Title Page
Abstract
Contents
NOMENCLATURE 9
CHAPTER 1. INTRODUCTION 22
1.1. General introduction 22
1.2. Motivation and necessity of research 25
1.3. Objectives 28
1.4. Study outline 30
CHAPTER 2. BACKGROUND CONCEPTS 32
2.1. Surface jet flow behind BFS 32
2.2. Submerged wall jet flow behind sluice gate 34
CHAPTER 3. LITERATURE REVIEW 37
3.1. Surface jet flow behind BFS 37
3.1.1. Flow and turbulence structure in separation zone 37
3.1.2. Flow-sediment interaction in separation zone 39
3.1.3. Effect of BFS angle on reattachment length 40
3.2. Local scour by horizontal wall jet flow 43
CHAPTER 4. METHODOLOGY 47
4.1. Numerical simulation using OpenFOAM 48
4.2. Large Eddy Simulation (LES) 50
4.3. Coupling of LES and DEM 52
4.4. Incorporation of air phase into LES-DEM model 56
4.5. Measurement of reattachment length 58
4.6. Visualization of vortex structure 58
4.7. Bedload transport rate 59
4.8. Quadrant analysis for flow structure 60
4.9. Quadrant analysis for bedload transport 61
CHAPTER 5. Computational Setup and Application 62
5.1. Surface jet flow behind various inclined BFSs 62
5.2. Submerged wall jet flow with air injection behind sluice gate 66
CHAPTER 6. MODEL VALIDATION 72
6.1. Validation against surface jet flow over BFS 72
6.1.1. Validation of hydrodynamic model 72
6.1.2. Validation of LES-DEM coupling model 82
6.2. Validation against submerged wall jet flow 86
6.2.1. Validation of numerical model against mean velocity 87
6.2.2. Validation of numerical model against scouring dimensions 88
CHAPTER 7. RESULTS 92
7.1. Surface jet flow behind various inclined BFSs 92
7.1.1. Near-bed flow structure 92
7.1.2. Sediment flux 104
7.1.3. Quadrant analysis for flow structure 107
7.1.4. Quadrant analysis for bedload transport 111
7.2. Submerged wall jet flow with air injection behind sluice gate 116
7.2.1. Bed profile and sediment flux 116
7.2.2. Flow and turbulence structures 133
7.2.3. Quadrant analysis for bedload transport 159
CHAPTER 8. CONCLUSIONS 163
REFERENCES 171
Appendix 193
초록 198
Table 1. Previous studies on flow and sediment behaviors by separation flow in surface jet flow. 42
Table 2. Previous studies on flow characteristics and scouring by horizontal wall jet flow. 46
Table 3. Configuration of the numerical simulation for surface jet flow. 66
Table 4. Length scale in the numerical domain. 68
Table 5. Configuration of the numerical simulation for submerged wall jet flow. 71
Table 6. R² and RMS values between the simulation results and experimental data from Ruck and Makiola (1993) and Nakagawa and Nezu (1987). 81
Table 7. Comparison of percentage of time occupied by each turbulence event between the observation data by Nelson et al. (1995) and simulation results. 85
Table 8. Comparison of percentage of each turbulence event weighted by bedload transport rate between the observation data by Nelson et al. (1995) and simulation results. 85
Table 9. Experimental configuration from Chatterjee et al. (1994). 87
Table 10. Comparison of the scour hole's dimensions between the simulation and empirical formula from Chatterjee et al. (1994). 90
Table 11. Near-bed flow information and bedload transport rate. 104
Table 12. Ratio of time (in percentage) by each turbulence event in various BFS angles. 108
Table 13. Ratio (in percentage) of bedload transport rate during each turbulence event in various BFS angles. 115
Table 14. Dimensions of scour hole with and without air injection in the central vertical plane. 132
Table 15. Maximum mean velocity and turbulence intensity in y axis at x = 0 in the central vertical plane. 157
Table 16. Near-bed mean velocity and turbulence intensity at x = 0 and y = 5 mm in the central vertical plane. 158
Table 17. Ratio (in percentage) of bedload transport rate during each turbulence event with and without air injection in wall jet flow. 162
Figure 1. Flow chart of the research procedure 31
Figure 2. Schematic diagram of different flow regimes over BFS suggested by Wu and Rajaratnam (1998). 33
Figure 3. Schematic diagram of submerged wall jet flow behind sluice gate. 35
Figure 4. Boundary layer of submerged wall jet flow, readapted from Dey et al. (2010). 36
Figure 5. Conceptual model of a vortex tube formation behind dune proposed by Müller and Gyr (1986). 38
Figure 6. Coupling algorithm between LES and DEM 55
Figure 7. Schematic illustration of the fluids (water and air) and sediment based on the volume fraction in a numerical cell. 57
Figure 8. Schematic diagram of the computational domain with various inclined BFSs (diagram is not to the scale). 65
Figure 9. Schematic diagram of the computational domain for wall jet flow behind a sluice gate (diagram is not to the scale) 70
Figure 10. Streamwise velocity (a, b, c) and turbulence intensity (d, e, f) profiles behind the step at Re=15000, α = 10°, 30°, 90°, and ER=1. 48 (Blue line is the... 75
Figure 11. Streamwise velocity (a, b, c) and turbulence intensity (d, e, f) profiles behind the step at Re=47000, α = 10°, 30°, 90°, and ER=1. 48 (Blue line is the... 76
Figure 12. Streamwise velocity (a, b, c, d, e) profiles behind the step at Re=64000, α = 10°, 15°, 25°, 30°, 90°, and ER=1. 48 (Blue line is the location of reattachment... 77
Figure 13. Streamwise velocity (a, b, c, d, e, f) profiles behind the step at Re=15000, α = 10°, 20°, 25°, 30°, 45°, 90°, and ER=2 (Blue line is the location of... 78
Figure 14. Streamwise velocity (a, b, c, d, e) profiles behind the step at Re=47000, α = 10°, 25°, 30°, 45°, 90°, and ER=2 (Blue line is the location of reattachment... 79
Figure 15. Streamwise velocity (a, b, c, d) profiles behind the step at Re=64000, α = 10°, 25°, 45°, 90°, and ER=2 (Blue line is the location of reattachment point in... 80
Figure 16. Streamwise velocity (a), streamwise turbulence intensity (b), and vertical turbulence intensity (c) profiles behind the step (Blue line is the location of... 81
Figure 17. Near-bed streamwise velocity (a), streamwise turbulence intensity (b), and vertical turbulence intensity (c) profiles behind the step (Dotted... 84
Figure 18. Mean bedload transport rate in the streamwise direction behind the BFS(Circle=simulation data; Circle (filled)=observation by Nelson et al. (1995)). 85
Figure 19. Experimental setup of Chatterjee et al. (1994). 86
Figure 20. Comparison of vertical distribution of normalized streamwise velocity between simulation and experiment 88
Figure 21. Relationships of dimensions of scour hole and scour volume from Chatterjee et al. (1994). Red dots represent the experimental sets. 89
Figure 22. Scour hole's dimensions formed by simulation and estimated by Chatterjee et al. (1994). 91
Figure 23. Mean streamwise velocity for CaseN10 (a), CaseN20 (b), CaseN30 (c), and CaseN90 (d). Solid line represents the reattachment point. 94
Figure 24. Streamwise turbulence intensity for CaseN10 (a), CaseN20 (b), CaseN30 (c), and CaseN90 (d). Solid line represents the reattachment point. 95
Figure 25. Vertical turbulence intensity for CaseN10 (a), CaseN20 (b), CaseN30 (c), and CaseN90 (d). Solid line represents the reattachment point. 96
Figure 26. Separation zone with time-averaged velocity vectors in the central section of the z-axis for CaseN10 (a), CaseN20 (b), CaseN30 (c), and CaseN90 (d). 97
Figure 27. Streamwise velocity profiles behind the step measured in the central vertical plane for CaseN10 (a), CaseN20 (b), CaseN30 (c), and CaseN90 (d). Blue... 98
Figure 28. Streamwise turbulence intensity profiles behind the step measured in the central vertical plane for CaseN10 (a), CaseN20 (b), CaseN30 (c), and CaseN90 (d).... 99
Figure 29. Vertical turbulence intensity profiles behind the step measured in the central vertical plane for CaseN10 (a), CaseN20 (b), CaseN30 (c), and CaseN90 (d).... 101
Figure 30. Coherent vortex structures visualized by Q-criterion (isosurface: Q=600) for CaseN10 (a), CaseN20 (b), CaseN30 (c), and CaseN90 (d) at different instants. 103
Figure 31. Mean bedload transport rate downstream of the various inclined BFSs (the dash lines show the locations of reattachment points associated with step angles). 105
Figure 32. Joint frequency distributions of u' and v' measured at x = xb (a), xb + 5H (b), and xb + 10H (c) for CaseN10, and x = xr (d), xr + 5H (e), xr + 10H (f) for CaseN20.[이미지참조] 109
Figure 33. Joint frequency distributions of u' and v' measured at x = xr -2. 5H (a, d), xr (b, e), and xr + 5H (c, f) for CaseN30 (a-c) and CaseN90 (d-f).[이미지참조] 110
Figure 34. Joint frequency distributions of u' and v' weighted by qx measured at x = xb (a), xb + 5H (b), xb + 10H (c) for CaseN10, and x = xr (d), xr + 5H (e), xr + 10H (f) for CaseN20.[이미지참조] 113
Figure 35. Joint frequency distributions of u' and v' weighted by qx measured at x = xr -2. 5H (a, d), xr (b, e), and xr + 5H (c, f) for CaseN30 (a-c) and CaseN90 (d-f).[이미지참조] 114
Figure 36. Bedform changes over time in CaseNA. 118
Figure 37. Bedform changes over time in CaseRA2Q025. 119
Figure 38. Bedform changes over time in CaseRA2Q05. 120
Figure 39. Bedform changes over time in CaseRA2Q1. 121
Figure 40. Bedform changes over time in CaseRA20Q025. 122
Figure 41. Bedform changes over time in CaseRA20Q05. 123
Figure 42. Bedform changes over time in CaseRA20Q1. 124
Figure 43. Bedform changes over time in CaseRA40Q025. 125
Figure 44. Bedform changes over time in CaseRA40Q05. 126
Figure 45. Bedform changes over time in CaseRA40Q1. 127
Figure 46. Comparison of bedload transport rate at various time intervals for CaseNA and CaseRA2Q025-Q1. 129
Figure 47. Comparison of bedload transport rate at various time intervals for CaseNA and CaseRA20Q025-Q1. 130
Figure 48. Comparison of bedload transport rate at various time intervals for CaseNA and CaseRA40Q025-Q1. 131
Figure 49. Comparison of mean velocity (a) and turbulent kinetic energy (b) contours in the central vertical plane (z/W=0.5) for CaseNA. 134
Figure 50. Comparison of mean velocity (a) and turbulent kinetic energy (b) contours in the central vertical plane (z/W=0.5) for CaseNA. 137
Figure 51. Comparison of mean velocity (a, b) and turbulence intensity (c, d) contours in the central vertical plane (z/W=0.5) for CaseRA2Q025. 138
Figure 52. Comparison of mean velocity (a, b) and turbulence intensity (c, d) contours in the central vertical plane (z/W=0.5) for CaseRA2Q05. 139
Figure 53. Comparison of mean velocity (a, b) and turbulence intensity (c, d) contours in the central vertical plane (z/W=0.5) for CaseRA2Q1. 140
Figure 54. Comparison of mean velocity (a, b) and turbulence intensity (c, d) contours in the central vertical plane (z/W=0.5) for CaseRA20Q025. 141
Figure 55. Comparison of mean velocity (a, b) and turbulence intensity (c, d) contours in the central vertical plane (z/W=0.5) for CaseRA20Q05. 142
Figure 56. Comparison of mean velocity (a, b) and turbulence intensity (c, d) contours in the central vertical plane (z/W=0.5) for CaseRA20Q1. 143
Figure 57. Comparison of mean velocity (a, b) and turbulence intensity (c, d) contours in the central vertical plane (z/W=0.5) for CaseRA40Q025. 144
Figure 58. Comparison of mean velocity (a, b) and turbulence intensity (c, d) contours in the central vertical plane (z/W=0.5) for CaseRA40Q05. 145
Figure 59. Comparison of mean velocity (a, b) and turbulence intensity (c, d) contours in the central vertical plane (z/W=0.5) for CaseRA40Q1. 146
Figure 60. Comparison of mean velocity (a, b) and turbulence intensity (c, d) profiles in the central vertical plane (z/W=0.5) between CaseNA and CaseRA2Q025-Q1. 149
Figure 61. Comparison of mean velocity (a, b) and turbulence intensity (c, d) profiles in the central vertical plane (z/W=0.5) between CaseNA and CaseRA20Q025-Q1. 150
Figure 62. Comparison of mean velocity (a, b) and turbulence intensity (c, d) profiles in the central vertical plane (z/W=0.5) between CaseNA and CaseRA40Q025-Q1. 151
Figure 63. Relation between the maximum scour depth and near-bed mean velocity (a), turbulence intensity (b), maximum mean velocity (c), and turbulence intensity (d) in the central vertical plane at x = 0 between CaseNA and CaseRA2. 152
Figure 64. Relation between the maximum scour depth and near-bed mean velocity (a), turbulence intensity (b), maximum mean velocity (c), and turbulence intensity (d) in the central vertical plane at x = 0 between CaseNA and CaseRA20. 153
Figure 65. Relation between the maximum scour depth and near-bed mean velocity (a), turbulence intensity (b), maximum mean velocity (c), and turbulence intensity (d) in the central vertical plane at x = 0 between CaseNA and CaseRA40. 154
Figure 66. Vortex structures visualized by Q-criterion (isosurface: Q=300) at a time instant for CaseNA (a) and CaseRA20Q1 (b). 156
Figure 67. Joint frequency distributions of u' and v' weighted by qx measured at x = 0. 015 m (a, d), 0. 075 m (b, e), and 0. 175 m (c, f) for CaseNA (a, b, c) and CaseRA20Q1 (d, e, f). 161
Figure 68. Schematic diagram of backward-facing step flow, re-adapted from Sodja, (2007). 197