分叉微通道换热器对流换热性能的数值模拟

doi:10.7523/j.ucas.2024.071

摘要/Abstract

摘要：

受叶脉等自然分叉结构的启发，采用数值模拟的方法研究分叉微通道换热器基本单元的对流换热情况。在固定第1级通道参数的基础上，改变分叉结构第2级通道的宽度，详细分析通道内的温度场以及流场，得到入口到第2级通道各个位置处的压降、对流换热系数和综合换热评价系数。结果显示，分叉结构起到增强流体扰动和打断并形成新流体边界层的作用，强化换热的同时也使得温度分布更均匀。在第2级流道1 mm以内，内部流动入口效应影响较大，当分叉后水力直径与分叉前水力直径比值为0.54时，综合换热评价系数最大；在第2级流道1 mm以外，当分叉后水力直径与分叉前水力直径比值为0.80时，综合换热评价系数最大。

关键词: 微通道换热器, 强化传热, 分叉结构, 分形

Abstract:

Inspired by the natural bifurcation structure such as leaf veins， this paper uses numerical simulation to study the convective heat transfer of the basic unit of the bifurcated microchannel heat sink. On the basis of fixing the parameters of the first-stage-channel， changing the width of the second-stage-channel of the bifurcated structure， and analyzing the temperature field and flow field in the channel in detail， the pressure drop， convective heat transfer coefficient and comprehensive heat transfer evaluation coefficient from the inlet to the second-stage were obtained. The results show that the bifurcation structure can enhance the fluid disturbance， interrupt and form a new fluid boundary layer， strengthen the heat transfer and make the temperature distribution more uniform. Within 1 mm of the inlet of the second-stage-channel diameter， the inlet effect of internal flow is more influential， and the comprehensive heat transfer evaluation coefficient reaches its maximum when the ratio of hydraulic diameter after bifurcation to that before bifurcation is 0.54. When the ratio of hydraulic diameter bifurcation is 0.80， the comprehensive heat transfer evaluation coefficient reaches its maximum outside the second-stage-channel above 1 mm. The research can be used as a reference and guidance for the optimal design of bifurcated microchannel heat sinks.

Key words: microchannel heat sink, enhanced heat transfer, bifurcated structure, fractal

中图分类号:

TK124

柯伟宣, 穆建超, 王豪, 蔡可蒙, 刘捷. 分叉微通道换热器对流换热性能的数值模拟[J]. 中国科学院大学学报, 2026, 43(4): 478-487.

Weixuan KE, Jianchao MU, Hao WANG, Kemeng CAI, Jie LIU. Numerical simulation of convective heat transfer performance of bifurcated microchannel heat sink[J]. Journal of University of Chinese Academy of Sciences, 2026, 43(4): 478-487.

图/表 15

图1 自然界当中的分叉结构

Fig.1 Bifurcated structures in nature

图2 分叉微通道换热器单元三维模型

Fig.2 3D model of bifurcated microchannel heat sink unit

表1 本文第2级通道宽度的变化值及对应的高宽比和水力直径比

Table 1 Value of the second-stage-channel width and the corresponding aspect ratio and hydraulic diameter ratio

W₂/mm	0.10	0.11	0.12	0.13	0.15	0.17	0.20	0.22	0.24	0.30
$α 2$	6.00	5.50	5.00	4.50	4.00	3.50	3.00	2.75	2.50	2.00
β	0.43	0.46	0.50	0.54	0.60	0.67	0.75	0.80	0.86	1.00

表1 本文第2级通道宽度的变化值及对应的高宽比和水力直径比

Table 1 Value of the second-stage-channel width and the corresponding aspect ratio and hydraulic diameter ratio

W₂/mm	0.10	0.11	0.12	0.13	0.15	0.17	0.20	0.22	0.24	0.30
$α 2$	6.00	5.50	5.00	4.50	4.00	3.50	3.00	2.75	2.50	2.00
β	0.43	0.46	0.50	0.54	0.60	0.67	0.75	0.80	0.86	1.00

表2 材料物性参数

Table 2 Material property parameters

	$ρ$ /(kg·m^-3)	$C p$ /(J·(kg·K)^-1)	$μ$ /(mPa·s)	$k$ /(W·(m·K)^-1)
水	998.2	4 128	1.003	0.6
硅	2 328.0	700	—	148.0

表2 材料物性参数

Table 2 Material property parameters

	$ρ$ /(kg·m^-3)	$C p$ /(J·(kg·K)^-1)	$μ$ /(mPa·s)	$k$ /(W·(m·K)^-1)
水	998.2	4 128	1.003	0.6
硅	2 328.0	700	—	148.0

图3 本文的数值模拟与实验结果对比

Fig.3 Comparison of the numerical simulation and experimental results

图4 网格剖分示意图

Fig.4 Grid division diagram

表 3 网格无关性验证

Table 3 Grid independence validation

网格量	最小网格尺寸/mm	$h ¯$ /(W·m^-2·K^-1)	$h ¯$ 相对偏差/%	$Δ P$ /Pa	$Δ P$ 相对偏差/%
12 100 774	0.002	30 142	0.0	6 005	0.0
9 499 880	0.003	29 961	-0.6	5 992	-0.2
8 599 340	0.004	30 054	-0.3	5 787	-3.6
7 713 785	0.005	29900	-0.8	5 998	-0.1

表 3 网格无关性验证

Table 3 Grid independence validation

网格量	最小网格尺寸/mm	$h ¯$ /(W·m^-2·K^-1)	$h ¯$ 相对偏差/%	$Δ P$ /Pa	$Δ P$ 相对偏差/%
12 100 774	0.002	30 142	0.0	6 005	0.0
9 499 880	0.003	29 961	-0.6	5 992	-0.2
8 599 340	0.004	30 054	-0.3	5 787	-3.6
7 713 785	0.005	29900	-0.8	5 998	-0.1

图5 α2=2.75模型在y=0 mm和y=-0.5 mm位置处的截面温度云图

Fig.5 Isothermal contours section at y=0 mm and y=-0.5 mm of the α2=2.75 model

图6 α2=4.50模型在y=0 mm和y=-0.5 mm位置处的截面温度云图

Fig.6 Isothermal contours section at y=0 mm and y=-0.5 mm of the α2=4.50 model

图7 α2=2.75模型不同区域的温度分布和流线分布

Fig.7 Isothermal and streamline contours of different regions of the α2=2.75 model

图8 α2=4.50模型不同区域的温度分布和流线分布

Fig.8 Isothermal and streamline contours of different regions of the α2=4.50 model

图9 在 uin=3 m/s， Re =1 050情况下，第2级通道不同位置处的换热系数

Fig.9 Heat transfer coefficients at different positions of the second-stage-channel when uin=3 m/s， Re =1 050

图10 在uin=3 m/s，Re=1 050情况下，入口到出口不同位置处的总压力

Fig.10 Total pressure at different positions from inlet to outlet when uin=3 m/s， Re=1 050

图11 在uin=3 m/s， Re=1 050情况下，通道边界入口到出口不同位置处的温度

Fig.11 Temperature at different positions from the entrance to the exit of the channel boundary when uin=3 m/s，Re=1 050

图12 第2级通道不同位置处的综合换热系数

Fig.12 Comprehensive heat transfer coefficient at different positions of the second-stage-channel

参考文献 22

[1]	Bailey C. Thermal management technologies for electronic packaging： current capabilities and future challenges for modelling tools［C］//2008 10th Electronics Packaging Technology Conference. Singapore： IEEE， 2008：527-532. DOI：10.1109/EPTC.2008.4763487 .
[2]	He Z Q， Yan Y F， Zhang Z E. Thermal management and temperature uniformity enhancement of electronic devices by micro heat sinks： a review［J］. Energy， 2021， 216： 119223. DOI：10.1016/j.energy.2020.119223 .
[3]	Nadjahi C， Louahlia H， Lemasson S. A review of thermal management and innovative cooling strategies for data center［J］. Sustainable Computing： Informatics and Systems， 2018， 19： 14-28. DOI：10.1016/j.suscom.2018.05.002 .
[4]	Moore G E. Cramming more components onto integrated circuits［J］. Proceedings of the IEEE， 1998， 86（1）： 82-85. DOI： 10.1109/JPROC.1998.658762 .
[5]	Peng M， Chen L， Ji W T， et al. Numerical study on flow and heat transfer in a multi-jet microchannel heat sink［J］. International Journal of Heat and Mass Transfer， 2020， 157： 119982. DOI：10.1016/j.ijheatmasstransfer.2020.119982 .
[6]	Lee J， Mudawar I. Fluid flow and heat transfer characteristics of low temperature two-phase micro-channel heat sinks-Part 1： experimental methods and flow visualization results［J］. International Journal of Heat and Mass Transfer， 2008， 51（17/18）： 4315-4326. DOI：10.1016/j.ijheatmasstransfer.2008.02.012 .
[7]	Lee J， Mudawar I. Low-temperature two-phase microchannel cooling for high-heat-flux thermal management of defense electronics［J］. IEEE Transactions on Components and Packaging Technologies， 2009， 32（2）： 453-465. DOI：10.1109/TCAPT.2008.2005783 .
[8]	Colgan E G， Furman B， Gaynes M，et al. High performance and subambient silicon microchannel cooling［J］. Journal of Heat Transfer， 2007，129（8）：1046-1051. DOI：10.1115/1.2724850 .
[9]	Yan Y F， Yan H Y， Yin S Y， et al. Single/multi-objective optimizations on hydraulic and thermal management in micro-channel heat sink with bionic Y-shaped fractal network by genetic algorithm coupled with numerical simulation［J］. International Journal of Heat and Mass Transfer， 2019， 129： 468-479. DOI：10.1016/j.ijheatmasstransfer.2018.09.120 .
[10]	郝俊娇，潘日，周刚，等. 高热流密度电子元件中热管散热技术的进展［J］. 化工进展， 2015， 34（5）： 1220-1224， 1231. DOI： 10.16085/j.issn.1000-6613.2015.05.006 .
[11]	Tuckerman D B， Pease R F W. High-performance heat sinking for VLSI［J］. IEEE Electron Device Letters， 1981， 2（5）： 126-129. DOI：10.1109/EDL.1981.25367 .
[12]	Sui Y， Teo C J， Lee P S， et al. Fluid flow and heat transfer in wavy microchannels［J］. International Journal of Heat and Mass Transfer， 2010， 53（13/14）： 2760-2772. DOI：10.1016/j.ijheatmasstransfer.2010.02.022 .
[13]	Wang R J， Wang J W， Lijin B Q， et al. Parameterization investigation on the microchannel heat sink with slant rectangular ribs by numerical simulation［J］. Applied Thermal Engineering， 2018， 133： 428-438. DOI：10.1016/j.applthermaleng.2018.01.021 .
[14]	Cheng X， Wu H Y. Enhanced flow boiling performance in high-aspect-ratio groove-wall microchannels［J］. International Journal of Heat and Mass Transfer， 2021， 164： 120468. DOI：10.1016/j.ijheatmasstransfer.2020.120468 .
[15]	Weir B S， MacDonald N. Trees and networks in biological models［J］. Biometrics， 1984， 40（4）： 1210. DOI：10.2307/2531182 .
[16]	Murray C D. The physiological principle of minimum work： i. the vascular system and the cost of blood volume［J］.Proceedings of the National Academy of Sciences of the United States of America， 1926， 12（3）： 207-214. DOI：10.1073/pnas.12.3. 207 .
[17]	Bejan A， Errera M R. Deterministic tree networks for fluid flow： geometry for minimal flow resistance between a volume and one point［J］. Fractals， 1997， 5（4）： 685-695. DOI： 10.1142/s0218348x97000553 .
[18]	Pence D. Reduced pumping power and wall temperature in microchannel heat sinks with fractal-like branching channel networks［J］. Microscale Thermophysical Engineering， 2003， 6（4）： 319-330. DOI：10.1080/10893950290098359 .
[19]	Senn S M， Poulikakos D. Laminar mixing， heat transfer and pressure drop in tree-like microchannel nets and their application for thermal management in polymer electrolyte fuel cells［J］. Journal of Power Sources， 2004， 130（1/2）： 178-191. DOI：10.1016/j.jpowsour.2003.12.025 .
[20]	Ma C B， Sun Y N， Wu Y J， et al. A bio-inspired fractal microchannel heat sink with secondary modified structure and sub-total-sub fluid transmission mode for high heat flux and energy-saving heat dissipation［J］. International Journal of Heat and Mass Transfer， 2023， 202： 123717. DOI： 10.1016/j.ijheatmasstransfer.2022.123717 .
[21]	Peng H， Guo W H， Li M L. Thermal-hydraulic and thermodynamic performances of liquid metal based nanofluid in parabolic trough solar receiver tube［J］. Energy， 2020， 192： 116564. DOI：10.1016/j.energy.2019.116564 .
[22]	Chai L， Xia G D， Wang L， et al. Heat transfer enhancement in microchannel heat sinks with periodic expansion-constriction cross-sections［J］. International Journal of Heat and Mass Transfer， 2013， 62： 741-751. DOI：10.1016/j.ijheatmasstransfer.2013.03.045 .