Please use this identifier to cite or link to this item:
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/28734
Title: | 二維對稱漩渦對融合動力學之研究 The merging dynamics of two-dimensional symmetric vortex pair |
Authors: | BO-HAN WU 吳柏翰 |
Advisor: | 黃美嬌 |
Keyword: | 對稱漩渦對,融合,類渦片結構,交換帶,橢圓漩渦, symmetric vortex pair,merger,sheet-like structure,exchange band,elliptic vortex, |
Publication Year : | 2007 |
Degree: | 碩士 |
Abstract: | 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. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/28734 |
Fulltext Rights: | 有償授權 |
Appears in Collections: | 機械工程學系 |
Files in This Item:
File | Size | Format | |
---|---|---|---|
ntu-96-1.pdf Restricted Access | 2.52 MB | Adobe PDF |
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.