Robust Aerodynamic Design Optimization Using Polynomial Chaos

Abstract

This paper investigates the potential of polynomial chaos methods, when used in conjunction with computational fluid dynamics, to quantify the effects of uncertainty in the computational aerodynamic design process. The technique is shown to be an efficient and accurate means of simulating the inherent uncertainty and variability in manufacturing and flow conditions and thus can provide the basis for computationally feasible robust optimization with computational fluid dynamics. This paper presents polynomial chaos theory and the nonintrusive spectral projection implementation, using this to demonstrate polynomial chaos as a basis for robust optimization, focusing on the problem of maximizing the lift-to-drag ratio of a two-dimensional airfoil while minimizing its sensitivity to uncertainty in the leading-edge thickness. The results demonstrate that the robustly optimized designs are significantly less sensitive to input variation, compared with nonrobustly optimized airfoils. The results also indicate that the inherent geometric uncertainty could degrade the on-design as well as the offdesign performance of the nonrobust airfoil. This leads to the further conclusion that the global optimum for some design problems is unreachable without accounting for uncertainty.