Use of 2-D and 3-D unsteady RANS in the computation of wall bounded buoyant flows

•RANS closures applied in natural convection cavities at high Ra values.•Extended version of the AWF introduced in EDF open-source CFD software.•Proposed AWF strategy substantially improves predictions.•Three-dimensionality significantly affects flow and thermal developments. The present study numerically investigates the performance of a range of RANS turbulence closures with different near-wall treatments in the prediction of natural convection flows. Comparisons are performed of both 2-D and 3-D steady and time-dependent computations in differentially heated cavities, which involve very simple geometries, but give rise to complex flow physics of relevance to cooling applications, including safety features of nuclear reactors. The turbulence closures assessed include eddy-viscosity and second-moment closures and involve low-Reynolds-number versions (LRN) which fully resolve the viscous sublayer, as well as high-Reynolds-number versions (HRN) which adopt wall function treatments to prescribe boundary conditions for the wall shear stress and heat flux. In the 2-D computations of the tall rectangular cavity, there are only small deviations in the predictions of different models, and these are mainly confined to the local Nusselt number comparisons. Among the LRN models, the second-moment EBRSM is in good agreement with the data, while the LRN eddy-viscosity models under-estimate the Nusselt number levels. The HRN models, when used with the standard log-law-based wall function, over-estimate the Nusselt number. During the course of the present investigation, a new, more general, version of the Analytical Wall Function (AWF) has been developed and introduced to the open-source CFD code utilised. Here, this more general numerical wall treatment brings the HRN k-ε predictions of the Nusselt number to very close agreement with the experimental data. In the 2-D square cavity computations, the simulations focus on a high Rayleigh number (Ra) of 1011, for which DNS data has recently become available. At such high Ra value all the models are challenged due to the unsteadiness of the flow and the presence of a largely stationary and laminar core, and thin turbulent boundary layers. Assessment of different 3-D configurations of the same square cavity demonstrates that the effect of the turbulent mixing in the third (z) direction is significant, but can be taken into account by introducing a cavity depth of D=0.15H, matching that used in the DNS study. The deviations i