Fluid mechanics of the interface region between two porous layers

Allan, Fathi M.; Hamdan, M. H.

doi:10.1016/s0096-3003(01)00016-9

Cited by 23 publications

(12 citation statements)

References 3 publications

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“…through ground layers where each layer constitutes a subdomain. In fact, our motivation for this work stems from our interest in modeling fluid flow through multilayer porous medium, where many works have been conducted in this regard [18][19][20][21][22]. The present work generalizes earlier works on two-layer porous medium, [18,19].…”

Section: Introductionmentioning

confidence: 62%

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A numerical scheme for multi-point special boundary-value problems and application to fluid flow through porous layers

Hajji¹

2011

Applied Mathematics and Computation

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Section: Introductionmentioning

confidence: 62%

“…There has been a lot of work on fluid flow through porous media [17][18][19][20][21][22][23][24][25][26] and references therein. For example, the book by Chen et al [17] gives an excellent account on computational methods for multiphase flows in porous media.…”

Section: Flow Through Porous Mediamentioning

confidence: 99%

A numerical scheme for multi-point special boundary-value problems and application to fluid flow through porous layers

Hajji¹

2011

Applied Mathematics and Computation

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“…However experimental measurement of µ e is not a trivial matter, if not impossible (Nield and Bejan, 1992). Therefore in the present work in accordance with the published literature, µ e is set to be equal to the fluid viscosity µ (Hsu and Cheng, 1985;Kaviany, 1986;Allan and Hamdan, 2002).…”

Section: Governing Equationsmentioning

confidence: 93%

“…It was shown that at very high Da, the porous matrix provides only a negligible resistance against a flow regime and a velocity profile similar to a free flow system is observed. Allan and Hamdan (2002) studied the velocity profile at the interface between two different porous media. They concluded that the velocity distribution in the two porous regions and at the interface is influenced by the Darcy parameters of the two porous layers.…”

Section: Introductionmentioning

confidence: 99%

Finite Element Modelling of Flow Through a Porous Medium Between Two Parallel Plates Using The Brinkman Equation

et al. 2006

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Despite the widespread use of the Darcy equation to model porous flow, it is well known that this equation is inconsistent with commonly prescribed no slip conditions at flow domain walls or interfaces between different sections. Therefore, in cases where the wall effects on the flow regime are expected to be significant, the Darcy equation which is only consistent with perfect slip at solid boundaries, cannot predict velocity and pressure profiles properly and alternative models such as the Brinkman equation need to be considered. This paper is devoted to the study of the flow of a Newtonian fluid in a porous medium between two impermeable parallel walls at different Darcy parameters (Da). The flow regime is considered to be isothermal and steady. Three different flow regimes can be considered using the Brinkman equation: free flow (Da > 1), porous flow (high permeability, 1 > Da > 10 −6 ) and porous flow (low permeability Da < 10 −6 ). In the present work the described bench mark problem is used to study the effects of solid walls for a range of low to high Darcy parameters. Both no-slip and slip conditions are considered and the results of these two cases are compared. The range of the applicability of the Brinkman equation and simulated results for different cases are shown.

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“…While it is understood that this effective viscosity should depend on the interfacial geometry of the porous system (Vafai 2005;Givler and Altobelli 1994;Lundgren 1972;Koplik et al 1983;Auriault 2009a, b), its actual relation with other parameters, such as porosity, remains an issue under debate. This uncertainty is attested by the number of experimental (Givler and Altobelli 1994), theoretical (Lundgren 1972;Koplik et al 1983;Allan and Hamdan 2002;Auriault 2009a, b), and numerical investigations (Martys et al 1994;Nabovati and Amon 2012) that reported contradictory results, predicting either an increase or decrease inμ eff i with respect to fluid viscosity. Due to the aforementioned lack of consensus, we have introduced the generic representationμ e i =μ/ f i (φ), where f i (φ) is some function of porosity φ offering the possibility of employing more generic formulas for this parameter (subject to the consistency constraint f i (1) = 1).…”

Section: Problem Statementmentioning

confidence: 99%

Stokes–Brinkman–Darcy Solutions of Bimodal Porous Flow Across Periodic Array of Permeable Cylindrical Inclusions: Cell Model, Lubrication Theory and LBM/FEM Numerical Simulations

Silva

Ginzburg

2016

Transp Porous Med

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An analytical study is devised for the problem of bimodal porous flow across a periodic array of permeable cylindrical inclusions. Such a configuration is particularly relevant for porous media systems of dual granulometry, an idealization often taken, e.g. in the modelling of membranes and fibrous applications. The double-porosity system is governed by the Stokes-Brinkman-Darcy equations, the most general description in this class of flow problems characterized by the permeabilities of the surrounding matrix and inclusions, their porosities and the relative volume fraction. We solve this problem with the Kuwabara cell model and lubrication approach, providing analytical solutions for the system effective permeability in closed analytical form. The ensemble of results demonstrates the self-consistency of the bimodal solutions in eight possible limit configurations and supports the validity of the Beavers-Joseph interface stress jump condition for transmission from the open Stokes flow to low-permeable Darcy region. At the same time, these solutions bring further insight on the relative significance of the governing parameters on the effective permeability, with a focus on the role of the effective viscosity (porosity) distribution. Furthermore, although the cell model is restricted to relatively small volume fractions in open flow, its validity extends in lesspermeable background flow inside Brinkman/Brinkman description. In turn, the lubrication approximation remains more adequate in the opposite limit of the dense impermeable inclusions. These conclusions are drawn from comparisons with the numerical solutions obtained with the developed lattice Boltzmann model and the standard finite element method. The two methods principally differ in the treatment of the interface conditions: implicit and explicit, respectively. The purpose of this task is therefore twofold. While the numerical schemes help quantifying the validity limits of the theoretical approach, the analytical solutions offer a non-trivial benchmark for numerical schemes in highly heterogeneous soil.

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Fluid mechanics of the interface region between two porous layers

Cited by 23 publications

References 3 publications

A numerical scheme for multi-point special boundary-value problems and application to fluid flow through porous layers

A numerical scheme for multi-point special boundary-value problems and application to fluid flow through porous layers

Finite Element Modelling of Flow Through a Porous Medium Between Two Parallel Plates Using The Brinkman Equation

Stokes–Brinkman–Darcy Solutions of Bimodal Porous Flow Across Periodic Array of Permeable Cylindrical Inclusions: Cell Model, Lubrication Theory and LBM/FEM Numerical Simulations

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