Part I Shock Waves in Complex Liquids
1 Shock Waves in Bubbly Liquids
Leen van Wijngaarden ..................................... 3
1.1 Introduction ........................................... 3
1.2 Elements of Bubble Dynamics ............................ 3
1.3 Nonlinear Compressive Waves ............................ 9
1.4 Mechanisms Opposing Steepening of Compressive
Waves ................................................. 11
1.4.1 Viscous Stresses ............................... 11
1.4.2 Dispersion ..................................... 11
1.4.3 Relaxation ..................................... 12
1.5 Strong Shock Waves .................................... 14
1.6 Shock Waves of Moderate and Weak Strength ............. 17
1.7 Solitons in bubbly flows .............................. 28
References ................................................. 31
2 Interaction of a Shock Wave with a Single Bubble
Yukio Tomita ............................................ 35
2.1 Introduction .......................................... 35
2.2 Violent Bubble Collapse and Liquid Jet Formation ...... 37
2.3 Shock Wave-Bubble Interaction near Boundaries ......... 48
2.4 Bubble Collapse Induces High Temperature and
Sonohuninescence ...................................... 59
References ................................................. 63
3 Shock Induced Cavitation
Valery K. Kedrinskii .................................... 67
3.1 Introduction .......................................... 67
3.2 Real Liquid State (Nucleation Problems) ............... 68
3.3 Bubble Clusters ....................................... 72
3.3.1 Formation Mechanisms ........................... 72
3.3.2 Mathematical Model of Cavitating Liquid ........ 73
3.3.3 Comparison with Experiments .................... 75
3.3.4 Dynamic Strength of Liquid ..................... 76
3.3.5 Tensile Stress Relaxation (Cavitation
in a Vertically Accelerated Tube) .............. 77
3.4 Methods of Hydrodynamic Pulse Tubes and
Experimental Technique ................................ 80
3.4.1 Hydrodynamic Tube of Rarefaction ............... 80
3.4.2 Hydrodynamic Shock Tube, Pulse X-Ray Method
and Resolution of Cavitation Zone Dynamics ..... 80
3.4.3 "Frozen" Profile of Mass Velocities in a
Cavitation Zone ................................ 83
3.5 Comparison of the Initial Stages of Disintegration
of Solids and Liquids ................................. 85
3.5.1 Liquids ........................................ 85
3.5.2 Solids ......................................... 88
3.6 Shock Waves, Bubbles, and Biomedical Problems ......... 89
3.6.1 General Questions and Statements ............... 89
3.6.2 Some Results on Modeling of ESWL
Applications ................................... 92
References ................................................. 95
4 Shocks in Cryogenic Liquids
Masahide Murakami ....................................... 99
4.1 Cryogenic Fluids and Superfluid Liquid Helium ......... 99
4.1.1 Cryogenic Fluids .............................. 100
4.1.2 Superfluid Liquid Helium (He II) .............. 102
4.2 Shock Waves in He II ................................. 112
4.2.1 Compression Shock Wave ........................ 112
4.2.2 Thermal Shock Wave ............................ 116
4.2.3 Superfluid Shock Tube Facility ................ 122
References ................................................ 130
Part II Shock Waves and Phase Transition
5 Shock Waves in Fluids with Interphase Transport
of Mass, Momentum and Energy (Vapour Droplet Mixtures
and Solid-Particle-Laden Gases)
Abhijit Guha ........................................... 135
5.1 Introduction ......................................... 135
5.2 Relaxation Gas Dynamics for Pure Vapour Droplet
Mixtures and Detailed Structure of Shock Waves ....... 137
5.2.1 Relaxation Phenomena .......................... 137
5.2.2 Gas Dynamics .................................. 143
5.2.3 Detailed Structue of Shock Waves .............. 148
5.3 Integral Analysis: Jump Conditions for Pure
Vapour-Droplet Flows ................................. 156
5.3.1 Stationary Shock Waves ........................ 156
5.3.2 Jump Relations for Pure Vapour-Droplet
Flow .......................................... 159
5.3.3 Unsteady Development of Shock Waves ........... 162
5.4 Coupled Relaxation Processes and Thermal Choking ..... 165
5.4.1 Differential Approach ......................... 165
5.4.2 Integral Approach ............................. 167
5.5 Shock Waves in Vapour-Droplet Flow with a
Carrier Gas .......................................... 168
5.5.1 Introduction .................................. 168
5.5.2 Jump Conditions Across Normal Shock
Waves when both Boundary Conditions
are Equilibrium States ........................ 171
5.5.3 Limiting Wetness Fraction ..................... 174
5.5.4 Jump Conditions Across Shock Waves with
Complete Evaporation of Liquid Phase
(y2 = 0) ...................................... 174
5.6 Shock Waves in a Solid Particle-Laden Gas ............ 176
5.6.1 Equilibrium Gas Dynamics for Gas-Particle
Mixture ....................................... 176
5.6.2 Relaxation Phenomena .......................... 177
5.6.3 Comparative Magnitudes of Relaxation Times
and Structure of Shock Waves .................. 179
5.6.4 Jump Conditions ............................... 179
5.7 Interpretation of Total Pressure and Total
Temperature .......................................... 180
References ........................................... 185
6 Condensation Discontinuities and Condensation Induced
Shock Waves
Can E. Delale. Günter H. Schnerr.
Marinus E.H. van Dongen ................................ 187
6.1 Introduction ......................................... 187
6.2 Kinetics of Condensation and Condensation Models ..... 188
6.2.1 Nucleation ..................................... 188
6.2.2 Droplet Growth ................................. 190
6.3 Flows with Heat Addition ............................. 190
6.3.1 Subcritical Flows ............................. 199
6.3.2 Supercritical Flows ........................... 199
6.4 Condensation Induced Shock Waves in Nozzle Flows ..... 202
6.4.1 Quasi-One-Dimensional Nozzle Flows ............ 202
6.4.2 Two-Dimensional Transonic Nozzle Flows
with Nonequilibrium Condensation .............. 209
6.4.3 Unsteady Self-Excited Periodic Flows .......... 214
6.4.4 Condensation Induced Shock Waves in
Prandtl-Meycr Flows ........................... 220
6.4.5 Condensation Induced Shock Waves in
Unsteady Rarefaction Waves .................... 223
6.4.6 Future Perspectives ........................... 227
References ................................................ 228
7 Liquefaction Shock Waves
Gerd Е.A. Meier ........................................ 231
7.1 Introduction ......................................... 231
7.2 Retrograde Fluids and their Role in Gasdynamics ...... 232
7.2.1 Introductary Remarks .......................... 232
7.2.2 The Liquefaction Shock Wave History ........... 233
7.2.3 Fluid Properties of Retrograde Substances ..... 234
7.2.4 Gasdynamic Aspects of Fluid Properties ........ 235
7.2.5 One-Dimensional Treatment of Real Gas
Flows ......................................... 237
7.2.6 Initial Flow Experiments with Retrograde
Fluids with Shock Waves ....................... 238
7.3 Experimental Details of Liquefaction Shock Wave
Studies .............................................. 244
7.3.1 Objectives of the Experiments ................. 244
7.3.2 Experimental Arrangement of the First
Tests ......................................... 244
7.3.3 Experimental Results for Partial
Liquefaction Shocks ........................... 248
7.3.4 Experimental Results for Complete
Liquefaction Shocks ........................... 251
7.3.5 Photographic Observations of the
Liquefaction Shock Wave ....................... 254
7.3.6 Shock-Boundary-Layer Interaction
Region ........................................ 256
7.3.7 Experimental Results for Liquefaction
Shocks from an Open Shock Tube ................ 256
7.4 Concluding Remarks ................................... 257
References ................................................ 259
Part III Shock Waves Interacting with Solid Foams,
Textiles, Porous and Granular Media
8 Experimental Studies of Shock Wave Interactions
with Porous Media
Beric Skews ............................................ 271
8.1 Introduction ......................................... 271
8.2 Thin Barriers ........................................ 272
8.2.1 Perforated Rigid Plates ....................... 272
8.2.2 Textiles ...................................... 275
8.2.3 Movable Sheets ................................ 280
8.3 Thick Slabs .......................................... 280
8.3.1 Rigid Skeletons ............................... 282
8.3.2 Compressible Foams ............................ 284
8.4 Particle Beds ........................................ 292
8.5 Conclusion ........................................... 293
References ................................................ 294
9 Linear Waves and Shock Waves in Flexible and Rigid
Porous Media
Darid Simeulders and Marinus van Dongen ................ 297
9.1 Introduction ......................................... 297
9.2 Acoustic Bulk Properties ............................. 298
9.2.1 Thermal Effects ............................... 299
9.2.2 One-Dimensional Field Equations ............... 301
9.2.3 Low-Frequency Limit ........................... 304
9.2.4 High-Frequency Limit .......................... 305
9.2.5 Loose Frame Limit ............................. 306
9.2.6 Stiff Frame Limit ............................. 308
9.2.7 Incompressible Fluid Limit .................... 309
9.3 Wave Interactions and Wave Reflections ............... 310
9.4 Nonlinear Models ..................................... 312
9.4.1 Head-on Collision of Shock Waves with
Rigid Porous Media ............................ 314
9.4.2 Head-on Collision of Shock Waves with
Flexible Porous Media ......................... 318
9.5 Conclusions .......................................... 322
References ................................................ 323
10 Shock Waves in Granular Media
Victor Golub and Olga Mirova ......................... 325
10.1 Introduction ......................................... 325
10.2 Shock Adiabat of a Solid ............................. 325
10.3 Shock Adiabat in Granular Material ................... 327
10.4 Processes of Deformation Under Shock-Wave
Loading .............................................. 331
10.4.1 Models Used in Calculations .................. 331
10.4.2 Phenomenology of the Process of Shock
Compaction of Granular Materials ............. 335
10.4.3 Key Features of the Thermodynamics
of Shock Compaction of Granular Media ........ 338
10.4.4 Analysis of Thermodynamic Models of
Heterogeneous Heating of Granular Medium
Under Conditions of Shock-Wave
Deformation .................................. 342
10.4.5 Conditions Required for Developing
High-Strength Compacts ....................... 345
10.5 Attenuation of Explosive Wave as a Result
of Deterioration of Granular Material ................ 346
References ................................................ 350
Index ..................................................... 353
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