Page 74 - 《爆炸与冲击》2026年第01期

第 46 卷 王天召，等： 水下接触爆炸气泡脉动特性的理论研究 第 1 期

自由场气泡在最大半径、初始条件以及脉动周期间的定量关系。理论推导表明，接触爆炸气泡最大半
径、初始半径、脉动周期分别为自由场工况的 2 1/3 倍（理论比例系数 1.26），实际工况中因流体可压缩性、
气泡不稳定变形等因素导致的能量损失，上述比例系数略大于实际值。
(2) 采用 LS-DYNA 对自由场与接触爆炸工况进行有限元模拟，结果表明接触爆炸气泡的最大半径
与脉动周期均显著大于自由场，模拟值与理论预测的误差在 5% 以内。实验研究中，接触爆炸气泡的最
大半径（10.60 cm）和周期（16.97 ms）较自由场（9.59 cm，15.97 ms）分别增加约 10% 和 6%，与理论误差趋
势一致，验证了模型的适用性。
本文的模型建立在流体无黏且不可压缩假设基础上，忽略了气泡脉动过程中的能量损失，通过实验
与数值模拟结果，验证了模型对于小当量浅水爆炸气泡的适用性。未来研究将综合考虑流体可压缩性、
黏性效应及复杂边界条件等因素的影响，以提升模型的普适性。

参考文献：
[1] LAMB H. The early stages of a submarine explosion [J]. The London, Edinburg and Dublin Philosophical Magazine and
Journal of Science, 1923: 257–265. DOI: 10.1080/14786442308634111.
[2] RAYLEIGH L. On the pressure developed in a liquid during the collapse of a spherical [J]. The London, Edinburg and Dublin
Philosophical Magazine and Journal of Science, 1917: 94–98. DOI: 10.1080/14786440808635681.
[3] KELLER J, KOLODNER I I. Damping of underwater explosion bubble oscillations [J]. Journal of Apply Physics, 1956, 27:
1152. DOI: 10.1063/1.1722221.
[4] KELLER J, MIKSIS M. Bubble oscillations of large amplitude [J]. Journal of the Acoustical Society of American, 1980, 68:
628. DOI: 10.1121/1.384720.
[5] PROSPERETTI A, LEZZI A. Bubble dynamics in a compressible liquid. part 1. first-order theory [J]. Journal of Fluid
Mechanics , 1986: 457–478. DOI: 10.1017/S0022112086000460.
[6] 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.
[7] GEERS T L. Transient response analysis of complex submerged structures [J]. Journal of the Acoustical Society of America,
1974, 55(S1): 26–26. DOI: 10.1121/1.1919626.
[8] GEERS T L, HUNTER K S. An integrated wave-effects model for an underwater explosion bubble [J]. Journal of the
Acoustical Society of America, 2002, 111(4): 1584–1601. DOI: 10.1121/1.1458590.
[9] GEERS T L. Residual potential and approximate methods for three-dimensional fluid-structure interaction problems [J].
Journal of the Acoustical Society of America, 1971, 49(5B): 1505–1510. DOI: 10.1121/1.1912526.
[10] COLE R H. Underwater explosions [M]. Princeton: Princeton University Press, 1948.
[11] HUNTER K S, GEERS T L. Pressure and velocity fields produced by an underwater explosion [J]. Journal of the Acoustical
Society of America, 2004, 115(4): 1483–1496. DOI: 10.1121/1.1648680.
[12] VERNON T A. Whipping response of ship hulls from underwater explosion bubble loading [R]. Dartmouth: National
Defence, Research and Development Branch, 1986.
[13] ZHANG A M, LI S M, CUI P, et al. A unified theory for bubble dynamics [J]. Physics of Fluids, 2023, 35(3): 033323. DOI:
10.1063/5.0145415.
[14] ZHANG A M, LI S M, XU R Z, et al. A theoretical model for compressible bubble dynamics considering phase transition and
migration [J]. Journal of Fluid Mechanics, 2024, 999: A58. DOI: 10.1017/jfm.2024.954.
[15] 周霖, 谢中元, 陈勇. 炸药水下爆炸气泡脉动周期工程计算方法 [J]. 兵工学报, 2009, 30(9): 1202–1205. DOI: 10.3321/j.
issn:1000-1093.2009.09.010.
ZHOU L, XIE Z Y, CHEN Y. Engineering calculation method of bubble pulsation period for underwater explosion of
explosives [J]. Acta Armamentarii, 2009, 30(9): 1202–1205. DOI: 10.3321/j.issn:1000-1093.2009.09.010.
[16] 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): 2508–2516. DOI: 10.
12382/bgxb.2021.0560.
WANG S S, LIANG C, GAO Y, et al. Engineering model of overpressure peak of secondary pressure wave in deep water

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