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研究生:陳壽德
研究生(外文):Shou-Te Chen
論文名稱:利用修正後之特徵寬度擴散渦漩法模擬共轉渦漩流場融合過程之研究
論文名稱(外文):The Study of Using Corrected Core Spreading Vortex Method for Simulating The Merging Process of Co-ratating Vortices
指導教授:黃美嬌黃美嬌引用關係
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
畢業學年度:94
語文別:中文
論文頁數:93
中文關鍵詞:渦漩法渦泡分裂渦泡融合共轉渦漩
外文關鍵詞:Vortex MethodCore SpreadingVortex SplittingVortex MergingCo-rotating Vortices
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本論文利用修正後之軸擴散渦漩法來模一對擁有相同強度,並且彼此繞著對方旋轉的渦漩流場。原本的軸擴散渦漩法並無法正確地收斂至Navier-stokes方程式,為了改善上述缺點,可以使用splitting方法來限制模擬中渦泡之特徵寬度大小,將特徵寬度較大的母渦泡分裂為數個特徵寬度較小之子渦泡,避免其特徵寬度太大使得誤差超出容忍範圍。我們將splitting方法再加以修正,保留了分裂前的母渦泡,使其以弱於分裂前之強度存在著。為了避免多次splitting過程造成渦泡數量過多,增加模擬時間,我們將強度、特徵寬度相似,且距離非常接近的渦泡融合(merge)成為一顆,藉此控制渦泡數量。
在模擬過程中,兩個渦漩慢慢地靠近對方,最後會融為一體。融合過程主要可以分為四個階段,其中convective stage為整個過程的核心部份。兩個渦漩在此階段會有明顯的形狀改變,且開始彼此靠近。最後,有學者提到若是使用rotating reference frame (即觀察者隨著渦漩移動) 觀察流場之流線圖形,其流場原點附近之流線圖形會由saddle圖形變為center圖形,即使此時兩渦漩尚未達到fully merge階段。我們認為其原因與觀察者的旋轉速度有關。因此我們嘗試去探討此兩者之間的關聯性。
Simulations for a pair of equal-strength co-rotating vortices in use of improved core spreading vortex method is discussing in the thesis. The core spreading vortex methods generally have the problem of no correct convergence to the Navier-Stokes equations. To be correct, the core size of simulated vortex elements cannot be too large. The technique of splitting a fat vortex element into some thin ones in order to fix the convergence problem is convenient and efficient. In particular, it keeps the method purely Lagrangian. A new splitting method in which several weaker child vortices surround a thinned but still strong parent vortex is proposed. The computational amount on the other hand is kept reasonably large by merging similar and close-by vortices.

According to previous experiment research, it is found that complete merging undergoes four stages with physical meaning. The second (convective) stage represents the heart of the vortex merging process. The vortices become markedly deformed, and closer. It is also found that the time required for merging is inversely proportional to the square root of the Reynolds number. If one observes the streamlines in a rotating reference frame(observer moves with the vortices), then one finds the central saddle point vanishes, despite the fact that the vorticity still has two distinct peaks and mergers is not complete. We think that it is concerned with the rotating speed of the observer. Eventually, we try to find out the relationship between the rotating speed of the observer and the streamline patterns.
目錄

中文摘要 v
英文摘要 vii
表目錄 xi
圖目錄 xii
符號說明
第一章 緒論 1
1-1 離散渦漩法 1
1-2 研究動機與目的 6
1-3 論文架構 8
第二章 數值方法 9
2-1 Core-spreading vortex method(CVM) 9
2-2 渦泡分裂方法(Splitting Method) 13
2-2-1 Splitting Scheme I 13
2-2-2 Splitting Scheme IV 14
2-3 渦泡融合方法(Merging Method 16
第三章 Co-rotating Vortices 流場 20
3-1 起始條件 20
3-1-1 起始條件之產生 20
3-1-2 參數設定 21
3-1-3 起始條件之驗證 22
3-2 模擬流場介紹 24
3-2-1 參數設定 24
3-2-2 Co-rotating Vortices融合過程 25
3-2-3 改變雷諾數及b0對於d(t) 的影響 27
3-3 Laminar and turbulent vortex merger 29
3-3-1 Lamiar vortex merger 29
3-3-2 Turbulent vortex merger 31
第四章 使用Rotating Reference Frame之流場探討 33
4-1 流場介紹 33
4-2 臨界旋轉速度 35
4-3 結果討論 39
第五章 結論 41
參考文獻 43
參考文獻

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