Three transcritical cycles are studied based on an air-source heat pump water heater (ASHPWH) system with optimal control strategy in the paper. Schematics and corresponding pressure-enthalpy diagrams of the systems with the three cycles analyzed in this study are shown in Figures 1–3.

The isentropic and actual compression processes are respectively illustrated by the dashed line ′′1–2s′′ (and ′′3–4s′′ in Figure 3) and the solid line ′′1–2′′ (and ′′3–4″ in Figure 3) in the pressure-enthalpy diagrams. Similarly, the lines ′′4–5s′′ and ′′4–5″ express isentropic and actual expansion processes respectively in Figure 3. On the basis of the first and second laws of thermodynamics, a model is proposed to evaluate and compare the performance of the three cycles carefully. The studied ASHPWH systems are assumed to operate based on optimal control strategy during simulation.

The thermodynamic model is conducted based on the following assumptions:

(1) The three studied cycles are all operated under steady conditions.

The parameters of external conditions have a significant effect on the system performance. The external environment temperature and hot water inlet/outlet temperature of the studied ASHPWH systems in this paper are specified based on the Chinese standards GB/T 21362-2008 (GB/T 21362-2008, 2008) and GB/T 23137-2008 (GB/T 23137-2008, 2008), which are shown in Table 1.

In order to overcome the shortcomings discussed in the literature and improve the application possibility of CO₂/R41 azeotropy mixture in the refrigeration industry, the optimum mass ratio of composition is defined and determined in this study.

According to the Standard of the U. S. Department of Transportation DOT 173 .115 (Wang et al., 2002), working fluid with the LFLv higher than 13% or the difference between UFLv and LFLv less than 12% can be identified as non-flammable fluid (i.e., A1 security level). Table 2 shows the UFLv and LFLv of the CO₂/R41 mixture with various volume fractions of composition. It is obvious that the increase of volume fraction of R41 can decrease the UFLv and LFLv and their difference. Under the condition of A1 security level, the maximum volume fraction of R41 is 48% in a CO₂/R41 mixture. As can be observed from the existing literature, the thermodynamic performance of a refrigeration/heat pump system with CO₂/R41 refrigerant can be improved continuously by increasing the fraction of R41. Therefore, when the safety and thermodynamic property are considered comprehensively, the optimum volume ratio of CO₂/R41 azeotropy refrigerant is identified to be 0.52/0.48, which can be converted into the optimum mass ratio, i.e., the optimum mass ratio is 0.583/0.417.

The main thermo-physical properties of the CO₂/R41 mixture with the optimum ratio can be obtained, as shown in Table 3. Therefore, the CO₂/R41 mixture (0.583/0.417, mass ratio) is eco-friendly and particularly strong for a transcritical cycle because of its low critical temperature (i.e., 37.67°C).

It is well known that the COP of a refrigeration/heat pump system can be directly affected by the high pressure. So, the optimum high pressure (p _opt ) should be accurately determined to ensure the accuracy of the simulation results from the proposed thermodynamic model. For a single-stage transcritical cycle with a throttling valve when pure CO₂ refrigerant is used, there are several correlations that can be employed to obtain the optimum high pressure with enough accuracy. However, relevant correlations are scarce for calculating the optimum high pressure in a CO₂/R41 cycle, CO₂ two-stage cycle, and CO₂ expander cycle. In our present work, one iterative method is proposed to calculate the optimum high pressure of the above cycles. Equation 13 provided in (Hu et al., 2018) is a classic correlation to obtain the optimum high pressure of a single-stage transcritical CO₂ cycle and is therefore used to verify the accuracy of the proposed iterative method. p o p t = 4.9 + 2.256 T g c , o − 0.17 T k + 0.002 T g c , o 2 × 10 − 1 (13) where p _opt is the optimum high pressure, in Mpa; T _k is the evaporation temperature, in °C; and T _gc,o is the outlet temperature of the gas cooler, in °C.

Table 4 shows the values of the optimum high pressure that are obtained by Eq. 13 and the proposed iterative method. It is noted that the calculation results of the optimum high pressure using Eq. 13 and the iterative method are respectively marked as p _opt,equ and p _opt,ite . It can be seen that the maximum error between Eq. 13 and the iterative method is less than 1.2%, which indicates that the proposed iterative method in this study has enough accuracy, i.e., the established thermodynamic model is reasonable.

In this study, the optimum ratio of the CO₂/R41 mixture is calculated and then the performance of three different cycles (i.e., CO₂/R41 cycle, CO₂ two-stage cycle, and CO₂ expander cycle) are evaluated and compared under the same conditions, i.e., −10°C ≤ T _k ≤ 0°C, 35°C ≤ T _gc,o ≤ 45°C.

Figure 5 shows the optimum high pressure (p _opt ) of the three studied cycles with various parameters of the evaporation temperature (T _k ) and the outlet temperature of the gas cooler (T _gc,o ). It is observed that the optimum high pressure of the CO₂/R41 cycle is more than 26.9% lower than that of CO₂ expander cycle under the same condition. In addition, the optimum high pressure of CO₂/R41 cycle is more than 32.6% lower than that of CO₂ two-stage cycles under the same condition. The decrease in operating pressure can help to improve the tightness and safety of a refrigeration system. Meanwhile, the tube thickness of the heat exchanger and connecting tubes can be appropriately reduced so as to lower the manufacturing cost of the device.

Figure 6 exhibits the effect of the evaporation temperature (T _k ) and the outlet temperature of the gas cooler (T _gc,o ) on the specific refrigerating capacity of the three studied cycles. It is observed that the CO₂/R41 cycle has a higher specific refrigerating capacity than the other two cycles. Take the specific condition (T _k = 0°C and T _gc,o = 35°C) as an example: the difference of specific refrigerating capacity between CO₂/R41 cycle and CO₂ expander cycle can reach 23.73%, while it can reach 22.66% for the specific refrigerating capacity between CO₂/R41 cycle and CO₂ two-stage cycle.

Figure 7 depicts the maximum COP of the three studied cycles with various evaporation temperatures (T _k ) and the outlet temperature of the gas cooler (T _gc,o ). The expander can recover a portion of the expansion work for driving the compressor, which leads to a significantly higher COP of a CO₂ expander cycle. Moreover, the CO₂/R41 cycle is observed to have a higher COP compared with the CO₂ two-stage cycle when the outlet temperature of the gas cooler is less than 39°C. For instance, when T _k = 0°C and T _gc,o = 35°C, the maximum COP of the CO₂/R41 cycle is about 4.6% higher than that of CO₂ two-stage cycle.

Excess discharge temperature is a serious problem in CO₂ compressors, because the superheated refrigerant vapor may reduce the viscosity of lubricating oil, which affects the reliability and safety of the compressor. It is universally acknowledged that the most significant advantage of a two-stage cycle is its ability to reduce the discharge temperature of a compressor, as shown in Figure 8. It can be found that the difference in discharge temperature between the CO₂/R41 cycle and CO₂ expander cycle is negligible and is reduced with the decrease of T _gc,o . Under the specific condition of T _k = 0°C and T _gc,o = 35°C, the discharge temperature of CO₂/R41 cycle is even lower than that of CO₂ expander cycle, by about 0.4°C. Therefore, the CO₂/R41 cycle is competitive with the CO₂ expander cycle in terms of exhaust temperature, especially at a lower T _gc,o .

Since the compression ratio has a significant influence on wear and how leakproof the equipment is during the operation, it can affect the reliability and safety of the equipment. Therefore, it is an important performance index for a compressor. Figure 9 depicts the compression ratio of the compressor in the three studied cycles under various conditions. It is observed that for a low T _gc,o , the differences of the compression ratio among the three studied cycles are very small, while the compression ratio of the CO₂ expander cycle is obviously lower than that of both CO₂/R41 cycle and CO₂ two-stage cycle for a high T _gc,o . For example, the differences in the compression ratio between CO₂/R41 cycle and CO₂ expander cycle is less than 1.24% when T _gc,o is 35°C and is about 10% when T _gc,o is 45°C.

For a compressor, isentropic efficiency is an important parameter affecting the comprehensive performance of a vapor compression refrigeration/heat pump cycle. It expresses the power consumption ratio between the isentropic compression process and the actual compression process. Figure 10 shows the isentropic efficiencies of the compressor in the three studied cycles under various conditions. In the CO₂ two-stage cycle, the inter-stage pressure can be given from the geometric mean value of low and high pressures. According to Eqs 2, 6, it can be seen that the isentropic efficiency of the high-pressure compressor (HP) is equal to that of the low-pressure compressor (LP). It is noted that the value of compressor isentropic efficiency in the CO₂ two-stage cycle represents that of a single compressor (i.e., HP or LP) in Figure 10. In CO₂ two-stage cycle and CO₂/R41 cycle, the isentropic efficiency of the compressor varies little with the change of T _k and T _gc,o , especially for CO₂ two-stage cycle. Meanwhile, it can be seen that the differences in the compressor isentropic efficiency between the CO₂/R41 cycle and CO₂ two-stage cycle are very small (i.e., less than 0.0057) under the studied conditions. In contrast, the operation condition has an obvious effect on the isentropic efficiencies of a compressor in the CO₂ expander cycle.

It is well known that the transcritical cycle is suitable for application in heat pump water heater systems. Since the temperature glide of the refrigerant in gas coolers can be perfectly coupled to that of the heated water, the three studied transcritical cycles are used in an ASHPWH system in the present work. In order to identify and quantify the thermodynamic losses, the exergy efficiency of an ASHPWH system under three transcritical cycles are analyzed in detail on the basis of the second law of thermodynamics. Figure 11 delineates the variation of exergy efficiency of the ASHPWH system under three transcritical cycles for various parameters of T _gc,o and T _k . It can be seen that the system exergy efficiency under the CO₂/R41 cycle is higher than that under CO₂ two-stage cycle when the outlet temperature of the gas cooler is less than 39°C (i.e., T _gc,o ≤ 39°C).

Table 5 shows the irreversible loss of each component in the studied systems under a specific condition (i.e., T _k = 0°C and T _gc,o = 35°C). It can be found that the gas cooler and throttling valve are the two main components in terms of irreversible loss in the studied systems. Due to the large pressure drop, the throttle valve produces a large irreversible loss in a refrigeration/heat pump system, which leads to low exergy efficiency for the system, as shown in Figure 11. However, the throttling valve is still usually used as a component in a CO₂ refrigeration/heat pump system, because it has been difficult to design and manufacture an expander which can be satisfactorily used in a high-pressure CO₂ refrigeration/heat pump system.