Shape optimization for the noise induced by the flow over compact bluff bodies

Abstract

A shape optimization for tonal noise generated aerodynamically at low Mach number is performed for a cylinder with polygonal cross-section. Acoustic quantities are derived from a hybrid analytical formula, with aeroacoustic sources obtained from the incompressible solution of the direct Navier-Stokes equations in 2D at Re = 150; the solid domain is modelled by an Immersed Boundary Method. The optimization is done with the Particle Swarm Optimization (PSO) technique and performed in a cluster where each cost function evaluation is an independent flow simulation. The precision on the 4 main shape parameters is set to 0.001, consistently with the convergence criteria in time, grid and swarm. Optimal shapes for minimum drag and minimum acoustic power are relatively similar. A large range between the optimal shapes is obtained: factor 1.8 for drag and 20 dB for the acoustic power. The reduction of noise is associated with long and bluffer geometries, while the louder flows are associated with highly interacting shear layers obtained with back pointing triangles. The fluctuating lift is the major quantity to control noise at fixed length, while increasing the aspect ratio tends to reduce the noise for globally all geometries. An overall correlation between mean drag and fluctuating suction is also noticed.