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超声场下刚性界面附近溃灭空化气泡的速度分析

郭策 祝锡晶 王建青 叶林征

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超声场下刚性界面附近溃灭空化气泡的速度分析

郭策, 祝锡晶, 王建青, 叶林征

Velocity analysis for collapsing cavitation bubble near a rigid wall under an ultrasound field

Guo Ce, Zhu Xi-Jing, Wang Jian-Qing, Ye Lin-Zheng
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  • 为了揭示刚性界面附近气泡空化参数与微射流的相互关系, 从两气泡控制方程出发, 利用镜像原理, 建立了考虑刚性壁面作用的空化泡动力学模型. 数值对比了刚性界面与自由界面下气泡的运动特性, 并分析了气泡初始半径、气泡到固壁面的距离、声压幅值和超声频率对气泡溃灭的影响. 在此基础上, 建立了气泡溃灭速度和微射流的相互关系. 结果表明: 刚性界面对气泡振动主要起到抑制作用; 气泡溃灭的剧烈程度随气泡初始半径和超声频率的增加而降低, 随着气泡到固壁面距离的增加而增加; 声压幅值存在最优值, 固壁面附近的气泡在该最优值下气泡溃灭最为剧烈; 通过研究气泡溃灭速度和微射流的关系发现, 调节气泡溃灭速度可以达到间接控制微射流的目的.
    Acoustic cavitation bubble and its production extreme physics such as shockwaves and micro-jets on a solid wall have attracted great interest in the application of ultrasound (e.g., ultrasonic medical, ultrasonic cleaning, and ultrasonic machining). However, the prediction and control of micro-jets induced by ultrasonic field have been a very challenging work, due to the complicated mechanisms of collapsing of cavitation bubbles. In order to determine the interaction of micro-jet with the key parameters that influence the acoustic cavitation, the dynamics of bubble growth and collapse near a rigid boundary in water is investigated. Using the method of mirror image, a revised bubble dynamics equation in radial oscillation for a bubble near a plane rigid wall is derived from the double-bubble equation (the Doinikov equation). In the present equation, the gas inside the bubble is assumed to be the van der Waals gas, and the weak compressibility of the liquid is also assumed. The revised equation is then employed to simulate numerically the dynamical behaviors of a bubble, using the fourth-order Runge-Kutta method with variable step size adaptive control. Numerical simulations of the motion characteristics and collapse velocities of a bubble near a rigid boundary or a free boundary have been performed, under various conditions of initial bubble radius, spacing between the center of the bubble and the wall, acoustic pressure and ultrasonic frequency, in order to explain the effects of these key parameters on the acoustic cavitation intensity. It is shown that, compared with free boundary, the effect of rigid boundary on the bubble plays a significant role in suppressing the bubble oscillation. The intensity of bubble collapsing is reduced as the increase of the initial bubble radius and ultrasonic frequency, and increased by enlarging the spacing between the center of the bubble and the wall. There exists an optimal acoustic pressure (almost 3.5 times bigger than the ambient pressure), at which the collapse of a bubble near a rigid wall can be the most violent. Furthermore, the relationship between the collapse velocity of a bubble near a rigid boundary and its micro-jet is described. Results demonstrate that the velocity of micro-jet is dependent on that of bubble collapse, and it can be controlled by adjusting the velocity of bubble collapse indirectly. Calculation results of the micro-jet in this paper are compared with some numerical and experimental results given in the literature and good apparent trends between them are obtained. These results will give important implications for further understanding the dynamics of cavitation bubble on a solid wall induced by the ultrasonic field and its different requirements in engineering applications.
      通信作者: 郭策, guoce1027@163.com
    • 基金项目: 国家自然科学基金(批准号: 50975265, 51275490)和山西省自然科学基金(批准号: 2013011024-5)资助的课题.
      Corresponding author: Guo Ce, guoce1027@163.com
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 50975265, 51275490) and the Natural Science Foundation of Shanxi Province, China (Grant No. 2013011024-5).
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    Brujan E A, Matsumoto Y 2012 Microfluid Nanofluid 13 957

    [3]

    Brujan E A, Ikeda T, Matsumoto Y 2008 Exp. Thermal Fluid Sci. 32 1188

    [4]

    Vignoli L L, Barros A L, Thom R C, et al. 2013 Eur. J. Phys. 34 679

    [5]

    Merouani S, Hamdaoui O, Rezgui Y, et al. 2014 Ultrasonic 54 227

    [6]

    Wang Y C, Yao M C 2013 Ultrason. Sonochem. 20 565

    [7]

    Zarepour H, Yeo S H 2012 Int. J. Mach. Tools Manufact. 62 13

    [8]

    Tsuboi R, Kakinuma Y, Aoyama T, et al. 2012 Procedia CIRP 1 342

    [9]

    Grossmann S, Hilgenfeldt S, Lohse D 1997 J. Acoust. Soc. Am. 102 1223

    [10]

    Behnia S, Sojahrood A J, Soltanpoor W, et al. 2009 Ultrason. Sonochem. 16 502

    [11]

    Mahdi M, Ebrahimi R, Sham M 2011 Phys. Lett. A 375 2348

    [12]

    Doinikov A A, Zhao S K, Dayton P A 2009 Ultrasonics 49 195

    [13]

    Mettin R, Doinikov A A 2009 Appl. Acoust. 70 1330

    [14]

    Wang L, Tu J, Guo X S, et al. 2014 Chin. Phys. B 23 124302

    [15]

    Wang C H 2010 Ph. D. Dissertation (Xi'an: Shaanxi Normal University) (in Chinese) [王成会 2010 博士学位论文 (西安: 陕西师范大学)]

    [16]

    Doinikov A A 2001 Phys. Rev. E 64 026301

    [17]

    Wang C H, Cheng J C 2013 Sci. China: Phys. Mech. Astron. 56 1246

    [18]

    Ida M 2009 Phys. Rev. E 79 016307

    [19]

    Li F C, Cai J, Huai X L, Liu B 2013 J. Thermal Sci. 22 242

    [20]

    Shen Z Z, Lin S Y 2011 Acta Phys. Sin 60 104302 (in Chinese) [沈壮志, 林书玉 2011 物理学报 60 104302]

    [21]

    Qian M L, Cheng Q, Ge C Y 2002 Acta Acustica 27 289 (in Chinese) [钱梦騄, 程茜, 葛曹燕 2002 声学学报 27 289]

    [22]

    Hegedűs F, Klapcsik K 2015 Ultrason. Sonochem. 27 153

    [23]

    Chen H S, Li J, Chen D, Wang J D 2008 Wear 265 692

    [24]

    Chen X G, Yan J C, Gao F, et al. 2013 Ultrason. Sonochem. 20 144

    [25]

    Wang X F 2009 Cavitating and Supercavitating Flows Theory and Applications (Beijing: National Defence Industry Press) p29 (in Chinese) [王献孚 2009 空化泡和超空化泡流动理论及应用 (北京: 国防工业出版社) 第29页]

    [26]

    Blake J R, Gibson D C 1987 Ann. Rev. Fluid Mech. 19 99

    [27]

    Ohl C, Arora M, Ikink R, et al. 2006 Biophys. J. 91 4285

    [28]

    Tzanakis I, Hadfield M, Henshaw I 2011 Exp. Thermal Fluid Sci. 35 1544

    [29]

    Rayleigh L 1917 Phil. Mag. 34 94

  • [1]

    Benjamin T B, Ellis A T 1966 Phil.Trans. R. Soc. Lond. A 260 221

    [2]

    Brujan E A, Matsumoto Y 2012 Microfluid Nanofluid 13 957

    [3]

    Brujan E A, Ikeda T, Matsumoto Y 2008 Exp. Thermal Fluid Sci. 32 1188

    [4]

    Vignoli L L, Barros A L, Thom R C, et al. 2013 Eur. J. Phys. 34 679

    [5]

    Merouani S, Hamdaoui O, Rezgui Y, et al. 2014 Ultrasonic 54 227

    [6]

    Wang Y C, Yao M C 2013 Ultrason. Sonochem. 20 565

    [7]

    Zarepour H, Yeo S H 2012 Int. J. Mach. Tools Manufact. 62 13

    [8]

    Tsuboi R, Kakinuma Y, Aoyama T, et al. 2012 Procedia CIRP 1 342

    [9]

    Grossmann S, Hilgenfeldt S, Lohse D 1997 J. Acoust. Soc. Am. 102 1223

    [10]

    Behnia S, Sojahrood A J, Soltanpoor W, et al. 2009 Ultrason. Sonochem. 16 502

    [11]

    Mahdi M, Ebrahimi R, Sham M 2011 Phys. Lett. A 375 2348

    [12]

    Doinikov A A, Zhao S K, Dayton P A 2009 Ultrasonics 49 195

    [13]

    Mettin R, Doinikov A A 2009 Appl. Acoust. 70 1330

    [14]

    Wang L, Tu J, Guo X S, et al. 2014 Chin. Phys. B 23 124302

    [15]

    Wang C H 2010 Ph. D. Dissertation (Xi'an: Shaanxi Normal University) (in Chinese) [王成会 2010 博士学位论文 (西安: 陕西师范大学)]

    [16]

    Doinikov A A 2001 Phys. Rev. E 64 026301

    [17]

    Wang C H, Cheng J C 2013 Sci. China: Phys. Mech. Astron. 56 1246

    [18]

    Ida M 2009 Phys. Rev. E 79 016307

    [19]

    Li F C, Cai J, Huai X L, Liu B 2013 J. Thermal Sci. 22 242

    [20]

    Shen Z Z, Lin S Y 2011 Acta Phys. Sin 60 104302 (in Chinese) [沈壮志, 林书玉 2011 物理学报 60 104302]

    [21]

    Qian M L, Cheng Q, Ge C Y 2002 Acta Acustica 27 289 (in Chinese) [钱梦騄, 程茜, 葛曹燕 2002 声学学报 27 289]

    [22]

    Hegedűs F, Klapcsik K 2015 Ultrason. Sonochem. 27 153

    [23]

    Chen H S, Li J, Chen D, Wang J D 2008 Wear 265 692

    [24]

    Chen X G, Yan J C, Gao F, et al. 2013 Ultrason. Sonochem. 20 144

    [25]

    Wang X F 2009 Cavitating and Supercavitating Flows Theory and Applications (Beijing: National Defence Industry Press) p29 (in Chinese) [王献孚 2009 空化泡和超空化泡流动理论及应用 (北京: 国防工业出版社) 第29页]

    [26]

    Blake J R, Gibson D C 1987 Ann. Rev. Fluid Mech. 19 99

    [27]

    Ohl C, Arora M, Ikink R, et al. 2006 Biophys. J. 91 4285

    [28]

    Tzanakis I, Hadfield M, Henshaw I 2011 Exp. Thermal Fluid Sci. 35 1544

    [29]

    Rayleigh L 1917 Phil. Mag. 34 94

计量
  • 文章访问数:  2314
  • PDF下载量:  264
  • 被引次数: 0
出版历程
  • 收稿日期:  2015-09-11
  • 修回日期:  2015-10-31
  • 刊出日期:  2016-02-05

超声场下刚性界面附近溃灭空化气泡的速度分析

  • 1. 中北大学机械与动力工程学院, 太原 030051
  • 通信作者: 郭策, guoce1027@163.com
    基金项目: 国家自然科学基金(批准号: 50975265, 51275490)和山西省自然科学基金(批准号: 2013011024-5)资助的课题.

摘要: 为了揭示刚性界面附近气泡空化参数与微射流的相互关系, 从两气泡控制方程出发, 利用镜像原理, 建立了考虑刚性壁面作用的空化泡动力学模型. 数值对比了刚性界面与自由界面下气泡的运动特性, 并分析了气泡初始半径、气泡到固壁面的距离、声压幅值和超声频率对气泡溃灭的影响. 在此基础上, 建立了气泡溃灭速度和微射流的相互关系. 结果表明: 刚性界面对气泡振动主要起到抑制作用; 气泡溃灭的剧烈程度随气泡初始半径和超声频率的增加而降低, 随着气泡到固壁面距离的增加而增加; 声压幅值存在最优值, 固壁面附近的气泡在该最优值下气泡溃灭最为剧烈; 通过研究气泡溃灭速度和微射流的关系发现, 调节气泡溃灭速度可以达到间接控制微射流的目的.

English Abstract

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