本文主要利用數值方法探討單一圓柱與圓柱陣列在剪切流場內的運動模式，觀察圓柱陣列於剪切流內是否具有流體-彈性振動(Fluid-Elastic Vibration)，並對不同圓柱間距比、剪切參數以及質量比和圓柱的排列型態等參數，對於圓柱運動軌跡與振幅之影響，做詳細的分析。
研究中運用計算流體力學軟體Fluent 6.3.26版本，求解此類問題；以SIMPLEC演算法將連續與動量守恆方程式做交替運算，並與圓柱運動方程式相結合，利用動網格技術，使圓柱體受到流場作用力的影響而產生運動；於不同流場條件下，模擬流場型態和圓柱運動模式，觀察流體引致振動對圓柱體的影響。
根據研究可得，均勻流場中單一圓柱體的流場型態和運動模式與相關文獻互相吻合。另外，在剪切流場中圓柱陣列體的探討方面，以矩形與菱形的圓柱體排列方式下，調整圓柱間相對距離和改變剪切參數值，來觀察出有流體-彈性振動現象的產生，與單一圓柱體相比較，其發生流體-彈性振動之臨界流速均小於單一圓柱體，代表著圓柱陣列流場較易發生流體-彈性振動。

The present study is aimed to explore dynamical behavior of the fluid- elastic vibration of cylindrical arrays and single cylinder in shear flow by numerical simulations .The effects of the shear parameter, spacing(P/D) 、mass ratio and arrangement of cylinders on fluid-elastic vibration of the cylinders are investigated
Continuity and momentum equations are solved alternatively by using a CFD package, Fluent 6.3.26. Dynamic meshing techniques together with the cylinder motion equations are employed in the simulation. Under different flow conditions, flow types and cylinder motion models, lock-in and vortex-induced vibration are studied.
According to the research the motion and flow types of a single cylinder in uniform flow are in good agreement with the previous studies in literatures. In shear flow, however, as the shear parameter increases, the fluid vortex-induced vibration of the cylinder is induced, and thus amplitude of the cylinder increases considerably. Further, cylindrical arrays in the shear flow are studied. Cylindrical arrays arrangements (rectangle and rhombus) 、 the distance between cylinders and regulate shear parameter are the factors to cause fluid-elastic vibration. Compared with the single cylinder motion, cylindrical arrays motion’s critical flow velocity is smaller than the single cylinder motion, which means cylindrical arrays motion are more subject to fluid-elastic vibration.

中文摘要 I
Abstract II
目錄 IV
符號說明 IX
第一章 緒論 1
1.1 研究動機 1
1.2 文獻回顧 4
1.2.1 均勻流場中單一圓柱 4
1.2.2 剪切流場中單一圓柱 4
1.2.3 均勻流場矩形陣列圓柱 6
1.2.4 剪切流場矩形陣列圓柱 7
1.2.5 剪切流場中的菱形陣列圓柱 8
1.2.6 流體-彈性振動 9
1.3 研究目的 10
1.4 研究中所使用的無因次參數定義 11
第二章 模擬理論與數值參數設定 13
2.1 理論分析 13
2.1.1數值方法 14
2.1.2 流體統御方程式 14
2.1.3 圓柱運動方程式 15
2.1.4 數值運算流程 16
2.2 數值方法 19
2.2.1 SIMPLEC演算法 20
2.3 流場與數值參數設定 21
2.3.1 流場的基本假設與邊界條件設定 21
2.3.2 流場計算域(Domain)的設定 22
2.3.3 流場系統的網格設定 22
2.3.4 時間步階( Time Step )的設定與測試 23
第三章 結果與討論 25
3.1 單一圓柱之理論驗證 25
3.1.1 升力係數與阻力係數變化 25
3.1.2 史卓荷數變化 26
3.2 均勻流場中單一彈性圓柱的運動模式 26
3.2.1 無因次速度與圓柱振幅變化 27
3.2.2 無因次速度與頻率比 28
3.2.3 質量比對圓柱振幅的影響 28
3.2.4 圓柱運動軌跡變化 29
3.3 剪切流場中單一彈性圓柱的運動模式 30
3.3.1 剪切參數對圓柱振幅的影響 31
3.4 均勻流場中彈性矩形圓柱陣列的運動模式 32
3.4.1矩形圓柱陣列的模型架構 33
3.4.2 均勻流場中矩形圓柱陣列的流場特性分析 33
3.5 剪切流場中彈性並列圓柱陣列的振動 34
3.6 剪切流場中彈性矩形圓柱陣列的振動 36
3.6.1 剪切參數對矩形圓柱陣列的振動影響 36
3.6.2 剪切流場中矩形圓柱陣列的振動軌跡 37
3.6.3 剪切流場中間距比對矩形圓柱陣列的振動影響 39
3.7 剪切流場中彈性菱形圓柱陣列的振動 41
3.7.1 剪切參數對菱形圓柱陣列的運動模式影響 41
3.7.2 剪切流場中質量比對菱形陣列的影響 43
3.7.3剪切流場中菱形陣列圓柱流速改變的運動軌跡 44
第四章 結論與建議 46
參考文獻 49
圖檔 54
圖 2-1 剪切流場中質量-阻尼-彈簧(Mass-Damper-Spring)模型示意圖 54
圖2-2 二維圓柱運動運算流程圖 55
圖2-3 SIMPLEC演算法流程圖 56
圖2-4 二維圓柱陣列與剪切流場的邊界條件示意圖 57
圖2-5 (a) 流場系統的網格分佈圖 (b) 陣列圓柱周圍網格放大圖 58
圖3-1 剪切流場中圓柱平均阻力與升力係數隨雷諾數變化之關係圖 59
圖3-2 不同雷諾數下之史卓荷數隨剪切參數的變化 60
圖3-3 均勻流場中圓柱y方向無因次振幅與無因次速度變化趨勢 61
圖3-4-1 彈簧阻尼系統之圓柱體在發生鎖定現象區域內的無因次流體速度與頻率比的關係圖Feng(1968) 62
圖3-4-2 彈簧阻尼系統之圓柱體在發生鎖定現象區域內的無因次流體速度與頻率比的關係圖 63
圖3-5 均勻流場中圓柱Y方向無因次振幅與無因次速度關係圖 64
圖3-6 不同無因次速度下之單一圓柱運動軌跡 65
圖3-7 不同無因次速度下之單一圓柱運動軌跡 Jauvtis(2004) 66
圖3-8 單根圓柱在區域性網格內不同剪切參數的振動 67
圖3-9 圓柱陣列分別在均勻流場中的振動 68
圖3-10 圓柱陣列在均勻流場中的X軸方向振動 69
圖3-11 圓柱陣列在均勻流場中不同的質量比之流場振動 70
圖3-12 均勻流場中圓柱陣列不同間距比的振動 71
圖3-13(a)流場系統的網格分佈圖 (b)並列圓柱周圍網格邊界圖 72
圖3-14 並列圓柱陣列在剪切流場中的振動 73
圖3-15並列圓柱陣列在剪切流場中的振動 74
圖3-16 剪切流場中剪切參數對並列圓柱陣列的振動影響 75
圖3-17 剪切流場圓柱陣列尾流渦度週期等值圖 76
圖3-18 圓柱陣列在剪切流場中不同的間距比渦漩示意圖 Lam (2007) 77
圖3-19 剪切流場中的圓柱陣列在不同剪切參數振動 78
圖3-20 剪切流場圓柱陣列尾流渦度週期等值圖 79
圖3-21 圓柱陣列C3跟C4在不同剪切參數下的振動 80
圖3-22 剪切流場中圓柱陣列C2在K=0.1的運動軌跡圖 81
圖3-23 剪切流場中圓柱陣列C3在K=0.1的運動軌跡圖 82
圖3-24 剪切流場中矩形圓柱陣列質量比的關係圖 83
圖3-25 剪切流場圓柱陣列尾流渦度週期等值圖 84
圖3-26 剪切流場圓柱陣列尾流渦度週期等值圖 85
圖3-27 剪切參數K=0.1時的圓柱陣列振動 86
圖3-28 圓柱陣列在不同間距比時的剪切流場振動 87
圖3-29 菱形陣列在剪切流場的示意圖 88
圖3-30 (a) 流場系統的網格分佈圖 (b) 菱形圓柱周圍網格放大圖 89
圖3-31 剪切參數對菱形陣列圓柱振動的影響 90
圖3-32 剪切流場中菱形陣列圓柱的振動 91
圖3-33 剪切流場並列圓柱在不同剪切參數下的尾流渦度週期圖 93
圖3-34 剪切流場中菱形陣列圓柱的振動 94
圖3-35 剪切流場中剪切參數對菱形圓柱陣列的振動影響 95
圖3-36 菱形陣列圓柱在剪切流場內的振動軌跡 98

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