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 CO2 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-Benard 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

https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.2020.0111

Vigorous convection in porous media.

We perform a numerical study of the heat transfer and flow structure of Rayleigh-Benard (RB) convection in (in most cases regular) porous media, which are comprised of circular, solid obstacles located on a square lattice. This study is focused on the role of porosity $\phi$ in the flow properties during the transition process from the traditional RB convection with $\phi=1$ (so no obstacles included) to Darcy-type porous-media convection with $\phi$ approaching 0. Simulations are carried out in a cell with unity aspect ratio, for the Rayleigh number $Ra$ from $10^5$ to $10^{10}$ and varying porosities $\phi$, at a fixed Prandtl number $Pr=4.3$, and we restrict ourselves to the two dimensional case. For fixed $Ra$, the Nusselt number $Nu$ is found to vary non-monotonously as a function of $\phi$; namely, with decreasing $\phi$, it first increases, before it decreases for $\phi$ approaching 0. The non-monotonous behaviour of $Nu(\phi)$ originates from two competing effects of the porous structure on the heat transfer. On the one hand, the flow coherence is enhanced in the porous media, which is beneficial for the heat transfer. On the other hand, the convection is slowed down by the enhanced resistance due to the porous structure, leading to heat transfer reduction. For fixed $\phi$, depending on $Ra$, two different heat transfer regimes are identified, with different effective power-law behaviours of $Nu$ vs $Ra$, namely, a steep one for low $Ra$ when viscosity dominates, and the standard classical one for large $Ra$. The scaling crossover occurs when the thermal boundary layer thickness and the pore scale are comparable. The influences of the porous structure on the temperature and velocity fluctuations, convective heat flux, and energy dissipation rates are analysed, further demonstrating the competing effects of the porous structure to enhance or reduce the heat transfer.

From Rayleigh-B\'enard convection to porous-media convection: how porosity affects heat transfer and flow structure

https://repository.tudelft.nl/islandora/object/uuid%3A3d826726-15a9-4cda-9940-3f5c4ee5ddf8/datastream/OBJ/download

Flow and heat transfer measurements in natural convection in coarse-grained porous media

https://repository.tudelft.nl/islandora/object/uuid%3Aeb26ff62-53fa-44ff-a296-56cd33e4ca0f/datastream/OBJ/download

Daniel J. Keene

Papers

Thermal Convection in Porous Media at High Rayleigh Numbers