Proceedings of the 8 th International Symposium on Experimental and Computational Aerothermodynamics of Internal Flows Lyon, July 2007 M. Kaczorowski et al. http://www.lmfa.ec-lyon.fr/ISAIF8/ Paper reference : ISAIF8-00130 Analysis of Turbulent Free Convection in a Rectangular Rayleigh-Bénard Cell M. Kaczorowski and C. Wagner DLR – Institute of Aerodynamics and Flow Technology, Bunsenstr. 10, D-37073 Göttingen, Germany The present study compares results of direct numerical simulations of thermal convection within a rectangular geometry with Rayleigh-Bénard convection in infinitely extended fluid layers and cylindrical geometries. It is shown that boundary layer thicknesses show similar tendencies in the rectangular geometry and the infinitely ex- tended fluid layer simulated by Hartlep et al. [6], but the quasi two-dimensional geometry of the rectangular cell delays the transition to a 3-D flow. Energy spectra are evaluated at different locations of the flow field. The spec- tra recorded in the centre of the cell show the same exponential scaling within the equilibrium range as those ob- tained by Verzicco and Camussi [11] in a slender cylindrical container. However, it is observed that within the thermal boundary layer significantly more turbulent energy is held by the small scales which is reflected by a fuller spectrum and a smaller exponent. Analysis of the thermal dissipation rates indicates that there are three dis- tinct regimes, with the small scale contributions growing rapidly for increasing Rayleigh number, whereas the large scale contributions remain almost constant. Keywords: DNS, thermal dissipation rate, boundary layer, energy spectrum Introduction A well-studied, but yet not fully understood problem in fluid mechanics is the Rayleigh-Bénard convection, where fluid between horizontal walls is heated from be- low and cooled from above. The Rayleigh number 3 T Ra gH α κν ∆ = (1) is a non-dimensional characteristic measure of the forces driving thermal convection determined by the height H of the fluid layer, the temperature difference between hot and cold wall ∆T, the gravitational acceleration g and the fluid properties α, κ and ν which are the thermal expan- sion coefficient, thermal diffusivity and kinematic vis- cosity respectively. Typically, numerical experiments of the Rayleigh-Bénard problem assume periodic boundary conditions in horizontal direction or a cylindrical con- tainer. However, Daya and Ecke [2] studied the impact of the container shape on the turbulent properties, and in- terestingly found that temperature and velocity fluctua- tions strongly depend upon the geometry while global properties, such as heat transfer, remain unchanged within measurement accuracy. In recent studies Verzicco and Camussi [10,11] have carried out direct numerical simulations of turbulent convection within cylindrical containers of low aspect ratio Γ = D / H, where D denotes the diameter of the container. They found that for a container of aspect ratio unity and Pr = 0.7 there is a transition from δ θ > δ u to δ θ < δ u around Ra = 2 × 10 7 , where δ θ and δ u denote the ther- mal and the kinetic boundary layer thickness respectively.