Modern Developments in Gas Dynamics: Based upon a course on Modern Developments in Fluid Mechanics and Heat Transfer, given at the University of California at Los Angeles

393 Pages·1995·6.97 MB·English

by  W. H. T. Loh (auth.)

MODERN
DEVELOPMENTS
IN GAS DYNAMICS
MODERN
DEVELOPMENTS
IN GAS DYNAMICS
Based upon a course on Modern Developments in Fluid Mechanics
and Heat Transfer, given at the University of California at Los Angeles
Edited by W. H. T. Loh
Manager, Science and Technology
Space Division, North American Rockwell Corporation
Downey, California
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PLENUM PRESS • NEW YORK - LONDON • 1969
Library of Congress Catalog Card Number 69-14561
ISBN-13: 978-1-4615-8626-5 e-ISBN-13: 978-1-4615-8624-1
DOl: 10.1007/978-1-4615-8624-1
© 1969 Plenum Press, New York
Softcover reprint of the hardcover 1st edition 1969
A Division of Plenum Publishing Corporation
227 West 17th Street, New York, N. Y. 10011
United Kingdom edition published by Plenum Press, London
A Division of Plenum Publishing Company, Ltd.
Donington House, 30 Norfolk Street, London W. C. 2, England
All rights reserved
No part of this publication may be reproduced in any
form without written permission from the publisher.
To
Our Late Teacher Theodore von Karman
PREFACE
During the last decade, the rapid growth of knowledge in the field
of fluid mechanics and heat transfer has resulted in many significant ad
vances of interest to students, engineers, and scientists. Accordingly, a
course entitled "Modern Developments in Fluid Mechanics and Heat
Transfer" was given at the University of California to present significant
recent theoretical and experimental work. The course consisted of seven
parts: I-Introduction; II-Hydraulic Analogy for Gas Dynamics; 111-
Turbulence and Unsteady Gas Dynamics; IV-Rarefied and Radiation
Gas Dynamics; V-Biological Fluid Mechanics; VI-Hypersonic and
Plasma Gas Dynamics; and VII-Heat Transfer in Hypersonic Flows.
The material, presented by the undersigned as course instructor and
by various guest lecturers, could easily be adapted by other universities for
use as a text for a one-semester senior or graduate course on the subject.
Due to the extensive notes developed during the University of California
course, it was decided to publish the material in three volumes, of which
the present is the first. The succeeding volumes will be entitled "Selected
Topics in Fluid and Bio-Fluid Mechanics" and "Introduction to Steady and
Unsteady Gas Dynamics."
Finally, I must express a word of appreciation to my wife Irene and to
my children, Wellington Jr. and Victoria, who made it possible for me to
write and edit this book in the very quiet atmosphere of our home.
W. H. T. LOH
March 1968
University of California
Los Angeles, California
vii
CONTENTS
Chapter 1
Theory of the Hydraulic Analogy for Steady and Unsteady Gas
Dynamics 1
by W. H. T. Loh
Introduction. . .
1. Two-Dimensional Steady Flow Analogy 2
1.1. Energy Equation . . 2
1.2. Continuity Equation 3
1.3. Irrotational Motion 5
1.4. Summary . . . . . 7
2. Hydraulic Jumps (Shocks) . 8
2.1. Shock Polars .... 11
2.2. Water Depths in Hydraulic Jump 18
2.3. Energy Loss during Hydraulic Jump 27
2.4. Summary . . . . . . . . . . . . . 30
3. One-Dimensional Unsteady Gas Dynamics by Hydraulic
Analogy ........... . 31
3.1. Two-Dimensional Steady Flow 32
3.2. One-Dimensional Unsteady Flow 33
3.3. Equations of Standing Waves . . 38
3.4. Summary of Analogous Equations 39
3.5. Discussion. . . . . . . . . . . 40
4. Hydraulic Analogy for Longitudinal Plane Waves. Deriva-
tion of Equations of Standing Waves . . . . . 42
4.1. Continuity Equation . . . . . . . . . . . . . .. 42
4.2. Equation of Thermodynamics and Equation of Hy-
draulics .... 44
4.3. Equation of Motion . . . . . . . . . 45
4.4. Wave Equations ...... '.' .. . 47
4.5. Equation of Wave Propagation Velocity 48
4.6. Summary . . . .. ...... . 49
ix
x Contents
5. Experimental Verification . . . . . . . . . . . . .. 51
5.1. Equations for Experimental Model. . . . . . .. 51
5.2. Analogous Quantities for Hydraulic Model Design. 56
Appendix A . 56
Appendix B 57
Notation . 59
References 60
Chapter 2
Combined Heat and Mass Transfer Processes 63
by E. R. G. Eckert
Introduction. . . . 63
1. Conservation Equations . 63
2. Constitutive Equations . 67
3. Laminar Boundary Layer Equations 69
4. Solutions of the Laminar Boundary Layer Equations 72
4.1. Heat Transfer 72
4.2. Mass Transfer . . . . 74
4.3. Example. . . . . . . 75
5. Turbulent Boundary Layers 78
*- *-
6. Correction Equations for Pr 1 and Le 1 79
Notation . 80
References 82
Chapter 3
Hypersonic Viscous Flows . 83
by Arthur Henderson, Jr.
1. Induced-Pressure Effects. 83
1.1. Introduction . . . . 83
1.2. Basic Considerations 34
1.3. Flat Plate a = 0 . . 86
1.4. Blunt Wedge 90
2. Closed-Form Local Similarity 93
2.1. Local Similarity Defined 93
2.2. Compressible Similar Solutions 96
2.3. Closed-Form Local-Similarity Solutions 99
Contents xi
3. Boundary Layer Transition . . . . . 100
4. Turbulent Boundary Layer . . . . . 114
4.1. Effect of Wall-Temperature Ratio 114
4.2. Virtual Origin . . . . . . . . . 116
4.3. Transformation of Compressible Boundary Layer Pro-
files. 118
Notation . 124
References 125
Chapter 4
Hypersonic Gas Dynamics of Slender Bodies 131
by H. K. Cheng
Introduction. . 131
1. Inviscid Flows and Related Problems 132
1.1. Entropy and Speed Defects . . . 132
1.2. The Shock-LayerjEntropy-Wake Interaction. 138
1.3. Blow-Hard ............... 144
1.4. Minimizing Drag. . . . . . . . . . . . . 145
2. The Outer-Edge Problem of the Hypersonic Boundary Layer
on a Slender Body. . . . . . . . . . . . . . .. 145
2.1. The Outer-Edge Problem . . . . . . . . . . . .. 145
2.2. The Scales Associated with the Viscous Transition Layer 147
2.3. The Transition Layer in the Strong- and Weak-Inter-
action Regimes Involving Power-Law Shocks. .. 150
2.4. The Outer-Edge Problem for the Flat Plate in the Strong
Interaction Regime: w = 1 . . . . . . . . .. 155
3. Transverse Curvature and Gross Flow in the Strong-Interac-
tion Regime . . . . . . . . . . . . . . . . . ., 161
3.1. A Strong-Interaction Formulation of Hypersonic Vis-
cous Flow around Asymmetrical Slender Bodies 162
3.2. The Needle in the Strong-Interaction Regime . .. 165
3.3. The Needle Problem in the Weak-Shock Regimes . 175
Acknowledgment. 179
References 179
xii Contents
Chapter 5
Hypersonic Blunt-Body Gas Dynamics 183
by J. F. McCarthy, Jr.
Introduction. . . . . . 183
1. Classification of Body Shapes 184
2. Blunt-Body Flow Fields. 186
3. Flow Regimes . . . . . 187
4. Flow-Field Gas Properties 189
5. Inviscid-Flow Analysis . . 190
5.1. Methods of Analysis-Subsonic-Transonic Region 190
5.2. Method of Analysis-Supersonic Region 205
6. Viscous-Flow Analysis. . . . . . . . . . . 206
6.1. Methods of Analysis-Boundary Layer. 208
6.2. Improved Boundary-Layer Analysis 210
7. Interactions of Viscous-Inviscid Flow. 213
7.1. Separated Flow. . . . . . . 214
7.2. Base and Wake Flow Fields 219
8. Wake Flows .' 223
9. Summary 227
Notation . 228
References 231
Chapter 6
Rarefied Gas Dynamics ............. 235
by S. A. Schaaf
Introduction. . . 235
1. Elements of Kinetic Theory 236
2. Free-Molecular Flow 245
3. Slip Flow 250
References 254
Contents xiii
Chapter 7
Fundamentals of Radiation Gas Dynamics 255
by S. I. Pai
Introduction . 255
1. Fundamentals of Radiative Transfer 257
2. Fundamental Equations of Radiation Gas Dynamics 263
3. Initial and Boundary Conditions of Radiation Gas Dynamics 267
4. Similarity Parameters of Radiation Gas Dynamics. . . . 270
4.1. Dimensionless Parameters of Ordinary Gas Dynamics 271
4.2. Dimensionless Parameters of Radiation Gas Dynamics 273
5. Radiation Mean Free Path . . . 276
6. Wave Motion in a Radiating Gas 278
7. Shock Waves . . . . . . . . . 282
7.1. Rankine-Hugoniot Relations in Radiation Gas Dy-
namlcs 282
7.2. Shock-Wave Structure 285
8. Two-Dimensional Channel Flows of an Ionized, Radiating
Gas .......... . 286
9. Unsteady Laminar Boundary Layer on an Infinite Plate. . 292
10. A Uniform Flow of a Radiating Gas Over a Semiinfinite
Plate . . . . . . . . . . . . . . . . . . . . . . 298
11. Stagnation-Point Heat Transfer in Radiation Gas Dynamics 304
Acknowledgment . 306
Notation . 306
References 309
Chapter 8
Some Problems of Radiative Transfer 311
by F. K. Moore
Introduction. . . . . . . . . . . . . . . . . . . . . . . 311
1. Absorption Coefficients for Radiative Transfer Calculation 312
1.1. Gray-Gas Approximations 312
1.2. Piecewise Gray Models . . 316
1.3. Models for Band Radiation 318