Influence of Shape Parameterization on a Benchmark Aerodynamic Optimization Problem

Abstract

This paper presents an investigation into the influence of shape parameterization and dimensionality on the optimization of a benchmark case described by the American Institute of Aeronautics and Astronautics Aerodynamic Design Optimization Discussion Group. This problem concerns the drag minimization of a National Advisory Committee for Aeronautics 0012 under inviscid flow conditions at and subject to a local thickness constraint. The work presented here applies six different shape-parameterization schemes to this optimization problem with between four and forty design variables. The parameterization methods used are Bézier-surface free-form deformation, B-splines, class-function/shape-function transformations, Hicks–Henne bump functions, a radial-basis-function-domain-element method, and a singular-value-decomposition method. The optimization framework used consists of a gradient-based sequential-quadratic-programming optimizer coupled with the Stanford University Unstructured adjoint Euler solver, which enables the efficient calculation of the design-variable gradients. Results for all the parameterization methods are presented with the best results for each technique converging to two distinct optimized airfoil shapes with drag counts ranging between 25 and 56 (from an initial value of 469). The optimal result was achieved with the B-spline method with 16 design variables. Further analysis of results is then presented to investigate the design spaces, numerical error, flow behavior, and the presence of hysteresis.