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研究生:張光宇
研究生(外文):Kuang-Yu Chang
論文名稱:多孔性介質與流體性質對於環狀混合對流場穩定性的影響
指導教授:李石頓李石頓引用關係
指導教授(外文):Shih-Tuen Lee
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:機械工程學研究所
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:92
中文關鍵詞:多孔性介質穩定性分析福海門數改良式達西數布雷克門
外文關鍵詞:porous mediumstability analysisForchheimer numbermodified Darcy numberBrinkman
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本研究之目的在探討不同的改良式達西數(modified Darcy number,Da*)、福海門數(Forchheimer number,Fo)與改良式普朗特數(modified Prandtl number,Pr*)對環狀管內混合對流場穩定性的影響。本文採用改良式布雷克曼-福海門-達西模型(Brinkman-Forchheimer-extended Darcy model)來模擬流體於高滲透率的多孔性介質中的流動行為,並使用膺頻譜謝比雪夫定置法(Pseudospectral Chebyshev collocation method)處理數值問題。
本研究假設內徑與內外徑間距的比值(縱橫比)為2.414,內管溫度較外管高,在此情況下縱橫比、Pr* 對穩定性的影響較明顯。計算的結果顯示,Da* 與Pr* 對於流場的穩定性有極顯著的影響,而Fo的影響則在Da* 或Re或Pr* 較大時較明顯;越低的Pr*與越低的Da*與越高的Fo可建構出較穩定的流動;縱橫比的減少或Pr*的降低或Da*的增加將有助於非對稱擾動的產生;就影響的程度而言,縱橫比與Pr*是影響流場穩定性的最主要因素,其次為Da*,Fo的影響程度則視Pr*、Da*與Re的大小決定。

The purpose of this study is to find the effects of the modified Darcy number Da*, Forchheimer number Fo and modified Prandtl number Pr* on the linear stability characteristics of mixed-convection flow in the annular tubes. In this study the flow in the high specific permeability porous medium is simulated by Brinkman-Forchheimer-extended Darcy model, and the Pseudospectral Chebyshev collocation method is employed in the numerical calculation.
In this study, the ratio(aspect ratio)of the inner radius to the distance between the inner and outer tubes is assumed to be 2.414, and temperature of the inner wall is higher than that of outer wall. In this situation, more significant effects of the aspect ratio, Pr* on the stability characteristics can be found. Calculation results show that the modified Darcy number and the modified Prandtl number have important effects on the stability characteristics. Forchheimer number has more significant effect as the modified Darcy number or the Reynolds number or the modified Prandtl number is large. The lower modified Prandtl number, and modified Darcy number and the higher Forchheimer number are, the more stable flow is. It’s easy to induce axisymmetric disturbances as the aspect ratio decreases or the modified Prandtl number decreases or the modified Darcy number increases. Aspect ratio and the modified Prandtl number play most important roles in the flow stability, the effect of the modified Darcy number is secondary, and the importance of the Forchheimer number depends on the magnitudes of the modified Pandtl number, modified Darcy number and Reynolds number.

誌 謝………………………………………………………………i
摘 要………………………………………………………………ii
英 文 摘 要………………………………………………………iii
表 目 錄 …………………………………………………………v
圖 目 錄 …………………………………………………………vi
符 號 說 明………………………………………………………viii
目 錄 ……………………………………………………………xii
第 一 章前言……………………………………………………1
1.1緒論……………………………………………………1
1.2文獻回顧………………………………………………2
1.3本文研究方向…………………………………………6
第 二 章數學模式………………………………………………7
2.1統御方程式……………………………………………7
2.2邊界條件………………………………………………8
2.3無因次化方程式………………………………………9
2.4基礎狀態………………………………………………11
2.5線性穩定性分析………………………………………12
第 三 章數值方法………………………………………………16
3.1膺頻譜謝比雪夫定置法………………………………16
3.2準確度分析……………………………………………19
3.3能量平衡分析…………………………………………21
第 四 章結果與討論……………………………………………23
4.1基礎層流速度分佈……………………………………24
4.2中性穩定曲線分佈結果………………………………25
4.2.1Pr*=1、Da*=1時的中性穩定曲線分佈………………25
4.2.2Pr*=1、Da*=0.01時的中性穩定曲線分佈 ………… 27
4.2.3Pr*=1、Da*=0.0001時的中性穩定曲線分佈 ………29
4.2.4小結……………………………………………………31
4.2.5Pr*=10、Da*=1時的中性穩定曲線分佈 ……………32
4.2.6Pr*=10、Da*=0.01時的中性穩定曲線分佈………… 33
4.2.7Pr*=10、Da*=0.0001時的中性穩定曲線分佈………35
4.2.8小結……………………………………………………37
4.2.9Pr*=100、Da*=1時的中性穩定曲線分佈……………37
4.2.10Pr*=100、Da*=0.01時的中性穩定曲線分佈 ………40
4.2.11Pr*=100、Da*=0.0001時的中性穩定曲線分佈 ……42
4.2.12小結……………………………………………………44
4.3縱橫比的影響…………………………………………44
4.4Pr*、熱剪應力模態與熱浮力模態 …………………46
第 五 章結論……………………………………………………47
參 考 文 獻………………………………………………………49
附 錄 一謝比雪夫多項式特性…………………………………54
附 錄 二式(3-6)~(3-8)的係數 ………………………………55
附 錄 三邊界條件的展開………………………………………59
附 錄 四能量平衡關係式的推導………………………………60
表 …………………………………………………………………64
圖 …………………………………………………………………72

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