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SHOCK WAVE–BOUNDARY-LAYER INTERACTIONS

Shock wave–boundary-layer interaction (SBLI) is a fundamental phenomenon in gasdynamics that is observed in many practical situations, ranging from transonic aircraftwings to hypersonic vehicles and engines. SBLIs have the potential to pose serious prob-lems in a flowfield; hence they often prove to be critical – or even design-limiting – issuesfor many aerospace applications.

This is the first book devoted solely to a comprehensive state-of-the-art explanationof this phenomenon with coverage of all flow regimes where it occurs. The book includesa description of the basic fluid mechanics of SBLIs plus contributions from leading inter-national experts who share their insight into their physics and the impact they have inpractical flow situations. This book is for practitioners and graduate students in aerody-namics who wish to familiarize themselves with all aspects of SBLI flows. It is a valuableresource for specialists because it compiles experimental, computational, and theoreticalknowledge in one place.

Holger Babinsky is Professor of Aerodynamics at the University of Cambridge and aFellow of Magdalene College. He received his Diplom-Ingenieur (German equivalent ofan MS degree) with distinction from the University of Stuttgart and his PhD from Cran-field University with an experimental study of roughness effects on hypersonic SBLIs.From 1994 to 1995, he was a Research Associate at the Shock Wave Research Centreof Tohoku University, Japan, where he worked on experimental and numerical investi-gations of shock-wave dynamics. He joined the Engineering Department at CambridgeUniversity in 1995 to supervise research in its high-speed flow facilities. Professor Babin-sky has twenty years of experience in the research of SBLIs, particularly in the develop-ment of flow-control techniques to mitigate the detrimental impact of such interactions.He has authored and coauthored many experimental and theoretical articles on high-speed flows, SBLIs, and flow control, as well as various low-speed aerodynamics subjects.Professor Babinsky is a Fellow of the Royal Aeronautical Society, an Associate Fellowof the American Institute of Aeronautics and Astronautics (AIAA), and a Member ofthe International Shock Wave Institute. He serves on a number of national and interna-tional advisory bodies. Recently, in collaboration with the U.S. Air Force Research Lab-oratories, he organized the first AIAA workshop on shock wave–boundary-layer predic-tion. He has developed undergraduate- and graduate-level courses in Fluid Mechanicsand received several awards for his teaching.

John K. Harvey is a Professor in Gas Dynamics at Imperial College and is a visiting pro-fessor in the Department of Engineering at the University of Cambridge. He obtainedhis PhD in 1960 at Imperial College for research into the roll stability of slender deltawings, which was an integral part of the Concorde development program. In the early1960s, he became involved in experimental research into rarefied hypersonic flows, ini-tially with Professor Bogdonoff at Princeton University and subsequently back at Impe-rial College in London. He has published widely on the use of the direct-simulationMonte Carlo (DSMC) computational method to predict low-density flows, and he hasspecialized in the development of suitable molecular collision models used in thesecomputations to represent reacting, ionized, and thermally radiating gases. He has alsobeen active in the experimental validation of this method. Through his association withCUBRC, Inc., in the United States, he has been involved in the design and construc-tion of three major national shock tunnel facilities and in the hypersonic aerodynamicresearch programs associated with them. Professor Harvey has also maintained a stronginterest in low-speed experimental aerodynamics and is a recognized expert on the aero-dynamics of F1 racing cars. Professor Harvey is a Fellow of the Royal Aeronautical Soci-ety and an Associate Fellow of the American Institute of Aeronautics and Astronautics.

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Shock Wave–Boundary-LayerInteractions

Edited by

Holger BabinskyUniversity of Cambridge

John K. HarveyImperial College






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Shock wave–boundary-layer interactions / [edited by] Holger Babinsky, John Harvey.p. cm. – (Cambridge aerospace series)

Includes bibliographical references and index.ISBN 978-0-521-84852-7 (hardback)1. Shock waves. 2. Boundary layer. I. Babinsky, Holger. II. Harvey,John (John K.) III. Title. IV. Series.TL574.S4S575 2011629.132′37–dc22 2011001978

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To my late mother – Holger Babinsky






Brief Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . page 1

Holger Babinsky and John K. Harvey

2 Physical Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Jean Delery

3 Transonic Shock Wave–Boundary-Layer Interactions . . . . . . . . . . . . . 87

Holger Babinsky and Jean Delery

4 Ideal-Gas Shock Wave–Turbulent Boundary-Layer Interactions(STBLIs) in Supersonic Flows and Their Modeling:Two-Dimensional Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

Doyle D. Knight and Alexander A. Zheltovodov

5 Ideal-Gas Shock Wave–Turbulent Boundary-Layer Interactions inSupersonic Flows and Their Modeling: Three-DimensionalInteractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202

Alexander A. Zheltovodov and Doyle D. Knight

6 Experimental Studies of Shock Wave–Boundary-LayerInteractions in Hypersonic Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . 259

Michael S. Holden

7 Numerical Simulation of Hypersonic ShockWave–Boundary-Layer Interactions . . . . . . . . . . . . . . . . . . . . . . . . . 314

Graham V. Candler

8 Shock Wave–Boundary-Layer Interactions Occurring inHypersonic Flows in the Upper Atmosphere . . . . . . . . . . . . . . . . . . 336

John K. Harvey

vii






viii Brief Contents

9 Shock-Wave Unsteadiness in Turbulent Shock Boundary-LayerInteractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373

P. Dupont, J. F. Debieve, and J. P. Dussauge

10 Analytical Treatment of Shock Wave–Boundary-LayerInteractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395

George V. Inger

Index 459






Contents

Contributors page xvii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1 Structure of the Book 21.1.1 George Inger 3

1.2 Intended Audience 4

2 Physical Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.1 Shock Wave–Boundary-Layer Interactions: Why TheyAre Important 5

2.2 Discontinuities in Supersonic Flows 62.2.1 Shock Waves 62.2.2 The Shock-Polar Representation 72.2.3 Shock Intersections and the Edney Classification

of Shock-Shock Interferences 112.2.4 Shock Waves, Drag, and Efficiency: The Oswatitsch

Relationship 162.3 On the Structure of a Boundary-Layer Flow 19

2.3.1 Velocity Distribution through a Boundary Layer 192.3.2 The Multilayer Structure 242.3.3 The Boundary-Layer Response to a Rapid Pressure

Variation 252.4 Shock Waves and Boundary Layers: The Confrontation 26

2.4.1 The Basic SBLI in Two-Dimensional Flows 262.4.2 The Boundary-Layer–Shock-Pressure-Jump Competition 28

2.5 Interactions without Separation: Weakly Interacting Flows 312.5.1 The Incident-Reflecting Shock 31

Overall Flow Organisation 31Shock Penetration in a Rotational Layer 33

2.5.2 Ramp-Induced Shock 352.5.3 Normal Shock and Transonic Interactions 362.5.4 Upstream Influence Scaling 38

2.6 Interaction Producing Boundary-Layer Separation: StronglyInteracting Flows 39

ix






x Contents

2.6.1 Separation Caused by an Incident Shock 39Overall Flow Organisation 39The Outer Inviscid-Flow Structure 40

2.6.2 Ramp-Induced Separation 442.6.3 Normal Shock-Induced Separation or Transonic

Separation 472.7 Separation in Supersonic-Flow and Free-Interaction Processes 51

2.7.1 The Free-Interaction Theory 512.7.2 Incipient Shock-Induced Separation in Turbulent Flow 55

2.8 Transitional SBLIs 562.9 Specific Features of Hypersonic Interactions 59

2.9.1 Shock Pattern and Flowfield Organisation 592.9.2 Wall-Temperature Effect 602.9.3 Wall-Heat Transfer in Hypersonic Interactions 612.9.4 Entropy-Layer Effect 642.9.5 Real-Gas Effects on SBLI 66

2.10 A Brief Consideration of Three-Dimensional Interacting Flows 672.10.1 Separation in Three-Dimensional Flow 672.10.2 Topology of a Three-Dimensional Interaction 702.10.3 Reconsideration of Two-Dimensional Interaction 73

2.11 Unsteady Aspects of Strong Interactions 742.12 SBLI Control 77

2.12.1 Mechanisms for Control Action 772.12.2 Examination of Control Techniques 79

Active Control 81Passive Control 81Wall Contouring 82

2.13 Concluding Remarks 82Appendix A: Discontinuities in Supersonic Flow and theRankine-Hugoniot Equations 83

3 Transonic Shock Wave–Boundary-Layer Interactions . . . . . . . . . . . . . 87

3.1 Introduction to Transonic Interactions 873.2 Applications of Transonic SBLIs and Associated

Performance Losses 873.2.1 Transonic Airfoils and Cascades 88

Shock Losses on Transonic Wings 903.2.2 Supersonic Engine Intakes 933.2.3 Internal Flows 95

3.3 Normal SBLIs in Detail 953.3.1 Attached-Flow Interaction 96

Region I (Upstream of Main Shock) 101Region II (Downstream of Main Shock) 103Inflow–Shape-Factor Effects 103

3.3.2 The Onset of Shock-Induced Separation 1043.3.3 Separated SBLIs 107

Boundary-Layer Behavior in Separated TransonicInteractions 110






Contents xi

3.3.4 Other Effects on Transonic SBLIs 114Confinement Effects (Channels) 114Surface-Curvature Effects 117Sweep Effects 118

3.3.5 Large-Scale Unsteadiness of Normal SBLIs 1183.4 Control of Transonic SBLIs 123

3.4.1 Shock Control 1243.4.2 Methods of Shock Control 127

Contoured-Surface Bump 127‘Passive’ Control 129Other Methods of Shock Control 130Three-Dimensional Shock-Control Methods 130

3.4.3 Methods of Boundary-Layer Control 132

4 Ideal-Gas Shock Wave–Turbulent Boundary-Layer Interactions(STBLIs) in Supersonic Flows and Their Modeling:Two-Dimensional Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

4.1 Introduction 1374.1.1 Problems and Directions of Current Research 1374.1.2 Computational Fluid Dynamics 138

4.2 Two-Dimensional Turbulent Interactions 1414.2.1 Normal STBLI: Flow Regimes and Incipient Separation

Criteria 1424.2.2 Examples of NSTBLI Numerical Modeling 1484.2.3 Gas Dynamics Flow Structure in Compression Ramps

and Compression-Decompression Ramps with Examplesof Their Numerical Modeling 151

4.2.4 Incipient Separation Criteria, STBLI Regimes, and ScalingLaws for CR and CDR Flows 159

4.2.5 Heat Transfer and Turbulence in CR and CDR Flows 1664.2.6 Unsteadiness of Flow Over CR and CDR Configurations

and Its Numerical Modeling 1694.2.7 Oblique Shock Wave–Turbulent Boundary-Layer

Interaction 1854.3 Summary 193

5 Ideal-Gas Shock Wave–Turbulent Boundary-Layer Interactions inSupersonic Flows and Their Modeling: Three-DimensionalInteractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202

5.1 Introduction 2025.2 Three-Dimensional Turbulent Interactions 2025.3 Three-Dimensional Nature of Separated Flows 203

5.3.1 Introduction 2035.3.2 STBLI in the Vicinity of Sharp Unswept Fins 205

5.3.2.1 Flow Regimes and Incipient Separation Criteria 205






xii Contents

5.3.2.2 Flow Structure and Its Numerical Prediction 2155.3.2.3 Secondary-Separation Phenomenon and Its

Prediction 2215.3.3 Sharp Swept Fin and Semi-Cone: Interaction Regimes

and Scaling Laws 2255.3.4 Swept Compression Ramp Interaction and Its Modeling 2305.3.5 Double Sharp-Fin Interaction 237

5.4 Summary 253

6 Experimental Studies of Shock Wave–Boundary-LayerInteractions in Hypersonic Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . 259

6.1 Introduction 2596.2 SBLI in Laminar Two-Dimensional and Axisymmetric

Hypersonic Flows 2636.2.1 Introduction 2636.2.2 Salient Characteristics for Laminar Regions of SBLI

in Hypersonic Flows 2636.2.3 Boundary-Layer Models of Shock Wave–Laminar

Boundary-Layer Interaction 2656.2.4 Early Navier-Stokes Validation Studies 2686.2.5 Recent Navier-Stokes and DSMC Code-Validation Studies

of Hypersonic SBLIs 2736.3 SBLI in Turbulent and Transitional Flows 275

6.3.1 Introduction 2756.3.2 Characteristics of Turbulent SBLI in Two-Dimensional

Configurations 2766.3.3 Navier-Stokes Prediction of Shock Wave–Turbulent

Boundary-Layer Interaction in Hypersonic Flow 2806.3.4 SBLI in Turbulent Hypersonic Flow on Axisymmetric

Configurations: Comparison Between Measurements andComputations 281

6.3.5 Swept and Skewed SBLIs in Turbulent Supersonicand Hypersonic Flows 285

6.3.6 Shock-Wave Interaction in Transitional Flows OverAxisymmetric/Indented Nose Shapes 289

6.4 Characteristics of Regions of Shock-ShockBoundary-Layer Interaction 2926.4.1 Introduction 2926.4.2 Shock-Shock Heating in Laminar, Transitional,

and Turbulent Interactions 2936.4.3 Comparison Between Measurements in Laminar Flows

and Navier-Stokes and DSMC Predictions 2956.5 SBLI Over Film- and Transpiration-Cooled Surfaces 296

6.5.1 Introduction 2966.5.2 Shock Interaction with Film-Cooled Surfaces 2976.5.3 Shock Interaction with Transpiration-Cooled Surfaces 298






Contents xiii

6.5.4 Shock-Shock Interaction on Transpiration-Cooled LeadingEdges 299

6.6 Real-Gas Effects on Viscous Interactions Phenomena 3006.6.1 Introduction 3006.6.2 Studies of Real-Gas Effects on Aerothermal

Characteristics of Control Surfaces on a U.S. Space ShuttleConfiguration 305

6.7 Concluding Remarks 308

7 Numerical Simulation of Hypersonic ShockWave–Boundary-Layer Interactions . . . . . . . . . . . . . . . . . . . . . . . . . 314

7.1 Introduction 3147.2 Hypersonic SBLI Physics 315

7.2.1 Shock Wave–Laminar Boundary-Layer Interactionsat High Mach Number 315

7.2.2 Hypersonic Compression-Corner Flows 3177.2.3 Hypersonic Shock-Shock Interactions 321

7.3 Numerical Methods for Hypersonic Shock–Boundary-LayerInteraction Flows 324

7.4 Example: Double-Cone Flow for CFD Code Validation 3277.5 Conclusions 332Acknowledgments 333

8 Shock Wave–Boundary-Layer Interactions Occurring inHypersonic Flows in the Upper Atmosphere . . . . . . . . . . . . . . . . . . 336

8.1 Introduction 3368.2 Prediction of Rarefied Flows 337

8.2.1 Classical Kinetic Theory for Dilute Gases 3378.3 Characteristics of Rarefied Flows 338

8.3.1 Structural Changes that Occur in Rarefied Flows 3398.4 Examples of SBLIs in Rarefied Hypersonic Flows 343

8.4.1 Introduction 3438.4.2 SBLIs on a Hollow-Cylinder–Flare Body 3448.4.3 Velocity-Slip and Temperature-Jump Effects 3498.4.4 SBLIs Occurring on a Sharp Biconic Body 3538.4.5 Flows Involving Chemical Reactions 359

8.5 Concluding Remarks 363Appendix A: Kinetic Theory and the DSMC Method 365

A.1 Particle-Simulation Methods 366A.2 The DSMC Method 366

9 Shock-Wave Unsteadiness in Turbulent Shock Boundary-LayerInteractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373

9.1 Introduction 3739.2 The Upper Branch: Unseparated Flows 3739.3 The Lower Branch: Separated Flows 376

9.3.1 Introduction 376






xiv Contents

9.3.2 Separated Flows with Far Downstream Influence 3769.3.3 Separated Flows without Far-Downstream Influence 377

9.3.3.1 General Organization 3779.3.3.2 Separated Flows: Frequency Content 382

9.4 Conclusions: A Tentative Classification of Unsteadinessand Related Frequencies 389

10 Analytical Treatment of Shock Wave–Boundary-LayerInteractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395

10.1 Introduction 39510.1.1 Motivation for Analytical Work in the Computer Age 39510.1.2 Scope of the Present Survey 39610.1.3 Content 396

10.2 Qualitative Features of SBLIs 39710.2.1 High-Reynolds-Number Behavior: Laminar versus

Turbulent 39710.2.2 General Scenario of a Nonseparating SBLI 398

10.2.2.1 Incident-Oblique Shock 39810.2.2.2 Compression Corner 399

10.2.3 Basic Structure of the Interaction Zone 40010.2.3.1 Triple Deck: General Features 40010.2.3.2 Further Local Subdivisions 401

10.3 Detailed Analytical Features of the Triple Deck 40110.3.1 Middle Deck 401

10.3.1.1 General Aspects 40110.3.1.2 Purely Laminar Flows 40510.3.1.3 Turbulent Flows at Large Reynolds Numbers 405

10.3.2 Inner Deck 40610.3.2.1 General Aspects 40610.3.2.2 Laminar Flows 40910.3.2.3 Turbulent Flows 409

10.3.3 Middle-Inner-Deck Matching 41110.3.3.1 Laminar Flows 41110.3.3.2 Turbulent Flows 412

10.3.4 Inviscid-Pressure–Flow Deflection Relationships for theOuter Deck 413

10.3.5 Combined Matching of All Decks 41510.3.5.1 Laminar Flows 41510.3.5.2 Turbulent Flows 416

10.3.6 Summary of Scaling Properties and Final CanonicalForms of Triple-Deck Equations 41710.3.6.1 Laminar Flows 41810.3.6.2 Turbulent Flows 420

10.4 Application to Laminar-Flow Interactions 42210.4.1 Supersonic Adiabatic Flows 422

10.4.1.1 General Aspects 42210.4.1.2 Free Interaction and Upstream Influence 423






Contents xv

10.4.1.3 Wall-Pressure Distribution and IncipientSeparation 427

10.4.1.4 Linearized Solutions 42810.4.2 Hypersonic Nonadiabatic Flows 428

10.4.2.1 Streamline Divergence Effect 42810.4.2.2 Upstream Influence 42810.4.2.3 Incipient Separation 43010.4.2.4 Interactive Heat Transfer 430

10.4.3 Transonic Regime 43310.4.4 Three-Dimensional Interactions 434

10.5 Application to Turbulent Interactions 43510.5.1 Supersonic/Hypersonic Interactions in Asymptotic

Theory 43510.5.1.1 Upstream Region 43510.5.1.2 Downstream Region 437

10.5.2 Transonic Flows in Asymptotic Theory 44010.5.2.1 Small-Scale Features 44010.5.2.2 Purely Supersonic Flows 44010.5.2.3 Mixed Supersonic/Subsonic Flows 442

10.5.3 Three-Dimensional Effects 44210.6 Limitations of the Triple-Deck Approach 443

10.6.1 Laminar Flows 44310.6.2 Turbulent Flows 445

Appendix A The Wall-Slip Boundary Conditions 446Appendix B Evaluation of Boundary-Layer Profile Integrals andRelated Matters 448

B.1 Limit Expression in the Laminar Interaction Theory 448B.2 Evaluation of Im for Laminar Flow 449B.3 Evaluation of Im for Turbulent Flow 449

Appendix C Summary of Constants in the Scaling Relationships forLaminar Flow 450

C.1 Supersonic–Hypersonic Flow 450C.2 Adiabatic Shockless Transonic Flow 450

Appendix D Nomenclature 451D.1 Subscripts 453D.2 Special Symbols 453

Index 459






Contributors

Holger Babinsky (Editor and Chapter 3) Department of Engineering, University ofCambridge, Cambridge CB2 1PZ, UK [email protected]

John K. Harvey (Editor and Chapter 8) Department of Aeronautics, Imperial Col-lege, London SW7 2AZ, UK; Department of Engineering, University of Cambridge,Cambridge CB2 1PZ, UK [email protected]

Graham V. Candler (Chapter 7) Department of Aerospace Engineering & Mechan-ics, University of Minnesota, Minneapolis, MN 55455-0153, USA [email protected]

J. F. Debieve (Chapter 9) Institut Universitaire des Systemes Thermiques Indus-triels, Universite d’Aix-Marseille, UMR CNRS 6595, Marseille, France

Jean Delery (Chapters 2 and 3) ONERA, 29 Avenue Division Le Clerc 92320Chatillon, France [email protected]

P. Dupont (Chapter 9) Institut Universitaire des Systemes Thermiques Industriels,Universite d’Aix-Marseille, UMR CNRS 6595, Marseille, France

J. P. Dussauge (Chapter 9) Institut Universitaire des Systemes Thermiques Indus-triels, Universite d’Aix-Marseille, UMR CNRS 6595, Marseille, France [email protected]

Michael S. Holden (Chapter 6) CUBRC, 4455 Genesee Street, Buffalo, NY 14225,USA [email protected]

George V. Inger (Chapter 10) Formerly at Department of Aerospace and OceanEngineering, Virginia Polytechnic Institute and State University, Blacksburg, VA24060, USA

Doyle D. Knight (Chapters 4 and 5) Department of Mechanical and AerospaceEngineering, Rutgers – The State University of New Jersey, Piscataway, NJ 08854-8058, USA [email protected]

Alexander A. Zheltovodov (Chapters 4 and 5) Khristianovich Institute of Theoreti-cal and Applied Mechanics, Siberian Branch of Russian Academy of Science, RussiaNovosibirsk 630090, Russia [email protected]

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