Far-Field Aeroacoustic Shape Optimization using Large Eddy Simulation

This study presents a shape optimization framework that combines a Flux Reconstruction (FR) spatial discretization, Large Eddy Simulation (LES), the Ffowcs-Williams and Hawkings (FW-H) formulation, and the gradient-free Mesh Adaptive Direct Search (MADS) optimization algorithm. We emphasize the necessity of duplicating the data surface to achieve accurate far-field noise prediction in spanwise periodic problems using the FW-H formulation. The proposed parallel implementation of the optimization framework ensures consistent runtime per optimization iteration, regardless of the number of design parameters, thereby addressing a common limitation of many gradient-free algorithms. The framework is demonstrated through far-field aeroacoustic shape optimization of NACA 4-digit airfoils at a Reynolds number of 23,000. The objective function minimizes the Overall Sound Pressure Level (OASPL) at a far-field observer positioned 10 unit chords below the trailing edge, while preserving the mean lift coefficient and reducing the mean drag coefficient. The optimized airfoil achieves an OASPL reduction of $5.9\mathrm{dB}$ and over 14% decrease in mean drag, while maintaining the mean lift coefficient. These results underscore the feasibility and effectiveness of the proposed approach for practical shape optimization applications.