低比转速离心叶轮的POD代理模型优化方法
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摘要
针对离心泵叶轮水力优化过程中须不断预估叶型控制参数扰动对内流场变化的敏感性、计算量随控制参数的维数呈指数倍增长等不足,提出了基于本征正交分解(POD)代理模型的低比转速离心叶轮优化方法.采用泰勒多项式对离心泵叶片型线进行参数化控制,由控制参数扰动得到叶片型线的初始样本集,由叶片型线参数及叶轮CFD内流场数据构建样本快照集.采用POD方法预测各控制参数扰动下的流场,由此预估目标函数对控制变量的敏感性,并沿梯度矢量方向不断优化更新叶片型线.分析结果表明:POD代理模型能够快速地对流场进行精确的预测,大大减少离心泵优化设计的计算量.
Aiming at the problem that in the hydraulic optimization of centrifugal pump impeller,the sensitivity of pump inner flow field to the blade shape control parameters repeatedly must be predicted,and the amount of calculation is increasing exponentially with the dimensions of the control parameters,the optimization method of low specific speed centrifugal pump impeller based on the proper orthogonal decomposition(POD) surrogate model was proposed.The blade was parameterized by Taylor polynomial,and the experiment samples were designed by introducing small perturbations of the control parameters.The snapshot set consisted of the control parameter for blade shape and the flow field data.The POD method was used to predict the flow field perturbation response with the perturbation of control parameters,and the sensitivity of the objective function was predicted.The blade shape was updated continuously along the gradient vector.The analysis results show that the POD surrogate model can accurately predict the flow field and greatly reduce the calculation amount of centrifugal pump optimization.
Aiming at the problem that in the hydraulic optimization of centrifugal pump impeller,the sensitivity of pump inner flow field to the blade shape control parameters repeatedly must be predicted,and the amount of calculation is increasing exponentially with the dimensions of the control parameters,the optimization method of low specific speed centrifugal pump impeller based on the proper orthogonal decomposition(POD) surrogate model was proposed.The blade was parameterized by Taylor polynomial,and the experiment samples were designed by introducing small perturbations of the control parameters.The snapshot set consisted of the control parameter for blade shape and the flow field data.The POD method was used to predict the flow field perturbation response with the perturbation of control parameters,and the sensitivity of the objective function was predicted.The blade shape was updated continuously along the gradient vector.The analysis results show that the POD surrogate model can accurately predict the flow field and greatly reduce the calculation amount of centrifugal pump optimization.
引文
[1]MOHAMMADI B,PIRONNEAU O.Applied shape optimization for fluids[M].Oxford:Oxford University,2010.
[2]IULIANO E,PEREZ E A.Application of surrogate-based globaloptimization to aerodynamic design[M].Berlin:Springer International Publishing,2016.
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[4]卢金铃,席光,祁大同.反问题与神经网络相结合的混流泵叶片优化设计[J].西安交通大学学报,2004,38(3):308-312.
[5]ANTONY Jameson.Aerodynamic design via control theory[J].Journal of Scientific Computing,1998,3(3):402-407.
[6]MOHAMMADI B,PIRONNEAU O.Applied shape design for fluids[M].Oxford:Oxford University Press,2000.
[7]MOHAMMADI B.Incomplete sensitivity and shape optimization[J].Control and Cybernetics,2010,39(3):615-626.
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[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.
[10]BUI-THANH T,DAMODARAN M,WILLCOX KE.Aerodynamic data reconstruction and inverse design using proper orthogonal decomposition[J].AIAA Journal,2004,42(8):1505-1516.
[11]OYAMA A,NONOMURA T,FUJII K.Data mining of Pareto optimal transonic airfoil shapes using proper orthogonal decomposition[J].Journal of Aircraft,2010,47(5):1756-1762.
[12]TOAL D J J,BRESSLOFF N W,KEANE A J.Geometricfiltration using POD for aerodynamic design optimization[C]//Proceedings of the Collection of Technical Papers-26th AIAA Applied Aerodynamics Conference.Honolulu:IEEE,2008:18-21.
[13]CAI X,LADEINDE F.A comparison of two PODmethods for airfoil design optimization[C]//Proceedings of AIAA.Honolulu:IEEE,2005:AIAA2005-4912.
[14]段焰辉,蔡晋生,刘秋洪.基于代理模型方法的翼型优化设计[J].航空学报,2011,32(4):617-627.
[15]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.
[16]ZHANG Renhui,GUO Rong,YANG Junhu,et al.Inverse method of centrifugal pump impeller based on proper orthogonal decomposition(POD)method[J].Chinese Journal of Mechanical Engineering,2017,30:1025-1031.
[17]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].农业机械学报,2017,48(6):381-386.
[2]IULIANO E,PEREZ E A.Application of surrogate-based globaloptimization to aerodynamic design[M].Berlin:Springer International Publishing,2016.
[3]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.
[4]卢金铃,席光,祁大同.反问题与神经网络相结合的混流泵叶片优化设计[J].西安交通大学学报,2004,38(3):308-312.
[5]ANTONY Jameson.Aerodynamic design via control theory[J].Journal of Scientific Computing,1998,3(3):402-407.
[6]MOHAMMADI B,PIRONNEAU O.Applied shape design for fluids[M].Oxford:Oxford University Press,2000.
[7]MOHAMMADI B.Incomplete sensitivity and shape optimization[J].Control and Cybernetics,2010,39(3):615-626.
[8]ALISON L,MARSDE N,WANG Meng,et al.Shape optimization for aerodynamic noise control[J].Center for Turbulence Research Annual Research Briefs,2001,11:241-247.
[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.
[10]BUI-THANH T,DAMODARAN M,WILLCOX KE.Aerodynamic data reconstruction and inverse design using proper orthogonal decomposition[J].AIAA Journal,2004,42(8):1505-1516.
[11]OYAMA A,NONOMURA T,FUJII K.Data mining of Pareto optimal transonic airfoil shapes using proper orthogonal decomposition[J].Journal of Aircraft,2010,47(5):1756-1762.
[12]TOAL D J J,BRESSLOFF N W,KEANE A J.Geometricfiltration using POD for aerodynamic design optimization[C]//Proceedings of the Collection of Technical Papers-26th AIAA Applied Aerodynamics Conference.Honolulu:IEEE,2008:18-21.
[13]CAI X,LADEINDE F.A comparison of two PODmethods for airfoil design optimization[C]//Proceedings of AIAA.Honolulu:IEEE,2005:AIAA2005-4912.
[14]段焰辉,蔡晋生,刘秋洪.基于代理模型方法的翼型优化设计[J].航空学报,2011,32(4):617-627.
[15]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.
[16]ZHANG Renhui,GUO Rong,YANG Junhu,et al.Inverse method of centrifugal pump impeller based on proper orthogonal decomposition(POD)method[J].Chinese Journal of Mechanical Engineering,2017,30:1025-1031.
[17]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].农业机械学报,2017,48(6):381-386.