Near-Field Aeroacoustic Shape Optimization at Low Reynolds Numbers

Abstract

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 free-stream Mach number of $M_\infty = 0.15$, resulting in a $7.9dB$ noise reduction. The second case considers tandem cylinders at $Re=200$ and $M_\infty = 0.2$, 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 $M_\infty = 0.2$ to reduce trailing edge noise. The airfoil's shape is optimized to generate a new 4-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 $0dB$ and the drag coefficient is decreased by $24.95\%$. These results demonstrate the feasibility of shape optimization using MADS and FR for aeroacoustic design.

Figures (25)

• Figure 1: The computational element $\Omega_k$ with solution points in black, flux points in red, and mapping points in blue, for a $\mathcal{P}2$ discretization.
• Figure 2: Search and poll steps of the MADS optimization techniques for iteration $k$ for the NACA example.
• Figure 3: The geometry of a two-dimensional cavity.
• Figure 4: The computational domain of the open cavity.
• Figure 5: The time history of drag coefficient of the open cavity.