A shape optimization procedure for cylinders aeolian tone

A shape optimization procedure is presented. It is dedicated to the noise generated by obstacle flows. The cost function is the acoustic power efficiency, which is derived directly from the fluctuations of the aerodynamic force through for a single formula from the hypothesis of tonal noise. The force is estimated from the direct solution of the 2D incompressible, unsteady flow in laminar regime over a convex symmetrical obstacle without incidence. The no-slip condition at the boundary is assured by an Immersed Boundary Method, that allows the use of the same mesh for all the geometries. The shape of the obstacle is defined by 4 Bézier curves, constrained by second-order continuity leading to 4 degrees of freedom: the aspect ratio, the position of the maximum cross section and two curvature parameters (up and downstream). The optimization is performed via a Particle Swarm Optimization (PSO) routine. Several tests are performed increasing complexity so that coefficients of the PSO be adjusted to the present response surface. There is up to 16 dB of difference between the power efficiency of the extrema configurations for a fixed aspect ratio (AR) and 8 dB for constrained surface or perimeter. For an AR of 1.5, the optimal shape leads to 3dB less acoustic power than the ellipse of same AR. The shapes that minimize acoustic power are relatively different from those that minimize the mean drag.