Journal of Mechanical Science and Technology

, Volume 32, Issue 5, pp 2119–2126 | Cite as

Numerical simulation of the freezing process of a water drop attached to a cold plate

  • Truong V. VuEmail author
  • Khoa V. Dao
  • Binh D. Pham


This paper presents a direct numerical work on the freezing process of a water drop that is either sessile on or pendant from a cold plate. The numerical technique used is an axisymmetric front-tracking method to represent interfaces that separate different phases. The sessile drop corresponds to positive Bond numbers Bo (i.e., Bo > 0), and the pendant drop represents the other values of Bo. Numerical results show that pendant drops break up into liquid drops when gravity dominates the force induced by surface tension at Bo < 0. That is, a decrease in Bo enhances the breakup of the freezing drop. The breakup also depends significantly on the initial shape of the drop in terms of the contact angle at the plate ϕ0, that is, increasing ϕ0 induces breakup. In addition, the drop rapidly completes freezing due to breakup. In the case of non-breakup, the increase in Bo reduces the solidified drop height and decreases the time to complete solidification. The freezing process also consumes minimal time with small ϕ0. The solidified drop after solidification has a cone near the axis of symmetry due to volume expansion of water upon solidification. This shape of the solidified drop is in accordance with the experimental observation.


Direct numerical simulation Freezing Front-tracking Gravity Water drop 


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  1. [1]
    Y. Cao, Z. Wu, Y. Su and Z. Xu, Aircraft flight characteristics in icing conditions, Progress in Aerospace Sciences, 74 (2015) 62–80.CrossRefGoogle Scholar
  2. [2]
    N. Dalili, A. Edrisy and R. Carriveau, A review of surface engineering issues critical to wind turbine performance, Renewable and Sustainable Energy Reviews, 13 (2) (2009) 428–438.CrossRefGoogle Scholar
  3. [3]
    K. Mensah and J. M. Choi, Review of technologies for snow melting systems, J. of Mechanical Science and Technology, 29 (12) (2015) 5507–5521.CrossRefGoogle Scholar
  4. [4]
    D. M. Anderson, M. G. Worster and S. H. Davis, The case for a dynamic contact angle in containerless solidification, J. of Crystal Growth, 163 (3) (1996) 329–338.CrossRefGoogle Scholar
  5. [5]
    O. R. Enríquez, Á. G. Marín, K. G. Winkels and J. H. Snoeijer, Freezing singularities in water drops, Physics of Fluids, 24 (9) (2012) 091102.CrossRefGoogle Scholar
  6. [6]
    J. H. Snoeijer and P. Brunet, Pointy ice-drops: How water freezes into a singular shape, American J. of Physics, 80 (9) (2012) 764–771.CrossRefGoogle Scholar
  7. [7]
    H. Hu and Z. Jin, An icing physics study by using lifetimebased molecular tagging thermometry technique, International J. of Multiphase Flow, 36 (8) (2010) 672–681.CrossRefGoogle Scholar
  8. [8]
    Z. Jin, X. Cheng and Z. Yang, Experimental investigation of the successive freezing processes of water droplets on an ice surface, International J. of Heat and Mass Transfer, 107 (2017) 906–915.CrossRefGoogle Scholar
  9. [9]
    X. Zhang, X. Wu and J. Min, Freezing and melting of a sessile water droplet on a horizontal cold plate, Experimental Thermal and Fluid Science, 88 (2017) 1–7.CrossRefGoogle Scholar
  10. [10]
    G. A. Satunkin, Determination of growth angles, wetting angles, interfacial tensions and capillary constant values of melts, J. of Crystal Growth, 255 (1–2) (2003) 170–189.CrossRefGoogle Scholar
  11. [11]
    H. Itoh, H. Okamura, C. Nakamura, T. Abe, M. Nakayama and R. Komatsu, Growth of spherical Si crystals on porous Si3N4 substrate that repels Si melt, J. of Crystal Growth, 401 (2014) 748–752.CrossRefGoogle Scholar
  12. [12]
    A. Sanz, The crystallization of a molten sphere, J. of Crystal Growth, 74 (3) (1986) 642–655.CrossRefGoogle Scholar
  13. [13]
    M. Nauenberg, Theory and experiments on the ice-water front propagation in droplets freezing on a subzero surface, European J. of Physics, 37 (4) (2016) 045102.CrossRefGoogle Scholar
  14. [14]
    X. Zhang, X. Wu, J. Min and X. Liu, Modelling of sessile water droplet shape evolution during freezing with consideration of supercooling effect, Applied Thermal Engineering, 125 (2017) 644–651.CrossRefGoogle Scholar
  15. [15]
    W. W. Schultz, M. G. Worster and D. M. Anderson, Solidifying sessile water droplets, Interactive Dynamics of Convection and Solidification, Kluwer Academic Publishers, 209-226.Google Scholar
  16. [16]
    A. Virozub, I. G. Rasin and S. Brandon, Revisiting the constant growth angle: Estimation and verification via rigorous thermal modeling, J. of Crystal Growth, 310 (24) (2008) 5416–5422.CrossRefGoogle Scholar
  17. [17]
    G. Chaudhary and R. Li, Freezing of water droplets on solid surfaces: An experimental and numerical study, Experimental Thermal and Fluid Science, 57 (2014) 86–93.CrossRefGoogle Scholar
  18. [18]
    H. Zhang, Y. Zhao, R. Lv and C. Yang, Freezing of sessile water droplet for various contact angles, International J. of Thermal Sciences, 101 (2016) 59–67.CrossRefGoogle Scholar
  19. [19]
    T. V. Vu, G. Tryggvason, S. Homma, J. C. Wells and H. Takakura, A front-tracking method for three-phase computations of solidification with volume change, J. of Chemical Engineering of Japan, 46 (11) (2013) 726–731.CrossRefGoogle Scholar
  20. [20]
    T. V. Vu, G. Tryggvason, S. Homma and J. C. Wells, Numerical investigations of drop solidification on a cold plate in the presence of volume change, International J. of Multiphase Flow, 76 (2015) 73–85.MathSciNetCrossRefGoogle Scholar
  21. [21]
    P. Dimitrakopoulos, Gravitational effects on the deformation of a droplet adhering to a horizontal solid surface in shear flow, Physics of Fluids, 19 (12) (2007) 122105.CrossRefzbMATHGoogle Scholar
  22. [22]
    S. M. Tilehboni, E. Fattahi, H. H. Afrouzi and M. Farhadi, Numerical simulation of droplet detachment from solid walls under gravity force using lattice Boltzmann method, J. of Molecular Liquids, 212 (2015) 544–556.CrossRefGoogle Scholar
  23. [23]
    T. V. Vu, A. V. Truong, N. T. Hoang and D. K. Tran, Numerical investigations of solidification around a circular cylinder under forced convection, J. of Mechanical Science and Technology, 30 (11) (2016) 5019–5028.CrossRefGoogle Scholar
  24. [24]
    T. V. Vu and J. C. Wells, Numerical simulations of solidification around two tandemly-arranged circular cylinders under forced convection, International J. of Multiphase Flow, 89 (2017) 331–344.CrossRefGoogle Scholar
  25. [25]
    T. V. Vu, Three-phase computation of solidification in an open horizontal circular cylinder, International J. of Heat and Mass Transfer, 111 (2017) 398–409.CrossRefGoogle Scholar
  26. [26]
    C.-C. Liao, Y.-W. Chang, C.-A. Lin and J. M. McDonough, Simulating flows with moving rigid boundary using immersed-boundary method, Computers & Fluids, 39 (1) (2010) 152–167.CrossRefzbMATHGoogle Scholar
  27. [27]
    Z. Jin, S. Jin and Z. Yang, Visualization of icing process of a water droplet impinging onto a frozen cold plate under free and forced convection, J. of Visualization, 16 (1) (2013) 13–17.CrossRefGoogle Scholar
  28. [28]
    L. Huang, Z. Liu, Y. Liu, Y. Gou and L. Wang, Effect of contact angle on water droplet freezing process on a cold flat surface, Experimental Thermal and Fluid Science, 40 (2012) 74–80.CrossRefGoogle Scholar
  29. [29]
    F. H. Harlow and J. E. Welch, Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface, Physics of Fluids, 8 (12) (1965) 2182–2189.MathSciNetCrossRefzbMATHGoogle Scholar
  30. [30]
    N. Al-Rawahi and G. Tryggvason, Numerical simulation of dendritic solidification with convection: Two-dimensional geometry, J. of Computational Physics, 180 (2) (2002) 471–496.CrossRefzbMATHGoogle Scholar
  31. [31]
    A. Esmaeeli and G. Tryggvason, Computations of film boiling. Part I: Numerical method, International J. of Heat and Mass Transfer, 47 (25) (2004) 5451–5461.CrossRefzbMATHGoogle Scholar

Copyright information

© The Korean Society of Mechanical Engineers and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Transportation EngineeringHanoi University of Science and TechnologyHanoiVietnam

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