Wing Section Optimization for Supersonic Viscous Flow

Abstract

To improve the performance of a highly swept supersonic wing, it is desirable to have an automated design method that also includes a higher fidelity to the flow physics. With this impetus, an aerodynamic optimization methodology incorporating the thin-layer Navier-Stokes equations and sensitivity analysis had previously been developed. Prior to embarking upon the full wing design task, the present investigation concentrated on the identification of effective optimization problem formulations and testing the feasibility of the employed methodology, by defining two-dimensional test cases. Starting with two distinctly different initial airfoils, two independent optimizations resulted in shapes with similar features: cambered, parabolic profiles with sharp leading- and trailing-edges. Secondly, an outboard wing section normal to the subsonic portion of the leading edge, which had a high normal angle-of attack, was considered. The optimization resulted in a shape with twist and camber that eliminated the adverse pressure gradient, hence, exploiting the leading-edge thrust. The wing section shapes obtained in all the test cases included the features predicted by previous studies. This was considered as a strong indication that the flow field analyses and sensitivity coefficients were computed and provided to the present gradient-based optimizer correctly. Also, from the results of the present study, effective optimization problem formulations could be deduced to start a full wing shape optimization.