Towards Adjoint-Based Methods for Aeroacoustic Control

S. Scott Collis+ , Kaveh Gayour+, Matthias Heinkenschloss , Michael Ulbrich, and Stefan Ulbrich

+Department of Mechanical Engineering and Materials Science Rice University, Houston, TX 77005-1892, USA

*Department of Computational and Applied Mathematics Rice University, Houston, TX 77005-1892, USA

**Lehrstuhl für Angewandte Mathematik und Mathematische Statistik

Zentrum Mathematik

Technische Universität München

AIAA Paper 2001-0821

39th Aerospace Sciences Meeting & Exhibit

January 8-11, 2001, Reno, Nevada.

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Abstract

This paper is concerned with the numerical solution of optimal boundary control problems governed by the unsteady two-dimensional compressible Navier-Stokes equations. Specifically, we will present results 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 strike the wall. The control is the temporal and spatial distribution of wall-normal velocity which is used to minimize a 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 two optimal control calculations using different objectives and different control regularizations.