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研究生： 黃礪德
Huang, Li-Te
論文名稱： 沿著流線向三液滴的相互作用
Streamwise Interaction of Three Drops
指導教授： 林大惠
Lin, Ta-Hui
學位類別： 碩士
Master
系所名稱： 工學院 - 機械工程學系
Department of Mechanical Engineering
論文出版年： 2015
畢業學年度： 103
語文別： 英文
論文頁數： 127
中文關鍵詞： 液滴碰撞 、液滴相互作用 、液滴間距 、火焰結構 、液滴蒸發率
外文關鍵詞： Drop Collision, Drop Interaction, Drop Spacing, Flame Structure, Drop Vaporization
相關次數： 點閱：126  下載：1 
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    • 本研究以自由液滴法研究三顆液滴在一對流環境下，流線向之相互影響性。實驗參數分別為：液滴直徑(di)、液滴初始間距(Si = s/di)、冷流場環境與熱流場環境(vg)，s為兩顆液滴之中心距離，使用流體為水與十二烷。本研究主要分為水液滴在冷流場環境與熱流場環境下，流線向之相互作用，以及十二烷液滴在熱流場環境下，流線向之相互作用兩部分。
    實驗結果顯示，當三顆液滴在落下飛行的過程中，由於後方液滴會受到前方液滴的尾流影響，並且由於阻力係數(CD)較低的因素，進而發生後方液滴追撞前方液滴的現象。研究結果指出，增加液滴之間距離(s)、增加液滴初始間距(Si)、減少三顆液滴雷諾數(Re)可發現液滴碰撞點(xc)位置會有延後發生的現象。第一次液滴碰撞點(xc)在液滴初始間距(Si)為2.5和5時，隨著雷諾數降低呈線性變化延後，然而在液滴初始間距(Si)為10時，隨著雷諾數降低呈曲線變化延後。第二次液滴碰撞只發生在液滴初始間距(Si)為2.5和5，其液滴碰撞點(xc)隨著雷諾數降低呈曲線變化延後。第一次液滴追撞行為模式可分為同軸碰撞與非同軸碰撞，其中增加液滴直徑(di)會使震盪頻率增加，此外第二次液滴追撞行為模式只有非同軸碰撞，並且沒有規律的震盪頻率發生。
    三顆十二烷液滴在熱流場環境下，由於會有蒸發與燃燒的現象發生，因此液滴之間的相互作用與水液滴完全不同。十二烷液滴在落下飛行的過程中，液滴碰撞型態分為三種，包含發生於前兩顆液滴碰撞或後兩顆液滴碰撞，也有三顆液滴沒有碰撞的現象發生。這是由於液滴的火焰會使得局部環境溫度與流場對流產生變化，進而影響三顆液滴在飛行過程的縱向與側向間距變化，以及液滴碰撞與火焰型態的轉換模式。

    The interaction of three drops in the direction of the stream is studied experimentally using a free-falling drop apparatus which provides different gaseous flows, cold flow (vg = 0 - 0.5 m/s) and a hot flow (vg = 2.5 m/s). Both water and dodecane were used in the experiments, and thus there are two main parts to discuss.
    In the downward movement of three aligned drops with given values of di and Si, the first two drops first merge into a large drop, which then merges with the remaining drop. It was found that the position of the merging drop collisions which resulted in merged shifted downstream with larger initial drop diameter, larger initial drop spacing, and higher initial gas velocity due to the weakened wake effect. The initial drop spacing (Si) was more dominated to interaction of three drops. The leading merged collision included along the same axis condition and under the off-center condition, but the final merged collision occurred only under the off-center condition. The oscillation period of the leading merged increased with increasing initial drop diameter, but the final merged did not exhibit a oscillate cycle.
    Three aligned dodecane drops moved downward only in hot flow. The three dodecane drops were affected by the interactions among the thermal expansion, convective effect caused by the different flame structures in the combustion chamber, and exhibited three main merged modes. The different flame structure would affect the vaporization rate (k) of all drops.

    Contents Contents Ⅰ List of Tables Ⅲ List of Figures Ⅳ Nomenclature XI 1. Introduction 1 1.1 Dynamics characteristics of drops 2 1.1.1 Three drop collisions 2 1.1.2 Drop interactions 4 1.2 Combustion characteristics of drop interactions 11 1.3 Objectives 18 2. Experimental apparatus and methods 19 2.1 Drop generation system 19 2.2 Combustion system 20 2.3 Experimental methods 21 3. Results and discussion 23 3.1 Dynamic characteristics of three water drops 23 3.1.1 Velocity of drops 23 3.1.2 Reynolds numbers of drops 27 3.1.3 Drag coefficients of drops 30 3.1.4 Variation of water drop spacing with different positions 31 3.1.5 Merging process of drops 33 3.2 Combustion characteristics of three dodecane drops 41 3.2.1 Flame streak image 41 3.2.2 Variation of drop spacing with different positions 42 3.2.3 Flame transition process 46 3.2.4 Vaporization rate of drops 52 4. Conclusions 55 4.1 Dynamics characteristics of three water drops 55 4.2 Combustion characteristics of three dodecane drops 56 5. References 57 Tables and figures 64 List of publications 127 List of Tables Table 2.1. Properties of water and dodecane 64 Table 2.2. Experimental parameters of three water drops 64 Table 2.3. Experimental parameters of three dodecane drops 64 List of Figures Figure 2.1. Experimental apparatus 65 Figure 2.2(a). Drop string severance system 65 Figure 2.2(b). Drop string severance disk 66 Figure 2.3. The direction of flow injected into the quartz tube 66 Figure 2.4. Variation of drop and gas velocity with x [48] 67 Figure 2.5. Axial temperature distribution inside the combustion chamber [48] ……………………………………………68 Figure 2.6. Image of Three-drops with different Si 69 Figure 2.7. Image of axial drop spacing (Sx) and transverse drop spacing (Sy) 69 Figure 2.8. Image of merged drop and trailing drop, axial drop spacing (Sx3) and transverse drop spacing (Sy3) 70 Figure 3.1. Image of water drops at different positions (x) 70 Figure 3.2(a). Variation of water drop velocity (v) at different positions (x) for various initial gas velocities (vg). (Si ≈ 2.5 and di ≈ 900 µm) 71 Figure 3.2(b). Variation of water drop velocity (v) at different positions (x) for various initial gas velocities (vg). (Si ≈ 5 and di ≈ 900 µm) 72 Figure 3.2(c). Variation of water drop velocity (v) at different positions (x) for various initial gas velocities (vg). (Si ≈ 10 and di ≈ 900 µm) 73 Figure 3.2(d). Variation of water drop velocity (v) at different positions (x) for various initial gas velocities (vg). (Si ≈ 2.5 and di ≈ 700 µm) 74 Figure 3.2(e). Variation of water drop velocity (v) at different positions (x) for various initial gas velocities (vg). (Si ≈ 5 and di ≈ 700 µm) 75 Figure 3.2(f). Variation of water drop velocity (v) at different positions (x) for various initial gas velocities (vg). (Si ≈ 10 and di ≈ 700 µm) 76 Figure 3.2(g). Variation of water drop velocity (v) at different positions (x) for various initial gas velocities (vg). (Si ≈ 2.5 and di ≈ 500 µm) 77 Figure 3.2(h). Variation of water drop velocity (v) at different positions (x) for various initial gas velocities (vg). (Si ≈ 5 and di ≈ 500 µm) 78 Figure 3.2(i). Variation of water drop velocity (v) at different positions (x) for various initial gas velocities (vg). (Si ≈ 10 and di ≈ 500 µm) 79 Figure 3.3(a). Variation in the Reynolds number (Re) of a water drop at different positions (x) for various initial gas velocities (vg). (Si ≈ 2.5 and di ≈ 900 µm) 80 Figure 3.3(b). Variation in the Reynolds number (Re) of a water drop at different positions (x) for various initial gas velocities (vg). (Si ≈ 5 and di ≈ 900 µm) 81 Figure 3.3(c). Variation in the Reynolds number (Re) of a water drop at different positions (x) for various initial gas velocities (vg). (Si ≈ 10 and di ≈ 900 µm) 82 Figure 3.3(d). Variation in the Reynolds number (Re) of a water drop at different positions (x) for various initial gas velocities (vg). (Si ≈ 2.5 and di ≈ 700 µm) 83 Figure 3.3(e). Variation in the Reynolds number (Re) of a water drop at different positions (x) for various initial gas velocities (vg). (Si ≈ 5 and di ≈ 700 µm) 84 Figure 3.3(f). Variation in the Reynolds number (Re) of a water drop at different positions (x) for various initial gas velocities (vg). (Si ≈ 10 and di ≈ 700 µm) 85 Figure 3.3(g). Variation in the Reynolds number (Re) of a water drop at different positions (x) for various initial gas velocities (vg). (Si ≈ 2.5 and di ≈ 500 µm) 86 Figure 3.3(h). Variation in the Reynolds number (Re) of a water drop at different positions (x) for various initial gas velocities (vg). (Si ≈ 5 and di ≈ 500 µm) 87 Figure 3.3(i). Variation in the Reynolds number (Re) of a water drop at different positions (x) for various initial gas velocities (vg). (Si ≈ 10 and di ≈ 500 µm) 88 Figure 3.3(j). Variation in the Reynolds number (Re) of a water drop at different positions (x) for the hot flows. (Si ≈ 2.5, 5, 10 and di ≈ 500, 700, 900 µm) 89 Figure 3.4(a). Variation in the drag coefficient (CD) of a water drop at different positions (x) for various initial gas velocities (vg). (Si ≈ 2.5 and di ≈ 900 µm) 90 Figure 3.4(b). Variation in the drag coefficient (CD) of a water drop at different positions (x) for various initial gas velocities (vg). (Si ≈ 5 and di ≈ 900 µm) 91 Figure 3.4(c). Variation in the drag coefficient (CD) of a water drop at different positions (x) for various initial gas velocities (vg). (Si ≈ 10 and di ≈ 900 µm) 92 Figure 3.4(d). Variation in the drag coefficient (CD) of a water drop at different positions (x) for various initial gas velocities (vg). (Si ≈ 2.5 and di ≈ 700 µm) 93 Figure 3.4(e). Variation in the drag coefficient (CD) of a water drop at different positions (x) for various initial gas velocities (vg). (Si ≈ 5 and di ≈ 700 µm) 94 Figure 3.4(f). Variation in the drag coefficient (CD) of a water drop at different positions (x) for various initial gas velocities (vg). (Si ≈ 10 and di ≈ 700 µm) 95 Figure 3.4(g). Variation in the drag coefficient (CD) of a water drop at different positions (x) for various initial gas velocities (vg). (Si ≈ 2.5 and di ≈ 500 µm) 96 Figure 3.4(h). Variation in the drag coefficient (CD) of a water drop at different positions (x) for various initial gas velocities (vg). (Si ≈ 5 and di ≈ 500 µm) 97 Figure 3.4(i). Variation in the drag coefficient (CD) of a water drop at different positions (x) for various initial gas velocities (vg). (Si ≈ 10 and di ≈ 500 µm) 98 Figure 3.4(j). Variation in the drag coefficient (CD) of a water drop at different positions (x) for the hot flows. (Si ≈ 2.5, 5, 10 and di ≈ 900 µm) 99 Figure 3.5. Dimensionless spacing of axial direction as a function of x for three water drops. (Si ≈ 2.5 and di ≈ 500, 700, 900 µm) 100 Figure 3.6. Dimensionless spacing of axial direction as a function of x for three water drops. (Si ≈ 5 and di ≈ 500, 700, 900 µm) 101 Figure 3.7. Dimensionless spacing of axial direction as a function of x for three water drops. (Si ≈ 10 and di ≈ 500, 700, 900 µm) 102 Figure 3.8. Dimensionless spacing of transverse direction as a function of x for three water drops. (Si ≈ 2.5 and di ≈ 500, 700, 900 µm) 103 Figure 3.9. Dimensionless spacing of transverse direction as a function of x for three water drops. (Si ≈ 5 and di ≈ 500, 700, 900 µm) 104 Figure 3.10. Dimensionless spacing of transverse direction as a function of x for three water drops. (Si ≈ 10 and di ≈ 500, 700, 900 µm) 105 Figure 3.11. The leading merging position for two water drops (xc) as a function of the initial gas velocity (vg). (Si ≈ 2.5, 5, 10 and di ≈ 500, 700, 900 µm) 106 Figure 3.12. The final merging position for two water drops (xc) as a function of the initial gas velocity (vg). (Si ≈ 2.5, 5 and di ≈ 500, 700, 900 µm) 107 Figure 3.13. The minimum value of Re for the leading merged collision (di ≈ 500, 700, 900 µm). 108 Figure 3.14. The minimum value of Re for the final merged collision (di ≈ 500, 700, 900 µm) 109 Figure 3.15. The rear-ending process of merging collision of two water drops along the same axis, as di ≈ 900 µm. (Cold flow) 110 Figure 3.16. The period of water drop oscillation in cold flow. (8 t - 38 t is for 1 cycle.) 111 Figure 3.17. Rear-ending process of the final merged collision of two drops under the off-center condition, as di ≈ 900 µm 111 Figure 3.18. Images of flame streak 112 Figure 3.19. Image of merged drop and trailing drop, axial drop spacing (Sx) and transverse drop spacing (Sy) 113 Figure 3.20. Variation of the Reynolds number (Re) of a dodecane drop at different positions (x) (Si ≈ 2.5 and di ≈ 900 µm) 114 Figure 3.21. Variation of the Reynolds number (Re) of a dodecane drop at different positions (x) (Si ≈ 5 and di ≈ 900 µm) 115 Figure 3.22. Variation of the Reynolds number (Re) of a dodecane drop at different positions (x) (Si ≈ 10 and di ≈ 900 µm) 116 Figure 3.23. Dimensionless spacing of axial direction as a function of x for three dodecane drops 117 Figure 3.24. Dimensionless spacing of transverse direction as a function of x for three dodecane drops 118 Figure 3.25. Image of three diesel drops ignition period. (x = 17cm) 119 Figure 3.26. Variation of flame transition of dedecane drop at different positions (x) in hot flow, as Si ≈ 5 and di ≈ 900 µm. (Mode I) 120 Figure 3.27. Variation of flame transition of dedecane drop at different positions (x) in hot flow, as Si ≈ 5 and di ≈ 900 µm. (Mode II) 120 Figure 3.28. Variation of flame transition of dedecane drop at different positions (x) in hot flow, as Si ≈ 5 and di ≈ 900 µm. (Mode III) 121 Figure 3.29. Variation of flame transition of dedecane drop at different positions (x) in hot flow, as Si ≈ 10 and di ≈ 900 µm. (Mode III) 122 Figure 3.30. Variation of drop diameter squared (d2) with time for various Si. 123 Figure 3.31. Variation of vaporization rate (k) at different initial drop spacing. (Mode I). 124 Figure 3.32. Variation of vaporization rate (k) at different initial drop spacing. (Mode II). 125 Figure 3.33. Variation of vaporization rate (k) at different initial drop spacing. (Mode III). 126 Nomenclature As Surface area of the drop (m2) Cp CD Water Heat capacity (J/kg-K) Drag coefficient di Initial drop diameter (μm) dt Instantaneous drop diameter k Vaporization rate constant (cm2/s) kg Air thermal conductivity (W/m•K) Re Reynolds number Si Initial drop spacing Sx1 Axial drop spacing between leading drop and middle drop Sx2 Sx3 Axial drop spacing between middle drop and trailing drop Axial drop spacing between leading merged drop and the other drop Sy1 Transverse drop spacing between leading drop and middle drop Sy2 Sy3 Transverse drop spacing between middle drop and trailing drop Transverse drop spacing between leading merged drop and the other drop s Center-to-center distance between drops v Velocity of drop (m/s) vg Initial gas velocity (m/s) x Position in combustion chamber (cm) ρw Water density of dodecane (kg/m3) Δt Interval of frames in high speed filming (10000 fps) ΩO2 Ambient oxygen concentration (%) μ Viscosity (N.s/m2) σ Surface tension (N/m)

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