Gradient-free aerodynamic shape optimization using Large Eddy Simulation

Abstract

In this paper we demonstrate the ability to perform gradient-free aerodynamic shape optimization using Large Eddy Simulation (LES) with the Mesh Adaptive Direct Search (MADS) optimization algorithm. We first outline the challenges associated with performing gradient-based optimization using LES, specifically chaotic divergence of the adjoint. We then introduce a Dynamic Polynomial Approximation (DPA) procedure, which allows the high-order solution polynomial representation used by the flow solver to be increased, or decreased, depending on the poll size being used by MADS. This allows rapid convergence towards the optimal design space using lower-fidelity simulations, followed by automatic transition to higher-fidelity simulations when close to the optimal design point. We demonstrate the utility of MADS for optimization of simple chaotic problems, specifically the Lorenz system. We then demonstrate the utility of DPA for aerodynamic optimization of a low Reynolds SD7003 airfoil, highlighting the benefits of the binary DPA approach. Finally, we perform aerodynamic optimization of a turbulent SD7003 airfoil with a final design that increases the mean lift to drag ratio by 32% relative to experimental data, demonstrating that shape optimization using LES and MADS is feasible for aerodynamic design.