# Turbulent Rayleigh-Bénard convection in cylindrical containers

Rayleigh-Bénard convection is one of the classical problems in fluid mechanics, where a fluid between two horizontal plates is heated from below and cooled from above. At a sufficiently high-temperature difference, the onset of turbulent convection can be observed, in which large thermal structures are detaching from the thermal boundary layers, transporting hot and cold fluid through the core region, respectively.

Most of the theoretical and numerical investigations of natural convection rely on the Oberbeck-Boussinesq (OB) approximation. This means that almost all physical fluid properties are assumed to be constant, except the density in the buoyancy term which is considered to vary linearly with the temperature.

Aiming at more realistic flow predictions, the OB approximation is applicable only if the temperature difference imposed between the bottom and the top plate of Rayleigh cell is small enough and variations of the fluid’s material properties are negligible.

In natural convection, the temperature- and pressure-dependences of the material properties can influence significantly the global flow structures as well as mean flow characteristics such as the mean heat flux (the Nusselt number) and the centre temperature. The deviations of the latter in non-Oberbeck-Boussinesq (NOB) convection from those of OB convection are recognized as NOB effects.

Within the project, well-resolved three-dimensional Direct Numerical Simulations (DNS) of incompressible NOB and OB convection in cylindrical Rayleigh cells are conducted using a highorder finite volume method. Hence, it is possible to analyze the temporal and spatial evolution of all relevant turbulent flow structures and their impact on large-scale transport mechanisms.

The main focus of the here presented investigations is thereby devoted to the analysis of coherent flow structures and their interaction with thermal and viscous boundary layers, the convective heat transport and the influence of very large Prandtl numbers.

# Contact:

Prof. Dr. Claus Wagner

German Aerospace Center (DLR)

Institute of Aerodynamics and Flow Technology, Department Ground Vehicles

Göttingen

Phone: +49 551 709-2261