Microscopic flow near the surface of two-dimensional porous media. Part 2. Transverse flow

Larson, R. E.; Higdon, J. J. L.

doi:10.1017/s0022112087001149

Cited by 182 publications

(105 citation statements)

References 6 publications

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“…The fact that the total number of stagnation points in the square arrays of cylinders is very sensitive to the orientation of the mean flow has been noted earlier by Larson and Higdon. 12 These investigators have illustrated the changes in the flow field through detailed streamline plots. In particular, their streamline plots at area fraction of 0.4 clearly show six stagnation points when the mean flow is almost parallel to one of the principal lattice directions and two stagnation points otherwise.…”

Section: A Periodic Arraysmentioning

confidence: 99%

Nusselt number for flow perpendicular to arrays of cylinders in the limit of small Reynolds and large Peclet numbers

Wang

Sangani

1997

Physics of Fluids

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The problem of determining the Nusselt number N, the nondimensional rate of heat or mass transfer, from an array of cylindrical particles to the surrounding fluid is examined in the limit of small Reynolds number Re and large Peclet number Pe. N in this limit can be determined from the details of flow in the immediate vicinity of the particles. These are determined accurately using a method of multipole expansions for both ordered and random arrays of cylinders. The results for N/Pe1/3 are presented for the complete range of the area fraction of cylinders. The results of numerical simulations for random arrays are compared with those predicted using effective-medium approximations, and a good agreement between the two is found. A simple formula is given for relating the Nusselt number and the Darcy permeability of the arrays. Although the formula is obtained by fitting the results of numerical simulations for arrays of cylindrical particles, it is shown to yield a surprisingly accurate relationship between the two even for the arrays of spherical particles for which several known results exist in the literature suggesting thereby that this relationship may be relatively insensitive to the shape of the particles.

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Section: A Periodic Arraysmentioning

confidence: 99%

Nusselt number for flow perpendicular to arrays of cylinders in the limit of small Reynolds and large Peclet numbers

Wang

Sangani

1997

Physics of Fluids

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“…We recall that the viscosity in the Brinkman equation is not known and the use of it seems to be justified only in the case of a high porosity (see the discussion in [28]). Furthermore, Larson and Higdon undertook a detailed numerical simulation of two configurations (axial and transverse) of a shear flow over a porous medium in [21]. Their conclusion was that a macroscopic model based on Brinkman's equation gives "reasonable predictions for the rate of decay of the mean velocity for certain simple geometries, but fails for to predict the correct behavior for media anisotropic in the plane normal to the flow direction".…”

Section: Introductionmentioning

confidence: 99%

Effective interface conditions for the forced infiltration of a viscous fluid into a porous medium using homogenization

Carraro

Goll

Marciniak-Czochra

et al. 2015

Computer Methods in Applied Mechanics and Engineering

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It is generally accepted that the effective velocity of a viscous flow over a porous bed satisfies the Beavers-Joseph slip law. To the contrary, in the case of a forced infiltration of a viscous fluid into a porous medium the interface law has been a subject of controversy. In this paper, we prove rigorously that the effective interface conditions are: (i) the continuity of the normal effective velocities; (ii) zero Darcy's pressure and (iii) a given slip velocity. The effective tangential slip velocity is calculated from the boundary layer and depends only on the pore geometry. In the next order of approximation, we derive a pressure slip law. An independent confirmation of the analytical results using direct numerical simulation of the flow at the microscopic level is given, as well.

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“…James & Davis 2001). Numerical simulations have been carried out in the Stokes regime (Larson & Higdon 1987), for flow over banks of cylinders (Sahraoui & Kaviany 1992;Zhang & Prosperetti 2009) and for arrays of cubes (Breugem, Boersma & Uittenbogaard 2005;Chandesris & Jamet 2009;Valdés-Parada et al 2009). …”

Section: Introductionmentioning

confidence: 99%

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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Microscopic flow near the surface of two-dimensional porous media. Part 2. Transverse flow

Cited by 182 publications

References 6 publications

Nusselt number for flow perpendicular to arrays of cylinders in the limit of small Reynolds and large Peclet numbers

Nusselt number for flow perpendicular to arrays of cylinders in the limit of small Reynolds and large Peclet numbers

Effective interface conditions for the forced infiltration of a viscous fluid into a porous medium using homogenization

Pressure-driven flow in a channel with porous walls

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