Article(id=1295068255320830655, tenantId=1146029695717560320, journalId=1210938733613449225, issueId=1295068190569164906, articleNumber=null, orderNo=null, doi=10.19666/j.rlfd.202509009, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1756656000000, receivedDateStr=2025-09-01, revisedDate=1760630400000, revisedDateStr=2025-10-17, acceptedDate=1762272000000, acceptedDateStr=2025-11-05, onlineDate=1786697933272, onlineDateStr=2026-08-14, pubDate=1782316800000, pubDateStr=2026-06-25, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1786697933272, onlineIssueDateStr=2026-08-14, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1786697933272, creator=13701087609, updateTime=1786697933272, 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=144, endPage=153, ext={EN=ArticleExt(id=1295068257166324416, articleId=1295068255320830655, tenantId=1146029695717560320, journalId=1210938733613449225, language=EN, title=Experimental study on convective heat transfer characteristics of supercritical carbon dioxide in horizontal-vertical L-shaped turning tube, columnId=1211002405299294959, journalTitle=Thermal Power Generation, columnName=Thermal energy science research, runingTitle=null, highlight=null, articleAbstract=
[Objective]

In practical energy and chemical engineering systems, pipeline layouts often exhibit complex multi-directional configurations due to equipment arrangement, spatial constraints, and process requirements, rather than simple straight horizontal or vertical sections. This is particularly evident in applications such as compact heat exchangers for supercritical carbon dioxide (S-CO2) Brayton cycles, nuclear reactor cooling circuits, and chemical transport pipelines, where the working fluid frequently undergoes abrupt changes in flow direction. Among these configurations, the L-shaped bend, a classic directional-changing structure that connects horizontal and vertical pipe sections, is especially common and plays a crucial role in achieving spatial redirection of the working fluid. Therefore, investigating the heat transfer characteristics of S-CO2 in L-shaped bends is of significant importance. This study aims to investigate the effect of buoyancy-induced density stratification in a heated horizontal section on the subsequent heat transfer in a vertical upward flow under different experimental parameters.

[Methods]

An experimental system with high expandability was established, featuring a single-cycle S-CO2 heat transfer test platform utilizing stainless steel circular pipes with adjustable lengths and bend angles. Experiments were conducted to study the flow and heat transfer characteristics of S-CO2 inside a horizontal-to-vertical L-shaped turning pipe.

[Results]

The experimental results reveal two distinct types of “asymmetric heat transfer deterioration” in the turning pipe: one characterized by asymmetry in the severity of deterioration, and the other by asymmetry in its location. When the wall heat flux is increased, wall temperature peaks indicating heat transfer deterioration appear in the vertical section, with unequal peak values on the two sides, representing asymmetry in severity. A further increase in wall heat flux shifts the deterioration position toward the inlet, while the enthalpy at which deterioration initiates remains unchanged, indicating that the wall heat flux does not affect the onset enthalpy of deterioration. When the heat flux is raised sufficiently for the deterioration to advance to the inlet of the vertical section, the wall temperature peak on the inner side occurs earlier than that on the outer side, demonstrating asymmetry in the location of deterioration.

[Conclusion]

The study demonstrates that asymmetry in severity originates from non-uniform cross-sectional mass flow distribution caused by temperature stratification extending from the horizontal section. In contrast, asymmetry in location occurs under high-temperature and high-heat-flux conditions due to the earlier fulfillment of deterioration criteria within the inner-side boundary layer. This research elucidates the coupling effect between buoyancy and flow redirection in L-shaped pipes, providing an experimental basis for the design of related heat exchange equipment.

, authors=Siyuan FENG, Banghui ZHANG, Zhennan LIU, Ming GAO, Yan REN, Qiguo YANG, authorsList=Siyuan FENG, Banghui ZHANG, Zhennan LIU, Ming GAO, Yan REN, Qiguo YANG, authorCompany=null, correspAuthors=Ming GAO, 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=1295068258646913743, articleId=1295068255320830655, tenantId=1146029695717560320, journalId=1210938733613449225, language=CN, title=超临界二氧化碳在水平-竖直L形转向管内对流换热特性实验研究, columnId=1211002405437706993, journalTitle=热力发电, columnName=热能科学研究, runingTitle=null, highlight=null, articleAbstract=
【目的】

为了探究在不同实验参数下,超临界二氧化碳在水平加热段中由浮升力造成的密度分层现象对后续垂直上升流动中换热的影响。

【方法】

进行了水平-竖直L形转向管道中的加热流动实验。

【结果】

实验结果表明,水平-竖直L形转向管道中会出现2种独特的“不对称传热恶化”现象:一种为恶化程度不对称,一种为恶化位置不对称。研究表明,恶化程度不对称源于水平段延续的温度分层导致截面质量流速不均;而恶化位置不对称则在高温高热流下,由内侧边界层提前达到恶化条件所致。

【结论】

该研究揭示了L形管内浮升力与流动转向的耦合效应,为相关换热设备的设计提供了实验依据。

, authors=冯思源, 张帮辉, 刘圳男, 高明, 任燕, 杨其国, authorsList=冯思源, 张帮辉, 刘圳男, 高明, 任燕, 杨其国, authorCompany=null, correspAuthors=高明, authorNote=

冯思源(2001),男,硕士研究生,主要研究方向为超临界二氧化碳换热特性,

, correspAuthorsNote=
高明(1982),男,博士,教授,主要研究方向为强化传热传质,
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Study on the “pseudo-boiling” mechanism of flow and heat transfer of supercritical fluid in a vertical tube[D]. 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Models and main parameters of the experimental parameter measuring elements

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名称品牌、型号量程精度/%
压力变送器WIKA、A-100~40 MPa0.25
压差变送器ColliHigh、JYB-31510~40 MPa0.25
温度变送器WIKA、TR10-H–100~450 ℃0.25
质量流量计首科实华、SincerityDNF-10~700 kg/h0.20
电流互感器彼爱琪、BH-0.66-50II0~500 A0.20
电压表银燕台技、S3-VD-1T-05A4B50 V0.20
热电偶开普森、K型–40~260 ℃0.40
), ArticleFig(id=1295068266427347720, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1295068255320830655, language=CN, label=表1, caption=

实验参数测量元件的型号及其主要参数

, figureFileSmall=null, figureFileBig=null, tableContent=
名称品牌、型号量程精度/%
压力变送器WIKA、A-100~40 MPa0.25
压差变送器ColliHigh、JYB-31510~40 MPa0.25
温度变送器WIKA、TR10-H–100~450 ℃0.25
质量流量计首科实华、SincerityDNF-10~700 kg/h0.20
电流互感器彼爱琪、BH-0.66-50II0~500 A0.20
电压表银燕台技、S3-VD-1T-05A4B50 V0.20
热电偶开普森、K型–40~260 ℃0.40
), ArticleFig(id=1295068266515428105, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1295068255320830655, language=EN, label=Tab.2, caption=

Measurement uncertainties of relevant experimental parameters

, figureFileSmall=null, figureFileBig=null, tableContent=
测量参数实验范围相对不确定度/%
压力p/MPa7.8~9.80.50
主流温度Tb/℃19.5~58.90.26
壁面温度Tw/℃41.2~157.80.43
电压U/V3.75~9.870.07
电流I/A96.9~312.20.46
壁面热流密度qw/(kW·m–29.95-65.862.90
对流换热系数hx/(kW·(m2·K)–11.04~7.263.10
), ArticleFig(id=1295068266582536970, tenantId=1146029695717560320, journalId=1210938733613449225, articleId=1295068255320830655, language=CN, label=表2, caption=

相关实验参数的测量不确定度

, figureFileSmall=null, figureFileBig=null, tableContent=
测量参数实验范围相对不确定度/%
压力p/MPa7.8~9.80.50
主流温度Tb/℃19.5~58.90.26
壁面温度Tw/℃41.2~157.80.43
电压U/V3.75~9.870.07
电流I/A96.9~312.20.46
壁面热流密度qw/(kW·m–29.95-65.862.90
对流换热系数hx/(kW·(m2·K)–11.04~7.263.10
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超临界二氧化碳在水平-竖直L形转向管内对流换热特性实验研究
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冯思源 , 张帮辉 , 刘圳男 , 高明 , 任燕 , 杨其国
热力发电 | 热能科学研究 2026,55(6): 144-153
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热力发电 |热能科学研究 2026 , 55 (6) : 144 -153
超临界二氧化碳在水平-竖直L形转向管内对流换热特性实验研究
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冯思源 , 张帮辉, 刘圳男, 高明 , 任燕, 杨其国
作者信息
  • 上海理工大学能源与动力工程学院,上海 200093
通讯作者:
高明(1982),男,博士,教授,主要研究方向为强化传热传质,
作者简介:

冯思源(2001),男,硕士研究生,主要研究方向为超临界二氧化碳换热特性,

Experimental study on convective heat transfer characteristics of supercritical carbon dioxide in horizontal-vertical L-shaped turning tube
Siyuan FENG , Banghui ZHANG, Zhennan LIU, Ming GAO , Yan REN, Qiguo YANG
Affiliations
  • School of Energy and Power Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China
出版时间: 2026-06-25 doi: 10.19666/j.rlfd.202509009
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【目的】

为了探究在不同实验参数下,超临界二氧化碳在水平加热段中由浮升力造成的密度分层现象对后续垂直上升流动中换热的影响。

【方法】

进行了水平-竖直L形转向管道中的加热流动实验。

【结果】

实验结果表明,水平-竖直L形转向管道中会出现2种独特的“不对称传热恶化”现象:一种为恶化程度不对称,一种为恶化位置不对称。研究表明,恶化程度不对称源于水平段延续的温度分层导致截面质量流速不均;而恶化位置不对称则在高温高热流下,由内侧边界层提前达到恶化条件所致。

【结论】

该研究揭示了L形管内浮升力与流动转向的耦合效应,为相关换热设备的设计提供了实验依据。

超临界二氧化碳  /  对流换热  /  L形管道  /  传热
[Objective]

In practical energy and chemical engineering systems, pipeline layouts often exhibit complex multi-directional configurations due to equipment arrangement, spatial constraints, and process requirements, rather than simple straight horizontal or vertical sections. This is particularly evident in applications such as compact heat exchangers for supercritical carbon dioxide (S-CO2) Brayton cycles, nuclear reactor cooling circuits, and chemical transport pipelines, where the working fluid frequently undergoes abrupt changes in flow direction. Among these configurations, the L-shaped bend, a classic directional-changing structure that connects horizontal and vertical pipe sections, is especially common and plays a crucial role in achieving spatial redirection of the working fluid. Therefore, investigating the heat transfer characteristics of S-CO2 in L-shaped bends is of significant importance. This study aims to investigate the effect of buoyancy-induced density stratification in a heated horizontal section on the subsequent heat transfer in a vertical upward flow under different experimental parameters.

[Methods]

An experimental system with high expandability was established, featuring a single-cycle S-CO2 heat transfer test platform utilizing stainless steel circular pipes with adjustable lengths and bend angles. Experiments were conducted to study the flow and heat transfer characteristics of S-CO2 inside a horizontal-to-vertical L-shaped turning pipe.

[Results]

The experimental results reveal two distinct types of “asymmetric heat transfer deterioration” in the turning pipe: one characterized by asymmetry in the severity of deterioration, and the other by asymmetry in its location. When the wall heat flux is increased, wall temperature peaks indicating heat transfer deterioration appear in the vertical section, with unequal peak values on the two sides, representing asymmetry in severity. A further increase in wall heat flux shifts the deterioration position toward the inlet, while the enthalpy at which deterioration initiates remains unchanged, indicating that the wall heat flux does not affect the onset enthalpy of deterioration. When the heat flux is raised sufficiently for the deterioration to advance to the inlet of the vertical section, the wall temperature peak on the inner side occurs earlier than that on the outer side, demonstrating asymmetry in the location of deterioration.

[Conclusion]

The study demonstrates that asymmetry in severity originates from non-uniform cross-sectional mass flow distribution caused by temperature stratification extending from the horizontal section. In contrast, asymmetry in location occurs under high-temperature and high-heat-flux conditions due to the earlier fulfillment of deterioration criteria within the inner-side boundary layer. This research elucidates the coupling effect between buoyancy and flow redirection in L-shaped pipes, providing an experimental basis for the design of related heat exchange equipment.

supercritical carbon dioxide  /  convective heat transfer  /  L-shaped pipe  /  heat transfer
冯思源, 张帮辉, 刘圳男, 高明, 任燕, 杨其国. 超临界二氧化碳在水平-竖直L形转向管内对流换热特性实验研究. 热力发电, 2026 , 55 (6) : 144 -153 . DOI: 10.19666/j.rlfd.202509009
Siyuan FENG, Banghui ZHANG, Zhennan LIU, Ming GAO, Yan REN, Qiguo YANG. Experimental study on convective heat transfer characteristics of supercritical carbon dioxide in horizontal-vertical L-shaped turning tube[J]. Thermal Power Generation, 2026 , 55 (6) : 144 -153 . DOI: 10.19666/j.rlfd.202509009
CO2化学性质稳定、密度较高、制备成本低,可作为动力循环的一种工质[1-2]。在超临界状态下,超临界二氧化碳(S-CO2)以其高温环境循环效率更高、透平体积更小、临界参数更低、工质腐蚀性更小等优点而备受关注[3-7],其在提高发电效率和降低碳排放方面展现了巨大潜力,被广泛认为是在新一代发电系统中极具潜力的替代工质。早在1950年,Sulzer[8]就已经提出了以超高参数S-CO2作为工质的动力循环发电系统。现今,S-CO2布雷顿循环已被证明相较于水蒸气朗肯循环具有更多优势[9],被认为未来可以取代或部分取代水蒸气朗肯循环[10]。随着科学技术的发展,S-CO2已经在火电、光电、核电、余热利用、舰船等诸多领域中[11-15]展现出巨大潜力,有望成为下一代能源系统的革命性技术。
在整个S-CO2布雷顿循环发电系统中,S-CO2的管内流动换热随处可见,其在不同工况下的管内流动换热特性都关系换热器及受热管道的设计。因此,研究S-CO2管内流动换热机理与特性非常关键。在S-CO2管内加热流动时,会产生传热恶化现象,具体表现为局部区域换热能力突然急剧减弱,产生明显的壁温峰值。同时传热恶化在水平管道中和垂直管道中的表现有所不同,近年来已有大量学者展开研究。王振川等[16]进行了小管径中的S-CO2的管内传热恶化实验,对内径为1 mm的垂直不锈钢光管进行实验,发现在小管径中S-CO2在向上流动时也会出现明显传热恶化,并认为该现象是受浮升力影响的,并且还向光管中插入螺旋结构进行对比实验,发现螺旋结构可有效抑制传热恶化现象。Kim等人[17]对S-CO2在垂直细管内向上及向下流动的实验研究,发现壁温分布强烈依赖于流动方向,并指出在物性剧烈变化条件下,流动加速效应相较于浮力效应对传热的影响占主导地位。Kumar等人[18]对水平小管径中S-CO2流动换热进行了三维数值模拟,特别强调浮力的影响,认为由密度分层引起浮力诱导的局部二次环流对管内换热模式产生影响,使管道下半部分传热延迟恶化,引发明显的热不对称性。
虽然已有许多学者对S-CO2在水平、竖直管道中的换热特性进行了研究,然而,当流动方向发生90°转变时,水平段产生的浮升力诱导二次流和温度分层将与转弯处的离心力、惯性力发生复杂相互作用,显著改变垂直入口段的流场和热边界条件,使得换热特性相较于直管更为复杂,因此目前对于S-CO2在水平-竖直转向L型管道中的换热特性研究较少。并且,在实际的能源与化工工程系统中,由于设备布局、空间约束及工艺流程的需要,管道系统往往呈现出复杂的多走向特征,而非简单的水平或垂直管道。特别是在诸如S-CO2布雷顿循环的紧凑式换热器、核反应堆冷却回路以及化工输送管道中,工质频繁地经历流动方向的剧烈改变。其中,L形弯管作为连接水平与竖直管段的经典转向结构尤为常见,是实现工质空间转向输送的关键部件。因此,对L形弯管内S-CO2的换热特性研究尤为重要。本文在对水平管中的换热特性的研究基础上,开展了水平-竖直转向L形管道中的S-CO2加热流动实验,以研究水平管中的温度分层现象[19-20]对后续垂直流动中换热的影响。除了常规的传热恶化及多峰值传热恶化[21]现象以外,在此实验中发现了一种新的传热恶化现象,即由水平段密度分层导致的垂直段中两侧不对称的传热恶化现象,本文将此现象定义为“不对称传热恶化”,并对这一现象产生的机理进行分析说明。
图1为已搭建的S-CO2管内单循环换热实验平台的系统,此系统实验空间扩展性高,可通过设置不同长度、角度的不锈钢圆形管道,实现不同角度、流向下的超临界管内流动换热特性实验。
该实验系统由主循环系统、增压系统以及冷却系统3个子系统构成。搭建完成的实验系统的主要技术指标为:最大压力25 MPa,最高温度350 ℃,最高入口雷诺数Re为106,最大加热功率20 kW。图2为实验台现场照片,其中标注了实验系统的各主要部件。正式实验前,对系统进行保压测试和热平衡测试,确保在目标工况下压力波动在±0.1 MPa以内,温度波动在±0.5 ℃以内。关键工况进行了重复性实验,结果表明壁温测量值的重复性误差在±1.0 ℃以内。
增压系统包括高纯CO2气瓶、减压阀、过滤器、增压泵、空气压缩机、冷冻干燥机、电磁阀及管道等。空气压缩机产生的压缩空气,经过冷冻干燥机干燥后,输入增压泵中驱动增压泵工作,气瓶中的低压高纯CO2经过减压阀和过滤器后进入增压泵增压并输入实验系统中。
冷却系统包括冷水机、PPR水管与冷却器,通过冷水机中的水泵将冷水送至冷却器中对加热后的高温CO2进行冷却,离开冷却器的热水回到冷水机的水箱中进行冷却完成冷却循环。冷水机中的水箱容量为1 000 L,冷却器为一台印刷电路板式换热器(PCHE),能够有效将实验后的CO2冷却回液态。
主循环系统由高压三柱塞循环泵、脉冲阻尼器、真空泵、调节阀、电加热系统、实验管道、绝缘接头、压力变送器、压差变送器、温度变送器、科里奥利质量流量计、冷却器、缓冲罐、背压阀、恒温槽、水冷头、数据采集仪、K型热电偶、热电偶定位器、控制终端组成。
对S-CO2的流动传热特性研究需要同时测量大量实验参数,如流量、温度、压力等。所有压力变送器、压差变送器、热电偶和质量流量计进行定期标定,并在实验前进行了零点校验,确保测量精度。相关仪器的型号、量程、精度如表1所示。
本实验使用内径9.4 mm、外径12.7 mm的316L不锈钢管作为实验管道,管道中间通过折弯器弯出一个半径38 mm的90°转弯,连接在实验系统中,具体加热长度为水平段500 mm,垂直段900 mm,转弯处长度为60 mm,总加热长度1 460 mm,此外进出口处有200 mm长的稳流段,两端连接绝缘接头防止漏电,外侧包裹外径50 mm的橡塑管绝热。
热电偶布置方式如图3所示,在水平段每隔100 mm为1个测温位置,在每个测温位置的管道顶部和底部分别布置1根热电偶,管道转弯处每隔23°为1个测温点,同样每个测温点布置2个对应热电偶,转弯段总长60 mm,共计10个测温点。垂直段中,每隔50 mm布置1对热电偶,需要注意的是,本文的内侧、外侧并非管道内外壁面,而是将原本水平段的内壁面顶侧的延伸段定义为内侧,内壁面底侧的延伸段定义为外侧。测温截面间距的差异是基于预实验的观察结果,即水平段温度分层发展较为平缓,而垂直段,尤其是在传热恶化可能发生的区域,壁温变化非常剧烈。减小垂直段测温间距是为了更精确地捕捉传热恶化峰的起始、峰值和恢复过程。在两端电极夹具的外侧管道与水平段橡塑保温棉管外侧各布置了1根热电偶。
由于本实验中存在垂直实验段,故垂直段橡塑保温棉管的外侧同样布置1根热电偶用于计算垂直段散热损失,具体计算将于下节说明。
本节对实验中重要数据的处理方法与计算公式进行简要叙述,对于CO2的热物理性质,通过NIST(national institute of science and technology)数据库REF-PROP得到。在本实验中,实验段的热损失主要为铜电极板的自然对流散热损失Q1,该损失主要以自然对流形式散失至周围环境,其与绝缘接头及管道接触处的导热损失相对较小,一并计入该部分损失,以及保温橡塑管道上的自然对流散热损失Q2。实验通过在管道上直接施加交流电进行电加热,通过记录的电压U与电流I计算电加热功率Qel而总热损失功率Qloss为2种热损失功率之和Q1+Q2,因此得到实验的输入功率Qin的计算式:
Qin=QelQloss=UIQ1Q2
经过多次实验测试,总热损失功率占比Qloss/Qel低于1%,因此实验段外壁面视为绝热。当热平衡时,流体吸热功率Qth为:
Qth=qm(hb,ohb,i)
式中:qm为质量流量;hb,i为实验段进口处主流比焓;hb,o为实验段出口处主流比焓,两者由进出口的温度压力查询NIST数据库得到。
由于加热方式为直接在管道上施加电流,因此视作均匀的壁面热流密度条件。可由式(3)、式(4)计算得到内壁面热流密度qw及体积热流密度qv
qw=QthπdiL
qv=Qthπ(do2di2)L
式中:L为实验段长度;do为管道外径;di为管道内径。
对于均匀的壁面热流密度条件,实验段中的主流焓将沿加热段长度线性上升,由进口处主流温度、压力从NIST数据库查得进口处主流比焓hb,i后,由式(5)计算沿程主流比焓ib
ib=hb,i+LxLQelqm
式中:Lx为加热长度。
本实验采取直接在管道上增加低压高电流实现加热,发热量是均匀的,故认为水平段的热流是均匀的。利用基于一维稳态导热公式推导出的内壁温计算公式,从热电偶测得的外壁温计算出管道内壁温[22]。本文采用的一维稳态导热模型基于均匀内热源和圆周方向绝热的假设。在直管段该假设近似成立。然而,在弯管段,离心力作用可能导致外侧热流密度高于内侧,且周向壁温分布不均,此时一维模型会引入一定误差。未来工作需通过三维数值模拟或更精细地测量来修正弯管段的换热计算。忽略管壁温度沿轴向和周向的变化,将圆柱坐标系下的导热微分方程(式(6))改写为有内热源的一维稳态导热形式(式(7))。
ρctτ=1rr(λrtr)+1r2φ(λtφ)+z(λz)+qv
ddr(λrdtdr)+qvr=0
据上文,本实验中,实验段外壁面视为绝热,可有以下边界条件(式(8)):
{r=do2,dtdr=0,t=Tw,or=di2,t=Tw,i
式中:r为半径;t为温度;Tw,i为管道内壁面温度;Tw,o为管道外壁面温度;λ为管壁导热系数。
将式(8)代入式(7)中并进行两次积分计算,可得内壁温计算公式:
Tw,i=Tw,o+116λqv(do2di2)qvdo28λln(dodi)
最终可通过式(10)计算管内沿程对流换热系数hx,并进一步通过式(11)计算沿程Nu[16]
hx=qwTw,iTb
Nu=hxdiλb
式中:Tb为主流定性温度;λb为流体导热系数,两者均由沿程焓ib与流体压力查询NIST数据库得到。
传热系数无法直接测量,其是由多个直接测得量计算得到的间接测得量[23]。间接测得量的不确定度ΔY的计算公式为:
ΔY=(YXjΔXj)2
式中:ΔXj为直接测得量Xj的不确定度。各参数不确定度如表2所示。
图4展示了水平-竖直转向管道在壁面热流密度qw分别为10、20、30、40、50、60 kW/m2时的内壁温及局部对流换热系数的沿程变化。实验参数分别为:压力p=8.7 MPa,质量流速G=370 kg/(s·m2),入口温度Tin=18.5 ℃。
不同壁面热流密度下,S-CO2在水平段都产生了程度不同的温度分化,并且这一温度分化将会延续到垂直段中对垂直流动时的换热产生影响。将整理出的对流换热系数与内壁温结果分别标于图4中,图4横坐标为基于式(5)计算的主流焓ib,纵坐标分别为内壁温Tw,i和局部对流换热系数hx。如图4a)所示,以2条蓝色点划线区分管道水平段、转弯段、垂直段3个区域,下面图片均使用该方式进行管道区域划分,后续不再赘述。
图4a)—图4d)中,内、外侧的壁温沿程均匀上升,传热模式属于正常传热,但由于水平温度分层的影响,垂直段内侧壁温全程高于外侧壁温。如图4e)、图4f)所示,当壁面热流密度提高到30 kW/m2时,内、外侧内壁温从主流焓约为270.0 kJ/kg的位置突然开始急剧上升,出现传热恶化现象,并且外侧内壁温的上升速度比内侧内壁温更快,两侧的内壁温在主流焓为277.8 kJ/kg处同时到达壁温峰值,但是外侧内壁温峰值比内侧内壁温峰值更高,最高内侧内壁温58.7 ℃,最高外侧内壁温62.6 ℃。此后两侧内壁温开始急剧下降,直到内壁温回归到正常传热模式应有温度后又开始均匀上升,但经历过传热恶化之后,两侧内壁温从内侧壁温高于外侧壁温转变为外侧壁温高于内侧壁温,这是两侧传热恶化程度不同导致的。
图4d)、图4g)、图4h)中,随着壁面热流密度继续上升至40 kW/m2时,传热恶化壁温峰值向入口端移动,并且两侧内壁面的壁温峰值位置不再一致,内侧壁温峰值比外侧更接近入口端。2个壁温峰值对应位置的主流焓分别为276.4 kJ/kg和278.8 kJ/kg,这与图4c)中的壁温峰值主流焓277.8 kJ/kg十分接近,说明随着壁面热流密度提高,传热恶化对应的主流焓值几乎不变,而由于加热功率提高,使得主流焓更快到达传热恶化对应的焓值点,从而使壁温峰值产生了向入口端移动的现象。
随着壁面热流密度进一步上升,如图4e)、图4f)所示,当之前实验中对应的传热恶化主流焓值移动到转弯段出口时,恶化发生位置前移至转弯段,该处的流动与热边界条件发生改变,导致首次传热恶化对应的焓值发生偏移;S-CO2离开转弯段进入垂直段后,传热急剧恶化,发生壁温飞升。在后续垂直段流动中,内壁温出现了新的峰值,如图4f)所示,在垂直段下游,当主流焓达到约290.0 kJ/kg和330.0 kJ/kg时,内外侧壁温相继出现了第2个和第3个显著的峰值,即二次、三次传热恶化,其特征同样是壁温急剧升高且局部换热系数显著下降。这表明流体在经历第1次恶化恢复后,在向下游流动的过程中再次出现了某种导致恶化发生的条件。
图5为单侧传热恶化现象。本文实验中出现了与传统的S-CO2垂直流动换热实验不太相同的现象,将其定义为“不对称传热恶化”,其特点在如下。
1)恶化程度不对称 在垂直管道的同一高度位置处,内侧内壁面与外侧内壁面由传热恶化导致的壁温峰值不同。通过多次实验数据总结,水平-竖直转向管道中发生传热恶化时,如图4c)图5所示,一般内侧的壁温峰值比外侧更高,在一些情况下甚至会产生只有内侧出现壁温峰值的情况,即发生了单侧的传热恶化。
2)恶化位置不对称 内侧内壁面与外侧内壁面由传热恶化导致的首次壁温峰值出现在垂直段的不同高度位置。如图4d)所示,出现位置不对称的传热恶化时内侧内壁面先出现壁温峰值,通过对多次实验结果统计发现,外侧内壁面先发生传热恶化的情况一般出现在靠近垂直段的出口端处。
不对称传热恶化的发生与水平加热段中的温度分层存在着直接联系,S-CO2在水平管中将会由于浮力效应的影响而产生明显的温度分层,并且在转弯段出口处存在明显的内壁温分布不对称,这说明水平段中的温度分层在转弯段中延续,并在垂直段中持续存在。水平段产生的温度分层流体进入弯管后,在离心力作用下,密度较大的外侧流体有向外拱的趋势,而密度较小的内侧流体有向内聚集的趋势。这可能导致在弯管出口截面,即垂直段入口,温度场和速度场分布不再是简单的上下分层,而是演变为一种不对称的、可能带有双涡结构二次流的复杂分布。外侧平均密度依然较大,但流速分布可能因二次流而发生改变。这个复杂的垂直段入口初始条件,是导致后续出现不对称传热恶化的直接原因。正是这种复杂的入口条件,使得垂直段内侧和外侧的近壁流体层处于不同的热工水力状态。对于外侧,密度大、惯性力强,但流经弯管后其流动结构可能被二次流削弱或增强;对于内侧,密度小、流动性好,但易受离心力作用而聚集。这种差异导致当水平管中近壁面超临界流体从类液态向类气态转变时,大幅增加了流体比体积,同时削弱了黏性与流体剪切力,导致在温度分层的同时在不同温度的流体层之间产生了滑移,抑制了湍流涡流的产生,最终使得温度分层延续到了垂直段之中。而在单纯的垂直上升流中,入口条件是均匀对称的,因此不会产生这种周向的不对称性。
对于垂直管中的传热恶化,传统的浮力效应解释[24]一般认为,在垂直管中近壁面流体温度升高越过临界点时,剧烈变化的流体物性使得管道截面径向密度梯度增大,产生了强烈的浮升力。并且在上升流动中(图6),由于浮力方向与流动方向一致,使近壁面流体发生流动加速,将径向流体速度分布由“U”型转变为“M”型,这种速度分布的变化使得湍流层流化,从而恶化了传热。
垂直管道中的温度分层将导致管截面质量流速分布不均,管道外侧壁面附近流体具有更高密度,使其引发比内侧更强烈的传热恶化,因此实验中外侧内壁温峰值普遍高于内侧内壁温峰值。随着壁面热流密度提高,传热恶化位置向垂直段入口端移动,由于温度分层延续的影响,内侧内壁面边界层温度高于外侧,导致内侧提前进入传热恶化,这是造成内侧壁温峰值大部分情况下比外侧更接近垂直段入口端的原因。而在一些情况下,入口温度高到一定程度或壁面热流密度达到一定程度时,内侧近壁面流体层平均温度较低,能够引发比较明显的流动加速,从而导致流体速度分布向半“M”型转变,即只有外侧出现壁温峰值的单侧恶化现象。
此前也有学者报道垂直管中S-CO2的多次传热恶化现象,张海松[25]将多次恶化现象解释为管道内局部蒸发动量力和局部惯性力交替起主导作用,导致类气层厚度与内壁温出现振荡。本文实验中也出现了多次传热恶化现象,如图7所示,其恶化特点与前人研究相同,发生多次传热恶化时每次出现的壁温峰值逐渐降低。但与完全的垂直流动不同的是,在水平-竖直转向管道中由于水平段温度分层的影响,即使在二次恶化与三次恶化时,其温度峰值也不相同,说明局部蒸发动量力受管道内质量流速分布的影响,在周向上分布不均匀,即周向上的类气层厚度发生了不均匀变化。
本文使用水平段500 mm、垂直段900 mm、内径9.4 mm的管道进行水平-竖直转向L形管道中的S-CO2对流换热实验研究。通过不同壁面热流密度的对比实验,探究水平受热流动中的温度分层现象对垂直流动的影响,得出以下结论。
1)根据实验结果发现,水平段中的温度分层将会通过转弯段延续到垂直段中,当壁面热流密度不高时,垂直段中不发生传热恶化,壁面温度均匀上升,但受温度分层影响,内侧内壁温始终高于外侧内壁温。
2)传热恶化存在对应的发生焓值,且水平-竖直转向管道中会出现独特的“不对称传热恶化”现象。提升壁面热流密度后,垂直段中出现传热恶化壁温峰值,但两侧壁温峰值不相同,即“不对称传热恶化”现象中的恶化程度不对称的传热恶化现象,继续提高壁面热流密度,传热恶化位置将向入口端移动,但发生恶化的焓值位置没有变化,壁面热流密度并不影响传热恶化发生焓值位置。继续提高壁面热流密度,传热恶化位置前移到垂直段入口位置时,内侧的壁温峰值将会与外侧错位,比外侧更早出现壁温峰值,即“不对称传热恶化”现象中的位置不对称传热恶化现象。
后续研究将进行数值模拟工作,以期在后续研究中与实验结果相互印证,更完整地揭示L形管内S-CO2的换热机理。并开展不同管径的对比实验,设置平行的垂直管实验段,以量化弯管效应的影响,进一步揭示“不对称传热恶化”的产生条件与尺度效应。
  • 上海市自然科学基金项目(25ZR1401261)
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doi: 10.19666/j.rlfd.202509009
  • 接收时间:2025-09-01
  • 首发时间:2026-08-14
  • 出版时间:2026-06-25
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  • 收稿日期:2025-09-01
  • 修回日期:2025-10-17
  • 录用日期:2025-11-05
基金
Natural Science Foundation of Shanghai(25ZR1401261)
上海市自然科学基金项目(25ZR1401261)
作者信息
    上海理工大学能源与动力工程学院,上海 200093

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高明(1982),男,博士,教授,主要研究方向为强化传热传质,
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