Numerical research on time domain ship motions coupled with sloshing at different liquid levels and forward speeds

Abstract In the present study, an reasonable numerical method based on the potential flow theory and boundary element method (BEM) for solving time domain ship motion coupling with sloshing is proposed. Ship motion is solved based on the three dimensional (3D) time domain potential flow theory with forward speed using the BEM. The 3D fully nonlinear time domain potential flow theory and BEM are also adopted to simulate the nonlinear sloshing phenomenon and then numerically coupled with ship motion in a same time step. A corresponding parallel numerical solver is also developed to investigate the coupling effects between 6 degrees of freedom (DOF) ship motion and internal sloshing. To validate the numerical solver and better understand these coupling effects, numerical research on liquid level and forward speed effects is conducted. The developed numerical solver is also validated from previous model experimental results. Computational and experimental results of ship motion response amplitude operators (RAOs) are in reasonable agreement for both 15000 GT and S175 models with liquid tank. The natural frequency of sloshing varies with changes in liquid levels, and coupling effects become more obvious when the natural frequency of sloshing is close to excited frequency of a ship. Our accurate numerical results on the liquid level effects of roll motions indicate that the numerical method proposed can solve the engineering problem related to liquefied natural gas (LNG) and liquefied petroleum gas (LPG) ships traveling through ocean waves. The numerical behavior of a coupling system with forward speed shows that a liquid tank can reduces the resonance frequency of roll motion and has a limited effect on pitch motion. However, as forward speeds increase, such effects follow a gradually increasing trend.