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
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
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 Psexidosteady
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 ................................................. 308
5.2 Reports ............................................... 332
References ............................................ 332
Index ......................................................... 339
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