MODELING OF POROUS MEDIA BY THE LATTICE BOLTZMANN METHOD


  • A.A. Avramenko Institute of Engineering Thermophysics of the National Academy of Sciences of Ukraine
  • A.I. Tyrinov Institute of Engineering Thermophysics of the National Academy of Sciences of Ukraine
  • V.E. Domashev Institute of Engineering Thermophysics of the National Academy of Sciences of Ukraine
  • A.V. Kovalenko Institute of Engineering Thermophysics of the National Academy of Sciences of Ukraine

Abstract

The principles of modeling heat and mass transfer and hydrodynamics of flows in porous media using the lattices Boltzmann method are considered. The methodology for implementing the Darcy law for the lattices Boltzmann method is shown.

In contrast to traditional numerical schemes based on discretization of continuous medium equations, the lattices Boltzmann method is based on microscopic models and mesoscopic kinetic equations. The fundamental idea of the lattices Boltzmann method is to build such simplified kinetic models that include the existing physics of microscopic or mesoscopic processes so that the macroscopic averaged properties correspond to the required macroscopic equations. The main premise of using this simplified method is that the macroscopic dynamics of a fluid is the result of the collective behavior of many microscopic particles of the system.

There are two approaches to modeling porous media using the lattices Boltzmann method. The first of them consists in modeling the spatial structure of the simulated system. Therefore, no additional factors need to be considered. The second approach is that the integrated characteristics of the porous medium (Darcy and Forheimer laws) are used to take into account the effect of porosity on the flow.

The purpose of this paper is to show the realization of the linear law of hydrodynamic drag (Darcy) in porous media for the lattices Boltzmann method. Usually, the main goal of direct modeling is to determine the integral characteristics of a porous medium.

The work considers the flow of fluid through a porous channel, which is formed between two flat walls. A method for implementing the Darcy law in the lattices Boltzmann method is shown.

This work will help to simulate the heat transfer and hydrodynamics of flows in porous media without the use of commercial packages.

References

1. Vargas M. et al. Steady natural convection in a cylindrical cavity //International communications in heat and mass transfer. 2002, V. 29, No.2, P. 213–221
2. Avramenko A. A. et al. Dean instability of nanofluids with radial temperature and concentration non-uniformity //Physics of Fluids. 2016, V. 28, No.3, P. 034104.
3. Kuznetsov A. V., Avramenko A. A. A minimal hydrodynamic model for a traffic jam in an axon //International Communications in Heat and Mass Transfer. 2009, V.36, No.1, P. 1–5.
4. Avramenko A. A. et al. Investigation of stability of a laminar flow in a parallel-plate channel filled with a fluid saturated porous medium //Physics of Fluids. 2005, V.17, No.9, P. 094102.
5. Avramenko A. A., Kuznetsov A. V. The onset of convection in a suspension of gyrotactic microorganisms in superimposed fluid and porous layers: effect of vertical throughflow //Transport in porous media. 2006, V. 65, No2, P. 159.
6. Kuznetsov A. V., Avramenko A. A. A 2D analysis of stability of bioconvection in a fluid saturated porous medium—estimation of the critical permeability value //International communications in heat and mass transfer. 2002, V. 29, No2, P. 175–184.
7. Kuznetsov A. V., Avramenko A. A. Stability analysis of bioconvection of gyrotactic motile microorganisms in a fluid saturated porous medium //Transport in porous media. 2003, V. 53, No1, P. 95–104.
8. Cheng Z. et al. The effect of pore structure on non-Darcy flow in porous media using the lattice Boltzmann method //Journal of Petroleum Science and Engineering. 2019, V. 172, P. 391–400.
9. Leclaire S. et al. Generalized three-dimensional lattice Boltzmann color-gradient method for immiscible two-phase pore-scale imbibition and drainage in porous media //Physical Review E. 2017, V. 95, No3, P. 033306.
10. Liu H. et al. Multiphase lattice Boltzmann simulations for porous media applications //Computational Geosciences. 2016, V. 20, No4, P. 777–805.
11. Sadeghi R. et al. Three-dimensional lattice Boltzmann simulations of high density ratio two-phase flows in porous media //Computers & Mathematics with Applications. 2018, V. 75, No7, P. 2445–2465.
12. Hyväluoma J. et al. Lattice Boltzmann simulation of flow-induced wall shear stress in porous media //Transport in Porous Media. 2018, V. 121, No2, P. 353–368.
13. Sheikholeslami M. Lattice Boltzmann method simulation for MHD non-Darcy nanofluid free convection //Physica B: Condensed Matter. 2017, V. 516, P. 55–71.
14. He X., Luo L. S. Theory of the lattice Boltzmann method: From the Boltzmann equation to the lattice Boltzmann equation //Physical Review E. 1997, V. 56, No6, P. 6811.
15. P.L. Bhatnagar, E.P. Gross, M. Krook. A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems// Physical Review. 1954, No. 94, P. 511–525.
16. Y. Peng, C. Shu, Y.T. Chew, A 3D incompressible thermal lattice Boltzmann model and its application to simulate natural convection in a cubic cavity// J. Comput. Physics. 2004, V.193, No1, P. 260–274.
17. A.I. Tyrinov, A.A. Avramenko, B.I. Basok, B.V. Davydenko, Modeling of flows in a microchannel based on the Boltzmann lattice equation// J. Eng. Phys. Thermophys. 2012, V.85, No1, P. 65–72.
18. C.H. Liu, K.-H. Lin, H.-C. Mai, C.-A. Lin. Thermal boundary conditions for thermal lattice Boltzmann simulations// Computers & Mathematics with Applications, 2010, V.59, No7, P. 2178–2193.
19. Avramenko A. A. et al. Heat Transfer in Porous Microchannels with Second-Order Slipping Boundary Conditions //Transport in Porous Media. 2019, V.129, No3. P. 673–699.

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Published
2020-07-07
How to Cite
Avramenko, A., Tyrinov, A., Domashev, V., & Kovalenko, A. (2020). MODELING OF POROUS MEDIA BY THE LATTICE BOLTZMANN METHOD. Thermophysics and Thermal Power Engineering, 42(3), 23-28. https://doi.org/https://doi.org/10.31472/ttpe.3.2020.2
Section
Heat and Mass Transfer Processes and Equipment, Theory and Practice of Drying