Towards Adjoint-Based methods for Aeroacoustic control

This paper is concerned with the numerical solution of optimal boundary control problems governed by the unsteady two-dimensional compressible Navier-Stokes equations. Specifically, results are presented for a model problem consisting of two counter-rotating viscous vortices above an infinite wall which, due to the self-induced velocity field, propagate downward and interact with the wall. The wall boundary control is the temporal and spatial distribution of wall-normal velocity which is used to minimize cost functional of interest. The motivation for this work is on-blade control of aeroacoustic noise generated by blade-vortex interaction. We discuss some problem formulation issues, especially the choice of regularization terms; we outline our adjoint computations; and we present results from optimal control calculations using two different objectives and different control reguiarizations.