Study on weakly nonlinear motions of ship advancing in waves and influences of steady ship wave

Time domain Rankine source method incorporated with HOBEM is developed and applied to solve motion of ship advancing with steady forward speed in waves. Steady ship wave (SW) potential is solved beforehand and is applied in both boundary conditions of free surface and ship hull for solving time domain ship motion. nti-terms in body boundary condition are computed with ship wave potential, time domain free surface conditions of radiation and diffraction problems are derived by use of ship wave potential. Since steady incoming flow has significant influences on ship motions, the two simplified steady flow models of uniform stream (US) and double body flow (DB) are also applied in time domain simulations for the comparative studies. In addition, nonlinear Froude-Krylov and restoring forces are used in ship motions equation. A numerical program is originally coded by Fortran and is used to solve motions of four types of hulls, which are Series60 ship, Wigley-1, S-175 container ship and a full formed tanker, at various speeds. The results of added mass, damping coefficients, wave exciting forces and ship motions are in generally good agreement with related model tests data. It shows that both hydrodynamic coefficients and ship motions obtained by SW and DB are apparently more accurate than by US. The accuracy of motions is improved for ships with complex and full formed hulls by the present method, which takes SW as steady flow. Numerical results of ship motions are affected by both the different free surface conditions due to different steady flow models and m(j)-terms, while added mass and damping coefficients are mainly influenced by m(j)-terms. More physical phenomenon are detailedly investigated and discussed.