was prepared as an account of work
sponsored by the United States Government and
two of its subcontractors. Neither the United
States nor the United States Department of Energy,
nor any of their employees, nor any of their contractors, subcontractors, or their employees,
makes any warranty, express or implied, or assumes
any legal liability or responsibility for the
accuracy, completeness or usefulness of any
information, apparatus, product or process disclosed, or represents that its use would not
infringe privately owned rights.
DEVELOPMENT OF A MODEL TO PREDICT
FLOW OSCILLATIONS IN LOW-FLOW SODIUM BOILING
by
Alan E. Levin
Peter Griffith
Energy Laboratory,
Department of Nuclear Engineering and
Department of Mechanical Engineering
Massachusetts Institute of Technology
Cambridge, Massachusetts 02139
Topical Report of the
MIT Sodium Boiling Project
sponsored by
U. S. Department of Energy,
General Electric Co. and
Hanford Engineering Development Laboratory
Energy Laboratory Report No. MIT-EL-80-006
April 1980
-4-
ABSTRACT
An experimental and analytical program has been carried
out in order to better understand the cause and effect of flow
oscillations in boiling sodium systems.
These oscillations
have been noted in previous experiments with liquid sodium,
and play an important part in providing cooling during Lossof-Piping Integrity
(LOPI) accidents that have been postulated
for the Liquid Metal-Cooled Fast Breeder Reactor.
The experimental program involved tests performed in a
small scale water loop.
These experiments showed that voiding
oscillations, similar to those observed in sodium, were present
in water, as well.
An analytical model, appropriate for either
sodium or water, was developed and used to describe the water
flow behavior.
The results of the experimental program indicate that water
can be successfully employed as a sodium simulant, and further,
that the condensation heat transfer coefficient varies significantly during the growth andcollapse of vapor slugs during oscillations.
It is this variation, combined with the temperature
profile of the unheated zone above the heat source, which determines the oscillatory behavior of the system.
The analytical program has produced a model which qualitatively does a good job in predicting the flow behavior in the
wake experiment.
Quantitatively, there are some discrepancies
between the predicted and observed amplitudes of the oscillations.
These discrepancies are attributable both to uncertainties in the
experimental measurements and inadequacies in modelling the behavior of the condensation heat transfer coefficient.
Currently,
-5-
several parameters, including the heat transfer coefficient,
unheated zone temperature profile, and amount of mixing between hot and cold fluids during oscillations, are set by the
user, and have a deterministic effect on the behavior of the
model.
Additionally, criteria for the comparison of water and
sodium experiments have been developed. These criteria have
not been fully tested.
Several recommendations for future study are proposed,
in order to advance the capability of modelling the phenomena
observed.
-6-
ACKNOWLEDGEMENT
Funding for this project was provided by the United States
Department of Energy, the General Electric Co., and the Hanford
Engineering Development Laboratory. This support was deeply
appreciated.
The authors also thank Dr. William Hinkle and Prof. Neil
Todreas for their helpful suggestions, Messrs. Joseph Caloggero
and Fred Johnson for their help in acquiring materials for and
constructing the Water Test Loop, and Messrs. Chris Mulcahy
and Lee Shermelhorn for their help with the data acquisition
system.
The work described in this report was performed primarily
by the principal author, Alan E. Levin, who has submitted the
same report in partial fulfillment for the ScD degree in Nuclear
Engineering at MIT.
-7-
TABLE OF CONTENTS
PAGE
Title Page . . . . . . . . . . . . . . . . . . . .
Abstract . .
.
.
.
.
.
.
.
.
3
4
....................
Acknowledgements . . . . . . . . . . . . . . . . .
6
. . . . . . . . . . . . . . . .
7
*
. 12
List of Tables . . . . . . . . . . . . . . . . . .
15
Table of Contents
List of Figures
Nomenclature . .
. . . . . . . ................
.
.
.
.
.
.
.
.
.
*.......
.. .
16
INTRODUCTION . . . . . . . . . . . . .
20
1.1
Background . . . . . . . . . . . . . . . .
20
1.2
Scope of the Work
. . . . . . . . . . . .
22
CHAPTER 1:
CHAPTER 2:
. . . . . . . . . . . . .
27
2.1
Overall Concept
2.2
The Hydrodynamic Model . .
2.3
The Thermal Model
2.4
Solution of the Equations
2.5
Limitations of the Model . .
CHAPTER 3:
.
27
.
.
.
.
.
.
.
28
. . . . . . . . . . . .
33
. . . . . . . .
36
.
.
.
.
.
.
.
.
.
THE ANALYTICAL MODEL . .
.
.
.
.
.
41
CRITERIA FOR THE COMPARISON OF BOILING
SODIUM TO WATER
43
. . . . . . . . . .
3.1
Background . . . . . . . . . . . . . . . .
43
3.2
Momentum Equations . . . . . . . . . . . .
45
3.3
The Compressibility Equation . .
3.4
The Energy Equation
.
.
..
.
.
.
.
.
47
-8-
TABLE OF CONTENTS
(Cont.)
PAGE
3.5
Comparison of Sodium Data to Water Data . . .
CHAPTER 4:
EXPERIMENTAL APPARATUS AND
PROCEDURES . . . . . . . .
.
.
.
.
4.1
Background and Experimental Apparatus
4.2
Experimental Set-up and Procedure ...
4.3
.
. . 53
.
. . 53
4.2.1
Pretest Set-up and Calibration . . .
4.2.2
Experimental Procedure . .
.
62
.
62
.
.
.
.
.
.
64
4.2.2.1
Stagnant Flow Tests . .
.
.
.
.
.
64
4.2.2.2
Forced Convection Testing . . .
.
67
.
. . 68
EXPERIMENTAL AND ANALYTICAL RESULTS.
. . 70
Safety Precautions . .
CHAPTER 5:
5.1
52
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
70
Stagnant Flow Tests . .
.
.
.
.
.
.
.
.
70
Experimental Results
5.1.1
.
. .
.
5.1.1.1
Data Analysis
. . . . . . . . . .
70
5.1.1.2
Test 4 . . . . . . . . . . . . . .
73
5.1.1.3
Test 5 . . . . . . . . . . . . . .
77
5.1.1.4
Test 6 . . . . . . . . . . . . . .
81
5.1.1.5
Test 7 . . . . . . . . . . . . . .
85
5.1.1.6
Tests 8 and 9
. . . . . . . . . .
85
.
.
5.1.2
Forced Convection Testing . .
5.1.3
Sources of Error and Uncertainties
in Experimental Tests .........
.
.
.
92
-9-
TABLE OF CONTENTS (Cont.)
PAGE
5.1.3.1
Stagnant Flow Tests . .
.
.
.
.
95
5.1.3.2
Forced Convection Testing .
.
.
.
96
5.1.3.3
Other Sources of Error
5.1.4
5.1.5
5.2
.
97
.....
Calculation of Condensation Heat
Transfer Coefficient . . . . . . .
..
98
Comparison of Water Data to
Sodium Data . . . . . . . . .
.
.
.
.
101
.
.
.
.
.
103
Analytical Results . .
.
.
.
.
.
5.2.1
Features of Analytical Simulations .
5.2.2
Comparison of Analytical and Experimental Test Results . . . . . . . . .
CHAPTER 6:
CONCLUSIONS AND RECOMMENDATIONS FOR
FUTURE STUDY . . . . . . . . . . . .
.
114
131
.
................
. .....
6.1
Conclusions
6.2
Recommendations for Future Work . .
.
.
.
.
REFERENCES . . . . . . . . . . . . . . . . . . . .
APPENDIX A:
The Computer Code FLOSS ........ .
.
. ..
.
.
.
.
.
.
104
131
132
135
138
138
A.1
General Description . .
A.2
Solution of the Hydrodynamic and
Thermal Models . . . . . . . . . .
.
.
.
.
138
. .
.
.
.
.
.
139
.
.
.
.
.
.
.
141
. .
.
.
.
.
.
.
141
A.3
A.2.1
The Hydrodynamic Model
A.2.2
The Thermal Model . .
The Structure of the Code
.
-10-
TABLE OF CONTENTS
(Cont.)
PAGE
.
.
. .
.
.....
141
A.3.1
FLOSS-MAIN Program.
A.3.2
Subroutine HYDRO . . . . . . . . . .
A.3.3
Subroutine HEAT . . . . . . . . . .
A.3.4
Subroutine AREA.
A.3.5
Subroutine HTCOEF . .
A.3.6
Subroutine PGUESS . . . . . . .
A.3.7
Subroutine RESIN. ...
A.3.8
Subroutine FFACTP.
A.3.9
Subroutine PROP . .
A.3.10
A.4
.
.
143
143
.
............
145
. ............
145
. 146
. . .
148
............
.
.
.
Subroutine PLOTTER . ..
.
.
.
.
.
.
.
.
150
...........
150
..........
.
.
.
148
.
.
150
Description and Use of the Computer
Controlled Data Acquisition System. . .
152
Restrictions on Code Use.
APPENDIX B:
.
.
152
..................
B.1
Background. .....
B.2
Hardware.
......
..................
152
B.3
Software.
.....
...................
155
B.4
Operation of the CCDAS . . . . . . . . . .
APPENDIX C:
C.1
Data Conversion and Presentation . .
APPENDIX D:
D.1
Example of Experimental Results. .
.
....
.
.
Calculation of Condensation Heat
Transfer Coefficients . . . ........
Calculational Method . . . . . . . . . . .
. 158
161
. 161
. 171
. 171
-11-
TABLE OF CONTENTS
(Cont.)
PAGE
APPENDIX E:
Computer Input and Output . .
.
.
.
.
175
.
.
.
.
175
E.1
Contents of the Appendix . .
E.2
The FLOSS Code
.
.
.
.
.
.
.
.
.
.
176
E.3
Sample Input to FLOSS . .
.
.
.
.
.
.
.
.
.
197
E.4
FLOSS Output . . .
APPENDIX F:
. .
.
.
.
.
.
.
.
.
199
A Comparison of FLOSS to the SAS
Computer Code . . . . . . . . . .
.
.
244
.
.
.
.
.
.
.
.
.
F.1
The SAS Code. .
.
.
.
.
.
. . .
.
244
F.2
Comparing FLOSS to SAS. . .
.
.
.
. . . .
.
245
.
. .
.
.
-12-
LIST OF FIGURES
PAGE
FIGURE
1.1
Potential Sequence of Events for a Lossof-Piping-Integrity Accident
1.2
Potential Sequence of Events for a Lossof-Flow Accident
2.1
Model of Loop Used for Calculation
2.2
Flow Chart of FLOSS Code Solution Scheme
4.1
Schematic of the M.I.T.-Water Test Loop
4.2
Pump Performance Characteristics
5.1
Results of Test 4 - Oscillations in
Bubble Length
5.2
Results of Test 4 - Temperature of First
Unheated Node
5.3
Results of Test 5 - Oscillations
Length
5.4
Results of Test 5 - Temperature of First
Unheated Node
5.5
Results of Test 6 - Oscillations in Bubble
Length
5.6
Results of Test 6 - Temperature of First
Unheated Node
5.7
Results of Test 7 - Oscillations in Bubble
Length
5.8
Results of Test 7 - Temperature of First
Unheated Node
5.9
Results of Test 8 - Oscillations in Bubble
Length
5.10
Results of Test 8 - Temperature of First
Unheated Node
in
Bubble
-13-
LIST OF FIGURES (Cont.)
PAGE
FIGURE
Results of Test 9 - Oscillations in Bubble
Length
90
Results of Test 9 - Temperature of First
Unheated Node
91
5.13
Results of Forced Convection Test Temperature of First Unheated Node
93
5.14
Example of THORS Results - Volumetric
Flow Oscillations
102
5.15
Computer Generated Plot - Simulation of
Test 9: Volumetric Flow Rates in Legs
1 and 2
105
5.16
Computer Generated Plot - Simulation of
Test 9: Bubble Pressure
106
5.17
Computer Generated Plot - Simulation of
Test 9: Total Bubble Length
107
5.18
Computer Generated Plot - Simulation of
Test 9: Bubble Lengths in Legs 1 and 2
108
5.19
Comparison of Analytical Results for
Different Heat Transfer Coefficients Test 4 Conditions
109
Comparison of Analytical Results for
Different Heat Transfer Coefficients Test 6 Conditions
110
Comparison of Analytical Results for
Different Heat Transfer Coefficients Test 9 Conditions
111
5.22
Analytical vs. Experimental Results Test 4: Bubble Length
115
5.23
Analytical vs. Experimental Results Test 5: Bubble Length
116
5.11
5.12
5.20
5.21
-14-
LIST OF FIGURES (Cont.)
PAGE
FIGURE
5.24
Analytical vs. Experimental Results Bubble Length
Test 6:
117
5.25
Analytical vs. Experimental Results Bubble Length
Test 7:
118
5.26
Analytical vs. Experimental Results Test 8: Bubble Length
119
5.27
Analytical vs. Experimental Results Bubble Length
Test 9:
120
5.28
Analytical vs. Experimental Results Test 9:
Bubble Lengths, No Delay Time
Adjustment
122
5.29
Analytical vs. Experimental Results Unheated Zone Temperature
Test 4:
125
5.30
Analytical vs. Experimental Results Unheated Zone Temperature
Test 5:
126
5.31
Analytical vs. Experimental Results Unheated Zone Temperature
Test 6:
127
5.32
Analytical vs. Experimental Results Unheated Zone Temperature
Test 7:
128
5.33
Analytical vs. Experimental Results Unheated Zone Temperature
Test 8:
129
5.34
Analytical vs. Experimental Results Unheated Zone Temperature
Test 9:
130
A.1
Method for Guessing Pressures in FLOSS
147
A.2
Numbering System for Components in FLOSS
149
B.1
Schematic of Data Acquisition System
156
B.2
Data Acquisition Flow Chart
160
-15-
LIST OF TABLES
PAGE
TABLE
3.1
Comparison of Water and Sodium Properties
44
4.1
List of Loop Components
56
4.2
Experimental Conditions
65
5.1
Example of Condensation Heat Transfer
Coefficients
99
C.1
Example of Results from Test 4
164
C.2
Example of Results from Test 5
165
C.3
Example of Results from Test 6
166
C.4
Example of Results from Test 7
167
C.5
Example of Results from Test 8
168
C.6
Example of Results from Test 9
169
C.7
Example of Results from Test 10
(Forced Convection)
170
Comparison of FLOSS to SAS
247
F.1
-16-
NOMENCLATURE
Symbol
Explanation
Units
. 2
A
Area
Co
Turbulent drift flux parameter
C
Specific heat
D
Diameter
in
F
Body force
lbf
f
Volumetric body force (Eq. 2.1)
f
Friction factor
g
Acceleration of gravity
ft/sec
H
Entha ipy
BTU
h
Specific enthalpy
BTU/Ibm
h
Heat transfer coefficient
BTU/hr-ft 2 oF
I
Inertance
2
5
lb f-sec /ft
Ja
Jakob number
k
Thermal conductivity
L
Length
in
m
Mass
ibm
P
Pressure
2
lb /in
P
Power (App. D)
kw,BTU/hr
Q
Volumetric flow rate
ft3/sec
q
Heat
R
Resistance
in
BTU/lbmOF
lbf/ft
3
2
BTU/hr-ftoF
BTU
lb -sec/ft
f
5
-17-
NOMENCLATURE (Cont.)
Explanation
Symbol
Units
lbf-sec2/ft
5
R'
Resistance
Re
Reynolds number
St
Stanton number
T
Temperature
t
Time
sec
U
Internal Energy
BTU
V
Volume
ft
v
Velocity
ft/sec
w
Work
BTU
x
Length scale
oF
3
in
Void fraction
Error
Viscosity
lbm/hr-ft
Density
lbm/ft
Surface tension
lbf/ft
Shear stress
lbf/in
3
2
-18-
NOMENCLATURE (Cont.)
Subscripts
acc
Acceleration
b
Bubble
com
Compressible volume
con
Condensation
evap
Evaporation
fg
Difference between saturated vapor
and liquid
fric
Frictional
g
Vapor
grayv
Gravitational (hydrostatic)
H
Hydrodynamic
i
Index
1
Liquid
net
Net
S
Source
sat
Saturation
sys
System
T
Thermal
tot
Total
o0
Reference
1
Bypass leg
-19-
NOMENCLATURE
(Cont.)
Subscripts (Cont.)
Unheated zone
Compressible volume
Superscripts
Indicates dimensionless quantity
Time step
-20-
CHAPTER I
INTRODUCTION
1.1
Background
The liquid metal-cooled fast breeder reactor
(LMFBR) is currently under consideration as the prototype
for the next generation of nuclear power plants to be built
in the United States, Europe, and Japan.
A thoroughly diff-
erent concept than present day water cooled reactors (LWR's),
the LMFBR employs liquid sodium as a coolant.
This permits
operation of the reactor at high temperature and low pressure, thus increasing power cycle efficiency.
It also
allows the use of a compact core with a high power density,
which is then surrounded with a blanket of depleted uranium.
This configuration permits breeding - the production of more
fuel than is consumed - to occur.
Along with the above advantages inherent in the
LMFBR, there are several disadvantages.
The fact that sod-
ium is opaque means that the reactor cannot be easily inspected by direct visual means.
come highly radioactive.
The coolant may also be-
Perhaps the most significant draw-
back is the possible effects of sodium boiling.
When a
light water reactor sustains an accident which causes the
-21-
coolant to boil, the reactor tends to shut itself off due
to the decrease in the density of the moderator.
In the
LMFBR, however, the boiling of the coolant would shift the
neutron spectrum in the reactor so as to increase the power,
thus creating a possible "autocatalytic" reaction that would
cause the reactor power to increase rapidly.
There are also circumstances wherein the boiling
of the coolant, while not causing large power excursions,
could still have serious detrimental effects on the reactor
core.
In particular, the loss-of-piping-integrity (LOPI)
accident must be considered.
In such an accident, a coolant
inlet pipe breaks, similar to the loss-of-coolant accident
in the LWR.
In the case of the LMFBR, this pipe rupture
causes a rapid decrease in flow rate.
It is assumed in the
analysis of this accident that the reactor has been shut
down by control rods (scrammed).
However, the residual heat
remaining in the fuel due to decay of fission products and
stored energy, may be sufficient to cause coolant boiling.
There is significant uncertainty about the behavior of
sodium during boiling.
One school of thought asserts that,
under conditions such as might occur during a LOPI, voiding
process would propagate rapidly due to the high thermal conductivity of sodium, causing a rapid dryout of parts of the
core, followed possibly by wide scale core melting and sub-
-22-
sequent loss of coolable core geometry.
It is also possible, though, that mitigating factors might come into play to prevent such a rapid dryout.
Under this scenario, the stored heat would be rapidly removed
without deleterious effects, and subsequent natural circulation and/or forced flow would be sufficient to remove the
continuing decay power.
Figures 1.1 and 1.2 are taken from the Department
of Energy's report on sodium boiling (1),
and illustrate
the complex sequences of events which have been developed
for sodium boiling accidents.
The heavy lines indicate the
most likely sequences.
1.2
Scope of the Work
This project was conceived as an attempt both to
model and simulate sodium boiling behavior, as part of the
total D.O.E. effort in this area.
Results from the Thermal-
Hydraulic Out-of-Reactor Safety Facility
(THORS) tests at
Oak Ridge National Laboratory have indicated that stable
sodium boiling may be expected under low-power, low flow
conditions, such as might occur during a LOPI (2); current
models do not accurately predict this type of behavior.
In
addition, significant flow oscillations occurred during some
of these experiments.
Upon analysis of the THORS results,
it appeared that these oscillations might aid in postponing
-23-
FIGURB 1.1
POTENTIAL SEQUENCE OF EVENTS FOR A LOSSOF-PIPING-INTEGRITY ACCIDENT
-24-
FIGURE 1.2
POTENTIAL SEQUENCE OF EVENTS FOR A LOSSOF-FLOW ACCIDENT
-25-
the dryout of the core.
Since sodium experimentation is both costly and
rather hazardous, due to sodium's tendency to ignite spontaneously in oxygen, a simpler approach was developed, using
water as a simulant.
1.
The objectives of this project were:
Development of a simple, one-dimensional model for
flow oscillations under low-power, low-flow conditions.
This model should be easily understood
and incorporate the necessary physical basis for
the flow behavior to be modelled.
2.
Performance of a series of experiments - with waterto ascertain whether the model would predict observed behavior, as well as to demonstrate the
suitability of water as a simulant for liquid
sodium.
3.
Establishment of a set of criteria through which
water and sodium experiments might be compared.
4.
Comparison of data from the experiment to sodium
data using the criteria developed under 3.
The fourth objective was to be met through com-
parison of the results obtained from the water experiments
to those from the Sodium Boiling Test Facility (SBTF) at
ORNL.
The following chapters will cover development of
-26-
the model, choice of the simulant, criteria for the comparison of water and sodium experimental results, the design of
the M.I.T. Water Test Loop, and the results and analysis of
experiments performed on the WTL.
the SBTF will also be included.
A brief description of
Finally, the conclusions
from this work are presented, along with recommendations
for future work in this area.
-27-
CHAPTER 2
THE ANALYTICAL MODEL
2.1
Overall Concept
The modelling of two-phase flow is an extremely
complex task, due to the interactions of the phases with
each other, as well as with their surroundings.
Because
of this fact, the model developed for this work was derived
so as to keep the vapor phase essentially separated from
the liquid.
In addition, the flow oscillations to be
modelled involve the expansion and contraction of a vapor
space surrounded by two nearly incompressible liquid columns.
The growth and collapse of such a bubble can be the result
of either of two effects:
a hydrodynamic effect, whereby
the vapor space grows or collapses due to the differential
pressure between the bubble and the liquid, or a thermal
effect, through which the amount of vapor increases or decreases through the evaporation or condensation of the vapor.
This second mechanism requires the transfer of heat, either
latent or sensible, whereas the first does not.
The two
effects do not occur independently, however; the collapse
of a steam bubble due to hydrodynamic effects would tend
to increase the bubble pressure.
This would then raise the
saturation temperature of the bubble and cause condensation
-28-
to occur, possibly causing further collapse and starting the
cycle again.
Due to the two possible methods of bubble growth
and collapse, the model has been developed so as to incorporate both of these factors.
This approach was proposed
by Ford (3) in his freon experiments and modelling.
While
Ford's original reasoning was followed, the details of the
models differ, as well as the methods of solution.
In developing this model, the objective was to
produce what would eventually be a module in a large systemscale code.
There was no attempt made, therefore, to model
the single phase flow configuration prior to the inception
of boiling and flow oscillations, nor were there any means
provided to carry the calculation past the point at which
the limitations of model occur.
The model limitations are
discussed in Section 2.5, and recommendations for further
calculational tools are presented in Chapter 6.
2.2
The Hydrodynamic Model
The system under consideration for the develop-
ment of this model is illustrated in Fig. 2.1.
The vapor
space is assumed to be at constant pressure throughout, and
the top of the upper plenum is assumed to be at atmospheric
pressure.
The liquid is considered to be incompressible,
and acts essentially as a piston.
The vapor space is not
-29-
Patm
t e
Plenum
PBubble
Primary
Section
A-I
FIGURE 2.1
LOOP MODEL FOR CALCULATION
-30-
assumed to be incompressible; in fact, its compressibility
is one of the driving forces in the oscillations.
The system is assumed to be in a fixed configuration, with the vapor slug totally separated from the liquid.
This "fixed-regime" type of model allows a simple mathematical description of the system.
The momentum equation for one-dimensional, incompressible, single phase flow in a pipe is
dv
1
dp
dt
p
dx
1 dT
p ::-y = f x
(2 1)
Integrating over the volume:
p
dv
z AL dt
= AAP -
shearT A
K
A
F
x
(2.2)
This equation can be rearranged to show the contribution
of each term:
APtottt = AP acc+
acc
APfric
fric + APgrav
grav
(2 3)
The first term represents the acceleration of the fluid;
the second is the pressure drop due to friction, and the
third term represents the pressure drop due to body forces,
in this case, gravity.
If
dv
the area is assumed constant, the term pALdv
ddQ
can be expressed as pL -, where Q is the volumetric flow
rate, vA.
-31-
Dividing Eq. (2.3) by the area, and combing the
gravitational and total pressure drops
dQ
P9L
AP'
=A
( 2.4)
Ashear
dt+
A
where AP' = AP
tot
- AP
.
grav
The frictional term is now expressed, as is customarily done, using a friction factor, f:
2
L Pv
t
A
shear
AT
4f
AP
K
D
2
fric
A
_
(2.5)
Casting the equation in terms of the volumetric flow rate,
Q,
L
_
_
(2.6)
2f Dfric
D
A2
AP fi
Equation (2.4) now becomes
AP'
=
(p-L
A
pL
The term A
indicated by I.
dQ
dt
+
2f
D
A
Q
(2.7)
A2
is the inertance of the fluid column
The term 2fLpQ/DA 2 is the effective resist-
ance due to friction on the fluid, and is indicated by R.
Thus
AP'
=
dQ
dt
+
RQ
(2.8)
-32-
This form of the equation is commonly used in system dynamics,
and allows the creation of an electrical analog, with pressure drop paralleling voltage and volumetric flow rate analogous to current.
The coefficients I and R would correspond
to circuit inductances and resistances, respectively.
In Eq. (2.8), the pressure drop AP' represents the
non-gravitational pressure difference between the vapor space
and the constant upper plenum pressure, and is common to the
two liquid legs.
The equation for the vapor space is also derived
from system dynamics.
For a compressible volume, the con-
servation of mass equation states
d
dm
dt
dt
(PV )
gg
p Q
gg
(2.9)
thus
Q
g
=
V
-
p
d
d
dt
dV
+
-dt
(2.10)
If the motion of the boundaries of the compressible volume
is examined, it is seen that the motion of the liquid legs,
hereafter referred to as Q1 and Q 2 , sum to the volume change,
dV
Therefore,
--.
dt
V
dp
(2.11)
= ---9
Q
3
dt
p
com
g
-33-
Using Eq. 2.8, the equations for the two liquid
legs shown in Fig. 2.1 can be expressed as
AP'
=
I
dQ1
d
1 dt
+
R Q1
1 1
(2.12)
AP'
=
dQ2
I2 !2 dt
+
R2 Q2
2 2
(2.13)
since
dv
Q1
+
Q2
As stated above,
(2.14)
dt
Eqs.
(2.14) and (2.11) can be combined to
define a source volumetric flow rate, Qs, such that
Q0
+ Q2 + Q3
=
Q
(2.15)
The four equations, 2.8 (one for each liquid leg),
2.11, and 2.12 comprise the hydrodynamic model.
2.3
The Thermal Model
The thermal model for bubble growth is derived
directly from the first law of thermodynamics for a closed
system.
That law states:
6q
-
6W
=
6U
(2.16)
The definition of enthalpy
H = U + PV
(2.17)
-34-
is
substituted into Eq.
(2.16).
Realizing that the term
6W represents pressure-volume work done by the system, so
that
6W
=
(2.18)
P6V
and making this substitution,
as well, Eq.
(2.16) becomes
6q - P6V = 6H - P6V - V6P
(2.19)
6q
(2.20)
or
+
V6P = 6H
Equation (2.20)
is now divided by 6t, and the
limit is taken as 6t approaches zero.
This gives the diff-
erential form of the equation
+
dP
dt
dt
dH
(2.21)
dt
The enthalpy term for a two-phase system can be separated
into its components.
H
=
dH
-:
m h
Thus
+ m h
(2.22)
and
dh 9
dh
g dt
dma
dt
dm
g dt
(2.23)
-35-
The system of bubble and surrounding liquid is chosen to be
large enough so that the mass fluxes across the system boundThis choice of a closed system sets a model
aries are zero.
This assumption is valid only when the vapor
limitation.
through-flow in the bubble is
very small, a condition which
exists for small bubble lengths only, as in the early stages
From the definition of a closed system,
of a transient.
therefore
dm
dm
=
0
(2.24)
dt
and
dm
- 9=
dt
dm
dt
(2.25)
Substituting into Eq. (2.20):
IT
d
S=
dm
(h - h
L
g
ddt
dh
dh
m
+m
gdt
m dt
The last two terms represent the change in
ible heat of the system.
(2.26)
sens-
For small changes in temperature
and pressure, these contributions are negligible when compared to the latent heat of vaporization, (h - h£)
or hfg.
Thus,
dH
h
dt
dm
dm
fgdt
(2.27)
-36-
Substituting back into Eq. (2.18) yields
dm
dq + V
dt
dP
dt
=h
V
dp
dm
(2 .28)
fg dt
Since mg = p V
g
gg
dm
=
dt
g
dV
-
P
+
dt
(2.29)
dt
and
dv
dt
V
+
p
g
dp
dt
+
=
(
dt
V
dP
V gP/@h
g
gf
hfg
(2.30)
It should be noted that the left hand side of
Eq.
(2.30) corresponds exactly to the source flow Qs
(2.15)] derived in Section 2.2.
[Eq.
Equation (2.30) comprises
the thermal model for the system.
2.4
Solution of the Equations
The thermal and hydrodynamic equations for the
system are solved simultaneously and iteratively to find
the net source flow and the bubble behavior.
The solution
is accomplished by means of a digital computer, using a
program developed as part of this project.
To review, the equations that must be solved are
-37-
dQl
+
AP'
=
I1
AP'
=
dQ2
12 dt 2 +
2
Q
3
=
1 dt
V
p
g
(2.31)
Q
1 1
2
R'2 Q
2
(2.32)
2 2
dp
d
dt
(net
s
R'
(2.11)
+
V
)/ph
= Q1 + Q
3
(2.30)
In rewriting these equations, the subscripts 1
and 2 refer to the two legs noted on Fig. 2.1; subscript
3 refers to the bubble itself.
the bubble is symbolized by
The total net heat flow to
net.
Since the resistance
term, R, depends on Q [Eq. (2.7], a new coefficient, R',
has been introduced in Eqs. (2.31) and (2.32), such that
'
=
2f
D
--
21
(2.33)
A
There is still a dependence of R' on Q, since the
friction factor, f, is a function of the Reynolds number
and
Re
=
pQD
Ap
(2.34)
However, since this dependence is normally to a small fraction power in turbulent flow, the form in Eq. (2.33) has
-38-
been retained.
The number of bypass legs that are part of Leg 1
in Fig. 2.1 is immaterial since, by the analogy of parallel
resistances and inductances, these can be combined into an
effective single bypass leg.
Additional resistances, such
as elbows, tees, and other flow obstructions can be accomodated using an equivalent resistance concept, as well.
The solution scheme employed in the computer program sets the equations up in finite-difference form and
solves them iteratively.
Equations (2.31) and (2.32) are
approximated by first order, explicit finite difference
equations, while Eqs. (2.11) and (2.30) are solved by implicit first order difference equations.
Details of the
solution scheme may be found in Appendix A.
The iterative
technique itself consists of the following steps:
1.
The pressure in the bubble is guessed, as well as
the bubble lengths and vapor volumes, above and
within the heater. The split must be made due to
the fact that in the heated zone, evaporation
occurs, while in the unheated section above the
heater, evaporation occurs. Thus, in order to derive the net heat input to the vapor space, which
is the difference between evaporation and condensation, the bubble must be split into two parts.
The common vapor space pressure ties the two parts
together.
2.
The pressure guess allows the determination of the
properties in the bubble, since the assumption is
made that all vapor (as well as the liquid film on
the walls of the heater) is at saturation. The
liquid density is assumed to be constant, and
-39-
equal to that at saturation. This allows direct
solution of Eqs. (2.11) and (2.27), since net heat
input is a function of temperature and power to the
heater. Other iterative loops determine the amount
of power that goes into heating up or cooling the
heater wall as pressure changes and the temperature
profile of the liquid in the unheated section, as
heat is introduced into this liquid by condensation.
3.
Equations (2.31) and (2.32) are solved as described
above.
4.
The source flow (Q1 +Q +Q ) calculated from the
thermal model is compareA to that calculated from
the hydrodynamic model. If these two flows are
different by more than a specified convergence
error limit, a new pressure is guessed and the calculation starts again from step 1.
5.
If the two source flows are within the specified
error, new bubble lengths and vapor volumes are
calculated and compared to those that were guessed
in step 1. If these are within a specified tolerance, time is incremented and the transient calculation proceeds. If they are not within the error
limit, a new guess is made of bubble lengths and
volumes, and the calculation returns to step 1 for
another iteration.
A flow chart is shown in Fig. 2.2 illustrating
this technique.
As noted in step 2 above, a temperature-time hisory of the upper unheated zone is calculated.
This is done
in order to allow calculation of the condensation of vapor
which occurs in that part of the test section.
The model
used for this calculation is a nodal-averaged temperature
scheme, whereby the upper section is split into a number
of nodes, each with a single temperature, and new temper-
-40Guess Pressure
. . .
in
Voided Region
Calculate
Properties
From Tables
No
First
Iteration
at time=t?
Yes
Guess
Bubble Lengths
and vapor volumes
in Legs 1 and 2
Calculate QI
Q2 'Q3'Qs f r om
Hydrodynamic
model
Calculate Qs'
Unheated Zone
Temperature
Profile from
Thermal Model
?
No
Yes
Dce s
Lb (Guess)
No
Lb (Calculated)
Yes
Tiime=t+ZIFIGURE
2.2
FLOW CHART OF FLOSS CODE SOLUTION
SCHEME
-41-
atures are calculated based on the flow of liquid into and
out of each node, as well as any condensation which might
occur.
The changing temperature in the unheated section
determines the thermal contribution to bubble growth and
collapse, and changes in the amplitude and period of oscillations may be related to this factor.
of this fact is found in Chapter 5.
Further discussion
Details of the temper-
ature calculational scheme can be found in Appendix A.
The method of solution outlined in this section
has proven to yield satisfactory and physically realistic
results.
These results, along with comparison to experi-
mental results can also be found in Chapter 5.
2.5
Limitations of the Model
A "fixed-regime" model is valid only insofar as
the regime that is fixed actually exists physically.
Once
conditions proceed to a point where the assumptions incorporated into the model are no longer justifiable, the model
is no longer useful in describing the system.
In the case of the model presented here, the
model is valid for small bubble lengths and vapor volumes.
Due to the assumptions made in both the hydrodynamic and
thermal portions of the model, any deviation from a slugflow regime would cause the model to fail.
In addition,
liquid and vapor through-flows are neglected in the formu-
-42-
lation of the thermal model.
When the bubble becomes large
enough to encourage substantial natural circulation flow,
this assumption becomes invalid.
For these reasons, once
net evaporation exceeds net condensation, causing the bubble
to grow without collapse, the transient calculation is stopped,
and the assumption is made that another calculational tool
can be used to determine subsequent occurrences.
-43-
CHAPTER 3
CRITERIA FOR THE COMPARISON OF BOILING
LIQUID SODIUM TO WATER
3.1
Background
The application of data from water experimentation
to the question of what occurs during the boiling of liquid
sodium requires that a group of criteria be developed with
which to compare water data to sodium data.
Several such
criteria will be proposed in this chapter.
Clearly, the physical characteristics and properties of the two fluids are quite different, especially those
properties dealing with heat transport.
Therefore, heat
conduction is not included in the comparison criteria.
It
is assumed that different temperature profiles may exist
under the same flow conditions in water and sodium, and
differences arising from this fact must be considered.
However, from inspection of the equations of the model presented in Chapter 2, it can be seen that the properties
that affect the equations are largely hydrodynamic in nature,
and there is substantially less disparity between water and
liquid sodium in this area.
Table 3.1 lists both thermal
and hydrodynamic properties of each fluid for comparison.
-44-
Table 3.1
Comparison of Water and Sodium Properties
Fluid Property
Tsat
P
pz/P
Water at 14.7 psia
Sodium at 25 psia
(Reactor Conditions)
212 0 F
1670 0 F
3
59.8 lbm/ft'
46.4 lbm/ft
0.0373 lbm/ft
0.025 lbm/ft
3
1650
1603
hfg
970.3 BTU/lbm
1650 BTU/lbm
Cp
1.0 BTU/lbmoF
0.31 BTU/lbmoF
0.687 lbm/hr-ft
0.363 lbm/hr-ft
0.004 lbf/ft
%0.012
0.394 BTU/hr-ftoF
31.5 BTU/hr-ftoF
lb /ft
-45-
The criteria developed in this chapter, then, are
mainly hydrodynamic in nature, and may be used under these
special circumstances to compare boiling water to boiling
liquid sodium.
3.2
Momentum Equations
The approach that is taken throughout this chapter
involves the non-dimensionalization of the basic equations.
The momentum equation,
for Unidimensional,
dv
_
dt
as presented in Chapter 2
single phase flow in a oipe is:
1
d
p
dx
2
d2v - f
P
2
x
(2.1)
is, in this case, due to gravity;
The body force--f
xthus
dv
1
dp
dt
p
dx
P
2
d v2
dy2
g
(3.1)
Non-dimensionalization is accomplished by choosing new variables that are dimensionless.
For the momentum
equation, these variables are:
v
=
v*
=
v/v 0
t*
=
tvo/
o/p
oop
(3.2)
-46-
y*
=
p*=
y/D
p/p 2 ,
P*
=
P/P
x*
=
x/D
P1*
=
P/Pz
The quantity P
is a reference pressure, and D
is the diameter, and serves as a reference length scale.
Substituting these quantities into Eq. (3.1)
yields
Vo
2
D
dv*
o
dt*
pPD
*
dP*
P
Vo
p* dx*
p
D2 p* dy* 2
1
* d2v
g
(3.3)
Simplifying, and applying the definition of v
[Eq. (3.2)] to the first term on the right hand side:
dv* _ 1
p*
dt*
dp*
dx*
P9£
pz voD
_*
p*
d 2 v*
d*2
dy*
Dg
-1v 2
(3.4)
(3.4)
The coefficient of the second term on the right
hand side of the equation is the inverse of the Reynolds
number.
This is the first of the comparison criteria.
The
Froude number also appears, as the last term in Eq. (3.4).
Although this sets another criterion, it reduces essentially
to a density ratio for systems of similar geometry and
pressure.
Applying the definition of v0 to the expression
-47-
Dg
yields the result
2
v
0
Dg
vo
E = PzDg
94 g(3.5)
P
2
0
o
Since the liquid densities of sodium and water
are similar, this criterion is satisfied.
The choice of
another geometry, however, would necessitate consideration
of this parameter.
The appearance of the Reynolds number is not alAs stated above, the driving factors
together unexpected.
in the oscillatory flow behavior tend to be chiefly hydrodynamic in nature; thus, the prime basis for hydrodynamic
scaling should appear.
3.3
The Compressibility Equation
The term expressing the compressibility effects
is
Q
g
=
V
dp
-2
dt
p
'
(2.11)
The volumetric flow rate is defined in Chapter 2
as
=
Av
Av =
-1
Q
g
Thus
V
p
dp
dt
(3.6)
-48-
or
V
dp
pg
dt
-2
x
A
dt
"9
(3.7)
Once again, dimensionless variables are chosen:
V
x*
=
x/D
A*
=
A/D
*
=
V /D
=
t/T
g
t*
p*=
2
(3.8)
3
g
Pg/p
Equation (3.7) now becomes
3A •
D A*
T
D3V *P
D a
dx*
dt*
pT
k
dp*
dt*
(3.9)
Simplifying:
=
A*
dx*
dtA*
g
P
g
dp *
dt*
(3.10)
-49-
The second dimensionless group, then is the liquidto-vapor density ratio, PZ/p
.
This term behaves as a kind
of variable spring constant, since it changes with pressure,
and along with the length of the bubble and heat transfer,
helps to determine the oscillatory behavior of the system.
From the table of properties, it is clear that the density
ratios for sodium and water at pressures near atmospheric
are similar.
3.4
The Energy Equation
The energy equation, as derived in Chapter 2, is
dV
dt
VdP
dp
V
9 +
__1 =
9
pg
dt
(4 +
9
at
)ph
g fg27)
(2.27)
The left hand side of the equation is equivalent
to a volumetric vapor generation rate, Qs.
The term VdP/dt
is very small compared with the net heat flow, 4, and is
neglected.
Thus
Qs
net / ghfg
(3.11)
The source flow, Qs , can be expressed, as in the
previous section, in terms of an equivalent velocity and
area:
-50-
net/ ghfg
=
Avs
(3.12)
The velocity, v , is now non-dimensionalized:
s
v *=
V s/v
Avo s*
=
(3.13)
Then
net/pghfg
(3.14)
and finally
vs
net/pgVo A hfg
=
(3.15)
The net heat input includes both power input to
the lower part of the bubble, as well as condensation which
occurs when vapor enters the unheated section above the
heat source.
The vapor generation occurs via evaporation
at the liquid-vapor interface, at saturation, and the condensation is due to the interaction of saturated vapor with
If this heat input is expressed in terms
subcooled liquid.
of an equivalent heat transfer coefficient and temperature
difference, Eq. (3.15) becomes
h
v*
=
4
=
s
)
(T-T
eq
Pgv
(3.16)
sat
hfg
where
net
heq A (T-Tsat
)
(3.17)
-51-
The quantity on the right hand side of Eq. (3.16)
is the Jakob number, Ja, multiplied by the Stanton number,
St, since
C (_sat)
p Cpt
Ja
=
St
=
(3.18)
pghfg
pg hfg
and
h
h
(3.19)
More importantly, this combination serves as a
kind of power-to-flow ratio, normalized by the latent heat
of vaporization.
It is this term which should be used as
a comparison criterion.
The factor of differing saturation
temperatures is also taken into account.
One factor which
appears indirectly in Eq. (3.16) is the condensation in the
unheated zone, since it is combined with the heat input
term.
The condensation potential in the unheated section
appears to be the primary driving force in the flow oscillations under study, a fact that will be discussed more
fully in Chapter 5.
The heat input to the system is effec-
tively a constant over the duration of the experiments, and
it is this condensation term which provides the variation in
4net and the ultimate potential for bubble growth and collapse.
The characterization of the condensation heat trans-
fer in order to determine this potential is therefore crucial.
-52-
3.5
Comparison of Sodium Data to Water Data
The Sodium Boiling Test Facility (SBTF) at Oak
Ridge National Laboratory is almost an exact analog of the
original MIT Water Test Loop, as described in Chapter 4.
The SBTF also has a pump to provide for forced-flow experimentation; however, it does not include a bypass loop at
this time.
The SBTF is a sodium loop, heated indirectly over
its three-foot heated length by a quadelliptical radiant
furnace.
At the inception of this program, it was expected
that some data would be available from SBTF in order to
provide a direct comparison to water data.
While several
of the natural circulation tests performed on the original
WTL have been reproduced, budgetary and experimental problems have forced a delay in the performance of forced-flow
and flow oscillation testing.
It is anticipated that these
types of experiments will be performed in the near future,
providing a direct test of the comparison criteria herein
proposed.
-53-
CHAPTER 4
EXPERIMENTAL APPARATUS AND PROCEDURES
4.1
Background and Experimental Apparatus
The expense and hazard involved in the use of
liquid metals as an experimental medium led to the concept
of the first M.I.T. Water Test Loop, constructed by Dr. W.
D. Hinkle in 1976.
The WTL was intended to be a simple,
easy-to-operate alternative to complex sodium boiling facilities such as THORS.
ported by Hinkle (4),
The first experiments performed and reinvolved natural circulation tests
only, to determine critical heat fluxes under low-power
conditions.
These results, along with comparison criteria
developed by Hinkle, were compared to sodium data obtained
under similar conditions from the SBTL loop at Oak Ridge (5).
Water was chosen as the simulant in the initial series of
tests because of the similar liquid-to-vapor density ratios
for the two liquids.
Other similarity criteria were not
considered.
Flow oscillations such as those observed in the
THORS tests could not be modelled using Hinkle's approach,
and so a more involved and sophisticated test program was
developed.
The performance of these experiments required
that the Water Test Loop be modified somewhat from its
-54 -
original design.
Figure 4.1 shows the loop in its current
configuration; Table 4.1 lists the dimensions and properties
of the loop.
The modifications consisted of the addition of
a pump and a bypass leg, which would allow operation in
either forced or natural circulation.
Four ball valves
were installed at the bypass to provide the means to change
flow configurations.
In addition, an orifice flange was
added upstream of the inlet plenum to provide the capacity
to vary the inlet flow resistance.
Whereas the entire
"primary" section - that part between the two plena con-
sisting of the heater and unheated inlet and outlet sectionshad been steel, the new loop was built with Pyrex glass
tubing making up as much of the unheated sections as practical.
This allowed visual observation of bubble growth and
collapse patterns during a transient.
The instrumentation was also altered considerably
for the new tests.
Thermocouples had previously been fast-
ened to the outside of the entire metal primary section,
and strain-gauge type pressure transducers were installed
in the inlet plenum, heater inlet and heater outlet.
was no flow measuring instrument included.
was by means of a chart recorder.
There
Data acquisition
The modified version of
the loop retained the thermocouples on the outside of the
heater rod; however, the Pyrex sections were split into
-55-
11"
-1'
To City Water
- 8
-]-J
-16
7
19
2
3
<18
15
9.5'
7
7
3'
144
'
9H
Note:
FIGURE
jL
To City I
13
12
Numbers refer to Table 4.1 on following page
4.1
SCHEMATIC OF THE M.I.T. WATER TEST LOOP
-56-
Table 4.1.
Component Number
List of Loop Components
Function
Heater Tube -
0.25" OD
Pyrex Tubing -
6mm OD
Swagelok Tee for Thermocouple
Insertion
Orifice for AP Transducer
Cooling/Heating Coil for Plenum
Upper Plenum -
8"I.D.
x 8"
ht.
Stainless Steel Bypass Pipe 1" I.D.
Ball Valve for Flow Control
Pump
Orifice Flange
Lower Plenum 8"
I.D.
x 8"
ht.
Heat Exchange Loop Pump
Heat Exchanger
Connection to 7kw DC Generator
Insulator and Tyco Pressure
Transducer
Validyne AP Cell across Orifice
Thermocouple on Outside of
Heater Tube
Thermocouple Inserted into
Swagelok Tee
Data Acquisition System
-57-
smaller zones, with each end inserted into a Swagelok tee.
The third port of the tee was used for insertion of a thermocouple directly into the fluid stream.
The thermocouples
were sealed into the ports using RTV Silicone Rubber Sealant.
All thermocouples were copper-constantan.
Pressure transducers of the same type that Hinkle
used were retained for the heater inlet and outlet.
inlet plenum transducer was not used.
The
These gauges were
Tyco type AB, with a range of 0-6 psig.
When excited by a
6-volt dry cell battery, the response was linear, at a rate
of 20 mv/psi.
For the new set of experiments, it was desired to
have measurement of inlet and outlet flow rates.
To accomp-
lish this, flow orifices were installed just downstream of
the inlet plenum and upstream of the outlet plenum.
The
orifices were about 80% of the test section diameter.
They
were made this way so as to cause as little interference
with the flow as possible, while still generating enough
of a pressure drop to measure flow rate.
Pressure drop
measurements were made using Validyne DPl5 differential
pressure transducers.
These instruments can be adjusted
as to the range of their output, from about ± 0-1 to ± 010 volts full scale.
The transducers themselves are vari-
able reluctance devices with interchangeable diaphragms,
-58-
permitting operation from ± 0-0.1 psid upward.
In order to
provide response as accurate as possible and to avoid pinning
the data acquisition system at its maximum output, a range
of ± 0-1 volt was chosen, with the lower transducer set for
+ 0-1.0 psid, and the upper transducer for ± 0-0.5 psid.
The Validyne transducers were supplied with their own carrier
demodulators, which served as both a power source and voltage
output device.
Calibration of these transducers was done
in place, using both upflow and downflow.
The loop was run in visual observation tests
immediately after construction.
On the basis of these ob-
servations and sodium test results, the decision was made
to purchase a fast-scan data acquisition system, in order
to collect data at a rapid enough rate to be able to trace
the oscillatory motion.
The system chosen was a Perkin-
Elmer Low-Level Real Time Analog System (RTAS).
The RTAS
has the capability of scanning individual data points at
rates up to 8000 points per second.
permits inputs of ± 0-1.0 volts.
The low level system
To collect and store the
data, a Perkin-Elmer Model 1610 minicomputer was acquired.
This machine is a 16-bit computer with 64000 bytes of
memory, with dual floppy disk drives to provide input-output capability.
A Perkin-Elmer 550 CRT terminal was used
as the system console, and a Perkin-Elmer 650 Thermal Printer
-59-
was connected to the rear of the CRT to provide hard copy
output, if desired.
Operating system software, including
FORTRAN support,was supplied by Perkin-Elmer.
Using the
1610 computer and driver programs developed by Perkin-Elmer
for the RTAS, data acquisition was done at the rate of 600
points per second.
The RTAS input supports twenty-four
individual instruments, and scans were performed twenty-five
times per second.
The instrumentation consisted of:
The
two Validyne differential pressure transducers, the two Tyco
gauge pressure transducers, and nineteen thermocouples, one
each in the inlet and outlet plena, eight tied onto the outside of the heater at approximately 4.5 inch intervals, and
nine in the unheated zones.
The twenty-fourth point was
connected to an RTD temperature reference on the RTAS termination panel to provide an equivalent ice-point for the
thermocouples.
The computer, through its line-frequency
clock, is able to generate interupts at
per second.
up to 120 times
Each interupt allows the RTAS to scan all 24
points at the maximum scan rate.
The interupt interval
chosen for these experiments was 40 milliseconds.
More
detail on the data acquisition system can be found in
Appendix B.
Power was supplied to the test section by a
7 kilowatt DC generator.
The test section was directly
-60-
heated (resistance heating) by the generator.
Power was
measured using a Hewlett Packard Model 3465 B Digital Multimeter.
The voltage drop across the test section heater tube
was measured, and multiplied by the generator current output.
Generator current was ascertained by means of a calibrated
shunt providing 50 4v output at 1000 amperes.
The remainder of the test section, aside from the
bypass legs, consisted of a heat transfer loop to cool the
plena.
The lower plenum was cooled by direct fluid exchange,
whereby fluid was removed, pumped through a small heat exchanger, and returned to the plenum.
The upper plenum, which
was open to the atmosphere to provide a constant reference
pressure, was cooled by a copper coil loop inside the plenum.
Water was run from the city water pipes through this copper
coil, and the temperature of this water could be varied, so
as to hold the plenum at the desired temperature.
Both the main test section pump and the heat exchanger loop pump were Jabsco "Sturdi-Puppy" self-priming
vane pumps, rated at 5 gpm at 8.5 psi.
Figure 4.2 repre-
sents the pump curve.
The bypass legs were stainless steel piping.
The
large size of these pipes in relation to the primary tubing
was to negate any significant bypass effect on flow dynamics.
-61-
100.0
10.0
GALLONS
PER
MINUTE
1.0
0.1
10.0
1.0
0.1
AP
FIGURE 4.2
(psi)
PUMP PERFORMANCE CHARACTERISTICS
-62-
4.2
Experimental Set-up and Procedure
4.2.1
Pretest Set-up and Calibration
Prior to each set of experiments, several steps
were followed to insure readings from instruments were as
accurate as possible.
With the loop filled, the battery
for the Tyco pressure transducers was checked to make certain it still was charged at 6 volts.
The transducers
themselves were then checked for offset from zero.
This
was accomplished by checking the output from each transducer with a digital multimeter to ascertain the output,
and then subtracting from that reading 20 my for each psi
of water head above the transducer.
The second step involved the calibration-in-place
of the Validyne differential pressure transducers.
Each
transducer was calibrated in both upflow and downflow.
Calibration in upflow was accomplished via a two step
method.
The loop was run at the beginning of the experi-
mental program with the bypass line opened and the power
at a low level.
Using the thermocouples directly upstream
and downstream of the heater, a heat balance was performed.
Knowing the amount of power input and the temperature size
of the water across the heater, it was then possible to
determine the flow rate.
This single point was used to
calibrate the transducers in upflow, with the assumption
-63-
of linear transducer response.
For downflow calibration,
the primary side of the loop was isolated to prevent recirculation effect on the transducer.
Water was then with-
drawn from the lower plenum through the hole where the plenum
pressure transducer had been mounted in Hinkle's experiment.
Initially, since the water could be withdrawn at variable
rates, several different measurements were made.
The flow
was collected for a timed interval, then measured to find
the flow rate.
The rate of withdrawal was sufficiently
small, so that the driving pressure on the primary side did
not change appreciably.
time.
This insured constant flow over
The calibration with several points verified the
linearity assumption made in upflow, and in later calibrations, only one point was taken for downflow calibrations.
The transducers themselves were first bled, and then zeroed
using the carrier demodulator adjusting dial.
Output was
again read using a digital multimeter.
Before beginning experimentation, the loop was
operated for several minutes to remove all trapped air
bubbles from the system.
The final step before beginning the experiment
was to load the data acquisition system controller programs
into memory.
Once this was accomplished, the data collection
procedure could be started by simply pressing on key
-64-
the system console.
4.2.2
Experimental Procedure
The experimental procedure for each run was basi-
cally the same, with the exception of the final test.
The
last experiment will therefore be dealt with separately.
The conditions for all tests analyzed are presented in Table
4.2.
4.2.2.1
Stagnant Flow Testing
Three preliminary tests were run under stagnant
flow conditions to test all of the equipment and to practice
data-taking procedures.
Six additional experiments were
then run in which data was acquired and converted.
Preliminary analytical work using the computer
model indicated that the temperature profile in the unheated zone was perhaps the single most important parameter
in determining flow oscillatory behavior.
It was therfore
decided to run the experiment in the same way each time,
varying only that temperature profile.
The temperature profile was established by running
the loop with bypass flow.
This made the velocity in the
primary section sufficiently low that any temperature ranging from the lower plenum temperature to saturation could
be established in the unheated zone by varying heater power.
The temperature would then be uniform from the top of the
-65-
Table 4.2.
Test Number
Experimental Conditions
Unheated
Zone Temperature(oF) Heater
Stagnant/
Power
Forced Convection Prior to Boiling
(kw)
Inception
S
75
0.544
102
0.544
80
0.209
100
0.326
117
0.417
140
0.390
%175 decreasing
to %95 at top
1.09
-66-
heater to the upper plenum, where the temperature was controlled using the heat transfer loop.
Losses to the sur-
roundings were assumed to be negligible.
The temperature
of the upper unheated zone was measured by connecting an
Omega Model 403A digital thermometer connected to the first
thermocouple downstream of the heater and in the water.
Once the temperature profile was established, the
pump was stopped and the generator was disconnected from
the heater.
The bypass valve was then closed.
The flow
path, therefore, consisted of the primary loop with no bypass and a stalled pump in the downcomer.
The pump was
stalled to permit as little natural circulation as possible
to raise the temperature of the unheated zone.
Some leak-
age flow through the stalled pump was present, however.
The power was then set at the desired level and applied in
a step-change fashion to the test section.
Shortly before
the inception of boiling, the data acquisition system was
started.
Boiling and flow oscillations then were observed
and data acquired.
Upon termination of the data acquisition
program in approximately fifteen seconds, the pump was restarted to bring the loop down below saturation at all points.
Power was then measured using the procedure outlined in a
previous section, and the generator was then shut off.
arations were then made for the next run.
Prep-
-67-
After the termination of experimentation, data
reduction was accomplished using the data acquisition computer.
A conversion program was written for the instru-
mentation present using calibration information to convert
the Tyco transducer readings to psig and the Validyne transducer readings to flow rate.
verted by a four step method.
The thermocouples were conUsing calibration information
supplied with the RTD temperature reference, the temperature
of the thermocouple termination panel was determined.
This
temperature was then converted to millivolts for copperconstantan thermocouples using a standard curve fit with a
320 F reference power.
This number was then added to each
thermocouple reading.
Finally, the adjusted thermocouple
output was converted to temperature using a standard curve
fit for a 320 F reference temperature.
As a last step,
bubble lengths in the heated and unheated zones were calculated by a stepwise integration of the flow rates with time.
Results of these calculations, and the accuracy of the
derived data, will be discussed in Chapter 5.
4.2.2.2
Forced Convection Testing
One experiment was performed using forced, instead of stagnant, flow.
This was done both to examine the
effect of a nonuniform temperature profile in the unheated
zone, and to determine the effect that forced flow would
-68-
the oscillatory behavior.
Procedures for pretest calibra-
tion and set-up were the same as described in Section 4.2.1.
In this experiment, though, the run was started with the
bypass closed and the pump running.
This generated a flow
rate so large as to make the temperature rise across the
heater very small.
The bypass was then opened and data
acquisition began simultaneously.
The opening of the bypass
reduced flow drastically to the primary section, allowing
boiling to begin.
Termination of the experiment and data
reduction were then performed as outlined in Section 4.2.2.1.
4.3
Safety Precautions
During all tests, the behavior of the bubble was
observed visually in the Pyrex section.
This was done to
provide verification of the results derived through data
reduction, and also to insure that the heater was not about
to reach critical heat flux (CHFJ.
Since the heater was
clamped at both ends, the rapid heatup of the tube associated with CHF would have caused severe distortion (bowing)
of the tube, possibly resulting in permanent heater deformation.
The Pyrex was also checked to make certain that it
did not crack.
A small amount of leakage was observed, due to
the many fittings as well as the manner in which the thermocouples were sealed into the unheated zone.
Leaks that were
-69-
small enough to have no appreciable effect on the experiment
were ignored.
Large leaks, however, were resealed.
-70-
CHAPTER 5
EXPERIMENTAL AND ANALYTICAL RESULTS
5.1
Experimental Results
5.1.1
Stagnant Flow Tests
5.1.1.1
Data Analysis
Data reduction for each experiment was carried out
as described in Chapter 4.
Upon examination of the data,
several facts were immediately evident.
The differential pressure transducer upstream of
the upper plenum was nearly useless in trying to determine
the bubble length in the unheated section.
because of the presence of air in the water.
This was true
Since the
loop was operated open to the atmosphere, it was not degassed, and the water used to fill the loop had a substantial amount of dissolved air in it.
At boiling inception,
this air was stripped out from the steam, and upon condensation, did not dissolve once again into the water, but instead travelled up the test section to the upper plenum.
When these bubbles came near the Validyne transducer, they
so distorted the differential pressure reading that any
attempt to deduce the flow rate or to integrate the flow
rate to find the bubble length yielded unrealistic results,
based on what was observed visually during the experiment.
-71-
In addition, the Validyne transducer just downstream of the lower plenum registered extremely large pressure drops at times during each run.
This pheonomenon was
attributed to a "water hammer" effect due to vapor condensation.
This conclusion was reached due to the fact that
these large pressure drops always occured immediately after
the bubble lengths, as calculated from the flow rate, reached zero.
After peaking rapidly these shock waves would die
away rapidly as well, until the next bubble growth-collapse
cycle.
The passage of these pressure waves across the ori-
fice taps at the bottom of the test section caused large
differential pressures to be recorded by the Validyne transducers, although the flow itself was not significantly affected, due to the high rate of speed of the wave.
However,
since flow rates are inferred from the readings of the Validynes, the response of the transducers to these pressure
waves tended to distort flow rate measurements.
No other
distortion, such as that mentioned for the upper transducer
due to air bubbles, was noted for the lower Validyne.
Several examples of experimental results are
shown in Appendix C.
The flow rate readings shown in seve-
ral of the tables illustrates clearly the effect of the
"water hammer" shock waves.
-72-
The thermocouples performed rather well, although
there were cases of bead breakage and subsequent failure
to function.
In general, though, those couples connected
to the outside of the heater tube tended to respond very
slowly to changes in temperature inside the tube.
This is
understandable due to the time lag resulting from the tube
wall thickness.
The thermocouples in the fluid, though,
responded rapidly to temperature changes and were quite
valuable in determining bubble movement.
All of the stagnant flow tests exhibited the same
basis characteristics.
Upon boiling inception, the vapor
bubble would begin to grow outward in both directions from
the top of the heater.
This tended to push warm fluid into
the upper unheated zone, causing the temperature of that
fluid to rise.
In addition, condensation would deposit
heat in this fluid.
When the bubble grew far enough so that
net condensation exceeded net evaporation, it would then begin to collapse.
This, in turn, would pull the colder fluid
above the bubble down into the heated zone, dropping the
temperature at that point below saturation.
This cycle was
followed by the aforementioned "water hammer" shock effect,
and then a short waiting period would occur while the water
at the top of the heater was reheated to saturation.
cycle would repeat itself several times.
This
The amplitude
-73-
and frequency of the bubble growth-collapse cycle tended to
change over the course of the transient, due to the changing
temperature profile in the unheated zone.
In the subsequent sections, each test will be examined individually in order to discuss its characteristics.
5.1.1.2
Test 4
After the first three preliminary tests, the first
run to be analyzed was number 4.
A plot of calculated bubble lengths in the heater
versus time is presented in Fig. 5.1.
Due to the anomalies
in flow rate readings, from which the bubble length is calculated, mentioned in the previous section, these measurements can be treated only as approximate.
However, several
pieces of valuable information are discernable from these
data.
The first thing to notice is, in general, the extremely rapid collapse of the bubbles after they have reached their peak lengths.
This is likely due to the variation
in condensation heat transfer during the oscillation cycle.
This point will be discussed at length in a later section,
due to its importance in determining bubble growth and
collapse.
Although the growth-collapse pattern appears to be
somewhat random at first, after about two seconds, a pattern
30.
25.0
20.0
LB
(In.
15 .
10.
5.
FIGURE 5.1
TIE (Seconds)
RESULTS OF TEST 4 - OSCILLATIONS IN BUBBLE LENGTH
-75-
of increasing and then decreasing bubble length becomes
apparent.
This looks very much like a "beat pattern" that
is experienced in sound waves.
It results from the super-
position of two somewhat different frequencies.
In this
case, it appears that the short frequency is indeed the
bubble oscillation frequency.
The longer wave pattern is
probably due to a sort of "enthalpy wave" flow instability.
This instability results, at low flow rates, when a large
amount of fluid is heated to saturation.
Upon boiling in-
ception, its density decreases, and the fluid accelerates
out of the heated zone.
It is replaced by colder fluid from
below, which increases the density of the fluid once again,
and decelerates the column back to its original condition.
This beat pattern behavior is consistent with results of
liquid metal experiments, another point which will be examined in more detail in a subsequent section.
The temperature at the first thermocouple in the
fluid downstream of the heater is shown in Fig. 5.2 as a
function of time.
This plot clearly illustrates the temp-
erature oscillations which occur as the bubble grows and
collapses.
Another point to note is the waiting period evident after each bubble collapse.
Part of this time is
artifically induced by the pressure waves from the water
220
210
200
190
180
170
160
(°F)
150
140
130
120
110
100
90
80
70
60
FIGURE 5.2
FIGURE 5.2 OFE
RESULTS
(S
onds)
RESULTS OF TEST WZ4TEMPERATURE OF FIRST UNHEATED NODE
-77-
However, some of this period is caused by
hammer effect.
the necessity to heat the water back to saturation after a
bubble collapses.
A final point to note is the amplitude of the
Since the flow rates are inferred from the
oscillation.
pressure transducers, and bubble length is inferred by
integrating the flow rate curve, several sources of uncertainty are available to distort the calculation.
In addi-
tion, since the readings from the upper Validyne were highly
unreliable, the bubble length above the heater can be inferred only by applying information gained from the analytical study.
This point will be elaborated upon in the sec-
tion on the comparison of analytical and experimental results, and when the condensation heat transfer coefficient
is discussed.
5.1.1.3
Test 5
The power to the heater in Test 5 was the same as
that in Test 4; however the temperature in the upper unheated
zone was approximately 250 F higher.
The purpose of this run,
then, was to compare it with the previous run to determine
the effect of that temperature on the oscillatory flow behavior.
A plot of bubble length within the heater versus
time is presented in Fig. 5.3, and temperature of the fluid
just downstream of the heater versus time is shown in Fig.
30.0
25.0
L
B
20.0
(In.)
15.0
10.0
5.0
0
TrIE (Seconds)
FIGURE 5.3
RESULTS OF TEST 5 - OSCILLATIONS IN BUBBLE LENGTH
-79-
5.4.
There are some significant differences between Tests
4 and 5 which should be noted, as well as a few similarities.
The similarities basically relate to the character
of the flow oscillations in general.
The same pattern as
that described in the previous section is evident.
Some
slight evidence of the "beating" that appeared in Test 4
shows again between about 1.5 and 3.5 seconds.
However,
the difference in amplitude is not as significant in Test
5 as in Test 4, a fact that can be attributed to the difference in unheated zone temperature.
A second similarity is
the waiting period between oscillations that was noted in
Test 4.
However, this waiting period tends to be shorter
in this test.
The higher upper zone temperature means that
less time is needed to return the fluid to saturation.
The main differences between the two runs is the
difference in oscillation frequency and amplitude over the
transient.
The average frequency - number of oscillations
divided by transient time - is less in this test than in
Test 4.
seconds.
This difference is especially clear after t=4
Related to this fact is the slightly larger ampli-
tude of the oscillations.
However, the amplitude of the
oscillation is more an inertial effect than a thermal one.
Therefore, while the difference in amplitude is not particularly large, for bubbles of similar lengths in the two tests,
220
T
f
160
V
00
0o
(OF)
150
-
140
130
120
110
100 0
1
2
3
TIME (Seconds)
FIGURE 5.4
RESULTS OF TEST 5 - TEMPERATURE OF FIRST UNHEATED NODE
-81-
the collapse time in Run #5 is significantly longer, due to
the lower temperature difference in condensation.
This shows
that bubble collapse, in the initial stage at least, is
largely thermal in nature.
The remaining four stagnant flow tests were run at
However, no attempt
lower powers than the first two tests.
was made to keep the power exactly the same in the four
tests.
The temperature of the unheated zone was increased
from test to test, though, to further explore the influence
of this temperature on flow behavior.
5.1.1.4
Test 6
Conditions during Test 6 featured a very low power
as well as a low temperature in the unheated zone.
The re-
sults of this test are presented in Fig. 5.5 and 5.6.
The
same general pattern of flow behavior prevails in this test
as in the previous two.
The beat pattern is especially
clear between about 2.5 and 6.5 seconds.
However, the
amplitudes of the oscillations in this case are smaller
than in the previous tests, a fact attributable mainly to
the extremely low power level.
The average frequency of the
oscillations is also much more rapid.
This is due partly
to the power level and partly to the low upper zone temperature.
An interesting point to note is that there appears
5
4
LB
00
3
(In.)
2
0
0
1
FIGURE 5.5
2
3
4
5
•
6
A
7
TIIE (Seconds)
RESULTS OF TEST 6 - OSCILLATIONS IN BUBBLE LENGTH
8
9
10
220
210
200
190
180
170
T 160
f
(oF)150
0a
140
130
120
110
100
90
80
70 60
0
I
1
2
FIGURE 5.6
7
8
6
5
TIME (Seconds)
RESULTS OF TEST 6 - TEMPERATURE OF FIRST UNHEATED NODE
3
4
9
10
-84-
to be less of a waiting period in this test than in previous tests.
With a low power and low temperature, this is
perhaps the reverse of what would be expected.
However,
the low amplitudes of the oscillations in this case mean
that less cold fluid is pulled down during bubble collapse
to mix with the hot fluid at the top of the heater.
Even
though the power is low, this decreased mixing effect contributes to a short waiting period.
The effect of the low
upper zone temperature is seen primarily in the extremely
fast bubble collapse times.
In virtually every cycle, the
collapse rate is quite rapid, creating the asymmetrical
growth-collapse curve.
One additional feature to note is
the long temperature coastdown between about 5 and 7 seconds.
This temperature decrease was very likely due to two effects.
First, there was some loss of heat to the environment, and
although those losses were generally quite small, this contributed to the cooling.
Second, and more important is the
fact that there was a dense, low temperature column of water
sitting on top of a warmer, lower density region.
During
the waiting period, then, colder water diffused into the
warmer zone, causing some cooling to occur.
The effect of
this was to increase the waiting period, as seen between
about 6 and 7 seconds in Fig. 5.5.
-85-
5.1.1.5
Test 7
The power and unheated zone temperature for this
test were both higher than their respective values in Test
6.
It is perhaps in this run that the features of the flow
behavior that have been discussed previously are most clearly
seen.
Figures 5.7 and 5.8 illustrate the bubble growth and
temperature oscillations.
In particular, the superposition
of oscillatory patterns to create the "beating" seen in
Tests 4, 5, and 6 is quite evident throughout the run.
Not
only does the beat pattern recur, but the beat frequency and
average amplitude of the envelope each increase.
This be-
havior is consistent with the higher power and temperature
condition.
The average frequency of the oscillation is
slightly less than in Test 6, as is the waiting period between bubble growth cycle.
In addition, the amplitudes of
the oscillations, reflected by the maximum bubble lengths,
are clearly larger.
5.1.1.6
Tests 8 and 9
The last two stagnant flow tests are presented
in Figs. 5.9 through 5.12.
In each case, the features dis-
cussed in the previous sections pertaining to bubble growth
patterns, beating,and amplitudes and frequencies can be
seen.
The fact that each test essentially reproduces the
same behavior, with changes attributable to slightly differ-
10.
9.
8.
7.
LB 6.
(Ln.)
4.
3.
2.
1.
TI1T (Seconds)
FIGURE 5.7
RESULTS OF TEST 7 - OSCILLATIONS IN BUBBLE LENGTH
220
210
200
190 T
(OF)
180
f
170 160 I
150
140 130 120 110 100
90
I
80
0
1
I
I
2
3
4-
I
5
I
6
I
7
I
8
TIME (Seconds)
FIGURE 5.8
RESULTS OF TEST 7 - TEMPERATURE OF FIRST UNHEATED NODE
I
9
10
-UIIIIIC .
~---
13 12
11 10.
9
LB
8
(In,)
7
co
6
5
4
3
2-
1
00
1
FIGURE 5.9
2
3
4
5
TI IE (Seconds)
RESULTS OF TEST 8 -
6
OSCILLATIONS
7
8
9
IN BUBBLF LENGTH
10
220
210 200 190 180
170
T
(OF~160
I
150
140
130
120
110 100
0
I
1
I
2
FIGURE 5.10
3
4
5
TIME (Seconds)
6
7
8
RESULTS OF TEST 8 - TEMPERATURE OF FIRST UNHEATED NODE
9
10
__
20
]I
15
L
-
I
10
LB,-
AI
10
--
(In.)
0
1
2
3
4
5
6
7
TIME ( Seconds)
FIGURE 5.11
RESULTS OF TEST 9 - OSCILLATIONS IN BUBBLE LENGTH
8
9
10
220
210 200 190 180 T
-
170
H
fI
(°F)
160
150
140
130 120
0
1
I
2
I
3
I
4
I
5
I
6
I
7
I
8
TIME (Seconds)
FIGURE 5.12
RESULTS OF TEST 9 - TEMPERATURE OF FIRST UNHIEATED NODE
I
9
10
-92-
ing test conditions indicate that the same basic mechanisms
are at work in creating the oscillatory flow behavior.
5.1.2
Forced Convection Testing
Only one experiment was performed with non-stagnant
flow.
The results of this experiment are presented in Fig.
5.13.
Only the temperature downstream of the heater is shown
for this run, due to the highly ambiguous bubble length results for this run.
The reason for the ambiguous results
will be discussed shortly.
The features discussed in relation to stagnant
flow oscillatory behavior are largely absent in this test,
and the reason for this is quite evident.
The test was carried out by opening the bypass
valve and allowing the flow to coast down from approximately
10-15 feet per second to approximately 0.7 feet per second.
However, during this time, the power was constant at a
level of about 1.09 kilowatts.
Under these conditions, the
water in the unheated zone was able to heat up to a substantially higher temperature than was present in the stagnant flow tests.
The result of this high temperature at
bubble inception was to allow the growth of the vapor volume
to such an extent that net condensation never exceeded net
evaporation by enough to collapse the bubbles, and steady
state forced convection two-phase flow eventually was
220
210
200
190
180
170
160
Tf
150
(OF)
140
130
120
110
100
90
80
70
FIGURE 5.13
TIME (Seconds)
RESULTS OF FORCED CONVECTION TEST - TEMPERATURE OF
FIRST UNHEATED NODE
-94-
established.
This is the reason for the ambiguous bubble
length readings after data reduction.
Since no real flow
oscillations occurred, except for the normal variations
associated with "steady" two-phase flow, integration of the
flow rate did not give dependable void readings.
In any
case, the vapor present was mainly in the form of small
bubbles, not a single vapor slug.
This fact in itself would
indicate a different flow behavior than that present in the
stagnant flow tests.
It was believed that setting the power
high enough to allow boiling inception before the establishment of high unheated zone temperatures might possibly lead
to critical heat flux and subsequent damage to the test
section.
This was not desirable, and further forced con-
vection tests were not conducted.
There were also instru-
mentation problems associated with the forced convection
tests, as well as the same sources of uncertainty as in the
other tests.
These will be discussed in the following sec-
tion.
5.1.3
Sources of Error and Uncertainties in Experimental Tests
Several factors were present in the experiments
that created, or had the potential to create, errors in the
measurement of key parameters.
These factors were differ-
ent in the two different types of experiments, and will be
-95-
examined separately.
5.1.3.1
Stagnant Flow Tests
The sources of uncertainty and error in the stagnant flow tests are connected mainly with two factors:
the
dissolved air in the water being used, and the water hammer
effects mentioned in Section 5.1.1.
The presence of air on the water has been previously discussed.
After becoming liberated from the water in
boiling, some of the air formed bubbles which travelled upward through the remainder of the test section.
As already
noted, these bubbles rendered the flow rate readings from
the upper differential pressure transducer virtually meaningless.
However, not all of the air travelled up out of
the test section.
Some of it very likely remained mixed
with the steam in the bubble.
Upon bubble collapse due to
condensation, the air would remain to cushion the oscillation.
Some of the very low amplitude oscillations seen in
the experimental results may indeed be the result of these
air bubbles.
The effect of the water hammer pressure waves on
the flow rate measurements has also been mentioned previously in Section 5.1.1.2.
The extremely high artificial flow
rates inferred from differential pressure measurements during these pressure waves certainly distorted the bubble
-96-
length calculations.
This effect also made it more diffi-
cult to calculate condensation heat transfer coefficients.
It is also probable that the waiting period between bubble
growth-collapse cycles is partially due to the decay of
these pressure waves, although part of that period is undoubtedly genuine.
One further possible effect of these
waves involves the measurement of flow rates late in the
course of the transients.
In this case, though the waves
generated by the water hammer do tend to decay rapidly,
they also propagate throughout the test section, and would
tend to reflect back and forth from the two plena.
It is
possible that, given enough growth-collapse cycles, as
sufficient intensity could still remain to distort flow
rate readings throughout the cycle, and not just at the
beginning and end of the cycles.
This may possible account
for the behavior between about 7.5 and 9 seconds in Run 8
(Fig. 5.9),
for example.
5.1.3.2
Forced Convection Testing
The uncertainties present in this test are largely
due to an effect related to the water hammer pressure waves
noted in the previous section.
When the bypass valve was
opened to permit the flow to coast down, severe pressure
waves resulted from this flow disturbance.
As a result,
the flow rate readings inferred from the pressure trans-
-97-
ducers are quite unreliable during the first part of the
transient.
5.1.3.3
Other Sources of Error
In both types of tests, there are sources of error
related to the nature of the instruments themselves.
The
Validyne transducers proved to be extremely difficult to
calibrate and to maintain in a zero-output condition at
zero flow.
This zero drift was compensated in both the
calibration procedure and in the conversion program, but
some uncertainties were still possible.
The Tyco gauge
pressure transducers functioned quite well, in general, and
few uncertainties exist in the readings from these instruments.
The thermocouples also functioned well, in general.
However, thermocouples do have characteristic response times,
and cannot record temperature changes instantaneously.
The
thermocouples in the fluid responded quite rapidly, and the
readings were considered reliable.
The thermocouples fast-
ened onto the outside of the metal tube tended to respond
much more slowly, due to the time constant of the tube
itself,
the time constant of the thermocouple, and the con-
tact resistance of the thermcouple bead with the metal tube.
The resultant response time of these thermocouples was somewhat less rapid, and the readings less reliable.
Temper-
ature changes related to the flow oscillations were not re-
-98-
corded by these thermocouples.
One final source of error was the data acquisition
system itself.
When the RTAS was tested, small offsets-
were found in the output of each channel.
These offsets
were subtracted from the instrument readings during data
reduction, but there is no way of knowing if these offsets
were truly constant during a run.
In addition, the data
acquisiton system error band as per manufacturer's specifications was on the order of 0.5%, full scale.
This inher-
ent error also contributed somewhat to experimental error.
5.1.4
Calculation of Condensation Heat Transfer
Coefficient
Examination of the bubble growth-collapse patterns
reveals an extremely asymmetrical behavior.
Instead of a
bubble collapse which parallels the growth curve, what is
seen is a relatively long growth period, followed by a
rapid collapse.
This indicates a non-uniform heat transfer
coefficient over the bubble growth-collapse cycle.
In
order to ascertain the nature of this non-uniformity, several calculations were performed to determine the condensation
heat transfer coefficient.
Results of the calculations for various experiments are shown in Table 5.1.
Details of the calculational
method can be found in Appendix D.
-99-
Table 5.1
Test Number
Example of Condensation Heat
Transfer Coefficients
Bubble Condition
Growth
Heat Transfer
Coefficien
(BTU/hr-ft OF)
hA
(BTU/hroF)
168.5
6.71
3167.1
62.71
325.7
10.91
4456.3
180.03
25.0
0.19
Collapse
192.0
2.88
Growth
102.4
0.36
Collapse
871.2
25.53
Growth
102.2
1.62
3587.2
100.80
109.9
2.86
3457.5
67.08
Collapse
Growth
Collapse
Growth
Collapse
Growth
Collapse
-100-
The most interesting aspect of the results is the
extremely large magnitude of the heat transfer coefficient
during bubble collapse.
The reason for this behavior in-
volves another type of flow instability.
accelerates
into a liquid medium, small waves may form at
the liquid-vapor interface.
bilities.
When a vapor
This is due to Taylor insta-
The waves may then break up into small droplets
of liquid, creating a mist-flow regime at the very end of
the bubble.
This type of behavior was documented by Ford
(3) in his Freon experiments.
Since the heat transfer co-
efficient shown is based on an area which does not account
for any such mechanisms, the result is a coefficient which
is quite large.
The important parameter is the product of
the heat transfer coefficient and the heat transfer area,
and this is also shown in Table 5.1.
sents the heat removal rate (q/AT).
This product repreThe calculational
method employed to determine the heat removal contains
some assumptions, as presented in Appendix D, which might
tend to distort the actual numbers; however, the way in
which the condensation changes over the period of the
bubble growth-collapse cycle is indisputable.
The fact that the heat transfer coefficient effects
the oscillatory behavior of the system implies that a circular situation exists; that is, that the system behavior
-101-
in turn affects the heat transfer coefficient.
The more
violent the oscillation, the greater the acceleration of
vapor into fluid, and the more extensive the fluid misting
effect becomes.
This is one reason for the behavior noted
in Test 6 - the oscillation amplitude was so small and vapor
generation reasonably slow, that the heat transfer coefficient did not have a chance to increase to the same magnitude as in the higher-power experiments.
Although it is qualitatively clear what is happening to the heat transfer coefficient in this type of flow,
quantifying the behavior mechanistically is more difficult,
and was not conceived as part of this work.
Further dis-
cussion of this point can be found in Chapter 6.
5.1.5
Comparison of Water Data to Sodium Data
Although the Sodium Boiling Test Facility was not
able to operate in a mode precisely comparable to the WTL,
is is interesting to compare the results of the water experiments to LOPI experiments carried out in the THORS
facility at ORNL.
It should be noted that the THORS faci-
lity is a multipin bundle, in which two-dimensional effects
may be important.
However, examination of the results of
one of the LOPI tests reveals some interesting parallels.
Figure 5.14 shows the results from THORS test
71H-101.
Note that the parameter plotted is flow rate
-102-
Io~
I-[,
II
0
-I
"I
10.0
H
-0.O
-1
0.0
5.0
329/77
THNR567.
10.0
15.0
20.0
13 25 32 rESf 71HItuN 101
FIURE 3.14
EX
25.0
30.0
35.0
0.0
50.0
4O5.Q
55.0
60.0
SECCNIS
LE 'OF IORPS
ESULTS -
OSCILLATIONS
O).,.ETMIPJC F
T7
-103-
versus time; however, since the flow oscillates about the
zero-flow point, it is clear that the integration of the
curve to show the bubble length would show the same characThe most outstanding point is the beat pattern
teristics.
that appears during the course of the oscillation cycle.
This characteristic is quite similar to the pattern seen in
several of the water tests.
In addition, there is a change
in flow oscillation frequency over the transient, which
again parallels the water results.
One other area in which a comparison between water
and sodium tests can be drawn is the subject of noncondensable gases.
Mention has already been made about some of
the effects on dissolved air in the water.
It must be
noted that in a sodium system, inert gas blankets are used
to preclude the potentially dangerous contact of sodium and
oxygen.
As a result, these gases become dissolved in the
sodium, and can behave in much the same manner as air in
water.
Sodium systems cannot be examined visually during
experimentation, of course, to determine the presence of
inert gas in the sodium vapor; however, the presence of noncondensables in water experiments should not be considered
as a non-prototypic parameter.
5.2
Analytical Results
The results of computer simulations of the stag-
-104-
nant flow tests are presented in Fig. 5.15 through 5.33.
The features of the simulations themselves will be discussed
in the next section.
Comparison of analytical results to
those obtained experimentally will be discussed in the
Section 5.2.2.
5.2.1
Features of Analytical Simulations
The information obtained from a computer run in-
cludes data on flow rates, bubble pressures, areas, and
bubble lengths and volumes.
An example of the actual out-
put from the computer is presented in Appendix E.
There
exists, as part of the program, a subroutine which picks
specific pieces of information and plots them, using a
library plotting routine.
Examples of these plots are pre-
sented in Figs. 5.15 through 5.18.
The conditions for this
run correspond to those shown in the output in Appendix E.
Some of the features to be noted in the plots include the rapid oscillation of all variables plotted as the
bubble flows and collapses.
Note also, the slight delay
between oscillatory cycles and the asymmetric pattern of
the growth-collapse cycle.
Figures 5.19 through 5.21 present a slightly
different perspective.
In these plots, the bubble length
within the heater is shown.
The conditions for these runs
correspond to some of the stagnant-flow test conditions.
4
I
F
I
I
t-"1
+
*
3
x
2 -
U
c-n
TiNI
2
+
S
2
0
0n
Q
H
II
0
LL2
1.
W22
-1-2
0!
"
2
-
,
2
-3-
0
-4
0
2
4
G
9
i0
12
TIME (SEC)
FIGURE 5.15
CCUPUThr
(M]ffTE PIR -
TLUATIMA ('
T E R P 9:
VOILETRIC TOVW RATES IN
LEGS 1 AND 2
22
20
-, 18
H
LU
oncrLi
U
l ,h
14
12 -
10
0
2
4
G
9
10
TIME (SEC)
FIGURE 5,16
COMPUTER GENERATED PLOT , SIMULATION OF TEST 9:
BUBBLE PRESSURE
12
3.0
2.5 -
,..,
o~n
4
2.0
LU
(I
zZ
H
4
1.5
I
I
C3D
z
i
1.0
E4-
I
~0.5
0.0
0
2
4
G
9
j0
TIME (SEC)
FIGURE 5.17
COMPUTER GENERATED PLOT - SIMULATION OF TEST 9:
TOTAL BUBBLE LENGTH
12
1.5
1I
I
zu0.5
1.0
LII
L
1
0)
Lu -0.5
-1.0
zI
-1.5
0
2
4
6
9
i0
12
TIME (SEC)
FIGURE 5.18
COMPUTER GENERATED PLOT - SIMULATION OF TEST 9:
BUBBLE LENGTHS IN LEGS
1 AND 2.
-
h
con
= 1500 BTU/hr-ftL°F
2.0
LB
C)
(In.)
1.0
II
1.0
FIGURE 5.19
2.0
TIME (Seconds)
3.0
4.0
COMPARISON OF ANALYTICAL RESULTS FOR DIFFERENT HEAT TRANSFER
COEFFICIENTS -
TEST 4 CONDITIONS
5.0
1.5
1'
1.0
II
LB
(In,)
1i
0.5
I
I
I
0I
1.0
2.0
3.0
4.0
5.0
T]E (Seconds)
FIGURE 5.20
COMPARISON OF ANALYTICAL RESULTS FOR DIFFERENT HEAT TRANSFER
COEFFICIENTS - TEST 6 CONDITIONS
6.0
1.5
1.0
L
B
(In.)
0.5
0
1.0
FIGURE 5.21
2.0
3.0
4.0
TIBE (Seconds)
COMPARISON OF ANALYTICAL RESULTS FOR DIFFERENT HEAT TRANSFER
COEFFICIENTS - TEST 9 CONDITIONS
5.0
-112-
However, the condensation heat transfer coefficient has been
varied so as to provide a comparison between the results for
different heat removal rates.
It is not surprising that, when a high heat transfer coefficient is used, the cycle period is slightly smaller,
and the amplitude of the cycle is considerably smaller.
This
is due largely to the manner in which the code is currently
set up.
When the temperature nodal pattern is input to the
code, the first node is normally made quite small - on the
order of an inch - and the temperature therein is set at saturation.
This permits no condensation to occur in that node.
This is done for two reasons.
First, from a physical stand-
point, some hot fluid must flow into the unheated zone before the inception of boiling, due to natural circulation.
The resistance of the stalled pump during the stagnant flow
tests, however, made the natural circulation flow rate quite
small.
Therefore, this relatively small volume of fluid
was used as a saturated length.
This "zone of no condensation"
permits growth of the bubble at the start of the cycle.
In
addition, the heat transfer coefficient, when input as a
constant, as was done in these runs, must be set very high,
to correspond to the large heat removal rate attained during bubble collapse.
The small initial saturated node pro-
-113-
vides a de facto variation in condensation heat transfer coefficient.
More preferable, of course, would be a mechan-
istic model of the variation of the heat transfer coefficient
during the cycle.
However, such a model does not presently
exist.
The choice of the length of the saturated node
and the condensation heat transfer coefficient together
provides a "dial" which the user may adjust.
The combin-
ation of these two parameters, along with the temperature
profile chosen for the unheated zone, legislates, for all
intents and purposes, the length of the bubble during the
transient.
Changes in the temperature profile by virtue
of the heat input to or output from the unheated zone during the transient also provide some change in the cycle
period and amplitude, and this, too, is demonstrated in all
of the figures.
The variation of the heat transfer coefficient
during the cycle in the simulations is correct in a broad
sense - low at the beginning and high at the peak, and it
was felt that trying to vary either the temperature profile
or the heat transfer coefficient without some mechanistic
base would cause more difficulties than it would solve.
The results of this decision are discussed in the next section.
-114-
5.2.2
Comparison of Analytical and Experimental
Test Results
The parameter which is best suited for comparison
between the experimental tests and analytical simulations
is the bubble length with the heater.
combination of reasons.
This is true for a
First and foremost, this bubble
length is the most reliable nonthermal datum that can be
derived from the experimental results.
The experimentally
determined flow rates were subject to effects that do not
show up analytically (non-condensables, "water hammer", etc.).
Second, this parameter illustrates quite clearly the frequency, amplitude, and asymmetrical behavior of the oscillations.
The bubble length within the heater is plotted,
therefore, in Figs. 5.22 through 5.27, for each stagnant
flow test and its corresponding computer simulation.
The
simulations plotted here correspond to the high heat transfer coefficient runs, examples of which were shown and explained in Section 5.2.1.
however:
One small change has been made,
the waiting period between oscillations has been
adjusted in the analytical results to agree with that determined experimentally.
Therefore, what is shown is
actually a cycle-by-cycle comparison of the results.
The reason for the adjustment involves the method
__
30.0
25.0
Experimental Data
20.0
-Computer Simulatio9,
h
= 3000 BTU/hr-ft F
20
con
L
B
uI
15.0
(In.)
10.0
5.0
1
2
3
5
4
TIME
FIGURE 5.22
6
7
8
9
(Seconds)
ANALYTICAL VS. EXPERIMENTAL RESULTS - TEST 4:
BUBBLE LENGTH
10
30.0
25.0
20.0
15.0
LB
(In.)
10,0
5,0
0
FIGURE 5,23
TIME (Seconds)
ANALYTICAL VS. EXPERIMENTAL RESULTS - TEST 5:
BUBBLE LENGTH
3
L-
IL
-I__I
LB
(In.)
TI2E (Seconds)
FIGURE 5.24
ANALYTICAL VS. EXPERIMENTAL RESULTS - TEST 6:
BUBBLE LENGTH
__
__
10 .1
9.1
8.
7.'
L
6.1
LB
5.1
(In.)4.
3.
2.
1.
0
1
FIGURE 5.25
2
3
ANALYTICAL VS.
4
TIME
5
(Seconds)
6
7
EXPERIMENTAL RESULTS - TEST 7:
8
9
BUBBLE LENGTH
10
15
14 -
Experimental Data
13 -
Computer Simulation,
h
= 4000 BTU/hr-ft 2 OF
con
12 11
10
L
B
(In.)
9
H
)8
8-
7
6
5
4
3
2
1
___1
' A
i
4'
0
1
FIGURE 5.26
2
4
5
6
7
TIME (Seconds)
ANALYTICAL VS. EXPERIMENTAL RESULTS - TEST 8:
3
8
BUBBLE LENGTH
9
10
LB
10
(In.)
TI4E (Seconds)
FIGURE 5.27
ANALYTICAL VS.
EXPERIMENTAL RESULTS -
TEST 9:
BUBBLE LENGTH
-121-
by which the waiting period is determined in the code.
The
program uses the First Law of thermodynamics to increment
the temperature of the initial node back to saturation.
However, the temperature after bubble collapse is determined
by mixing an arbitrary amount of fluid at saturation with
the colder fluid from above the heater.
While this arbit-
rary amount of fluid is chosen from the standpoint of how
much physical mixing can occur, it is essentially another
user-adjustable "dial".
In addition, the large positive
flow rate readings produced by the "water hammer" effect
probably had a tendency to bias the calculations of bubble
length to some extent.
This would have shown up most in
the waiting period between cycles, due to the decay of
these pressure waves.
In light of these facts, it was felt
that to try to adjust the code to correspond to the actual
experimental output would not be a productive exercise.
To demonstrate how the actual computer output corresponds
to the experimental results, Fig. 5.28 has been included on
the following page.
This is a combination of Fig. 5.11 and
Fig. 5.18, and plots length versus time, calculated without
adjusting the delay time against the experimental data.
The difference in calculated versus experimental period can
also be deduced by examining the temperature versus time
plots in Fig. 5.29 through 5.34.
LB
10-
(In.)
5-
S1
5AA
2
3
4
5
6
7
8
9
TI7.E (Seconds)
FIGURE 5.28
ANALYTICAL VS. EXPERIMENTAL RESULTS - TEST 9:
TIME ADJUSTMENT
BUBBLE LENGTHS, NO DELAY
10
-123-
In every case, the first and most obvious fact
that is apparent is that the experimental results give much
larger bubble lengths than the analytical results.
reasons for this are twofold.
The
First, the previously men-
tioned bias in the experimental flow rate readings, due to
pressure waves, tends to distort the bubble lengths determined from those readings.
Second, the way in which the
condensation heat transfer coefficient varies, both experimentally and analytically, has been discussed in previous
sections.
Although the variations in heat transfer coeffi-
cient throughout the entire cycle have not been accounted
for analytically, it is interesting to note that, in almost
every case, the initial rise of the bubble growth pattern
is very close analytically to what is seen experimentally.
This confirms the lack of condensation during this period
of the cycle.
In a few cases, in Test 6 especially, the
entire cycle is very closely simulated, as well.
This
would tend to confirm the large jump in condensation heat
transfer when the bubble begins to collapse.
are more correct qualitatively, though.
Other tests
The fact that
there is a mismatch in the experimental and analytical heat
transfer coefficients during various times of the cycle explains much of the quantitative disagreement between the
two types of results.
-124-
Figures 5.29 through 5.34 show the temperature
of the first fluid thermocouple in the experiment compared
to that of the first non-saturated analytical node, for each
stagnant flow test.
Note that while the values of the tem-
peratures are not correct quantitatively, in every case, and
that the flow oscillatory patterns are somewhat variant, the
trends between experimental temperature results and computer
simulations agree quite well.
From
a qualitative standpoint, then, the analy-
tical results and the experimental results agree quite well.
In general, the period of the oscillatory cycles, as well as
the asymmetric shape of the cycle curve are in close agreement.
In addition, the variation of the amplitude and period
during the transient agree fairly well.
Due to the large
uncertainties in the experimental results, this qualitative
agreement in the areas mentioned are much more important than
the quantitative disagreement in the actual magnitude of the
parameters measured.
220
210
200
190
180
170
160
Tf
150
(oF )
140
130
120
110
100
90
80
70
60
TIME
FIGURE 5.29
A
FTICIL VS. EXPIERT!
MIr
(seconds)
iTAL RESULTS - TEST 4:
UNHEATED ZONE TPERAIJRE
220
210
200
190
180
170
Tf 160
0
CF
(
)50
140
130
120
110
100
90
TIME (Seconds)
FIGURE 5.30
ANALYTICAL VS.
EXPERIMENTAL RESULTS - TEST 5:
UNTHEATED ZONE TEMPERATURE
-
-
I
-
I
-- I-C
~-i I12 r
220
210 200 190 -
A4A..
180
170 L
160
150
Tf
(OF)
I
140
130
120 -
p
110
Experimental Data
100
Computer Simulation, 2
h
= 2000 BTU/hr-ft oF
90
con
80
70
60
0
I
1
I
2
I
3
j
I
5
4
TIME
FIGURE 5.31
I
6
1
7
I
8
(Seconds)
ANALYTICAL VS. EXPERIMENTAL RESULTS - TEST 6:
ZONE TEMPERATURE
UNHEATED
I
9
10
220
210 ._ .
200
190 180 170 160
T
(OF)
150
f
140
Experimental Data
130
120
_
Computer Simulation
h
con
110
= 3000 BTU/hr-ft
OF
100
90
80
0
I
.I
I
I
1
2
3
4
I
I
I
I
I
5
6
7
8
9
TIME (Seconds)
FIGURE 5.32
ANALYTICAL VS. EXPERIMENTAL RESULTS - TEST 7:
ZONE TEMPERATURE
UNHEATED
10
'
//t
Experimental Data
I
Computer Simulation
h
= 4000
o
BTU/hr-ft
2
FIGURE 5.33
3
456
TIME (Seconds)
ANALYTICAL VS. EXPERIMENTAL RESULTS - TEST 8:
ZONE TEMPERATURE
UNHEATED
F
________
_
_~
220
210
200
190
180
Tf
(OF)
170
-
(f) 1 7 6 0
__
Experimental Data
6
11o60-
150 -
.
..
140
Computer Simulation, 2
h con = 6000 BTU/hr-ft °F
•
130 I
120
0
1
FIGURE 5.34
I
2
I
3
ANALYTICAL VS.
I
4
I
I
I
I
5
6
TIME (Seconds)
7
8
9
I
EXPERIMENTAL RESULTS - TEST 9:
ZONE TEMPERATURE
UNHEATED
10
-131-
CHAPTER 6
CONCLUSIONS AND RECOMMENDATIONS
FUTURE STUDY
6.1
Conclusions
The results of the experimental and analytical
work performed for this project have led to the following
conclusions.
1.
A model has been developed which will qualitatively
describe the processes occurring during flow oscillations of the type studied.
2.
Experiments with water indicate that sodium behavior can be successfully simulated using water, despite the large disparity in the physical makeup
and properties of the two liquids.
3.
A set of criteria has been proposed whereby water
and sodium data can be compared. Only a very
limited amount of mostly qualitative testing of
these criteria has been done as part of this work,
however.
4.
The temperature profile in the unheated region
downstream of the source of heat for the fluid
(i.e. core, heater pin, heater tube) has a significant effect in determining the behavior of the
system during oscillations.
5.
The heat transfer coefficient for condensation
also has a significant effect on the flow oscillIn addition, the coefficient changes over
ations.
perhaps two orders of magnitude during the oscillations, due to the microscale processes at the
liquid-vapor interface, and this change may be one
of the driving forces during oscillatory behavior.
6.
The existence of flow oscillations helps to draw
cool fluid down from the unheated zone into the
top of the heated zone. This behavior may well
-132-
delay dryout of the heater walls and any subsequent
temperature excursions, which might otherwise prove
detrimental to providing adequate core cooling during transients.
7.
6.2
More study is needed in many of the areas delineated
in points 1-6.
Recommendations for Future Work
The scope of this project was such that it did not
allow detailed study of the condensation heat transfer coefficient.
The type of behavior seen was not completely
anticipated, and the experiment was not constructed in a
way which would easily lead to the development of a mechanistic model of the condensation process during flow oscillations.
Clearly, further work is needed in this area.
The criteria proposed for the comparison of sodium
and water data have been tested only superficially.
It
would be useful if the SBTF experiment at ORNL were to be
operated in such a way that low-power, low-flow oscillations
could be generated for comparison to WTL results.
Data from
THORS and the multipin experiments is useful from a qualitative standpoint, but the existence of two-dimensional effects
due to the radically different experimental geometry may
distort efforts to quantitatively compare the data.
The model which has been developed for this project makes a good start toward describing, from a physical
basis, the parameters which affect flow oscillatory behavior.
-133-
However, it is far from complete, especially with respect
to the heat transfer calculational scheme.
Further work is
required on the model in this area, as well as in the area
of expanding the model to a multidimensional tool.
A con-
siderable amount of work is underway presently to determine
whether multidimensional effects exist in large LMFBR fuel
pin bundles.
The existence of a multidimensional model to
aid in this work would be helpful, and consistent with the
original objective of this work to provide a model which
might become a module in a large systems code.
Experimentally, there appears to be a wide range
of options regarding the simulation of sodium behavior using
water.
It is clear that certain types of flow behavior can
be modelled using water instead of liquid sodium, namely,
those types which depend mainly on hydrodynamic processes,
rather than thermal ones.
Consideration must be given to
using small scale water experiments for preliminary investigations of sodium behavior, so that otherwise unexpected
effects which might have an adverse effect on sodium experiments may be avoided.
Further work on the effect of loop dynamics on
flow behavior should be performed.
The means to do this
on the Water Test Loop currently exists to some extent,
using variable flow orifices in the orifice flange upstream
-134-
of the inlet plenum.
A parametric study using the
FLOSS
model might also be valuable.
Finally, more work is needed in quantifying the
effect of unheated zone temperature profiles on flow oscillations.
Judging from the experimental results obtained in
this work, there may, for a certain power, be an optimum
temperature profile which would provide the best means of
accident abatement.
The design of LMFBR cores so that such
effects could be used to maximum advantage would be the
ultimate result of such future work.
-135-
REFEREUCES
1.
W.D. Hinkle, et.al., "LMFBR Safety and Sodium Boiling,
A State of the Art Report", Department of Energy (June,
1978).
2.
R.J. Ribando, et al., "Sodium Boiling in a Full Length
19-Pin Simulated Fuel Assembly (THORS Bundle 6A)",
ORNL/TM-6553, Oak Ridge National Laboratory (January,
1979).
3.
W.D. Ford, "Bubble Growth and Collapse in Narrow Tubes
with Nonuniform Temperature Profiles", ANL-7746, Argonne
National Laboratory (December, 1970).
4.
W.D. Hinkle, "Water Tests for Determining Post Voiding
Behavior in the LMFBR", M.I.T. Report MIT-EL-76-005,
M.I.T. Energy Laboratory (June, 1976).
5.
P.W. Garrison, R.H. Morris and B.H. Montgomery, "Dryout Measurements for Sodium Natural Convection in a
Vertical Channel", ORNL/TM-7018, Oak Ridge National
Laboratory (December, 1979).
6.
A Computer Programme for the SubR.W. Bowring, "HAMBO:
channel Analysis of the Hydraulic and Burnout Characteristics of Rod Clusters", AEEW-R 582, UKAEA (1968).
7.
A.E. Levin, "Simulation of Flow Behavior in BWR Coolant
Channels During Transients", S.B. Thesis, M.I.T. (June,
1975).
8.
G.H. Golden and J.V. Tokar, "Thermophysical Properties
of Sodium", ANL-7323, Argonne National Laboratory
(August, 1967).
9.
Perkin-Elmer Computer Systems Division, "OS/16 Operator's Handbook", Perkin-Elmer Corporation (1975).
10.
Perkin-Elmer Computer Systems Division, "OS/16 User's
Handbook", Perkin-Elmer Corporation (1976).
11.
Perkin-Elmer Computer Systems Division, "FORTRAN IV
Reference Manual and User Guide", Perkin-Elmer Corporation (1976).
-136-
12.
Perkin-Elmer Computer Systems Division, "FORTRAN IV
Run Time Support", Perkin-Elmer Corporation (1977).
13.
J. Aberle, et al., "Sodium Boiling Experiments in a 7Pin Bundle under Flow Rundown Conditions", KFK 2378,
GFK, Karlsruhe, FRG.
14.
A.E. Bergles, "Review of Instabilities in Two-Phase
Systems", Proc. NATO Advanced Study Institute in Two
Phase Flows and Heat Transfer, V.1, Hemisphere Publishing Corp., Washington, D.C. (1977).
15.
J. Costa and P. Charlety, "Forced Convection Boiling of
Sodium in a Narrow Channel", in Liquid Metal Heat Transfer and Fluid Dynamics, A.S.M.E. (1970).
16.
A.W. Cronenberg, "A Thermohydrodynamic Model for Molten
UO2-Na Interaction, Pertaining to Fast-Reactor FuelFailure Accidents", ANL-7947, Argonne National Laboratory (June, 1972).
17.
M.H. Fontana, "THORS Bundle 6A Boiling Stability Test
Results", Report presented at D.O.E. Conference, Boston
(August, 1977).
18.
P.W. Garrison, SBTF Test Results, Personal Communication
(January, 1979).
19.
R.E. Henry, et al., "OPERA Single-Pin Coastdown Expulsion
and Reentry Test", ANL-75-17, Argonne National Laboratory
(February, 1975).
20.
W. Kowalchuk and A.A. Sonin, "A Model for Condensation
Oscillations in a Vertical Pipe Discharging Steam into
a Subcooled Water Pool", NUREG/CR-022, M.I.T. (June,
1978).
21.
W. Peppler and E. G. Schlechtendahl, "Experimental and
Analytical Investigations of Sodium Boiling Events in
Narrow Channels", Proc. Winter Annual Meeting, ASME,
in Liquid Metal Heat Transfer and Fluid Dynamics,
A.S.M.E. (November, 1970).
-137-
22.
M. Pezzilli, et al., "The NEMI Code for Sodium Boiling,
and its Experimental Basis", in Liquid Metal Heat Transfer and Fluid Dynamics, A.S.M.E. (1970).
23.
T.A. Shih, "The SOBOIL Program - A Transient, Multichannel, Two-Phase Flow Model for Analysis of Sodium
Boiling in LMFBR Fuel Assemblies, G.E. ST-TN-79008,
General Electric Corp., A.R.S.D.
24.
M.G. Stevenson, et al., "Current Status and Experimental
Basis of the SAS LMFBR Accident Analysis Code System",
CONF-740401-P3, Proc. Fast Reactor Safety Mtg., Beverly
Hills, CA (April, 1974).
25.
D.H. Thompson, et al., "SLSF In-Reactor Experiment P3AInterim Post-Test Report", ANL/RAS 77-, Argonne National
Laboratory (November, 1977).
26.
J.G. Collier, Convective Boiling and Condensation, McGraw-Hill Book Company, LTD, London (1972).
27.
R.H. Sabersky, A.J. Acosta, and E.G. Hauptmann, Fluid
Flow, 2nd Ed., The MacMillan Co., New York (1971).
28.
W.M. Rohsenow and H.Y. Choi, Heat, Mass and Momentum
Transfer, Prentice-Hall, Inc., New Jersey (1961).
29.
M. Clark, J. and K.F. Hansen, Numerical Methods of
Reactor Analysis, Academic Press, New York (1964).
30.
R.H. Perry and C.H. Chilton, Eds., Chemical Engineers'
Handbook, 5th Ed., McGraw Hill Book Company, New York
(1973).
31.
R.L. Powell, et al., "Thermocouple Reference Tables
Based on the IPTS-68", NBS Monograph 125, U.S. National
Bureau of Standards (March, 1974).
32.
F.E. Dunn, et. al., "The SAS2A LMFBR Accident Analysis
Computer Code," ANL/RAS 73-39, Argonne National Laboratory (December, 1973).
33.
R.E. Barry and R.E. Balshizer, "Condensation of Sodium
at High Heat Fluxes," Proc. 3rd Int. Heat Transfer Conf.,
V.II (1966).
-138-
APPENDIX A
THE COMPUTER CODE FLOSS
A.l.
General Description of the Code
The computer code FLOSS is a relatively small and
simple program designed to solve the equations for the hydrodynamic and thermal models.
It was developed as part of this
project, and is envisioned as a module of a large system-scale
code at some future time.
Because of this ultimate aim,
many complicating features, such as sophisticated heat transfer models, were omitted.
In addition, since the model deals
only with a fixed regime, single phase flow before the transient and two-phase flow after the transient have not been
modelled.
Instead, the primary aim was to develop a code
which could be easily understood and would take small amounts
of computer time to run, yet would include as much of the
essential physics of the problem as possible.
This aim has
been, for the most part, achieved.
A.2.
Solution of the Hydrodynamic and Thermal Models
The solution scheme for the equations presented
in Chapter 2 is an amalgam of different techniques for
finite difference solutions of differential equations.
The
entire code is semi-implicit, with an iterative scheme described in Chapter 2.
-139-
A.2.1
The Hydrodynamic Model
The equations for the hydrodynamic model are:
dQl
AP'
=
+
d
I
R I'Q 2
1
1 dt
d2
=
AP'
Q=
3
(2.28)
1
2
dQ + R 'Q2
I
2 dt 2
2 2
V
dp
p2
g
'
dt
(2.29)
(2.11)
The first two equations are solved using a firstorder, explicit finite difference scheme.
The equations can
be rearranged into the form
dQ2
at
AP '
Q 2
Q
2
(A.1)
where i can be either 1 or 2.
This is then transformed into a finite difference
equation:
n-n
n
Qi - Qi
At
AP'n
=
n
1
R'n-1
n-1 22
___
(Qn-l)
(Q)
i
n
(A.2)
(A.2)
1
where n is a time index.
The final form of the equation, upon rearrangement of terms, is
-140-
n
Qi1
At
n-1
= Qin- +
'n
1
I.
'n-1 (Q.n-12)]
'n
[APn - R.
1
(A.3)
1
Equation (2.11) is solved by an implicit, first
order finite difference approximation
n
3
g
n
(A.4)
n-i
n
At
Because of the explicit nature of the equations
solved by Eq. (A.3), special attention must be paid to the
time step.
The time step size is limited by the Courant
condition
Ax
At
> v
-
(A.5)
That is, the time step must be small enough that the velocity does not allow the calculation to cross more than one
node.
This becomes important during the temperature profile
calculation in the unheated zone.
During condensation, the
rapidity of the bubble collapse creates extremely large velocities, relative to the bubble growth period.
For this rea-
on, a variable time step is employed in the solution of Eq.
(A.3).
If the solution fails to converge at a large time
step, the step is reduced by a factor of two, and the solution procedure is repeated.
If convergence is not achieved
-141-
after several successive reductions, it is assumed the bubble
has collapsed entirely or undergone an expulsion.
The method
for dealing with this problem is discussed in Section A.3.1.
A.2.2
The Thermal Model
The equation for the thermal model is
(n
Q
S
net
+
V dP
g )/ph
dt
g fg
(2.27)
This equation is also solved by an implicit, firstorder finite difference approximation
Q
s
A.3
n
=
[q
n
net
+
V
n
g
(
pn - Pn-
n
n)]/(p
At
n
) (A.5)
h
g
fg
The Structure of the Code
To provide ease of handling and understanding,
the code is split into a main section and several subroutines.
Each routine is briefly explained in this section.
A.3.1
FLOSS-MAIN Program
The MAIN portion of the code provides the basic
framework for the simulation of transients.
In addition,
schemes for variable time step size and non-convergence
restarting are included.
Initially, data are input and con-
-142-
verted to an internally consistent set of units, a proper
call sequence for the actual calculational subroutines is
established, initial conditions are established, and output
is arranged to be easily readable.
One of the limitations that has been determined by
use of the code is the necessity to generate a sufficient
amount of vapor during the initial time step of the transient.
By trial and error, the amount of power required for this
to occur is such that
(Input Power) * (time step)
-
0.025 kw-sec
This is the only initial constraint.
(A.6)
However, for
very low powers, large initial time steps must be used.
The
code, through the variable time step calculation, will adjust
the size of the time step as necessary to allow convergence.
If convergence does not occur, as described in
Chapter 2, that is, if the thermal and hydrodynamic models
cannot be made to generate the same bubble size, a check is
made of the temperature in the initial node downstream of
the heater.
If this temperature is below the saturation
temperature at initial pressure, as is usually the case, it
is an indication that the bubble has collapsed entirely,
and the calculation is restarted.
This is accomplished by
-143-
assuming that a small amount of fluid at the top of the heater,
originally at saturation, is mixed with the lower temperature
fluid in the first unheated node.
The mean temperatures of
this fluid is then determined, and a heat balance is performed on this fluid, using the heater power as a heat source.
The temperature of the fluid in this node is thereby increased, while temperatures in the upper nodes of the unheated
zone are held constant.
When the temperature in the first
node reaches saturation, the calculation of the transient
proceeds anew.
In this way, the "waiting period" seen ex-
perimentally is reproduced.
If the temperature of the initial unheated node
is greater than or equal to saturation at nonconvergence, it
is assumed that an expulsion of fluid has occurred, and the
transient is ended at that point.
A.3.2
Subroutine HYDRO
This subprogram solves the hydrodynamic model, as
previously outlined in A.2.1.
The differencing scheme is
established, as well as the iterative scheme for calculation
of the bubble lengths and volumes.
Error convergence limits,
read in as data, are applied in this routine.
A.3.3. Subroutine HEAT
This routine solves the thermal model, as previously described.
The bubble is split into two volumes, one in
-144-
the heated zone and one in the unheated zone.
The heat in-
puts and outflows are calculated separately for each "halfbubble", and the total size is then determined.
Convergence
criteria are set up such that not only must the total bubble
size be consistent, but the two separate zones must also
converge.
There also exists the means to account for wall
heat capacity effects.
In addition, the unheated zone temperature profile
is calculated.
The method for this calculation is quite in-
volved, and the code listing should be referred to in order
to understand the details of the scheme.
To summarize the
scheme, a search is performed to locate the vapor-liquid
interface at each time step.
That having been accomplished,
the temperature of each node is then calculated on a volumeaveraged basis:
T.
1
n
=
(T
n-l
1
V.
1
n
+ ..T.
1
n-l
dV
13
+
n-1
i/
At
n-l
n-l
np
Cp
n-
)/ V
i
(A.7)
In Eq. (A.7), i and
j
represent the volume being
calculated and the adjacent volume respectively.
This vol-
ume is either above or below volume i, depending on whether
the bubble is expanding or contracting.
The term T.n-Vi .n
1
1
represents the temperature of the node at the previous time
step multiplied by the volume of that fluid remaining in
-145-
the node at the current time step.
The second term repre-
sents the temperature of the adjacent node, multiplied by
the amount of fluid pushed from node j into node i by bubble
movement, and the final term represents any heat input to the
node due to condensation at liquid vapor intervaces multiplied by the volume over which the heat transfer occurs.
This sum is then divided by the nodal liquid volume, the result being the volume-averaged temperature of the node.
This
procedure is performed for each node at each time step, during each iteration.
A.3.4
Subroutine AREA
This short subprogram calculates the cross-section-
al area of the bubble, based on a weighted average of the
film thickness.
A constant void fraction is assumed at ini-
tial bubble formation, equal to the inverse of the turbulent
velocity drift flux constant, i.e. 1/C .
Subsequent evapor-
0
ation in the heated zone is accountable for areal changes.
The void fraction in the unheated zone remains 1/C
0
at all
times.
A.3.5
Subroutine HTCOEF
This portion of the code calculates the condensa-
tion heat transfer coefficient for the upper unheated zone.
Three options exist for the determination of this parameter:
a constant heat transfer coefficient which has been input
-146-
as data (KHT=1); the Dittus-Boelter correlation, based on
vapor velocity and properties (KHT=2); or an option that
allows the user to input his own correlation or model (KHT=3).
If the first option is chosen, the heat transfer coefficient
does not change at all over the period of the transient; however heat transfer rates may be changed by changing the unheated zone temperature profile.
A.3.6
Subroutine PGUESS
This subroutine contains the logic for guessing the
pressure during the iterative process described in Chapter 2.
For each pressure guess, an error is calculated based on the
difference between the hydrodynamic and thermal flow rate:
E=
(QH-QT)/[(IQH
+
QTI )/2]
This error may be positive or negative.
(A.8)
If positive, the
pressure is reduced until a negative error is generated.
If the error is negative, the pressure is subsequently
increased.
When two errors exist of opposite sign, a method
of successive linear approximations is employed to continue
guessing the pressure until the convergence limits are
reached.
This method is shown in Fig.
represented by this linear method is
A.1 .
The equation
-147-
Guessed
SGuessed
FIGURE A.1
METHOD FOR GUESSING PRESSURES IN FLOSS
-148-
AP E +
P=
B
where B is the y-intercept.
(A.9)
The method has proven to be re-
liable, and, for the most part, rapidly convergent.
A.3.7
Subroutine RESIN
This routine calculates resistances and inertances
for solution of the hydrodynamic equations.
It also contains
the logic for deriving equivalent values for parallel bypass
The numbering
loops, using an analog to electrical systems.
scheme for this calculation is shown in Fig.
A.2
.
The
scheme must be followed exactly as shown for the code to
calculate the bypass equivalent vales properly.
A.3.8
Subroutine FFACTR
This subprogram calculates the friction factors
for the previous subroutine RESIN, for determination of resistance terms.
The calculation is based on the Reynolds
number of the liquid flow in each part of the system.
If
the Reynolds number is less than 2000, the laminar value
f
is used.
16
Re
(A.10)
-149-
1, (3 (m-l)+6) ]
L
I- (2,2)
((2,1)
bubble
(1,1)
-(1,2)
FIGURE A.2
NUMBERING SYSTEM FOR COMPONENTS IN FLOSS
-150-
For 2000 <Re <50000
f = 0.0791 Re 0.0 2 5
(A.11)
If Re > 50000
f = 0.046 Re 0. 0 2 0
A.3.9
(A.12)
Subrountine PROP
This routine calculates properties of either water
or liquid sodium, depending on the option chosen.
The water
properties are based on polynomial expressions derived by
Bowring (6),
and are taken from Levin (7).
The sodium
properties were derived by Golden and Tokar (8).
A.3.10
Subroutine PLOTTER
The Joint Computer Facility at M.I.T. maintains
a FORTRAN library subroutine called PICTR which enables
computer developed plots to be made using a VARIAN electrostatic plotter.
This subroutine contains the logic which
sets up the output from a simulated transient in a form to
be used by the PICTR routines.
Information on these rou-
tines is available from the JCF.
A.4
Restrictions on Code Use
Several restrictions on the use of the code have
-151-
been noted already in this Appendix.
These will be reviewed,
and some other restrictions explained.
1.
The energy input to the model during the start of
the transient must be about 0.025 kw-sec.
2.
The Courant condition Ax > v applies during rapid
bubble movement. This restriction is automatically
considered in the inclusion of a variable time step
calculation.
3.
The nodalization scheme for the unheated zone is
very flexible, as it allows an input not only of
the nodal temperatures, but of nodal lengths as
well. The initial node should be very short - on
the order of two inches or less - and the temperature should be at or near saturation, to allow
bubble growth. It is believed that these are the
conditions that physically prevail at bubble initiation. The remainder of the nodal lengths should
be chosen judiciously.
Too long a length will cause
the nodal averaged temperature to be far too low,
compared to reality, while too short a length would
cause temperatures to be too high, and unnecessarily
restrict time step size. A sample problem is shown
in Appendix D. For most transients, nodel lengths
on the order of 0.4 - 1.0 foot have been found to
be satisfactory. The scheme for calculation of
nodal temperature also breaks down if the bubble
interface crosses two nodal interfaces in the same
time step. This presents an additional restriction
for which the Courant condition must account.
Choice of nodal lengths must therefore be chosen
such that time step sizes do not become so small
as to significantly increase code execution time.
4.
The error criterion for convergence of the thermalto-hydrodynamic comparison has been kept relatively
high for most simulations, to cut down on computer
time requirements. Reduction of the convergence
limit appears to have little effect on the values
generated by the code. The convergence criteria
for bubble lengths and volumes are related to the
error convergence limit, and must be set to approximately the same value. The sample input in Appendix D illustrates this fact.
Ax
-152-
APPENDIX B
DESCRIPTION AND USE OF THE COMPUTER
DATA ACQUISITION SYSTEM
B.1
Background
The general structure of the CCDAS apparatus has
been previously described in Chapter 4.
The purpose of
this appendix is to describe the hardware, software, and
operating procedures associated with the system in more detail.
The system is now operating as a data acquisition
and data conversion unit in the M.I.T. Heat Transfer Laboratory.
B.2
Hardware
The CCDAS is built from several different components
in order to provide a wide range of usage, both as a computer and as a data acquisition system.
The heart of the system is a Perkin-Elmer Model
1610 Minicomputer.
This is a 16-bit machine, with a current-
ly installed capacity of 64 kilobytes of semiconductor memory.
The memory may be expanded to as much as 128 kilobytes
in 32 kb increments.
The computer is equipped with a line
frequency clock, which can provide processor interrupts at
up to twice the line frequency (120 hz).
Processor options
on the HTL computer include a precision integral clock,
-153-
a battery backup system, and a hardware multiplication/
division unit.
The PIC will provide interrupts at a rate
faster than the line frequency clock, if necessary.
The
battery backup system provides a power system backup to
preserve information in memory in the event of a power
failure.
The hardware multiply/divide option allows the
computer to perform these operations directly, instead of
through software programming.
This allows the operations
to be done much more quickly.
These are several peripherals which are connected
to the minicomputer.
The system command console is a Per-
kin -Elmer Model 550 CRT.
This is an essential piece of
equipment, since the minicomputer itself has no built-in
command-issuing unit.
The CRT is a standard type of visual
display unit, with a keyboard and viewing screen, providing interactive use of the computer.
In addition, the CRT
has a printer port built into the back of the unit, which
allows connection to a CRT page printer.
The page printer
used in this system is the Perkin -Elmer Model 650 "Pussycat" Thermal Printer.
The printer will print 24 lines, a
full screen display, automatically upon receipt of 24-line
feed signals from the CRT.
The printer is a single buffer
machine, which does not allow data to be received and
stored while printing is taking place.
Therefore the dis-
play must be advanced twenty-four lines and then halted,
-154-
printing permitted, and then display scrolling advanced in
order to allow printing of all information.
Data and program storage are provided by a dual
floppy disk system.
Each disk contains space for up to 256
kilobytes of information, either in ASCII (source) or binary
(object or image) form.
The last peripheral is the data acquisition unit,
itself.
The RTAS (see Chapter 4) currently allows up to 24
instruments to be connected for input to the computer, and
capacity may be expanded to 32 channels in 4-channel increments, in the present configuration.
The termination panel
is supplied with a calibrated Resistance Temperature Device
(RTD) to serve as an equivalent ice-point for thermocouples.
If the RTD is used, it must be connected to one of the RTAS
channels.
Maximum scanning speed is 8000 points per second.
Data is stored in the computer by means of software programming.
Each data point is stored as a number ranging from
-2048 to +2047.
To convert these data to meaningful infor-
mation, the value must be multiplied by a gain factor, which
is set by the user.
Each channel has a variable gain, which
is set through input to the controlling software, which
ranges from ±20 to ±1000 millivolts, full scale; the gain
factor is then the full scale output divided by 2048.
This
-155-
configuration provides a very flexible system which is not
difficult to operate.
The system is shown schematically in
Fig. B.1.
B.3
Software
The sofware supplied by Perkin-Elmer includes sup-
port for all peripherals, and is currently configured for
the FORTRAN computer language.
Support for other languages
is available from the vendor.
The computer is controlled by an operating system,
created by means of a system generation (SYSGEN).
The SYSGEN
procedure, which can be performed by the vendor or the user,
sets the operating environment for the system, and tells
the computer which peripherals are available and which processing options are necessary for the user's requirements.
The SYSGEN is performed by using several assembly language
programs supplied by Perkin-Elmer.
These include a Configu-
ration Utility Program (CUP), which sets the system environment, and three packages which tell the computer how to perform functions in the given environment.
These are the
Command Processor, The File Manager, and the System Executive.
Once a SYSGEN is performed using these programs, the
resultant operating system must be loaded into the computer
before any operations can be performed.
The present system provides support for the RTAS,
-156-
To Experimental
Loop Instruments
I
RTAS
with
RTD Temperature
Reference
PI Clock LF Clock
Hardware Mult/Div
1610
Computer
Battery Backup
CRT
Thermal
Printer
FIGURE B.1
I
r
Dual
System
Floppy
Console
Disk
Drives
SCHEMATIC OF COMPUTER SYSTEM
-157-
CRT, and floppy disk drives.
It also includes a partition
system for the memory, which allows several programs to be
held in memory simultaneously, although only one program may
be active at a time.
Currently, the system is configured for
five foreground partitions and one background partition; the
size of each partition may be set by the user.
There is also
a system partition, which must be allowed to exist for the
computer to process information.
The software for FORTRAN programming includes a
FORTRAN compiler and a run-time library.
The former pro-
gram allows the FORTRAN source programming to be converted
to binary code, and the latter provides support for library
mathematical and real-time routines.
Linkage between user
programs and FORTRAN library functions is provided through
use of the vendor-supplied Task Establishment Utility Program.
This program also converts the output from the FOR-
TRAN compiler (object code) to executable code (image code).
The remaining software that has been supplied by
Perkin-Elmer includes several driver programs to allow the
RTAS to be operated.
This software includes both assembly
language and FORTRAN programming.
The function of the pro-
gramming is to provide for generation of interrupts, data
sampling, data storage, disk allocation, and transfer of
acquired data from computer memory to disk.
Once the data
-158-
have been put onto the floppy disk, further data processing
may be accomplished through user-written data conversion
programming.
B.4
Operation of the CCDAS
-The operation of the CCDAS involves several steps
and will be explained briefly in this section.
A detailed
instruction manual is under preparation at this time, and
Perkin-Elmer's own handbooks are also valuable references.
Initially, the system is started up using the operating system described in Section B.3.
The foreground par-
titions are then set to accomodate two programs:
a test
supervisory program (TSTSUP) and a data acquisition system
driver, program (DATACQ).
Logical input and output units
are then assigned by the user.
vided by the RTAS.
The input to DATACQ is pro-
The input to TSTSUP is provided by the
user and includes:
1)
The name of the file in which acquired data is to
be stored.
2)
The time interval at which interrupts are to be
generated.
3)
The number of channels to be sampled.
4)
The list of channels and their respective gains,
in the order in which sampling is to be done.
5)
The number of scans to be made.
The number of scans to be performed (item 5) is
-159-
determined by dividing the total transient time, which is not
an input, by the sampling interval (item 2).
The TSTSUP program is activated upon the user's
START command on the console.
This command is issued about
5 seconds before the sampling period is to begin, to allow
the programs to start properly.
The initial program reads
the input data, opens a file on one of the floppy disks for
RTAS output, then initiates the DATACQ program and pauses.
The DATACQ program generates interrupts at the desired intervals.
Each interrupt allows the scanning to proceed.
This
is done at the maximum rate, and the data is stored in complete memory.
After several scans, DATACQ sends a signal
to TSTSUP, and TSTSUP activates a small data-logging subroutine, which transfers data from computer memory to the
file opened initially by TSTSUP.
This procedure continues
until the number of samples input as item 3 have been
acquired.
The program then ceases execution.
The user may
then load a conversion program into the computer which reads
the data from the floppy disk, and converts it, using the
gain factors described in the previous section, plus any
conversion tables (e.g., calibration curves, thermocouple
tables), to engineering units or millivolts, depending on
the user's desire.
A flowchart of the data acquisition procedure is
shown in Fig. B.2.
-160-
TSTSUP
FIGURE B.2
DATA ACQUISITION FLOW CHART
-161-
APPENDIX C
EXAMPLE OF EXPERIMENTAL RESULTS
C.1.
Data Conversion and Presentation
After the acquisition of data as described in
Appendix B, this information was converted to temperatures,
pressures, and flow rates by use of calibration information
and thermocouple tables, as described in Chapter 4.
In addi-
tion, a stepwise integration of the flow rates was performed
to estimate the length of the vapor bubbles above and below
the top of the heater.
As explained in Chapter 5, the read-
ings of flow rate from the upper AP transducers proved to be
quite unreliable.
Also, since 375 points were required for
each instrument for each transient, it would be impractical
to present every piece of data acquired.
Therefore, an ex-
ample of the output from each stagnant flow experiment will
be shown in the first six tables.
The data shown include:
1.
The flow rate, as determined by the lower LP cell.
2.
The temperature of the first thermocouple in the
fluid downstream of the top of the heater.
3.
The length of the bubble below the top of the
heater.
There are two important points to be made with
respect to items 1 and 3.
First, a negative flow rate
indicates bubble growth downward.
A positive flow rate
-162-
indicates bubble collapse.
The second point, then, in-
volves the large positive flow rates generated after bubble
collapse.
These readings were attributed in Chapter 5 to.
"water hammer" effects due to bubble collapse.
This effect
is clearly shown, for example, in Table C.4, at 1.8 and 2.4
seconds.
Since a positive flow rate corresponds to bubble
collapse, it is clear that continuing to integrate these
flow rates after the bubble length has reached zero would
provide non-physical results.
Thus, upon bubble collapse
to zero length, no further integration is performed until a
negative flow rate is generated.
which the results appear.
This explains the form in
The data are presented at 0.2-
second intervals, which represents five data-taking cycles.
Apparent mismatches in flow rate, bubble length, and temperature are attributable in every case to the fact that the
duration of bubble growth-collapse cycle is not exactly a
multiple of 0.2 seconds; therefore, in Table C.1, for instance, at 0.4 seconds, a positive flow rate (bubble collapsing) is shown, whereas the bubble length is greater than
at 0.2 seconds.
This indicates that the bubble grew con-
siderably after 0.2 seconds, and had just begun to collapse
at 0.4 seconds.
Results from the forced convection test are difficult to decipher because of the effects on the fluid of the
valve movement when the flow rate was reduced.
Qualitatively,
-163-
the results indicate that, after boiling inception, the flow
oscillates slightly due to normal fluctuations that occur
during "steady" two-phase flow.
However, there are no
real oscillations similar to those in the stagnant flow
tests.
The temperature downstream of the heater is shown,
however, to indicate the high temperature at boiling inception, which caused the transition immediately to bubbly,
steady two-phase flow.
Table C.1 - Example of Results from Test 4
Time After Boiling
Inception
Flow Rate
(10- 4 ft3/sec)
Calculated Bubble
Length (In)
__
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
3.2
3.4
3.6
3.8
4.0
4.2
4.4
4.6
4.8
5.0
-0.02
-3.34
1.14
-0.26
0.17
5.41
1.60
-0.28
-0.81
14.49
4.05
-0.22
-1.61
9.20
5.00
0.05
-1.57
10.51
-4.23
0.68
6.63
28.66
-10.35
8.32
4.97
1.72
0.00
2.89
12.19
5.86
4.86
1.88
0.00
0.24
1.69
0.00
0.00
0.10
6.60
2.57
0.00
0.00
2.81
0.00
4.33
3.60
0.00
0.00
7.60
22.39
0.00
0.00
Temperature
At First TC
Downstream of
__ Heater (OF)
74.64
94.63
163.32
144.52
157.78
171.12
173.54
184.05
182.11
193.30
173.93
174.72
172.29
188.30
176.59
173.54
169.62
167.27
171.98
174.72
206.66
181.72
162.93
197.82
210.82
194.45
Table C.2 - Example of Results from Test 5
Time After Boiling
Inception
Flow Rate
(10 4ft /sec)
Calculated Bubble
Length (In)
Temperature
At First TC
Downstream of
Heater (0 F)
I
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
3.2
3.4
3.6
3.8
4.0
4.2
4.4
4.6
4.8
5.0
-0.01
0.41
0.22
-4.01
4.61
-0.46
5.51
-0.47
-3.50
24.92
-3.11
2.94
13.30
-0.31
-6.69
26.09
2.74
-0.34
-2.49
6.33
11.72
15.07
8.47
-13.62
6.24
1.92
0.00
0.36
0.11
2.38
4.70
0.22
0.00
0.22
8.83
0.00
2.03
12.00
0.00
0.14
11.83
0.00
0.00
0.16
10.02
0.14
0.00
0.00
0.00
11.54
26.40
10.81
102.21
106.40
115.46
148.93
172.21
159.68
166.40
161.27
182.03
178.92
169.94
189.38
190.92
178.92
189.76
206.96
195.83
188.22
204.68
212.25
211.12
208.47
200.49
181.26
198.20
193.99
Table C.3 - Example of Results from Test 6
Time After Boiling
Inception
Flow Rate
(10 4ft /sec)
Calculated Bubble
Length (In)
Temperature
At First TC
Doetnstrea Oo Heater
T F
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
3.2
3.4
3.6
3.8
4.0
4.2
4.4
4.6
4.8
5.0
-0.03
-0.84
-0.27
21.99
-0.52
0.02
10.99
-1.18
1.99
4.51
-1.81
11.92
1.33
-0.84
10.56
-0.26
-0.30
-0.30
-0.18
5.73
0.18
-0.46
-0.45
2.21
1.97
-0.26
0.00
0.92
3.14
0.00
0.49
2.80
0.00
1.09
1.78
0.00
1.93
0.00
0.00
1.16
0.00
0.14
2.38
0.14
1.26
0.00
0.12
1.03
3.84
0.00
0.00
0.17
78.12
81.55
152.63
156.22
148.24
155.42
154.23
152.63
163.04
162.56
160.58
175.13
163.75
170.83
166.90
160.98
178.95
166.11
163.35
158.60
155.03
151.04
168.47
161.38
159.40
154.63
Table C.4 - Example of Results from Test 7
Time After Boiling
Inception
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
3.2
3.4
3.6
3.8
4.0
4.2
4.4
4.6
4.8
5.0
Flow Rate
(10-4 ft3/sec)
0.02
-0.03
-0.52
-0.10
-1.02
-0.15
-0.14
16.88
-3.69
31.88
-0.86
-2.90
27.07
-2.07
8.53
1.47
-2.82
8.60
-0.15
-1.46
8.53
-0.33
-0.14
25.50
-2.88
11.78
Calculated Bubble
Length (In)
0.00
0.53
0.42
0.05
1.13
0.07
0.18
0.00
3.52
0.00
0.62
7.32
0.00
1.55
3.71
0.00
4.48
0.00
0.07
2.74
0.00
0.31
1.57
0.00
2.41
2.51
Temperature
At First TC
Downstream
of Heater (OF)
99.56
105.85
110.43
115.91
131.02
141.56
164.30
160.35
155.59
173.73
149.68
161.14
163.91
149.20
182.30
163.51
165.09
179.27
170.20
169.42
172.95
167.85
177.24
176.07
166.67
183.85
Table C.5 - Example of Results from Test 8
Time After Boiling
Inception
0.0
0.2
0.4
0.6
0.6
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
3.2
3.4
3.6
3.8
4.0
4.2
4.4
4,6
4.8
5.0
Flow Rate
(10-4 ft3/sec)
-0.03
-0.03
1.36
-1.73
13.36
-1.40
15.64
-2.65
24.70
-0.40
-2.10
15.96
-2.18
12.92
-0.12
-0.11
3.84
-4.77
19.92
4.23
-0.24
-6.59
19.34
7.04
-2.88
-0.26
Calculated Bubble
Length (In)
0.00
0.66
0.00
1.38
0.00
1.55
0.00
2.12
0.00
0.18
8.81
0.00
1.73
0.00
0.13
0.64
0.00
6.14
0.00
0.00
0.11
8.83
0.00
0.00
1.86
10.50
Temperature
At First TC
Downstream of
Heater (°F)
116.64
124.14
128.56
158.75
174.50
185.07
176.91
171.05
178.86
167.83
187.77
183.52
179.56
182.28
178.78
199.21
182.28
186.54
193.47
209.09
193.09
197.00
207.66
211.44
195.77
205.76
Table C.6 - Example of Results from Test 9
Time After Boiling
Inception
Flow Rate
(10 4ft /sec)
Calculated Bubble
Length (In)
_
1.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
3.2
3.4
3.6
3.8
4.0
4.2
4.4
4.6
4.8
5.0
-0.03
-3.62
-1.39
28.40
-1.46
8.00
7.31
-3.34
10.00
25.07
-5.90
-0.42
24.54
-0.37
-6.63
11.66
2.23
-0.66
-0.75
7.18
-1.81
4.35
13.43
-0.89
-7.25
46.76
0.00
2.82
14.18
0.00
1.34
1.04
0.00
2.74
0.11
0.00
4.19
16.84
0.00
0.22
11.26
0.00
0.00
0.55
4.42
0.00
1.68
1.24
0.00
0.44
13.33
0.00
Temperature
At First TC
Downstream of
Heater (0 F)
_____
139.20
146.53
199.29
188.62
187.38
174.96
171.91
169.16
192.39
195.08
172.61
193.16
205.38
190.85
188.93
188.54
188.16
186.30
206.14
194.77
188.54
210.00
211.43
186.61
185.45
209.17
-170-
Table C.7 - Example of Results.from Test 10
(Forced Convection)
Time After Boiling
Inception
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
3.2
3.4
3.6
3.8
4.0
4.2
4.4
4.6
4.8
5.0
Temperature at First TC
Downstream of Heater (0 F)
165.39
167.35
169.71
171.67
175.58
179.09
179.79
181.42
186.46
180.65
185.68
180.65
187.54
194.16
194.92
178.62
174.02
185.68
180.18
199.06
184.14
204.08
194.92
210.90
212.79
218.06
-171-
APPENDIX D
CALCULATION OF CONDENSATION HEAT
TRANSFER COEFFICIENTS
D.1
Calculational Method
Results from the reduction of the experimental
data were used to estimate the magnitude of the condensation heat transfer coefficient during different stages of
the bubble growth-collapse cycle.
These calculated heat
transfer coefficients were then used as a guide to the selection of input parameters to the model.
The only assumption that was made for these calculations was that the upper and lower halves of the bubble
were approximately equal in length.
An assumption of this
sort was necessary due to the unreliable flow rate readings
from the upper AP cell.
The assumption of equal lengths
was chosen because of the approximately equal inertances
of the two halves of the loop (see Chapter 2).
Although
the lower loop contains all of the bypass and downcomer
piping, the fact that most of this piping was approximately
six times the diameter of the primary side (and therefore
36 times the area) means that the relative contribution of
this piping to the loop inertance was quite small.
Using this assumption, calculations were performed
-172-
for each of the stagnant flow experiments during bubble growth
and collapse.
Examples of these calculations are shown in
the remainder of this Appendix.
The reasons for the large
change in magnitude of the heat transfer coefficient have
been fully explored in Chapter 5.
-173-
For Test 4
Data Taking Conditions
At = 0.04
Test Conditions P = 0.544 kw = 1857.2 BTU/hr
t = 12.32 sec, Bubble is growing
At
p = 18.63 psia
T
= 192 0 F
liq
+
T sa-
223 0 F,
hfg
963 BTU/lbm
pg
0.045 ibm/ft
-
3
At = 31 0 F
L 1 = 13.08", Q 1 = 15.23 x
- 4 ft3/sec
10
10
ft /sec
Assume
L 1 =L
l
A
2
= A
1
L = 26.16"
2
- 4 ft 3
V = 2.29 x 10
Thus
A = 3.98 x 102 ft"
2
. = 1/C
°
dp
SinceV
p 0.002 lbm/ft3/psi
; Ap =-0.21 psi, dp
_ V dp
dp
p dt dp
Since Vp dp
Qs
=
Ql+Q2 +Acom = 2(15.23x10
-4 ) +
-3
4s =
g hfg Qs =
evap =
evp
(L/L)
/HTR
(2.99xi
p =
13
- 3)
( 3.08)
36hr
2.29
0.045
0.045
(-0.21)(0.002))
0.04
2.99 x 10-3 ft3/sec
(0.045)(963)(3600)
1857.2 =
= 466.9
BT
674.8 BTU
'
BTU
hr
-174-
qcon
=
qevap
h con
At
- q
BTU
= 207.9 BTU
hr
s
207.9
-2)(31)
(3.98x
(3.98x10 ) (31)
con/
BTU
2
hrft2 OF
= 168.5
t = 14.76 sec, Bubble is collapsing
p = 16.52 psia
-+
T
~
-
~
220F, p
sat
-
g
hf
fg
T liq
li
= 214.5 OF
+
= 6.48" , Q
t3 ,
0.041 ibm/ft
= 965
9
BTU
AT = 5.5 OF
=-0.34 ft3/sec, Ap =-0.04 psi,
d- = 0.0023 ibm/ft
3
psi
dp
Same assumptions are made,
-4
V = 1.1 x 10
Thus
ft
3
3
x 10-2
=
A1.98
ft
A =1.98 x 10
Qs -0.68xl0 4+ 1
s
4
(0
-5
=(-7.42x10 5 ) (0.041) (965)(3600)
1857.2 = 334.3
36
=
evap
s=
344.9
=
-0.04
0.041
S(6.48
con
-4
BTU/hr
5 ft3
-7.42xl0 -5 ft
sec
BTU
= 10.6 BTU
BTU
hr
= 3344.9/[1.98xi0-2 ) (5.5)]
) (5.5)]
hcon = 44.9/[1.98x10
-
3167.1
BTU
hrft 2OF
-175-
APPENDIX E
COMPUTER INPUT AND OUTPUT
E.1
Contents of the Appendix
This appendix contains a copy of the FLOSS com-
puter code, a sample input to the code, and a sample of
output from the code, as printed out by the computer.
-176-
E.2
The FLOSS Code
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13.275
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0.166E-06
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16.128
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0.121E-04
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449
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TIME STEP
T: 6.730
RESTART
69.730
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-244-
APPENDIX F
A COMPARISON OF FLOSS TO THE SAS COMPUTER CODE
F.1
THE SAS Code
Argonne National Laboratory developed the first
SAS computer code, SASlA, in 1970.
The code has undergone
virtually continuous revision and updating since then, and
is currently in its fourth generation, with SAS4A.
The
code is a one dimensional, multichannel code, for the purpose of studying accidents involving sodium voiding in the
LMFBR.
It contains calculational modules for transient and
steady state thermalhydraulics, both in single phase and
two phase flow.
In addition, it has the means to consider
fuel and clad melting and motion, fission gas release, and
other factors present during postulated LMFBR accidents.
The code is structured so as to be able to follow an entire
reactor accident from the initiation phase through until
gross fuel motion and reactor disassembly begin.
Other
codes, such as VENUS, can then use the SAS results to predict the events during the core disruptive phase of the
accident.
The current SAS model can handle multiple bubbles
in a single channel, and multiple channels across the core.
However, each bundle is considered as a unit which behaves
one-dimensionally.
Therefore, although corewide incoheren-
-245-
cies in voiding behavior can be tracked, multi-dimensional
bubble behavior across a single bundle cannot be considered.
Due to its versatility, the SAS code is one of the most
widely used tools in the United States LMFBR accident analysis program.
F.2
Comparing FLOSS to SAS
Since the FLOSS code also uses a one-dimensional
thermal-hydrodynamic model to calculate conditions during
a transient, it is not surprising to find that the equations
used in both codes are quite similar.
The technique used
to track the solution of the transient was derived from one
of the reports used in the development of the original SAS
code, as well.
Though the intent of this project was not
to reproduce SAS, the system of solution for both codes is
basically similar.
The major differences between SAS and FLOSS are in
scope and in the handling of the heat transfer during condensation.
The scope of SAS is far greater than that of
FLOSS; in fact, the FLOSS code would comprise no more than
two or three modules in the entire SAS code.
This is due
to the assumption made when the project was begun that
FLOSS would eventually become a module in a larger, systemscale code.
The second difference is more fundamental.
The SAS code contains only a single input for a constant
-246-
heat transfer coefficient.
In the manual consulted (32)
this value was set at approximately 11000 BTU/hr-ft2 0 F,
which falls in the range suggested by Barry and Balzhiser
(33).
However, there is no methodology presented for des-
cribing the changes in condensation heat transfer which
have been documented here.
The FLOSS code accomplishes
this change in heat transfer by slightly changing the initial temperature profile, thereby causing a step change in
heat transfer coefficient.
The high value of the coeffi-
cient causes the code to underpredict experimental results.
However, the failure of SAS to consider this phenomenon may
lead to overprediction of experimental results causing an
unrealistically conservative solution.
Table F.1, presented
on the next page, spotlights some of the areas where further
research is needed to improve the predictive abilities of
SAS.
The entire question of multidimensional effects in
sodium boiling is another area with which neither FLOSS nor
SAS are capable of dealing.
As mentioned in Chapter 6,
this, as well as several other questions, remain to be resolved in further research.
Table F.1
Issue
Initial Temperature Profile
in Unheated Zone
Comparison of FLOSS to SAS
Water (FLOSS)
Experimentally determined, except
for small saturated zone at start
SAS
As calculated
during initial
stages of
transient
of unheated zone
Initial Temperature Profile
in Core (Heated
Zone)
Not considered
As calculated
Condensation
Heat Transfer
Step change from
Constant
zero to values
approximating
those present
during bubble
collapse
Recommendations for Sodium
work
A physically realistic and
accurate temperature profile is necessary to adequately characterize the
flow behavior. This factor
is one of the prime determinants of how the flow will
behave. It is essential
that any simulation which
purports to chart the best
estimate of the oscillation
take account of the importance of this factor, and
calculate an accurate temperature profile history as
well.
The identical comment as
above is applicable here,
as well. This profile will
also influence flow behavior,
especially if it is steep.
Investigation is needed to
determine whether the sodium
condensation coefficient behaves like the water coefficient. A mechanistic model
for h
versus time over
the pernod of an oscillation, accounting for interfacial breakup and augmentation of heat transfer, is
needed.
Table F.1
Comparison of FLOSS TO SAS (Cont.)
Issue
Water (FLOSS)
SAS
Recommendations for Sodium
Work
Loop Dynamics
Present implicit
in model
Present in
later versions
of SAS
The characteristics of the
external loop can have a
significant effect on flow
oscillatory behavior.
Investigation into the relevance of simulant behavior
to sodium behavior is clearly needed.
Comparison of
Simulants to
Sodium
Non-condensable
gas
Implicit in choice
of heat transfer
coefficient
Implicit in
choice of heat
transfer co-
efficient
While work has been done regrading condensation in liquid metals, the presence of
non-condensibles in sodium
systems provides both a
mechanism for nucleation and
a retarding factor in condensation. Work is needed to
provide accurate models for
the effect of these noncondensibles on heat transfer.
This is especially relevant
if fission gases are released into the coolant.