低比转数离心泵叶轮内流场重构与模态分析
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摘要
针对传统离心泵水力性能优化设计的复杂性,提出采用本征正交分解-径向基函数(POD-RBF)混合代理模型方法对离心泵叶轮内流场进行重构分析。由三次Bezier曲线对低比转数离心泵二维叶片型线进行参数化控制,通过对叶片包角、进出口安放角等控制参数进行适量的扰动得到叶片型线的样本集。由叶片型线参数及叶轮CFD内流场数据构成样本的快照矢量集,根据几何相似及网格变形方法插值得到各相似节点的流场参数,依据本征正交分解法(POD)将快照集分解为一系列正交基的线性组合。由径向基函数(RBF)拟合目标叶型所对应的正交基系数,实现了对目标叶轮内流场的重构。采用POD-RBF方法对MH48-12. 5型低比转数离心泵叶轮内流场进行了重构,其压力预测均方根误差为0. 84%,速度预测误差基本在0. 5 m/s以内,流场预测所需时间约为CFD计算的1/240。对样本集进行POD基模态分析,得到了各阶基模态流场特征及能量分布特性。
According to the complexity of traditional hydraulic performance optimization design of centrifugal pump,the hybrid surrogate model method which is the combination of proper orthogonal decomposition and radial basis function was proposed for the flow reconstitution of centrifugal pump impeller. The blade of low specific speed centrifugal pump was parameterized by cubic Bezier curve,and the experiment samples can be designed by introducing small perturbation of control parameters which included wrap angle,inlet and outlet blade angles. The snapshot set consisted of the control parameter for blade shape and the flow field data. According to the geometric similarity of the impeller flow passage and the mesh deformation technology,the flow field data of the similar position were interpolated. The snapshot set can be decomposed as linear combination of orthogonal basis by using proper orthogonal decomposition. The orthogonal basis coefficients for the objective blade were fitted by using radial basis function. The flow field data of the objective impeller were reconstructed. In the calculation case for the type of MH48-12. 5 centrifugal pump,the flow field in impeller was reconstructed. The root-mean-square error for pressure prediction was 0. 84%,and the velocity prediction error was within 0. 5 m/s. The computation time for the flow field prediction was less than 1/240 of the CFD. POD base modal analysis was carried out on the sample set. The base modal characteristic of flow field and its energy distribution were analyzed.
According to the complexity of traditional hydraulic performance optimization design of centrifugal pump,the hybrid surrogate model method which is the combination of proper orthogonal decomposition and radial basis function was proposed for the flow reconstitution of centrifugal pump impeller. The blade of low specific speed centrifugal pump was parameterized by cubic Bezier curve,and the experiment samples can be designed by introducing small perturbation of control parameters which included wrap angle,inlet and outlet blade angles. The snapshot set consisted of the control parameter for blade shape and the flow field data. According to the geometric similarity of the impeller flow passage and the mesh deformation technology,the flow field data of the similar position were interpolated. The snapshot set can be decomposed as linear combination of orthogonal basis by using proper orthogonal decomposition. The orthogonal basis coefficients for the objective blade were fitted by using radial basis function. The flow field data of the objective impeller were reconstructed. In the calculation case for the type of MH48-12. 5 centrifugal pump,the flow field in impeller was reconstructed. The root-mean-square error for pressure prediction was 0. 84%,and the velocity prediction error was within 0. 5 m/s. The computation time for the flow field prediction was less than 1/240 of the CFD. POD base modal analysis was carried out on the sample set. The base modal characteristic of flow field and its energy distribution were analyzed.
引文
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7廖福,张洪.基于遗传算法低比转速离心泵的优化设计[J].中国农机化学报,2016,37(2):233-236.LIAO Fu,ZHANG Hong.Optimization design of lower speed pump based on genetic algorithm[J].Journal of Chinese Agricultural Mechanization,2016,37(2):233-236.(in Chinese)
8张人会,郭苗,杨军虎,等.基于伴随方法的离心泵叶轮优化设计[J].排灌机械工程学报,2014,32(11):943-947.ZHANG Renhui,GUO Miao,YANG Junhu,et al.Blade shape optimization of centrifugal pump impeller with adjoint method[J].Journal of Drainage and Irrigation Machinery Engineering,2014,32(11):943-947.(in Chinese)
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10 CHATTERJEE A.An introduction to the proper orthogonal decomposition[J].Current Science,2000,78(7):808-817.
11段焰辉,蔡晋生.基于Gappy POD方法的翼型流场分析[J].航空工程进展,2010,1(1):40-44.DUAN Yanhui,CAI Jinsheng.Airfoil flow analysis based on Gappy POD method[J].Advances in Aeronautical Science and Engineering,2010,1(1):40-44.(in Chinese)
12白俊强,邱亚松,华俊.改进型Gappy POD翼型反设计方法[J].航空学报,2013,34(4):762-771.BAI Junqiang,QIU Yasong,HUA Jun.Improved airfoil inverse design method based on Gappy POD[J].Acta Aeronautica et Astronautica Sinica,2013,34(4):762-771.(in Chinese)
13邱亚松,白俊强,华俊.基于本征正交分解和代理模型的流场预测方法[J].航空学报,2013,34(6):1249-1260.QIU Yasong,BAI Junqiang,HUA Jun.Flow field estimation method based on proper orthogonal decomposition and surrogate model[J].Acta Aeronautica et Astronautica Sinica,2013,34(6):1249-1260.(in Chinese)
14刘南,白俊强,邱亚松,等.基于本征正交分解的气动外形设计空间重构方法研究[J].西北工业大学学报,2015,33(2):171-177.LIU Nan,BAI Junqiang,QIU Yasong,et al.Investigating aerodynamic shape design space reconstruction using proper orthogonal decomposition(POD)[J].Journal of Northwestern Polytechnical University,2015,33(2):171-177.(in Chinese)
15 QIU Y,BAI J.Stationary flow fields prediction of variable physical domain based on proper orthogonal decomposition and kriging surrogate model[J].Chinese Journal of Aeronautics,2015,28(1):44-56.
16罗佳奇,段焰辉,夏振华.基于自适应本征正交分解混合模型的跨音速流场分析[J].物理学报,2016,65(12):181-189.LUO Jiaqi,DUAN Yanhui,XIA Zhenhua.Transonic flow reconstruction by an adaptive proper orthogonal decomposition hybrid model[J].Acta Physica Sinica,2016,65(12):181-189.(in Chinese)
17 ZHANG R H,GUO R,YANG J H,et al.Inverse method of centrifugal pump impeller based on proper orthogonal decomposition(POD)method[J].Chinese Journal of Mechanical Engineering,2017,30(4):1-7.
18张人会,吴昊,杨军虎,等.基于本征正交分解法的液环泵气液两相流场重构[J/OL].农业机械学报,2017,48(6):381-386.http:∥www.j-csam.org/jcsam/ch/reader/view_abstract.aspx?file_no=20170650&flag=1.DOI:10.6041/j.issn.1000-1298.2017.06.050.ZHANG Renhui,WU Hao,YANG Junhu,et al.Reconstruction for gas-liquid flow of liquid-ring pump based on proper orthogonal decomposition[J/OL].Transactions of the Chinese Society for Agricultural Machinery,2017,48(6):381-386.(in Chinese)
19 SIROVICH L.Turbulence and the dynamics of coherent structures.I-Coherent structures.II-Symmetries and transformations.III-Dynamics and scaling[J].Quarterly of Applied Mathematics,1987,45(3):561-571.
20 BUHMANN M D.Radial basis functions[J].Acta Numerica,2000,9(5):1-38.
2王伟,施卫东,蒋小平,等.基于正交试验及CFD的多级离心泵叶轮优化设计[J].排灌机械工程学报,2016,34(3):191-197.WANG Wei,SHI Weidong,JIANG Xiaoping,et al.Optimization design of multistage centrifugal pump impeller by orthogonal experiment and CFD[J].Journal of Drainage and Irrigation Machinery Engineering,2016,34(3):191-197.(in Chinese)
3王旭鹤,祝宝山,曹树良,等.可逆式水泵水轮机转轮的三维反问题优化设计[J].农业工程学报,2014,30(13):78-85.WANG Xuhe,ZHU Baoshan,CAO Shuliang,et al.Optimal design of reversible pump-turbine runner[J].Transactions of the CSAE,2014,30(13):78-85.(in Chinese)
4郭鹏程,罗兴锜,刘胜柱.基于三维紊流数值计算的离心泵叶轮优化设计[J].机械工程学报,2004,40(4):181-184.GUO Pengcheng,LUO Xingqi,LIU Shengzhu.Optimized redesign of the centrifugal impeller based on numerical analysis of 3Dturbulent flow[J].Chinese Journal of Mechanical Engineering,2004,40(4):181-184.(in Chinese)
5张剑慈,崔宝玲,李昳,等.低比转速开式叶轮高速离心泵的优化设计系统[J].机械工程学报,2006,42(7):19-23.ZHANG Jianci,CUI Baoling,LI Ying,et al.Numerical simulation and experimental study on fluidic flowmeter[J].Chinese Journal of Mechanical Engineering,2006,42(7):19-23.(in Chinese)
6张人会,樊家成,杨军虎,等.基于自由曲面变形方法的离心泵叶片载荷优化[J/OL].农业机械学报,2015,46(10):38-43.http:∥www.j-csam.org/jcsam/ch/reader/view_abstract.aspx?file_no=20151006&flag=1.DOI:10.6041/j.issn.1000-1298.2015.10.006.ZHANG Renhui,FAN Jiacheng,YANG Junhu,et al.The optimization of the centrifugal pump blade load based on free form deformation[J/OL].Transactions of the Chinese Society for Agricultural Machinery,2015,46(10):38-43.(in Chinese)
7廖福,张洪.基于遗传算法低比转速离心泵的优化设计[J].中国农机化学报,2016,37(2):233-236.LIAO Fu,ZHANG Hong.Optimization design of lower speed pump based on genetic algorithm[J].Journal of Chinese Agricultural Mechanization,2016,37(2):233-236.(in Chinese)
8张人会,郭苗,杨军虎,等.基于伴随方法的离心泵叶轮优化设计[J].排灌机械工程学报,2014,32(11):943-947.ZHANG Renhui,GUO Miao,YANG Junhu,et al.Blade shape optimization of centrifugal pump impeller with adjoint method[J].Journal of Drainage and Irrigation Machinery Engineering,2014,32(11):943-947.(in Chinese)
9张人会,郭广强,杨军虎,等.基于不完全敏感性方法的低比转速离心叶轮优化研究[J].机械工程学报,2014,50(4):162-166.ZHANG Renhui,GUO Guangqiang,YANG Junhu,et al.Optimization research on low specific speed centrifugal impeller based on incomplete sensitivities method[J].Journal of Mechanical Engineering,2014,50(4):162-166.(in Chinese)
10 CHATTERJEE A.An introduction to the proper orthogonal decomposition[J].Current Science,2000,78(7):808-817.
11段焰辉,蔡晋生.基于Gappy POD方法的翼型流场分析[J].航空工程进展,2010,1(1):40-44.DUAN Yanhui,CAI Jinsheng.Airfoil flow analysis based on Gappy POD method[J].Advances in Aeronautical Science and Engineering,2010,1(1):40-44.(in Chinese)
12白俊强,邱亚松,华俊.改进型Gappy POD翼型反设计方法[J].航空学报,2013,34(4):762-771.BAI Junqiang,QIU Yasong,HUA Jun.Improved airfoil inverse design method based on Gappy POD[J].Acta Aeronautica et Astronautica Sinica,2013,34(4):762-771.(in Chinese)
13邱亚松,白俊强,华俊.基于本征正交分解和代理模型的流场预测方法[J].航空学报,2013,34(6):1249-1260.QIU Yasong,BAI Junqiang,HUA Jun.Flow field estimation method based on proper orthogonal decomposition and surrogate model[J].Acta Aeronautica et Astronautica Sinica,2013,34(6):1249-1260.(in Chinese)
14刘南,白俊强,邱亚松,等.基于本征正交分解的气动外形设计空间重构方法研究[J].西北工业大学学报,2015,33(2):171-177.LIU Nan,BAI Junqiang,QIU Yasong,et al.Investigating aerodynamic shape design space reconstruction using proper orthogonal decomposition(POD)[J].Journal of Northwestern Polytechnical University,2015,33(2):171-177.(in Chinese)
15 QIU Y,BAI J.Stationary flow fields prediction of variable physical domain based on proper orthogonal decomposition and kriging surrogate model[J].Chinese Journal of Aeronautics,2015,28(1):44-56.
16罗佳奇,段焰辉,夏振华.基于自适应本征正交分解混合模型的跨音速流场分析[J].物理学报,2016,65(12):181-189.LUO Jiaqi,DUAN Yanhui,XIA Zhenhua.Transonic flow reconstruction by an adaptive proper orthogonal decomposition hybrid model[J].Acta Physica Sinica,2016,65(12):181-189.(in Chinese)
17 ZHANG R H,GUO R,YANG J H,et al.Inverse method of centrifugal pump impeller based on proper orthogonal decomposition(POD)method[J].Chinese Journal of Mechanical Engineering,2017,30(4):1-7.
18张人会,吴昊,杨军虎,等.基于本征正交分解法的液环泵气液两相流场重构[J/OL].农业机械学报,2017,48(6):381-386.http:∥www.j-csam.org/jcsam/ch/reader/view_abstract.aspx?file_no=20170650&flag=1.DOI:10.6041/j.issn.1000-1298.2017.06.050.ZHANG Renhui,WU Hao,YANG Junhu,et al.Reconstruction for gas-liquid flow of liquid-ring pump based on proper orthogonal decomposition[J/OL].Transactions of the Chinese Society for Agricultural Machinery,2017,48(6):381-386.(in Chinese)
19 SIROVICH L.Turbulence and the dynamics of coherent structures.I-Coherent structures.II-Symmetries and transformations.III-Dynamics and scaling[J].Quarterly of Applied Mathematics,1987,45(3):561-571.
20 BUHMANN M D.Radial basis functions[J].Acta Numerica,2000,9(5):1-38.