Rarefied Gas Dynamics

This book provides a coherent and easy accessible approach to rarefied gas dynamics. The author addresses young researchers and professionals who look for a consistent introduction as well as scientists and engineers who deal with molecular gas dynamics in their routine work. It is the first monograph which includes advanced topics like oscillatory flows and sound propagation in the rarefied gas flows. The reader is introduced to the main concepts and recent results of rarefied gas dynamics. No prior knowledge of gas dynamics is needed to develop a sound understanding of the underlying principles of thermodynamics, modern analytical and numerical methods of modelling. The author includes different theoretical and computational methodologies like model kinetic equations, the discrete velocity method, and Monte Carlo methods. It is beneficial to have all of them in one place, since these methods often have different domains of applicability. Most results are given without using mathematical derivations. Readers who want to study this field deeper can choose from a long list of references. Audience: Researchers, engineers and professionals who deal with rarefied gas dynamics in their routine work and need quickly to learn main concepts and results of this field. Advanced and PhD students in physics, mathematics, mechanical engineering and chemical engineering.

Auteur
Professsor Felix Sharipov graduated from the Moscow University of Physics and Technology, Faculty of Aerophysics and Space Research, and the Ural State Technical University. Since 1988 he is active in rarefied gas dynamics, since 1992 at the Federal University of Parana in Brazil. His research interests are numerical methods of rarefied gas dynamics applied to microfluidics, vacuum technology and aerothermodynamics. His group develops both probabilistic and deterministic approaches. Prof. Sharipov was organizer of numerous vacuum gas dynamics meetings, and published over a hundred journal articles, conference papers, and book chapters. He is a member of editorial board of international journal ?Vacuum?

Résumé

Aimed at both researchers and professionals who deal with this topic in their routine work, this introduction provides a coherent and rigorous access to the field including relevant methods for practical applications. No preceding knowledge of gas dynamics is assumed.

Contenu

Preface XIII

List of Symbols XV

List of Acronyms XXI

1 Molecular Description 1

1.1 Mechanics of Continuous Media and Its Restriction 1

1.2 Macroscopic State Variables 2

1.3 Dilute Gas 3

1.4 Intermolecular Potential 4

1.4.1 Definition of Potential 4

1.4.2 Hard Sphere Potential 4

1.4.3 Lennard-Jones Potential 5

1.4.4 Ab initio Potential 5

1.5 Deflection Angle 7

1.6 Differential Cross Section 8

1.7 Total Cross Section 9

1.8 Equivalent Free Path 10

1.9 Rarefaction Parameter and Knudsen Number 10

2 Velocity Distribution Function 13

2.1 Definition of Distribution Function 13

2.2 Moments of Distribution Function 15

2.3 Entropy and Its Flow Vector 18

2.4 Global Maxwellian 18

2.5 Local Maxwellian 20

3 Boltzmann Equation 23

3.1 Assumptions to Derive the Boltzmann Equation 23

3.2 General Form of the Boltzmann Equation 23

3.3 Conservation Laws 25

3.4 Entropy Production due to Intermolecular Collisions 27

3.5 Intermolecular Collisions Frequency 27

4 GasSurface Interaction 31

4.1 General form of Boundary Condition for Impermeable Surface 31

4.2 DiffuseSpecular Kernel 33

4.3 CercignaniLampis Kernel 34

4.4 Accommodation Coefficients 34

4.5 General form of Boundary Condition for Permeable Surface 37

4.6 Entropy Production due to GasSurface Interaction 38

5 Linear Theory 43

5.1 Small Perturbation of Equilibrium 43

5.2 Linearization Near Global Maxwellian 43

5.3 Linearization Near Local Maxwellian 46

5.4 Properties of the Linearized Collision Operator 47

5.5 Linearization of Boundary Condition 48

5.5.1 Impermeable Surface Being at Rest 48

5.5.2 Impermeable Moving Surface 49

5.5.3 Permeable Surface 50

5.5.4 Linearization Near Reference Maxwellian 50

5.5.5 Properties of Scattering Operator 50

5.5.6 Diffuse Scattering 51

5.6 Series Expansion 51

5.7 Reciprocal Relations 53

5.7.1 General Definitions 53

5.7.2 Kinetic Coefficients 54

6 Transport Coefficients 57

6.1 Constitutive Equations 57

6.2 Viscosity 58

6.3 Thermal Conductivity 59

6.4 Numerical Results 61

6.4.1 Hard Sphere Potential 61

6.4.2 Lennard-Jones Potential 61

6.4.3 Ab Initio Potential 62

7 Model Equations 65

7.1 BGK Equation 65

7.2 S-Model 67

7.3 Ellipsoidal Model 69

7.4 Dimensionless Form of Model Equations 70

8 Direct Simulation Monte Carlo Method 73

8.1 Main Ideas 73

8.2 Generation of Specific Distribution Function 74

8.3 Simulation of GasSurface Interaction 75

8.3.1 Kernel Decomposition 75

8.3.2 Diffuse Scattering 75

8.3.3 CercignaniLampis Scattering 76

8.4 Intermolecular Interaction 77

8.5 Calculation of Post-Collision Velocities 78

8.6 Calculation of Macroscopic Quantities 80

8.7 Statistical Scatter 81

9 Discrete Velocity Method 83

9.1 Main Ideas 83

9.2 Velocity Discretization 85

9.2.1 Onefold Integral 85

9.2.2 Twofold Integral 86

9.3 Iterative Procedure 87

9.4 Finite Difference Schemes 88

9.4.1 Main Principles 88

9.4.2 One-Dimensional Planar Flows 89

9.4.3 Two-Dimensional Planar Flows 90

9.4.4 One-Dimensional Axisymmetric Flows 93

9.4.5 Full Kinetic Equation 96

10 Velocity Slip and Temperature Jump Phenomena 97

10.1 General Remarks 97

10.2 Viscous Velocity Slip 98 <p&gt...