Gradient-Free Aerodynamic Shape Optimization using PyFR and MADS

Abstract

The development of next-generation aircraft will rely on our ability to perform shape optimization using high-fidelity Computational Fluid Dynamics (CFD). Whereas previous low-fidelity solvers, such as the Reynolds Averaged Navier-Stokes (RANS) approach, are amenable to gradient based optimization, high-fidelity fidelity solvers, such as Large Eddy Simulation (LES), are not. LES resolves unsteady turbulent structures, resulting in chaotic divergence of the flow and objective functions when perturbed. As a result, classical sensitivity analysis via the adjoint or tangent methods is unconditionally unstable. In this presentation we demonstrate the utility of a gradient-free Mesh Adaptive Direct Search (MADS) approach for performing shape optimization with LES. We first demonstrate the suitability of MADS for optimizing model problems, specifically the Lorenz system. We then use MADS coupled with PyFR to perform shape optimization of an SD7003 airfoil and two independent optimizations of a T106D turbine cascade. Results demonstrate >20% performance improvement relative to reference designs for both cases. Importantly, these results are obtained within days via two independent levels of parallelism. This demonstrates that aerodynamic shape optimization using LES is now feasible, and that it can be used for practical aerospace geometries.