微管流之層流與紊流模擬

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姓名

陳達建(Ta-Chien Chen) 查詢紙本館藏

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機械工程學系

論文名稱

微管流之層流與紊流模擬
(Laminar and turbulent flow simulation for the microchannels)

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摘要(中)

中文摘要

本文以數值模擬微管流層流與紊流的熱流場特性，流道包括梯形微管道、平行板與圓管，水力直徑範圍在Dh=50μm–1.81mm；使用軟體FEMLAB的數值解並與實驗數據與傳統理論作比對。其中模擬微小圓管（Dh=50–101μm）層流場以黏性粗糙度模式 (RVM) 來分析粗糙度效應。結果顯示在Re <400條件下，梯形微管道摩擦因子（f）數值解與實驗數據與理論解相符。層流微小圓管中，採用RVM模式的數值解會使流動阻抗降提高因而降低體積流率；f數值解與實驗數據相近但低於傳統理論解。在Re >1500，因流場可能進入過渡區而使本文RVM數值解與Mala (1999) 的RVM數值解偏離實驗結果。小圓管紊流計算使用k-ε模式與壁面定律，但在4000< Re <10000範圍的f數值解皆高於實驗量測與傳統理論解約30%，由於標準k-ε模式只適用於高雷諾數及受限於軟體無法調整紊流模式的經驗係數，導致本文紊流模擬誤差過高。

比較Gao等人(2001)與楊建裕等人(2001)的熱傳實驗結果，發現平板流道高等於0.4mm和0.7mm的局部Nu計算值與實驗數據相近。而對在高雷諾數(Re=1687) 圓管流，靠近出口的局部Nu值的實驗值與數值預測結果皆高於傳統理論解，根據實驗的解釋是因為管長不足以達到完全發展溫度場，造成實驗量測與數值預測高於層流理論解。

摘要(英)

本文以數值模擬微管流層流與紊流的熱流場特性，流道包括梯形微管道、平行板與圓管，水力直徑範圍在Dh=50μm–1.81mm；使用軟體FEMLAB的數值解並與實驗數據與傳統理論作比對。其中模擬微小圓管（Dh=50–101μm）層流場以黏性粗糙度模式 (RVM) 來分析粗糙度效應。結果顯示在Re <400條件下，梯形微管道摩擦因子（f）數值解與實驗數據與理論解相符。層流微小圓管中，採用RVM模式的數值解會使流動阻抗降提高因而降低體積流率；f數值解與實驗數據相近但低於傳統理論解。在Re >1500，因流場可能進入過渡區而使本文RVM數值解與Mala (1999) 的RVM數值解偏離實驗結果。小圓管紊流計算使用k-ε模式與壁面定律，但在4000< Re <10000範圍的f數值解皆高於實驗量測與傳統理論解約30%，由於標準k-ε模式只適用於高雷諾數及受限於軟體無法調整紊流模式的經驗係數，導致本文紊流模擬誤差過高。
比較Gao等人(2001)與楊建裕等人(2001)的熱傳實驗結果，發現平板流道高等於0.4mm和0.7mm的局部Nu計算值與實驗數據相近。而對在高雷諾數(Re=1687) 圓管流，靠近出口的局部Nu值的實驗值與數值預測結果皆高於傳統理論解，根據實驗的解釋是因為管長不足以達到完全發展溫度場，造成實驗量測與數值預測高於層流理論解。A numerical study was performed to analyze the laminar and turbulent flow and heat transfer characteristics for various types microchannel flow. The types of microchannel flow including the parallel plate, circular tube and the trapezoidal duct, where the hydraulic diameter ranging from 50μm to 4mm. Numerical solution using the software FEMLAB are compared with experiment and theory. In addition, the roughness viscosity model (RVM) was adopted to simulate the roughness effect in the circular tube (Dh=50–101μm). Results show that when Re<400, predictions of friction factors (f) of the laminar flow in the trapezoidal duct are agreed with the experimental data and the theory. For laminar microtube flow, solutions using RVM would induce higher flow resistance and thus reduce the volume flowrate. Prediction of friction factors matches experimental data but are lower than conventional theory. When Re>1500, present solutions using RVM disagree with Mala’s (1999) RVM solutions due to the early transition to turbulent flow at Re=1500. Calculation for turbulent microtube flow are performed using the k-ε model and law of the wall, and higher f’s (about 30%) values than experiment and theory is found in the flow regime of 4000 For the case of heat transfer in the parallel plate, calculations of the local Nu compare well with available experimental measurement for the channel height equal to 0.4mm and 0.7mm. In the microtube flow at high Re (Re=1687), both experimental and numerical results of Nu close to the exit of tube are higher than the classical theory. Based on experiment’s explanation, the tube is not long enough for flow reaching the thermal fully developed condition, and thus cause experimental and numerical data higher than the theatrical value.

關鍵字(中)

★ 紊流k-ε模式
★ 黏性粗糙度模式
★ 紊流
★ 數值模擬
★ 微管流

關鍵字(英)

★ Turbulent flow
★ k-ε turbulence model
★ Roughness viscosity model
★ Numerical simulation
★ 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 vii
圖目錄 viii
符號說明 xi
第一章緒論 1
1.1 研究動機 1
1.2 文獻回顧 2
1.3 微管道與傳統管道的熱流現像偏差原因 7
1.4 研究方向 13
第二章數值模擬方法 14
2.1 有限元素法簡介 14
2.2 數值模擬軟體（FEMLAB）介紹 15
2.3. 統御方程式與流場邊界條件 16
2.3.1 梯形管流場數值模擬 16
2.3.2 紊流流場數值模擬 16
2.3.3 層流微小管RVM數值模擬 19
2.3.4 層流熱傳數值模擬 20
2.3.5 邊界條件與壁面定律(Law of the wall) 21
第三章數值模擬結果與討論 24
3.1 層流數值模擬結果 24
3.1.1 梯形管格點數分析 24
3.1.2 速度分佈 26
3.1.3 壓力梯度 27
3.1.4 摩擦因子值比較 28
3.2 層流微小圓管RVM數值模擬結果 29
3.2.1 粗糙度黏性比較 29
3.2.2 速度剖面比較 29
3.2.3 體積流率比較 30
3.2.4 摩擦因子比較 31
3.3 紊流數值模擬結果 32
3.3.1速度分佈 32
3.3.2壓力分佈 33
3.3.3摩擦因子比較 33
3.4 熱傳數值模擬結果比較 34
3.4.1 溫度分佈 35
3.4.2 局部Nu比較 35
第四章結論與建議 37
參考文獻 40

參考文獻

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指導教授

吳俊諆(Jiunn-Chi Wu)

審核日期

2003-7-16

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