Rarefied Gas Dynamics: From Basic Concepts to Actual Calculations

Rarefied Gas Dynamics: From Basic Concepts to Actual Calculations

by Carlo Cercignani
     
 

ISBN-10: 0521659922

ISBN-13: 9780521659925

Pub. Date: 02/28/2014

Publisher: Cambridge University Press

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…  See more details below

Overview

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.

Product Details

ISBN-13:
9780521659925
Publisher:
Cambridge University Press
Publication date:
02/28/2014
Series:
Cambridge Texts in Applied Mathematics Series, #21
Edition description:
New Edition
Pages:
338
Product dimensions:
5.98(w) x 8.98(h) x 0.83(d)

Table of Contents

Prefacexi
Introductionxiii
1Boltzmann Equation and Gas-Surface Interaction1
1.1Introduction1
1.2The Boltzmann Equation2
1.3Molecules Different from Hard Spheres9
1.4Collision Invariants11
1.5The Boltzmann Inequality and the Maxwell Distributions15
1.6The Macroscopic Balance Equations16
1.7The H-Theorem21
1.8Equilibrium States and Maxwellian Distributions24
1.9Model Equations26
1.10The Linearized Collision Operator29
1.11Boundary Conditions30
References38
2Problems for a Gas in a Slab: General Aspects and Preliminary Example40
2.1Introduction40
2.2Couette Flow for Bounce-Back Boundary Conditions43
2.3Couette Flow at Small Mean Free Paths50
2.4Couette Flow at Large Mean Free Paths58
2.5Rarefaction Regimes64
2.6Moment Methods for Plane Couette Flow67
2.7Perturbations of Equilibria75
References80
3Problems for a Gas in a Slab or a Half-Space: Discussion of Some Solutions82
3.1Use of Models82
3.2Transformation of Models into Pure Integral Equations85
3.3Variational Methods87
3.4Poiseuille Flow98
3.5Half-Space Problems103
3.6Numerical Methods113
3.7The Direct Simulation Monte Carlo Method117
3.8A Test Case: Couette Flow with Reverse Reflection119
3.9Accurate Numerical Solutions of the Linearized Boltzmann Equation122
References124
4Propagation Phenomena and Shock Waves in Rarefied Gases129
4.1Introduction129
4.2Propagation of Discontinuities130
4.3Shear, Thermal, and Sound Waves135
4.4Shock Waves141
4.5Monte Carlo Simulation and the Problem of Shock Wave Structure152
4.6Concluding Remarks156
References157
5Perturbation Methods in More than One Dimension162
5.1Introduction162
5.2Linearized Steady Problems162
5.3Linearized Solutions of Internal Problems168
5.4Linearized Solutions of External Problems170
5.5The Stokes Paradox in Kinetic Theory173
5.6The Continuum Limit180
5.7Free Molecular Flows189
5.8Nearly Free Molecular Flows192
5.9Expansion of a Gas into a Vacuum194
5.10Concluding Remarks199
References200
6Polyatomic Gases, Mixtures, Chemistry, and Radiation204
6.1Introduction204
6.2Mixtures205
6.3Polyatomic Gases209
6.4The H-Theorem for Classical Polyatomic Molecules216
6.5Chemical Reactions220
6.6Ionization and Thermal Radiation225
6.7Concluding Remarks226
References227
7Solving the Boltzmann Equation by Numerical Techniques230
7.1Introduction230
7.2The DSMC Method231
7.3Applications of the DSMC Method to Rarefied Flows234
7.4Vortices and Turbulence in a Rarefied Gas241
7.5Qualitative Differences between the Navier-Stokes and the Boltzmann Models252
7.6Discrete Velocity Models256
7.7Concluding Remarks263
References266
8Evaporation and Condensation Phenomena273
8.1Introduction273
8.2The Knudsen Layer near an Evaporating Surface277
8.3The Knudsen Layer near a Condensing Surface285
8.4Influence of the Evaporation-Condensation Coefficient290
8.5Moderate Rates of Evaporation and Condensation293
8.6Effects due to the Presence of a Noncondensable Gas and to the Internal Degrees of Freedom299
8.7Evaporation from a Finite Area304
8.8Concluding Remarks306
References307
Index313

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