微细通道内的流动和传热特性研究

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摘要

微尺度内的传热与传质在微电机、微生物工程、微电子工程、航空航天和材

料处理等领域有着广泛的应用前景。从上个世纪 80 年代中期开始，微通道内的流

体流动和传热现象就成为国际电子学界和传热学界的热点问题。近年来的各国研

究者研究表明尺度微细化后的规律已明显不同于常规尺度条件下的流动和传热现

象，这使微细尺度传热形成一个新的学科分支。本文对微通道内流动和换热特性

进行了理论和实验研究，主要内容包括：

1. 微通道内单相气体层流流动换热理论模型研究。将常规通道中的 Graetz 问

题扩展到微圆管内的流动和换热。综合考虑了微通道内的稀薄效应和滑移区的速

度滑移和温度跳跃边界条件，求解得到了常壁温条件下扩展的 Graetz 问题的精确

解析解。得到了温度分布，局部努塞尔数 Nux，热充分发展段的努塞尔数 Nu∞，

温度跳跃值s，平均温度m，进而讨论了 Nux, Nu∞, s和m随Kn 数的变化关系。

分析结果表明滑移边界对微通道内的层流换热产生了很大的影响，速度滑移和温

度跳跃的综合作用使 Nu 数随着 Kn 的增加而减小。

2. 实验测定微通道内单相层流充分发展段摩擦阻力因子。实验测定了去离子

水在微通道（管内径 d=0.65mm 的圆管）内层流（Re 数范围：55～420）充分发展

区压降随 Re 数的变化关系，经过数据处理得到了微通道内的 Poiseuille 数（ Po=f·Re）

与Re 数的依变关系（常规通道内在此 Re 数范围内 Po=64）。实验结果表明：在 55

＜Re＜170 区域，f·Re 随着 Re 数的增加急剧增大；在 170＜Re＜420 区域，f·Re

随着 Re 数的增加增大，但是相较于前面的区域增长的趋势放缓。此实验结果与常

规通道内 f·Re 值为常数的理论完全不同。将实验数据按照最小二乘法分两部分进

行数据回归，得到了 f·Re 随Re 数变化分段函数表示的函数表达。

3. 微通道内沸腾起始点（ONB）研究。实验测定微通道（管内径 d=0.65mm

的圆管）内去离子水分别在质量流率为 353.84、445.04、562.56（kg/m2s）工况下

的过冷沸腾起始点，并将实验得到的 ONB 处对应的热流密度和壁面过热度关系与

传统预测关联式（Davis 和Anderson 理论关系式和 Bergles 和Rohesenow 经验关联

式）和基于微通道建立的 ONB 关联式进行比较。根据微通道内单相层流充分发展

段摩擦阻力因子实验结果对常规管道内的沸腾起始点关联式进行修正，得到了适

用于微通道的沸腾起始点处的热流密度和壁面过热度的关联式。预测关联式展现

了很好的预测结果。

4. 提出了常/微通道的划分应该有单相流动换热和两相流动换热之分的观念。

对于管道内单相气体流动和换热提出了以滑移区的出现（Kn≥10-3）作为常/微通

道划分的衡量；对于管道内单相液体流动换热，由于液体的分子自由程很小，不

能用 Kn 数来衡量液体，所以管道内单相液体流动换热的常/微通道划分与气体流

动换热的划分也应不同，本文中提出了以摩擦阻力常数 f·Re 的数值发生改变时对

应管道直径（或者其他相关参数）作为常/微通道划分参数；对于管道内的流动沸

腾换热提出了采用流动沸腾中的气泡脱离直径作为常/微通道划分参数。

5. 微通道内的流动沸腾换热实验研究。详细论述了去离子水在 d=0.65mm 的

圆形管道内的流动沸腾换热实验研究，得到了局部换热系数随干度的变化关系。

进而根据换热系数的变化趋势讨论了微通道内饱和流动沸腾区主导的换热机制，

并将其他研究者实验得到的微通道内流动沸腾区主导的换热机制与本实验比较，

已发表的饱和流动沸腾区换热主导机制的判定准则均不能有效地判别本实验的主

导换热机制。本实验饱和流动沸腾区得到的数据与已发表的预测关联式进行比较，

两种基于微通道建立的关联式 Jatuporn 和Thome 关联式能基本上预测在实验工况

0＜x＜0.35 区域换热系数大体上随干度的增加而减小趋势外，其他的关联式都失

效了；对实验过程中发现的低干度区的烧毁现象进行了分析。

关键词：微细通道扩展的 Graetz 问题摩擦因子沸腾起始点流动沸

腾换热机制流动沸腾换热系数烧毁现象

ABSTRACT

The heat and mass transfer in microchannels is need for the fields of MEMS,

Microbial Engineering, aerospace and materials processing in the future. Since the early

80s, the heat and mass transfer in microchannels has been the hot issue in the

International academic of heat transfer. The obvious differences of heat and mass

transfer were reported by the researchers between in microchannels and conventional

channels. That makes it a new subject branch. In this paper, the theoretical analysis and

experimental research of heat and mass transfer in micro-/mini-channels are made, the

contents are flowing:

1. Laminar flow and heat transfer of gas in microchannels. This paper extended

the original Graetz problem to slip-flow in microtube. The extended Graetz problem in

slip-flow with the isothermal boundary condition on the wall was solved. In

mathematical model of this problem, conventional energy equation was used, both the

rarefaction effects of gas flowing in the microtube and the velocity slip and the

temperature jump condition of slip-flow were taken into account. The analytical

solution was obtained by solving the energy equation with the method of separation of

variables. In the end, the temperature distribution, the local Nusselt number Nux, the

thermally fully-developed Nusselt number Nu∞, dimensionless temperature jump s, and

the bulk mean temperature distribution m were obtained. From the results，it can be

concluded that the convective heat transfer in microtubes is affected largely by the

velocity slip and temperature jump condition. Considering the boundary condition of

both the velocity slip and temperature jump make the Nu decreases as Kn increases.

2. Full developed laminar flow friction factor in microchannels. An experiment

has been conducted to measure the friction factor of laminar ﬂow (Re:55～420) of

deionized water in microtube with diameter of 0.65mm. It is shown that the friction

constant of this microtube is greatly influenced by the Reynolds number. It is different

with the conventional tube. The laminar apparent friction constant increases with the

increase of the Reynolds number. This increase is more obvious at large Reynolds

numbers than that at low Reynolds numbers. Based on the data points, a correlation

equation for the friction constant of a fully developed laminar flow of deionized water

in this microtube is obtained in terms of the Reynolds number.

3. Onset of Nucleate Boiling (ONB) in microtube. The present study is aimed at

experimentally identifying the onset of nucleate boiling in forced convective ﬂow in a

microtube. The experimental data is compared with existing correlations (conventional

correlations and presented correlations based on microchannels), and develops a new

correlation satisfied to microtube by revise the conventional correlation with the friction

constant. The correlation show good agreement with the experimental dates.

4. Macro-to-microscale transition. The new classification and size ranges are

proposed based on single phase heat transfer and two phases heat transfer. For single

phase heat transfer of gases, the appearance of slip flow (Kn≥10-3) should as to be the

transition boundary; For single phase heat transfer of liquids, the channel diameter

correspond to transition of friction constant of fully developed laminar flow could as to

be the transition boundary; The bubble diameter of departing could as to be the

transition boundary for two-phase processes.

5. Flow boiling heat transfer in microchannels. An experiment has been conducted

to measure the local flow boiling heat transfer of deionized water in microtube with

diameter of 0.65mm. The relation of local boiling heat transfer coefficient verified with

thermodynamic equilibrium quality is acquired. The findings from the experimental

investigation are discussed, and fundamental differences from macro-channel results

identified. This is followed by assessment of some popular macrochannel correlations

and presented correlations specially developed for mini/micro-channels, through

comparison between correlation predictions and the present experimental data. A new

phenomenon of tube burning in low thermodynamic equilibrium quality is found in this

experiment, the possible reasons are discussed.

Key words: microchannel, extended Graetz problem, friction factor,

ONB, heat transfer mechanism, heat transfer coefficient,

burning phenomenon

摘要

ABSTRACT

第一章绪论 .................................................................................................................. 1

§1.1 课题的来源及意义 ............................................................................................. 1

§1.2 国内外研究现状 ................................................................................................. 2

§1.2.1 微通道内单相气体流动换热 ...................................................................... 2

§1.2.2 微通道内单相流动摩擦因子 ...................................................................... 3

§1.2.3 微通道内的沸腾起始点 .............................................................................. 4

§1.2.4 微通道内的流动沸腾换热 .......................................................................... 5

§1.3 本文工作 ............................................................................................................. 8

第二章微通道内滑移区的 Graetz 问题解析解 ........................................................... 9

§2.1 概述滑移边界条件和 Graetz 问题 .................................................................... 9

§2.2 滑移区 Graetz 问题模型 ................................................................................... 10

§2.3 结果分析 ........................................................................................................... 13

§2.4 本章小结 ........................................................................................................... 17

第三章微细管道内流动和换热实验装置系统 .......................................................... 18

§3.1 实验装置系统 ................................................................................................... 18

§3.2 实验段 ............................................................................................................... 20

§3.3 测量方法 ........................................................................................................... 22

§3.4 不确定度分析 ................................................................................................... 24

§3.5 本章小节 ........................................................................................................... 25

第四章微通道内的沸腾起始点（ONB）研究 .......................................................... 26

§4.1 微通道内沸腾起始点和摩擦阻力因子研究概述 ........................................... 26

§4.1.1 微通道内沸腾起始点研究概述 ................................................................ 26

§4.1.2 微通道内摩擦阻力因子研究概述 ............................................................ 29

§4.2 实验测定微通道内的摩擦阻力因子 ............................................................... 31

§4.2.1 实验数据处理 ............................................................................................ 31

§4.2.2 实验结果与分析 ........................................................................................ 32

§4.3 微通道内的沸腾起始点 ................................................................................... 34

§4.3.1 实验数据处理 ............................................................................................ 34

§4.3.2 实验结果与分析 ........................................................................................ 36

§4.3.3 建立适用于微通道的 ONB 关联式 ......................................................... 40

§4.4 本章小结 ........................................................................................................... 41

第五章微通道内流动沸腾换热 .................................................................................. 42

§5.1 常/微通道划分 .................................................................................................. 42

§5.1.1 概述 ............................................................................................................ 42

§5.1.2 基于单相流动换热提出的常/微通道划分 ............................................... 44

§5.1.3 基于流动沸腾换热提出的常/微通道划分 ............................................... 46

§5.2 微通道内流动沸腾换热实验数据处理 ........................................................... 46

§5.3 微通道内的流动沸腾换热实验结果分析 ....................................................... 47

§5.3.1 微通道内流动沸腾换热机制 .................................................................... 47

§5.3.2 微通道内流动沸腾换热系数 .................................................................... 50

§5.3.3 微通道内低干度区的烧毁现象 ................................................................ 54

§5.4 本章小结 ........................................................................................................... 57

第六章总结 .................................................................................................................. 58

§6.1 研究内容总结 ................................................................................................... 58

§6.2 下一步工作展望 ............................................................................................... 59

符号说明 ........................................................................................................................ 60

附录 ................................................................................................................................ 62

参考文献 ........................................................................................................................ 65

在读期间公开发表论文和承担科研项目及取得成果 ................................................ 73

致谢 .............................................................................................................................. 74

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摘要：

摘要微尺度内的传热与传质在微电机、微生物工程、微电子工程、航空航天和材料处理等领域有着广泛的应用前景。从上个世纪80年代中期开始，微通道内的流体流动和传热现象就成为国际电子学界和传热学界的热点问题。近年来的各国研究者研究表明尺度微细化后的规律已明显不同于常规尺度条件下的流动和传热现象，这使微细尺度传热形成一个新的学科分支。本文对微通道内流动和换热特性进行了理论和实验研究，主要内容包括：1.微通道内单相气体层流流动换热理论模型研究。将常规通道中的Graetz问题扩展到微圆管内的流动和换热。综合考虑了微通道内的稀薄效应和滑移区的速度滑移和温度跳跃边界条件，求解得到了常壁温条件下扩展的Graetz问...

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