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清华大学学报(自然科学版)  2015, Vol. 55 Issue (9): 1003-1009    
  核能与新能源工程 本期目录 | 过刊浏览 | 高级检索 |
基于三维管道模型的快速边界元法在阴极保护分析中的应用
刘立祺, 王海涛
清华大学 核能与新能源技术研究院, 先进核能技术协同创新中心, 先进反应堆工程与安全教育部重点实验室, 北京 100084
Fast boundary element method based on a 3D pipe model for analyzing cathodic protection
LIU Liqi, WANG Haitao
Key Laboratory of Advanced Reactor Engineering and Safety of the Ministry of Education, Collaborative Innovation Center of Advanced Nuclear Energy Technology, Institute of Nuclear and New Energy Technology, Tsinghua University, Beijing 100084, China
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摘要 该文采用边界元法(BEM)对包含大规模管道结构的阴极保护系统进行分析。为降低管道上的单元数量和单元积分计算量, 提出一种三维管道边界元模型, 将管道离散为线单元且保留管道圆柱面积分。为了能够在普通微机上模拟大规模阴极保护系统, 使用快速多极算法(FMM)加速边界元方程的求解。针对阴极极化边界条件引入的非线性问题, 采用迭代算法求解。数值算例表明: 采用该文线单元离散管道, 相比常规三角形单元, 可将单元数量降低一个数量级; 快速多极算法可以求解自由度为50 000量级的大规模阴极保护问题。
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刘立祺
王海涛
关键词 阴极保护边界元法(BEM)管道模型线单元快速多极算法(FMM)    
Abstract:The boundary element method (BEM) was used to analyze a cathodic protection (CP) system consisting of large pipeline structures. A three-dimensional pipe boundary element model was used to reduce the number of elements on the pipelines as well as the element integral computations. The pipelines were meshed with line elements with the boundary integrals were based on the original shapes. The large-scale CP problem was solved on a common desktop computer using the fast multipole method (FMM) to accelerate the BEM. The nonlinearity introduced by the polarization curve at the cathode was solved iteratively. The numerical results demonstrate that the number of elements can be reduced by one order of magnitude when discretizing pipelines with these line elements compared with triangular elements and that the FMM can solve large CP problems with up to 50 000 dimension of freedoms (DOFs).
Key wordscathodic protection    boundary element method (BEM)    pipe model    line elements    fast multipole method (FMM)
收稿日期: 2013-04-10      出版日期: 2015-11-09
ZTFLH:  TG174.41  
通讯作者: 王海涛, 研究员, E-mail: wanght@mail.tsinghua.edu.cn     E-mail: wanght@mail.tsinghua.edu.cn
引用本文:   
刘立祺, 王海涛. 基于三维管道模型的快速边界元法在阴极保护分析中的应用[J]. 清华大学学报(自然科学版), 2015, 55(9): 1003-1009.
LIU Liqi, WANG Haitao. Fast boundary element method based on a 3D pipe model for analyzing cathodic protection. Journal of Tsinghua University(Science and Technology), 2015, 55(9): 1003-1009.
链接本文:  
http://jst.tsinghuajournals.com/CN/  或          http://jst.tsinghuajournals.com/CN/Y2015/V55/I9/1003
  图1 线单元Sj 的柱坐标系Cylinder-1
  图2 非线性边界条件迭代求解流程图
  图3 包含两条管道的长方体模型示意
  图4 极化曲线
  图5 算例1管道电流和电位分布
  图6 包含5×5×4=100条管道的长方体模型平面示意图
  图7 中心位置管道的电位分布
  图8 阴极保护系统分析模型示
  图9 罐底极化曲线
  图10 整体电位分布
  图11 阴极保护系统中间管道电位分布
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