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考虑水蒸气蒸发和冷凝的球状泡群中泡的动力学特性

徐珂 许龙 周光平

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考虑水蒸气蒸发和冷凝的球状泡群中泡的动力学特性

徐珂, 许龙, 周光平

Dynamic characteristics of bubbles in spherical bubble group considering evaporation and condensation of water vapor

Xu Ke, Xu Long, Zhou Guang-Ping
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  • 为了深入探究空化泡群中气泡的动力学特性, 建立了超声驱动下考虑水蒸气的蒸发和冷凝的泡群中泡的动力方程. 基于该方程, 研究了泡群中泡的位置、泡的数量、泡的初始半径对其动力学特性的影响, 探究了超声作用下球状泡群中气泡半径、能量、温度、压力和气泡内水蒸气分子数的变化规律. 结果表明: 泡群中泡的运动受到周围气泡的抑制作用; 泡群中泡的初始半径大小对泡群中泡的半径、能量、温度、压力和气泡内水蒸气分子数有显著影响; 泡群中泡的位置距离泡群中心越远, 泡的膨胀半径越大; 随着泡群中泡的数目增加, 泡的振幅减小; 超声频率增加, 泡群中泡的空化效应减弱; 超声声压增加, 泡群中泡的空化效应增加. 研究结果为超声空化泡群的研究提供了理论参考.
    In order to explore the dynamic characteristics of bubbles in the cavitation bubble cluster in detail, the dynamic equation of a bubble with arbitrary location inside the bubble cluster is established in this paper, based on the interactions between bubbles inside the bubble cluster driven by ultrasound. The effects of evaporation and condensation of the water vapor are also taken into account in the derivation process. Based on the proposed equation, the influences of the bubble position, number of bubbles, and initial radius of bubbles on the dynamic characteristics of cavitation bubbles are studied, and the corresponding change laws of the bubble radius, energy, temperature, pressure, as well as the number of water vapor molecules in a bubble are investigated under ultrasound. The calculation results are shown below. 1) Comparing with an isolated bubble, the oscillation of a bubble inside the bubble cluster is suppressed by its surrounding bubbles, which leads to the fact that the vibration amplitude of a bubble inside the bubble cluster is smaller, and that the internal energy, maximum temperature, maximum pressure and the number of water molecules in the bubble all become smaller. As the distance between the bubble and the center of the bubble cluster increases, the vibration amplitude of the bubble become larger. 2) The initial radii of the bubbles in the bubble cluster can significantly affect the normalized vibration amplitude, collapse time, internal energy, temperature, and pressure of bubbles, as well as the number of water vapor molecules in bubbles of the bubble cluster. 3) As the number of bubbles in the bubble cluster increases, the vibration amplitudes of the bubbles decrease. 4) The higher the ultrasonic frequency, the smaller the oscillation amplitude of the bubble; the smaller the maximum pressure and energy of the bubble, the larger the minimum value of the internal pressure and temperature of the bubble and the less the number of water molecules in the bubble. When the ultrasonic frequency increases, the cavitation effects of bubbles in the bubble cluster are suppressed. 5) As the ultrasonic sound pressure increases, the oscillation amplitudes of the bubbles in the bubble cluster increase, the maximum values of the bubbles' radii increase, the collapse times of the cavitation bubbles increase, and the number of oscillations of bubbles decreases after the cavitation bubbles have collapsed. Additionally, the maximum value of internal energy, temperature, pressure, and the number of water molecules in the bubble also increase as the ultrasonic sound pressure increases, while the minimum value of the pressure and temperature of the bubble decrease. Besides, when the ultrasonic sound pressure increases, the cavitation effects of the bubbles in the bubble cluster turn stronger. This paper focuses on the dynamic characteristics of ultrasonic cavitation bubble cluster from the theoretical aspect and the results can be further applied to experimental analysis.
      通信作者: 许龙, xulong@cjlu.edu.cn
    • 基金项目: 国家自然科学基金(批准号: 12074354, 11574277)资助的课题
      Corresponding author: Xu Long, xulong@cjlu.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 12074354, 11574277)
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    张婵, 郑爽英 2009 水资源与水工程学报 20 136

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    Eddingsaas N C, Suslick K S 2006 Nature 444 163Google Scholar

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    Suslick K S, Didenko Y, Fang M M, Hyeon T, Kolbeck K J 2000 Philos. Trans. R. Soc. London, Ser. B 357 335Google Scholar

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    Flannigan D J, Hopkins S D, Camara C G, Putterman S J, Suslick K S 2006 Phys. Rev. Lett. 96 204301Google Scholar

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    Xu H, Suslick K S 2010 Phys. Rev. Lett. 104 244301Google Scholar

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    Liu K, Zhang J G, Qu C J, Li Z H 2012 China Petroleum and Chemical Standard and Quality 32 93Google Scholar

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    Luo X M, Gong H Y, He Z L, Zhang P, He L M 2021 Ultrason. Sonochem. 70 105337Google Scholar

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    冯若, 李化茂 2000 应用声学 19 35Google Scholar

    Feng R, Li H M 2000 Appl. Acoust. 19 35Google Scholar

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    程效锐, 张舒研, 房宁 2018 应用化工 47 1753Google Scholar

    Cheng X R, Zhang S Y, Fang N 2018 Appl Chemical Industry 47 1753Google Scholar

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    Xiong Y D 2002 Appl. Acoust. 21 33Google Scholar

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    高贤娴, 陈伟中, 黄威, 徐俊峰, 徐兴华, 刘亚楠, 梁越 2009 科学通报 54 408Google Scholar

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    苟杰, 陈伟中 2012 中国科学: 物理学 力学 天文学 42 217

    Gou J, Chen W Z 2012 Sci. China, Ser. G 42 217

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    沈阳, 朱彤, 由美雁, 糜彬, 韩进, 谢元华, 李现瑾, Kyuichi Yasui 2015 高校化学工程学报 29 809Google Scholar

    Shen Y, Zhu D, You M Y, Mei B, Han J, Xie Y H, Li X J, Kyuichi Y 2015 Journal of Chemical Engineering of Chinese Universities 29 809Google Scholar

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    Lin Z Y, Zhu X J, Yao L 2019 Ultrason. Sonochem. 59 104744Google Scholar

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    沈壮志, 吴胜举 2012 物理学报 61 124301Google Scholar

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    王成会, 莫润阳, 胡静, 张明铎 2017 中国科学: 物理学 力学 天文学 47 59

    Wang C H, Mo R Y, Hu J, Zhang M D 2017 Sci. China, Ser. G 47 59

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    张鹏利, 林书玉, 朱华泽, 张涛 2019 物理学报 68 134301Google Scholar

    Zhang P L, Lin S Y, Zhu H Z, Zhang T 2019 Acta Phys. Sin. 68 134301Google Scholar

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    Shen Z Z 2020 Chin. Phys. B 29 417Google Scholar

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    清河美, 那仁满都拉 2020 物理学报 69 184301Google Scholar

    Qing H M, Naranmandula 2020 Acta Phys. Sin. 69 184301Google Scholar

  • 图 1  单泡、泡群中心的泡和泡群表面的泡的动力学特性 (a) 气泡归一化半径随时间的变化曲线; (b) 气泡内内能随时间的变化曲线; (c) 气泡内温度随时间的变化曲线; (d) 气泡内压力随时间的变化曲线; (e) 气泡内水分子数量随时间的变化曲线

    Fig. 1.  Dynamical behaviors of a single bubble, a bubble at the center of a bubble group and a bubble on the surface of a bubble group: (a) Change curve of the normalized radius with the time for the bubble; (b) change curve of the internal energy in the bubble with the time; (c) change curve of the temperature in the bubble with the time; (d) change curve of the pressure in the bubble with the time; (e) change curve of the number of water molecules in the bubble with the time.

    图 2  泡群中不同初始半径的泡的动力学特性 (a) 气泡归一化半径随时间的变化; (b) 气泡内内能随时间的变化曲线; (c) 气泡内温度随时间的变化曲线; (d) 气泡内压力随时间的变化曲线; (e) 气泡内水分子数量随时间的变化曲线

    Fig. 2.  Dynamic characteristics of the bubbles with different initial radii in bubble group: (a) Change curve of the normalized radius with the time; (b) change curve of the internal energy in the bubble with the time; (c) change curve of the temperature in the bubble with the time; (d) change curve of the pressure in the bubble with the time; (e) change curve of the number of water molecules in the bubble with the time.

    图 3  泡群中不同位置的泡的动力学特性

    Fig. 3.  Dynamic characteristics of bubbles at different positions in a bubble group.

    图 4  不同频率下泡群中泡的动力学特性 (a) 气泡归一化半径随时间的变化; (b) 气泡内内能随时间的变化曲线; (e) 气泡内水分子数量随时间的变化曲线

    Fig. 4.  Dynamic characteristics of the bubbles in bubble groups at different frequencies: (a) Change curve of the normalized radius with the time for the bubble; (b) change curve of the internal energy in the bubble with the time; (c) change curve of the temperature in the bubble with the time; (d) change curve of the pressure in the bubble with the time; (e) change curve of the number of water molecules in the bubble with the time.

    图 5  不同声压下泡群中泡的动力学特性 (a) 气泡归一化半径随时间的变化; (b) 气泡内内能随时间的变化曲线; (c) 气泡内温度随时间的变化曲线; (d) 气泡内压力随时间的变化曲线; (e) 气泡内水分子数量随时间的变化曲线

    Fig. 5.  Dynamic characteristics of bubbles in bubble groups under different sound pressures: (a) Change curve of the normalized radius with the time for the bubble; (b) change curve of the internal energy in the bubble with the time; (c) change curve of the temperature in the bubble with the time; (d) change curve of the pressure in the bubble with the time; (e) change curve of the number of water molecules in the bubble with the time.

  • [1]

    莫润阳, 林书玉, 王成会 2009 应用声学 8 389Google Scholar

    Mo R, Lin S Y, Wang C H 2009 Appl. Acoust. 8 389Google Scholar

    [2]

    张婵, 郑爽英 2009 水资源与水工程学报 20 136

    Zhang C, Zheng S Y 2009 Journal of Water Resources and Water Engineering 20 136

    [3]

    Suslick K S 1989 Sci. Am. 260 80Google Scholar

    [4]

    Eddingsaas N C, Suslick K S 2006 Nature 444 163Google Scholar

    [5]

    Suslick K S, Didenko Y, Fang M M, Hyeon T, Kolbeck K J 2000 Philos. Trans. R. Soc. London, Ser. B 357 335Google Scholar

    [6]

    Flannigan D J, Hopkins S D, Camara C G, Putterman S J, Suslick K S 2006 Phys. Rev. Lett. 96 204301Google Scholar

    [7]

    Xu H, Suslick K S 2010 Phys. Rev. Lett. 104 244301Google Scholar

    [8]

    刘坤, 张建国, 屈策计, 李忠厚 2012 中国石油和化工标准与质量 32 93Google Scholar

    Liu K, Zhang J G, Qu C J, Li Z H 2012 China Petroleum and Chemical Standard and Quality 32 93Google Scholar

    [9]

    Luo X M, Gong H Y, He Z L, Zhang P, He L M 2021 Ultrason. Sonochem. 70 105337Google Scholar

    [10]

    冯若, 李化茂 2000 应用声学 19 35Google Scholar

    Feng R, Li H M 2000 Appl. Acoust. 19 35Google Scholar

    [11]

    程效锐, 张舒研, 房宁 2018 应用化工 47 1753Google Scholar

    Cheng X R, Zhang S Y, Fang N 2018 Appl Chemical Industry 47 1753Google Scholar

    [12]

    熊宜栋 2002 应用声学 21 33Google Scholar

    Xiong Y D 2002 Appl. Acoust. 21 33Google Scholar

    [13]

    Hilgenfeldt S, Lohse D, Brenner M P 1996 Phys. Fluids 8 2808Google Scholar

    [14]

    Kyuichi Y 1997 Phys. Rev. E 56 6750Google Scholar

    [15]

    Toegel R, Lohse D 2003 J. Chem. Phys. 118 1863Google Scholar

    [16]

    高贤娴, 陈伟中, 黄威, 徐俊峰, 徐兴华, 刘亚楠, 梁越 2009 科学通报 54 408Google Scholar

    Gao X X, Chen W Z, Huang W, Xu J F, Xu X H, Liu Y N, Liang Y 2009 Chin. Sci. Bull. 54 408Google Scholar

    [17]

    苟杰, 陈伟中 2012 中国科学: 物理学 力学 天文学 42 217

    Gou J, Chen W Z 2012 Sci. China, Ser. G 42 217

    [18]

    沈阳, 朱彤, 由美雁, 糜彬, 韩进, 谢元华, 李现瑾, Kyuichi Yasui 2015 高校化学工程学报 29 809Google Scholar

    Shen Y, Zhu D, You M Y, Mei B, Han J, Xie Y H, Li X J, Kyuichi Y 2015 Journal of Chemical Engineering of Chinese Universities 29 809Google Scholar

    [19]

    Lin Z Y, Zhu X J, Yao L 2019 Ultrason. Sonochem. 59 104744Google Scholar

    [20]

    An Y 2011 Phys. Rev. E 83 066313Google Scholar

    [21]

    沈壮志, 吴胜举 2012 物理学报 61 124301Google Scholar

    Shen Z Z, Wu S J 2012 Acta Phys. Sin. 61 124301Google Scholar

    [22]

    王成会, 莫润阳, 胡静, 张明铎 2017 中国科学: 物理学 力学 天文学 47 59

    Wang C H, Mo R Y, Hu J, Zhang M D 2017 Sci. China, Ser. G 47 59

    [23]

    张鹏利, 林书玉, 朱华泽, 张涛 2019 物理学报 68 134301Google Scholar

    Zhang P L, Lin S Y, Zhu H Z, Zhang T 2019 Acta Phys. Sin. 68 134301Google Scholar

    [24]

    Shen Z Z 2020 Chin. Phys. B 29 417Google Scholar

    [25]

    清河美, 那仁满都拉 2020 物理学报 69 184301Google Scholar

    Qing H M, Naranmandula 2020 Acta Phys. Sin. 69 184301Google Scholar

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出版历程
  • 收稿日期:  2021-01-08
  • 修回日期:  2021-05-15
  • 上网日期:  2021-06-07
  • 刊出日期:  2021-10-05

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