A potential based panel method for 2-D hydrofoils

Abstract

A potential based panel method for the hydrodynamic analysis of 2-D hydrofoils moving beneath the free surface with constant speed without considering cavitation is described. By applying Green's theorem and the Green function method, an integral equation for the perturbation velocity potential is obtained under the potential flow theory. Dirichlet type boundary condition is used instead of Neumann type boundary condition. The 2-D hydrofoil is approximated by line panels which have constant source strength and constant doublet strength distributions. The free surface condition is linearized and the method of images is used for satisfying this free surface condition. All the terms in fundamental solution (Green function) of perturbation potential are integrated over a line panel. Pressure distribution, lift, residual drag and free surface deformations are calculated for NACA4412, symmetric Joukowski and van de Vooren profile types of hydrofoil. The results of this method show good agreement with both experimental and numerical methods in the literature for the NACA4412 and symmetric Joukowski profile types. The lift and residual drag values of the van de Vooren profile are also presented. The effect of free surface is examined by a parametric variation of Froude number and depth of submergence.