The Radiation Problem of a Submerged Oblate Spheroid in Finite Water Depth Using the Method of the Image Singularities System

Abstract

This study examines the hydrodynamic parameters of a unique geometry that could be used effectively for wave energy extraction applications. In particular, we are concerned with the oblate spheroidal geometry that provides the advantage of a wider impact area on waves, closer to the free surface where the hydrodynamic pressure is higher. In addition, the problem is formulated and solved analytically via a method that is robust and most importantly very fast. In particular, we develop an analytical formulation for the radiation problem of a fully submerged oblate spheroid in a liquid field of finite water depth. The axisymmetric configuration of the spheroid is considered, i.e., the axis of symmetry is perpendicular to the undisturbed free surface. In order to solve the problem, the method of the image singularities system is employed. This method allows for the expansion of the velocity potential in a series of oblate spheroidal harmonics and the derivation of analytical expressions for the hydrodynamic coefficients for the translational degrees of freedom of the body. Numerical simulations and validations are presented taking into account the slenderness ratio of the spheroid, the immersion below the free surface and the water depth. The validations ensure the correctness and the accuracy of the proposed method. Utilizing the same approach, the whole process is implemented for a disc as well, given that a disc is the limiting case of an oblate spheroid since its semi-minor axis approaches zero.