Boundary conditions at a naturally permeable wall

Beavers, G. S.; Joseph, Daniel D.

doi:10.1017/s0022112067001375

Cited by 2,711 publications

(2,011 citation statements)

References 2 publications

Supporting

Mentioning

1,916

Contrasting

Unclassified

Order By: Relevance

“…One reason for these differences might be the difference between the Darcy numbers in the two cases. If the Darcy number is estimated using the pore sizes quoted in Beavers & Joseph (1967) we find 5.9×10 −3 and 3.4×10 −3 for the two data sets reproduced in figure 12, to be compared with, e.g. κ/a 2 6 × 10 −2 for our model porous medium with β = 0.303.…”

Section: Effective Slip At the Porous Medium Interfacementioning

confidence: 72%

“…Even ignoring the Reynolds number dependence, which was negligible in the parameter range of Beavers & Joseph (1967), it would seem that the parameter α has some dependence on the type of flow rather than being dependent 'only on the properties of the fluid and the permeable material' as postulated by these authors.…”

Section: Effective Slip At the Porous Medium Interfacementioning

confidence: 97%

“…When the porosity is significant, the difference from (1.1) can be appreciable also with a γ ∼ O(1). Beavers & Joseph (1967) define a parameter Φ expressing the increase in the flow rate with respect to that produced by the same pressure gradient in a plane no-slip channel. The same quantity is readily calculated from (8.4) with the result (2009) also find a result of this type, but with the important feature that their procedure adds a term proportional to the pressure gradient.…”

Section: Effective Slip At the Porous Medium Interfacementioning

confidence: 99%

“…A different approach was initiated by Beavers & Joseph (1967) where U = U (z) is the mean velocity in the flow direction x, U i is the slip velocity at the porous medium interface z = 0, κ is the permeability and α is a phenomenological dimensionless parameter. The Darcy velocity U D , which represents the mean flow rate per unit area in the bulk of the porous medium, is given by 2) in which dP /dx is an imposed mean pressure gradient and µ is the fluid viscosity.…”

Section: Introductionmentioning

confidence: 99%

“…In this picture, on traversing the interface, the velocity undergoes a discontinuity from U Much of this work relies on a variety of hypotheses and assumptions which, while eminently plausible, it has proven difficult to scrutinize in detail. The early experimental work, such as the original one of Beavers & Joseph (1967) and related subsequent studies, gave only indirect evidence as to the nature of the interfacial phenomena. More recent attempts, such as those of Goharzadeh et al (2005), Morad & Khalili (2009) and Pokrajac & Manes (2009), have difficulties resolving the flow very near the porous medium interface.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Pressure-driven flow in a channel with porous walls

Liu

Prosperetti

2011

J. Fluid Mech.

View full text Add to dashboard Cite

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.

show abstract

Section: Effective Slip At the Porous Medium Interfacementioning

confidence: 72%

Section: Effective Slip At the Porous Medium Interfacementioning

confidence: 97%

Section: Effective Slip At the Porous Medium Interfacementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Pressure-driven flow in a channel with porous walls

Liu

Prosperetti

2011

J. Fluid Mech.

View full text Add to dashboard Cite

show abstract

Analysis of singular perturbations on the Brinkman problem for fictitious domain models of viscous flows

Angot

1999

Math. Meth. Appl. Sci.

View full text Add to dashboard Cite

We show the justification of a formulation by fictitious domain to study incompressible viscous flows inside fluid–porous–solid systems by using the Brinkman model in a heterogeneous fictitious porous medium covering the whole auxiliary domain. The singular perturbations of this problem are analysed when the permeability of the medium tends to infinity in the fluid domain and/or to zero in the solid domain. In addition, the viscosity inside the solid body may possibly tend to infinity. The strong convergence of the solutions is established. Some error estimates on the solution are derived as a function of the penalty parameter. The error bound on the resulting applied force for the flow around a bluff obstacle is also given. Copyright © 1999 John Wiley & Sons, Ltd.

show abstract

Combined Free and Porous Flow in the Subsurface

Das

Nassehi

2004

Water Encyclopedia

View full text Add to dashboard Cite

The presence of a fluid layer adjacent to a porous medium is common in many environmental, chemical, mechanical and petroleum engineering problems. The flow behavior in the fluid layer is determined by the properties of the fluid (e.g., viscosity and density) and surface (e.g., pressure and shear) and body (e.g., gravity, and electric field) forces. However, flow in the porous medium depends additionally on the properties of the medium which include, among others, porosity and permeability. In fluid dynamic analysis of groundwater systems, it is commonly found that water flows through combined free (nonporous) and porous pathways between surface and subsurface systems. Such coupled regimes may also be present due to construction of industrial utilities and structures in the ground. Important engineering processes that may involve combined free and porous flow domains are, for example, fluid losses/leaks from underground pipes and storage tanks in old gas works sites; dig‐and‐treat, pump‐and‐treat, and permeable reactive barrier technologies for groundwater treatment; and drilling/extraction of oil from underground reservoirs. However, in most cases, the associated transport phenomena are determined by natural hydroenvironmental conditions. These include, for example, combined surface and subsurface flow, lake–groundwater interactions, seepage through preferential flow channels and macropores, circulatory flows and rise and fall of groundwater, glaciology, and multiple karstic regions interfaced with granular porous sections. The subdomains in coupled flow systems are generally distinguished by an interfacial surface, which represents the transitional zone for contaminants/fluid mobility from free to porous sections or vice versa. To gain on understanding of the combined flow behavior, it is necessary to develop realistic methodologies for evaluating mass and momentum transfer across the free/porous flow interfaces.

show abstract

Boundary conditions at a naturally permeable wall

Cited by 2,711 publications

References 2 publications

Pressure-driven flow in a channel with porous walls

Pressure-driven flow in a channel with porous walls

Analysis of singular perturbations on the Brinkman problem for fictitious domain models of viscous flows

Combined Free and Porous Flow in the Subsurface

Contact Info

Product

Resources

About