A second-order slender-body approach for computing wave induced forces with application to a simplified semi-submersible FOWT model

Abstract

This paper presents a slender-body approximation to evaluate the first- and second-order wave loads acting on a floating structure comprised of slender cylinders. It combines Rainey’s equation, which can be seen as an extension of the inertial part of Morison’s equation to include nonlinear terms, with Pinkster’s formulation for the low-frequency second-order loads on floating bodies. The objective is to obtain expressions that allow the evaluation of second-order wave loads considering the mean body position, so that an Inverse Fast Fourier Transform algorithm can be used to efficiently compute the second-order wave loads in a real sea condition directly in time domain. Similarly to Morison’s equation, this approach is incapable of modeling wave scattering and radiation effects, but this is acceptable as long as the diameters of the cylinders that compose the structure are small in face of the length of the incoming waves. To verify the method, it is applied to the computation of the slow motions of a simplified semi-submersible FOWT model, first under the action of bichromatic waves and then of an irregular sea, and the results are compared with the ones obtained with WAMIT, OpenFAST and experiments.