本文主要利用數值方法探討單一圓柱與三圓柱在剪切流場內的運動模式，觀察圓柱於剪切流內是否具有流體-彈性振動(Fluid-Elastic Vibration)，並另外針對不同圓柱間距比、剪切參數以及質量比等參數，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，觀察鎖定(Lock-In)現象以及流體-彈性振動對圓柱體的影響。
研究結果顯示，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，而在剪切流場中，隨著剪切參數的增加，圓柱出現流體-彈性振動的情形，使圓柱振幅大幅提升。另外，在剪切流場中雙圓柱體的探討方面，以並列、縱列與交錯的圓柱體排列方式下，調整圓柱間相對距離，均觀察出有流體-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，代表著雙圓柱體流場較易發生流體-彈性振動。

The present study aims to explore dynamical behavior of the fluid- elastic vibration of a single cylinder and three cylinders in shear flow by numerical simulations. This paper investigates the effects of the shear parameter, mass ratio, and spacing(P/D) on fluid-elastic vibration of the cylinders.
Continuity equation and momentum equations are solved alternatively 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 fluid-elastic vibration are studied.
The results show that motion and flow types of a single cylinder in uniform flow are in agreement with the previous studies in literatures. In shear flow, however, as the shear parameter increases, the fluid-elastic vibration of the cylinder is induced, and thus amplitude of the cylinder increases considerably. Further, three cylinders in the shear flow are studied. Three cylinders arrangements (classified as side-by-side, tandem ,and stagger) and the distance between cylinders are the factors to cause fluid-elastic vibration. Compared with the single cylinder motion, three cylinders motion’s critical flow velocity is smaller than that of the single cylinder motion, which means two cylinders motion are more subject to fluid-elastic vibration.

中文摘要----------------------------------------------------------------------------I
英文摘要---------------------------------------------------------------------------II
目錄--------------------------------------------------------------------------------III
圖目錄--------------------------------------------------------------------------VIII
表目錄---------------------------------------------------------------------------XX
符號說明-----------------------------------------------------------------------XXI

第一章 緒論-----------------------------------------------------------------------1
1.1 研究動機------------------------------------------------------------1
1.2 文獻回顧------------------------------------------------------------3
1.2.1均勻流場中單一圓柱--------------------------------------3
1.2.2 剪切流場中單一圓柱-------------------------------------4
1.2.3 均勻流場中並列及縱列雙圓柱-------------------------5
1.2.4 均勻流場中交錯排列三圓柱----------------------------7
1.2.5 流體-彈性振動---------------------------------------------8
1.3 研究目的----------------------------------------------------------9
1.4本研究中所使用的無因次參數-----------------------------10

第二章 模擬理論與數值參數設定------------------------------------------12
2.1 理論分析----------------------------------------------------------12
2.1.1 數值方法---------------------------------------------------13
2.1.2 流體統御方程式------------------------------------------13
2.1.3 圓柱運動方程式------------------------------------------14
2.1.4 數值運算流程---------------------------------------------16
2.1.5 PISO演算法-----------------------------------------------19
2.2流場與數值參數設定--------------------------------------------20
2.2.1流場的基本假設與邊界條件設定---------------------20
2.2.2流場計算域(Domain)的設定與測試------------------21
2.2.3流場系統的網格設定與測試---------------------------22
2.2.4時間步階的設定與測試---------------------------------24

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
3.1.3 流場型態變化---------------------------------------------27
3.2均勻流場中單一彈性圓柱之運動模式探討-----------------28
3.2.1 無因次速度與圓柱振幅變化---------------------------28
3.2.2 無因次速度與頻率比變化------------------------------29
3.2.3 質量比對圓柱振幅之影響------------------------------30
3.2.4 均勻流場中之圓柱運動軌跡變化------------------31
3.3剪切流場中單一彈性圓柱之運動模式探討-----------------32
3.3.1 剪切參數對圓柱振幅之影響---------------------------32
3.3.2 剪切流場中之圓柱運動軌跡變化---------------------34
3.4 均勻流場中彈性雙圓柱之運動模式探討-------------------35
3.4.1 並列固定雙圓柱之流場特性分析---------------------36
3.4.2 並列彈性雙圓柱之運動模式探討---------------------37
3.4.3 縱列固定雙圓柱之流場特性分析---------------------38
3.4.4 縱列彈性雙圓柱之運動模式探討---------------------40
3.5均勻流場中彈性三圓柱直線排列之運動模式探討--------41
3.5.1並列固定三圓柱之流場特性分析 ( θ=90˚)-----------42
3.5.2並列彈性三圓柱之運動模式探討 ( θ=90˚)-----------43
3.5.3縱列固定三圓柱之流場特性分析 ( θ=0˚)------------44
3.5.4縱列彈性三圓柱之運動模式探討 ( θ=0˚)------------45
3.5.5斜直線固定三圓柱之流場特性分析 ( θ=45˚及
θ= -45˚)-----------------------------------------------------46

3.5.6斜直線彈性三圓柱之運動模式探討 ( θ=45˚及
θ= -45˚)---------------------------------------------------47
3.6剪切流場中彈性三圓柱直線排列之運動模式探討--------48
3.6.1剪切參數對並列三圓柱之運動模式的影響
( θ=90˚)-----------------------------------------------------48
3.6.2剪切參數對縱列三圓柱之運動模式的影響( θ=0˚)--49
3.6.3剪切參數對斜直線三圓柱之運動模式的影響
( θ=45˚)-----------------------------------------------------50
3.6.4剪切參數對斜直線三圓柱之運動模式的影響
( θ= -45˚)---------------------------------------------------51
3.7均勻流場中彈性三圓柱交錯排列之運動模式探討--------52
3.7.1交錯排列固定三圓柱之流場特性分析 ( θ=0˚)------53
3.7.2交錯排列固定三圓柱之運動模式探討 ( θ=0˚)------53
3.7.3交錯排列固定三圓柱之流場特性分析 ( θ=180˚)---54
3.7.4交錯排列固定三圓柱之運動模式探討 ( θ=180˚)---55
3.7.5交錯排列固定三圓柱之流場特性分析 ( θ=90˚
與 -90˚)----------------------------------------------------56
3.7.6交錯排列固定三圓柱之運動模式探討 ( θ=90˚
與 -90˚)----------------------------------------------------57
3.8剪切流場中彈性三圓柱直線排列之運動模式探討--------58

3.8.1剪切參數對交錯排列三圓柱之運動模式的影響
( θ= 0˚)----------------------------------------------------58
3.8.2剪切參數對交錯排列三圓柱之運動模式的影響
( θ= 180˚)-------------------------------------------------59
3.8.3剪切參數對交錯排列三圓柱之運動模式的影響
( θ= 90˚)---------------------------------------------------60
3.8.4剪切參數對交錯排列三圓柱之運動模式的影響
( θ= -90˚)--------------------------------------------------61
第四章 結論與建議------------------------------------------------------------62
參考文獻-------------------------------------------------------------------63

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