臺灣博碩士論文加值系統

本文以數值模式之方法，研究均勻流場之中，圓柱橫向振動對昇力的影響機理。模式以Navier-Stokes方程式與投影法求解出流場，再以波譜分析解析昇阻力時間序列，並分析出渦流射出之頻率與能量
。當流體流經圓柱，圓柱之橫向振動將影響渦流，渦流將對圓柱作用，進而產生與固定圓柱不同之昇力與阻力。本文先利用流線圖、等壓圖、以及渦度圖等三種圖形，研究觀察渦流的方法與渦流之特性。再以等壓圖與壁壓圖分析圓柱振動對昇力的影響。最後綜合討論不同圓柱振動頻率對於昇力之影響機理。研究結果顯示，等壓圖是觀察渦流較適當的方法。在鎖定區間內，圓柱振動頻率愈大，渦流能量愈強，並且使壁壓分佈愈扭曲，進而產生愈大之昇力。緩衝區間內，渦流受到弱化，導致渦流能量較小，與壁壓分佈扭曲較少，最後造成較小的昇力。

This study set up a numerical simulation that used to discuss mechanism of the lift for a transversely oscillating cylinder. The Navier-Stokes equation is solved by a primitive method for the flow field. Then, a spectrum analysis is used to analyze the time series of the lift force to obtain the frequency and the energy of the shed vortices. The transverse vibration of the cylinder will affect vortex shedding when fluid flows over the cylinder. The vortices of vibrating cylinder will cause different lift and drag from those of fixed cylinder. This article uses three type of figure, i.e. streamline figure, pressure figure, and vorticity figure, to study the observation methods and characteristics of vortex. Then uses pressure figure and wall pressure figure to analyze the effect of cylinder vibration to the lift. Finally comprehensively discusses the mechanism of cylinder vibrating frequency to the lift. The results showed that pressure figure is the best for the observation of vortices. In the lock-on region, higher cylinder vibrating frequency gave greater vortex energy, more distorted wall pressure distribution , and larger lift. In the buffer region, vortice were weakened with less energy, and less distortion of the wall pressure, and finally caused lower lift.

謝誌 ………………...………….…………………… I

中文摘要 ………………...………….…………………… II

英文摘要 ………………...………….…………………… III

目 錄 …………………...……….…………………… IV
表 目 錄 …………………...……….…………………… VII
圖 目 錄 …………………...……….…………………… VIII
符號說明表 …………………...……….…………………… XII

第一章 概論
1.1 概述……………………………………………….……… 1
1.2 研究目的……………….………………………………… 2
1.3 前人研究……………………………………….………… 3
1.3.1 圓柱為固定之狀況………………………………... 3
1.3.2 圓柱為強制運動之狀況…………………………... 5
1.3.3 往復橫向振動圓柱之主要研究成果 …………… 6
1.3.4 數值方法概述 …………………………………… 8
1.4 章節介紹…………………………………………………. 9

第二章 理論分析
2.1 流場部份......…………………………………………....... 11
2.1.1 制御方程式……………………………………….. 11
2.1.2 起始條件………………………………………….. 14
2.1.3 邊界條件………………………………………….. 14
2.1.3.1 內邊界條件………………………………. 14
2.1.3.2 外邊界條件………………………………. 15
2.1.4 作用力…………………………………………….. 15
2.2 圓柱運動部分……………….………………………….... 16

第三章 數值方法模式
3.1 流場計算數值解法大綱…………………………………. 19
3.2 起始條件…………………………………………………. 21
3.3 邊界條件…………………………………………………. 22
3.3.1 內邊界條件………………………………. 22
3.3.2 外邊界條件………………………………. 23
3.4 座標轉換…....……………………………………………. 23
3.5 網格系統…….……………………………………… 27
3.6 昇力與阻力係數………………………..................... 29
3.6.1 求解昇力與阻力係數……………………………. 29
3.6.2 以波譜分析方法分析昇力與阻力係數之時間序列………………………………………………….
31
3.7 求解流線函數 ……………………………..............
33
3.8 求解渦度 ………………………………………....
34
3.9 計算圓柱運動……………………………………………. 35
3.10 時階 的限制……………………………………...
36
3.11 其他說明………………………………………………… 37
3.11.1 二階段計算及計算時間……………………... 37
3.11.2 慣性座標之流線…………………………………. 38

第四章 結果與討論
4.1 往復橫向振動圓柱計算結果驗證………………………. 40
4.1.1 時間平均阻力…………………………………….
4.1.2 昇力之虛部……………………………………….
40
41

4.2 頻率區間概述…...……………………………………….. 42
4.2.1 振動頻率的分區………………………………….
4.2.2 振動頻率對昇力中各頻率能量的影響………….
42
44

4.2.3 振動頻率對昇力的影響………………………….. 45
4.3 觀察渦流的方法與渦流之特性.………………………… 46
4.3.1 何種圖形較能顯示渦流…………………………. 48
4.3.2 附著渦流…………………………………………. 51
4.3.3 渦流的射出…………………….………………… 52
4.3.4 自由渦流…………………………………………. 53
4.4 圓柱振動頻率對昇力之影響機理……….……………. 55
4.4.1 昇力之計算……….………………………….. 55
4.4.2 壁壓圖分佈與昇力之關係………………….…… 56
4.4.3 渦流與壁壓圖之關係……………………………. 57
4.4.4 頻率與渦流之關係………..……………………... 58
4.4.5 綜合討論….………………………………… 59

第五章 結論與建議
5.1 結論…………………………………..…………………... 62
5.2 建議………………………………………………………. 64

參考文獻…………………………………………………….. 65

表……………………………………………………………... 69

圖……………………………………………………………... 73

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