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Article(id=1236323802506916594, tenantId=1146029695717560320, journalId=1210938733613449225, issueId=1236323797054312545, articleNumber=null, orderNo=null, doi=10.19666/j.rlfd.202411233, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1730390400000, receivedDateStr=2024-11-01, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1772692164303, onlineDateStr=2026-03-05, pubDate=1758729600000, pubDateStr=2025-09-25, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1772692164303, onlineIssueDateStr=2026-03-05, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1772692164303, creator=13701087609, updateTime=1772692164303, updator=13701087609, issue=Issue{id=1236323797054312545, tenantId=1146029695717560320, journalId=1210938733613449225, year='2025', volume='54', issue='9', pageStart='1', pageEnd='178', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1772692163003, creator=13701087609, updateTime=1772692223569, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1236324051153646111, tenantId=1146029695717560320, journalId=1210938733613449225, issueId=1236323797054312545, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1236324051153646112, tenantId=1146029695717560320, journalId=1210938733613449225, issueId=1236323797054312545, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=118, endPage=124, ext={EN=ArticleExt(id=1236323802808906486, articleId=1236323802506916594, tenantId=1146029695717560320, journalId=1210938733613449225, language=EN, title=Design of high-efficiency and low-resistance channels for printed circuit heat exchangers based on boundary layer redevelopment, columnId=1236323798149025895, journalTitle=Thermal Power Generation, columnName=Special topic on low carbon power technology, runingTitle=null, highlight=null, articleAbstract=

Based on the application of micro-channel printed circuit heat exchangers in fields such as thermoelectric power generation and aerospace, a high-efficiency, low-resistance, and easy-to-manufacture transverse slotted channel is proposed using the theory of boundary layer re-development, and the heat transfer is enhanced. Numerical simulations are employed to study the flow and heat transfer characteristics of both straight and slotted channels. The mechanisms of heat transfer enhancement and flow resistance reduction in the transverse slotted channel are investigated. The results show that the entrance effect can significantly enhance heat transfer with a minimal increase in flow resistance. The transverse slotted channel creates multiple entrance effects in the slotted regions by inducing flow separation, which leads to periodic boundary layer redevelopment, thereby greatly enhancing local convective heat transfer. Additionally, due to the relatively small velocity gradient in the slotted regions, local resistance is effectively reduced. As a result, the proposed transverse slotted channel improves the heat transfer capability of the channel by 2.24%~2.59%, reduces the resistance by 6.66%~7.91%, and increases the overall heat transfer performance by 9.87%~11.02%.

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基于微细通道印刷电路板式换热器在热力发电、航空航天等领域的应用，以及边界层再发展理论，提出了一种高效低阻且易加工的横向开槽式通道，对通道换热进行强化。采用数值模拟方法研究平直通道及开槽通道的流动传热特性，探究横向开槽通道的传热强化及流动减阻机理。结果表明：入口效应可以在较小流阻增加的前提下大幅强化传热；横向开槽通道可以在开槽区域通过流动分离实现多次入口效应，使流动边界层周期性再发展，从而大幅强化局部对流换热；开槽区域速度梯度较小，可以有效降低局部阻力。提出的横向开槽通道可使通道换热能力提升2.24%~2.59%，阻力降低6.66%~7.91%，综合换热性能提升9.87%~11.02%。

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于婷俐（1980），男，硕士，高级工程师，主要研究方向为火电厂动力机械与换热器，。

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于婷俐（1980），男，硕士，高级工程师，主要研究方向为火电厂动力机械与换热器，。

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于婷俐（1980），男，硕士，高级工程师，主要研究方向为火电厂动力机械与换热器，。

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Dimensions of the models

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参数模型
Case 0Case 1Case 2
通道总长L/mm555
开槽间距l/mm11
开槽宽度W/mm0.10.2
开槽区域占比/%3.857.41
水力直径/mm50.0052.5355.67
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模型尺寸参数

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参数模型
Case 0Case 1Case 2
通道总长L/mm555
开槽间距l/mm11
开槽宽度W/mm0.10.2
开槽区域占比/%3.857.41
水力直径/mm50.0052.5355.67
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基于边界层再发展的高效低阻印刷电路板式换热器通道设计
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于婷俐
热力发电 | 低碳电力技术研究专题 2025,54(9): 118-124
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热力发电 | 低碳电力技术研究专题 2025, 54(9): 118-124
基于边界层再发展的高效低阻印刷电路板式换热器通道设计
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于婷俐
作者信息
  • 国能双鸭山发电有限公司，黑龙江　双鸭山　155136

    • 于婷俐（1980），男，硕士，高级工程师，主要研究方向为火电厂动力机械与换热器，。

Design of high-efficiency and low-resistance channels for printed circuit heat exchangers based on boundary layer redevelopment
Tingli YU
Affiliations
  • Guoneng Shuangyashan Power Generation Co Ltd, Shuangyashan 155136, China
出版时间: 2025-09-25 doi: 10.19666/j.rlfd.202411233
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摘要
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基于微细通道印刷电路板式换热器在热力发电、航空航天等领域的应用，以及边界层再发展理论，提出了一种高效低阻且易加工的横向开槽式通道，对通道换热进行强化。采用数值模拟方法研究平直通道及开槽通道的流动传热特性，探究横向开槽通道的传热强化及流动减阻机理。结果表明：入口效应可以在较小流阻增加的前提下大幅强化传热；横向开槽通道可以在开槽区域通过流动分离实现多次入口效应，使流动边界层周期性再发展，从而大幅强化局部对流换热；开槽区域速度梯度较小，可以有效降低局部阻力。提出的横向开槽通道可使通道换热能力提升2.24%~2.59%，阻力降低6.66%~7.91%，综合换热性能提升9.87%~11.02%。

印刷电路板换热器  /  入口效应  /  横向开槽通道  /  流动传热特性  /  高效低阻强化

Based on the application of micro-channel printed circuit heat exchangers in fields such as thermoelectric power generation and aerospace, a high-efficiency, low-resistance, and easy-to-manufacture transverse slotted channel is proposed using the theory of boundary layer re-development, and the heat transfer is enhanced. Numerical simulations are employed to study the flow and heat transfer characteristics of both straight and slotted channels. The mechanisms of heat transfer enhancement and flow resistance reduction in the transverse slotted channel are investigated. The results show that the entrance effect can significantly enhance heat transfer with a minimal increase in flow resistance. The transverse slotted channel creates multiple entrance effects in the slotted regions by inducing flow separation, which leads to periodic boundary layer redevelopment, thereby greatly enhancing local convective heat transfer. Additionally, due to the relatively small velocity gradient in the slotted regions, local resistance is effectively reduced. As a result, the proposed transverse slotted channel improves the heat transfer capability of the channel by 2.24%~2.59%, reduces the resistance by 6.66%~7.91%, and increases the overall heat transfer performance by 9.87%~11.02%.

printed circuit heat exchanger  /  entrance effect  /  transverse slotted channel  /  thermal-hydraulic performance  /  high-efficiency and low-resistance enhancement
于婷俐. 基于边界层再发展的高效低阻印刷电路板式换热器通道设计. 热力发电, 2025 , 54 (9) : 118 -124 . DOI: 10.19666/j.rlfd.202411233
Tingli YU. Design of high-efficiency and low-resistance channels for printed circuit heat exchangers based on boundary layer redevelopment[J]. Thermal Power Generation, 2025 , 54 (9) : 118 -124 . DOI: 10.19666/j.rlfd.202411233
正文
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协同吸气式火箭发动机（synergetic air-breathing rocket engine，SABRE）中的氢氦回热器对空间要求极高[1]，需要具有高传热系数以及高紧凑度（8 000 m2/m3以上）[2]。为此，Huang等人[3]提出采用基于增材制造的三周期极小曲面（triply periodic minimal surface，TPMS）换热器，该类型换热器在相同水力直径下的传热系数与紧凑度均高于因高效紧凑特性受到广泛关注的印刷电路板式换热器（printed circuit heat exchanger，PCHE）。然而，受限于技术，金属3D打印得到的通道水力直径通常在毫米级，无法满足8 000 m2/m3的紧凑度要求。因此，通常选用通道水力直径为50 μm左右的微米级PCHE作为氢氦回热器[4]。
PCHE通道构型对其流动传热性能影响显著，目前，国内外学者对此已经开展了大量研究，主要包括直通道[5]、“之字形”通道[6]、S形肋片通道[7]、翼型肋片通道[8-10]以及基于前几种通道的改进型通道[11-13]。S形肋片和翼型肋片等非连续型通道相对于直通道、“之字形”通道等连续型通道具有更好的流动传热性能[14]，但由于肋片接触面积较小，其耐压性能弱于连续型通道[15]。因此，针对氢氦回热器的高压工况（~20 MPa），主要采用连续型通道。目前，众多学者针对连续型通道PCHE开展了广泛研究，包括流动换热特性的实验研究[16]与数值研究[17]，“之字形”通道几何参数[18]和截面形状[19]的优化，PCHE的流动传热预测模型[20]以及结构和工况参数的影响[21]等。此外，为进一步提升通道的流动传热性能，研究者也提出了多种改进通道，如蜷曲型通道[22]、渐扩通道[23]及变径通道[24]等。
在氢氦回热器微米级通道中，受限于加工技术，传统高效低阻的强化传热方式大多难以实现，因此发展高效低阻且易加工的新型通道至关重要。在通道入口附近，由于流动边界层与热边界层较薄，传热效率显著高于通道充分发展段，该现象称为“入口效应”[25]。若能够在通道内实现多次入口效应，则可以显著强化通道的传热性能，该方法称为边界层再发展理论。基于该理论，Xu等人[26]通过在三角形热沉散热通道上开设横向的梯形槽，实现了通道内多次入口效应，在显著强化换热的同时使通道阻力有一定程度降低。然而，如何在微米级PCHE通道内实现边界层的再发展尚少有研究。鉴于此，本文提出了一种横向开槽通道，使流体通过开槽区域时发生扰动，从而在开槽区域下游通道入口处形成较均匀的入口速度分布，进而实现多次入口效应。进一步地，采用数值模拟方法揭示横向开槽通道强化传热与流动减阻机理。研究结果将为高效低阻易加工的PCHE通道设计提供理论支撑。
1　物理模型及简化
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以航空发动机中的微米级氢氦回热器为例，研究横向开槽通道对PCHE流动传热性能的影响。考虑到模型的周期性和开槽后相邻通道可能出现的串流现象，选取3个热通道和3个冷通道作为计算单元，通道的上、下、左、右4个表面均设置为周期性边界条件[27]，如图1所示。其中，冷、热通道的横截面均为边长为a的正方形；为保证PCHE整体结构强度，壁厚∆t≥a/2[4]。模型固体基板选用316不锈钢，冷流体为氢气，入口温度Tcin=35 K，入口雷诺数Rec=100~500，工作压力pc=20 MPa。热流体选用氦气，进口温度Thin=700 K，工作压力ph=6 MPa，流量与冷侧相同。流体和固体的交界面采用耦合边界，即流体侧与固体侧的温度与热流密度处处相等。由于高压（20 MPa），工质在微米级通道内流动时克努森数（Kn）仍低于0.001，因此，流动依然处于连续介质区。
对于横向开槽通道（图2），为使开槽区域产生较明显的入口效应，通道打断位置选择在由流动边界层发展导致传热性能较弱的区域，开槽间距l=1 mm。模型各参数如表1所示。其中，Case 0为基础平直通道，Case 1和Case 2分别为不同开槽宽度通道。需指出，开槽区域会增大流体区域体积并减小换热面积，但由于开槽区域体积占比较小，对水力直径影响较小（表1），因此，本文未考虑开槽对水力直径的影响。为方便对比，后续将以入口水力直径作为特征长度进行分析。
2　数值方法及验证
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模拟工况中，冷、热流体的入口雷诺数为100~ 500，流动处于层流状态，因此选用层流模型对微米级PCHE单元结构进行模拟。数值计算的控制方程，包括连续方程、动量方程和能量方程，如式(1)—式(4)所示。
∂∂xi(ρui)=0
∂∂xj(ρuiuj)=−∂p∂xi+∂∂xj[μ(∂ui∂xi+∂uj∂xj)−23μ∂uk∂xkδij]
∂∂xj(ρHui)=∂∂xi(λ∂T∂xi)
对固体区域只求解能量方程：
∂∂xi(λs∂T∂xi)=0
式中：ρ、ρμ、λ分别为密度、动力黏度与导热系数；u、p、T分别为速度、压力与温度；H为流体焓值；下标i、j、k分别代表各物理量在x、y、z方向的分量。
式(1)—式(4)使用有限体积法（finite volume method，FVM）求解，速度压力耦合采用SIMPLE算法，对流项采用二阶迎风格式离散，扩散项采用QUICK格式。计算的收敛准则为能量方程的残差低于10–8，其他方程残差低于10–6。计算过程中考虑氢气与氦气的物性随温度的变化，物性参数通过NIST数据库查询得到。
引入努塞特数Nu与阻力因子f分别评价通道内的流动传热性能，定义式为：
Nu=hDhλ
f=2∇pDhρu2
式中：∇p为压力梯度；h为对流传热系数，定义式见式(7)。
h=qTw−Tf
式中：q为内壁热流密度；Tw与Tf分别为内壁温度与流体温度。
对于沿程Nu与f的计算，∇p为局部压力梯度；h计算时选取了局部内壁温度与截面流体平均温度。而对于通道平均Nu与f的计算，∇p为通道进、出口的压力梯度；h计算时，Tw与Tf分别选取了通道内壁面与流体区域的平均温度。
为了评价2种横向开槽通道的综合换热性能，引入等流量条件下的综合换热因子PEC：
PEC=Nu/Nu0f/f0
式中：Nu0与f0分别代表平直通道的Nu与f。
选取网格数量分别为90万、145万、295万、445万和600万的5套网格进行数值模型的网格无关性验证，结果见图3。可以看出，当采用第3套网格（295万）时，努塞特数Nu和压降与最密网格计算值误差小于3%。综合考虑计算机资源和准确性，最终选择第3套网格进行后续数值计算。
由于目前对微米级PCHE的实验研究数据较少，将数值计算所得通道内平均努塞特数及阻力因子与文献中对层流工况下毫米级“之字形”通道PCHE的实验测试数据[20]进行比对，以验证数值计算方法的有效性，结果如图4所示。可以看出，数值模拟结果与文献实验结果在Re=100~500范围内符合良好，通道平均努塞特数与阻力因子最大误差均不超过10%，验证了本文数值模型的准确性。
3　计算结果及分析
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3.1　平直通道内流动换热特性
图5展示了平直通道（Case 0）PCHE中冷通道内沿程Nu分布情况。可以看出：在入口处，由于入口效应的作用，通道局部Nu很大；随着流动发展，Nu逐渐降低，并最终趋于一个定值，达到充分发展状态。该现象与常规尺度通道中局部Nu的分布规律相同。与常物性流体在正方形通道内等热流边界条件下充分发展段的Nu相比，PCHE通道内充分发展段的Nu略高，这是由于在PCHE中，沿程热流密度并非定值，以冷通道为例，壁面热流密度在中后段逐渐升高，在流体变物性的协同作用下，通道内扰动增强，使换热效果优于常物性流体。此外，随着入口质量流量的增加，入口段长度增加，Nu也随之增加，因而通道整体换热效果增强。
图6展示了平直通道PCHE中冷通道内沿程f·Re的分布情况。与Nu分布规律类似：入口处f·Re较高，随着流动发展，f·Re降低；对于较低Re工况（Rec=100~200），f·Re逐渐趋于定值，达到充分发展，此时f·Re与常物性流体层流状态下正方形通道内充分发展段的f·Re相近。而随着入口Re增大（Rec=300~500），入口段长度增加，f·Re在通道出口处仍有较明显的下降趋势，说明此时流动还未达到完全充分发展状态，导致通道内阻力较高。
需注意，在入口处，f·Re迅速降低至较低水平并开始缓慢下降；而局部Nu在入口段的下降速度较为平缓，存在一个较大的强化换热区域。该现象说明，入口效应可以在大幅强化换热的同时将通道的阻力增加控制在一个较小的范围内。因此，利用入口效应可以在小幅增加压降损失的前提下显著增强换热，从而有效提升通道的综合换热特性。
3.2　横向开槽通道流动换热特性
根据上述分析，提出了一种横向开槽通道的PCHE，通过流体在槽道内的扰动使其进入开槽区域下游通道时可在入口处形成较为均匀的速度分布，从而在通道内实现多次入口效应。图7对比了3种通道的Nu。可以看出：通道Nu随着流量的增加而增大；相同流量下，3种通道中Case 2的Nu最大，Case 1次之，Case 0最小；相对于Case 0，Case 1可使Nu提升0.33%~0.96%，Case 2可使Nu提升2.24%~2.59%。该结果表明，横向开槽通道的换热性能优于平直通道，且开槽宽度越大，换热性能越高。
图8展示了3种通道的阻力性能。可以看出：通道阻力因子f随着流量增大而减小；相同流量下，Case 2阻力因子最小而Case 0阻力因子最大；相对于Case 0，Case 1的阻力因子降低了3.00%~3.08%，Case 2的阻力因子降低了6.66%~7.91%。该结果表明，横向开槽可以有效降低通道内的流动阻力，且开槽宽度较大的通道流动减阻效果更加明显。
3种通道PEC因子对比如图9所示。可以看出，由于横向开槽通道的流动换热性能均优于传统平直通道，因此2种通道的综合换热因子相较于平直通道均有提升，其中，Case 1的PEC因子可提升3.46%~4.51%，Case 2可提升9.87%~11.02%。
3.3　横向开槽通道局部流动换热特性
为分析横向开槽通道强化换热及流动减阻机理，图10和图11分别展示了mc=4.5×10–7时3种通道的沿程局部Nu和局部f·Re对比。由图10可以看出，在槽道下游通道入口处，局部Nu显著提升，且在下游处存在一段换热较强的区域，出现了类似入口效应的现象，因此开槽通道换热效果显著优于传统平直通道。通过对比Case 1和Case 2可以看出，较大的开槽宽度可以使入口效应更显著，这是由于开槽宽度较大时，开槽区域流体扰动更充分，使得开槽下游入口速度分布更均匀（图12）。由图11可以看出，在开槽区域，横向开槽通道的局部f·Re显著下降，且其下降幅度大于槽道下游通道入口处局部f·Re增加幅度，因此横向开槽通道阻力性能亦优于传统直通道。值得注意的是，在开槽区域下游，f·Re为负数，这是由于流体对迎来流壁面的垂直冲击会导致局部压力增大，从而出现逆压力梯度现象，如图12b)所示。
冷通道下游最后一个横向开槽通道附近（z=3.8~4.3 mm）的流线及压力云图如图12所示。由图12a)可以看出，每个开槽区域均存在一对对称的漩涡，使得流体由传统通道中与壁面直接接触改为与开槽区域内流体接触，导致该区域的速度梯度明显减小，开槽区域的流动阻力显著降低。此外，开槽区域的旋涡有足够的空间充分发展，因此可有效削弱流体对迎来流壁面的垂直冲击，从而降低下一段通道入口的局部压力梯度，如图12b)所示，使阻力相对开槽宽度较小的通道有所降低。
4　结论及展望
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针对微米级PCHE，基于边界层再发展理论，提出了一种高效低阻易加工的横向开槽式通道，通过实现多次入口效应显著增强传热，并采用数值模拟方法对横向开槽通道的流动传热特性及其强化机理开展了研究，得到以下结论。
1）入口效应可在大幅强化换热的同时将通道的阻力增加控制在较小范围内，因此，有效利用入口效应将有效提升通道的综合换热特性。
2）横向开槽通道可以在有效强化换热的同时大幅降低通道流动阻力，从而显著提升通道综合换热性能，2种开槽通道分别使综合换热性能提升3.46%~4.51%和9.87%~11.02%。
3）较大的开槽宽度有利于流体的充分混合以及降低开槽区域的速度梯度，从而使传热性能更高而阻力更低。
需指出，本文主要基于边界层再发展理论对横向开槽PCHE通道设计进行初步探索，证明其有效性，但开槽后同样面临局部机械性能下降等问题。同时，开槽通道的综合性能还可以通过几何参数优化进一步提升，未来可针对横向开槽PCHE的机械性能及几何参数优化进一步开展研究。
文献
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doi: 10.19666/j.rlfd.202411233
  • 接收时间：2024-11-01
  • 首发时间：2026-03-05
  • 出版时间：2025-09-25
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  • 收稿日期：2024-11-01
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    国能双鸭山发电有限公司，黑龙江　双鸭山　155136
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2种不同金属材料的力学参数
科
Family		 属数
Number of
genus		 种数
Number of
species		 占总种数比例
Percentage of
total species (%)		 属
Genus		 种数
Number of
species		 占总种数比例
Percentage of total
species (%)
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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