Numerical Computation Of Nonlinear Wave Forces On A 3D Floating Body With Forward Speed

There are more and more applications of numerical method, i.e. Numerical Wave Tank (NWT), to research the interaction of ship and offshore structure with wave and current. In this paper, the nonlinear diffraction problem is studied with potential flow theory in frequency domain for three-dimensional floating body sailing in waves on deep water. This problem includes nonlinear diffraction problem and nonlinear wave making problem.It is harder to solve accurately such nonlinear water wave problem because of the nonlinear free-surface condition; various kinds of approximations are developed. In this paper, by adopting the Stokes nonlinear wave theory of deep water, the total flow velocity potential and wave elevation are decomposed into first-order and higher order ones, and the nonlinear free-surface condition is expanded by Stokes perturbation technique. The free-surface condition of diffraction problem contains nonlinear wave making velocity potential. The radiation condition of the first-order diffraction problem is dealt with by the numerical method just in the same way as that is applied in steady wave making problem, and the method is extended to the second-order diffraction problem.Time domain is the most popular method to solve nonlinear wave flow. But it takes both computer time and memory. Frequency domain is suitable for computing linear problem in common sense, and it is widely used and works well in the first-order linear problem. In this paper, the frequency domain is developed to solve the first and second diffraction problems by assuming the perturbation is steady and periodic, and the need of computer power decreases largely.Boundary element method is the most widely used method for potential flow. In this paper, NURBS method is used to describe the body surface accurately, the body surface and its differentiation are continuous; the de-singularized method isused to numerically compute the problems, so there is no singularity, no irregular frequency. And the differentiation of potential on body surface can be carried out directly.In this paper, the major factors which have effects on the numerical convergence includ the inner distance of the sources submersed into the body surface, the distance moved upward above the mean free-surface, the computing range of free surface, and the collocation point interval (or number). With enough free-surface range and collocation point number, this paper discusses the effects of the two kinds of distances on the numerical convergence, proposes the expressions for the inner distance, and has obtained consistent and convergence results.In this paper, choosing submerged spheroids and Wigley hulls as computing models, the computed wave resistance and first-order wave exciting force are in good agreement with the other published results. The second-order wave exciting force, nonlinear wave making and nonlinear diffraction wave contour are calculated also. The effect of the nonlinearity on total wave exciting force and wave contour is discussed.The key of this paper is the solution of the second-order double-frequency wave exciting force for a floating body sailing in waves by solving second-order diffraction potential. All computed results show the theory and numerical methods in this paper are correct and valid. Although this paper deals with a floating body all methods can be used to the fixed offshore structures in waves and current.