臺灣博碩士論文加值系統

過去一般低速液體噴流斷裂的研究，大多僅獲得噴流斷裂的結果及液滴的形成，但卻不能提供噴流內部流場的結構變化，而無法了解真正噴流斷裂的機制。在本研究中，首先，將考慮由圓管噴嘴等速射出之液體噴流，並假設該噴流表面在一開始時，受到一微小的餘弦波擾動，如此，則可採用微小擾動原理，導出流體連續及動量擾動方程式(包括軸向及徑向)，再沿著噴流與擾動波表面之數值柵格推導積分方程式。則整組方程式可利用TVD法，以電腦來求數值解。所得之數值解將包括噴流半徑的變化、噴流內部的軸向與徑向擾動速度變化、液滴的形成與大小變化，尤其是噴流內部流場結構的計算結果，可用為分析噴流斷裂的機制。這些計算結果，相當精確的符合文獻上之實驗結果，顯示本研究的噴流斷裂模式的可行性。
對於高速液體噴流，本研究考慮液體噴流由圓管噴嘴等速射出，並假設該噴流表面在一開始時，受到一微小的餘弦波擾動，將藉由微小擾動原理所推導的流體連續及動量擾動方程式(包括軸向及徑向)，進一步推導出表面不穩定波成長率之擴散方程式。在本研究中進行該擴散方程式的全解分析，並利用不穩定波成長率的計算結果，提出霧化模式以計算高速液體噴流霧化液滴的大小。在本研究中液滴大小以計算SMD（Sauter Mean Diameter）為主，並以文獻中之實驗結果比較，以證實本研究的高速噴流斷裂與霧化模式之精確性及適用性。

Most past studies regarding the breakup of low speed liquid jets only predicted the jet breakup and drop formation without providing any structural information in the internal flow field for understanding the jet breakup mechanism. In the present study, a cylindrical liquid jet issued from a nozzle at a constant velocity was first considered. It was assumed that the jet surface was initially disturbed with a consinusoidal wave with an infinitesimal amplitude. By the method of small perturbation, the equations of motion were derived, including continuity, and axial and radial momentum equations. The continuity and momentum equations in the transient form were integrated on an adaptive grid, conforming the jet and surface wave shape. The system of equations were numerically solved by a TVD (i.e. Total Variation Diminishing) scheme. The solutions included jet radius variations, axial and radial velocities in the disturbed flow field, and the formation of main and satellite drops. Among them, the numerical results of the flow structure were especially useful for analyzing the jet breakup mechanism. By comparing with measurement data in the literature, the present computational results showed a fairly good correspondence and indicated the practice of the numerical model in the present study.
For the high speed jet breakup, the present study also considered a cylindrical liquid jet issued from a nozzle at a constant velocity with the same assumption as the low speed jet. In the high speed model, the dispersion equation for governing the growth rates of unstable waves on the jet surface was derived from the perturbation equations of continuity and momentum equations. The general solutions for the dispersion equation were used to compute the drop sizes in the high speed jet atomization by an atomization model which was proposed in the present study. The Sauter mean diameters (SMD) of the drops in the atomization process were compared with experimental data in the literature to validate the accuracy and suitability of the present models for the jet breakup and atomization of high speed liquid jets.

中文摘要
英文摘要
目錄--------------------------------------------------------I
表目錄------------------------------------------------------III
圖目錄------------------------------------------------------Ⅳ
符號說明----------------------------------------------------Ⅶ
第一章 簡介--------------------------------------------------1
1-1 研究動機-------------------------------------------------1
1-2 文獻回顧-------------------------------------------------2
1-3 研究目標-------------------------------------------------7
第二章 理論模式----------------------------------------------9
2-1低速液體噴流理論模式--------------------------------------10
2-1-1 間接模擬理論----------------------------------------10
2-1-2 直接模擬理論----------------------------------------15
2-2高速液體噴流理論模式--------------------------------------20
2-2-1 高速液體噴流破裂模式--------------------------------22
2-2-2 高速液體噴流霧化模式--------------------------------27
第三章 結果與討論--------------------------------------------30
3-1低速液體噴流之斷裂----------------------------------------30
3-1-1 低速噴流不穩定波成長--------------------------------30
3-1-2 直接數值分析與非線性間接理論之比較--------------- -37
3-1-3 附隨液滴的形成--------------------------------------46
3-1-4 噴流斷裂的機制--------------------------------------53
3-2 高速液體噴流之斷裂---------------------------------------67
3-2-1 高速噴流不穩定波成長--------------------------------67
3-2-2 噴流表面破裂與霧化----------------------------------81
第四章 結論與建議--------------------------------------------90
4-1 低速液體噴流之結論與建議---------------------------------90
4-2 高速液體噴流之結論與建議---------------------------------94
參考文獻-----------------------------------------------------97

1. 陳炳輝，噴墨印表頭簡介，微系統科技協會季刊，第3期，pp.38-44，民國90年1月。
2. Lefevre, A. H., “Atomization and Sprays”, Hemisphere Publishing Corporation, 1989.
3. M. Van Thiel, M. Wilkins and A. Mitchell, “Shaped Charge Sequencing”, Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., vol. 12, pp. 283-288, 1975.
4. Plateau, J., “Statique Experimentale et Theorique des Liquids Soumie aux Seules Forces Moleculaire”, vol. 1, 2. Paris: chanthier villars, pp. 450-495, 1873.
5. Rayleigh, L., “On the Capillary Phenomenon of Jets”, Procedings of Royal society, London, 29, pp. 71-97, 1879.
6. Weber, C., “Zum Zerfall eines Flussigkeitsstrahles(On the Disruption of Liquid Jets)”, Z. Angew, Math. Mech., vol. 11, pp. 136, 1931.
7. Chandrasekhar, S., “The Capillary Instability of a Liquid Jet”, Hydrodynamic and Hydromagnetic Stability, Oxford University Press, Oxford, pp. 537-542, 1961.
8. Donnely, R. J., and Glaberson, W., “Experiment on the Capillary Instability of a Liquid Jet”, Proc. Roy. Soc.,(London), vol. A290. pp. 547-556, 1965.
9. Goedde, E. F. and Yuen, M. C., “Experiments on Liquid Jet Instability”, J. Fluid Mechanics, vol. 40, pp. 495-512, 1970.
10. Taylor, G. I., “Generation of Ripples by Wind Blowing over Viscous Fluids”, The Scientific Papers of G. I. Taylor, ed. G. k. Batchelor, Cambridge University Press, Cambridge, vol. 3, pp.244-254, 1962.
11. Sterling, M. and Sleicher, C. A., “The Instability of Capillary Jets”, J. Fluid Mech., vol. 68, pp. 477-495, 1975.
12. Hoyt, J. W. and Taylor, J. J., “Waves on Water Jets”, J. Fluid Mech., vol. 83, 1977.
13. Lin, S. P. and Reitz, R. D., “Drop and Spray Formation From a Liquid Jet”, Annu. Rev. Fluid Mech., vol. 30, pp. 85-105, 1998.
14. Lasheras, J. C., Villermaux, E., and Hopfinger, E. J., “Break-up and Atomization of a Round Water Jet by a High Speed Annular Air Jet”, J. Fluid Mech., vol. 357, pp. 351-379, 1998.
15. Chou, P. C. and Flis, W. J., “Recent Development in Shaped Charge Technology”, Propellants, Explosives, Pyrotechnics, 11, pp. 98-114, 1986.
16. Birkhoff, G., MacDougall, D. P., Pugh, E. M., and Taylor, G., “Explosives with Lined Cavities”, J. Appl. Phys., vol. 19, pp. 563-582, 1948.
17. Pugh, E. M., Eichelberger, R. J., and Rostoker, N., “Theory of Jet Formation by Charges with Lined Conical Cavities”, J. Appl. Phys., Vol. 23, pp. 532-536, 1952.
18. Karpp, R. R. and Simon, J., “An Estimate of the Strength of a Copper Shaped Charge Jet and the Effect of Strength on the Breakup of a Stretching Jet”, US Army Ballistic Research Labs., BRL Report No. 1893 : AD # B012141, June 1976.
19. Chou, P. C. and Carleone, J., “Breakup of Shaped-Charge Jets”, Proc. 2nd Int. Symp. on Ballistics, Dayton Beach, FL, 9-11 March 1976.
20. Chou, P. C. and Carleone, J., “The Stability of Shaped Charge Jet”, J. Appl. Phys., vol. 48, pp. 4187-4195, 1977.
21. Carleone, J., Chou, P. C., and Ciccarelli, R. D., “Shaped-Charge Jet Stability and Penetrations”, US Army Ballistic Research Labs., BRL Report No. 351, Sep. 1977.
22. Miller, C. W., “A New Approach to the Numerical Analysis of Shaped Charge Jets”, Proc. 6th Int. Symp. on Ballistics, Orlando, FL, Oct. 1981.
23. Rayleigh, Lord, “On the Instability of Jets”, Proceedings of London Math. Society, vol. 10, pp. 4, 1879.
24. Rayleigh, Lord, Theory of Sound, London, Macmillan, 2nd ed. (reprinted in 1945, New York, Dover), 1896.
25. Reitz, R. D. and Bracco, F. V., “Mechanism of Atomization of a Liquid Jet”, Phys. Fluids, vol. 25, pp. 1730-1742, 1982.
26. Lin, S. P. and Kang, D. J., “Atomization of a Liquid Jet”, Phys. Fluids, Vol.30, No.7, pp. 2000-2006, 1987.
27. Yuen M. C., “Non-linear Capillary Instability of a Liquid Jet”, J. Fluid Mechanics, vol.33, Part.l, pp. 151-163, 1968.
28. Wang, D. P., “Finite Amplitude Effect on the Stability of a Jet of Circular Cross Section”, J. Fluid Mechanics, vol. 34, pp. 299-313, 1968.
29. Lee, H. C., “Drop Formation in a Liquid Jet”, IBM Journal of Res. Development, vol. 18, pp. 364-369, 1974.
30. Nayfeh, A. H., “Nonlinear Stability of a Liquid Jet”, Phys. Fluids, vol. 13, pp. 841-847, 1970.
31. Lafrance, P., “Nonlinear Breakup of a Laminar Liquid Jet”, Phys. Fluids, vol. 18, pp. 428-432, 1975.
32. Rutland, D. F. and Jameson, G. J., “Theoretical Predition of the Sizes of Drops Formed in the Breakup of Capillary Jets”, Chem. Engn. Sci. vol. 25, pp. 1689-1698, 1970.
33. Chaudhary, K. C. and Redekopp, L. G., “The Nonlinear Capillary instability of a Liquid Jet. Part I,II,III”, J. Fluid Mechanics., vol. 96, Part.2, pp. 257-298, 1980.
34. Fromm, J. E., “Numerical Calculation of the Fluid Dynamics of Drop-on-Demand Jets,” IBM Journal of Res. Development, vol. 28, no. 3 pp. 322-333, 1984.
35. Childs, R. E., and Mansour, N. M.,”Simulation of Fundamental Atomization Mechanism in Fuel Sprays,” AIAA-88-0238, 1988.
36. Shokoohi, F., and Elrod, H. G., “Numerical Investigation of the Disintegration of Liquid Jets,” J. Comp. Phys., vol. 71, pp. 324-342, 1987.
37. Sellens, R. W., “A One-dimensional Numerical Model of Capillary Instability”, Atomization and Sprays, vol. 2, pp. 239-251, 1992.
38. Hilbing, J. H., Heister, S. D. and Spangler, C. A., “A Boundary-Element Method for Atomization of a Liquid jet”, Atomization and Sprays, vol. 5, pp. 621-638, 1995.
39. Hilbing, J. H. and Heister, S. D., “Droplet Size Control in Liquid Jet Breakup”, Phys. Fluids, vol. 8, No.6, 1996.
40. Carleone, J., Chou, P. C., and Walter, W. P., “An Improved Shaped-Charge Jet Breakup Calculation and Measurement of Jet Properties”, US Army Ballistic Res. Labs., BRL Report No. ARBRL-CR-00445, Jan. 1981.
41. Chuech, S. G., Przekwas, A. J. and Yang H. Q., “ Direct Simulation for The Instability and Breakup of Laminar Liquid Jets”, AIAA-90-2066,1990.
42. Schlighting, H., “Boundary-Layer Theory”, 7th edition, McGraw-Hill Book, pp. 457-458, 1979.
43. Levich, V. G., “Physicochemical Hydrodynamics”, Prentice-Hall, Englewood Cliffs, 1962.
44. Yee, H. C., “Upwind and Symmetric Shock-Capturing Schemes”, NASA Technical Memorandum No. 89464, NASA Ames Research Center, Moffett Field, California, May 1987.
45. Chuech, S. G., Przekwas, A. J. and Singhal, A. K., “Numerical Modeling for Primary Atomization of Liquid Jets”, AIAA J. of Propulsion and Power, vol. 7, No.6, pp. 879-886, 1991.
46. Defay, R. and Prigogine, I., “Surface Tension and Absorption”, Jone Wiley and Sons, Inc., New York.
47. Grant, R. P. and Middleman, “Newtonian Jet Stability”, A.I.Ch.E. Journal, vol. 12, No.4, pp. 669-678, 1966.
48. Rutland, D. F. and Jameson, G. J., “A Non-linear Effect in the Capillary Instability of Liquid Jets”, J. Fluid Mechanics, vol. 46, pp. 267-272, 1971.
49. Phinney, R. E., “Stability of a Laminar Viscous Jet-The Influence of the Initial Disturbance Level”, A.I.Ch.E. Journal, vol. 18, pp. 432-434, 1972.
50. Bogy, D. B., “Drop Formation in a Circular Liquid Jet”, Annual Review Fluid Mechanics, vol. 7, pp. 207-228, 1979.
51. Wu, K-J., Reitz, R. D., and Bracco, F. V., “Measurements of Drop Size at the Spray Edge Near the Nozzle in Atomizing Liquid Jets”, Phys. Fluids, vol. 29, No.4, pp.941-951, 1986.
52. Meister, B. J. and Scheele, G. E., “Prediction of Jet Length in Immiscible Liquid System”, A.I.Ch.E. Journal, vol. 15, pp. 689, 1969.
53. Smith, S. W. J., and Moss, H., Proc. Roy. Soc. (London) A93, pp.373, 1917.