Analytical fluid dynamics

805 Pages·2001·9.45 MB·English

by  George Emanuel

Analytical
Fluid
Dynamics
SECOND EDITION
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Analytical
Fluid
Dynamics
SECOND EDITION
George Emanuel
Professor
Department of Mechanical and Aerospace Engineering
University of Texas, Arlington
Arlington, Texas
CRC Press
Boca Raton London New York Washington, D.C.
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Library of Congress Cataloging-in-Publication Data
Emanuel, George
Analytical fluid dynamics / George Emanuel.-2nd ed.
p. cm.
Includes bibliographical references and index.
ISBN 0-8493-9114-9 (alk paper)
1. Fluid dynamics. I. Title.
[DNLM: 1. Hepatitis B virus. QW 710 G289h]
QA911 .E43 2000
532′.05-dc21 99-089453
CIP
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Dedication
Dedicated with love to my wife and companion, Lita
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Preface
The objectives of this edition remain the same as the first. The analysis and formulation are provided
for a variety of selected topics in inviscid and viscous fluid dynamics, it is hoped with physical
insight. In part, this means formulating the appropriate equations and then transforming them into
a suitable form for the specific flow under scrutiny. The approach is applied to viscous boundary
layers, shock waves, Prandtl–Meyer flow, etc. Sometimes a solution is obtained; other times a final
answer requires numerical computation. Of crucial interest, however, is the analytical process itself
and the coinciding physical interpretation.
A more in-depth coverage of topics is favored compared to a broad one that bypasses crucial or
difficult details. At the graduate level, I believe an intensive approach is preferable. The book tries
to avoid too much repetition of undergraduate course material. Of course, some repetition is both
useful and unavoidable. When it occurs, however, the level and manner of treatment are different,
often markedly so, from those at the undergraduate level. I have attempted whenever possible to
point out the assumptions and limitations of the topic under discussion. Conversely, an attempt is
made to discuss why a particular topic is worthy of study. For instance, a solution may be useful as
a first (or initial value) estimate for CFD calculations. The rate of convergence is usually accelerated
by having a reasonable initial flow field. Analytical solutions, such as those provided by the substi-
tution principle, can be used to verify Euler or Navier–Stokes codes. An analytical approach often
yields suitable first estimates for parameters of interest. In this regard, some of the homework
problems are designed to give the student practice in obtaining “back-of-the-envelope” solutions. My
personal motivation, however, still remains the beauty and elegance of analytical fluid dynamics
(AFD).
As mentioned in the preface to the first edition, much of the material in that edition was unique.
This is even truer for this edition, where all of the added material is unique to this text. The chapters
covering a calorically imperfect gas flow, sweep, shock wave interference with an expansion,
unsteady one-dimensional flow, and the force and moment analysis are new. In addition, the
thermodynamic chapter is largely new as are Appendices B and C. The chapters that remain from
the first edition have been revised to improve the clarity of the presentation.
When appropriate, topics where future research is warranted are pointed out. Fluid dynamics,
including the AFD specialty, is very much alive and growing. Consequently, not everything in this
text is complete or polished. A variety of major topics are not discussed. These topics include
turbulent flow, CFD, experimental methods, etc., that are major subjects in themselves.
I owe a debt of gratitude to the many friends and colleagues who have contributed to this
undertaking, especially past and present students. It is indeed a pleasure to acknowledge their
comments and assistance. I particularly thank Dr. Jose Rodriguez, Professor Frank K. Lu, and
Professor Milton Van Dyke for his comments on Chapter 23. I am especially in debt to Susan
Houck for her superb typing and preparation of the manuscript.
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Contents
Part I: Basic Concepts
Outline of Part I.................................................................................................................................3
Chapter 1 Background Discussion
1.1 Preliminary Remarks.................................................................................................................5
1.2 Euler and Lagrange Formulations............................................................................................5
1.3 The Stress Tensor....................................................................................................................16
1.4 Relation between Stress and Deformation-Rate Tensors.......................................................19
1.5 Constitutive Relations.............................................................................................................22
1.6 Integral Relations....................................................................................................................25
References........................................................................................................................................29
Problems...........................................................................................................................................29
Chapter 2 The Conservation Equations
2.1 Preliminary Remarks...............................................................................................................33
2.2 Mass Equation.........................................................................................................................33
2.3 Transport Theorem..................................................................................................................34
2.4 Linear Momentum Equation...................................................................................................35
2.5 Inertial Frame..........................................................................................................................36
2.6 Angular Momentum Equation................................................................................................39
2.7 Energy Equation......................................................................................................................41
2.8 Viscous Dissipation.................................................................................................................44
2.9 Alternate Forms for the Energy Equation..............................................................................46
Reference..........................................................................................................................................48
Problems...........................................................................................................................................49
Chapter 3 Classical Thermodynamics
3.1 Preliminary Remarks...............................................................................................................53
3.2 Combined First and Second Laws..........................................................................................53
3.3 Potential Functions..................................................................................................................56
3.4 Open System...........................................................................................................................58
3.5 Coupling to Fluid Dynamics..................................................................................................63
3.6 Compressible Liquid or Solid.................................................................................................73
3.7 Second Law.............................................................................................................................75
References........................................................................................................................................83
Problems...........................................................................................................................................84
Chapter 4 Kinematics
4.1 Preliminary Remarks...............................................................................................................89
4.2 Definitions...............................................................................................................................89