Unsteady Three-Dimensional Transonic Flow Computations Using Field Element Method

Abstract

An unsteady field element (or called, integral equation) scheme for solving the full-potential equation has been developed for unsteady transonic wing flows. The unsteady full-potential equation is formulated in a moving frame of reference, and it is written in the Poisson’s equation where unsteady term is included in nonhomogeneous term. Integral equation solution in terms of velocity field is obtained by the Green’s theorem. The solution consists of a wing surface integral term of vorticity distribution, a wake surface integral term of free-vortex sheet and a volume integral term of compressibility and unsteadiness over a small limited domain around the wing. The solution is accomplished by a time-marching, iterative procedure. The Murman-Cole type-difference scheme is used to compute derivatives of density, and shocks are captured automatically. The scheme has been applied to the flow around a rectangular wing at transonic speeds undergoing acceleration motion. The time history of the wing surface pressure distributions has been presented.