Characteristics of flow in the wake region of a bluff vertical cylinder in the presence of waves,currents and combined wave current flows 4

Appendix F Time Series of CFD Calculated Wave Elevations Figure F1: Wave height monitors in the wave tank at (a) x=-0.84 m, (b) x=+0.84 m, (c) x=+9.24 m for combined waves and currents, C = 50 mm/s, downstream cylinder placed at x = ½ D, y=0.6D. Figure F2: Wave height monitors in the wave tank at (a) x=-0.84 m, (b) x=+0.84 m, (c) x=+9.24 m for combined waves and currents, C = 75 mm/s, downstream cylinder placed at x = ½ D, y=0.6D. Figure F3: Wave height monitors in the wave tank at (a) x=-0.84 m, (b) x=+0.84 m, (c) x=+9.24 m for combined waves and currents, C = 100 mm/s, downstream cylinder placed at x = ½ D, y=0.6D. Figure F4: Wave height monitors in the wave tank at (a) x=-0.84 m, (b) x=+0.84 m, (c) x=+9.24 m for waves only, downstream cylinder placed at x = ½ D, y=0.6D. Figure F5: Wave height monitors in the wave tank at (a) x=-0.84 m, (b) x=+0.84 m, (c) x=+9.24 m for combined waves and currents, C = 50 mm/s, downstream cylinder placed at x = ½ D, y=0. Figure F6: Wave height monitors in the wave tank at (a) x=-0.84 m, (b) x=+0.84 m, (c) x=+9.24 m for combined waves and currents, C = 75 mm/s, downstream cylinder placed at x = ½ D, y=0. Figure F7: Wave height monitors in the wave tank at (a) x=-0.84 m, (b) x=+0.84 m, (c) x=+9.24 m for combined waves and currents, C = 100 mm/s, downstream cylinder placed at x = ½ D, y=0. Figure F8: Wave height monitors in the wave tank at (a) x=-0.84 m, (b) x=+0.84 m, (c) x=+9.24 m for waves only, downstream cylinder placed at x = ½ D, y=0. Figure F9: Wave height monitors in the wave tank at (a) x=-0.84 m, (b) x=+0.84 m, (c) x=+9.24 m for combined waves and currents, C = 50 mm/s, Single Cylinder Run. Figure F10: Wave height monitors in the wave tank at (a) x=-0.84 m, (b) x=+0.84 m, (c) x=+9.24 m for combined waves and currents, C = 75 mm/s, Single Cylinder Run. Figure F11: Wave height monitors in the wave tank at (a) x=-0.84 m, (b) x=+0.84 m, (c) x=+9.24 m for combined waves and currents, C = 100 mm/s, Single Cylinder Run. Figure F12: Wave height monitors in the wave tank at (a) x=-0.84 m, (b) x=+0.84 m, (c) x=+9.24 m for waves only, Single Cylinder Run. 344 Wave Height Plots along wave tank at positions x = -0.83 m, 0.83 m and 9.24 m Currents C = 50 mm/s Waves T = 0.7 s Wave Height H = 25 mm Downstream Cylinder Position: WHM X = -2 m ½ D Downstream, 100 mm lateral offset WHM WHM X = 10 m X=0m Figure F1: Wave height monitors in the wave tank at (a) x=-0.84 m, (b) x=+0.84 m, (c) x=+9.24 m for combined waves and currents, C = 50 mm/s, downstream cylinder placed at x = ½ D, y=0.6D. 345 Wave Height Plots along wave tank at positions x = -0.83 m, 0.83 m and 9.24 m Currents C = 75 mm/s Waves T = 0.7 s Wave Height H = 25 mm Downstream Cylinder Position: WHM X = -2 m ½ D Downstream, 100 mm lateral offset WHM WHM X = 10 m X=0m Figure F2: Wave height monitors in the wave tank at (a) x=-0.84 m, (b) x=+0.84 m, (c) x=+9.24 m for combined waves and currents, C = 75 mm/s, downstream cylinder placed at x = ½ D, y=0.6D. 346 Wave Height Plots along wave tank at positions x = -0.83 m, 0.83 m and 9.24 m Currents C = 100 mm/s Waves T = 0.7 s Wave Height H = 25 mm Downstream Cylinder Position: WHM X = -2 m ½ D Downstream, 100 mm lateral offset WHM WHM X = 10 m X=0m Figure F3: Wave height monitors in the wave tank at (a) x=-0.84 m, (b) x=+0.84 m, (c) x=+9.24 m for combined waves and currents, C = 100 mm/s, downstream cylinder placed at x = ½ D, y=0.6D. 347 Wave Height Plots along wave tank at positions x = -0.83 m, 0.83 m and 9.24 m Currents C = mm/s Waves T = 0.7 s Wave Height H = 25 mm Downstream Cylinder Position: WHM X = -2 m ½ D Downstream, 100 mm lateral offset WHM WHM X = 10 m X=0m Figure F4: Wave height monitors in the wave tank at (a) x=-0.84 m, (b) x=+0.84 m, (c) x=+9.24 m for waves only, downstream cylinder placed at x = ½ D, y=0.6D. 348 Wave Height Plots along wave tank at positions x = -0.83 m, 0.83 m and 9.24 m Currents C = 50 mm/s Waves T = 0.7 s Wave Height H = 25 mm Downstream Cylinder Position: WHM ½ D Downstream, mm lateral offset WHM WHM X = 10 m X=0m X = -2 m Figure F5: Wave height monitors in the wave tank at (a) x=-0.84 m, (b) x=+0.84 m, (c) x=+9.24 m for combined waves and currents, C = 50 mm/s, downstream cylinder placed at x = ½ D, y=0. 349 Wave Height Plots along wave tank at positions x = -0.83 m, 0.83 m and 9.24 m Currents C = 75 mm/s Waves T = 0.7 s Wave Height H = 25 mm Downstream Cylinder Position: WHM ½ D Downstream, mm lateral offset WHM WHM X = 10 m X=0m X = -2 m Figure F6: Wave height monitors in the wave tank at (a) x=-0.84 m, (b) x=+0.84 m, (c) x=+9.24 m for combined waves and currents, C = 75 mm/s, downstream cylinder placed at x = ½ D, y=0. 350 Wave Height Plots along wave tank at positions x = -0.83 m, 0.83 m and 9.24 m Currents C = 100 mm/s Waves T = 0.7 s Wave Height H = 25 mm Downstream Cylinder Position: WHM ½ D Downstream, mm lateral offset WHM WHM X = 10 m X=0m X = -2 m Figure F7: Wave height monitors in the wave tank at (a) x=-0.84 m, (b) x=+0.84 m, (c) x=+9.24 m for combined waves and currents, C = 100 mm/s, downstream cylinder placed at x = ½ D, y=0. 351 Wave Height Plots along wave tank at positions x = -0.83 m, 0.83 m and 9.24 m Currents C = mm/s Waves T = 0.7 s Wave Height H = 25 mm Downstream Cylinder Position: WHM ½ D Downstream, mm lateral offset WHM WHM X = 10 m X=0m X = -2 m Figure F8: Wave height monitors in the wave tank at (a) x=-0.84 m, (b) x=+0.84 m, (c) x=+9.24 m for waves only, downstream cylinder placed at x = ½ D, y=0. 352 Wave Height Plots along wave tank at positions x = -0.83 m, 0.83 m and 9.24 m Currents C = 50 mm/s Waves T = 0.7 s Wave Height H = 25 mm Single Cylinder Run WHM WHM WHM X = 10 m X=0m X = -2 m Figure F9: Wave height monitors in the wave tank at (a) x=-0.84 m, (b) x=+0.84 m, (c) x=+9.24 m for combined waves and currents, C = 50 mm/s, Single Cylinder Run. 353 t = 60T’ t = 61T’ t = 62T’ t = 63T’ t = 64T’ t = 65T’ t = 66T’ t = 67T’ t = 68T’ t = 69T’ t = 70T’ t = 71T’ t = 72T’ 385 t = 73T’ t = 74T’ t = 75T’ t = 76T’ t = 77T’ Figure H6. Iso surface plots of wave and currents run, C = 75 mm/s, T = 0.7s, at time intervals of T’. (At Stable Beating. Downstream cylinder spacing at x = ½ D, y = 0.6 D). 386 t = 60T’ t = 61T’ t = 62T’ t = 63T’ t = 64T’ t = 65T’ t = 66T’ t = 67T’ t = 68T’ t = 69T’ t = 70T’ t = 71T’ t = 72T’ 387 t = 73T’ t = 74T’ t = 75T’ t = 76T’ t = 77T’ Figure H7. Iso surface plots of wave and currents run, C = 100 mm/s, T = 0.7s, at time intervals of T’. (At Stable Beating. Downstream cylinder spacing at x = ½ D, y = 0.6 D). 388 t = 60T’ t = 61T’ t = 62T’ t = 63T’ t = 64T’ t = 65T’ t = 66T’ t = 67T’ t = 68T’ t = 69T’ t = 70T’ t = 71T’ t = 72T’ 389 t = 73T’ t = 74T’ t = 75T’ t = 76T’ t = 77T’ Figure H8. Iso surface plots of wave only run, T = 0.7s, at time intervals of T. (At Steady State. Downstream cylinder spacing at x = ½ D, y = 0.6 D). 390 t = 60T’ t = 61T’ t = 62T’ t = 63T’ t = 64T’ t = 65T’ t = 66T’ t = 67T’ t = 68T’ t = 69T’ t = 70T’ t = 71T’ t = 72T’ 391 t = 73T’ t = 74T’ t = 75T’ t = 76T’ t = 77T’ Figure H9. Iso surface plots of wave and currents run, C = 50 mm/s, T = 0.7s, at time intervals of T’. (At Stable Beating. Downstream cylinder spacing at x = ½ D, y = 0). 392 t = 45T’ t = 46T’ t = 47T’ t = 48T’ t = 49T’ t = 50T’ t = 51T’ t = 52T’ t = 53T’ t = 54T’ t = 55T’ t = 56T’ t = 57T’ 393 t = 58T’ t = 59T’ t = 60T’ t = 61T’ t = 62T’ Figure H10. Iso surface plots of wave and currents run, C = 75 mm/s, T = 0.7s, at time intervals of T’. (At Stable Beating. Downstream cylinder spacing at x = ½ D, y = 0). 394 t = 60T’ t = 61T’ t = 62T’ t = 63T’ t = 64T’ t = 65T’ t = 66T’ t = 67T’ t = 68T’ t = 69T’ t = 70T’ t = 71T’ t = 72T’ 395 t = 73T’ t = 74T’ t = 75T’ t = 76T’ t = 77T’ Figure H11. Iso surface plots of wave and currents run, C = 100 mm/s, T = 0.7s, at time intervals of T’. (At Stable Beating. Downstream cylinder spacing at x = ½ D, y = 0). 396 t = 60T’ t = 61T’ t = 62T’ t = 63T’ t = 64T’ t = 65T’ t = 66T’ t = 67T’ t = 68T’ t = 69T’ t = 70T’ t = 71T’ t = 72T’ 397 t = 73T’ t = 74T’ t = 75T’ t = 76T’ t = 77T’ Figure H12. Iso surface plots of wave only run, T = 0.7s, at time intervals of T’. (At Steady State. Downstream cylinder spacing at x = ½ D, y = 0). 398 Appendix I Derivation of Similarity Scale factors Using Dimensional Analysis. In physical modeling, flow conditions at model scale are considered to be similar to the prototype if the following three conditions are satisfied: a. Similarity of form (Geometric Similarity), b. Similarity of motion (Kinematic Similarity), c. Similarity of forces (Dynamic Similarity). Geometric similarity means that the ratios of all the prototype lengths to the model lengths are equivalent. For kinematic similarity to be satisfied, the ratios of the prototype velocities to the model velocities must be equivalent. For free surface flow modelling, the basic relevant parameters for dimensional analysis are classified into the following three groups: a. The fluid properties and physical constants, which are the density of water, ρ (units in kg/m3), dynamic viscosity of water, μ (units in N s/m2), the time interval characteristic of unsteady state flow, t (units in s), and the acceleration of gravity, g (units in m/s2), b. Flow geometry, described by the characteristic lengths, L (units in m), c. Flow properties, described by the velocities V (units in m/s) and the pressure difference to drive the fluid flow, ΔP (units in Pa). Using the above basic parameters, dimensional analysis yields: 𝐹1 (𝜌, 𝜇, 𝑡, 𝑔, 𝐿, 𝑉, ∆𝑃) = (I.1) Since there are seven basic parameters, the dimensions of these can be characterized into the three basic measures of mass (M), length (L) and time (T). Buckingham π – theorem states that the basic quantities can be grouped into independent dimensionless parameters: 𝐹2 � 𝑉 �𝑔𝐿 ; 𝜌𝑉 ∆𝑃 ; 𝜌𝑉𝐿 𝜇 ; 𝐿 𝑉𝑡 (I.2) � These four dimensionless parameters have distinctive characteristics. 399 The first parameter, gravity force. 𝑉 , is the Froude number (Fr), characterizing the ratio of the inertia force to the �𝑔𝐿 The second parameter, force to pressure force. The third parameter, 𝜌𝑉 ∆𝑃 𝜌𝑉𝐿 𝜇 , is the Euler number (Eu), that is proportional to the ratio of the inertial , is the Reynolds number (Re), which characterise the ratio of the inertia force to the viscous force. This parameter can be rewritten as water. 𝑉𝐿 𝛾 , where ϒ is the kinematic viscosity of 𝐿 The fourth parameter, , is the Strouhal number, and it characterizes the ratio of the local 𝑉𝑡 acceleration to convective acceleration. For model studies using geometrically similar models, complete dynamic similarity is achieved if and only if each of the four dimensionless parameters has the same value in both model and prototype. Using a scale ratio N, where N is the ratio of a parameter in the prototype to the same parameter in the model, for complete similarity, NV =1 Ng NL for Froude similarity to be satisfied, (I.3) NL =1 NV N t for Convective Acceleration (Strouhal Number) similarity to be satisfied, (I.4) NP =1 N ρ NV for Euler Number similarity to be satisfied and, (I.5) N L NV =1 Nυ for Reynolds Number similarity to be satisfied. (I.6) 400 [...]... T=0.7s, at time intervals of T’ (At Stable Beating Downstream cylinder spacing at x = 1 ½ D, y = 0.6 D) Figure H8 Iso surface plots of wave only run, T = 0.7s, at time intervals of T (At Steady State Downstream cylinder spacing at x = 1 ½ D, y = 0.6 D) Figure H9 Iso surface plots of wave and currents run, C =50mm/s, T=0.7s, at time intervals of T’ (At Stable Beating Downstream cylinder spacing at x = 1 ½... surface plots of wave and currents run, C =75mm/s, T =0.7s, at time intervals of T’ (At Stable Beating Downstream cylinder spacing at x = 1 ½ D, y = 0) Figure H11 Iso surface plots of wave and currents run, C=100mm/s, T=0.7s, at time intervals of T’ (At Stable Beating Downstream cylinder spacing at x = 1 ½ D, y = 0) Figure H12 Iso surface plots of wave only run, T = 0.7s, at time intervals of T’ (At... surface plots of wave and currents run, C =50mm/s, T =0.7s, at time intervals of T’ (At Stable Beating Downstream cylinder spacing at x = 1 ½ D, y = 0.6 D) Figure H6 Iso surface plots of wave and currents run, C =75mm/s, T =0.7s, at time intervals of T’ (At Stable Beating Downstream cylinder spacing at x = 1 ½ D, y = 0.6 D) Figure H7 Iso surface plots of wave and currents run, C=100mm/s, T=0.7s, at.. .Wave Height Plots along wave tank at positions x = -0.83 m, 0.83 m and 9. 24 m Currents C = 75 mm/s Waves T = 0.7 s Wave Height H = 25 mm Single Cylinder Run WHM 1 X = -2 m WHM 2 WHM 3 X = 10 m X=0m Figure F10: Wave height monitors in the wave tank at (a) x=-0. 84 m, (b) x=+0. 84 m, (c) x=+9. 24 m for combined waves and currents, C = 75 mm/s, Single Cylinder Run 3 54 Wave Height Plots along wave tank at... beating Wave only, T = 0.7 s run Downstream cylinder placed at x = 1 ½ D, y = 0 373 Appendix H Iso Surface Plots of Numerical Wave Tank Figure H1 Iso surface plots of wave and currents run, C= 50 mm/s, T=0.7s, at time intervals of T’ (First 24T’ s of run Downstream cylinder spacing at x = 1 ½ D, y = 0.6 D) Figure H2 Iso surface plots of wave and currents run, C= 75 mm/s, T=0.7s, at time intervals of. .. m and 9. 24 m Currents C = 100 mm/s Waves T = 0.7 s Wave Height H = 25 mm Single Cylinder Run WHM 1 X = -2 m WHM 2 WHM 3 X = 10 m X=0m Figure F11: Wave height monitors in the wave tank at (a) x=-0. 84 m, (b) x=+0. 84 m, (c) x=+9. 24 m for combined waves and currents, C = 100 mm/s, Single Cylinder Run 355 Wave Height Plots along wave tank at positions x = -0.83 m, 0.83 m and 9. 24 m Currents C = 0 mm/s Waves... intervals of T’ (First 24T’ s of run Downstream cylinder spacing at x = 1 ½ D, y = 0.6 D) Figure H3 Iso surface plots of wave and currents run, C=100mm/s, T=0.7s, at time intervals of T’ (First 24T’ s of run Downstream cylinder spacing at x = 1 ½ D, y = 0.6 D) Figure H4 Iso surface plots of wave only run, T = 0.7s, at time intervals of T (First 24T’ s of run Downstream cylinder spacing at x = 1 ½ D, y =... plots at every 2T increment at steady state beating Wave only, T = 0.7 s run Downstream cylinder placed at x = 1 ½ D, y = 0.6 D Figure G8 Vorticity plots at every 2T increment at steady state beating Wave only, T = 0.7 s run Downstream cylinder placed at x = 1 ½ D, y = 0.6 D Figure G9 Velocity vector plots at every 2Te increment at steady state beating C = 50 mm/s, T = 0.7 s run Downstream cylinder placed... steady state beating Wave only, T = 0.7 s run Downstream cylinder placed at x = 1 ½ D, y = 0 Figure G16 Vorticity plots at every Te increment at steady state beating Wave only, T = 0.7 s run Downstream cylinder placed at x = 1 ½ D, y = 0 357 Vector Plots (CFD Simulation) Currents C = 50 mm/s Wave Period T = 0.7 s Spacing x =1½D Offset y = 0.6 D Time = 64T Time = 64T + 2Te Time = 64T + 4Te Time = 64T... s Wave Height H = 25 mm Single Cylinder Run WHM 1 X = -2 m WHM 2 WHM 3 X = 10 m X=0m Figure F12: Wave height monitors in the wave tank at (a) x=-0. 84 m, (b) x=+0. 84 m, (c) x=+9. 24 m for waves only, Single Cylinder Run 356 Appendix G CFD Calculated Velocity Vector and Vorticity Plots Figure G1 Velocity vector plots at every 2Te increment at steady state beating C = 50 mm/s, T = 0.7 s run Downstream cylinder . 344 Appendix F Time Series of CFD Calculated Wave Elevations Figure F1: Wave height monitors in the wave tank at (a) x=-0. 84 m, (b) x=+0. 84 m, (c) x=+9. 24 m for combined waves and currents,. wave tank at (a) x=-0. 84 m, (b) x=+0. 84 m, (c) x=+9. 24 m for combined waves and currents, C = 50 mm/s, Single Cylinder Run. Figure F10: Wave height monitors in the wave tank at (a) x=-0. 84 m,. combined waves and currents, C = 100 mm/s, Single Cylinder Run. Figure F12: Wave height monitors in the wave tank at (a) x=-0. 84 m, (b) x=+0. 84 m, (c) x=+9. 24 m for waves only, Single Cylinder