  In this paper, we investigated the feasibility of gradient-free aeroacoustic
shape optimization. The sound pressure level at a near-field observer is
computed directly from the flow field, and the shape is optimized with the
objective of minimizing the sound pressure level at this observer. The Flux
Reconstruction (FR) approach, is used to study the flow over two-dimensional
objects at low Reynolds numbers. The Sound Pressure Level (SPL) is computed
using a direct acoustic approach at an observer in the near field. Aeroacoustic
shape optimization is performed using the gradient-free Mesh Adaptive Direct
Search (MADS) technique. A $7\%$ noise reduction is achieved for flow over an
open deep cavity with a length-to-depth ratio of $L/D=4$ at Reynolds number of
$Re=1500$ based on the cavity depth and free-stream Mach number of $M_\infty =
0.15$. The second case considers tandem cylinders at $Re=200$ and $M_\infty =
0.2$. Over $12\%$ noise reduction is achieved by optimizing the distance
between the cylinders and their diameter ratio. Finally, a baseline NACA0012
airfoil is optimized at $Re=10000$ 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 the SPL while ensuring the baseline
time-averaged lift coefficient is maintained and prevent any increase in the
baseline time-averaged drag coefficient. The optimized airfoil is silent with
$0~dB$ noise and the drag coefficient is decreased by $24.95\%$. These results
demonstrate the feasibility of shape optimization using MADS and FR for
aeroacoustic design.
