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Shock Wave and High Pressure Phenomena Series Editor-in-Chief L. Davison, USA Y. Horie, USA Founding Editor R. A. Graham, USA Advisory Board V. E. Fortov, Russia Y. M. Gupta, USA R. R. Asay, USA G. Ben-Dor, Israel K. Takayama, Japan F. Lu, USA Shock Wave and High Pressure Phenomena L.L. Altgilbers, M.D.J. Brown, I. Grishnaev, B.M. Novac, I.R. Smith, I. Tkach, and Y. Tkach: Magnetocumulative Generators T. Antoun, D.R. Curran, G.I. Kanel, S.V. Razorenov, and A.V. Utkin: Spall Fracture J. Asay and M. Shahinpoor (Eds.): High-Pressure Shock Compression of Solids S.S. Batsanov: Effects of Explosion on Materials: Modification and Synthesis Under High-Pressure Shock Compression R. Cherét: Detonation of Condensed Explosives L. Davison, D. Grady, and M. Shahinpoor (Eds.): High-Pressure Shock Compression of Solids II L. Davison and M. Shahinpoor (Eds.): High-Pressure Shock Compression of Solids III L. Davison, Y. Horie, and M. Shahinpoor (Eds.): High-Pressure Shock Compression of Solids IV L. Davison, Y. Horie, and T. Sekine (Eds.): High-Pressure Shock Compression of Solids V A.N. Dremin: Toward Detonation Theory Y. Horie, L. Davison, and N.N. Thadhani (Eds.): High-Pressure Shock Compression of Solids VI R. Graham: Solids Under High-Pressure Shock Compression J.N. Johnson and R. Cherét (Eds.): Classic Papers in Shock Compression Science V.F. Nesterenko: Dynamics of Heterogeneous Materials M. Suc´eska: Test Methods of Explosives J.A. Zukas and W.P. Walters (Eds.): Explosive Effects and Applications G.I. Kanel, S.V. Razorenov, and V.E. Fortov: Shock-Wave Phenomena and the Properties of Condensed Matter V.E. Fortov, L.V. Altshuler, R.F. Trunin, and A.I. Funtikov: High-Pressure Shock Compression of Solids VII L.C. Chhabildas, L. Davison, and Y. Horie (Eds.): High-Pressure Shock Compression of Solids VIII D. Grady: Fragmentation of Rings and Shells M. V. Zhernokletov and B. L. Glushak (Eds.): Material Properties under Intensive Dynamic Loading R.P. Drake: High-Energy-Density Physics G. Ben-Dor: Shock Wave Reflection Phenomena ABC G. Ben-Dor Reflection Phenomena Shock Wave With 194 Figures Second Edition Series Editors-in-Chief: Lee Davison 39 Can˜oncito Vista Road Tijeras, NM 87059, USA E-mail: leedavison@aol.com Yasuyuki Horie AFRL/MNME Munitions Directorate 2306 Perimeter Road Eglin AFB, FL 32542, USA E-mail: yasuyuki.horie@eglin.af.mil ISSN 8063-7200 ISBN This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable for prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springer.com c© The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: WMX design GmbH, Heidelberg Printed on acid-free paper 5 4 3 2 1 0 Ben Gurion University of Negev Institute for Applied Research Beer-Sheva, Israel E-mail: bendorg@bgumail.bgu.ac.il 978-3-540-71381-4 2nd ed. Springer Berlin Heidelberg New York ISBN 978-3-540-97707-2 Springer Berlin Heidelberg New York LATEXTypesetting by the author and SPi using a Springer marco package SPIN: 11519492 54/SPi Gabi Ben-Dor Library of Congress Control Number: 2007928738 1st ed. Springer-Verlag Berlin Heidelberg , 20071991 To Professor Ozer Igra who introduced me to the world of shock tubes and waves, to Professor Irvine Israel Glass who led me into the world of shock wave reflection phenomena, to my colleagues all over the world with whom I have been investigating the fascinating phenomena of shock wave reflection for over 30 years, and finally, to Ms. Edna Magen, and our three children, Shai, Lavi and Tsachit, who provided me with an excellent atmosphere and support to accomplish all my goals. Acknowledgment I would like to thank Dr. Li Huaidong, currently at the Jet Propulsion Laboratory, California Institute of Technology, in Pasadena, who was my Ph.D. student and Post Doctoral Fellow during the years 1992–1997, for his invaluable contribution to many of the findings of my researches in the area of shock wave reflection, which are the reason for putting together this second edition of my monograph. Preface Nothing is more exciting to a scientist than realizing that his/her areas of expertise are developing and that the state-of-the-knowledge yesterday is out- dated today. The distinguished philosopher Ernst Mach first reported the phenomenon of shock wave reflection over 125 years ago in 1878. The study of this fasci- nating phenomenon was then abandoned for a period of about 60 years until Professors John von Neumann and Bleakney initiated its investigation in the early 1940s. Under their supervision, 15 years of intensive research related to various aspects of the reflection of shock waves in pseudosteady flows were carried out. It was during this period that the four basic shock wave reflec- tion configurations, regular, single-Mach, transitional-Mach and double-Mach reflections, were discovered. Then, for a period of about 10 years from the mid-1950s until the mid-1960s, the investigation of the reflection phenom- enon of shock waves was kept on a low flame all over the world (e.g. Australia, Japan, Canada, USA, USSR, etc.) until Professor Tatyana Bazhenova from the USSR, Professor Irvine Israel Glass from Canada, and Professor Roy Hender- son from Australia re-initiated the study of this and related phenomena. Under their scientific leadership, numerous findings related to this phenomenon were reported. Probably the most productive research group in the mid-1970s was that led by Professor Irvine Israel Glass in the Institute of Aerospace Studies of the University of Toronto. In 1978, exactly 100 years after Ernst Mach first reported his discoveries on the reflection phenomenon; I published my Ph.D. thesis in which, for the first time, analytical transition criteria between the various shock wave reflection configurations were established. For reasons which for me are yet unknown, the publication of my Ph.D. findings triggered intensive experimental and analytical studies of the shock wave reflection phenomenon over a variety of geometries and properties of the reflecting surface and in a variety of gases. The center of the experimental investigation was shifted from Canada to Japan, in general, and to the Shock Wave Research Center that was led by Professor Kazuyoshi Takayama, in particular. Under his supervision flow visualization techniques reached such linjy 高亮 VIII Preface a stage that the phrase “cannot be resolved experimentally” almost ceased to exist in the scientific dictionary, especially after Dr. Harald Kleine joined his research group for a couple of years. In the same year that I published my Ph.D. thesis, I published my first journal paper related to the shock wave reflection phenomenon. This paper, entitled “Nonstationary Oblique Shock Wave Reflections: Actual Isopycnics and Numerical Experiments” was co-authored with my Ph.D. supervisor, Pro- fessor Irvine Israel Glass. In the conclusion to the paper we wrote Undoubt- edly, numerical codes will evolve in the future which will reliably predict not only RR and SMR but also CMR and DMR in real gases. I wish my lot- tery predictions were as successful as this prediction, since probably the most remarkable progress in the study of the shock wave reflection phenomenon in the following decade (i.e., in the 1980s) was made by American compu- tational fluid dynamicists, who demonstrated that almost nothing is beyond their simulation capability. At one time, it was feared that the computational fluid dynamicists would put the experimentalists out of business. Fortunately, this did not occur. Instead, experimentalists, computational fluid dynami- cists, and theoreticians worked together in harmony under the orchestration of Professor John Dewey, who realized, in 1981, that scientists interested in the reflection phenomenon of shock waves will benefit the most if they meet once every one/two years and exchange views and ideas. In 1981, he initiated the International Mach Reflection Symposium, which became the framework for excellent cooperation between scientists from all over the world who are interested in better understanding the shock wave reflection phenomenon. Ten years later, in 1991, I completed writing my monograph entitled Shock Wave Reflection Phenomena, which summarized the state-of-the-knowledge at that time. Three major developments, which shattered this state-of-the-knowledge, took place in the 15 years that has passed since then. – The first (in the early 1990s), was the discovery of the hysteresis phenom- enon in the reflection of shock waves in steady flows. – The second (in the mid-1990s), was a re-initiation of a abandoned approach considering an overall shock wave diffraction process that results from the interaction of two sub-processes, namely, the shock-wave reflection process and the shock-induced flow deflection process. This approach led to the development of new analytical models for describing the transitional- and the double-Mach reflections; and – The third (in the late 1990s and the mid-2000s), was the resolution of the well-known von Neumann paradox. As a result, only one out of the four main chapters of the monograph could be still considered as relevant and providing updated information. Unlike this chapter, the other four are simply outdated. Consequently, the monograph has been re-written, to again describe the state-of-the-knowledge of the fascinating Preface IX phenomena of shock wave reflection, which I have been investigating for over three decades. As a final remark I would like to point out that this book comes as close as possible to summarizing almost all that I know about shock wave reflection phenomena from a phenomenological point of view. Thirty-one years ago, when I first met Professor Irvine Israel Glass, I almost knew nothing about the reflection of shock waves. When he assigned me the investigation of this phenomenon, I thought that it would take a lifetime to understand and explain it. Now I can state wholeheartedly that I was lucky to have been assigned to investigate this fascinating phenomenon and to have met and worked under the supervision of Professor Irvine Israel Glass. I have been even luckier to become a part of a wonderful group of scientists from all over the world with whom I have been collaborating throughout the past thirty years, and with whom I hope to continue collaborating in the future. linjy 高亮 Contents 1 General Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Introduction and Historical Background . . . . . . . . . . . . . . . . . . . . 3 1.2 Reasons for the Reflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.2.1 Reason for the Reflection in Steady Flows . . . . . . . . . . . . 11 1.2.2 Reasons for the Reflection in Pseudosteady and Unsteady Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.3 Analytical Approaches for Describing Regular and Mach Reflections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.3.1 Two-Shock Theory (2ST) for an Inviscid Flow . . . . . . . . 14 1.3.2 Three-Shock Theory (3ST) for an Inviscid Flow . . . . . . . 16 1.4 Shock Polars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 1.4.1 Shock-Polar Presentation of the Flow Field Near the Reflection Point of a Regular Reflection . . . . . . 21 1.4.2 Shock-Polar Presentation of the Flow Field Near the Triple Point of a Mach Reflection . . . . . . . . . . . 22 1.5 Suggested RR ��� IR Transition Criteria . . . . . . . . . . . . . . . . . . . . 25 1.5.1 Detachment Criterion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 1.5.2 Mechanical-Equilibrium Criterion . . . . . . . . . . . . . . . . . . . 29 1.5.3 Sonic Criterion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 1.5.4 Length-Scale Criterion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 1.5.5 Summary, Critique, and Discussion . . . . . . . . . . . . . . . . . . 33 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 2 Shock Wave Reflections in Steady Flows . . . . . . . . . . . . . . . . . . . 39 2.1 Categories of Steady Reflection Phenomena . . . . . . . . . . . . . . . . . 42 2.1.1 Curved Incident Shock Wave Reflections over Straight Reflecting Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 2.1.2 Straight Incident Shock Wave Reflections over Curved Reflecting Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 2.1.3 Curved Incident Shock Wave Reflections over Curved Reflecting Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 XII Contents 2.1.4 Straight Incident Shock Wave Reflections over Straight Reflecting Surfaces . . . . . . . . . . . . . . . . . . . . 44 2.2 Modifications of the Perfect Inviscid Two- and Three-Shock Theories . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 2.2.1 Nonstraight Discontinuities . . . . . . . . . . . . . . . . . . . . . . . . . 49 2.2.2 Viscous Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 2.2.3 Thermal Conduction Effects . . . . . . . . . . . . . . . . . . . . . . . . 51 2.2.4 Real Gas Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 2.3 Prediction of the Mach Reflection Shape and the Mach Stem Height . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 2.3.1 Assumptions and Concepts of the Models . . . . . . . . . . . . . 54 2.3.2 Governing Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 2.3.3 Derivation of a General Expression for a Curved Line as a Function of Some Boundary Conditions at Its Ends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 2.3.4 Estimation of the Strength of the Expansion Waves that are Reflected at the Slipstream . . . . . . . . . . . . . . . . . 66 2.3.5 Geometric Relations of the Wave Configuration Shown in Figs. 2.12 and 2.15 . . . . . . . . . . . . . . . . . . . . . . . . 67 2.3.6 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 2.4 Hysteresis Processes in the RR � MR Transition . . . . . . . . . . . . 76 2.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 2.4.2 Hysteresis Processes in the Reflection of Symmetric Shock Waves . . . . . . . . . . . . . . . . . . . . . . . . . 79 2.4.3 Hysteresis Process in the Reflection of Asymmetric Shock Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 2.4.4 Hysteresis Process in the Reflection of Axisymmetric (Conical) Shock Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 3 Shock Wave Reflections in Pseudosteady Flows . . . . . . . . . . . . 135 3.1 “Old” State-of-the-Knowledge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 3.1.1 Reflection Configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 3.1.2 The Transition Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 3.1.3 Second Triple Point Trajectory and Some Critical Remarks Regarding the Old State-of-the-Knowledge . . . 151 3.2 “New” (Present) State-of-the-Knowledge . . . . . . . . . . . . . . . . . . . 156 3.2.1 Introductory Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 3.2.2 Shock-Diffraction Process . . . . . . . . . . . . . . . . . . . . . . . . . . 157 3.2.3 Transition Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 3.2.4 Single-Mach Reflection (SMR) . . . . . . . . . . . . . . . . . . . . . . 161 3.2.5 Formation of Transitional-Mach Reflection (TMR) or Double-Mach Reflection (DMR) . . . . . . . . . . . . . . . . . . 161 3.2.6 Transitional-Mach Reflection (TMR) . . . . . . . . . . . . . . . . . 162 3.2.7 Double-Mach Reflection – DMR. . . . . . . . . . . . . . . . . . . . . 167 Contents XIII 3.2.8 SMR � PTMR/TMR/DMR and the TMR � DMR Transition Criteria and Domains of Different Types of Reflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 3.2.9 Triple-Mach Reflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176 3.2.10 Summary of the New State-of-the-Knowledge . . . . . . . . . 177 3.2.11 Domains and Transition Boundaries . . . . . . . . . . . . . . . . . 179 3.2.12 Weak Shock Wave Reflection Domain . . . . . . . . . . . . . . . . 180 3.3 Summary, Critique, and Discussion . . . . . . . . . . . . . . . . . . . . . . . . 190 3.4 Modifications of the Perfect Inviscid Two- and Three-Shock Theories . . . . . . . . . . . . . . . . . . . . . . . . . . . 194 3.4.1 Nonsteady Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194 3.4.2 Nonstraight Discontinuities . . . . . . . . . . . . . . . . . . . . . . . . . 195 3.4.3 Real Gas Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196 3.4.4 Viscous Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 3.4.5 Thermal Conduction Effects . . . . . . . . . . . . . . . . . . . . . . . . 222 3.4.6 Noninfinitely Thin Contact Discontinuity . . . . . . . . . . . . . 224 3.4.7 Non-Self-Similar Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 3.5 Additional Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230 3.5.1 Flow Deflection Domains . . . . . . . . . . . . . . . . . . . . . . . . . . . 230 3.5.2 Shock Wave Diffraction Domains . . . . . . . . . . . . . . . . . . . . 232 3.5.3 Comparison Between Steady and Pseudosteady Reflection Domains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235 4 Shock Wave Reflections in Unsteady Flows . . . . . . . . . . . . . . . . 247 4.1 Constant Velocity Shock Wave Reflections Over Nonstraight Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250 4.1.1 Shock Wave Reflections Over Cylindrical Concave Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250 4.1.2 Shock Wave Reflections Over Cylindrical Convex Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282 4.1.3 Shock Wave Reflections Over Double Wedges . . . . . . . . . 291 4.2 Nonconstant Velocity Shock Wave Reflections Over Straight Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297 4.3 Spherical Shock Wave Reflections Over Straight and Nonstraight Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304 5 Source List . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307 5.1 Scientific Journals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 308 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .