The paper considers two problems of thermal convection of an incompressible liquid in a horizontally extended layer: with lateral heat supply and with heating of the horizontal layer from below-the Rayleigh-Benard problem. An influence of boundary conditions and Prandtl numbers on the convective flow structure and temperature distribution is considered. The solutions of these problems are obtained using numerical modeling. The simulation is based on the numerical solution of a system of non-stationary 2D Navier-Stokes equations for an incompressible fluid, as well as for the Rayleigh-Benard problem for the case of a two-layers gas-liquid system. Navier-Stokes equations are solved using two numerical methods: the finite difference method and the control volume method. To verify the models, the results of calculations obtained by different numerical methods were compared with each other and compared with experimental data. The paper presents the results of numerical simulation of convective flows and heat and mass transfer in horizontal liquid layers under different defining dimensionless parameters and boundary conditions. The non-linear features of convective flows in horizontal liquid layers are shown, in particular, the occurrence of a counter-flow inside the layer-a liquid flow with a direction opposite to the main convective flow. The influence of boundary conditions and Rayleigh and Prandtl numbers on the existence of a countercurrent is considered. A simulation of the convective flow of a liquid in a horizontal layer when heated from the side at small Prandtl numbers, as well as at a Prandtl number equal to zero, is performed. The simulation results showed that for laminar convection (the Rayleigh number is greater than 10^5), the flow with Prandtl numbers equal to or less than 10^-2 is qualitatively different from the flow of a liquid with a zero Prandtl number. Therefore, the approximation of the zero value of the Prandtl number may not always be correct. Nonlinear peculiarities of convective flows in horizontal liquid layers are presented. It is shown that in long horizontal layers laterally heated only by thermal laminar convection (without the presence of impurities and concentration convection), it is possible to create a stable vertical density stratification of the fluid and, as a result, lead to the appearance of layered structures.
Федюшкин А.И. Влияние чисел Рэлея, Прандтля и граничных условий на конвективные течения жидкости в горизонтальных слоях. Математическое моделирование и численные методы. 2020. № 1. с. 28–44.