中开多级离心泵效率优化计算方法

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Optimization calculation method for efficiency of multistage split case centrifugal pump

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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.

Keywords： multistage centrifugal pump ; hydraulic loss model ; key design variables ; approximate model ; muti-objective optimization

TONG Shui-guang, ZHAO Hang, LIU Hui-qin, TONG Zhe-ming, YU Yue, TANG Ning, WU Wei-jie, LI Jin-fu, CONG Fei-yun, ZHANG Hao, WANG Yin-hua, HAO Guo-shuai. Optimization calculation method for efficiency of multistage split case centrifugal pump. Journal of Zhejiang University(Engineering Science)[J], 2019, 53(5): 988-996 doi:10.3785/j.issn.1008-973X.2019.05.021

1.1. 优化设计方案

MSD中开多级（10级）离心泵的设计要求如下：体积流量qV=100 m3/h，扬程H=80 m（每级）,转速n=2 950 r/min，配套电机的额定输出功率Pr=355 kW，通过计算得到比转速 ${n_{\rm{s}}} = 67.09$. 设计目标为10级整体效率η=70%. 该单级离心泵效率的优化设计方案如图1所示.

图 1

Fig.1   Optimal design scheme of singlestage centrifugal pump

1.2. 离心泵变量范围

Tab.1  Range of design variables of multistage pump

 设计变量 范围 Z [3, 7] $\,{\beta _1}$ $[{10^ \circ }, \;{35^ \circ }]$ $\,{\beta _2}$ $[{14^ \circ },\;{24^ \circ }]$ ${D_2}$ $[10.4{{\left( {{n}_{{\rm{s}}}}/100 \right)}^{-{1}/{2}\;}}{{(q_{V}/n)}^{{1}/{3}\;}},\;11.1{{\left( {{n}_{{\rm{s}}}}/100 \right)}^{-{1}/{2}\;}}{{(q_{V}/n)}^{^{{1}/{3}\;}}}]$ ${b_2}$ $[0.85{{\left( {{n}_{{\rm{s}}}}/100 \right)}^{{5}/{6}\;}}{{(q_{V}/n)}^{{1}/{3}\;}},\;1.2{{\left( {{n}_{{\rm{s}}}}/100 \right)}^{{5}/{6}\;}}{{(q_{V}/n)}^{{1}/{3}\;}}]$ ${D_{\rm{s}}}$ $[12{{(q_{V}/n)}^{{1}/{3}\;}},\;15{{(q_{V}/n)}^{{1}/{3}\;}}]$ ${D_{\rm{h}}}$ $[8.5{{(q_{V}/n)}^{{1}/{3}\;}},\;11.7{{(q_{V}/n)}^{{1}/{3}\;}}]$ $\varphi$ $[{{140}^{\circ }},\;{{180}^{\circ }}]$ $\theta$ $[{{18}^{\circ }},\;{{28}^{\circ }}]$ ${D_3}$ $[1.03{{D}_{2}},\;1.06{{D}_{2}}]$ $Y$ $[0.8,\;2.0]$

1.3. 设计变量的灵敏度分析

$\Delta {h_1} = {K_1}{W_1}/\left( {2g} \right),$

$\Delta {h_2} = {K_2}Z{\lambda _{\rm{a}}}{l_{\rm{a}}}{W_{\rm{a}}}^2/\left( {2g{D_{\rm{a}}}} \right),$

$\Delta {h_3} = {K_3}\left| {{W_1}^2 - {W_2}^2} \right|/\left( {2g} \right),$

$\Delta {h_4} = {K_4}({{8{Q_{\rm{s}}}^2}})/({{{{\text{π}} ^2}g{D_1}^4}}),$

$\Delta {h_5} = {K_5}\left( {{V_{{\rm{m}}2}}^2 + {V_{{\rm{u}}2}}^2 - {V_{\rm{s}}}^2} \right)/\left( {2g} \right).$

$\mathop y\limits^ \wedge ({{x}}) = \mathop {{\beta}} \limits^ \wedge f({{x}}) + {{{r}}^{\rm{T}}}({{x}}){{{R}}^{ - 1}}({{Y}} - \mathop {{\beta}} \limits^ \wedge {{F}}).$

2种二次响应面计算模型和径向基高斯响应面计算模型的均方根误差和决定系数如表2所示. 比较完全RSF与不完全RSF模型的均方根误差和决定系数，完全RSF模型拟合准确度较高，所以在后续计算模型中选择完全RSF模型进行运算，简称RSF. RSF、RBF的均方根误差接近0，决定系数接近1.0，说明2种近似模型的拟合准确度均较高.

Tab.2  Validity test of response surface model

 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

图 6

Fig.6   Comparison of approximate model predicted hydraulic power with CFD numerical calculation result

图 7

Fig.7   Comparison of approximate model predicted hydraulic power with CFD numerical calculation result

3.2. 基于二代非劣排序遗传算法寻优

$\left. \begin{array}{l} {f_1} = {H_{\max }},{f_2} = {\eta _{\max }}, \\ {{x}} = \left[ {{D_2},\;{b_2},\;{\beta _2}} \right]. \\ \end{array} \right\}$

$H \geqslant (1 + 3\text{% }){H_{\rm{r}}}.$

3种不同近似模型的总效率为

$\eta = {\eta _{\rm{m}}}{\eta _{\rm{V}}}{\eta _{\rm{h}}}.$

${\eta _{\rm{V}}} = ({{1 + 0.68{n_{\rm{s}}}^{ - 2/3}}})^{-1},$

${\eta _{\rm{m}}} = 1 - {{0.07}}/{{{{({{{n_{\rm{s}}}}}/{{100}})}^{{7}/{6}}}}}.$

Tab.3  Pareto optimal solution and CFD numerical simulation analysis of four calculation models

 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

图 5

Fig.5   Comparison of approximate model predicted head value with CFD numerical calculation result

图 8

Fig.8   Full flow performance prediction of singlestage centrifugal pump with impeller 1 and 2

$\eta = 66 \text{%}$ 水平线与效率曲线交于2点，体积流量分别为q1q2，高效区相对宽度定义为L = $\left({{{q_2} - {q_1}}}\right)/{q_{V{\rm{r}}}}$，则叶轮1、2的高效区相对宽度分别为

${L_1} = ({{179.2 - 63.5}})/{{100}} = 1.157,$

${L_2} = ({{193.9 - 69.4}})/{{100}} = 1.245.$

参考文献 原文顺序 文献年度倒序 文中引用次数倒序 被引期刊影响因子

[J]. 西华大学学报: 自然科学版, 2016, (3): 89- 92

YANG Jun-hu, BIAN Zhong, ZHONG Chun-lin, et al

Method for selecting centrifugal pump impeller outlet angle based on calculation of centrifugal pump impeller's hydraulic loss

[J]. Journal of Xihua University: Natural Science, 2016, (3): 89- 92

GAO Jiang-yong. Study on optimization of centrifugal pump impeller's and volute's parameters [D]. Handan: Hebei University of Engineering, 2008.

[J]. 机械设计, 2013, (12): 19- 22

NIE Song-hui, ZHU Bai-lin, LIAO Shu-tao, et al

Optimization design of centrifugal pump based on genetic algorithm

[J]. Journal of Machine Design, 2013, (12): 19- 22

[J]. 农业机械学报, 2013, 44 (5): 59- 65

WANG Chun-lin, PENG Hai-bo, DING Jian, et al

Optimization for vortex pump based on response surface method

[J]. Transactions of the Chinese Society for Agricultural Machinery, 2013, 44 (5): 59- 65

[J]. 机械工程学报, 2015, (15): 33- 38

WANG Wen-jie, YUAN Shou-qi, PEI Ji, et al

Two-point hydraulic optimization of pump impeller based on kriging model and neighborhood cultivation genetic algorithm

[J]. Journal of Mechanical Engineering, 2015, (15): 33- 38

BELLARY S A I, HUSAIN A, SAMAD A

Effectiveness of meta-models for multi-objective optimization of centrifugal impeller

[J]. Journal of Mechanical Science and Technology, 2014, 28 (12): 4947- 4957

BELLARY S A I, ADHAV R, SIDDIQUE M H, et al

Application of computational fluid dynamics and surrogate-coupled evolutionary computing to enhance centrifugal-pump performance

[J]. Engineering Applications of Computational Fluid Mechanics, 2016, 10 (1): 171- 181

HEO M, MA S, SHIM H, et al

High-efficiency design optimization of a centrifugal pump

[J]. Journal of Mechanical Science and Technology, 2016, 30 (9): 3917- 3927

[J]. 江苏大学学报: 自然科学版, 2007, 28 (5): 405- 408

TAN Ming-gao, LIU Hou-lin, YUAN Shou-qi

Calculation of hydraulic loss in centrifugal pumps

[J]. Journal of Jiangsu University: Natural Science Edtion, 2007, 28 (5): 405- 408

WANG Dan. Optimization design of low specific-speed centrifugal pump based on genetic algorithm [D]. Lanzhou: Lanzhou University of Technology, 2016.

[J]. 上海交通大学学报, 2015, 49 (5): 695- 701

MA Yi, MA Zhong-qiang, ZHANG Sheng-chang, et al

A novel design method for impeller of medium specific speed non-overload multistage centrifugal pump

[J]. Journal of Shanghai Jiaotong University, 2015, 49 (5): 695- 701

[J]. 华中科技大学学报: 自然科学版, 2015, 43 (4): 54- 57

ZHANG Yu, QIN Gang, ZHANG Yun-qing, et al

Kriging based muti-objective optimization for hydraulic performance of centrifugal pump

[J]. Journal of Huazhong University of Science and Technology: Natural Science Edition, 2015, 43 (4): 54- 57

GAO Jiang-yong. Study on optimization of centrifugal pump impeller's and volute's parameters [D]. Handan: Hebei University of Engineering, 2008.

BABAYIGIT O, KOCAASLAN O, AKSOY M H, et al. Numerical identification of blade exit angle effect on the performance for a multistage centrifugal pump impeller [J]. EPJ Web of Conferences, 2015, 92: 2003.

Analysis of effect of impeller geometry including blade outlet angle on the performance of multi-pressure pumps: Simulation and experiment

[J]. Mechanika, 2017, 23 (1): 107- 119

KOCAASLAN O, OZGOREN M, BABAYIGITO, et al

Numerical investigation of the effect of number of blades on centrifugal pump performance

[J]. AIP Conference Proceedings, 2017, 1863 (1): 030028

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