Towards a better analytical modelling of the thermodynamic behaviour of phase change materials

Abstract Modelling of latent heat thermal storage systems is mainly achieved with an analytical formulation describing the thermodynamic state of the phase change material (PCM). In literature, different models exist to describe the evolution of the liquid fraction, the effective heat capacity and the enthalpy as a function of temperature. The main issue is to correctly establish these behaviour laws and to identify the thermophysical properties of each PCM. Analytical models proposed in literature often have obvious limitations, such as the presence of discontinuities or the impossibility to represent asymmetric phase change dynamics. Such approaches a priori do not allow to model accurately the thermodynamic behaviour of the PCM. Given the limitations identified on existing models, a new analytical model is proposed in this paper. Moreover, it is not uncommon to observe the presence of two heat flux peaks during the phase change process of a PCM, as with the studied PCM (RT58). Therefore, we propose a method to model the two heat flux peaks, which are rarely considered in literature. PCM properties are determined thanks to a four-step identification process, using experimental data and the different analytical models studied. Based on the numerical modelling of the rectangular container used for the experiments, and on the identified thermodynamic properties of the enclosed PCM, a comparative study between the new analytical model and existing models is carried out. It appears that modelling only a single heat flux peak is not satisfactory for the studied PCM, and taking into account a second heat flux peak decreases the error on the exchanged energy by a factor of 2.5 to 6.5 depending on models. The new model leads to an accuracy gain of a factor of 1.5 to 3.3 compared with existing models. We do not recommend the model based on a linear evolution of the liquid fraction as the resulting error is between 1.6 and 3.3 times greater than for the other models. The study carried out is based on both melting and solidification processes, and concerns a PCM which does not undergo supercooling.