Numerical analysis of natural convection in sodium plenum below the grid plate of a fast reactor during a severe accident

Heat transfer characteristics of liquid sodium are quite different from that of normal liquids because of its very low Prandtl number. Empirical correlations for convective heat transfer in sodium are rather limited because of inherent difficulties in performing sodium experiments. In this paper, transient and steady natural convection developing inside a cylindrical enclosure heated from the top and cooled along the vertical side wall is studied by a numerical analysis. This problem is of relevance to the safety analysis of sodium cooled pool type fast reactor. The focus of the present investigation is to determine the effect of plate thickness on the natural convection heat transfer characteristics. For the case of a thick top plate, in the transient regime, heat transfer is conduction dominated and Nusselt number is found to be inversely proportional to square root of time as in the case of a thin plate. But the steady state heat transfer coefficient between the lower surface of thick hot plate and liquid sodium is less by about 25% than for a thin plate at the same temperature as the lower surface. The reason for this behaviour is traced to the weaker convective current developed in the case of a thick plate. Based on detailed parametric studies, a correlation for Nusselt number is derived with a correlation coefficient of 0.99, for use in the reactor safety analysis. The Nusselt number is found to be a function of Boussinesq number, thermal conductivity ratio between the wall material and liquid sodium and non-dimensional thickness of the plate. The validity of the correlation is further checked by applying it to different data sets not used for the derivation of the correlation.

► We study natural convection of sodium in cylindrical enclosures.
► Influence of enclosure wall thickness and conductivity ratio is studied.
► Nusselt number correlations are proposed for use in LMFBR safety analysis.