Mechanics of Turbulence of Multicomponent Gases

Mechanics of Turbulence of Multicomponent Gases

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English

Description

Turbulence in multicomponent reacting gas mixtures is an important mechanism underlying numerous natural phenomena closely related to the study of our space environment. This book develops a new mathematical approach for modelling multicomponent gas turbulence that adequately describes the combined processes of dynamics and heat and mass transfer when chemical kinetics and turbulent mixing are equally important. The developed models include the evolutionary transfer equations for the single-point second correlation moments of turbulent fluctuations of thermohydrodynamical parameters. The phenomenological approach to the closure problem in hydrodynamic equations of mean motion at the level of the first order moments is based on the thermodynamics of irreversible processes and enables defining relationships in a more general form as compared to those conventionally deduced using the mixing path concept. Based on the developed approach, turbulent exchange factors for a planetary upper atmosphere are evaluated, and a turbulent model of a protoplanetary accretion gas-dust disk involving heat and mass transfer and coagulation is also considered.
As compared to previously published books on the problem of turbulence, this book deals, for the first time, with the complicated models of reacting gas mixtures. It is intended for graduate and postgraduate students in the fields of fluid gas dynamics, astrophysics, space physics, planetary sciences, and aeronomy, and especially for those dealing with computer modelling of the processes in such natural media. The book may also be of interest to specialists in the relevant fields of ecology, engineering, and material processing.

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Published 01 January 1983
Reads 11
EAN13 0306480921
License: All rights reserved
Language English

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FOREWORD
CONTENTS
P A R T 1 SEMIEMPIRICAL MODELING OF TURBULENT MULTICOMPONENT GASES
CHAPTER 1 TURBULENCE IN NATURAL MEDIA
1.1.TURBULENT MOTION OF A FLUID. GENERAL CONSIDERATIONS 1.1.1.GEOPHYSICAL TURBULENCE 1.1.2.SOME METHODS OF TURBULENCE SIMULATION 1.1.3.TURBULENT DIFFUSION 1.1.4.THE DYNAMIC NATURE OF TURBULENCE 1.2.TURBULENCE IN ATMOSPHERES OF PLANETS 1.2.1.PLANETARY ATMOSPHERES 1.2.2.DYNAMICS OF THE ATMOSPHERES OF EARTH AND VENUS 1.2.3.DYNAMICS OF THE MARTIAN ATMOSPHERE 1.2.4.GENERAL CIRCULATION OF THE ATMOSPHERES OF GIANT PLANETS 1.3.TURBULENCE IN THE UPPER ATMOSPHERE OF PLANETS 1.3.1.THE UPPER ATMOSPHERES OF THE TERRESTRIAL PLANETS 1.3.2.TURBULENT DIFFUSION IN THE ATMOSPHERE OF TERRESTRIAL PLANETS 1.3.3.THE UPPER ATMOSPHERES OF THE GIANT PLANETS 1.4.ASTROPHYSICAL AND COSMOGONIC MODELS 1.4.1.THE BIRTH AND EVOLUTION OF STARS 1.4.2.THE ROLE OF TURBULENCE IN THE EVOLUTION OF THE UNIVERSE 1.4.3.THE ORIGIN OF PLANETARY SYSTEMS 1.4.4.PLASMA TURBULENCE SUMMARY
CHAPTER 2 REGULAR MOTION OF GASEOUS MIXTURES INVOLVING PHYSICOCHEMICAL INTERACTIONS OF THE COMPONENTS
2.1.INITIAL BALANCE EQUATIONS AND CONSERVATION LAWS FOR REGULAR MOTIONS IN GASEOUS MIXTURES 2.1.1.DIFFERENTIAL EQUATIONS FOR MATERIAL BALANCE
VII
1
6
6 7 12 13 16 17 18
21 23
27 35
36
39 46 49 49
56 57 62 64
65
65 67
VIII
2.1.2.THE CONSERVATION EQUATION FOR THE MOMENTUM OF THE TOTAL CONTINUUM 2.1.3.DIVERSE ENERGY EQUATIONS FOR MULTICOMPONENT MEDIA 2.1.4.THE EQUATION OF STATE FOR A MIXTURE OF IDEAL GASES 2.1.5.THE COMPLETE SYSTEM OF HYDRODYNAMIC EQUATIONS FOR GAS MIXTURES 2.2. THE SECOND LAW OF THERMODYNAMICS: THE RATE OF ENTROPY ORIGIN IN GASEOUS MIXTURES 2.2.1.THE ONSAGER PRINCIPLE 2.2.2. THE EVOLUTIONARY ENTROPY TRANSFER EQUATION FOR MULTICOMPONENT GASEOUS MIXTURES 2.3. DEFINING RELATIONS FOR DIFFUSION AND HEAT FLUXES IN CONTINUOUS MULTICOMPONENT MIXTURES 2.3.1.LINEAR CONSTITUENT RELATIONS FOR MOLECULAR FLUXES OF DIFFUSION AND HEAT 2.3.2.THE STEFANMAXWELL RELATIONS FOR MULTICOMPONENT DIFFUSION 2.3.3. THE GENERALIZED STEFANMAXWELL RELATIONS BASED ON THE METHODS OF THERMODYNAMICS OF IRREVERSIBLE PROCESSES 2.3.4. THE TOTAL HEAT FLUX IN AN IDEAL MULTICOMPONENT MEDIA 2.3.5. FORMULAS FOR THE MULTICOMPONENT DIFFUSION COEFFICIENTS 2.3.6. MULTICOMPONENT DIFFUSION IN THE UPPER ATMOSPHERE SUMMARY
CHAPTER 3 TURBULENT MOTION OF MULTICOMPONENT MIXTURES WITH VARIABLE THERMOPHYSICAL PROPERTIES
3.1.MEAN MOTION OF A TURBULENT MULTICOMPONENT MIXTURE WITH VARIABLE DENSITY 3.1.1.CHOICE OF THE AVERAGING OPERATOR AVERAGED CONSERVATION LAWS FOR A TURBULIZED 3 . 1 . 2 . MIXTURE 3.2. TURBULENT FLOWS OF REACTING GASEOUS MIXTURES 3.2.1. THE AVERAGE THERMAL EQUATION OF STATE FOR IDEAL GAS MIXTURES 3.2.2. THE AVERAGED HYDRODYNAMIC EQUATIONS FOR A MIXTURE 3.2.3. THE AVERAGE CHEMICAL REACTION RATE IN TURBULENT FLOWS 3.3. DEFINING RELATIONS FOR TURBULENT FLOWS IN MULTICOMPONENT MEDIA
71
73
78
79
82 83
87
89
89
94
97
104
105
107 111
112
113 114
118 135
135
136
138
147
3.3.1. THE GRADIENT HYPOTHESIS 3.3.2. MODELING THE TURBULENT TRANSPORT COEFFICIENTS 3.3.3. THE DEFINITION OF CORRELATIONS INVOLVING DENSITY FLUCTUATIONS SUMMARY
CHAPTER 4 EVOLUTIONARY TRANSFER MODELS FOR THE SECOND CORRELATION MOMENTS
IX
147
155
158 165
166
4.1. THE GENERAL FORM OF THE TRANSFER EQUATION FOR PAIR CORRELATIONS IN A COMPRESSIBLE FLOW167 4.1.1. DIFFERENTIAL TRANSFER EQUATIONS FOR FLUCTUATIONS168 4.1.2.EVOLUTIONARY TRANSFER EQUATION: THE GENERAL FORM170 4.2.TURBULENT ENERGY BALANCE EQUATIONS FOR COMPRESSIBLE MULTICOMPONENT MEDIA172 4.2.1.THE EQUATIONS FOR THE TURBULENT STRESS TENSOR173 4.2.2.THE TRANSFER EQUATION FOR TURBULENT ENERGY IN COMPRESSIBLE MULTICOMPONENT MIXTURES179 4.3. TRANSFER EQUATIONS FOR THE PAIR CORRELATIONS OF MIXTURE ENTHALPY AND CONCENTRATIONS OF COMPONENTS184 4.3.1.THE TRANSFER EQUATION FOR TURBULENT HEAT FLUXES185 4.3.2. A PROGNOSTIC EQUATION FOR MEANSQUARE FLUCTUATIONS OF THE MIXTURE ENTHALPY187 4.3.3. CORRELATIONS INCLUDING FLUCTUATIONS OF THE SUBSTANCE PRODUCTION SOURCE189 4.3.4. THE TRANSFER EQUATION FOR TURBULENT DIFFUSION FLUXES191 4.3.5. THE EVOLUTIONARY TRANSFER EQUATION FOR CORRELATIONS WITH MIXTURE ENTHALPY AND COMPOSITION PULSATIONS192 4.3.6. THE TRANSFER EQUATION FOR CORRELATION MOMENTS OF MIXTURE COMPOSITION PULSATIONS194 4.3.7.THE TURBULENCE SCALE196 4.3.8.THE EVOLUTIONARY TRANSFER EQUATION FOR THE SCALAR DISSIPATION RATE198 4.3.9. ALGEBRAIC CLOSURE MODELS200 SUMMARY205
CHAPTER 5 THE STEFANMAXWELL RELATIONS AND THE HEAT FLUX FOR TURBULENT MULTICOMPONENT CONTINUUM MEDIA
206
X
5.1.THE BALANCE EQUATION FOR THE AVERAGED ENTROPY IN TURBULENT FLOWS OF GASEOUS MIXTURES 5.1.1.THE GENERAL FORM OF THE EVOLUTIONARY EQUATION FOR THE WEIGHTEDMEAN ENTROPY 5.1.2.THE BALANCE EQUATION FOR ENTROPY AND ENTROPY PRODUCTION FOR THE TURBULENT CHAOTIC SUBSYSTEM 5.1.3.THE BALANCE EQUATION FOR THE TOTAL TURBULIZED CONTINUUM ENTROPY 5.2. DEFINING RELATIONS FOR MULTICOMPONENT TURBULIZED MEDIA: THE THERMODYNAMIC APPROACH 5.2.1. LINEAR KINEMATIC CONSTITUTIVE RELATIONS 5.2.2.TURBULENT DIFFUSION AND HEAT FLUXES IN DEVELOPED TURBULENT FLOWS 5.3.THE STEFANMAXWELL RELATION AND THE HEAT FLUX FOR TURBULENT MIXTURES. 5.3.1.THE STEFANMAXWELL RELATION 5.3.2. THE HEAT FLUX IN TURBULENT MULTICOMPONENT MEDIA SUMMARY
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217 217
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223 223
227 228