A 3D IEM for Compressible Wing Flows With and Without Shocks

Abstract

An integral equation (or called field-panel, field-boundary element) scheme for solving the full-potential equation for incompressible and compressible flows with and without shocks 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 wing (or a general body) surface (boundary elements) integral term(s) of vorticity/source distribution(s), wake surface (boundary elements) integral term(s) of free-vortex sheet(s), a volume (field-elements) integral term of compressibility over a small limited domain around the source of disturbance, and a shock surface (boundary elements) integral term of source distributions. Solution is obtained through an iterative procedure for non-linear compressible flows. To be consistent with the mixed-nature of transonic flows, the Murman-Cole type-difference scheme is used to compute the derivatives of the density. The present scheme is applied to flows around a rectangular wing with circular-arc section at incompressible, high- subsonic and transonic flow conditions.