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 本文主要在於模擬不可壓縮非牛頓流體，自鉛直的毛細管或孔洞，承受時變的起始壓力下的流出情形。本文設定不同形式的時變壓力梯度與流體特性，模擬具自由邊界軸對稱的液滴，並假設初使流場狀態為靜止，突然施加時變壓力梯度至液滴流場。本文採用FLOW-3D計算流力模式，使用半隱性有限差分法(Semi-Implicit Finite-Difference)配合體積分率法(Fractional Volume of Fluid, VOF)與自由網格法(Fractional Area/Volume Obstacle Representation, FAVOR)，為了節省計算時間與加速趨近數值解，使用了鬆弛法(Successive Over-Relaxation, SOR)來求解動量方程式之數值近似解。數值結果可觀察出液體在流出毛細管或孔洞其自由表面的演變，提供滴管動力一個易於理解的說明，並可得在不同的壓力梯度定義下液滴內的速度與壓力場圖，並進一步求得流體體積與時間之關係，以提供液體控制系統之參考。關鍵詞：自由表面、液滴、有限差分法、體積分率法
 The main objective of this study is to simulate the dynamics of a droplet of incompressible non-Newtonian fluids from a vertical capillary tube or an orifice into an ambient gas. The study simulates an axisymmetric drop with a free surface in suddenly applied time-dependent pressure gradients. The droplet is initially at rest, then a time-dependent pressure gradient is suddenly imposed on the fluid.The momentum equations are solved numerically by using Semi-Implicit Finite-Difference Method, Fractional Volume of Fluid Method and Fractional Area/Volume Obstacle Representation Method. To speed up the convergence of numerical iterations, we use Successive Over-Relaxation Method. Numerical solutions show that the evolution of free surface gives a comprehensive image to the capillary tube dynamics. It also shows the developing velocity and pressure profiles under different kinds of pressure gradients. The study also considers further the relation between volume of fluid and time to provide references to the flow control system of the micropipette.Keywords: Free Surface, Droplet, Finite-Difference Method, Fractional Volume Fluid Method.
 中文摘要 I英文摘要 II目錄III圖表目錄 V符號說明Ⅷ第一章　導論 11-1研究背景與目的 11-2文獻回顧 51-3本文結構7　第二章　理論分析82-1 流體描述與基本假設82-1-1 卡瑞爾模型流體102-1-2 自由表面112-1-3 基本假設122-2統御方程式132-2-1連續方程式132-2-2動量方程式132-2-3 自由界面方程式152-3初始條件與邊界條件162-3-1初始條件162-3-2邊界條件16第三章　數值方法183-1 FLOW-3D® 套裝軟體之說明183-2網格定義說明與差分方程式203-2-1網格定義說明203-2-2差分方程式說明233-3-3數值的精確度263-3計算流程293-4 動力相似與無因次化30第四章　結果與討論294-1 牛頓流體314-2 非牛頓流體344-3 模擬結果的驗證37第五章結論與未來展望385-1 結論385-2 未來展望40參考文獻41
 1.張大昌 “圓管內非牛頓流體之驅動流場分析” 中原大學機械工程研究所碩士論文，(2000)。2.E. A. Hauser, H. E. Edgerton, and W. B. Tucker, “The application of the high-speed motion picture camera to the research on the surface tension of liquid,” J. Phys Chem. 40, 973 (1936).3.H. E. Edgerton, E. A. Hauser, and W. B. Tucker, “Studies in drop formation as revealed by the high-speed motion camera,” J. Phys Chem. 41, 1017 (1937)4.D. H. Peregrine, G. Shoker, and A. Symon, “The bifurcation of liquid bridges,” J. Fluid Mech 212, 25 (1990).5.X. D. Shi, M. P. Brenner, and S. R. Nagel,” A cascade of structure in a drop falling from a faucet, ” Science 265, 219 (1994)6.X. Zhang and O. A. Basaran, “An experimental study of dynamics of drop formation,” Phys. Fluids 7, 1184(1995)7.M. P. Brenner, J. Eggers, K Joseph, S. R. Nagel, and X. D. Shi, “Break-down of scaling in droplet fission at high Reynolds numbers,” Phys. Fluids 9, 1573 (1997).8.H. C. Lee, “drop formation in a liquid jet,” IBM J. Res. Dev. 18, 364 (1974).9.R. M. S. M. Schulkes, “Dynamics of liquid jets revisited,” J. Fluid Mech. 250, 635 (1993).10.R. M. S. M. Schulkes, “Nonlinear dynamics of liquid columns: A comparative study,” Phys. Fluids 5, 2121 (1993).11.S. E. Bechtel, M. G. Forest, and K. J. Lin, “Closure to all orders in 1D models for slender viscoelastic jets: An integrated theory for axisymmetric, torsionless flows,” Stability Appl. Anal. Continuous Media 2, 59 (1992).12.J. Eggers and T. F. Dupont, “Drop formation in a one-dimensional approximation of the Navier-Stokes equation,” J. Fluid Mech. 262, 205 (1994)13.D. T. Papageorgiou, “Analytical description of the breakup of liquid jets,” Phys. Fluids Mesh 301, 109 (1995)14.Edward D. Wilkes, Scott D. Phillips, Osman A. Basaran, “Computational and experimental analysis of dynamics of drop formation,” Phys. Fluids 11, 12 (1999)15.Cryer, S. A., and Steen P. H., ”Collapse of the soap-film bridge: quasistaic description,” J. Colloid Interface Sci. 154, 276. (1992)16.Jyi-Tyan Yeh, “Simulation and Industrial Applications of Inkjet,” 第七屆全國計算流體力學學術研討會, B-26 (2000)17.Harlow, F.H., and Welch, J.E., ”Numerical Calculation of Time-Depend Viscous Incompressible Flow of Fluid with free Surface,” Physics of Fluids, 8, pp. 2182-2189. (1965)18.Harlow, F.H., and Welch, J.E., ”Numerical Study of Large Amplitude Free Surface Motions,” Physics of Fluids, 9, pp. 842-851. (1966)19.Patrick J. Roache, Computation Fluid Dynamics, pp.196-20120.J. Timmermans, The Physico-Chemical Constants of Binary Systems in Concentrated Solutions (Interscience, New York, 1960), Vol. 4.21.R. M. S. M. Schulkes, "The evolution and bifurcation of a pendant drop," J. Fluid Mech. 278, 83 (1994).
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