The critical issues of the optimization design of centrifugal pump are introduced in detail, and the main obstacle is the complicated implicit relation between the pump hydraulic performance and its interior passage geometry shape. The parametric design methods of centrifugal impeller proposed previously are introduced, which include the method based on NURBS surface, the method based on free-form deformation (FFD) and the method based on partial differential equation (PDE). To reduce the computational cost, the partial differential equation method is used to parametric design of the centrifugal impeller, and the boundary condition was parameterized. The parameters a(u,v) are consider as constant. The response surface methodology (RSM) is proposed to optimize the design of pump impeller. The objective function can be approximated based on trial results. Analyze the response surface model, and we find that the 2nd order polynomial cannot be used to simulate the complicated relation between the design object and the control variables. So the partial differential equations were proposed to construct the hypersurface response of objective function. The boundary-value problem of hyperspace is numerically solved. According to the optimization analysis, we can get the optimum design of pump impeller. The calculation case shows that the proposed theory and method are rational.

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