*2.1. PCM Hysteresis*

The hysteresis may be explained as the dependence of the state of a system on its history or the lagging of an effect behind the cause of this state. This effect applies to the phase-change phenomenon. Many researchers have already dealt with the hysteresis effect during simulation modeling, revealing the effects of this phenomenon on simulation results with real conditions [9]. Biswas et al. [23] conducted PCM measurements using heat-flow meter apparatus for freezing and melting cycles and used them to model different simulation scenarios both with and without hysteresis. The results showed that including the hysteresis effect significantly impacts the calculated thermal performance of the PCM layer. Barz and Sommer [24] also confirmed that the phase transition of PCM is significantly affected by hysteresis phenomena. According to their results, the static hysteresis model and the macro kinetic models showed qualitatively consistent results.

Delcroix et al. [25], Mehling et al. [26], Berardi and Gallardo [27] proved that PCM thermal features are sensitive to the testing method and stated that DSC (di fferential scanning calorimetry) test results are not directly applicable to building simulations as the process of charging and discharging in PCM mixed in other porous materials is hardly represented by testing samples of a few grams. In particular, Delcroix et al. [25] and Mehling et al. [26] analyzed hysteresis as a function of the cooling and heating rates and noticed that the hysteresis tested in DSC is low (around 1 ◦C) at low cooling and heating rates, while it can reach up to around 7–8 ◦C at higher rates that can be found in real conditions. The authors did not comment in this context on the whole volume complexity of phase change. Mehling et al. [26] also advised adjustments to measure methods and conditions to PCM application to include the subcooling e ffect in enthalpy curves.

Mandilaras et al. presented a new hybrid methodology for the precise determination of the effective heat capacity and enthalpy curves of PCMs [28]. They combined DSC testing with dynamic operated heat flow apparatus followed by the numerical optimization of the obtained experimental enthalpy curves. Fateha et al. included the hysteresis e ffect in their numerical and experimental investigation of an insulation layer with PCM [29]. However, no switching between the melting and freezing curves was explored during the cycle. When using the hysteresis model for enthalpy, they were able to identify a strong agreemen<sup>t</sup> between measurements and simulations.

Kumarasamy et al. elaborated on the numerical schemes for the testing and simulation of encapsulated PCM with temperature hysteresis [30]. Their results showed that encapsulation greatly altered the thermal response of PCM in terms of the phase change temperatures and hysteresis. The authors suggested that in such a case, a Computer Fluid Dynamics-based conduction-dominant scheme should be incorporated into the simulation. Moreles et al. investigated the application of PCM, considering the hysteresis of phase change and only complete phase transitions [31]; based on a developed numerical model, a graphical method of optimized PCM selection was, hence, proposed.

All the previously discussed papers were based on former versions of the EnergyPlus ™ program in which the PCM parameters did not take into account the hysteresis e ffect. In the simplified enthalpy–temperature function, only one curve representing both the melting and solidifying process was given. However, the latest releases of EnergyPlus ™ 9.2 (released on September 27, 2019) take into account two separate freezing and melting curves with user-specified temperature data [20]. In this algorithm, an actual value of the specific heat that is used in the simulation process is not only dependent on the current state of the PCM but also on the former state as in symbolic Equation:

$$c\_p = f(T\_{i; \text{new}}; T\_{i; \text{prev}}; \text{PhaseState}\_{\text{new}}; \text{PhaseState}\_{\text{prev}}) \tag{1}$$

where *cp* is the specific heat, and *Ti* is the previous and new *i*-node temperature. The values of PCM thermal conductivity and density should be entered for the liquid and solid states. It should be noted that the current description of the new algorithm related to hysteresis is unclear in the program documentation, as it is not entirely clear what 'temperature di fference' refers to in this context and which PCM data should be introduced [20].

One of the first papers on the new hysteresis algorithm embedded in EnergyPlus ™ was written by Goia et al. [32]. Unfortunately, the hysteresis algorithm was only briefly highlighted in this paper, and the authors' input data was not presented. The simulation results were compared against experimental data obtained from the small-scale dynamic tests performed with the heat-flow apparatus. It was expected that a new algorithm that enables modelling of hysteresis would closely follow the real mode of phase change and thus the precision of the PCM simulations. Goia et al. confirmed these expectations stating that the numerical results were significantly better than those obtained with more conventional models. However, in the case of an incomplete phase change of PCM, the obtained results were regarded as 'questionable'.
