Preface ....................................................... ix
1 Basic Equations ............................................. 1
1.1 Introduction ........................................... 1
1.2 Thermodynamics ......................................... 1
1.3 Conservation Equations ................................. 3
1.4 Characteristic Equations ............................... 5
1.5 Acoustic Waves ......................................... 9
1.6 Acoustic Radiation from a Spherical Expanding Piston .. 11
1.7 Waves of Finite Amplitude ............................. 14
1.8 The Piston Problem .................................... 16
1.9 Shockwaves ............................................ 20
1.10 Detonation and Deflagration Waves ..................... 26
2 Weak Shock Theory .......................................... 31
2.1 Introduction .......................................... 31
2.2 Properties of Weak Shocks ............................. 32
2.3 Chandrasekhar's Solution .............................. 35
2.4 Oswatitsch's Solution ................................. 37
2.5 Friedrichs' Theory .................................... 41
2.6 Decay of a Piston Driven Shock ........................ 45
2.7 Whitham's Theory ...................................... 48
3 Shock Propagation in a Non-uniform Cross-sectional Area
Tube ....................................................... 56
3.1 Introduction .......................................... 56
3.2 Chester's Theory ...................................... 56
3.3 Chisnell's Theory ..................................... 60
3.4 Whitham's Theory ...................................... 64
4 Blast Wave Theory .......................................... 67
4.1 Introduction .......................................... 67
4.2 Basic Equations ....................................... 68
4.3 The Energy Integral ................................... 70
4.4 Integrals of the Similarity Equations ................. 75
4.5 Closed Form Solution for Blasts ....................... 78
4.6 Properties of the Constant Energy Solution ............ 81
4.7 Variable Energy Blasts ................................ 83
5 Homentropic Explosions ..................................... 87
5.1 Introduction .......................................... 87
5.2 The Shock Tube Problem ................................ 88
5.3 Propagation of Chapman-Jouguet Detonations ............ 91
5.4 Piston Driven Explosion ............................... 94
6 The Snow-Plow Approximation ............................... 102
6.1 Introduction ......................................... 102
6.2 Basic Equations ...................................... 102
6.3 Constant Energy Blast Waves .......................... 107
6.4 Explosion of a Finite Spherical Charge ............... 113
6.5 Piston Driven Explosions ............................. 116
7 The Brindley-Kirkwood Theory .............................. 121
7.1 Introduction ......................................... 121
7.2 Basic Equations ...................................... 122
7.3 The Energy Integral .................................. 124
7.4 The Fourth Equation .................................. 127
7.5 The Shock Decay Equation ............................. 128
7.6 The Asymptotic Weak Shock Regime ..................... 132
7.7 Explosion of a Pressurized Sphere .................... 134
8 Non-similar Solutions for Finite Strength Blast Waves ..... 136
8.1 Introduction ......................................... 136
8.2 Basic Formulation .................................... 136
8.3 Perturbation Solution ................................ 139
8.4 Quasi-similar Solution ............................... 144
8.5 Integral Method ...................................... 155
9 Implosions ................................................ 164
9.1 Introduction ......................................... 164
9.2 Implosions ........................................... 164
9.3 Solution in the State Plane .......................... 167
9.4 Shock Propagation in a Non-uniform Density Medium .... 169
9.5 The Sharp Blow Problem ............................... 173
9.6 Exact Solution for γ = 1.4 ........................... 175
9.7 Determination of A ................................... 177
9.8 Converging Blast Waves ............................... 180
Bibliography ................................................. 195
Index ........................................................ 199
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