Investigation of Coupling Effects of Double Bubbles Based on the EFEM and the Unified Bubble Equation

XU Liuyi; LI Shimin; WANG Shiping; LIU Yunlong; ZHANG Aman

doi:10.21656/1000-0887.450018

Volume 45 Issue 7

Jul. 2024

Turn off MathJax

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2024 > 45(7): 835-849

XU Liuyi, LI Shimin, WANG Shiping, LIU Yunlong, ZHANG Aman. Investigation of Coupling Effects of Double Bubbles Based on the EFEM and the Unified Bubble Equation[J]. Applied Mathematics and Mechanics, 2024, 45(7): 835-849. doi: 10.21656/1000-0887.450018

Citation:

PDF( 5530 KB)

Investigation of Coupling Effects of Double Bubbles Based on the EFEM and the Unified Bubble Equation

doi: 10.21656/1000-0887.450018

College of Shipbuilding Engineering, Harbin Engineering University,Harbin 150001， P.R. China

Received Date: 2024-01-25
Rev Recd Date: 2024-04-02
Publish Date: 2024-07-01

Abstract

Abstract

Based on the Eulerian finite element method (EFEM), an axially symmetric numerical model was established for 2-bubble underwater pulsation. The accuracy of the model and the convergence of the mesh were fully verified by comparison with the unified bubble equation and experimental results. The calculation results show that, the unified bubble equation is more accurate than other bubble theories in predicting the bubble dynamic behavior and the pressure load in the flow field. Combined with the EFEM and the unified bubble equation, the effects of buoyancy parameter δ and strength parameter ε on the coupling law of double bubbles were studied. For buoyancy parameter δ≤0.15, the upper bubble will produce a vertical downward jet under the action of the lower bubble, and the lower bubble boundary is like the solid wall boundary. For δ increasing to 0.2, the influence of the lower bubble on the upper bubble weakens, the buoyancy effect becomes more prominent and the jet direction of the upper bubble is vertical upward. Strength parameter ε has no obvious effect on the coupling between bubbles, but its effect on the bubble jet velocity decreases significantly for ε≥150.
- bubble dynamics,
- EFEM,
- unified bubble equation,
- bubble coupling

(Contributed by LIU Yunlong, M.AMM Youth Editorial Board & ZHANG Aman, M.AMM Editorial Board)

FullText(HTML)

References(47)

References

[1]	LI S, MEER D V D, ZHANG A M, et al. Modelling large scale airgun-bubble dynamics with highly non-spherical features[J]. International Journal of Multiphase Flow, 2020, 122 : 103143. doi: 10.1016/j.ijmultiphaseflow.2019.103143
[2]	LANGHAMMER J, LANDRØ M. High-speed photography of the bubble generated by an airgun[J]. Geophysical Prospecting, 1996, 44 (1): 153-172. doi: 10.1111/j.1365-2478.1996.tb00143.x
[3]	CUI P, ZHANG A M, WANG S P. Shock wave emission and ice breaking effect of multiple interacting bubbles[J]. Ocean Engineering, 2021, 234 : 109175. doi: 10.1016/j.oceaneng.2021.109175
[4]	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. doi: 10.1017/jfm.2020.400
[5]	PITT W, HUSSEINI G, STAPLES B. Ultrasonic drug delivery: a general review[J]. Expert Opinion on Drug Delivery, 2004, 1 (1): 37-56. doi: 10.1517/17425247.1.1.37
[6]	CHEN H, HWANG J. Ultrasound-targeted microbubble destruction for chemotherapeutic drug delivery to solid tumors[J]. Journal of Therapeutic Ultrasound, 2013, 1 (1): 10. doi: 10.1186/2050-5736-1-10
[7]	张阿漫, 明付仁, 刘云龙, 等. 水下爆炸载荷特性及其作用下的舰船毁伤与防护研究综述[J]. 中国舰船研究, 2023, 18 (3): 139-154. https://www.cnki.com.cn/Article/CJFDTOTAL-JCZG202303014.htm ZHANG Aman, MING Furen, LIU Yunlong, et al. Review of research on underwater explosion related to load characteristics and ship damage and protection[J]. Chinese Journal of Ship Research, 2023, 18 (3): 139-154. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JCZG202303014.htm
[8]	陈岩武, 孙远翔, 王成. 水下爆炸载荷下舰船双层底部结构的毁伤特性[J]. 兵工学报, 2023, 44 (3): 670-681. https://www.cnki.com.cn/Article/CJFDTOTAL-BIGO202303004.htm CHEN Yanwu, SUN Yuanxiang, WANG Cheng. Damage characteristics of ships double bottom structure subjected to underwater explosion[J]. Acta Armamentarii, 2023, 44 (3): 670-681. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-BIGO202303004.htm
[9]	闫秋实, 常松, 李述涛. "北溪"天然气管道爆炸毁伤探讨与分析[J]. 防护工程, 2022, 44 (6): 1-6. doi: 10.3969/j.issn.1674-1854.2022.06.001 YAN Qiushi, CHANG Song, LI Shutao. Exploration and analysis on explosion damage of "Beixi" natural gas pipeline[J]. Protective Engineering, 2022, 44 (6): 1-6. (in Chinese) doi: 10.3969/j.issn.1674-1854.2022.06.001
[10]	TIAN Z L, LIU Y L, ZHANG A M, et al. Analysis of breaking and re-closure of a bubble near a free surface based on the Eulerian finite element method[J]. Computers & Fluids, 2018, 170 : 41-52.
[11]	TONG S Y, ZHANG S, WANG S P, et al. Characteristics of the bubble-induced pressure, force, and impulse on a rigid wall[J]. Ocean Engineering, 2022, 255 : 111484. doi: 10.1016/j.oceaneng.2022.111484
[12]	吕可, 邹佳俊, 陈颖, 等. 近刚性壁面异相双气泡耦合及射流增强效应研究[J]. 力学学报, 2023, 55 (8): 1605-1617. https://www.cnki.com.cn/Article/CJFDTOTAL-LXXB202308001.htm LÜ Ke, ZOU Jiajun, CHEN Ying, et al. Study on the interaction and jet enhancement effect of two out-of-phase bubbles near a rigid boundary[J]. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55 (8): 1605-1617. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-LXXB202308001.htm
[13]	王诗平, 张阿漫, 刘云龙, 等. 同相气泡耦合特性实验研究[J]. 力学学报, 2012, 44 (1): 56-64. https://www.cnki.com.cn/Article/CJFDTOTAL-LXXB201201010.htm WANG Shiping, ZHANG Aman, LIU Yunlong, et al. Experimental study on interaction of inphase bubbles[J]. Chinese Journal of Theoretical and Applied Mechanics, 2012, 44 (1): 56-64. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-LXXB201201010.htm
[14]	FONG S W, ADHIKARI D, KLASEBOER E, et al. Interactions of multiple spark-generated bubbles with phase differences[J]. Experiments in Fluids, 2009, 46 : 705-724. doi: 10.1007/s00348-008-0603-4
[15]	AVACHAT S, ZHOU M. Response of submerged metallic sandwich structures to underwater impulsive loads[J]. Journal of Mechanics of Materials, 2015, 10 (1): 17-41.
[16]	HIGDON C E. Water barrier ship self defense lethality[J]. Naval Engineers Journal, 2010, 112 (4): 121-135.
[17]	MAKUTA T, TAKEMURA F, HIHARA E, et al. Generation of micro gas bubbles of uniform diameter in an ultrasonic field[J]. Journal of Fluid Mechanics, 2006, 548 : 113-131.
[18]	KELLER J B, MIKSIS M J. Bubble oscillations of large amplitude[J]. Journal of Acoustical Society of America, 1980, 68 : 628-633.
[19]	ZHANG A M, LI S M, CUI P, et al. A unified theory for bubble dynamics[J]. Physics of Fluids, 2023, 35 (3): 28.
[20]	ZHANG A M, LI S M, CUI P, et al. Theoretical study on bubble dynamics under hybrid-boundary and multi-bubble conditions using the unified equation[J]. Science China: Physics Mechanics & Astronomy, 2023, 66 (12): 16. http://www.zhangqiaokeyan.com/academic-journal-cn_science-china-information-sciences_thesis/02012116945541.html
[21]	ZHANG A M, LI S M, CUI P, et al. Interactions between a central bubble and a surrounding bubble cluster[J]. Theoretical and Applied Mechanics Letters, 2023, 13 (3): 100438.
[22]	谈乃正, 李世民, 詹立蕾, 等. 基于气泡统一方程的声场双气泡耦合作用研究[J]. 哈尔滨工程大学学报, 2024, 45 (2): 1-9. https://www.cnki.com.cn/Article/CJFDTOTAL-HEBG202402001.htm TAN Naizheng, LI Shimin, ZHAN Lilei, et al. A study on the coupling effect of double bubbles in sound field based on the unified equation for bubble dynamics[J]. Journal of Harbin Engineering University, 2024, 45 (2): 1-9. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-HEBG202402001.htm
[23]	LI S M, ZHANG A M, CUI P, et al. Vertically neutral collapse of a pulsating bubble at the corner of a free surface and a rigid wall[J]. Journal of Fluid Mechanics, 2023, 962 : 41.
[24]	LI S, ZHANG A M, HAN R. 3D model for inertial cavitation bubble dynamics in binary immiscible fluids[J]. Journal of Computational Physics, 2023, 494 : 112508.
[25]	黄晓婷, 孙鹏楠, 彭玉祥, 等. 基于新型轴对称无网格方法的水下爆炸冲击波和气泡运动数值模拟[J]. 同济大学学报(自然科学版), 2023, 51 (6): 818-826. https://www.cnki.com.cn/Article/CJFDTOTAL-TJDZ202306003.htm HUANG Xiaoting, SUN Pengnan, PENG Yuxiang, et al. Numerical simulation of underwater explosion shock waves and bubbles based on a novel axisymmetric meshless method[J]. Journal of Tongji University(Natural Science), 2023, 51 (6): 818-826. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-TJDZ202306003.htm
[26]	LI M K, ZHANG A M, MING F R, et al. A coupled smoothed particle hydrodynamics-finite volume method for three-dimensional modeling of bubble dynamics[J]. Physics of Fluids, 2023, 35 (5): e17922.
[27]	ZHANG Y F, LIU L T, WANG J X, et al. Study on the impact characteristics of underwater explosion bubble jets induced by plate structure[J]. Ocean Engineering, 2022, 266 : 19.
[28]	GONG S W. Transient response of stiffened composite submersible hull to underwater shock and bubble[J]. Composite Structures, 2019, 213 : 243-251.
[29]	XU L Y, TIAN Y, LIU X B, et al. Numerical investigation on jet penetration capacity of hypervelocity shaped charge in underwater explosion[J]. Ocean Engineering, 2023, 281 : 114668.
[30]	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.
[31]	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.
[32]	LIU W T, MING F R, ZHANG A M, et al. Continuous simulation of the whole process of underwater explosion based on Eulerian finite element approach[J]. Applied Ocean Research, 2018, 80 : 125-135.
[33]	HE M, WANG S P, REN S F, et al. Numerical study of effects of stand-off distance and gravity on large scale bubbles near a breach[J]. Applied Ocean Research, 2021, 117 (3): 102946.
[34]	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.
[35]	LIU W T, ZHANG A M, MIAO X H, et al. Investigation of hydrodynamics of water impact and tail slamming of high-speed water entry with a novel immersed boundary method[J]. Journal of Fluid Mechanics, 2023, 958 : A42.
[36]	唐皓, 刘云龙, 冯集团, 等. 水下爆炸异相气泡动力学特性的Euler有限元数值模拟研究[J]. 应用数学和力学, 2023, 44 (8): 895-908. doi: 10.21656/1000-0887.440047 TANG Hao, LIU Yunlong, FENG Jituan, et al. Eulerian finite-element numerical simulation investigation on the dynamic characteristics of out-of-phase bubbles in underwater explosions[J]. Applied Mathematics and Mechanics, 2023, 44 (8): 895-908. (in Chinese) doi: 10.21656/1000-0887.440047
[37]	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 : 046107.
[38]	HAN R, ZHANG A M, LI S, et al. Experimental and numerical study of the effects of a wall on the coalescence and collapse of bubble pairs[J]. Physics of Fluids, 2018, 30 (4): 042107.
[39]	LI S, ZHANG A M, HAN R, et al. Experimental and numerical study of two underwater explosion bubbles: coalescence, fragmentation and shock wave emission[J]. Ocean Engineering, 2019, 190 : 106414.
[40]	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.
[41]	WANG C, KHOO B C. An indirect boundary element method for three-dimensional explosion bubbles[J]. Journal of Computational Physics, 2004, 19 (4): 451-480.
[42]	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.
[43]	LI S, KHOO B C, ZHANG A M, et al. Bubble-sphere interaction beneath a free surface[J]. Ocean Engineering, 2018, 169 : 469-483.
[44]	BENSON D J, OKAZAWA S. Contact in a multi-material Eulerian finite element formulation[J]. Computer Methods in Applied Mechanics and Engineering, 2004, 193 (39): 4277-4298.
[45]	LIU Y L, ZHANG A M, TIAN Z L, et al. Dynamical behavior of an oscillating bubble initially between two liquids[J]. Physics of Fluids, 2019, 31 : 09211.
[46]	LIU Y L, ZHANG A M, TIAN Z L, et al. Investigation of free-field underwater explosion with Eulerian finite element method[J]. Ocean Engineering, 2018, 166 : 182-190.
[47]	佟施宇. 近场水下爆炸与典型结构耦合特性实验与数值研究[D]. 哈尔滨: 哈尔滨工程大学, 2022. TONG Shiyu. Experimental and numerical study on coupling characteristics of near-field underwater explosion and typical structures[D]. Harbin: Harbin Engineering University, 2022. (in Chinese)