Abstract: The paper presents an aerodynamic shape optimization of the last stage of a 4.5-stage com-pressor by a gradient-based optimization method that adopts the continuous adjoint approach. An adjoint mixing-plane formulation is used to compute the adjoint solutions for multi-stage turbomachines. Firstly, a conventional preliminary design method with empirical correlations are used to produce a base design of a 4.5-stage low-speed and low compression ratio compressor with an inlet guide vane. Then the last stage is redesigned by the adjoint method to reduce the flow losses at the operation condition near stall through modifying the aerodynamic shape and stagger angle of the stator blade. The cost function is defined as a weighted sum of entropy production and the deviation from a given mass flow rate, enforcing the constraint on mass flow rate. Finally, a multi-point design optimization approach by using the adjoint method is employed to improve the performance of the last stage at two different operation conditions. The optimization show that the adjoint-based multi-stage design can improve the aerodynamic performance of a multi-stage compressor by profile modifications.

Key words: aerodynamic design optimization, adjoint method, multi-stage, multi-point, mixing-plane, flow separation, compressor