Towards the Fully-coupled Numerical Modelling of Floating Wind Turbines

Abstract The aim of this study is to model the interactions between fluids and solids using fully nonlinear models. Non- linearity is important in the context of floating wind turbines, for example, to model breaking waves impacting on the structure and the effect of the solid's elasticity. The fluid- and solid-dynamics equations are solved using two unstructured finite-element models, which are coupled at every time step. Importantly, the coupling ensures that the action-reaction principle is satisfied at a discrete level, independently of the order of representation of the discrete fields. To the authors’ knowledge, the present algorithm is novel in that it can simultaneously handle: (i) non- matching fluid and solid meshes, (ii) different polynomial orders of the basis functions on each mesh, and (iii) different fluid and solid time steps. First, results are shown for the flow past a fixed actuator-disk immersed in a uniform flow and representing a wind turbine. The present numerical results for the velocity deficit induced by the disk are shown to be in good agreement with the semi-analytical solution, for three values of thrust coefficients. The presence of a non-zero fluid viscosity in the numerical simulation affects wake recovery and fluid entrainment around the disk. Second, the dynamic response of a cylindrical pile is computed when placed at an interface between air and water. The results qualitatively demonstrate that the present models are applicable to the modelling of multiple fluids interacting with a floating solid. This work provides a first-step towards the fully coupled simulation of offshore wind turbines supported by a floating spar.