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研究生:姚煥堂
研究生(外文):YAO HUAN-TANG
論文名稱:有限體積法在高雷諾數矩形流道之流場與溫度場之分析
論文名稱(外文):High Reynolds Number Flow Field and Temperature Field Analysis with the Finite Volume Method in the Rectangular Duct
指導教授:莊福盛
學位類別:碩士
校院名稱:國立臺灣科技大學
系所名稱:機械工程系
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2001
畢業學年度:89
語文別:中文
論文頁數:62
中文關鍵詞:有限體積法矩形流道高雷諾數等溫邊界
外文關鍵詞:finite volume methodRectangular Ducthigh Reynolds numberisothermal
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摘要
本文主要是使用數值的方法之有限體積法 (finite volume method)來計算高雷諾數在具阻礙物之矩形流道內流體的發展 (developing) 情形,但流體限定在是層流(laminar)的情況下,配合等溫 (isothermal) 的邊界條件下,求出速度分佈與溫度分佈。此外還針對不同阻礙物高度與矩形流道高度之比 (F/H) ,加以分析其在矩形流道之速度與溫度分佈 ,由速度圖和溫度圖來探討對熱傳效果的影響。

Abstract
The purpose of this study is to use the finite volume method of the numerical method to investigate high Reynolds number flow in the developing situation of fluid in a rectangular duct with baffles.The flow is laminar and with isothermal boundary. The influences of various factors, such as the ratio of obstacle’s height and rectangle’s height (F/H) on the velocity and temperature distributions are studied.

目 錄
中文摘要 ........................i
英文摘要 ........................ii
誌謝 ..........................iii
目錄 .........................v
圖索引 ........................viii
表索引 ........................xi
符號索引 .......................xii
第一章 緒論.........................1
1.1 前言..........................1
1.2 文獻回顧........................2
1.2.1 數值方法......................2
1.2.2 矩形流道......................3
1.3 研究目的........................4
1.4 內容大綱........................5
第二章 理論分析.......................6
2.1 幾何模型........................6
2.2 基本假設........................7
2.3 統御方程式.......................7
2.4 邊界條件........................8
第三章 數值分析.......................11
3.1 格點配置 .......................11
3.2差分方程式 ......................12
3.2.1 連續方程式....................12
3.2.2 動量方程式....................13
3.2.3 能量方程式....................16
3.3 演算過程........................18
3.4 收斂條件........................20
第四章 結果與討論......................29
4.1 程式測試與分析.....................29
4.2 速度場分析.......................30
4.3 溫度場分析.......................32
第五章 結論與展望......................57
5.1 結論..........................57
5.2 未來展望........................58
參考文獻 .........................59
圖索引
圖2.1 具阻礙物之矩形流道幾何模型..............10
圖3.1 交錯式網格節點配置圖 ................21
圖3.2 連續方程式示意圖...................22
圖3.3 X方向動量方程式控制體積圖 .............23
圖3.4 Y方向動量方程式控制體積圖..............24
圖3.5 X方向動量方程式二維離散網格節點示意圖........25
圖3.6 Y方向動量方程式二維離散網格節點示意圖........26
圖3.7 T能量方程式二維離散網格節點示意圖..........27
圖3.8 程式流程圖......................28
圖4.1 平板流道,在 位置的速度剖面圖.........34
圖4.2 平板流道,在 位置的速度剖面圖.........35
圖4.3 平板流道,在 位置的速度剖面圖.........36
圖4.4 平板流道,在 位置的速度剖面圖.........37
圖4.5 阻礙物高與矩形高比為1/3,
雷諾數為1000之速度圖................38
圖4.6 阻礙物高與矩形高比為1/3,
雷諾數為1400之速度圖................39
圖4.7 阻礙物高與矩形高比為1/3,
雷諾數為1800之速度圖................40
圖4.8 阻礙物高與矩形高比為1/2,
雷諾數為1000之速度圖................41
圖4.9 阻礙物高與矩形高比為1/2,
雷諾數為1400之速度圖................42
圖4.10 阻礙物高與矩形高比為1/2,
雷諾數為1800之速度圖................43
圖4.11 阻礙物高與矩形高比為2/3,
雷諾數為1000之速度圖................44
圖4.12 阻礙物高與矩形高比為2/3,
雷諾數為1400之速度圖................45
圖4.13 阻礙物高與矩形高比為2/3,
雷諾數為1800之速度圖................46
圖4.14 阻礙物高與矩形高比為1/3,
雷諾數為1000配合等溫邊界之等溫線分佈圖.......47
圖4.15 阻礙物高與矩形高比為1/3,
雷諾數為1400配合等溫邊界之等溫線分佈圖.......48
圖4.16 阻礙物高與矩形高比為1/3,
雷諾數為1800配合等溫邊界之等溫線分佈圖.......49
圖4.17 阻礙物高與矩形高比為1/2,
雷諾數為1000配合等溫邊界之等溫線分佈圖.......50
圖4.18 阻礙物高與矩形高比為1/2,
雷諾數為1400配合等溫邊界之等溫線分佈圖.......51
圖4.19 阻礙物高與矩形高比為1/2,
雷諾數為1800配合等溫邊界之等溫線分佈圖.......52
圖4.20 阻礙物高與矩形高比為2/3,
雷諾數為1000配合等溫邊界之等溫線分佈圖.......53
圖4.21 阻礙物高與矩形高比為2/3,
雷諾數為1400配合等溫邊界之等溫線分佈圖.......54
圖4.22 阻礙物高與矩形高比為2/3,
雷諾數為1800配合等溫邊界之等溫線分佈圖.......55
表索引
表4.1 不同格點數之 與 比較表 ...........56

參考文獻
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[6] S. V. Patanker, D. Rafiinejda and D. B. Spalding, 1975,"Calculation of Three-Dimensional Boundary Layer with Solution of All Three Momentum Equations", Computational Methods Application Mechanical Engineering, Vol. 6.pp. 245-253.
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[10] R. J. Goldstein, and D. K. Kreid, 1967,"Measurement of Laminar Flow Development in a Square Duct Using a Laser-Doppler Flowmeter", Journal of Applied Mechanics, Vol. 34.pp. 35-41.
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[17] J. B. Aparecido and R. M. Cotta, 1990,"Thermally Developing Laminar Flow Inside Rectangular Ducts", International Journal Heat and Mass Transfer, Vol. 33.pp. 288-301.
[18] C. H. Cheng and C. J. Weng, 1993,"Developing Flow of Mixed Convection in a Vertical Rectangular Duct with One Heating Wall", Numerical Heat Transfer, Part A, Vol. 24.pp. 432-442.
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