Rarefied Gas Dynamics: From Basic Concepts to Actual Calculations

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The aim of this book is to present the concepts, methods, and applications of kinetic theory to rarefied gas dynamics. After introducing the basic tools, problems in plane geometry are treated using approximation techniques (perturbation and numerical methods). These same techniques are later used to deal with two- and three-dimensional problems. The models include not only monatomic but also polyatomic gases, mixtures, and chemical reactions. A special chapter is devoted to evaporation and condensation phenomena.

Each section is accompanied by problems that are mainly intended to demonstrate the use of the material in the text and to outline additional subjects, results, and equations. This will help ensure that the book can be used for a range of graduate courses in aerospace engineering or applied mathematics.

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Editorial Reviews

From the Publisher
"...Carlo Cercignani has produced a unique book that may be a harbinger of the future." AIAA Journal

"...for persons not too familiar with kinetic theory, it presents a readable and carefully written introduction to the basics of the theory." Mathematical Reviews

" Rarefield Gas Dynamics: From Basic Concept to Actual Calculations is a great comprehensive refernce that is certainly worth the low cost." Appl Mech Rev vol 54, no 5 Sept 01

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Product Details

Table of Contents

Preface xi
Introduction xiii
1 Boltzmann Equation and Gas-Surface Interaction 1
1.1 Introduction 1
1.2 The Boltzmann Equation 2
1.3 Molecules Different from Hard Spheres 9
1.4 Collision Invariants 11
1.5 The Boltzmann Inequality and the Maxwell Distributions 15
1.6 The Macroscopic Balance Equations 16
1.7 The H-Theorem 21
1.8 Equilibrium States and Maxwellian Distributions 24
1.9 Model Equations 26
1.10 The Linearized Collision Operator 29
1.11 Boundary Conditions 30
References 38
2 Problems for a Gas in a Slab: General Aspects and Preliminary Example 40
2.1 Introduction 40
2.2 Couette Flow for Bounce-Back Boundary Conditions 43
2.3 Couette Flow at Small Mean Free Paths 50
2.4 Couette Flow at Large Mean Free Paths 58
2.5 Rarefaction Regimes 64
2.6 Moment Methods for Plane Couette Flow 67
2.7 Perturbations of Equilibria 75
References 80
3 Problems for a Gas in a Slab or a Half-Space: Discussion of Some Solutions 82
3.1 Use of Models 82
3.2 Transformation of Models into Pure Integral Equations 85
3.3 Variational Methods 87
3.4 Poiseuille Flow 98
3.5 Half-Space Problems 103
3.6 Numerical Methods 113
3.7 The Direct Simulation Monte Carlo Method 117
3.8 A Test Case: Couette Flow with Reverse Reflection 119
3.9 Accurate Numerical Solutions of the Linearized Boltzmann Equation 122
References 124
4 Propagation Phenomena and Shock Waves in Rarefied Gases 129
4.1 Introduction 129
4.2 Propagation of Discontinuities 130
4.3 Shear, Thermal, and Sound Waves 135
4.4 Shock Waves 141
4.5 Monte Carlo Simulation and the Problem of Shock Wave Structure 152
4.6 Concluding Remarks 156
References 157
5 Perturbation Methods in More than One Dimension 162
5.1 Introduction 162
5.2 Linearized Steady Problems 162
5.3 Linearized Solutions of Internal Problems 168
5.4 Linearized Solutions of External Problems 170
5.5 The Stokes Paradox in Kinetic Theory 173
5.6 The Continuum Limit 180
5.7 Free Molecular Flows 189
5.8 Nearly Free Molecular Flows 192
5.9 Expansion of a Gas into a Vacuum 194
5.10 Concluding Remarks 199
References 200
6 Polyatomic Gases, Mixtures, Chemistry, and Radiation 204
6.1 Introduction 204
6.2 Mixtures 205
6.3 Polyatomic Gases 209
6.4 The H-Theorem for Classical Polyatomic Molecules 216
6.5 Chemical Reactions 220
6.6 Ionization and Thermal Radiation 225
6.7 Concluding Remarks 226
References 227
7 Solving the Boltzmann Equation by Numerical Techniques 230
7.1 Introduction 230
7.2 The DSMC Method 231
7.3 Applications of the DSMC Method to Rarefied Flows 234
7.4 Vortices and Turbulence in a Rarefied Gas 241
7.5 Qualitative Differences between the Navier-Stokes and the Boltzmann Models 252
7.6 Discrete Velocity Models 256
7.7 Concluding Remarks 263
References 266
8 Evaporation and Condensation Phenomena 273
8.1 Introduction 273
8.2 The Knudsen Layer near an Evaporating Surface 277
8.3 The Knudsen Layer near a Condensing Surface 285
8.4 Influence of the Evaporation-Condensation Coefficient 290
8.5 Moderate Rates of Evaporation and Condensation 293
8.6 Effects due to the Presence of a Noncondensable Gas and to the Internal Degrees of Freedom 299
8.7 Evaporation from a Finite Area 304
8.8 Concluding Remarks 306
References 307
Index 313
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