Effect of Marangoni Convection on Solidification of Phase Change Materials Infiltrated in Porous Media in Presence of Voids

Abstract

Void formation is encountered in the form of air pockets during preparation of composite thermal energy storage systems, consisting of phase change materials (PCM) infiltrated into a high-conductivity porous structure. The presence of voids within the pores of a porous structure degrades the thermal and phase change behavior of such composites. Recent work devoted to multiphase modeling of the infiltration of PCM in liquid state into porous media and formation of voids showed that among the various contributing driving forces (i.e. gravity, pressure gradient and interfacial forces), the interfacial forces (resulting from surface tension and contact angle) play a significant role at the pore level. Additionally, modeling the solidification and melting of PCM within the pores in presence of a void revealed that there is a temperature gradient along the interface between the PCM and void. Considering the surface tension as the major driving force at the pore level, this temperature gradient is large enough to give rise to a gradient in surface tension that then triggers the Marangoni convection at the interface. Thus, as a convection mechanism, it affects the phase change process as well as the interface shape. Therefore, in this paper, the effects of the Marangoni convection on PCM solidification time and shape of the interface was investigated at the pore level. A numerical approach was employed for solidification of a PCM based on the combination of the Volume-of-fluid (VOF) and enthalpy-porosity methods, including the variation of the surface tension with temperature, i.e. Marangoni effects. A two-dimensional model of a pore was developed based on the average geometric features of the pores in a porous structure with interconnecting pores. Following the grid independence study, the transient simulation of solidification was performed, whereas the PCM within the pore and the air within the void were treated as incompressible liquid and compressible gas, respectively. The liquid density change during the solidification was included to explicate the formation of shrinkage void and its distribution within the pores. The PCM solidification time and shape of the final interface between the PCM and air pocket (representing the amount and distribution of the shrinkage void evolving during the solidification) were extracted and compared between the cases with and without Marangoni convection. For verification purposes, the volume of the predicted infiltration void is in agreement with experimental measurements and the volume of the shrinkage void shows a good agreement with theoretical volume change. The final shape of the interface was justified and turned out to be in agreement with the prevailing Marangoni convection pattern.