Numerical and Experimental Study of Solidification in a Spherical Shell

The present study explores numerically and experimentally the process of a phase-change material (PCM) solidification in a spherical shell. At the initial state, the PCM liquid occupies 98.5% of the shell. The upper segment of 1.5% contains air, which flows in as the solidification progresses. In the experiments, a commercially available paraffin wax is used. Its properties are engaged in the numerical simulations. The investigation is performed for solidification in spherical shells of 20 mm, 40 mm, 60 mm, and 80 mm in diameter at the wall uniform temperature, which varied from $10°C$ to $40°C$ below the mean solidification temperature of the phase-change material. Transient numerical simulations are performed using the FLUENT 6.2 software and incorporate such phenomena as flow in the liquid phase, volumetric shrinkage due to solidification, and irregular boundary between the PCM and air. The numerical model is validated versus the experimental results. Shrinkage patterns and void formation are demonstrated. Dimensional analysis of the results is performed and presented as the PCM melt fractions versus the product of the Fourier and Stefan numbers. This analysis leads to a generalization that encompasses the cases considered herein.