Optimal Control of Aeroacoustic Noise Generated by Cylinder Vortex Interaction

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Abstract
This paper presents an optimal control formulation and solution for an idealized Blade Vortex Interaction (BVI) problem. This problem consists of the interaction of an inviscid vortex pair with a circular cylinder in a steady Mach 0.3 uniform flow with wall-normal velocity used as control on the cylinder surface. This model problem captures the fundamental noise generation process of the BVI phenomena while mitigating many of the complexities of the full rotorcraft problem. The optimal control problem is solved using a gradient based method where gradient information is computed from a continuous adjoint analysis of the governing unsteady Euler equations. The BVI wave packet is targeted by defining an objective function that measures the square amplitude of pressure fluctuations in an observation region over a time interval of interest. When the observation region encloses the entire flow a 6 dB reduction in overall BVI noise is obtained. When the observation region is limited to the region of greatest BVI noise, a 13dB reduction is obtained. The optimal control, unlike most common mitigation methods, does not target the interaction directly — instead, the computed boundary control modulates the potential flow about the cylinder, producing a wave packet of the correct amplitude and phase to approximately cancel the BVI noise in the observation region.

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