3-D Integral-Equation Method for Calculating the Effects of Tank-Wall Interference on Hydrodynamic Forces Acting on a Ship

Abstract

A 3-D integral-equation method is developed for predicting the hydrodynamic forces acting on and resulting motions of a ship, with the effects of tank-wall interference included. The proposed calculation method is restricted to the zero-speed problem, but provides in principle an exact solution for a body of arbitrary geometry. The integral equations for the radiation and diffraction velocity potentials on the body surface are derived by applying Green's theorem, and solved numerically with a discretization of the body in panels, with the velocity potential assumed constant on each panel. The Green function satisfying the tank-wall boundary condition is provided by first considering an infinite number of mirror images and then obtaining a closed-form expression for the resultant infinite series. Computed added mass, damping coefficient, and wave-exciting force for a hemisphere and for a ship with two planes of symmetry are compared with corresponding experiments which are also carried out in the present study. Virtually perfect agreement exists between experiments and numerical predictions, suggesting the validity of the present integral-equation method. Based on these reliable numerical computations, the characteristics of ship motions in a resticted waterway are studied