Computation of Turbulent Free Convection in Oblique Porous Enclosures Using a Macroscopic Two-Equation Model

Computations for turbulent natural convection within an inclined cavity totally filled with a fluid saturated porous medium are presented. The finite volume method in a generalized coordinate system is applied. The inclined walls are maintained at constant but different temperatures, while the horizontal walls are kept insulated. Governing equations are written in terms of primitive variables and are recast into a general form, Flow and heat transfer characteristics, (streamlines, isotherms and average Nusselt number), are investigated for a wide range of values of Rayleigh number and inclined angle. The turbulent model used is the standard k-ε model with a wall function. In this work, the turbulence model is first switched off and the laminar branch of the solution is found. Subsequently, the turbulence model is included so that the solution merges 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 relaminarization phenomenon. Present solutions are compared with published results and the influence of the inclination angle on Ra_cr is analyzed. For Ra_m greater than around 10⁴, both laminar and turbulent flow solutions deviate, indicating that such critical value for Ra_m was reached.