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ANALYSIS AND MODELLING OF THE TURBULENT DIFFUSION OF TURBULENT HEAT FLUXES IN NATURAL CONVECTION

Laltu Chandra
Forschungszentrum Karlsruhe, Institut fur Kern- und Energietechnik, Postfach 3640, Karlsruhe 76021, Germany

Gunther Grotzbach
Forschungszentrum Karlsruhe, Institut fur Kern- und Energietechnik, Postfach 3640, Karlsruhe 76021, Germany

Abstract

Stably and unstably thermally stratified fluid layers are often encountered in practice ranging form environment to industry. There are examples of counter gradient heat fluxes occurring in such fluid layers containing a combination of both types of stratification. Simple standard heat flux models as employed e.g. in the k-ε-σ t framework need to be improved for representing such behaviour of the turbulent heat fluxes. More complex algebraic models or even in some cases the full transport equations for the turbulent heat fluxes are therefore required. There, the triple correlation u'ju'kT' appears as an important closure term in the turbulent diffusion. Usually, this is modelled following the Daly and Harlow approximation, which has already been found to be not sufficiently accurate in buoyant flows. In this paper, the transport equation for this triple correlation will be analyzed using Direct Numerical Simulation (DNS) data of two different flow types, for a internally heated fluid layer (IHL) and for Rayleigh-Bénard convection (RBC). Based on this study a Reynolds- Averaged Navier Stokes (RANS) model for the above closure term will be derived. Finally, this will be validated using the DNS data of both RBC and IHL which have different Rayleigh (Ra) and Prandtl (Pr) numbers.