Modeling of Phase Change Hysteresis During Partial Phase Change with the "Shift"-method

For phase change materials (PCM) a difference between melting and crystallization temperature can occur, the so-called supercooling. This hysteresis effect reduces the potential of a high storage density for latent heat storages as the narrow temperature range of the phase change is broadened. For the investigation of PCM for different applications by numerical modelling, like for battery temperature control or latent thermal energy storage, this hysteresis effect as well as partial phase change must be considered as due to operational condition a a partial melting and crystallization is likely to occur. Therefore, phenomenological methods based on the experimentally determined enthalpy-temperature relations for melting and crystallization can be applied. Doing so it is a challenge to model the behavior when the heating is changed to cooling and vice versa during phase transition. The study presents a new phenomenological method which is called "shift"-method. It is derived especially but not only for PCMs with a multistage phase change during crystallization, like it can occur for microencapsulated PCMs. For these materials first a supercooled major phase change followed by a second phase change with larger supercooling associated to rotator phases can be observed. The presented method is verified by experimental results and compared to an existing modelling approach called "curve-scale"-method. Therefore, partial melting and crystallization processes of a PCM composite are experimentally characterized with differential scanning calorimetry (DSC). Additionally, both methods are integrated in a Modelica / Dymola model of a passive battery cooling system with the PCM composite which is validated against experimental results. With both methods the temperature evolution with time can be described with a deviation of less than 2 %. According to the results the benefits and drawbacks of the methods are discussed.