Optimal Transpiration Boundary Control for Aeroacoustics
S. Scott Collis
Department of Mechanical Engineering and Materials Science
Kaveh Ghayour
Department of Computational and Applied Mathematics and
Department of Mechanical Engineering and Materials Science
Matthias Heinkenschloss
Department of Computational and Applied Mathematics
Rice University
AIAA Journal, Vol. 41, No. 7 (2003), pages 1257-1270.
Abstract
We consider the optimal boundary control of aeroacoustic noise
governed by the two-dimensional unsteady compressible Euler equations. The
control is the time and space varying wall-normal velocity on a subset of an
otherwise solid wall. The objective functional to be minimized is a measure
of acoustic amplitude. Optimal transpiration boundary control of aeroacoustic
noise introduces challenges beyond those encountered in direct aeroacoustic
simulations or in many other optimization problems governed by compressible
Euler equations. One nontrivial issue that arises in our optimal control
problem is the formulation and implementation of transpiration boundary
conditions. Since we allow suction and blowing on the boundary, portions of
the boundary may change from inflow to outflow, or vice versa, and different
numbers of boundary conditions must be imposed at inflow versus outflow
boundaries. Another important issue is the derivation of adjoint equations
which are required to compute the gradient of the objective function with
respect to the control. Among other things, this is influenced by the choice
of boundary conditions for the compressible Euler equations. This paper
describes our approaches to meet these challenges and presents results for
three model problems. These problems are designed to validate our
transpiration boundary conditions and their implementation, study the accuracy
of gradient computations, and assess the performance of the computed
controls.
Note: This paper is an expanded version of the
AIAA Paper 2002-2757,
Optimal Control of Aeroacoustic Flows:Transpiration Boundary Control.