An inverse method for the design of transonic airfoils and wings

Abstract

A design method for transonic airfoils and wings based on the solution of the Euler/Navier-Stokes equations is described. The applied design strategy is an inverse design method based on the work of Takanashi. The difference between the computed pressure distribution of a given geometry and the prescribed target pressure distribution is iteratively reduced by the solution of an inverse formulated transonic small perturbation equation (TSP-equation). In this design method an analysis code is required, such as the Euler/Navier-Stokes code CEVCATS/FLOWer developed at DLR. It is shown that Takanashi's method must be modified in order to ensure the convergence of the design in transonic flow. In addition a smoothing algorithm based on Bézier curves is used to obtain a smooth surface. In order to estimate the accuracy and convergence of the design method, a redesign of a known transonic airfoil and wing is conducted. In all designed cases very accurate results are obtained within a small number of design cycles.