Aerodynamic Shape Optimization Using Sensitivity Analysis on Third-Order Euler Equations

Previously, the authors have shown an aerodynamic optimization method with two design variables using sensitivity analysis on the first-order-accurate discretization of the Euler equations. Two advancements of this method are reported in this article. First, nonlinear fluid dynamic phenomena including flow discontinuities are better predicted by an improved flow prediction method which uses the third-order accurate discretization of the Euler equations. Using this method, the flowfield of a modified shape which generates shocks and other large gradients is predicted based on the shock-free flowfield of the original shape and without solving the flowfield equations. Secondly, every surface grid point is used as a design variable, which virtually eliminates all geometrical restrictions on the shape as it is optimized for the specified objective. This improved algorithm is demonstrated by optimizing the ramp shape of a scramjet-afterbody configuration for maximum axial thrust. Starting with totally different initial designs, virtually identical shapes are obtained as the optimum. The method is more efficient than the traditional design methods for a few reasons, which include the use of flow predictions and the elimination of a priori guessing of possible shapes from which the optimum is to be selected.