Control theory based airfoil design using Euler equations

Abstract

This paper describes the implementation of optimization techniques based on control theory for airfoil with Euler equations.The Frechet derivative of the cost function is determined via the solution of an adjoint partial differential equation,and the boundary shape is then modified in a direction of descent.The advantage is that the cost function variation is independent on the flow field variation,with the result that the gradient of cost function with respect to arbitrary number of design variables can be determined without the need for additional flow field evaluations.So each design cycle requires the numerical solution of both the flow and the adjoint equations leading to a computational cost roughly equal to the cost of two flow solutions.Results are presented for both the inverse problem and drag minimization.