Aerodynamic design of cascades by using an adjoint equation method

Abstract

A continuous adjoint equation method is developed for the aerodynamic design of cascade blades in a two-dimensional, inviscid, and compressible flow. A cost function based on a prescribed target pressure distribution is defined and the purpose of design is to minimize the value of the cost function. The adjoint equations and the corresponding boundary conditions are derived based on the Euler equations, the flow boundary conditions, and the definition of the cost function. Gradient information is obtained by solving the adjoint equations. A one-dimensional search algorithm is used to perform the optimization in the calculated gradient direction. Multigrid method is applied to accelerate the computation for both the Euler and the adjoint equations. Three transonic cascade blade design cases are tested. The results show that the method is effective and efficient for turbomachinery blade design. The effect of shape functions on the performance of the design method is discussed. © 2003 by the authors. Published by the American Institute of Aeronautics and Astronautics, Inc.