Skip to main content
SpringerLink
Log in

A pseudopotential-based multiple-relaxation-time lattice Boltzmann model for multicomponent/multiphase flows

  • Research Paper
  • Published:
Acta Mechanica Sinica Aims and scope Submit manuscript

Abstract

In this paper, a pseudopotential-based multiple-relaxation-time lattice Boltzmann model is proposed for multicomponent/multiphase flow systems. Unlike previous models in the literature, the present model not only enables the study of multicomponent flows with different molecular weights, different viscosities and different Schmidt numbers, but also ensures that the distribution function of each component evolves on the same square lattice without invoking additional interpolations. Furthermore, the Chapman-Enskog analysis shows that the present model results in the correct hydrodynamic equations, and satisfies the indifferentiability principle. The numerical validation exercises further demonstrate that the favorable performance of the present model.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Giovangigli, V.: Multicomponent Flow Modeling. Bikhauser, Boston (1999)

    Book  MATH  Google Scholar 

  2. Prosperetti, A., Tryggvason, G.: Computational Methods for Multiphase Flow. Cambridge University Press, Cambridge (2007)

    Book  Google Scholar 

  3. Guo, Z., Zheng C.: Theory and Applications of Lattice Boltzmann Method. Science Press, Beijng (2009)

    Google Scholar 

  4. Succi, S.: The Lattice Boltzmann Equation for Fluid Dynamics and Beyond. Oxford University Press, Oxford (2001)

    MATH  Google Scholar 

  5. Chen, S., Doolen, G. D: Lattice Boltzmann method for fluid flows. Annu. Rev. Fluid Mech. 30, 329–364 (1998)

    Article  MathSciNet  Google Scholar 

  6. Aidun, C. K., Clausen J. R.: Lattice Boltzmann method for complex flows. Annu. Rev. Fluid Mech. 42, 439–472 (2010)

    Article  MathSciNet  Google Scholar 

  7. Gunstensen, A. E., Rothman, D. H, Zaleski, S., et al.: Lattice Boltzmann model of immiscible fluids. Phys. Rev. A 43, 4320–4327 (1991)

    Article  Google Scholar 

  8. Flekkoy, E. G.: Lattice BGK models for miscible fluids. Phys. Rev. E 47, 4247–4257 (1993)

    Article  Google Scholar 

  9. Shan, X., Chen, H.: Lattice Boltzmann model for simulating flows with multiple phases and components. Phys. Rev. E 47, 1815–1819 (1993)

    Article  Google Scholar 

  10. Shan, X., Doolen, G.: Multicomponent lattice-Boltzmann model with interparticle interaction. J. Stat. Phys. 81, 379–393 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  11. Shan, X.: Diffusion in a multicomponent lattice Boltzmann model. Phys. Rev. E 54, 3614–3620 (1996)

    Article  Google Scholar 

  12. Swift, M. R., Orlandini, E. O., Osborn, W. R., et al.: Lattice Boltzmann simulations of liquid-gas and binary fluid systems. Phys. Rev. E 54, 5041–5051 (1996)

    Article  Google Scholar 

  13. Luo, L. S., Girimaji, S. S.: Theory of the lattice Boltzmann method: Two-fluid model for binary mixtures. Phys. Rev. E 67, 036302 (2003).

    Article  Google Scholar 

  14. Guo, Z., Zhao, T. S.: Discrete velocity and lattice Boltzmann models for binary mixtures of nonideal fluids. Phys. Rev. E 68, 035302 (2003)

    Article  Google Scholar 

  15. Guo, Z., Zhao, T. S.: Finite-difference-based lattice Boltzmann model for dense binary mixtures. Phys. Rev. E 71, 026701 (2005)

    Article  Google Scholar 

  16. McCracken, M., Abraham J.: Lattice Boltzmann methods for binary mixtures with different molecular weights. Phys. Rev. E 71, 046704 (2005)

    Article  Google Scholar 

  17. Arcidiacono, S., Karlin, I. V., Mantzaras, J., et al.: Lattice Boltzmann model for the simulation of multcomponent mixtures. Phys. Rev. E 76, 046703 (2007)

    Article  Google Scholar 

  18. Asinari, P.: Semi-implicit-linearized multiple-relaxation-time formulation of lattice Boltzmann scheme for mixture modeling. Phys. Rev. E 73, 056705 (2006)

    Article  MathSciNet  Google Scholar 

  19. Asinari, P., Luo L. S.: A consistent lattice Boltzmann equation with baroclinic coupling for mixture. J. Comput. Phys. 227, 3879–3895 (2008)

    Article  MathSciNet  Google Scholar 

  20. Zheng, L., Guo, Z., Shi, B., et al.: Finite-difference-based multiple-relaxation-times lattice Boltzmann model for binary mixtures. Phys. Rev. E 81, 016706 (2010)

    Article  Google Scholar 

  21. Martys, N. S., Chen, H.: Simulation of multicomponent fluids in complex three-dimensional geometries by the lattice Boltzmann method. Phys. Rev. E 53, 743–750 (1996)

    Article  Google Scholar 

  22. Kang, Q., Zhang, D., Chen, S.: Displacement of a threedimensional immiscible droplet in a duct. J. Fluid Mech. 545, 41–66 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  23. Pan, C., Hilpert, M., Miller, C. T.: Lattice-Boltzmann simulation of two-phase flow in porous media. Water Resour. Res. 40, W01501 (2004)

    Article  Google Scholar 

  24. Li, H., Pan, C., Mill, C. T.: Pore-scale investigation of viscous coupling effects for two-phase flow in porous media. Phys. Rev. E 72, 026705 (2005)

    Article  Google Scholar 

  25. Yu, Z., Hemminger, O., Fan, L. S.: Experimental and lattice Boltzmann simulation of two-phase gas-liquid flows. Chem. Eng. Sci. 62, 7172–7183 (2007)

    Article  Google Scholar 

  26. Sankaranarayanan, K., Shan, X., Kevrekidis, I.G., et al.: Analysis of drag and virtual mass forces in bubbly suspensions using an implicit formulation of the lattice Boltzmann method. J. Fluid Mech. 452, 61–96 (2002)

    Article  MATH  Google Scholar 

  27. Huang, H., Jr., Thorne, D. T., Schaap, M. G., et al.: Proposed approximation for contact angles in Shan-and-Chen-type multicomponent multiphase lattice Boltzmann models. Phys. Rev. E 76, 066701 (2007)

    Article  Google Scholar 

  28. Qian, Y.H., d’Humires, D., Lallemand, P.: Lattice BGK models for Navier-Stokes equation. Europhys. Lett. 17, 478–484 (1992).

    Article  Google Scholar 

  29. He, X, Luo, L. S.: Theory of the lattice Boltzmann method: From the Boltzmann equation to the lattice Boltzmann equation. Phys. Rev. E 56, 6811–6817 (1997)

    Article  Google Scholar 

  30. Ginzbourg, I., Verhaeghe, F., d’Humieres, D.: Two-relaxationtime lattice Boltzmann scheme: About parametrization, velocity, pressure and mixed boundary condtions. Commun. Comput. Phys. 3, 427–478 (2008)

    MathSciNet  Google Scholar 

  31. d’Humieres, D.: Generalized lattice Boltzmann equations. Prog. Astronaut. Aeronaut. 159, 450–457 (1992)

    Google Scholar 

  32. Lallemand, P., Luo, L.S., Theory of the lattice Boltzmann method: Dispersion, dissipation, isotropy, Galilean invariance, and stability. Phys. Rev. E 61, 6546–6562 (2000)

    Article  MathSciNet  Google Scholar 

  33. Luo, L. S., Liao, W., Chen X., et al.: Numerics of the lattice Boltzmann method: Effects of the collision models on the lattice Boltzmann simulations. Phys. Rev. E 83, 056710 (2011)

    Article  Google Scholar 

  34. Pan, C., Luo, L. S., Miller, C. T.: An evaluation of lattice Boltzmann schemes for porous media flow simulation. Comput. Fluids 35, 898–909 (2006)

    Article  MATH  Google Scholar 

  35. Chai, Z., Shi, B., Guo, Z., et al.: Multiple-relaxation-time lattice Boltzmann model for generalized Newtonian fluid flows. J. Non-Newtonian Fluid Mech. 166, 332–342 (2011)

    Article  Google Scholar 

  36. Chai, Z., Shi B., Guo Z., et al.: Gas flow through square array of circular cylinders with Klinkenberg effect: A lattice Boltzmann study. Commun. Comput. Phys. 8, 1052–1073 (2010)

    Google Scholar 

  37. Du, R., Shi, B., Chen X.: Multi-relaxation-time lattice Boltzmann model for incompressible flow. Phys. Lett. A 359, 564–572 (2006)

    Article  MATH  Google Scholar 

  38. Asinari, P.: Multiple-relaxation-time lattice Boltzmann scheme for homogeneous mixture flows with external force. Phys. Rev. E 77 056706 (2008)

    Article  Google Scholar 

  39. Guo Z., Asinari, P., Zheng C.: Lattice Boltzmann equation for microscale gas flows of binary mixtures. Phys. Rev. E 79, 026702 (2009)

    Article  Google Scholar 

  40. Yu, Z., Fan L. S.: Multirelaxation-time interaction-potentialbased lattice Boltzmann model for two-phase flow. Phys. Rev. E 82, 046708 (2010)

    Article  Google Scholar 

  41. Guo, Z., Zheng, C., Shi, B.: Discrete lattice effects on the forcing term in the lattice Boltzmann method. Phys. Rev. E 65, 046308 (2002)

    Article  Google Scholar 

  42. Chao J., Mei R., Singh R., et al.: A filter-based, massconserving lattice Boltzmann method for immiscible multiphase flows. Int. J. Numer. Meth. Fluids 66, 622–647 (2011)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China

    Zhen-Hua Chai & Tian-Shou Zhao

Authors
  1. Zhen-Hua Chai
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tian-Shou Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tian-Shou Zhao.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chai, ZH., Zhao, TS. A pseudopotential-based multiple-relaxation-time lattice Boltzmann model for multicomponent/multiphase flows. Acta Mech Sin 28, 983–992 (2012). https://doi.org/10.1007/s10409-012-0123-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10409-012-0123-6

Keywords

Search

Navigation