The effect of finite depth on 2D and 3D cavitating hydrofoils

Abstract

The iterative numerical method that has been developed for cavitating hydrofoils and surface piercing bodies moving inside a numerical towing tank is modified and extended to the case of fully submerged, both two- and three-dimensional cavitating hydrofoils in water of finite depth, and the effects of subcritical speed, critical speed and supercritical speed are investigated in detail. The iterative numerical method based on Green’s theorem allows separating the cavitating hydrofoil problem, the free surface problem and finite bottom problem both in two and three dimensions. The cavitating hydrofoil surface, the free surface and the surface of finite bottom are modeled with constant strength dipole and constant strength source panels. While the kinematic boundary condition is applied on the hydrofoil surface, a dynamic condition is applied with a cavity closure condition on the cavity surface. The source strengths on the free surface are expressed in terms of perturbation potential by applying the linearized free surface conditions. No radiation condition is enforced for downstream and transverse boundaries. The source strengths on the bottom surface are zero because of vanishing normal velocity. The method is applied to 2D and 3D cavitating hydrofoils, and the effect of finite bottom on lift and drag coefficients, cavity number and wave elevation is investigated.