Contribution to elliptic relaxation modelling of turbulent natural and mixed convection

The paper reports on recent developments in modelling and numerical computations of natural and mixed convection based on newly developed quasi-linear algebraic heat flux and buoyancy extended stress models in the framework of the eddy-viscosity elliptic-relaxation approach. The DNS based ‘a priori’ testing of generic cases of turbulent natural convection (the side- and heated-from-below configurations) demonstrated that significant improvements are obtained in predictions of turbulent heat flux components when compared with more conventional proposals from the literature [including simple- and generalized gradient diffusion hypotheses (SGDH, GGDH), as well as algebraic flux models (AFM)]. The five equations ( k – ε – v 2 ¯ – f – θ 2 ¯ ) model is then applied to the computation of several 2D and 3D natural and mixed convection flows in turbulent regime. For all simulated cases, good agreements with available experimental and earlier numerical simulations are obtained. It is proved that the new model provides a rational compromise between physically sounder wall treatment and computational robustness making it possible to use moderately dense computational grids.