Tackling Turbulent Flows in Engineering (eBook)

Tackling Turbulent Flowsin Engineering 2
Preface 4
Contents 7
1 Basics of Fluid Mechanics and Convective Heat Transfer 11
Abstract 11
1.1…Fluid Properties 11
1.1.1 Viscosity 11
1.1.2 Density 12
1.1.3 Thermal Conductivity 12
1.1.4 Surface Tension 13
1.1.5 Speed of Sound and Mach Number 13
1.1.6 Newtonian and Non-Newtonian Fluids 13
1.2…Treatments and Visualization of Fluid 14
1.2.1 Eulerian and Lagrangian Approaches 14
1.2.2 Streamline, Streakline and Pathline 14
1.2.3 Integral and Differential Treatments 15
1.3…Vorticity and Irrotational Flow 16
1.4…Force, Strain and Stress 17
1.5…Fluid Acceleration 19
1.6…Mass Conservation 19
1.7…Conservation of Linear Momentum 20
1.8…Navier--Stokes Equations 21
1.9…Conservation of Energy 21
1.10…Boundary Conditions 22
1.10.1 No Slip and No Temperature Jump Conditions 22
1.10.2 Inlet and Outlet 23
1.10.3 Interface 23
1.11…Convective Heat Transfer 23
1.12…Examples 25
1.12.1 Flow Normal to an Infinite Circular Cylinder 25
1.12.2 Thermal Boundary-Layer Inside a Heated Circular Tube 27
1.13…Concluding Remarks 28
References 28
2 Fluid Turbulence 29
Abstract 29
2.1…Physical Description 29
2.2…Stability of Laminar Flows 32
2.3…Transition and Onset of Turbulence 32
2.4…Types of Turbulent Flows 33
2.5…Significance of Turbulent Flows and Heat Transfer 34
2.6…Turbulence in the Vicinity of a Solid Wall 35
2.7…Task of a Turbulence Model 38
2.8…Concluding Remarks 39
References 39
3 Characteristics of Some Important Turbulent Flows 40
Abstract 40
3.1…Boundary-Layer Flow Past a Flat Plate 40
3.2…Forced and Free Convections 43
3.3…Simple Free Shear Flows 44
3.4…Circular Pipe and Parallel Plates 47
3.5…Separated Flows 49
3.6…Concluding Remarks 51
References 51
4 Reynolds-Averaged Governing Equations and Closure Problem 52
Abstract 52
4.1…Types of Reynolds-Averaging 52
4.1.1 Time-Average 53
4.1.2 Spatial-Average 53
4.1.3 Ensemble-Average 53
4.2…RANS and Scalar Equations 55
4.3…Closure Problem 56
4.4…Concluding Remarks 57
References 57
5 Models Based on Boussinesq Approximation 58
Abstract 58
5.1…Boussinesq Approximation 58
5.2…Models Based on Boussinesq Approximation 59
5.2.1 Mixing Length Models 59
5.2.2 One Equation Model 62
5.2.2.0 Based on Equation for Turbulence Kinetic Energy 62
5.2.2.0 Based on Equation for Eddy Viscosity 64
5.2.3 Two Equation Models 65
5.3…Limitations of Boussinesq Approximation 65
5.4…Examples 65
5.5…Concluding Remarks 65
References 66
6 k-- epsilon and Other Two Equations Models 67
Abstract 67
6.1…Introduction 67
6.2…Standard k-- epsilon Model 67
6.3…Exact Transport Equations for k and epsilon 68
6.4…Modelled Transport Equations for k and epsilon 68
6.5…Features of the k-- epsilon Model 70
6.6…Boundary Conditions 70
6.7…Treatment of Wall 71
6.7.1 Wall Functions Approach 71
6.7.1.1 Standard Wall Functions 71
6.7.1.2 Non-Equilibrium Wall Functions 72
6.7.1.3 Enhanced Wall Treatments 73
6.7.2 Low Reynolds Number Models 73
6.8…Example: Oscillatory Boundary Layers 75
6.9…Some Modern Variants of k-- epsilon Model 75
6.9.1 RNG k-- epsilon Model 76
6.9.2 Realizable k-- epsilon Model 76
6.9.3 k-- omega Model 77
6.10…V2f Model 78
6.11…Shear Stress Transport k-- omega Model 80
6.12…Other Two Equation Models 81
6.13…Modifications to k-- epsilon Model for Buoyancy Driven Flows 81
6.14…Other Modifications 84
6.15…Concluding Remarks 85
References 86
7 Reynolds-Stress and Scalar Flux Transport Model 88
Abstract 88
7.1…Introduction 88
7.2…Modeled Equations for Reynolds Stress Transport Model 88
7.2.1 Modeling of Turbulent Transport 89
7.2.2 Modeling of Pressure Strain 90
7.2.3 Modeling of Dissipation 90
7.3…Exact Transport Equation for Scalar Flux 91
7.4…Boundary Conditions 91
7.5…Treatment of Solid Walls 92
7.6…Features of Reynolds-Stress and Scalar Flux Transport Model 93
7.7…Algebraic Stress and Scalar Flux Models 93
7.8…Examples 94
7.9…Concluding Remarks 95
References 96
8 Direct Numerical Simulation and Large Eddy Simulation 97
Abstract 97
8.1…Introduction 97
8.2…Direct Numerical Simulation 98
8.3…Large Eddy Simulation 99
8.4…Subgrid Scale Models for LES 101
8.4.1 Smagorinsky SGS Model 101
8.4.2 Dynamic SGS Model 102
8.4.3 Scale Similarity SGS Model 103
8.5…DNS vis-à-vis LES 103
8.6…Detached Eddy Simulation and Hybrid Models 103
8.7…Treatment of Walls in LES 104
8.7.1 Wall Models That Use Equilibrium Laws 105
8.7.2 Velocity and Temperature TBLE Wall Model 106
8.8…Initial, Boundary Conditions and Duration of Computations 108
8.9…Concluding Remarks 109
References 110
9 Some Case Studies 111
Abstract 111
9.1…Heat Exchangers 111
9.2…Stirred Vessels 113
9.3…Flow in a Tundish Used in Steel Making 114
9.4…Turbulent Plume 115
9.5…LES and DES of Particle Deposition in a Human Throat 117
9.6…Unsteady Cross Ventilation in Buildings 118
9.7…Effect of Turbulent Prandtl Number on Film Cooling 119
9.8…Flow Over Rough Walls with Suction 120
9.9…Separated Convection Due to Backward Facing Step 120
9.10…Concluding Remarks 120
References 121
10 Conclusions and Recommendations 122
Abstract 122
10.1…Tackling Turbulence 122
10.2…CFD Issues 124
References 124
Index 125