黃美嬌臺灣大學：機械工程學研究所吳柏翰WU, BO-HANBO-HANWU2007-11-282018-06-282007-11-282018-06-282007http://ntur.lib.ntu.edu.tw//handle/246246/61515本篇論文利用Leonard之面積擴散渦漩法，結合Huang所提出的渦泡分裂與融合機制，來模擬二維黏性與無黏性對稱漩渦對的融合現象，探討其融合機制與動力學特性。 在無黏性流場部分，本研究的重點為因對流而從一漩渦跑向另一顆漩渦附近之渦度結構，稱之為類渦片結構，驗證此結構是造成漩渦融合的主因。接著我們從兩方面探討類渦片結構產生的原因：漩渦對流場的流線型態點明了exchange band的重要性；Yasuda模型說明一漩渦受到另一顆漩渦影響時的變形情形。此外，我們以『對稱橢圓漩渦對模型』探討漩渦變形與exchange band的存在關係。由於流體在無黏性流場時只受到壓力的作用，因此在本論文也探討壓力隨時間變化情形。最後探討兩漩渦初始中心距離對漩渦融合的影響。在黏性流場部分，研究再次驗證類渦片結構的產生與融合的關係，並觀察流線與壓力隨時間的變化情形，此外也探討擴散效應與雷諾數對融合過程的影響。 總結兩部分研究結果顯示，當兩漩渦距離夠近時，漩渦受另一顆漩渦影響而變形，部分渦度先進入exchange band，再對流至對方附近而產生了類渦片結構，從而造成兩漩渦融合。初始距離愈大，除了漩渦變形量愈小外，漩渦距離exchange band愈遠，兩因素有加乘的效果。因此，當初始距離大於某一臨界值時，渦度無法進入exchange band，類渦片不會產生，兩漩渦也就不會有融合的現象發生。而黏度會造成漩渦擴散，使得原不會進入exchange band的渦度會因擴散而進入，因此融合早晚會發生；此外，黏度也會減緩漩渦非軸對稱的變形。In use of Leonard’s vortex blob method, resurrected by Huang’s blob splitting and merging schemes, this thesis simulates the merging process of a 2D symmetry vortex pair and investigates the merging mechanism and dynamics associated with viscous and inviscid flows. When the flow is inviscid, we focus on the formation of a sheet-like structure which circulation is advected from one vortex to the other and verify it is responsible for the merger. Then from two aspects, we attempt to explain why such a sheet-like structure is generated. The streamline patterns illuminate the importance of the exchange band, and the Yasuda model explains the deformation of one vortex due to the straining of the other. Moreover, we build a symmetric elliptic vortex model to explore the relationship between the vortex deformation and the exchange band. In inviscid flow the pressure force is the only force. Its variation in time is also studied. Finally we investigate the influence of the initial distance between two vortices. In viscous flows, we verify the cause of merger again, namely the formation of the sheet-like structure. The temporal variations in the streamline patterns and in the pressure field are observed. The effect of diffusion or Reynolds number on the merging process is investigated as well. To summarize, the investigation shows that when the vortices are close enough, vortices are deformed due to the mutual straining, partial vorticity enters into the exchange band and is advected toward the other vortex, and the sheet-like structure is thus formed, which causes merger. The larger the distance between vortices, the smaller the deformation is, and the farther the vortex is away from the exchange band. Therefore, when the distance is larger than some critical value, vortices will not merge. When the flow is viscous, nonetheless, vorticity will diffuse into the exchange band sooner or later and vortices will eventually merge. Moreover, the viscous effect will also relax the asymmetric deformation of vortices.口試委員審定書 i 致謝 ii 中文摘要 iii 英文摘要 iv 表目錄 ix 圖目錄 x 第一章 緒論.................................................................................................1 第二章 數值方法介紹.................................................................................4 2.1 渦泡方法.......................................................................................7 2.2 分裂機制.......................................................................................8 2.3 融合機制.......................................................................................9 2.4 渦度場的建造.............................................................................11 2.5 程式流程.....................................................................................12 2.6 測試例：Burger vortex之擴散...................................................13 2.7 壓力場的計算.............................................................................14 2.7.1 統御方程式......................................................................14 2.7.2 邊界條件..........................................................................15 2.7.3 空間映射..........................................................................15 2.7.4 有限差分法......................................................................16 2.7.5 收斂測試..........................................................................17 第三章 無黏性流場.................................................................................19 3.1 準確性測試................................................................................20 3.2 漩渦形變....................................................................................21 3.3 類渦片結構................................................................................22 3.4 exchange band............................................................................23 3.5 Yasuda模型................................................................................25 3.6 融合機制....................................................................................28 3.7 橢圓漩渦對模型........................................................................29 3.7.1 inner core region大小.....................................................29 3.7.2 漩渦與exchange band相對關係....................................31 3.8 壓力場........................................................................................31 3.9 兩漩渦初始距離的影響............................................................33 3.9.1 漩渦中心點的運動.........................................................33 3.9.2 類渦片結構的影響.........................................................33 第四章 黏性流場.....................................................................................35 4.1 準確性測試................................................................................35 4.1.1 之選擇......................................................................36 4.1.2 之選擇..........................................................................37 4.1.3 渦泡分裂與融合方式.....................................................37 4.2 漩渦形變....................................................................................37 4.3 類渦片結構................................................................................39 4.4 壓力場........................................................................................39 4.5 雷諾數的影響............................................................................40 4.5.1 黏度的效應.....................................................................40 4.5.2 漩渦中心點的運動.........................................................40 4.5.3 類渦片結構的影響.........................................................41 第五章 結論與未來展望.........................................................................42 參考文獻.....................................................................................................44 附錄A..........................................................................................................472583907 bytesapplication/pdfen-US對稱漩渦對融合類渦片結構交換帶橢圓漩渦symmetric vortex pairmergersheet-like structureexchange bandelliptic vortexthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/61515/1/ntu-96-R94522118-1.pdf