Numerical analysis of ship motion coupled with tank sloshing

The effects of tank sloshing are usually ignored or linearized in ship motion analysis. Recent studies show that the nonlinearity caused by the coupling of tank sloshing and ship motion can be significant in a certain frequency range. The tank sloshing can be excited by the ship motion, at the same time, the tank sloshing induces an impact load on the tank wall, which has a significant influence on the ship motion. In this paper, a time domain equation has been built to obtain the results of coupling effects which is more accurate than the results obtained from the frequency domain equation considering the effects of damping. In solving of the time domain equation, hydrodynamic coefficients and wave loads are obtained by a program Hydrostar which is based on the potential theory in frequency domain. The radiation force is integrated in time domain by using impulse response function (IRF) approach. The liquid motion in the tank is simulated in time domain by computational fluid dynamics (CFD) program which has high accuracy in simulating tank sloshing. The tank sloshing force and moment computed by CFD program based on volume of fluid (VOF) method are then applied as an external force of the ship motion. The simulated results of ship motion are in turn used as the excitation of tank sloshing and repeated by ensuing time steps. This time domain method is accurate in solving coupling effects of ship motion and tank sloshing, because it combines the advantages of potential flow theory and viscous flow theory. The response amplitude operator (RAO) of ship motion of computation and experiment is proved in good agreement.