Unsteady transonic wing flow computations using field-boundary element methods

Abstract

An unsteady integral equation (or called field-panel, field-boundary element) scheme for solving the full-potential equation for transonic unsteady wing flows has been developed. The unsteady full-potential equation has been written in a moving frame of reference, in the form of the Poisson's equation. Compressibility and unsteadiness have 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 a wing surface (boundary elements) integral term of vorticity distribution, a wake surface (boundary elements) integral term of free-vortex sheet and a volume (field-elements) integral term of compressibility and unsteadiness over a small limited domain around the wing. Numerical solutions are obtained by a time-marching, iterative procedure. Time-derivative term is calculated by a second-order backward finite-difference scheme. To be consistent with the mixed-nature of 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 at transonic speed undergoing acceleration motion and transient pitching motion, respectively. The time history of wing surface pressure distributions has been presented.