Fundamentals ofJet Propulsion with Applications
This introductory text on air-breathingjet propulsion focuses on the basic operating
principles ofjet engines and gas turbines. Previous coursework in fluid mechanics
and thermodynamics is elucidated and applied to help the student understand and
predict the characteristics of engine components and various types of engines and
power gas turbines. Numerous examples help the reader appreciate the methods
and differing, representative physical parameters. A capstone chapter integrates
the text material in a portion of the book devoted to system matching and analysis
so that engine performance can be predicted for both on- and off-design conditions.
The book is designed for advanced undergraduate and first-year graduate students
in aerospace and mechanical engineering. A basic understanding offluid dynamics
and thermodynamics is presumed. Although aircraft propulsion is the focus, the
material can also be used to study ground- and marine-based gas turbines and
turbomachinery and some advanced topics in compressors and turbines.
Ronald D. Flack is a Professor, former Chair of Mechanical and Aerospace Engi­
neering, a~d former Director of the Rotating Machinery and Controls (ROMAC)
Industrial Research Program at the University of Virginia. Professor Flack began
his career as an analytical compressor design engineer at Pratt & Whitney Air­
craft. He is an kSME Fellow and is actively involved in research on experimental
internal flows in turbomachines and fluid film bearings.
Fundamentals ofJet Propulsion
with Applications
RONALD D. FLACK
University of Virginia
r
II
,
~lN CAMBRIDGE
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UNIVERSITY PRf:SS
CAMBRIDGE UNIVERSITY PRESS
Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, Sao Paulo
Cambridge University Press
40 West 20th Street, New York, NY 100 114211, USA
www.cambridge.org
Information on this title: www.caInbridge.org/9780521819831
© Cambridge University Press 2005
This book is in copyright. Subject to statutory exception
and to the provisions of relevant collective licensing agreements,
no reproduction of any part may take place without
the written permission of Cambridge University Press.
First published 2005
Printed in the United States of America
A catalog record for this publication is available from the British Library.
Library ofCongress Cataloging in Publication Data
Flack, Ronald D., 1947­
Fundamentals ofjet propulsion with applications / Ronald D. Flack, Jr.
p.
cm. - (Cambridge aerospace series; 17)
Includes bibliographical references and index.
ISBN 0-521-81983-0 (hardback)
I. Jet engines.
I. Title.
II. Series.
TL 709.F5953 2005
621.43' 52 - dc22
2004020358
On the cover is the PW 4000 Series - 112-inch fan(courtesy of Pratt & Whitney)
ISBN-13 978-0-521-81983-1 hardback
ISBN-IO 0-521-81983-0 hardback
Cambridge University Press has no responsibility for
the persistence or accuracy of URLs for external or
third-party Internet Web sites referred to in this book
and does not guarantee that any content on such
Web sites is, or will remain, accurate or appropriate.
Dedicated to Harry K. Herr, Jr.
(Uncle Pete)
who quietly helped me find the right career direction
Contents
Preface
Foreword
Part I
page xv
xix
Cycle Analysis
Introduction
1.1
1.2
3
History of Propulsion Devices and Turbomachines
Cycles
1.2.1
Brayton Cycle
1.2.2
Brayton Cycle with Regeneration
1.2.3
Intercooling
1.2.4 Steam-Topping Cycle
Classification of Engines
1:3.1
Ramjet
1.3.2 Turbojet
1.3.3
Turbojet with Afterburner
1.3.4
Turbofan
. 1.3.5
Turbofan with Afterburner
1.3.6 Turboprop
Unducted Fan (UDF)
1.3.7
1.3.8
Turboshaft
1.3.9
Power-Generation Gas Turbines
1.3.10 Comparison of Engine Types
Engine Thrust
Turbojet
1.4.1
Turbofan with a Fan Exhaust
1.4.2
1.4.3
Turboprop
Performance Measures
1.5.1
Propulsion Measures
Power-Generation Measures
1.5.2
Summary,
,
1.3
1.4
1.5
1.6
2
3
10
10
13
14
15
16
16
17
19
20
25
27
29
29
30
32
34
35
38
40
41
41
42
42
Ideal Cycle Analysis
46
2;1 Introduction
46
47
48
51
53
2.2
Components
2.2.1
I)i~ser
Compressor
2.2.2
2.2.3 .. Fan
..2 .2.4
Turbine
2.2.5
Propeller
vii
55
56
ix
Contents
4.2.4 Combined Area Changes and Friction
4.3 Supersonic
4.3.1 Shocks
4.3.2 Internal Area Considerations
4.3.3 Additive Drag
4.3.4 "Starting" an Inlet
4.4 Performance Map
4.5 Summary
244
5 Nozzles
5.1 Introduction
5.2 Nonideal Equations'
5.2.1 Primary Nozzle
5.2.2 Fan Nozzle
5.2.3 Effects of Efficiency on Nozzle Performance
5.3 Converging Nozzle
5.4 Converging-Diverging Nozzle
5.5 Effects of Pressure Ratios on Engine Performance
5.6 Variabl~N ozzle
5.7 Performance Maps
5.7.1 Dimensional Analysis
5.7.2 TrenQs
5.8 Thrust Reversers and Vectoring
5.8.1 Reversers
5.8.2 Vectoring
5.9 Summary
6 Axial Flow Compressors and Fans
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
215
216
216
225
229
232
235
236
Introduction
Geometry
Velocity Polygons or Triangles
Single-Stage Energy Analysis
6.4.1 Total Pressure Ratio
6.4.2 Percent Reaction
6.4.3 Incompressible Flow
6.4.4 Relationships of Velocity Polygons.to Percent Reaction and
Pressure Ratio
Performance Maps
6.5.1 Dimensional Analysis
6.5.2 Trends
6.5.3 Experimental Data
6.5.4 Mapping Conventions
6.5.5 Surge Control
Limits on Stage Pressure Ratio
Variable Stators
6.7.1 Theoretical Reasons'
6.7.2 Turning Mechanism
"Twin Spools
6.8.1' Theoretical Reasons
o
244
244
244
245
245
246
247
256
258
260
260
261
265
265
267
270
276
276
277
283
286
287
287
288
289
299
299
300
301
302
303
303
307
307
312
312
312
Contents
x
6.9
6.10
6.11
6.12
6.8.2 Mechanical Implementation
6.8.3 Three Spools
Radial Equilibrium
6.9.1. Differential Analysis
6.9.2 Free Vortex
6.9.3 Constant Reaction
Streamline Analysis Method
6.10.1 Flow Geometry
6.10.2 Working Equations
Performance of a Compressor Stage
6.11.1 Velocity Polygons
6.11.2 Lift and Drag Coefficients
6.11.3 Forces
6.11.4 Relationship of Blade Loading and Performance
6.11.5 Effects of Parameters
6.11.6 Empiricism Using Cascade Data
6.11.7 Further Empiricism
6.11.8 Implementation of General Method
Summary
7 Centrifugal Compressors
7.1
7.2
7.3
7.4
7.5
7.6
7.7
7.8
Introduction
Geometry
Velocity Polygons or Triangles
Single-Stage Energy Analysis
7.4.1 Total Pressure Ratio
7.4.2 Incompressible Flow (Hydraulic pumps)
7.4.3 Slip
7.4.4 Relationships of Velocity Polygons to Pressure Ratio
Performance Maps
7.5.1 Dimensional Analysis
7.5.2 Mapping Conventions
Impeller Design Geometries
7.6.1 Eye Diameter
7.6.2 Basic Blade Shapes
7.6.3 Blade Stresses
7.6.4 Number of Blades
7.6.5 Blade Design
Vaned Diffusers
Summary
8 Axial Flow Turbines
8.1 Introduction
8.2 Geometry
8.2.1 Configuration
8.2.2 Comparison with Axial Flow Compressors
8.3 Velocity Polygons or Triangles
8.4 Single-Stage Energy Analysis
8.4.1 Total Pressure Ratio
314
315
316
316
317
318
320
321
322
331
332
335
340
341
342
346
351
354
355
374
374
374
378
380
381
381
382
386
390
390
390
391
392
392
392
393
394
394
397
406
406
407
407
409
413
416
417
Contents
xi
8.4.2
8.4.3
8.4.4
Percent Reaction
Incompressible Flow (Hydraulic Turbines)
Relationships of Velocity Polygons to Percent Reaction
and Performance
8.5 Performance Maps
8.5.1 Dimensional Analysis
8.5.2 Mapping Conventions
8.6 Thermal Limits of Blades and Vanes
8.6.1 Blade Cooling
8.6.2 Blade and Vane Materials
8:6.3 Blade and Vane Manufacture
8.7 Streamline Analysis Method
8.8 Summary
9 Combustors and Afterburners
9.1 Introduction
9.2 Geometries
9.2.1 Primary Combustors
9.2.2 <Afterbumers
9.3 Flame Stability, Ignition, and Engine Starting
9.3.1 Flame Stability
,9.3.2 Ignition and Engine Starting
9.4 Adiabatic Flame Temperature
9.4.1 Chemistry
9.4.2 Thermodynamics
9.5 Pressure Losses
9.5.1 Rayleigh Line Flow
9.5.2 Fanno Line Flow
9.5.3 Combined Heat Addition and Friction
9.5.4 Flow with a Drag Object
9.6 Performance Maps
9.6.1 Dimensional Analysis'
9.6.2 Trends
9.7 Fuel Types and Properties
9.8 Summary
10
417
418
419
425
425
425
427
428
429
430
433
434
440
440
441
441
445
447
447
448
449
450
451
456
456
457
458
459
461
461
462
463
465
Ducts and Mixers
471
10.1 Introduction
10.2 Total Pressure Losses
10.2.1 Fanno Line Flow
10.2.2 Mixing Process
10.2.3 Flow with a Drag Object
10.3 Summary
471
471
471
473
475
477
~
~
Part III System Matching and Analysis
11 Matching of Gas Turbine Components
11.1 ." Introduction
11.2 Component Matching
481
481
482
o
Contents
xii
11.2.1 Gas Generator
11.2.2 Jet Engine
11.2.3 Power-Generation Gas Turbine
11.2.4 Component Modeling
11.2.5 Solution of Matching Problem
11.2.6 Other Applications
11.2.7 Dynamic or Transient Response
11.3 Matching of Engine and Aircraft
11.4 Use of Matching and Cycle Analysis in Second-Stage Design
11.5 Summary
Part IV
482
484
486
487
492
499
499
508
511
512
Appendixes
Appendix A
Standard Atmosphere
527
Appendix B
Isentropic Flow Tables
530
Appendix C
Fanno Line Flow Tables
548
Appendix D
Rayleigh Line Flow Tables
5.58
Appendix E
Normal Shock Flow Tables
568
Appendix F
Common Conversions
583
Appendix G
Notes on Iteration Methods
585
G.l
G.2
G.3
Introduction
Regula Falsi
Successive Substitutions
585
585
588
One-Dimensional Compressible Flow
591
H.l
H.2
H.3
H.4
H.5
H.6
H.7
H.8
H.9
H.I0
H.ll
H.12
H.13
H.14
591
591
593
595
597
598
600
601
Appendix H
Appendix I
Introduction
Ideal Gas Equations and Stagnation Properties
Variable Specific Heats
Isentropic Flow with Area Change
Fanno Line Flow
Rayleigh Line Flow
Normal Shocks
Oblique Planar Shocks
Flow with a Drag Object
Mixing Processes
Generalized One-Dimensional Compressible Flow
Combined Area Changes and Friction
Combined Heat Addition and Friction
Combined Area Changes, Heat Addition, and Friction
Turbomachinery Fundamentals
1.1
1.2
Introduction
Single-Stage Energy Analysis
1.2.1 Total Pressure Ratio
1.2.2 Percent Reaction
1.2.3 Incompressible Flow
604
605
607
608
609
610
613
613
613
613
618
618
xiii
Contents
1.3
Similitude
1.3.1 Dimensional Analysis - Compressible Flow
620
620
623
628
631
References
Ans\t1-'ers to Selected Problems
Index
o