Determination of the Slip Constant in the Beavers‐Joseph Experiment for Laminar Fluid Flow through Porous Media Using a Meshless Method

Mierzwiczak, Magdalena; Fraska, Agnieszka; Grabski, Jakub Krzysztof

doi:10.1155/2019/1494215

Cited by 16 publications

(10 citation statements)

References 24 publications

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“…The Stokes-Darcy problem is well studied for isotropic porous media (interface location, fitting of parameter α, see e.g. [25,29,36]). However, this is not the case for anisotropic media.…”

Section: Validation Casementioning

confidence: 99%

Effective coupling conditions for arbitrary flows in Stokes-Darcy systems

Eggenweiler¹,

Rybak²

2020

Preprint

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Boundary conditions at the interface between the free-flow region and the adjacent porous medium is a key issue for physically consistent modeling and accurate numerical simulation of flow and transport processes in coupled systems due to the interface driven nature of such processes. Interface conditions available in the literature have several weak points: most of them are suitable only for flows parallel to the fluid-porous interface, some are restricted to specific boundary value problems, and others contain unknown model parameters which still need to be deter-mined. These facts severely restrict the variety of applications that can be successfully modeled. We propose new interface conditions which are valid for arbitrary flow directions. These coupling conditions are rigorously derived using the theory of homogenization and boundary layers. All effective parameters appearing in these conditions are computed numeri-cally based on the geometrical configuration of the coupled system. The developed conditions are validated by comparison of numerical simulation results for the coupled Stokes-Darcy model and the pore-scale resolved model. In addition, the new interface conditions are compared with the classical conditions to demonstrate the advantage of the proposed conditions.

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Section: Validation Casementioning

confidence: 99%

Effective coupling conditions for arbitrary flows in Stokes-Darcy systems

Eggenweiler¹,

Rybak²

2020

Preprint

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“…Importance of this flow configuration in the current work is that it provides for a vehicle to study the effects of flow direction on the BJ slip parameter. This might be an important methodology from a cost-effective vantage point as experiments to approximate slip parameters could be costly, and some elegant theoretical methods of estimation are complicated and potentially time-consuming, [25]. With the availability of more data on the slip parameter for Darcy layers, experiments and/or techniques presented in [25] can estimate the most accurate value(s) for flow down an incline.…”

Section: Introductionmentioning

confidence: 99%

“…This might be an important methodology from a cost-effective vantage point as experiments to approximate slip parameters could be costly, and some elegant theoretical methods of estimation are complicated and potentially time-consuming, [25]. With the availability of more data on the slip parameter for Darcy layers, experiments and/or techniques presented in [25] can estimate the most accurate value(s) for flow down an incline. Our proposed relations can then be used to estimate the corresponding slip parameter(s) for the Forchheimer layer.…”

Section: Introductionmentioning

confidence: 99%

A Modified Beavers and Joseph Condition for Gravity-Driven Flow over Porous Layers

2021

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Gravity-driven flow through an inclined channel over a semi-infinite porous layer is considered in order to obtain a modification to the usual Beavers and Joseph slip condition that is suitable for this type of flow. Expressions for the velocity, shear stress, volumetric flow rates, and pressure distribution across the channel are obtained together with an expression for the interfacial velocity. In the absence of values for the slip parameter when the flow is over a Forchheimer porous layer, this work provides a relationship between the slip parameters of the Darcy and Forchheimer layers. Expressions for the interfacial velocities in both cases are obtained. This original work is intended to provide baseline analysis and a benchmark with which more sophisticated types of flow, over porous layers in an inclined domain can be compared.

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“…Although the question concerning the correct value of the Beavers-Joseph parameter is known for decades, to the best of the authors knowledge, no systematic study on determination of this parameter has been published. In case of cylindrical grains and parallel flows to the porous bed, the optimal value of the Beavers-Joseph slip coefficient was obtained in [27]. In the literature, α BJ = 1 is typically used even if this is not the optimal choice [12,28,29].…”

Section: Introductionmentioning

confidence: 99%

A modification of the Beavers-Joseph condition for arbitrary flows to the fluid-porous interface

Strohbeck¹,

Eggenweiler²,

Rybak³

2021

Preprint

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Physically consistent coupling conditions at the fluid-porous interface with correctly determined effective parameters are necessary for accurate mathematical modeling of various applications described by coupled free-flow and porous-medium problems. To model single-fluid-phase flows at low Reynolds numbers in such coupled systems, the Stokes/Darcy equations are typically used together with the conservation of mass across the fluid-porous interface, the balance of normal forces and the Beavers-Joseph condition on the tangential component of velocity. In the latter condition, the value of the Beavers-Joseph slip coefficient α BJ is uncertain, however, it is routinely set α BJ = 1 that is not correct for many applications. In this paper, three flow problems (pressure-driven flow, lid-driven cavity over porous bed, general filtration problem) with different pore geometries are studied. We determine the optimal value of the Beavers-Joseph parameter for unidirectional flows minimizing the error between the pore-scale resolved and macroscale simulation results. We demonstrate that the Beavers-Joseph slip coefficient is not constant along the fluid-porous interface for arbitrary flow directions, thus, the Beavers-Joseph condition is not applicable in this case.

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Determination of the Slip Constant in the Beavers‐Joseph Experiment for Laminar Fluid Flow through Porous Media Using a Meshless Method

Cited by 16 publications

References 24 publications

Effective coupling conditions for arbitrary flows in Stokes-Darcy systems

Effective coupling conditions for arbitrary flows in Stokes-Darcy systems

A Modified Beavers and Joseph Condition for Gravity-Driven Flow over Porous Layers

A modification of the Beavers-Joseph condition for arbitrary flows to the fluid-porous interface

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