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研究生:闕志哲
研究生(外文):Chih-Che Chueh
論文名稱:建構於動態非結構網格之定命性渦元法
論文名稱(外文):A Deterministic Vortex Method on Dynamic Unstructured Grids
指導教授:張建成張建成引用關係
指導教授(外文):Chien-Cheng Chang
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:應用力學研究所
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:2004
畢業學年度:92
語文別:中文
論文頁數:96
中文關鍵詞:Vortex Method
外文關鍵詞:渦元法
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傳統的數值方法用來求解不可壓縮流時,會遭遇數值方面的不穩定,因此在本文中使用穩定性相當高之Chang 和 Chern之渦元法搭配有限體積法來求解不可壓縮流,其渦旋度方程式之對流項利用面積加權算則來處理;此外在格點產生方面,因為非結構網格在處理複雜的邊界外形時較為快速,所以我們利用非結構網格取代結構性網格。將Chang的渦元法結合非結構性網格,可以分析更複雜的幾何形狀,而不在是侷限在某些特定的基本幾何形狀。本文主要是在驗證並探討Chang的渦元法結合非結構性網格之正確性與可靠性,因此測試的幾何形狀還是停留在圓柱、方柱、機翼(NACA0012)。除此之外,還利用機翼作俯仰運動,來測試動態網格的可用性,用來分析運動中的物體。
本文計算圓柱瞬間啟動流場比較Chang的新演算法之一階準確與舊演算法之二階準確渦元法,發現對於非結構網格來說,由於擴散理論的標準取值方面對於舊演算法之二階準確有實際上困難,而原本Chang 和 Chern渦元法是在結構性網格上發展,由於網格形狀規則,故對 的正確估算較容易,但對於網格形狀不規則的非結構網格來說,準確估算 時有實際上的困難,若勉強按擴散理論的標準取值找出一接近的 ,此時據以計算所得之圓柱阻力係數與Chang 和 Chern作比較時,發現整體流場趨勢相同,但數值上皆有些差距,這顯示不能依擴散理論的標準取值獲正確之 引起了數值不收斂的問題。經改成使用新演算法之一階準確(new approach)時,由於使用完全顯式(fully explicit scheme) 方法,因此 不受擴散理論的標準取值限制,計算結果與之比較非常吻合,但 必須取的很小( 很大會造成顯式法的數值不穩定)。
目 錄

第一章 導論..............................................1
1-1研究目的與動機……..………………………………….1
1-2文獻回顧..............................................2
1-3全文概要..............................................4

第二章 非結構網格產生法………………….......6
2-1概念……………...………………………………………6
2-2波前步進法……...………………………………………8
2-3動態網格產生法…...…………………………………..11
2-4靜態網格產生應用實例……………………….………12
2-5動態網格產生應用實例……………………….………15

第三章 非結構網格渦元法……...….………….18
3-1概念………………………………...…………………..18
3-2控制方程式………….………………..………………..19
3-2-1二維那維爾史托克方程式……………………..19
3-2-2邊界條件………………………………………..20
3-3渦元法之時間差分………………………..….……….21
3-4有限體積法與空間離散………..….……….………….27
3-5牛頓疊代法與隱式近似LU矩陣分解法…..………... 31
3-6數值邊界條件…………….…………………..………..32
3-6-1渦度數值邊界條件……………………………..32
3-6-2流線函數數值邊界條件………………………..33
3-7壓力、阻力與升力係數….…………………..………...35
3-8面積加權算則…………………..….……..…..………..39

第四章 結果與討論……………….……………40
4-1概念……………………………………………...……..40
4-2穩態黏性流流經圓柱〈Re=40〉………….……..……..41
4-3穩態黏性流流經圓柱〈Re=300,550,1000〉......43
4-4黏性流流經旋轉圓柱體之渦旋分離〈Re=1000〉…….44
4-5黏性流流經方柱體〈Re=1000〉……………………….44
4-6黏性流流經固定機翼NACA0012〈Re=1000〉………45
4-7模擬機翼等速拉升攻角 NACA0012〈Re=1000〉……46
4-8機翼作正弦函數俯仰運動 NACA0012〈Re=1000〉…47

第五章 結論與未來展望……………….………80
5-1結 論……………………………….…………………80
5-2未來展望與工作…………………….…………………81

附錄A 資料結構……………….………………83
參考文獻……………….……………….............91
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