臺灣博碩士論文加值系統

本研究主要探討厚邊界層中，有限長旋轉圓柱之 Magnus 效應。藉由分析圓柱流場中的無因次參數，如：雷諾數 (Reynolds number, Re)、斯特勞哈爾數 (Strouhal number, St)、長寬比 (Aspect ratio, AR)、轉速比 (Rotation ratio, α) 以及高度比 (Gap ratio, SG)。研究不同條件下，Magnus 效應對流場造成的影響。
實驗中，所使用之水洞為一開放式的渠道，並以甘油作為工作液體。並以長 188 (mm)，直徑 30 (mm)，AR=6.3，且與渠道壁間距 12 (mm) 之旋轉圓柱，在 Re=70-150、α=0-2、SG=3.6 之參數範圍中，使用三種不同方法，對流場進行分析：
第一，透過雷射光頁將流場顯影，再利用 PIV 影像分析法，繪製出流場概況。
第二，利用 LDA 雷射系統，對流場中特定位置之示蹤粒子，進行速度量測。
第三，藉由 Load Cell 量測不同參數下，圓柱所受之升、阻力。
同時，以商業軟體 Ansys/Fluent 進行數值模擬，將所得之計算結果，與實驗結果進行比較，完成最後的驗證。
本研究的結果顯示，3D 流場有許多現象與 2D 流場出現不同的區別：
I α=0
因AR值較低，渦漩剝離現象延後至 Re=70 時，才發生。
II α≠0
一旦圓柱開始旋轉，渦漩及停滯點皆會向上發生偏轉。隨著轉速比的增加，平均升力係數呈線性趨勢增加；平均阻力係數則先下降後增加。當轉速達臨界轉速比時，圓柱出現渦漩抑制，尾流不再發生震盪。

This article is to report on an experimental investigation of the Magnus effect of a horizontally lying circular cylinder, rotating in flow with thick boundary layer.
The experiments were performed in an open water channel with using the glycerol as the working fluid.
The aspect ratio (AR=L⁄D) of the cylinder is fixed at 6.3, and the gap ratio (SG=H/D) is fixed at 3.6. Furthermore, the Reynolds number (Re=ρDU⁄μ) varies from 70 to 150, and the spin ratio (α=Ωa⁄U) varies from 0 to 2 which rotates in counterclockwise.
In these regime of parameters, the flow is found to be different from the 2D model about the middle cross section:
I α=0
Because of the lower aspect ratio, the vortex shedding is delayed. But it still can be found at Re≥70.
II α≠0
The flow becomes unsymmetric as soon as the cylinder starts rotating. Then, the stagnation point and the vortex in the wake will deflect upwardly. As the spin ratio becomes larger, the coefficient of the mean lift force will increase linearly; the coefficient of the mean drag force will go down slightly in the beginning, and then increase dramatically. If the spin ratio becomes larger and reaches the critical value, the vortex shedding will be suppressed suddenly.

誌謝 i
摘要 ii
Abstract iii
目錄 iv
圖目錄 vii
表目錄 xi
第一章 序論 1
1.1 研究背景與動機 1
1.2 靜止圓柱相關文獻 2
1.2.1 卡門渦街 (Kármán vortex street) 2
1.2.2 低雷諾數下之卡門渦街 3
1.2.3 高雷諾數下之卡門渦街 5
1.2.4 卡門渦街相關文獻總結 6
1.3 Magnus 效應相關文獻 7
1.3.1 低雷諾數下，圓柱周圍之 Magnus 效應相關文獻 7
1.3.2 高雷諾數下，圓柱周圍之 Magnus 效應相關文獻 12
1.3.3 Magnus 效應相關文獻總結 14
第二章 基礎理論 15
2.1 勢流理論 15
2.1.1 勢流理論 15
2.1.2 基本勢流解 16
2.1.3 勢流分析 21
2.2 黏性流理論 23
2.2.1 黏性流理論 23
2.2.2 黏性流分析 28
第三章 實驗方法 35
3.1 實驗設備 35
3.1.1 水平式循環水洞 35
3.1.2 微細氣泡產生器 36
3.1.3 高速攝影機 37
3.1.4 雷射光頁產生器(Illumination) 39
3.1.5 數位單眼相機 40
3.1.6 LDA雷射系統 41
3.1.7 Load Cell 42
3.1.8 音叉式黏度計 42
3.1.9 圓柱系統 44
3.2 實驗架設 45
3.3 實驗方法 48
3.3.1 雷射光頁顯影 48
3.3.2 粒子影像測速 48
3.3.3 PIVlab 49
3.3.4 LDA 52
3.3.5 Load Cell 53
第四章 數值方法 54
4.1 網格建構 54
4.1.1 網格類型 54
4.1.2 網格設定 55
4.1.3 邊界條件 56
4.2 控制方程式 56
4.3 數值方法 56
4.3.1 空間離散 57
4.3.2 時間離散 57
4.3.3 壓力-速度耦合關係處理 59
第五章 結果與討論 60
5.1 驗證分析 60
5.1.1 水洞量測 60
5.2 旋轉圓柱 67
5.2.1 速度場分析 67
5.2.2 頻率分析 74
5.2.3 受力分析 77
第六章 結論與未來展望 82
6.1 結論 82
6.1.1 Magnus effect 82
6.2 未來展望 83
參考文獻 84

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