臺灣博碩士論文加值系統

本文主要探討振盪流流經單方及並列雙方柱之渦漩行為。藉由改變流場參數雷諾數、KC數(Keulegan-Carpenter number)及另一參數方柱間隙比(g*)的影響。文中利用流場可視化實驗及數值模擬方法來探討流體流經方柱周圍所形成之流場變化，並在數值模擬結果中記錄流場訊息升力係數及阻力係數來探討柱體受力之情形。
研究結果得知當雷諾數固定時，隨著$KC$值的增加，流體流經單方柱之流場型態會由對稱依附在柱體表面之渦漩對，轉變為對稱分離之渦漩對及渦漩逸散等三種型態，流場記錄之訊息阻力係數呈現指數函數遞減。當KC值固定時在不同雷諾數下流場型態則大致相似，阻力係數則沒有太大的變化。
在並列雙方柱之振盪流場則另外受到間隙比(g*)的影響。間隙比變小流體流經間隙處形成噴流的型式，且流場發生不對稱連續渦漩對情形較早發生。在間隙比增大時，流體流經並列雙方柱易造成並列方柱兩側的流場型態不相同。流場記錄之訊息因子阻力係數及升力係數可明顯觀察改變，其中阻力係數隨間隙比增大而減小，上、下個別方柱所受之阻力係數為相同變化。此外當間隙比等於方柱邊長時，所得之升力係數較為規則變化。
本研究亦藉由頻譜分析及相位圖探討流場由穩定秩序(order)轉變至混亂(chaos)過程，並以關聯性(correlation)探討並列雙方柱之上、下方柱受力關聯性。

The behaviour of vortices induced by a single square cylinder and a pair of side-by-side square cylinders in an oscillating flow is investigated. The flow patterns in the vicinity of square cylinders are visualized using the experimental
approach and the numerical model. Meanwhile, force coefficients exerted on square cylinders are determined numerically.
The results reveal that the flow patterns for an oscillating flow past a single cylinder can be divided into three modes:
(i) a pair of attached vortices, (ii) a pair of separation and symmetric vortices, and (iii) vortex shedding as Keulegan-Carpenter number increases. Reynolds number does not affect the flow field apparently. In addition, the in-line force coefficient decreases exponentially as Keulegan-Carpenter number increases.
For an oscillating flow past a pair of side-by-side cylinder, the gap ratio plays a vital role in the flow variation. The
jet-like structure is found when fluids flow through the gap. In addition, the gap causes the earlier appearance of asymmetric
vortex shedding. The in-line force and lift force coefficients of two square cylinders are determined numerically and analyzed using the spectrum analysis and phase diagrams. In terms of those results, the transition of the flow field from the order state to the chaotic state is demonstrated.

1 導論
1.1 前言
1.2 文獻回顧
1.3 論文目的
1.4 論文大綱
2 數學模式與數值方法
2.1 控制方程式
2.2 初始條件與邊界條件
2.2.1 初始條件
2.2.2 邊界條件
2.3 動量方程式之離散
2.3.1 時間項之離散
2.3.2 對流與擴散項之離散
2.4 連續方程式之離散
2.5 SOLA演算法則
2.6 鬆弛係數
2.7 網格產生與計算點的配置
2.8 流場訊息計算
2.9 數值模式驗證
2.10 總結
3 流場可視化實驗
3.1 實驗器材及設備
3.1.1 拖曳台車與實驗水槽
3.1.2 實驗模型
3.1.3 影像擷取設備與雷射器材
3.1.4 質點軌跡影像觀察
3.2 實驗步驟
3.3 總結
4 振盪流場與單一方柱體之交互作用
4.1 振盪流場參數
4.2 數值運算設定
4.2.1 流場數值運算設定
4.3 網格獨立性及邊界設定
4.3.1 邊界測試
4.3.2 網格獨立性測試
4.4 流場分析
4.4.1 流場型態分析
4.4.2 力量分析
4.5 總結
5 振盪流場與兩平行排列方形柱體之交互作用
5.1 數值運算設定
5.2 渦漩流場分析
5.3 力量分析
5.4 振盪流流經並列雙方柱之渦漩逸出混沌現象分析
5.4.1 頻譜及相位分析
5.4.2 雙方柱之受力相關聯性分析
5.5 總結
6 結論與建議
6.1 結論
6.2 建議
參考文獻

[1] Bearman, P.W., Graham, J.M.R., Obasaju, E.D. and Drossopulos, G.M. 1984, The influence of corner radius on the forces experienced by cylindrical bluff bodies in oscillatory flow. Applied Ocean Research 6, 83-89.
[2] Bearman, P.W., and Obasaju, E.D. 1982, An experimental study of pressure fluctuations on fixed and oscillating square-section cylinders. Journal of Fluid Mechanics 119, 297-321.
[3] Chen, L., Tu, J.Y. and Yeoh, G.H. 2003, Numerical simulation of turbulent wake flows behind two side-by-side cylinders. Journal of Fluids and Structures 18, 387-403.
[4] Davis, R.W., Moore, E.F. and Purtell, L.P. 1984, A numerical-experimental study of confined flow around rectangular cylinders. Physics of Fluids 27, 46-59.
[5] Davis, R.W. and Moore, E.F. 1982, A numerical study of vortex shedding from rectangles. Journal of Fluid Mechanics 116, 475-506.
[6] Franke, R., Rodi, W. and Schonung, B. 1990, Numerical calculation of laminar vortex-shedding flow past cylinders. Journal of Wind Engineering and Industrial Aerodynamics 35, 237-257.
[7] Tannehill, J.C., Anderson, D.A. and Pletcher, R.H. 1997, Computational Fluid Mechanics and Heat Transfer 2nd ed., Taylor and Francis Co., Philadelphia, USA.
[8] Keulegan, G.H. and Carpenter, L.H. 1958 Forces on cylinders and plates in an oscillating fluid. Journal of Research of the National Bureau of Standards. 60.
[9] Leonard, B.P. 1979, A stable and accurate convective modeling procedure based on quadratic upstream interpolation. Computer Methods in Applied Mechanics and Engineering 19, 59-98.
[10] Luo, S.C., Li, L.L. and Shah, D.A. 1999, Aerodynamic stability of the downstream of two tandem square-section cylinders. Journal of Wind Engineering and Industrial Aerodynamics 79, 79-103.
[11] Obasaju, E.D., Bearman, P.W. and Graham, J.M.R. 1988, A study of forces, circulation and vortex patterns around a circular cylinder in oscillating flow. Journal of Fluid Mechanics 196, 467-494.
[12] Okajima, A. 1982, Strounal numbers of rectangular cylinders. Journal of Fluid Mechanics 123, 379-398.
[13] Okajima, A., Ueno, H. and Sakai, H. 1992, Numerical simulation of flow laminar and turbulent flows around rectangular cylinders. Internation Journal for Numerical Methods in Fluids 15, 999-1012.
[14] Okajima, A. 1990,Numerical simulation of flow around rectangular cylinders. Journal of Wind Engineering and Industrial Aerodynamics 33, 171-180.
[15] Sarpkaya, T. 1986, Force on a circular cylinder in viscous oscillating flow at low Keulegan-Carpenter numbers. Journal of Fluid Mechanics165, 61-71.
[16] Saha, A.K., Muralidhar, K. and Biswas, G. 2000, Transition and chaos in two-dimensional flow past a square cylinder. Journal of Engineering Mechanics126, 523-532.
[17] Sumer, B.M. and Fredsoe, J. 1997, Hydrodynamics around cylindrical structures, World Scientific Publish Co., Singapore.
[18] Sumer, B.M., Fredsoe, J. and Jensen, K. 1994, A note on spanwise correlation on a freely vibrating cylinder in oscillatory flow. Journal of Fluids and Structures8, 231-238.
[19] Wong, P.T.Y., Ko, N.W.M. and Chiu, A.Y.W. 1995, Flow characteristics around two parallel adjacent square cylinders of different sizes. Journal of Wind Engineering and Industrial Aerodynamics54/55, 263-275.
[20] Williamson, C.H.K. 1985, Evolution of a single wake behind a pair of bluff bodies. Journal of Fluid Mechanics159, 1-18.
[21] Williamson, C.H.K. 1985, Sinusoidal flow relative to circular cylinders. Journal of Fluid Mechanics 155, 141-174.
[22] Williamson, C.H.K. and Roshko, A. 1988, Vortex formation in the wake of oscillating cylinder. Journal of Fluids and Structures 2, 355-381.
[23] Peng, Y.F., Shiau, Y.H. and Hwang R.R. 2003, Transition in a 2-D lid- driven cavity flow. Computers & Fluids32, 337-352.
[24] Zheng, W. and Dalton, C. 1999, Numerical prediction of force on rectangular cylinders in oscillating viscous flow. Journal of Fluids and Structures13, 225-249.
[25] 程繹中 2002，並列雙方柱後尾流場之混沌現象，國立台灣科技大學機械研究所碩士論文.
[26] 張尚鈞 2003，振盪流場與單一方柱交互作用之數值與實驗研究，國立台灣科技大學機械研究所碩士論文.