ABSTRACT

The water-entry problem for arbitrary two-dimensional bodies was solved in the time domain by a boundary element method based on desingularized Cauchy's formula. The Euler-Lagrangian method is employed to trace the free surface. The body surface and the free-surface profile are represented by non-uniform rational B-splines (NURBS) curves. Gaussian quadrature is applied to discretize the non-singular boundary integral equations. A numerical scheme has been developed to treat the corner singularity at the intersection point of body and the free-surface boundaries. The developed numerical method has been applied to compute the free surface elevation and pressure distribution on wedge surfaces. Numerical results were compared with analytical solutions.

INTRODUCTION

When a ship travels in heavy seas, the large-amplitude ship motion can result in bow-flare water impact. It will subsequently cause severe damages to ship structures. It is essential to predict the pressure distribution induced by the bow-flare impact in ship design. It can be achieved by solving the Laplace equations with nonlinear freesurface boundary conditions or by solving the Navier-Stokes equations. In the solution based on the potential flow theory, the bow-flare impact problem is commonly simplified into a two-dimensional water-entry problem, in which it is assumed that the initial velocity of the boy entering calm water is equal to the relative velocity of the body and the moving free surface.

The wedge water-entry problem has been extensively studies by many researchers. The theoretical analysis of the similarity flow induced by the wedge entry was first conducted Wagner(1932). Armand and Cointe(1986), Cointe(1991) and Howison et al.(1991) extended Wagner's theory to analyze the wedge entry problem using matched asymptotic expansions for wedges with small deadrise. Furthermore, Dobrovol'skaya(1969) developed an analytical solutions in terms of a nonlinear singular integral equation for the problem of the symmetrical entry of a wedge into calm water.