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Table 2. Consistency verifications of model values and experimental results.

Table 2 Consistency verifications of model values and experimental results.

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Figure 1. Refrigeration cycle represented on the entropy-temperature plan (s-T): 1-2 compressor; 2-3 condenser; 3-4 expansion valve; 4—1 evaporator. eee eee ee ee ee nee ee NN a NN mee I I NE NE ID NE NE EN The difficulties that are encountered while practically performing the reversed Carnot cycle can be overcome by performing the ideal reverse steam compression cycle [34]. In this case, as shown on the plan entropy-temperature (ST) in Figure 1, the heat absorption continues until reaching the condition of dry saturated steam (point 2), so that subsequent isentropic compression occurs in the superheated steams zone (segment 1-2).
Figure 1. Refrigeration cycle represented on the entropy-temperature plan (s-T): 1-2 compressor; 2-3 condenser; 3-4 expansion valve; 4—1 evaporator. eee eee ee ee ee nee ee NN a NN mee I I NE NE ID NE NE EN The difficulties that are encountered while practically performing the reversed Carnot cycle can be overcome by performing the ideal reverse steam compression cycle [34]. In this case, as shown on the plan entropy-temperature (ST) in Figure 1, the heat absorption continues until reaching the condition of dry saturated steam (point 2), so that subsequent isentropic compression occurs in the superheated steams zone (segment 1-2).
Figure 2. Refrigeration cycle represented on the enthalpy-pressure plan (p-H).
Figure 2. Refrigeration cycle represented on the enthalpy-pressure plan (p-H).
Table 1. Heat pump performance. The described calculation model has been validated by comparing the calculated data with those 2.3. Test Case
Table 1. Heat pump performance. The described calculation model has been validated by comparing the calculated data with those 2.3. Test Case
Figure 3. Plan of an outdoor test cell: HP (Heat Pump); D (Datalogger); T (Temperature sensors): T1 and T2 at 1.8 m in height, T4 and T5 at 0.5 m; G (Globe-thermometer); RH (Relative Humidity).
Figure 3. Plan of an outdoor test cell: HP (Heat Pump); D (Datalogger); T (Temperature sensors): T1 and T2 at 1.8 m in height, T4 and T5 at 0.5 m; G (Globe-thermometer); RH (Relative Humidity).
The thermal model of the envelope focuses on the idea of using the lumped solution’s uttermost important features to build a 3R1C module (Figure 5) suitable for the representation of heat gains, losses and dynamic response of a single element of the building envelope. A whole system RC scheme is then assembled, connecting these modules according to the structure of the building envelope, through the internal air temperature node.
The thermal model of the envelope focuses on the idea of using the lumped solution’s uttermost important features to build a 3R1C module (Figure 5) suitable for the representation of heat gains, losses and dynamic response of a single element of the building envelope. A whole system RC scheme is then assembled, connecting these modules according to the structure of the building envelope, through the internal air temperature node.
Figure 5. A 3 Resistance 1 Capacitance (3R1C) module.
Figure 5. A 3 Resistance 1 Capacitance (3R1C) module.
The EER values in the different running hours of the system are not constant but vary between 2.59 and 4.63. These results are in compliance with those ex pected, but 7% of the calculated values are lower than 3.2, which differ from what expected. The causes of this inconsistency may be found in the analysis of the refrigerant temperatures in the condenser and in the evaporator: the temperature of the cool reservoir, i.e., in the evaporator, is much higher than between these values and the cooling power; indeed, the E lower than 350 W. The model shows an insufficiency in the expected value. There is a correlation ER outliers correspond to a cooling power the modeling of the refrigerant flow rate modulation made by the inverter that causes an incorrect calculation of the refrigerant temperature in the evaporator. The first evaluation concerns the calculation of the EER. The calculation procedure is based on the second law efficiency, adapted to an hourly assessment. The method provides hourly values of EER, one for each time at which the heat pump is running. The results are shown in Figure 6.
The EER values in the different running hours of the system are not constant but vary between 2.59 and 4.63. These results are in compliance with those ex pected, but 7% of the calculated values are lower than 3.2, which differ from what expected. The causes of this inconsistency may be found in the analysis of the refrigerant temperatures in the condenser and in the evaporator: the temperature of the cool reservoir, i.e., in the evaporator, is much higher than between these values and the cooling power; indeed, the E lower than 350 W. The model shows an insufficiency in the expected value. There is a correlation ER outliers correspond to a cooling power the modeling of the refrigerant flow rate modulation made by the inverter that causes an incorrect calculation of the refrigerant temperature in the evaporator. The first evaluation concerns the calculation of the EER. The calculation procedure is based on the second law efficiency, adapted to an hourly assessment. The method provides hourly values of EER, one for each time at which the heat pump is running. The results are shown in Figure 6.
The difference between the simplified model and EnergyPlus is equal to 9 kWh and lower than 9%. The EnergyPlus model is a black box that does allows to input physical numbers. In fact, the calculation of consumption is obtained through the determination of biquadratic and quadratic performance curves that parameterizes the variation of the energy input to cooling output ratio (EER), i.e., aS a function of the indoor wet-bulb temperature. The graph shows, however, that EnergyPlus overestimates the real consumption (11.9%).
The difference between the simplified model and EnergyPlus is equal to 9 kWh and lower than 9%. The EnergyPlus model is a black box that does allows to input physical numbers. In fact, the calculation of consumption is obtained through the determination of biquadratic and quadratic performance curves that parameterizes the variation of the energy input to cooling output ratio (EER), i.e., aS a function of the indoor wet-bulb temperature. The graph shows, however, that EnergyPlus overestimates the real consumption (11.9%).
Figure 8. Indoor temperature comparison. Figure 8 shows the trend of the indoor temperature related to the calculated values with the simplified model (blue line), with the EnergyPlus v.8.4 model (orange line) and measured (red line). The green line represents the detected external temperature over the considered period. All the environmental parameters have hourly step representations. The trends of the calculated and measured data are almost equal except for the first hours of 13 August due the initialization of the simulation.
Figure 8. Indoor temperature comparison. Figure 8 shows the trend of the indoor temperature related to the calculated values with the simplified model (blue line), with the EnergyPlus v.8.4 model (orange line) and measured (red line). The green line represents the detected external temperature over the considered period. All the environmental parameters have hourly step representations. The trends of the calculated and measured data are almost equal except for the first hours of 13 August due the initialization of the simulation.
Figure 9. Comparison of the measured and calculated average daily powers through the energy signature method. 3.2. Validation
Figure 9. Comparison of the measured and calculated average daily powers through the energy signature method. 3.2. Validation
ALLO ila sien ibaa alulirc. After careful analysis of the data, 93.4% of the points is placed within the confidence interval 95% (Figure 10). In order to define the nature of the points that fall outside the range considered, it has been expanded in the above range, as previously described. In this way, it is found that more than 98.1% of the points arise within a confidence interval of 99%, with a 4.7% difference that represents the number of spurious or scattered points. It is possible to draw the same consideration in energy consumption (Figure 11). Starting from a confidence interval at 95%, 92% of the points fall inside. By extending the confidence interval at 99%, it is found that 98.7% fall within it.
ALLO ila sien ibaa alulirc. After careful analysis of the data, 93.4% of the points is placed within the confidence interval 95% (Figure 10). In order to define the nature of the points that fall outside the range considered, it has been expanded in the above range, as previously described. In this way, it is found that more than 98.1% of the points arise within a confidence interval of 99%, with a 4.7% difference that represents the number of spurious or scattered points. It is possible to draw the same consideration in energy consumption (Figure 11). Starting from a confidence interval at 95%, 92% of the points fall inside. By extending the confidence interval at 99%, it is found that 98.7% fall within it.
Figure 11. Bland-Altman plot: energy consumption. 4. Conclusions
Figure 11. Bland-Altman plot: energy consumption. 4. Conclusions
Nomenclature
Nomenclature
Related topics:
EngineeringHeat pumpCarnot cycle
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