Effects of buoyancy-driven convection on melting within spherical containers

A computational study of the effects of buoyancy-driven convection on constrained melting of phase change materials within spherical containers is presented. The computations are based on an iterative, finite-volume numerical procedure using primitive-dependent variables, whereby the time-dependent continuity, momentum and energy equations in the spherical coordinate system are solved. A single-domain enthalpy formulation is used for simulation of the phase change phenomenon. The effect of phase change on convection is accounted for using a Darcyʹs law-type porous media treatment. Early during the melting process, the conduction mode of heat transfer is dominant, giving rise to concentric temperature contours. As the buoyancy-driven convection is strengthened due to the growth of the melt zone, melting in the top region of the sphere is much faster than in the bottom region due to the enhancement of the conduction mode of heat transfer. When buoyancy effects are very marked, as many as three time-dependent recirculating vortices are observed. In comparison to the diffusion-controlled melting, buoyancy-driven convection accelerates the melting process markedly. The Prandtl number plays an important role in the melting process. With the Rayleigh number fixed, changing the Prandtl number from 0.03 to 1.0 and 50 brings about totally different flow and melting patterns. The computational findings are verified through qualitative constrained melting experiments using a high-Prandtl number wax as the phase change material.