Supersonic Flow and Shock WavesThe Springer edition of this book is an unchanged reprint of Courant and Friedrich's classical treatise which was first published in 1948. The basic research for it took place during World War II, but there are many aspects which still make the book interesting as a text and as a reference. It treats basic aspects of the dynamics of compressible fluids in mathematical form, and attempts to present a systematic theory of nonlinear wave propagation, particularly in relation to gas dynamics. Written in the form of an advanced textbook, it accounts for classical as well as some fairly recent developments. The authors intend their audience to be engineers, physicists and mathematicians alike. |
Contents
Compressible Fluids | 1 |
Qualitative differences between linear and nonlinear waves | 2 |
A General Equations of Flow Thermodynamic Notions | 3 |
Ideal gases polytropic gases and media with separable energy | 6 |
Mathematical comments on ideal gases | 8 |
Solids which do not satisfy Hookes law | 10 |
Discrete media | 12 |
Conservation of energy | 15 |
ChapmanJouguet processes | 211 |
Jouguets rule | 215 |
Determinacy in gas flow involving a reaction front | 218 |
Solution of flow problems involving a detonation process | 222 |
Solution of flow problems involving deflagrations | 224 |
Detonation as a deflagration initiated by a shock | 226 |
Deflagration zones of finite width | 227 |
Detonation zones of finite width ChapmanJouguet hypothesis | 231 |
Enthalpy | 17 |
Isentropic flow Steady flow Subsonic and supersonic flow | 18 |
Vector form of the flow equations | 19 |
Bernoullis law | 21 |
Limit speed and critical speed | 23 |
B Differential Equations for Specific Types of Flow | 25 |
Nonsteady flows | 28 |
Lagranges equations of motion for onedimensional and spherical flow | 30 |
AppendixWave Motion in Shallow Water | 32 |
Mathematical Theory of Hyperbolic Flow Equations for Functions of Two Variables | 37 |
Differential equations of second order type | 38 |
Characteristic curves and characteristic equations | 40 |
Characteristic equations for specific problems | 45 |
The initial value problem Domain of dependence Range of influence | 48 |
Propagation of discontinuities along characteristic lines | 53 |
Characteristic lines as separation lines between regions of different types | 55 |
Characteristic initial values | 56 |
Supplementary remarks about boundary data | 57 |
Simple waves Flow adjacent to a region of constant state | 59 |
The hodograph transformation and its singularities Limiting lines | 62 |
Systems of more than two differential equations | 70 |
Appendix | 75 |
OneDimensional Flow | 79 |
A Continuous Flow | 80 |
Domain of dependence Range of influence | 82 |
More general initial data | 84 |
Riemann invariants | 87 |
Integration of the differential equations of isentropic flow | 88 |
Remarks on the Lagrangian representation | 91 |
B Rarefaction and Compression Waves | 92 |
Distortion of the wave form in a simple wave | 96 |
Particle paths and crosscharacteristics in a simple wave | 97 |
Rarefaction waves | 99 |
Escape speed Complete and incomplete rarefaction waves | 101 |
Centered rarefaction waves | 103 |
Explicit formulas for centered rarefaction waves | 104 |
Remark on simple waves in Lagrangian coordinates | 106 |
Compression waves | 107 |
Appendix to Part B | 110 |
Shocks | 116 |
Historical remarks on nonlinear flow | 118 |
Discontinuity surfaces | 119 |
Basic model of discontinuous motion Shock wave in a tube | 120 |
Jump conditions | 121 |
Shocks | 124 |
Contact discontinuities | 126 |
Models of shock motion | 129 |
Discussion of the mechanical shock conditions | 130 |
Sound waves as limits of weak shocks | 131 |
Shock conditions in Lagrangian representation | 132 |
Shock relations derived from the differential equations for viscous and heatconducting fluids | 134 |
Hugoniot relation Determinacy of the shock transition | 138 |
Basic properties of the shock transition | 141 |
Critical speed and Prandtls relation for polytropic gases | 146 |
Shock relations for polytropic gases | 148 |
The state on one side of the shock front in a polytropic gas determined by the state on the other side | 150 |
Reflection of a shock on a rigid wall | 152 |
Shock strength for polytropic gases | 154 |
Weak shocks Comparison with transitions through simple waves | 156 |
Nonuniform shocks | 160 |
Approximate treatment of nonuniform shocks of mod erate strength | 161 |
Decaying shock wave Nwave | 164 |
Formation of a shock | 168 |
Remarks on strong nonuniform shocks | 171 |
Interactions | 172 |
Survey of results | 176 |
Riemanns problem Shock tubes | 181 |
Method of analysis | 182 |
The process of penetration for rarefaction waves | 191 |
Interactions treated by the method of finite differences | 197 |
E Detonation and Deflagration Waves | 204 |
Assumptions | 207 |
Various types of processes | 208 |
The width of the reaction zone | 232 |
AppendixWave Propagation in ElasticPlastic Material | 235 |
The equations of motion | 238 |
Impact loading | 240 |
Stopping shocks | 243 |
Interactions and reflections | 245 |
Isentropic Irrotational Steady Plane Flow | 247 |
A Hodograph Method | 248 |
Special flows obtained by the hodograph method | 252 |
The role of limiting lines and transition lines | 256 |
B Characteristics and Simple Waves | 259 |
Characteristics in the hodograph plane as epicycloids | 262 |
Characteristics in the uvplane continued | 264 |
Simple waves | 266 |
Explicit formulas for streamlines and cross Mach lines in a simple wave | 271 |
Flow around a bend or corner Construction of simple waves | 273 |
Compression waves Flow in a concave bend and along a bump | 278 |
Supersonic flow in a twodimensional duct | 282 |
Interaction of simple waves Reflection on a rigid wall | 286 |
Jets | 289 |
Transition formulas for simple waves in a polytropic gas | 290 |
Oblique Shock Fronts | 294 |
Relations for oblique shock fronts Contact discon tinuities | 297 |
Shock relations in polytropic gases Prandtls formula | 302 |
General properties of shock transitions | 304 |
Shock polars for polytropic gases | 306 |
Discussion of oblique shocks by means of shock polars | 311 |
Flows in corners or past wedges | 317 |
InteractionsShock Reflection | 318 |
Regular reflection of a shock wave on a rigid wall | 319 |
Regular shock reflection continued | 327 |
Analytic treatment of regular reflection for polytropic gases | 329 |
Configurations of several confluent shocks Mach reflec tion | 331 |
Configurations of three shocks through one point | 332 |
Mach reflections | 334 |
Stationary direct and inverted Mach configuration | 335 |
Results of a quantitative discussion | 338 |
Pressure relations | 342 |
Modifications and generalizations | 343 |
Mathematical analysis of threeshock configuration | 346 |
Analysis by graphical methods | 347 |
E Approximate Treatments of Interactions Airfoil Flow | 350 |
Decaying shock front | 354 |
Flow around a bump or an airfoil | 356 |
Flow around an airfoil treated by perturbation methods linearization | 357 |
Alternative perturbation method for airfoils | 364 |
F Remarks about Boundary Value Problems for Steady Flow | 367 |
Flow in Nozzles and Jets | 377 |
De Laval nozzle | 380 |
Various types of nozzle flow | 383 |
Shock patterns in nozzles and jets | 387 |
Thrust | 392 |
Perfect nozzles | 394 |
Flow in Three Dimensions | 397 |
Supersonic flow along a slender body of revolution | 398 |
Resistance | 404 |
B Conical Flow | 406 |
The differential equations | 408 |
Conical shocks | 411 |
Other problems involving conical flow | 414 |
Spherical Waves | 416 |
Analytical formulations | 418 |
Progressing waves | 419 |
Special types of progressing waves | 421 |
Spherical quasisimple waves | 424 |
Spherical detonation and deflagration waves | 429 |
Other spherical quasisimple waves | 431 |
Reflected spherical shock fronts | 432 |
Concluding remarks | 433 |
| 435 | |
| 453 | |
| 455 | |
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Common terms and phrases
adiabatic ahead angle assume assumption boundary conditions burnt gas centered simple wave characteristic equations compression wave conservation conservation laws consider constant corresponding cusp deflagration density depends derivatives determined detonation differential equations discontinuity discussion duct entropy Figure function given heat conduction hence hodograph Hugoniot curve incident shock initial value initial value problem integral curve interaction intersection isentropic linear mathematical nozzle oblique shock obtain one-dimensional p₁ parameters Particle Paths piston polytropic gases possible prescribed pressure quantities rarefaction wave reflected shock region regular reflection Section shock conditions shock front shock line shock polar shock wave simple wave solution sonic sound speed stationary steady flow straight Mach lines stream function streamline subsonic supersonic flow surface theory time-like tion unburnt gas v)-plane wall zero zone μ² ρο ρυ
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