Turbulent convective heat transfer in thin vertical fluid layers
Turbulent Rayleigh-Benard convection in bounded vertical layers is studied in numerical simulations. The influence of layer thickness on convective heat transfer is investigated in detail. In this work we study the ability of two-dimensional and quasi-two-dimensional mathematical models to describe the characteristics of heat transfer in the thin layers. These models require much less computing resources in comparison to three-dimensional direct numerical simulations of turbulent convection. Three statements of the problem are considered: two-dimensional (2D), three-dimensional (3D) and quasi-two-dimensional (Q2D). The Q2D model uses the modified 2D equations, which are derived from the 3D Boussinesq equations under the assumption of a laminar transverse velocity profile. The 2D and Q2D simulations were performed using our own code, whereas the 3D simulations were carried out using open source CFD software OpenFOAM Extend 3.1. It is shown that the flow structure strongly affects the Nusselt number value. In thin layers the convective heat transfer increases despite a decrease in the intensity of the large-scale flow. It is shown, that the friction on lateral boundaries, even in frame of a rough model of linear friction, which was used in the Q2D simulations strongly affects the structure of the turbulent convective flow, changes its local and integral characteristics. The comparison with 3D numerical results demonstrates that the Q2D results qualitatively reproduce the dependence of the Nusselt number on the layer thickness, but underestimate the values of the Nusselt numbers by 30%. Also 2D results reveal poor correlation with the real structure of fluid flow in the domain for any aspect ratio.