## Turbulent natural convection in a porous square cavity computed with a macroscopic $$\kappa$$–$$\epsilon$$ model.(English)Zbl 1121.76339

Summary: Detailed numerical computations for laminar and turbulent natural convection within a square cavity filled with a fluid saturated porous medium are presented. Heated vertical walls are maintained at constant but different temperatures, while horizontal surfaces are kept insulated. The macroscopic $$\kappa - \varepsilon$$ turbulence model with wall function is used to handle turbulent flows in porous media. In this work, the turbulence model is first switched off and the laminar branch of the solution is found when increasing the Rayleigh number, $$Ra_{\text{m}}$$. Computations covered the range $$10 < Ra_{\text{m}} < 10^6$$ and $$10^{-10} < Da < 10^{-7}$$ and made use of the finite volume method. Subsequently, the turbulence model is included and calculations start at high $$Ra_{\text{m}}$$, merging to the laminar branch for a reducing $$Ra_{\text{m}}$$ and for $$Ra_{\text{m}}$$ less than a certain critical Rayleigh number, $$Ra_{\text{cr}}$$. This convergence of results as $$Ra_{\text{m}}$$ decreases can be seen as a characterization of the laminarization phenomenon. For $$Ra_{\text{m}}$$ values less than around $$10^4$$, both laminar and turbulent flow solutions merge, indicating that such critical value for $$Ra_{\text{m}}$$ was reached. Results further indicate that when the parameters porosity, $$Pr$$, conductivity ratio between the fluid and the solid matrix and the $$Ra_{\text{m}}$$ are kept fixed, the lower the Darcy number, the higher the average Nusselt number at the hot wall.

### MSC:

 76F35 Convective turbulence 76R10 Free convection 76S05 Flows in porous media; filtration; seepage 76F60 $$k$$-$$\varepsilon$$ modeling in turbulence 76M12 Finite volume methods applied to problems in fluid mechanics 80A20 Heat and mass transfer, heat flow (MSC2010)
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