The dynamic response of floating offshore wind turbine platform in wave–current condition Open Access

The increasing demand for renewable energy has led to the growth of wind energy, with floating offshore wind turbines (FOWTs) being a promising solution for generating energy in deep water where traditional turbines are unable to operate. FOWTs also benefit from greater and more consistent wind resources in deeper water and eliminate the visual impact associated with near-shore turbines.^1,2 Several FOWT designs, such as OC4 DeepCwind,³ Hywind,⁴ and TetraSpar,⁵ have been developed extensively. For FOWTs, their applications are expected to expand to more diverse locations, which may present more complex sea states, resulting in more significant challenges in ensuring adequate stability, power output, and reliability under diverse operating conditions, for the design of FOWT, and this has been investigated extensively both numerically and experimentally in our previous studies^6–8 and other researchers.^9–14 

In addition to wave–platform interaction, the appearance of water current in some areas of sea may lead to additional platform motion, known as vortex-induced motion (VIM). This phenomenon usually occurs when a cylindrical structure or a bluff body is moored or elastically mounted in the presence of current. The amplitude of the response can be particularly high when the frequency of vortex shedding becomes synchronized with the structure vibration frequency.^15,16 Such synchronization is known as lock-in, and it occurs over a wide range of flow velocity.

The VIM of cylinders and monocolumn platforms has been extensively studied experimentally.^17–19 It was found that the platform follows a classic eight-shaped orbital trajectory for some cases. This low-frequency response, especially in cross-flow (CF) direction, may result in potential damage to FOWT's mooring system and cause fatigue problem.²⁰ The in-line (IL) motion is relatively small compared to that in the CF direction.

Compared to wave, current–platform interaction gets less attention during the design process of FOWT platform. This is partially because the water current caused by wind has a characteristic speed of 0.05–0.5 m/s, which is less than the minimal threshold required for VIM to occur. The speed of tidal current is usually larger than surface current, whose maximum value can be as large as 4.5 m/s as observed in some channel areas,²¹ with a water depth ranging from 40 to 110 m, but this velocity is much smaller in deep, open ocean. However, in certain locations, such as the Gulf Stream, the current velocity at the free surface can exceed 2 m/s, which is sufficiently large to induce VIM for a floating platform having cylinders, such as SPAR.^22–24 The semi-submersible (SS) platform, on the other hand, has a smaller aspect ratio (draft/characteristic length), which has been investigated by Gonçalves et al.^25,26 Their experimental findings confirmed that VIM occurs even at a relatively low current speed for two SS platforms with different geometric dimensions. Other research regarding VIM of different platforms can also be found recently.^27,28 Due to the inherent disadvantage of potential-flow theory method, in which fluid is assumed irrotational and non-viscous, numerical analysis involving offshore structure–fluid interaction has been conducted using the finite element method²⁹ (FEM) or computational fluid dynamics (CFD) method. The later considers viscosity of fluid directly by solving the Navier–Stokes equation with turbulence models.^30–34 In their studies, the formation and shedding of the vortices due to VIM is clearly observed.

A combined colinear wave–current interaction with four square columns platform is further studied experimentally.^35,36 The findings indicated that the adding of wave sometimes tends to have little impact on VIM, while mitigating VIM entirely in other cases. This is further observed in the studies of Maximiano et al.³⁷ and Li et al.³⁸ A detailed examination on the fluid flow vorticity field indicated that the reduced amplitude of VIM is caused by the wave interaction with current and platform, changing the vortex shedding pattern, and thus the vortex shedding frequency.

While VIM mitigation by waves is observed in past studies, most of existing investigations are focused on the flow condition where wave and current are aligned. In reality, it is very likely the angle between the wave and current can vary in different sea states. For instance, in the project of LIFE50+ for a 10 MW wind turbine, the wave and current inter-angle ranges from 82.5° to 150° at three deployment sites with a water depth over 50 m.³⁹ It is, therefore, critical to understand the wave–current–structure interaction under various angles and flow conditions.

In this paper, the dynamic response of the floating platform in complex sea conditions is numerically studied using a high-fidelity CFD tool.⁴⁰ We aim at illustrating the underlying mechanisms that are related to the wave–current interaction with FOWT platforms using this tool. The rest of the paper is organized as follows. The numerical method including the governing equations of the fluid dynamics, the structural dynamics, and the mooring system will first be presented in Sec. II, together with a description of the physical problem to be studied and the parameters for both the OC4 DeepCwind platform by National Renewable Energy Laboratory (NREL) and the BW IDEOL platform with Électricité de France. Section III displays the numerical results, where the wave-only, current-only conditions are first examined for two FOWT platforms as comparisons. Then, the combined wave–current condition studies for the OC4 platform at various wave–current angles and wave parameters are conducted, and the conclusions are drawn in the last section.

The wave–current interaction of the FOWT platform is simulated using an integrated toolbox based on the OpenFOAM code. Particularly, the solver is a multiphase flow solver interFoam in OpenFOAM. To apply mooring lines as restraints, an in-house code is integrated into interFoam. Additionally, a wave generation boundary condition and active wave absorbing scheme are implemented in the simulation.⁶ 

The two platforms studied are OC4 semi-submersible platform and a barge IDEOL platform as shown in Fig. 2. The OC4 semi-submersible platform model is based on a 1:73 model test performed at the University of Tokyo by Gonçalves et al.²⁶ The platform is made up of four columns, one central column with a smaller diameter and three offset columns with larger diameters. Columns are connected by crossbars in between. There are base columns attached below the side columns. In the experiment, the model was restrained by four perpendicular mooring lines. The main parameters, including the equivalent stiffness of the mooring system, are summarized in Table I. The natural frequencies of the platform in IL and CF directions are 9.4 and 9.6 s, respectively, which were obtained via free decay tests.

The barge IDEOL platform is a 1:50 model, which was experimentally tested in the National Research Institute of Fisheries Engineering (NRIFE) wave tank in Japan,⁴⁶ shown in Fig. 2(b). The width of the barge semi-submersible platform is 0.82 m, with a draught of 0.14 m. The skirt with 0.055 m width is attached at the bottom to reduce the dynamics motion response. Compared to the OC4 platform, this barge platform has a simpler geometry and is easier to construct, with a larger area of water plane and smaller draft. To constrain the platform, three catenary mooring lines are applied. The nominal diameter of these studless chains is 3 mm with a total length of 8 m. The geometric parameters of the platform can be found in Fig. 2 and Table I.

In ocean engineering, the geometry of a platform significantly influences its motion response, particularly in interaction with water currents. The above-mentioned two platforms exhibit distinct geometries, primarily differentiated by their waterplane (WP) area. The IDEOL barge platform, akin to a hollowed-out box, has a substantially larger WP area compared to the SS platform. This expands WP area results in a shallower draft and a reduced aspect ratio (defined as draft/characteristic length). In a vortex-induced motion (VIM) study, a lower aspect ratio typically exhibits enhanced three-dimensional characteristics at the platform's bottom edge, subsequently altering the motion amplitude.

The computational domain is shown in Fig. 3 with top and side views. The boundary conditions are set as follows: The zero-gradient pressure condition is applied at the inlet and outlet boundaries with the air speed equal to zero, while the fluid velocity is given by a build-in boundary based on the wave theory, for the generation of inflow wave–current condition and wave absorbing. For those cases with oblique incident waves, the front boundary is imposed the same settings as the inlet boundary condition for wave generating. A non-slip wall boundary condition is applied to the bottom.

To accurately model the motion of platform under both wave and current conditions, it is essential to ensure that the mesh resolution meets different mesh density requirements. For instance, to capture VIM, the separation of the boundary layer around the structure and the vortex street at the downstream should be accurately modeled. Therefore, CFD mesh is refined at the near wall field region as well as the wake region. To reduce the overall cell numbers of the computational domain, a hybrid mesh is used, which is made up of the near-field structured mesh (red one) and the far-field unstructured mesh as shown in Fig. 4. Within the boundary layer, the thickness of the mesh is set that the y+ around the platforms ranges from 1.0 to 4.0. The surface cell on the platform is 1/100 of the characteristic length D. At the near field of the structure, the average cell size is 1/50D. At the far field region, to ensure the accuracy of numerical wave generation, the cells near air–water free surface are refined. In particular, at least eight cells are used along the z direction per wave height and at least 180 cells per wavelength.

The convergence test of the numerical simulation is conducted, and the results are shown in Table II. Three mesh sets with different cell counts are used, with which the normalized IL and CF motions (A_x/D and A_y/D) are compared, as well as the frequency of the cross-flow oscillation f/f_n. The disparity between the medium and fine cases is less significant than that between the intermediate and coarse cases. This suggests that the intermediate grid is sufficient fine for the current research. Similarly, for the sensitivity study with different time steps, the predicted motion hardly changes when UΔt/D < 0.002. Considering the cost of computational time, a time step of UΔt/D = 0.002 is chosen for the CFD modeling in this study.

PIMPLE [a combination of Pressure Implicit with Splitting of Operator (PISO) and Semi-Implicit Method for Pressure-Linked Equations (SIMPLE)] algorithm is utilized to solve the pressure–velocity coupling. A second-order Crank–Nicolson scheme is used for temporal discretization. The second-order upwind scheme is adopted for convective terms. Gradient terms are handled via a second-order cell-limited Gauss linear scheme. The total cell of the simulation is around 350 × 10⁶ for both platforms. The computations are made in parallel with five nodes (180 cores) for each case on Cirrus HPC (http://www.cirrus.ac.uk). The average simulation time is 3T_n per day, which may vary depending on the specific cases.

When waves and currents coexist, their respective motions become coupled. To decouple this effect, we start with a comparative study on a fluid–structure interaction either induced by wave or current separately for both OC4 and IDEOL platforms. Because of their different geometric characteristics, it is expected to observe different dynamic motion responses. For the validation purpose, the comparison between our CFD results with experimental testing has been done for waves interaction with IDEOL platform. Other validations for this CFD tool can be found from our previous publications on (a) wave–structure interaction for floating platforms,^8,47 (b) wave energy devices,⁴⁴ and (c) the current–structure interaction for the OC4 platform with VIM studies.^31,48

Either current or wave interaction with OC4 platform is first studied, and the flow conditions are listed in Table III. Figure 5 displays the amplitude of the motion response in the current-only scenario along with the experimental data, in which IL component (A_cx) and CF component (A_cy) are plotted against flow velocities. They are calculated by multiplying the root mean square (RMS) displacement by $2$ and then normalized with the characteristic length, which is D_s for the OC4 platform and W_B for the IDEOL platform.

In VIM analysis, the freestream velocity is commonly normalized using the natural frequency of the system (f_n). The reduced velocity is defined as V_r = U/f_nD, where U and D are the flow velocity and characteristic length of the structure. It can be rewritten as V_r = UT_n/D, where T_n is the natural frequency of structure. From a physical perspective, the numerator can be considered as the distance that the constant fluid flows over the structure in one natural vibration period. Thus, V_r is an indicator for the ratio between this distance and the structural dimension. In this study, cases with different V_r are achieved by only varying the flow velocity; meanwhile, Re number is also synchronized with V_r since they are both a representative of the flow velocity.

The plot indicates that the CFD predictions are in good agreement with the experiments. The IL motion is significantly smaller compared to that of CF motion with A_cx/D being less than 0.1, indicating that the IL movement of platform is not dominant. The CF motion response shown in Fig. 5(b), however, reveals a very typical current–structure interaction VIM phenomenon. In particular, the lock-in region ranges from V_r = 5 to 10, in which the maximum A_cy/D characterized by VIM reaches a value of 0.41 at V_r = 8.1. At real sea conditions, the full-scale current velocity in the lock-in region can vary from 1.0 to 1.45 m/s. Therefore, it is expected to observe significant platform motion within this velocity range.

The added mass coefficient in the CF direction (C_a) also agrees well with the experiment as shown in Fig. 6, which is defined as C_a = $−R fft F y t fft y ̇ t/m,$ where F_y(t), y are the hydrodynamic force and displacement in the CF direction, respectively. R() represents the real part of the complex number, and fft represents the fast Fourier transform (FFT) operator. The large and positive values of C_a with V_r < 9.9 denote the synchronization with the vortex shedding frequency. As the velocity increases, C_a decreases and becomes negative after V_r > 9.9, indicating the end of resonance.

The resonance in the lock-in region is also reflected by the time-series and the corresponding FFT analysis shown in Fig. 7, where a dominant VIM motion can be observed at V_r = 8.1 in the lock-in region. With a smaller V_r = 3.7, the periodic motion exists but has a lower frequency and smaller amplitude. At larger V_r beyond lock-in region, the amplitude is small but with higher-order frequency components.

The vorticity field is plotted and examined in Fig. 8 to reflect the typical vortex shedding associated with VIM phenomenon. It is seen that with the increase in V_r, the vorticity becomes stronger, and the flow field becomes more irregular. Within the lock-in region at V_r = 8.1 [Figs. 8(d)–8(f)], the vortices generate alternately from both sides of column and then shed from either side of the column at a frequency equal to the lock-in frequency f_n. An anti-clockwise vortex is observed when the platform reaches y_min in Fig. 7(e), and another anti-clockwise vortex is observed, while a clockwise vortex is shed when y_max at (f), revealing a typical 2P mode for the wake in VIM. At V_r = 3.7, no obvious vortex shedding is observed, which associates with a smaller motion in the CF direction.

In addition to the above-mentioned current-only condition, the wave-only condition is also examined for OC4 to set up a baseline model for the subsequent wave–current investigations. Figure 9 shows the predicted surge response amplitude operators (RAO) with various wave heights (H) and wave periods (T). It is seen that the RAO increases with T, as the platform's structure natural period aligns more closely with it, increasing the motion response. The RAO relationship with H is rather complex due to enhanced mooring forces with increasing H, as well as the higher nonlinearity with larger H. Therefore, the variation follows a nonlinear trend.

The IDEOL platform is analyzed starting with the current-only scenarios. The response amplitudes in IL and CF directions are shown in Fig. 10, with the parameters summarized in Table IV. It is seen that barge-type platform has an even smaller IL motion compared with the OC4 platform. The motion in the CF direction is also relatively smaller. For the largest reduced velocity of V_r = 9.6 (U = 2.3 m/s at full scale), the maximum A_cy/D is less than 0.2. Only at this largest V_r, the periodic platform motion characterized by VIM becomes notable, as shown in the time-series plots in Fig. 11.

Compared to the OC4 platform, the VIM phenomena are less profound, which might be due to several reasons.

First, the most pronounced vortex-induced motion (VIM) for the SS platform occurs around V_r = 8.1. Comparatively, for the IDEOL platform to experience significant VIM, it requires a much higher reduced velocity of at least 10.0 or even higher, as can be seen in Fig. 10. Thus, the VIM of IDEOL platform is not obvious. In addition, the aspect ratio of the IDEOL platform is 0.17, which is much smaller than that of 1.64 for the OC4 platform. This finding agrees with the research by Goncalves et al. that the response of CF motion of a cylinder weakens as its aspect ratio decreases. The VIM could be even negligible if the aspect ratio is less than 0.3.¹⁸ 

Then, the dynamic response of IDEOL platform for the wave-only condition is studied for a series of wave periods (Table IV). In the experiment, the wave heights varied from 2.5 to 7.5 m. In this validation, an intermediate wave height of H = 5 m is chosen. Figure 12 shows the predicted RAOs in comparison with the experiment (EXP) and numerical modeling (SIM) data. In the SIM studies, the potential-flow-based method is used, the hydrodynamic coefficient is obtained by Ansys Aqwa software, and the dynamic response is calculated using DNV-GL's Bladed software package⁴⁶ to couple the hydrodynamic loads. The RAOs are normalized by the wave amplitude for heave and surge motions, while the pitch response is normalized by kH/2 Fig. 12.

For the wave periods studied, an averaged RAO for the surge and heave are typically 0.84 and 1.0, respectively, from CFD and EXP. However, the pitch RAO reveals an initial increasing and then decreasing trend. The peak RAO occurs at T = 14.1 s. It is evident that better agreement between the present CFD predictions and the experimental data has been reached than the results obtained from the potential-flow-based tool (SIM). One explanation for the improved accuracy of CFD modeling over the potential theory method is that the later linearizes the wave–air free-surface equation at the time-averaged positions; therefore, the nonlinear effect of fluid–structure interaction, represented by the changing wetted surfaces, is not very well captured.⁴⁶ As shown in Fig. 13, the green water can be observed clearly showing the changing wetted surface. Also, for the CFD modeling, tuning the viscous damping to fit the experiments is not required, which is usually needed for a viscous-modified potential flow model.

In the above two sections for current-only and wave-only cases, it is observed that the VIM phenomena are more profound for a semi-submersible platform than a barge platform. Therefore, the following studies on a combined wave–current–structure interaction will be focused on OC4 semi-submersible platform.

It is well known that in a real sea state, current and wave do not always exist alone, and the extreme loading condition for a FOWT platform may occur with specific combinations of wave and current. In our previous study on a colinear wave–current condition,³⁸ it was found that the current-induced CF motion can be mitigated with the addition of waves, depending on V_r under investigation. This conclusion is consistent with others' findings. Some other studies also found that if the wave and current were non-colinear, the mitigation became less obvious.^49,50 To investigate this phenomenon, this section is dedicated to examining the impact of the angle of the flow direction between current and wave (θ) on the platform's dynamic responses. Three angles varying from θ = 0° to 90° are selected. Typical wave period and wave height are T = 2.0 s, H = 0.09 m. The current speed varies from 0.05 to 0.20 m/s, leading to the reduced velocity V_r ranging from 2.3 to 11.6, as shown in Table V.

The responses of platform are shown in Fig. 14 with different angles. Given a combined wave–current condition, the IL motion varies a little with reduced velocity, indicating that varying current speed does not affect IL motion significantly, as shown in Fig. 14(a). However, the IL motion is noticeably impacted by angles variation (θ). In fact, with θ = 0°, A_x/D is the largest and close to A_w in the wave-only cases, while θ = 90°, A_x/D is the smallest and close to that in the current-only cases. Unlike the above IL response, CF motion varies significantly with reduced velocity and the peak values can be clearly captured [Fig. 14(b)]. As the angle θ increases, A_y/D increases across all V_r. Therefore, for safety design purposes, it is recommended to pay more attention to those cases with θ = 90°. Beyond the lock-in region, with θ > 0°, A_y/D are greater than those observed in the current-only cases and close to A_w. However, within the lock-in region, with increasing θ to 90°, A_y/D is always larger than that of either wave-only or current-only. The large CF motion in this wave–current condition is induced by the non-zero wave–current angle. As the velocity components along the y axis increase with the angle, CF response increases due to the enlarged inertia wave force acting on the platform. In addition, the flow field and VIM are altered with a combined wave–current interaction.

However, the variation of a_c with V_r resembles the pattern of current-only cases, with the peak amplitude occurring at V_r = 8.1 and decreasing beyond this V_r. This indicates that the VIM effect still exists even with waves. Hence, the response peaks in the wave–current cases depicted in Fig. 14 are primarily due to the current's contribution within the lock-in region. A comparison between Figs. 15(a) and 15(b) indicates that larger θ leads to an amplified VIM. It is also worthwhile to note that with a larger angle, the a_c near the peak value at Vr = 8.1 also increases, which means that the VIM becomes significant for a wider range of reduced velocities with the addition of waves.

The effects of angle are also reflected in dominant frequencies, as analyzed in Fig. 16. For current-only cases, f_y increases with V_r and locks onto f_c in the lock-in region, leading to a large motion response. For cases with θ = 0°, f_y is the same as that of current-only. However, for those with 0° < θ < 90°, outside the lock-in region, f_y is close to f_w indicating the platform's motion is dominated by waves. Within the lock-in region f_y = f_c, the resonance occurs. With an increasing θ, the lock-in region becomes wider, revealing a more vulnerable platform due to large-scale motions under a wide range of current velocity. The time-series distribution of y/D and their FFT analysis displayed in Fig. 17 reinforce the above observations. In fact, two dominant frequencies appear in relation to f_c and f_w. Outside lock-in region, the low-frequency components are not as prominent compared to the high-frequency components. Within the lock-in region, the low-frequency component is substantially large and increases with angles. In addition to the above dominant frequencies, other spikes are also noted, which might be caused by the nonlinear coupling between the vibration of platform and fluid flow. The difference frequency f_diff  = f_w − f_c and sum frequency f_sum = f_w + f_c exist, although with a relatively small magnitude, which is also noticeable in the cases with 90° with heir magnitudes increasing with angle.

It should be noted that the symmetric vortex pair does not provide net force along the CF direction, but it interferes with the vortex formed by the steady flow. Moreover, the flow in the −x direction caused by the waves mitigates the generation of a complete vortex due to a steady current, leading to a possible reduction in the cross-flow motion.

Compared to the cases with θ = 0°, the vortex field for θ = 90° in Fig. 19 shows more asymmetric characteristics. Since the waves propagate along the y axis, the flow along the x axis is less affected. As a result, when a vortex forms, it is periodically stretched and carried by oscillatory flow in the CF direction, causing it to split into smaller vortices. At (y/D)_max and (y/D)_min in Figs. 19(a) and 19(e), a large vortex is generated on one side of the offset column, but breaks down into small eddies. The vortex from the central small column presents a 2S mode with one clockwise and one counterclockwise vortex detaching from the central column within one cycle. Moreover, the shed vortex not only moves downstream but also along the CF direction, bringing it closer to the platform and increasing the chances of encountering between the clockwise and counterclockwise vortices, thereby changing the motion frequency. This is clearly depicted from Figs. 19(b) and 19(c), where V_y is positive, while V_y is negative at Fig. 19(f). It is clearly indicated that when the wave and current are colinear, oscillatory flow mitigates the generation of a complete vortex due to current; thus, the VIM is mitigated. The disturbed vortex field by the symmetric vortex from the oscillatory flow contributes to this trend.

The platform motion trajectory with different θ and V_r is shown in Fig. 20. For current-only cases, the platform experiences significant motion displacement within the lock-in region at V_r = 8.1. The predominant motion is along the y axis, and the movement along the x axis is limited. This pattern of movement is similar to that in the study on a four-square column semi-submersible platform, where a typical eight-shaped trajectory is not found.²⁵ 

Previous studies on colinear wave–current–structure interaction indicated that the CF response was not only affected by the reduced velocity, but also influenced by the wave parameters, i.e., the wave height and wave period (Gonçalves et al.^35,36). In addition, our findings from Sec. III C for various θ values reveal that the largest CF motion occurs at θ = 90°. In this section, the investigation is focused on the study of wave–current–platform interaction at θ = 90° for a series of wave heights and wave periods (Table VI). The reduced velocity is fixed at V_r = 8.1, where the strongest VIM occurs.

The effect of wave parameters on the platform's response is shown in Fig. 21. It is seen that the IL motion is relatively small compared with the large platform dimensions. The overall CF motion is larger than that observed in the current-only cases and increases with wave period T. The motion response is also influenced by wave height H. As H increases, A_y/D approaches that of wave-only cases. A_y/D decreases monotonically with H for T = 1.5 s. However, peaks are observed for T = 2.0 s and T = 2.6 s, and the peak A_y/D is seen at H = 0.04 and 0.07 m, respectively. This concludes an important finding, e.g., waves with a small wave height may also lead to large platform motion under the wave–current condition.

This can be further inferred by decomposing the motion amplitude shown in Fig. 22(a). For cases with small H < 0.06 m, the motion induced by current, indicated by a_c, varies between 0.4 < a_c/D < 0.5, which is larger than that observed in current-only cases, indicating an enhanced VIM effect. However, for H > 0.06 m, a_c decreases significantly with increasing H, indicating a mitigated VIM effect by waves. Meanwhile, a_w becomes dominant after H > 0.11 m, and the motion is locked onto f_w rather than f_c, as shown in Fig. 22(b). The shift in the predominant influence from currents to waves can also be observed from the time histories of y/D and FFT plots in Fig. 23. As H increases, the low-frequency motion induced by current becomes less prominent. The FFT analysis indicates the appearance of difference frequencies and sum frequency components, especially for θ = 90°. These frequencies are only excited when the contribution of current and wave to the system's energy is roughly equivalent. As H increases, the energy at f_c weakens, causing above two frequencies to become less significant.

The differences in wave parameters are also reflected in the vorticity field shown in Fig. 24 for H = 0.04 m. Compared with larger H = 0.09 m in Fig. 19, the vortex herein are less disturbed by waves, thus leading to a larger CF motion response. The vortex shedding appears at the 2P mode, with two pairs of vortices shed in one cycle, such as the vortex A₁ and B₁ at instant b and A₂ and B₂ at instant e. As the wave period decreases, the vortex flow exhibits greater levels of turbulence and disorder, as seen from Figs. 25(a) and 25(c). Additionally, the vortex motion is observed to occur in close proximity to the structure with smaller T.

Figure 26 plots velocity ratio (α′) as a function of KC number with θ = 90°. For the wave parameters examined, most cases are within a regime where VIM is obvious, thus associated with a large CF motion. For those falling into inertia force regime, the response is mainly wave-dominant.

This study explores the fluid–structure interaction of floating offshore wind turbines under various scenarios, including wave-only, current-only, and wave–current conditions in which the motion response is one of the main concerns. The CFD package OpenFOAM with further developed models is used for the simulation. To reduce the computational size for wave–current cases, a hybrid mesh and active wave absorbing scheme are utilized. The comparison study shows that a semi-submersible platform has a larger aspect ratio, exhibits a larger cross-flow (CF) motion, and experiences the lock-in phenomenon for the reduced velocities considered. Conversely, a barge platform, with a larger cross-surface area and low aspect ratio, shows a much smaller motion. Obvious vortex-induced motion (VIM) is not seen with selected V_r, indicating that there is little chance for a floating barge platform undergoing a lock-in phenomenon.

The angle between the directions of wave and current significantly affects the platform's CF motion, with a mitigated VIM and small CF motion being observed when the wave and current are colinear or having a small angle. Increasing the angle from 0° to 90° leads to a more significant VIM and larger CF motion, with the oscillation frequency being more synchronized with the system's natural frequency. The motion displacement reaches its maximum at angle of 90°, where the motion induced by wave and current are in the same direction and coupled nonlinearly. A combination of largest wave height and the most significant VIM does not result in the largest CF motion. The motion can be even larger for smaller wave height, in some cases. The study of Keulegan–Carpenter number (KC numbers) and velocity ratio shows that the motion is mitigated if the problem is inertia-force dominant, whereas motion will be enhanced if it is drag-force dominated.

The interaction effect factor (IEF), which represents the motion ratio in wave–current condition compared to the sum motion in wave and current conditions separately, is evaluated. For large wave height and small wave period, the ratio is lower than 0.75, suggesting that the interaction of wave and current mitigates the sum of their individual motion. However, the most extreme motion does not necessarily take place with the largest wave height. With a smaller wave height, the ratio may be larger than 1.0. Remarkably, the interaction of wave and current could sometimes amplify the IEF to values as high as 1.35. At the design stage of floating offshore wind turbines platforms, these coupling effects have generally not been accounted for though it is sometimes critical as we illustrated. Therefore, our findings offer valuable insight for engineers considering the installation of wind turbines in regions where currents and waves coexist, potentially leading to more efficient and safer designs.

Although with the above findings, one limitation of the present study is the omission of wind loads and the resultant motion responses and critical elements in the interaction between FOWTs and current/waves. This is because the load generated by the upper turbine can alter the pitch and yaw motion, potentially influencing the vortex shedding around the structure. Although our current model does not include an aerodynamic simulation for wind turbines, future work is planned to expand the model's capabilities to address this aspect.

This work used the Cirrus UK National Tier-2 HPC Service at EPCC (http://www.cirrus.ac.uk) funded by the University of Edinburgh and EPSRC (EP/P020267/1) and ARCHIE-WeSt High-Performance Computer (www.archie-west.ac.uk) based at the University of Strathclyde. This research was supported by the National Natural Science Foundation of China (Grant Nos. 52271282 and 51909189), Guangdong Basic and Applied Basic Research Foundation (2022A1515010846), and Tsinghua Shenzhen International Graduate School via the Scientific Research Start-Up Funds (QD2021023C). Xiang Li thanks China Scholarship Council (CSC) and University of Strathclyde (UoS) for financial support during his Ph.D. study in the UK.

The authors have no conflicts to disclose.

Xiang Li: Conceptualization (equal); Investigation (equal); Methodology (equal); Validation (equal); Writing – original draft (equal); Writing – review & editing (equal). Qing Xiao: Conceptualization (equal); Methodology (equal); Project administration (equal); Resources (equal); Supervision (equal); Writing – original draft (equal); Writing – review & editing (equal). Enhao Wang: Conceptualization (supporting); Resources (supporting); Writing – review & editing (supporting). Christophe Peyrard: Conceptualization (supporting); Resources (supporting). Rodolfo Trentin Gonçalves: Conceptualization (supporting); Writing – review & editing (supporting).

The data that support the findings of this study are available within the article.