Inverse Design of a Displacement Body with a discrete Adjoint Method

Abstract

Wind tunnel experiments at German Aerospace Center (DLR) for the analysis of laminar turbulent transition showed that a nearly linearly decreasing pressure distribution at a plate is able to suppress Tollmien-Schlichting boundary layer instabilities. Nevertheless, this pressure distribution leads to the growth of nonlinear instabilities in cross flow direction. Within up-ucoming research projects at DLR it is intended to further investigate this cross flow boundary layer instabilities. The experimental setup consists of a flat plate, a displacement body mounted above the plate and an additional supporting wing. The supporting wing prevents flow separations. The displacement body imposes the particular pressure distribution upon the upper side of the plate. However, contour and position of the displacement body is not known by detail. Therefore, the given pressure distribution is to be recreated by an inverse design procedure. The task can be seen as a design optimisation to a given pressure function. To provide a fast evaluation the discrete adjoint method of the TAU-Code is used. The problem's cost function is regarded as the residual of the current and the target pressure.