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Investigations on the Droplet Impact onto a Spherical Surface with a High Density Ratio Multi-Relaxation Time Lattice-Boltzmann Model

Published online by Cambridge University Press:  03 June 2015

Duo Zhang ,
K. Papadikis  and
Sai Gu
Duo Zhang
Affiliation:
Xi’an Jiaotong-Liverpool University, No. 111 Ren’ai Road, Suzhou Dushu Lake Higher Education Town, Suzhou, China 215123 School of Engineering, University of Liverpool, Brownlow Hill, Liverpool, L69 7ZX, United Kingdom
K. Papadikis*
Affiliation:
Xi’an Jiaotong-Liverpool University, No. 111 Ren’ai Road, Suzhou Dushu Lake Higher Education Town, Suzhou, China 215123
Sai Gu
Affiliation:
School of Engineering, Cranfield University, Bedfordshire MK43 0AL, United Kingdom
*
*Corresponding author.Email:[email protected]
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Abstract

In the current study, a two-dimensional multi-relaxation time (MRT) lattice Boltzmann model which can tolerate high density ratios and low viscosity is employed to simulate the liquid droplet impact onto a curved target. The temporal variation of the film thickness at the north pole of the target surface is investigated. Three different temporal phases of the dynamics behavior, namely, the initial drop deformation phase, the inertia dominated phase and the viscosity dominated phase are reproduced and studied. The effect of the Reynolds number, Weber number and Galilei number on the film flow dynamics is investigated. In addition, the dynamic behavior of the droplet impact onto the side of the curved target is shown, and the effect of the contact angle, the Reynolds number and the Weber number are investigated.

Keywords

76T10Multiphase flowMRT Lattice Boltzmannhigh-density-ratiodroplet impactfilm thicknessdynamic behavior
Type
Research Article
Information
Communications in Computational Physics , Volume 16 , Issue 4 , October 2014 , pp. 892 - 912
Copyright
Copyright © Global Science Press Limited 2014

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References

[1]Rein, M., Phenomena of liquid drop impact on solid and liquid surface, Fluid Dyn. Res., 38(1993), 61.CrossRefGoogle Scholar
[2]Yarin, A. L., Drop impact dynamics: Splashing, spreading, receding, bouncing…, Annu. Rev. Fluid Mech., 38(2006), 159–192.Google Scholar
[3]Rioboo, R., Marengo, M. and Tropea, C., Time evolution of liquid drop impact onto solid, dry surfaces, Exp. Fluids, 33(2002), 112–124.Google Scholar
[4]Asai, A., Shioya, M., Hirasawa, S. and Okazaki, T., Impact of an ink drop on paper, J. Imaging Sci. Techn., 37(1993), 205–207.Google Scholar
[5]Scheller, B. L. and Bousfield, D. W., Newtonian drop impact with a solid surface, AIChE J., 41(1995), 1357–1367.Google Scholar
[6]Pasandideh-Fard, M., Qiao, Y. M., Chandra, S. and Mostaghimi, J., Capillary effects during droplet impact on a solid surface, Phys. Fluids, 8(1996), 650.Google Scholar
[7]Mao, T., Kuhn, D. C. S. and Tran, H., Spread and rebound of liquid droplets upon impact on flat surfaces, AIChE J., 43(1997), 2169–2179.CrossRefGoogle Scholar
[8]Roisman, I. V., Rioboo, R. and Tropea, C., Normal impact of a liquid drop on a dry surface: Model for spreading and receding, Proc. R.Soc. London, Ser. A 458(2002), 1411–1430.CrossRefGoogle Scholar
[9]Hung, L. S. and Yao, S. C., Experimental investigation of the impaction of water droplets on cylindrical objects, Int. J. Multiphase Flow, 25(1999), 1545–1559.CrossRefGoogle Scholar
[10]Hardalupas, Y., Taylor, A. M. K. P. and Wilkins, J. H., Experimental investigation of submillimeter droplet impingement onto spherical surfaces, Int. J. Heat Fluid Flow, 20(1999), 477485.Google Scholar
[11]Bakshi, S., Roisman, L. V. and Tropea, C., Investigations on the impact of a drop onto a small spherical target, Phys. Fluids, 19(2007), 032102.Google Scholar
[12]Trapaga, G. and Szekely, J., Mathematical modeling of the isothermal impingement of liquid droplets in spraying processes, Metall. Trans. B, 22(1991), 901–914.Google Scholar
[13]Bussmann, M. and Afkhami, S., Drop impact simulation with a velocity-dependent contact angle, Chem. Eng. Sci., 62(2007), 7214.Google Scholar
[14]Pasandideh-Fard, M., Bussmann, M., Chandra, S. and Mostaghimi, J., Simulating droplet impact on a substrate of arbitrary shape, Atomization Spray., 11(2001), 397–414.Google Scholar
[15]Liu, H., Krishnan, S., Marella, S. and Udaykumar, H. S., Sharp interface Cartesian grid method II: A technique for simulating droplet interactions with surfaces of arbitrary shape, J. Comput. Phys., 210(2005), 32–54.Google Scholar
[16]Ge, Y. and Fan, L. S., Droplet-particle collision mechanics with film-boiling evaporation, J. Fluid Mech., 573(2007), 331–337.Google Scholar
[17]Shan, X. and Chen, H., Simulation of nonideal gases and liquid-gas phase transitions by the lattice Boltzmann equation, Phys. Rev. E, 49(1994), 2941–2948.Google Scholar
[18]Swift, M. R., Orlandini, E., Osborn, W. R. and Yeomans, J. M., Lattice Boltzmann simulations of liquid-gas and binary fluid systems, Phys. Rev. E, 54(1996), 5041–5052.Google Scholar
[19]He, X., Chen, S. and Zhang, R., A lattice Boltzmann scheme for incompressible multiphase flow and its application in simulation of Rayleigh-Taylor instability, J. Comput. Phys., 152(1999), 642–663.Google Scholar
[20]Inamuro, T., Ogata, T., Tajima, S. and Konishi, N., A lattice Boltzmann method for incompressible two-phase flows with large density differences, J. Comput. Phys., 198(2004), 628–644.CrossRefGoogle Scholar
[21]Yan, Y. Y. and Zu, Y. Q., A lattice Boltzmann method for incompressible two-phase flows on partial wetting surface with large density ratio, J. Comput. Phys., 227(2007), 763–775.Google Scholar
[22]Briant, A. J., Papatzacos, P. and Yeomans, J. M., Lattice Boltzmann simulations of contact line motion in a liquid-gas system, Philos. Trans. Roy. Soc. Lond. A, 360(2002), 485–495.CrossRefGoogle Scholar
[23]Lee, T. and Lin, L., Lattice Boltzmann simulations of micron-scale drop impact on dry surfaces, J. Comput. Phys., 229(2010), 8045–8063.Google Scholar
[24]Kaehler, G. and Wagner, A. J., Derivation of hydrodynamics for multi-relaxation time lattice Boltzmann using the moment approach, Commun. Comput. Phys., 13(2013), 614–628.Google Scholar
[25]Wang, L., Guo, Z. L., Shi, B. C. and Zheng, C. G., Evaluation of three lattice Boltzmann models for particulate flows, Commun. Comput. Phys., 13(2013), 1151–1172.Google Scholar
[26]Li, Q. X., Hong, N., Shi, B. C. and Chai, Z. H., Simulation of power-law fluid flows in two-dimensional square cavity using multi-relaxation-time lattice Boltzmann method, Commun. Comput. Phys., 15(2014), 265–284.Google Scholar
[27]Gupta, A. and Kumar, R., Droplet impingement and breakup on a dry surface, Comput. Fluids, 39(2010), 1696–1703.Google Scholar
[28]Gupta, A. and Kumar, R., Two-dimensional lattice Boltzmann model for droplet impingement and breakup in low density ratio liquids, Commun. Comput. Phys., 10(2011), 767–784.Google Scholar
[29]Shen, S. Q., Bi, F. F. and Guo, Y. L., Simulation of droplets impact on curved surfaces with lattice Boltzmann method, Int. J. Heat Mass Tranf., 55(2012), 69386943.Google Scholar
[30]Li, Q., Luo, K. H. and Li, X. J., Forcing scheme in pseudopotential lattice Boltzmann model multiphase flows, Phys. Rev. E, 86(2012), 016709.Google Scholar
[31]Yuan, P. and Schaefer, L., Equations of state in a lattice Boltzmann model, Phys. Fluids, 18(2006), 042101.Google Scholar
[32]Guo, Z., Z, C. and Shi, B., Discrete lattice effects on the forcing term in the lattice Boltzmann method, Phys. Rev. E, 65(2002), 046308.Google Scholar
[33]Yu, Z. and Fan, L. S., Multirelaxation-time interaction-potential-based lattice Boltzmann model for two-phase flow, Phys. Rev. E, 82(2010), 046708.Google Scholar
[34]Li, Q., Luo, K. H. and Li, X. J., Lattice Boltzmann modeling of multiphase flows at large density ratio with an improved pseudopotential model, Phys. Rev. E, 87(2013), 053301.Google Scholar