Influence of the Geometry on Rayleigh-Bénard Convection

Abstract

Direct numerical simulations (DNS) of Rayleigh-Bénard convection in a cube and a cylinder with equal diameter and height are performed to investigate the main responses of the system, namely heat flux and motion. Differences in the latter two quantities for the two geometries suggest a transition between different flow states in the cube, which is not observed in the cylinder due to its rotational symmetry. A method is introduced to analyse the flow dynamics in the cube, which relies on the temperature distribution at the lateral walls. It reveals that above a certain Rayleigh number the global flow structure in the cube is organized in a diagonal manner and not longer parallel to the walls, which leads to differences in the heat flux and the kinetic energy in the cylindrical and the cubic sample.

Boundary layers and wind in turbulent thermal convection

“…To avoid the above mentioned difficulties because of the azimuthal symmetry of a cylindrical container, for further studies box-shaped containers are used. In chapter 10 (published as a conference proceeding in a book by Springer [156]), the mean heat flux (which is related to the thickness of the thermal BL), the mean kinetic energy and the global flow in a cubic container and in a cylindrical one are evaluated and compared for Pr = 0.786 and Ra between 10 5 and 10 7 .…”