Aerodynamic shape optimization of a transonic fan by an adjoint-response surface method

An adjoint-response surface method is developed to provide efficient surrogate model in a parametrized design space for aerodynamic optimization of turbomachinery blades. Our goal is to improve the adiabatic efficiency or equivalently reduce the entropy generation through blade row with a mass flow rate constraint. Firstly, an aerodynamic sensitivity analysis is conducted with a viscous adjoint method to find the suitable number of control points on the suction surface of the transonic NASA rotor 67. Then quadratic polynomial (QP) based response surfaces of 4, 6 and 8 parameters are examined to validate the advantages of the gradient-enhanced model. In the following 24-parameter aerodynamic design optimization case, a steepest descent optimization (SDO) based on adjoint gradient is conducted, then QP based response surface model is constructed using both the values of cost function and its adjoint gradients with respect to geometry control parameters. We present the geometric features, overall aerodynamic improvements and flow details of optimal designs given by SDO and gradient-enhanced response surface model (GERSM). The effects of blade reshaping on shock system, tip clearance flow and flow separation at hub are examined. Also, off-design performances are analyzed regarding both adiabatic efficiency and stall margin.