A Semi-Theoretical Approach to a Correlation for the Thermal Conductivity of a Beryllium Pebble Bed

Abstract

In the framework of the European Fusion Technology Programme, Lithium ceramics and Beryllium packed pebble beds are foreseen to be used as Tritium breeders and neutron multipliers, respectively, for the Helium Cooled Pebble Bed breeding blanket of a fusion power reactor operating with a D-T plasma. The present work is focused on the semi-theoretical investigation of the thermal conductivity of single size Beryllium pebble beds, starting from the main hypothesis that this conductivity depends linearly on pebble bed local temperature and total volumetric strain and introducing a method to determine the coefficients of such dependence on the basis of the results obtained by the SUPER-PEHTRA experiments. It has been mainly assumed that the SUPER-PEHTRA Beryllium pebble bed can be considered as a homogeneous, isotropic, and linear elastic medium, and that the analytical solution of the direct static problem of the thermo-elasticity for such a system has been used to fit the experimental thermal distributions, uncovering the best values for the thermal conductivity function coefficients. This thermal conductivity has been used together with a constitutive model, realistically taking into account the pebble bed mechanical behavior to reproduce the experimental tests. The results of the analyses agree quite well with the experimental ones, thus encouraging the use of the derived thermal conductivity correlation for Beryllium pebble beds undergoing low volumetric strain.