Floating wind power requires cost-effective, and hence typically small support platforms.
Wave loads on small semi-submersible floating wind turbines are sensitive to wind-induced inclination.
A time-domain model allows to integrate hydrodynamic, aerodynamic, and gyroscopic forces, and observe their coupling.
The effect of wave load alterations on floating wind turbine dynamics is investigated for inline and cross wind and waves.
Significant ‘inclination effects’ are found. Experimental results uncaptured by the classic modelling approach are explained.
This study focusses on the coupling effects arising from the changes in the hydrodynamic behaviour of a semi-submersible floating wind turbine when it undergoes large inclinations under wind loading. By means of a range of time-domain simulations, it is shown that both the hull geometric nonlinearity effect and the alteration of viscous hydrodynamic forces can significantly affect the dynamics of a typical floating wind turbine operating in waves at rated conditions. The consequences of said effects for both aligned and misaligned wind and waves are explored. In general terms inclinations are found to increase motions, where the modes that are more affected depend on the relative direction between incident wind and waves. Understanding the sources of aero-hydrodynamic coupling is key to providing sound design and modelling guidelines for the coming generation of floating wind turbines.
In recent years floating wind power has been increasingly regarded as an attractive option for the production of low-carbon electricity, thanks to the potential to unlock vast resources which are unexploitable using fixed substructures; these are expected to become gradually unviable for depths beyond 50–60 m  and . Being able to deploy wind turbines in deep water will be crucial to determine the scale of the industry within regions where the maritime continental shelf is steep. In spite of the presence of vast shallow areas especially in the North Sea, an estimate of the technical resource potential in Europe indicates a deep-water share of about 70% . Estimates for France range between 60%  and 80% . In Japan, now a prominent country in floating wind developments, 80% of the offshore wind resources are located in deep water according to .
Different from most conventional offshore floating structures, floating wind turbines (FWTs) are relatively small bodies which can exhibit stronger nonlinearities in their dynamic behaviour. Moreover, they are designed with the purpose of maximising the aerodynamic interaction related to wind energy extraction, which gives raise to unusually large aerodynamic load to displacement ratios. This constitutes an important source of dynamic coupling, especially as FWT platforms tend to evolve toward more optimised, lightweight solutions. Characterising the mechanical behaviour of a floating wind turbine for design and verification purposes requires the coupling of wind turbine aerodynamics and control with offshore hydromechanics. The understanding of such coupled dynamics under complex met-ocean loading has recently been the driver of a novel generation of coupled offshore dynamic models designed for the requirements of FWT mechanical simulation, such as FAST ,  and , HAWC2  and , FloVAWT , Simo-Riflex  and , and CALHYPSO of EDF R&D, the software used in the present study.
1.1. Small offshore structure hydrodynamics
Compact floating platforms can exhibit increased hydrodynamic complexity when subjected to ocean waves compared to their larger counterparts; for example it is more likely to come across regimes where hydrodynamic drag plays an important part in excitation, as it was observed experimentally on the DeepCwind-OC4 platform by Ref. , and explained numerically in Ref. . These phenomena typically affect structures featuring sharp-edged motion control devices, tanks, and pontoons, which accentuate flow separation. Surface proximity effects can also manifest on these appendices when their submergence is limited, such as increased vertical wave loading (conjectured in Ref. ) and run-up . As shown by the experimental campaign carried out by Ref.  on a CALM buoy equipped with a skirt, a semi-empirical numerical model implementing linear potential diffraction/radiation and a Re-independent drag force formulation can satisfactorily (but not comprehensively, as explained in 1.2) represent the hydrodynamic forces acting on this type of structure for the calculation of dynamic response. Similar conclusions have been drawn by Ref.  whilst comparing numerical and experimental motion results for a compact water-injection platform concept, the predecessor of the WindFloat platform design. An analogous numerical-experimental comparison carried out for the engineering design of WindFloat itself broadly confirmed the accuracy of this type of numerical model . Next follows a brief close-up on water entrapment device hydrodynamics and the main related modelling challenges.
1.2. Water entrapment plates
The water entrapment principle, often utilised in the hydrodynamic design of FWTs, provides a passive motion control tool through the installation of relatively low-cost appendices. Pioneered by Principle Power with the WindFloat prototype, the heave plate appendix consists in a thin reinforced structure installed coaxially below the platform’s columns, as visible in Fig. 1. The dynamic stability provided by the use of heave plates, coupled with the extra static stability insured by a closed-loop active ballasting system, reportedly allowed the WindFloat prototype to adopt conventional aerogenerator technology .