Analysis of heat transfer and fluid flow during melting inside a spherical container for thermal energy storage

A numerical model of heat transfer and fluid flow during melting of a phase change material (PCM) inside a closed and uniformly heated spherical shell has been developed to investigate the thermal performance of the system. The control volume discretization technique has been used to solve the conservation equations for mass, momentum, and energy along with the enthalpy-porosity method to track the melting front. The study focused on PCMs with a melting temperature in the range of operation of concentrated solar thermal power (CSP) generation. A comprehensive analysis has been performed in order to determine the influence of the Grashof, Stefan and Prandtl numbers on the melting dynamics of capsules with various diameters (20, 30, 40, and 50 mm). Also the effects of the shell material and initial temperature of the system on the thermal performance have been analyzed. Correlations have been proposed for the melt fraction and average Nusselt number as a function of the main dimensionless parameters that characterized this problem. In order to support the validity of the developed model, the predicted results of a validation case are compared with the experimental results reported by Tan [1] and are found to be in good agreement.