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Article(id=1320037418196119704, tenantId=1146029695717560320, journalId=1316781260334530699, issueId=1320037383882519364, articleNumber=null, orderNo=null, doi=10.3969/j.issn.1005-0329.2025.12.008, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1751644800000, receivedDateStr=2025-07-05, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1792651045606, onlineDateStr=2026-10-22, pubDate=1767110400000, pubDateStr=2025-12-31, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1792651045606, onlineIssueDateStr=2026-10-22, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1792651045606, creator=13701087609, updateTime=1792651045606, updator=13701087609, issue=Issue{id=1320037383882519364, tenantId=1146029695717560320, journalId=1316781260334530699, year='2025', volume='53', issue='12', pageStart='1', pageEnd='118', issueExtLink='null', onlineDate='null', pubDate='1767110400000', pubDateStr='2025-12-31', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1792651037426, creator='13701087609', updateTime=1792656182714, updator='13701087609', preIssue=null, nextIssue=null, articleTotal=null, ext={EN=IssueExt(id=1320058964839093145, tenantId=1146029695717560320, journalId=1316781260334530699, issueId=1320037383882519364, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1320058964839093146, tenantId=1146029695717560320, journalId=1316781260334530699, issueId=1320037383882519364, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null, downloadFileDto=null}, startPage=64, endPage=76, ext={EN=ArticleExt(id=1320037418355503257, articleId=1320037418196119704, tenantId=1146029695717560320, journalId=1316781260334530699, language=EN, title=Influence of pile‑soil parameters on thermo‑mechanical coupling characteristics of energy pipe piles with phase change materials, columnId=null, journalTitle=Fluid Machinery, columnName=null, runingTitle=null, highlight=null, articleAbstract=

To investigate the influence of pile‑soil parameters on the thermo‑mechanical coupling characteristics of energy pipe piles with phase change materials，a combined method of 3D numerical simulation and experimental validation was adopted to analyze the effects of heat exchange tube form，pile material，soil type，and layered conditions.The results show that the heat exchange capacity per unit pile depth follows a descending order for coaxial pipe，double U‑tube，and single U‑tube heat exchangers，measuring 81，71.44，54.51 W/m，respectively，at the end of operation.The coaxial pipe configuration delays the recovery of the summer phase change material （PCM-S） under long‑term operation，expands the thermal influence zone of the surrounding soil，and intensifies the changes in the mechanical performance of the pile.Different pipe pile materials lead to variations in heat exchange capacity and PCM-S liquefaction rate due to differences in thermal conductivity：during the PCM-S phase change period，C80 exhibits the highest heat exchange，while C100 shows the lowest；after phase change completion，C100 achieves the highest heat exchange （55.77 W/m），and C80 the lowest （54.5 W/m）.The axial force and side friction resistance of the pile are highest for C80，followed by C90，and lowest for C100.Increasing the thermal conductivity of the soil enhances heat exchange performance and reduces the thermo‑mechanical response of the pile.In layered soils，an arrangement with increasing thermal conductivity from top to bottom is most conducive to heat exchange，and high thermal conductivity soil layers accelerate heat diffusion，reducing thermo‑mechanical changes in the pile.This research provides a theoretical basis for the optimal design of pile‑soil parameters in energy pipe piles with phase change materials.

, authors=Weibo YANG, Jiayan ZHAO, Jiaheng ZHU, Tianzheng QIAO, Feng WANG, authorsList=Weibo YANG, Jiayan ZHAO, Jiaheng ZHU, Tianzheng QIAO, Feng WANG, authorCompany=null, correspAuthors=null, authorNote=null, correspAuthorsNote=null, copyrightStatement=null, copyrightOwner=null, extLink=null, articleAbsUrl=null, sourceXml=null, magXml=null, pdfUrl=null, pdf=null, pdfFileSize=null, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=null, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=null, mapNumber=null, fund=null), CN=ArticleExt(id=1320037426723139783, articleId=1320037418196119704, tenantId=1146029695717560320, journalId=1316781260334530699, language=CN, title=桩土参数对相变能源管桩热-力耦合特性的影响, columnId=1317484287230853622, journalTitle=流体机械, columnName=设计计算, runingTitle=null, highlight=null, articleAbstract=

为探究桩土参数对相变能源管桩热-力耦合特性的影响，采用三维数值模拟与试验验证相结合的方法，分析了换热管形式、桩体材料、土体类型及分层条件的影响。结果表明，套管、双U型与单U型换热管的单位桩深换热量依次递减，运行结束时分别为81，71.44，54.51 W/m；套管形式在长期运行下会延缓夏季相变材料（PCM-S）的恢复，并扩大桩周土体热影响范围，加剧桩身力学性能变化。不同管桩材料因导热系数差异，导致换热量与PCM-S液化率不同：PCM-S相变期间，C80换热量最大，C100最小；相变完成后，C100换热量最高（55.77 W/m），C80最低（54.5 W/m）。桩身轴力与侧摩阻力以C80最大，C90次之，C100最小。土体导热系数增大可提升换热性能并减小桩身热-力学响应；在分层土中，导热系数自上而下递增的布置最有利于换热，且高导热土层能加速热扩散，降低桩身热-力学变化。研究可为相变能源管桩的桩土参数优化设计提供理论依据。

, authors=杨卫波, 赵佳燕, 朱家恒, 谯田正, 汪峰, authorsList=杨卫波, 赵佳燕, 朱家恒, 谯田正, 汪峰, authorCompany=null, correspAuthors=null, authorNote=

杨卫波（1975），男，博士，教授，博导，主要从事地源热泵与浅层地热能利用方面的研究，通信地址：225127江苏省扬州市邗江区华扬西路196号扬州大学扬子津东校区电气与能源动力工程学院，E-mail：。

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杨卫波（1975），男，博士，教授，博导，主要从事地源热泵与浅层地热能利用方面的研究，通信地址：225127江苏省扬州市邗江区华扬西路196号扬州大学扬子津东校区电气与能源动力工程学院，E-mail：。

"}, bioImg=null, bioContent=

杨卫波（1975），男，博士，教授，博导，主要从事地源热泵与浅层地热能利用方面的研究，通信地址：225127江苏省扬州市邗江区华扬西路196号扬州大学扬子津东校区电气与能源动力工程学院，E-mail：。

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language=CN, orderNo=3, keyword=相变材料), Keyword(id=1320037432188317932, tenantId=1146029695717560320, journalId=1316781260334530699, articleId=1320037418196119704, language=CN, orderNo=4, keyword=热-力耦合), Keyword(id=1320037432247038189, tenantId=1146029695717560320, journalId=1316781260334530699, articleId=1320037418196119704, language=CN, orderNo=5, keyword=数值模拟)], refs=[Reference(id=1320037440874721566, tenantId=1146029695717560320, journalId=1316781260334530699, articleId=1320037418196119704, doi=null, pmid=null, pmcid=null, year=null, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=1, rfOrder=0, authorNames=null, journalName=null, refType=null, unstructuredReference=BOZIS D，PAPAKOSTAS K，KYRIAKIS N.On the evaluation of design parameters effects on the heat transfer efficiency of energy piles［J］.Energy & Buildings，2010，43（4）：1020-1029., articleTitle=null, refAbstract=null), Reference(id=1320037440992162079, tenantId=1146029695717560320, 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unstructuredReference=SUN T F.Numerical simulation and experimental study on thermal‑mechanical coupling characteristics of energy pile under cyclic temperature load［D］.Yangzhou：Yangzhou University，2022., articleTitle=null, refAbstract=null)], funds=null, companyList=[AuthorCompany(id=1320037427213873352, tenantId=1146029695717560320, journalId=1316781260334530699, articleId=1320037418196119704, xref=null, ext=[AuthorCompanyExt(id=1320037427226456265, tenantId=1146029695717560320, journalId=1316781260334530699, articleId=1320037418196119704, companyId=1320037427213873352, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=College of Electrical，Energy and Power Engineering，Yangzhou University，Yangzhou 225127，China), AuthorCompanyExt(id=1320037427247427786, tenantId=1146029695717560320, journalId=1316781260334530699, articleId=1320037418196119704, companyId=1320037427213873352, language=CN, country=null, province=null, 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（a）管桩部分 （b）整体计算区域

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（a）单U型管 （b）双U型管 （c）套管

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（a）单U型管 （b）双U型管 （c）套管

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（a）桩身位移 （b）桩身轴力 （c）桩身侧摩阻力

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（a）桩身位移 （b）桩身轴力 （c）桩身侧摩阻力

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（a）桩身位移 （b）桩身轴力 （c）桩身侧摩阻力

, figureFileSmall=L+oDYDeNpRh4ta2WJXfjIA==, figureFileBig=YMS4T7wdrn5b3aW2j7etIg==, tableContent=null), ArticleFig(id=1320037440128135444, tenantId=1146029695717560320, journalId=1316781260334530699, articleId=1320037418196119704, language=EN, label=Tab.1, caption=

Simulation calculation conditions

, figureFileSmall=null, figureFileBig=null, tableContent=
参数名称数值参数名称数值
U型管外径/mm25土体初始温度/℃17.5
U型管内径/mm20土体密度/（kg·m-3）1 600
两支管间距/mm100土体比热容/（J·kg-1·K-1）1 640
套管外径/mm75土体导热系数/（W·m-1·K-1）0.688
套管内径/mm70换热管密度/（kg·m-3）950
管桩长度/m14换热管导热系数/（W·m-1·K-1）0.42
管桩外径/m0.5换热管比热容/（J·kg-1·K-1）2 300
管桩内径/m0.25管桩密度/（kg·m-³）2 490
夏季PCM密度/（kg·m-3）855.4管桩导热系数/（W·m-1·K-1）1.78
夏季PCM导热系数/（W·m-1·K-1）0.186管桩比热容/（J·kg-1·K-1）800
夏季PCM相变
温度/℃		20.15夏季PCM相变
潜热/（J·g-1）		136
), ArticleFig(id=1320037440199438613, tenantId=1146029695717560320, journalId=1316781260334530699, articleId=1320037418196119704, language=CN, label=表1, caption=

模拟计算条件

, figureFileSmall=null, figureFileBig=null, tableContent=
参数名称数值参数名称数值
U型管外径/mm25土体初始温度/℃17.5
U型管内径/mm20土体密度/（kg·m-3）1 600
两支管间距/mm100土体比热容/（J·kg-1·K-1）1 640
套管外径/mm75土体导热系数/（W·m-1·K-1）0.688
套管内径/mm70换热管密度/（kg·m-3）950
管桩长度/m14换热管导热系数/（W·m-1·K-1）0.42
管桩外径/m0.5换热管比热容/（J·kg-1·K-1）2 300
管桩内径/m0.25管桩密度/（kg·m-³）2 490
夏季PCM密度/（kg·m-3）855.4管桩导热系数/（W·m-1·K-1）1.78
夏季PCM导热系数/（W·m-1·K-1）0.186管桩比热容/（J·kg-1·K-1）800
夏季PCM相变
温度/℃		20.15夏季PCM相变
潜热/（J·g-1）		136
), ArticleFig(id=1320037440283324694, tenantId=1146029695717560320, journalId=1316781260334530699, articleId=1320037418196119704, language=EN, label=Tab.2, caption=

Parameters of pipe piles with different materials

, figureFileSmall=null, figureFileBig=null, tableContent=
参数C80混凝土C90混凝土C100混凝土
导热系数/（W·m-1·K-1）1.752.052.3
密度/（kg·m-3）2 5002 5502 600
压缩模量/GPa424650
), ArticleFig(id=1320037440363016471, tenantId=1146029695717560320, journalId=1316781260334530699, articleId=1320037418196119704, language=CN, label=表2, caption=

不同材料管桩参数

, figureFileSmall=null, figureFileBig=null, tableContent=
参数C80混凝土C90混凝土C100混凝土
导热系数/（W·m-1·K-1）1.752.052.3
密度/（kg·m-3）2 5002 5502 600
压缩模量/GPa424650
), ArticleFig(id=1320037440442708248, tenantId=1146029695717560320, journalId=1316781260334530699, articleId=1320037418196119704, language=EN, label=Tab.3, caption=

Parameters of different soil types

, figureFileSmall=null, figureFileBig=null, tableContent=
土体类型密度/（kg·m-3）导热系数/（W·m-1·K-1）比热容/（J·kg-1·K-1）压缩模量/MPa泊松比黏聚力/kPa内摩擦角/（°）
砂土1 8001.81 260350.291528
黏土1 5001.371 100200.36018
岩土2 5003.21 4006000.32027
), ArticleFig(id=1320037440509817113, tenantId=1146029695717560320, journalId=1316781260334530699, articleId=1320037418196119704, language=CN, label=表3, caption=

不同类型土体参数

, figureFileSmall=null, figureFileBig=null, tableContent=
土体类型密度/（kg·m-3）导热系数/（W·m-1·K-1）比热容/（J·kg-1·K-1）压缩模量/MPa泊松比黏聚力/kPa内摩擦角/（°）
砂土1 8001.81 260350.291528
黏土1 5001.371 100200.36018
岩土2 5003.21 4006000.32027
), ArticleFig(id=1320037440568537370, tenantId=1146029695717560320, journalId=1316781260334530699, articleId=1320037418196119704, language=EN, label=Tab.4, caption=

Different types of layered soil

, figureFileSmall=null, figureFileBig=null, tableContent=
分层第一层第二层第三层
1粉质黏土泥岩砂岩
2砂岩泥岩粉质黏土
3泥岩
), ArticleFig(id=1320037440631451931, tenantId=1146029695717560320, journalId=1316781260334530699, articleId=1320037418196119704, language=CN, label=表4, caption=

不同分层土体类型

, figureFileSmall=null, figureFileBig=null, tableContent=
分层第一层第二层第三层
1粉质黏土泥岩砂岩
2砂岩泥岩粉质黏土
3泥岩
), ArticleFig(id=1320037440702755100, tenantId=1146029695717560320, journalId=1316781260334530699, articleId=1320037418196119704, language=EN, label=Tab.5, caption=

Physical property parameters of different soil types

, figureFileSmall=null, figureFileBig=null, tableContent=
土体类型粉质黏土泥岩砂岩
密度/（kg·m-3）1 9402 6102 445
导热系数/（W·m-1·K-1）1.51.992.49
比热容/（J·kg-1·K-1）1 755868.51 016
压缩模量/MPa5.331526
泊松比0.30.335.5
黏聚力/kPa16.83060
内摩擦角/（°）9.72030
), ArticleFig(id=1320037440782446877, tenantId=1146029695717560320, journalId=1316781260334530699, articleId=1320037418196119704, language=CN, label=表5, caption=

不同类型土体物性参数

, figureFileSmall=null, figureFileBig=null, tableContent=
土体类型粉质黏土泥岩砂岩
密度/（kg·m-3）1 9402 6102 445
导热系数/（W·m-1·K-1）1.51.992.49
比热容/（J·kg-1·K-1）1 755868.51 016
压缩模量/MPa5.331526
泊松比0.30.335.5
黏聚力/kPa16.83060
内摩擦角/（°）9.72030
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桩土参数对相变能源管桩热-力耦合特性的影响
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杨卫波 , 赵佳燕 , 朱家恒 , 谯田正 , 汪峰
流体机械 | 设计计算 2025,53(12): 64-76
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流体机械 |设计计算 2025 , 53 (12) : 64 -76
桩土参数对相变能源管桩热-力耦合特性的影响
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杨卫波 , 赵佳燕, 朱家恒, 谯田正, 汪峰
作者信息
  • 扬州大学 电气与能源动力工程学院，江苏 扬州 225127
作者简介:

杨卫波（1975），男，博士，教授，博导，主要从事地源热泵与浅层地热能利用方面的研究，通信地址：225127江苏省扬州市邗江区华扬西路196号扬州大学扬子津东校区电气与能源动力工程学院，E-mail：。

Influence of pile‑soil parameters on thermo‑mechanical coupling characteristics of energy pipe piles with phase change materials
Weibo YANG , Jiayan ZHAO, Jiaheng ZHU, Tianzheng QIAO, Feng WANG
Affiliations
  • College of Electrical，Energy and Power Engineering，Yangzhou University，Yangzhou 225127，China
出版时间: 2025-12-31 doi: 10.3969/j.issn.1005-0329.2025.12.008
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摘要
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为探究桩土参数对相变能源管桩热-力耦合特性的影响，采用三维数值模拟与试验验证相结合的方法，分析了换热管形式、桩体材料、土体类型及分层条件的影响。结果表明，套管、双U型与单U型换热管的单位桩深换热量依次递减，运行结束时分别为81，71.44，54.51 W/m；套管形式在长期运行下会延缓夏季相变材料（PCM-S）的恢复，并扩大桩周土体热影响范围，加剧桩身力学性能变化。不同管桩材料因导热系数差异，导致换热量与PCM-S液化率不同：PCM-S相变期间，C80换热量最大，C100最小；相变完成后，C100换热量最高（55.77 W/m），C80最低（54.5 W/m）。桩身轴力与侧摩阻力以C80最大，C90次之，C100最小。土体导热系数增大可提升换热性能并减小桩身热-力学响应；在分层土中，导热系数自上而下递增的布置最有利于换热，且高导热土层能加速热扩散，降低桩身热-力学变化。研究可为相变能源管桩的桩土参数优化设计提供理论依据。

能源管桩  /  桩土参数  /  相变材料  /  热-力耦合  /  数值模拟

To investigate the influence of pile‑soil parameters on the thermo‑mechanical coupling characteristics of energy pipe piles with phase change materials，a combined method of 3D numerical simulation and experimental validation was adopted to analyze the effects of heat exchange tube form，pile material，soil type，and layered conditions.The results show that the heat exchange capacity per unit pile depth follows a descending order for coaxial pipe，double U‑tube，and single U‑tube heat exchangers，measuring 81，71.44，54.51 W/m，respectively，at the end of operation.The coaxial pipe configuration delays the recovery of the summer phase change material （PCM-S） under long‑term operation，expands the thermal influence zone of the surrounding soil，and intensifies the changes in the mechanical performance of the pile.Different pipe pile materials lead to variations in heat exchange capacity and PCM-S liquefaction rate due to differences in thermal conductivity：during the PCM-S phase change period，C80 exhibits the highest heat exchange，while C100 shows the lowest；after phase change completion，C100 achieves the highest heat exchange （55.77 W/m），and C80 the lowest （54.5 W/m）.The axial force and side friction resistance of the pile are highest for C80，followed by C90，and lowest for C100.Increasing the thermal conductivity of the soil enhances heat exchange performance and reduces the thermo‑mechanical response of the pile.In layered soils，an arrangement with increasing thermal conductivity from top to bottom is most conducive to heat exchange，and high thermal conductivity soil layers accelerate heat diffusion，reducing thermo‑mechanical changes in the pile.This research provides a theoretical basis for the optimal design of pile‑soil parameters in energy pipe piles with phase change materials.

energy pipe pile  /  pile‑soil parameters  /  phase change material  /  thermo‑mechanical coupling  /  numerical simulation
杨卫波, 赵佳燕, 朱家恒, 谯田正, 汪峰. 桩土参数对相变能源管桩热-力耦合特性的影响. 流体机械, 2025 , 53 (12) : 64 -76 . DOI: 10.3969/j.issn.1005-0329.2025.12.008
Weibo YANG, Jiayan ZHAO, Jiaheng ZHU, Tianzheng QIAO, Feng WANG. Influence of pile‑soil parameters on thermo‑mechanical coupling characteristics of energy pipe piles with phase change materials[J]. Fluid Machinery, 2025 , 53 (12) : 64 -76 . DOI: 10.3969/j.issn.1005-0329.2025.12.008
正文
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0　引言
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地源热泵因其节能、环保、高效及适应性好等优势而在建筑节能领域得到广泛应用。然而，传统地源热泵的钻孔费用高、占地面积大制约了其大面积推广。为此，有人提出将地埋管直接埋入建筑桩基中，从而构成能源桩［1］。能源桩不仅降低了钻孔埋管费用，而且节省埋管占地空间，是替换传统地埋管最为理想的新型埋管技术。
管桩是一种高预应力混凝土建筑地基，在其中心空腔埋入换热管回填后可构成能源管桩。它不仅可以有效利用地下空间，而且相较于传统实体能源桩，具有施工便捷、无需破坏桩身结构及回填与埋管更灵活等优势。将相变材料（phase change materials，PCM）作为能源管桩回填材料一部分的相变能源管桩（phase change energy pipe pile，PCEPP），可以在增强蓄能换热效果的同时，降低桩体温度与热应变幅度，增强桩体力学性能稳定性，成为近年来暖通、结构等多学科交叉领域研究的一个热点。
针对相变能源管桩，CAO等［2-3］模拟了PCEPP的热响应特性，并对比了水、普通灌浆和PCM回填下能源管桩的换热性能，结果表明，PCM能有效提高能源管桩的换热能力，在连续运行时，普通灌浆和PCM回填下能源管桩换热性能优于水回填，并且对PCM进行改进后更有利于换热。HU等［4-5］模拟了PCM的相变温度、导热系数及相变潜热对能源管桩换热性能的影响，得出较高的相变温度更有利于缓解能源桩及周围土体的积冷问题，较高的潜热和导热系数有利于换热性能的提升，适度降低潜热可减少热堆积，维持周期性热响应稳定性。WANG等［6-7］对新型石蜡/石墨PCM作为管桩回填物进行了研究，结果表明，新型PCM能有效提高储热能力与桩体换热性能，减少桩内的温度波动，且较高的石墨体积分数能提升换热性能。崔宏志等［8］开展了蓄热增强型混凝土管桩和普通管桩的对比试验，得出螺旋布管方式能够优化换热路径，管桩中心填充PCM能提高换热性能，采用PCM与导热翅片的复合方式不会提高换热性能，但能有效减少桩体及桩周土体温度的影响。XIA等［9］在管桩中将金属翅片和螺旋换热管进行集成，得出集成后其换热性能更好，并且能减少桩身热应力，大幅提高对PCM的利用率。
综上所述，目前PCEPP的研究主要集中于普通回填材料与PCM回填材料的对比，PCM物性参数、新型PCM等因素对PCEPP热力学特性的影响，而关于桩土参数对PCEPP热-力耦合特性影响的研究较少。为此，本文进一步探讨不同桩埋管形式、管桩材料、桩周土体类型及土体分层形式下PCEPP的热-力耦合特性。
1　计算模型
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1.1　物理模型
PCEPP运行过程中涉及埋管、回填土、回填PCM、管桩及桩周土体间的导热与PCM固液相变传热及由传热导致的热变形，是一个复杂的相变-热-力耦合过程，为便于模型建立，作以下假设。
（1）埋管、回填原土、PCM、管桩、循环介质及桩周土体均为各向同性材料，且除PCM外，物性参数均不随温度而改变。
（2）桩土初始温度相同，土体远边界温度保持不变，忽略土体在竖直方向的传热及土体表面与空气之间的对流换热。
（3）忽略埋管与回填材料、回填材料与管桩内壁、管桩外壁与土体之间的接触热阻。
（4）认为桩身与桩周土体之间为纯导热过程。
（5）PCM与桩周土体或埋管间无对流换热，仅有导热的传热过程。
（6）桩身变形为弹性变形，桩周土体变形为弹塑性变形，桩土间摩擦系数恒定。
基于上述假设，建立如图1所示的PCEPP物理模型。
其中，土体计算区域为2×2×15 m3，夏季相变材料（summer phase change materials，PCM-S）回填于管桩内壁与一根预先放置的同心套管（底部封口，直径0.104 m）外壁所形成的环状空间内，其回填内外直径分别为0.104，0.25 m，回填深度为14 m；冬季相变材料（winter phase change materials，PCM-W）封装于圆管中，并将其置于管桩空腔中心，其回填半径为0.035 m，回填深度为13 m。U型换热管内外直径分别0.025，0.032 m，U型两支管间距为0.2 m，U型管深度为13.5 m。
1.2　数值模型
1.2.1　管内流体流动控制方程
换热管内循环介质流动处于湍流状态，流体不可压缩，采用Realizable k-ε湍流模型，控制方程如下［10］。
连续性方程：
∂u∂x+∂v∂y+∂w∂z=0
动量方程：
ρf(∂u∂t+u∂u∂x+v∂u∂y+w∂u∂z)=-∂P∂x+μ(∂2u∂x2+∂2u∂y2+∂2u∂z2)
ρf(∂v∂t+u∂v∂x+v∂v∂y+w∂v∂z)=-∂P∂y+μ(∂2v∂x2+∂2v∂y2+∂2v∂z2)
ρf(∂w∂t+u∂w∂x+v∂w∂y+w∂w∂z)=-∂P∂z+μ(∂2w∂x2+∂2w∂y2+∂2w∂z2)
能量方程：
∂Tf∂t+u∂Tf∂x+v∂Tf∂y+w∂Tf∂z=α(∂2Tf∂x2+∂2Tf∂y2+∂2Tf∂z2)
式中，u，v，w分别为x，y，z三个坐标上的速度矢量分量，m/s；ρf为流体密度，kg/m3；t为时间，s；P为压强，Pa；μ为流体动力黏度，Pa·s；ν为运动黏度，m2/s；Tf为埋管内流体温度，℃。
1.2.2　流体与管内壁间换热方程
管内循环流体与管内壁间为对流换热，可表示为：
-λp∂Tp∂rr=R=h(Tf-Tp)
式中，λp为管材导热系数，W/（m·K）；Tp为管壁温度，℃；r为U型管内半径，m；h为对流换热系数，W/（m2·K）；Tf为管内流体温度，℃。
h可表示为：
h=0.02Ref0.8Prfnλf /2r
式中，λf为管内循环流体导热系数，W/（m·K）。
1.2.3　桩土导热控制方程
桩体与土体传热为瞬态导热过程，可表示为：
ρcCc∂Tc∂t=∇⋅λc∇Tc+qc
式中，ρc为材料密度，kg/m3；Cc为材料比热容，J/（kg·K）；Tc为材料温度，K；λc为材料导热系数，W/（m·K）；qc为体积热源，W/m3。
1.2.4　相变传热控制方程
采用Fluent中基于焓-多孔介质方法的凝固/熔化模型来模拟相变过程，其控制方程如下［11］。
能量方程：
∂∂t(ρH)+∇(ρvH)=∇(λΔT)+Se
Se=ρCp∂(∇H)∂τ
式中，ρ为相变材料密度，kg/m³；H为相变材料焓，J；v为流体流速，m/s；λ为相变材料导热系数，W/（m·K）；T为相变材料温度，K；Se为源项；Cp为相变材料比热容，J/（kg·K）。
动量方程：
∂(ρv)∂τ+∇⋅(ρviv⃗)=∇⋅(μ∇vi)-∂ρ∂xi+ρgi+Si
Si=(1-β)2β3+εAmush(v-vp)
式中，vi为i方向上的速度分量，m/s；μ为运动黏度，m2/s；Si为i方向上的修正源项；ε表示为避免分母为0而引入的很小的常数；Amush为模糊区常数；vp为牵引速度，m/s。
连续性方程：
∂ρ∂τ+∇⋅(ρv⃗)=0
1.2.5　桩土本构模型
管桩混凝土强度远大于桩周土体，运行过程中，土体的变形会超过屈服极限进入到弹塑性变形阶段，而混凝土管桩始终保持弹性变形阶段，因此，管桩桩身采用理想状态下的弹性本构模型［12］，其表达式如下：
σ=DT(εObs+αcΔT)
式中，DT为弹性矩阵；εObs为桩身受热产生的观测应变；αc为桩身混凝土的热膨胀系数，℃-1；ΔT为桩身温度相对于初始温度的变化值，℃。
桩周土体采用Mohr-Coulomb弹塑性模型，如下式所示［13］：
F=Rmcq-ptanϕ-c=0
Rmc=13cosϕsin(Θ+π3)+13cos(Θ+π3)tanϕ
式中，Rmc为Π平面上描述屈服面形状的一个度量参数；ϕ和Θ分别为桩周土体的内摩擦角和偏极角，（°）；c，q和p分别为桩周土体黏聚力、偏应力和平均有效应力。
1.2.6　地应力
初始地应力是指土体在重力作用下而形成的应力，采用初始地应力定义法对数值模型的地应力进行平衡，初始地应力根据下式计算：
σz=γZ
σh=K0σZ
式中，σz为竖向初始地应力，Pa；γ为土体重度，N/m2；Z为土体深度，m；σh为水平向初始地应力，Pa；K0为侧向土压力系数。
1.3　网格划分
基于Workbench平台中的Spaceclaim模块建立PCEPP的数值模型，并导入至Meshing模块进行网格划分。模型采用自动网格划分方法，其上半部分为规则形状且深度较大，采用扫掠方式并以较大网格间距划分，以降低网格数量；下半部分则采用六面体网格划分，以保证网格质量。PCEPP为筒状结构，采用面网格划分以进一步减少网格数量。桩周土体区域的网格密度设置为由内向外逐渐稀疏。网格划分示意如图2所示。
为了在保证网格质量的情况下提高计算精度与效率，选取2.13×106，2.51×106，2.86×106，3.07×106，4.34×106五种网格方案进行相应试算。分别以进口流速0.6 m/s，进口温度35 ℃运行8 h，通过对比出口温度变化差异比较其网格质量，选取最佳网格数。通过计算，综合考虑计算精度与时间，可得网格数量为3.07×106、时间步长为120 s较为合适。
1.4　模型独立性验证
试验台如图3所示，为确保相变能源管桩模型计算的准确性，建立与相变能源管桩试验台尺寸一致的数值模型。
通过对比夏季工况下运行8 h过程中，桩身换热量及桩顶位移的试验数据与模拟结果，验证该相变能源管桩模型计算结果的可靠性。结果如图4，5所示。
由图4（a）和图5（a）可以看出，相变能源管桩桩身换热量与桩顶位移的模拟值与试验值变化趋势基本一致，但试验值整体低于模拟值。该差异主要源于数值模型对实际条件的简化，以及试验过程中环境因素对数据采集的干扰。进一步由图4（b）与图5（b）可知，桩身换热量与桩顶位移的平均相对误差分别为1.9%和4.87%，实时最大误差分别为5.11%和7.8%，各项误差均处于可接受范围内，从而验证了相变能源管桩数值模型在热-力耦合特性计算方面的准确性。
2　性能评价指标
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PCEPP热力学特性包括其换热性能及力学特性两方面，主要性能评价指标包括换热性能、PCM贡献率、桩身轴力和侧摩阻力。
2.1　换热性能
采用单位桩深换热量评价PCEPP的换热性能，计算公式如下：
ql=Cfm˙(Tin-Tout)l
式中，ql为单位桩深换热量，W/m；Cf为流体比热容，J/（kg·℃）；m˙为管内流体质量流量，kg/s；Tin，Tout分别为桩埋管的进口与出口流体温度，℃；l为桩深，m。
2.2　PCM贡献率
引入PCM贡献率，用于反映其在换热过程中相变潜热在总换热量中的占比，计算公式如下：
η=(βE-βS)mLQall×10-6
式中，η为PCM贡献率；βS，βE分别为运行初始与结束时刻PCM的液相率；m为PCEPP内填充的PCM质量，kg；L为相变潜热，J/kg；Qall为总换热量，MJ。
2.3　桩身轴力
运行过程中桩体受热发生膨胀，而桩周土体会对桩身产生附加轴向应力，计算公式如下［14］：
Ppile=σpileApile=-EApileεT-Rstr
式中，Ppile为桩身轴力，kN；σpile为桩身应力，kPa；Apile为桩身横截面积，m2；E为桩身混凝土弹性模量，kPa；εT-Rstr为桩身约束应变，με。
εT-Rstr可表示为：
εT-Rstr=αcΔT-εT-Obs
式中，αc为桩身材料的热膨胀系数，℃-1；ΔT为桩身温度变化值，℃；εT-Obs为观测应变。
2.4　侧摩阻力
桩身在土体中由于热胀冷缩会与桩周土体产生相对位移，由于不同深度的约束不同，导致桩侧摩阻力分布也不同，规定侧摩阻力向上为正，向下为负，相邻两层应变计之间的平均桩侧摩阻力计算公式如下［15-16］：
fS,mob,j=(σT,j-σT,j-1)(D2-d2)/4DΔL
式中，D为管桩外径，m；d为管桩内径，m；ΔL为相邻两层应变计之间的间距；j表示从桩顶到桩底应变计的位置，j=1，2，3...。
3　模拟结果与分析
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利用CFD软件对上述模型进行求解，运行周期为10天，每天运行8 h、恢复16 h，桩埋管换热介质入口温度为35 ℃，循环流量为0.294 L/s，桩体、PCM及桩周土体初始温度设定为17.5 ℃，模拟计算参数如表1所示［17］。
3.1　换热管形式的影响
选取图6所示的单U型管、双U型管、套管3种典型换热管进行对比研究。图中，夏季相变材料PCM-S采用筒状回填形式布置于管桩内壁，冬季相变材料PCM-W采用圆管封装后布置于管桩内部空腔中心。
不同换热管形式下，单位桩深换热量和PCM-S液相率随时间变化分别如图7，8所示。由图7可以看出，套管换热器的单位桩深换热量最大，其次为双U型管，单U型管最小。这主要是因为一方面套管换热器的换热表面积较大，且流量一定时管内流速较低，换热介质换热时间更长；另一方面，结合图8可看出，套管换热器的PCM-S液相率在第1天时最大，双U型管其次，单U型管最小，从而导致套管及双U型管因相变释放的潜热量也较大。进一步由图8可知，不同换热管形式下PCM-S完成相变的时间也不一致，如套管、双U型管及单U型管的PCM-S分别在运行第1，2及4天完全相变，其原因在于套管换热器的换热面积最大，而单U型管换热面积最小。由此可看出，换热面积是影响PCEPP换热性能及PCM相变状态的主要因素之一。
不同换热管形式运行结束时7 m深截面温度云图如图9所示。
从图9可以看出，套管换热器的PCEPP对桩土温度变化的影响最大，其次为双U型管与单U型管，其原因在于3种换热管换热性能的差异，套管换热器因换热量大，从而导致土体的热影响范围更大。
不同换热管形式下桩身位移、桩身轴力与侧摩阻力沿桩深分布分别如图10，11所示。
由图10（a）与图11（a）可以看出，运行第1天，3种换热管形式下桩身位移、轴力变化均较小，这主要是因为桩身位移与轴力主要受到桩身温度变化的影响，结合图8可知，运行第1天时，由于PCM-S的相变缓冲作用，导致桩身温度变化较小，因此，桩身位移与轴力变化较小。
进一步分析图10（b）与图11（b）可知，运行第10天时，单U型管、双U型管及套管的桩顶位移、最大轴力及桩顶侧摩阻力分别为0.091，0.765，0.809 mm；19.96，24.61，28.66 kN；-5.888，-10.835，-15.360 kPa。可以看出，套管换热器对桩身位移、桩身轴力及侧摩阻力的影响最大，这是因为套管换热器的PCEPP桩身温度变化最大，进而导致了桩身力学性能变化最大；而单U型管桩身温度变化最小，其力学性能变化最小。综上所述，套管换热器能大幅度提升PCEPP的换热效果，但PCM-S的相变速率会加快，并增大对桩身及桩周土体温度的影响程度，导致桩身力学性能变化的增大；单U型管虽然换热性能一般，但能增大PCM-S的使用效率，对桩身及桩周的温度影响最小，且对桩身受热引起的变形与热应力幅度影响较小。
3.2　管桩材料的影响
管桩材料物性参数的差异会影响并改变其热-力耦合特性，为此选取C80，C90，C100这3种混凝土制成的能源管桩进行研究，不同材料管桩的物性参数见表2［18］，计算结果见图12、图13。由图12（a）可以看出，运行前5天，C80的单位桩深换热量始终最大，其次为C90，而C100最小，如运行第1天，3种材料对应的单位桩深换热量分别为69.94，68.90，67.85 W/m。进一步由图12（b）可得，运行前4天，C80的PCM-S液相率变化最快，使用效果较好，从而使得其单位桩深换热量最大；但运行至第5天时PCM-S均已经完全相变，此时，换热性能主要受桩体导热系数影响，如运行第10天，3种材料对应的单位桩深换热量分别为54.50，55.26，55.77 W/m。
进一步由图13（a）可以看出，不同材料下桩身位移沿桩深的变化规律一致，但C80的桩身位移最大，C90其次，C100最小，如3种材料对应的桩顶位移分别为0.09，0.07，0.06 mm，这主要是由于3种材料的导热系数差异，使得桩体温度变化不同。这也同样导致对应的桩身轴力与桩侧摩阻力沿桩深分布存在差异，正如图13（b）（c）所示，C80的桩轴力与桩侧摩阻力最大，其次为C90，C100的最小。显然，低导热系数的C80管桩的桩体温度变化大，导致桩身的位移量、轴力及侧摩阻力增大，而高导热系数的C100桩身温度低，因此，桩身位移量、轴力及侧摩阻力较小。
3.3　土体类型的影响
PCEPP的热力学性能与桩周土体类型紧密相关。为此，选取砂土、黏土、岩土3种典型土壤进行对比分析，3种土体类型参数见表3［18］。
不同土体类型下单位桩深换热量随时间变化如图14所示。
从图可以看出，岩土中单位桩深换热量最大，砂土次之，黏土最小，如运行第1天，黏土、砂土、岩土中的单位桩深换热量分别为75.72，94.91，134.68 W/m，这主要是由于3种土体类型导热性不同而导致其导热能力的差异（见表3）。
不同土体类型PCM-S液相率与贡献率随时间变化如图15所示。由图15（a）可以看出，运行第1天，岩土中PCM-S液相率变化最大，黏土最小，因此，由于相变潜热的释放也会增大岩土中PCEPP的换热量。进一步分析图15（b）可以发现，从PCM-S贡献率上看，岩土并非最大，这是因为岩土的高导热性与高热容，导致显热传递作用超过PCM-S的潜热贡献而占据主导地位；而砂土、黏土因导热性差，显热传递不足，因此，PCM的潜热贡献率更高。这说明在土体导热系数较大时，土体导热系数是影响换热量的主要因素。由图15（a）还可以看出，不同桩周土体类型下PCM液相率均为第1天变化较大，第2天后完成相变。但第1天岩土中液相率变化最大，砂土其次，黏土中液相率变化最小，分别达到了99.5%，81.0%，61.7%，恢复期PCM-S液相率分别恢复了19.6%，41.2%，51.3%，这说明提升桩周土体类型的导热系数可增大运行过程中PCM的使用效果，但会减缓PCM-S的恢复速率。此外，不同桩周土体类型中PCEPP的PCM-S均在第3天完全融化，因此，在实际运行过程中应当在导热系数较高的土体中加大PCM-S的使用量。
不同桩周土体类型下管桩力学参数沿桩深分布规律如图16所示。可以看出，PCEPP在不同桩周土体类型中的桩身位移变化趋势相似，桩身位移均随运行时间呈现向两端累加增大的状态，如在第10天运行结束后，PCEPP在黏土、砂土、岩土中的桩顶位移量分别达到1.26，0.733，0.744 mm；从图16（b）（c）还可以看出，运行10天后，3种土体中最大桩身轴力及桩顶侧摩阻力分别为28.14，25.76，23.90 kN；-7.25，-6.43，-3.51 kPa。由此可以看出，由于桩周土体导热性差异导致其热扩散能力不同，使得PCEPP在不同桩周土体中的温度变化不同，从而会出现不同的热胀冷缩状况及力学性能变化。岩土导热系数最大，桩体散热效果最好，因此，桩体温度变化最小，对应桩体在岩土中的力学性能变化最小，黏土因其导热系数小，导致桩体力学性能变化最大。
3.4　土体分层的影响
实际工程中，桩周土体沿深度并非均匀一致，而是会沿深度方向出现分层。为此，选取3种不同土体分层类型进行数值模拟，具体分层土体类型及对应的不同土体参数见表4与表5［19］。
不同土体分层单位桩深换热量随时间变化如图17所示。可以看出，运行初期不同土体分层下PCEPP单位桩深换热量相差不大，但随运行时间的增加逐渐产生差异（分层1>分层3>分层2）。运行10天后，分层1，2，3下的单位桩深换热量分别为112.08，101.86，104.76 W/m。这是因为分层1的上层导热系数低、下层导热系数高，运行过程中，换热管内介质温度会沿深度方向逐渐降低，上层土体导热性能低但温差大，下层土体层温差小但导热性能好，因此，有利于循环介质与桩周土体之间的热量交换。分层2的土体导热系数由上往下依次递减，虽然上层导热系数与温差均较大，但下层土体的导热系数较小且温差也较小，进而减小了换热量；分层土体3为均匀导热系数，换热量正好位于两者之间。
不同土体分层PCM液相率随时间变化如图18所示。从图可以看出，不同土体分层形式下PCEPP中PCM-S的液相率变化规律相同，第1天时，由于温差较大，PCM-S的液相率变化最为剧烈，分层1~3的液相率分别达到了83.0%，80.5%及85.5%，分层2土体中PCM-S液相率变化最小，分层3最大，其原因为分层2中土体与桩身的换热性能较差，导致PCM-S液相率变化最小。由此可以看出，PCM-S液相率的变化与桩周土体导热系数有着密切关系，而PCM-S液相率则在PCM-S未完全发生相变前决定着换热量的大小。
运行结束时不同土体分层形式下桩体力学参数沿桩深分布规律如图19所示。由图19（a）可以看出，运行10天后，在分层3土体中，桩身位移呈现向两端变大的趋势；在分层1土体中，桩身整体呈向上拱的形变；而在分层2中，桩身位移呈现向下沉的形变。如分层1，2，3中桩顶及桩底位移量分别为1.45，0.142，0.875 mm及-0.048，-1.338，-1.080 mm。
此外，由图19（b）可知，在3种分层土体中，桩身最大轴力分别为27.57，30.72和31.93 kN，其对应出现深度分别为3，11，8 m。这主要是由于在分层1的土体中，桩身上端温度变化较大，膨胀时受土体侧向约束限制，膨胀力主要向上传递，桩身下端温度变化较小，膨胀量小，位移受限，因此整体上呈现向上形变的趋势；在分层2的土体中，桩身温度变化沿深度方向逐渐增大，因此，整体上呈现出向下沉降的趋势；而分层3土体为均匀土体，因此，桩身位移均匀向两端递增，桩身轴力同样受到温度影响，在温度变化剧烈部位产生较大的轴力；桩身侧摩阻力因桩土间的相对位移产生，桩身位移越大，其侧摩阻力越大。
文中仅针对夏季工况展开分析，对于冬季工况，由于相变材料回填于管桩中心，其相变温度难以被有效调控，目前尚未进行深入研究。后续工作将对此种回填形式在冬季工况下的热-力耦合特性进行深入研究。
4　结论
收起
（1）换热管形式对PCEPP的热-力耦合特性影响较大，套管换热器因其换热面积较大，换热性能最好，其次为双U型管与单U型管，如运行结束时其单位桩深换热量分别为81，71.44，54.51 W/m；但套管长期运行会导致PCM-S的恢复效果减慢，并且会增大对土体的热影响范围及桩身力学性能的变化。
（2）C80管桩在短时间运行中换热性能最好；C100在长时间运行中换热性能最好，并且C100的桩身力学性能变化最小。如运行第10天，C80，C90，C100对应的单位桩深换热量分别为54.50，55.26，55.77 W/m，桩顶位移分别为0.09，0.07，0.06 mm。
（3）桩周土体类型对PCEPP的热-力耦合特性有显著影响。PCEPP在岩土中换热效果最好，砂土次之，黏土最差，如运行结束时，其单位桩身换热量分别为134.68，94.92，75.75 W/m。且桩周土体导热系数越大，PCM-S融化速率也越快。从力学角度上看，土体导热系数越大，桩体温度变化越小，其力学性能变化越小。
（4）对于桩周土体不同分层形式，土体导热系数从上向下增大的分层形式更有利于PCEPP的换热，导热系数大的土体层热扩散更快，桩身受到的热-力学性能影响更小。

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doi: 10.3969/j.issn.1005-0329.2025.12.008
  • 接收时间：2025-07-05
  • 首发时间：2026-10-22
  • 出版时间：2025-12-31
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    扬州大学 电气与能源动力工程学院，江苏 扬州 225127
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