Stokes–Darcy system, small-Darcy-number behaviour and related interfacial conditions

Lyu, Wenqi; Wang, Xiaoming

doi:10.1017/jfm.2021.509

Cited by 11 publications

(9 citation statements)

References 41 publications

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“…Relatively impervious materials, like limestone or granite, can have permeabilities between 10 −18 and 10 −15 m 2 , while more porous media, like sorted gravel or sand, can have permeabilities in the range 10 −10 Π 10 −7 m 2 (Bear 1972;Nield & Bejan 2017). The resulting Darcy numbers in experiments and/or simulations are small (typically 10 −10 ≤ Da ≤ 10 −5 ), highlighting the necessity to study the relevant small-Darcy regime in more depth, as done in Lyu & Wang (2021). This observation spurred McCurdy et al (2019) to develop a simple model to predict the critical depth ratio d * that distinguishes shallow convection from deep convection.…”

Section: Non-dimensional Systemmentioning

confidence: 99%

“…Relatively impervious materials, like limestone or granite, can have permeabilities between and , while more porous media, like sorted gravel or sand, can have permeabilities in the range (Bear 1972; Nield & Bejan 2017). The resulting Darcy numbers in experiments and/or simulations are small (typically ), highlighting the necessity to study the relevant small-Darcy regime in more depth, as done in Lyu & Wang (2021).…”

Section: The Coupled Navier–stokes–darcy Systemmentioning

confidence: 99%

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Predicting convection configurations in coupled fluid–porous systems

2022

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A ubiquitous arrangement in nature is a free-flowing fluid coupled to a porous medium, for example a river or lake lying above a porous bed. Depending on the environmental conditions, thermal convection can occur and may be confined to the clear fluid region, forming shallow convection cells, or it can penetrate into the porous medium, forming deep cells. Here, we combine three complementary approaches – linear stability analysis, fully nonlinear numerical simulations and a coarse-grained model – to determine the circumstances that lead to each configuration. The coarse-grained model yields an explicit formula for the transition between deep and shallow convection in the physically relevant limit of small Darcy number. Near the onset of convection, all three of the approaches agree, validating the predictive capability of the explicit formula. The numerical simulations extend these results into the strongly nonlinear regime, revealing novel hybrid configurations in which the flow exhibits a dynamic shift from shallow to deep convection. This hybrid shallow-to-deep convection begins with small, random initial data, progresses through a metastable shallow state and arrives at the preferred steady state of deep convection. We construct a phase diagram that incorporates information from all three approaches and depicts the regions in parameter space that give rise to each convective state.

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Section: Non-dimensional Systemmentioning

confidence: 99%

Section: The Coupled Navier–stokes–darcy Systemmentioning

confidence: 99%

Predicting convection configurations in coupled fluid–porous systems

2022

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“…All filtration processes involve such coupling. For many natural and engineering applications involving such coupled processes, the Darcy number is very small [23]. Therefore, it is of significant interest to investigate the small Darcy number regime of the coupled system.…”

Section: Introductionmentioning

confidence: 99%

“…There are competing theories within the fluid community such as the continuity of the full velocity, the continuity of the pressures, the continuity of the stress tensor, among others [22]. In a recent work [23], the authors investigated these issues in the linearized regime, i.e. the Stokes-Darcy system.…”

Section: Introductionmentioning

confidence: 99%

Small Darcy number limit of the Navier–Stokes–Darcy system

Lyu,

Wang

2024

Nonlinearity

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We study the small Darcy number behavior of the Navier–Stokes–Darcy system with the conservation of mass, Beavers–Joseph–Saffman–Jones condition, and the Lions balance of the normal-force interface boundary conditions imposed on the interface separating the Navier–Stokes flow and Darcy flow. We show that the asymptotic behavior of the coupled system, at small Darcy number, can be captured by two semi-decoupled Darcy number independent sequences: a sequence of (linearized) Navier–Stokes equations, and a sequence of Darcy equations with appropriate initial and boundary data. Approximate solutions to any order of the small parameter (Darcy number) can be constructed via the two sequences. The local in time validity of the asymptotic expansion up to second order is presented. And the global in time convergence is derived under the assumption that the Reynolds number is below a threshold value.

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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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Stokes–Darcy system, small-Darcy-number behaviour and related interfacial conditions

Abstract: Abstract

Cited by 11 publications

References 41 publications

Predicting convection configurations in coupled fluid–porous systems

Predicting convection configurations in coupled fluid–porous systems

Small Darcy number limit of the Navier–Stokes–Darcy system

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

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