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研究生: 彭寶華
Peng, Bou-Hua
論文名稱: 探討不同縫寬開縫圓柱渦流流量計對於流場特性之影響
Influence of Widths of Slit on Vortex Shedding behind Slit circular cylinder
指導教授: 苗君易
Miau, Jiun-Jih
學位類別: 碩士
Master
系所名稱: 工學院 - 航空太空工程學系
Department of Aeronautics & Astronautics
論文出版年: 2008
畢業學年度: 96
語文別: 中文
論文頁數: 153
中文關鍵詞: 粒子影像測速儀渦流流量計希爾伯-黃轉換
外文關鍵詞: vortex meter, PIV, HHT
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  • 如何改善渦流流量計流場一直是受到許多研究人員所重視,而利用開縫圓柱來改善流場之研究也行之有年。許多專家都已經證實開縫圓柱能有效加強量測訊號強度,並大幅改善訊號品質。但甚少有人探討開縫圓柱其縫寬對於其流場特性之影響。本論文利用熱線(hot-wire)測速儀在風洞中進行實驗,探討不同縫寬(s/d)之渦流流量計流場二維性,並且在水洞中利用粒子影像測速儀(PIV)及視流實驗觀測其流場之變化。
    由PIV實驗結果得知,可透過縫寬比(s/d)的增加來使渦流流量計渦流溢放頻率相對提高。且當雷諾數介於2400至11400時,s/d=0.15之渦流流量計穩定度最高。且透過視流實驗,發現開縫圓柱渦流流量計縫寬比(s/d)越大,其流場分離點亦隨之往前。透過hot-wire實驗之量測,利用交叉相關係數分析兩根探針不同間距(z)之訊號,判斷其側向波長長度變化,且透過與信號雜訊分析結果結合,吾人發現當雷諾數30000及50000時,開縫圓柱渦流流量計的確具有大幅改善流場訊號品質及增加流場二維性之能力,且s/d=0.15之流場訊號品質及流場二維性皆最佳。最後透過希爾伯-黃轉換(HHT)分析,吾人發現當渦流流量計流場二維性越強,其輸出瞬時頻率強度越強且穩定。

    The phenomenon of vortex shedding due to uniform flow over a circular cylinder with a normal slit was investigated in this study. Experiments were made for five cylinder models whose slit widths in terms of s/d, where s and d denote the width and the cylinder diameter, respectively, were 0, 0.05, 0.15, 0.20 and 0.30. For the experiments made in a water channel, the techniques of Particle Image Velocimetry (PIV) and flow visualization were employed. The PIV data obtained at the Reynolds numbers between 2,400 and 11,400 reveal a trend that the vortex shedding frequency reduced gets increased as s/d gets higher. More interestingly noted is that for the case of s/d= 0.15, the process of vortex shedding appears to be most periodic in time, which quantitatively can also be indicated by the signal quality defined. Results of flow visualization indicate that flow in the slit is oscillating in accordance with the frequency of vortex shedding, which in fact causes suction or blowing to flow over the circular cylinder. Thus, unsteady motions in the slit are realized very effective to modify the vortex shedding process.
    Experiments made in a wind tunnel were aimed to examine the two-dimensionality of vortex shedding by means of spanwise correlation of hot-wire measurements at the Reynolds numbers between 30,000 and 50,000, for the five cylinder models studied. Results obtained indicate that the vortex shedding structures in the case of s/d=0.15 behave most two-dimensional. Hilbert-Huang Transformation (HHT) analysis of the velocity signals measured further show that among the five cases studied, the case of s/d=0.15 appears to be the one whose instantaneous vortex shedding frequency is most stabilized in time and its amplitude is the highest in value.

    中文摘要....………………………………………………….……………...I 英文摘要....……………………………………………………………......III 致謝………………………………………………………………………IV 目錄....………………..……………………………………………..........VI 表目錄.………………....………………………………………….............X 圖目錄.……………….………………………………………............. …XI 符號說明……………………………….............................................. .XVIII 第一章 序論………………………………………………………………..1 1.1 研究動機與目的……………………………………………...……..1 1.2 文獻回顧…………………………………………………………….2 1.2.1 粒子影像測速儀……………………………..………....…........2 1.2.2 二維圓柱流場…………………………………………………..4 1.2.3 三維圓柱流場…………………………………………………..4 1.2.4 鈍形體渦流流量計……………………………………………..7 第二章 實驗設備及模型……………………………………………….…10 2.1 風洞實驗設備…...…………………………………………........10 2.1.1 風洞設備…………………………………………………...…10 2.1.2量測儀器與訊號擷取系統…………………………………….10 2.2水洞實驗設備…..…………………………………………………11 2.2.1循環式水洞..……………………………………………...……11 2.2.2視流實驗原理及實驗架設……………………………….……11 2.2.2.1視流實驗原理…..………………….....…………...……11 2.2.2.2視流實驗架設…..………………………...…………….12 2.2.3 PIV技術原理及實驗系統架設……………...…...……...……12 2.2.3.1 PIV技術原理方法…….…………….…………………12 2.2.3.2 PIV量測系統架設…….…………….………………...12 2.2.3.3 實驗模型…..………………………...…………..….....14 第三章 實驗步驟及方法………………………………………………...15 3.1 參數分析…………………………………………………...……...15 3.1.1 雷諾數……………………………………………...…...……...15 3.1.2 無因次頻率………………………………………...…...……...15 3.1.3 無因次頻率線性分析……………………………...…...……...16 3.2 二維流場分析………………………………………...…...………16 3.2.1 渦流溢放頻率之量測……………………………...…...……...17 3.2.2 快速傅立葉轉換………………………………….........…………17 3.2.3 流場渦度通量之計算…………………………….........…………18 3.3 三維流場分析………………………………….........……………….18 3.3.1 希爾伯- 黃轉換…………………………….........……………….18 3.3.2 信號雜訊比………………………………….........………………19 3.3.3 交叉相關係數……………………………….........………………20 第四章 實驗結果與討論………………………………………………...…22 4.1 PIV及視流實驗結果…………………………...…………………...22 4.1.1 圓柱尾流流場分析………………………...………….………...22 4.1.1.1 PIV資料可視化……………………...…………………...22 4.1.1.2 PIV資料數據化……………………...…………………...23 4.1.2 渦流流量計尾流流場分析………………...……………………24 4.1.2.1 PIV資料可視化……………………...…………………..24 4.1.2.2 PIV資料數據化……………………...…………………..24 4.2 Hot-wire實驗結果…………………………...……………………..26 4.2.1 圓柱尾流流場分析………………………...………….………..26 4.2.1.1 交叉相關係數………………………...……….….……..27 4.2.2 渦流流量計尾流流場分析…………………...…….….….........28 4.2.2.1 交叉相關係數………………………...……….….……..28 4.2.2.2 無因次頻率…………………...….….…………………..29 4.2.2.3 希爾伯-黃轉換……………………...……....……...……30 第五章 結論與建議………………………...……….….………………..…31 5.1 結論………………………...……….….…………………………...31 5.2 建議………………………...……….….…………………….……..33 5.2.1 PIV……………………...……….….………………………........33 5.2.2 hot-wire………………...……….….…………………….……....33 參考文獻.........................................................................................................35 表目錄 表1.1 開縫圓柱縫寬比(s/d)………………………………………….38 表3.1 不同雷諾數下各個渦流流量計之高速攝影機取樣頻率……39 表3.2 不同雷諾數下各個渦流流量計之高速攝影機曝光時間……39 表3.3 IMF 1至IMF 6之號雜訊比(Re=50000,s/d=0.15)…………...…40 表4.1 縫寬比(s/d)與無因次頻率(St)之交叉相關數(x=1d,y=-0.75d).41 表4.2 各個渦流流量計之無因次線性誤差,2400<Re<11400………41 表4.3 各個渦流流量計之交叉相關分析係數(Re=30000,y=1.5d)…..42 表4.4 各個渦流流量計之交叉相關分析係數(Re=50000,y=1.5d)…..42 表4.5 各個渦流流量計之交叉相關分析係數(Re=30000,y=2d)…......43 表4.6 各個渦流流量計之交叉相關分析係數(Re=50000,y=2d)……..43 表4.7 縫寬比(s/d)與無因次頻率(St)之交叉相關數…………………44 表4.8各個渦流流量計之無因次線性誤差,2400<Re<50000………....44 表4.9 不同縫寬比(s/d)渦流流量計瞬時頻率平均強度(Amp_mean)..45 圖目錄 圖1.1 PIV技術構成示意圖【3】…………………………………………46 圖1.2 PIV系統應用於量測直升機旋轉翼【4】…………………………46 圖1.3 PIV系統應用於量測升力機翼尾流【4】…………………………47 圖1.4 立體數位PIV示意圖【4】…………………………………………47 圖1.5 PIV位移統計圖,”peak-locking”(左),改善(右) 【7】…………..48 圖1.6 經過霧化之DEHS粒子尺度分佈 【6】…………………………..48 圖1.7 Auto-correlation及Cross-correlation示意圖【7】………………….49 圖1.8 流動分離現象示意圖【9】……………………………………………49 圖1.9 圓柱表面摩擦力及壓力分佈,Re=2.6×105【10】…………………..50 圖1.10 圓柱油流實驗,+90°一側的視流結果,Re=3.09×105【9】…….50 圖1.11 圓柱局部速度訊號【22】…………………………………………..51 圖1.12 圓柱側向波長比較示意圖【22】…………………………………..51 圖1.13 圓柱側向波長示意圖,Re=600【22】……………………………..52 圖1.14 開縫圓柱示意圖【24】…………………………………………….52 圖1.15 開縫圓柱表面壓力分佈【24】…………………………………….53 圖1.16 無因次頻率與開縫圓柱角度分佈圖【24】………………………53 圖1.17 無因次頻率與雷諾數關係圖【25】……………………………….54 圖1.18 不同開縫比(s/d)之開縫圓柱無因次頻率【25】………………….54 圖1.19 開縫圓柱(s/d=0.08)之縫內震盪速度與壓力【25】………………..55 圖1.20 圓柱縫槽流場示意圖【25】………………………………………..55 圖1.21 流量計設備示意圖【26】………………………………………….56 圖1.22 周期訊號標準差vs流量示意圖(d=14mm,w=2mm)【26】……….56 圖1.23 非線性誤差vs 阻滯比【26】……………………………………….57 圖1.24 梯型鈍形體示意圖【27】……………………………………………57 圖1.25 工作流體(水)校正曲線【27】………………………………………58 圖 1.26 鈍形體組合流場示意圖【28】……………………………………..58 圖 1.27 不同外型條件之圓柱【29】………………………………………..59 圖1.28 hot-wire探針量測圓柱(C1)、開縫圓柱(S1)及開縫凹槽圓柱(SN1)在 x/D=5處之渦流溢放訊號【29】………………………………………..60 圖2.1 風洞外型示意圖………………………………………………..........61 圖2.2 DANTEC 55M01型定溫式熱線測速儀…………………………….61 圖2.3 水洞外型示意圖……………………………………………………..62 圖2.4 開縫圓柱渦流流量計示意圖…………………………………..........62 圖2.5 PIV系統示意圖…………………………………………………..….63 圖2.6 Innva 70氬離子雷射光源與光學設備……………………………....63 圖2.7 模型架設示意圖:(a)PIV實驗; (b)風洞實驗………………………64 圖2.8 開縫圓柱模型示意圖……………………………………………….65 圖2.9 渦流流量計示意圖…………..………………………………………65 圖3.1 圓柱流場之無因次頻率與雷諾數相關圖【11】……………………66 圖3.2 圓柱流場之平均流場示意圖(8000張,擷取頻率200hz,曝光時間 4.997ms,Re=11400)…………………………………………………………66 圖3.3原始訊號及內建模態函數……………………………………...........67 圖3.4內建模態函數快速傅立葉轉換……………………………………..67 圖3.5頻譜分析圖…………….……………………………………….........68 圖3.6交叉相關係數分析結果示意圖…………….………………….........69 圖4.1圓柱尾流流場(Re=2700,T=2.76sec)…..………………………......70 圖4.2 分析圓柱尾流流場(x=1d,y=-0.75d)示意圖………………………....71 圖4.3 圓柱尾流流場(x=1d,y=-0.75d)之速度分佈………………………...72 圖4.4 圓柱尾流流場(x=1d,y=-0.75d)之無因次頻率……………………..73 圖4.5分析圓柱尾流流場示意圖……………………………………….…74 圖4.6圓柱尾流流場之渦漩通量…………………………………………..75 圖4.7 s/d=0.3渦流流量計尾流流場(Re=1.14×104,T≒0.495sec)…..……..76 圖4.8 s/d=0.2渦流流量計尾流流場(Re=1.14×104,T≒0.5sec)………….…77 圖4.9 s/d=0.15渦流流量計尾流流場(Re=1.14×104,T≒0.54sec)…………78 圖4.10 s/d=0.05渦流流量計尾流流場(Re=1.14×104,T≒0.57sec)………..79 圖4.11 s/d=0.3渦流流量計分離點示意圖;Re=4600…………………..80 圖4.12 s/d=0.2渦流流量計分離點示意圖;Re=4600………………….80 圖4.13 s/d=0.15渦流流量計分離點示意圖;Re=4600…………………81 圖4.14 s/d=0.05渦流流量計分離點示意圖;Re=4600…………………81 圖4.15 分析開縫圓柱(s/d=0.05, Re=4600)瞬時流場示意圖……………82 圖4.16 分析開縫圓柱(s/d=0.15, Re=4600)瞬時流場示意圖……………82 圖4.17 分析開縫圓柱(s/d=0.2, Re=4600)瞬時流場示意圖……….........83 圖4.18 分析開縫圓柱(s/d=0.3, Re=4600)瞬時流場示意圖………..........83 圖4.19 分析開縫圓柱(s/d=0.05, Re=1.14×104)縫口流場示意圖….........84 圖4.20 分析開縫圓柱(s/d=0.05, Re=1.14×104)尾流流場示意圖….........84 圖4.21 開縫圓柱縫寬比(s/d)與無因次頻率關係(St)示意圖(1d,-0.75d)…85 圖4.22開縫圓柱(s/d=0.05;x=-0d,y=-0.525d)之速度分佈…………………86 圖4.23 開縫圓柱(s/d=0.05;x=1d,y=-0.75d)之速度分佈…………..……...87 圖4.24 開縫圓柱(s/d=0.05;x=0d,y=-0.525d)之無因次頻率……….……...88 圖4.25 開縫圓柱(s/d=0.05;x=1d,y=-0.75d)之無因次頻率………..……...89 圖4.26 開縫圓柱(s/d=0.15;x=0d,y=-0.525d)之速度分佈…………………90 圖4.27 開縫圓柱(s/d=0.15;x=1d,y=-0.75d)之速度分佈…………..……...91 圖4.28 開縫圓柱(s/d=0.15;x=0d,y=-0.525d)之無因次頻率……….……...92 圖4.29 開縫圓柱(s/d=0.15;x=1d,y=-0.75d)之無因次頻率………..……...93 圖4.30 開縫圓柱(s/d=0.2;x=0d,y=-0.525d)之速度分佈…………….........94 圖4.31 開縫圓柱(s/d=0.2;x=1d,y=-0.75d)之速度分佈…………………..95 圖4.32 開縫圓柱(s/d=0.2;x=0d,y=-0.525d)之無因次頻率……………….96 圖4.33 開縫圓柱(s/d=0.2;x=1d,y=-0.75d)之無因次頻率…………..........97 圖4.34 開縫圓柱(s/d=0.3;x=0d,y=-0.525d)之速度分佈………………….98 圖4.35 開縫圓柱(s/d=0.3;x=1d,y=-0.75d)之速度分佈…………………..99 圖4.36 開縫圓柱(s/d=0.3;x=0d,y=-0.525d)之無因次頻率……………....100 圖4.37 開縫圓柱(s/d=0.3;x=1d,y=-0.75d)之無因次頻率…………........101 圖4.38 開縫圓柱縫寬比(s/d)與無因次頻率關係(St)示意圖(0d,-0.75d)...102 圖4.39 渦流流量計無因次頻率分佈圖…………………………………..103 圖4.40 渦流流量計無因次頻率線性誤差分佈圖………………………..103 圖4.41 不同縫寬比(s/d)渦流流量計Qs分佈圖(x=1d,y=-0.75d)…………104 圖4.42 不同縫寬比(s/d)渦流流量計Er分佈圖(x=1d,y=-0.75d)…………104 圖4.43 不同縫寬比(s/d)渦流流量計Qs分佈圖(x=0d,y=-0.525d)………..105 圖4.44 不同縫寬比(s/d)渦流流量計Er分佈圖(x=0d,y=-0.525d)………..105 圖4.45 不同縫寬比(s/d)渦流流量計之渦流通量(x=0.5d截面)…..……...106 圖4.46 渦流流量計原始訊號交叉相關係數(x=1d,y=1.5d)…..………….107 圖4.47 渦流流量計原始訊號交叉相關係數(x=1.5d,y=1.5d)……………108 圖4.48 渦流流量計原始訊號交叉相關係數(x=1d,y=2d)……….………109 圖4.49 渦流流量計原始訊號交叉相關係數(x=2d,y=2d)……………….110 圖4.50 圓柱流場Hw1、Hw2原始訊號 (x=1.5d,y=1.5d;Re=30000)……111 圖4.51 圓柱流場Hw1、Hw2原始訊號 (x=1d,y=1.5d;Re=30000) …….112 圖4.52 圓柱流場Hw1、Hw2原始訊號 (x=1d,y=2d;Re=30000)……….113 圖4.53 圓柱流場Hw1、Hw2原始訊號 (x=1d,y=2d;Re=30000)……….114 圖4.54 圓柱流場Hw1、Hw2不同位置交叉相關係數分佈…………….115 圖4.55 不同開縫比(s/d)之Hw1、Hw2交叉相關係數分佈…………….115 圖4.56 不同開縫比(s/d)之Hw1、Hw2交叉相關係數分佈……………..116 圖4.57 不同開縫比(s/d)之Hw1、Hw2交叉相關係數分佈……..………116 圖4.58 不同縫寬比(s/d)之無因次頻率分佈……..………………………117 圖4.59 不同雷諾數之無因次頻率分佈……..……………………………117 圖4.60 渦流流量計無因次頻率線性誤差分佈圖……………………..…118 圖4.61 不同渦流流量計之快速傅立葉分析(x=1d,y=1.5d;Re=30000).....119 圖4.62 不同渦流流量計之快速傅立葉分析(x=1.5d,y=1.5d;Re=30000)..120 圖4.63 不同渦流流量計之快速傅立葉分析(x=1d,y=2d;Re=30000)........121 圖4.64 不同渦流流量計之快速傅立葉分析(x=2d,y=2d;Re=30000)........122 圖4.65 不同渦流流量計之雜訊比(x=1d,y=1.5d)………………………..123 圖4.66 不同渦流流量計之雜訊比(x=1.5d,y=1.5d) ……………………..124 圖4.67 不同渦流流量計之雜訊比(x=1d,y=2d) ………………………….125 圖4.68 不同渦流流量計之雜訊比(x=2d,y=2d)…………………………..126 圖4.69 不同s/d渦流流量計之無因次分佈……………...………………127 圖4.70 不同渦流流量計HHT;Re=50000;(1d,1.5d)...............................128 圖4.71 不同渦流流量計HHT;Re=50000;(1.5d,1.5d) ...........................129 圖4.72 不同渦流流量計HHT;Re=50000;(1d,2d) .................................130 圖4.73 不同渦流流量計HHT;Re=50000;(2d,2d)..................................131

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