Numerical optimization of compressor blade profile based on the control theory

An aerodynamic optimization method based on the control theory has been applied to the axial compressor 2-D blade profile design.The correspondent adjoint equations on the basis of Euler equations and the relevant boundary conditions were deduced in detail.The solving method for the adjoint equations was also proposed.The procedure to conduct an optimized design of a compressor 2-D blade profile could be divided into three steps.First,the required surface pressure distribution is pre-specified and set as the objective function.Second,the parameterized blade profile is seen as a set of the design variables,and the gradients of objective function to the design variables can be calculated by solving the adjoint equations.Third,a new blade profile is obtained by using the BFGS optimization algorithm,and this process is repeated until a converged profile is obtained.The proposed method has been validated by three illustrations.