A nonlinear asymptotic model for the inertial flow at a fluid-porous interface

Angot, Philippe; Goyeau, Benoı̂t; Ochoa‐Tapia, J. Alberto

doi:10.1016/j.advwatres.2020.103798

Cited by 10 publications

(6 citation statements)

References 71 publications

(188 reference statements)

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“…The flow of fluids in composite porous-clear domains is a prevalent phenomenon in many natural and industrial applications. Consequently, such has been the focus of several research studies, covering both laminar and turbulent flow considerations [1][2][3][4][5][6][7][8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Turbulent Flow through and over a Compact Three-Dimensional Model Porous Medium: An Experimental Study

Arthur¹

2021

Fluids

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There are several natural and industrial applications where turbulent flows over compact porous media are relevant. However, the study of such flows is rare. In this paper, an experimental investigation of turbulent flow through and over a compact model porous medium is presented to fill this gap in the literature. The objectives of this work were to measure the development of the flow over the porous boundary, the penetration of the turbulent flow into the porous domain, the attendant three-dimensional effects, and Reynolds number effects. These objectives were achieved by conducting particle image velocimetry measurements in a test section with turbulent flow through and over a compact model porous medium of porosity 85%, and filling fraction 21%. The bulk Reynolds numbers were 14,338 and 24,510. The results showed a large-scale anisotropic turbulent flow region over and within the porous medium. The overlying turbulent flow had a boundary layer that thickened along the stream by about 90% and infiltrated into the porous medium to a depth of about 7% of the porous medium rod diameter. The results presented here provide useful physical insight suited for the design and analyses of turbulent flows over compact porous media arrangements.

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Section: Introductionmentioning

confidence: 99%

Turbulent Flow through and over a Compact Three-Dimensional Model Porous Medium: An Experimental Study

Arthur¹

2021

Fluids

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“…Based on the choice of the underlying flow models in the free-flow region and the porous medium, different sets of coupling conditions at the fluidporous interface are available in the literature. Interface conditions for the Navier-Stokes/Darcy-Forchheimer model are developed in [2,[17][18][19]. Coupling conditions for the Stokes equations and multiphase Darcy's law together with the transport of chemical species and energy are proposed in [15].…”

Section: Introductionmentioning

confidence: 99%

“…However, some of these interface conditions contain unknown model parameters, which still need to be determined before the conditions can be used in numerical simulations, e.g. [4,19,22]. Other alternative coupling concepts, where the effective coefficients can be computed based on the pore geometry, are either derived only for unidirectional flows parallel or perpendicular to the porous layer [6,10,20] or they are not validated for arbitrary flow directions [7,31].…”

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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“…There are other alternative coupling concepts in the literature for Stokes-Darcy problems, e.g. (Angot et al, , 2021Lācis et al, 2020;Ochoa-Tapia & Whitaker, 1995) which are beyond the scope of this manuscript. Pore-network models (Blunt, 2017) consider a simplified yet equivalent representation of the porous geometry by separating the void space into larger pore bodies connected by narrow pore throats.…”

Section: Introductionmentioning

confidence: 99%

“…There are many mathematical approaches when dealing with a regression problem such as PCE representation that lead to a sparse solution. These approaches have led to the emergence of numerous sparse solvers in the compressed sensing (Arjoune et al, 2017), as well as in the sparse PCE. In (Lüthen et al, 2021), the authors provide a comprehensive survey of the proposed solvers in the context of PCE.…”

Section: Introductionmentioning

confidence: 99%

Uncertainty-aware Validation Benchmarks for Coupling Free Flow and Porous-Medium Flow

Mohammadi¹,

Eggenweiler²,

Flemisch³

et al. 2021

Preprint

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A correct choice of interface conditions and useful model parameters for coupled freeflow and porous-medium systems is vital for physically consistent modeling and accurate numerical simulations of applications. We consider the Stokes-Darcy problem with different models for the porous-medium compartment and corresponding coupling strategies: the standard averaged model based on Darcy's law with classical or generalized interface conditions as well as the pore-network model. We study the coupled flow problems' behaviors considering a benchmark case where a pore-scale resolved model provides the reference solution and quantify the uncertainties in the models' parameters and the reference data. To achieve this, we apply a statistical framework that incorporates a probabilistic modeling technique using a fully Bayesian approach. A Bayesian perspective on a validation task yields an optimal bias-variance tradeoff against the reference data. It provides an integrative metric for model validation that incorporates parameter and conceptual uncertainty. Additionally, a model reduction technique, namely Bayesian Sparse Polynomial Chaos Expansion, is employed to accelerate the calibration and validation processes for computationally demanding Stokes-Darcy models with different coupling strategies. We perform uncertainty-aware validation, demonstrate each model's predictive capabilities, and make a model comparison using a Bayesian validation metric.

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A nonlinear asymptotic model for the inertial flow at a fluid-porous interface

Cited by 10 publications

References 71 publications

Turbulent Flow through and over a Compact Three-Dimensional Model Porous Medium: An Experimental Study

Turbulent Flow through and over a Compact Three-Dimensional Model Porous Medium: An Experimental Study

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

Uncertainty-aware Validation Benchmarks for Coupling Free Flow and Porous-Medium Flow

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