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.
[1]Kim J S,Park W G. Optimized inverse design method for pump impeller[J]. Mechanics Research Communications, 2000, 27(4): 465-473.[2]Lehnhuser T,Schfer M. A numerical approach for shape optimization of fluid flow domains[J]. Computer Methods in Applied Mechanics and Engineering, 2005, 194(50/51/52): 5221-5241.[3]Zangeneh M, Goto A, Harada H. On the role of threedimensional inverse design methods in turbomachinery shape optimization[J]. Journal of Mechanical Engineering, 1999, 213(1): 27-42.[4]Zangeneh M, Goto A, Takemura T. Suppression of secondary flows in a mixedflow pump impeller by application of three dimensional inverse design method—Part 1:Design and numerical validation[J]. Journal of Turbomachinery,1996, 118(7): 536-542.[5]Seo S J, Kim K Y. Design optimization of forwardcurved blades centrifugal fan with response surface method[C]∥Proceedings of the ASME Heat Transfer/Fluids Engineering Summer Conference, 2004:551-556[6]张人会,杨军虎,刘宜. 基于曲面迭代的离心泵数值叶片模型[J]. 机械工程学报,2006,42(10): 70-72.Zhang Renhui, Yang Junhu, Liu Yi. Numerical model of centrifugal pump blade based on iteration of surface[J]. Chinese Journal of Mechanical Engineering, 2006, 42 (10): 70-72. (in Chinese)[7]Zhang Renhui, Yang Junhu, Li Rennian. Parametric control of the hydraulic machinery impeller based on freeform deformation[J]. Procedia Engineering, 2012, 31: 909-913.[8]张人会,杨军虎,李仁年.离心泵叶轮的参数化设计[J].排灌机械,2009,27(5): 310-313.Zhang Renhui, Yang Junhu, Li Rennian. Investigation on parametric design of centrifugal pump blade[J].Drainage and Irrigation Machinery, 2009,27(5): 310-313. (in Chinese)[9]潘雷,谷良贤.分块响应面法研究[J].计算机工程与应用,2009,45(19): 37-39.Pan Lei, Gu Liangxian. Research on improved response surface method [J]. Computer Engineering and Applications, 2009, 45(19): 37-39. (in Chinese)[10]董峰,蔡文立,石教英. 超曲面:一种三维有限元数据场的造型表示方法[J].计算机研究与发展, 1997, 34(12): 908-912.Dong Feng, Cai Wenli, Shi Jiaoying. Hyperpatch:a modeling approach to representing three dimensional FEM data field[J]. Journal of Computer Research and Development, 1997, 34 (12): 908-912. (in Chinese)