Skip to main content
SpringerLink
Log in

Lattice Boltzmann Method for Sprays

  • Chapter
  • First Online:
Book cover Handbook of Atomization and Sprays

Abstract

Among the noncontinuum-based computational techniques, the lattice Boltzman method (LBM) has received considerable attention recently. In this chapter, we will briefly present the main elements of the LBM, which has evolved as a minimal kinetic method for fluid dynamics, focusing in particular, on multiphase flow modeling. We will then discuss some of its recent developments based on the multiple-relaxation-time formulation and consistent discretization strategies for enhanced numerical stability, high viscosity contrasts, and density ratios for simulation of interfacial instabilities and multiphase flow problems. As examples, numerical investigations of drop collisions, jet break-up, and drop impact on walls will be presented. We will also outline some future directions for further development of the LBM for applications related to interfacial instabilities and sprays.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 469.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 599.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 599.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Ashgriz, N. and Y. Poo. Coalescence and Separation in Binary Collisions of Liquid Drops. J. Fluid Mech. 221: 183–204 (1990).

    Article  Google Scholar 

  2. Asinari, P. Viscous Coupling based Lattice Boltzmann Model for Binary Mixtures. Phys. Fluids 067102: 1–22 (2005).

    MathSciNet  Google Scholar 

  3. Bhatnagar, P., E. Gross, and M. Krook. A Model for Collision Processes in Gases, I. Small Amplitude Processes in Charged and Neutral One-Component Systems. Phys. Rev. 94: 511–525 (1954).

    Article  MATH  Google Scholar 

  4. Carnahan, N. and K. Starling. Equation of State for Nonattracting Rigid Spheres. J. Chem. Phys. 51: 635–636 (1969).

    Article  Google Scholar 

  5. Chapman, S. and T. Cowling. Mathematical Theory of Non-Uniform Gases. Cambridge University Press, London (1964).

    Google Scholar 

  6. Chen, S. and G. Doolen. Lattice Boltzmann Method for Fluid Flows. Annu. Rev. Fluid Mech. 30: 329–364 (1998).

    Article  MathSciNet  Google Scholar 

  7. d’Humieres, D., I. Ginzburg, M. Krafczyk, P. Lallemand, and L.-S. Luo. Multiple-Relaxation-time Lattice Boltzmann Models in Three Dimensions. Phil. Trans. Roy. Soc. Lond. Ser. A 360: 437–351 (2002).

    Article  MATH  MathSciNet  Google Scholar 

  8. Gunstensen, A.K., D.H. Rothman, S. Zaleski, and G. Zanetti. Lattice Boltzmann Model of Immiscible Fluids. Phys. Rev. A 43: 4320–4327 (1991).

    Article  Google Scholar 

  9. Harris, S. An Introduction to the Theory of the Boltzmann Equation. Dover Publications, New York (2004).

    Google Scholar 

  10. He, X. and G. Doolen. Thermodynamic Foundations of Kinetic Theory and Lattice Boltzmann Models for Multiphase Flows. J. Stat. Phys. 107: 1572–4996 (2002).

    Article  Google Scholar 

  11. He, X. and L.-S. Luo. 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 

  12. He, X., X. Shan, and G. Doolen. Discrete Boltzmann Equation Model for Nonideal Gases. Phys. Rev. E 57: R13–R16 (1998).

    Article  Google Scholar 

  13. He, X., S. Chen, and R. Zhang. A Lattice Boltzmann Scheme for Incompressible Multiphase Flow and its Application in Simulation of Rayleigh–Taylor Instability. J. Comput. Phys. 152: 642–663 (1999).

    Article  MATH  MathSciNet  Google Scholar 

  14. Holdych, D.J., D. Rovas, J.G. Georgiadis and R.O. Buckius. An Improved Hydrodynamic Formulation for Multiphase Flow Lattice Boltzmann Models. Int. J. Modern Phys. C 9: 1393–1404 (1998).

    Article  Google Scholar 

  15. Inamuro, T., N. Konishi, and F. Ogino. A Galilean Invariant Model of the Lattice Boltzmann Method for Multiphase Fluid Flows Using Free-Energy Approach. Comput. Phys. Commun. 129: 32–45 (2000).

    Article  MATH  MathSciNet  Google Scholar 

  16. Inamuro, T., T. Ogata, S. Tajima, and N. Konishi. A Lattice Boltzmann Method for Incompressible Two-phase Flows with Large Density Ratios. J. Comput. Phys. 198: 628–644 (2004).

    Article  MATH  Google Scholar 

  17. Junk, M., A. Klar, and L.-S. Luo. Asymptotic Analysis of the Lattice Boltzmann Equation. J. Comput. Phys. 210: 676–704 (2005).

    Article  MATH  MathSciNet  Google Scholar 

  18. Kikkinides, E.S., A.G. Yiotis, M.E. Kainourgiakis, and A.K. Stubos. Thermodynamic Consistency of Liquid-Gas Lattice Boltzmann Methods. Phys. Rev. E 78: 036702 (2008).

    Google Scholar 

  19. Lallemand, P. and L.-S. Luo, Theory of the Lattice Boltzmann Method: Dispersion, Isotropy, Galilean Invariance, and Stability. Phys. Rev. E 61: 6546–6562 (2000).

    Article  MathSciNet  Google Scholar 

  20. Lee, T. and C.-L. Lin. A Stable Discretization of the Lattice Boltzmann Equation for Simulation of Incompressible Two-Phase Flows at High Density Ratio. J. Comput. Phys. 206: 16 (2005).

    Article  MATH  MathSciNet  Google Scholar 

  21. Luo, L.-S. Theory of the Lattice Boltzmann Method: Lattice Boltzmann Models for Nonideal Gases. Phys. Rev. E 62: 4982–4996 (2000).

    Article  MathSciNet  Google Scholar 

  22. McCracken, M.E. and J. Abraham. Multiple-Relaxation-Time Lattice-Boltzmann Model for Multiphase Flow. Phys. Rev. E 71: 036701 (2005a).

    Google Scholar 

  23. McCracken, M.E. and J. Abraham. Simulations of Liquid Break up with an Axisymmetric, Multiple Relaxation Time, Index-Function Lattice Boltzmann Model. Int. J. Mod. Phys. C 16: 1671–1682 (2005b).

    Article  MATH  Google Scholar 

  24. Mukherjee, S. and J. Abraham. A Pressure-Evolution-Based Multi-Relaxation-Time High-Density-Ratio Two-Phase Lattice-Boltzmann Model. Comput. Fluids 36: 1149–1158 (2007a).

    Article  MATH  Google Scholar 

  25. Mukherjee, S. and J. Abraham. Lattice Boltzmann Simulations of Two-Phase Flow with High Density Ratio in Axially Symmetric Geometry. Phys. Rev. E. 75: 026701 (2007b).

    Google Scholar 

  26. Mukherjee, S. and J. Abraham. Investigations of Drop Impact on Dry Walls with a Lattice Boltzmann Model. J. Colloid Interface Sci. 312: 341–354 (2007c).

    Article  Google Scholar 

  27. Mukherjee, S. and J. Abraham. Crown Behavior in Drop Impact on Wet Walls. Phys. Fluids 19: 052103 (2007d).

    Google Scholar 

  28. Nourgaliev, R., T.N. Dinh, T.G. Theofanous, and D. Joseph. The Lattice Boltzmann Equation Method: Theoretical Interpretation, Numerics and Implications. Int. J. Multiphase Flow 29: 117–169 (2003).

    Article  MATH  Google Scholar 

  29. Premnath, K.N. and J. Abraham. Lattice Boltzmann Model for Axisymmetric Multiphase Flows. Phys. Rev. E, 71: 056706 (2005a).

    Google Scholar 

  30. Premnath, K.N. and J. Abraham. Simulations of Binary Drop Collisions with a Multiple-Relaxation-Time Lattice-Boltzmann Model. Phys. Fluids 17: 122105 (2005b).

    Google Scholar 

  31. Premnath, K.N. and J. Abraham. Three-Dimensional Multi-Relaxation Time (MRT) Lattice-Boltzmann Models for Multiphase Flow. J. Comput. Phys. 224: 539–559 (2007).

    Article  MATH  MathSciNet  Google Scholar 

  32. Premnath, K.N., McCracken, M.E. and J. Abraham. A Review of Lattice Boltzmann Methods for Multiphase Flows Relevant to Engine Sprays. SAE Trans: J. Engines, 114: 929–940 (2005).

    Google Scholar 

  33. Qian, J. and C. Law. Regimes of Coalescence and Separation in Droplet Collision. J. Fluid Mech. 331: 59–80 (1997).

    Article  Google Scholar 

  34. Roisman, I. Dynamics of Inertia Dominated Binary Drop Collisions. Phys. Fluids 16: 3438–3449 (2004).

    Article  MathSciNet  Google Scholar 

  35. Rowlinson, J. and B. Widom. Molecular Theory of Capillarity. Clarendon Press, Oxford (1982).

    Google Scholar 

  36. Sankaranarayanan, K., I.G. Kevrekidis, S. Sundaresan, J. Lu and G. Tryggvason. A Comparative Study of Lattice Boltzmann and Front-Tracking Finite-Difference Methods for Bubble Simulations. Int. J. Multiphase Flow 29: 109–116 (2003).

    Article  MATH  Google Scholar 

  37. Sbragaglia, M., R. Benzi, L. Biferale, S. Succi, K. Sugiyama, and F. Toschi. Generalized Lattice Boltzmann Method with Multirange Pseudopotential. Phys. Rev. E 75: 026702 (2007).

    Google Scholar 

  38. Shan, X. and H. Chen. Lattice Boltzmann Model of Simulating Flows with Multiple Phases and Components. Phys. Rev. E 47: 1815–1819 (1993).

    Article  Google Scholar 

  39. Shan, X., X.-F. Yuan, and H. Chen. Kinetic Theory Representation of Hydrodynamics: A Way Beyond the Navier-Stokes Equation. J. Fluid Mech. 550: 413–441 (2006).

    Article  MATH  MathSciNet  Google Scholar 

  40. Stone, H. and L. Leal. Relaxation and Breakup of an Initially Extended Drop in an Otherwise Quiescent Fluid. J. Fluid Mech. 198: 399–427 (1989).

    Article  Google Scholar 

  41. Stone, H., B. Bentley, and L. Leal. An Experimental Study of Transient Effects in the Breakup of Viscous Drops. J. Fluid Mech. 173: 131–158 (1986).

    Article  Google Scholar 

  42. Succi, S. The Lattice Boltzmann Equation for Fluid Dynamics and Beyond. Oxford University Press, New York (2001).

    MATH  Google Scholar 

  43. Swift, M., S. Orlandini, W. Osborn, and J. Yeomans. Lattice Boltzmann Simulations of Liquid-Gas Binary-fluid Systems. Phys. Rev. E 54: 5041–5042 (1996).

    Article  Google Scholar 

  44. Wagner, A.J. Thermodynamic Consistency of Liquid-Gas Lattice Boltzmann Simulations. Phys. Rev. E 74: 056703 (2006).

    Google Scholar 

  45. Wolf-Gladrow, D. Lattice-Gas Cellular Automata and Lattice Boltzmann Models, Lecture Notes in Mathematics, No. 1725. Springer, Berlin (2000).

    Google Scholar 

  46. Zheng, H.W., C. Shu, and Y.T. Chew. A Lattice Boltzmann Model for Multiphase Flows with Large Density Ratio. J. Comput. Phys. 218: 353–371 (2006).

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mechanical Engineering, University of Wyoming, Laramie, USA

    K. N. Premnath

Authors
  1. K. N. Premnath
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. Abraham
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to K. N. Premnath .

Editor information

Editors and Affiliations

  1. Dept. Mechanical &, Industrial Engineering, University of Toronto, King's College Road 5, Toronto, M5S 3G8, Ontario, Canada

    Nasser Ashgriz

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer US

About this chapter

Cite this chapter

Premnath, K.N., Abraham, J. (2011). Lattice Boltzmann Method for Sprays. In: Ashgriz, N. (eds) Handbook of Atomization and Sprays. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-7264-4_20

Download citation

  • DOI: https://doi.org/10.1007/978-1-4419-7264-4_20

  • Published:

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4419-7263-7

  • Online ISBN: 978-1-4419-7264-4

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation