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Numerical analysis of hollow droplet impact on a flat surface

Zheng Zhi-Wei Li Da-Shu Qiu Xing-Qi Cui Yun-Jing

Numerical analysis of hollow droplet impact on a flat surface

Zheng Zhi-Wei, Li Da-Shu, Qiu Xing-Qi, Cui Yun-Jing
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  • Many researches of a dense droplet impacting on a flat surface have been reported in the literature. However, the mechanism of a hollow droplet impacting on a flat surface has not yet been well addressed. A mathematical model is developed in the present research to resolve this impacting process. The model couples level set and volume of fluid method, and considers heat transfer and contact resistance between the droplet and surface. The validation of the model is carried out by comparing simulation results with experiment data. Different impact behaviors are observed in the impacting processes of both the dense droplet and the hollow droplet on a flat surface, obtained from the simulation result. The hydrodynamics and heat transfer behaviors of the hollow droplet impacting on a flat surface and the formation of central jetting are also explored. The effects of impact velocity and surface wettability on the impacting behavior of the hollow droplet are also analyzed. The results show that in the impacting process, the hollow droplet presents a spread and central jetting pattern, accompanying liquid shell contraction and breakup, while only spread and liquid shell contraction are observed in the dense droplet impacting process. It is also observed that the central jetting of the hollow droplet peels off the surface in the final impacting stage. The dimensionless spread factor for the hollow droplet is less than that of the dense droplet with the same initial kinetic energy in spread stage. The pressure gradient inside the hollow droplet is the main factor resulting in the spread and central jetting. The temperature distribution in the liquid shell and the surface is more uniform than in the central jetting, which is caused by the secondary breakup of the liquid shell. The spread factor of the hollow droplet remains unchanged as the impact velocity increases but is closely related to the surface wettability. The spread factor of the hydrophilic surface is larger than that of the hydrophobic surface. The effects of the surface wettability on the spread factor gradually reduce with the increase of the impact velocity. The effects of the impact velocity on the dimensionless jet length and the average wall heat flux are significant, while the surface wettability plays a negligible role in them. Improving the impact velocity increases the dimensionless length of the central jetting and the average wall heat flux, but this influence diminishes under a high impact velocity condition. Neither the dimensionless time spans of reaching the maximum spread factor nor the maximum average wall heat flux for the hollow droplet is influenced by the impact velocity and surface wettability and the development of the spread falls behind the heat transfer. Furthermore, the maximum spread factor increases with Reynolds number, and when Reynolds number is higher than 500, the increase in the maximum spread factor is no longer significant.
      Corresponding author: Li Da-Shu, lstax01@163.com;apvshi@upc.edu.cn ; Qiu Xing-Qi, lstax01@163.com;apvshi@upc.edu.cn
    • Funds: Project supported by the National Science and Technology Major Project of the Ministry of Science and Technology of China(Grant No. GZH201200602-01) and the Fundamental Research Funds for the Central Universities of Ministry of Education of China(Grant No. 15CX06052A).
    [1]

    Moreira A L N, Moita A S, Panao M R 2010 Prog. Energ. Combust. 36 554

    [2]

    Li D S, Qiu X Q, Yu L, Xu J, Duan X L, Zheng Z W 2014 Ind. Heating 43 1 (in Chinese)[李大树, 仇性启, 于磊, 许京, 段小龙, 郑志伟2014工业加热43 1]

    [3]

    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]

    [4]

    Rioboo R, Tropea C, Marengo M 2001 Atomization Spray 11 155

    [5]

    Bi F F, Guo Y L, Shen S Q, Chen J X, Li Y Q 2012 Acta Phys. Sin. 61 184702 (in Chinese)[毕菲菲, 郭亚丽, 沈胜强, 陈觉先, 李熠桥2012物理学报61 184702]

    [6]

    Li D S, Qiu X Q, Cui Y J, Zheng Z W, Ma P Y, Qi F L 2014 T. Chin. Soc. Agric. Mach. 45 25 (in Chinese)[李大树, 仇性启, 崔运静, 郑志伟, 马培勇, 祁风雷2014农业机械学报45 25]

    [7]

    Kwon T J 2003 Ph. D. Dissertation(West Lafayette:Purdue University)

    [8]

    Yokoi K 2011 Soft Matter 7 5120

    [9]

    Solonenko O P, Gulyaev I P, Smirnov A V 2008 Tech. Phys. Lett. 34 1050

    [10]

    Shukla R K, Kumar A 2015 J. Therm. Spray Techn. 24 1368

    [11]

    Gulyaev I P, Solonenko O P, Gulyaev P Y, Smirnov A V 2009 Tech. Phys. Lett. 35 885

    [12]

    Gulyaev I P, Solonenko O P 2013 Exp. Fluids 54 1

    [13]

    Solonenko O P, Smirnov A V, Gulyaev I P 2008 The 5th International Workshop on Complex Systems Sendai, Japan, September 26——28, 2008982 561

    [14]

    Shinoda K, Murakami H 2010 J. Therm. Spray Techn. 19 602

    [15]

    Kumar A, Gu S 2012 Int. J. Heat Fluid Fl. 37 189

    [16]

    Kumar A, Gu S, Tabbara H, Kamnis S 2013 Surf. Coat. Techn. 220 164

    [17]

    Tabbara H, Gu S 2012 Int. J. Heat Mass Trans. 55 2081

    [18]

    Brackbill J U, Kothe D B, Zemach C 1992 J. Comput. Phys. 100 335

    [19]

    Yokoi K 2013 J. Comput. Phys. 232 252

    [20]

    Guo Y, Wei L, Liang G, Shen S 2014 Int. Commun. Heat Mass 53 26

    [21]

    Yang B H 2013 Ph. D. Dissertation(Chongqing:Chongqing University)(in Chinese)[杨宝海2013博士学位论文(重庆:重庆大学)]

    [22]

    Ubbink O, Issa R I 1999 J. Comput. Phys. 153 26

    [23]

    Liang C, Wang H, Zhu X, Chen R, Ding Y D, Liao Q 2013 CIESC J. 64 2745 (in Chinese)[梁超, 王宏, 朱恂, 陈蓉, 丁玉栋, 廖强2013化工学报64 2745]

    [24]

    Liu D W, Ning Z, L M, Yan K, Sun C H 2016 Chin. J. Comput. Mech. 33 3027 (in Chinese)[刘冬薇, 宁智, 吕明, 阎凯, 孙春华2016计算力学学报33 3027]

    [25]

    Song Y C, Ning Z, Sun C H, L M, Yan K, Fu J 2013 J. Combust. Sci. Technol. 19 549 (in Chinese)[宋云超, 宁智, 孙春华, 吕明, 阎凯, 付娟2013燃烧科学与技术19 549]

    [26]

    Šikalo Š, Marengo M, Tropea C, Ganic E N 2002 Exp. Therm. Fluid Sci. 25 503

  • [1]

    Moreira A L N, Moita A S, Panao M R 2010 Prog. Energ. Combust. 36 554

    [2]

    Li D S, Qiu X Q, Yu L, Xu J, Duan X L, Zheng Z W 2014 Ind. Heating 43 1 (in Chinese)[李大树, 仇性启, 于磊, 许京, 段小龙, 郑志伟2014工业加热43 1]

    [3]

    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]

    [4]

    Rioboo R, Tropea C, Marengo M 2001 Atomization Spray 11 155

    [5]

    Bi F F, Guo Y L, Shen S Q, Chen J X, Li Y Q 2012 Acta Phys. Sin. 61 184702 (in Chinese)[毕菲菲, 郭亚丽, 沈胜强, 陈觉先, 李熠桥2012物理学报61 184702]

    [6]

    Li D S, Qiu X Q, Cui Y J, Zheng Z W, Ma P Y, Qi F L 2014 T. Chin. Soc. Agric. Mach. 45 25 (in Chinese)[李大树, 仇性启, 崔运静, 郑志伟, 马培勇, 祁风雷2014农业机械学报45 25]

    [7]

    Kwon T J 2003 Ph. D. Dissertation(West Lafayette:Purdue University)

    [8]

    Yokoi K 2011 Soft Matter 7 5120

    [9]

    Solonenko O P, Gulyaev I P, Smirnov A V 2008 Tech. Phys. Lett. 34 1050

    [10]

    Shukla R K, Kumar A 2015 J. Therm. Spray Techn. 24 1368

    [11]

    Gulyaev I P, Solonenko O P, Gulyaev P Y, Smirnov A V 2009 Tech. Phys. Lett. 35 885

    [12]

    Gulyaev I P, Solonenko O P 2013 Exp. Fluids 54 1

    [13]

    Solonenko O P, Smirnov A V, Gulyaev I P 2008 The 5th International Workshop on Complex Systems Sendai, Japan, September 26——28, 2008982 561

    [14]

    Shinoda K, Murakami H 2010 J. Therm. Spray Techn. 19 602

    [15]

    Kumar A, Gu S 2012 Int. J. Heat Fluid Fl. 37 189

    [16]

    Kumar A, Gu S, Tabbara H, Kamnis S 2013 Surf. Coat. Techn. 220 164

    [17]

    Tabbara H, Gu S 2012 Int. J. Heat Mass Trans. 55 2081

    [18]

    Brackbill J U, Kothe D B, Zemach C 1992 J. Comput. Phys. 100 335

    [19]

    Yokoi K 2013 J. Comput. Phys. 232 252

    [20]

    Guo Y, Wei L, Liang G, Shen S 2014 Int. Commun. Heat Mass 53 26

    [21]

    Yang B H 2013 Ph. D. Dissertation(Chongqing:Chongqing University)(in Chinese)[杨宝海2013博士学位论文(重庆:重庆大学)]

    [22]

    Ubbink O, Issa R I 1999 J. Comput. Phys. 153 26

    [23]

    Liang C, Wang H, Zhu X, Chen R, Ding Y D, Liao Q 2013 CIESC J. 64 2745 (in Chinese)[梁超, 王宏, 朱恂, 陈蓉, 丁玉栋, 廖强2013化工学报64 2745]

    [24]

    Liu D W, Ning Z, L M, Yan K, Sun C H 2016 Chin. J. Comput. Mech. 33 3027 (in Chinese)[刘冬薇, 宁智, 吕明, 阎凯, 孙春华2016计算力学学报33 3027]

    [25]

    Song Y C, Ning Z, Sun C H, L M, Yan K, Fu J 2013 J. Combust. Sci. Technol. 19 549 (in Chinese)[宋云超, 宁智, 孙春华, 吕明, 阎凯, 付娟2013燃烧科学与技术19 549]

    [26]

    Šikalo Š, Marengo M, Tropea C, Ganic E N 2002 Exp. Therm. Fluid Sci. 25 503

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  • Received Date:  04 June 2016
  • Accepted Date:  26 September 2016
  • Published Online:  05 January 2017

Numerical analysis of hollow droplet impact on a flat surface

    Corresponding author: Li Da-Shu, lstax01@163.com;apvshi@upc.edu.cn
    Corresponding author: Qiu Xing-Qi, lstax01@163.com;apvshi@upc.edu.cn
  • 1. College of Chemical Engineering, China University of Petroleum, Qingdao 266580, China;
  • 2. CNOOC Research Institute, Beijing 100028, China;
  • 3. College of Machinery and Electrical Engineering, China University of Petroleum, Qingdao 266580, China
Fund Project:  Project supported by the National Science and Technology Major Project of the Ministry of Science and Technology of China(Grant No. GZH201200602-01) and the Fundamental Research Funds for the Central Universities of Ministry of Education of China(Grant No. 15CX06052A).

Abstract: Many researches of a dense droplet impacting on a flat surface have been reported in the literature. However, the mechanism of a hollow droplet impacting on a flat surface has not yet been well addressed. A mathematical model is developed in the present research to resolve this impacting process. The model couples level set and volume of fluid method, and considers heat transfer and contact resistance between the droplet and surface. The validation of the model is carried out by comparing simulation results with experiment data. Different impact behaviors are observed in the impacting processes of both the dense droplet and the hollow droplet on a flat surface, obtained from the simulation result. The hydrodynamics and heat transfer behaviors of the hollow droplet impacting on a flat surface and the formation of central jetting are also explored. The effects of impact velocity and surface wettability on the impacting behavior of the hollow droplet are also analyzed. The results show that in the impacting process, the hollow droplet presents a spread and central jetting pattern, accompanying liquid shell contraction and breakup, while only spread and liquid shell contraction are observed in the dense droplet impacting process. It is also observed that the central jetting of the hollow droplet peels off the surface in the final impacting stage. The dimensionless spread factor for the hollow droplet is less than that of the dense droplet with the same initial kinetic energy in spread stage. The pressure gradient inside the hollow droplet is the main factor resulting in the spread and central jetting. The temperature distribution in the liquid shell and the surface is more uniform than in the central jetting, which is caused by the secondary breakup of the liquid shell. The spread factor of the hollow droplet remains unchanged as the impact velocity increases but is closely related to the surface wettability. The spread factor of the hydrophilic surface is larger than that of the hydrophobic surface. The effects of the surface wettability on the spread factor gradually reduce with the increase of the impact velocity. The effects of the impact velocity on the dimensionless jet length and the average wall heat flux are significant, while the surface wettability plays a negligible role in them. Improving the impact velocity increases the dimensionless length of the central jetting and the average wall heat flux, but this influence diminishes under a high impact velocity condition. Neither the dimensionless time spans of reaching the maximum spread factor nor the maximum average wall heat flux for the hollow droplet is influenced by the impact velocity and surface wettability and the development of the spread falls behind the heat transfer. Furthermore, the maximum spread factor increases with Reynolds number, and when Reynolds number is higher than 500, the increase in the maximum spread factor is no longer significant.

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