Rigid body dynamic response of a floating offshore wind turbine to waves: Identification of the instantaneous centre of rotation through analytical and numerical analyses

Floating Offshore Wind Turbines (FOWT) can harness the abundant offshore wind resource at reduced installation requirements. However, a further decrease in the development risks through higher confidence in the design and analysis methods is needed. The dynamic behaviour of FOWT systems is complex due to the strong interactions between the large translational and rotational motions and the diverse loads, which poses a challenge. While the methods to study the FOWT's general responses are well established, there are no methods to describe the highly complex time-dependent rotational motion patterns of FOWT. For a rigid body in general plane motion, an Instantaneous Centre of Rotation (ICR) can be identified as a point at which, at a given moment, the velocity is zero. However, it is common to assume a centre of rotation fixed in space and time, arbitrarily set at the centre of floatation or gravity. Identification of the ICR is crucial as it may lead to better motion reduction methods and can be leveraged to improve the designs. This includes better-informed fairlead placement and the reduction of aerodynamic load variability. In this paper, we propose a two-fold approach for the identification of the ICR: an analytical solution in the initial static equilibrium position, and a time-domain numerical approach for dynamic analysis in regular and irregular waves to understand the motion patterns and ICR sensitivity to environmental conditions. Results show that the ICR of FOWT depends on wave frequency and, at low frequencies, on wave height, due to the nonlinear viscous drag and mooring loads. An unexpected but interesting result is that the surge-heave-pitch coupling introduced by the mooring system leads to a dynamic phenomenon of signal distortion known as ”clipping” in the nonlinear audio signal processing area, which, through the introduction of higher harmonics, is responsible for the ICR sensitivity to motion amplitude.