Turbulence modeling of natural convection in enclosures: A review

In this paper a review of recent developments of turbulence models for natural convection in enclosures is presented. The emphasis is placed on the effect of the treatments of Reynolds stress and turbulent heat flux on the stability and accuracy of the solution for natural convection in enclosures. The turbulence models considered in the preset study are the two-layer k − ɛ model, the shear stress transport (SST) model, the elliptic-relaxation (V2-f) model and the elliptic-blending second-moment closure (EBM). Three different treatments of the turbulent heat flux are the generalized gradient diffusion hypothesis (GGDH), the algebraic flux model (AFM) and the differential flux model (DFM). The mathematical formulation of the above turbulence models and their solution method are presented. Evaluation of turbulence models are performed for turbulent natural convection in a 1:5 rectangular cavity ( Ra = 4.3×10 10 ) and in a square cavity with conducting top and bottom walls ( Ra = 9 1.58×10 9 ) and the Rayleigh-Benard convection ( Ra = 2 × 10 6 ∼ Ra = 10 9 ). The relative performances of turbulence models are examined and their successes and shortcomings are addressed.