Boundary conditions at a planar fluid–porous interface for a Poiseuille flow

Chandesris, Marion; Jamet, Dominique

doi:10.1016/j.ijheatmasstransfer.2005.12.010

Cited by 150 publications

(124 citation statements)

References 23 publications

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“…The equations were originally written in terms of an effective viscosity as a coefficient in the viscous term. Since then it has been shown (Chandesris & Jamet 2006) that using volume averaging and 72 E. Ahmadi, R. Cortez and H. Fujioka assuming a homogeneous porous region results in an effective viscosity equal to the fluid viscosity divided by the porosity, µ/φ, so we use this formulation here. When the permeability of the medium is small, k 1, the viscous term can be neglected and the equation reduces to Darcy's law.…”

Section: Introductionmentioning

confidence: 99%

“…This case of a porous medium surrounded by a Stokes flow has been a topic of active investigation with the main goal of deriving appropriate boundary conditions at the interface (Beavers & Joseph 1967;Beavers, Sparrow & Magnuson 1970;Richardson 1971;Saffman 1971;Taylor 1971;Neale & Nader 1974;Howes & Whitaker 1985;Goyeau et al 2003;Chandesris & Jamet 2006;Valdés-Parada, Goyeau & Ochoa-Tapia 2007;Tlupova & Cortez 2009;Valdés-Parada et al 2009, 2013.…”

Section: Introductionmentioning

confidence: 99%

“…One difficulty with this expression lies on the fact that the expression for β depends on the velocity, which is an unknown of the problem. To reduce the complexity in determining β, Chandesris & Jamet (2006) used matched asymptotics to derive the interface jump condition…”

Section: Introductionmentioning

confidence: 99%

“…The quantities γ and λ depend on k and φ in the transition region. For example, if we assume φ and 1/k transition linearly, then (Chandesris & Jamet 2006) 10) or if those variations are following a hyperbolic tangent, then…”

Section: Introductionmentioning

confidence: 99%

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Boundary integral formulation for flows containing an interface between two porous media

2017

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A system of boundary integral equations is derived for flows in domains composed of a porous medium of permeability k 1 , surrounded by another porous medium of different permeability, k 2 . The incompressible Brinkman equation is used to describe the flow in the porous media. We first apply a boundary integral representation of the Brinkman flow on each side of the dividing interface, and impose continuity of the velocity at the interface to derive the final formulation in terms of the interfacial velocity and surface forces. We discuss relations between the surface stresses based on the additional conditions imposed at the interface that depend on the porosity and permeability of the media and the structural composition of the interface. We present simulated results for test problems and different interface stress conditions. The results show significant sensitivity to the choice of the interface conditions, especially when the permeability is large. Since the Brinkman equation approaches the Stokes equation when the permeability approaches infinity, our boundary integral formulation can also be used to model the flow in sub-categories of Stokes-Stokes and Stokes-Brinkman configurations by considering infinite permeability in the Stokes fluid domain.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Boundary integral formulation for flows containing an interface between two porous media

2017

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“…Ochoa-Tapia & Whitaker (1995), Alazmi & Vafai (2001), Goyeau et al (2003), Chandesris & Jamet (2006, Nield & Bejan (2006) and Hirata et al (2007a). These models generally use Darcy's law (or Darcy-Brinkman for high porosities; cf.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear stability of the one-domain approach to modelling convection in superposed fluid and porous layers

Hill

Carr

2010

Proc. R. Soc. A.

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Studies of the nonlinear stability of fluid/porous systems have been developed very recently. A two-domain modelling approach has been adopted in previous works, but was restricted to specific configurations. The extension to the more general case of a Navier-Stokes modelled fluid over a porous material was not achieved for the twodomain approach owing to the difficulties associated with handling the interfacial boundary conditions. This paper addresses this issue by adopting a one-domain approach, where the governing equations for both regions are combined into a unique set of equations that are valid for the entire domain. It is shown that the nonlinear stability bound, in the one-domain approach, is very sharp and hence excludes the possibility of subcritical instabilities. Moreover, the one-domain approach is compared with an equivalent two-domain approach, and excellent agreement is found between the two.

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A numerical method for forced convection in porous and homogeneous fluid domains coupled at interface by stress jump

Chen

Winoto

Low

2007

Numerical Methods in Fluids

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SUMMARYA numerical method was developed for flows involving an interface between a homogeneous fluid and a porous medium. It is based on the finite volume method with body-fitted and multi-block grids. The Brinkman-Forcheimmer extended model was used to govern the flow in the porous medium region. At its interface, the flow boundary condition imposed is a shear stress jump, which includes the inertial effect, together with a continuity of normal stress. The thermal boundary condition is continuity of temperature and heat flux.The forced convection through a porous insert over a backward-facing step is investigated. The results are presented with flow configurations for different Darcy numbers, 10 −2 to 10 −5 , porosity from 0.2 to 0.8, Reynolds number from 10 to 800, and the ratio of insert length to channel height from 0.1 to 0.3. The heat transfer is improved by using porous insert. To enhance the heat transfer with minimal frictional losses, it is preferable to have a medium length of insert with medium Darcy number, and larger Reynolds number. The interfacial stress jump coefficients and 1 were varied from −1 to 1, and within this range the average and local lower-wall Nusselt numbers are not sensitive to the parameters.

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Boundary conditions at a planar fluid–porous interface for a Poiseuille flow

Cited by 150 publications

References 23 publications

Boundary integral formulation for flows containing an interface between two porous media

Boundary integral formulation for flows containing an interface between two porous media

Nonlinear stability of the one-domain approach to modelling convection in superposed fluid and porous layers

A numerical method for forced convection in porous and homogeneous fluid domains coupled at interface by stress jump

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