Treatment of turbulent heat fluxes with the elliptic-blending second-moment closure for turbulent natural convection flows

In this paper a comparative study on the treatment of the turbulent heat fluxes with the elliptic-blending second-moment closure for natural convection flows is presented. Three different cases for treating the turbulent heat fluxes are considered. Those are the generalized gradient diffusion hypothesis (GGDH), the algebraic flux model (AFM) and the differential flux model (DFM). These models are implemented in a computer code especially designed for an evaluation of turbulent models. Calculations are performed for turbulent natural convection flows in an 1:5 rectangular cavity (Ra = 4.3 × 1010) and in a square cavity with conducting top and bottom walls (Ra = 1.58 × 109). The calculated results are compared with the available experimental data. The results show that the GGDH, AFM and DFM models produce sufficiently accurate solutions for the turbulent natural convection in an 1:5 rectangular cavity where the strength of the thermal stratification is weak in a central region of the cavity. However, the GGDH model produces very erroneous solutions for the turbulent natural convection in a square cavity with conducting walls where the Rayleigh number is relatively small and the thermally stratified region is dominant. The AFM and DFM produce very accurate solutions for both cases without invoking any numerical problems.