2014 1(14)

Back to table of content

   Short abstract

 

Pages:

30 - 38

Language:

RU

Ref.:

21


Click to get extended abstract


Download paper: [RU]

2014_1(14)_5.pdf

 

 

SIMULATIONS OF PHASE TRANSITIONS WITH HEAT AND MASS TRANSFER BY THE LATTICE BOLTZMANN METHOD

Kupershtokh A.L.1, Medvedev D.A.1,2, Gribanov I.I.1

1 Lavrentyev Institute of Hydrodynamics SB RAS, Novosibirsk, Russia
2 Novosibirsk State University, Novosibirsk, Russia


Citation:

Kupershtokh, A.L., Medvedev, D.A. and Gribanov, I.I., (2014) Simulations of phase transitions with heat and mass transfer by the lattice Boltzmann method, Modern Science: Researches, Ideas, Results, Technologies, Iss. #1(14), PP. 30 - 38.


Keywords:

Lattice Boltzmann Equation Method; phase transitions; equations of state; dynamics of multiphase flows; surface tension; heat- and mass-transfer; computer simulations; parallel computations; graphical processing units


Abstracts:

We propose a new method for the computation of heat and mass transfer for the modeling of flow of a medium with liquid-vapor phase transitions using the lattice Boltzmann equations (LBE). When the phase boundaries are present, it is necessary to consider the equation of energy transfer. A second set of LBE distribution functions is introduced in the form of a passive scalar that describes the transfer of internal energy. In order to eliminate the spurious diffusion of energy at the interface with a high density ratio, special pseudo-forces are introduced to prevent the passive scalar from expansion. The thermal conductivity and the pressure work are taken into account in the energy equation. In order to avoid interface tracking in the LBE method, the latent heat of evaporation and condensation is accounted in the energy equation for the inner region of a thin liquid-vapor transition layer. Several simple tests were carried out to demonstrate all the aspects of the processes considered. It is shown that the Galilean invariance and the scaling of thermal conduction processes hold. The proposed method has low scheme diffusion for the internal energy and can be applied for modeling a wide range of flows of two-phase media with the mass and heat transfer.


References:

  1. Chen S., Doolen G.D. Lattice Boltzmann method for fluid flow // Annu. Rev. Fluid Mech. - 1998. V. 30. P. 329-364.

  2. Aidun C.K., Clausen J.R. Lattice-Boltzmann Method for Complex Flows // Annu. Rev. Fluid Mech. 2010. V. 42. P. 439-472.

  3. Shan X., Chen H. Lattice Boltzmann model for simulating flows with multiple phases and components // Phys. Rev.E. 1993. V. 47, N 3. P. 1815-1819.

  4. Qian Y.H., Chen S. Finite size effect in lattice-BGK models // International Journal of Modern Physics C. 1997. Vol. 8, N 4. P. 763-771.

  5. Kupershtokh, A.L. (2012). "Three-dimensional simulations of two-phase liquid-vapor systems on GPU using the lattice Boltzmann method", Numerical Methods and Programming, Vol. 13, pp. 130-138.

  6. Kupershtokh, A.L. (2012). "Three-dimensional LBE simulations on hybrid GPU-clusters of the decay of a binary mixture of liquid dielectrics with a solute gas to a system of gas-vapor channels", Numerical Methods and Programming, Vol. 13, pp. 384-390.

  7. Kupershtokh, A.L. (2014). "Three-dimensional LBE simulations of a decay of liquid dielectrics with a solute gas into the system of gas-vapor channels under the action of strong electric fields", Computers and Mathematics with Applications, Vol. 67, No. 2, pp. 340-349.

  8. Alexander F.J., Chen S., and Sterling J.D. Lattice Boltzmann thermohydrodynamics // Phys. Rev.E. 1993. V. 47, N 4. P. R2249- R2252.

  9. Qian, Y.H. (1993). "Simulating thermohydrodynamics with lattice BGK models", Journal of Scientific Computing, Vol. 8, No. 3, pp. 231-242.

  10. Chen, Y., Ohashi, H. and Akiyama, M. (1994). "Thermal lattice Bhatnagar-Gross-Krook model without nonlinear deviations in macrodynamical equations", Phys. Rev. E, Vol. 50, No. 4, pp. 2776-2783.

  11. Zhang R., Chen H. Lattice Boltzmann method for simulations of liquid-vapor thermal flows // Phys. Rev.E. 2003. V. 67, N 6. P. 066711.

  12. Shan X. Simulation of Rayleigh-Bénard convection using a lattice Boltzmann method // Physical Review E. 1997. V. 55, N 3. P. 2780-2788.

  13. He X., Chen S. and Doolen G.D. (1998). "A novel thermal model for the lattice Boltzmann method in incompressible limit", Journal of Computational Physics, Vol. 146, No. 2, pp. 282-300.

  14. Guo, Z., Zheng, C., Shi, B. and Zhao, T.S. (2007). "Thermal lattice Boltzmann equation for low Mach number flows: Decoupling model", Phys. Rev. E, Vol. 75, No. 3, pp. 036704.

  15. Li, Q., He, Y.L., Wang, Y. and Tao, W.Q. (2007). "Coupled double-distribution-function lattice Boltzmann method for the compressible Navier - Stokes equations", Phys. Rev. E, Vol. 76, No. 5, pp. 056705.

  16. Kupershtokh, A.L. (2004). "Incorporating a body force term into the lattice Boltzmann equation", Vestnik NGU (Quart.J. of Novosibirsk State Univ.), Series: Math., Mech. and Informatics, Vol. 4, No. 2, pp. 75-96.

  17. Kupershtokh A.L. Criterion of numerical instability of liquid state in LBE simulations // Computers and Mathematics with Applications, 2010. V. 59, N 7. P. 2236-2245.

  18. Kupershtokh, A.L. (2005). "Simulation of flows with liquid-vapor interfaces by the lattice Boltzmann method", Vestnik NGU (Quart.J. of Novosibirsk State Univ.), Series: Math., Mech. and Informatics, Vol. 5, No. 3, pp. 29-42.

  19. Kupershtokh A.L., Medvedev D.A., Karpov D.I. On equations of state in a lattice Boltzmann method // Computers and Mathematics with Applications, 2009. Vol. 58, N 5. P. 965-974.

  20. Kupershtokh, A.L. (2011). "A lattice Boltzmann equation method for real fluids with the equation of state known in tabular form only in regions of liquid and vapor phases", Computers and Mathematics with Applications, Vol. 61, No. 12, pp. 3537-3548.

  21. Kupershtokh, A.L., Medvedev, D.A. and Gribanov, I.I. (2014). "Modeling of thermal flows in a medium with phase transitions using the lattice Boltzmann method", Numerical Methods and Programming, Vol. 15, pp. 317-328.

 

 
     

© SPIC "Kappa", LLC 2009-2016