Non-Equilibrium Reacting Gas Flows (eBook)

Kinetic Theory of Transport and Relaxation Processes

Ekaterina Nagnibeda, Elena Kustova (Autoren)

eBook Download: PDF

2009 | 2009
XIV, 252 Seiten
Springer Berlin (Verlag)
978-3-642-01390-4 (ISBN)

Infos

In the present monograph, we develop the kinetic theory of transport phenomena and relaxation processes in the flows of reacting gas mixtures and discuss its applications to strongly non-equilibrium conditions. The main attention is focused on the influence of non-equilibrium kinetics on gas dynamics and transport properties. Closed systems of fluid dynamic equations are derived from the kinetic equations in different approaches. We consider the most accurate approach taking into account the state-to-state kinetics in a flow, as well as simplified multi-temperature and one-temperature models based on quasi-stationary distributions. Within these approaches, we propose the algorithms for the calculation of the transport coefficients and rate coefficients of chemical reactions and energy exchanges in non-equilibrium flows; the developed techniques are based on the fundamental kinetic theory principles. The theory is applied to the modeling of non-equilibrium flows behind strong shock waves, in the boundary layer, and in nozzles. The comparison of the results obtained within the frame of different approaches is presented, the advantages of the new state-to-state kinetic model are discussed, and the limits of validity for simplified models are established.

The book can be interesting for scientists and graduate students working on physical gas dynamics, aerothermodynamics, heat and mass transfer, non-equilibrium physical-chemical kinetics, and kinetic theory of gases.

Inhalt

Preface 6
Contents 9
Introduction 12
Kinetic Equations and Method of Small Parameter 17
Energy of Internal Degrees of Freedom: Macroscopic Gas Parameters 17
{/it Rotational and Vibrational Energy of Molecules} 17
{/it Distribution Function and Macroscopic Parameters} 20
{/it Specific Heats} 23
Kinetic Equations for Distribution Functions in Reacting Gas Mixtures 27
Small Parameters in Kinetic Equations and the Method of Different Scales 30
Modification of the Chapman–Enskog Method for Gases with Rapid and Slow Processes 36
State-to-State Approach 44
Zero-Order Distribution Function 44
Closed Set of Governing Equations 48
First-Order Distribution Function 50
Transport Terms 53
Production Terms 56
Multi-Temperature Models in Transport and Relaxation Theory 63
Generalized Treanor Distribution for a Gas Mixture 64
Macroscopic Parameters and Specific Heats 70
Governing Equations in the Multi-Temperature Approach 73
First-Order Distribution Function 75
First-Order Transport Terms 80
Production Terms 83
Strongly Non-equilibrium Quasi-stationary Distribution in a Pure Gas 88
{/it Zero-Order Distribution Function} 88
{/it Equations for Macroscopic Parameters} 94
{/it Vibrational Relaxation Time and Specific Heats} 95
Transport Processes in a Gas with Strong Vibrational Excitation 98
{/it First-Order Distribution Function} 98
{/it Transport Terms} 101
One-Temperature Model for Chemically Non-equilibrium Gas Mixtures 104
Zero-Order Distribution, Macroscopic Parameters and Set of Governing Equations 104
First-Order Distribution Function: Transport and Production Terms 109
Transition to Chemical Equilibrium Regime 113
Algorithms for the Calculation of Transport Coefficients 117
State-to-State Approach 117
{/it Expansions in the Sonine and Waldmann-Trübenbacher Polynomials} 118
{/it Systems of Equations for the Expansion Coefficients} 121
Quasi-stationary Approaches 127
{/it Multi-Temperature Approach} 127
{/it One-Temperature Approach} 134
Bracket Integrals 136
{/it State-to-State Approach} 137
{/it Multi-Temperature Approach} 143
{/it One-Temperature Approach} 148
$/Omega$-Integrals and Relaxation Times 150
{/it $/Omega$-Integrals} 151
{/it Relaxation Times} 157
Simplified Formulas for Transport Coefficients in the State-to-State Approach 158
Transition Between Transport Terms in Different Approaches 164
A Single-Component Gas: The Generalized Eucken Formula 168
Reaction Rate Coefficients 176
State-to-State Approach: Zero-Order Chapman–Enskog Approximation 177
{/it Rate Coefficients for Vibrational Energy Transitions} 178
{/it Dissociation Rate Coefficients} 182
Quasi-stationary Approaches 187
First-Order Approximation of the Chapman–Enskog Method 193
Non-Equilibrium Kinetics and Transport Processes Behind Shock Waves 196
State-to-State Kinetics in Binary Mixtures with Dissociation and Recombination 196
Diffusion and Heat Transfer 201
Vibrational and Chemical Kinetics and Transport Processes in Air Mixtures 203
Heat Transfer and Diffusion in a Non-equilibrium Boundary Layer 208
Equations for a Non-equilibrium Boundary Layer in the State-to-State Approach 209
A Flow of N_{2}/N Mixture Near the Non-catalytic Surface 213
A Flow of O_{2}/O Mixture Near the Catalytic Surfaces 217
Non-equilibrium Kinetics and Its Influence on the Parameters of Nozzle Flows 226
Flow Equations, Non-equilibrium Distributions and Macroscopic Parameters 226
The Influence of Non-equilibrium Kinetics on Gas Dynamics and Transport Processes 233
Conclusion 239
References 241
Index 254

Produkt-Details

• Erscheint lt. Verlag: 9.7.2009
• Reihe/Serie: Heat and Mass Transfer
• Reihe/Serie: Heat and Mass Transfer
• Zusatzinfo: XIV, 252 p.
• Verlagsort: Berlin
• Sprache: englisch
• Themenwelt: Naturwissenschaften ► Physik / Astronomie
• Themenwelt: Technik ► Maschinenbau
• Schlagworte: chemical reactions • Diffusion • Distribution • fluid- and aerodynamics • gas mixture • heat transfer • multi temperature distribution • Shock waves • state-to-state kinetic model • thermodynamics
• ISBN-10: 3-642-01390-2 / 3642013902
• ISBN-13: 978-3-642-01390-4 / 9783642013904