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脉动气泡在黏性介质中的声发射

申潇卓 吴鹏飞 林伟军

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脉动气泡在黏性介质中的声发射

申潇卓, 吴鹏飞, 林伟军

Acoustic emission of pulsating bubbles in viscous media

Shen Xiao-Zhuo, Wu Peng-Fei, Lin Wei-Jun
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  • 在气泡辐射声问题中一直被使用的气泡声发射公式并未考虑介质的黏性在声波传播过程中产生的影响. 本文结合气泡的边界条件, 对黏性介质中的声波方程进行求解, 给出黏性介质中经过修正的气泡的声发射公式, 进行气泡动力学方程求解和有限元仿真等数值计算后发现, 在考虑介质的黏性时, 本文提出的黏性介质中气泡声发射公式所计算出的声压小于经典气泡声发射公式计算出的声压, 并且随着介质黏度、超声频率以及传播距离的增加, 二者之间的误差逐渐增大.
    The classical single bubble’s acoustic emission equation has been used to describe the sound filed radiated by bubble for a long time. Because this formula does not consider the influence of the medium viscosity in the process of sound wave propagation, it is more reasonable to modify it in some special cases.Based on the boundary condition of the bubbles, i.e. the vibration velocity of the bubble wall is equal to the particle vibration velocity of the external medium at the bubble boundary, the acoustic wave equation in spherical coordinate system in viscous medium is solved, and the modified acoustic emission formula of the bubble in the viscous medium is given.The bubble radius R(t) is obtained numerically from the bubble dynamics equation by using the fourth-fifth order Runge-Kutta method. Then the bubble's radiation sound field is obtained by using the direct substitution method and the finite element (The pressure acoustics module; two-dimensional (2D) axisymmetric geometric model) method, respectively. The modified expression ppresent given in this work is more accurate to describe the bubble’s radiation than the classical expression pclassical in the cases of high-viscosity, high-frequency and long-distance. In these cases, continuing to measure the acoustic emission of bubbles by using the classical expression may have an influence on the characteristics of cavitation, such as the inaccurate descriptions of parameters such as cavitation intensity and cavitation threshold.
      通信作者: 吴鹏飞, wpf@mail.ioa.ac.cn
    • 基金项目: 中国科学院基础前沿研究计划从0到1原始创新项目(批准号: ZDBS-LY-SLH037)、中国科协青年人才托举工程(批准号: 2022-2024QNRC001)和中国科学院青年创新促进会(批准号: 2023031)资助的课题.
      Corresponding author: Wu Peng-Fei, wpf@mail.ioa.ac.cn
    • Funds: Project supported by the Basic Frontier Research Program of the Chinese Academy of Sciences from 0 to 1 Original Innovation Project (Grant No. ZDBS-LY-SLH037), the Young Elite Scientists Sponsorship Program by China Association for Science and Technology (Grant No. 2022-2024QNRC001), and the Youth Innovation Promotion Association of Chinese Academy of Sciences (Grant No. 2023031).
    [1]

    柯乃普R T, 达利 J W, 哈米特 F G著(水利水电科学研究所译)1981 空化与空蚀(北京: 水利出版社)第8—11页

    Knapp R T, Daily J W, Hammitt F G (translated by China Institute of Water Resources and Hydropower) 1981 Cavitation (Beijing: China Water & Power Press) pp8–11

    [2]

    汪德昭, 尚尔昌 2013 水声学(北京: 科学出版社)第376, 590页

    Wang D Z, Shang E C 2013 Underwater Acoustics (Beijing: Science Press) pp376, 590

    [3]

    Wan M X, Feng Y, Haar G T 2015 Cavitation in Biomedicine: Principles and Techniques (Berlin, Heidelberg: Springer) pp1–5, 47–49

    [4]

    Du G H, Wu J R 1990 J. Acoust. Soc. Am. 87 965

    [5]

    Ye Z 1997 J. Acoust. Soc. Am. 101 809Google Scholar

    [6]

    Zilonova E, Solovchuk M, Sheu T W 2019 Phys. Rev. E 99 023109Google Scholar

    [7]

    Kou S Y, Chen W Z, Wu Y R, Zhao G Y 2023 Ultrason Sonochem 94 106352Google Scholar

    [8]

    Yuan Y, An Y 2021 Int. Commun. Heat Mass 126 105378Google Scholar

    [9]

    Qin D, Zou Q Q, Li Z Y, Wang W, Wan M X, Feng Y 2021 Acta Phys. Sin. 70 154701 [秦对, 邹青钦, 李章勇, 王伟, 万明习, 冯怡 2021 物理学报 70 154701]Google Scholar

    Qin D, Zou Q Q, Li Z Y, Wang W, Wan M X, Feng Y 2021 Acta Phys. Sin. 70 154701Google Scholar

    [10]

    Liu R, Huang C Y, Wu Y R, Hu J, Mo R Y, Wang C H 2024 Acta Phys. Sin. 73 084303 [刘睿, 黄晨阳, 武耀蓉, 胡静, 莫润阳, 王成会 2024 物理学报 73 084303]Google Scholar

    Liu R, Huang C Y, Wu Y R, Hu J, Mo R Y, Wang C H 2024 Acta Phys. Sin. 73 084303Google Scholar

    [11]

    Shen X Z, Wu P F, Lin W J 2024 Ultrason Sonochem 107 106890Google Scholar

    [12]

    Zhang H L 2012 Theoretical Acoustics (revised version) (Beijing: Higher Education Press pp221–223) [张海澜 2012 理论声学 (修订版) (北京: 高等教育出版社) 第221—223页]

    Zhang H L 2012 Theoretical Acoustics (revised version) (Beijing: Higher Education Press pp221–223)

    [13]

    Currie G I 2003 Fundamental Mechanics of Fluids (3rd Ed.) (Boca Raton: CRC Press) pp30-33

    [14]

    Filonets T, Solovchuk M 2022 Ultrason Sonochem 88 106056Google Scholar

    [15]

    Keller J B, Miksis M 1980 J. Acoust. Soc. Am. 68 628Google Scholar

    [16]

    Lauterborn W, Kurz T 2010 Rep. Prog. Phys. 73 106501Google Scholar

  • 图 1  脉动气泡示意图

    Fig. 1.  Schematic of a pulsating bubble.

    图 2  气泡半径及辐射声压曲线, f = 20 kHz, pa = 100 kPa, R0 = 15 μm, r = 1000 μm (a) μ = 0.005 Pa·s; (b) μ = 0.025 Pa·s; (c) μ = 0.075 Pa·s; (d) μ = 0.1 Pa·s

    Fig. 2.  Bubble radius and radiation sound pressure curves, f = 20 kHz, pa = 100 kPa, R0 = 15 μm, r = 1000 μm: (a) μ = 0.005 Pa·s; (b) μ = 0.025 Pa·s; (c) μ = 0.075 Pa·s; (d) μ = 0.1 Pa·s.

    图 3  气泡半径及辐射声压曲线, f = 4500 kHz, pa = 200 kPa, R0 = 3 μm, r = 1000 μm (a) μ = 1 Pa·s; (b) μ = 2 Pa·s; (c) μ = 4 Pa·s; (d) μ = 6 Pa·s

    Fig. 3.  Bubble radius and radiation sound pressure curves, f = 4500 kHz, pa = 200 kPa, R0 = 3 μm, r = 1000 μm: (a) μ = 1 Pa·s; (b) μ = 2 Pa·s; (c) μ = 4 Pa·s; (d) μ = 6 Pa·s.

    图 4  气泡声辐射的有限元计算模型 (a) 二维轴对称几何模型; (b) 局部网格划分1; (c) 局部网格划分2

    Fig. 4.  Finite element model for calculating bubble acoustic radiation: (a) Two-dimensional axisymmetric geometric model; (b) localised grid division 1; (c) localised grid division 2.

    图 5  不同黏度下气泡辐射声压, f = 4000 kHz, R0 = 3 μm, pa = 200 kPa, r = 8000 μm (a) μ = 0.25 Pa·s; (b) μ = 0.5 Pa·s; (c) μ = 1 Pa·s

    Fig. 5.  Sound pressure curves of bubble radiation under different viscosity, f = 4000 kHz, R0 = 3 μm, pa = 200 kPa, r = 8000 μm: (a) μ = 0.25 Pa·s; (b) μ = 0.5 Pa·s; (c) μ = 1 Pa·s.

    图 6  不同频率下气泡辐射声压, R0 = 3 μm, pa = 200 kPa, r = 3000 μm, μ = 1 Pa·s (a) f = 2000 kHz; (b) f = 4000 kHz; (c) f = 8000 kHz

    Fig. 6.  Sound pressure curves of bubble radiation under different frequency, R0 = 3 μm, pa = 200 kPa, r = 3000 μm, μ = 1 Pa·s: (a) f = 2000 kHz; (b) f = 4000 kHz; (c) f = 8000 kHz.

    图 7  不同距离下气泡辐射声压, f = 4000 kHz, R0 = 3 μm, pa = 200 kPa, μ = 1 Pa·s (a) r = 1000 μm; (b) r = 4500 μm; (c) r = 8000 μm

    Fig. 7.  Sound pressure curves of bubble radiation under different distance, f = 4000 kHz, R0 = 3 μm, pa = 200 kPa, μ = 1 Pa·s: (a) r = 1000 μm; (b) r = 4500 μm; (c) r = 8000 μm.

    表 1  数值计算中参数的含义及取值

    Table 1.  Definition and value of parameters in numerical calculation.

    参数 含义 取值
    σ/(N·m–1) 表面张力系数 0.056
    c/(m·s–1) 声速 1549
    c0/(m·s–1) 理想介质中的声速 1500
    ρ/(kg·m–3) 密度 1100
    p0/kPa 环境静压 101.3
    pv/kPa 泡内水蒸气压 2.33
    κ 绝热指数 1.4
    下载: 导出CSV
  • [1]

    柯乃普R T, 达利 J W, 哈米特 F G著(水利水电科学研究所译)1981 空化与空蚀(北京: 水利出版社)第8—11页

    Knapp R T, Daily J W, Hammitt F G (translated by China Institute of Water Resources and Hydropower) 1981 Cavitation (Beijing: China Water & Power Press) pp8–11

    [2]

    汪德昭, 尚尔昌 2013 水声学(北京: 科学出版社)第376, 590页

    Wang D Z, Shang E C 2013 Underwater Acoustics (Beijing: Science Press) pp376, 590

    [3]

    Wan M X, Feng Y, Haar G T 2015 Cavitation in Biomedicine: Principles and Techniques (Berlin, Heidelberg: Springer) pp1–5, 47–49

    [4]

    Du G H, Wu J R 1990 J. Acoust. Soc. Am. 87 965

    [5]

    Ye Z 1997 J. Acoust. Soc. Am. 101 809Google Scholar

    [6]

    Zilonova E, Solovchuk M, Sheu T W 2019 Phys. Rev. E 99 023109Google Scholar

    [7]

    Kou S Y, Chen W Z, Wu Y R, Zhao G Y 2023 Ultrason Sonochem 94 106352Google Scholar

    [8]

    Yuan Y, An Y 2021 Int. Commun. Heat Mass 126 105378Google Scholar

    [9]

    Qin D, Zou Q Q, Li Z Y, Wang W, Wan M X, Feng Y 2021 Acta Phys. Sin. 70 154701 [秦对, 邹青钦, 李章勇, 王伟, 万明习, 冯怡 2021 物理学报 70 154701]Google Scholar

    Qin D, Zou Q Q, Li Z Y, Wang W, Wan M X, Feng Y 2021 Acta Phys. Sin. 70 154701Google Scholar

    [10]

    Liu R, Huang C Y, Wu Y R, Hu J, Mo R Y, Wang C H 2024 Acta Phys. Sin. 73 084303 [刘睿, 黄晨阳, 武耀蓉, 胡静, 莫润阳, 王成会 2024 物理学报 73 084303]Google Scholar

    Liu R, Huang C Y, Wu Y R, Hu J, Mo R Y, Wang C H 2024 Acta Phys. Sin. 73 084303Google Scholar

    [11]

    Shen X Z, Wu P F, Lin W J 2024 Ultrason Sonochem 107 106890Google Scholar

    [12]

    Zhang H L 2012 Theoretical Acoustics (revised version) (Beijing: Higher Education Press pp221–223) [张海澜 2012 理论声学 (修订版) (北京: 高等教育出版社) 第221—223页]

    Zhang H L 2012 Theoretical Acoustics (revised version) (Beijing: Higher Education Press pp221–223)

    [13]

    Currie G I 2003 Fundamental Mechanics of Fluids (3rd Ed.) (Boca Raton: CRC Press) pp30-33

    [14]

    Filonets T, Solovchuk M 2022 Ultrason Sonochem 88 106056Google Scholar

    [15]

    Keller J B, Miksis M 1980 J. Acoust. Soc. Am. 68 628Google Scholar

    [16]

    Lauterborn W, Kurz T 2010 Rep. Prog. Phys. 73 106501Google Scholar

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  • 收稿日期:  2024-06-12
  • 修回日期:  2024-07-15
  • 上网日期:  2024-07-31
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