Application of the Integral Equation Method to Flows Around a Wing with Circular-Arc Section

Abstract

An integral equation (or called field-panel, field-boundary element) scheme for solving the full-potential equation for transonic flows has been developed. The full-potential equation has been written in the form of the Poisson’s equation. Compressibility has been treated as non-homogeneity. The integral equation solution in terms of velocity field is obtained by the Green’s theorem. The solution consists of surface (boundary elements) integral term(s) of vorticity/source distributions), wake surface (boundary elements) integral term(s) of free-vortex sheet(s) and a volume (field-elements) integral term of compressibility over a small limited domain around the source of disturbance. Solution procedure is an iterative procedure for non-linear flows. To consist with the mixed-nature of transonic flows, the Murman-Cole type-difference scheme is used to compute the derivatives of the density for non-linear flows. The present scheme is applied to flows around a rectangular wing with circular-arc section.