Transitional regimes and rotation effects in Rayleigh–Bénard convection in a slender cylindrical cell

Abstract

In this paper we analyze transitional regimes and mean flow structures for the thermally driven convective flow in a cylindrical cell of aspect-ratio (diameter over cell height) Γ = 1 / 2 . The investigation is carried out through the numerical integration of the three-dimensional unsteady Navier–Stokes equations with the Boussinesq approximation. In particular the critical Rayleigh numbers for the onset of convection, for the unsteady, chaotic and turbulent regimes are computed for two values of the Prandtl number and comparisons with cylindrical cells of larger aspect-ratio are performed. The effect of the background rotation on the flow dynamics is also described showing that the heat transfer increase, already evidenced in the literature, is only obtained for a range of rotation rates. The rotation can enhance or inhibit the heat transfer and, at low Rayleigh numbers, it is a very effective way to inhibit vertical motions and to prevent horizontal thermal gradients. This is highly desirable in solidification and crystal growth processes where thermally induced motions cause material defects and crystal inhomogeneities.