Momentum transport at a fluid–porous interface

Goyeau, Benoı̂t; Lhuillier, Daniel; Gobin, D.; Velarde, Manuel G.

doi:10.1016/s0017-9310(03)00241-2

Cited by 284 publications

(261 citation statements)

References 52 publications

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“…This study was supported by National Science Foundation under grants CBET-0625138 and CBET-0754344. let us assume (Goyeau et al 2003) that a possible description is provided by a generalized Darcy-Brinkman equation. For a porous medium occupying the halfspace z 6 0 exposed to a fluid flowing in the direction x (see figure 1) the flow is then described by…”

Section: Discussionmentioning

confidence: 99%

“…However, questions arise as to the proper viscosity parameter to use in the Brinkman model (see e.g. Koplik et al 1983;Martys, Bentz & Garboczi 1994;Goyeau et al 2003;Le Bars & Worster 2006) and, furthermore, the predicted length scale for the penetration of the flow into the porous medium is found to be at variance with the available data (see e.g. Goharzadeh, Khalili & Jørgensen 2005;Ghisalberti 2009;Morad & Khalili 2009;Pokrajac & Manes 2009).…”

Section: Introductionmentioning

confidence: 99%

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Pressure-driven flow in a channel with porous walls

Liu

Prosperetti

2011

J. Fluid Mech.

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The finite-Reynolds-number three-dimensional flow in a channel bounded by one and two parallel porous walls is studied numerically. The porous medium is modelled by spheres in a simple cubic arrangement. Detailed results on the flow structure and the hydrodynamic forces and couple acting on the sphere layer bounding the porous medium are reported and their dependence on the Reynolds number illustrated. It is shown that, at finite Reynolds numbers, a lift force acts on the spheres, which may be expected to contribute to the mobilization of bottom sediments. The results for the slip velocity at the surface of the porous layers are compared with the phenomenological Beavers-Joseph model. It is found that the values of the slip coefficient for pressure-driven and shear-driven flow are somewhat different, and also depend on the Reynolds number. A modification of the relation is suggested to deal with these features. The Appendix provides an alternative derivation of this modified relation.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Pressure-driven flow in a channel with porous walls

Liu

Prosperetti

2011

J. Fluid Mech.

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“…Structures composed of a porous medium adjacent to a fluid flow are often seen in industrial processes (wastewater treatment, filtration, thermal insulation), environmental phenomena (groundwater pollution, sea water flow above coral reefs) and biological settings (bacterial biofilms) (Manem & Rittmann 1992;Costerton, Stewart & Greenberg 1999;Goyeau et al 2003;Lowe et al 2008;Bear & Cheng 2010). 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%

“…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%

“…Introducing a thin transition layer between the fluid and porous regions, an expression for β was derived based on the variation in velocity, the geometry of the interface and the variations of the porous material properties (Goyeau et al 2003). 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.…”

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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Reactive mold filling in resin transfer molding processes with edge effects

Ding

Jia

Yang

et al. 2009

J of Applied Polymer Sci

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Reactive mold filling is one of the important stages in resin transfer molding processes, in which resin curing and edge effects are important characteristics. On the basis of previous work, volume-averaging momentum equations involving viscous and inertia terms were adopted to describe the resin flow in fiber preform, and modified governing equations derived from the NavierStokes equations are introduced to describe the resin flow in the edge channel. A dual-Arrhenius viscosity model is newly introduced to describe the chemorheological behavior of a modified bismaleimide resin. The influence of the curing reaction and processing parameters on the resin flow patterns was investigated. The results indicate that, under constant-flow velocity conditions, the curing reaction caused an obvious increase in the injection pressure and its influencing degree was greater with increasing resin temperature or preform permeability. Both a small change in the resin viscosity and the alteration of the injection flow velocity hardly affected the resin flow front. However, the variation of the preform permeability caused an obvious shape change in the resin flow front. The simulated results were in agreement with the experimental results. This study was helpful for optimizing the reactive mold-filling conditions.

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Momentum transport at a fluid–porous interface

Cited by 284 publications

References 52 publications

Pressure-driven flow in a channel with porous walls

Pressure-driven flow in a channel with porous walls

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

Reactive mold filling in resin transfer molding processes with edge effects

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