Calculation of Three-Dimensional Steady Cavitation by a Simple Surface Panel Method

Abstract

This paper presents a calculation method for the 3-D steady cavitating hydrofoil problem. The method is based on a simplified surface panel method “SQCM” which satisfies the Kutta condition at a time even for the 3-D problem. Hess and Smith type source panels are distributed on the hydrofoil and cavity surface. Discrete vortices are distributed on the camber surface according to Lan's QCM (Quasi-Continuous vortex lattice Method). The boundary conditions to determine these singularities are the constant pressure condition on the cavity surface and the zero normal velocity condition on the hydrofoil and camber surfaces. The cavity shape in each spanwise section is determined so that the zero normal velocity condition is satisfied.In the present method, a cavity length for each spanwise section is given first. Then the singularities, the cavitation number and the cavity shapes are determined. These steps are repeated until the cavity shapes are unchanged. Next, the cavity length is corrected by comparing the obtained cavitation number with the objective cavitation number in each section. By using the corrected cavity length, the calculation is restarted from the beginning. Above described procedure is repeated until the obtained cavitation number is converged to the objective cavitation number in each section. Cavity shapes, pressure distributions and forces acting on hydrofoils are calculated for four kinds of hydrofoils. Good agreements are obtained between the calculated results and the experimental data.