Near-Field Aeroacoustic Shape Optimization at Low Reynolds Numbers

We investigate the feasibility of gradient-free aeroacoustic shape optimization using the flux reconstruction (FR) approach to study two-dimensional flow at low Reynolds numbers. The overall sound pressure level (OASPL) is computed via the direct acoustic approach, and optimization is performed using the gradient-free mesh adaptive direct search (MADS) algorithm. The proposed framework is assessed across three problems. First, flow over an open cavity is investigated at a Reynolds number of Re=1500 and freestream Mach number of M infinity=0.15, resulting in a 7.9 dB noise reduction. The second case considers tandem cylinders at Re=200 and M infinity=0.2, achieving a 16.5 dB noise reduction by optimizing the distance between the cylinders and their diameter ratio. Finally, a NACA0012 airfoil is optimized at Re=10,000 and M infinity=0.2 to reduce trailing edge noise. The airfoil's shape is optimized to generate a new four-digit NACA airfoil at an appropriate angle of attack to reduce OASPL while maintaining the baseline time-averaged lift coefficient and preventing an increase in the baseline time-averaged drag coefficient. The optimized airfoil is silent at 0 dB and the drag coefficient is decreased by 24.95%. These results demonstrate the feasibility of shape optimization using MADS and FR for aeroacoustic design.