本文主要探討自由液滴的阻力分析。在實驗中以脈波驅動壓電片產生穩定液滴，在室溫室壓下（17~23℃，1atm）的靜止空氣中自由落下，拍攝其運動過程，並採用水、正十六烷及正庚烷三種不同物理性質為液滴種類，量測下落時間與速度關係及液滴直徑，由此求出加速度及其所受阻力。實驗上可分兩大部分，一為單一、孤立自由下落液滴的阻力分析，主要研究孤立液滴在加速過程中及其本身性質對阻力的影響；二為穩態自由下落液滴串的阻力分析，目的在研究液滴間的距離對阻力的影響。將實驗結果無因次化，以 、 、 及 表達，觀察並討論其趨勢關係，並探討在不同燃油液滴下之間的比較。實驗中雷諾數範圍在5~200之間，實驗誤差在 以內。

In this study we investigated the effect of freely-falling droplets on drag force. A single stream of mono-sized stable droplets were generated by piezo-electric transducer and fell into quiescent surrounding air, then we recorded the trajectory of droplets by CCD camera. The species of droplets included water, hexadecane and heptane. By measuring the velocity and diameter of droplet with time, we got the acceleration profile of droplets and the drag force of droplet along the path. Our experiments included two parts. One was the effect of acceleration and properties on the drag coefficient in isolated droplet；the other was the influence of droplet spacing on the drag coefficient in steady, monodisperse droplet stream. We then tried to nondimensionalize the experiment data as CD, Re, Ac, and S/d ratio. The range of Reynolds numbers were from 5 to 200 and experimental uncertainties were typically less than 5 percent.

中文摘要………………………………………………………………Ⅰ
英文摘要………………………………………………………………II
目錄……………………………………………………………………Ⅲ
圖表&照片目錄…………………………………………………………Ⅵ
附表目錄………………………………………………………….. …………Ⅷ
符號說明……………………………………………………………………Ⅸ
第一章 緒論…………………………………………………………1
1－1 前言……………………………………………………1
1－2 文獻回顧………………………………………………3
1－3 實驗動機與目的………………………………………6
第二章 基本原理………………………………………………8
2－1 液滴形狀………………………………………10
2－1.1液滴的變形……………………………11
2－1.2液滴尺寸的縮小………………………12
2－2 液滴內部環流的影響…………………………12
2－3 液滴表面流體性質的影響……………………14
2－4 液滴表面揮發現象的影響……………………15
2－5 液滴外圍流場的影響…………………………16
2－6 單一連續下落液滴串之間相互影響…………18
第三章 實驗設備與步驟………………………………………20
3－1 實驗裝置………………………………………20
3－1.1 液滴產生方法與電子控制裝置…………20
3－1.2 液滴產生裝置與測試平台………………22
3－1.3 液滴產生與拍攝裝置之升降機構………23
3－1.4 影像拍攝系統……………………………24
3－1.5 影像處理系統……………………………25
3－2 實驗步驟……………………………………………26
3－2.1 實驗操作與拍攝……………………………26
3－2.2 實驗數據讀取與分析處理…………………30
第四章 結果與討論……………………………………………33
4－1穩態連續下落液滴串之阻力探討……………………34
4－2單滴自由下落液滴之阻力分析…………………38
4－3 實驗數據之不準確度分析……………………………42
第五章 結論……………………………………………………48
參考文獻…………………………………………………………..49
圖表&照片………………………………………………………..……53
附 表…………………………………………………………..……99

[1] Stokes, G. G., “On the Effect of Internal Friction of Fluid on the Motion of Pendulums,” Cambridge Phil. Trans., Vol. 9, pp. 8, 1851.
[2] Oseen, C. W., “Uber die Stokes’sche Formel und ubereine verwandte Aufgabe in der Hydrodynamik,” Ark. f. Math. Astron. och. Fys., Vol. 6, No. 29., 1910.
[3] Proudaman, I., and Pearson, J. R. A., ”Expansions at Small Reynolds Numbers for the Flow Past a Sphere and Circular Cylinder,” J. Fluid Mech., Vol. 2, pp. 237, 1957.
[4] Kassoy, D. R., Adamson, J. R., and Messiter, A. F., “Compressible Low Reynolds Number Flow around a Sphere,” The Physics of Fluids, Vol.9, No. 4, pp. 671, 1966.
[5] Hadamard, J., “Movement Permanent Lent D’une Sphere Liquid Visqueuse Dans un Liquid Visqueux,” C. R. Acad Sci. Paris Ser. A-B, Vol. 152, pp. 1735, 1911.
[6] Elzingam, E. R., and Banchero, J. T., ”Some Observations on the Mechanics of Drops in Liquid-Liquid Systems,“ AIChE J., Vol. 7, pp. 394, 1961.
[7] Chao, B. T., ”Motion of Spherical Gas Bubbles in a Viscous Liquid at Large Reynolds Number,” Physics of Fluids, Vol. 5, pp. 69, 1962.
[8] Hamielec, E. A., Hoffman, T. W., and Ross, L. L., “Numerical Solution of the Navier-Stokes Equation for Flow Past Sphere：Part 1. Viscous Flow Around Sphere with and without Radial Mass Efflux,” AIChE J., Vol. 13, No. 2, pp. 212, 1967.
[9] Ahmed, H. A., and Hamielec, A. E., ”A Theoretical and Experiment Investigation of the Effect on Internal Circulation on the Drag of Spherical Droplet Falling at Terminal Velocity in Liquid Media,” Ind. Eng. Chem. Fundam, Vol. 14, pp. 308, 1975.
[10] Hubbard, G. L., Denny, V. E., and Mills, A. F., “Droplet Evaporation；Effects of Transients and Variable Properties,” Int. J. Heat Mass Transfer, Vol. 18, pp. 1003, 1975.
[11] Buzzard, J. L., and Nedderman, R. M., ”The Drag Coefficients of Liquid Droplets Accelerating Through Air,” Chemical Engineering Science, Vol. 22, pp. 1577, 1967.
[12] Yuen, M. C., and Chen, L. W., ”On Drag of Evaporating Liquid Droplets,” Combustion Science and Technology , Vol. 14, pp. 147, 1976.
[13] Chuchottaworn, P., Fujinami, A., and Asano, K., ”Experimental study of Evaporation of Volatile Pendant Drop under High Mass Flux Condition,” J. Chem. Eng. of Japan, Vol. 17, No. 1, pp. 7, 1984.
[14] Hu, S., and Kintner, R. C., “The Fall of Single Liquid Drops Through Water,” AIChE J., Vol. 1, pp. 42, 1955.
[15] Basaran, O. A., Scott, T. C., Byers, C. H., “Drop Oscillations in Liquid-Liquid System,” AIChE J., Vol. 35, No. 8, pp. 1263, 1989.
[16] Srikrishna, M., Sivaji, K., and Narasimhamurty, G. S. R., “Mechanics of Liquid Drops in Air,” Chem. Eng. J., Vol. 24, pp. 27, 1982.
[17] Irvine, T. F., Gyves, Jr. T., and Smith, T., ”Drag Relationships for Liquid Droplets Settling in a Continous Liquid,” AIChE J., Vol. 39 , No. 1, pp. 37, 1993.
[18] Humphery, J. A. C., Hummel, R. L., and Smith, J. W., ”Note on the Mass Transfer Enhancement due to Circulation in Growing Drop,” Chem. Eng. Sci., Vol. 29, pp. 634, 1974.
[19] Johnson, G., and Marschall, E., “On the Temperature Jump in Liquid/Liquid Direct Contact Heat Exchangers,” Int. J. Multiphase Flow, Vol. 12, pp. 127, 1986.
[20] Mulholland, J. A., Srivastava, R. K., and Wendt, J. O. L., “Influence of Droplet Spacing on Drag Coefficient in Nonevaporating, Monodisperse Streams,” AIAA Journal, Vol. 26, No. 10, pp. 1231, 1988.
[21] Zhu, C., Liang, S. C., and Fan, L. S., “Particle Wake Effects on the Drag Force of an Interactive Particle,” International Journal of Multiphase Flow, Vol. 20, No. 1, pp. 117, 1994.
[22] Virepinte, J. F., Adam, O., Lavergne, G., and Biscos, Y., “Droplet Spacing on Drag Measurement and Burning Rate for Isothermal and Reacting Conditions,” Journal of Propulsion and Power, Vol. 15, No. 1, pp. 97, 1999.
[23] Law, C. K., “Recent Advances in Droplet Vaporization and Combustion,” Prog. Energy Combust. Sci., Vol. 8, pp. 171, 1982.
[24] Jacques, M., Rivero, M., and Fabre, J., ”Accelerated Flows Past a Rigid Sphere or a Spherical Bubble. Part 1. Steady Straining Flow,” J. Fluid Mech., Vol. 284, pp. 97, 1995.
[25] Beard, K. V., and Pruppacher, H. R., “A determination of the terminal velocity and drag of small water drops by means of a wind tunnel,” J Atmos Sci, Vol. 26, pp. 1066, 1969.
[26] Warnica, W. D., Renksizbulut, M., and Strong, A. B., “Drag Coefficients of Spherical Liquid Droplets Part 1: Quiescent Gaseous Fields,” Experiments in Fluids, Vol. 18, pp. 258, 1995.
[27] Biswal, L. D., Datta, and Som, S. K., “Transport Coefficients and Life History of a Vaporising Liquid Fuel Droplet Subject to Retardation in a Conventive Ambience,” International Journal of Heat and Fluid Flow, Vol. 20, pp. 68, 1999.
[28] Kline, S. J., and McClintock, F. A., “Describing Uncertainties in Single-Sample Experiments,” Mech. Eng., pp. 3, January 1953.
[29] 黃耀德, ”兩連續自由下落液滴之阻力分析與現象,”國立台灣大學機械工程學研究所碩士論文, 1999.
[30] editor-in-chief, David, R. L., “CRC Handbook of chemistry and physics,” CRC Press, 2000-2001.
[31] executive editor, Reiner L., “Beilstein Handbook of Organic Chemistry,” New York：Springer, fourth edition. 1985.
[32] Sujith, R. I., Waldherr, G. A., Jagoda, J. I., and Zinn, B. T., ”On the Effect of Evaporation on Droplet Drag,” J. of Fluids Eng., Vol. 118, pp. 862, 1996.
[33] Le Clair, B. P, Hamielec, A. E., Pruppacher, H. R., and Hall, W. D., “A Theoretical and Experimental Study of the Internal Circulation in Water Drops Falling at Terminal Velocity in Air,” J. Atmos Sci, Vol. 29, pp. 728, 1972.
[34] Jog, M. A., Ayyaswamy, P. S., and Cohen, I. M., “Evaporation and Combustion of a Slowly Moving Liquid Fuel Droplet： Higher-Order Theory,” Journal of Fluid Mechanics, Vol. 307, pp. 135, 1996.
[35] Chisnell, R. F., “The Unsteady Motion of a Drop Moving Vertically Under Gravity,” J. Fluid Mech., Vol. 176, pp. 443, 1987.
[36] Munson, B. R., Young, D. F., and Okiishi, T. H., ”Fundamentals of Fluid Mechanics,” John Wiley & Sons, New York, 1994.
[37] Clift, R., Grace, J. R., and Weber, M. E., “Bubbles, Drops and Particles,” Academic, New York, 1978.
[38] White, F. M., ”Viscous Fluid Flow,” McGraw-Hill International Edition., 2nd edition, 1991.