Numerical investigation of 3-D wing moving over free surface in water of finite depth

Abstract

Three-dimensional (3-D) wing moving steadily over free water surface with the effects of finite depth has been investigated numerically by an iterative boundary element method (IBEM) developed originally before for cavitating 3-D hydrofoils advancing under free surface. The IBEM has been modified and extended to do this. The fluid is assumed inviscid, incompressible and the flow irrotational. All variables and equations are made non-dimensional. In this way the convergence of numerical scheme is achieved very quickly and consistently. The IBEM is based on the Green’s theorem. The wing problem (including its wake), the free surface problem and the bottom surface problem are solved separately with the effects of each other via their potential values. The 3-D wing surface, the free surface and bottom surface are modeled with constant strength source and constant strength doublet panels. The kinematic boundary condition is applied both on the wing surface and on the bottom surface. On the other hand, the linearized kinematic and dynamic combined condition is applied on the free water surface. The method is first applied to a rectangular wing with a high aspect ratio to compare the pressure distribution on mid-section strip with that of two-dimensional method. Later, the IBEM is applied to a tapered swept-back wing and the effects of finite depth on wing performance have been investigated. It is found that the shallower water depth caused an increase in Kelvin wedge angle, wave height and wave length as compared with in infinite depth case. It is also found that a decrease depth of bottom surface is caused an increase in loading on the wing.

Journal of Naval Architecture and Marine Engineering, 21(1), 2024, P: 1- 14