面積擴散渦漩法無滑移邊界條件之研發

Development of a Core-Spreading Vortex Method with No-Slip Boundary Condition

蘇煥勛(Huan-Syun Su)

指導教授 ： 黃美嬌

國立臺灣大學/工學院/機械工程學研究所/碩士(2007年)

https://doi.org/10.6342/NTU.2007.02169

摘要

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。

關鍵字

渦漩方法 ； 無滑移邊界條件 ； 面積擴散 ； 殘留渦度

並列摘要

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.

並列關鍵字

Vortex method ； No-slip boundary condition ； Core spreading ； residual vorticity

參考文獻

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