A twice expansion analysis method in the time-domain for wave action on a floater translating with a large amplitude. (15th May 2016) - Teng, Bin; Jin, Ruijia; Cong, Longfei
Abstract: A twice expansion method in the time-domain was proposed for computing wave interaction with a body experiencing large amplitude drift motion. The body displacement was divided into two components, a low frequency and a high frequency oscillations. The low frequency oscillation was computed by a wavelet transform method with time matching in the computation, and was called as the instantaneous mean position. Then the first and the second order boundary conditions were established at the instantaneous mean position and the still free surface by a perturbation expansion method which would guarantee that the expansion factors are always small. The velocity potential was separated into the incident, the scattering and the steady disturbance potentials. The scattering and the steady disturbance potentials were computed by solving integral equations respectively. Numerical examinations were carried out for a forced moving truncated cylinder in waves and wave interaction with a spar platform with mooring system in deep water. The comparisons were made between the results from the present twice expansion method and the direct expansion method. The comparisons show that the present method can consider the changes in the phase and the encounter frequency of wave loads due to body drift motion at low frequency. The body response at the natural frequency of the spar platform from the twice expansion method is smaller than that from the direct expansion method, but is larger at lower frequency. The peak frequency of the response amplitude from the present method moves to lower frequency, as the influence of wave drift damping is included in the model. Highlights: A twice expansion method is proposed for the problem of wave interaction with a body experiencing large amplitude drift motion to overcome the inapplicability of the direct perturbation expansion when expansion parameter is not small. A wavelet transform technique is used to find the instantaneous mean position of body motion with the time marching computation. Meshes on the free surface and body surface translate with the mean position. The method can work out the phase change of the incident wave force and the variation of encounter frequency between waves and body. The motion response at nearby of the natural frequency of the platform from the present method is different from that from the direct expansion method, as the wave drift damping force is included.