Prediction of Cavitation on Two- and Three-Dimensional Hydrofoils by an Iterative BEM

Abstract

SUMMARY The potential based boundary element methods are applied for the cavity prediction for both two- and three-dimensional (2-D and 3-D) hydrofoils. The problems are treated with source and doublet distributions on the panel surface by the use of Dirichlet type boundary conditions. An iterative solution approach is used to determine the cavity shape of partially cavitating hydrofoils. In the case of specified cavitation number and cavity length, the iterative solution method proceeds by addition or subtraction of a displacement thickness on the cavity surface of the hydrofoil. The appropriate cavity shape is obtained so that the dynamic boundary condition on the cavity surface and the kinematic boundary condition on the whole foil surface including the cavity are satisfied. For a given cavitation number the cavity length of 2-D hydrofoil is determined according to the minimum error criterion among different cavity lengths which satisfy the dynamic boundary condition on the cavity surface. In the three-dimensional hydrofoil problem the prediction of cavity is exactly the same as in the case of two-dimensional method in span wise locations by the transformation of the pressure distribution from analysis of three dimensional to two dimensional. The three dimensional effects at each span wise locations are considered by the multiplication of the cavitation number by a coefficient which varies along the cavity length. The coefficient represents the ratio of the pressure coefficient from two dimensional hydrofoil to three dimensional hydrofoil. The two dimensional hydrofoil problem is investigated for the NACA-16006 and NACA-16012 sections with two angles of attack. The results are compared with those obtained by a commercial CFD code (FLUENT) and the other potential based boundary element code PCPAN. For the three dimensional cavitation prediction an application is carried out and the results are compared with CFD. Consequently, it is shown that the results from the developed two and three dimensional prediction methods are in a good agreement with those obtained from CFD and PCPAN.