Gradient-Free Aeroacoustic Shape Optimization Using Large Eddy Simulation

We present an aeroacoustic shape optimization framework that relies on high-order Flux Reconstruction (FR), the gradient-free Mesh Adaptive Direct Search (MADS) optimization algorithm, and Large Eddy Simulation (LES). Our parallel implementation ensures consistent runtime for each optimization iteration, regardless of the number of design parameters, provided sufficient resources are available. The objective is to minimize the Overall Sound Pressure Level (OASPL) at a near-field observer by computing it directly from the flow field. We evaluate this framework across three problems. First, an open deep cavity is considered at a free-stream Mach number of $M_\infty=0.15$ and Reynolds number of $Re=1500$, reducing the OASPL by $12.9~dB$. Next, we considered tandem cylinders at $Re=1000$ and $M_\infty=0.2$, achieving over $11~dB$ noise reduction by optimizing cylinder spacing and diameter ratio. Lastly, a baseline NACA0012 airfoil at $Re=23000$ and $M_\infty=0.2$ is optimized to generate a new 4-digit NACA airfoil at an appropriate angle of attack to minimize the OASPL while ensuring the baseline time-averaged lift coefficient is maintained and prevent any increase in the baseline time-averaged drag coefficient. The OASPL and mean drag coefficient are reduced by $5.7~dB$ and more than $7\%$, respectively. These results highlight the feasibility and effectiveness of our aeroacoustic shape optimization framework.