Gasdynamics : theory and applications

462 Pages·1986·14.396 MB·English

by  George Emanuel

Gasdynamics:
Theory and Applications
George Emanuel
The University of Oklahoma
Norman, Oklahoma
AIAA EDUCATION SERIES
J. S. Przemieniecki
Series Editor-in-Chief
Air Force Institute of Technology
Wright-Patterson Air Force Base, Ohio
Published by
American Institute of Aeronautics and Astronautics, Inc.
1633 Broadway, New York, N.Y. 10019
Texts Published in the AIAA Education Series
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Frank J. Regan, 1984
Aerothermodynamics of Gas Turbine and Rocket Propulsion
Gordon C. Gates, 1984
Aerothermodynamics of Aircraft Engine Components
Gordon C. Gates, Editor, 1985
Aircraft Combat Survivability Analysis and Design
Robert E. Ball, 1985
Intake Aerodynamics
J. Seddon and E.L. Goldsmith, 1985
Composite Materials for Aircraft Structures
Brian C. Hoskin and Alan A. Baker, Editors, 1986
American Institute of Aeronautics and Astronautics, Inc.
New York, New York
Library of Congress Cataloging in Publication Data
Emanuel, George.
Gasdynamics, theory and applications.
(AIAA education series)
Includes index.
1. Gasdynamics. 2. Fluid dynamics. 3. Aerodynamics,
Supersonic. I. Title. II. Series.
QC168.E6 1986 620.1'074 86-10771
ISBN 0-930403-12-6
Copyright © 1986 by the American Institute of Aeronautics and
Astronautics, Inc. All rights reserved. Printed in the United States of
America. No part of this publication may be reproduced, distributed, or
transmitted, in any form or by any means, or stored in a data base or
retrieval system, without the prior written permission of the publisher.
Foreword
Gasdynamics: Theory and Applications by George Emanuel is the
seventh in the Education Series of textbooks and monographs pub-
lished by the American Institute of Aeronautics and Astronautics
(AIAA). Embracing a broad spectrum of theory and applications of
many different disciplines of aerospace, including aerospace design
practice, the Education Series develops both teaching texts and
reference materials for practicing engineers and scientists. George
Emanuel's text clearly serves both aims.
Emanuel covers all the important aspects of gasdynamics, with
particular emphasis on compressible-flow theory and applications.
The book is divided into two parts. Part I covers thermodynamic laws,
conservation equations, steady streamtube flow, normal and oblique
shock waves, Prandtl-Meyer flow and shock expansion theory, nozzle
and diffuser flow, heat transfer, and unsteady one-dimensional flow.
Part II deals with more advanced topics, such as shock waves, two-
dimensional flow, theory of characteristics, aerodynamic windows,
flows with shock waves, and waverider aerodynamics. The text should
prove to be of great value for senior-level undergraduate and graduate
courses and as a reference for the practicing aerospace engineer.
J. S. PRZEMIENIECKI
Editor-in-Chief
AIAA Education Series
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Table of
Contents
ix Preface
PART I
1 Chapter 1. Introduction
3 Chapter 2. Thermodynamics
2.1 First Law of Thermodynamics
2.2 State Variables
2.3 Entropy
2.4 Reciprocity
2.5 Equations of State
2.6 Specific Heats
2.7 Isentropic Process
2.8 Second Law of Thermodynamics
2.9 Speed of Sound
Problems
23 Chapter 3. One-Dimensional Conservation
Equations
3.1 Streamtube Flow
3.2 Substantial Derivative
3.3 Conservation Equations
3.4 Change in Entropy
3.5 Acoustic Approximation
3.6 Summary
Problems
39 Chapter 4. Steady Streamtube Flow
4.1 Integrated Form of the Governing Equations
4.2 Isentropic Relations
4.3 Area and Mass Flow Rate
Problems
49 Chapter 5. Normal and Oblique Shock Waves
5.1 Steady, Normal Shock Waves
5.2 Oblique Shock Waves
Problems
69 Chapter 6. Prandtl-Meyer Flow
and Shock-Expansion Theory
6.1 Prandtl-Meyer Flow
6.2 Shock-Expansion Theory
Problems
89 Chapter 7. Nozzle and Diffuser Flow
7.1 Nozzle Flow
7.2 Diffuser Flow
Problems
113 Chapter 8. Ducts with Area Change,
Heat Transfer, and Friction
8.1 Influence Coefficient Method
8.2 Rayleigh Flow
8.3 Fanno Flow
Problems
147 Chapter 9. Unsteady, One-Dimensional Flow
9.1 Normal Shock Waves
9.2 Reflected Normal Shock Waves
9.3 Method of Characteristics
9.4 Unsteady Expansion Waves
Problems
181 Chapter 10. Applications of Unsteady,
One-Dimensional Flow
10.1 Shock-Tube Flow
10.2 Piston Expansion Tube
Problems
PART II
Theory
197 Chapter 11. Governing Equations
11.1 Volume Dilatation
11.2 Conservation Equations
11.3 Conservative Form
11.4 Boundary and Initial Conditions
Problems
203 Chapter 12. Shock Waves
12.1 One-Dimensional Flow
12.2 Oblique Shock Waves
Problems
213 Chapter 13. Transformation of the Conservation
Equations
13.1 General Theory
13.2 Steady Two-Dimensional or Axisymmetric
Flow—I
13.3 Steady Two-Dimensional or Axisymmetric
Flow—II
13.4 Natural Coordinates
13.5 Hodograph Transformation
Problems
249 Chapter 14. Definitions and Theorems
14.1 Basic Concepts
14.2 Stream and Potential Functions
14.3 Homogeneity of the Conservation Equations
Problems
273 Chapter 15. Exact Solutions of Steady
Homentropic Flow of a Perfect Gas
15.1 Preliminary Remarks
15.2 Spiral Flow
15.3 Supersonic Flow Past a Cone
Problems
283 Chapter 16. Theory of Characteristics
16.1 Steady Two-Dimensional or Axisymmetric Flow
16.2 Compatibility and Characteristic Equations
Problems
Applications
307 Chapter 17. Minimum-Length Nozzles
17.1 Preliminary Remarks
17.2 Curved Sonic Line MLN
17.3 Straight Sonic Line MLN
17.4 MLN Comparisons
Problems
329 Chapter 18. Aerodynamic Window
18.1 Preliminary Remarks
18.2 Theory for a Free-Vortex AW
18.3 Design Procedure
Problems
347 Chapter 19. Flows with Shock Waves
19.1 Preliminary Remarks
19.2 Stability of Shock Waves
19.3 Flow Over a Compressive Ramp
19.4 Formation of Shock Waves in Jets
19.5 Shock Wave Reflection from a Wall
in Steady Flow
19.6 Pseudo-Steady Flow Over a Planar
Compressive Ramp
19.7 Shock Wave Interference
Problems
399 Chapter 20. Waverider Aerodynamics
20.1 Preliminary Remarks
20.2 Caret-Shaped Waveriders
20.3 C and C for an Arbitrary Waverider
L D
20.4 Waveriders Derived from a Conical Flowfield
Problems
415 Appendix A. SI Units and Nomenclature
419 Appendix B. Thermodynamic Summary
421 Appendix C. Stream tube Flow Equations
423 Appendix D. Normal and Oblique Shock
Summary
425 Appendix E. Shock Wave Angle 0 vs Flow
Deflection Angle 0
427 Appendix F. Prandtl-Meyer Flow Summary
429 Appendix G. Shock-Expansion Summary
431 Appendix H. Nozzle Flow Summary
433 Appendix I. Summary of Equations for Ducts
with Area Change, Heat Transfer, and Friction
435 Appendix J. Rayleigh Flow Summary
437 Appendix K. Fanno Flow Summary
439 Appendix L. Unsteady, Normal Shock Summary
441 Appendix M. Reflected Shock Wave Summary
443 Appendix N. Jacobian Theory
447 Subject Index
Preface
Over the past four decades, a number of texts on compressible flow
have appeared. Gasdynamics: Theory and Applications presents tradi-
tional material in a new way, as, for example, on unsteady flow in
Chaps. 9 and 10 and conical flow in Chap. 15. The material in Part II
is largely unavailable in other books.
Part I contains introductory material suitable for a one-semester
senior-level course. To assist the student, the chapters in Part I
contain many fully worked examples; and the appendices give concise
summaries of the material.
Part II contains ample material for a one-semester first-year
course at the graduate level. The subject matter builds directly on Part
I, but is more analytically oriented. Part II is subdivided into theory,
Chaps. 11-16, and applications, Chaps. 17-20. In both parts of the
text, but especially in Part II, unresolved issues or difficulties are
exposed; gasdynamics is an evolving subject, a point that should be
brought home to students.
The material in Part II should provide a useful background for
other advanced courses, such as transonic or hypersonic flow, and
particularly for computational fluid dynamics (CFD). That is, Part II
—largely unavailable in other books—bridges the gap between tradi-
tional gasdynamics and CFD, making this text do double service as a
useful reference book.
Although not designed for a course in CFD, Gasdynamics: The-
ory and Applications includes many topics important to CFD, such as
Jacobian theory, homogeneity, and the conservative form, which is
given special treatment and considerable emphasis. Other topics of
more general significance, such as shock waves, conical flow, and
transformation theory, are treated in a manner consistent with CFD.
Gasdynamics: Theory and Applications emphasizes supersonic gas-
dynamics, in which the continuum flow is inviscid and adiabatic and
body forces are negligible. Hence, the book does not consider viscous
layers, magnetohydrodynamics, and rarefied gas flows. The book
attempts to strike a balance between theory and applications. The
applications often justify the assumptions of a nonreactive, non-
radiating, nondiffusing perfect gas and a steady, two-dimensional or
axisymmetric flow. The theory is tailored somewhat to these condi-
tions.
ix