Simulation of turbulent natural convection in a porous cylindrical annulus using a macroscopic two-equation model

Abstract

This work presents numerical computations for laminar and turbulent natural convection within a horizontal cylindrical annulus filled with a fluid saturated porous medium. Computations covered the range 25 < Ra m < 500 and 3.2 × 10 −4 > Da > 3.2 × 10 −6 and made use of the finite volume method. The inner and outer walls are maintained at constant but different temperatures. The macroscopic k– ε turbulence model with wall function is used to handle turbulent flows in porous media. First, the turbulence model is switched off and the laminar branch of the solution is found when increasing the Rayleigh number, Ra m. Subsequently, the turbulence model is included and calculations start at high Ra m, merging to the laminar branch for a reducing Ra m. This convergence of results as Ra m decreases can be seen as an estimate of the so-called laminarization phenomenon. Here, a critical Rayleigh number was not identified and results indicated that when the porosity, Prandtl number, conductivity ratio between the fluid and the solid matrix and Ra m are kept fixed, the lower the Darcy number, the higher is the difference of the average Nusselt number given by the laminar and turbulent models.