A Boundary Element Method for the Analysis of the Flow Around 3-D Cavitating Hydrofoils

Abstract

The three-dimensional steady cavitating hydrofoil problem is treated in nonlinear theory by employing a low-order potential-based boundary element method. The cavity extent and shape are determined for given cavitation number by satisfying the three-dimensional kinematic and dynamic boundary conditions on the hydrofoil surface beneath the cavity and on the portion of the wake sheet overlapped by the cavity. A unified discretization and algorithm is developed to predict the occurrence of general cavity planforms, including partial cavitation, supercavitation, and mixed partial/supercavitation. The cavity planform is determined iteratively by searching for the planform which corresponds to a closed cavity at all spanwise locations. Cavity shapes predicted by the present method, applied in two dimensions, are compared to the converged nonlinear cavity shapes and are found to differ only slightly for a range of foil thicknesses and angles of attack. The accuracy of the 3-D method is gaged by satisfying Green's formula, subject to a kinematic boundary condition, on a modified foil consisting of the union of the original foil and the cavity predicted by the present method. Comparing the resulting pressure distribution to the pressure distribution from the present method shows that the dynamic boundary condition is satisfied to within acceptable accuracy.