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Article(id=1295068234907148782, tenantId=1146029695717560320, journalId=1210938733613449225, issueId=1295068190569164906, articleNumber=null, orderNo=null, doi=10.19666/j.rlfd.202509085, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1758988800000, receivedDateStr=2025-09-28, revisedDate=1762358400000, revisedDateStr=2025-11-06, acceptedDate=1763395200000, acceptedDateStr=2025-11-18, onlineDate=1786697928405, onlineDateStr=2026-08-14, pubDate=1782316800000, pubDateStr=2026-06-25, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1786697928405, onlineIssueDateStr=2026-08-14, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1786697928405, creator=13701087609, updateTime=1786697928405, updator=13701087609, issue=Issue{id=1295068190569164906, tenantId=1146029695717560320, journalId=1210938733613449225, year='2026', volume='55', issue='6', pageStart='1', pageEnd='192', issueExtLink='null', onlineDate='null', pubDate='1782316800000', pubDateStr='2026-06-25', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=1, specialIssue=null, createTime=1786697917835, creator='13701087609', updateTime=1786698816898, updator='13701087609', preIssue=null, nextIssue=null, articleTotal=null, ext={EN=IssueExt(id=1295071961596584952, tenantId=1146029695717560320, journalId=1210938733613449225, issueId=1295068190569164906, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1295071961596584953, tenantId=1146029695717560320, journalId=1210938733613449225, issueId=1295068190569164906, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null, downloadFileDto=null}, startPage=73, endPage=82, ext={EN=ArticleExt(id=1295068235108475375, articleId=1295068234907148782, tenantId=1146029695717560320, journalId=1210938733613449225, language=EN, title=Performance optimization of heat storage unit with tree-branch fins and foam metal composite structure, columnId=1295068192326574197, journalTitle=Thermal Power Generation, columnName=Energy storage technology research, runingTitle=null, highlight=null, articleAbstract=
[Objective]

To achieve recovery and utilization of low-grade waste heat, we proposed a phase change thermal storage unit incorporating “tree-branch fins + foam metal”, and co-optimized its structural and material parameters using response surface methodology and orthogonal experiments.

[Methods]

Under typical operating conditions (80 ℃, 0.005 m/s), tree-branch fins reduced the melting time of the phase change material (PCM) by 10.7% compared to straight fins, with optimal parameters including a length ratio of 1.143, a width ratio of 1.057, and a branching angle of 68.987°. Regarding system structure, the counterflow arrangement of dual heat exchanger tubes decreased the melting time to 558 s, and further filling with foam metal shortened it to 181 s. Although increasing porosity enhances the proportion of PCM, it weakens the structural support of the metal framework, thereby prolonging the melting time.

[Results]

In conclusion, the integration of tree-branch fins and foam metal significantly improves the thermal storage performance of phase change thermal storage devices. Subsequently, staged thermal energy storage can improve the efficiency of heat storage. The optimal configuration for a three-stage cascade is put forward: Stage I: 0.9 porosity nickel foam + n-octadecane; Stage II: 0.5 porosity nickel foam + n-octadecane; Stage III: 0.5 porosity nickel foam + stearic acid PCM.

[Conclusion]

It can provide an integrated design basis for the efficient capture and reuse of low-grade waste heat at 50~60 ℃.

, authors=Xu HAN, Xilu BO, authorsList=Xu HAN, Xilu BO, authorCompany=null, correspAuthors=Xilu BO, 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=1295068238560387606, articleId=1295068234907148782, tenantId=1146029695717560320, journalId=1210938733613449225, language=CN, title=树杈翅片与泡沫金属复合储热单元性能优化研究, columnId=1236714914694361723, journalTitle=热力发电, columnName=储能技术研究, runingTitle=null, highlight=null, articleAbstract=
【目的】

针对低品位余热的高效回收与利用，提出了一种“树杈翅片+泡沫金属”的相变储热单元，并通过响应面法与正交试验对结构与材料参数进行协同优化。

【方法】

在典型工况（80 ℃、0.005 m/s）下，树杈翅片较直翅片可将PCM熔化时间缩短10.7%，其最优参数为长度比1.143、宽度比1.057、分支角68.987°。系统结构方面，双换热管逆流可将熔化时间降至558 s，进一步填充泡沫金属后缩短至181 s。提高孔隙率虽增加相变材料比例，但会削弱金属骨架作用，延长熔化时间。

【结果】

综上所述，采用树杈翅片和泡沫金属可显著提升相变储热装置的储热效果。进一步地，采用梯级储热可提高储热效率，提出三级级联的最优配置为：第1段0.9孔隙率泡沫镍+相变材料正十八烷，第2段0.5孔隙率泡沫镍+相变材料正十八烷，第3段0.5孔隙率泡沫镍+相变材料硬脂酸。

【结论】

研究结论可为50~60 ℃低品位余热的高效捕获与再利用提供一体化设计依据。

, authors=韩旭, 薄熙禄, authorsList=韩旭, 薄熙禄, authorCompany=null, correspAuthors=薄熙禄, authorNote=

韩旭（1991），男，副教授，博士，主要研究方向为综合能源系统，储能技术，。

, correspAuthorsNote=
薄熙禄（2000），男，硕士研究生，主要研究方向为综合能源系统，储能技术，。
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韩旭（1991），男，副教授，博士，主要研究方向为综合能源系统，储能技术，。

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韩旭（1991），男，副教授，博士，主要研究方向为综合能源系统，储能技术，。

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caption=Liquid fraction solidification curves of foam metal materials, figureFileSmall=A/XCBOh+sdOp57nnKUrYCw==, figureFileBig=4uHXX5WLJhaELjlNBYEtxQ==, tableContent=null), ArticleFig(id=1295068243035710031, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1295068234907148782, language=CN, label=图17, caption=泡沫金属材料液相分数凝固曲线, figureFileSmall=A/XCBOh+sdOp57nnKUrYCw==, figureFileBig=4uHXX5WLJhaELjlNBYEtxQ==, tableContent=null), ArticleFig(id=1295068243090235984, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1295068234907148782, language=EN, label=Fig.18, caption=Liquid fraction melting curves of PCMs, figureFileSmall=Xj1515bzFXHQYjPzgy7pAg==, figureFileBig=xK6k4O8h301ycRLrxu2WfQ==, tableContent=null), ArticleFig(id=1295068243157344849, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1295068234907148782, language=CN, label=图18, caption=相变材料液相分数熔化曲线, figureFileSmall=Xj1515bzFXHQYjPzgy7pAg==, figureFileBig=xK6k4O8h301ycRLrxu2WfQ==, tableContent=null), ArticleFig(id=1295068243278979666, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1295068234907148782, language=EN, label=Fig.19, caption=Solidification curves of liquid fraction of PCMs, figureFileSmall=DEGVo8JfOZCN+Ix44l6+wQ==, figureFileBig=S+bRBdW/6b8PnJMz0bHM5Q==, tableContent=null), ArticleFig(id=1295068243341894227, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1295068234907148782, language=CN, label=图19, caption=相变材料液相分数凝固曲线, figureFileSmall=DEGVo8JfOZCN+Ix44l6+wQ==, figureFileBig=S+bRBdW/6b8PnJMz0bHM5Q==, tableContent=null), ArticleFig(id=1295068243413197396, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1295068234907148782, language=EN, label=Tab.1, caption=

Thermophysical property parameters

, figureFileSmall=null, figureFileBig=null, tableContent=
项目RT35水
密度/（kg·m–3）815.0998.2
定压比热容/（J·kg–1·K–1）2 0004 182
热导率/（W·m–1·K–1）0.20.6
热膨胀系数/K–10.000 60.001 003
相变潜热/（J·kg–1）170 000
熔化温度/K309
凝固温度/K302
), ArticleFig(id=1295068243476111957, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1295068234907148782, language=CN, label=表1, caption=

热物性参数

, figureFileSmall=null, figureFileBig=null, tableContent=
项目RT35水
密度/（kg·m–3）815.0998.2
定压比热容/（J·kg–1·K–1）2 0004 182
热导率/（W·m–1·K–1）0.20.6
热膨胀系数/K–10.000 60.001 003
相变潜热/（J·kg–1）170 000
熔化温度/K309
凝固温度/K302
), ArticleFig(id=1295068243559998038, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1295068234907148782, language=EN, label=Tab.2, caption=

Test design

, figureFileSmall=null, figureFileBig=null, tableContent=
编号长度比A宽度比B角度CR1/s
11.001.00501 109.33
21.001.25601 200.05
31.001.50701 114.33
41.001.75551 122.24
51.252.00651 105.33
61.251.00501 200.98
71.251.25601 212.17
81.251.50701 227.88
91.501.75551 189.67
101.502.00651 135.67
111.501.00501 155.33
121.501.25601 184.00
131.751.50701 198.33
141.751.75551 154.00
151.752.00651 205.00
161.751.00501 189.67
172.001.25601 198.33
182.001.50701 219.99
192.001.75551 200.15
202.002.00651 191.67
), ArticleFig(id=1295068243631301207, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1295068234907148782, language=CN, label=表2, caption=

试验设计

, figureFileSmall=null, figureFileBig=null, tableContent=
编号长度比A宽度比B角度CR1/s
11.001.00501 109.33
21.001.25601 200.05
31.001.50701 114.33
41.001.75551 122.24
51.252.00651 105.33
61.251.00501 200.98
71.251.25601 212.17
81.251.50701 227.88
91.501.75551 189.67
101.502.00651 135.67
111.501.00501 155.33
121.501.25601 184.00
131.751.50701 198.33
141.751.75551 154.00
151.752.00651 205.00
161.751.00501 189.67
172.001.25601 198.33
182.001.50701 219.99
192.001.75551 200.15
202.002.00651 191.67
), ArticleFig(id=1295068243702604376, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1295068234907148782, language=EN, label=Tab.3, caption=

Analysis of variance table

, figureFileSmall=null, figureFileBig=null, tableContent=
来源平方和自由度均方FP
模型27 404.1993 044.9120.21<0.000 1**显著
A8 040.8618 040.8653.37<0.000 1**
B2 304.0812 304.0815.290.002 9**
C907.261907.266.020.034 0*
AB799.931799.935.310.043 9*
AC450.251450.252.990.114 5
BC49.98149.980.330.577 3
A23 483.5613 483.5623.120.000 7**
B22 916.1312 916.1319.360.001 3**
C213 002.43113 002.4386.31<0.000 1**
残差1 506.5510150.65
失拟项805.215161.041.150.441 6不显著
纯误差701.345140.27
总和28 910.7419
), ArticleFig(id=1295068243803267673, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1295068234907148782, language=CN, label=表3, caption=

方差分析

, figureFileSmall=null, figureFileBig=null, tableContent=
来源平方和自由度均方FP
模型27 404.1993 044.9120.21<0.000 1**显著
A8 040.8618 040.8653.37<0.000 1**
B2 304.0812 304.0815.290.002 9**
C907.261907.266.020.034 0*
AB799.931799.935.310.043 9*
AC450.251450.252.990.114 5
BC49.98149.980.330.577 3
A23 483.5613 483.5623.120.000 7**
B22 916.1312 916.1319.360.001 3**
C213 002.43113 002.4386.31<0.000 1**
残差1 506.5510150.65
失拟项805.215161.041.150.441 6不显著
纯误差701.345140.27
总和28 910.7419
), ArticleFig(id=1295068243882959450, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1295068234907148782, language=EN, label=Tab.4, caption=

Thermophysical property parameters of metallic foams

, figureFileSmall=null, figureFileBig=null, tableContent=
热物性参数镍钛铝钢铜
密度/（kg·m–3）8 9004 8502 7198 0308 978
定压比热容/（J·kg–1·K–1）460.60544.25871.00502.48391.00
热导率λ/（W·m–1·K–1）91.747.44202.4016.27387.60
), ArticleFig(id=1295068243950068315, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1295068234907148782, language=CN, label=表4, caption=

泡沫金属材料热物性参数

, figureFileSmall=null, figureFileBig=null, tableContent=
热物性参数镍钛铝钢铜
密度/（kg·m–3）8 9004 8502 7198 0308 978
定压比热容/（J·kg–1·K–1）460.60544.25871.00502.48391.00
热导率λ/（W·m–1·K–1）91.747.44202.4016.27387.60
), ArticleFig(id=1295068244029760092, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1295068234907148782, language=EN, label=Tab.5, caption=

Orthogonal experimental table

, figureFileSmall=null, figureFileBig=null, tableContent=
序号第1段第2段第3段相变时间/s
1D1E1F1D1E1F1D1E1F1599.7
2D1E2F2D3E4F5D2E2F2985.0
3D1E3F3D5E2F4D3E3F3737.0
4D1E4F4D2E5F3D4E4F4688.7
5D1E5F5D4E3F2D5E5F51 236.3
6D2E1F2D2E2F2D3E4F5945.7
7D2E2F3D4E5F1D4E5F1753.3
8D2E3F4D1E3F5D5E1F2921.7
9D2E4F5D3E1F4D1E2F3956.0
10D2E5F1D5E4F3D2E3F4648.3
11D3E1F3D3E3F3D5E2F4729.7
12D3E2F4D5E1F2D1E3F5953.7
13D3E3F5D2E4F1D2E4F1833.3
14D3E4F1D4E2F5D3E5F21 053.0
15D3E5F2D1E5F4D4E1F3653.7
16D4E1F4D4E4F4D2E5F3631.3
17D4E2F5D1E2F3D3E1F4938.0
18D4E3F1D3E5F2D4E2F51 003.0
19D4E4F2D5E3F1D5E3F1684.7
20D4E5F3D2E1F5D1E4F2974.7
21D5E1F5D5E5F5D4E3F21 216.3
22D5E2F1D2E3F4D5E4F3667.7
23D5E3F2D4E1F3D1E5F4641.0
24D5E4F3D1E4F2D2E1F51 012.0
25D5E5F4D3E2F1D3E2F1716.3
), ArticleFig(id=1295068244105257565, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1295068234907148782, language=CN, label=表5, caption=

正交实验

, figureFileSmall=null, figureFileBig=null, tableContent=
序号第1段第2段第3段相变时间/s
1D1E1F1D1E1F1D1E1F1599.7
2D1E2F2D3E4F5D2E2F2985.0
3D1E3F3D5E2F4D3E3F3737.0
4D1E4F4D2E5F3D4E4F4688.7
5D1E5F5D4E3F2D5E5F51 236.3
6D2E1F2D2E2F2D3E4F5945.7
7D2E2F3D4E5F1D4E5F1753.3
8D2E3F4D1E3F5D5E1F2921.7
9D2E4F5D3E1F4D1E2F3956.0
10D2E5F1D5E4F3D2E3F4648.3
11D3E1F3D3E3F3D5E2F4729.7
12D3E2F4D5E1F2D1E3F5953.7
13D3E3F5D2E4F1D2E4F1833.3
14D3E4F1D4E2F5D3E5F21 053.0
15D3E5F2D1E5F4D4E1F3653.7
16D4E1F4D4E4F4D2E5F3631.3
17D4E2F5D1E2F3D3E1F4938.0
18D4E3F1D3E5F2D4E2F51 003.0
19D4E4F2D5E3F1D5E3F1684.7
20D4E5F3D2E1F5D1E4F2974.7
21D5E1F5D5E5F5D4E3F21 216.3
22D5E2F1D2E3F4D5E4F3667.7
23D5E3F2D4E1F3D1E5F4641.0
24D5E4F3D1E4F2D2E1F51 012.0
25D5E5F4D3E2F1D3E2F1716.3
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树杈翅片与泡沫金属复合储热单元性能优化研究
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韩旭 , 薄熙禄
热力发电 | 储能技术研究 2026,55(6): 73-82
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热力发电 |储能技术研究 2026 , 55 (6) : 73 -82
树杈翅片与泡沫金属复合储热单元性能优化研究
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韩旭（1991），男，副教授，博士，主要研究方向为综合能源系统，储能技术，。

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韩旭 , 薄熙禄
作者信息
  • 华北电力大学河北省低碳高效发电技术重点实验室，河北 保定 071003
通讯作者:
薄熙禄（2000），男，硕士研究生，主要研究方向为综合能源系统，储能技术，。
作者简介:

韩旭（1991），男，副教授，博士，主要研究方向为综合能源系统，储能技术，。

Performance optimization of heat storage unit with tree-branch fins and foam metal composite structure
Xu HAN , Xilu BO
Affiliations
  • Hebei Key Laboratory of Low-Carbon and High-Efficiency Power Generation Technology, North China Electric Power University, Baoding 071003, China
出版时间: 2026-06-25 doi: 10.19666/j.rlfd.202509085
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摘要
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【目的】

针对低品位余热的高效回收与利用，提出了一种“树杈翅片+泡沫金属”的相变储热单元，并通过响应面法与正交试验对结构与材料参数进行协同优化。

【方法】

在典型工况（80 ℃、0.005 m/s）下，树杈翅片较直翅片可将PCM熔化时间缩短10.7%，其最优参数为长度比1.143、宽度比1.057、分支角68.987°。系统结构方面，双换热管逆流可将熔化时间降至558 s，进一步填充泡沫金属后缩短至181 s。提高孔隙率虽增加相变材料比例，但会削弱金属骨架作用，延长熔化时间。

【结果】

综上所述，采用树杈翅片和泡沫金属可显著提升相变储热装置的储热效果。进一步地，采用梯级储热可提高储热效率，提出三级级联的最优配置为：第1段0.9孔隙率泡沫镍+相变材料正十八烷，第2段0.5孔隙率泡沫镍+相变材料正十八烷，第3段0.5孔隙率泡沫镍+相变材料硬脂酸。

【结论】

研究结论可为50~60 ℃低品位余热的高效捕获与再利用提供一体化设计依据。

相变储热  /  树杈翅片  /  响应面法  /  翅片参数优化  /  泡沫金属
[Objective]

To achieve recovery and utilization of low-grade waste heat, we proposed a phase change thermal storage unit incorporating “tree-branch fins + foam metal”, and co-optimized its structural and material parameters using response surface methodology and orthogonal experiments.

[Methods]

Under typical operating conditions (80 ℃, 0.005 m/s), tree-branch fins reduced the melting time of the phase change material (PCM) by 10.7% compared to straight fins, with optimal parameters including a length ratio of 1.143, a width ratio of 1.057, and a branching angle of 68.987°. Regarding system structure, the counterflow arrangement of dual heat exchanger tubes decreased the melting time to 558 s, and further filling with foam metal shortened it to 181 s. Although increasing porosity enhances the proportion of PCM, it weakens the structural support of the metal framework, thereby prolonging the melting time.

[Results]

In conclusion, the integration of tree-branch fins and foam metal significantly improves the thermal storage performance of phase change thermal storage devices. Subsequently, staged thermal energy storage can improve the efficiency of heat storage. The optimal configuration for a three-stage cascade is put forward: Stage I: 0.9 porosity nickel foam + n-octadecane; Stage II: 0.5 porosity nickel foam + n-octadecane; Stage III: 0.5 porosity nickel foam + stearic acid PCM.

[Conclusion]

It can provide an integrated design basis for the efficient capture and reuse of low-grade waste heat at 50~60 ℃.

phase change thermal energy storage  /  tree-branch fins  /  response surface methodology  /  fin parameter optimization  /  metal foam
韩旭, 薄熙禄. 树杈翅片与泡沫金属复合储热单元性能优化研究. 热力发电, 2026 , 55 (6) : 73 -82 . DOI: 10.19666/j.rlfd.202509085
Xu HAN, Xilu BO. Performance optimization of heat storage unit with tree-branch fins and foam metal composite structure[J]. Thermal Power Generation, 2026 , 55 (6) : 73 -82 . DOI: 10.19666/j.rlfd.202509085
正文
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太阳能、风能等可再生能源固有的间歇性和不稳定性，导致其在时间和空间上与能源需求存在显著的错配[1-3]。为有效解决这一问题，利用低品位余热，通过就地换热、储热及梯级耦合等技术进行跨时段、跨环节调配，能显著提高一次能源利用效率，减少不必要的补燃和用电，从而有效降低碳排放。
在众多储能技术中，热储能技术（TES）因其能有效缓解能源供需不平衡而备受瞩目[4-5]。其中，潜热储能主要依赖于相变材料（PCM）的储热和释热过程，在余热回收和太阳能收集等领域应用广泛。但PCM自身导热性较低，严重限制了其储热效率和充放热速率[6]。针对PCM导热性差的缺点，研究人员提出了被动增强技术，主要通过填充纳米颗粒、增加翅片、使用金属泡沫等方式进行改善。增加翅片能大幅增加换热面积，从而改善PCM的热交换性能，缩短相变过程时间[7]，被证明是有效的传热强化手段之一。
在储热装置中应用翅片的研究已非常深入，且翅片形状对传热性能有显著影响[8]。V形、树枝形、环形及纵向翅片等多种结构都被证实能提升传热效果。Hicham等人[9]研究发现，在三级级联潜热储热装置中使用纵向翅片可显著缩短熔化时间。Hao等人[10]则指出，树状翅片能显著加速PCM的熔融，比无翅片装置缩短了47.7%的熔融时间。Yang等人[11]在竖直管壳式相变储热装置中加入泡沫金属后，完全熔化时间和完全凝固时间分别减少了85.83%和95.83%。此外，翅片结构的参数优化也成为研究热点[12]。Li等人[13]研究了10种翅片结构参数组合，发现最优参数配置可以将熔化时间缩短54.1%。Yang等人[14]研究表明，不同数量的翅片配置可能导致熔化时间差异高达72.85%。Huang等人[15]结合了分形翅片与矩形翅片，与单一翅片相比，熔化时间缩短了41.1%。Arici等人[16]研究发现，调整翅片的长度和位置，可使熔化时间缩短13%～68%。
尽管翅片结构的优化在改善换热效果方面成效显著，但现有研究多侧重于翅片的参数、分布和排列方式，对翅片优化与泡沫金属材料协同应用的研究相对不足。金属泡沫材料不仅可以增加换热面积，还能促进热量传递的均匀性，具有良好的传热强化效果。然而，当使用参数各异的多种金属泡沫时，其强化效果会受到接触热阻的影响。基于上述背景，本文针对低品位余热回收问题，设计了一种结合树杈翅片结构与泡沫金属材料的相变储热单元。旨在深入探讨树杈翅片结构参数及泡沫金属材料相关影响因素对换热效果的具体作用，为优化相变储热装置的设计提供重要的理论指导。
1　模型与方法
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1.1　物理模型
配备有树杈翅片的相变储热装置如图1所示，其由一个载水的铜传热管和一个与PCM集成的外管组成，相变材料填充在管与壳中间，水在管内流动。采用ANSYS Workbench仿真平台建立相变储热单元的几何模型，采用套管式换热器模型，内管为热流体，内管直径为12 mm，外管直径为48 mm，壁厚为2 mm，管长为200 mm，外管填充有相变材料。通过热流体将热量传递给相变材料进行储热，在内管外侧开设有8个树杈翅片，翅片总长度为16 mm，根部厚度为2 mm，分叉角度为60°。选取RT35作为相变材料，水作为传热流体，管道壁面材料为钢，翅片材料为铜，热物性参数如表1所示。
1.2　数学模型
为保证求解效率并提高求解准确性，做如下假设：1）循环介质和相变材料的热物性与温度无关；2）相变材料的热物性参数各向同性且均匀；3）流体为不可压缩牛顿流体，自然对流为层流；4）仅考虑浮力项的密度变化，相变材料的密度满足Boussinesq假设；5）储热单元外壁绝热；6）忽略熔化过程中相变材料的体积变化；7）泡沫金属为多孔介质区域。
在多孔介质相变过程中，采用Enthalpy-Porosity模型进行求解，流体依然遵循流体力学的3大控制方程，但需考虑固液两相区自然对流的影响，因此连续性方程必须考虑密度的变化，控制方程如下：
连续性方程：
∂ρ∂τ+∇(ρV¯)=0
动量方程：
∂(ρu)∂τ+ρ[(u⋅∇)u]=−∇p+μ∇2u+Su
∂(ρu)∂τ+ρ[(u⋅∇)u]=−∇p+μ∇2u+Sν
能量方程：
∂(ρh)∂τ+∇⋅(ρhV¯)=∇⋅(λ∇T)
式中：u为速度矢量，m/s；ρ为流体密度，kg/m3；p流体压力，MPa；μ为流体动力黏度，Pa·s；T为流体温度，℃；λ为流体的热导率，W/（m·K）。
Su=(1−β)2(β3+ξ)Amushu
Sν=(1−β)2(β3+ξ)Amushν+ρrefgδ(h−href)cp
式中：Amush为糊状区常数，取104~107；ξ为修正系数，小于0.000 1，防止除以0；δ为体膨胀系数；ρref为参考密度，kg/m3；href为比焓值，J/kg；β为液相率；cp为比热容，J/（kg·K）。
β={0,T<TsT−TsTf−Ts,Ts⩽T⩽Tf1,T>Tf
式中：Ts、Tf分别为固相和液相的温度，℃。
比焓：
h=∫TrefTcpdT+βLp
在糊状区内的比热容和热导率均为线性变化：
λ=λs+β(λf−λs)
cp=cp,s+β(cp,f−cp,s)
式中：Lp为相变潜热，J/kg；cp，s、cp，f为固相和液相的比热容，J/（kg·K）；λs为固相热导率，W/（m·K）；λf为液相热导率，W/（m·K）。
换热流体、相变材料区域以及管道壁面是模型的主要组成部分，在进行模型仿真计算时，要对其初始条件以及边界条件进行相关设定。
入口水温和入口流速分别设置为80 ℃和0.005 m/s；管道外壁面设置为绝热边界条件，即热量在此表面不进行热交换；本文忽略了储热单元外边界与周围环境之间的换热；水的温度为80 ℃，PCM初始温度为25 ℃；翅片与PCM之间的界面为耦合边界。
1.3　模型验证
基于上述模型及边界条件，使用Ansys Fluent 2022的凝固/熔化模型，采用SIMPLE算法（压力-速度耦合）、二阶逆风离散（能量/动量）及PRESTO格式（压力方程），糊状区常数取初始值。网格独立性验证显示，当网格数量从623 141增至1 173 923时，储热平均温度曲线变化趋势近似。网格数量达到813 496后，温度变化趋于平缓，故选择813 496进行仿真。时间步长独立性方面，5.0、1.0、0.5 s的3组仿真结果差异较小（图3）。考虑到精度与效率，最终选定1 s作为时间步长。
为评估本节数值模拟的可信度，建立了与文献[17]中相同的相变材料模型，所涉及的物性参数及边界条件均依据文献设置，图4为本文模型与Zhang等人[17]研究结果的对比。
Zhang等人通过实验分析了相变储热单元在蓄-释热过程中的换热性能，通过布置测点对储热体内温度进行了分析，本研究对所布置测点的温度进行了计算。由于在实验过程中受环境温度以及实验设备等因素的影响，使得实验结果与仿真模拟之间存在一定的误差，经过计算比较，所验证的测点温度与仿真计算的结果最大误差不超过5%。
为验证本文所提出的树状翅片在增强相变储热单元的储热效果，本节对常见直肋与树状翅片进行了有效性验证，其中直翅片套管式换热器模型横截面如图5所示。图5中内管为热流体，内管直径为12 mm，外管直径为48 mm，壁厚为2 mm，管长为200 mm，外管填充有相变材料；内管外侧开设有8个翅片，翅片长度为16 mm，厚度为2 mm，其余设置均与树杈翅片换热器模型一致。
为探究树状翅片对相变储热单元储热性能的强化机理，同时避免翅片体积及翅片材料的影响，本节所建立的物理模型均保持相同的翅片体积和翅片材料，常规直肋与树状翅片的计算结果如图6和图7所示。本文所建立的直肋和树状翅片体积误差仅为1.6%，可以近似认为体积一致。从图6及图7的计算结果可以看出，树状翅片具有良好的传热性能，且树杈翅片的相变材料平均温度升高趋势明显快于直翅片。值得注意的是，在储热初期，此时的相变材料未开始熔化，自然对流尚未建立，此时的热量传递主要依靠导热，树杈翅片的优势并不明显，相变材料平均温度曲线与液相率曲线之间的差距较小；当储热时间超过800 s时，相变材料熔化区域逐渐扩大，自然对流强度逐渐加强，在靠近翅片处形成低粘度液层，树杈翅片的强化效果逐渐明显。树杈翅片与传统直翅片相比，在空间上具有多级、分叉的热通道特点，将热流体热量从多个路径传入相变材料深层，各分支温度场之间相互叠加，缩短平均导热路径，将内管热流量在径向均匀散开，使相变材料均匀吸热。配置树杈翅片相变储热罐的相变材料平均温度明显高于传统直翅片，相变材料的熔化时间从1 374 s缩短至1 227 s，减少了10.7%。
图8为不同翅片温度云图。从图8可以看出，添加树杈翅片可以将内管热流体的热量更快地传递至相变材料区域，对比发现树枝翅片的相变材料区域温度更加均匀，温度分布趋于一致，而直翅片区域温度显著高于相变材料区域，相变材料不能充分吸收内管热流体的热量，导致其换热流体的出口温度大于树杈翅片相变储热单元。
2　结果与分析
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2.1　储热装置翅片结构对储热效果的影响
为探究树杈翅片对相变储热装置储热效果的影响，本文对翅片的长度比、宽度比和分支角度进行了参数分析和优化设计，分别取5组进行分析。储热计算时，换热工质的入口温度为80 ℃，入口流速为0.005 m/s，管道外壁面设置为绝热边界，并采用响应面优化算法确定最佳翅片形状。树杈翅片套管换热器模型如图9所示，树杈翅片的长度比、宽度比和分叉角度分别为L2与L1之比、W2与W1之比和α。
本文设置了5组不同长度比的翅片结构，长度比分别为1.00、1.25、1.50、1.75和2.00，宽度比均为1.00，分支角度均为60°，计算结果如图10所示。对比不同翅片长度比相变材料出口温度曲线可以看出：长度比为1.75时，中期储热效果最佳，温度曲线表现出较快的上升趋势，表明此时的储热性能较好；不同长度比对相变储热装置储热性能的影响较小，在储热中期具有较大差异，在初期及末期改变长度比的影响较小。最终计算结果显示，当长度比从1.00提升至1.25时，相变材料的熔化时间从1 251 s缩短至1 154 s，降低了7.75%。储热结束后5组长度比翅片的相变材料温度分别为64.23、64.80、63.21、63.74、64.39 ℃，长度比为1.25时，相变储热装置的熔化时间最短，且储热效果最好，平均温度提升了0.89%。
在储热初期，翅片根部逐渐升温，此时相变材料逐渐熔化形成薄液膜，改变长度对短程导热的影响较弱，因此5组长度比的区别并不明显。随着储热工质的不断加热，相变材料熔化区域逐渐扩大，树杈翅片的覆盖率逐渐起到主导作用，因此改变翅片长度比具有显著作用。储热末期相变材料即将完全熔化，此时的固液区域远离翅片呈现孤岛形态，长度比对储热速率的边际影响减弱。
本文设置了5组不同宽度比的翅片结构，分别为1.00、1.25、1.50、1.75和2.00，长度比均为1，分支角度均为60°。最终计算结果显示，随着翅片宽度比的不断提高，相变储热装置的储热效果不断提高。当宽度比从1.00提高到2.00时，相变材料熔化时间从1 251 s降低至1 156 s，降低了95 s，即7.59%；储热完成后相变材料的平均温度从64.23 ℃提高至65.04 ℃，提高了0.81 ℃，即1.26%。
增加相变储热装置的翅片宽度比，可以提高翅片截面积，从而提高翅片换热效率，其本质上是拓宽导热主通道，缩短换热工质到相变材料之间的等效导热路径，从而提高翅片的传热效率。
m=hPkAc
式中：m为翅片效率，m–1；h为对流换热系数，W/（m2·K）；P为翅片与流体的湿周，m；k为翅片材料的热导率，W/（m·K）；Ac为翅片截面积，m2。
在储热中期，储热性能明显提升，此时相变材料的熔化进入对流增强阶段，翅片不仅继续发挥导热翅片的传统作用，更在内部熔融相变材料的诱发下，部分转化为流体流动的自然浮升环路，进一步拓宽对流通道。
翅片分支角度影响翅片的传热深度，当分支角度较大时，翅片覆盖面积扩大，无翅片区域面积降低，会对翅片远端覆盖不足，形成换热效率较小的“冷点”。因此，本文对树杈翅片的分支角度进行了单因素分析，设置了5组分支角度进行分析，分别为50°、55°、60°、65°和70°，其长度比和宽度比均为1，边界条件和参数设置均与上文相同。计算结果显示，当分支角度为65°时，储热性能最好，相变材料熔化时间从1 151 s提高至1 164 s，提高了1.13%，相变材料的平均温度从64.23 ℃提高至66.65 ℃，提高了3.77%。
单因素分析在探究某一独立因素的影响机理时，具有明显的优势，但对于多因素复杂的影响机理时，往往难以分析，因此本文采用响应面分析的方法，设计20组不同长度比、宽度比和角度的相变储热单元模型，对翅片结构进行优化，不同试验设计如表2所示，表中试验指标R1为熔化时间（s）。
表3为方差分析。表3中F值作为方差分析中的核心检验统计量，其数值大小直接反映了组间变异与组内变异之间的相对比例。该比值的增大，意味着不同处理组之间均值差异的幅度相较于内部随机波动而言更为显著。P值则是在原假设成立的前提下，所观测到的当前样本数据（或更极端情况）出现的概率。模型F值为20.21表示模型显著。模型中P值小于0.050 0表明模型项显著，P值小于0.010 0表明模型项极显著。表3中A的P值小于0.000 1，B的P值为0.002 9，C的P值为0.034 0，AB的P值为0.043 9，A2的P值为0.000 7，B2的P值小于0.001 3，C2的P值小于0.000 1，可知A、B、C、AB、A2、B2、C2是显著模型项。失拟项的F值为1.15，P值为0.441 6，表明失拟项模型不显著，模型拟合较好，数据较可靠，模型回归线性方程为：
R1=1211.93+22.42A+12B−7.53C−10AB+7.5AC+2.5BC−11.77A2−10.77B2−22.74C2
由式（12）可知，影响R1的各因素关系为A>B>C，响应面法得出的最优模型为长度比为1.143、宽度比为1.057、角度为68.987°。
2.2　储热装置相变单元对储热效果的影响
为进一步提高相变储热装置的储热效果，本节对上文所提出的结构进行了优化设计，引入双通道相变储热装置和泡沫金属。其中，换热流体的双通道采用逆流布置，入口速度和入口温度与上文保持一致，换热工质的入口温度为80 ℃，入口流速为0.005 m/s。采用逆流布置可提高换热流体与相变材料的温差，从而提高换热效率，提高相变储热装置内部相变材料温度的均匀性。双换热管道结构如图11所示。
泡沫金属填充相变材料模型所涉及的热物性参数、边界条件以及孔隙率与粘性阻力系数均依据Xu等人[18]进行设置，采用多孔介质模型与凝固熔化模型，并将泡沫金属区域设置为多孔介质区域，区域内各项同性，材料设置为金属材料填充相变材料。
有（无）泡沫金属的双换热管道模型的液相分数对比曲线如图12所示，单（双）换热管道有（无）泡沫金属模型的温度云图如图13所示。其中，图13中[1]、[2]、[3]、[4]为同一时刻单换热管道无泡沫金属、单换热管道复合泡沫金属、双热管道无泡沫金属、双换热管道复合泡沫金属的温度云图。从图12及图13可以看出：采取双换热管道逆流的方式可以大幅提高储热效率。仿真计算结果显示，相变材料熔化时间缩短至558 s，储热结束时相变材料的最高温度从64.23 ℃提高至79.94 ℃，提高了24.46%；同时在相变材料区域添加泡沫金属可以大幅缩短相变储热装置的储热时间，相变材料的熔化时间从558 s缩短至181 s，缩短了67.56%。
进一步的，泡沫金属作为三维高导热骨架能显著缩短换热工质传入相变材料的路径，提高相变材料与金属骨架的接触面积，从而降低温度梯度、加快固–液界面的推进，在充放热中期明显缩短熔化/凝固时间。
在储热中期的换热效果显著提高，相变材料液相率曲线更早接近平台期，传热时间缩短，使用泡沫金属的三维骨架将换热工质的热量更快地散开到相变材料内部，缩短了相变材料的导热路径并降低了界面热阻，可以显著加快储热响应速度。由于相变材料的热导率较低，热量很难从换热管传递至相变材料深处，而泡沫金属依靠其出色的导热性能，将热量从换热管很快传递至相变材料深处。
在相变中后期，液相率不断提高，相变材料熔化区域不断扩大，此时热量的传递方式为导热与对流。采用泡沫金属使相变材料区域温度趋于一致，抑制了相变材料的自然对流，传热方式以导热为主。
相变材料种类、泡沫金属材料、泡沫金属孔隙率对相变储热装置的换热效果有显著影响[18]，为探究每一个参数对相变储热单元的储热释热效果的影响，设置了5组不同泡沫金属孔隙率，分别为0.5、0.6、0.7、0.8和0.9，泡沫金属材料均为铜，相变材料的相变温度均为28.85 ℃；5组不同泡沫金属材料，分别为泡沫镍、泡沫钛、泡沫铜、泡沫铝和泡沫钢，孔隙率均为0.7，相变材料的相变温度均为28.85 ℃；5组不同相变材料，分别为正十八烷、硬脂酸、石墨烯复合相变材料、十四醇和RT35，其孔隙率均为0.7，泡沫金属材料为铜来进行仿真计算，入口温度为80 ℃，入口流速为0.005 m/s；释热计算时，入口温度为25 ℃，初始温度为50 ℃，管道外壁面设置为绝热边界条件，部分计算结果如图14—图19所示。其中5种泡沫金属材料的热物性参数见表4。
对比不同孔隙率的凝固熔化曲线可以看出，随着孔隙率的增加，储热性能逐渐降低，当孔隙率从0.6增加至0.9时，相变材料区域增加，金属骨架区域减小，相变时间从173 s增加至204 s，增加了17.92%。由于金属材料的热导率较高，可以大幅提高相变材料的等效导热系数，从而提高相变材料的换热效果。提高孔隙率意味着相变材料中填充的金属骨架体积分数降低，相变材料占比增多，因此相变材料的熔化相变时间增加。此外，泡沫金属材料可以显著缩短储热中期的导热路径，提升液相前沿的推进速度；在释热阶段，同样能把相变材料深部热量更快地抽回到冷却水侧，尤其在温差较小、自然对流弱的工况下优势更明显，泡沫金属材料的储热效果主要由金属材料的热导率决定，从图16中可以看出，使用铜泡沫时相变时间为181 s，而相变时间最长的为217 s。
将不同参数的相变储热单元梯级配置可以使换热流体在流动过程中始终与相邻的相变材料保持较小的温差，避免了单级系统因温差逐渐减小导致的换热速率下降问题。为了进一步提高相变储热单元的储热性能，本节将相变储热单元划分为3个不同参数的单元进行计算，并选取最优组合。单因素分析可量化单一特定因素对目标的影响，在描述参数独立影响方面具有优势，然而，在揭示相变材料、泡沫金属材料与孔隙率之间的复杂相互作用时存在一定的局限性。为了克服局限性并更全面优化冷却效果，同时减少仿真模拟的次数，本节采用正交试验方法，对相变储热单元参数的最优组合进行优化设计，正交实验设计如表5所示。其中，D1—D5分别为正十八烷、硬脂酸、石墨烯复合相变材料5组相变材料、十四醇和RT35，E1—E5分别为0.5、0.6、0.7、0.8、0.9 5组孔隙率，F1—F5分别为泡沫铜、泡沫铝、泡沫钢、泡沫钛和泡沫镍5组泡沫金属材料。
根据上述仿真结果，利用极差分析法确定正交试验中各因素对评价指标的影响程度。具体计算公式如下：
Kij=∑Tmaxij(i=L,H,W,j=1,2,3,4)
kij=Kij/n
R=max(kij)−min(kij)
式中：n为水平数；Kij为第i列因素第j水平所对应的试验结果之和；kij为Kij的平均值，平均值是用来描述某一因素或水平下试验结果的中心趋势或典型水平的。平均值越小，代表该因素或水平下的试验指标整体水平偏低。根据kij的大小可以判断因素i的最佳水平，以确定最优组合。极差R，定义为第i列因素各水平下的最大平均值与最小平均值之差，以此衡量该因素对实验结果的影响。R值的大小直接反映了试验因子对结果的影响幅度，当R值增大时，意味着数据的离散程度增大，进而说明该因素对试验指标的影响更为显著。基于上述计算方法，分别针对相变储热装置的相变时间以及最大热应力进行了极差分析，并得出了相应的分析结果。
以相变储热装置相变时间为评价指标计算极差，可以得到各因素对相变储能装置换热性能影响的主次顺序。以相变储热装置的相变时间为优化目标时，相变材料种类的影响最大、其次为泡沫金属材料种类，影响最小的为泡沫金属孔隙率。第1段相变单元配置为在孔隙率为0.9的泡沫镍中填充正十八烷，第2段相变单元配置为在孔隙率为0.5的泡沫镍中填充正十八烷，第3段相变单元配置为在孔隙率为0.5的泡沫镍中填充硬脂酸相变材料。
3　结论
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本文针对50~60 ℃低品位余热回收场景，围绕“树杈翅片+泡沫金属”结构开展了强化传热研究。通过对相变储热装置树杈翅片的长度比、宽度比及分支角度进行响应面分析，确定各因素影响程度为长度比>宽度比>角度，并获得最优几何参数（长度比1.143，宽度比1.057，角度68.987°）。在相变储热单元设计中，通过正交实验优化泡沫金属孔隙率、泡沫金属与相变材料种类，提出多联级配置方案：第1段采用0.9孔隙率泡沫镍与相变材料正十八烷，第2段和第3段采用0.5孔隙率泡沫镍分别搭配相变材料正十八烷与硬脂酸。该优化设计显著提升了低品位余热的回收效率，为工业废热利用提供了有效技术路径。
基金
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  • 河北省自然科学基金项目(E2023502025)
  • 国家自然科学基金项目(52106010)
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2026年第55卷第6期
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doi: 10.19666/j.rlfd.202509085
  • 接收时间：2025-09-28
  • 首发时间：2026-08-14
  • 出版时间：2026-06-25
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  • 收稿日期：2025-09-28
  • 修回日期：2025-11-06
  • 录用日期：2025-11-18
基金
Natural Science Foundation of Hebei Province(E2023502025)
河北省自然科学基金项目(E2023502025)
National Natural Science Foundation of China(52106010)
国家自然科学基金项目(52106010)
作者信息
    华北电力大学河北省低碳高效发电技术重点实验室，河北 保定 071003

通讯作者:

薄熙禄（2000），男，硕士研究生，主要研究方向为综合能源系统，储能技术，。
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2种不同金属材料的力学参数
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Number of
species		 占总种数比例
Percentage of
total species (%)		 属
Genus		 种数
Number of
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鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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