三维快速多极边界元法分析地埋管群传热问题  

3D Fast Multipole Boundary Element Method Analysis of Heat Exchange Performance of Buried Pipe Groups

作　　者：宋子欣 胡宗军[1] 胡斌 牛忠荣[1] SONG Zixin;HU Zongjun;HU Bin;NIU Zhongrong(College of Civil Engineering,Hefei University of Technology,Hefei 230009,P.R.China)

机构地区：[1]合肥工业大学土木与水利工程学院,合肥230009

出　　处：《应用数学和力学》2023年第7期797-808,共12页Applied Mathematics and Mechanics

基　　金：国家自然科学基金项目(11272111)。

摘　　要：基于三节点三角形线性单元,为克服单元跨叶子积分难题,将三维位势问题快速多极边界元法与几乎奇异积分的半解析算法相结合,实现了三维边界元法中几乎奇异积分的准确计算,该方法适用于U型地埋管薄体结构的换热分析.在制冷、制热两种工况下研究了U型地埋管壁厚对换热量的影响,并进一步分析了管群间的热相互作用.计算结果显示,当管壁导热系数一定时,管壁越厚,对管内流体和土壤之间的换热影响越大.当钻孔间距一定时,管群中埋管数量越多,热干扰现象越强烈,提高管群换热量的主要措施是降低管群间热干扰.因准确计算了几乎奇异积分,三维快速多极边界元法可以有效计算薄体和厚体耦合的三维热传导问题.该文方法和分析结果可为地埋管换热器系统的工程应用提供参考.Based on the 3⁃node triangular linear element and to overcome the element cross⁃leaf integration problem,a new 3D fast method was formulated for 3D potential problems through combination of the fast mul⁃tipole boundary element method(FMBEM)with the semi⁃analytical algorithm of nearly singular integral,to re⁃alize the accurate calculation of the nearly singular integral in the 3D boundary element method(BEM).This method is applicable to the heat exchange of thin⁃wall structures of U⁃type buried pipe groups.In the cooling and heating conditions,the effects of the wall thickness of the U⁃type buried pipe group were analyzed by means of the new FMBEM,and the thermal interaction between multiple buried pipes was discussed.The cal⁃culation results show that,for a constant thermal conductivity of the pipe wall,the thicker the pipe wall is,the greater the effect on the heat exchange between the pipe fluid and the soil will be.For a constant borehole spacing,the bigger the number of buried pipes in a group is,the stronger the thermal interference between the pipes will be.The main strategy to increase the heat exchange of the pipe group is to reduce the thermal inter⁃ference between the heat exchange pipes.Due to the accurate calculation of the nearly singular integral,the proposed 3D FMBEM can effectively solve the 3D heat exchange problems of thin⁃thick coupled bodies.This method and the results for the provide references for the engineering application of buried pipe heat exchangers.

关 键 词：地埋管群换热器 几乎奇异积分 薄体 传热 快速多极边界元法 

分 类 号：O39[理学—工程力学]