工程科学学报.第43卷，第11期：1569-1576.2021年11月 Chinese Journal of Engineering,Vol.43,No.11:1569-1576,November 2021 https://doi.org/10.13374/j.issn2095-9389.2020.05.03.003;http://cje.ustb.edu.cn 能源桩三维螺旋线热源的瞬态传热模型 李庆文12，郑明阳》，乔兰12，隋智力4☒ 1)北京科技大学土木与资源工程学院，北京1000832)北京科技大学城市地下空间工程北京市重点实验室，北京1000833)中铁第四勘 察设计院集团有限公司，武汉4300614)北京城市学院城市建设学部.北京100083 ☒通信作者，E-mail:szl803@126.com 摘要将螺旋埋管等效为三维螺旋线热源，考虑螺旋埋管能源桩的传热过程，运用格林函数和第一型曲线进行积分，推导 给出了考虑时间、空间位置、埋管参数和岩土体热物理性质4参数的螺旋埋管能源桩的温度场解析解，建立高精度三维螺旋 埋管能源桩的传热模型.并通过在数值模拟软件中建立螺旋埋管能源桩三维模型，依据边界条件，求解得出三维螺旋埋管能 源桩温度场数值解.对比结果表明：所建立的能源桩三维螺旋线热源模型具有很高的解析精度.最后，基于解析模型讨论了 螺旋埋管能源桩换热温度场的空间分布和时间效应， 关键词能源桩：螺旋埋管：传热模型：温度场：解析解 分类号TU470 Transient heat transfer model of a three-dimensional spiral heat source in an energy pile LI Qing-wen2),ZHENG Ming-yang.QIAO Lan2).SUI Zhi- 1)School of Civil and Resource Engineering,University of Science and Technology Beijing,Beijing 100083,China 2)Beijing Key Laboratory of Urban Underground Space Engineering,University of Science and Technology Beijing,Beijing 100083,China 3)China Railway Siyuan Survey and Design Group Co.,LTD.,Wuhan 430061,China 4)Urban Construction School,Beijing City University,Beijing 100083,China Corresponding author,E-mail:sz1803@126.com ABSTRACT An energy pile is a new type of ground source heat pump system.A heat exchanger is casted into the concrete pile foundation of a building structure for the purpose of heating or cooling the building through heat exchange between the pile foundation and surrounding soil.An energy pile can be developed rapidly because of its high heat transfer efficiency and stable structure and because it requires no additional drilling requirements.In the long-term operation,energy piles have to bear both the overlying and thermal loads caused by changes in the temperature field.Thus,accurately evaluating the temperature field of an energy pile and its surrounding soil is one of the key problems in the design and application of energy piles.To improve the heat transfer efficiency of energy piles,U-type,W-type,spiral type,and similar types of coils have been developed to be casted into the energy pile.Results of thermal efficiency analysis show that the spiral type coil has the best heating and cooling performance and was nearly 150%more thermally efficient than the double U-type coil.Thus,a spiral coil is selected as the main coils'form in the current practical application. However,due to the complex heat exchange structure of the spiral pipe,the present analytical model had to be simplified to accurately characterize the temperature field characteristics of a spiral pipe casted in an energy pile.In this paper,the spiral pipe was regarded as a three-dimensional spiral heat source.Considering the existing heat transfer model,an analytical solution of the temperature field was obtained by integrating green's function and the first curve function;then,the high-precision,three-dimensional (3-D)heat transfer model of the spiral pipe was established considering the time,space,buried pipe parameters,and thermal property of host soil.In 收稿日期：202005-03 基金项目：北京市教育委员会科技计划一般资助项目(KM202011418001):中央高校基本科研业务费专项资金资助项目(FRF-BD-19-004A)能源桩三维螺旋线热源的瞬态传热模型 李庆文1,2)，郑明阳3)，乔    兰1,2)，隋智力4) 苣 1) 北京科技大学土木与资源工程学院，北京 100083    2) 北京科技大学城市地下空间工程北京市重点实验室，北京 100083    3) 中铁第四勘 察设计院集团有限公司，武汉 430061    4) 北京城市学院城市建设学部，北京 100083 苣通信作者， E-mail: szl803@126.com 摘    要    将螺旋埋管等效为三维螺旋线热源，考虑螺旋埋管能源桩的传热过程，运用格林函数和第一型曲线进行积分，推导 给出了考虑时间、空间位置、埋管参数和岩土体热物理性质 4 参数的螺旋埋管能源桩的温度场解析解，建立高精度三维螺旋 埋管能源桩的传热模型. 并通过在数值模拟软件中建立螺旋埋管能源桩三维模型，依据边界条件，求解得出三维螺旋埋管能 源桩温度场数值解. 对比结果表明：所建立的能源桩三维螺旋线热源模型具有很高的解析精度. 最后，基于解析模型讨论了 螺旋埋管能源桩换热温度场的空间分布和时间效应. 关键词    能源桩；螺旋埋管；传热模型；温度场；解析解 分类号    TU470 Transient heat transfer model of a three-dimensional spiral heat source in an energy pile LI Qing-wen1,2) ，ZHENG Ming-yang3) ，QIAO Lan1,2) ，SUI Zhi-li4) 苣 1) School of Civil and Resource Engineering, University of Science and Technology Beijing, Beijing 100083, China 2) Beijing Key Laboratory of Urban Underground Space Engineering, University of Science and Technology Beijing, Beijing 100083, China 3) China Railway Siyuan Survey and Design Group Co., LTD., Wuhan 430061, China 4) Urban Construction School, Beijing City University, Beijing 100083, China 苣 Corresponding author, E-mail: szl803@126.com ABSTRACT    An  energy  pile  is  a  new  type  of  ground  source  heat  pump  system.  A  heat  exchanger  is  casted  into  the  concrete  pile foundation of a building structure for the purpose of heating or cooling the building through heat exchange between the pile foundation and  surrounding  soil.  An  energy  pile  can  be  developed  rapidly  because  of  its  high  heat  transfer  efficiency  and  stable  structure  and because  it  requires  no  additional  drilling  requirements.  In  the  long-term  operation,  energy  piles  have  to  bear  both  the  overlying  and thermal loads caused by changes in the temperature field. Thus, accurately evaluating the temperature field of an energy pile and its surrounding soil is one of the key problems in the design and application of energy piles. To improve the heat transfer efficiency of energy piles, U-type, W-type, spiral type, and similar types of coils have been developed to be casted into the energy pile. Results of thermal  efficiency  analysis  show  that  the  spiral  type  coil  has  the  best  heating  and  cooling  performance  and  was  nearly  150% more thermally efficient than the double U-type coil. Thus, a spiral coil is selected as the main coils’ form in the current practical application. However, due to the complex heat exchange structure of the spiral pipe, the present analytical model had to be simplified to accurately characterize the temperature field characteristics of a spiral pipe casted in an energy pile. In this paper, the spiral pipe was regarded as a three-dimensional spiral heat source. Considering the existing heat transfer model, an analytical solution of the temperature field was obtained  by  integrating  green ’s  function  and  the  first  curve  function;  then,  the  high-precision,  three-dimensional  (3-D)  heat  transfer model  of  the  spiral  pipe  was  established  considering  the  time,  space,  buried  pipe  parameters,  and  thermal  property  of  host  soil.  In 收稿日期: 2020−05−03 基金项目: 北京市教育委员会科技计划一般资助项目（KM202011418001）；中央高校基本科研业务费专项资金资助项目（FRF-BD-19-004A） 工程科学学报，第 43 卷，第 11 期：1569−1576，2021 年 11 月 Chinese Journal of Engineering, Vol. 43, No. 11: 1569−1576, November 2021 https://doi.org/10.13374/j.issn2095-9389.2020.05.03.003; http://cje.ustb.edu.cn