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浙江大学学报(工学版)
Journal of ZheJiang University (Engineering Science)  2019, Vol. 53 Issue (5): 988-996    DOI: 10.3785/j.issn.1008-973X.2019.05.021
    
Optimization calculation method for efficiency of multistage split case centrifugal pump
Shui-guang TONG1(),Hang ZHAO1,Hui-qin LIU1,Zhe-ming TONG1,Yue YU1,Ning TANG1,Wei-jie WU1,Jin-fu LI2,Fei-yun CONG1,*(),Hao ZHANG3,Yin-hua WANG4,Guo-shuai HAO5
1. School of Mechanical Engineering, Zhejiang University, Hangzhou 310027, China
2. Hangzhou Alkali Pump Co. Ltd, Hangzhou 310030, China
3. Hangzhou Resource Power Equipment Co. Ltd, Hangzhou 311202, China
4. Hangzhou Hangfa Electrical Equipment Co. Ltd, Hangzhou 311215, China
5. Shenyang Turbine Machinery Co. Ltd, Shenyang 110869, China
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Abstract  

The optimization calculation method of the hydraulic efficiency and the relative width of high efficient area for centrifugal pumps was researched. The multi-objective optimization calculation method of the approximate models was proposed based on the hydraulic loss model. Optimization design of multi-stage dual split centrifugal pump was conducted as an example. The key design variables were selected out through sensitivity analysis based on the hydraulic loss model. The hydraulic loss model, the complete quadratic response surface function (RSF) model, the radial basis Gaussian response surface function (RBF) model and the Kriging response surface function (KRG) model were used respectively to optimize the key design variables of centrifugal pumps. The accuracy and efficiency of the four methods were analyzed as well. Results showed that the calculation time of the first optimization method based on the theoretical formula was the shortest, but the error was big. The latter three optimization methods were based on the computational fluid dynamics (CFD) numerical simulation analysis and the results were accurate. The results of RSF model were the most accurate and the calculation time was short. The calculation results of RSF was the most accurate, followed by that of RBF, and the worst was that of KRG by the comparison of the calculation accuracies of the three approximate models. The Pareto optimal solution based on RSF had the head of 83.77 m and the efficiency of 77.26% with the design flow. The Pareto optimal solution based on RBF had the head of 83.09 m and the efficiency of 76.63% with the design flow.

Key words： multistage centrifugal pump      hydraulic loss model      key design variables      approximate model      muti-objective optimization     
Received: 26 April 2018      Published: 17 May 2019
CLC:  TH 311  
Corresponding Authors: Fei-yun CONG     E-mail: cetongsg@163.com;cloudswk@zju.edu.cn
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Shui-guang TONG
Hang ZHAO
Hui-qin LIU
Zhe-ming TONG
Yue YU
Ning TANG
Wei-jie WU
Jin-fu LI
Fei-yun CONG
Hao ZHANG
Yin-hua WANG
Guo-shuai HAO
Cite this article:

Shui-guang TONG,Hang ZHAO,Hui-qin LIU,Zhe-ming TONG,Yue YU,Ning TANG,Wei-jie WU,Jin-fu LI,Fei-yun CONG,Hao ZHANG,Yin-hua WANG,Guo-shuai HAO. Optimization calculation method for efficiency of multistage split case centrifugal pump. Journal of ZheJiang University (Engineering Science), 2019, 53(5): 988-996.

URL:

http://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2019.05.021     OR     http://www.zjujournals.com/eng/Y2019/V53/I5/988


中开多级离心泵效率优化计算方法

对离心泵水力效率及高效区相对宽度的优化计算方法进行研究，在水力损失模型的基础上提出基于近似模型的多目标优化计算方法. 以中开多级离心泵的优化设计为例，基于水力损失模型进行设计变量灵敏度分析，选出关键设计变量. 分别利用水力损失、完全二次响应面（RSF）、径向基高斯响应面（RBF）和克里金响应面（KRG）4种近模型优化离心泵的关键设计变量，分析4种效率优化计算方法的精确性和有效性. 结果表明：基于理论公式计算的第1种优化方法耗时少，但结果误差较大；后3种优化方法基于计算流体动力学（CFD）数值仿真分析，结果准确，其中RSF模型的结果最精确且计算时间较短. 比较3种不同近似模型的计算精度，RSF的计算结果最精确，RBF结果次之，KRG结果最差. 在设计流量下，基于RSF的Pareto最优解的扬程为83.77 m，效率为77.26%，基于RBF的Pareto最优解的扬程为83.09 m，效率为76.63%.


关键词： 多级离心泵,  水力损失模型,  关键设计变量,  近似模型,  多目标优化 
Fig.1 Optimal design scheme of singlestage centrifugal pump
设计变量 范围
Z [3, 7]
$\,{\beta _1}$ $[{10^ \circ }, \;{35^ \circ }]$
$\,{\beta _2}$ $[{14^ \circ },\;{24^ \circ }]$
${D_2}$ $ [10.4{{\left( {{n}_{{\rm{s}}}}/100 \right)}^{-{1}/{2}\;}}{{(q_{V}/n)}^{{1}/{3}\;}},\;11.1{{\left( {{n}_{{\rm{s}}}}/100 \right)}^{-{1}/{2}\;}}{{(q_{V}/n)}^{^{{1}/{3}\;}}}]$
${b_2}$ $ [0.85{{\left( {{n}_{{\rm{s}}}}/100 \right)}^{{5}/{6}\;}}{{(q_{V}/n)}^{{1}/{3}\;}},\;1.2{{\left( {{n}_{{\rm{s}}}}/100 \right)}^{{5}/{6}\;}}{{(q_{V}/n)}^{{1}/{3}\;}}]$
${D_{\rm{s}}}$ $ [12{{(q_{V}/n)}^{{1}/{3}\;}},\;15{{(q_{V}/n)}^{{1}/{3}\;}}]$
${D_{\rm{h}}}$ $ [8.5{{(q_{V}/n)}^{{1}/{3}\;}},\;11.7{{(q_{V}/n)}^{{1}/{3}\;}}]$
$\varphi $ $ [{{140}^{\circ }},\;{{180}^{\circ }}]$
$\theta $ $ [{{18}^{\circ }},\;{{28}^{\circ }}]$
${D_3}$ $ [1.03{{D}_{2}},\;1.06{{D}_{2}}]$
$Y$ $ [0.8,\;2.0]$
Tab.1 Range of design variables of multistage pump
Fig.2 Effect curve of univariate on external characteristic values of singlestage centrifugal pump
Fig.3 Sensitivity analysis for design variables of centrifugal pump
Fig.4 Mesh model of singlestage centrifugal pump
近似模型 RMSE/% R2/%
H P η H P η
不完全RSF 0.10 0.24 0.26 96.96 94.41 82.34
完全RSF 0.08 0.15 0.21 97.81 97.78 89.33
RBF 0.10 0.22 0.25 97.19 95.46 84.20
Tab.2 Validity test of response surface model
Fig.6 Comparison of approximate model predicted hydraulic power with CFD numerical calculation result
Fig.7 Comparison of approximate model predicted hydraulic power with CFD numerical calculation result
模型 D2/mm b2/mm β2/（°） 模型理论计算值 CFD仿真计算值 误差/%
H/m P/kW η/% H/m P/kW η/% H P η
HLoss 273.9 14.0 17.0 82.40 26.51 75.98 76.89 24.55 74.10 7.15 7.98 3.78
RSF 279.0 13.0 15.0 84.19 26.11 77.32 83.77 26.03 77.26 0.50 0.31 0.08
RBF 277.0 14.5 15.0 83.13 26.30 75.85 83.09 26.00 76.63 0.50 1.15 1.02
KRG 275.0 15.5 15.0 84.06 26.69 75.02 82.13 25.98 75.81 2.35 2.73 1.04
Tab.3 Pareto optimal solution and CFD numerical simulation analysis of four calculation models
Fig.5 Comparison of approximate model predicted head value with CFD numerical calculation result
Fig.8 Full flow performance prediction of singlestage centrifugal pump with impeller 1 and 2
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