Turbulent Heat Flux Modelling by Using Elliptic-Blending k-ε-ζ-f RANS Model

We report the results for two buoyancy-driven benchmark cases, heatdriven square cavity at Ra = 10(11), and Rayleigh- Benard convection at Ra = 10(9), by using the elliptic-blending eddy viscosity k-epsilon-zeta-f model (or just-f), and three different formulations of the turbulent heat flux, namely the Simple Gradient Diffusion Hypothesis (SGDH), the General Gradient Diffusion Hypothesis (GGDH) and the Algebraic heat Flux Model (AFM). The zeta-f model is well-posed for computing turbulent heat transfer since it contains an approximation of the normal Reynolds stress in the wall-normal direction that is needed in GGDH and AFM formulations. Furthermore, the modelling of the wall-blocking effect by using the elliptic-relaxation approach is physically more sound than the commonly used damping functions. This work is motivated by the recently held 17(th) ERCOFTAC SIG15/MONACO2025 workshop on turbulent natural convection flows in differentially heated cavities, [1], which demonstrated superior performance of the zeta-f model in predicting the main flow features for the selected cases.