Effects of pore scale on the macroscopic properties of natural convection in porous media

Gasow, Stefan; Lin, Zhe; Zhang, Hao Chun; Кузнецов, А. В.; Avila, Marc; Jin, Yan

doi:10.1017/jfm.2020.164

Cited by 22 publications

(81 citation statements)

References 28 publications

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“…Although DNS is too expensive for engineering applications, it is a powerful tool to gain a better understanding of the physics of convection in porous media and serves as a foundation for developing macroscopic models. Recently, we performed pore-scale-resolving DNS of natural convection in porous media composed of a simple porous matrix (Gasow et al 2020). Our DNS results showed that the boundary layer thickness for convection in porous media is determined by the pore size instead of the Rayleigh number.…”

Section: Introductionmentioning

confidence: 98%

A macroscopic two-length-scale model for natural convection in porous media driven by a species-concentration gradient

et al. 2021

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The modelling of natural convection in porous media is receiving increased interest due to its significance in environmental and engineering problems. State-of-the-art simulations are based on the classic macroscopic Darcy–Oberbeck–Boussinesq (DOB) equations, which are widely accepted to capture the underlying physics of convection in porous media provided the Darcy number, $Da$ , is small. In this paper we analyse and extend the recent pore-resolved direct numerical simulations (DNS) of Gasow et al. (J. Fluid Mech, vol. 891, 2020, p. A25) and show that the macroscopic diffusion, which is neglected in DOB, is of the same order (with respect to $Da$ ) as the buoyancy force and the Darcy drag. Consequently, the macroscopic diffusion must be modelled even if the value of $Da$ is small. We propose a ‘two-length-scale diffusion’ model, in which the effect of the pore scale on the momentum transport is approximated with a macroscopic diffusion term. This term is determined by both the macroscopic length scale and the pore scale. It includes a transport coefficient that solely depends on the pore-scale geometry. Simulations of our model render a more accurate Sherwood number, root mean square (r.m.s.) of the mass concentration and r.m.s. of the velocity than simulations that employ the DOB equations. In particular, we find that the Sherwood number $Sh$ increases with decreasing porosity and with increasing Schmidt number $(Sc)$ . In addition, for high values of $Ra$ and high porosities, $Sh$ scales nonlinearly. These trends agree with the DNS, but are not captured in the DOB simulations.

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Section: Introductionmentioning

confidence: 98%

A macroscopic two-length-scale model for natural convection in porous media driven by a species-concentration gradient

et al. 2021

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“…In the following sections, we just show the results for one set of layout. A reasonable estimate of Da can be obtained based on the Kozeny's equation (Nield & Bejan 2006;Gasow et al 2020). With the empirical model coefficient β = 150, the minimum Darcy number reached in this study is Da = 6.2 × 10 −6 .…”

Section: Numerical Modelmentioning

confidence: 66%

“…Here we report a numerical study on the transport of fluid particles and heat transfer in random porous media based on pore-scale modelling. In pore-scale models, the detailed flow features in the pores are resolved, which are useful for constructing appropriate macroscopic models and understanding the microscopic mechanisms underlying the macroscopic flow properties (Gasow et al 2020;Wood, He & Apte 2020).…”

Section: Introductionmentioning

confidence: 99%

Lagrangian dynamics and heat transfer in porous-media convection

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“…It seems likely that progress in understanding this limit will come from a mixture of experiments, numerical studies in which the pore-scale is fully resolved (cf. [86]) and continuum modelling using extensions of Darcy's Law like the Brinkman model or extended Hele-Shaw models (cf. [55]).…”

Section: (A) Heterogeneities and Interaction With Topography Or Flowmentioning

confidence: 99%

“…Some studies have explored the break-down of Darcy’s Law for low and moderate Ra convection using the Lattice–Boltzmann method to describe flow between the pores of the medium (e.g. [85]), while Gasow et al [86] recently presented direct numerical simulations of high- Ra two-sided convection that resolved flow on the pore scale through an idealized network. They found that resolving flow on the pore scale can lead to a reduction in the convective flux, and also demonstrated that the pore-scale dynamics can affect both the small (proto-plume and boundary-layer) scales and the large (megaplume) scales of the macroscopic flow.…”

Section: Two-sided Convectionmentioning

confidence: 99%

Vigorous convection in porous media

Hewitt

2020

Proc. R. Soc. A.

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The problem of convection in a fluid-saturated porous medium is reviewed with a focus on ‘vigorous’ convective flow, when the driving buoyancy forces are large relative to any dissipative forces in the system. This limit of strong convection is applicable in numerous settings in geophysics and beyond, including geothermal circulation, thermohaline mixing in the subsurface and heat transport through the lithosphere. Its manifestations range from ‘black smoker’ chimneys at mid-ocean ridges to salt-desert patterns to astrological plumes, and it has received a great deal of recent attention because of its important role in the long-term stability of geologically sequestered CO 2 . In this review, the basic mathematical framework for convection in porous media governed by Darcy’s Law is outlined, and its validity and limitations discussed. The main focus of the review is split between ‘two-sided’ and ‘one-sided’ systems: the former mimics the classical Rayleigh–Bénard set-up of a cell heated from below and cooled from above, allowing for detailed examination of convective dynamics and fluxes; the latter involves convection from one boundary only, which evolves in time through a series of regimes. Both set-ups are reviewed, accounting for theoretical, numerical and experimental studies in each case, and studies that incorporate additional physical effects are discussed. Future research in this area and various associated modelling challenges are also discussed.

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Effects of pore scale on the macroscopic properties of natural convection in porous media

Cited by 22 publications

References 28 publications

A macroscopic two-length-scale model for natural convection in porous media driven by a species-concentration gradient

A macroscopic two-length-scale model for natural convection in porous media driven by a species-concentration gradient

Lagrangian dynamics and heat transfer in porous-media convection

Vigorous convection in porous media

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