Two-dimensional horizontal motion of two floaters with internal flow using higher-order multi-modal method

Abstract

Existing studies have concentrated on the problem of sloshing itself and coupling with body motion has only been conducted using a single-dominant method. Moreover, although the problem of secondary resonance induced by an internal fluid with sufficiently deep tank depths has been studied by the introduction of the two-mode dominant method; however, sloshing below critical tank depths still needs considerable research. This study investigated the two-dimensional horizontal motion of the two rectangular boxes, including the internal flow. The hydrodynamic coefficients were calculated using the constant panel method, and the effect of the internal fluid was calculated using the multimodal method based on the Bateman-Luke variational principle. Consequently, the characteristics of the internal fluid motion were categorized by the ratio of the internal fluid depth(h) to the tank length(l). For h/l value below the critical depth ration (approximately 0.337 for a rectangular water tank), the single-dominant method was considered inappropriate for describing the sloshing phenomenon precisely. Thus, this study aimed to develop higher-order multimodal methods. The numerical results were compared with previous experimental data. Furthermore, a parametric study of the modal damping was conducted.