The main equipment of the transcritical CO₂ heat pump system includes a compressor, gas cooler, internal heat exchanger, expansion device, and evaporator. To meet the frequency conversion requirements of the compressor, a high-performance open-loop vector converter from an inverter is used. The specific parameters of the apparatuses are shown inTable 1. The accuracy of the measurement devices is listed inTable 2. The experiment flow chart and the experimental facilities are shown in Figure 1 and Figure 2, respectively.

Figure 3 presents the theoretical pressure-enthalpy diagram of the transcritical CO₂ heat pump system. It can be seen from the figure that 1–2 is the compression process of CO₂ in the compressor, and CO₂ changes from the subcritical state to the supercritical state; 2–3 is the isobaric exothermic process of CO₂ in the gas cooler, and water is heated; 3–4 is the re-exothermic process in the high-pressure side of the internal heat exchanger with constant pressure; 4–5 is the isoenthalpic expansion process in the expansion valve; 5–6 is the isobaric endothermic process in the evaporator, and the air is cooled; 6–1 is the re-endothermic process in the low-pressure side of the internal heat exchanger with constant pressure.

The actual operating conditions can be controlled by the compressor frequency, the discharge pressure, and the ambient temperature. The compressor frequency is controlled by the frequency converter in the range of 20–40Hz. Through two parallel expansion devices, the discharge pressure adjustment is within 7000–11600kPa. The discharge pressure 7310kPa is the minimum pressure for the CO₂ supercritical condition, and the discharge pressure 11600kPa is the top limit for system safety. Since the evaporator is installed outdoor, the experiments are carried out in different periods to meet the requirement of ambient temperature. The experiment is performed in November and December when the ambient temperature is 15±1°C; the experiment is performed in September when the ambient temperature is 30±1°C. In addition, the inlet water is at a temperature of 15°C and a flow rate of 0.5 m³/h. According to the test, the range of the outlet water temperature is 45–90°C when the ambient temperature is 15°C; the range of the outlet water temperature is 55–100°C when the ambient temperature is 30°C. The specific operating conditions are shown inTable 3.

Theoretical system COP _th is defined as Eq. 1: C O P th = Q ˙ gc , th W ˙ com , th = m ˙ ⋅ Δ h gc m ˙ ⋅ Δ h com . (1)

It also could be calculated with: C O P = h 2 − h 3 h 2 − h 1 . (2)

The heating capacity of water Q ˙ gc = V w ⋅ ρ w ⋅ C p , w ⋅ Δ T w , (3) Δ T w = Q ˙ gc V w ⋅ ρ w ⋅ C p , w . (4)

The compressor work ( W ˙ com ) can be calculated by the volumetric efficiency ( η v ), the isentropic efficiency ( η i s ), and the mechanical efficiency ( η m ). η v = 0.999526 − 0.08724 ( P d i s / P s u c ) , (5) η i s = 1.014896 − 0.08538 ( P d i s / P s u c ) , (6) η m = 0.77854 + 0.0003 n − 0.075676 ( P d i s / P s u c ) . (7)

The physical parameters of CO₂ are calculated using REFPROP.

According to the method proposed by Kline and McClintock (Kline, 1953), the uncertainty of the experimental results is calculated in this study. The calculation process of summing the square of errors is as follows: δ R = [ ∑ i = 1 j ( ∂ R ∂ x i δ x i ) 2 ] 1 / 2 , (8) δ C O P = [ ( ∂ C O P ∂ Q ˙ gc , w δ Q ˙ gc , w ) 2 + ( ∂ C O P ∂ W ˙ com δ W ˙ com ) 2 ] 1 / 2 . (9)

Based on the accuracy of the measuring device and the experimental data, the maximum uncertainty of COP is 5.3487%.

It can be seen from Figure 4 that the changing trends of COP are almost the same under the same ambient temperature and different compressor frequencies. All changing trends first rise rapidly and then decrease after reaching the peak value. The downward trend of COP gradually flattens with increase in the compressor frequency. The peak values of the COP move in the direction of the increase in discharge pressure with the increase of the ambient temperature. It is worth noting that, the peak value of the COP at the ambient temperature of 15°C is larger than that at the ambient temperature of 30°C except for 20 and 35Hz. The specific data of maximum COP is listed in Table 4.

According to Eq. 2, the COP _th is the ratio of the enthalpy difference between the gas cooler and the compressor.

To analyze the reason for the change of the system COP, the enthalpy difference variation trend of the compressor and the gas cooler at the compressor frequency of 20Hz is proposed.

It can be seen from Figure 5 that although the increase of compressor enthalpy difference is flat, however, the increase of gas cooler enthalpy difference is obvious when the discharge pressure is less than 7920kPa for an ambient temperature of 15°C. And this inflection point is 8680kPa for an ambient temperature of 30°C. The ratio of the enthalpy difference between the gas cooler and the compressor is the system COP _th by Eq. 2, so the inflection points of the enthalpy difference ratio can reflect the variation trend of the system COP. Therefore, the reason for the variation trend of the gas cooler enthalpy difference can be analyzed to obtain the reason for the change of the system COP.

Figure 6 shows the inlet and outlet enthalpy of the gas cooler under different compressor discharge pressure. It can be seen from the figure that the inlet enthalpy of the gas cooler has a little change as the discharge pressure increases. Whereas, the outlet enthalpy of the gas cooler decreases significantly as the discharge pressure increases before it reaches the inflection point, which is 7920kPa for ambient temperature of 15°C and 8680kPa for ambient temperature of 30°C. So, the rapid decline of the gas cooler outlet enthalpy is the reason for the rapid increase in system COP.

Drawing the variation trend of the gas cooler outlet enthalpy in the P-h diagram. The conclusions can be extracted from Figure 7 that the gas cooler outlet temperature begins to drop as the discharge pressure increases. The gas cooler outlet temperature was maintained near 15 °C due to the influence of convective heat transfer and the inlet water temperature (15°C), so the variation trend of the gas cooler outlet temperature in the second half matches the variation trend of the 15°C-isothermal line. The inflection points of the ambient temperature of 15 and 30°C are 7920 and 8680kPa, respectively, so these discharge pressures are chosen as the demarcation point in the P-h diagram. Since the isotherm is above the critical point of CO₂ (7310kPa, 31.1°C) is almost horizontal and the CO₂ outlet temperature of the gas cooler drops slowly, it is almost the same as the isotherm variation trend. The change in the CO₂ outlet temperature and the isotherm of the gas cooler lead to a rapid drop in the enthalpy of the CO₂ gas cooler. As the discharge pressure increases, the temperature of the gas cooler outlet rapidly decreases, and the enthalpy value of the gas cooler outlet rapidly increased after the demarcation point. The change in the increased rate of the gas cooler outlet enthalpy is the main reason for the change in the system COP.

The heating capacity of water can be calculated by Eq. 3, and the water temperature difference of the gas cooler can be calculated by Eq. 4 Because the fluctuation of the V w , ρ w , and C p , w is very small during the experiments, the amount of heat absorbed by the water directly affects the water temperature difference of the gas cooler. The inlet water temperature of the gas cooler is maintained at 15°C, and so the greater the heating capacity, the higher the GCW will be.

As shown in Figures 8A,B, the GCW, and the heating capacity have a similar variation trend. It can be seen that the GCW and the heating capacity, at other compressor frequencies except 40Hz, all increase to a peak value and then decrease with increasing pressure discharge. The heating capacity increases about 34.8%, 41.3%, 38.1%, and 47.3%, respectively, while the GCW increases about 15.3%, 19.5%, 28.3%, and 34.8%, respectively, when the ambient temperature is 15°C. In addition, the heating capacity increases about 47.5%, 58.7%, 49.1%, and 50.2%, respectively, while the GCW increases 39.1%, 37.9%, 35.2%, and 50.5%, respectively, when the ambient temperature is 30°C. Therefore, it can be concluded that the GCW is mainly affected by the heating capacity.

It is worth noting that all parameters of 40Hz, except the heating capacity of 15°C, continue to rise within the experimental range, and there is no downward trend. The peak values of heating capacity and GCW with the discharge pressure at 15 and 30°C for all frequencies are shown in Figure 9. It can be seen from the figure that the corresponding discharge pressure increase with the compressor frequency, whether it is the heating capacity or the GCW. Hence, it can be inferred that the discharge pressure corresponding to the maximum heating capacity and GCW of 40Hz will be greater than that of 35Hz. However, the system will automatically stop when the discharge pressure rises to 11600kPa because this system has high-pressure protection. Therefore, the GCW (15 and 30°C) and the heating capacity (30°C) of 40Hz do not show the peak value within the experimental range.

The GCW at different ambient temperatures can be calculated by Eq. 14. The input dynamic parameters of different ambient temperature are shown inTable 6. The input fixed parameters are m ˙ w , T w , in , and L gc , their specific values are 0.14 kg s⁻¹, 15°C, and 18 m, respectively, which are the same as the input parameters at ambient temperatures 15 and 30°C. Taking the compressor frequency of 20Hz as an example, the variation trends of the GCW are shown in Figure 13.

It can be seen from Figure 13 that the maximum GCWs for all ambient temperatures occur at the discharge pressure of about 9800kPa. Although increasing ambient temperature can result in a slightly increased system COP, it does not mean that the GCW increases with ambient temperature. For example, the maximum GCW is 60.4°C in this figure and occurs at the ambient temperature of 21°C. The other main variation trend is that the decreasing rates of GCW decrease as the ambient temperature increases. After the discharge pressure increases to 10500kPa, the GCW at an ambient temperature of 27°C is higher than that of the other ambient temperatures in the same discharge pressure.

At an ambient temperature of 20°C, the GCWs of different compressor frequencies can be calculated by Eq. 14 to determine the effect of compressor frequency on GCW and the accuracy of the prediction model. The input variable parameters of the CO₂ inlet temperature and compressor pressure ratio at the ambient temperature of 20°C and different compressor frequencies are shown inTable 7. The input fixed parameters maintain unchanged. The calculation results of GCW are shown in Figure 14.

It can be seen from Figure 14 that the GCW variation trends of different discharge pressures at an ambient temperature of 20°C are almost the same as the experimental results at ambient temperatures of 15 and 30°C. These three sets of GCWs at different ambient temperatures rise first and then decrease with the increase of compressor frequency. In addition, the peak points of GCW shift in the direction of the high discharge pressure with an increase in the compressor frequency. Compared to Figure 15, the curve at an ambient temperature of 20°C is smoother than the curves at ambient temperatures of 10 and 30°C, because the curve at the ambient temperature of 20°C is generated by the calculated results. The maximum GCWs and the discharge pressures corresponding to three ambient temperatures at different compressor frequencies are shown in Figure 15.

The figure shows that at the same compressor frequency, the increase in the ambient temperature does not mean that the GCW is improved. When the compressor frequencies are 25Hz, 35Hz, and 40Hz, the GCWs at an ambient temperature of 20°C are all higher than that at the ambient temperature of 30°C. This result is the same as the result discussed above. But the variation trends of the discharge pressure at the maximum GCW display some regularity. Regardless of the compressor frequency, the discharge pressure at the maximum GCW increases as the ambient temperature increases. Based on the abovementioned conclusion, it can be determined that the ambient temperature is not the main factor affecting the GCW.

The system COP of the ambient temperature of 20°C at different compressor frequencies can be calculated by the correlations, which are presented by Qin et al. (Wang W. et al., 2021). The calculation process of the system COP and Q ˙ gc , w is shown in Eqs. 1, 3. The equations for compressor efficiency are shown in Eqs. 5, 7.

At first, the CO₂ mass flow rate can be calculated by the volumetric efficiency. And then, the rate of work done on the refrigerant can be calculated by the isentropic efficiency. In addition, the rate of work into the compressor can be calculated by mechanical efficiency. At last, the system COP corresponds to the same GCW at different compressor frequencies and the ambient temperature of 20°C can be obtained. The specific calculation results as shown in Figure 16.

The figure shows the system COP at the same GCW decreases as increase of compressor frequency. The system COP of 40Hz decreases most significantly, and the maximum decrease value reaches 0.85. As illustrated in Figure 13, the variation range of the GCW is extended by increasing the compressor frequency. For example, the variation range of 20Hz is from 44.87 to 60.57°C, but the variation range of 40Hz is extended to 111.46°C from 68.59°C. Based on the abovementioned discussion, it can be concluded that when all compressor frequencies can meet the requirements of GCW at the same ambient temperature and water inlet condition, a lower compressor frequency is a better choice for the system operation.