Chapter Discussion on Beat Phenomenon in the Wake of a Bluff Cylinder 7.1 Origin of the beat phenomenon Both experiments and CFD numerical simulations are used in this study to investigate the beat phenomenon present in the wake of a bluff cylinder in combined waves and currents flow This phenomenon is backed by anecdotal evidence in industry model tests where collinear waves and currents acting inline on a flexibly mounted upstream SPAR cylindrical structure and a downstream TAD structure have caused large relative displacements between the two structures In this study, a bluff upstream cylinder, and a slender downstream cylinder placed at various locations in the wake of the bluff cylinder are subjected to collinear waves and currents to study the origin of this beat phenomenon Amplitude modulations in wave elevations and velocities are clearly evident in combined flows where the Uc / Uw ratio is less than 2.86 The corresponding frequency spectra of the time series is typically characterized by two dominant peaks, one at the encounter wave frequency, and a secondary frequency that is close to the encounter wave frequency This beat phenomenon diminishes at higher Uc / Uw ratios, beyond which beating is small, and the frequency spectra are then primarily characterized by the encounter wave frequency and the Strouhal frequency Mapping of the kinematics at the various locations in the wake of the bluff cylinder from x = D to ½ D and y = to 1.1 D reveal that modulation in the velocity time series occurs in the wake region within the y = 0.6 D offset bound, and is strong at the location x = ½ D, y = 0.6 D Wave elevation records at a lateral position 20 mm alongside the upstream cylinder also exhibit similar beating frequencies Force measurements on the downstream slender cylinder reveal similar modulation in the X and Y direction force time series At both downstream cylinder placements at x = ½ D, y = and 0.6D, combined wave current flows create a large increase in the transverse Y forces, compared to wave only flow The presence of currents does not alter the in-line X forces significantly, but introduces modulation features in the force signatures 172 At stable beating, wave elevation plots of the wave tank show that the surface profiles change with a periodicity corresponding to the beat period The velocity vector plots in CFD, as well as vorticity plots, show that flow around the downstream cylinder over each successive wave period has similar periodic change in the flow patterns that correspond with the beat period These observations are clearly not present in wave only simulations Further examination of the iso-surface plots and the velocity vector plots are made at steady beating, for both downstream cylinder locations at x = ½ D, y = and y = 0.6 D These plots are taken over consecutive encounter wave periods, aligned at the instant when maximum flow velocities are observed over the sides of the downstream cylinder This phase alignment is chosen so that features of the flow in the upstream cylinder wake and around the downstream cylinder can be clearly examined over successive encounter wave periods Figure 122 show this comparison for downstream cylinder location at x = ½ D, y = 0, for wave only flow, while Figures 123, 124 and 125 show the plots for combined wave current flows at Uc / Uw = 0.86, 1.29 and 1.72 respectively It is seen from the plots that the differential in the velocities over the sides of the downstream cylinder corresponds to the differentials in wave heights at the downstream cylinder location where a higher velocity differential corresponds to a higher local wave height The variation of the differentials in the local wave heights over successive encounter wave periods is more obvious at lower current speeds This relates to the more obvious beating features in the velocity and force signatures at lower Uc / Uw In Figure 122, at higher currents of C = 100 mm/s (Uc / Uw = 1.72), where the beat period is 4.12s, it is observed that the differential features in the local wave heights around the downstream cylinder are diminished Correspondingly, the differentials in the flow velocities over the sides of the downstream cylinder are reduced From the plots in wave only flows in Figure 122, it is clear that the local wave height features and the velocity vectors around the downstream cylinder repeat itself over successive wave period, with very little variation Hence, the wave height records and the velocity time signatures not portray any modulation features Similar observations are seen when the downstream cylinder is at x = ½ D, y = 0.6 D Again, in wave only flow, Figure 126 shows that both the local wave height and velocity vector features replicate themselves over successive wave periods Combined wave current flow plots for Uc / Uw = 0.86, 1.29 and 1.72 are shown in Figures 127, 128 and 129 respectively It is observed that in combined wave current flows when the downstream cylinder is placed at a Y offset location to the 173 upstream bluff cylinder, its presence further disturbs the free stream, enhancing asymmetry in the wave heights around it This region of asymmetrical features extends upstream to around the bluff cylinder The flow is consequently affected, and this explains the highly modulated features observed in the Y force signatures, as seen in Figure 114 of Chapter Based on the above observations, it is clear that the spatial features of the flow around and in the wake of the bluff upstream cylinder remain invariant over successive wave period in waves only flows However, with the introduction of currents to the wave flow, wave current interaction together with flow separation over the bluff cylinder have a temporal influence on the salient features of the wake flow that repeats itself over every beat period, resulting in modulated time series signatures over successive encounter wave period evident in velocity, force and iso-surface measurements The presence of the downstream cylinder has little role in altering the temporal characteristics in these combined wave current flows However, when placed at a Y offset to the incoming flow, the downstream cylinder enhances the asymmetry in wake flow velocities and local wave surface elevations and is most evident in the force records, where pronounced modulated signatures are recorded These beat features are more obvious at low Uc / Uw ratios, where the contribution of waves in the flow is more significant At higher current flows, the role of flow reversal due to waves is reduced, and hence, beating features are diminished 174 Time = 57T Time = 57T + 2T Time = 57T + 4T Time = 57T + 6T Time = 57T + 8T Time = 57T + 10T Time = 57T + 12T Time = 57T + 14T Figure 122: Velocity vector plots and corresponding local iso surface plots over two successive wave periods T, for wave only flow, T = 0.7 s Downstream cylinder location at x = ½ D, y = 175 Time = 55T Time = 55T + 2Te Time = 55T + 4Te Time = 55T + 6Te Time = 55T + 8Te Time = 55T + 10Te Time = 55T + 12Te Time = 55T + 14Te Figure 123: Velocity vector plots and corresponding local iso surface plots over two successive encounter wave periods Te, for C = 50 mm/s, T = 0.7 s Downstream cylinder location at x = ½ D, y = 176 Time = 113T Time = 113T + 2Te Time = 113T + 4Te Time = 113T + 6Te Time = 113T + 8Te Time = 113T + 10Te Time = 113T + 12Te Time = 113T + 14Te Figure 124: Velocity vector plots and corresponding local iso surface plots over two successive encounter wave periods Te, for C = 75 mm/s, T = 0.7 s Downstream cylinder location at x = ½ D, y = 177 Time = 77T Time = 77T + Te Time = 77T + 2Te Time = 77T + 3Te Time = 77T + 4Te Time = 77T + 5Te Time = 77T + 6Te Time = 77T + 7Te Figure 125: Velocity vector plots and corresponding local iso surface plots over each successive encounter wave periods Te, for C = 100 mm/s, T = 0.7 s Downstream cylinder location at x = ½ D, y = 178 Time = 82T Time = 82T + 2T Time = 82T + 4T Time = 82T + 6T Time = 82T + 8T Time = 82T + 10T Time = 82T + 12T Time = 82T + 14T Figure 126: Velocity vector plots and corresponding local iso surface plots over two successive wave periods T, for wave only flow, T = 0.7 s Downstream cylinder location at x = ½ D, y = 0.6 D 179 Time = 64T Time = 64T + 2Te Time = 64T + 4Te Time = 64T + 6Te Time = 64T + 8Te Time = 64T + 10Te Time = 64T + 12Te Time = 64T + 14Te Figure 127: Velocity vector plots and corresponding local iso surface plots over two successive encounter wave periods Te, for C = 50 mm/s, T = 0.7s Downstream cylinder location at x = ½ D, y = 0.6 D 180 Time = 64T Time = 64T + 2Te Time = 64T + 4Te Time = 64T + 6Te Time = 64T + 8Te Time = 64T + 10Te Time = 64T + 12Te Time = 64T + 14Te Figure 128: Velocity vector plots and corresponding local iso surface plots over two successive encounter wave periods Te, for C = 75 mm/s, T = 0.7s Downstream cylinder location at x = ½ D, y = 0.6 D 181 Figure A81: X – velocities in cylinder wake, combined wave current flow, T=0.7s, at location x= D, y = 1.1 D, for C = (a) 150, (b) 125, (c) 100, (d)75, (e) 50mm/s, (f) wave only Figure A82: Y – velocities in cylinder wake, combined wave current flow, T=0.7s, at location x= D, y = 1.1 D, for C = (a) 150, (b) 125, (c) 100, (d)75, (e) 50mm/s, (f) wave only 265 Figure A83: X – velocities in cylinder wake, combined wave current flow, T=1.0s, at location x= D, y = 1.1 D, for C = (a) 150, (b) 125, (c) 100, (d)75, (e) 50mm/s, (f) wave only Figure A84: Y – velocities in cylinder wake, combined wave current flow, T=1.0s, at location x= D, y = 1.1 D, for C = (a) 150, (b) 125, (c) 100, (d)75, (e) 50mm/s, (f) wave only 266 Figure A85: X – velocities in cylinder wake, combined wave current flow, T=2.0s, at location x= D, y = 1.1 D, for C = (a) 150, (b) 125, (c) 100, (d)75, (e) 50mm/s, (f) wave only Figure A86: Y – velocities in cylinder wake, combined wave current flow, T=2.0s, at location x= D, y = 1.1 D, for C = (a) 150, (b) 125, (c) 100, (d)75, (e) 50mm/s, (f) wave only 267 Figure A87: X – velocities in cylinder wake, current only flow, at location x = D, y= 0, for currents (a) 150, (b) 125, (c) 100, (d) 75, (e) 50 mm/s Figure A88: Y – velocities in cylinder wake, current only flow, at location x = D, y= 0, for currents (a) 150, (b) 125, (c) 100, (d) 75, (e) 50 mm/s 268 Figure A89: X – velocities in cylinder wake, combined wave current flow, T=0.7s, at location x= D, y=0, for C = (a) 150, (b) 125, (c) 100, (d)75, (e) 50mm/s, (f) wave only Figure A90: Y – velocities in cylinder wake, combined wave current flow, T=0.7s, at location x= D, y=0, for C = (a) 150, (b) 125, (c) 100, (d)75, (e) 50mm/s, (f) wave only 269 Figure A91: X – velocities in cylinder wake, combined wave current flow, T=1.0s, at location x= D, y=0, for C = (a) 150, (b) 125, (c) 100, (d)75, (e) 50mm/s, (f) wave only Figure A92: Y – velocities in cylinder wake, combined wave current flow, T=1.0s, at location x= D, y=0, for C = (a) 150, (b) 125, (c) 100, (d)75, (e) 50mm/s, (f) wave only 270 Figure A93: X – velocities in cylinder wake, combined wave current flow, T=2.0s, at location x= D, y=0, for C = (a) 150, (b) 125, (c) 100, (d)75, (e) 50mm/s, (f) wave only Figure A94: Y – velocities in cylinder wake, combined wave current flow, T=2.0s, at location x= D, y = 0, for C = (a) 150, (b) 125, (c) 100, (d)75, (e) 50mm/s, (f) wave only 271 Figure A95: X – velocities in cylinder wake, current only flow, at location x = D, y = 0.6 D, for currents (a) 150, (b) 125, (c) 100, (d) 75, (e) 50 mm/s Figure A96: Y – velocities in cylinder wake, current only flow, at location x = D, y = 0.6 D, for currents (a) 150, (b) 125, (c) 100, (d) 75, (e) 50 mm/s 272 Figure A97: X – velocities in cylinder wake, combined wave current flow, T=0.7s, at location x= D, y =0.6 D, for C = (a) 150, (b) 125, (c) 100, (d)75, (e) 50mm/s, (f) wave only Figure A98: Y – velocities in cylinder wake, combined wave current flow, T=0.7s, at location x= D, y =0.6 D, for C = (a) 150, (b) 125, (c) 100, (d)75, (e) 50mm/s, (f) wave only 273 Figure A99: X – velocities in cylinder wake, combined wave current flow, T=1.0s, at location x= D, y =0.6 D, for C = (a) 150, (b) 125, (c) 100, (d)75, (e) 50mm/s, (f) wave only Figure A100: Y – velocities in cylinder wake, combined wave current flow, T=1.0s, at location x= D, y =0.6 D, for C = (a) 150, (b) 125, (c) 100, (d)75, (e) 50mm/s, (f) wave only 274 Figure A101: X – velocities in cylinder wake, combined wave current flow, T=2.0s, at location x= D, y =0.6 D, for C = (a) 150, (b) 125, (c) 100, (d)75, (e) 50mm/s, (f) wave only Figure A102: Y – velocities in cylinder wake, combined wave current flow, T=2.0s, at location x= D, y = 0.6 D, for C = (a) 150, (b) 125, (c) 100, (d)75, (e) 50mm/s, (f) wave only 275 Figure A103: X – velocities in cylinder wake, current only flow, at location x = D, y = 1.1 D, for currents (a) 150, (b) 125, (c) 100, (d) 75, (e) 50 mm/s Figure A104: Y – velocities in cylinder wake, current only flow, at location x = D, y = 1.1 D, for currents (a) 150, (b) 125, (c) 100, (d) 75, (e) 50 mm/s 276 Figure A105: X – velocities in cylinder wake, combined wave current flow, T=0.7s, at location x= D, y=1.1 D, for C = (a) 150, (b) 125, (c) 100, (d)75, (e) 50mm/s, (f) wave only Figure A106: Y – velocities in cylinder wake, combined wave current flow, T=0.7s, at location x= D, y =1.1 D, for C = (a) 150, (b) 125, (c) 100, (d)75, (e) 50mm/s, (f) wave only 277 Figure A107: X – velocities in cylinder wake, combined wave current flow, T=1.0s, at location x= D, y =1.1 D, for C = (a) 150, (b) 125, (c) 100, (d)75, (e) 50mm/s, (f) wave only Figure A108: Y – velocities in cylinder wake, combined wave current flow, T=1.0s, at location x= D, y =1.1 D, for C = (a) 150, (b) 125, (c) 100, (d)75, (e) 50mm/s, (f) wave only 278 Figure A109: X – velocities in cylinder wake, combined wave current flow, T=2.0s, at location x= D, y =1.1 D, for C = (a) 150, (b) 125, (c) 100, (d)75, (e) 50mm/s, (f) wave only Figure A110: Y – 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