Four different types of a single drop dripping down a hole under gravity by lattice Boltzmann method

Document Type: Research Paper

Authors

1 دانشیار دانشکده مهندسی مکانیک دانشگاه تهران

2 PhD student in School of Mechanical Eng.

Abstract

In this paper the dynamic of a droplet on a surface with a hole is investigated under gravitational effect by using lattice Boltzmann method. Incompressible two-phase flow with high density ratio proposed by Lee is considered. Cahn’s theory is used to observe the wettability of the surface in contact with liquid and gas phases. Several parameters such as contact angle, surface tension and gravitational acceleration are studied to demonstrate their effects on the deformation of the droplet. To evaluate the results, the benchmark problems for equilibrium contact angle, capillary rise and Laplace law are conducted and a satisfactory agreement with analytical results is shown. Based on this study, four typical deformations of a droplet dripping down a hole can be observed; equilibrium drop on the top of the surface, equilibrium drop under the bottom of the surface, splashing and dripping of the drop. It is seen that at low Ohnesorge numbers the droplet deforms slightly and tends to retain its state. Moreover any increase in the Archimedes number magnifies the tendency to pass through the hole. Also, the relationship between the volume of the remaining droplet on the surface and Archimedes and Ohnesorge numbers is investigated. It is found that by increasing the Archimedes number, the volume of the remaining droplet on the surface reaches a constant value that is dependent on geometric parameters.

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Main Subjects


[1]           M. C. Sukop and D. T. Thorne, Lattice Boltzmann Modeling: An introduction for Geoscientists and Engineers. Berlin: Springer, 2005.

[2]           H. X and L. Ls, "A priori derivation of the lattice Boltzmann equation," Phys Rev E, vol. 55, p. R6333, 1997.

[3]           S. Chen and G. D. Doolen, "Lattice Boltzmann method for fluid flows," Ann. Rev. Fluid Mech. , vol. 30, pp. 329-364, 1998.

[4]           S. Succi, The Lattice Boltzmann Equation for Fluid Dynamics and Beyound, 2001.

[5]           A. Fakhari and M. H. Rahimian, "SIMULATION OF AN AXISYMMETRIC RISING BUBBLE BY A MULTIPLE RELAXATION TIME LATTICE BOLTZMANN METHOD," International Journal of Modern Physics B, vol. 23, 2009.

[6]           M. Taghilou and M. H. Rahimian, "Investigation of two-phase flow in porous media using lattice Boltzmann method," Computers & Mathematics with Applications, vol. 67, pp. 424–436, 2014.

[7]           H. Safari, M., M. H. Rahimian, M Krafczyk , "Consistent simulation of droplet evaporation based on the phase-field multiphase lattice Boltzmann method," Physical Review E 90 (3), 033305, 2014.

[8]           A. Begmohammadi, M. H. Rahimian, M. Farhadzadeh, and M. A. Hatani, "Numerical simulation of single-and multi-mode film boiling using lattice Boltzmann method," Computers & Mathematics with Applications, vol. 71, pp. 1861–1874, 2016.

[9]           M. A. Hatani, M. Farhadzadeh, and M. H. Rahimian, "Investigation of vapor condensation on a flat plate and horizontal cryogenic tube using lattice Boltzmann method," International Communications in Heat and Mass Transfer, vol. 66, pp. 218–225, 2015.

[10]         H. Amirshaghaghi, M. H. Rahimian, and H. Safari, "Application of a two phase lattice Boltzmann model in simulation of free surface jet impingement heat transfer " International Communications in Heat and Mass Transfer, vol. 75, pp. 282–294, 2016.

[11]         A. L. Yarin and D. A. Weiss, "Impact of drops on solid surfaces: self-similar capillary waves, and splashing as a new type of kinematic discontinuity," J Fluid Mech, vol. 283, pp. 283-141, 1995.

[12]         D. Morton, M. Rudman, and L. Jong-Leng, "An investigation of the flow regimes resulting from splashing drops," Phys Fluid, vol. 12, 2000.

[13]         S. Mukherjee and J. Abraham, "Lattice Boltzmann simulations of two-phse flow with high density ratio in axially symmetric geometry," Phys Rev E, vol. 75, p. 026701, 2007.

[14]         S. Sikalo, M. Marengo, C. Tropea, and E. N. Ganic, "Analysis of impact of droplets on horizontal surfaces," Exp. Therm. Fluid Sci., vol. 25, pp. 503-510, 2005.

[15]         S. Sikalo, C. Tropea, and E. N. Ganic, "Dynamic wetting angle of spreading droplet," Exp. Therm. Fluid Sci., vol. 29, pp. 795-802, 2005.

[16]         S. Sikalo, C. Tropea, and E. N. Ganic, "Impact of droplets onto inclined sufraces," J. Colloid Interf. Sci., vol. 286, pp. 661-669, 2005.

[17]         R. Haghani, M. H. Rahimian, and M. Taghilou, "LBM Simulation of a Droplet Dripping Down a Hole," Eng. App. Comp. Fluid Mech., vol. 7, pp. 461-470, 2013.

[18]         S. F. Lunkad, V. V. Buwa, and K. D. P. Nigam, "Numerical simulations of drop impact and spreading on horizontal and inclined surface," Chem. Eng. Sci., vol. 62, pp. 7214-7224, 2007.

[19]         X. He, X. Shan, and G. D. Doolen, "Discrete Boltzmann equation model for nonideal gases," Physical Review E, vol. 57, pp. R13--R16, 1998.

[20]         T. Lee, "Effects of incompressibility on the elimination of parasitic currents in the lattice Boltzmann equation method for binary fluids," Com. Math. App., vol. 58, pp. 987-994, 2009.

[21]      T. Lee and L. Liu, "Lattice Boltzmann simulations of micron-scale drop impact on dry surfaces," J. Com. Phy., vol. 229, pp. 8045-8063, 2010