Direct numerical simulation study of the effect of horizontal flow on mixed convection in porous media

A direct numerical simulation (DNS) study is performed on mixed convection in a chamber filled with a porous medium composed of staggered circular elements. Natural convection is driven by a temperature difference between the two walls, while forced convection is caused by a prescribed horizontal force. The Rayleigh number in the range 1000 ≤ 𝑅𝑎 ≤ 20000, pore-scale Rayleigh number in the range 1.2 ≤ 𝑅𝑎𝐾 ≤ 39.2, Peclet–Rayleigh number ratio in the range 0 ≤ 𝑃 𝑒𝐾∕𝑅𝑎𝐾 ≤ 1, Prandtl number 𝑃 𝑟 = 250, and porosity 𝜙 = 0.46 and 0.56 are considered in the DNS study. The DNS results reveal that pore-scale dispersion caused by natural convection is significant due to the large 𝑅𝑎𝐾. It enhances the merging of small plumes in the boundary layer and reduces the mega-plume number. The horizontal flow has two competing effects on heat transfer. It weakens vertical macroscopic advection and pore-scale dispersion, and thus reduces the heat transfer. However, it also weakens small-scale horizontal motions in the boundary layer, which prevents the mega-plumes from merging and enhances the heat transfer. Consequently, the mega-plume number increases at 𝑅𝑎 = 1000 as 𝑃 𝑒𝐾∕𝑅𝑎𝐾 rises from 0 to 1. At 𝑅𝑎 = 20000, the mega-plume number increases as 𝑃 𝑒𝐾∕𝑅𝑎𝐾 increases from 0 to 0.1; however, it decreases as 𝑃 𝑒𝐾∕𝑅𝑎𝐾 increases to 1, due to strong dispersion caused by the horizontal flow. The overall effect of the horizontal flow is mainly to reduce the Nusselt number. The Nusselt number follows the scaling law 𝑁𝑢 ∼ 𝑅𝑎𝑎, where 𝑎 can be approximated as 𝑎 = 0.5 − 2.5 × 10−6𝑃 𝑒 for the present DNS cases.