PORE-SCALE MODELLING OF FLUID FLOW IN PENETRABLE SPHERES USING THE PROJECTION METHOD FOR INCOMPRESSIBLE NAVIER-STOKES EQUATIONS
https://doi.org/10.55452/1998-6688-2021-18-2-6-11
Abstract
The direct numerical simulation (DNS) is an effective and useful tool in the two-phase fluid flow studying. The projection method on the staggered grid was applied in this paper to solve the incompressible Navier-Stokes equations in irregular domains at the pore-scale level (irregular boundary is presented by its level-set function). The permeability of porous medium which was constructed by the random positioning of penetrable spheres of equal radii were numerically calculated and validated by comparing with theoretical estimations of permeability based on the numerical solution of the lattice-Boltzmann equation in irregular domains in previous works. All numerical calculations were performed using PARIS simulator.
Supporting agencies: This research is funded by the Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan (Grant No. AP08052055), which is gratefully acknowledged by the authors.
About the Authors
Zh. K. Akasheva
Satbayev University
Kazakhstan
Kazakhstan
Akasheva Zhibek Kairatovna - Deputy Head of the Research Laboratory «Computational Modeling and Information Technologies»
050000, Almaty
A. A. Kudaikulov
Satbayev University
Kazakhstan
Kazakhstan
Kudaikulov Aziz Anarbayevich - PhD, Professor
050000, Almaty
B. K. Assilbekov
Satbayev University
Kazakhstan
Kazakhstan
Assilbekov Bakytzhan Kalzhanovich – PhD, Head of the Research Laboratory «Computational Modeling and Information Technologies»
050000, Almaty
D. A. Bolysbek
Satbayev University; Al-Farabi Kazakh National University
Kazakhstan
Kazakhstan
Bolysbek Darezhat Abilseyituly - Researcher at the Research Laboratory «Computational Modeling and Information Technologies»
050000, Almaty
References
1. J. Koplik. Creeping flow in two-dimensional networks. J. Fluid Mech., 1982, vol. 119, pp. 219-247.
2. H. J. Vogel, J. Tolke, V.P. Schulz, M. Krafczyk and K. Roth. Comparison of a Lattice-Boltzmann Model, a Full-Morphology Model, and a Pore Network Model for Determining Capillary Pressure-Saturation Relationships. Vadose Zone J., 2005, vol. 4, pp. 380-388.
3. D.H. Rothman. Cellular-automaton fluids: A model for flow in porous media. Geophysics, 1988, vol. 53, no. 4, pp. 509-518.
4. S. Succi, E. Foti and F. Higuera. Three-Dimensional Flows in Complex Geometries with the Lattice Boltzmann Method, Europhys. Lett., 1989, vol. 10, no. 5, pp. 433-438.
5. A. Lemmer and R. Hilfer. Parallel domain decomposition method with non-blocking communication for flow through porous media. Journal of Computational Physics, 2015, vol. 281, pp. 970-981.
6. C. Manwart, U. Aaltosalmi, A. Koponen, R. Hilfer and J. Timonen. Lattice-Boltzmann and finite-difference simulations for the permeability for three-dimensional porous media. Physical Review E, 2002, vol. 66, no. 1.
7. S. Geller, M. Krafczyk, J. Tolke, S. Turek and J. Hron. Benchmark computations based on lattice-Boltzmann, finite element and finite volume methods for laminar flows. Computers & Fluids, 2006, vol. 35, pp. 888-897.
8. M.J. Blunt, B. Bijeljic, H. Dong, O. Gharbi, S. Iglauer, P. Mostaghimi, A. Paluszny, C. Pentland. Pore-scale imaging and modelling. Advances in Water Resources, 2013, vol. 51, pp. 197–216.
9. P.J. Roache. Computational fluid dynamics, Hermosa Publishers, 1985, isbn 0-913-47805-9.
10. R. Peyret and T.D. Taylor. Computational methods for fluid flow, 1983, Springer, New York, isbn 978-3-540-13851-8, 978-3-642-85952-6.
11. D.L. Brown, R. Cortez and M.L. Minion. Accurate projection methods for the incompressible Navier-Stokes equations, J. Comput. Phys., 2001, vol. 168, no. 2, pp. 464-499.
12. A. Cancelliere, C. Chang, E. Foti, D.H. Rothman and S. Succi. The permeability of a random medium: Comparison of simulation with theory, Phys. Fluids A, 1990, vol. 2, pp. 2085-2088.
13. H.L. Weissberg and S. Prager. Viscous Flow through Porous Media. III. Upper Bounds on the Permeability for a Simple Random Geometry, Physics of Fluids, 1970, vol. 13, no. 12, pp. 2958-2965.
14. H.C. Brinkman. A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles, Appl. Sci. Res., 1949, vol. A1, pp. 27-34.
15. S. Torquato. Random Heterogeneous Materials: Microstructure and Macroscopic Properties, 2002, Springer, New York, isbn 0-387-95167-9.
16. S. Zaleski. PARIS simulator code, http://www.ida.upmc.fr/~zaleski/paris.
Review
For citations:
Akasheva Zh.K., Kudaikulov A.A., Assilbekov B.K., Bolysbek D.A. PORE-SCALE MODELLING OF FLUID FLOW IN PENETRABLE SPHERES USING THE PROJECTION METHOD FOR INCOMPRESSIBLE NAVIER-STOKES EQUATIONS. Herald of the Kazakh-British technical university. 2021;18(2):6-11. https://doi.org/10.55452/1998-6688-2021-18-2-6-11
Views:
418
Email this article 