黃美嬌臺灣大學：機械工程學研究所蘇煥勛Su, Huan-SyunHuan-SyunSu2007-11-282018-06-282007-11-282018-06-282007http://ntur.lib.ntu.edu.tw//handle/246246/60990本論文以Leonard之面積擴散渦漩法（Core spreading vortex method）及Huang之渦泡分裂融合修正法為基礎，開發一滿足無滑移、無穿透邊界條件之數值模擬工具。其中，無穿透邊界條件是利用於邊界上放置渦片（vortex sheet）結構來滿足，並以邊界元素法求得其適當強度，藉渦片產生之速度抵銷外界流場於邊界上之滑移速度。而渦片之環量（circulation）隨時間擴散進流場之現象則藉由Koumoutsakos之理論，以邊界上之等效渦度通量（vorticity flux）求解擴散方程式，得解析解後，再將之離散為邊界附近之新渦泡。 為避免部分新渦泡太過接近邊界，我們引入了「殘留渦度」的概念，將離邊界甚近之環量轉為渦片形式留在邊界上，以減少環量進入物體內部之誤差。此外既有渦泡也可能因對流或其他數值誤差造成過於靠近邊界，因此我們也設計一專門處理過於靠近邊界渦泡之方法（NWB），以其他計算元素取代這些渦泡，降低進入物體內部之環量，進而降低渦片強度計算上的擾動（fluctuations）。最後研究以瞬間啟動圓柱流作為測試流場，將模擬結果與前人之數值模擬及實驗結果比較，驗證了本方法之可行性與準確度。Based on the core-spreading vortex method developed by Leonard and the blobs-splitting-and-merging scheme developed by Huang, this thesis develops a new numerical method for two-dimensional viscous incompressible flows with solid boundaries. The no-penetration boundary condition is satisfied by placing a vortex sheet along the boundary, which strength must be adapted to cancel the slip velocity on the boundary induced by all the other flow components. The strength of the vortex sheet is computed in the present work by the constant panel method. To simulate the diffusion of the vortex sheet into the flow field as time goes on, Koumoutsakos’ analytical solution is employed, in which an effective vorticity flux is derived and used for solving the vorticity diffusion equation. The solution is then discretized into blobs (called “ -blobs”) in the vicinity of the boundary. Moreover, to prevent the vorticity from entering into the body, the concept of “residual vorticity” is introduced in the sense that partial circulation of the vortex sheet is remained at the boundary without being diffused into the flow field. Blobs very close to the wall are thus unnecessary. Moreover, blobs may move too close to the boundary because of advection errors or other numerical errors. It may cause serious fluctuations in evaluating the strength of the vortex sheet. In order to reduce the fluctuations, these near-wall blobs (NWB) are also manipulated in use of the concept of “residual vorticity”. Finally, we apply the so-developed solver to a simulation of the flow past an impulsively started circular cylinder at different Reynolds numbers. The simulation results are compared with previous experimental as well as numerical data. The validity and the accuracy of this newly developed Navier-Stokes solver are confirmed.口試委員會審定書……………………………………………………………. i 誌謝…………………………………………………………………………...... ii 中文摘要……………………………………………………………………...... iii 英文摘要…………………...…………………………………………………... iv 目錄…………………...…………………………………………………........... v 圖目錄………………...…………………………………………………........... vii 第一章 引言………...…………………………………………………........... 1 1.1研究背景..…………………………………………………………..….. 1 1.2研究目的……………………………………………………..……..….. 3 1.3論文架構……………………………………………………..…………. 4 第二章 二維黏性不可壓縮流場統御方程式………………………………. 5 第三章 面積擴散渦漩法……..……………………………………………... 7 3.1理論基礎……………………………………………………………..… 7 3.2渦泡分裂……………………………………………………………….. 9 3.3渦泡融合..……………………………………………………………… 11 3.3.1同向融合………………………………………………………... 11 3.3.2異向融合………..…………………………………………….... 14 第四章 固體邊界條件……..………………………………………….…….. 15 4.1邊界渦度密度方程式……………...……….………………………….. 15 4.1.1理論基礎……………..…………………………………………. 15 4.1.2離散渦度密度方程式..…………………………………………. 16 4.1.3解析解………………..…………………….…………………… 17 4.1.4方法比較……………..…………………………………………. 18 4.2邊界渦度之擴散…………………...…………….…………………….. 19 4.2.1理論基礎……………..…………………………………………. 19 4.2.2渦度積分法…………..…………………………………………. 20 4.2.3平板擴散法…………..…………………………………………. 22 4.3邊界渦泡之處理…………………...………………….……………….. 23 4.3.1取代法（NWB1）……..………………………………………….. 24 4.3.2重新分配法一（NWB2）……………………………………… 26 4.3.3重新分配法二（NWB3）……………………………………… 27 第五章 時間積分法及流程設計……………………………………...…….. 28 5.1對流之時間積分法………………...…………….…………………….. 28 5.2邊界渦度擴散之時間積分法……...…………….…………………….. 29 5.2.1梯形法………………..…………………………………………. 30 5.2.2交替法………………..…………………………………………. 31 5.2.3啟動瞬間之特殊處理..…………………………………………. 32 5.3其他特殊處理……………………...…………….…………………….. 33 第六章 結果與討論…………………………………………………………. 35 6.1梯形法及交替法之比較…………...…………….…………………….. 36 6.2邊界渦泡處理法之比較…………...…………….…………………….. 37 6.3邊界渦度擴散網格及NWB3網格之參數探討..…………………….. 39 6.4其他流場觀測……………………...………….……………………….. 40 6.4.1 Re = 550瞬間啟動圓柱流..……………………………………. 41 6.4.2 Re = 3000瞬間啟動圓柱流……………………………………. 43 第七章 結論與展望…………………………………………………...…….. 45 參考文獻…………………………………………………………………….… 47 附錄A………………………………………………………………………….. 50 附錄B………………………………………………………………………….. 512033889 bytesapplication/pdfen-US渦漩方法無滑移邊界條件面積擴散殘留渦度Vortex methodNo-slip boundary conditionCore spreadingresidual vorticitythesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/60990/1/ntu-96-R94522108-1.pdf