Abstract
In this paper, we follow the pore-level simulation approach to investigate fluid flow over an open-porous interface using the lattice Boltzmann method. As this approach does not require any specific treatment for the interface, the predicted pore-level velocity field is averaged and used to evaluate the available macroscopic boundary conditions for the interface. Two most common interface boundary conditions are evaluated, and the unknown fitting parameters in them are calculated as a function of porosity of the porous region. Analytical solutions of the velocity profile in the close vicinity of the interface are used to validate the numerical methodology. It is shown that the predicted numerical results for penetration depth in the porous region, flow rate in open channel, and velocity profile in the open and porous regions are in excellent agreement with the predictions of the two available models, if the proposed values of their fitting parameters are used.
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References
Auriault J.L.: On the domain of validity of Brinkman’s equation. Transp Porous Med. 79(2), 215–223 (2010)
Bear J.: Dynamics of Fluids in Porous Media. Dover Publications, New York (1988)
Beavers G.S., Joseph D.D.: Boundary conditions at a naturally permeable wall. J. Fluid Mech. 30(1), 197–207 (1967)
Beavers G.S., Sparrow E.M., Masha B.A.: Boundary condition at a porous surface which bounds a fluid flow. Am. Inst. Chem. Eng. (AIChE) J. 20(3), 596–597 (1974)
Chandesris M., Jamet D.: Boundary conditions at a planar fluid-porous interface for a Poiseuille flow. Int. J. Heat Mass Transfer 49(13–14), 2137–2150 (2006)
Chandesris M., Jamet D.: Boundary conditions at a fluid-porous interface: An a priori estimation of the stress jump coefficients. Int J Heat Mass Transfer 50(17–18), 3422–3436 (2007)
Chandesris M., Jamet D.: Jump conditions and surface-excess quantities at a fluid/porous interface: A multi-scale approach. Transp. Porous Med. 78(3), 419–438 (2009)
Deng C., Martinez D.M.: Viscous flow in a channel partially filled with a porous medium and with wall suction. Chem. Eng. Sci. 60(2), 329–336 (2005)
Duman T., Shavit U.: An apparent interface location as a tool to solve the porous interface flow problem. Transp. Porous Med. 78(3), 509–524 (2009)
Goyeau B., Lhuillier D., Gobin D., Velarde M.G.: Momentum transport at a fluid-porous interface. Int. J. Heat Mass Transfer 46(21), 4071–4081 (2003)
Gupte S.K., Advani S.G.: Flow near the permeable boundary of a porous medium: An experimental investigation using LDA. Exp. Fluids 22(5), 408–422 (1996)
Gupte S.K., Advani S.G.: Flow near the permeable boundary of an aligned fiber preform: An experimental investigation using laser doppler anemometry. Polym. Compos. 18(1), 114–124 (1997)
James D.F., Davis A.M.J.: Flow at the interface of a model fibrous porous medium. J. Fluid Mech. 426, 47–72 (2001)
Larson R.E., Higdon J.J.L.: Microscopic flow near the surface of two-dimensional porous media. Part 1. Axial flow. J. Fluid Mech. 166, 449–472 (1986)
Larson R.E., Higdon J.J.L.: Microscopic flow near the surface of two-dimensional porous media. Part 2. Transverse flow. J. Fluid Mech. 178, 119–136 (1987)
Llewellin E.W.: LBFlow: An extensible lattice Boltzmann framework for the simulation of geophysical flows. Part I: Theory and implementation. Comput. Geosci. 36(2), 115–122 (2010)
Llewellin E.W.: LBFlow: An extensible lattice Boltzmann framework for the simulation of geophysical flows. Part II: Usage and validation. Comput. Geosci. 36(2), 123–132 (2010)
Min J.Y., Kim S.J.: A novel methodology for thermal analysis of a composite system consisting of a porous medium and an adjacent fluid layer. J. Heat Transfer 127(6), 648–656 (2005)
Nabovati A., Sousa A.C.M.: Fluid flow simulation at open-porous medium interface using the lattice Boltzmann method. Int. J. Numer. Methods Fluids 56(8), 1449–1456 (2008)
Nabovati A., Llewellin E.W., Sousa A.C.M.: A general model for the permeability of fibrous porous media based on fluid flow simulations using the lattice Boltzmann method. Compos. A 40(6–7), 860–869 (2009)
Nabovati A., Llewellin E.W., Sousa A.C.M.: Through-thickness permeability prediction of three-dimensional multifilament woven fabrics. Compos A 41(4), 453–463 (2010)
Neale G., Nader W.: Formulation of boundary conditions at the surface of a porous medium. Soc. Petrol. Eng. J. 14(5), 434–436 (1974)
Nield D.A.: The Beavers–Joseph boundary condition and related matters: A historical and critical note. Transp. Porous Media 78(3), 537–540 (2009)
Nield D.A., Kuznetsov A.V.: The effect of a transition layer between a fluid and a porous medium: Shear flow in a channel. Transp. Porous Media 78(3), 477–487 (2009)
Ochoa-Tapia J.A., Whitaker S.: Momentum transfer at the boundary between a porous medium and a homogeneous fluid-I. Theoretical development. Int. J. Heat Mass Transfer 38(14), 2635–2646 (1995)
Ochoa-Tapia J.A., Whitaker S.: Momentum transfer at the boundary between a porous medium and a homogeneous fluid-II. Comparison with experiment. Int. J. Heat Mass Transfer 38(14), 2647–2655 (1995)
Richardson S.: A model for the boundary condition of a porous material. Part 2. J. Fluid Mech. 49(2), 327–336 (1971)
Saffman P.G.: On the boundary condition at the surface of a porous medium. Stud. Appl. Math. 50(2), 93–101 (1971)
Sahraoui M., Kaviany M.: Slip and no-slip velocity boundary conditions at interface of porous, plain media. In. J. Heat Mass Transfer 35(4), 927–943 (1992)
Sahraoui, M., Kaviany, M.: Slip and no-slip temperature boundary conditions at interface of porous, plain media: convection. Part 1. Formulation. 1992 National Heat Transfer Conference, San Diego, California, 6th edn. HTD-vol. 193, pp. 25–33 (1993)
Succi S.: The Lattice Boltzmann Equation for Fluid Mechanics and Beyond. Oxford University Press, Oxford (2001)
Sukop M.C., Thorne D.T.: Lattice Boltzmann Modeling: An Introduction for Geoscientists and Engineers. Springer, Berlin (2006)
Taylor G.I.: A model for the boundary condition of a porous material. Part 1. J. Fluid Mech. 49(2), 319–326 (1971)
Valdés-Parada F.J., Ochoa-Tapia J.A., Alvarez-Ramirez J.: On the effective viscosity for the Darcy–Brinkman equation. Phys. A 385(1), 69–79 (2007a)
Valdés-Parada F.J., Ochoa-Tapia J.A., Alvarez-Ramirez J.: Diffusive mass transport in the fluid-porous medium inter-region: Closure problem solution for the one-domain approach. Chem. Eng. Sci. 62(21), 6054–6068 (2007b)
Valdés-Parada F.J., Alvarez-Ramirez J., Goyeau B., Ochoa-Tapia J.A.: Computation of jump coefficients for momentum transfer between a porous medium and a fluid using a closed generalized transfer equation. Transp. Porous Med. 78(3), 439–457 (2009)
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Nabovati, A., Amon, C.H. Hydrodynamic Boundary Condition at Open-Porous Interface: A Pore-Level Lattice Boltzmann Study. Transp Porous Med 96, 83–95 (2013). https://doi.org/10.1007/s11242-012-0074-1
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DOI: https://doi.org/10.1007/s11242-012-0074-1