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 本文主要目的為發展新的三維邊界元素法，模擬水下爆炸氣泡破裂變形的過程，並探討氣泡破裂時所生射流速度之大小。在數值方法上，本文提出新的氣泡表面切線速度求法。為了驗証數值模式的準確性，本模式模擬在不考慮重力影響下氣泡膨脹收縮的一維運動，並與Rayleigh-Plesset方程的解比較。在確定數值模式的準確性之後，本文探討了水下爆炸氣泡在無限流場中或平面固體邊界附近破裂之特性。本文數值結果顯示，氣泡在無限流場中破裂時，其射流與重力方向相反且射流速度會隨著水深增加而變大。當氣泡在平面固體邊界附近破裂時，射流方向受固體邊界效應及重力影響。在相同條件下，以固體邊界在氣泡上方時氣泡射流速度最大，而固體邊界在氣泡下方時射流速度最小。
 In the present study a new three-dimensional boundary element method was developed to simulate the collapse of an underwater-explosion bubble. In order to verify the accuracy of the new scheme, this model was applied to determine the one-dimensional bubble pulsation. The numerical results agree well with the solutions obtained from Rayleigh-Plesset equation. After having verified the accuracy of this model, the bubble collapse in the free flow field as well as near a plane solid boundary was investigated. The velocity of the collapse-induced jet was determined and compared systematically. The numerical results show that as a bubble collapses in a free flow field, the formed jet is in the opposite direction of the gravity and the jet velocity increases with the depth of the bubble location. When the bubble collapses near a plane solid boundary, the direction of the jet depends on the gravity and the relative position of the boundary to the bubble. Under the same conditions, the jet velocity has its maximum value when the collapse occurs beneath the solid boundary; on the contrary it has the minimum value as the collapse occurs above a solid boundary.
 中文摘要 …………………………………………………………… I 英文摘要 ……………………………………………………………… II 誌謝 …………………………………………………………………… III 目錄 …………………………………………………………………… V 圖目錄 ……………………………………………………………… VII 符號說明 …………………………………………………………… X 第一章 緒論 1-1 前言 ………………………………………………………… 1 1-2 水下爆炸氣泡運動之特性 ………………………………… 1 1-3 文獻回顪 …………………………………………………… 3 1-4 本文組織 …………………………………………………… 6 第二章 理論分析 2-1 氣泡運動方程式 …………………………………………… 7 2-2 邊界積分方程式 …………………………………………… 9 2-3 起始條件 …………………………………………………… 12 第三章 數值方法 3-1 邊界元素的取法 …………………………………………… 14 3-2 元素法線方向與Jacobian的計算 ………………………… 16 3-3 邊界積分式的離散化 ……………………………………… 18 3-4 核函數的積分 ……………………………………………… 20 3-5 節點速度 …………………………………………………… 22 3-6 體積的計算 ………………………………………………… 25 3-7 計算流程 …………………………………………………… 26 第四章 結果與討論 4-1 數值模式準確性之驗證 …………………………………… 27 4-2 氣泡在無限流場中破裂之過程 …………………………… 30 4-3 氣泡在平面固體邊界附近破裂之過程 …………………… 33 第五章 結論與建議 5-1 結論 ………………………………………………………… 35 5-2 建議 ………………………………………………………… 36 參考文獻 …………………………………………………………… 37 附錄A ……………………………………………………………… 64
 1. Benjamin, T. B. and A. T. Eillis, “Cavitation : The Collapse of Cavitation Bubbles and the Pressures thereby Produced against Solid Boundaries”, Philosophical Trans. of the Royal Society of London, Vol. 260, pp. 221-240, 1966.2. Blake, J. K. and D. C. Gibson, “Growth and Collapse of a Vapour Cavity near a Free Surface”, J. Fluid Mech. Vol.111, pp. 123-140, 1981.3. Chahine, G. L., “Interaction Between an Oscillating Bubble and a Free Surface”, J. Fluid Engr. Vol.99, pp. 709-716, 1977.4. Chahine, G. L., T. O. Perdue, and C. B. Tucker, “Interaction Between an Underwater Explosion Bubble and a Solid Submerged Body”, Tech. Report 86029-1, Traycor Hydronautics, Inc. 1988.5. Cole, R. H., “Underwater Explosions”, Princeton University Press, 1948.6. Curtis, F. G. and O. W. Patrick, “Applied Numerical Analysis”, 6th Edition, Addison-Wesley, inc., p389-390, 1999.7. Eric, B. B., F. C. Graham, and J. O. Tinsley, “Finite Elements”, Volumn I, Englewood Cliffs, New Jersey, U.S.A., 1981.8. Ellis, A. T., “Observations on Bubble Collapse”, Calif. Inst. Of Tech. Hydrodyn. Lab. Rdp. 21-12, 1952.9. Goertner, J. F., J. R. Hendrickson, and R. G. Leemon, “Model Studies of the Behavior of Underwater Explosion Bubbles in Contact with a Rigid Bottom,” NOLTR 68-207, 1969.10. Guerri, L., G. Lucca, and A. Prosperitti, “A Numerical Method for the Dynamics of Nonspherical Cavitation Bubbles”, JPL. Vol. 82-7, pp. 175-181, 1980.11. Hayami, K., “A Projection Transformation Method for Nearly Singular Boundary Element Integrals”, Lecture Notes in Engineering, Vol. 73, Springer Verlag, 1992.12. Kane, J. H., “Boundary Element Analysis in Engineering Continuum Mechanics”, Prentice-Hall, Inc. New Jersey, 1994.13. Keller, J. B. and I. I. Kolodner, “Damping of Underwater Explosion Bubble Oscillations”, J. Acoust. Soc. Am. Vol.27, pp. 1152-1161, 1956.14. Knapp, R. T. and A. Hollander, “Laboratory Investigations of the Mechanism of Cavitation”, Trans. ASME. Vol 70, pp. 419-435, 1948.15. Kornfeld, M. and L. L. Suvarov, “On the Destructive Action of Cavitation”, J. Appl. Phys, Vol. 15, pp. 495-503, 1944.16. Lauterborn, W., “Numerical Investigation of Nonlinear Osaillations of Gas Bubbles in Liquids”, J. Acoust. Soc. Am. Vol. 59, pp. 283-293, 1976.17. Lauterborn, W. and H. Bolle, “Experimental Investigation of Cavitation-Bubble Collapse in the Neighbourhood of a Solid Boundary “, J. Fluid Mech., Vol. 72, part2, pp. 391-399, 1975.18. Naudi, C. F. and A. T. Ellis, ”On the Mechanism of Cavitation Damage by Nonhemispherical Cavities Collapsing in Contact with a Solid Boundary”, J. Basic Engineering, pp. 648-656, 1961.19. Panton, R. L., “Incompressible Flow”, John Wiley&Sons, 1984.20. Plesset, M. S. and R. B. Chapman, “Collapse of an Initially Spherical Vapour Cavity in the Neighborhood of a Solid Boundary”, J. Fluid Mech., Vol. 47, part2, pp. 283-290, 1971.21. Poritsky, H., “The Collapse or Growth of a Spherical Bubble or Cavity in a Viscous Fluid”, In: Proceedings of the First U.S. National Congress on Applied Mechanics , pp. 813-821, 1952.22. Rayleigh, L., “On the PressureDeveloped in a Liquid During the Collapse of a Spherical Cavity”, Phil. Mag., Vol. 334, pp. 94-98, 1917.23. Snay, H. G., J. F. Goertner, and R. S. Price, “Small Scale Experiments to Determine Migration of Explosion Gas Globes towards Submarines”, Naval Ordance Lab. Report 2280, 1952.24. Swift, E. and J. C. Decius, “Measurement of Bubble Pulse Phenomena, III Radius and Period Studies”, Underwater Explosion Research, Vol. II-The Gas Globe, ONR., 1950.25. Wilkerson, S. A., “Boundary Integral Technique for Explosion bubble Collapse Analysis”, ASME Energy-Sources Technology Conference and Exhibition, Publication no. 89-OCN-2. Houston, Texas, Jan. 22-25,1989.26. Wilkerson, S. A., “A Boundary Integral Approach to Three-Dimensional Underwater Explosion Bubble Dynamics”, PHD. Thesis, The Johns Hopkins University, 1990.27. 林志榮，”水下爆炸單一氣泡收縮及噴出破裂過程之動力行為”，國立成功大學造船暨船舶機械工程研究所碩士論文，1997。28. 尹孝元，”水下爆炸氣泡之動力分析”，國立成功大學水利暨海洋工程研究所碩士論文，1996。29. 周明忠，”水下爆炸氣泡動力行為及壓力場之研究”，國立成功大學造船暨船舶機械工程研究所碩士論文，1998。30. 林志榮，涂季平，黃清哲，”水下爆炸單一氣泡收縮及噴出破裂過程之動力行為”，中國土木水利工程學刊，第十卷，第一期，9-16頁，1998。
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 1 水下爆炸氣泡之動力分析 2 水下爆炸氣泡動力行為及壓力場之研究 3 水下爆炸單一氣泡收縮及噴出破裂過程之動力行為 4 氣泡在固體邊界附近破裂之數值模擬 5 水下爆炸效應之研究 6 水下爆炸氣泡軌跡之研究

 1 30. 林志榮，涂季平，黃清哲，”水下爆炸單一氣泡收縮及噴出破裂過程之動力行為”，中國土木水利工程學刊，第十卷，第一期，9-16頁，1998。 2 【37】張永慶, “資料庫中介軟體與WWW”, 網路通訊雜誌, 第62期, pp. 44-49, 1996年9月.

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