Numerical investigation of secondary load cycle and ringing response of a vertical cylinder

A numerical wave tank is established based on two-phase FVM model and VOF method and verified with the physical experiment in Grue et al. (1994). Focusing waves with different wave steepness passing a vertical cylinder are investigated by Numerical simulations. The phenomenon called ‘secondary load cycle’ which may lead to ringing response, is observed and discussed. The presence of secondary load cycle could be related to Froude Number (Fr). The possible transition region of the present and absent secondary load cycle is Fr = 0.4. Sub and super harmonic wave components appear in the propagation of waves, second-order wave theory could give a good prediction. Morison equation with linear wave theory could predict well the wave forces of vertical cylinder with small steepness without the secondary load cycle, but cannot capture the crests/troughs of the wave forces with the secondary load cycle. Crest improvements are achieved by second-order wave theory. A spectral analysis based on wavelet transform is applied to wave loads. The frequency of the secondary load may be up to 13 times the wave frequency, which may cause the ringing response expanding to a higher frequency range. Strong ringing response occurs in steep wave, it could be extended up to 15 times wave trough-to-trough frequency due to the secondary load cycle. The damping has slightly influence on the peak of resonance response, but it will lead to faster decay of subsequent response, if the damping ratio is large.