二维电磁场-流体-温度场耦合仿真节点数据映射算法研究
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摘要
在二维电磁场-流体-温度场耦合分析中,针对电磁场计算域与流体-温度场仿真域网格不匹配的情况,需要引入异构网格节点数据映射算法来实现数据的传递。为将电磁场损耗准确映射到流体-温度场的相关网格单元和节点上,提出快速映射法和径向基函数法,并结合两种方法的优点提出异构网格节点数据映射的混合算法。结合具有解析解的算例和换流变压器铁心漏磁场映射的实例,验证三种算法的可行性;讨论网格疏密对映射算法精度的影响;分析比较径向基函数法、快速映射法和混合算法的映射精度,并从计算效率方面对径向基函数法和快速映射法进行对比。结果表明:快速映射法、径向基函数法和混合算法各具优缺点,对不同算例,需要根据其模型和网格特点选择适当的映射算法,以满足精度要求,为二维电磁场-流体-温度场耦合仿真奠定了基础。
In the analysis of the 2D coupling electromagnetic-fluid-thermal fields, which the meshes in electromagnetic domain don't match the meshes in the fluid-thermal domain, the mapping method of the node data need to be studied. In order to map electromagnetic losses to fluid-thermal field accurately, this paper proposed the fast projection algorithm and the radial basis function(RBF) scheme, and presented the mixed method combing the advantages of the two proposed methods. Based on the examples with analytical solutions and the leakage magnetic field mapping of a converter transformer, the feasibility of the three methods were verified, the effects of the grid density on the mapping algorithm accuracy was discussed, the mapping accuracy of the three methods were compared, and the computational efficiency of the fast projection algorithm and the RBF schemes were studied. The result shows that three methods have advantages and disadvantages. For different applications, it is necessary to choose a proper mapping algorithm according to the model and grid features. Above research lay a foundation for the 2D coupling electromagnetic-fluid-thermal fields.
In the analysis of the 2D coupling electromagnetic-fluid-thermal fields, which the meshes in electromagnetic domain don't match the meshes in the fluid-thermal domain, the mapping method of the node data need to be studied. In order to map electromagnetic losses to fluid-thermal field accurately, this paper proposed the fast projection algorithm and the radial basis function(RBF) scheme, and presented the mixed method combing the advantages of the two proposed methods. Based on the examples with analytical solutions and the leakage magnetic field mapping of a converter transformer, the feasibility of the three methods were verified, the effects of the grid density on the mapping algorithm accuracy was discussed, the mapping accuracy of the three methods were compared, and the computational efficiency of the fast projection algorithm and the RBF schemes were studied. The result shows that three methods have advantages and disadvantages. For different applications, it is necessary to choose a proper mapping algorithm according to the model and grid features. Above research lay a foundation for the 2D coupling electromagnetic-fluid-thermal fields.
引文
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[17]李永明,黄宏佩,张淮清.基于径向基函数法的特高压直流输电线路地面标称电场计算[J].重庆大学学报,2013,36(1):75-80.Li Yongming,Huang Hongpei,Zhang Huaiqing.Nominal electric field calculation at the ground level of UHVDC transmission lines based on radial basis function method[J].Journal of Chongqing University,2013,36(1):75-80.
[18]吴宇飞.径向基函数插值在叶轮流固耦合分析中的应用[J].风机技术,2012(3):34-39.Wu Yufei.Application of radial basis functions interpolation schemes in fluid-structure interaction analysis of impeller[J].Compressor Blower&Fan Technology,2012(3):34-39.
[19]Boer A D,Zuijlen A H V,Bijl H.Review of coupling methods of for non-matching meshes[J].Computer Methods in Applied Mechanics&Engineering,2007,196(8):1515-1525.
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[21]盛剑霓.电磁场数值分析[M].北京:科学出版社,1984.
[22]郭健.变压器铁心空载损耗分布的一种二维有限元计算方法[J].变压器,2007,44(3):22-25.Guo Jian.Two dimensional finite element method to calculate no-load loss distribution of transformer core[J].Transformer,2007,44(3):22-25.
[23]刘东升,张俊杰,赵峰,等.特高压特大容量变压器三维涡流场计算和防止局部过热技术的研究[J].变压器,2009,46(9):1-5.Liu Dongsheng,Zhang Junjie,Zhao Feng,et al.3D eddy current field calculation and partial overheat protection technology research of UHV large transformer[J].Transformer,2009,46(9):1-5.
[24]刘深深.气动力/热/结构多场耦合数据传递方法研究[D].绵阳:中国空气动力研究与发展中心,2014.
[25]葛志广,宋俊杰.高精度磁法数据网格化方法的选取[J].工程地球物理学报,2010,7(2):169-172.Ge Zhiguang,Song Junjie.The griding methods of selection about the data of high-precision magnetic[J].Chinese Journal of Engineering Geophysics,2010,7(2):169-172.
[2]李伟力,孙佳慧,孙宏丽,等.汽轮发电机稳态与负序工况下转子涡流损耗计算和温度场分析[J].电工技术学报,2012,27(9):59-63.Li Weili,Sun Jiahui,Sun Hongli,et al.Calculation and analysis of eddy loss and temperature field in rotor of synchronous generator under steady state and negative sequence[J].Transactions of China Electrotechnical Society,2012,27(9):59-63.
[3]杜海,曲延滨,张鹏.新型旋转电磁热机流体流动与传热的耦合计算与实验[J].电工技术学报,2015,30(12):291-297.Du Hai,Qu Yanbin,Zhang Peng.Coupling calculation and experiment of fluid flow and heat transfer of a new rotating induction heater[J].Transactions of China Electrotechnical Society,2015,30(12):291-297.
[4]徐永明,蒋治国,艾萌萌.潜油电动机隔磁段电磁-热-力耦合特性研[J].电工技术学报,2015,30(15):172-178.Xu Yongming,Jiang Zhiguo,Ai Mengmeng.Coupling characteristics research on electromagnetism and temperature and force of the magnetic isolated segment in the submersible motor[J].Transactions of China Electrotechnical Society,2015,30(15):172-178.
[5]韩芳旭.换流变压器谐波损耗及热问题的计算与分析[D].沈阳:沈阳工业大学,2011.
[6]刘赟,俞集辉,程鹏.基于电磁-热耦合场的架空输电线路载流量分析与计算[J].电力系统保护与控制,2015,43(9):28-34.Liu Yun,Yu Jihui,Cheng Peng.Analysis and calculation on the ampacity of overhead transmission lines based on electromagnetic-thermal coupling fields[J].Power System Protection and Control,2015,43(9):28-34.
[7]张宇娇,秦威南,刘东圆,等.面向电磁装置磁-热耦合分析的异型网格映射方法[J].电工技术学报,2016,31(13):141-148.Zhang Yujiao,Qin Weinan,Liu Dongyuan,et al.Nonmatching meshes mapping method in coupled magnetic and thermal analysis of electromagnetic devices[J].Transactions of China Electrotechnical Society,2016,31(13):141-148.
[8]贺鸿鹏.基于COMSOL的OCT传感单元的多物理场研究与设计[D].北京:华北电力大学,2014.
[9]李宜伦,王泽济,杨仕友,等.热轧带钢厂边部加热涡流温度场仿真分析[J].电工技术学报,2013,28(增刊2):105-110.Li Yilun,Wang Zeji,Yang Shiyou,et al.Numerical simulation of the eddy current and temperature fields in the edge heating hot strip mill[J].Transactions of China Electrotechnical Society,2013,28(S2):105-110.
[10]石碧薇.变压器在谐波条件下的损耗及热问题分析[D].保定:华北电力大学,2014.
[11]Barber C B,Dobkin D P,Huhdanpaa H T.The quickhull algorithm for convex hulls[J].ACM Transactions on Mathematical Software,1996,22(4):469-483.
[12]孙学功.多物理场耦合界面数据传递的仿真研究[J].计算机仿真,2015,32(1):23-28.Sun Xuegong.Simulation of data exchange of multi physics coupling surfaces[J].Computer Simulation,2015,32(1):23-28.
[13]宋少云.多场耦合问题的协同求解方法研究与应用[D].武汉:华中科技大学,2007.
[14]吴宇飞.叶轮流固耦合界面不匹配网格的数据传递[D].大连:大连理工大学,2012.
[15]王泽忠.简明电磁场数值计算[M].北京:机械工业出版社,2011.
[16]吴宗敏.径向基函数、散乱数据拟合与无网格偏微分方程数值解[J].工程数学学报,2002,19(2):1-12.Wu Zongmin.Radial basis function scattered data interpolation and the meshless method of numerical solution of PDEs[J].Journal of Engineering Mathematics,2002,19(2):1-12.
[17]李永明,黄宏佩,张淮清.基于径向基函数法的特高压直流输电线路地面标称电场计算[J].重庆大学学报,2013,36(1):75-80.Li Yongming,Huang Hongpei,Zhang Huaiqing.Nominal electric field calculation at the ground level of UHVDC transmission lines based on radial basis function method[J].Journal of Chongqing University,2013,36(1):75-80.
[18]吴宇飞.径向基函数插值在叶轮流固耦合分析中的应用[J].风机技术,2012(3):34-39.Wu Yufei.Application of radial basis functions interpolation schemes in fluid-structure interaction analysis of impeller[J].Compressor Blower&Fan Technology,2012(3):34-39.
[19]Boer A D,Zuijlen A H V,Bijl H.Review of coupling methods of for non-matching meshes[J].Computer Methods in Applied Mechanics&Engineering,2007,196(8):1515-1525.
[20]Chamdrupatla T R,Belegundu A D.工程中的有限元方法[M].北京:机械工业出版社,2005.
[21]盛剑霓.电磁场数值分析[M].北京:科学出版社,1984.
[22]郭健.变压器铁心空载损耗分布的一种二维有限元计算方法[J].变压器,2007,44(3):22-25.Guo Jian.Two dimensional finite element method to calculate no-load loss distribution of transformer core[J].Transformer,2007,44(3):22-25.
[23]刘东升,张俊杰,赵峰,等.特高压特大容量变压器三维涡流场计算和防止局部过热技术的研究[J].变压器,2009,46(9):1-5.Liu Dongsheng,Zhang Junjie,Zhao Feng,et al.3D eddy current field calculation and partial overheat protection technology research of UHV large transformer[J].Transformer,2009,46(9):1-5.
[24]刘深深.气动力/热/结构多场耦合数据传递方法研究[D].绵阳:中国空气动力研究与发展中心,2014.
[25]葛志广,宋俊杰.高精度磁法数据网格化方法的选取[J].工程地球物理学报,2010,7(2):169-172.Ge Zhiguang,Song Junjie.The griding methods of selection about the data of high-precision magnetic[J].Chinese Journal of Engineering Geophysics,2010,7(2):169-172.