**4. Results**

To assess the correctness of the new EnergyPlus ™ algorithm, the simulation results have been compared to the results of measurements conducted in the climate chambers shown in Figure 3. A wall, located between the warm and cold chamber, was made of 15 cm expanded polystyrene covered with the standard gypsum panel on the warm side. Two material samples were glued to the gypsum panel. One of them was a modified gypsum panel (50 × 60 cm) containing 30% by mass of PCM Micronal. The second one was a reference standard gypsum panel of the same size and thickness (12.5 mm) as the PCM panel. The principle of the presented research was based on a comparison of surface temperature fluctuations and energy accumulation in the PCM and the reference standard samples. In this way, the authors wanted to examine the e fficiency of the added PCM wall cladding as a form of overheating protection in a hot summer environment.

**Figure 3.** Full-scale climate chambers (cold chamber on the left and warm chamber on the right).

The melting temperature of the PCM panel, as declared by the manufacturer, was 23 °C.

Before the experiment, a sample of PCM was tested in the calorimeter DSC214 (Polyma–Netzsch), and measured latent heat was equal to 127.7 J/g. The PCM 23 e ffective phase change temperature range measured was very wide: 17.8 ◦C ÷ 31.5 °C. Both gypsum boards were initially tested for thermal conductivity using the Laser Comp Fox 314 plate apparatus. The tests were performed for di fferent temperature ranges referring to the melting temperature of PCM. In the first case, the average temperature below the phase change temperature range was adopted and the value of thermal conductivity λ was 0.159 W/mK. In the second case, only a part of the material was in the liquid state (the temperature of the heating plate was 40 ◦C and the cooling plate was 20 °C). In these conditions, the λ-value was equal to 0.162 W/mK. In the third case, the temperature of both plates exceeded the phase change value, so all the PCM material contained in the tested plate was in the liquid state during the test, and the λ-value was equal to 0.164 W/mK. The observed small di fferences in the thermal conductivity coe fficients (max. 2.8%) can be treated as negligible and were not included in further analysis.

Three temperature sensors were placed on the surface of both gypsum panels (K-type thermocouples, measurement class 2, sensors attached to the surface with adhesive paper tape). The heat flow on both surfaces of the sample plates was measured by means of Ahlborn 118SI silicone heat-flow transducers (sensor size 120 × 120 mm), measurement class A. Air temperature was measured by means of the Pt 100 and Pt 1000 sensors, measurement class B, protected with an aluminum foil against thermal radiation. All the measurements and data recording were performed by the Ahlborn Almemo 5690 data acquisition system and the Data-Control 4.2 program.

Temperature fluctuations in the warm chamber corresponded to the conditions that occur in a room during a hot summer day. However, the technical capabilities of the control system only allowed stepped (non-continuous) changes. Four testing cycles were conducted as reported in Table 1.


**Table 1.** Testing cycles of the boundary conditions.

The temperature in the warm chamber was gradually changing during the daily cycle within the range 18 ÷ 37 °C. The daily maximum temperature was maintained for 4 hours at the same level, which was long enough to enable the phase change in the whole volume of PCM. During the whole night, a constant temperature of 18 °C was maintained in the chamber; therefore, after each cycle, it was possible to discharge the total amount of energy stored in the tested materials during the day to the surrounding environment. The air temperature in the cold chamber was maintained at a constant 18 °C in two tests, and in the other two tests, it was variable in a similar way as was the case in the warm chamber. The last two cycles were close to the conditions that occur during hot summer days. A simulation model of the climate chambers with the sample wall between the chambers was created in the EnergyPlus™ software. As in the real conditions, the modeled wall consisted of a 15 cm layer of expanded polystyrene and gypsum board, to which a layer of phase-changing material was attached. It was assumed that the conditions of heat exchange between the outer shell of the chamber and the surrounding environment were adiabatic. A dynamically changing cycle of air temperature inside the warm chamber was assumed. This was consistent with the cycle of the experimental measurements. The same model was used as the reference variant of the standard gypsum board.

Measured and calculated temperature fluctuations during one selected day of cycle 0129 are presented in Figure 4. The red curve shows the daily internal air temperature cycle that was a driving force of the fluctuations and the boundary condition both in the experiment and the simulation.

The scheduled maximum temperature of 36 °C was maintained for more than three hours. The curves obtained from numerical calculations and the measurements were, in general, very close to each other, with the exception of the surface temperature of the reference gypsum plate. The relatively low thermal capacity of the standard material in which heat is stored only in a sensible way resulted in a significantly higher temperature of the gypsum surface when the internal air temperature was rising and much lower temperature during the cooling stage. The gypsum plate cooled quicker than the PCM. The results of the simulation by means of both algorithms (with and without the hysteresis effect) fit perfectly with each other and very closely followed the measurements during the heating stage. This means that the enthalpy characteristic introduced to the simplified algorithm without hysteresis followed the heating curve of the PCM.

**Figure 4.** Measured versus simulated temperature fluctuations of the phase change materials' (PCM) surface.

As could be expected, significant discrepancies may be observed during the cooling stage, when the solidification process starts. Within the wide range of phase change, but still, before the phase change temperature declared by the producer (23 °C) was reached, the model without hysteresis (orange curve) showed a surface temperature higher than the other models due to the single characteristic curve. The new model that takes into account the effect of hysteresis closely followed the measured values. Below the phase change temperature, this relationship was reversed.

Figure 5 shows the heat flux values on the internal surface of the PCM board obtained from measurements and computer simulations. One simulation was conducted on the model without taking into account phase change hysteresis and the second one with this effect. The cycle begins with the discharge phase of the wall's thermal capacity (negative flux value). Then, as a result of the internal temperature increase in the tested space, heat flux released from the wall decreased, and then the process of recharging (plus flux value) began. The significant differences between both simulation models may be noticed in the second phase of the research cycle, especially in cooling mode. The maximum instantaneous heat flux value was high and equal to 62 <sup>W</sup>/m2. During the whole measuring period, the PCM panel accumulated around 180 Wh/m2.

To assess the accumulation efficiency of the PCM board, Figure 6 shows the results of measurement and simulation of heat flux on the internal surface of the reference gypsum board. The heat exchange on the surface of the standard panel took place according to a similar scenario as before, but the instantaneous heat flux values were definitely lower. In the case of material without phase change, the graph obtained from the simulation was very close to the measurement results. The maximum momentary heat flux value was, in this case, equal to 32 <sup>W</sup>/m<sup>2</sup> and accumulated during the whole cycle amount of energy was only 36 Wh/m2.

**Figure 5.** Measured versus simulated heat flux density on the internal surface of the PCM panel.

**Figure 6.** Measured versus simulated heat flux density on the internal surface of the standard gypsum panel.

During the full phase transition cycle, the entire volume of PCM material could accumulate 5 times more energy than a standard material of the same volume. The application of PCM wall panels substantially enlarged the storage capacity of the wall and also enabled a decrease in cooling power demand. All these measures support the improvement in space thermal comfort.

#### **5. Discussion of the Simulation Precision**

Figure 7 presents the temperature difference between the results of measurements and calculations for the two variants of the simulation algorithm. The maximum momentary error of simulation occurred in the case of the algorithm without hysteresis and was equal to 0.96 K.

**Figure 7.** Absolute momentary errors of simulation.

The average results of relative error calculation for all the temperature testing cycles are shown in Figure 8. In the case of cycle 0130, the mean relative error of the variant without hysteresis was 5.38 times larger than that of the variant with hysteresis. The lowest disproportion may be observed in the case of cycle 0203, the mean relative error was 1.71 times larger than in the case of the variant with hysteresis. The average ratio between the errors of both compared algorithms in the four tested cycles of measurements was 3.35. It should be noted that the errors related to the algorithm with hysteresis were close to the errors of the simulation of the standard materials (reference plate), i.e., precision of the applied simulation software.

**Figure 8.** Mean error of surface temperature estimation in four cycles of measurements.

Figure 9 shows mean absolute errors of simulation of the heat flux density at the internal surface of tested samples. The inclusion of the hysteresis effect in the simulation algorithm reduced simulation error in three cycles of simulation only to a small extent. Better accuracy of heat flux evaluation could be expected only in the case of standard building material, in which only sensible heat accumulation takes place. Relatively high fluctuations can be caused on the one hand by the large variation in the

value of heat fluxes and on the other hand, by much lower, than in case of temperature, precision of the heat flux measurement (5%). However, the absolute error values allowed a rough estimation of the room's cooling load and may be used as a simple designing tool.

**Figure 9.** Mean error of surface temperature estimation in four cycles of measurements.
