Effects of Pressure-Induced Density Changes in the Thermal Energy Absorbed by a Micro-Encapsulated Phase-Change Material

Abstract

Density changes produced by pressure increments during melting of a spherically confined phase-change material have an impact on the thermal energy absorbed by the heat storage unit. Several authors have assumed incompressible phases to estimate the volume change of the phase-change material and the thermal balance at the liquid–solid interface. This assumption simplifies the problem but neglects the contribution of density changes to the thermal energy absorbed. In this work, a thermal balance at the interface that depends on the rate of change of the densities and on the shape of the container is found by imposing total mass conservation. The rigidity of the container is tuned through the coupling constant of an array of springs surrounding the phase-change material. This way, the behavior of the system can be probed from the isobaric to the isochoric regimes. The sensible and latent heat absorbed during the melting process are obtained by solving the proposed model through numerical and semi-analytical methods. Comparing the predictions obtained through our model, it is found that even for moderate pressures, the absorbed thermal energy predicted by other authors can be significantly overestimated.

Effects of Total Thermal Balance on the Thermal Energy Absorbed or Released by a High-Temperature Phase Change Material

“…The sensible heat absorbed by a PCM can be conceived in four stages, as discussed in Refs. [ 14 , 25 ]. These stages can be used to show that latent heat is absorbed through the bulk latent heat of the PCM and not the apparent latent heat previously defined [ 29 ].…”

“…The method is described in Refs. [ 13 , 14 ], and a brief description of the semi-analytical method will be given in this part of the section. The liquid and solid domains are divided into m and n regions, respectively.…”

“…The latent heat and melting temperature of salts used as HTPCMs have been determined through molecular dynamics and ab initio simulations [ 10 ]. Mass accommodation methods have been developed to include the effects of density variations produced by pressure increments during melting of encapsulated PCMs [ 4 , 11 , 12 , 13 , 14 ]. The pressure increments on spherically microencapsulated HTPCMs have been predicted through models that assume incompressible solid phases [ 4 ].…”

“…The pressure increments on spherically microencapsulated HTPCMs have been predicted through models that assume incompressible solid phases [ 4 ]. The latent heat energy density is diminished by pressure increments, and different models have been proposed to estimate the latent heat during melting of encapsulated PCMs [ 4 , 5 , 14 ]. The research has been focused on improving the desired thermodynamic properties of PCMs to enhance the heat energy transfer rates between the PCM and the HTF, and increase the thermal energy density of PCMs.…”

“…On the other hand, high-order approximations to the spatial derivative involved in this type of boundary conditions are needed when using FDMs, in order to reach the expected state of the system at thermodynamic equilibrium [ 23 ]. Semi-analytical approaches have also been used to find solutions for the liquid–solid interface dynamics through the heat balance integral method (HBIM) [ 23 , 24 ] and the refined heat balance integral method (RHBIM) [ 13 , 14 , 25 ]. Finally, the accuracy of the proposed solutions to the moving boundary problem when the system is subjected to different types of boundary conditions has been tested with the available similarity solutions, other numerical solutions, or experimental results [ 26 , 27 , 28 ].…”