Natural convection of compressible and incompressible gases in undeformable porous media under cold climate conditions

A numerical model for convective heat and mass transport of compressible or incompressible gas flows with soil-water phase change is presented. In general, the gaseous phase is considered as compressible and the model accounts for adiabatic processes of compression heating and expansion cooling. The inherently compressible gaseous phase may nevertheless be considered as incompressible by adopting the Oberbeck–Boussinesq approximations. The numerical method used to solve the equations that describe natural convection is based on a Galerkin finite element formulation with adaptive mesh refinement and dynamic time step control. As most existing numerical studies have focused on the behavior of incompressible fluids, model substantiation examines the influence of fluid compressibility on two-widely used benchmarks of steady-state convective heat and mass transport. The relative importance of the effect of pressure-compressibility cooling is shown to increase as the thermal gradient approaches the magnitude of the adiabatic gradient. From these results, it may be concluded that pore-air compressibility cannot be neglected in medium to large-sized enclosures at small temperature differentials. After demonstrating its ability to solve fairly complex transient problems, the model is used to further our understanding of the thermal behavior of the toe drain at the LA2-BSU dam in the province of Quebec, Canada.