以數值模擬探討微管流之物理效應

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姓名

林冠宏(Kuan-Hung Lin) 查詢紙本館藏

畢業系所

機械工程學系

論文名稱

以數值模擬探討微管流之物理效應
(Investigations of physical effects in microchannels by numerical simulation)

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摘要(中)

本文是利用FEMLAB軟體（依據有限元素法）模擬可壓縮氣體在微流道（平行板以及圓管）的熱流特性和物理效應，並與解析解、實驗數據以及他人的數值結果比對。馬赫數與雷諾數分別介於0.5×10-3 有鑒於前人（陳家勇,="" 2002）的數值解並未考慮邊界上不連續的滑動速度、溫度躍昇現象，使其數值解並不完備。因此，為補足前人在探討微管流物理效應之不足，除了滑動流之修正外，本文也考慮多重物理效應（稀薄效應、壓縮性、黏滯消散以及可逆功）對流場熱流特性的影響；而這些效應在傳統管多被忽略。同時利用三種滑動模式探討克德森數在落入過渡流後的速度與壓降分佈。由數值結果發現：1)="" 隨進口壓力的增加，非線性壓力分佈愈明顯；2)="" 滑動流之質量流率高於不可滑動流；3)="" 流體之壓縮性隨進口壓力增高而增大，加上流場並不會形成完全發展流，因此摩擦係數已不再是定值，而是局部馬赫數之函數；4)="" 隨管徑縮減，黏性耗散愈明顯；5)="" 當克德森數逐漸落入過渡流後，利用一階滑動邊條件所得之速度分佈會愈趨扁平，與兩種修正模式之差異也愈大，隨克德森數之增高此現象愈明顯，修正模式所得之速度分佈則仍是維持類似拋物線的型態。

摘要(英)

本文是利用FEMLAB軟體（依據有限元素法）模擬可壓縮氣體在微流道（平行板以及圓管）的熱流特性和物理效應，並與解析解、實驗數據以及他人的數值結果比對。馬赫數與雷諾數分別介於0.5×10-3 有鑒於前人（陳家勇, 2002）的數值解並未考慮邊界上不連續的滑動速度、溫度躍昇現象，使其數值解並不完備。因此，為補足前人在探討微管流物理效應之不足，除了滑動流之修正外，本文也考慮多重物理效應（稀薄效應、壓縮性、黏滯消散以及可逆功）對流場熱流特性的影響；而這些效應在傳統管多被忽略。同時利用三種滑動模式探討克德森數在落入過渡流後的速度與壓降分佈。由數值結果發現：1) 隨進口壓力的增加，非線性壓力分佈愈明顯；2) 滑動流之質量流率高於不可滑動流；3) 流體之壓縮性隨進口壓力增高而增大，加上流場並不會形成完全發展流，因此摩擦係數已不再是定值，而是局部馬赫數之函數；4) 隨管徑縮減，黏性耗散愈明顯；5) 當克德森數逐漸落入過渡流後，利用一階滑動邊條件所得之速度分佈會愈趨扁平，與兩種修正模式之差異也愈大，隨克德森數之增高此現象愈明顯，修正模式所得之速度分佈則仍是維持類似拋物線的型態。
This work studies the compressible gaseous flow in microchannels (diameter size ranging from 0.01 μm to 0.01 m) using the FEMLAB software. Simulations are performed by solving Navier-Stokes equations with modification wall boundary conditions (slip velocity and temperature jump). The flow regime simulated is from the slip flow upto the transitional flow, which consist of the following flow parameters: 0.224≦Kn≦3.44, 10-3≦Re≦800 and 0.5x10-3≦Ma≦0.84. In order to thoroughly analyze various physical effects in the microchannel flow, this work studies multiphysics effects (rarefaction, compressibility, viscous dissipation, reversible work) on the thermal-flow characteristics of the microchannel. Results reveal several interesting features: 1) as the inlet pressure increase, the streamwise nonlinear pressure distribution appears visibly
2) the slip flow has a higher mass flowrate than that of the nonslip flow
3) compressibility effect cause the local friction factor increases with increasing local Ma
4) due to high velocity gradients in the microchannel flow, viscous dissipation and reversible work can not be neglected
5) first-order slip velocity gives unrealistically over-prediction of velocity at transitional flow regime, and the new continuum based slip model is extended successfully to the transitional flow regime..

關鍵字(中)

★ 黏滯消散
★ 壓縮效應
★ 稀薄效應
★ 微管流

關鍵字(英)

★ Microchannel flow
★ Compressibility
★ Rarefaction
★ Viscous dissipation

論文目次

目錄
頁次
摘要 I
英文摘要 III
目錄 V
表目錄 VII
圖目錄 VIII
符號說明 XIII
第一章前言 1
1.1 研究動機 1
1.2 微小管道中之熱流現象 2
1.3 文獻回顧 8
1.4 研究目的 15
第二章數值分析 16
2.1 有限元素法（Finite Element Method） 16
2.2 形狀函數 17
2.3 統馭方程式 18
2.4 通式(General form)與弱式(Weak form) 21
2.5 邊界條件與起始條件 25
2.6 摩擦係數與摩擦係數鈕索數 28
第三章結果與討論 29
3.1 稀薄效應與壓縮效應 29
3.2 切線動量調整係數對流場的影響 32
3.3 溫度躍昇 34
3.4 黏滯消散與可逆功 35
3.5 修正滑動速度 37
第四章結論與建議 39
4.1 結論 39
4.2 建議 40
參考文獻 42
附錄 A 46

參考文獻

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指導教授

吳俊諆(Jiunn-Chi Wu)

審核日期

2003-7-14

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