Contents

Certificate of approval . . . i

Certificate . . . iii

Declaration . . . v

Curriculum vita . . . vii

Acknowledgements . . . ix

Contents . . . xi

List of figures . . . xvi

List of tables . . . xxiii

Nomenclature . . . xxiv

Abstract . . . xxxi

1 Introduction and Literature Review 1 1.1 Introduction to jet . . . 2

1.2 Applications of jets . . . 4

1.3 Literature review . . . 4

1.3.1 Literature related to turbulent offset jet and wall jet flows in the quiescent medium . . . 4

1.3.2 Literature related to turbulent offset jet and wall jet flows in an external stream . . . 8

1.3.3 Literature related to buoyancy-opposed jet flow . . . 10

1.3.4 Literature related to turbulent natural convection flow in a cavity . . . 12

1.4 Objectives of the present study . . . 15

2 Mathematical Formulation 17 2.1 Introduction . . . 17

xi

2.2 High-Reynolds number standard k − model and low-Reynolds

numberk−models . . . 17

2.3 Different turbulence models considered . . . 18

2.3.1 Standardk−model . . . 18

2.3.2 Launder and Sharma model . . . 18

2.3.3 Yang and Shih model . . . 19

2.3.4 Low-Reynolds numberk−ωmodel . . . 19

2.3.5 Shear stress transport model . . . 20

2.4 Governing equations for forced convection flow . . . 20

2.4.1 Turbulent transport equations for standardk−model, YS model and LS model . . . 21

2.4.2 Turbulent transport equations for SST model . . . 22

2.5 Governing equations for natural convection flow in a cavity . . . 24

2.5.1 Turbulent transport equations for YS model . . . 25

2.5.2 Turbulent transport equations for SST model . . . 26

2.5.3 Turbulent transport equations for the low-Reynolds num- berk−ωmodel . . . 27

2.5.4 Modeling of turbulent heat flux . . . 29

2.5.5 Buoyancy production term . . . 30

2.6 Governing equations for mixed convection flow . . . 30

2.6.1 YS model . . . 30

2.7 Numerical scheme and method of solution . . . 31

3 A Comparative Study of Flow Characteristics of Wall-bounded Jets Using Different Turbulence Models 33 3.1 Introduction . . . 33

3.2 Boundary conditions . . . 34

3.3 Results and discussion . . . 35

3.3.1 Reattachment length and skin friction coefficient . . . 35

3.3.2 Similarity solution . . . 38

3.3.3 Velocity profile(u⁺−y⁺) . . . 39

3.3.4 Variation of local maximum axial velocity(Umax) . . . 45

3.3.5 Jet half-width(Y0.5)variation alongX-direction . . . 48

3.3.6 Moffatt vortices . . . 52

3.3.7 Pressure distribution(P)in the domain . . . 53

3.3.8 Reynolds shear stress(^u_U^v2 0 )distribution . . . 53

3.3.9 Evolution of the momentum flux in the axial direction . . . . 60

3.4 Summary . . . 63

4 A Comparative Study of Heat Transfer Characteristics of Wall-bounded

Jets Using Different Turbulence Models 65

4.1 Introduction . . . 65

4.2 Boundary conditions . . . 66

4.3 Results and discussion . . . 66

4.3.1 Study of wall-bounded jets in the quiescent medium . . . . 66

4.3.1.1 Thermal characteristics of heated offset jet and wall jet flows over adiabatic surface . . . 66

4.3.1.2 Contour plots and temperature profile at various axial locations . . . 67

4.3.1.3 Decay of local maximum axial temperature and similarity solution for temperature . . . 74

4.3.1.4 Thermal characteristics of wall jet flow under isothermal and constant heat flux boundary con- ditions . . . 77

4.3.1.5 Temperature profile in the thermal sublayer and entire thermal boundary layer . . . 79

4.3.1.6 Similarity solution for temperature and axial vari- ation of local heat transfer coefficient . . . 79

4.3.1.7 Temperature profile in wall coordinates (T⁺−y⁺) . 83 4.3.2 Study of wall-bounded jet in the presence of an external moving stream . . . 85

4.3.2.1 Velocity similarity profile and velocity profile (u⁺− y⁺) . . . 85

4.3.2.2 Temperature profile and variation of local heat transfer coefficient . . . 88

4.4 Summary . . . 90

5 Effects of Freestream Motion on Flow and Heat Transfer Characteristics of Turbulent Offset Jet 91 5.1 Introduction . . . 91

5.2 Boundary conditions . . . 92

5.3 Results and discussion . . . 93

5.3.1 Reattachment length, streamlines and vector plots . . . 93

5.3.2 Velocity profile and the decay of local maximum axial velocity 94 5.3.3 Entrainment volume flow rate . . . 96

5.3.4 Velocity similarity profile and skin friction coefficient . . . . 98

5.3.5 Logarithmic velocity profile and velocity defect law profiles . 99 5.3.6 Axial variation ofY0.5 . . . 100

5.3.7 Thermal characteristics of heated jet submitted to adiabatic

wall . . . 103

5.3.8 Thermal characteristics of unheated jet submitted to the isothermal/isoflux surface . . . 106

5.4 Summary . . . 107

6 Investigation on the Relative Performance of Various Low-Reynolds Number Turbulence Models for Buoyancy-driven Flow in a Tall Cavity 109 6.1 Introduction . . . 109

6.2 Problem description . . . 112

6.3 Boundary conditions . . . 112

6.4 Results and discussion . . . 112

6.4.1 Non-dimensional velocity profile(v⁺−x⁺)and variation of vertical velocity . . . 112

6.4.2 Non-dimensional temperature profile(T⁺−x⁺)and varia- tion of temperature . . . 117

6.4.3 Variation of local Nusselt number and transition location . . 120

6.4.4 Wall shear stress . . . 122

6.4.5 Variation of turbulent kinetic energy and Reynolds stress . . 122

6.4.6 Shearing and swirling zone . . . 125

6.4.7 Flux Richardson number . . . 128

6.5 Summary . . . 130

7 Numerical Investigation of a Buoyancy-Opposed Wall Jet Flow 131 7.1 Introduction . . . 131

7.2 Geometrical details . . . 132

7.3 Boundary condition . . . 133

7.4 Results and discussion . . . 133

7.5 Summary . . . 151

8 Conclusion and Scope for Future Work 153 8.1 Scope for future study . . . 155 A Validation of the Computer Code and Grid Independence Study for

Chapter 3 157

B Grid independence study for Chapter 4 161

C Grid Independence Study for Chapter 5 163

D Grid Independence Study for Chapter 6 165

E Grid Independence Study for Chapter 7 169

Bibliography 171