Theoretical and numerical analysis on phase change materials (PCM): A case study of the solidification process of erythritol in spheres

Phase change materials (PCM) present great potential for energy efficiency gains in thermal systems by storing solar energy or waste heat in industrial processes. This is due to the great amount of energy stored per mass unit within a small temperature range. In this paper we focus, by means of the numerical investigation, on the solidification process of the PCM erythritol in spheres, having 10, 20, 30 and 40 mm diameter, under wall temperatures of 10, 15, 20, 25, 30 and 40 K below the phase change temperature of the material. The problem is considered two-dimensional in geometry and transient in time. The numerical model here adopted consists of mass, momentum, energy and volume fraction equations. The results have been initially validated by comparison with data found in literature. Afterwards, analysis of the convective streams on the liquid PCM, liquid fraction, heat flux in the sphere wall and total solidification times have been widely illustrated. The liquid fraction suffers a sharp reduction at the beginning of the solidification process due to the high heat flux at the initial times. As the solid layer adjacent to the shell increases, it causes an augmentation of thermal resistance, significantly reducing the heat flux. The shape of the curve representing the solid fraction shows similarity with the S-curve pattern of solidification. The total solidification time proved to be dependent on both the diameter length and the temperature difference DT (between phase change material and wall temperature), being its influence reduced for lower temperature values. Finally, the liquid fraction results, as a function of Fourier and Stefan numbers, have been employed to amend a dimensionless correlation found in literature.