Prediction of pore-scale-property dependent natural convection in porous media at high Rayleigh numbers

Abstract

Natural convection in porous media has received increasing attention in recent years due to its significance in engineering applications. This process is traditionally analyzed by the solution of the classical Darcy-Oberbeck-Boussinesq (DOB) equations. According to the DOB equations, natural convection in porous media is exclusively dependent on the Rayleigh-Darcy number, Ra, while the Sherwood number, Sh, has a linear relationship with Ra at high Rayleigh numbers. However, these predictions conflict with experimental observations. In this study, we have performed a pore-scale resolved direct numerical simulation (DNS) study of natural convection in periodic porous media composed of two-dimensional square and circular obstacles. Based on our analysis, a new correlation of Sh for large Rayleigh numbers (Ra≥1000), low Darcy numbers Da, and high Schmidt numbers Sc (Da/Sc≤2×10−8) has been proposed, expressed as Sh=aRa1−0.2φ2+1, where a=0.011±0.002 is a pore-scale geometric parameter. The new correlation has been validated over a wide range of Rayleigh numbers, porosity values, and pore-scale geometries. Our DNS results also show that, with a decrease of porosity, it becomes more difficult for mega-plumes with low wavenumbers to enter the boundary layer. Low wavenumber motions decay much faster with a decrease of Da than the pore-scale motions near the wall. The volume-averaged dissipation rate nondimensionalized using the pore size εˆi has the scaling law εˆi∼Da in the internal region and εˆi∼Da1/2 in the near-wall region. We expect that these characteristics obtained from DNS also apply to natural convection in porous media with much lower Darcy numbers.