Title: Optimum aerodynamic design using CFD and control theory
Abstract: This paper describes the implementation of optimization techniques based on control theory for airfoil and wing design.The theory is applied to a system defined by the partial differential equations of the flow, with control by the boundary as a free surface.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.This process is repeated until an optimum solution is approached.Each design cycle requires the numerical solution of both the flow and the adjoint equations, leading t o a computational cost roughly equal t o the cost of two flow solutions.The cost is kept low by using multigrid techniques, which yield a sufficiently accurate solution in about 15 iterations.Satisfactory designs are usually obtained with 10-20 design cycles.