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Application of biharmonic equation in impeller profile optimization design of an aero-centrifugal pump

Xianwei Liu (School of Power and Energy, Northwestern Polytechnical University, Xi’an, China)
Huacong Li (Northwestern Polytechnical University, Xi’an, China)
Xinxing Shi (Northwestern Polytechnical University, Xi’an, China)
Jiangfeng Fu (Northwestern Polytechnical University, Xi’an, China)

Engineering Computations

ISSN: 0264-4401

Article publication date: 14 June 2019

Issue publication date: 15 August 2019




The purpose of this paper is to improve the hydraulic efficiency without changing the overall dimension. The blade profile optimization design of the aero-centrifugal pump based on the biharmonic equation surrogate model has been studied.


First of all, Bezier curves and linear function are used to control the annular angle distribution and the stacking angle of blade profile under the MATLAB platform. Grid independence analysis has been studied to find the finest mesh scheme. After the precision comparison of test data and computation fluid dynamics 15 sets of design parameters are carried out as the boundary condition of the biharmonic equation. The efficiency surrogate model of the biharmonic equation is constructed via iteratively solving of a discrete difference equation. The other two surrogate models of response surface model (RSM) and radial basis function neural network surrogate model (RBFNNSM) are compared with the biharmonic equation surrogate model by the standard of modified complex correlation coefficient R2 and root mean square deviation (RSME). Finally, the artificial fish swarm algorithm has been used to find the global optimal design parameters with the objective function of highest efficiency.


The results show that the design parameters code conversion method can reduce the number of optimization parameters from five to three, makes the design space become a cube, and compared with RSM and RBFNNSM, the biharmonic equation surrogate model has higher precision with R2 is 0.8958, RSME is 0.1382. The final optimum result of AFSA is at the point of [1 −1 −1]. The internal flow field analysis shows that after optimization the outlet relative velocity becomes more uniform and the wake effect has been significantly decreased. The hydraulic efficiency of the optimized pump is about 59.45 per cent increasing 5.4 per cent compared with a prototype pump.


This study developed a new method to optimize the design parameters of aero-centrifugal pump impeller based on biharmonic equation surrogate model, which had a good agreement with experimental values within just 15 sets of the original design. The optimization results shows that the method can improve the hydraulic efficiency significantly.



Liu, X., Li, H., Shi, X. and Fu, J. (2019), "Application of biharmonic equation in impeller profile optimization design of an aero-centrifugal pump", Engineering Computations, Vol. 36 No. 5, pp. 1764-1795.



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