壓縮微管流的熱流分析

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姓名

陳家勇(Chia-Yung Chen) 查詢紙本館藏

畢業系所

機械工程學系

論文名稱

壓縮微管流的熱流分析
(Thermal fluid analysis of compressible microchannel flow)

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摘要(中)

本文以數值模擬探討微管道的壓縮層流之熱流特性，管道水力直徑小於4 m，壁面設定為無滑移流條件。流速範圍有二，一是Main=0.07~0.21，Re=1~10；二是Main=(3~12)×10-4，Re=(1.2~8.9)×10-3。數值解顯示壓縮層流在入口處有速度陡升現象，且不論微管道多長，都不會形成完全發展流；而入口流速愈大，出口流速急遽增加現象愈明顯。
非滑移流中的速度剖面類似滑移流，愈靠近出口處愈平坦；且入口流速愈大情況愈明顯。而入口處的速度剖面，因流體在壁面的黏滯性加熱呈現凹陷狀。考慮加熱壁面時，壁溫愈高時，流場的紐索數愈低，且流體需流過較長距離，紐索數才能達到定值。
與非壓縮流場比較，壓縮效應使得壓力分佈呈非線性分佈，且在出口處壓力梯度與速度梯度同時達到最大值。且入出口壓力比愈大時，非線性的壓力分佈現象愈明顯。
模擬結果顯示在微型流道中，因流道尺寸效應，入口流速雖然極低(Main~10-3)，仍會因為入口流速的些微不同，造成流場差異頗大的壓力分佈。

摘要(英)

This numerical study analyzed the thermal-flow characteristics of the compressible laminar flow over the microchannel (dh < 4μm). The channel wall is assumed as non-slip flow condition. Two flow regimes were considered: 1) Ma=0.07~0.21, Re=1~10; 2) Ma=(3~12)×10-4, Re=(1.2~8.9)×10-3. Numerical results show that the compressible laminar flow has abrupt velocity jump near the channel entrance, and the fully developed flow can never be achieved no matter how long the channel is. In addition, further increases inlet velocity, more significant increasing of velocity at the outlet is predicted.
The predicted velocity of present non-slip flow has a flat profile, which is similar to the solution of the slip flow simulation, and the velocity distribution is flatter as the flow approaches the outlet. Near the inlet, velocity profiles have a concave shape due to the viscosity heating at wall. For the heating wall case, the Nusselt number is inversely proportional to the wall temperature. When the wall temperature is higher, the flow needs longer channel to reach a constant Nusselt number.
Comparing with the incompressible flow, nonlinear pressure distribution is obtained due to the compressibility effect. Both pressure and velocity gradient reach the maximum value at the outlet. Furthermore, enforcing higher pressure ratio (inlet value to outlet value), more significant nonlinear level of pressure distribution is observed.
Because of the channel size effect, even the inlet velocity is very low (Main~10-3), numerical results reveal that a slight velocity difference makes a huge dissimilar pressure distribution in microchannel.

關鍵字(中)

★ 壓縮層流
★ 數值模擬
★ 熱對流
★ 微管流

關鍵字(英)

★ compressible laminar flow
★ numerical simulation
★ heat convection
★ microchannel flow

論文目次

目錄頁次
中文摘要…………………………………………………………………… i
英文摘要…………………………………………………………………... ii
目錄………………………………………………………………….……… iv
表目錄…………..…………………………………………………..……… vi
圖目錄…………………………………………………………………….... vii
符號說明………….………………………………………………………. ix
第一章導論…………………………………………….……………………….1
1.1 研究動機……………………………………………………………..………..1
1.2 流體在微小管中的熱流現象………………………………….……………...2
1.3文獻回顧…………………………………………………………………….. 3
1.3.1實驗量測…………………………………………………….……………..3
1.3.2物理機制與解釋…………………………………………….……….…… 6
1.4 研究方向……………………………………………………………………..12
第二章數值方法……….………….……………………………………….. 14
2.1有限元素法(Finite-Element Method)簡介……………………………………14
2.2統御方程式和邊界條件的設定………………………………………………15
2.3無因次化後的統御方程式……………………………………………………17
2.4 FIDAP使用的數值演算法…………………………………………………...18
2.4.1 分離變數法……………………………………………….………….….19
2.4.2 數值收斂條件…………………………………………….…………... ..21
2.5 FIDAP的解題步驟…………………………………………………………...21
2.6前處理階段、處理階段和後處理階段簡介…………………………………22
第三章結果與討論………………………………………………………… .24
3.1 低流速平行板流場之模擬…………………………………………………..25
3.1.1 物性參數及網格設定…………………………………………………...25
3.1.2 結果比較………………………………………………………………...25
3.2 壓縮流與非壓縮流的比較…………………………………………………..31
3.3極低流速平行板流場之模擬………………………………………………...32
3.3.1 物性參數及網格設定…………………………………….……………..33
3.3.2 結果比較………………………………………………………………...33
3.4 入口處流速的陡升現象及不同壁溫下的熱流現象分析…………………..37
3.4.1 物理量參數及網格設定………………………………….……………. 38
3.4.2 結果比較……………………………………………………………..….38
第四章結論…………………………………………………………………..42
參考文獻……………………………………………..…………….……………74
表目錄
頁次
表1 Harley等人(1995)模擬平行板流場的物性參數 69
表2 流場格點密度與流場流速範圍關係，格點在流場y方向的延伸率均為1.2 69
表3 本文的模擬流場與Harley等人(1995)的流場差異，(a) Main=0.07，(b) Main=0.21 70
表4 Chen等人(1998)模擬平行板流場的物性參數，參數值依據溫度T=314 K 71
表5 (a) Chen等人(1998)模擬非滑移流、滑移流的水平流速範圍，(b) 本文模擬非滑移流場的物性參數，雷諾數根據表4流場出口物性參數，Chen的物性參數為Re=(1.2~8.9)×10-3，Maout=(5~35)×10-4，Knout=0.055 72
表6 Kavehpour等人(1997)模擬平行板流場的物性參數 73
圖目錄
頁次
圖1 平行板流場的部份格點分佈 45
圖2 不同的流場格點密度時，流場中的水平流速分佈 45
圖3 流場中心沿水平方向的物性分佈與Harley等人(1995)的數據比較，入口流速Main=0.07 46
圖4 流場中心沿水平方向的物性分佈，入口流速Main=0.21 47
圖5 流場中心沿水平方向的水平速度剖面，入口流速Main=0.07 48
圖6 沿水平方向的水平速度剖面與Harley等人(1995)的數據比較，入口流Main=0.21 49
圖7 沿水平方向的水平速度剖面 (a) Beskok(1994)，(b)本文數值解 50
圖8 沿水平方向的垂直速度剖面與Harley等人(1995)的數據比較，入口流速Main=0.21 51
圖9 沿水平方向的流場溫度剖面與Harley等人(1995)的數據比較，入口流速Main=0.21 52
圖10 沿水平方向的流場壓力剖面與Harley等人(1995)的數據比較，入口流速Main=0.21 53
圖11 不同的壓力比(PR)，壓縮流在微型流道沿水平方向的壓力分佈 54
圖12 不同的壓力比(PR)，壓縮流在微型流道沿水平方向的水平速度分佈 55
圖13 不同壓力比(PR)條件下，壓縮性對於質流量率的影響，為出口處的質流量率 56
圖14 沿水平方向的流場中心壓力分佈與Chen等人(1998) 的數據比較，(a) 依據非滑移模式下的入口流速，(b) 依據滑移模式下的入口流速 57
圖15 Chen等人(1998) 分別在滑移流、非滑移流模式，沿水平方向的流場中心水平速度分佈 58
圖16 沿水平方向的流場中心壓力分佈與Pong等人(1994)的實驗數據比較 59
圖17 分別以Chen等人(1998) 在滑移流與非滑移流模式下(PR=2.02)的入口流速為模擬流場依據時的剪應力分佈 60
圖18 (a) 沿水平方向的流場中心水平速度分佈與Chen等人(1998)的非滑移流數據比較，(b) Guo(2000)的數值模擬，實驗數據出處 Li等人(2000) 61
圖19 沿水平方向的水平速度剖面與Chen等人(1998) 的非滑移流數據比較 62
圖20 與Chen等人(1998 )的質流量－壓力比比較 63
圖21 與Arkilic等人(1995)的質流量－壓力比，實驗數據比較　　64
圖22 沿水平方向的流場中心物性分佈 (a) Kavehpou(1997)，(b) 本文數值解，u＊=u/uin，ρ*=ρ/ρin，Knin=0.005，Re=0.01 65
圖23 入口處溫度剖面與Kavehpour等人(1997)的數據比較，Knin=0.01，Re=0.01 66
圖24 入口處水平流速剖面與Kavehpour等人(1997)的數據比較，Knin=0.01，Re=0.01 67
圖25 流場入口處在不同壁溫下的紐索數分佈比較，(a) 本文結果，(b) Kavehpour (1997)數值解 68

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指導教授

吳俊諆(Jiunn-Chi Wu)

審核日期

2002-7-12

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