Numerical Analysis of 2-D and 3-D Cavitating Hydrofoils Under a Free Surface

Abstract

A method which models two- or three-dimensional cavitating hydrofoils moving with constant speed under a free surface is described. An integral equation is obtained by applying Green's theorem on all surfaces of the fluid domain. This integral equation is divided into two parts:the cavitating hydrofoil problem, andthe free-surface problem. These two problems are solved separately, with the effects of one on the other being accounted for in an iterative manner. The cavitating hydrofoil surface and the free surface are modeled with constant strength dipole and source panels. The source strengths on the free surface are expressed in terms of the second derivative of the potential with respect to the horizontal axis by applying the linearized free-surface conditions. The induced potential by the cavitating hydrofoil on the free surface and by the free surface on the hydrofoil are determined in an iterative sense. In order to prevent upstream waves the source strengths from some distance in front of the hydrofoil to the end of the truncated upstream boundary are enforced to be equal to zero. No radiation condition is enforced at the downstream boundary or at the transverse boundary. The method is applied to 2-D and 3-D hydrofoil geometries in fully wetted or cavitating flow conditions and the predictions are compared with those of other methods in the literature.

A numerical method for the prediction of wave pattern of surface piercing cavitating hydrofoils

“…It is assumed that the fluid is inviscid and incompressible and the flow field is irrotational. Formulation of this problem can be given as follows [2,7].…”

“…The cavity closure and detachment (inception) points depend on the pressure where falls to the critical one, (see for instance Figs 15 and 23 of reference [7]). The cavity height (taken normal to the cavity surface) is h c and determined by integrating the following partial differential equation…”

“…φ W is the potential jump across the wake surface, and n + is the unit vector normal to wake surface pointing upwards. In the present study, the iterative method developed before [7,8]…”

“…The flow around a cavitating two-dimensional hydrofoil by Kelvin type of singularities and by applying the linearized free surface conditions were modelled by Lee et al [6]. An IBEM was described for both two-dimensional S Bal and three-dimensional cavitating hydrofoils under the linearized free surface by Bal et al [7] and Bal and Kinnas [8], respectively. The method was also applied to swept and V types of cavitating hydrofoils and some design tables and figures were given by Bal [9].…”

“…In the present study, however, the IBEM given by Bal et al [7] and Bal and Kinnas [8] is modified and extended to include the surface piercing cavitating hydrofoils (or vertical struts) into the calculations. This IBEM allows solving the cavitating hydrofoil problem and the free surface problem separately, with the effects of one problem on the other accounted for by the values of induced potential.…”