DNS Based Analysis and Modeling of the Turbulent Heat Transfer by Natural Convection in Liquid Lead-Bismuth

Results of a direct numerical simulation for Rayleigh-Be´nard convection with Pr = 0.025 are used to analyze the transport equations for the turbulent heat flux. These results show the importance of the pressure diffusion and of the pressure scrambling term in the budget of turbulent heat flux equations. Analysis using the two-point correlation method shows, that a suitable model for the pressure scrambling term may give good approximation of the total temperature pressure gradient correlation, if the flow field is locally dominated by small structures. DNS results show, that a standard pressure scrambling model predicts the total temperature pressure gradient correlation acceptably well for this type of flow. DNS based analysis of the standard pressure scrambling model indicates, that an application of the mixed time scale may improve the model and reduce the number of empirical coefficients.