A Numerical Calculation of Hydrodynamic Forces on a Seagoing Ship by 3-D Source Technique With Forward Speed

Abstract

In this paper, the hydrodynamic forces of a surface ship advancing in waves at constant forward speed are numerically calculated by using the 3-D source distribution techniques. The paper also deals with the numerical calculations of free surface flow around an advancing ship in calm water as well as in waves. The body boundary condition is linearised about the undisturbed position of the body and the free surface condition is linearised about the mean water surface. The potential is represented by a distribution of sources over the surface of the ship and its waterline. The problem is solved by the method of singularities distributed over the hull surface. Hess & Smith method is used to obtain the density of these singularities. The numerical solution of the surface ship case is approximately obtained by considering the hull as a position of plane polygonal elements, bearing a constant singularity distribution. The velocity potential of any particular point in the free surface around the moving hull is determined by using the 3-D Green function with forward speed which satisfies the boundary conditions for a pulsating source in the fluid. Contours of wave patterns around moving surface ships are calculated from the velocity potential. The numerical accuracy of the computer code is firstly checked by calculating the velocity potential of a translating, pulsating unit source with arbitrary frequency and forward speed. Free surface wave patterns generated by a Wigley hull advancing with steady forward speed are calculated by using this code. Some corresponding hydrodynamic coefficients of heave and pitch modes for the Wigley hull has been calculated. Exciting forces and motion amplitudes are also investigated. The numerical result of this code is validated by comparing the calculated results with the experimental ones and those calculated by other methods. From the comparison, the results predicted by the present calculations are found in fairly good agreement with the experiment. Finally, the effects of motion amplitude on the free surface elevation are analyzed. These will be helpful for the accurate estimation of sea keeping problems for a ship advancing in waves.