Thermal Non-Equilibrium in Heterogeneous Media (eBook)

Preface 8
Contents 9
Nomenclature 12
List of Figures 15
List of Tables 18
Overview 19
1 Heterogeneous Media 20
1.1 Introduction 20
1.2 Outline of This Book 24
References 25
2 Modeling of Thermal Non-equilibrium 27
2.1 Introduction 27
2.2 Governing Equations 28
2.2.1 Local Instantaneous Transport Equations 28
2.2.2 Double-Decomposition of Variables 29
2.2.3 Macroscopic Flow Equations 30
2.2.4 Macroscopic Energy Equations 32
2.2.5 Correlations for Interfacial Heat Transfer, h_{i} 35
2.3 Periodic Cell 36
2.3.1 Numerical Method and Boundary Conditions 36
2.3.2 Film Coefficient Hi 38
2.3.3 A Correlation for Interstitial Heat Transfer 39
2.4 Laminar Flow in a Channel 43
2.4.1 Non-dimensional Parameters 43
2.4.2 Numerical Method and Boundary Conditions 44
2.4.3 Local Nusselt Numbers 44
2.5 Turbulent Flow in a Channel 46
2.6 Chapter Summary 55
References 58
3 Moving Systems 60
3.1 Introduction 60
3.2 Macroscopic Laminar Model for Fixed and Moving Beds 60
3.2.1 Fixed Bed 61
3.2.2 Moving Bed 61
3.3 Turbulence Model for Flow Equations 62
3.3.1 Fixed Bed 63
3.3.2 Moving Bed 64
3.4 Thermal Transport 65
3.4.1 Two-Energy Equation Model 65
3.4.2 Interfacial Heat Transfer Coefficient 67
3.4.3 Wall Treatment and Boundary Conditions 68
3.5 Results for Laminar Parallel Flow 69
3.5.1 Effect of Reynolds Number, {/varvec {Re}_{ D}} 69
3.5.2 Effect of Slip Ratio, {/varvec {u}_{ s} /{u}_{ D}} 73
3.5.3 Effect of Darcy Number, {/varvec {Da}} 73
3.5.4 Effect of Porosity, {/varvec { /phi}} 73
3.5.5 Effect of Thermal Capacity Ratio {/varvec (/rho c_{p} )_{s} /(/rho c_{p} )_{f}} 74
3.5.6 Effect of Thermal Conductivity Ratio {/varvec k_{s} /k_{f}} 75
3.6 Results for Turbulent Parallel Flow 77
3.6.1 Effect of Reynolds Number, {/varvec Re_{D}} 77
3.6.2 Effect of Slip Ratio, {/varvec {u}_{ s} /{u}_{ D}} 77
3.6.3 Effect of Darcy Number, {/varvec Da} 80
3.6.4 Effect of Porosity, {/varvec /phi} 81
3.7 Chapter Summary 83
References 84
4 Combustion Systems 86
4.1 Introduction 86
4.2 Porous Burners 86
4.3 Macroscopic Flow 87
4.3.1 Macroscopic Continuity Equation 87
4.3.2 Macroscopic Momentum Equation 88
4.3.3 Turbulence Modeling 88
4.4 Heat Transfer 89
4.4.1 Local Thermal Non-equilibrium Model (LTNE) 89
4.5 Combustion Modeling 91
4.5.1 Mass Transport for Fuel 91
4.5.2 Chemical Reaction 92
4.6 Heat Release 93
4.6.1 Double-Decomposition of Variables 93
4.6.2 Macroscopic Fuel Consumption 94
4.7 Numerical Results 98
4.7.1 Simulation Details and Boundary Conditions 98
4.7.2 Grid Independence Study 98
4.7.3 One Dimensional Combustor 98
4.8 Chapter Summary 102
References 104
5 Double Diffusion 106
5.1 Introduction 106
5.2 Mass Transport 107
5.3 Averaging Operators 109
5.4 Time Averaging for Buoyant Flows 110
5.5 Volume Averaging 112
5.5.1 Mean Continuity Equation 112
5.5.2 Mean Momentum Transport 112
5.5.3 Macroscopic Turbulence Field 113
5.6 Two-Energy Equation Model (2EEM) 113
5.6.1 Interfacial Heat Transfer, /bf{h_{i}} 115
5.7 Mass Transport 116
5.8 Double-Diffusion Effects with a 2EEM Model 117
5.8.1 Mean Flow 117
5.8.2 Turbulent Field 118
5.9 Chapter Summary 121
References 121
6 Final Remarks 123
References 123