臺灣博碩士論文加值系統

本文係以實驗與小波方法研究具有不同直徑的並列雙圓柱下游尾流被鎖定之特性，藉以了解外加擾動頻率對於並列雙圓柱下游尾流結構被鎖定的影響。本文的實驗是在低速循環迴路式的水槽中進行，以螢光染液釋放法紀錄流場可視化，以瞭解並列雙圓柱近域尾流定性演化的情形，並佐以雷射都卜勒測速儀系統對尾流場進行整個截面之定量流場量測。
主要內容為：固定切線速度擾動振幅，變化外加擾動振幅以及外加擾動頻率並利用小波分析，探討具有不同直徑(d/D=1/2)的並列雙圓柱下游尾流被鎖定的特性。研究結果顯示：(1)當具有大直徑之圓柱受到外加擾動影響時，並列雙圓柱下游的寬、窄域尾流被鎖定的區域均往單一圓柱特徵頻率的方向偏移；且在適當的擾動頻率時，雙圓柱均被鎖定在不同頻率段，形成雙鎖定的現象；(2)當小圓柱受到外加擾動時，寬域尾流的鎖定範圍以不受擾動的寬域尾流特徵頻率(fw*=fw/fos= 0.9)為中心向兩側擴張，而窄域尾流則是在無因次擾動頻率為fe*=0.9~1.2與fe*= 2.2~3.2間發生被鎖定現象，其中頻段fe*=0.9~1.2中則是寬域和窄域尾流同時發生被鎖定現象；而在頻段fe*=2.2~3.2之鎖定則僅有窄域尾流被鎖定。(3)藉由小波分析，間隙流中之特徵頻率因外加擾動的影響，從原與窄域尾流相同頻率轉為與外加擾動相同頻率。由此可知：外加擾動直接影響被擾動的尾流結構，也確實是經由間隙流的媒介而間接影響到另一個尾流結構。

The experimental investigation is to study, based on wavelet analysis, the locked-on characteristics of wakes behind two side-by-side circular cylinders with various excitation frequencies in the low-speed water channel. Quantitative velocity measurements and qualitative dye flow visualization were performed by way of the LDA system and the laser sheet technique, respectively.
In this study, two side-by-side circular cylinders has different diameters (d/D=1/2). The net gap ratio between two cylinders is 3D/4, and the Reynolds number based on the large cylinder diameter is 1160. One of the cylinders is perturbed in front of an oscillatory rotation about it’s center with a constant amplitude of tangential velocity.
It is found that：(1) When the large cylinder is perturbed at various excitation frequencies, the locked-on band of the narrow and the wide wakes behind each cylinder tend to shift towards the natural shedding frequency of the individual cylinder. When the excited at proper frequency, both the wide and the narrow wakes behind two circular cylinders are locked-on simultaneously but at the distinct frequency. This is called double lock-on phenomena. (2) When the small cylinder is perturbed at various excitation frequencies, the locked-on bandwidth of the wide wakes is located with fe*=0.7~0.9. The locked-on bandwidth of the narrow wakes is located at fe*=2.2~3.2. And the double locked-on of both wakes happens to be within fe*=0.9~1.2. (3) By wavelet transformation and analysis, it is shown that the characteristics frequency of the gap flow is dominated by the frequency of narrow wake when unperturbed. However, the responding frequency in gap flow is dominated by the characteristics frequency of the wide wake when the wide wake is excited near it’s nature shedding frequency. This reveals the direct evidences of flow coupling between the wide and narrow wakes.

目 錄
摘要
目錄……………………………………………………………………Ⅰ
圖表目錄………………………………………………………………Ⅳ
符號說明………………………………………………………………Ⅶ
第一章 緒 論 1
1-1 研究動機 1
1-2文獻回顧 2
1-3 本文結構 4
第二章 實驗設備與方法 5
2-1 循環式水槽 5
2-2 速度量測系統 6
2-3 實驗模型系統配置 7
2-4 圓柱振盪系統 8
2-5 流場可視化 9
2-6速度量測步驟 9
第三章 小波理論與傅立葉分析 12
3-1 傅立葉分析 12
3-2 短時傅立葉分析 13
3-3 小波轉換 14
3-4 連續小波轉換 15
3-5 訊號分析與測試結果 16
3-5-1 模擬訊號 16
3-5-2傅立葉轉換(FFT) 16
3-5-3小波分析(wavelet analysis) 16
第四章 實驗結果與討論 18
4-1 流場結構可視化 18
4-1-1 未擾動時，並列雙圓柱近域尾流結構 18
4-1-2 外加擾動頻率fe=0.5Hz時，並列雙圓柱近域尾
流結構 18
4-1-3 外加擾動頻率fe=0.63Hz時，並列雙圓柱近域尾
流結構 19
4-2 並列雙圓柱尾流結構能量的分佈 20
4-3 並列雙圓柱尾流結構被鎖定的響應頻率 21
4-4 並列雙圓柱下游尾流場的頻譜特性 22
4-4-1 外加擾動頻率對並列雙圓柱近域尾流結構的影響 22
4-4-2 外加擾動頻率對尾流響應頻率的影響 25
4-5 寬、窄域尾流在小波分析下的偏態值與峰度 27
第五章 結論 29
第六章 建議與未來發展方向 32
圖 表 目 錄
圖2-1 閉回路式循環水槽本体及各部名稱說明圖--------------------------34
圖2-2 自組式的FLDV量測系統各要件示意圖-----------------------------35
圖2-3 量測模型配置圖-----------------------------------------------------------36
圖2-4 直徑20mm圓柱模型各組成元件與尺寸圖--------------------------37
圖2-5 直徑10mm圓柱模型各組成元件與尺寸圖--------------------------38
圖2-6 (a)FLDV量測座標示意圖 (b)並列雙圓柱與外加擾動方式
的示意圖--------------------------------------------------------------------39
圖2-7 (a)伺服馬達組立俯視圖 (b)伺服馬達系統配置圖------------------40
圖2-8 流場可視化實驗配置側視圖--------------------------------------------41
圖2-9 實驗量測系統座標圖-----------------------------------------------------42
圖3-1 Haar的圖形-----------------------------------------------------------------43
圖3-2 傅立葉轉換、短時傅立葉轉換與小波轉換之時頻關係圖
(a)傅立葉轉換的時頻關係圖 (b)短時傅立葉轉換的時頻
關係圖(c)小波轉換的時頻關係圖-------------------------------------44
圖3-3 母小波經尺度因子及平移因子作用示意圖 (a)尺度刻度
為1時 (b)尺度刻度為2時 (c)平移參數b為1時------------------45
圖3-4 連續小波轉換--------------------------------------------------------------46
圖3-5 (a)原始的模擬訊號 (b)模擬訊號之能量頻率圖---------------------47
圖3-6 (a)小波轉換後之等高線圖 (b)瞬間頻率的最大值與最大
值之統計值----------------------------------------------------------------48
圖4-1 G/D=3/4，d/D=1/2，fe=0Hz流場可視化照片------------------------49
圖4-2 G/D=3/4，d/D=1/2，fe=0.5Hz流場可視化照片---------------------52
圖4-3 G/D=3/4，d/D=1/2，fe=0.63Hz流場可視化照片-------------------55
圖4-4 (a)未加擾動時，截面X/D=2.5寬、窄域特徵頻率之能量
隨著高度之變化 (b)外加擾動fe=0.5Hz時，截面X/D=2.5
寬窄域特徵頻率隨著高度之變化--------------------------------------58
圖4-5 未加擾動時，寬窄域下游尾流能量圖(a)窄域尾流能量圖
(b)寬域尾流能量圖------------------------------------------------------59
圖4-6 大圓柱受到外加擾動fe=0.5 Hz時，寬、窄域下游尾流能
量圖 (a)窄域尾流能量圖 (b)寬域尾流能量圖---------------------60
圖4-7 並列雙圓柱尾流結構流場的響應頻率與外加擾動頻率關
係圖之比較。(a)大圓柱受到外加旋轉擾動 (b)小圓柱受到
外加旋轉擾----------------------------------------------------------------61
圖4-8 G/D=3/4，d/D=1/2，fe=0Hz並列雙圓柱尾流之能量頻譜圖。
左列為快速傅立葉轉換所得之頻譜圖，右列為小波轉換所
統計而得各頻率發生機率圖-------------------------------------------62
圖4-9 G/D=3/4，d/D=1/2，fe=0.5Hz並列雙圓柱尾流之能量頻譜
圖。左列為快速傅立葉轉換所得之頻譜圖，右列為小波轉
換所統計而得各頻率發生機率圖--------------------------------------65
圖4-10 G/D=3/4，d/D=1/2，fe=0.63Hz並列雙圓柱尾流之能量頻
譜圖。左列為快速傅立葉轉換所得之頻譜圖，右列為小波
轉換所統計而得各頻率發生機率圖----------------------------------68
圖4-11 G/D=3/4，d/D=1/2，fe=1.16Hz並列雙圓柱尾流之能量頻
譜圖。左列為快速傅立葉轉換所得之頻譜圖，右列為小波
轉換所統計而得各頻率發生機率圖----------------------------------71
圖4-12 G/D=3/4，d/D=1/2，fe=1.83Hz並列雙圓柱尾流之能量頻
譜圖。左列為快速傅立葉轉換所得之頻譜圖，右列為小波
轉換所統計而得各頻率發生機率圖----------------------------------74
圖4-13 G/D=3/4，d/D=1/2，未外加擾動頻率fe=0Hz下，寬、窄
域尾流發生機率。--------------------------------------------------------77
圖4-14 G/D=3/4，d/D=1/2，大圓柱外加擾動頻率fe=0.5Hz下，寬
窄域尾流發生機率。-----------------------------------------------------81
圖4-15 不同的外加旋轉擾動時，由統計方法統計出由小波轉換後
的各頻率分佈圖，得到平均值、偏態值與峰度。左列為不
同外加擾動下，寬域各統計值，右列為窄域各統計值。---------85

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