Natural convection flow in a square cavity revisited: Laminar and turbulent models with wall functions

Numerical simulations have been undertaken for the benchmark problem of natural convection flow in a square cavity. The control volume method is used to solve the conservation equations for laminar and turbulent flows for a series of Rayleigh numbers (Ra) reaching values up to 1010. The k‐ϵ model has been used for turbulence modelling with and without logarithmic wall functions. Uniform and non‐uniform (stretched) grids have been employed with increasing density to guarantee accurate solutions, especially near the walls for high Ra‐values. ADI and SIP solvers are implemented to accelerate convergence. Excellent agreement is obtained with previous numerical solutions, while some discrepancies with others for high Ra‐values may be due to a possibly different implementation of the wall functions. Comparisons with experimental data for heat transfer (Nusselt number) clearly demonstrates the limitations of the standard k‐ϵ model with logarithmic wall functions, which gives significant overpredictions.