Characteristics of flow in the wake region of a bluff vertical cylinder in the presence of waves,currents and combined wave current flows 2

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 w

Chapter 7 Discussion on Beat Phenomenon in the Wake of a Bluff Cylinder7.1 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 2 ½

D and y = 0 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 = 1 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 = 1 ½ D, y = 0 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

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 = 1 ½ D, y = 0 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 = 1 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 do not portray any modulation features

Similar observations are seen when the downstream cylinder is at x = 1 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

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 6

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

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 = 1 ½ D, y = 0

Figure 123: Velocity vector plots and corresponding local iso surface plots over two successive encounter wave periods T , for C = 50 mm/s, T = 0.7 s

Figure 124: Velocity vector plots and corresponding local iso surface plots over two successive encounter wave periods T e , for C = 75 mm/s, T = 0.7 s

Downstream cylinder location at x = 1 ½ D, y = 0

Figure 125: Velocity vector plots and corresponding local iso surface plots over each successive encounter wave periods T e , for C = 100 mm/s, T = 0.7 s

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 = 1 ½ D, y = 0.6 D

Figure 127: Velocity vector plots and corresponding local iso surface plots over two successive encounter wave periods T , for C = 50 mm/s, T = 0.7s

Figure 128: Velocity vector plots and corresponding local iso surface plots over two successive encounter wave periods T e , for C = 75 mm/s, T = 0.7s

Downstream cylinder location at x = 1 ½ D, y = 0.6 D

Time = 64T + 2Te

Figure 129: Velocity vector plots and corresponding local iso surface plots over each successive encounter wave periods T e , for C = 100 mm/s, T = 0.7s

7.2 Beat Periods in Combined Wave Current Flows

Beat phenomenon is encountered in both the inline and transverse direction in combined wave and current flows at low Uc / Uw Both experiments and CFD simulations showed that the beat periods are similar in kinematics and forces signatures

The waves considered in this study is normalized by the modified Keulegan Carpenter number (KC’)

of the waves, calculated at the measurement location, 80mm below still water level KC’ is defined

as follows:

𝐾𝐶′=𝑈𝑤 𝑇

Where: Uw = Maximum wave particle velocity at 80mm below still water level,

T = Wave period in no currents flow,

z = Depth in fluid measured from still water level = 80 mm

Combining these two equations give:

The KC’ numbers for the three calibrated waves T = 0.7, 0.85 and 1.0 s of wave height H = 25 mm are presented in Table 22 below:

Table 22 Waves used in this study, and corresponding modified Keulegan Carpenter number KC’

Figure 130 below shows the normalized plots of the ratio of beat to wave frequency fb/fw versus the ratio of current to maximum wave velocity Uc/Uw, for modified Keulegan Carpenter numbers of KC’ = 0.25 to 0.35 (T = 0.7s, 0.85s and 1.0s), at tow speeds of C = 50 mm/s to 150 mm/s These plots showed that fb/fw generally increased with increasing ratios of Uc/Uw This translates to lower beat periods at higher currents It is observed that these beat periods are not necessarily equal in the X and Y directions At the y = 0 offset location, with the exception of T = 0.7s, the fb/fw ratio in the X direction are slighter larger than those in the Y direction At higher Uc/Uw ratios, the beat frequencies in both directions are identical Similar trends are observed at the y = 0.6 D offset location

In the force signatures spectra, the secondary peak corresponding to the shift in frequency is dominant for Uc/Uw < 1, and this peak gradually decreased with increasing Uc/Uw The frequency of this peak is slightly larger than the wave frequency At Uc/Uw > 1.75, the beat frequency increased substantially and deviated from a linear increase Spectra plots at higher Uc/Uw ratios showed that the corresponding peak in frequency shift is slightly smaller than the wave frequency, and this peak

is much smaller compared to the wave frequency Figure 131 shows the plots of fb/fw versus Uc/Uw

at KC’ = 0.25 and currents of C = 50 mm/s to 100 mm/s from experimental and CFD studies

The X and Y force beat frequencies in CFD simulations are identical in both directions The trend of the plots is similar to experiments The spectra from CFD simulations at y = 0 offset location show that the peak corresponding to shift in frequency is slightly larger than the wave frequency This is also observed for larger Uc/Uw ratios CFD simulations also brought out the existence of a third peak that is of slightly at lower frequency This third peak is small compared to the higher frequency peak

at steady beating

Figure 130 Normalized plot of ratio of beat to wave frequency vs U c / U w for downstream

cylinder placed at x = 1 ½ D, (a) y = 0, (b) y = 0.6 D

Figure 131 Comparison of beat frequencies between experiments and CFD simulations for

downstream cylinder placed at (a) y = 0, (b) y = 0.6 D

(a)

(b)

7.3 Drag Coefficients in the Bluff Cylinder Wake

Past research by Blevins (2005), Wu et al (2003) and Price et al (1984) determined the measured drag coefficient on a downstream cylinder in the wake of a cylinder to identify the drag deficient region in the wake The wake drag coefficients from the present study are calculated from the time averaged kinematics in the wakeand compared with those obtained by Price (1984), for a cylinder spacing of x = 1 ½ D

Figure 132 shows the CD plot by Price for an infinitely long cylinder in current flows of Re = 5.4 x 104, and a tabulation of the experimental wake drag coefficients CD’ in this study, calculated for currents and well as combined waves and currents

Figure 132 Comparison of experiment C D coefficients with plot from Price (1984)

In currents only flow, as a finite length cylinder is used in this study, the wake drag coefficients CD’ in currents is expected to have a smaller value due to the free end effects of a finite length cylinder These CD’ values do compare favourably with Price’s plot

In combined wave current flows, it is observed that at low wave periods (T < 1.0s) negative CD values are obtained Conversely, at large wave periods (T = 2.0s), positive CD values are obtained The reason for this observation can be explained in terms of the flow characteristics of the waves used

No waves

0.7 s 1.0 s 2.0 s

in the flow exceeds the drag forces In this wave flow regime, the drag component of the wave force does not play a significant role in the overall drag force of the combined flow Hence, the wake drag coefficient CD’ is largely dictated by the current flow contribution On the other hand, for large wave period (T = 2.0s), the flow is drag dominated, where wave inertia forces is small compared to wave drag forces In this respect, the drag forces component during flow reversal plays a significant role and the wake drag coefficient is diminished in the overall flow

7.4 Velocity Spectrum in Measured Flow Velocities at Location x = 1 ½ D Downstream

In this section, the velocity frequency spectra in the wake of the upstream cylinder at low KC’ numbers is examined and discussed The spectra of the velocities at location x = 1 ½ D downstream,

at y = 0 and 0.6 D offsets is presented in Table 23

In currents only flows, at the y = 0 location, the inline velocity spectra is characterized by a broad spectrum of low frequency peaks associated with turbulence, along with the Strouhal frequency, over the range of currents measured The signal in the transverse direction shows just a distinct Strouhal frequency These low frequencies are greatly reduced at y = 0.6 D offset location, and Strouhal frequency peak is clearly identified These turbulence effects are further reduced with decrease in current speeds, which is obvious, as smaller wake effects are expected with lower flow velocities past the cylinder

In combined wave and current flows at KC’ = 0.25, it is observed that the low turbulence frequencies

is amplified at lower Uc/Um ratios of 0.86 and 1.72, which are not observable at similar currents speeds in currents only flows However, these plots also showed that the Strouhal frequency peak is muted significantly These observations could be plausibly explained from the effects of waves in the flow The net increase in flow when combined wave crest and current velocities flow around the upstream cylinder attributed to the increase in turbulence related low frequencies However, due to flow reversal in each wave cycle, vortex shedding is not developed completely, hence a reduced Strouhal frequency peak

Double peaks related to the wave frequency and shift in frequency in the beat phenomenon is seen for Uc/Um < 1.72 in both Y offset locations, and is most obvious at y = 0.6 D offset

At KC’ = 0.35, low turbulence related frequencies are reduced at the y = 0 offset position, and for

Uc/Um < 1, current contributions are very small At this Uc/Um ratio, waves are observed to be diffracting significantly at the measured wake location, to the extent that wave frequency peak is prevailing in the transverse velocity spectra At higher Uc/Um ratios of 1.74 and 2.61, the flow in the transverse direction is dominated by vortex shedding, as evident from the strong Strouhal frequency peak The converse is true at y = 0.6 D offset, where low frequency turbulence related peaks are amplified for the said Uc/Um ratios This amplification is accompanied with a marked reduction in the Strouhal peak

Beat phenomenon related double peaks are observed at both Y offsets, but these are again more significant in the transverse direction at the y = 0.6 D offset position

A comparison of the KC’ = 0.25 and 0.35 plots show that wave diffraction plays a more significant role at lower KC’ wave flows, evident from the presence of wave frequency peaks in the transverse direction

It is clear from the combined wave current spectra plots that wave current interaction in the wake is enhancing turbulence in the wake

Table 23: Spectra of kinematics in the wake of the upstream cylinder, measured at x = 1 ½ D, y

= 0 and 0.6 D offsets, for (a) Current only flow, (b) combined wave current flow at KC’ = 0.25, (c) combined wave current flow at KC’ = 0.35

7.5 Effects of Beat Phenomenon on Simulated Motions of Downstream Cylinder

Prior industry model tests showed that the surge responses of the SPAR and TAD structures were significantly larger in combined wave current flow, as compared to wave only flow It is hypothesized that the beat phenomenon has a contribution in the increased surge responses To test this hypothesis, an idealized 1 degree of freedom motion model is used to determine the simulated surge motions of a flexibly mounted downstream cylinder, in different flow conditions using velocities mapped in the wake of the upstream bluff cylinder

The mapped kinematics in the cylinder wake show that beat phenomenon occurred over a sizable region in the wake of the upstream cylinder, at domain x = ½D to 2 D and y = 0 to 0.6 D This observation is also seen in the iso surface plots from CFD simulation, which showed that the diffracted waves behind the upstream cylinder are evident over a large area in the wake

Beat phenomenon in the kinematics and force measurements are most obvious for combined wave current combination of T = 0.7s, and C = 50 mm/s, at the location x = 1 ½ D, y = 0.6 D In view of this time dependent modulation in forces and kinematics, the surge motions will be significantly different compared to wave only flows The analysis below simulates the downstream cylinder’s responses

7.5.1 Idealized One Degree of freedom model

The surge motion responses of a downstream cylinder is estimated using the kinematics time series using a simplified 1-DOF motion model, as shown in Figure 133

The equation of motion in the system described above is written as:

x C D U u x(U u x)

t

u C D t

u D Kx x

∂

∂

=+

2

14

4

2 2

(7.4) Where: M = Mass of structure = D dl

4

2

π ρ

a 4

2

π ρ

U and U w represent the current velocity and maximum wave particle velocity respectively, and ẋ and

ẍ correspond to the cylinder velocity and acceleration A damping parameter value of 0.01 was

chosen to reflect the typical damping response of a TAD semi-submersible, scaled for this present study

The first, second and third terms on the right hand side of the equation denote the Froude Kryoff forces, diffraction forces and drag forces respectively This equation is rearranged in terms of the cylinder acceleration to give:

− + +

∂

∂ +

t

u C D M

M

m a

(7.5)Using an iterative procedure, the Newton Raphson’s method is used to estimate the response of the cylinder using the following initial conditions

At t =0, Initial displacement of downstream cylinder x=x o =0,

Initial velocity of downstream cylinder x= xo =0, Velocities from experiments and CFD, at the mapped location are used in the above model to compute the simulated surge responses

7.5.2 Surge Responses of Downstream Cylinder

The cylinder surge responses are analysed for two cylinder natural frequencies, one at fn = 0.5 Hz, and the other close to the beat frequency, fn = 0.108 Hz Figure 134and135 show the plots of the surge responses for these two natural frequencies, for downstream cylinder placement at y = 0 and 0.6 D offsets The plots in red and green are computed from experimental and CFD kinematics respectively Table 24 and 25 presents the standard deviation of the surge motion responses

Table 24 Standard deviation of surge responses of downstream cylinder at different natural

frequencies, and locations for waves only runs

Table 25 Standard deviation of surge responses of downstream cylinder at different natural

frequencies, and locations for combined waves and currents runs

The plots show that at a cylinder natural frequency of 0.5 Hz, away from the beat frequency, the surge responses of the downstream cylinder placed at x = 1 ½ D, y = 0, in combined wave current flow are slightly larger to that in wave only flows The surge response is increased significantly when the downstream cylinder is placed at an offset, x = 1 ½ D, y = 0.6 D in wave current flow

At a cylinder natural frequency of 0.108 Hz, close to the beat frequency, the surge response of the downstream cylinder in combined wave current flow, placed at x = 1 ½ D, y = 0, is more than three times than that observed in wave only flow The responses at y = 0.6 D offset are several times larger To put these numbers in perspective, a downstream cylinder with a natural frequency close

to the beat frequency in combined wave current flow can result in surge responses that are more than twice its diameter This illustrates the importance of identifying the beat frequencies that arise from combined wave current flows around a bluff body, so that any downstream structure in the wake can be appropriately designed to avoid possible resonant surge responses

Combined Waves and Currents, T = 0.7s, C = 50 mm/s

Figure 134 Comparison of simulated surge motions for downstream cylinder located at x = 1 ½

D, y = 0, from linear theory, experiments and CFD for:

(a) Wave only flow, T = 0.7s, fn = 0.5, (b)Wave current flow, T=0.7s, C=50mm/s, fn=0.5, (c) Wave only flow, T = 0.7s, fn=0.108,

(d) Wave current flow, T=0.7s, C=50mm/s, fn=0.108

(a)

(b)

(c)

(d)

Figure 135 Comparison of simulated surge motions for downstream cylinder located at x = 1 ½

D, y = 0.6 D, from linear theory, experiments and CFD for:

(b)Wave current flow, T=0.7s, C=50mm/s, fn=0.5, (c) Wave only flow, T = 0.7s, fn=0.108,

(d) Wave current flow, T=0.7s, C=50mm/s, fn=0.108

(a)

(b)

(c)

(d)

7.6 Vorticity patterns in upstream cylinder wake, with downstream cylinder at x = 1 ½ D, y = 0

The vorticity plots generated in CFD showed unique characteristics in the vortices in the wake of the upstream cylinder in combined wave current flows during beat phenomenon, where discrete vortices are formed in the wake over each wave cycle These discrete vortices appear in an asymmetrical formation, as shown in Figure 136, for the case of C = 50 mm/s, T = 0.7s The vorticity plots shown are taken at the instant when the wave crest is past the sides of the upstream cylinder

Figure 136 Vorticity plots showing vortex formation in the wake of the upstream cylinder for (a)

current only flow, C = 50 mm/s, (b) wave only flow, T = 0.7s, (c) combined wave current flow, C = 50 mm/s T = 0.7s (Red circles show vortex formation)

Currents Only

Waves Only

Combined wave currents

It is observed that in the currents only case, at Re = 8.3K, the separation point of the shear layers around the cylinder occurred close to the vertical centreline of the upstream cylinder Vorticity is observed in the wake close to the cylinder surface suggesting that turbulence exists in the wake Observation of the vorticity plots in a time sequence over the duration of run show that the vortex shedding behind the cylinder is alternate, where its shedding frequency agreed well with calculated values

In the waves only case (T = 0.7s, Rewave = 9.6K) it is seen that the separation point now occurred aft

of the vertical centreline, and the vortices formed are drawn towards the horizontal centreline, which is obvious as the wave diffracts around the cylinder This is to be expected as the flow in this

KC and Reynolds (wave) regime are largely creeping flow with limited separation, as shown in flow regime plots by Sarpkaya (1986) The vorticity features are strongest over the one half of the wave period cycle where the wave crest passes the cylinder However, the shear layers are not fully formed before the flow reversal half of the wave cycle took over, resulting in short vortices of limited length

In combined waves and currents, a separation angle similar to that in waves only simulation is observed, but the growth of the vortices is more similar to the currents only simulation Again, in combined waves and currents, flow reversal take place in each wave cycle, but with addition of currents, the vortex is more substantially formed in the flow of the forward half wave cycle, with distinct discrete vortices over each side of the cylinder These vortices did not form alternately per

se, but is observed to be asymmetrical over the cylinder wake Zhou (2000), in a numerical study of combined waves and currents on a cylinder using a discrete vortex method solver, also reported similar asymmetric discrete vortex formation, but at a lower Reynolds number, and KC >4, where they occurred for similar Uc /Uw ratios of less than 1

Chapter 8 Conclusions and Recommendations

8.1 Conclusions of this study

This thesis research is carried out to establish and understand the dynamics of the wave-current- structure interaction leading to the beat phenomenon that is observed in the wake of a bluff cylinder A hybrid approach comprising experiments and CFD has been successfully implemented to better understand the problem Temporal and spatial descriptions of flow field in the vicinity and wake of two interacting cylinders have been systematically captured through the use of PIV and point measurements in tow experiments complemented by adequately validated numerical simulations Case studies have also been successfully carried out in combined wave-current flows with the characteristic current to wave velocity ratio, Uc / Uw, ranging from 0.8 to 2.8, and wave KC numbers ranging from 0.25 to 0.50

The experiments are carried out using a specially designed and built constant speed tow carriage system with vibration suppression ability In particular, vibrations in the carriage chassis have been successfully isolated to a large extent from the instrumentation sub frame, hence leading to a relatively low noise environment for the experiments The carriage drive system has also incorporated intelligent electronics that enable user specified speed controls and ramp accelerations Constant speed during operations is ensured though a computer controlled continuous feedback motor system

Through the controlled experiments, it is shown that the beat phenomenon, in the form of amplitude modulation, exists both in the kinematics of the flow field and also in the force time histories acting on the downstream slender cylinder The beat signatures are most pronounced at locations downstream of the bluff cylinder, especially at x = 1 ½ D at the monitored locations Forces on a 50 mm horizontal slice of the downstream cylinder, located at 80 mm below still water level, show that the beating characteristics are especially strong if the downstream cylinder is located at x = 1 ½ D and y = 0.6 D Flow visualization using the PIV method ascertain that differentials in the flow patterns in the wake around both sides of the downstream cylinder led to the large modulated Y direction forces measured in combined wave current flows Amplitude modulated signatures are not observed in the experiments for waves only and currents only flows, hence, the beat phenomenon exists only in combined wave current flows For the range of Uc / Uw

considered, beating is most obvious at Uc / Uw = 0.86, and the level of modulation in the time history signatures diminishes at higher Uc / Uw ratios

Results obtained using STAR CCM+, a commercial software based on Detached Eddy Simulation (DES) and Volume of Fluids (VOF), have also yielded similar features consistent with the experimental studies The numerical simulations have also helped to elucidate the physics of wave-current-structure interactions leading to the beat phenomenon In particular, beating occurs when there is a variation of the flow velocities in the near field of the downstream cylinder over successive encounter wave periods This variation repeats itself with a periodicity corresponding to the beat period This is reflected in the vorticity plots of the flow in the wake where the vorticity patterns over each successive encounter wave period show a periodic swing over each beat period This variation of the flow velocities over the sides of the downstream cylinder is also correlated to the perturbations in the local wave surface elevations in the wake of the bluff cylinder, where a higher velocity variation corresponds to a larger differential in the local wave heights around the downstream cylinder For the range of Uc / Uw ratios considered in this study, the variation of the differentials in the local wave heights over successive encounter wave periods is more obvious at low current speeds This relates to the more obvious beating features in the velocity and forces signatures at low Uc / Uw At higher Uc / Uw ratios, the differential features in the local wave heights around the downstream cylinder diminishes Correspondingly, the variation in the flow velocities around the downstream cylinder is reduced

It is shown in this study that the beat phenomenon is due to the wave-current and bluff cylinder interaction, and the presence of the downstream cylinder has little effect in altering the beat frequencies in the combined wave current flow With an offset of 0.6 D in the downstream cylinder location away from the centreline of the upstream cylinder location, the presence of the downstream cylinder will enhance the asymmetric features of the wake flow velocities and temporal variations of the surface wave heights around the cylinders These led to a pronounced amplitude modulated force signature evident in the forces on the downstream cylinder

Modulated features in velocities, wave surface elevations and forces due to combined wave current flows are more obvious at low current to wave velocity ratios where the contribution of waves are dominant compared to currents At higher current flows, the role of flow reversal due to waves is reduced, and hence, modulated features are reduced Parametric studies for various current speeds show that the beat periods in combined wave current flows decrease with increasing Uc / Uw ratios

Using an idealized 1-DOF model, it is demonstrated that surge motion responses of the downstream cylinder can be greatly amplified in combined wave current flows, compared to wave only or current only flows This verifies earlier observations in industry model tests where a downstream TAD structure showed large responses in collinear wave current flows, and reinforces the importance of identifying the frequencies in the beat phenomenon arising from combined wave current flow around a bluff body, so that the downstream structure can be designed to avoid resonant responses due to wave-current-structure interaction

8.2 Recommendations for future work

In this study, the wake characteristics of combined wave current flows and the existence of the beat phenomenon in the kinematics and force time histories are successfully demonstrated through a hybrid experimental – numerical approach, leading to a better understanding of the occurrence of the beat phenomenon The hybrid approach has been adopted due to the limitations in both the experiments and numerical simulations

b To investigate the long term characteristics of the beat phenomenon in combined flows, a longer tow tank, or a current generation system in the tow tank will enable a longer experiment run for extended data records,

c The kinematics, forces and flow visualization in the conducted study is measured at a horizontal position 80mm below still water level This achieved the objective of understanding the flow characteristics at a level close to the still water level However, there is scope in further work to add on to this knowledge over different depth locations, to further understand the beat phenomenon around the cylinder, spanwise The effects of combined wave current flows around a truncated cylinder can concurrently be studied,

there is scope in further work to add on to this knowledge over different depth locations, to further understand the beat phenomenon around the cylinder, spanwise The effects of combined wave current flows around a truncated cylinder can concurrently be studied,

d Other recent researches had shown promise in installing a PIV system on a towing facility This is possible through miniaturized laser optics and streamlined underwater housing suitable for focusing laser light sheet under the water surface without too much disturbances to the flow field This endeavour would enable a full time history record of the wave-current-structure interaction which will help towards deciphering experimentally, the evolution of the beat phenomenon With improved 64 bit computer operating systems, an exponential increase in on-board random access memory would allow acquiring of substantially longer data records,

e More wave elevation monitoring devices can be attached near the bluff upstream cylinder

to measure the local wave elevations This will help monitor surface profile changes during the transient wave-current-structure interaction process leading to the beat phenomenon,

f The current study had been conducted with rigidly fixed cylinders and it would be useful to take the experiments further to allow for moving and tethered cylinders with non-rigid supports Miniature sized and light weight inertia meters and gyrometers are available in the market today that can monitor translational and rotational motions, as well as response velocities and accelerations Measuring motion responses experimentally is close to reality

as these sensors can be installed remotely within the flexibly mounted cylinders where data acquisition can be transferred using wireless technology By varying the natural frequency of the cylinder, the motion responses of this instrumented cylinder can be experimentally captured and benchmarked against the motion model of this study

The use of a CFD software package in modelling a numerical wave tank with combined wave current flows has produced results consistent with the experiments The next logical step in improving the CFD simulation would be the push for more compute-intensive simulations with open boundaries rather than a numerical wave tank This will remove uncertainly pertaining to the presence of the wall boundary in both the experiments and numerical computations

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Appendix A

Time Series of Experimental Kinematics

Figure A1: X – velocities in cylinder wake, current only flow, at location x = 1 ½ D, y = 0, for

currents (a) 150, (b) 125, (c) 100, (d) 75, (e) 50 mm/s

Figure A2: Y – velocities in cylinder wake, current only flow, at location x = 1 ½ D, y = 0, for

currents (a) 150, (b) 125, (c) 100, (d) 75, (e) 50 mm/s

Figure A3: X – velocities in cylinder wake, combined wave current flow, T = 0.7 s, at location x =

1 ½ D, y = 0, for currents (a) 150, (b) 100, (c) 50 mm/s, (d) wave only

Figure A4: Y – velocities in cylinder wake, combined wave current flow, T = 0.7s, at location x =

1 ½ D, y = 0, for currents (a) 150, (b) 100, (c) 50 mm/s, (d) wave only

Figure A5: X – velocities in cylinder wake, combined wave current flow, T = 1.0s, at location x =

1 ½ D, y = 0, for currents (a) 150, (b) 100, (c) 50 mm/s, (d) wave only

Figure A6: Y – velocities in cylinder wake, combined wave current flow, T = 1.0s, at location x =

1 ½ D, y = 0, for currents (a) 150, (b) 100, (c) 50 mm/s, (d) wave only

Figure A7: X – velocities in cylinder wake, combined wave current flow, T = 2.0s, at location x =

1 ½ D, y = 0, for currents (a) 150, (b) 100, (c) 50 mm/s, (d) wave only

Figure A8: Y – velocities in cylinder wake, combined wave current flow, T = 2.0s, at location x =

1 ½ D, y = 0, for currents (a) 150, (b) 100, (c) 50 mm/s, (d) wave only

Figure A9: X – velocities in cylinder wake, current only flow, at location x = 1 ½ D, y = 0.6 D, for

currents (a) 150, (b) 125, (c) 100, (d) 75, (e) 50 mm/s

Figure A10: Y – velocities in cylinder wake, current only flow, at location x = 1 ½ D, y = 0.6 D, for

currents (a) 150, (b) 125, (c) 100, (d) 75, (e) 50 mm/s

Figure A11: X – velocities in cylinder wake, combined wave current flow, T=0.7s, at location x= 1

½ D, y = 0.6 D, for C = (a) 150, (b) 125, (c) 100, (d)75, (e) 50mm/s, (f) wave only Figure A12: Y – velocities in cylinder wake, combined wave current flow, T=0.7s, at location x= 1

½ D, y = 0.6 D, for C = (a) 150, (b) 125, (c) 100, (d)75, (e) 50mm/s, (f) wave only Figure A13: X – velocities in cylinder wake, combined wave current flow, T=1.0s, at location x= 1

½ D, y = 0.6 D, for C = (a) 150, (b) 125, (c) 100, (d)75, (e) 50mm/s, (f) wave only Figure A14: Y – velocities in cylinder wake, combined wave current flow, T=1.0s, at location x= 1

½ D, y = 0.6 D, for C = (a) 150, (b) 125, (c) 100, (d)75, (e) 50mm/s, (f) wave only Figure A15: X – velocities in cylinder wake, combined wave current flow, T=2.0s, at location x= 1

Figure A16: Y – velocities in cylinder wake, combined wave current flow, T=2.0s, at location x= 1

½ D, y = 0.6 D, for C = (a) 150, (b) 125, (c) 100, (d)75, (e) 50mm/s, (f) wave only Figure A17: X – velocities in cylinder wake, current only flow, at location x = 1 ½ D, y = 1.1 D, for

currents (a) 150, (b) 125, (c) 100, (d) 75, (e) 50 mm/s

Figure A18: Y – velocities in cylinder wake, current only flow, at location x = 1 ½ D, y = 1.1 D, for

currents (a) 150, (b) 125, (c) 100, (d) 75, (e) 50 mm/s

Figure A19: X – velocities in cylinder wake, combined wave current flow, T=0.7s, at location x= 1

½ D, y = 1.1 D, for C = (a) 150, (b) 125, (c) 100, (d)75, (e) 50mm/s, (f) wave only Figure A20: Y – velocities in cylinder wake, combined wave current flow, T=0.7s, at location x= 1

½ D, y = 1.1 D, for C = (a) 150, (b) 125, (c) 100, (d)75, (e) 50mm/s, (f) wave only Figure A21: X – velocities in cylinder wake, combined wave current flow, T=1.0s, at location x= 1

½ D, y = 1.1 D, for C = (a) 150, (b) 125, (c) 100, (d)75, (e) 50mm/s, (f) wave only Figure A22: Y – velocities in cylinder wake, combined wave current flow, T=1.0s, at location x= 1

½ D, y = 1.1 D, for C = (a) 150, (b) 125, (c) 100, (d)75, (e) 50mm/s, (f) wave only Figure A23: X – velocities in cylinder wake, current only flow, at location x = 2 ½ D, y = 0, for

currents (a) 150, (b) 125, (c) 100, (d) 75, (e) 50 mm/s

Figure A24: Y – velocities in cylinder wake, current only flow, at location x = 2 ½ D, y=0, for

currents (a) 150, (b) 125, (c) 100, (d) 75, (e) 50 mm/s

Figure A25: X – velocities in cylinder wake, combined wave current flow, T=0.7s, at location x= 2

½ D, y=0, for C = (a) 150, (b) 125, (c) 100, (d)75, (e) 50mm/s, (f) wave only

Figure A26: Y – velocities in cylinder wake, combined wave current flow, T=0.7s, at location x= 2

½ D, y=0, for C = (a) 150, (b) 125, (c) 100, (d)75, (e) 50mm/s, (f) wave only

Figure A27: X – velocities in cylinder wake, combined wave current flow, T=1.0s, at location x= 2

½ D, y=0, for C = (a) 150, (b) 125, (c) 100, (d)75, (e) 50mm/s, (f) wave only

Figure A28: Y – velocities in cylinder wake, combined wave current flow, T=1.0s, at location x= 2

½ D, y=0, for C = (a) 150, (b) 125, (c) 100, (d)75, (e) 50mm/s, (f) wave only

Figure A29: X – velocities in cylinder wake, combined wave current flow, T=2.0s, at location x= 2

½ D, y=0, for C = (a) 150, (b) 125, (c) 100, (d)75, (e) 50mm/s, (f) wave only

Figure A30: Y – velocities in cylinder wake, combined wave current flow, T=2.0s, at location x= 2

½ D, y=0, for C = (a) 150, (b) 125, (c) 100, (d)75, (e) 50mm/s, (f) wave only

Figure A31: X – velocities in cylinder wake, current only flow, at location x = 2 ½ D, y= 0.6 D, for

currents (a) 150, (b) 125, (c) 100, (d) 75, (e) 50 mm/s

Figure A32: Y – velocities in cylinder wake, current only flow, at location x = 2 ½ D, y= 0.6 D, for

currents (a) 150, (b) 125, (c) 100, (d) 75, (e) 50 mm/s

Figure A33: X – velocities in cylinder wake, combined wave current flow, T=0.7s, at location x= 2

½ D, y= 0.6 D, for C = (a) 150, (b) 125, (c) 100, (d)75, (e) 50mm/s, (f) wave only Figure A34: Y – velocities in cylinder wake, combined wave current flow, T=0.7s, at location x= 2

½ D, y= 0.6 D, for C = (a) 150, (b) 125, (c) 100, (d)75, (e) 50mm/s, (f) wave only Figure A35: X – velocities in cylinder wake, combined wave current flow, T=1.0s, at location x= 2

½ D, y= 0.6 D, for C = (a) 150, (b) 125, (c) 100, (d)75, (e) 50mm/s, (f) wave only Figure A36: Y – velocities in cylinder wake, combined wave current flow, T=1.0s, at location x= 2

½ D, y= 0.6 D, for C = (a) 150, (b) 125, (c) 100, (d)75, (e) 50mm/s, (f) wave only Figure A37: X – velocities in cylinder wake, combined wave current flow, T=2.0s, at location x= 2

½ D, y= 0.6 D, for C = (a) 150, (b) 125, (c) 100, (d)75, (e) 50mm/s, (f) wave only Figure A38: Y – velocities in cylinder wake, combined wave current flow, T=2.0s, at location x= 2

½ D, y= 0.6 D, for C = (a) 150, (b) 125, (c) 100, (d)75, (e) 50mm/s, (f) wave only Figure A39: X – velocities in cylinder wake, current only flow, at location x = 2 ½ D, y= 1.1 D, for

currents (a) 150, (b) 125, (c) 100, (d) 75, (e) 50 mm/s

Figure A40: Y – velocities in cylinder wake, current only flow, at location x = 2 ½ D, y= 1.1 D, for

currents (a) 150, (b) 125, (c) 100, (d) 75, (e) 50 mm/s

Figure A41: X – velocities in cylinder wake, combined wave current flow, T=0.7s, at location x= 2

½ D, y= 1.1 D, for C = (a) 150, (b) 125, (c) 100, (d)75, (e) 50mm/s, (f) wave only Figure A42: Y – velocities in cylinder wake, combined wave current flow, T=0.7s, at location x= 2

½ D, y= 1.1 D, for C = (a) 150, (b) 125, (c) 100, (d)75, (e) 50mm/s, (f) wave only Figure A43: X – velocities in cylinder wake, combined wave current flow, T=1.0s, at location x= 2

½ D, y= 1.1 D, for C = (a) 150, (b) 125, (c) 100, (d)75, (e) 50mm/s, (f) wave only Figure A44: Y – velocities in cylinder wake, combined wave current flow, T=1.0s, at location x= 2

½ D, y= 1.1 D, for C = (a) 150, (b) 125, (c) 100, (d)75, (e) 50mm/s, (f) wave only Figure A45: X – velocities in cylinder wake, combined wave current flow, T=2.0s, at location x= 2

½ D, y= 1.1 D, for C = (a) 150, (b) 125, (c) 100, (d)75, (e) 50mm/s, (f) wave only Figure A46: Y – velocities in cylinder wake, combined wave current flow, T=2.0s, at location x= 2

½ D, y= 1.1 D, for C = (a) 150, (b) 125, (c) 100, (d)75, (e) 50mm/s, (f) wave only Figure A47: X – velocities in cylinder wake, current only flow, at location x = 1 ¼ D, y=0, for

currents (a) 150, (b) 125, (c) 100, (d) 75, (e) 50 mm/s

Figure A48: Y – velocities in cylinder wake, current only flow, at location x = 1 ¼ D, y=0, for

currents (a) 150, (b) 125, (c) 100, (d) 75, (e) 50 mm/s

Figure A49: X – velocities in cylinder wake, combined wave current flow, T=0.7s, at location x= 1

¼ D, y=0, for C = (a) 150, (b) 125, (c) 100, (d)75, (e) 50mm/s, (f) wave only

Figure A50: Y – velocities in cylinder wake, combined wave current flow, T=0.7s, at location x= 1

¼ D, y=0, for C = (a) 150, (b) 125, (c) 100, (d)75, (e) 50mm/s, (f) wave only

Figure A51: X – velocities in cylinder wake, combined wave current flow, T=1.0s, at location x= 1

¼ D, y=0, for C = (a) 150, (b) 125, (c) 100, (d)75, (e) 50mm/s, (f) wave only

Figure A52: Y – velocities in cylinder wake, combined wave current flow, T=1.0s, at location x= 1

¼ D, y=0, for C = (a) 150, (b) 125, (c) 100, (d)75, (e) 50mm/s, (f) wave only

Figure A53: X – velocities in cylinder wake, combined wave current flow, T=2.0s, at location x= 1

¼ D, y=0, for C = (a) 150, (b) 125, (c) 100, (d)75, (e) 50mm/s, (f) wave only

Figure A54: Y – velocities in cylinder wake, combined wave current flow, T=2.0s, at location x= 1

¼ D, y=0, for C = (a) 150, (b) 125, (c) 100, (d)75, (e) 50mm/s, (f) wave only

Figure A55: X – velocities in cylinder wake, current only flow, at location x = 1 ¼ D, y= 0.6 D, for

currents (a) 150, (b) 125, (c) 100, (d) 75, (e) 50 mm/s

Figure A56: Y – velocities in cylinder wake, current only flow, at location x = 1 ¼ D, y= 0.6 D, for

currents (a) 150, (b) 125, (c) 100, (d) 75, (e) 50 mm/s

Figure A57: X – velocities in cylinder wake, combined wave current flow, T=0.7s, at location x= 1

¼ D, y= 0.6 D, for C = (a) 150, (b) 125, (c) 100, (d)75, (e) 50mm/s, (f) wave only Figure A58: Y – velocities in cylinder wake, combined wave current flow, T=0.7s, at location x= 1

¼ D, y= 0.6 D, for C = (a) 150, (b) 125, (c) 100, (d)75, (e) 50mm/s, (f) wave only Figure A59: X – velocities in cylinder wake, combined wave current flow, T=1.0s, at location x= 1

¼ D, y= 0.6 D, for C = (a) 150, (b) 125, (c) 100, (d)75, (e) 50mm/s, (f) wave only Figure A60: Y – velocities in cylinder wake, combined wave current flow, T=1.0s, at location x= 1

¼ D, y= 0.6 D, for C = (a) 150, (b) 125, (c) 100, (d)75, (e) 50mm/s, (f) wave only Figure A61: X – velocities in cylinder wake, combined wave current flow, T=2.0s, at location x= 1

¼ D, y= 0.6 D, for C = (a) 150, (b) 125, (c) 100, (d)75, (e) 50mm/s, (f) wave only Figure A62: Y – velocities in cylinder wake, combined wave current flow, T=2.0s, at location x= 1

¼ D, y= 0.6 D, for C = (a) 150, (b) 125, (c) 100, (d)75, (e) 50mm/s, (f) wave only Figure A63: X – velocities in cylinder wake, current only flow, at location x = 1 ¼ D, y= 1.1 D, for

currents (a) 150, (b) 125, (c) 100, (d) 75, (e) 50 mm/s

Figure A64: Y – velocities in cylinder wake, current only flow, at location x = 1 ¼ D, y= 1.1 D, for

currents (a) 150, (b) 125, (c) 100, (d) 75, (e) 50 mm/s

Figure A65: X – velocities in cylinder wake, combined wave current flow, T=0.7s, at location x= 1

¼ D, y= 1.1 D, for C = (a) 150, (b) 125, (c) 100, (d)75, (e) 50mm/s, (f) wave only Figure A66: Y – velocities in cylinder wake, combined wave current flow, T=0.7s, at location x= 1

¼ D, y= 1.1 D, for C = (a) 150, (b) 125, (c) 100, (d)75, (e) 50mm/s, (f) wave only