Aerodynamic Design of Cascades by Using an Adjoint Equation Method," AIAA Paper 2003-1068, AIAA 41st Aerospace Sciences Meeting and Exhibit

A continuous adjoint equation method is developed for the aerodynamic design of cascade blades in a two-dimensional, inviscid, and compressible ow. A cost function based on a prescribed target pressure distribution is dened 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 ow boundary condi-tions, and the denition of the cost function. Gradient information is obtained by solving the adjoint equations. A one-dimensional search algorithm is used to perform the opti-mization 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 eective and ecient for turbomachinery blade design. The eect of shape functions on the performance of the design method is discussed. I