INTRODUCTION TO PHYSICAL GAS DYNAMICS
CHAPTER I INTRODUCTORY KINETIC THEORY 1 Introduction, 1 2 Molecular Model, 2 3 Pressure, Temperature, and Internal Energy, 4 4 Mean Free Path, 12 5 Transport Phenomena, 15 6 Molecular Magnitudes, 23 CHAPTER II EQUILIBRIUM KINETIC THEORY 1 Introduction, 27 2 Velocity Distribution Function, 27 3 Equation of State for a Perfect Gas, 31 27 4 Maxwellian Distribution-Condition for Equilibrium, 35 5 Maxwellian Distribution-Final Results, 42 6 Collision Rate and Mean Free Path, 48 7 Chemical Equilibrium and the Law of Mass Action, 55 CHAPTER III CHEMICAL THERMODYNAMICS 1 Introduction, 59 2 Thermodynamic Systems and Kinds of Equilibrium, 60 3 Conservation of Mass, 63 4 Conservation of Energy; First Law, 65 5 The Second Law, 66 59 6 The Gibbs Equation for a Chemically Reacting System, 70 7 Entropy Production in Chemical Nonequilibrium; Condition for Reaction Equilibrium, 75 H Mixtures of Perfect Gases, 77 9 Law of Mass Action, 82 10 Heat of Reaction; van't Hoff's Equation, 83 CHAPTER IV STATISTICAL MECHANICS 1 Introduction, 86 2 Macroscopic and Microscopic Descriptions, 88 3 Quantum Energy States, 89 4 Enumeration of Microstates, 93 5 Distribution over Energy States-General Case, 101 6 Distribution over Energy States-Limiting Case, 104 86 7 Relation to Thermodynamics; Boltzmann's Relation, 112 8 Thermodynamic Properties, 117 9 Properties Associated with Translational Energy, 120 10 Contribution of Internal Structure, 126 11 Monatomic Gases, 129 12 Diatomic Gases, 132 13 Chemically Reacting Systems and Law of Mass Action, 139 14 Dissociation-Recombination of Symmetrical Diatomic Gas, 148 CHAPTER V EQUILIBRIUM GAS PROPERTIES 1 Introduction, 152 2 Symmetrical Diatomic Gas, 152 3 Ideal Dissociating Gas, 157 4 Ionization Equilibrium; The Saha Equation, 162 5 Mixture of Gases, 165 6 Properties of Equilibrium Air, 171 CHAPTER VI EQUILIBRIUM FLOW 1 Introduction, 178 2 Steady Shock Waves, 179 3 Steady Nozzle Flow, 183 4 Prandtl-Meyer Flow, 187 5 Frozen Flow, 191 152 178 CHAPTER VII VIBRATIONAL AND CHEMICAL RATE PROCESSES 197 1 Introduction, 197 2 Vibrational Rate Equation, 198 3 Entropy Production by Vibrational Nonequilibrium, 206 4 Chemical Rate Eq uati -General Considerations, 210 5 Energy Involved in Collisions, 216 6 Rate Equation for Dissociation-Recombination Reactions, 222 7 Rate Equation for Complex Mixtures, 228 8 High-Temperature Air, 229 9 Symmetrical Diatomic Gas; Ideal Dissociating Gas, 232 10 Generalized Rate Equation, 234 11 Local Relaxation Time; Small Departures from Equilibrium, 236 CHAPTER VIII FLOW WITH VIBRATIONAL OR CHEMICAL NONEQUILIBRIUM 1 Introduction, 245 2 Basic Nonlinear Equations, 246 3 Equilibrium and Frozen Flow, 251 4 Acoustic Equations, 254 5 Frozen and Equilibrium Speeds of Sound, 259 6 Propagation of Plane Acoustic Waves, 26I 245 7 Equation for Small Departures from a Uniform Free Stream, 269 8 Flow over a Wavy Wall, 274 9 Linearized Flow behind a Normal Shock Wave, 28I 10 Equations for Steady Quasi-One-Dimensional Flow, 286 I I Nonlinear Flow behind a Normal Shock Wave, 290 I 2 Fully Dispersed Shock Wave, 292 13 Nozzle Flow, 293 I 4 Method of Characteristics, 300 15 Supersonic Flow over a Concave Corner, 305 16 Supersonic Flow over a Convex Corner, 310 ('IIAPTER IX NONEQUILIBRIUM KINETIC THEORY 1 Introduction, 3I 6 2 The Conservation Equations of Gas Dynamics, 3I 7 3 The Boltzmann Equation, 328 4 Equilibrium and Entropy, 334 5 The Equations of Equilibrium Flow, 344 6 Moments of the Boltzmann Equation, 346 7 Dynamics of a Binary Collision, 348 X The Evaluation of Collision Cross-Sections, 356 9 The Evaluation of Colli on Integrals, 361 10 Gas Mixtures, 368 3I 6 CHAPTER X FLOW WITH TRANSLATIONAL NONEQUILIBRIUM 375 1 Introduction, 375 2 The Bhatnagar-Gross-Krook Collision Model, 376 3 The Chapman-Enskog Solution of the Krook Equation, 379 4 The Chapman-Enskog Solution of the Boltzmann Equation, 385 5 The Navier-Stokes Equations, 390 6 Expansion in Sonine Polynomials, 394 7 Transport Properties, 403 8 Bulk Viscosity, 407 9 The Structure of Shock Waves, 412 10 Linearized Couette Flow, 424 CHAPTER XI RADIATIVE TRANSFER IN GASES 1 Introduction, 436 2 Energy Transfer by Radiation, 437 3 The Equation of Radiative Transfer, 443 4 Radiative Equilibrium, 446 5 The Interaction of Radiation with Solid Surfaces, 450 6 Emission and Absorption of Radiation, 452 7 Quasi-Equilibrium Hypothesis, 458 436 8 Forma??· Solution of the Equation of Radiative Transfer, 462 9 Simplifications and Approximations, 465 CHAPTER XII FLOW WITH RADIATIVE NONEQUILIBRIUM 473 1 Introduction, 473 2 Basic Nonlinear Equations, 474 3 Asymptotic Situations; Grey-Gas Approximation, 476 4 One-Dimensional Equations, 479 5 Linearized One-Dimensional Equations, 485 6 Differential Approximation, 491 7 Acoustic Equation, 496 8 Propagation of Plane Acoustic Waves, 499 9 Equation for Small Departures from a Uniform Free Stream, 505 10 Linearized Flow through a Normal Shock Wave, 508 II Nonlinear Flow through a Normal Shock Wave, 515