Rarefied Gas Dynamics: From Basic Concepts to Actual Calculations

by Carlo Cercignani

• ISBN13: 9780521659925
• ISBN10: 0521659922
• Format: Paperback
• Copyright: 2000-02-28
• Publisher: Cambridge University Press

Summary

This book presents 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, chemical reactions. A special chapter is devoted to evaporation and condensation phenomena. Each section is accompanied by problems which 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.

Table of Contents

Preface	xi
Introduction	xiii
Boltzmann Equation and Gas-Surface Interaction	1	(39)
Introduction	1	(1)
The Boltzmann Equation	2	(7)
Molecules Different from Hard Spheres	9	(2)
Collision Invariants	11	(4)
The Boltzmann Inequality and the Maxwell Distributions	15	(1)
The Macroscopic Balance Equations	16	(5)
The H-Theorem	21	(3)
Equilibrium States and Maxwellian Distributions	24	(2)
Model Equations	26	(3)
The Linearized Collision Operator	29	(1)
Boundary Conditions	30	(10)
References	38	(2)
Problems for a Gas in a Slab: General Aspects and Preliminary Example	40	(42)
Introduction	40	(3)
Couette Flow for Bounce-Back Boundary Conditions	43	(7)
Couette Flow at Small Mean Free Paths	50	(8)
Couette Flow at Large Mean Free Paths	58	(6)
Rarefaction Regimes	64	(3)
Moment Methods for Plane Couette Flow	67	(8)
Perturbations of Equilibria	75	(7)
References	80	(2)
Problems for a Gas in a Slab or a Half-Space: Discussion of Some Solutions	82	(47)
Use of Models	82	(3)
Transformation of Models into Pure Integral Equations	85	(2)
Variational Methods	87	(11)
Poiseuille Flow	98	(5)
Half-Space Problems	103	(10)
Numerical Methods	113	(4)
The Direct Simulation Monte Carlo Method	117	(2)
A Test Case: Couette Flow with Reverse Reflection	119	(3)
Accurate Numerical Solutions of the Linearized Boltzmann Equation	122	(7)
References	124	(5)
Propagation Phenomena and Shock Waves in Rarefied Gases	129	(33)
Introduction	129	(1)
Propagation of Discontinuities	130	(5)
Shear, Thermal, and Sound Waves	135	(6)
Shock Waves	141	(11)
Monte Carlo Simulation and the Problem of Shock Wave Structure	152	(4)
Concluding Remarks	156	(6)
References	157	(5)
Perturbation Methods in More than One Dimension	162	(42)
Introduction	162	(1)
Linearized Steady Problems	162	(6)
Linearized Solutions of Internal Problems	168	(2)
Linearized Solutions of External Problems	170	(3)
The Stokes Paradox in Kinetic Theory	173	(7)
The Continuum Limit	180	(9)
Free Molecular Flows	189	(3)
Nearly Free Molecular Flows	192	(2)
Expansion of a Gas into a Vacuum	194	(5)
Concluding Remarks	199	(5)
References	200	(4)
Polyatomic Gases, Mixtures, Chemistry, and Radiation	204	(26)
Introduction	204	(1)
Mixtures	205	(4)
Polyatomic Gases	209	(7)
The H-Theorem for Classical Polyatomic Molecules	216	(4)
Chemical Reactions	220	(5)
Ionization and Thermal Radiation	225	(1)
Concluding Remarks	226	(4)
References	227	(3)
Solving the Boltzmann Equation by Numerical Techniques	230	(43)
Introduction	230	(1)
The DSMC Method	231	(3)
Applications of the DSMC Method to Rarefied Flows	234	(7)
Vortices and Turbulence in a Rarefied Gas	241	(11)
Qualitative Differences between the Navier-Stokes and the Boltzmann Models	252	(4)
Discrete Velocity Models	256	(7)
Concluding Remarks	263	(10)
References	266	(7)
Evaporation and Condensation Phenomena	273	(40)
Introduction	273	(4)
The Knudsen Layer near an Evaporating Surface	277	(8)
The Knudsen Layer near a Condensing Surface	285	(5)
Influence of the Evaporation-Condensation Coefficient	290	(3)
Moderate Rates of Evaporation and Condensation	293	(6)
Effects due to the Presence of a Noncondensable Gas and to the Internal Degrees of Freedom	299	(5)
Evaporation from a Finite Area	304	(2)
Concluding Remarks	306	(7)
References	307	(6)
Index	313