Floating offshore wind turbine (FOWT) technology has attracted increasing attention over the past decades because of its ability to generate stable power at water depths exceeding 60 meters. According to Musial et al. (2023), the global installed capacity of floating offshore wind power is projected to reach 380–394 GW by 2032, representing an approximately sixfold increase from the current level. As a result, the advances in design and analysis technologies for floating platforms have become a critical focus in the field. FOWT platforms are commonly categorized into semi-submersible, tension leg platform (TLP), and spar types, among which semi-submersible platforms account for more than 80% of current projects (Robertson et al., 2014).

These structures typically consist of large cylindrical columns and must maintain stable motion performance under complex marine environments involving waves, wind, and currents (Roddier et al., 2010). In particular, the interactions between platform motions and the mooring system are related directly to the structural integrity and energy production efficiency of FOWT systems (Lefebvre and Collu, 2012).

Potential theory-based methods are used widely to analyze offshore structures. Popular commercial tools such as OrcaWave, WAMIT, and AQWA offer high computational efficiency and are well-suited for frequency-domain response analysis (MacCamy and Fuchs, 1954). On the other hand, potential theory inherently assumes inviscid flow and cannot account for nonlinear hydrodynamic behaviors such as viscous effects, flow separation, and turbulence (Morris-Thomas and Thiagarajan, 2004). Souza et al. (2024) proposed a calibrated hybrid approach that integrates potential theory with Morison-type viscous drag elements to address these limitations. Their method adjusts the drag coefficients based on model test data, assigning higher coefficients near the free surface to capture viscous excitation and lower coefficients at depth for damping. This enables the simultaneous representation of excitation and damping, which is particularly effective for the surge and heave responses in semi-submersible FOWTs. Nevertheless, difficulties remain in accurately predicting low-frequency damping effects. In contrast, computational fluid dynamics (CFD) analysis, which is based on the Navier–Stokes equations, can capture viscous and nonlinear fluid behaviors with higher fidelity (Kim et al., 2011). Recent studies have increasingly used CFD to complement the limitations of potential theory. For example, Burmester et al. (2018) performed surge decay tests on semi-submersible platforms using CFD and quantified the difference from potential theory results that neglected viscous damping. Mohseni et al. (2018) experimentally and numerically examined the wave run-up around cylindrical floaters, and Kim et al. (2023) implemented a nonlinear Morison drag model using CFD to estimate the damping coefficients of FOWTs. Rentschler et al. (2022) also compared CFD predictions against free-decay test data and evaluated the sensitivity of results to damping coefficient settings.

Recent approaches to overcome the limitations of potential theory have incorporated correction factors based on experimental or CFD results (Nam et al., 2008). Li et al. (2022) and Mian et al. (2024) analyzed the influence of mooring systems, wave conditions, and environmental parameters on the dynamic responses of floating systems using CFD, highlighting the necessity and limitations of correction factor applications. Bertozzi et al. (2024) proposed a numerical model calibration procedure to reproduce the dynamic response of the OC4-DeepCWind semi-submersible platform under bichromatic wave conditions, identifying the influence of uncertain parameters such as mooring line length and making accurate low-frequency response predictions through experiment-based calibration, including free-decay tests.

Nevertheless, most studies derived the correction factors based primarily on platform-only models. Hence, quantitative comparative studies evaluating whether the same correction factors apply to fully coupled systems, including towers and turbines, are lacking. Therefore, it is necessary to investigate whether the correction factors obtained under platform-only conditions can be reliably applied to fully coupled systems. In this study, CFD analyses were used to derive the correction factors for platform-only and fully coupled models, and the differences between them are compared and analyzed. The objective was to assess whether the correction factors obtained from simplified models are valid in more complex, fully coupled systems and suggest the potential need for revised correction methodologies where necessary.

CFD analysis was used as the reference to evaluate the differences from potential theory-based results and determine the optimal drag coefficients that minimize such discrepancies. Traditional free-decay-based damping estimation may not fully capture wave-induced nonlinear viscous effects. Hence, the drag coefficients were instead determined directly from the motion responses under wave conditions. Although all six rigid-body degrees of freedom were modeled in both numerical approaches, the analysis focused on three motion responses: surge, heave, and pitch. The comparisons were made based on the mean position changes and response amplitudes. These three components are dominant under the investigated loading conditions and are most relevant to the evaluation of viscous correction performance. The remaining DOFs (sway, roll, and yaw) showed negligible amplitudes and were excluded from the main comparative discussion.

Potential theory assumes an inviscid fluid. Hence, it does not account for viscous damping effects. Therefore, correction factors in the form of drag coefficients must be introduced to reflect viscous influences. The drag coefficients were applied separately to each component of the platform, including columns, pontoons, and their intersections, as shown in Fig. 4. The drag coefficients in the surge and heave directions were defined independently for each component. In particular, depth-dependent drag coefficients were assigned to the columns following the approach described by Souza et al. (2024), with higher values near the free surface to account for viscous excitation and lower values near the keel to represent damping. This configuration enhances the ability of the model to capture low-frequency responses without significantly increasing the computational cost.

Certain drag coefficient values were fixed based on the results reported by Wang et al. (2022), while the remaining values were determined through a parametric study aimed at identifying the optimal combinations. Sixty-four drag coefficient combinations were evaluated under the platform-only and fully coupled model conditions, resulting in 128 simulation cases. All cases were analyzed under identical environmental forcing conditions to ensure a consistent comparison with the CFD results. The simulation results for each combination were assessed by calculating the error in mean drift (or position) and response amplitude compared to CFD, and the optimal drag coefficient set was selected based on these evaluations. Table 4 lists the parameter ranges and increments used for the drag coefficients, which were applied separately to the column, pontoon, and intersection components of the platform in the surge and heave directions.

This section presents a quantitative comparison between the responses obtained from potential theory-based simulations and those from CFD simulations under various drag coefficient combinations. The analysis focused on three motion responses: surge, heave, and pitch. The results were evaluated based on the mean value (mean drift or position) and the response amplitude of each motion.

Figs. 5 and 6 show the surge responses for the platform-only model and the fully coupled model, respectively, under different drag coefficient combinations. In the case of surge motion, the mean drift increased gradually as the normal-direction drag coefficients increased. In contrast, the response amplitude remained relatively insensitive to changes in drag coefficients, suggesting that the drag primarily influenced the drift component. This trend was observed consistently in the platform-only and fully coupled models.

Figs. 7 and 8 display the heave response results. In heave motion, variations in the tangential-direction drag coefficient had minimal influence on the mean position and response amplitude. Hence, damping in the heave response is governed more significantly by other factors rather than drag forces. This characteristic was also observed consistently under the fully coupled and platform-only conditions.

In contrast, Figs. 9 and 10 reveal more complex interactions in the pitch response. The mean pitch response tended to decrease as the normal-direction drag coefficient increased. In addition, the tangential-direction drag coefficient has a direct impact on the pitch response amplitude. These findings suggest that pitch motion is highly sensitive to coupling effects with surge and heave responses. This sensitivity was similarly consistent across both fully coupled and platform-only conditions.

In summary, the influence of the drag coefficients on the motion responses of the platform varies according to the degree of freedom. For surge, the normal-direction drag coefficient increased the mean drift (or position) significantly, while the tangential-direction coefficient had a negligible influence. The contributions of the drag elements assigned to the pontoon and intersection regions were comparable. In the case of heave, the variations in the tangential-direction drag coefficient produced minimal changes in the response amplitude, suggesting that heave is governed more by hydrostatic restoring and environmental forces than by drag-induced damping. For pitch motion, the tangential-direction drag coefficient clearly affected the response amplitude, whereas the normal-direction coefficient had little effect.

Although the response trends of the platform-only and fully coupled models appeared qualitatively similar in Figs. 5–10, this alone does not confirm the validity of applying the calibrated drag coefficients across both models. A direct comparison with the CFD results was conducted to verify their applicability, as shown in Fig. 11. Time-domain responses were analyzed (Fig. 11) to investigate the impact of the drag coefficients on the response amplitudes. Only pitch motion was considered in this analysis because the surge and heave motions showed minimal sensitivity to drag coefficient variations.

In the time-series comparison, the normal-direction drag coefficients Cd_{IS surge} and Cd_{pontoon surge} were fixed at 1.0 and 2.0, respectively, while the Cd_heave value was varied from 1.0 to 4.0 to determine its effect on the pitch response amplitude. The accuracy of the potential theory-based predictions was evaluated using the CFD results as a reference. In addition to some differences in amplitude, the overall response trends in the time series closely matched those of the CFD results.

Table 5 lists the error rates in pitch response amplitude corresponding to each Cd_heave value. The analysis showed that, under fully coupled conditions, the lowest error of 2.27% occurred when Cd_heave = 2.0, while under platform-only conditions, the minimum error of −4.08% was observed at Cd_heave = 3.0. In contrast, the other coefficient values resulted in significantly larger errors, ranging from 10% to more than 30%, suggesting that the choice of drag coefficient has a substantial influence on the accuracy of the pitch response amplitude prediction. These results suggest that the drag coefficients derived from simulations considering only the floating platform may not accurately reproduce the dynamic response of fully coupled systems.

Based on previous results, the Cd_heave value of 2.0, which showed the highest prediction accuracy under the most extreme conditions in the fully coupled simulations, was fixed for subsequent analysis. Fig. 12 presents heatmaps visualizing the response errors between CFD and potential code results for the three motion responses: surge, heave, and pitch. Subfigures (a) to (c) correspond to the fully coupled condition, while (d) to (f) represent the platform-only condition. Although both conditions showed similar error patterns with respect to the changes in surge drag coefficients, the optimal drag coefficient combinations, i.e., those with the lowest error, differed between the two cases. In the surge response, for example, the lowest error under the fully coupled condition was observed at Cd_{IS surge} = 2 and Cd_{pontoon surge} = 4, whereas the minimum error occurred at Cd_{IS surge} = 4 and Cd_{pontoon surge} = 6 under the platform-only condition. Furthermore, the influence of the surge drag coefficients on the heave and pitch responses was relatively minor under the platform-only condition. In contrast, for the surge response itself, the platform-only model exhibited greater sensitivity to the drag coefficient variations. These observations suggest that the presence of a tower–turbine superstructure loads in the fully coupled model may reduce the sensitivity of potential-based simulations to normal-direction drag coefficients.

Fig. 13 compares the potential theory-based simulation results and CFD results, using four optimal surge drag coefficient combinations identified through the earlier heatmap analysis. These combinations were applied under fully coupled simulation conditions. The models are denoted as FS-op, FP-op, PS-op, and PP-op, where the first letter indicates the source of the drag coefficient (fully coupled or platform only), and the second letter represents the motion response (surge or pitch) in which the coefficients were optimized. The suffix “-op” indicates that the combination represents an optimal set of coefficients.

The results show that the FS-op combination yielded the lowest average error across all motion responses, followed by FP-op, PS-op, and PP-op, respectively, each showing relatively good agreement. Although the drag coefficient combinations derived from the platform-only simulations exhibited higher error rates overall, the prediction error for most motion responses, excluding pitch and heave, remained within 10% compared to the CFD results. Even for the heave and pitch responses, the discrepancies were limited to approximately 0.3 m and 1°, respectively, indicating that the practical differences were minor. This is mainly because the mean pitch angle observed in CFD was 1.84°, and the mean heave value was 0.62 m. Therefore, although the relative errors appeared large because of the small magnitudes, the actual differences were within acceptable engineering limits. In other words, although the percentage error may appear high because of the small scale of the mean response values, the absolute differences are sufficiently small that they are unlikely to have a significant impact on the engineering decisions or system design. These errors can be considered practically negligible when interpreted in the context of the overall platform size and motion scale.

These results suggest that the accuracy of the correction factors applied to potential theory simulations under fully coupled conditions can vary depending on how the coefficients are derived. Although fully coupled-based correction factors offer the most reliable prediction performance, the platform-only-based coefficients can still provide acceptable accuracy for certain motion responses. Fig. 14 shows the differences between the optimal correction factor combination derived from the fully coupled simulation (FS-op) and those obtained from the platform-only simulations (PS-op and PP-op). This comparison was used to evaluate quantitatively the prediction performance of the correction factors derived under platform-only conditions.

The results indicate that, excluding the pitch response, the differences between FS-op and the platform-only cases for surge, heave, and mooring line tension responses were all within 5%, showing that platform-only-based correction factors can achieve a reasonable predictive reliability. On the other hand, a noticeably larger discrepancy was observed in the pitch response, suggesting that pitch motion is particularly sensitive to how the drag coefficients are derived. The results from Fig. 14 suggest that applying drag coefficients calibrated using the platform-only model to a fully coupled system may lead to underprediction of pitch motion. Therefore, differences in model configuration, such as the inclusion of a tower and turbine, can significantly influence the applicability and accuracy of the correction factors, especially for pitch-dominant responses.

This study conducted CFD simulations for the platform-only model and the fully coupled model (including a tower and turbine), and quantitatively compared the motion response differences with potential theory-based simulations incorporating various correction factor combinations. The analyses were carried out using STAR-CCM+ and OrcaFlex, focusing on three motion responses: surge, heave, and pitch. In particular, the differences in the motion responses according to the normal-direction drag coefficient combinations were visualized through a heatmap analysis, and four optimal combinations (FS-op, FP-op, PS-op, and PP-op) were compared with CFD results to evaluate the applicability of the correction factors.

The correction factor set derived from the fully coupled model (FS-op) provided the highest prediction accuracy across all motion responses. The platform-only based correction factor sets (PS-op and PP-op) exhibited relatively higher errors in some responses. For the surge, heave, and mooring line tension responses, however, the platform-only coefficients maintained prediction errors within 10%. Although there was some loss in precision for the pitch response, the difference remained within approximately 1°, which is generally acceptable in practical applications. As shown in Fig. 14, correction factors derived under platform-only conditions could provide reasonable prediction accuracy even when applied to fully coupled simulations. On the other hand, correction factors based on fully coupled models yielded significantly more reliable predictions for the responses that are more sensitive to drag coefficients, such as pitch.

Although the correction factors derived from fully coupled CFD simulations are expected to provide the most accurate representation of coupled effects, they come at a high computational cost, approximately 16 days per case using 70 CPU cores. In contrast, platform-only CFD simulations require approximately five days on 50 cores. Considering this significant difference, using platform-only models to estimate correction factors may offer a practical alternative for early-stage design evaluations or parametric studies, where large numbers of cases must be analyzed.

This study contributes by systematically evaluating the effects of modeling configuration on the selection of correction factors for potential theory-based analysis through high-fidelity CFD simulations. It quantitatively shows that correction factors derived from platform-only simulations commonly used in engineering practice can be applied to more complex fully coupled systems to a certain extent, enhancing the practicality and generalizability of correction factor application.

This study was conducted under a single, extreme set of environmental conditions. Therefore, future research should cover various wave conditions, mooring system configurations, and platform geometries to ensure broader applicability and data robustness. Moreover, it is recommended that future evaluations of correction factors also consider structural performance indicators, such as stress and fatigue life, in addition to motion responses. In particular, the error analysis in this study is based on a single set of environmental conditions. Hence, further analysis is necessary under conditions where pitch or heave motions are more dominant. It is important to determine if the observed discrepancies remain relatively constant in absolute terms, or whether they increase significantly when expressed as a percentage of the response (i.e., relative error) under different environmental conditions. If the latter is observed, meaning that relative errors become disproportionately large in more dynamic scenarios, it may suggest that the current correction model lacks robustness and requires further refinement for broader applicability. Future studies should focus on environmental conditions where the pitch and heave responses are dominant to validate the applicability and robustness of the correction factors under more dynamic scenarios.