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浙江大学学报(工学版)
浙江大学学报(工学版)  2019, Vol. 53 Issue (5): 988-996    DOI: 10.3785/j.issn.1008-973X.2019.05.021
机械工程、化学工程     
中开多级离心泵效率优化计算方法
童水光1(),赵航1,刘会琴1,童哲铭1,余跃1,唐宁1,吴伟杰1,李进富2,从飞云1,*(),张昊3,王寅华4,郝国帅5
1. 浙江大学 机械工程学院，浙江 杭州 310027
2. 杭州碱泵有限公司，浙江 杭州 310030
3. 杭州力源发电设备有限公司，浙江杭州 311202
4. 杭州杭发发电设备有限公司，浙江 杭州 311215
5. 沈阳透平机械股份有限公司，辽宁 沈阳 110869
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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摘要：

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    
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
收稿日期: 2018-04-26 出版日期: 2019-05-17
CLC:  TH 311  
通讯作者: 从飞云     E-mail: cetongsg@163.com;cloudswk@zju.edu.cn
作者简介: 童水光(1960—)，男，教授，从事机械CAD/CAE研究. orcid.org/0000-0001-5908-7401. E-mail: cetongsg@163.com
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童水光
赵航
刘会琴
童哲铭
余跃
唐宁
吴伟杰
李进富
从飞云
张昊
王寅华
郝国帅

引用本文:

童水光,赵航,刘会琴,童哲铭,余跃,唐宁,吴伟杰,李进富,从飞云,张昊,王寅华,郝国帅. 中开多级离心泵效率优化计算方法[J]. 浙江大学学报(工学版), 2019, 53(5): 988-996.

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.

链接本文:

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

图 1  单级离心泵效率优化设计方案
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]$
表 1  多级泵设计变量取值范围
图 2  单变量对单级离心泵外特性值的影响曲线
图 3  离心泵设计变量灵敏度分析
图 4  单级离心泵计算网格模型
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
表 2  响应面模型有效性检验
图 6  近似模型水力功率预测值与CFD数值计算结果对比
图 7  近似模型效率预测值与CFD数值计算结果对比
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
表 3  4种计算模型Pareto最优解及CFD数值模拟分析
图 5  近似模型扬程预测值与CFD数值计算结果对比
图 8  叶轮1、2的单级离心泵全流量性能预测
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