A Finite-Difference, Frequency-Domain Numerical Scheme for the Solution of the Gust Response Problem

Abstract

A numerical method is developed for solving subsonic flows with convected, three-dimensional vortical waves around lifting airfoils. The first-order method that is presented fully accounts for the distortion effects of the nonuniform mean flow on the convected vorticity. The unsteady velocity is split into a vortical component which is a known function of the upstream flow conditions and the Lagrangian coordinates of the mean flow, and an irrotational field whose potential satisfies a nonconstant-coefficient, inhomogeneous, convective wave equation. Using an elliptic coordinate transformation, the unsteady boundary value problem is solved in the frequency domain on grids which are determined as a function of the Mach number and reduced frequency. Extensive comparisons are made with known solutions to unsteady vortical flow problems, and it is seen that the agreement is in general very good for reduced frequencies ranging from zero to four. © 1995 by Academic Press, Inc.