No abstract

No 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.

Front tracking and enthalpy methods used to study phase change processes are based on a local thermal energy balance at the liquid–solid interface where mass accommodation methods are also used to account for the density change during the phase transition. Recently, it has been shown that a local thermal balance at the interface does not reproduce the thermodynamic equilibrium in adiabatic systems. Total thermal balance through the entire liquid–solid system can predict the correct thermodynamic equilibrium values of melted (solidified) mass, system size, and interface position. In this work, total thermal balance is applied to systems with isothermal–adiabatic boundary conditions to estimate the sensible and latent heat stored (released) by KNO3 and KNO3/NaNO3 salts which are used as high-temperature phase change materials. Relative percent differences between the solutions obtained with a local thermal balance at the interface and a total thermal balance for the thermal energy absorbed or released by high-temperature phase change materials are obtained. According to the total thermal balance proposed, a correction to the liquid–solid interface dynamics is introduced, which accounts for an extra amount of energy absorbed or released during the phase transition. It is shown that melting or solidification rates are modified by using a total thermal balance through the entire system. Finally, the numerical and semi-analytical methods illustrate that volume changes and the fraction of melted (solidified) solid (liquid) estimated through a local thermal balance at the interface are not invariant in adiabatic systems. The invariance of numerical and semi-analytical solutions in adiabatic systems is significantly improved through the proposed model.

The Stefan problem regarding the formation of several liquid–solid interfaces produced by the oscillations of the ambient temperature around the melting point of a phase change material has been addressed by several authors. Numerical and semi-analytical methods have been used to find the thermal response of a phase change material under these type of boundary conditions. However, volume changes produced by the moving fronts and their effects on the thermal performance of phase change materials have not been addressed. In this work, volume changes are incorporated through an additional equation of motion for the thickness of the system. The thickness of the phase change material becomes a dynamic variable of motion by imposing total mass conservation. The modified equation of motion for each interface is obtained by coupling mass conservation with a local energy–mass balance at each front. The dynamics of liquid–solid interface configurations is analyzed in the transient and steady periodic regimes. Finite element and heat balance integral methods are used to verify the consistency of the solutions to the proposed model. The heat balance integral method is modified and adapted to find approximate solutions when two fronts collide, and the temperature profiles are not smooth. Volumetric corrections to the sensible and latent heat released (absorbed) are introduced during front formation, annihilation, and in the presence of two fronts. Finally, the thermal energy released by the interior surface is estimated through the proposed model and compared with the solutions obtained through models proposed by other authors.