微型平板流和圓管流的熱流特性：以數值探討壓縮和稀薄效應

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劉冠佑(Guan-You Liou) 查詢紙本館藏

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機械工程學系

論文名稱

微型平板流和圓管流的熱流特性：以數值探討壓縮和稀薄效應
(The thermal flow characteristics of the micro parallel flow and microtube flow: a numerical study on the effect of compressibility andrarefaction.)

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摘要(中)

本文是運用FEMLAB軟體模擬微管道的壓縮與非壓縮氣流，流場與熱傳的數值解並與理論解、數值解和實驗數據比對，流道包括平行板與圓管，管徑尺寸介於0.1~1000 。馬赫數(Ma)與雷諾數(Re)分別介於5.75×10-5< Ma <0.65以及8.97×10-3< Re <1000，而努森數之範圍則是涵蓋連續流到過渡流區域(7.23×10-4< Kn <2.07)。
壓縮流的模擬顯示隨入出口壓力比(PR)增加，壓力分佈非線性程度愈顯著，所以無法形成完全發展流。另一方面稀薄效應會隨管徑縮小而加強，它對流場的影響和壓縮效應互相牽制，即這二者對速度分佈、壓力分佈、摩擦常數和Nu的影響恰好相反。傳統上利用作為壓縮流的分界對於微流並不適用，應改用入出口壓力比和壓差來判別，本文數值解顯示即使入口Ma極低但在適當的PR條件下，就需考慮流場的壓縮效應。
對於大管道( )的摩擦常數與理論值相近，但隨管徑縮小（），摩擦常數會低於理論值。整體來說，微管流的的摩擦常數會隨著Re遞減與Kn增加而逐漸低於理論值。
在熱傳方面，發現當管徑縮小和Re增高，黏滯消散愈明顯。對於等溫加熱流場，黏滯消散效應會導致熱傳效率大幅降低，但對冷卻流場，卻會使提高熱傳效率。致於滑動流區域，隨著Kn增加，Nu會降低且偏離理論值。

摘要(英)

This work uses the software FEMLAB to simulate compressible and incompressible gas flow in microchannels. Both micro parallel flow and microtube flow were analyzed, where the hydraulic diameter Dh ranging from 0.1 to 1000 . Simulated parameters cover wide flow regime including: Mach number (5.75×10-5< Ma <0.65), Reynolds number (8.97×10-3< Re<103) and from the continuum flow upto transitional flow (Kn <2.07).
Solutions of compressible flow show that the nonlinearity of pressure distribution is proportional to the inlet/outlet pressure ratio (PR), which causes the condition of fully developed flow invalid. As Dh decreases, rarefaction effects gets intense and it is contradict with compressibility effects, which can be observed in characteristics of velocity, pressure distributions, friction constant, and Nusselt number (Nu). Traditional value of Ma>0.3 as the lower bound of compressible flow is not valid in the microchannel flow; instead one should use PR and pressure difference to identify the compressible flow. Numerical results indicate that the flow is compressible even at very low inlet Ma provided that value of PR is moderate.
Regarding the friction constant (C) analysis, for large microchannel size (Dh=100- 300 ) computed values of friction constant agrees well with the theory. But when the microchannel size reduces ( ), friction constant is lower than the theatrical value. Overall, the reduction of C in microchannel flow is proportional to the increment of Kn and the decrease of Re.
Characteristics of heat transfer were also studied. Effect of viscous dissipation becomes important as Dh reduces and Re increases. For heating flow viscous dissipation drastically lessens heat transfer rate, but for cooling flow the phenomena just opposite. In the slip flow regime and Kn increases, Nu tends to decrease and deviate from conventional theory.

關鍵字(中)

★ 微管流
★ 壓縮效應
★ 稀薄效應
★ 黏滯消散

關鍵字(英)

★ Viscous dissipation
★ Microchannel flow
★ Compressibility
★ Rarefaction

論文目次

中文摘要 i
英文摘要 ii
目錄 iii
表目錄 v
圖目錄 vi
符號說明 x
第一章緒論 1
1.1 前言 1
1.2 微管流的分類 3
1.3 微管流中之熱流現象 5
1.4 文獻回顧 9
1.5 研究方向 18
第二章數值分析 19
2.1 有限元素法 19
2.2 模擬軟體(FEMLAB)簡介 20
2.3 統御方程式 20
2.4 邊界條件與初始條件 24
2.5 通式(General form) 26
2.6 摩擦常數與紐索數 28
第三章結果與討論 31
3.1 數值解驗證 31
3.2 稀薄與壓縮效應 33
3.3 壓縮與非壓縮圓管流的比較：參數分析 34
3.3.1 判別壓縮與非壓縮圓管流場的臨界值 37
3.4 圓管流摩擦常數 38
3.5 滑動壓縮與非壓縮平板流的比較：參數分析 41
3.5.1 判別壓縮與非壓縮平板流場的臨界值 43
3.6 平板流摩擦常數 43
3.7 摩擦常數綜合比較 45
3.8 微流道熱傳分析 47
3.8.1 平板流熱傳分析 47
3.8.2 圓管流熱傳分析 48
第四章結論與建議 50
4.1 結論 50
4.2 建議 52
參考文獻 53
附錄 A 57

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指導教授

吳俊諆(Jiunn-Chi Wu)

審核日期

2004-7-1

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