請用此 Handle URI 來引用此文件:
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/28734
完整後設資料紀錄
DC 欄位 | 值 | 語言 |
---|---|---|
dc.contributor.advisor | 黃美嬌 | |
dc.contributor.author | BO-HAN WU | en |
dc.contributor.author | 吳柏翰 | zh_TW |
dc.date.accessioned | 2021-06-13T00:20:02Z | - |
dc.date.available | 2007-07-31 | |
dc.date.copyright | 2007-07-31 | |
dc.date.issued | 2007 | |
dc.date.submitted | 2007-07-25 | |
dc.identifier.citation | [1] McWilliams, J. C. (1984). “The emergence of isolated vortices in turbulent flow.” J. Fluid Mech. 146:21-43.
[2] Freymuth, P. (1966). “On transition in a separated boundary layer.” J. Fluid Mech. 25:683. [3] Winant, C. D., F. K. Browand (1974). “Vortex pairing: the mechanism of turbulent mixing layer growth at moderate Reynolds number.” J. Fluid Mech. 63:237. [4] Brown, G. L., A. Roshko (1974). “On density effects and large structure in turbulent mixing layers.” J. Fluid Mech. 64:775-816. [5] Zabusky, N. J., G. S. Deem (1971). “Dynamical evolution of two-dimensional unstable shear flows.” J. Fluid Mech. 47:353-379. [6] Roberts, K. V., J. P. Christiansen (1972). “Topics in computational fluid mechanics.” Comput. Phys. Comm. 3:14. [7] Christiansen, J. P., N. J. Zabusky (1973). “Instability, coalescence and fission of finite-area vortex structures.” J. Comput. Phys. 13:363-379. [8] Rossow, V. J. (1977). ”Convective merging of vortex cores in lift generated wakes.” J. Aircraft 14:283-290. [9] Meunier, P. and T. Leweke (2001). 'Three-dimensional instability during vortex merging.' Physics of Fluids 13(10): 2747-2750. [10] Cerretelli, C. and C. H. K. Williamson (2003). 'The physical mechanism for vortex merging.' Journal of Fluid Mechanics 475(475): 41-77. [11] Saffman, P. G.., R. Szeto (1980). “Equilibrium shapes of a pair of equal uniform vortices.” Physics of Fluids 23:2339-2342. [12] Overman, E. A., N. J. Zabusky (1982). “Evolution and merger of isolated vortex structures.” Physics of Fluids 25:1297-1305. [13] Dritschel, D. G. (1986). 'The nonlinear evolution of rotating configurations of uniform vorticity.' Journal of Fluid Mechanics 172: 157-182. [14] Melander, M. V., N. J. Zabusky and J. C. McWilliams (1988). 'Symmetric vortex merger in two dimensions: causes and conditions.' Journal of Fluid Mechanics 195: 303-340. [15] Meunier, P., S. Le Dizes, et al. (2005). 'Physics of vortex merging.' Comptes Rendus Physique 6(4-5): 431-450. [16] Velasco Fuentes, O. G. (2005). “Vortex filamentation: its onset and its role on axisymmetrization and merger.” Dyn. Atmos. Oceans 40:23. [17] Huang, M.-J. (2005). 'The physical mechanism of symmetric vortex merger: A new viewpoint.' Physics of Fluids 17(7): 074105. [18] Brandt, L. K. and K. K. Nomura (2006). 'The physics of vortex merger: Further insight.' Physics of Fluids 18(5): 051701. [19] Rosenhead, L. (1931). “The formation of Vortices from a Surface of Discontinuity.” Proc. Roy. Soc. London A 134:170-192. [20] 陳立杰, 黃美嬌 2006, 群對點快速面積擴散渦漩法之研發(Box-to-Point-based Fast Core-Spreading Vortex Method), 第13屆全國計算流體力學學術研討會 [21] Chorin, A. J. (1973). “Numerical study of slightly viscous flow.” J. Fluid Mech. 57:785-796. [22] Goodman, J. (1987). “Convergence of the random vortex method.” Commun. Pure Appl. Math. 40:189-220. [23] Long, D. G. (1988). “Convergence of the random vortex method in two dimensions.” J. Amer. Math. Soc. 1:779 [24] Degond, P., S. Mas-Gallic (1989). “The weighted particle method for convection-diffusion equations. Part I: the case of an isotropic viscosity.” Mathematics of Computation 53(188):485-507. [25] Fishelov, D. (1990). “A new vortex scheme for viscous flow.” Journal of Computational Physics 86:211-224. [26] Ogami, Y., T. Akamatsu (1991). “Viscous flow simulation using the discrete vortex model – the diffusion velocity method.” Computers & Fluid 19:433-441. [27] Leonard, A. (1980). “Vortex methods for flow simulations.” J. Comput. Phys. 37:289-335. [28] Greengard, C. (1985). “The core-spreading vortex method approximations the wrong equation.” J. Comput. Phys. 61:345-348. [29] Rossi, L. (1996). “Resurrecting core-spreading vortex methods: a new scheme that is both deterministic and convergent.” SIAM Journal on Scientific Computing 17:370-397. [30] Huang, M.-J. (2005). “Diffusion via splitting and remeshing via merging in vortex methods.” International Journal for Numerical Methods in Fluids 48(5): 521-539. [31] Shiels, D. (1998). “Simulation of controlled bluff body flow with a viscous vortex method” Ph.D. Thesis, California Institute of Technology, Pasadena, CA. [32] Rossi, L. (1997). “Merging computational elements in vortex simulations.” SIAM Journal on Scientific Computing 18:1014-1027. [33] Yasuda, I., G. R. Flierl (1997). 'Two-dimensional asymmetric vortex merger: merger dynamics and critical merger distance.' Dynamics of Atmospheres and Oceans 26(3): 159-181. [34] Yasuda, I. (1991). “Studies on the evolution of Kuroshio warm-core rings.” Ph.D Thesis, Uviversity of Tokyo, 219pp. [35] Kida, S. (1981). ' Motion of an Elliptic vortex in a uniform shear flow.' 50(10): 3517-3520. | |
dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/28734 | - |
dc.description.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。 | zh_TW |
dc.description.abstract | 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. | en |
dc.description.provenance | Made available in DSpace on 2021-06-13T00:20:02Z (GMT). No. of bitstreams: 1 ntu-96-R94522118-1.pdf: 2583907 bytes, checksum: 5e6d65bbf49aa8267b9885b564aa9d68 (MD5) Previous issue date: 2007 | en |
dc.description.tableofcontents | 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..........................................................................................................47 | |
dc.language.iso | zh-TW | |
dc.title | 二維對稱漩渦對融合動力學之研究 | zh_TW |
dc.title | The merging dynamics of two-dimensional symmetric vortex pair | en |
dc.type | Thesis | |
dc.date.schoolyear | 95-2 | |
dc.description.degree | 碩士 | |
dc.contributor.oralexamcommittee | 李石頓,顏瑞和,伍次寅 | |
dc.subject.keyword | 對稱漩渦對,融合,類渦片結構,交換帶,橢圓漩渦, | zh_TW |
dc.subject.keyword | symmetric vortex pair,merger,sheet-like structure,exchange band,elliptic vortex, | en |
dc.relation.page | 46 | |
dc.rights.note | 有償授權 | |
dc.date.accepted | 2007-07-27 | |
dc.contributor.author-college | 工學院 | zh_TW |
dc.contributor.author-dept | 機械工程學研究所 | zh_TW |
顯示於系所單位: | 機械工程學系 |
文件中的檔案:
檔案 | 大小 | 格式 | |
---|---|---|---|
ntu-96-1.pdf 目前未授權公開取用 | 2.52 MB | Adobe PDF |
系統中的文件,除了特別指名其著作權條款之外,均受到著作權保護,並且保留所有的權利。