Abstract The problems in the optimization design of centrifugal pump impeller were elaborated and it was found that the implicit relation between the hydraulic performance and the complicated geometry shape of impeller passages was a main obstacle. The existing parametric design methods for centrifugal pump impellers, such as the NURBS surface method, freesurface deformation method and partial differential equation method were introduced in detail. To reduce the computational cost, a partial differential equations method was used to control the geometry shape of centrifugal impellers parametrically, the boundary conditions of the equations were parameterized as well.Suppose the parameters a(u,v) are constant and the response surface methodology (RSM) was applied to optimize the design of centrifugal pump impellers, a 2nd order polynomial response surface was constructed according to the trial results.Unfortunately, it was identified that a 2nd order polynomial fails to present the complicated nonlinear relation between the objective function and the control variables. So the partial differential equations had to be proposed to construct the hypersurface response of objective function. Then a boundaryvalue problem of hyperspace was numerically solved. Eventually, an optimal design of pump impellers was achieved.The result of the optimized design case shows that the proposed theory and method are reasonable.
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