## 5 Optimization through Parametric Analysis under Variable Input Conditions  
After the model validation, design optimization was carried out through parametric analysis. The main application foreseen for the storage unit is use in residential heat pump systems, and, therefore, only short-term storage periods are foreseen. Accordingly, the main goal of the optimization was the improvement of the heat transfer, rather than the overall amount of energy stored. In order to guarantee that the simulation runs performed for optimization purposes were carried out under realistic operating conditions, the input to the simulations were the measured experimental values (flow rate and temperature of HTF, pressure and temperature in the refrigerant circuit). Therefore, an investigation time range of 4000 s was considered, corresponding to the time range of data availability from the experimental setup. Both charge and discharge processes were investigated. Given the peculiarity of the system, i.e., the charging of the storage directly through the heat exchange between the refrigerant of the compression cycle and the PCM, the main parameter affecting the charge of the storage was the number of stacked PCM layers in between the refrigerant channels. Indeed, as already discussed in [25] for a similar design, since the heat transfer is achieved only through thermal conduction, the main limitation to heat transfer is the thermal conductivity of the PCM. Accordingly, three cases were considered: one, two, and four consecutive PCM layers. For each case, the overall amount of PCM was not changed, only the number of parallel channels was changed. The overall amount of energy that the system can store was then constant for the investigated conditions. In Figure 5, the results of the parametric analysis are shown; in terms of temperatures in the refrigerant and PCM. The fluctuations in the average temperature of the refrigerant were due to the specific behavior of the heat pump tested in the lab and, more specifically, to the operation of the thermostatic valve. There is a clear difference in the temperature trend for the different cases examined; since the heat transfer for one layer of PCM is better, in the same time-span, all the material in the storage not only completes the phase change, but also sensible heat in the solid phase can be exploited, and the average temperature reached was \(-10\)\({}^{\circ}\)C. For the configuration with two PCM layers, the phase change was completed after 3500 s, and a final temperature of \(-2.5\)\({}^{\circ}\)C was reached. Instead, in the case of four PCM layers, after 4000 s, not all the material in the storage had completed the phase change, due to the penalization of the heat transfer induced by the low thermal conductivity of the material. The average thermal power exchanged between the refrigerant and the PCM is reported in Figure 6. For the temperature, during the first part of the charging, the fluctuations in the power are due to the fluctuations in pressure and temperature of the refrigerant, as a consequence of the opening/closing of the thermostatic expansion valve of the heat pump. It is possible to notice that the average power delivered to the user is higher for the case of one layer of PCM and decreases almost linearly with the increase in the number of PCM layers. It is, however, worth noting that the configuration of one PCM layer, despite being more efficient from the point of view of heat transfer, is also the least advantageous from the point of view of system volume and metal usage. Indeed, in order to keep the same amount of PCM, the amount of metal needed for the one-layer case is much higher than the four-layer, which already amounts to 60% of the overall empty weight of the heat exchanger. In particular, the weight for each additional channel is about 1.2 kg.