Eulerian Finite-Element Numerical Simulation Investigation on the Dynamic Characteristics of Out-of-Phase Bubbles in Underwater Explosions
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摘要: 该研究基于Euler有限元方法建立了水下爆炸异相气泡动力学模型,将计算结果和气泡统一理论以及异相爆炸试验进行对比验证计算模型的有效性. 通过和自由场单气泡进行对比分析,发现异相爆炸冲击波对气泡做功是异相爆炸气泡总能量增加的原因,相位差绝对值越接近π、距离参数越小气泡总能量损失越少,后产生的气泡会使先产生的气泡提前坍缩. 气泡的射流方向受相位差影响,相位差为零时产生对向射流,其他相位差产生反向射流.Abstract: An underwater explosion out-of-phase bubbles dynamics model was developed based on the Eulerian finite-element method, with the calculation results compared to the unified bubble theory and the out-of-phase explosion experiment to validate the calculation model. Compared with the case of a single bubble in the free field, it is found that the work done by the shock wave of the out-of-phase explosion on the bubble is the cause for the increase of the total energy of the bubble. The closer the absolute value of the phase difference is to π, the smaller the distance parameter is, and the less the total energy loss of the bubble is. The later bubble can cause the first bubble to collapse in advance. The jet direction of the bubble is influenced by the phase difference. When the phase difference is zero, jets are directed toward each other, but for other phase differences, the backward jets occur.edited-byedited-by1) (我刊编委张阿漫来稿)
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图 2 EFEM计算结果与气泡统一理论[40]计算结果对比
注 为了解释图中的颜色,读者可以参考本文的电子网页版本,后同.
Figure 2. Comparisons between the EFEM calculation results and the unified theory calculation results
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[1] 贺铭, 张阿漫, 刘云龙. 近场水下爆炸气泡与双层破口结构的相互作用[J]. 爆炸与冲击, 2020, 40(11): 111402. https://www.cnki.com.cn/Article/CJFDTOTAL-BZCJ202011004.htmHE Ming, ZHANG Aman, LIU Yunlong. Interaction of the underwater explosion bubbles and nearby double-layer structures with circular holes[J]. Explosion and Shock Waves, 2020, 40(11): 111402. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-BZCJ202011004.htm [2] 张阿漫, 王诗平, 彭玉祥, 等. 水下爆炸与舰船毁伤研究进展[J]. 中国舰船研究, 2019, 14(3): 1-13. doi: 10.19693/j.issn.1673-3185.01608ZHANG Aman, WANG Shiping, PENG Yuxiang, et al. Research progress in underwater explosion and its damage to ship structures[J]. Chinese Journal of Ship Research, 2019, 14(3): 1-13. (in Chinese) doi: 10.19693/j.issn.1673-3185.01608 [3] 贺啸秋, 熊永亮, 徐顺, 等. 底部加热肥皂泡上准二维湍流的数值模拟[J]. 应用数学和力学, 2022, 43(10): 1086-1104. doi: 10.21656/1000-0887.430143HE Xiaoqiu, XIONG Yongliang, XU Shun, et al. Numerical simulation of the quasi-2D turbulence on a half soap bubble heated at the bottom[J]. Applied Mathematics and Mechanics, 2022, 43(10): 1086-1104. (in Chinese) doi: 10.21656/1000-0887.430143 [4] 孙涛, 庞明军, 费洋. 气泡间距对受污染球形气泡界面性质和尾流的影响[J]. 应用数学和力学, 2020, 41(10): 1157-1170. doi: 10.21656/1000-0887.410099SUN Tao, PANG Mingjun, FEI Yang. Effects of bubble spacings on interface properties and wake flow for 2 contaminated spherical bubbles[J]. Applied Mathematics and Mechanics, 2020, 41(10): 1157-1170. (in Chinese) doi: 10.21656/1000-0887.410099 [5] VAN WIJNGAARDEN L. Mechanics of collapsing cavitation bubbles[J]. Ultrasonics Sonochemistry, 2016, 29: 524-527. doi: 10.1016/j.ultsonch.2015.04.006 [6] ZHANG S, KHOO B, ZHANG A M. Study of three-dimensional air gun bubble pulsation and the surrounding fluid pressure with finite volume method[J]. Ocean Engineering, 2021, 221: 108500. doi: 10.1016/j.oceaneng.2020.108500 [7] SUPPONEN O, OBRESCHKOW D, FARHAT M. Rebounds of deformed cavitation bubbles[J]. Physical Review Fluids, 2018, 3(10): 103604. doi: 10.1103/PhysRevFluids.3.103604 [8] 杜志鹏, 张磊, 谌勇, 等. 泡沫覆盖层对水下爆炸气泡射流防护机理缩比试验研究[J]. 应用数学和力学, 2022, 43(5): 569-576. doi: 10.21656/1000-0887.420367DU Zhipeng, ZHANG Lei, CHEN Yong, et al. Reduced-scale experiment study on the protective mechanism of foam coating against underwater explosion bubble jet[J]. Applied Mathematics and Mechanics, 2022, 43(5): 569-576. (in Chinese) doi: 10.21656/1000-0887.420367 [9] 彭玉祥, 张阿漫, 薛冰, 等. 强冲击作用下舰船结构毁伤的三维无网格SPH-RKPM方法数值模拟[J]. 中国科学: 物理学力学天文学, 2021, 51(12): 124614. https://www.cnki.com.cn/Article/CJFDTOTAL-JGXK202112014.htmPENG Yuxiang, ZHANG Aman, XUE Bing, et al. Numerical investigation of ship structure damage subject to strong impact using a 3D meshless SPH-RKPM method[J]. Scientia Sinica: Physica, Mechanica & Astronomica, 2021, 51(12): 124614. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JGXK202112014.htm [10] TANG H, LIU Y L, CUI P, et al. Numerical study on the bubble dynamics in a broken confined domain[J]. Journal of Hydrodynamics, 2020, 32(6): 1029-1042. doi: 10.1007/s42241-020-0078-1 [11] 李帅. 水下爆炸气泡射流载荷特性研究[D]. 博士学位论文. 哈尔滨: 哈尔滨工程大学, 2016.LI Shuai. Characteristics of the jet impact pressure generated by an underwater explosion bubble[D]. PhD Thesis. Harbin: Harbin Engineering University, 2016. (in Chinese) [12] 张阿漫, 曾令玉, 王诗平, 等. 水下爆炸气泡融合动态特性研究[J]. 应用数学和力学, 2010, 31(2): 163-170. doi: 10.3879/j.issn.1000-0887.2010.02.005ZHANG Aman, ZENG Lingyu, WANG Shiping, et al. Study on fusion dynamics of underwater explosion bubbles[J]. Applied Mathematics and Mechanics, 2010, 31(2): 163-170. (in Chinese) doi: 10.3879/j.issn.1000-0887.2010.02.005 [13] 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 [14] CHO Y S, BAEK S H, LEE J, et al. Interaction of two bubbles in water[J]. AIP Conference Proceedings, 2000, 505: 1145-1148. doi: 10.1063/1.1307304 [15] TOMITA Y, SATO K. Pulsed jets driven by two interacting cavitation bubbles produced at different times[J]. Journal of Fluid Mechanics, 2017, 819: 465-493. doi: 10.1017/jfm.2017.185 [16] CHEW L W, KHOO B C, KLASEBOER E, et al. Interaction of two differently sized bubbles in a free field[J]. International Journal of Modern Physics: Conference Series, 2012, 19: 180-184. doi: 10.1142/S2010194512008720 [17] LIANG W, CHEN R, ZHENG J, et al. Interaction of two approximately equal-size bubbles produced by sparks in a free field[J]. Physics of Fluids, 2021, 33(6): 067107. doi: 10.1063/5.0051550 [18] 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. DOI: 10.1017/jfm.2020.400. [19] LI S M, LIU Y L, WANG Q, et al. Dynamics of a buoyant pulsating bubble near two crossed walls[J]. Physics of Fluids, 2021, 33(7): 073310. doi: 10.1063/5.0057594 [20] ZHANG A M, WANG S P, HUANG C, et al. Influences of initial and boundary conditions on underwater explosion bubble dynamics[J]. European Journal of Mechanics B: Fluids, 2013, 42: 69-91. doi: 10.1016/j.euromechflu.2013.06.008 [21] HIRT C W, NICHOLS B D. 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 [22] LI T, WANG S, LI S, et al. Numerical investigation of an underwater explosion bubble based on FVM and VOF[J]. Applied Ocean Research, 2018, 74: 49-58. doi: 10.1016/j.apor.2018.02.024 [23] LEE J, SON G. A sharp-interface level-set method for compressible bubble growth with phase change[J]. International Communications in Heat and Mass Transfer, 2017, 86: 1-11. doi: 10.1016/j.icheatmasstransfer.2017.05.016 [24] OSHER S, FEDKIW R P. Level set methods: an overview and some recent results[J]. Journal of Computational Physics, 2001, 169(2): 463-502. doi: 10.1006/jcph.2000.6636 [25] ZHU Z, SONG Z, SHAO Z, et al. Simulation of imbibition in porous media with a tree-shaped fracture following the level-set method[J]. Physics of Fluids, 2021, 33(8): 082109. doi: 10.1063/5.0060519 [26] HUA J, STENE J F, LIN P. Numerical simulation of 3D bubbles rising in viscous liquids using a front tracking method[J]. Journal of Computational Physics, 2008, 227(6): 3358-3382. doi: 10.1016/j.jcp.2007.12.002 [27] LIU L, YAO X, ZHANG A, et al. Numerical analysis of the jet stage of bubble near a solid wall using a front tracking method[J]. Physics of Fluids, 2017, 29(1): 012105. doi: 10.1063/1.4974073 [28] TRYGGVASON G, BUNNER B, ESMAEELI A, et al. A front-tracking method for the computations of multiphase flow[J]. Journal of Computational Physics, 2001, 169(2): 708-759. doi: 10.1006/jcph.2001.6726 [29] BARRAS G, SOULI M, AQUELET N, et al. Numerical simulation of underwater explosions using an ALE method. The pulsating bubble phenomena[J]. Ocean Engineering, 2012, 41: 53-66. doi: 10.1016/j.oceaneng.2011.12.015 [30] 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 [31] HE M, LIU Y L, ZHANG S, et al. Research on characteristics of deep-sea implosion based on Eulerian finite element method[J]. Ocean Engineering, 2022, 244: 110270. doi: 10.1016/j.oceaneng.2021.110270 [32] LIU Y, ZHANG A M, TIAN Z, et al. Investigation of free-field underwater explosion with Eulerian finite element method[J]. Ocean Engineering, 2018, 166: 182-190. [33] TIAN Z L, LIU Y L, ZHANG A M, et al. Energy dissipation of pulsating bubbles in compressible fluids using the Eulerian finite-element method[J]. Ocean Engineering, 2020, 196: 106714. [34] TIAN Z L, ZHANG A M, LIU Y L, et al. A new 3-D multi-fluid model with the application in bubble dynamics using the adaptive mesh refinement[J]. Ocean Engineering, 2021, 230: 108989. [35] XU L Y, WANG S P, LIU Y L, et al. Numerical simulation on the whole process of an underwater explosion between a deformable seabed and a free surface[J]. Ocean Engineering, 2021, 219: 108311. [36] LIU N N, ZHANG A M, LIU Y L, et al. Numerical analysis of the interaction of two underwater explosion bubbles using the compressible Eulerian finite-element method[J]. Physics of Fluids, 2020, 32(4): 046107. [37] TIAN Z L, ZHANG A M, LIU Y L, et al. Transient fluid-solid interaction with the improved penalty immersed boundary method[J]. Ocean Engineering, 2021, 236(1): 109537. [38] 田昭丽. 改进的欧拉有限元方法及水下爆炸近场载荷特性研究[D]. 博士学位论文. 哈尔滨: 哈尔滨工程大学, 2020.TIAN Zhaoli. The improved Eulerian finite-element method and the near-field load characteristics of underwater explosion[D]. PhD Thesis. Harbin: Harbin Engineering University, 2020. (in Chinese) [39] LEE E, HORNIG H, KURY J. Adiabatic expansion of high explosive detonation products[R]. Livermore, CA, USA: University of California Radiation Laboratory at Livermore, 1968. [40] ZHANG A M, LI S M, CUI P, et al. A unified theory for bubble dynamics[J]. Physics of Fluids, 2023, 35(3): 033323. [41] LIU N N, ZHANG A M, CUI P, et al. Interaction of two out-of-phase underwater explosion bubbles[J]. Physics of Fluids, 2021, 33(10): 106103. -