Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-28T01:03:48.924Z Has data issue: false hasContentIssue false
  • English
  • Français

Multiphysic Two-Phase Flow Lattice Boltzmann: Droplets with Realistic Representation of the Interface

Published online by Cambridge University Press:  20 August 2015

Pablo M. Dupuy ,
María Fernandino ,
Hugo A. Jakobsen  and
Hallvard F. Svendsen
Pablo M. Dupuy*
Affiliation:
Department of Chemical Engineering, Norwegian University of Science and Technology, N-7491 Trondheim, Norway CSIRO - Mathematics, Informatics and Statistics, Melbourne, Australia. (Current affiliation)
María Fernandino*
Affiliation:
Department of Energy and Process Engineering, Norwegian University of Science and Technology, N-7491 Trondheim, Norway
Hugo A. Jakobsen*
Affiliation:
Department of Chemical Engineering, Norwegian University of Science and Technology, N-7491 Trondheim, Norway
Hallvard F. Svendsen*
Affiliation:
Department of Chemical Engineering, Norwegian University of Science and Technology, N-7491 Trondheim, Norway
*
Email:[email protected], [email protected]
Corresponding author.Email:[email protected]
Email:[email protected]
Email:[email protected]
Get access

Abstract

Free energy lattice Boltzmann methods are well suited for the simulation of two phase flow problems. The model for the interface is based on well understood physical grounds. In most cases a numerical interface is used instead of the physical one because of lattice resolution limitations. In this paper we present a framework where we can both follow the droplet behavior in a coarse scale and solve the interface in a fine scale simultaneously. We apply the method for the simulation of a droplet using an interface to diameter size ratio of 1 to 280. In a second simulation, a small droplet coalesces with a 42 times larger droplet producing on it only a small capillary wave that propagates and dissipates.

Keywords

82.70.-y02.70.Hm02.60.NmTwo-phase flowdiffuse interface modelmulti-scalereal interface
Type
Research Article
Information
Communications in Computational Physics , Volume 9 , Issue 5 , May 2011 , pp. 1414 - 1430
Copyright
Copyright © Global Science Press Limited 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Baden, S. B., Structured Adaptive Mesh Refinement (SAMR) Grid Methods, Springer-Verlag New York, Inc., Secaucus, NJ, USA, 1999.Google Scholar
[2]Cahn, J. W. and Hilliard, J. E., Free energy of a nonuniform system. I, interfacial free energy, J. Chem. Phys., 28(2) (1958), 258–267.Google Scholar
[3]Cahn, J. W. and Hilliard, J. E., Spinodal decomposition: a reprise, Acta. Metall. Mater., 19 (1971), 151–161.Google Scholar
[4]Chen, H., Filippova, O., Hoch, J., Molvig, K., Shock, R., Teixeira, C., and Zhang, R., Grid refinement in lattice Boltzmann methods based on volumetric formulation, Phys. A., 362 (2006), 158–167.Google Scholar
[5]Dupuy, P. M., Fernandino, M., Jakobsen, H. A., and Svendsen, H. F., Fractional step two-phase flow lattice Boltzmann model implementation, J. Stat. Mech. Theory. Exp., (2009), P06014.Google Scholar
[6]Dupuy, P. M., Fernandino, M., Jakobsen, H. A., and Svendsen, H. F., Using Cahn-Hilliard mobility to simulate coalescence dynamics, Comput. Math. Appl., 59 (2010), 2246–2259.Google Scholar
[7]Filippova, O. and Hänel, D., Grid refinement for lattice-BGK models, J. Comput. Phys., 147(1) (1998), 219–228.Google Scholar
[8]Jacqmin, D., Calculation of two-phase Navier-Stokes flows using phase-field modeling, J. Comput. Phys., 155(1) (1999), 96–127.Google Scholar
[9]Jamet, D., Torres, D. and Brackbill, J. U., On the theory and computation of surface tension: the elimination of parasitic currents through energy conservation in the second-gradient method, J. Comput. Phys., 182(1) (2002), 262–276.Google Scholar
[10]Kaufman, A., Fan, Z. and Petkov, K., Implementing the lattice Boltzmann model on commodity graphics hardware, J. Stat. Mech. Theory. Exp., 06 (2009), P06016.Google Scholar
[11]Lee, T. and Lin, Ching-Long, Pressure evolution lattice-Boltzmann-equation method for two-phase flow with phase change, Phys. Rev. E., 67(5) (2003), 056703.CrossRefGoogle ScholarPubMed
[12]Lee, T. and Lin, Ching-Long, A stable discretization of the lattice Boltzmann equation for simulation of incompressible two-phase flows at high density ratio, J. Comput. Phys., 206(1) (2005), 16–47.Google Scholar
[13]Li, Q. and Wagner, A. J., Symmetric free-energy-based multicomponent lattice boltzmann method, Phys. Rev. E., 76(3) (2007), 036701.Google Scholar
[14]Mattila, K., Hyvluoma, J., Rossi, T., Aspns, M., and Westerholm, J., An efficient swap algorithm for the lattice Boltzmann method, Comput. Phys. Commun., 176(3) (2007), 200–210.Google Scholar
[15]Pan, Y. and Suga, K., Numerical simulation of binary liquid droplet collision, Phys. Fluids., 17(8) (2005), 082105.Google Scholar
[16]Shu, C., Niu, X. D., Chew, Y. T., and Cai, Q. D., A fractional step lattice Boltzmann method for simulating high Reynolds number flows, Math. Comput. Sim., 72(2-6) (2006), 201–205.Google Scholar
[17]Stiebler, M., Tölke, J., and Krafczyk, M., Advection-diffusion lattice Boltzmann scheme for hierarchical grids, Comput. Math. Appl., 55(7) (2008), 1576–1584.Google Scholar
[18]Tölke, J., Freudiger, S., and Krafczyk, M., An adaptive scheme using hierarchical grids for lattice Boltzmann multi-phase flow simulations, Comput. Fluids., 35(8-9) (2006), 820–830, Proceedings of the First International Conference for Mesoscopic Methods in Engineering and Science.Google Scholar
[19]Wagner, A.J., Thermodynamic consistency of liquid-gas lattice Boltzmann simulations, Phys. Rev. E., 74(5) (2006), 056703.Google Scholar
[20]Wilke, J., Pohl, T., and Kowarschik, M., Cache performance optimizations for parallel lattice Boltzmann codes, Lect. Notes. Comput. Sc., 2790 (2003), 441–450.Google Scholar
[21]Yu, Z. and Fan, Liang-Shih, An interaction potential based lattice Boltzmann method with adaptive mesh refinement (AMR) for two-phase flow simulation, J. Comput. Phys., 228(17) (2009), 6456–6478.Google Scholar
[22]Zheng, H. W., Shu, C., and Chew, Y. T., Lattice boltzmann interface capturing method for incompressible flows, Phys. Rev. E., 72(5) (2005), 056705.CrossRefGoogle ScholarPubMed
[23]Zheng, H. W., Shu, C., and Chew, Y. T., A lattice Boltzmann model for multiphase flows with large density ratio, J. Comput. Phys., 218(1) (2006), 353–371.Google Scholar