Mathematical modeling of the interaction of a thermal convective flow and a moving body

A mathematical model developed to describe the interaction of a thermal convective flow with a moving body is presented. The model was implemented within the framework of the SigmaFlow computational software package, which is based on computational fluid dynamics methods. The thermal convective flow is described by the Navier-Stokes equations in the Boussinesq approximation, and the moving body model is implemented using the immersed boundary method. The article presents the results of verification of the proposed mathematical model by solving the following test problems: unsteady laminar flow around the cylinder; natural convection in the channel between two cylinders; developed convective flow in a closed rectangular area with a fixed plate. The results of a numerical study of the plate motion in a thermal convective flow in a closed volume (cuvette) with hot lower and cold upper walls are presented. The calculations showed that the moving plate has an impact on the dynamics of formation of large-scale cells, the local distribution of heat flux density on the lower wall and the integral heat flux. In particular, they revealed a local decrease in the heat flux under the plate, an increase in the number of large vortices in the cuvette and the destruction of the horizontal temperature gradient observed in the case of a fixed plate. In addition, for a fixed plate, the value of heat flux under it depends on its position, and in the case of a moving plate - on the position and direction of its movement. A qualitative comparison of calculations for two different Rayleigh numbers with the experimental data obtained at the Institute of Continuous Medium Mechanics of the Ural Branch of the Russian Academy of Sciences showed that the behavior of the plate is governed by similar regularities.