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Mathematics 2022, 10, 3167 16 of 27 5.1. Demand Profile ConsiderthecoolingdemandprofileQ ̇ref representedinFigure7.Theshapecould sec be similar to a typical supermarket load profile, but the specific power values have been tailored to the system under study described in Section 2. 950 850 750 650 550 450 350 Cooling demand profile 0 2 4 6 8 10 12 Time [h] Figure 7. Cooling demand profile. Please notice that the time window has been set to 12 h instead of considering a com- plete day due to the maximum charging/discharging periods for which the TES tank has been designed. As stated in [24], the latter has been devised to ensure full charge/discharge in 3 or 4 h periods at full charging/discharging power, that were regarded as most desirable due to the research aim of the refrigeration facility. Therefore, longer charging/discharging periods cannot be fulfilled by this TES tank, which would be necessary to address actual 24-hour time periods. However, notice that it is only a scaling factor, since, provided that the TES tank volume was high enough, 24-hour time periods could be addressed following the same control strategy. 5.2. Cooling Power Ranges Table 4 gathers the maximum and minimum values of the different cooling powers for the system under study [25], regarding operating modes 1 to 4, which have been justified in Section 3.2 to be the simplest and most likely to be scheduled. Notice that a minimum admissible value Tmin = 2 °C has been imposed on the degree of superheating SH when obtaining the cooling power limits in mode 1. As discussed in [25], most cooling power limits depend on γTES, since the cylindrical shell in sensible zone grows as the TES is charged/discharged. This growth involves higher thermal resistance, that modifies the achievable cooling powers as γTES evolves. Power ranges when the freezing/melting boundary is located approximately at the cylinder edge, halfway, and at the centre are detailed in Table 4. It must be remarked that, in the case of mode 2, the cooling demand is provided exclusively at the evaporator, and thus the TES tank is not involved and that is why the cooling power range does not depend on the freezing/melting boundary location. However, in mode 4, Q ̇ TES,sec depends on the charge ratio, which decreases as the TES is discharged. Operating mode 3 is merely a combination of the previously described modes, where two independent secondary fluid circuits are used, and thus the cooling power ranges are the same as those presented for modes 2 and 4. Nevertheless, when operating in mode 1, Q ̇ e,sec and Q ̇ TES are strongly correlated, because the refrigerant circulates through the evaporator and the TES tank, then both flows merge at the compressor intake (point A in Figure 1). Therefore, the ranges indicated in Table 4 are not completely rigorous, since they include some unachievable points. As an illustrative example, Figure 8 shows the steady-state map between Q ̇ e,sec and Q ̇ TES when the freezing boundary locates at the PCM cylinder centre, where the continuous lines represent the overall limits and the small crosses indicate a number of steady-state achievable points. Power [W]PDF Image | Refrigeration Systems with Thermal Energy Storage
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