Interaction of Shock Waves

328 Pages·1994·8.493 MB·English

by  R. S. Srivastava (auth.)

INTERACTION OF SHOCK WAVES
FLUID MECHANICS AND ITS APPLICATIONS
Volume 22
Series Editor: R. MOREAU
MADYLAM
Ecole Nationale Superieure d'Hydraulique de Grenoble
Bofte Postale 95
38402 Saint Martin d'Heres Cedex, France
Aims and Scope of the Series
The purpose of this series is to focus on subjects in which fluid mechanics plays a
fundamental role.
As well as the more traditional applications of aeronautics, hydraulics, heat and
mass transfer etc., books will be published dealing with topics which are currently
in a state of rapid development, such as turbulence, suspensions and multiphase
fluids, super and hypersonic flows and numerical modelling techniques.
It is a widely held view that it is the interdisciplinary subjects that will receive
intense scientific attention, bringing them to the forefront of technological advance
ment. Fluids have the ability to transport matter and its properties as well as
transmit force, therefore fluid mechanics is a subject that is particulary open to
cross fertilisation with other sciences and disciplines of engineering. The subject of
fluid mechanics will be highly relevant in domains such as chemical, metallurgical,
biological and ecological engineering. This series is particularly open to such new
multidisciplinary domains.
The median level of presentation is the first year graduate student. Some texts are
monographs defining the current state of a field; others are accessible to final year
undergraduates; but essentially the emphasis is on readability and clarity.
For a list of related mechanics titles, see final pages.
Interaction of Shock Waves
by
R. s. SRIVASTAVA
formerly of the
Defence Science Center
New Delhi, India
with a Foreword
by
Professor Sir James Lighthill, F.R.S.
SPRINGER SCIENCE+BUSINESS MEDIA, B.V.
Library of Congress Cataloging-in-Publication Data
Srivastava, Radhey Shyam, 1931-
Interaction of shock waves / by R.S. Srivastava ; with a foreword
by Sir James Lighthill.
p. cm. -- (Fluid mechanics and its applications v. 22)
Inc 1u des index.
ISBN 978-94-010-4474-5 ISBN 978-94-011-1086-0 (eBook)
DOI 10.1007/978-94-011-1086-0
1. Shock waves. 1. Tit le. 11. Se r ies.
OA927.S75 1994
532' .0593--dc20 94-20092
ISBN 978-94-010-4474-5
Printed on acid-free paper
AlI Rights Reserved
© 1994 Springer Science+Business Media Dordrecht
Originally published by Kluwer Academic Publishers in 1994
Softcover reprint of the hardcover 1s t edition 1994
No part of the material protected by this copyright notice may be reproduced or
utilized in any form or by any means, electronic or mechanical,
including photocopying, recording or by any information storage and
retrieval system, without written permission from the copyright owner.
Dedicated to
Professor Sir James LighthilJ, F.R.S.
who has been my guide and source of inspiraton
during all these years.
CONTENTS
FOREWORD ix
PREFACE
Xl
ACKNOWLEDGEMENTS
XlI
CHAPTER 1 INTRODUCTION
CHAPTER 2 REFLECTION OF SHOCK WAVES 7
CHAPTER 3 DIFFRACTION OF NORMAL SHOCK WAVE 25
CHAPTER 4 DIFFRACTION OF OBLIQUE SHOCK WAVE 73
CHAPTERS DIFFRACTION OF NORMAL SHOCK BY YAWED
WEDGES 157
CHAPTER 6 DIFFRACTION OF OBLIQUE SHOCK BY YAWED
WEDGES 187
CHAPTER 7 SHOCK INTERACTION WITH MOVING AEROFOIL 237
CHAPTER 8 DIFFRACTION OF SHOCK BY FLAT SURFACES 265
CHAPTER 9 APPROXIMATE THEORY ON DIFFRACTION OF SHOCKS 283
SOURCE LIST 303
INDEX 319
FOREWORD
One of the great twentieth-century achievements in the mechanics of fluids was the full
elucidation of the physics of shock waves and the later comprehensive development of
understanding of how shock waves propagate (i) through otherwise undisturbed fluid and
(ii) in interaction either with solid bodies or with independently generated fluid flows.
The interaction problems (ii) were soon found to raise some very special difficulties
(beginning with the common formation of "Mach stems" in shock-wave reflection) yet
they also turned out to possess enormous scientific interest as well as being highly
important in practical applications.
For all these reasons the appearance of this book on "Interaction of Shock Waves" by one
of the world's major contributors to knowledge in that field is most particularly to be
welcomed. It covers all those approaches to the subject which have been found fruitful,
and most satisfactorily goes into comprehensive detail about each. At last the important
achievements of the leading research workers, experimental as well as theoretical, on
shockwave interaction problems are brought together in a single convenient and well
written volume. I warmly congratulate the author and the publisher on having performed,
for the benefit of everyone interested in the mechanics of fluids, this immensely valuable
service.
James Lighthill
IX
PREFACE
This monograph attempts to give a connected account of the work on interaction
of shock waves. Earlier a review article entitled "On Aerodynamics of Blasts" by
H.F.Ludloff has appeared in Advances in applied mechanics in 1953 covering the work
carried out upto 1952. Subsequently, a survey article entitled "The reflection and
diffraction of shock waves" by D. C. Pack has appeared in the Journal of Fluid
Mechanics (1964) covering the work carried out during past ten years reckoned from
1963. The area covered mainly was with respect to diffraction of normal shock
waves. Several important contributions have appeared in recent years on problems
related to diffraction of oblique shock waves. The need, therefore, was felt to bring out
a recent account of the work on the subject.For analysing the problem related to
diffraction of oblique shocks, a complete understanding regarding reflection of shock
waves (normal and oblique) from the rigid boundaries is necessary. A chapter on
reflection of shock waves has therefore been included apart from the chapters dealing
with diffraction of shock waves. The entire available work on diffraction of oblique
shock waves is based on two classic papers by Sir James Lighthill on "The diffraction
of blast (1949, 1950)". In this monograph therefore Lighthill's theory on the subject
has been brought out in all its details although it has earlier also received majestic
treatment by H.F.Ludloff and D.C.Pack. A general account however, is given in the
introductory chapter of the monograph. More recently W.C.Griffith's reveiw article has
appeared in Journal of Fluid Mechanics (1981) dealing with shock interaction
problems, apart from other topics. The notations of the different authors whose work
has been included in the monograph has generally been retained.
I take the opportunity to sincerely record my gratitude to Sir James Lighthil1,
F.R.S. for inspiring me to write this monograph. I am grateful to Prof. Lighthil1 who
took pains in going through the manuscript and offered many valuable suggestions. In
fact he has been guiding me directly or indirectly over three decades and but for his
encouragement and help, the problems included in the monograph would not have been
completed. I wish to thank Prof. I. I. Glass for the invaluable support and help in the
successful completion of the experimental work, at UTIAS, Canada.
I would like to record my sincere thanks to Sankalp for his dedicated effort in
preparing the camera ready manuscript. I am indebted to my wife Vijay Laxmi for her
co-operation and help in the success of the project. Thanks are also due to Ravi,
Sunita, Sanjay, Smriti, Manoj and Sangeeta for their invaluable help.
A-3 / 260, Janakpuri
New Delhi - 110058 , INDIA R. S. SRIVASTAVA
xi
ACKNOWLEDGEMENTS
Due· acknowledgement is made to the authors and the publishers for their
permission to reproduce the figures from their publications. The list of the journals are
as follows:
1) American Institute of Aeronautics and Astronautics
(A.l.A.A.)(U.S.A)
2) Journal of Aeronautical Sciences (J.A.S.)(U.S.A.)
3) Journal of Fluid Mechanics (J.F.M.), (Cambridge
University Press,U.K.)
4) Proceedings of the Royal Society (Proc.Roy.Soc.) Series A,London(U.K.)
5) Reviews of Modern Physics (U.S.A.)
6) Physical Review (U.S.A.)
7) British Aeronautical Research Council (A.R.C.) (U.K.)
8) Quarterly Journal of Mechanics and Applied Mathematics (Q.J.M.A.M.)(U.K.)
Author's name and year of publication duly appear after every publication in the
manuscript. The details of the references, however, appear at the end of each chapter.
xii
CHAPTER- I
INTRODUCTION
The problems relating to the behaviour of a shock wave encountering either
another shock wave, or a rarefaction wave, or an interface separating two media (one of
which may be rigid) are described as 'Interaction of Shock Waves'. This subject,
associated with almost all the real physical situations involving shocks, is one of the
most important branches of modern mechanical science. This study is of great practical
importance in connection with blast effect on supersonic aircrafts from the view point
of weapon analysis and the vulnerability of either a missile or a re-entry vehicle to
blast. This branch of science inspite of its manifold utility has not received the
attention it warrants because of considerable difficulties involved in obtaining the
solution of the problems.
Amongst the interaction problems , reflection of shock waves from rigid
boundaries has received considerable attention durilng recent years and this topic may be
divided into three parts:-
i) Normal Reflection
ii) Oblique Reflection
iii) Mach Reflection
Normal reflection occurs when the shock impinges head on to an unyielding
surface with the plane of the shock parallel to that of the surface. Oblique reflection
occurs when a shock impinges with a small angle between the direction of propagation
of the shock and the plane of the reflecting surface. Mach reflection occurs when a
shock front impinges on a surface near grazing incidence. The details about the three
types of reflections have been incorporated in the chapter on 'Reflection of Shock
Waves'.
The other important topic of the study has been in the field of diffraction of
shock waves. A theoretical investigation of the flow field produced by the interaction
of plane shocks with an obstacle, stationary or moving, is difficult and the mathematical
complications prevent an explicit theory. The complication is not only because of the
non-linear nature of the problem but also because of the fact that the non-uniform shock
waves which occur imply variations in the entropy of the fluid and a loss of irrotational
character of the motion. The problems on diffraction of shock waves have been
attempted in two ways. The first is to linearilze the basic equations of motion on the
assumption that the incident shock is weak. Since the entropy change across a weak
shock is of third order in shock strength, the entropy variations are also effectively
excluded and in fact the problem belongs to the theory of acoustics. The method was