Direct numerical simulation study of stable anti-Rayleigh–Bénard convection in porous media up to moderate Rayleigh numbers

Abstract

This study investigates anti-Rayleigh–Bénard (anti-RB) convection in a two-dimensional or quasi-two-dimensional cavity filled with regular square or circular bars across a broad spectrum of Rayleigh numbers, Prandtl numbers, Darcy numbers, and porosities, utilizing direct numerical simulation. Anti-RB convection is characterized by thermal boundary conditions on the bottom and top walls that are opposite to those in classical Rayleigh–Bénard (RB) convection. The findings demonstrate that thermal convection is initiated by the porous matrix with adiabatic boundary conditions and plays a significant role in local heat transfer when the Rayleigh number is sufficiently large. However, the induced velocity remains confined within individual representative elementary volumes (REVs) and the effects of thermal convection in each REV counterbalance each other, leading to a negligible effect on global heat transfer in the stable anti-RB regime. Due to geometric effects, the Nusselt number is found to be less than unity when compared to anti-RB convection in void cavity. At elevated Rayleigh numbers, the system transitions to the unstable anti-RB regime, where flow intensification enhances global heat transfer. Within the investigated range of relevant variables, a model for the Nusselt number is developed exclusively for the stable anti-RB regime and regular porous media, revealing that when the Darcy number is sufficiently small, the Nusselt number is minimally influenced by the Rayleigh number, the Prandtl number, and the Darcy number but is sensitive to porosity due to its impact on inter-channel width. Furthermore, the local thermal dissipation rate is higher in vertical channels, while the local kinetic dissipation rate is larger in horizontal channels. An adjusted framework is introduced to model the global thermal dissipation rate. The normalized global thermal dissipation rate approaches unity across various Rayleigh numbers and porosities. These findings might provide valuable insights and predictive tools for the thermal management and mass storage/transport industries.