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研究生:陳玉芬
研究生(外文):Yu-Feng Chen
論文名稱:NAPPLE法則於各類型不可壓縮黏性流場之應用
論文名稱(外文):NAPPLE Algorithm for Various Flow Configurations of Incompressible Viscous Flows
指導教授:李雄略李雄略引用關係
指導教授(外文):Shong-Leih Lee
學位類別:博士
校院名稱:國立清華大學
系所名稱:動力機械工程學系
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:2002
畢業學年度:90
語文別:中文
論文頁數:129
中文關鍵詞:NAPPLE法則棋盤式誤差鬆弛係數自由液面收縮(阻塞)管道自然對流背向階梯
外文關鍵詞:NAPPLE AlgorithmCheckerboard errorunder-relaxation factorfreesurfaceconstricted tubenatural convectionbackward-facing step flow
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本文將在直角座標上求解不可壓縮流壓力場的「NAPPLE法則」推展至通用曲線座標系統上。NAPPLE法則基本上是利用差分後的動量方程式帶入差分後的連續方程式中所得到的一個壓力聯結方程式,但是NAPPLE法則最大的特點是在推導的過程中,採用一個特殊的近似假設,成功的使得壓力及速度間有很強的相聯性,如此除了可以避免棋盤式的誤差外,並可以使所求得的數值解不再和鬆弛係數(under-relaxation factor)有關,這一點也是NAPLLE法則和壓力權重內差(PWIN)等使用速度內差的方法之間最大不同的地方。除此之外,在求解的過程中,不需要利用壓力修正方程式,而是直接利用所推導的壓力聯結方程式求解壓力場。因此利用NAPPLE法則求解壓力時,就跟在求解熱傳導方程式一樣簡單。為了驗證NAPPLE法則的性能,求解包括(1)週期槽池明渠流流場;(2)完全發展圓管和背向階梯紊流流場;(3)阻塞圓管管道內的層流流場和紊流流場及(4)兩平行圓環間由於溫度差所造成的自然對流流場等六個不同類型的流場問題。在明渠流流場的計算結果中,除了說明了發生不連續液面的原因外,計算所得的液面高度和實驗驗證也只有不到5%的誤差。在計算阻塞管道層流流場及兩平行圓環間的自然對流流場時,除了計算結果和流線渦流法的結果相同外,並說明了自然對流流場在內圈圓環為上偏心時,所有計算結果均低於實驗結果是由於實驗時有Benard instability所造成的。至於在計算紊流流場時,除了在分離流的區域外,對其餘流場的模擬結果均具有很高的精確度。由以上的計算結果,證明曲線座標系統下的NAPPLE法則在計算本文所列舉不同類型不可壓縮流流場的準確性與適用性。
摘要 i
誌謝 ii
目錄 iii
圖表目錄 vii
符號說明 x
第一章 緒論 1
1.1 前言 1
1.2 文獻回顧 2
1.3 研究方法與內容 5
第二章 統御方程式與NAPPLE法則的推導 8
2.1 統御方程式 8
2.2 座標轉換 9
2.3差分方法 10
2-4曲線座標系統下壓力聯結方程式的推導 13
2.5 直角座標與曲線座標NAPPLE法則的可逆 16
第三章 自由液面的演算及紊流模式 18
3.1自由液面流 18
3.1.1統御方程式 18
3.1.2插分方法 22
3.1.3自由液面變遷的演算 26
3-2紊流模式 27
3.2.1統御方程式 27
3.2.2座標轉換 31
3.2.3 模式近壁區域的處理 33
第四章 週期槽池黏性明渠流 37
4.1 問題描速與基本假設 37
4.2理論分析與統御方程式 38
4.3實驗驗證方法 41
4.4結果與討論 41
第五章 正交格點系統下紊流流場之數值模擬 50
5.1完全發展圓管流流場 50
5.1.1問題描速及基本假設 50
5.1.2統御方程式 50
5.1.3計算結果 54
5.2背向階梯紊流流場 56
5.2.1問題描述與基本假設 56
5.2.2統御方程式 57
5.2.3結果與討論 58
第六章 阻塞管道內之流場計算 61
6.1層流場 61
6.1.1問題描述及基本假設 61
6.1.2 統御方程式及邊界條件 62
6.1.3結果與討論 63
6.2紊流場 66
6.2.1問題描述 66
6.2.2統御方程式及邊界條件 66
6.2.3結果與討論 68
第七章 兩平行圓環間的自然對流效應 69
7.1物理問題 69
7.2統御方程式及邊界條件 69
7.3結果與討論 71
第八章 結論 74
參考文獻 77
附錄A、圓柱座標系統的統御方程式 83
A.1 層流流場 83
A.1.1統御方程式 83
A.1.2 座標轉換 84
A.2紊流場 85
A.2.1統御方程式 85
A.2.2座標轉換 89
A.3 壓力聯結方程式 91
作者簡歷 128
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