A modified heat capacity method for unconstrained melting inside the spherical capsule for thermal energy storage

The spherical capsule is one of the most common geometrical configurations for latent heat thermal energy storage. This study develops a modified heat capacity method coupling with the volume of fluid model to calculate the unconstrained melting inside the spherical capsule. Based on the force balance of the sinking solid body PCM, the solid velocity is implicitly introduced and incorporated in the extended Darcy term. The forces exerted on the solid PCM are calculated through the volume integral. Then, the proposed model is used to simulate the reported unconstrained melting experiments inside a spherical capsule filled with n-octadecane. The influence of the mushy zone constant on the melting processes is discussed, and the natural convection, solid moving, heat transfer, and melting behaviors are analyzed. It is found that the melting rate decreases with the increase of the mushy zone constant. The present model with a suitable mushy zone constant can reasonably predict the unconstrained melting. Besides, the appropriate mushy zone constant tends to increase with a higher Ste number. The total charging heat transfer rate linearly decreases during the melting process after the melt layer shapes. The heat transfer rate of the contact melting below the solid PCM is about 60 %-80 % of the total heat transfer rate and is much higher than that of the natural convection above the solid PCM. The thickness of the melt layer between the bottom solid PCM and the capsule shell increases after the lifting phenomenon, and it is less than 1 % of the capsule diameter.