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

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 k(s)/k(f) and heat capacity ratio sigma) 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 k(s)/k(f) at sigma = 1 and Group 2 with varying sigma at k(s)/k(f) = 1) are examined to compare the Nu-Ra relations at different porosity (phi) and k(s)/k(f) and sigma 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, (phi) over bar = phi +(1 - phi)sigma, in the DOB model.