Effects of pore scale and conjugate heat transfer on thermal convection in porous media

Abstract

The study of thermal convection in porous media is of both fundamental and practical interest. Typically, numerical studies have relied on the volume-averaged Darcy–Oberbeck–Boussinesq (DOB) equations, where convection dynamics are assumed to be controlled solely by the Rayleigh number (Ra). Nusselt numbers (Nu) from these models predict Nu–Ra scaling exponents of 0.9–0.95. However, experiments and direct numerical simulations (DNS) have suggested scaling exponents as low as 0.319. Recent findings for solutal convection between DNS and DOB models have demonstrated that the ‘pore-scale parameters’ not captured by the DOB equations greatly influence convection. Thermal convection also has the additional complication of different thermal transport properties (e.g. solid-to-fluid thermal conductivity ratio ks/kf and heat capacity ratio σ) in different phases. Thus, in this work we compare results for thermal convection from the DNS and DOB equations. On the effects of pore size, DNS results show that Nu increases as pore size decreases. Mega-plumes are also found to be more frequent and smaller for reduced pore sizes. On the effects of conjugate heat transfer, two groups of cases (Group 1 with varying ks/kf at σ = 1 and Group 2 with varying σ at ks/kf = 1) are examined to compare the Nu–Ra relations at different porosity (ϕ) and ks/kf and σ values. Furthermore, we report that the boundary layer thickness is determined by the pore size in DNS results, while by both the Rayleigh number and the effective heat capacity ratio, $\bar{\phi } = \phi + (1 - \phi )\sigma$ , in the DOB model.

Convective mixing in porous media: a review of Darcy, pore-scale and Hele-Shaw studies

“…When the thickness of the thermal boundary layer is comparable to the averaged pore length scale ( ), the transition from one regime to the other occurs. In addition to the porous structure and the Rayleigh number, in case of thermal convection, the boundary layer thickness and the heat transfer coefficient are determined also by the value of thermal conductivity of the solid and liquid phases [ 76 , 77 ].

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“…While in the two-dimensional case [ 54 , 62 ] this scaling sets in at , in three-dimensional flows [ 58 , 59 ] the ultimate state is expected to take place at , which is beyond the present numerical capabilities. Pore-scale simulations have revealed a more complex scenario, in which the heat/mass transfer is also influenced by porosity [ 30 , 31 ], Schmidt number and relative conductivity of fluid and solid phases [ 76 , 77 ]. These extensive numerical campaigns have led to the development of physics-based correlations for as a function of the flow parameters.…”

Towards the understanding of convective dissolution in confined porous media: thin bead pack experiments, two-dimensional direct numerical simulations and physical models

“…They observed that the scaling crossover occurs when the thickness of the thermal boundary layer is comparable to the averaged pore length scale. In addition to the porous structure and the Rayleigh number, in case of thermal convection, the boundary layer thickness and the heat transfer coefficient are determined also by the value of thermal conductivity of the solid and liquid phases (Korba & Li 2022; Zhong, Liu & Sun 2023).…”

Numerical Investigation of Conjugate Heat Transfer and Natural Convection Using the Lattice-Boltzmann Method for Realistic Thermophysical Properties

“…For example, Paknahad et al [26] studied metal foam at pore scale using a regularized collision operator for the thermal solver, but only steady-state conditions were considered. In another study, Korba and Li [27] investigated thermal convection and conjugate heat transfer in porous media and resolved the turbulent flow through direct numerical simulation.…”