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液滴撞击液膜过程的格子Boltzmann方法模拟

黄虎 洪宁 梁宏 施保昌 柴振华

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液滴撞击液膜过程的格子Boltzmann方法模拟

黄虎, 洪宁, 梁宏, 施保昌, 柴振华

Lattice Boltzmann simulation of the droplet impact onto liquid film

Huang Hu, Hong Ning, Liang Hong, Shi Bao-Chang, Chai Zhen-Hua
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  • 本文采用格子Boltzmann方法对液滴撞击液膜过程进行了研究, 主要考察了雷诺数(Re)、韦伯数(We)、相对液膜厚度 (h) 以及表面张力 () 等物理参数对界面运动过程的影响. 首先, 随着Re数和We数的增加, 可以明显观察到液滴撞击液膜过程中形成的皇冠状水花以及卷吸现象; 当Re数较大时, 液体会发生飞溅, 由液体飞溅形成的小液滴则会继续下落, 并与液膜再次发生碰撞. 其次, 当相对液膜厚度较小时, 液滴撞击液膜并最终导致液膜断裂; 然而随着相对液膜厚度的增大, 尽管撞击过程溅起的液体会越来越多, 但是液膜并不会发生断裂. 再次, 随着表面张力的增大, 界面变形阻力增大, 撞击过程中产生的界面形变也逐渐减弱. 最后还发现皇冠(由液滴溅起形成)半径r 随时间满足r/(2R) Ut/(2R), 这一结果与已有结论是一致的.
    The process of the droplet impact onto the liquid film, as one of the basic multiphase problems, is very important in many fields of science and engineering. On the other hand, the problem is also very complicated since there are many parameters that may influence the process of the droplet impact on the liquid film. To clearly understand the physical phenomena appearing in the process droplet impact on the liquid film, a parametric study on this problem is conduced based on a recently developed lattice Boltzmann method in which a lattice Boltzmann model is used to solve the Navier-Stokes equations, and the other is adopted to solve the Cahn-Hilliard equation that is used to depict the interface between different phases. In this paper, we mainly focus on the effects of the Reynolds number (Re), the Weber number (We), the relative thickness of film (h) and the surface tension () on the dynamic behavior of interface between different phases, and the velocity and pressure fields are also presented. It is found that with the increase of Re and We, the phenomena of crown and entrainment can be observed obviously during the process of droplet impact onto the liquid film, and the radius of the crown seems not dependent on the We and Re where the relative thickness of film and surface tension are fixed to be 0.5 and 0.003. However, when Re becomes much larger, the splashing phenomenon is produced, and the small droplets caused by the splashing can fall and then impact onto the liquid film again. We also find that if the relative thickness of film is small, the surface tension, Re and We are set to be 0.003, 480 and 500, the film can break up during the process of the droplet impact onto the liquid film, while with the increase of relative thickness, although more liquid are induced in the splashing process, the film cant break up. In addition, with the increase of surface tension, the resistance which prevents the change of interface becomes large, and thus the change of interface is not large when the droplet impacts onto liquid film, as expected. And finally, a quantitative study on the relation between the radius of crown (formed by droplet impact onto liquid film) and the time is also performed, and the expression r/(2R) Ut/(2R) where the parameter is about 1.0 and is also independent of We and Re, can be used to describe the relation.
      通信作者: 柴振华, hustczh@hust.edu.cn
    • 基金项目: 国家自然科学基金(批准号: 51576079, 11272132)和湖北省自然科学基金(批准号: 2015CFB440)资助的课题.
      Corresponding author: Chai Zhen-Hua, hustczh@hust.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 51576079, 11272132) and the National Natural Science Foundation of Hubei Province, China (Grant No. 2015CFB440).
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    Mohamed-Kassim Z, Longmire E K 2003 Phys. Fluids 15 3263

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    Guo J H, Dai S Q, Dai Q 2010 Acta Phys. Sin. 59 2601 (in Chinese) [郭加宏, 戴世强, 代钦 2010 物理学报 59 2601]

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    Weiss D A, Yarin A L 1999 J. Fluid Mech. 385 229

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    Lee S H, Hur N, Kang S 2011 J. Mech. Sci. Tech. 25 2567

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    Xie H, Koshizuka S, Oka Y 2004 Int. J. Numer. Meth. Fluids 45 1009

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    Coppola G, Rocco G, Luca L D 2011 Phys. Fluids 23 0022105

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    Josseranda C, Zaleskib S 2003 Phys. Fluids 15 1650

    [13]

    Berberovi E, Hinsberg N P V, Jakirli S, Roisman I R, Tropea C 2009 Phys. Rev. E 79 036306

    [14]

    Liang G T, Guo Y L, Shen S Q 2013 Acta Phys. Sin. 62 024705 (in Chinese) [梁刚涛, 郭亚丽, 沈胜强 2013 物理学报 62 024705]

    [15]

    Wang Y, Shu C, Huang H B, Teo C J 2015 J. Comput. Phys. 280 404

    [16]

    Lee T, Lin C L 2005 J. Comput. Phys. 206 16

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    Li Q, Luo K H, Gao Y J, He Y L 2012 Phys. Rev. E 85 026704

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    Lee T, Liu L 2010 J. Comput. Phys. 229 8045

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    Rieber M, Frohn A 1999 Int. J. Heat Fluid Flow 20 445

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    Hai Q X, Zhong Z, Liang Q Z 2016 Chin. Phys. B 25 014702

    [21]

    Song B W, Ren F, Hu H B, Huang Q G 2015 Chin. Phys. B 24 014703

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    Chai Z H, Zhao T S 2012 Acta Mech. Sin. 28 983

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    Liang H, Shi B C, Guo Z L, Chai Z H 2014 Phys. Rev. E 89 053320

    [24]

    Huang J J, Huang H, Wang X 2015 Int. J. Numer. Meth. Fluids 77 123

  • [1]

    Yarin A L 2006 Annu. Rev. Fluid Mech. 38 159

    [2]

    Rioboo R, Tropea C, Marengo M 2001 Atom. Sprays 11 155

    [3]

    Thoroddsen S T 2002 J. Fluid Mech. 451 373

    [4]

    Yarin A L, Weiss D A 1995 J. Fluid Mech. 382 141

    [5]

    Wang A B, Chen C C 2000 Phys. Fluids 12 2155

    [6]

    Mohamed-Kassim Z, Longmire E K 2003 Phys. Fluids 15 3263

    [7]

    Guo J H, Dai S Q, Dai Q 2010 Acta Phys. Sin. 59 2601 (in Chinese) [郭加宏, 戴世强, 代钦 2010 物理学报 59 2601]

    [8]

    Weiss D A, Yarin A L 1999 J. Fluid Mech. 385 229

    [9]

    Lee S H, Hur N, Kang S 2011 J. Mech. Sci. Tech. 25 2567

    [10]

    Xie H, Koshizuka S, Oka Y 2004 Int. J. Numer. Meth. Fluids 45 1009

    [11]

    Coppola G, Rocco G, Luca L D 2011 Phys. Fluids 23 0022105

    [12]

    Josseranda C, Zaleskib S 2003 Phys. Fluids 15 1650

    [13]

    Berberovi E, Hinsberg N P V, Jakirli S, Roisman I R, Tropea C 2009 Phys. Rev. E 79 036306

    [14]

    Liang G T, Guo Y L, Shen S Q 2013 Acta Phys. Sin. 62 024705 (in Chinese) [梁刚涛, 郭亚丽, 沈胜强 2013 物理学报 62 024705]

    [15]

    Wang Y, Shu C, Huang H B, Teo C J 2015 J. Comput. Phys. 280 404

    [16]

    Lee T, Lin C L 2005 J. Comput. Phys. 206 16

    [17]

    Li Q, Luo K H, Gao Y J, He Y L 2012 Phys. Rev. E 85 026704

    [18]

    Lee T, Liu L 2010 J. Comput. Phys. 229 8045

    [19]

    Rieber M, Frohn A 1999 Int. J. Heat Fluid Flow 20 445

    [20]

    Hai Q X, Zhong Z, Liang Q Z 2016 Chin. Phys. B 25 014702

    [21]

    Song B W, Ren F, Hu H B, Huang Q G 2015 Chin. Phys. B 24 014703

    [22]

    Chai Z H, Zhao T S 2012 Acta Mech. Sin. 28 983

    [23]

    Liang H, Shi B C, Guo Z L, Chai Z H 2014 Phys. Rev. E 89 053320

    [24]

    Huang J J, Huang H, Wang X 2015 Int. J. Numer. Meth. Fluids 77 123

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出版历程
  • 收稿日期:  2015-11-23
  • 修回日期:  2015-12-28
  • 刊出日期:  2016-04-05

液滴撞击液膜过程的格子Boltzmann方法模拟

  • 1. 华中科技大学数学与统计学院, 武汉 430074;
  • 2. 武昌理工学院信息工程学院, 武汉 430223;
  • 3. 杭州电子科技大学物理系, 杭州 310018;
  • 4. 华中科技大学, 煤燃烧国家重点实验室, 武汉 430074
  • 通信作者: 柴振华, hustczh@hust.edu.cn
    基金项目: 国家自然科学基金(批准号: 51576079, 11272132)和湖北省自然科学基金(批准号: 2015CFB440)资助的课题.

摘要: 本文采用格子Boltzmann方法对液滴撞击液膜过程进行了研究, 主要考察了雷诺数(Re)、韦伯数(We)、相对液膜厚度 (h) 以及表面张力 () 等物理参数对界面运动过程的影响. 首先, 随着Re数和We数的增加, 可以明显观察到液滴撞击液膜过程中形成的皇冠状水花以及卷吸现象; 当Re数较大时, 液体会发生飞溅, 由液体飞溅形成的小液滴则会继续下落, 并与液膜再次发生碰撞. 其次, 当相对液膜厚度较小时, 液滴撞击液膜并最终导致液膜断裂; 然而随着相对液膜厚度的增大, 尽管撞击过程溅起的液体会越来越多, 但是液膜并不会发生断裂. 再次, 随着表面张力的增大, 界面变形阻力增大, 撞击过程中产生的界面形变也逐渐减弱. 最后还发现皇冠(由液滴溅起形成)半径r 随时间满足r/(2R) Ut/(2R), 这一结果与已有结论是一致的.

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