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Article(id=1295065208536453457, tenantId=1146029695717560320, journalId=1210938733613449225, issueId=1295064874678252123, articleNumber=null, orderNo=null, doi=10.19666/j.rlfd.202506103, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1750262400000, receivedDateStr=2025-06-19, revisedDate=1751817600000, revisedDateStr=2025-07-07, acceptedDate=1753027200000, acceptedDateStr=2025-07-21, onlineDate=1786697206862, onlineDateStr=2026-08-14, pubDate=1774368000000, pubDateStr=2026-03-25, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1786697206862, onlineIssueDateStr=2026-08-14, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1786697206862, creator=13701087609, updateTime=1786697206862, updator=13701087609, issue=Issue{id=1295064874678252123, tenantId=1146029695717560320, journalId=1210938733613449225, year='2026', volume='55', issue='3', pageStart='1', pageEnd='184', issueExtLink='null', onlineDate='null', pubDate='1774368000000', pubDateStr='2026-03-25', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1786697127264, creator='13701087609', updateTime=1786698874628, updator='13701087609', preIssue=null, nextIssue=null, articleTotal=null, ext={EN=IssueExt(id=1295072203708592834, tenantId=1146029695717560320, journalId=1210938733613449225, issueId=1295064874678252123, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1295072203708592835, tenantId=1146029695717560320, journalId=1210938733613449225, issueId=1295064874678252123, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null, downloadFileDto=null}, startPage=138, endPage=149, ext={EN=ArticleExt(id=1295065209836687702, articleId=1295065208536453457, tenantId=1146029695717560320, journalId=1210938733613449225, language=EN, title=Heat transfer-flow resistance decoupling optimization for a printed circuit heat exchanger in supercritical carbon dioxide energy storage system, columnId=1295064897772086250, journalTitle=Thermal Power Generation, columnName=New power generation technology, runingTitle=null, highlight=null, articleAbstract=
[Objective]

To enhance the heat exchanger efficiency in a carbon dioxide energy storage system, a printed circuit heat exchanger (PCHE) was employed as the core heat transfer component, with binary nitrate molten salt (solar salt) serving as the cold-side fluid and supercritical carbon dioxide (S-CO2) as the hot-side fluid. This study aims to investigate the key factors influencing the internal heat transfer process in PCHE and optimize the dominant structural parameters governing its thermal performance, thereby addressing the performance bottlenecks of heat exchangers in such energy storage systems.

[Methods]

Three key structural parameters of the Zigzag PCHE, such as channel diameter, turning angle, and number of turning cycles, were selected as independent variables. The overall heat transfer coefficient K (a core indicator of heat transfer capacity) and the ratio of the overall heat transfer coefficient to pressure drop K/ΔP (a key metric for evaluating the trade-off between heat transfer and flow resistance) were designated as response variables. A three-factor, three-level response surface methodology (RSM) was established to quantitatively analyze the effects of the three structural parameters and their pairwise interactions on the response variables. Parameter optimization of the heat exchange channels was subsequently performed based on the analytical results.

[Results]

Within the specified parameter ranges (channel diameter: 1.0~2.0 mm, turning angle: 5°~30°, number of turning cycles: 6~10), the results indicate that reducing the channel diameter, increasing the turning angle, or increasing the number of turning cycles can effectively improve the heat transfer efficiency of the Zigzag PCHE. Statistical analysis shows that the channel diameter has a highly significant impact on both K and K/ΔP, and the interaction between the channel diameter and the number of turning cycles also significantly influences these two response variables. The optimal parameter set for achieving the maximum K value (1 313 W/(m2·K)) was determined to be a channel diameter of 1.003 mm, a turning angle of 29.71°, and 9.935 turning cycles. Furthermore, the optimal combination for the comprehensive performance factor K/ΔP was found to be a channel diameter of 2.0 mm, a turning angle of 9.407°, and 6 turning cycles, yielding a K/ΔP value of 0.453 7 W/(m2·K·Pa) and a corresponding K value of 801.7 W/(m2·K). A comparative analysis reveals that the optimized PCHE volume is reduced by approximately one-tenth compared to conventional shell-and-tube heat exchangers.

[Conclusion]

This study confirms that variations in the channel diameter, turning angle, and number of turning cycles significantly affect the thermal performance of zigzag PCHEs. The response surface methodology proves effective in optimizing the channel structural parameters to enhance heat transfer performance. Moreover, PCHEs demonstrate remarkable compactness advantages in CO2 energy storage systems, making them well-suited for space-constrained operational environments. The findings provide reliable theoretical and data-driven support for the rational selection and engineering design of heat exchangers in related fields.

, authors=Shuxia YUAN, Rui XIN, Song WU, Kun YANG, Zheng LI, Zongdong ZHU, authorsList=Shuxia YUAN, Rui XIN, Song WU, Kun YANG, Zheng LI, Zongdong ZHU, authorCompany=null, correspAuthors=Rui XIN, 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=1295065214660137335, articleId=1295065208536453457, tenantId=1146029695717560320, journalId=1210938733613449225, language=CN, title=超临界二氧化碳储能系统印刷线路板式换热器的传热-流阻解耦优化, columnId=1295064897931469804, journalTitle=热力发电, columnName=新型发电技术, runingTitle=null, highlight=null, articleAbstract=
【目的】

为提升二氧化碳储能系统换热器效率，以太阳盐和超临界二氧化碳（S-CO2）作为冷、热侧流体，研究其在印刷线路板式换热器（printed circuit heat exchanger，PCHE）中的流动传热性能。

【方法】

选取通道直径、转折角度、转折周期数为自变量，以总换热系数K、换热系数与压降比K/ΔP为响应值，采用数值模拟结合响应曲面法，分析自变量及交互作用的影响并优化参数。

【结果】

在通道直径1.0~2.0 mm、转折角度5~30°、转折周期数6~10的范围内，减小通道直径、增大转折角度及转折周期数可提升换热效率；通道直径对K和K/ΔP影响极显著，其与转折周期数的交互作用也显著；确定K最优参数（直径1.003 mm、转折角度29.71°、转折周期数9.935时，K高达1 313W/（m2·K））、K/ΔP最优参数（直径2.0 mm、转折角度9.407°、转折周期数6时，K/ΔP达0.453 7W/（m2·K·Pa））；PCHE尺寸较传统管壳式换热器缩小约1/10。

【结论】

该研究证实了在Z型PCHE中，通道直径、转折角度和转折周期数的改变会影响换热性能，而响应曲面法可有效地优化通道结构参数来提升换热性能。并且PCHE在二氧化碳储能系统中紧凑性优势显著。

, authors=袁淑霞, 辛蕊, 吴松, 杨坤, 李铮, 朱宗栋, authorsList=袁淑霞, 辛蕊, 吴松, 杨坤, 李铮, 朱宗栋, authorCompany=null, correspAuthors=辛蕊, authorNote=

袁淑霞（1977），女，博士，教授，研究生导师，主要研究方向为传质传热、多项流动、分离、二氧化碳储能、清洁燃烧技术，。

, correspAuthorsNote=
辛蕊（1999），女，硕士研究生，主要研究方向为二氧化碳储能技术，。
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袁淑霞（1977），女，博士，教授，研究生导师，主要研究方向为传质传热、多项流动、分离、二氧化碳储能、清洁燃烧技术，。

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袁淑霞（1977），女，博士，教授，研究生导师，主要研究方向为传质传热、多项流动、分离、二氧化碳储能、清洁燃烧技术，。

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Research on flow and heat transfer performance of silicon carbide printed circuit heat exchanger[D]. Qingdao: Qingdao University of Science and Technology, 2023: 1., articleTitle=Research on flow and heat transfer performance of silicon carbide printed circuit heat exchanger, refAbstract=null)], funds=[Fund(id=1295065229466030548, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1295065208536453457, awardId=2024JC-YBMS-368; 2025JC-YBMS-425, language=EN, fundingSource=Natural Science Foundation Research Project of Shaanxi Province(2024JC-YBMS-368; 2025JC-YBMS-425), fundOrder=null, country=null), Fund(id=1295065230871122390, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1295065208536453457, awardId=2024JC-YBMS-368; 2025JC-YBMS-425, language=CN, fundingSource=陕西省自然科学基础研究计划项目(2024JC-YBMS-368; 2025JC-YBMS-425), fundOrder=null, country=null)], companyList=[AuthorCompany(id=1295065214949544312, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1295065208536453457, xref=null, ext=[AuthorCompanyExt(id=1295065214957932921, 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label=Fig.3, caption=Velocity (left) and temperature (right) distribution contour map at X=130 mm section, figureFileSmall=Yy7VNnv08R1tJ/WKr4+nzw==, figureFileBig=+QH9oD2abrRfacaAIHor3w==, tableContent=null), ArticleFig(id=1295065219122876844, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1295065208536453457, language=CN, label=图3, caption=X=130 mm截面处速度（左）与温度（右）分布云图, figureFileSmall=Yy7VNnv08R1tJ/WKr4+nzw==, figureFileBig=+QH9oD2abrRfacaAIHor3w==, tableContent=null), ArticleFig(id=1295065219391312301, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1295065208536453457, language=EN, label=Fig.4, caption=Variations of the overall heat transfer coefficient along the flow path, figureFileSmall=IK66ZKEoc8IKvzRHt1Lrdg==, figureFileBig=6UdKGVith5pa+vKTjpDIIg==, tableContent=null), ArticleFig(id=1295065219471004078, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1295065208536453457, language=CN, label=图4, caption=总换热系数沿程变化曲线, figureFileSmall=IK66ZKEoc8IKvzRHt1Lrdg==, figureFileBig=6UdKGVith5pa+vKTjpDIIg==, tableContent=null), ArticleFig(id=1295065219525530031, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1295065208536453457, language=EN, label=Fig.5, caption=Distribution of velocity streamlines of the hot side fluid at different turning angles, figureFileSmall=bBpg8M8PS4AQSy9pwv7ttw==, figureFileBig=geFDwzeUYXzu9bmja1I7qw==, tableContent=null), ArticleFig(id=1295065219806548401, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1295065208536453457, language=CN, label=图5, caption=不同转折角度下热侧流体速度流线分布云图, figureFileSmall=bBpg8M8PS4AQSy9pwv7ttw==, figureFileBig=geFDwzeUYXzu9bmja1I7qw==, tableContent=null), ArticleFig(id=1295065219903017394, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1295065208536453457, language=EN, label=Fig.6, caption=Velocity streamline diagram of three channels at the X=130 mm cross-section, 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interaction between turning angle and the number of turning cycle on the value of the comprehensive factor K/ΔP (D=1.5mm), figureFileSmall=GITpmqwbopNuPIBX1pKTow==, figureFileBig=A7tlO6VYzWvrKrtBl11/yw==, tableContent=null), ArticleFig(id=1295065224483197384, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1295065208536453457, language=CN, label=图15, caption=转折角度与转折周期数交互作用对综合因子K/ΔP值的响应曲面（D=1.5 mm）, figureFileSmall=GITpmqwbopNuPIBX1pKTow==, figureFileBig=A7tlO6VYzWvrKrtBl11/yw==, tableContent=null), ArticleFig(id=1295065224856490441, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1295065208536453457, language=EN, label=Tab.1, caption=

Model reliability verification

, figureFileSmall=null, figureFileBig=null, tableContent=
项目实验值[11]模拟值误差/%
冷通道压降ΔPc/Pa32 40030 649.35.40
热通道压降ΔPh/Pa47 00052 048.410.47
冷通道温差ΔTc/K253.1274.68.49
热通道温差ΔTh/K330.3300.029.17
), ArticleFig(id=1295065224919405002, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1295065208536453457, language=CN, label=表1, caption=

模型可靠性验证

, figureFileSmall=null, figureFileBig=null, tableContent=
项目实验值[11]模拟值误差/%
冷通道压降ΔPc/Pa32 40030 649.35.40
热通道压降ΔPh/Pa47 00052 048.410.47
冷通道温差ΔTc/K253.1274.68.49
热通道温差ΔTh/K330.3300.029.17
), ArticleFig(id=1295065225263337931, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1295065208536453457, language=EN, label=Tab.2, caption=

Factors and levels of the response test

, figureFileSmall=null, figureFileBig=null, tableContent=
水平因素
A-通道直径D/mmB-转折角度α/（°）C-转折周期数N/个
–11.056
01.5158
12.03010
), ArticleFig(id=1295065225661796813, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1295065208536453457, language=CN, label=表2, caption=

响应试验因素及水平

, figureFileSmall=null, figureFileBig=null, tableContent=
水平因素
A-通道直径D/mmB-转折角度α/（°）C-转折周期数N/个
–11.056
01.5158
12.03010
), ArticleFig(id=1295065226106393038, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1295065208536453457, language=EN, label=Tab.3, caption=

Main factor analysis response surface table for the PCHE

, figureFileSmall=null, figureFileBig=null, tableContent=
序号通道直径D/mm转折角度α/（°）转折周期数N/个K/（W·（m2·K）–1）K/ΔP/（W·（m2·K·Pa）–1）
11.0581 128.6610.038 9
22.058467.0300.284 4
31.03081 308.3990.020 4
42.0308538.0340.149 7
51.01561 148.8100.034 1
62.0156973.6570.505 7
71.015101 151.0370.032 7
82.01510474.6740.238 1
91.556691.6980.123 4
101.5306838.3720.075 1
111.5510738.6050.131 8
121.53010769.3620.059 8
131.5158703.3200.106 8
141.5158703.3200.106 8
151.5158703.3200.106 8
161.5158703.3200.106 8
171.5158703.3200.106 8
), ArticleFig(id=1295065226550989263, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1295065208536453457, language=CN, label=表3, caption=

PCHE主因素分析响应曲面

, figureFileSmall=null, figureFileBig=null, tableContent=
序号通道直径D/mm转折角度α/（°）转折周期数N/个K/（W·（m2·K）–1）K/ΔP/（W·（m2·K·Pa）–1）
11.0581 128.6610.038 9
22.058467.0300.284 4
31.03081 308.3990.020 4
42.0308538.0340.149 7
51.01561 148.8100.034 1
62.0156973.6570.505 7
71.015101 151.0370.032 7
82.01510474.6740.238 1
91.556691.6980.123 4
101.5306838.3720.075 1
111.5510738.6050.131 8
121.53010769.3620.059 8
131.5158703.3200.106 8
141.5158703.3200.106 8
151.5158703.3200.106 8
161.5158703.3200.106 8
171.5158703.3200.106 8
), ArticleFig(id=1295065226928476624, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1295065208536453457, language=EN, label=Tab.4, caption=

Regression analysis table of the overall heat transfer coefficient K

, figureFileSmall=null, figureFileBig=null, tableContent=
方差来源平方和自由度均方F值P值显著性
模型9.190×10591.020×10510.080 00.003 0***
A-通道直径6.520×10516.520×10564.300 0<0.000 1***
B-转折角度2.290×10412.290×1042.261 00.176 4
C-转折周期3.370×10413.370×1043.320 00.111 2
AB2.956×10312.956×1030.291 60.605 9
AC6.280×10416.280×1046.196 00.041 7**
BC3.359×10313.359×1030.331 40.582 9
A21.180×10511.180×10511.640 00.011 3**
B24.348×10214.348×1020.042 90.841 8
C21.850×10411.850×1041.829 00.218 3
残差7.100×10471.010×104
失拟项7.100×10432.370×104
误差040
总相关性9.900×10516
), ArticleFig(id=1295065227352101329, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1295065208536453457, language=CN, label=表4, caption=

总换热系数K回归方差分析

, figureFileSmall=null, figureFileBig=null, tableContent=
方差来源平方和自由度均方F值P值显著性
模型9.190×10591.020×10510.080 00.003 0***
A-通道直径6.520×10516.520×10564.300 0<0.000 1***
B-转折角度2.290×10412.290×1042.261 00.176 4
C-转折周期3.370×10413.370×1043.320 00.111 2
AB2.956×10312.956×1030.291 60.605 9
AC6.280×10416.280×1046.196 00.041 7**
BC3.359×10313.359×1030.331 40.582 9
A21.180×10511.180×10511.640 00.011 3**
B24.348×10214.348×1020.042 90.841 8
C21.850×10411.850×1041.829 00.218 3
残差7.100×10471.010×104
失拟项7.100×10432.370×104
误差040
总相关性9.900×10516
), ArticleFig(id=1295065227431793106, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1295065208536453457, language=EN, label=Tab.5, caption=

Regression variance analysis table of K/ΔP

, figureFileSmall=null, figureFileBig=null, tableContent=
方差来源平方和自由度均方F值P值显著性
模型0.206 6090.022 957.9840.006 053***
A-通道直径0.138 3010.138 3048.1000.000 224***
B-转折角度0.009 3510.009 353.2530.114 300
C-转折周期0.009 5210.009 503.3100.111 700
AB0.003 3710.003 371.1740.314 600
AC0.017 7310.017 736.1660.042 020**
BC0.000 1410.000 140.0490.830 900
A20.015 5710.015 575.4160.052 820*
B20.008 2610.008 262.8740.133 900
C20.005 1610.005 161.7960.222 100
残差0.020 1370.002 88
失拟项0.020 1330.006 71
误差040
总相关性0.226 7016
), ArticleFig(id=1295065227809280467, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1295065208536453457, language=CN, label=表5, caption=

K/ΔP的回归方差分析表

, figureFileSmall=null, figureFileBig=null, tableContent=
方差来源平方和自由度均方F值P值显著性
模型0.206 6090.022 957.9840.006 053***
A-通道直径0.138 3010.138 3048.1000.000 224***
B-转折角度0.009 3510.009 353.2530.114 300
C-转折周期0.009 5210.009 503.3100.111 700
AB0.003 3710.003 371.1740.314 600
AC0.017 7310.017 736.1660.042 020**
BC0.000 1410.000 140.0490.830 900
A20.015 5710.015 575.4160.052 820*
B20.008 2610.008 262.8740.133 900
C20.005 1610.005 161.7960.222 100
残差0.020 1370.002 88
失拟项0.020 1330.006 71
误差040
总相关性0.226 7016
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超临界二氧化碳储能系统印刷线路板式换热器的传热-流阻解耦优化
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袁淑霞 , 辛蕊 , 吴松 , 杨坤 , 李铮 , 朱宗栋
热力发电 | 新型发电技术 2026,55(3): 138-149
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热力发电 |新型发电技术 2026 , 55 (3) : 138 -149
超临界二氧化碳储能系统印刷线路板式换热器的传热-流阻解耦优化
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袁淑霞 , 辛蕊 , 吴松, 杨坤, 李铮, 朱宗栋
作者信息
  • 西安石油大学机械工程学院，陕西 西安 710065
通讯作者:
辛蕊（1999），女，硕士研究生，主要研究方向为二氧化碳储能技术，。
作者简介:

袁淑霞（1977），女，博士，教授，研究生导师，主要研究方向为传质传热、多项流动、分离、二氧化碳储能、清洁燃烧技术，。

Heat transfer-flow resistance decoupling optimization for a printed circuit heat exchanger in supercritical carbon dioxide energy storage system
Shuxia YUAN , Rui XIN , Song WU, Kun YANG, Zheng LI, Zongdong ZHU
Affiliations
  • School of Mechanical Engineering, Xi’an Shiyou University, Xi’an 710065, China
出版时间: 2026-03-25 doi: 10.19666/j.rlfd.202506103
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摘要
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【目的】

为提升二氧化碳储能系统换热器效率，以太阳盐和超临界二氧化碳（S-CO2）作为冷、热侧流体，研究其在印刷线路板式换热器（printed circuit heat exchanger，PCHE）中的流动传热性能。

【方法】

选取通道直径、转折角度、转折周期数为自变量，以总换热系数K、换热系数与压降比K/ΔP为响应值，采用数值模拟结合响应曲面法，分析自变量及交互作用的影响并优化参数。

【结果】

在通道直径1.0~2.0 mm、转折角度5~30°、转折周期数6~10的范围内，减小通道直径、增大转折角度及转折周期数可提升换热效率；通道直径对K和K/ΔP影响极显著，其与转折周期数的交互作用也显著；确定K最优参数（直径1.003 mm、转折角度29.71°、转折周期数9.935时，K高达1 313W/（m2·K））、K/ΔP最优参数（直径2.0 mm、转折角度9.407°、转折周期数6时，K/ΔP达0.453 7W/（m2·K·Pa））；PCHE尺寸较传统管壳式换热器缩小约1/10。

【结论】

该研究证实了在Z型PCHE中，通道直径、转折角度和转折周期数的改变会影响换热性能，而响应曲面法可有效地优化通道结构参数来提升换热性能。并且PCHE在二氧化碳储能系统中紧凑性优势显著。

二氧化碳储能系统  /  熔盐  /  印刷电路板式换热器  /  响应曲面法
[Objective]

To enhance the heat exchanger efficiency in a carbon dioxide energy storage system, a printed circuit heat exchanger (PCHE) was employed as the core heat transfer component, with binary nitrate molten salt (solar salt) serving as the cold-side fluid and supercritical carbon dioxide (S-CO2) as the hot-side fluid. This study aims to investigate the key factors influencing the internal heat transfer process in PCHE and optimize the dominant structural parameters governing its thermal performance, thereby addressing the performance bottlenecks of heat exchangers in such energy storage systems.

[Methods]

Three key structural parameters of the Zigzag PCHE, such as channel diameter, turning angle, and number of turning cycles, were selected as independent variables. The overall heat transfer coefficient K (a core indicator of heat transfer capacity) and the ratio of the overall heat transfer coefficient to pressure drop K/ΔP (a key metric for evaluating the trade-off between heat transfer and flow resistance) were designated as response variables. A three-factor, three-level response surface methodology (RSM) was established to quantitatively analyze the effects of the three structural parameters and their pairwise interactions on the response variables. Parameter optimization of the heat exchange channels was subsequently performed based on the analytical results.

[Results]

Within the specified parameter ranges (channel diameter: 1.0~2.0 mm, turning angle: 5°~30°, number of turning cycles: 6~10), the results indicate that reducing the channel diameter, increasing the turning angle, or increasing the number of turning cycles can effectively improve the heat transfer efficiency of the Zigzag PCHE. Statistical analysis shows that the channel diameter has a highly significant impact on both K and K/ΔP, and the interaction between the channel diameter and the number of turning cycles also significantly influences these two response variables. The optimal parameter set for achieving the maximum K value (1 313 W/(m2·K)) was determined to be a channel diameter of 1.003 mm, a turning angle of 29.71°, and 9.935 turning cycles. Furthermore, the optimal combination for the comprehensive performance factor K/ΔP was found to be a channel diameter of 2.0 mm, a turning angle of 9.407°, and 6 turning cycles, yielding a K/ΔP value of 0.453 7 W/(m2·K·Pa) and a corresponding K value of 801.7 W/(m2·K). A comparative analysis reveals that the optimized PCHE volume is reduced by approximately one-tenth compared to conventional shell-and-tube heat exchangers.

[Conclusion]

This study confirms that variations in the channel diameter, turning angle, and number of turning cycles significantly affect the thermal performance of zigzag PCHEs. The response surface methodology proves effective in optimizing the channel structural parameters to enhance heat transfer performance. Moreover, PCHEs demonstrate remarkable compactness advantages in CO2 energy storage systems, making them well-suited for space-constrained operational environments. The findings provide reliable theoretical and data-driven support for the rational selection and engineering design of heat exchangers in related fields.

carbon dioxide energy storage system  /  molten salt  /  printed circuit heat exchanger  /  response surface method
袁淑霞, 辛蕊, 吴松, 杨坤, 李铮, 朱宗栋. 超临界二氧化碳储能系统印刷线路板式换热器的传热-流阻解耦优化. 热力发电, 2026 , 55 (3) : 138 -149 . DOI: 10.19666/j.rlfd.202506103
Shuxia YUAN, Rui XIN, Song WU, Kun YANG, Zheng LI, Zongdong ZHU. Heat transfer-flow resistance decoupling optimization for a printed circuit heat exchanger in supercritical carbon dioxide energy storage system[J]. Thermal Power Generation, 2026 , 55 (3) : 138 -149 . DOI: 10.19666/j.rlfd.202506103
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目前，二氧化碳储能系统中常用的换热介质主要包括水和导热油。水具有高热容与高传热系数等优点，但高温换热需要在高压或超临界状态下进行，这对材料性能提出了挑战；导热油虽然具有优良的传热性能和较低的工作压力，但在高温下易分解，可能导致安全隐患。矿物油型导热油的使用温度一般在320 ℃以下，合成型导热油的使用温度则不超过350 ℃，而在基于布雷顿循环的二氧化碳电热储能（electrothermal CO2 energy storage，ET-CES）系统中，CO2温度需升高至400 ℃以上，此时导热油已无法满足换热需求。因此，需引入一种可适用于更高温度的蓄热介质——熔盐。
熔盐一般指无机盐或其混合物的熔融液体，如硝酸盐、氯化盐、碳酸盐以及硫酸盐等[1]。这些熔盐具备宽广的使用温度范围、低蒸汽压、低黏度、低成本、易获取等优点，在高温换热系统中展现出广泛的应用潜力[2]。普通换热器难以适应超临界二氧化碳（S-CO2）的高温高压环境，印刷电路板式换热器（printed circuit heat exchanger，PCHE）凭借其紧凑结构、高效换热、耐高温高压和耐腐蚀等特点，成为熔盐与S-CO2高温换热的理想选择。
近年来，针对不同流道结构的PCHE换热优化研究逐渐增多，主要涉及流道形式、工况和结构等。Chu等人[3]以S-CO2与水为换热工质，研究了直通道型PCHE的换热性能；Ngo等人[4]通过实验研究了以CO2为工质的Z型和S型2种流道PCHE的热工水力特性；Kim等人[5]建立了S-CO2的Z型PCHE的三维模型，并将数值模拟结果与Ishizuka等人[6]的实验结果进行了对比；Meshram等人[7]通过建立直线型和Z型通道PCHE的一维模型，模拟计算并拟合了努塞特数与摩擦因子间的关系式；Fu等人[8]以S-CO2和熔盐作为换热工质，分析了一种翼型翅片通道和直通道组合型PCHE的换热特性；Shi等人[9]构建了翼型PCHE三维数值模型对在4 000~20 500的雷诺数和300~600 ℃的温度范围内，研究熔盐与S-CO2在翼型通道PCHE内的传热及流动摩擦性能；Wang等人[10]设计并制造了一种翼形PCHE，并研究了熔盐在翼型通道内的对流换热特性；张虎忠[11]以S-CO2布雷顿循环为基础，采用数值模拟方法对以S-CO2分别与S-CO2和水为工质的PCHE进行研究；Baik等人[12]以S-CO2与液化天然气（liquefied natural gas，LNG）为工质，数值模拟了不同振幅和波长对波纹形PCHE的热工水力性能的影响；Zhou等人[13]采用PCHE作为CO2布雷顿循环系统中的预热器，将CO2/丁烷、CO2/丙烷和CO2/氙的混合物用作冷流体，熔盐用作热流体，对不同工况下混合熔盐相变换热器的热工水力特性进行了数值分析；李占英等[14]建立了S-CO2布雷顿循环回热器PCHE的动态仿真模型，研究不同冷、热侧入口温度以及流量对换热的影响；Guo等人[15]以S-CO2布雷顿循环为基础，对PCHE回热器采用分段式设计；姚业成等[16]研究了熔盐与S-CO2在Z型PCHE流道内的流动和换热特性，并对其结构进行了优化；纪宇轩[17]以S-CO2为工质，研究了一种新的梯型流道结构PCHE，并与直线型、Z型和S型流道进行对比，分析了4种结构的耦合传热和压降损失特性；Lee等人[18]选取半圆形、矩形、梯形和圆形4种通道截面来研究Z型通道截面形状对流动传热性能的影响；Xu等人[19]以S-CO2为工质，研究了矩形、倒圆角矩形、椭圆形和翼型4种不连续的肋片结构对PCHE热工水力性能的影响；Wang等人[20]设计了一种翼型PCHE，并以熔盐和导热油作为工质将其应用于太阳能发电系统中，同时将结果与现有直线型和Z型流道传热性能进行了对比。
根据以上文献调研结果发现，现有研究以采用控制变量法研究单个因素对换热性能的影响为主，事实上，换热性能是多个因素耦合作用的结果。鉴于现有控制变量法的局限性，本文选择Z型通道的PCHE作为CO2储能换热器，采用响应曲面法（response surface methodology，RSM），以太阳盐为冷流体、S-CO₂为热流体，研究基于PCHE的CO₂储能系统换热过程，选取3种通道结构参数作为自变量，考虑因素的交互作用，进行多因素耦合影响下的PCHE结构优化，以提高CO₂储能换热器的换热效率。
1　模型及方法
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1.1　几何模型
PCHE由多个相同的板片堆叠组成，若假设冷、热流体在各通道内均匀分配，则各通道结构和流动情况具有周期性，可以选取一个典型的冷热通道进行分析。通道在X轴的投影长度为260 mm，其中包括进、出口各10 mm的延长段（稳定流体流动，防止回流）。通道结构及尺寸示意如图1所示。
1.2　流动及传热模型
采用计算流体动力学软件Fluent对PCHE换热性能进行数值模拟。流体流动及换热过程遵循质量守恒方程、动量守恒方程和能量守恒方程：
∂∂t(ρ)+∇⋅(ρu→)=0
∂∂t(ρu→)+∇⋅(ρu→iu→)=∇⋅(μ⋅gradu→i)−∇p+Si
式中：ρ为流体密度，kg/m3；t为时间，s；u→为流体速度矢量，m/s；Si为源项，i=1，2，3。
∂(ρu→icPT)∂xi=∂∂xi(λ∂T∂xj)+ST
式中：cp为比热容，J/（kg·K）；T为温度，K；ST为黏性耗散项，W/m3。
1.3　换热经典数学模型
1）能量平衡
mccpc(Tc,out−Tc,in)=mhcph(Th,in−Th,out)
式中：mc、mh分别为冷、热流体的质量流量，kg/s；cpc、cph分别为冷、热流体的比热容，J/（kg·K）。
2）总换热系数K
K=QAΔT
式中：Q为换热量，W；A为换热面积，m2；ΔT为对数平均温差，K。
ΔT=ΔTin−ΔToutln(Tin/Tout)
式中：ΔTin为入口侧的冷、热流体温差，K；ΔTout为出口侧的冷热流体温差，K。
ΔTin=ΔTin,hot−ΔTout,cold
ΔTout=ΔTout,hot−ΔTin,cold
式中：下标hot、cold分别表示热、冷侧流体。
3）压降
ΔP=Pin−Pout
式中：Pin为流体进口压力，MPa；Pout为流体出口压力，MPa。
1.4　材料及边界条件
本文采用不锈钢作为固体材料，S-CO2作为热流体，太阳盐（0.6NaNO3-0.4KNO3）[21]作为冷流体进行换热。由于RNG k-ε模型能充分考虑涡对流动的影响、计算精度高且在熔盐换热中结果更接近实验值[22]，所以选用该模型作为湍流模型。设置通道外壁面互为2组周期性边界，两端进、出口延长段以及进、出口外壁面为绝热，其余为流体与固体耦合壁面，设置为Couple。速度-压力耦合采用SIMPLE算法，均设置为二阶迎风离散格式。冷、热流体逆向流动，均采用质量入口、压力出口。
在确定进、出口参数时考虑以下几点：
1）确保热侧流体放出的热量等于冷侧流体吸收的热量，以满足能量守恒定律；
2）结合二氧化碳储能系统的储能与释能2个过程，确保冷、热两侧的进、出口温度差保持一致；
3）保证整个系统中熔盐温度在其熔点（496.15 K）以上。
结合以上要求，确定了冷、热流体的进、出口参数为：冷流体（太阳盐）进口温度503 K，进口质量流量0.188 g/s，出口压力0.1 MPa；热流体（S-CO2）进口温度823 K，进口质量流量0.24 g/s，出口压力10 MPa。
1.5　网格无关性及可靠性验证
对建立的PCHE通道进行网格划分，并设置第1层为0.01 mm、增长率为1.2的边界层，边界层总厚度为0.053 7 mm。为避免由于网格本身特性造成的计算结果差异，根据前文所述物性及边界条件对模型进行网格无关性验证。分别以通道的总换热系数和冷、热侧通道的平均压降作为评判标准，结果如图2所示，最终选择第4套网格（2 171 076）作为后续计算的网格数。
此外，将模拟结果与已发表的CO2在Z型PCHE中换热的实验数据[11]进行对比，结果见表1。由表1可知，模拟值与实验值的最大误差为10.74%，在可接受范围，证明本文模型可靠。
1.6　响应曲面分析法
响应曲面分析法是一种高效的统计优化技术，适用于多变量系统的建模与优化。与控制变量法相比，该方法不仅能研究各因素对结果的影响规律，而且可以得到因素交互作用对结果的影响以及显著性，并最大限度地减少试验数量，节省时间和成本[23]；与传统正交实验方法相比，该方法能准确描述变量与响应值之间复杂的非线性关系。本文方差分析所用公式如下：
1）平方和
ST=∑i=1n(yi−y¯)2
式中：yi为第i个观测值；y-为所有测值的均值；n为观测值的总数。
2）自由度
dT=n−1
式中：n为样本的数量。
3）均方
MT=STdT
4）F值
F值用于检验模型或因素的显著性：
F=MMME
式中：MM为模型均方；ME为残差均方。
本文以Z型PCHE的通道直径D、转折角度α和转折周期数N为自变量，分别以总换热系数K和综合换热系数与压降的比值K/ΔP作为响应值，进行响应面分析，表2为响应试验因素及水平。
2　计算结果及分析
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2.1　通道直径对PCHE热侧流体流动特性及换热特性的影响
图3为垂直于流动方向的横截面（X=130 mm）上的流体速度与温度分布云图，此时通道转折角度α=15°，转折周期数N=8。由图3可以看出，3种通道直径的流体速度有明显区别，通道直径越小，速度梯度变化越大。这是由于在小直径通道内，流速增加，流体更容易达到湍流状态，从而使边界层厚度减小，流体的热量被很快带走，促进通道内的热量传递，增强了换热过程。所以D=1.0 mm时截面的温度梯度小，温度分布均匀。
图4为相应的通道总换热系数K沿程变化规律。Z型PCHE的周期性结构导致流体流速在流动方向上也呈周期性变化，且局部速度梯度变化剧烈，换热系数变化明显。图4显示，通道直径越大，总换热系数K越小，且变化范围越小。这是因为在Z型PCHE大直径通道中，通道的几何结构对流体流动状态影响较小，所以不会引起换热系数大幅波动。综合分析温度速度云图与总换热系数沿程变化曲线可知，在所选范围内，当通道直径D=1.0 mm时换热性能最优。
2.2　转折角度对PCHE热侧流体流动特性及涡流演化的影响
当通道直径D=1.5 mm，转折周期数N=10时，转折角度分别为5°、15°和30°时的热侧流体速度流线分布如图5所示。
由图5可以看出，转折角度的变化导致流体流动方向发生改变，惯性的存在使流体在转弯处产生二次流，并在离心力作用下，部分区域流体速度梯度增大，流速变化明显。当转折角度为5°时，通道趋近于直通道，流速波动小，流线比较规则，流动方向与通道方向一致，表明流体流动状态相对稳定，但流体扰动小不利于对边界层的破坏，换热效果差。随着转折角度的增大，流体的不规则运动越来越明显。当转折角度增大到30°时，流体速度开始剧烈变化，并且流体内部扰动强烈，出现复杂状态的流动，这能有效破坏热边界层，有利于换热。
图6为上述3种通道在同一截面（X=130 mm）处的速度流线图。由图6可知：转折角度为5°截面上的速度较低，在截面的中心轴线上，形成了2个不明显的涡结构，不利于热量的传递；转折角度为15°截面上整体平均速度有所提高，并出现了较明显的两个涡流，但涡强度较小，不能充分破坏边界层，换热能力较前者有所增加；转折角度为30°时通道截面内存在明显高速度区，形成了明显的涡结构，更接近卡门涡街的特征，这些交替脱落的涡流能很大程度地增加流体扰动，破坏热边界层，促进热量传递。因此，在所选范围内，当转折角度α=30°时通道换热性能最优。
2.3　转折周期数对PCHE热侧流体流动特性及涡流演化的影响
当通道直径D=1.0 mm、转折角度α=15°时，转折周期数N分别为6、8、10的通道在同一截面处（图7）的速度流线与温度分布云图如图8所示。图8中转折周期数N=6和N=8在截面处存在明显的高温区，温度从中心向外呈环状递减，且热量在中心聚集，向外传递不够充分，换热效果不太理想。这2种情况下的截面涡形状不够明显，虽在一定程度上增加了流体的扰动，但作用不大。N=10的高温区范围较小且较分散，整体上温度分布更均匀。通道截面处的流动更复杂，有明显的不对称和不规则涡流，使流体扰动增强，能更有效地破坏热边界层，使流体混合更充分，从而增强热量传递。因此，N=10时更利于热量的充分传递，实现高效换热。
图9显示了当转折周期数N为6、8、10时的冷、热侧通道进出口压降。
由图9可以看出，当转折周期数N增加时，进出口压降明显增加。这会使流体在流动中不断改变速度，产生局部涡流和剪切应力，导致流动阻力增大。转折周期数N的增加也会使流动过程中边界层被破坏和重建的次数增多，从而增加流体与壁面的摩擦力。
3　响应曲面分析及优化
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为研究各因素对PCHE换热性能的影响程度，得到其主影响因素，并分析各交互作用的影响，建立通道直径、转折角度和转折周期数的响应曲面分析表。采用前述数值模拟方法对表中不同组合参数的PCHE流动及换热性能进行数值模拟，以通道总换热系数K和换热系数与压降的比值K/ΔP作为响应值，进行响应曲面分析，各工况下的计算结果见表3。
表3中的17组模型均设置质量入口和压力出口：冷侧入口温度为503 K，进口质量流量0.188 g/s，出口压力为0.1 MPa；热侧入口温度取823 K，进口质量流量0.24 g/s，出口压力为10 MPa。
3.1　通道总换热系数K的方差及响应曲面分析
总换热系数K的回归方差分析见表4。其中：P<0.01为极显著，表示为“***”；P<0.05为显著，表示为“**”；P<0.10为较显著，表示为“*”[23]。
从表4可以看出，通道直径对总换热系数K的影响表现为极显著，通道直径与转折周期数协同作用对总换热系数K表现为显著。此外，A2的P值为0.011 3，小于0.05，表现为显著，表示通道直径的二次项效应对总换热系数K存在显著影响。即通道直径与总换热系数K之间存在非线性关系，且这种非线性关系不因随机因素产生。其余因素表现为不显著。可以通过P值大小判断出各因素对总换热系数K的影响程度：通道直径>转折周期数>转折角度。
图10为通道直径与转折角度协同作用对总换热系数K的响应曲面图，此时转折周期数为8个。由图10可以看出：总换热系数K随通道直径的减小而显著增加（从约550 W/（m2·K）增加到1 210 W/（m2·K）），而随转折角度的增大增加缓慢，约在通道直径为1.0 mm且转折角度为30°时取得最大值。
图11为通道直径与转折周期数交互作用对总换热系数K的响应曲面，此时转折角度为15°。由图11可知当转折周期数与通道直径同时作用时，总换热系数K随转折周期数的变化与通道直径有密切的关系：通道直径较小时，转折周期数的增加会使总换热系数K增大；而当通道直径较大时，转折周期数的增加会使总换热系数K减小。这是因为当通道直径较小时，转折周期数增加会使流体在通道内流动时更频繁地改变方向，在此过程中会使流体产生扰动，打破层流边界层，增强流体的湍流程度，从而增大流体与壁面间的对流换热系数，使总换热系数K增大。
图12为转折角度与转折周期数交互作用对总换热系数K的响应曲面图，此时通道直径为1.5 mm。由图12可知，总换热系数K均随着二者的增大而增大，转折周期数的影响比转折角度大，但总换热系数K的变化趋势都很小。
综上所述，当转折角度分别与另外两个因素交互作用时，对总换热系数K的影响均占主导地位。从响应曲面图可以得到这3种因素对通道总换热系数K的影响从大到小分别是：通道直径、转折周期数、转折角度。结合图10—图12和表4可以得出，当通道直径为1.003 mm、转折角度为29.71°、转折周期数为9.935时，总换热系数K可达到最大，即1 313 W/（m2·K）。
3.2　 K/ΔP的方差及响应曲面分析
总换热系数K与通道冷、热侧平均压降的比值K/ΔP的回归方差分析见表5。其中：P<0.01为极显著，表示为“***”；P<0.05为显著，表示为“**”；P<0.10为较显著，表示为“*”[24]。
从表5可以看出，通道直径对K/ΔP影响的P值表现为极显著，通道直径与转折周期数协同作用表现为显著，A2的P值表现为较显著，其余因素为不显著。通过P值大小可判断各因素对K/ΔP的影响程度为：通道直径>转折角度>转折周期数。
图13为当通道直径与转折角度交互作用且转折周期数N=8时，综合因子K/ΔP值的响应曲面。
由图13可以看出，综合因子K/ΔP值与通道直径的变化明显成正比。这是由于通道直径增大会使流速降低，流体的流动阻力随之降低，所以K/ΔP值增大。当转折角度较小时，K/ΔP值较大，此时大的转折角度会使流体流动方向大幅度改变，增加流动阻力，导致压降增加，从而使K/ΔP变小。
图14为当通道直径与转折周期数同时作用且转折角度为15°时，综合因子K/ΔP值的响应曲面。由图14可以看出，通道直径越大，K/ΔP值越大。这是由于通道直径增大会使流体流速降低，流动状态相对稳定，流动阻力减小，而转折周期数增加会使流动阻力增大，此时通道直径的变化对K/ΔP值的影响大，所以在转折周期数较小、通道直径较大时，K/ΔP可以取得最大值。
图15为当转折周期与转折角度同时作用且通道直径为1.5 mm时，综合因子K/ΔP值的响应曲面。由图15可以看出，K/ΔP值随转折角度的增大而减小，而转折周期数对其几乎没有影响。当转折周期数较小时，K/ΔP值较大，这是因为小的转折周期数会减少流体在通道内的转折，进一步减少了因流动方向改变而产生的局部阻力损失。
综上所述，在研究范围，对通道综合因子K/ΔP的影响从大到小分别是：通道直径、转折角度和转折周期数。结合图13—图15和表5可以得出，当通道直径为2.0 mm、转折角度为9.407°、转折周期数为6时，K/ΔP最高可达0.453 7 W/（m2·K·Pa）。
4　经济性分析
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中国科学院工程热物理研究所[25]设计加工了百千瓦级PCHE缩比样机。研究表明，在相同热负荷条件下，PCHE的体积大约为管壳式换热器的1/5。中国船舶重工集团公司七二五所[26]自主研发的用于5 MW超临界二氧化碳发电试验平台的PCHE，在相同热负荷下体积和重量约为传统管壳式换热器的1/6。周宇[27]得出在相同的热负荷下PCHE体积仅为传统管式换热器的1/5。韩俊杰[28]提出PCHE的单位体积换热能力远优于传统列管式换热器，且尺寸缩小了1/10。
以文中3种通道直径为例，假设S-CO2侧的质量流量为40 kg/s，当通道直径D=1.0 mm时，计算得到PCHE尺寸为614 mm×818 mm×260 mm；当D=1.5 mm时，PCHE尺寸为923 mm×1 230 mm×260 mm；当D=2.0 mm时，PCHE尺寸约为1 227 mm×1 636 mm×260 mm。同时，计算得到相同S-CO2质量流量下传统管壳式换热器的尺寸为φ850 mm×6 000 mm。对比发现，PCHE的尺寸比传统管壳式换热器缩小了约1/10。
从以上研究及产品可以看出，在二氧化碳相关领域中，PCHE可节约极大的占地空间和设备成本，具有显著优势。
5　结论
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本文以二氧化碳储能系统为基础，研究储能阶段换热部分S-CO2与储能介质熔盐在Z型通道PCHE中的传热，并以通道直径、转折角度及转折周期数为自变量，以通道总换热系数K和综合换热系数与压降的比值K/ΔP为因变量，建立了三水平三因素的正交实验，探究通道参数交互作用对熔盐与S-CO2间换热的影响，并寻找主要影响因素。结论如下：
1）在所选范围内，通道换热效率随通道直径的减小、转折角度的增加和转折周期数的增加而增大，但影响程度不同。
2）在3种通道结构参数范围内，各因素对总换热系数K的影响显著性排序为：通道直径>转折周期数>转折角度。其中，通道直径与转折周期数存在显著的交互效应。通过响应曲面法与回归方差分析发现，当通道结构参数为通道直径1.003 mm、转折角度29.71°、转折周期数9.935时，总换热系数K可达到峰值，1 313 W/（m2·K）。
3）在本研究参数范围内，通道结构参数对总换热系数与压降比K/ΔP的影响程度排序为：通道直径>转折角度>转折周期数。基于响应曲面分析与方差分析，得到使K/ΔP值最大化的最优结构参数为：通道直径2.0 mm、转折角度9.407°、转折周期数6，此时K/ΔP峰值为0.453 7 W/（m2·K·Pa），总换热系数K也维持在较高水平，为801.7 W/（m2·K）。
基金
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  • 陕西省自然科学基础研究计划项目(2024JC-YBMS-368; 2025JC-YBMS-425)
文献
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2026年第55卷第3期
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doi: 10.19666/j.rlfd.202506103
  • 接收时间：2025-06-19
  • 首发时间：2026-08-14
  • 出版时间：2026-03-25
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  • 收稿日期：2025-06-19
  • 修回日期：2025-07-07
  • 录用日期：2025-07-21
基金
Natural Science Foundation Research Project of Shaanxi Province(2024JC-YBMS-368; 2025JC-YBMS-425)
陕西省自然科学基础研究计划项目(2024JC-YBMS-368; 2025JC-YBMS-425)
作者信息
    西安石油大学机械工程学院，陕西 西安 710065

通讯作者:

辛蕊（1999），女，硕士研究生，主要研究方向为二氧化碳储能技术，。
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鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
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