×

A lattice Boltzmann model for thermal non-Newtonian fluid flows through porous media. (English) Zbl 1410.76362

Summary: Following recent studies by R. R. Huilgol and G. H. R. Kefayati [“From mesoscopic models to continuum mechanics: Newtonian and non-newtonian fluids”, J. Non-Newtonian Fluid Mech. 233, 146–154 (2016; doi:10.1016/j.jnnfm.2016.03.002); “A particle distribution function approach to the equations of continuum mechanics in Cartesian, cylindrical and spherical coordinates: Newtonian and non-Newtonian fluids”, J. Non-Newtonian Fluid Mech. 251, 119–131 (2018; doi:10.1016/j.jnnfm.2017.10.004)], that developed a thermal lattice Boltzmann method for different non-Newtonian fluids, we propose, in this paper, a general lattice Boltzmann method for thermal incompressible non-Newtonian fluids through porous media. Since no restrictions are placed on the constitutive equations in this method, the theoretical development can be applied to all fluids, whether they be Newtonian, or power law fluids, or viscoelastic and Bingham fluids. To validate the accuracy of the method, natural convection in a porous cavity is studied and compared with previous studies. Next, we employ the model to simulate natural convection of power-law and Bingham fluids in a porous cavity.

MSC:

76M28 Particle methods and lattice-gas methods
76A05 Non-Newtonian fluids
76S05 Flows in porous media; filtration; seepage
76R10 Free convection

Software:

HE-E1GODF
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Huilgol, R. R.; Kefayati, GHR, From mesoscopic models to continuum mechanics: newtonian and non-newtonian fluids, J Nonnewton Fluid Mech, 233, 146-154, (2016)
[2] Huilgol, R. R.; Kefayati, GHR, A particle distribution function approach to the equations of continuum mechanics in cartesian, cylindrical and spherical coordinates: newtonian and non-newtonian fluids, J Nonnewton Fluid Mech, 251, 119-131, (2018)
[3] Sochi, T., Non-newtonian flow in porous media, Polymer (Guildf), 51, 5007-5023, (2010)
[4] Nield, D. A.; Bejan, A., Convection in porous media, Vol., XXIV, (2006), Springer · Zbl 1256.76004
[5] Vafai, K., Handbook of porous media, (2005), Marcel Dekker: Marcel Dekker New York
[6] Quere, P. L.; de Roquefort, T. A., Computation of natural convection in two dimensional cavities with Chebyshev polynomials, J Comput Phys, 57, 210-228, (1985) · Zbl 0585.76128
[7] Quere, P. L., Accurate solutions to the square thermally driven cavity at high rayleigh number, Comput Fluids, 20, 29-41, (1991) · Zbl 0731.76054
[8] Nithiarasu, P.; Seetharamu, K. N.; Sundararajan, T., Natural convection heat transfer in a fluid saturated variable porosity medium, Int J Heat Mass Transf, 40, 3955-3967, (1997) · Zbl 0925.76660
[9] Nithiarasu, P.; Ravindran, K., A new semi-implicit time stepping procedure for buoyancy driven flow in a fluid saturated porous medium, Comput Meth Appl Mech Eng, 165, 147-154, (1998) · Zbl 0953.76052
[10] Guo, Z.; Zhao, T. S., A lattice Boltzmann model for convection heat transfer in porous media, Numer Heat Transf Part B, 47, 157-177, (2005)
[11] Liu, Q.; He, Y.-L.; Li, Q.; Tao, W.-Q., A multiple-relaxation-time lattice Boltzmann model for convection heat transfer in porous media, Int J Heat Mass Transf, 73, 761-775, (2014)
[12] Wang, L.; Mi, J.; Guo, Z., A modified lattice Bhatnagar-Gross-Krook model for convection heat transfer in porous media, Int J Heat Mass Transf, 94, 269-291, (2016)
[13] Das, D.; Biswal, P.; Roy, M.; Basak, T., Role of the importance of Forchheimer term for visualization of natural convection in porous enclosures of various shapes, Int J Heat Mass Transf, 97, 1044-1068, (2016)
[14] Das, D.; Basak, T., Role of discrete heating on the efficient thermal management within porous square and triangular enclosures via heatline approach, Int J Heat Mass Transf, 112, 489-508, (2017)
[15] Fu, S. C.; So, R. M.C.; Leung, R. M.C., Linearized-Boltzmann-type-equation-based finite difference method for thermal incompressible flow, Comput Fluids, 6, 67-80, (2012) · Zbl 1365.76191
[16] Frisch, U.; Hasslacher, B.; Pomeau, Y., Lattice gas automata for the Navier-Stokes equation, Phys Rev Lett, 56, 1505-1508, (1986)
[17] Frisch, U.; dHumres, D.; Hasslacher, B.; Lallemand, P.; Pomeau, Y.; Rivet, J. P., Lattice gas hydrodynamics in two and three dimensions, Complex Syst, 1, 649-707, (1987) · Zbl 0662.76101
[18] Wolfram, S., Cellular automaton fluids 1: basic theory, J Stat Phys, 45, 471-526, (1986) · Zbl 0629.76002
[19] Chen, S.; Doolen, G. D., Lattice Boltzmann method for fluid flows, Annu Rev Fluid Mech, 30, 329-364, (1998) · Zbl 1398.76180
[20] Bhatnagar, P. L.; Gross, E. P.; Krook, M., A model for collision processes in gases. i. small amplitude processes in charged and neutral one-component systems, Phys Rev Ser, 2, 94, 511-525, (1954) · Zbl 0055.23609
[21] Chen, S.; Wang, Z.; Shan, X. W.; Doolen, G. D., Lattice Boltzmann computational fluid dynamics in three dimensions, J Stat Phys, 68, 379-400, (1992) · Zbl 0925.76516
[22] Qian, Y. H.; dHumieres, D.; Lallemand, P., Lattice BGK models for Navier-Stokes equation, Europhys Lett, 17, 479-484, (1992) · Zbl 1116.76419
[23] Toro, E. F., Riemann solvers and numerical methods for fluid dynamics: a practical introduction, (1999), Springer · Zbl 0923.76004
[24] Lax, P. D.; Wendroff, B., Systems of conservation laws, Comm Pure Appl Math, 13, 217-237, (1960) · Zbl 0152.44802
[25] Khezzar, L.; Siginer, D.; Vinogradov, I., Natural convection of power law fluids in inclined cavities, Int J Therm Sci, 53, 8-17, (2012)
[26] Kim, G. B.; Hyun, J. M.; Kwak, H. S., Transient buoyant convection of a power-law non-newtonian fluid in an enclosure, Int J Heat Mass Transf, 46, 3605-3617, (2003) · Zbl 1042.76563
[27] Bingham, E. C., Fluidity and plasticity, (1922), McGraw-Hill: McGraw-Hill New York
[28] Papanastasiou, T. C., Flow of materials with yield, J Rheol, 31, 385-404, (1987) · Zbl 0666.76022
[29] Kefayati, G. H.R., Double-diffusive natural convection and entropy generation of Bingham fluid in an inclined cavity, Int J Heat Mass Transf, 116, 762-812, (2018) · Zbl 1408.76483
[30] Turan, O.; Chakraborty, N.; Poole, R. J., Laminar natural convection of Bingham fluids in a square enclosure with differentially heated side walls, J Non Newton Fluid Mech, 165, 901-913, (2010) · Zbl 1274.76301
[31] Huilgol, R. R.; Kefayati, GHR, Natural convection problem in a Bingham fluid using the operator-splitting method, J Non Newton Fluid Mech, 220, 22-32, (2015)
[32] Glowinski, R., Finite element methods for incompressible viscous flow, Handbook of Numerical Analysis, 9, 3-1176, (2003) · Zbl 1040.76001
[33] Kefayati, G. H.R.; Huilgol, R. R., Lattice Boltzmann method for simulation of mixed convection of a Bingham fluid in a lid-driven cavity, Int J Heat Mass Transf, 103, 725-743, (2016)
[34] Dimakopoulos, M.; Pavlidis, M.; Tsamopoulos, J., Steady bubble rise in Herschel Bulkley fluids and comparisons of predictions via the augmented lagrangian method with those via the Papanastasiou model, J Non Newton Fluid Mech, 200, 34-51, (2013)
[35] Blazek, J., Computational fluid dynamics: principles and applications, 347-350, (2001), Elsevier · Zbl 0995.76001
[36] Cebeci, T.; Shao, J. P.; Kafyeke, F.; Laurendeau, E., Computational fluid dynamics for engineers, 311-320, (2005), Springer
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.