Unsteady Motion of Continuous Media (eBook)

Front Cover 1
Unsteady Motion of Continuous Media 4
Copyright Page 5
Table of Contents 6
AUTHOR'S POREWORD TO THE ENGLISH EDITION 8
Editor's Foreword 10
Foreword 12
Introduction 13
Chapter I. Mathematical and Thermodynamic Methods of Gas Dynamics 16
1. Fundamental Thermodynamic Relationships In Gas Dynamics 16
2. Fundamental Equations of Gas Dynamics in the Eulerian Form 25
3. Fundamental Equations of Gas Dynamics in Lagrangian Form 34
4. Some Common Properties of the Motion of a Medium 41
5. Fundamental Equations of Gas Dynamics in Certain Special Cases 51
Chapter II. Investigation of the Fundamental Equation of Non-Stationary Gas Dynamics By the Method of Characteristics 69
6. Characteristics of the Equations of Gas Dynamics 69
7· Characteristics of Equations with Two Independent Variables 80
Chapter III. Self-Similar Motion of a Medium 93
8· Self-Similar Motion of a Gas With Central Symmetry 93
9. Self-Similar Symmetrical Motion in Certain Special Cases 105
10. Plane and Spatial Self-Similar Motions 113
Chapter IV. Solution of Equation for One-Dimensional Isentropic Motion of a Medium 123
11· Basic Transformations of the Equations 123
12. Special Solutions 127
13· General Solutions 136
14. General Solutions in Lagrangian Form 145
15. Fundamental Physical Laws of Wave Propagation 149
Chapter V. One-Dimensional Isentropic Motions of a Medium 157
16. Fundamental Relationships for Steady Isentropic Flows 157
17. Simple Rarefaction Wave Produced by Escape of Gas at Rest into a Vacuum 162
18. Reflection of Rarefaction Wave 166
19. Escape of a Column of Gas from Both Ends into a Vacuum 179
20. Escape of Gas from a Tube of Finite Length into Vacuum 184
21. Certain Cases of Unsteady Escape of Gas 191
22. Fundamental Laws of Nonstationary Escape of Gas 197
23. Compression Waves in One Direction 201
Chapter VI. Elementary Theory of Shock Waves 212
24. General Conditions at Discontinuities 212
25. Fundamental Properties of Shock Waves 215
26. Shock Waves in Polytropic Media 226
27. Plane Shock Wave 232
28. Oblique Shock Wave 238
29. Regular Reflection of Oblique Shock Waves 251
30. Irregular Reflection of Oblique Shock Waves 262
31. Flow of Gas Into a Tube with an Abrupt Change in Cross-Section. Mixing or Gas Streams 267
32. Nonstationary Reflection of Gas Jet From a Wall 275
33· Analysis of the Fundamental Properties of Shock Waves 283
34. Certain Examples of Motion of a Medium with Stationary Shock Waves 289
35. Acoustic Theory of Shock Waves 293
Chapter VII. Theory of Detonation Waves 298
36. Fundamental Laws and Equations of the Theory of Detonation and Deflagratian Waves 298
37. Analysis of the Possible Notions of the Medium Behind the Reaction Front 306
38. The Mechanisms of Combustion and Detonation 309
39· Detonation and Combustion Processes in Polytropic Media 316
40. Equation of State of Detonation Products of Condensed Explosives 325
41. General Thermodynamic Laws for Expanding Detonation Condensed Explosives 341
Chapter VIII. Plane Detonation Waves and Escape of Detonation Products 348
42. Propagation of a Plane Detonation Wave 348
43. Escape of Detonation Products 352
44. Fundamental Results of the Investigation of Detonation Waves and of the Escape of Detonation Products 368
45. Escape of Detonation Products into a Vacuum in the Case k = 3 372
46. Escape of Detonation Products from an Inclined Surface of Charge into a Vacuum 376
47. Reflection of a Plane Detonation Wave 387
48. Oblique Reflection of a Strong Detonation Wave from a Wall 396
49. Certain Cases of Propagation of Deflagration Waves 402
50. Shock Waves with Absorption of Energy on the Front 406
51. Condition on the Front of a Shock Wave in the Lagrangian Representation 408
52. Motion of a Medium with Detonation in the Lagrangian Representation 409
Chapter IX. Theory of Propagation of Nonstationary Shock Waves 432
53 . Initial Parameters of Shock Waves 432
54. Fundamental Equations and Boundary Conditions for a Plane Shock Wave 444
55. Initial Stage of Propagation of a Plane Wave on Escape of Instantaneous Detonation Products into Air 451
56. Limiting Acoustic Stage of the Process 458
57. Intermediate State of Motion of Shock Wave 467
58. Propagation of a Shock Wave in a Real Detonation. Certain Examples of Adiabatic Motions 475
59· Reflection of Plane Nonstationary Shock Wave from a Wall 487
60. Total Impulses in Escape of Compressed Gas or Detonation Products in an Infinite Tube Filled with Air 490
61. Escape of Gas into a Tube of Finite Length, Filled with Air 493
Chapter .. Three dimensional Motion of Gas 505
62· Cylindrical and Spherical Detonation Waves 505
63. Expansion of a Gaseous Sphere into Vacuum 513
64. Theory of Point Explosion. Strong Self-similar Shock Waves. Converging Strong Self-similar Wave 521
65. Cylindrical and Spherical Waves in the Acoustic Approximation 543
66. Approximate Methods of Integrating the Equations for Cylindrical and Spherical Waves 546
67. Dispersion of the Products of Instantaneous and Real Detonation in Air 550
Chapter XI. Unsteady Motion in Condensed Media 556
68. Propagation of Plane Shock Wave in Water upon Explosion 556
69. Cavitation of a Dense Medium at the Free Surface 567
70. Propagation of a Spherical Shock Wave in Water 572
71· Unsteady Motion of Water in Channels 579
72. Propagation of Strong Waves in Solids 583
Chapter XII. Propulsion of Bodies by a Gas Stream 602
73. Lagrange's Ballistic Problem 602
74. Lagrange's Problem with Gradual Liberation of Energy 611
75. Propulsion of Body in the Case of Constant Pressure at its Surface 620
Chapter XII. Motion of Gas in a Gravitational Field 623
76. One-dimensional Motion of Gas in a uniform Gravitational Field 623
77. Motion of Gas in Variable Gravitational Field 635
78. Steady Motion of Gas in a Gravitational Field 643
79. Certain General Laws of Eruption of Gas Masses from Heavenly Bodies 649
Chapter XIV. Limiting Motion of Rarefied and Very Dense Media 667
80. Solution of the Fundamental Equations of Gas Dynamics for a Rarefied Medium 667
81. Motion of a Rarefied Medium in a Gravitational Field 673
82. Equilibrium State of a Gravitating Medium 682
83. Motion of Rotating Masses of Rarefied Gas in a Gravitational Field 696
84. Fundamental Laws of Motion of Gas in its Own Gravitational Field 700
Chapter XV. Certain Problems in the Relativistic Mechanics of Solid Media 712
85. Fundamental Equations of the Relativistic Theory 712
86. Fundamental Thermodynamic Relations 723
87. Elements of the Theory of Shock Waves 732
88. Motion of Medium in the Relativistic Case 740
BIBLIOGRAPHY 753
AUTHOR INDEX 756
SUBJECT INDEX 757