流体黏性及表面张力对气泡运动特性的影响

艾旭鹏; 倪宝玉

doi:10.7498/aps.66.234702

摘要

基于气泡边界层理论，引入黏性修正，采用边界积分法，考虑黏性效应和表面张力在单气泡以及双气泡耦合作用过程中的影响.首先将建立的数值模型与Rayleigh-Plesset的解析解进行对比，发现二者符合良好，验证了数值模型的有效性；在此基础上，建立考虑流体弱黏性效应的双气泡耦合模型，研究流体黏性和表面张力作用下，气泡表面变形、射流速度、流场能量转换等物理量的变化规律；最后研究雷诺数和韦伯数对于气泡脉动特性的影响规律.结果表明，流体黏性会抑制气泡脉动和气泡射流发展，降低气泡半径和射流速度；表面张力不改变气泡脉动幅值，但缩短了脉动周期，提升气泡势能.

关键词:

气泡 /
边界层 /
黏性 /
表面张力

Abstract

Boundary integral simulation has been conducted to study the motion and deformation of bubbles with weak viscous and surface tension effects in fluid. Both normal and tangential stress boundary conditions are satisfied and the weak viscous effects are confined to the thin boundary layers around bubble surfaces, which is also known as boundary layer theory of bubble. By using this method, the influence of viscosity and surface tension of fluid on the motion of bubbles has been studied. Both axisymmetric and three-dimensional numerical results are compared with analytical results of Rayleigh-Plesset equation. Good agreement between them is achieved, which validates the numerical model. On this basis, interaction model between two vertically placed bubbles is established, by taking the surface tension, gravity, and viscous effects into consideration. Variations of physical quantities including bubble deformation, jet velocity, and energy of fluid are studied. Last but not least, the influence of viscosity and surface tension on the motion of a spherical bubble is investigated. It is found that viscous effects of fluid depress the pulsation of bubble and part of fluid energy is transformed into viscous dissipation energy. As a result, the development of bubble jet, the radius of the bubble, and the jet velocity are reduced gradually. On the other hand, the surface tension of fluid does not change the range of the bubble pulsation but reduces the period of the bubble pulsation and enhances the potential energy of the bubble. This model and numerical results aim to provide some references for bubble dynamics in bioengineering, chemical engineering, naval architecture, and ocean engineering, etc.

Keywords:

作者及机构信息

1.
哈尔滨工程大学船舶工程学院, 哈尔滨 150001

通信作者: 倪宝玉, nibaoyu@hrbeu.edu.cn

基金项目: 国家自然科学基金（批准号：51639004，51579054，11472088）、中央高校基本科研业务基金（批准号：HEUCFM170110，HEUCFP201701，HEUCFP201777）和哈尔滨工程大学学科创新引智计划资助的课题.

Authors and contacts

1.
College of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, China

Corresponding author: Ni Bao-Yu, nibaoyu@hrbeu.edu.cn

Funds: Supported by the National Natural Science Foundation of China (Grant Nos. 51639004, 51579054, 11472088), the Fundamental Research Funds for the Central Universities, China (Grant Nos. HEUCFM170110, HEUCFP201701, HEUCFP201777), and the 111 Project of Harbin Engineering University, China.

参考文献

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[5]	Rungsiyaphornrat S, Klaseboer E, Khoo B C, Yeo K S 2003 Comput. Fluids 32 1049
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[8]	Guo X, Cai C, Xu G, Yang Y, Tu J, Huang P, Zhang D 2017 Ultrason. Sonoche. 39 863
[9]	Zhang Y, Zhang Y, Li S 2017 Ultrason. Sonoche. 35 431
[10]	Liu L T, Yao X L, Zhang A M, Chen Y Y 2017 Phys. Fluids 29 012105
[11]	Miksis M J, Vanden-Broeck J M, Keller J B 1982 J. Fluid Mech. 123 31
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[14]	Georgescu S C, Achard J L, Canot E 2002 Euro. J. Mech. B-Fluids 21 265
[15]	Klaseboer E, Manica R, Chan D Y C, Khoo B C 2011 Eng. Anal. Bound. Elem. 35 489
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[20]	Zhang A M, Ni B Y 2014 Comput. Fluids 92 22
[21]	Li S, NI B Y 2016 Eng. Anal. Bound. Elem. 68 63
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施引文献

[1]	Boulton-Stone J M, Blake J R 1993 J. Fluid Mech. 254 437
[2]	Cui P, Zhang A M, Wang S P 2016 Phys. Fluids 28 117103
[3]	Xue Y Z, Cui B, Ni B Y 2016 Ocean Eng. 118 58
[4]	Sato K, Tomita Y, Shima A 1994 J. Acoust. Soc. Am. 95 2416
[5]	Rungsiyaphornrat S, Klaseboer E, Khoo B C, Yeo K S 2003 Comput. Fluids 32 1049
[6]	Chew L W, Klaseboer E, Ohl S W, Khoo B C 2011 Phys. Rev. E 84 0663078
[7]	Han R, Li S, Zhang A M, Wang Q X 2016 Phys. Fluids 28 062104
[8]	Guo X, Cai C, Xu G, Yang Y, Tu J, Huang P, Zhang D 2017 Ultrason. Sonoche. 39 863
[9]	Zhang Y, Zhang Y, Li S 2017 Ultrason. Sonoche. 35 431
[10]	Liu L T, Yao X L, Zhang A M, Chen Y Y 2017 Phys. Fluids 29 012105
[11]	Miksis M J, Vanden-Broeck J M, Keller J B 1982 J. Fluid Mech. 123 31
[12]	Lundgren S, Mansour N 1988 J. Fluid Mech. 194 479
[13]	Boulton-Stone J M 1995 J. Fluid Mech. 302 231
[14]	Georgescu S C, Achard J L, Canot E 2002 Euro. J. Mech. B-Fluids 21 265
[15]	Klaseboer E, Manica R, Chan D Y C, Khoo B C 2011 Eng. Anal. Bound. Elem. 35 489
[16]	Joseph D D, Wang J 2004 J. Fluid Mech. 505 365
[17]	Lind S J, Phillips T N 2012 Theor. Comp. Fluid Dyn. 26 245
[18]	Lind S J, Phillips T N 2013 Phys. Fluids 25 022014
[19]	Ni B Y, Li S, Zhang A M 2013 Acta Phys. Sin. 62 124704 (in Chinese)[倪宝玉, 李帅, 张阿漫 2013 62 124704]
[20]	Zhang A M, Ni B Y 2014 Comput. Fluids 92 22
[21]	Li S, NI B Y 2016 Eng. Anal. Bound. Elem. 68 63
[22]	Lamb H 1932 Hydrodynamics (sixth Ed.) (Cambridge:Cambridge University Press) pp580-581
[23]	Wu G X 1991 Appl. Ocean Res. 13 317
[24]	Rayleigh J W 1917 Philos. Mag. 34 94
[25]	Zhang A M, Wang S P, Wu G X 2013 Eng. Anal. Bound. Elem. 37 1179
[26]	Best J P 1993 J. Fluid Mech. 251 79

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