Document Type: Original Article

**Author**

Kerman Branch, Islamic Azad University, Iran

**Abstract**

In this paper, fluid flow between two parallel flat plates that are partially filled with two-dimension porous media is investigated numerically using single relaxation time (SRT) lattice Boltzmann method (LBM) at pore scale. The considered obstacles are random, circular, rigid and granular with uniform diameters. Single component and single-phase viscous Newtonian fluid are considered as working fluid. There are no overlaps between obstacles. It supposed incompressible, steady and laminar flow and no chemical reaction performed in porous media. Velocity vectors and streamlines in this domain depicted. The effect of varying Reynolds number on the pressure drop or pressure gradient and Darcy drag are studied. Dimensionless permeability calculated as a function of porosity and Knudsen number. To vary porosity, obstacles diameter changed but their places considered constant. With increasing Knudsen number, the dimensionless permeability is increased. In addition, effect of domain resolution on pressure gradient investigated. The results demonstrate that lattice Boltzmann method will be very useful in fluid flow simulation through porous media.

**Keywords**

[1] Ghia, U., Ghia, K. N. and Shin, C. T., "High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method", J. Computational Physics, Vol. 48 ,1982, pp. 387-411.

[2] Koseff, J. R. and Street, R. L., "The Lid-Driven Cavity Flow: A Synthesis of Qualitative and Quantitative Observations", J. Fluids Engineering, Vol. 106, 1984,, PP. 390-398.

[3] Migeon, C., Pineau, G., and Texier, A., "Three-dimensionality development inside standard parallel pipe lid-driven cavities at Re=1000", J. Fluids and Structure, Vol. 17, 2003, PP. 717-738.

[4] Ilegbusi, O. J. and Mat, M. D., "A comparison of predictions and measurements of kinematics mixing of two fluids in a 2D enclosure", App. Mathematical Modelling, Vol. 24, 2000, PP. 199-213.

[5] Vogel, M. J., Hirsa, A. H. and Lopez, J. M., "Spatio-temporal dynamics of a periodically driven cavity flow", J. Fluids Mechanics, Vol. 478, 2003, PP. 197-226.

[6] Cortes, A.B., Miller, J. D., "Numerical experiments with the lid driven cavity flow problem", J. Computers and Fluids, Vol. 23, 1994, PP.1005-1027.

[7] Fusegi, T., Hyun J. M., Kuwaharas, K. and Farouk B., "A numerical study of three dimensional natural convection in a differentially heated cubical enclosure", Int. J. Heat Mass Transfer, Vol. 34, 1991, PP. 1543-1557.

[8] Barakos, G., Mitsoulis E., and Assimacopoulos D., "Natural convection flow in a square cavity revisited: laminar and turbulent models with wall functions", Int. J. Numerical Methods Fluids, Vol. 18, 1994, PP. 695-719.

[9] Zhou, Y. C., "DSC solution for flow in a staggered double lid driven cavity", Int. J. Numerical Methods in Engineering, Vol. 57 2003, PP. 211–234.

[10] Wu, J.S., Shao, Y.L., "Simulation of lid-driven cavity flows by parallel lattice Boltzmann method using multi-relaxation-time scheme", Int. J. Numerical Methods in Fluids, Vol. 46, 2004, PP. 921-937.

[11] Siegmann, T., Schmidt, J.R. and Albensoeder, S., "Experiments on the flow stability in a double-lid-driven cavity", PAMM, Vol. 5 , 2005, PP. 551-552.

[12] Albensoeder, S. and Kuhlmann, H.C., "Accurate three-dimensional lid-driven cavity flow", J. Computational Physics, 206 (2005), PP. 536-558.

[13] Chen, C. L., "Numerical study of flow and thermal behavior of lid-driven flows in cavities of small aspect ratios", Int. J. Numerical Methods in Fluids, Vol. 52, 2006, PP. 785–799.

[14] Leriche, E., "Direct Numerical Simulation in a Lid-Driven Cavity at High Reynolds Number", Conference on Turbulence and Interactions, 2006.

[15] Rousse, D. R., "Numerical predictions of two-dimensional conduction, convection and radiation heat transfer- part 1", Int. J. Thermal Science, Vol. 39, 2000, PP. 315-331.

[16] Rousse, D. R., Gautier, G. and Sacadura J. F., "Numerical predictions of two-dimensional conduction, convection and radiation heat transfer- part 2", Int. J. Thermal Science, Vol. 39,2000, PP. 323-353.

[17] Talukdar, P. and Mishra, S. C., "Transient conduction and radiation heat transfer with heat generation in a participating medium using the collapsed dimension method", J. Numerical Heat Transfer, Vol. 39, 2001, PP. 79-100.

[18] Santanu, D., Nagendra, K. and Lakshmisha, N., "Simulation of laminar flow in a three-dimensional lid-driven cavity by lattice Boltzmann method", Int. J. Numerical Methods for Heat Fluid Flow, Vol. 19, 2009, PP. 790-815.

[19] Zhang, T. and Baochang, S., "Lattice Boltzmann simulation of lid-driven flow in trapezoidal cavities", J. Computers and Fluids, Vol. 39, 2010, PP. 1977–1989.

[20] Amiri, H., Mansouri, S. H. and Safavinejad, A., "Combined conductive and radiative heat transfer in an anisotropic scattering participating medium with irregular geometries", Int. J. Thermal Science, Vol. 49, 2010, PP. 492-503.

[21] Jafari, M., Farhadi, M., Sedighi, k. and Fattahi, E., "Numerical simulation of convection heat transfer in a lid-driven cavity with an open side", J. World Academy of Science Engineering and Technology, Vol. 59, 2011, PP. 435-439.

[22] Guermond, J. L. and Minev, P., "Start-up flow in a three-dimensional lid-driven cavity by means of a massively parallel direction splitting algorithm", Int. Journal for Numerical Methods in Fluids, Vol. 45, 2011, PP. 885–899.

[23] Lari, K., Baneshi, M., Gandjalikhan Nassab, S. A., Komiya, A. and Maruyama, S., "Combined heat transfer of radiation and natural convection in a square cavity containing participating gases", Int. J. Heat and Mass Transfer, Vol. 54, 2011, pp. 5087-5099.

[24] Modest, M. F., Radiative Heat Transfer, McGraw-Hill, New York, USA, 2006.

Volume 9, Issue 3

Summer 2016

Pages 31-40