An IEA 15MW semi-submersible FOWT in focused waves is investigated by using a consistent second-order hydrodynamic model in the time domain, uniquely formulated in the body-fixed coordinate system (BFCS). The quadratic drag loads on the cross sections along the horizontal pontoons are estimated based on the local Keulegan-Carpenter (KC) numbers instantaneously estimated in the time domain, and the required KC-dependent drag coefficients are pre-calculated by dedicated two-dimensional (2D) CFD analysis for the relevant cross sections. Soft linear springs in the horizontal plane are used to approximate the restoring mechanism due to mooring system. The proposed empirical viscous correction works very well in comparison to the model tests of free decays in calm water. For the FOWT exposed to focus waves, significant low-frequency (LF) surge and pitch motions are observed in the referred model tests, which are reproduced by the present second-order time-domain model with reasonably good accuracy. The linear model is shown to significantly underestimate the motion responses close to the wave-focusing time and the large-amplitude transient LF oscillations when the focused waves have propagated away.


Floating offshore wind turbines (FOWTs) are being widely installed to seize the renewable offshore wind energy in intermediate and deep seas. In the design of FOWTs, the evaluation of the loads and responses of the FOWTs in turbulent-wind and stochastic-wave conditions, especially extreme loading conditions is critical, while also difficult to accurately model through numerical methods, because of the complex coupling between aero-hydro-elasticity, etc. of the entire system. Therefore, numerical methods should be carefully validated through code-to-data comparisons and theoretical analysis.

Among these environmental loads on the FOWTs, the underwater contribution from the supporting platform, in principle the hydrodynamic loads induced from current and waves, as well as the mooring loads are of paramount significance in predicting the dynamic responses of the FOWTs, which are typically in forms of wave-frequency (WF) and low-frequency (LF) responses. Due to the high costs of Computational Fluid Dynamics (CFD) modeling (Wang et al., 2021a,b, 2022) and fully nonlinear modeling (Xu et al., 2019), using numerical models based on the first- and second-order weakly-nonlinear potential-flow theory and/or Morison equations has become a common practice for the hydrodynamic modeling of FOWTs (e.g., see Ishihara & Zhang, 2019, Jonkman, 2007, Zheng et al., 2020). The mainstream hydrodynamic models include the frequency-domain method, indirect time-domain method based on Cummins-type equations, and direct time-domain method. The challenges to the first two methods, which are mostly adopted in the state-of-the-art numerical tools WADAM, Hydrostar, etc., need to be addressed. The most obvious one is that it is not straightforward to include the nonlinear effects, for instance, the nonlinear viscous loads in these methods, particularly in the case of irregular waves where seastate-dependent viscous loads may be required to achieve accurate second-order LF load calculations (Sauder, 2021). On the other hand, the underlying hypothesis of these methods based on perturbation scheme and Taylor expansion at the equilibrium position in the Inertial Coordinate System (referred as IneCS hereafter) are easily violated when large-horizontal resonant motions occur. In fact, resonance extensively exists for moored FOWTs and can be excited by the nonlinear LF wave loads, or self-excited oscillations (Faltinsen et al., 1979), even of small amplitudes since the wave-radiation damping is negligible at the natural periods of the horizontal motions (e.g., see Pinkster, 1980, Verhagen & Van Sluijs, 1970). Thus, the effects of the LF motions, e.g. the LF displacements and velocities, on the second-order wave-excitation loads, wave-drift damping, and in return on the LF motions, should be carefully modeled for moored FOWTs.

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