The Effects of Container Geometries on the Flow of Large-Scale Circulation in Simulated Rayleigh-Benard Systems

Abstract

The purpose of this study was to explore the effects of cell geometry on heat transport, represented by a value known as the Nusselt number, and the large scale circulation (LSC) in numerically-simulated Rayleigh-Benard systems. In Rayleigh-Benard systems, we explore convection and conduction in a fluid-filled cell whose top and bottom plates are set at fixed cold and hot temperatures, respectively. Cell size is characterized by an aspect ratio, a ratio of side length or diameter to depth. Using the spectral element code Nek5000, we simulated fluid flow in a cylindrical cell of aspect ratio 1, a square cell of aspect ratio 1, a long rectangular cell of aspect ratio 2x1, and a short rectangular cell of aspect ratio 0.5x1 at a Rayleigh number of 1x10^7 and a Prandtl number of 0.7, simulating air in a cell with a dimensionless temperature difference ratio of 1x10^7. To measure the LSC, we extracted data at the perimeter of the cell and tracked the coordinate values of temperature extrema. We also compiled isosurface temperature field plots into animations as to observe the time evolution of our data. We found that after convection had settled in, the mean Nusselt numbers for the cells had a weak inverse relationship with the aspect ratio of the cell. We also found that the LSC has no apparent orientation preference in the cylindrical cell, while it appears to favor an orientation along the diagonal in the square and rectangular cells. These observations on Nusselt values on the LSC are consistent with laboratory experiments.