Effects of nonlinearity and viscous damping on the resonant responses in two-dimensional moonpools with a recess

Abstract

In this study, the nonlinear and viscous damping effects on the resonant responses inside a two-dimensional moonpool with a recess are investigated. Based on a fully nonlinear potential flow (FNPF) model, the nonlinear moonpool responses excited by the forced heave motion of a structure are simulated in the time domain. To consider the vortex-shedding damping effects in the moonpool, induced by both piston-type motion (the first harmonic component) and sloshing-type motions (the higher harmonic components), a pressure drop model based on Faltinsen and Timokha (2015) is developed and applied to the FNPF model (FNPF-V for short). The response amplitude operators (RAOs) of the higher harmonics, by which the nonlinear effects are evaluated, are computed by the FNPF-V model. It is found that the higher harmonics are noticeable for the excitation frequencies ω n / ( n + 1 ) ( n is a positive integer, ω n denotes the natural frequency of the n th sloshing mode), where secondary resonances can be triggered. In addition, it is found that the strong nonlinear interactions between the first and higher harmonics can lead to a significant amplification of the moonpool responses. The nonlinear behaviour (the secondary resonance, as well as the sum- and difference-frequency effects) is substantially enhanced as the excitation amplitude increases. Moreover, it is found that the length of the recess influences the nonlinear response of the moonpool in two respects with opposite effects. On the one hand, for the same first harmonic response, moonpools with a longer recess are more apt to exhibit nonlinearity. On the other hand, for the same external excitation, as the length of the recess increases, the first harmonic responses at the excitation frequencies ω n / ( n + 1 ) decrease, suppressing the nonlinear behaviour. • This paper studies the secondary resonances triggered by the piston-mode response. • A pressure drop model is introduced to consider the vortex-shedding effects. • The nonlinear interactions between different harmonic components are investigated. • The effects of recess length on the nonlinear response are analysed and interpreted.