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Title: | 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 The Study of Using Corrected Core Spreading Vortex Method for Simulating The Merging Process of Co-ratating Vortices |
Authors: | Shou-Te Chen 陳壽德 |
Advisor: | 黃美嬌 |
Keyword: | 渦漩法,渦泡分裂,渦泡融合,共轉渦漩, Vortex Method,Core Spreading,Vortex Splitting,Vortex Merging,Co-rotating Vortices, |
Publication Year : | 2005 |
Degree: | 碩士 |
Abstract: | 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. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/34939 |
Fulltext Rights: | 有償授權 |
Appears in Collections: | 機械工程學系 |
Files in This Item:
File | Size | Format | |
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ntu-94-1.pdf Restricted Access | 8.43 MB | Adobe PDF |
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