The Reynolds-stress model of turbulence applied to the natural-convection boundary layer along a heated vertical plate

Abstract The turbulent natural-convection boundary layer for air along a heated vertical plate is investigated numerically with an algebraic (ASM) and fully differential Reynolds-stress model (RSM). From the literature a set of model constants is selected, in such a way that the wall-heat transfer and mean-flow structure are predicted in close agreement with the experimental data. Sensitivity tests on RSM constants show which constants dominate the mean-flow prediction, and which constants only affect turbulence quantities. Wall modifications are employed to improve predictions of the near-wall turbulence. RSM calculations of the turbulence quantities agree well with available experimental data. ASM results are poorer, but still in qualitative agreement with experiments. Hence, in natural-convection boundary layers, the local-equilibrium assumption has only limited applicability. Furthermore, the eddy-viscosity concept used in the k − e model (KEM) is tested. The KEM gives good mean-flow results, but for a good prediction of the detailed turbulence structure the RSM is needed.