水下爆炸动力学的起源、发展与展望

王树山; 贾曦雨; 高源; 马峰; 卢熹; 张静骁; 孙雨荟; 梁策

doi:10.11993/j.issn.2096-3920.2023-0005

水下爆炸动力学的起源、发展与展望

doi: 10.11993/j.issn.2096-3920.2023-0005

王树山^{1, 2,},
贾曦雨^{1, 2, ,},
高源^{1, 2,},
马峰^{1, 2,},
卢熹^3,,
张静骁^4,,
孙雨荟^{1, 2},
梁策^{1, 2,}

1.
北京理工大学爆炸科学与技术国家重点实验室, 北京, 100081
2.
北京理工大学机电学院水下无人系统研究所, 北京, 100081
3.
沈阳理工大学装备工程学院, 辽宁沈阳, 110159
4.
兵器科学研究院, 北京, 100089

基金项目: 国家自然科学基金专项项目(12141201); 国家自然科学基金重点项目(U20A2071); 国家自然科学基金青年基金(12202061)

详细信息

作者简介:
王树山(1965-), 教授, 博士生导师, 主要研究方向为水中爆炸、战斗部威力评估等

通讯作者:
贾曦雨(1988-), 助理研究员, 主要研究方向为水中爆炸、高精度数值计算等

中图分类号: TJ410; U674
计量
- 文章访问数: 492
- HTML全文浏览量: 60
- PDF下载量: 138
- 被引次数: 0
出版历程
- 收稿日期: 2023-01-19
- 修回日期: 2023-02-16
- 录用日期: 2023-02-21
- 网络出版日期: 2023-03-03

Underwater Explosion Dynamics: Its Origin, Development, and Prospect

WANG Shu-shan^{1, 2
,},
JIA Xi-yu^{1, 2
, ,},
GAO Yuan^{1, 2
,},
MA Feng^{1, 2
,},
LU Xi^3
,,
ZHANG Jing-xiao^4
,,
SUN Yu-hui^{1, 2},
LIANG Ce^{1, 2
,}

1.
State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China
2.
Institute for Unmanned Underwater System, School of Mechatronical Engineering, Beijing Institute of Technology, Beijing 100081, China
3.
School of Equipment Engineering, Shenyang Ligong University, Shenyang 110159, China
4.
Ordnance Science and Research Academy of China, Beijing 100089, China

摘要

摘要: 水下爆炸动力学是研究炸药等含能物质水下爆轰后, 产物与水介质互作用的物理效应的专门学科, 多学科相互交叉、渗透的特点尤为突出。文中在充分、详尽的文献分析基础上, 首先讨论了水下爆炸动力学的研究范畴并梳理了其起源过程; 然后以水下爆炸冲击波、气泡、边界效应和深水爆炸为主题, 从理论认识与技术发展的角度概述了水下爆炸动力学的发展现状; 最后, 从水下爆炸载荷、水下爆炸毁伤和新技术的应用3个方面对水下爆炸动力学的发展方向进行了建议与展望。不仅可以为从事水下爆炸研究的科研人员提供有益的参考、借鉴以及思路的启迪, 还能够对水下爆炸动力学相关专业知识有迫切需求的非专业领域工作者提供入门指导。
- 水下爆炸 /
- 水下爆炸动力学 /
- 冲击波 /
- 深水爆炸
Abstract: Underwater explosion dynamics is a specialized discipline that studies the physical effects of the interaction between the products of underwater detonations of energetic materials, including explosives and water. The characteristics of multi-disciplinary interaction and penetration are particularly prominent. Based on a thorough literature analysis, this paper discusses the research scope of underwater explosion dynamics and summarizes its process of origin. Then, from the perspectives of theoretical understanding and technological development, the paper outlines the current state of development of underwater explosion dynamics, focusing on underwater explosion shock waves, bubbles, boundary effects, and deep-water explosions. Finally, suggestions for the development of underwater explosion dynamics are proposed and discussed in three aspects: underwater explosion loads, underwater explosion damage, and the application of new technologies. This paper not only provides useful references, inspirations, and ideas for researchers engaged in underwater explosion research but also serves as an introduction and guideline for non-professional field workers who have an urgent need for relevant professional knowledge of underwater explosion dynamics.
- underwater explosion /
- UNDEX dynamics /
- shock wave /
- deep-water explosion

HTML全文

图 1 不同爆轰理论产物状态比较

Figure 1. Comparison of states of different detonation theories

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图 2 典型水下爆炸冲击波高速分幅快照

Figure 2. High-speed framing snapshot of typical underwater explosion shock wave

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图 3 水下爆炸冲击波波速衰减特征

Figure 3. Attenuation characteristics of underwater explosion shock wave velocity

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图 4 典型水下爆炸冲击波压力-时间曲线

Figure 4. Pressure-time curve of typical underwater explosion shock wave

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图 5 水下爆炸冲击波峰值压力分布特征

Figure 5. Characteristics of peak pressure distribution of underwater explosion shock wave

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图 6 冲击波的反射现象

Figure 6. Reflection of a shock wave

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图 7 水下爆炸载荷曲线与气泡脉动示意图

Figure 7. Diagram of underwater explosion load curve and bubble pulsation

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图 8 早期水下爆炸试验装置示意图和所测气泡脉动的压力时程曲线

Figure 8. Schematic diagram of early underwater explosion test device and pressure time history curve of bubble pulsation measured

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图 9 用电气石传感器所测棉火药水下爆炸的信号

Figure 9. The signal of underwater explosion of cotton powder measured by tourmaline sensor

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图 10 早期水下爆炸冲击波和气泡光学测试结果

Figure 10. Optical test results of shock wave and bubble in early underwater explosion

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图 11 Ramsauer试验布置示意图(P*为炸点)

Figure 11. Ramsauer test layout diagram (P* is blast point)

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图 12 近自由面水下爆炸的不同水柱形态示意图

Figure 12. Diagram of different water column morphology of near free surface underwater explosion

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参考文献(212)

[1]	Holt M, Heiskell R H. Vortex Motion as Related to Migrated Steam Bubbles from Underwater Nuclear Explosions[R]. Washington, D. C.: Naval Research Laboratory, 1966, 1-15.
[2]	Li T, Zhang A M, Wang S P, et al. Nonlinear Interaction and Coalescence Features of Oscillating Bubble Pairs: Experimental and Numerical Study[J]. Physics of Fluids, 2019, 31(9): 092108. doi: 10.1063/1.5121380
[3]	Akhatov I, Lindau O, Topolnikov A, et al. Collapse and Rebound of a Laser-Induced Cavitation Bubble[J]. Physics of Fluids, 2001, 13(10): 2805-2819. doi: 10.1063/1.1401810
[4]	Turley W D, Lone B, Mance J G, et al. Experimental Observations of Shock-Wave-Induced Bubble Collapse and Hot-Spot Formation in Nitromethane Liquid Explosive[J]. Journal of Applied Physics, 2021, 129(14): 145102. doi: 10.1063/5.0039414
[5]	Zeng B, Chong K L, et al. Periodic Bouncing of a Plasmonic Bubble in a Binary Liquid by Competing Solutal and Thermal Marangoni Forces[J]. Proceedings of the National Academy of Sciences, 2021, 118(23): e2103215118. doi: 10.1073/pnas.2103215118
[6]	孙承纬. 应用爆轰物理[M]. 北京: 国防工业出版社, 2000.
[7]	Kury J W, Honig H C, Lee E L, et al. Metal Acceleration by Chemical Explosive[J]. Journal of Applied Physics, 1965, 36(2): 625-632.
[8]	Guirguis R H. Streamline Dynamics Method for Highly Curved Detonations[C]//Presented at the Tenth Symposium (International) on Detonation. Boston, MA Boston: Office of Naval Research, 1993.
[9]	Guirguis R H. Time-Dependent Equations of State for Aluminized Underwater Explosives[C]//Presented at the Tenth Symposium(Intemational) on Detonation. Boston, MA Boston: Office of Naval Research, 1993.
[10]	Guirguis R H. Relation between Early and Late Energy Release in Non-Ideal Explosives[C]//Proceedings of the 1994 Jannaf Pshs. Monterey, CA: Elsevier, 1995.
[11]	Miller P J, Guirguis R H. Experimental Study and Model Calculations of Metal Combustion in A1/AP Underwater Explosives[C]//Proceedings of the 1992 MRS Symposium. Boston, MA: Elsevier, 1993.
[12]	Guirguis R H. Energy Release in Non-ideal Explosives[J]. AIP Conference Proceedings, 1996, 370(1): 381-384.
[13]	毛致远, 段超伟, 胡宏伟, 等. 水下爆炸威力试验与评价方法综述[J]. 水下无人系统学报, 2022, 30(3): 384-390. doi: 10.11993/j.issn.2096-3920.2022.03.015 Mao Zhi-yuan, Duan Chao-wei, Hu Hong-wei, et al. Review of Testing and Evaluation Methods for Underwater Explosion Power[J]. Journal of Unmanned Undersea Systems, 2022, 30(3): 384-390. doi: 10.11993/j.issn.2096-3920.2022.03.015
[14]	Jia X, Wang S, Feng C, et al. A Practical Simulation of a Hexanitrohexaazaisowurtzitane(CL-20) Sphere Detonated Underwater with the Taylor Wave Solution and Modified Tait Parameters[J]. Physics of Fluids, 2021, 33(3): 036102. doi: 10.1063/5.0037300
[15]	Sachdev P L. Shock Waves and Explosions[M]. New York: Chapman and Hall/CRC, 2004.
[16]	Jia X, Wang S, Xu J, et al. Nonlinear Characteristics and Corrections of Near-Field Underwater Explosion Shock Waves[J]. Physics of Fluids, 2022, 34(3): 046108.
[17]	Moisson A. Des Explosions Au Sein de L'eau[R]. [S. l.]: Maritime et Coloniale, 1877.
[18]	Audic J. Étude Sur Les Effets Des Explosions Sous-Marines[R].[S. l.]: Rev. Maritime et Coloniale, 1877.
[19]	Abbot H L. Report upon Experiments and Investigations to Develop a System of Submarine Mines for Defending the Harbors of the United States[R]. Washington, D. C.: the U. S. Army, 1881.
[20]	Bertelli T. Studi Comparativi fra Alcune Vibrazioni Meccaniche Artificiali e le Vibrazioni Sismiche[M]//Annali dell’Ufficio Centrale Meteorologico e Geodinamico Italiano X[II], Parte IV. Roma: Tipografia del Senato, 1892: 5-44.
[21]	Armstrong G E. Torpedoes and Torpedo-vessels[R]. London: Bell, 1896.
[22]	Plach F. Die Gepresste Schiesswolle. Eine Abhandlung über die Beurtheilung, Verwendung und Behandlung Dieses Explosiv-Preparates für Torpedo-und Seeminen-Lehrcurse[M]. Pola: E. Schaff, 1891.
[23]	Blochmann R. Die Explosion unter Wasser[J]. Marine-Rundschau, 1898, 9: 197-227.
[24]	Hilliar H W. Experiments on the Pressure Wave Thrown out by Submarine Explosions[R]. [S.l.]: Engl. Dept. of Scientific Research & Experiment, 1919.
[25]	Keys D A. A Piezoelectric Method of Measuring Explosion Pressures[J]. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 1921, 42: 473-488. doi: 10.1080/14786442108633788
[26]	Keys D A. The Cathode-Ray Oscillograph and Its Application to the Exact Measurement of Explosion Pressures, Potential Changes in Vacuum Tubes and High Tension Magnetos[J]. Boston: J. Franklin Institute, 1923, 196: 576-591.
[27]	Wood A B. The Cathode Ray Oscillograph[J]. Proceedings of the Physical Society (Lond.), 1922, 35(1): 109-124.
[28]	Ramsauer C. Die Massenbewegung des Wassers bei Unterwasserexplosionen[J]. Annals of Physics, 1923, 72: 265-284.
[29]	Lamb H. On the Early Stages of a Submarine Explosion[J]. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 1923, 6(45): 257-265.
[30]	Weinert. Unterwasser Zeitlupen Aufnahmen von Gasblasenschwingungen[R]. Kiel: Berichte der Chemisch-physikalischen Versuchsanstalt der Kriegsmarine, 1941.
[31]	Haack W. Geschoßformen Kleinsten Wellenwiderstandes[R]. Lilienthal: Lilienthal-Gesell. Ber, 1941, 139: 14-29.
[32]	U. S. Navy. A Photographic Study of Small-Scale Underwater Explosions[R]. Montgomery MD: David W. Taylor Model Basin, Confidential Test Rept. , 1941.
[33]	Campbell D C. Motions of a Pulsating Gas Globe under Water-a Photographic Study[R]. Montgomery MD: David W. Taylor Model Basin Rept. , 1943.
[34]	Ewing M, Crary A. Multi Impulses from Underwater Explosions[R]. Massachusetts, the U.S.: Woods Hole Oceanogr, 1941.
[35]	Cole R H. Underwater Explosions[M]. Princeton, New Jersey: Princeton University Press, 1948.
[36]	Office of Naval Research. Underwater Explosion Research, Three Volume-set[R]. Washington, D. C.: Office of Naval Research, 1950.
[37]	Snay H G. Hydrodynamics of Underwater Explosions[C]//In: Symposium on Naval Hydrodynamic. Washington, D. C.: National Academy of Sciences , 1956.
[38]	Hopkinson B. British Ordnance Board Minutes: Report 13565[R]. London, UK: British Ordnance Office, 1915.
[39]	Cranz K J, Eberhard O, Becker K E. Lehrbuch der Ballistik Ergänzungen zum. Band II[M]. Berlin, Germany: Springer, 1926.
[40]	White E P. Effects of Impact and Explosions[R]. Washington, D. C.: NDRC, 1946.
[41]	Kirkwood J G, Bethe H. The Pressure Wave Produced by an Underwater Explosion, Basic Propagation Theory, Part 1[R]. Washington, D. C.: OSRD, 1942.
[42]	Kiciński R, Szturomski B. Pressure Wave Caused by Trinitrotoluene(TNT) Underwater Explosion—Short Review[J]. Applied Sciences, 2020, 10(10): 3433. doi: 10.3390/app10103433
[43]	Zamyshlyaev B V, Yakovlev Y S. Dynamic Loads in Underwater Explosion: AD 757183[R]. Washington, D. C.: Naval Intelligence Support Center, 1973.
[44]	Geers T L, Hunter K S. An Integrated Wave-Effects Model for an Underwater Explosion Bubble[J]. The Journal of the Acoustical Society of America, 2002, 111(4): 1584-1601. doi: 10.1121/1.1458590
[45]	Hunter K S, Geers T L. Pressure and Velocity Fields Produced by an Underwater Explosion[J]. The Journal of the Acoustical Society of America, 2004, 115(4): 1483-1496. doi: 10.1121/1.1648680
[46]	Temperley H N V, Craig J. Calculation from Thermodynamical and Hydrodynamical Considerations of Underwater Shock-waves for Spherical Charges[R]. Washington, D. C.: Department of the Navy, Office of Naval Research, 1950: 347-372.
[47]	Brinkley S R, Kirkwood J G. Theory of the Propagation of Shock Waves[J]. Physical Review, 1947, 71(9): 606. doi: 10.1103/PhysRev.71.606
[48]	Brinkley S R, Kirkwood J G. Theory of the Propagation of Shock Waves from Infinite Cylinders of Explosive[J]. Physical Review, 1947, 72(11): 1109. doi: 10.1103/PhysRev.72.1109
[49]	Best J P. A Generalisation of the Theory of Geometrical Shock Dynamics[J]. Shock Waves, 1992, 2(2): 125. doi: 10.1007/BF01415902
[50]	Best J P. The Dynamics of Underwater Explosions[D]. Wollongong: University of Wollongong, 1991.
[51]	Sachdev P L. On the Theory of Weak Spherical Shocks[J]. Indian Journal of Pure & Applied Mathematics, 1976, 7(11): 1-7.
[52]	Sachdev P L. Shock Waves and Explosions[M]. 1st ed. Florida: Chapman and Hall/CRC, 2004.
[53]	Rogers P H. Weak-shock Solution for Underwater Explosive Shock Waves[J]. Journal of the Acoustical Society of America, 1977, 62(6): 1412-1419. doi: 10.1121/1.381674
[54]	Kedrinskii V K. Hydrodynamics or Explosions[J]. Journal of Applied Mechanics and Technical Physics, 1988, 28(4): 491-515. doi: 10.1007/BF00916731
[55]	Kedrinskii V K. Hydrodynamics of Explosion: Experiments and Models[M]. Berlin Heidelberg: Springer, 2005.
[56]	Arons A B. Underwater Explosion Shock Wave Parameters at Large Distances from the Charge[J]. Journal of the Acoustical Society of America, 1954, 26(3): 343-346. doi: 10.1121/1.1907339
[57]	Chapman N R. Measurement of the Waveform Parameters of Shallow Explosive Charges[J]. The Journal of the Acoustical Society of America, 1985, 78(2): 672-681. doi: 10.1121/1.392436
[58]	Zhang J, Wang S, Jia X, et al. An Improved Kirkwood-Bethe Model for Calculating Near-Field Shockwave Propagation of Underwater Explosions[J]. AIP Advances, 2021, 11(3): 035123. doi: 10.1063/5.0040224
[59]	Penney W G. The Pressure-Time Curve for Underwater Explosions (I)[R]. Washington, D. C.: Department of the Navy, Office of Naval Research, 1950: 273-288.
[60]	Penney W G, Dasgupta H K. The Pressure-Time Curve for Underwater Explosions (II)[R]. Washington, D. C.: Department of the Navy, Office of Naval Research, 1950: 289-300.
[61]	Holt M, Berry F J. The Initial Propagation of Spherical Blast from Certain Explosives[J]. Proceedings of the Royal Society of London, 1954, 224(1157): 236-251.
[62]	Holt M. The Initial Behaviour of a Spherical Explosion. I. Theoretical Analysis[J]. Proceedings of the Royal Society of London, 1956, 234(1196): 89-109.
[63]	Holt M. The Initial Behaviour of a Spherical Explosion. II. Application to PETN Charges in Air and Water[J]. Proceedings of the Royal Society of London, 1956, 234(1196): 110-115.
[64]	Ai D K, Holt M. The Initial Growth of a Spherical Explosion in Sea Water[R]. USA: Defense Technical Information Center, 1957.
[65]	Berger S A, Holt M. Implosive Phase of a Spherical Explosion in Sea Water[J]. The Physics of Fluids, 1962, 5(4): 426. doi: 10.1063/1.1706635
[66]	李晓杰, 杨晨琛, 闫鸿浩, 等. 柱状含铝炸药水下爆炸近场的特征线法研究[J]. 爆炸与冲击, 2019, 39(2): 22-29. doi: 10.11883/bzycj-2017-0412 Li Xiao-jie, Yang Chen-chen, Yan Hong-hao, et al. Numerical Study of Near-field Underwater Explosion of Cylindrical Aluminized Explosive by the Method of Characteristics[J]. Explosion and Shock Waves, 2019, 39(2): 22-29. doi: 10.11883/bzycj-2017-0412
[67]	李晓杰, 张程娇, 闫鸿浩, 等. 水下爆炸近场非均熵流的特征线差分解法[J]. 爆炸与冲击, 2012, 32(6): 604-608. doi: 10.3969/j.issn.1001-1455.2012.06.008 Li Xiao-jie, Zhang Cheng-jiao, Yan Hong-hao, et al. Difference Method of Characteristics in Isentropic Flow of Underwater Explosion in Near-field Region[J]. Explosion and Shock Waves, 2012, 32(6): 604-608. doi: 10.3969/j.issn.1001-1455.2012.06.008
[68]	Flores J, Holt M. Glimm’s Method Applied to Underwater Explosions[J]. Journal of Computational Physics, 1981, 44(2): 377-387. doi: 10.1016/0021-9991(81)90058-9
[69]	Harten A, Engquist B, Osher S, et al. Uniformly High Order Accurate Non-Oscillatory Schemes III[J]. Comput. Phys., 1987, 71: 231-303. doi: 10.1016/0021-9991(87)90031-3
[70]	Jiang G, Shu C W. Efficient Implementation of Weighted ENO Schemes[J]. Journal of Computational Physics, 1996, 126: 202-228. doi: 10.1006/jcph.1996.0130
[71]	Balsara D S, Shu C W. Monotonicity Preserving Weighted Essentially Non-Oscillatory Schemes with Increasingly High Order of Accuracy[J]. Journal of Computational Physics, 2000, 160: 405-452. doi: 10.1006/jcph.2000.6443
[72]	Zhang S, Jiang S, Shu C. Development of Nonlinear Weighted Compact Schemes with Increasingly Higher Order Accuracy[J]. Journal of Computational Physics, 2008, 227(15): 7294-7321. doi: 10.1016/j.jcp.2008.04.012
[73]	Capdeville G. A Central WENO Scheme for Solving Hyperbolic Conservation Laws on Non-Uniform Meshes[J]. Journal of Computational Physics, 2008, 227(5): 2977-3014. doi: 10.1016/j.jcp.2007.11.029
[74]	刘君, 韩芳, 魏雁昕. 应用维数分裂方法推广MUSCL和WENO格式的若干问题[J]. 航空学报, 2022, 43(3): 133-142. doi: 10.7527/j.issn.1000-6893.2022.3.hkxb202203010 Liu Jun, Han Fang, Wei Yan-xin. MUSCL and WENO Schemes Problems Generated by Dimension Splitting Approach[J]. Acta Aeronautica et Astronautica Sinica, 2022, 43(3): 133-142. doi: 10.7527/j.issn.1000-6893.2022.3.hkxb202203010
[75]	Wang C, Zhang X, Shu C W, et al. Robust High Order Discontinuous Galerkin Schemes for Two-Dimensional Gaseous Detonations[J]. Journal of Computational Physics, 2012, 231(2): 653-665. doi: 10.1016/j.jcp.2011.10.002
[76]	Tan C, Wang C, Shu C-W, et al. Efficient Implementation of High-Order Inverse Lax-Wendroff Boundary Treatment for Conservation Laws[J]. Journal of Computational Physics, 2012, 231(6): 2510-2527. doi: 10.1016/j.jcp.2011.11.037
[77]	Shima A. Studies on Bubble Dynamics[J]. Shock Waves, 1997, 7(1): 33-42. doi: 10.1007/s001930050060
[78]	Plesset M S. The Dynamics of Cavitation Bubbles[J]. Journal of applied Mechanics, 1949, 16: 277-282. doi: 10.1115/1.4009975
[79]	Besant W H. Hydrostatics and Hydrodynamics[M]. London: Cambridge University Press, 1859.
[80]	Rayleigh L. On the Pressure Developed in a Liquid during the Collapse of a Spherical[J]. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 1917, 6(34): 94-98.
[81]	Herring C. Theory of the Pulsations of the Gas Bubble Produced by an Underwater Explosion[R]. Washington, D. C.: Department of the Navy, Office of Naval Research, 1950: 35-130.
[82]	Trilling L. The Collapse and Rebound of a Gas Bubble[J]. Journal of Applied Physics, 1952, 23(1): 14-17. doi: 10.1063/1.1701962
[83]	Gilmore F R. The Growth or Collapse of a Spherical Bubble in a Viscous Compressible Liquid[R]. Pasadena: California Institute of Technology, 1952.
[84]	Keller J B, Kolodner I I. Damping of Underwater Explosion Bubble Oscillation[J]. Journal of Applied Physics, 1956, 27: 1152-1161. doi: 10.1063/1.1722221
[85]	Flynn H G. Cavitation Dynamics. I. A Mathematical Formulation[J]. Acoustical Society of America Journal, 1975, 57(6): 1379-1396. doi: 10.1121/1.380624
[86]	Flynn H G. Cavitation Dynamics: II. Free Pulsations and Models for Cavitation Bubbles[J]. The Journal of the Acoustical Society of America, 1975, 58(6): 1160-1170. doi: 10.1121/1.380799
[87]	Lastman G J, Wentzell R A. Cavitation of a Bubble in an Inviscid Compressible Liquid, with Comparisons to a Viscous Incompressible Liquid[J]. Physics of Fluids, 1979, 22(12): 2259-2266. doi: 10.1063/1.862534
[88]	Cramer E. The Dynamics and Acoustic Emission of Bubbles Driven by a Sound Field[C]//Cavitation and Inhomogeneities in Underwater Acoustics. Berlin, Heidelberg: Springer, 1980: 54-63.
[89]	Rath H J. Free and Forced Oscillations of Spherical Gas Bubbles and Their Translational Motion in a Compressible Fluid[C]//Cavitation and Inhomogeneities in Underwater Acoustics. Berlin, Heidelberg: Springer, 1980: 64-71.
[90]	Keller J B, Miksis M. Bubble Oscillations of Large Amplitude[J]. The Journal of the Acoustical Society of America, 1980, 68(2): 628-633. doi: 10.1121/1.384720
[91]	Prosperetti A, Lezzi A. Bubble Dynamics in a Compressible Liquid. Part 1. First-order Theory[J]. Journal of Fluid Mechanics, 1986, 168: 457-478. doi: 10.1017/S0022112086000460
[92]	Lighthill M J. A Technique for Rendering Approximate Solutions to Physical Problems Uniformly Valid[J]. Phil Mag, 1949, 40(5): 1179-1120.
[93]	Kuo Y H. On the Flow of an Incompressible Viscous Fluid past a Flat Plate at Moderate Reynolds Numbers[J]. J Math and Phys, 1953, 32(1): 83-51.
[94]	Tsien H S. The Poincare-Lighthill-Kuo Method[J]. Advan Appl Math, 1956, 4(2): 281-349.
[95]	Lastman G J, Wentzell R A. Comparison of Five Models of Spherical Bubble Response in an Inviscid Compressible Liquid[J]. The Journal of the Acoustical Society of America, 1981, 69(3): 638-642. doi: 10.1121/1.385580
[96]	Tilmann P M. Nonlinear Sound-Scattering by Small Bubbles[C]//Cavitation and Inhomogeneities in Underwater Acoustics. Berlin, Heidelberg: Springer, 1980: 113-118.
[97]	Tomita Y, Shima A. High-speed Photographic Observations of Laser-Induced Cavitation Bubbles in Water[J]. Acta Acustica United with Acustica, 1990, 71(3): 161-171.
[98]	Tomita Y, Shima A, Sato K. Dynamic Behavior of Two-Laser-Induced Bubbles in Water[J]. Applied Physics Letters, 1990, 57(3): 234-236. doi: 10.1063/1.103726
[99]	Tomita Y, Shima A. On the Behavior of a Spherical Bubble and the Impulse Pressure in a Viscous Compressible Liquid[J]. Bulletin of JSME, 1977, 20(149): 1453-1460. doi: 10.1299/jsme1958.20.1453
[100]	Shima A, Tomita Y. The Behavior of a Spherical Bubble in Mercury/Report 2[J]. Rep. Inst. High Speed Mech, 1979, 19: 39.
[101]	Lezzi A, Prosperetti A. Bubble Dynamics in a Compressible Liquid. Part 2. Second-order Theory[J]. Journal of Fluid Mechanics, 1987, 185: 289-321. doi: 10.1017/S0022112087003185
[102]	Geers T L, Park C K. Optimization of the G&H Bubble Model[J]. Shock and Vibration, 2005, 12(1): 3-8. doi: 10.1155/2005/430767
[103]	Geers T L, Lagumbay R S, Vasilyev O V. Acoustic-Wave Effects in Violent Bubble Collapse[J]. Journal of Applied Physics, 2012, 112(5): 054910. doi: 10.1063/1.4748870
[104]	Wang Q X, Blake J R. Non-spherical Bubble Dynamics in a Compressible Liquid. Part 1. Travelling Acoustic Wave[J]. Journal of Fluid Mechanics, 2010, 659(1): 191-224.
[105]	Wang Q X, Blake J R. Non-spherical Bubble Dynamics in a Compressible Liquid. Part 2. Acoustic Standing Wave[J]. Journal of Fluid Mechanics, 2011, 679(1): 559-581.
[106]	Wang Q X. Non-spherical Bubble Dynamics of Underwater Explosions in a Compressible Fluid[J]. Physics of Fluids, 2013, 25(7): 072104. doi: 10.1063/1.4812659
[107]	Smith W R, Wang Q. Radiative Decay of the Nonlinear Oscillations of an Adiabatic Spherical Bubble at Small Mach Number[J]. Journal of Fluid Mechanics, 2018, 837: 1-18. doi: 10.1017/jfm.2017.658
[108]	Zhang A M, Cui P, Cui J, et al. Experimental Study on Bubble Dynamics Subject to Buoyancy[J]. Journal of Fluid Mechanics, 2015, 776: 137-160. doi: 10.1017/jfm.2015.323
[109]	Zhang A M, Yang W S, Huang C, et al. Numerical Simulation of Column Charge Underwater Explosion Based on SPH and BEM Combination[J]. Computers & Fluids, 2013, 71: 169-178.
[110]	Cui P, Zhang A M, Wang S, et al. Ice Breaking by a Collapsing Bubble[J]. Journal of Fluid Mechanics, 2018, 841: 287-309. doi: 10.1017/jfm.2018.63
[111]	Cui P, Zhang A M, Wang S P, et al. Experimental Investigation of Bubble Dynamics near the Bilge with a Circular Opening[J]. Applied Ocean Research, 2013, 41: 65-75. doi: 10.1016/j.apor.2013.03.002
[112]	Cui P, Zhang A M, Wang S P, et al. Experimental Study on Interaction, Shock Wave Emission and Ice Breaking of Two Collapsing Bubbles[J]. Journal of Fluid Mechanics, 2020, 897(A25): 1-40.
[113]	Xiao W, Zhang A M, Wang S P. Investigation of Bubble Dynamics of Underwater Explosion Based on Improved Compressible Numerical Model[J]. Applied Ocean Research, 2016, 59: 472-482. doi: 10.1016/j.apor.2016.07.007
[114]	Wang P P, Zhang A M, Ming F R, et al. A Novel Non-Reflecting Boundary Condition for Fluid Dynamics Solved by Smoothed Particle Hydrodynamics[J]. Journal of Fluid Mechanics, 2019, 860: 81-114. doi: 10.1017/jfm.2018.852
[115]	Zhang J, Wang S, Jia X, et al. An Engineering Application of Prosperetti and Lezzi Equation to Solve Underwater Explosion Bubbles[J]. Physics of Fluids, 2021, 33(1): 017118. doi: 10.1063/5.0033016
[116]	Wang S, Gui Q, Zhang J, et al. Theoretical and Experimental Study of Bubble Dynamics in Underwater Explosions[J]. Physics of Fluids, 2021, 33(12): 126113. doi: 10.1063/5.0072277
[117]	Hsieh D Y. On the Dynamics of Nonspherical Bubbles[J]. Journal of Basic Engineering, 1972, 94(3): 655-665. doi: 10.1115/1.3425522
[118]	Wang Q X, Yeo K S, Khoo B C, et al. Nonlinear Interaction between Gas Bubble and Free Surface[J]. Computers & Fluids, 1996, 25(7): 607-628.
[119]	Zhang A M, Liu Y L. Improved Three-Dimensional Bubble Dynamics Model Based on Boundary Element Method[J]. Journal of Computational Physics, 2015, 294: 208-223. doi: 10.1016/j.jcp.2015.03.049
[120]	Zhang S, Duncan J, Chahine G. The Final Stage of the Collapse of a Cavitation Bubble near a Rigid Wall[J]. Journal of Fluid Mechanics, 1993, 257: 147-181. doi: 10.1017/S0022112093003027
[121]	Zhang A, Li S, Cui J. Study on Splitting of a Toroidal Bubble near a Rigid Boundary[J]. Physics of Fluids, 2015, 27: 062102. doi: 10.1063/1.4922293
[122]	Han R, Li S, Zhang A M, et al. Modelling for Three Dimensional Coalescence of Two Bubbles[J]. Physics of Fluids, 2016, 28(6): 707-721.
[123]	Benson D J. Computational Methods in Lagrangian and Eulerian Hydrocodes[J]. Computer Methods in Applied Mechanics & Engineering, 1992, 99: 235-394.
[124]	Donea J, Giuliani S, Halleux J P. An Arbitrary Lagrangian-Eulerian Finite Element Method for Transient Dynamic Fluid-Structure Interactions[J]. Computer Methods in Applied Mechanics & Engineering, 1982, 33(1-3): 689-723.
[125]	Hu H H, Patankar N A, Zhu M Y. Direct Numerical Simulations of Fluid-Solid Systems Using the Arbitrary Lagrangian-Eulerian Technique[J]. Journal of Computational Physics, 2001, 169(2): 427-462. doi: 10.1006/jcph.2000.6592
[126]	Noh W F. CEL: A Time-Dependent, Two-Space-Dimensional, Coupled Eulerian-Lagrange Code[R]. Livermore, California: UNT Libraries Government Documents Department, 1963.
[127]	Gang Q, Henke S, Grabe J. Application of a Coupled Eulerian-Lagrangian Approach on Geomechanical Problems Involving Large Deformations[J]. Computers & Geotechnics, 2011, 38(1): 30-39.
[128]	Glimm J, Isaacson E, Marchesin D. Front Tracking for Hyperbolic Systems[J]. Advances in Applied Mathematics, 1981, 2(1): 91-119. doi: 10.1016/0196-8858(81)90040-3
[129]	Glimm J, Klingenberg C, McBryan O. Front Tracking and Two-Dimensional Riemann Problems[J]. Advances in Applied Mathematics, 1985, 6(3): 259-290. doi: 10.1016/0196-8858(85)90014-4
[130]	Chern I L, Glimm J, McBryan O. Front Tracking for Gas Dynamics[J]. Journal of Computational Physics, 1986, 62(1): 83-110. doi: 10.1016/0021-9991(86)90101-4
[131]	Roe P L. A New Approach to Computing Discontinuous Flows of Several Ideal Gases[R]. Erfurt: Canfield Institute of Technology, 1984.
[132]	Larouturou B. How to Preserve the Mass Fraction Positive when Computing Compressible Multi-Component Flows[J]. Journal of Computational Physics, 1991, 95(1): 59-84. doi: 10.1016/0021-9991(91)90253-H
[133]	Hirt C, Nichols B. Volume of Fluid(VOF) Method for the Dynamics of Free Boundaries[J]. Journal of Computational Physics, 1981, 39(1): 201-225. doi: 10.1016/0021-9991(81)90145-5
[134]	Osher S, Sethian J A. Fronts Propagating with Curvature-Dependent Speed: Algorithms Based on Hamilton-Jacobi Formulations[J]. Journal of Computational Physics, 1988, 79(1): 12-49. doi: 10.1016/0021-9991(88)90002-2
[135]	Fedkiw R P, Aslam T, Merriman B. A Non-Oscillatory Eulerian Approach to Interfaces in Multimaterial Flows(the Ghost Fluid Method)[J]. Journal of Computational Physics, 1999, 152(2): 457-492. doi: 10.1006/jcph.1999.6236
[136]	Fedkiw R P, Marquina A, Merriman B. An Isobaric Fix for the Overheating Problem in Multimaterial Compressible Flows[J]. Journal of Computational Physics, 1999, 148(2): 545-578. doi: 10.1006/jcph.1998.6129
[137]	Fedkiw R P. Coupling an Eulerian Fluid Calculation to a Lagrangian Solid Calculation with the Ghost Fluid Method[J]. Journal of Computational Physics, 2002, 175(1): 200-224. doi: 10.1006/jcph.2001.6935
[138]	Liu T G, Khoo B C, Yeo K S. Ghost Fluid Method for Strong Shock Impacting on Material Interface[J]. Journal of Computational Physics, 2003, 190(2): 651-681. doi: 10.1016/S0021-9991(03)00301-2
[139]	Hu X Y, Khoo B C. An Interface Interaction Method for Compressible Multifluids[J]. Journal of Computational Physics, 2004, 198(1): 35-64. doi: 10.1016/j.jcp.2003.12.018
[140]	Liu T G, Khoo B C, Wang C W. The Ghost Fluid Method for Compressible Gas-Water Simulation[J]. Journal of Computational Physics, 2005, 204(1): 193-221. doi: 10.1016/j.jcp.2004.10.012
[141]	Liu T G, Khoo B C. The Accuracy of the Modified Ghost Fluid Method for Gas-Gas Riemann Problem[J]. Applied Numerical Mathematics, 2007, 57: 721-733. doi: 10.1016/j.apnum.2006.07.013
[142]	Wang C W, Liu T G, Khoo B C. A Real Ghost Fluid Method for the Simulation of Multimedium Compressible Flow[J]. Siam Journal on Scientific Computing, 2006, 28(1): 278-302. doi: 10.1137/030601363
[143]	Xu L, Feng C, Liu T. Practical Techniques in Ghost Fluid Method for Compressible Multi-Medium Flows[J]. Communications in Computational Physics, 2016, 20(3): 619-659. doi: 10.4208/cicp.190315.290316a
[144]	Liu T G, Khoo B C, Xie W F. The Modified Ghost Fluid Method as Applied to Extreme Fluid-Structure Interaction in the Presence of Cavitation[J]. Commun. Comput. Phys., 2006, 1: 898-919.
[145]	Liu T G, Xie W F, Khoo B C. The Modified Ghost Fluid Method for Coupling of Fluid and Structure Constituted with Hydro-Elasto-Plastic Equation of State[J]. Siam Journal on Scientific Computing, 2007, 30(3): 1105-1130.
[146]	Xu L, Liu T G. Modified Ghost Fluid Method as Applied to Fluid-Plate Interaction[J]. Advances in Applied Mathematics & Mechanics, 2014, 6(1): 24-48.
[147]	Feng Z W, Kaboudian A, Rong J L, et al. The Simulation of Compressible Multifluid Mulit-Solid Interactions Using the Modified Ghost Method[J]. Comput. Fluids, 2017, 154: 12-26. doi: 10.1016/j.compfluid.2017.05.017
[148]	Gao S, Liu T G. 1D Exact Elastic-Perfectly Plastic Solid Riemann Solver and Its Multi-Material Application[J]. Adv. Appl. Math. Mech., 2017, 9(3): 621-650.
[149]	Shi R C, Qu Y G, Batra R C. Numerical Simulation of Underwater Explosion Wave Propagation in Water-Solid-Air/Water System Using Ghost Fluid/Solid Method[J]. Journal of Fluids and Structures, 2019, 90: 354-378. doi: 10.1016/j.jfluidstructs.2019.07.002
[150]	Xu L, Liu T G. Optimal Error Estimation of the Modified Ghost Fluid Method[J]. Commun. Comput. Phys., 2010, 8: 403-426. doi: 10.4208/cicp.110509.271009a
[151]	Xu L, Liu T G. Accuracies and Conservation Errors of Various Ghost Fluid Methods for Multimedium Riemann Problem[J]. J. Comput. Phys., 2011, 230: 4975-90.
[152]	Liu T G, Feng C L, Xu L. Modified Ghost Fluid Method with Acceleration Correction (MGFM/AC)[J]. Journal of Scientific Computing, 2019, 81(1): 1906-44.
[153]	Feng C L, Liu T G, Xu L, et al. Modified Ghost Fluid Method with Axisymmetric Source Correction(MGFM/ASC)[J]. Communications in Computational Physics, 2020, 28: 621-660. doi: 10.4208/cicp.OA-2019-0056
[154]	Wang C, Tang H, Liu T. An Adaptive Ghost Fluid Finite Volume Method for Compressible Gas-Water Simulations[J]. Journal of Computational Physics, 2008, 227(12): 6385-409. doi: 10.1016/j.jcp.2008.03.005
[155]	Kennard E H. Cavitation in an Elastic Liquid[J]. Physical Review, 1943, 63(5-6): 172. doi: 10.1103/PhysRev.63.172
[156]	Kennard E H. Explosive Load on Underwater Structures as Modified by Bulk Cavitation[R]. Washington D C: David Taylor Model Basin, 1943.
[157]	Arons A, Yennie D, Cotter T. Long Range Shock Propagation in Underwater Explosion Phenomena II[M]. Underwater Explosion Compendium, 1949: 107.
[158]	Walker R R, Gordon J D. A Study of the Bulk Cavitation Caused by Underwater Explosions[R]. US: David Taylor Model Basin Portsmouth Va Underwater Explosions Research Div, 1966.
[159]	Gaspin J B, Price R S. The Underpressure Field from Explosions in Water as Modified by Cavitation[R]. Silver Spring: Naval Ordnance Lab White Oak Md, 1972.
[160]	Didoszak J M. Parametric Studies of DDG-81 Ship Shock Trial Simulations[D]. Monterey: Naval Postgraduate School Monterey Ca, 2004.
[161]	Walters A P. Investigation of an Explicitly Modeled Solid Ocean Floor on a Shallow Water UNDEX Event[D]. Monterey: Naval Postgraduate School Monterey Ca, 2011.
[162]	Ahn S H. Investigation of Shallow UNDEX in Littoral Ocean Domain[D]. Monterey: Naval Postgraduate School Monterey Ca, 2014.
[163]	Costanzo F A, Gordon J D. A Solution to the Axisymmetric Bulk Cavitation Problem[R]. Shock and Vibration Bulletin, 1983(53): 33-51.
[164]	Kedrinskii V K. Negative Pressure Profile in Cavitation Zone at Underwater Explosion near Free Surface[J]. Acta Astronautica, 1976, 3(7-8): 623-32. doi: 10.1016/0094-5765(76)90166-1
[165]	Kedrinskii V K. Surface Effects from an Underwater Explosion (Review)[J]. Journal of Applied Mechanics and Technical Physics, 1978(19): 474-491.
[166]	Xie W F, Liu T G, Khoo B C. Application of a One-Fluid Model for Large Scale Homogeneous Unsteady Cavitation: The Modified Schmidt Model[J]. Computers and Fluids, 2006, 35(10): 1177-92. doi: 10.1016/j.compfluid.2005.05.006
[167]	Kleine H, Tepper S, Takehara K, et al. Cavitation Induced by Low-speed Underwater Impact[C]//26th International Symposium on Shock Waves. Berlin Heidelberg: Springer, 2009.
[168]	Cui P, Zhang A M, Wang S P. Small-charge Underwater Explosion Bubble Experiments Under Various Boundary Conditions[J]. Physics of Fluids, 2016(28): 117103.
[169]	余俊, 刘建湖, 盛振新, 等. 水下爆炸引起的近自由面空化机理研究[J]. 水动力学研究与进展A辑, 2022, 37(4): 483-491. doi: 10.16076/j.cnki.cjhd.2022.04.006 Yu Jun, Liu Jian-hu, Sheng Zhen-xin, et al. Research on Mechanism of Cavitation near Free Surface Induced by Underwater Explosion[J]. Chinese Journal of Hydrodynamics, 2022, 37(4): 483-491. doi: 10.16076/j.cnki.cjhd.2022.04.006
[170]	Cushing V J. On the Theory Bulk Cavitation[R]. Washington, D. C.: NDRC, 1969.
[171]	Holt M. Final Report on Contact[R]. Virginia: Defense Technical Information Center, 1979.
[172]	John F G, Coarrnor. The Interaction between Explosion and the Ocean Surface[R]. Washington D. C.: NDRC, 1979.
[173]	Britt J R. Linear Theory of Bottom Reflection[R]. Maryland: Naval Ordnance Lab White Oak MD, 1969.
[174]	Britt J R. Bottom Reflection of Underwater Explosion Shock Waves[J]. Computer Program, 1971(7): 110-132.
[175]	孙百连, 顾文彬, 蒋建平, 等. 浅层水中沉底的两个装药爆炸的数值模拟研究[J]. 爆炸与冲击, 2003, 23(5): 460-465. doi: 10.3321/j.issn:1001-1455.2003.05.013 Sun Bai-lian, Gu Wen-bin, Jiang Jian-ping, et al. Numerical Simulation of Explosion Shock Wave Interaction in Shallow-Layer Water[J]. Explosion and Shock Waves, 2003, 23(5): 460-465. doi: 10.3321/j.issn:1001-1455.2003.05.013
[176]	姚熊亮, 杨文山, 陈娟, 等. 沉底水雷爆炸威力的数值计算[J]. 爆炸与冲击, 2011, 31(2): 173-178. Yao Xiong-liang, Yang Wen-shan, Chen Juan, et al. Numerical Calculation of Explosion Power of Mines Lying on Seabed[J]. Explosion and Shock Waves, 2011, 31(2): 173-178.
[177]	Saito T, Marumoto M. Experimental and Numerical Studies of Underwater Shock Wave Attenuation[J]. Shock Waves, 2013, 13(2): 139-148.
[178]	杨莉, 汪玉, 杜志鹏, 等. 沉底装药水下爆炸冲击波传播规律[J]. 兵工学报, 2013, 34(1): 100-104. Yang Li, Wang Yu, Du Zhi-peng, et al. Research on Shock Wave Propagation of Underwater Explosion of Bottom Charge[J]. Acta Armamentarii, 2013, 34(1): 100-104.
[179]	杨莉, 汪玉, 汪斌, 等. 沉底装药水中爆炸现象的实验研究[J]. 爆炸与冲击, 2013, 33(2): 175-180. doi: 10.3969/j.issn.1001-1455.2013.02.010 Yang Li, Wang Yu, Wang Bin, et al. Experimental Investigation on Loading Characteristics of Underwater Explosion from a Bottom Charge[J]. Explosion and Shock Waves, 2013, 33(2): 175-180. doi: 10.3969/j.issn.1001-1455.2013.02.010
[180]	杨莉, 巨圆圆, 武堃, 等. 装药沉底爆炸峰值压力试验及数值模拟研究[J]. 兵工学报, 2014, 35(S2): 368-372. Yang Li, Ju Yuan-yuan, Wu Kun, et al. Experiment and Simulation on Peak Pressure of Underwater Explosion of a Bottom Charge[J]. Acta Armamentarii, 2014, 35(S2): 368-372.
[181]	王振雄, 顾文彬, 陈江海, 等. 浅水中爆炸水底介质对水中冲击波峰值压力影响的试验研究[J]. 振动与冲击, 2017, 36(4): 243-248. doi: 10.13465/j.cnki.jvs.2017.04.038 Wang Zhen-xiong, Gu Wen-bin, Chen Jiang-hai, et al. Experimental Study on the Influence of the Bottom Medium on the Peak Pressure of Explosion Shock Waves in Shallow Water[J]. Journal of Vibration and Shock, 2017, 36(4): 243-248. doi: 10.13465/j.cnki.jvs.2017.04.038
[182]	Slifko J F. Pressure-Pulse Characteristics of Deep Explosions as Functions of Depth and Range[R]. Washington, D. C.: NDRC, 1967.
[183]	Xiao P, Yang K. Experimental Results for Peak Pressure and Sound Exposure Level in Deep-Sea Explosions[J]. Acoustics Australia, 2015, 43(2): 175-178. doi: 10.1007/s40857-015-0020-9
[184]	Bernard Fridman. Theory of Underwater Explosion Bubbles[R]. New York: New York University, 1950.
[185]	Arons A B. Secondary Pressure Pulses due to Gas Globe Oscillation in Underwater Explosions. I. Experimental Data[J]. Journal of the Acoustical Society of America, 1948, 20(3): 271-276. doi: 10.1121/1.1906371
[186]	姚熊亮, 汪玉, 张阿漫. 水下爆炸气泡动力学[M]. 哈尔滨: 哈尔滨工程大学出版社, 2012.
[187]	王树山, 梁策, 高源, 等. 深水爆炸二次压力波超压峰值的工程模型[J]. 兵工学报, 2022, 43(10): 2508-16. Wang Shu-shan, Liang Ce, Gao Yuan, et al. Engineering Model for Calculating Secondary Pressure Wave Overpressure Peak in Deep Water Explosion[J]. Acta Armamentarii, 2022, 43(10): 2508-16.
[188]	钟帅. 模拟深水爆炸装药输出能量的研究[D]. 淮南: 安徽理工大学, 2007.
[189]	朱宽, 钟冬望, 何理, 等. 基于高速摄影技术模拟深水爆破环境下气泡脉动规律研究[J]. 工程爆破, 2015, 21(1): 5-9. doi: 10.3969/j.issn.1006-7051.2015.01.002 Zhu Kuan, Zhong Dong-wang, He Li, et al. Research on Blasting Bubble Pulsation Rules in Simulated Deepwater Environment Based on High-Speed Photography Technology[J]. Engineering Blasting, 2015, 21(1): 5-9. doi: 10.3969/j.issn.1006-7051.2015.01.002
[190]	Li L, You Y. Time-frequency Energy Analysis of Deepwater Explosion Shock Wave Signals Based on HHT[C]//MATEC Web of Conferences. France: EDP Sciences, 2021, 336: 01017.
[191]	郝轶, 周章涛, 张显丕. 球型密闭容器内水下爆炸载荷特性研究[C]//第十二届全国冲击动力学学术会议论文集. 宁波: 中国力学学会, 2015.
[192]	马坤, 初哲, 王可慧, 等. 小当量炸药深水爆炸气泡脉动模拟实验[J]. 爆炸与冲击, 2015, 35(3): 320-325. doi: 10.11883/1001-1455-(2015)03-0320-06 Ma Kun, Chu Zhe, Wang Ke-hui, et al. Experimental Research on Bubble Pulse of Small Scale Charge Exploded under Simulated Deep Water[J]. Explosion and Shock Waves, 2015, 35(3): 320-325. doi: 10.11883/1001-1455-(2015)03-0320-06
[193]	Liang H, Zhang Q, Long R, et al. Pulsation Behavior of a Bubble Generated by a Deep Underwater Explosion[J]. AIP Advances, 2019, 9(2): 025108. doi: 10.1063/1.5086361
[194]	张亮. 典型装药深水爆炸特性研究[D]. 北京: 北京理工大学, 2020.
[195]	孟龙, 黄瑞源, 王金相, 等. 小当量梯恩梯水下爆炸气泡脉动的数值模拟[J]. 兵工学报, 2020, 41(S1): 64-71. Meng Long, Huang Rui-yuan, Wang Jin-xiang, et al. Numerical Simulation of Bubble Pulsation of Small-scaled TNT in Underwater Explosion[J]. Acta Armamentarii, 2020, 41(S1): 64-71.
[196]	Gao Y, Wang S, Zhang J, et al. Effects of Underwater Explosion Depth on Shock Wave Overpressure and Energy[J]. Physics of Fluids, 2022, 34(3): 037108. doi: 10.1063/5.0081107
[197]	Dular M, Coutier-Delgosha O. Thermodynamic Effects during Growth and Collapse of a Single Cavitation Bubble[J]. Journal of Fluid Mechanics, 2013, 736: 44-66. doi: 10.1017/jfm.2013.525
[198]	Petkovek M, Dular M I R. Measurements of the Thermodynamic Effects in Cavitating Flow[J]. International Journal of Heat and Fluid Flow, 2013, 44(1): 756-763.
[199]	郭锐, 俞旸晖. 水下爆炸声学效应研究现状与展望[J]. 水下无人系统学报, 2022, 30(3): 266-282. doi: 10.11993/j.issn.2096-3920.2022.03.001 Guo Rui, Yu Yang-hui. Progress and Prospect of the Acoustic Effects of Underwater Explosions[J]. Journal of Unmanned Undersea Systems, 2022, 30(3): 266-282. doi: 10.11993/j.issn.2096-3920.2022.03.001
[200]	程巍, 滕鹏晓, 吕君, 等. 基于大气声传播理论的爆炸声源能量估计[J]. 物理学报, 2021, 70(24): 135-141. Chen Wei, Teng Peng-xiao, Lü Jun, et al. Energy Estimation of Explosion Sound Source Based on Atmospheric Sound Propagation Theory[J]. Acta Physica Sinica, 2021, 70(24): 135-141.
[201]	Ghoshal R, Mitra N. Underwater Explosion Induced Shock Loading of Structures: Influence of Water Depth, Salinity and Temperature[J]. Ocean Engineering, 2016, 126(1): 22-28.
[202]	Keil A H. The Response of Ships to Underwater Explosions[J]. SNAME, 1961(69): 366-410.
[203]	Reid W D. The Response of Surface Ships to Underwater Explosions[R]. Melbourne: DSTO Aeronautical and Maritime Research Laboratory, 1996.
[204]	Keil A H. Introduction to Underwater Explosion Research[R]. Portsmouth, Virginia: UERD, Norfolk Naval Ship Yard, 1956.
[205]	Pusey H C. Technical Information Support for Survivability[J]. The Shock and Vibration, Bullitin, 1983(53): 21-31.
[206]	Rajendran R, Narasimhan K. A Shock Factor Based Approach for the Damage Assessment of Plane Plates Subjected to Underwater Explosion[J]. The Journal of Strain Analysis for Engineering Design, 2006, 41(6): 417-425. doi: 10.1243/03093247JSA120
[207]	Rajendran R. Effective Shock Factors for the Inelastic Damage Prediction of Clamped Plane Plates Subjected to Non-Contact Underwater Explosion[J]. The Journal of Strain Analysis for Engineering Design, 2009, 44(3): 211-220. doi: 10.1243/03093247JSA463
[208]	姚熊亮, 曹宇, 郭君, 等. 一种用于水面舰船的水下爆炸冲击因子[J]. 哈尔滨工程大学学报, 2007, 28(5): 501-509. doi: 10.3969/j.issn.1006-7043.2007.05.004 Yao Xiong-liang, Cao Yu, Guo Jun, et al. Research on the Response of Warships to Impulsive Factor of Underwater Explosions[J]. Journal of Harbin Engineering University, 2007, 28(5): 501-509. doi: 10.3969/j.issn.1006-7043.2007.05.004
[209]	姚熊亮, 郭君, 曹宇, 等. 在水下爆炸冲击波作用下的新型冲击因子[J]. 中国造船, 2008, 49(2): 52-60. doi: 10.3969/j.issn.1000-4882.2008.02.007 Yao Xiong-liang, Guo Jun, Cao Yu, et al. A New Impulsive Factors on the Underwater Shock Load[J]. Shipbuilding of China, 2008, 49(2): 52-60. doi: 10.3969/j.issn.1000-4882.2008.02.007
[210]	胡俊波, 张志华, 李庆民. 基于冲击因子的两个装药延时起爆目标毁伤评估方法研究[J]. 振动与冲击, 2012, 31(4): 92-95. doi: 10.3969/j.issn.1000-3835.2012.04.018 Hu Jun-bo, Zhang Zhi-hua, Li Qing-min. Damage Evaluation of Underwater Target by Means of Two Explosions Initiated Successively with Time Delay Based on Impulsive Factor[J]. Journal of Vibration and Shock, 2012, 31(4): 92-95. doi: 10.3969/j.issn.1000-3835.2012.04.018
[211]	胡宏伟, 宋浦, 王建灵, 等. 炸药水中爆炸冲击因子的新型计算方法[J]. 爆炸与冲击, 2014, 34(1): 11-16. doi: 10.3969/j.issn.1001-1455.2014.01.003 Hu Hong-wei, Song Pu, Wang Jian-ling, et al. A New Calculation Method for Shock Factor of Underwater Explosion[J]. Explosion and Shock Waves, 2014, 34(1): 11-16. doi: 10.3969/j.issn.1001-1455.2014.01.003
[212]	王树山, 张静骁, 王传昊, 等. 水中爆炸冲击波对靶体结构的毁伤准则研究[J]. 火炸药学报, 2020, 43(3): 262-270. doi: 10.14077/j.issn.1007-7812.201909015 Wang Shu-shan, Zhang Jing-xiao, Wang Chuan-hao, et al. Damage Criterion of Underwater Explosion Shock Wave on Target[J]. Chinese Journal of Explosives & Propellants, 2020, 43(3): 262-270. doi: 10.14077/j.issn.1007-7812.201909015