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IIT Kharagpur
CONTENTS
Title Page i
Certificate of Approval iii
Certificate v
Acknowledgements vii
Declaration ix
List of Symbols xi
Abstract xiii
Contents xv
CHAPTER 1 INTRODUCTION 1
CHAPTER 2 LITERATURE REVIEW 11
CHAPTER 3 DEVELOPMENT OF INCOMPRESSIBLE NAVIER- STOKES SOLVER
45
3.1 Introduction 45
3.2 Governing Equations 46
3.3 Unstructured Grid Based Finite Volume Discretization of Governing Equations on Triangular Cells
47 3.4 Application of Consistent Flux Reconstruction Scheme
on Unstructured Grid
51
1.1 Overview 1
1.2 Motivation of the Present Work 5
1.3 Objectives and Scope of the Present Thesis 5
1.4 Organisation of the Thesis 6
2.1 Introduction 11
2.2 Potential Flow Models 11
2.3 Incompressible Navier-Stokes Solvers 13
2.3.1 Formulation 13
2.3.2 Discretization schemes 14
2.3.3 Variable location in a cell 15
2.3.4 Pressure calculation techniques 17
2.3.5 Differencing schemes 21
2.3.6 Solution algorithm and stability criteria 22 2.3.7 Pressure velocity coupling algorithm 23
2.3.8 Flux reconstruction schemes 25
2.3.9 Structured and unstructured grid based method 27 2.4 Flow Past Various Two-Dimensional Geometries 30
2.5 Summary of Literature Review 42
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3.5 The pressure-Poisson Equation 55
3.6 Initial condition and Boundary Conditions 57 3.7 Numerical Stability, Convergence and Accuracy of the
Solver
58 3.8 Conservation of Kinetic Energy for the Solver 59 3.9 Terminology Used in Flow Calculations 60 3.10 Application and Validation of CFRUNS Solver 63
3.9.1 Flow past a bluff body 64
3.9.2 Flow past streamlined body 70
3.10 Conclusion 73
CHAPTER 4 FLOW PAST TWO AND THREE CIRCULAR CYLINDERS IN SIDE-BY-SIDE AND TANDEM ARRANGEMENT
75
4.1 Introduction 75
4.2 Brief Description of the Flow Problem 76
4.3 Results and Discussion 77
4.3.1 Flow past two side-by-side circular cylinders 77
4.3.1.1 Wake dynamics 86
4.3.1.2 Flow statistics 88
4.3.2 Flow past three side-by-side and tandem circular cylinders
90
4.4 Conclusions 100
CHAPTER 5 FLOW PAST TWO AND THREE CIRCULAR CYLINDERS IN STAGGERED ARRANGEMENTS
103
5.1 Introduction 104
5.2 Brief Description of the Flow Problem 100
5.3 Results and Discussion 105
5.3.1 Flow past two circular cylinders in staggered arrangement
105 5.3.2 Flow past three circular cylinders in staggered
arrangement
108 5.3.2.1 Staggered cylinder of equal diameter 108 5.3.2.2 Staggered cylinder of unequal diameter 117
5.4 Conclusions 123
CHAPTER 6 FLOW PAST SINGLE AND TANDEM CYLINDRICAL BODIES IN THE VICINITY OF A PLANE WALL
125
6.1 Introduction 125
6.2 Brief Description of the Flow Problem 126
6.3 Results and Discussion 127
6.3.1 Unconfined flow past a cylindrical body at zero angle of incidence
127 6.3.2 Flow past a square cylinder placed in the vicinity of
a plane wall
130 6.3.3 Flow past a circular cylinder in the vicinity of a
fixed wall
134
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6.3.4 Flow past two tandem circular cylinders in the vicinity of a plane wall
138
6.3.4.1 when g* = 0.5 139
6.3.4.2 when g* = 1.0 141
6.3.5 Flow statistics 144
6.3.5.1 Lift and drag coefficients 144
6.3.5.2 Strouhal number 146
6.3.5.3 Stagnation and separation points 147
6.4 Conclusions 148
CHAPTER 7 FLOW PAST AIRFOILS 151
7.1 Introduction 151
7.2 Geometrical Description of the Flow Problem 153
7.3 Results and Discussion 153
7.4 Conclusions 162
CHAPTER 8 CLOSURE 163
8.1 Concluding Remarks 163
8.2 Significant Contributions of the Thesis 167
8.3 Future Scope of the Research 168
REFERENCES 169
Appendix A 181
Appendix B 183
Appendix C 185
Appendix D 187
Appendix E 189
About the Author
