本文主要利用數值方法探討單一圓柱與交錯排列圓柱在剪切流場中的運動行為，並與在均勻流場內的情形比較，觀察交錯排列圓柱置於兩種流場內是否會產生流體-彈性振動(Fluid-Elastic Vibration)，並針對不同圓柱的間距比、質量比和剪切流的剪切參數等參數對圓柱的振幅與運動軌跡之影響情形做探討。
研究中透過PISO演算法進行連續與動量方程式的交替運算，並結合圓柱的運動方程式，配合動網格技術，使圓柱在受到流體作用力時的運動能表現在網格上；並在不同的流場條件下，模擬圓柱的運動及其周圍流場之變化，觀察流體通過交錯排列圓柱時的鎖定(Lock-In)現象與流體-彈性振動。
研究結果可得，單一圓柱於兩種流場內的運動模式及流場型態與文獻相符，而在交錯排列圓柱方面，在均勻流場內，圓柱的振動為渦漩所主導，下游圓柱的鎖定區域大於上游圓柱，流體彈性振動發生於圓柱間存在小間距比時。在剪切流場中，當剪切參數越大或圓柱間距越小，圓柱越容易發生流體彈性振動。

The present study aims to explore dynamical behavior of the single cylinder and the staggered cylinder arrays in shear flow by numerical simulations. The results are compared with the case in uniform flow. After the observation of the fluid-elastic vibration in the staggered cylinder arrays in the two flows. This paper investigates the effects of the spacing(P/D), mass ratio and the shear parameter on the trajectories, oscillation amplitudes among the different cylinders.
Continuity equation and momentum equations are used to solve the aforementioned problems alternatively by PISO method. Dynamic meshing techniques together with the cylinder motion equations are employed in the simulation. Under the different conditions, flow types and cylinder motion models, lock-in and fluid-elastic vibration are studied when the flow crosses the staggered cylinder arrays.
The results show that the motion and the flow field around the single cylinder is consistent with the literature. In terms of the staggered cylinder arrays in uniform flow, the oscillation is dominated by the vortex shedding, and the lock-in area in the downstream cylinders is greater than the upstream cylinders. Fluid elastic vibration occurs in the small spacing between cylinders. In shear flow, when the shear parameters are larger or the spacing between cylinders are smaller, the more likely the fluid elastic vibration of the cylinders will occur.

中文摘要----------------------------------------------------------------------------I
英文摘要---------------------------------------------------------------------------II
目錄--------------------------------------------------------------------------------III
圖表目錄----------------------------------------------------------------VII
符號說明-----------------------------------------------------------------------XI

第一章 緒論-----------------------------------------------------------------------1
1.1 前言------------------------------------------------------------1
1.2 文獻回顧------------------------------------------------------------5
1.3 研究動機----------------------------------------------------------13
1.4 研究中所使用的無因次參數定義----------------------------14

第二章 模擬理論與數值參數設定------------------------------------------16
2.1 理論分析----------------------------------------------------------16
2.1.1 數值方法---------------------------------------------------17
2.1.2統御方程式-------------------------------------------------17
2.1.3紊流模式----------------------------------------------------18
2.1.4圓柱運動方程式-------------------------------------------20
2.1.5 數值運算流程---------------------------------------------21

2.2 PISO演算法------------------------------------------------------24

2.3流場的基本假設與邊界條件設定---------------------------26
2.3.1流場計算域測試--------------------------------------27
2.3.2流場系統的網格設定與測試---------------------------28
2.3.3時間步階的設定與測試---------------------------------30

第三章 結果與討論------------------------------------------------------------31
3.1 單一圓柱之運動模式探討-------------------------------------31
3.1.1均勻流場中之單根圓柱運動分析---------------------32
3.1.2無因次流速與圓柱振幅及渦漩剝離頻率之關係---32
3.1.3不同無因次速度時的運動軌跡變化------------------33
3.1.4不同質量比對圓柱振幅的影響------------------------34
3.1.5 流場型態的變化------------------------------------------35

3.2剪切流場中單一圓柱的運動分析----------------------------36
3.2.1升力係數和阻力係數的變化---------------------------36
3.2.2史卓荷數的變化-----------------------------------------37
3.2.3剪切流場中無因次流速與振幅的關係---------------38
3.2.4不同剪切參數對圓柱振幅之影響----------------------38
3.2.5剪切流場內之流速對圓柱運動軌跡的影響---------40
3.2.6不同剪切參數對圓柱運動軌跡及流場之影響------41

3.3彈性交錯排列雙圓柱之運動模式探討----------------------42
3.3.1均勻流場內交錯排列雙圓柱運動分析--------------43
3.3.2均勻流場內交錯排列雙圓柱的振幅分析-----------43
3.3.3均勻流場中之雙根交錯排列圓柱的運動軌跡分析
--------------------------------------------------------------44
3.3.4均勻流中的雙根交錯排列圓柱的流場型態及升、
阻力係數變化--------------------------------------------45

3.4剪切流場中之雙根交錯排列圓柱的運動分析-------------46
3.4.1剪切流場內之雙根交錯排列圓柱的振幅分析-----47
3.4.2剪切流場內之雙根交錯排列圓柱的運動軌跡-----47
3.4.3剪切流場內之雙根交錯排列圓柱周圍的流場變化
---------------------------------------------------------------49

3.5彈性陣列交錯排列圓柱的運動模式--------------------------50
3.5.1均勻流場內之陣列交錯排列圓柱的運動探討-----50
3.5.2均勻流場內之陣列交錯排列圓柱的運動軌跡變化
---------------------------------------------------------------523.5.3均勻流場中之質量比對陣列交錯排列圓柱運動
的影響------------------------------------------------------53

3.6剪切流場中之陣列交錯排列圓柱的運動探討-------------54
3.6.1剪切流場中之不同間距比的陣列交錯排列圓柱
運動分析-------------------------------------------------55
3.6.2剪切流場中之陣列交錯排列圓柱運動軌跡變化
-------------------------------------------------------------56
3.6.3剪切流場中之質量比對陣列交錯排列圓柱運動
影響-------------------------------------------------------57

第四章 結論與建議------------------------------------------------------------60
參考文獻--------------------------------------------------------------------------62

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