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研究生:許桓瑞
研究生(外文):Huan-Ruei Shiu
論文名稱:電雙層於微流道旁通過渡流之效應
論文名稱(外文):Effects of Electric Double Layer on Bypass Transition in Microchannel Flow
指導教授:陳希立陳希立引用關係
指導教授(外文):Sih-Li Chen
學位類別:博士
校院名稱:國立臺灣大學
系所名稱:機械工程學研究所
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2004
畢業學年度:93
語文別:英文
論文頁數:116
中文關鍵詞:微流體電雙層旁通過渡流微流道
外文關鍵詞:microfluidicEDLmicrochannelbypass transition
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本論文藉由高解析之直接數值模擬探討電雙層(EDL) 於旁通過渡流線性與非線性發展之影響,並以三種不同型態之局部擾動加以分析,首先為成對的反向渦旋,第二種為噴流式之軸對稱擾動,第三種為波動包之形式,且在低雷諾數下之電雙層流場以系統性的比較次臨界過渡區之巨觀尺度Poiseuille流場來探究此擾動場之發展。在線性發展階段中v與w方向擾動速度之發展在質與量上是極為相似的,於EDL效應下,在初始u為零之成對形式之渦旋擾動,建立起兩倍大之徑向渦度ωy,並且兩流場皆發展出傾斜的強力剪力層,整體來說,其兩近似之擾動場所顯示在三維線性機制下EDL流場生成之結構與Poiseuille流場有相當之強度。對於較大振福之擾動,即非線性成長,因EDL流場存在不穩定之反曲速度剖面,則其總動能大於Poiseuille流場,而且軸對稱擾動引起之能量成長較大於反向旋轉渦流,在過渡過程中之非線性交互作用,假若其擾動足夠強烈或是/並且雷諾數足夠高以克服暫態成長階段,即旁通過渡過程中的Tollmien-Schliching不穩定機制,觸發流場裂解而形成紊流斑。因此,在相同的流場條件下,局部擾動振幅會在比Poiseuille流場小於一個級數下之EDL流場下觸發流場裂解。
The effect of the electric double layer (EDL) on the bypass transition mechanism in the linear and nonlinear evolution stage is explored through direct numerical simulations of high resolution. Three kinds of localized disturbances are analyzed. The first one is a pair of counterrotating vortices, the second is a wall jet-like axisymmetric perturbation, while the third is a wave-packet. The time-space evolution of the perturbed field is throughly investigated at low Reynolds numbers in EDL flow by systematically comparing the results in the subcritical transition region of macro-scale Poiseuille flow. The wall normal and spanwise perturbation velocities development are both quantitatively and qualitatively similar in macro and micro flows in the linear stage. The streamwise velocity, which is initially zero for the pair of vortices and is set up by the generation of the wall normal vorticity is twice larger under the EDL effect. Both flows develop inclined strong streamwise shear layers. Overall is the close similarity of the disturbance evolution showing that the three dimensional linear mechanism in EDL flow lead to the structures that are at least as strong as in Poiseuille flow. For large amplitude perturbations, i.e. in the non linear regime the total kinetic energy associated with the EDL flow is larger compared with the Poiseuille flow because of the inherently unstable EDL inflexionnal velocity profile. The energy growth associated with axisymmetric perturbation is always larger than that associated with the counterrotating vortices. The nonlinear interactions trigger the breakdown and lead to turbulent spots, bypassing the transitional Tollmien-Schlichting instability mechanism, providing that the disturbance is strong enough and/or the Reynolds number is sufficiently high to overcome the transient growth stage. Thus the amplitude of the localized disturbance that lead to breakdown is an order of magnitude smaller in EDL flow compared to the macro flow under some circumstances.
Contents

Abstract ii
摘要 iii
Resum�� iv
Acknowledgments v
誌謝 vi
Contents vii
List of Figures ix
List of Tables xiv
Nomenclature xv
1. Introduction 1
1.1 Preliminary 1
1.2 Microscale effect 1
1.2.1 Molecular effect 1
1.2.2 Interfacial effect 3
1.2.3 Surface roughness effect 5
1.3 Transition in microchannel flow 6
1.4 Objectives 7
1.5 The scope and structure of the thesis 8
2. Electric Double Layer 10
2.1 Physical aspects of electric double layers 10
2.2 Equations governing 2D channel flow under the EDL effect 13
2.3 Instability analysis of 2D channel flow under the EDL effect 19
2.3.1 Inflexional inviscid instability 19
2.3.2 Linear stability analysis 21
3. Basic background of laminar-turbulent transition mechanism 25
3.1 “Short” Historical 25
3.2 Bypass transition 29
3.3 Aspects of Subcritical instability on EDL microchannel flow 35
4. Direct Numerical Simulations 39
4.1 Introduction 39
4.2 Computational domain and grid spacing 41
4.3 Governing equations 43
4.4 Localized initial disturbance 46
4.3.1 Counterrotating streamwise vortices 46
4.3.2 Axisymmetric disturbances 49
4.3.3 Wave-packet 50
5. Results and discussions 52
5.1 Parameters of EDL 52
5.2 Early linear evolution 57
5.3 Nonlinear evolution 65
5.3.1 EDL flow v.s. Poiseuille flow for QSV and AS 65
5.4 Strong Nonlinear evolution 89
5.4.1 AS v.s. CSV for EDL flow 89
5.4.2 EDL flow for wave-packet 99
6. Conclusion 104
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