E ﬀ ects of Intercooling and Inter-Stage Heat Recovery on the Performance of Two-Stage Transcritical CO 2 Cycles for Residential Heating Applications

: Due to the harmful e ﬀ ects of synthetic refrigerants, such as chloroﬂuorocarbons (CFCs) and hydrochloroﬂuorocarbons (HCFCs)n the environment, natural refrigerants like carbon dioxide (CO 2 ) have been attracting great interest. The higher inter-stage superheating of CO 2 makes it di ﬃ cult to predict the e ﬀ ects of the intercooling on heating performance of a two-stage transcritical CO 2 cycle. In addition, very little is known about the potential of inter-stage heat rejection recovery in the heating performance enhancement of this cycle. In order to explore the e ﬀ ects of intercooling and inter-stage heat rejection recovery potential, three “sub-cycles”—(1) a sub-cycle with heat recovery, (2) a sub-cycle without heat recovery, and (3) a sub-cycle without intercooling—were modeled in Engineering Equation Solver (EES) software for three commonly-used two-stage transcritical cycles: (1) an intercooler cycle, (2) a ﬂash cycle, and (3) a split cycle. Then, the discharge pressure and intermediate pressure were simultaneously optimized. Based on the optimization results, the heating performance of the sub-cycles for each cycle were compared. The results demonstrate that the incorporation of intercooling without heat recovery was detrimental to the heating performance in comparison to the absence of intercooling. It is also clear that there is a great potential for heating performance improvement through inter-stage heat recovery.


Introduction
Increased concern for the world energy crisis and environmental problems has led to greater interest in eco-friendly refrigerants that are suitable for high-efficiency heat pump applications. Due to the abolition of chlorofluorocarbons (CFCs) and hydrochlorofluorocarbons (HCFCs) in the Montreal Protocol and the regulation of Hydrofluorocarbon (HFCs) in the Kyoto Protocol, the "natural" refrigerants have attracted considerable attention. Among the existing natural refrigerants, carbon dioxide (CO 2 ) is considered especially attractive because it is nonflammable, nontoxic, free from mutagens and carcinogens, and very low in cost [1]. However, the major disadvantage of the CO 2 cycle that influences its acceptance in the market is its lower performance [2][3][4].
Multi-stage heat pump/refrigeration cycles are typically used for large temperature differences between the source and sink, which cannot be overcome with single-stage systems [5]. Also, multi-stage cycles are an effective solution to provide power savings and improve the system performance. Two-stage cycles are usually used in food refrigeration and air conditioning for cooling applications and space or domestic water heating for heating applications, especially in cold climates.
Due to the low critical temperature of CO 2 , in most areas of application, cycles are operated in transcritical conditions, and the existence of an "optimum" discharge pressure has received significant Energies 2019, 12, 4763 3 of 15 using ethane and CO 2 as refrigerants. The theoretical analysis of the cycle performance characteristics was carried out for both refrigerants according to the first and second laws of thermodynamics. Zhang et al. [23] conducted a sensitivity study for three typical expander-based transcritical CO 2 cycles, including a two-stage cycle. The sensitivities of the maximum COP to the key operating parameters, including the inlet pressure of the gas cooler, the temperatures at evaporator inlet and gas cooler outlet, the inter-stage pressure, and the isentropic efficiency of expander, were obtained.
In heating applications, Wang et al. [24] tested the heating COP variation with discharge pressure and intermediate pressure. The result confirmed both of the pressures' influence on the overall system heating performance, which is similar to that in cooling performance. Pitarch et al. [25] analyzed and optimized a two-stage split CO 2 cycle for heating applications regarding COP in terms of the discharge pressure. The classical estimate of the intermediate pressure was employed in this analysis. This finding differs from cooling cycle in that the heating COP decreases as the refrigerant is cooled down at the intercooler.
Many researchers have dealt with the two-stage transcritical CO 2 system for cooling applications while few paid attention to cycles for heating applications. In fact, the inter-stage superheating of compressed CO 2 vapor is far higher than that of traditional refrigerants [13]. For example, when R134a, R410a, and CO 2 are compressed between an evaporating temperature of 270 K and a condensing temperature of 290 K, R134a is superheated by only 2.88 K and R410a is superheated by 8.89 K, while CO 2 is superheated by 16.57 K. This feature leads to the difficulty in predicting whether the intercooling has a beneficial effect on the heating performance of the two-stage cycle. This is because the removal of heat decreases the second-stage work but it also reduces the amount of heat that can be released from the gas cooler. As a result, it is not apparent which of these opposing effects has a greater influence on heating COP. In addition, it would be a waste of energy if the inter-stage heat is rejected to the ambient environment. However, very little is known about the potential of inter-stage heat rejection recovery in the heating performance enhancement of two-stage transcritical CO 2 cycles.
In order to understand the effects of intercooling and inter-stage heat rejection recovery on the performance of two-stage transcritical CO 2 cycles for heating applications, three "sub-cycles" have been optimized and compared based on the models developed in EES 10.0 software (University of Wisconsin, WI, USA) for two-stage transcritical CO 2 cycles. Because both the two pressures could affect the performance, unlike using classical estimate of intermediate pressure in Pitarch et al. [25], the two optimal pressures for each sub-cycle were identified simultaneously in this study. The three sub-cycles were: (1) a sub-cycle with heat recovery (with HR), (2) a sub-cycle without heat recovery (without HR), and (3) a sub-cycle without intercooling (without IC). In terms of two-stage cycle selection for investigation, due to the unavailability of advanced expansion technology in the market and the findings that the throttling valve heating cycles are able to be applied to the advanced expansion cycles, in this study, the three commonly-used cycles with a throttling valve were investigated: (1) a basic two-stage compression intercooler cycle, (2) a flash cycle, and (3) a split cycle. This paper is organized as follows. First, the optimum discharge pressure from the second-stage compressor (P D ) and intermediate pressure (P M ) for each sub-cycle were identified simultaneously. Second, the heating coefficients of performance (COPs) of the sub-cycles over a range of evaporating temperatures were compared. Finally, the cause of the observed trends in the COP for each sub-cycle was explained based on heating capacity ( . Q) and compression work (W). flash tank at the inter-stage pressure, where the vapor will be drawn by the HP compressor and the liquid will be throttled to the evaporator pressure. (3) Split Cycle: The cycle incorporates an LP and HP compressor in series, and two expansion valves. The mass flow splits after the gas cooler, where one part expands through the valve and enters the evaporator, and the other part expands and is injected with the outgoing stream of the low-pressure compressor.

Cycles and Sub-Cycles under Analysis
To investigate the effects of intercooling and inter-stage heat rejection recovery on the heating performance of the above cycles, three sub-cycles were evaluated for each of the selected cycles. In this analysis, the heat rejected from the gas cooler was used for space heating and the civil water was used as coolant for the intercooler. The heat recovered through civil water can be used for domestic hot water (e.g., preheating or direct utilization), which makes this sub-cycle more practical.  The mass flow  splits after the gas cooler, where one part expands through the valve and enters the evaporator, and  the other part expands and is injected with the outgoing stream of the low-pressure compressor. To investigate the effects of intercooling and inter-stage heat rejection recovery on the heating performance of the above cycles, three sub-cycles were evaluated for each of the selected cycles. In this analysis, the heat rejected from the gas cooler was used for space heating and the civil water was used as coolant for the intercooler. The heat recovered through civil water can be used for domestic hot water (e.g., preheating or direct utilization), which makes this sub-cycle more practical.   the HP compressor and the liquid will be throttled to the evaporator pressure. (3) Split Cycle: The cycle incorporates an LP and HP compressor in series, and two expansion valves. The mass flow splits after the gas cooler, where one part expands through the valve and enters the evaporator, and the other part expands and is injected with the outgoing stream of the low-pressure compressor.
To investigate the effects of intercooling and inter-stage heat rejection recovery on the heating performance of the above cycles, three sub-cycles were evaluated for each of the selected cycles. In this analysis, the heat rejected from the gas cooler was used for space heating and the civil water was used as coolant for the intercooler. The heat recovered through civil water can be used for domestic hot water (e.g., preheating or direct utilization), which makes this sub-cycle more practical.   The layout of the sub-cycles are as follows: (1) Sub-cycle with heat recovery: In the sub-cycle with heat recovery, an intercooler was installed after the first-stage compressor. Both the heat rejected from the gas cooler and the heat rejected from the intercooler were included for heating capacity calculations. (2) Sub-cycle without intercooling: In the sub-cycle without intercooling, no intercooler was installed after the first-stage compressor. (3) Sub-cycle without heat recovery: In the sub-cycle without heat recovery, an intercooler was installed after the first-stage compressor. However, only the heat rejected from the gas cooler was included for heating capacity calculations. Table 1 shows the features of the three sub-cycles Table 1. The features of the three sub-cycles.

Name of the Sub-Cycle
Feature Abbreviation Sub-cycle with heat recovery With both intercooling and heat recovery with HR Sub-cycle without intercooling With neither intercooling or heat recovery without IC Sub-cycle without heat recovery With only intercooling without HR The heating COP of each sub-cycle for the intercooler cycle was defined as follows: The heating COP of each sub-cycle for the flash cycle was defined as follows: The heating COP of each sub-cycle for the split cycle was defined as follows: where is the heating capacity (kJ/s); is the compression work (kJ/s); is the mass flowrate of CO2 (kg/s); ℎ is the specific enthalpy of CO2 (kJ/kg). The layout of the sub-cycles are as follows: (1) Sub-cycle with heat recovery: In the sub-cycle with heat recovery, an intercooler was installed after the first-stage compressor. Both the heat rejected from the gas cooler and the heat rejected from the intercooler were included for heating capacity calculations.
(2) Sub-cycle without intercooling: In the sub-cycle without intercooling, no intercooler was installed after the first-stage compressor. (3) Sub-cycle without heat recovery: In the sub-cycle without heat recovery, an intercooler was installed after the first-stage compressor. However, only the heat rejected from the gas cooler was included for heating capacity calculations. Table 1 shows the features of the three sub-cycles. Table 1. The features of the three sub-cycles.

Name of the Sub-Cycle Feature Abbreviation
Sub-cycle with heat recovery With both intercooling and heat recovery with HR Sub-cycle without intercooling With neither intercooling or heat recovery without IC Sub-cycle without heat recovery With only intercooling without HR The heating COP of each sub-cycle for the intercooler cycle was defined as follows: The heating COP of each sub-cycle for the flash cycle was defined as follows: The heating COP of each sub-cycle for the split cycle was defined as follows: where .
Q is the heating capacity (kJ/s); .
W is the compression work (kJ/s); . m 1 is the mass flowrate of CO 2 (kg/s); h is the specific enthalpy of CO 2 (kJ/kg).

Thermodynamic Analysis
An Engineering Equation Solver (EES) [26] is a numerical equation-solving program with many built-in mathematical and thermophysical property functions useful for engineering calculations. The high accuracy thermodynamic and transport property database means that EES is widely used in thermodynamic and heat transfer fields. The reliability and the accuracy of the numerical models in this study depend on the compressor efficiency correlation, the temperature calculation of the internal heat exchanger (IHX), and the temperature difference between CO 2 and water, which are presented as follows from the former research results.
The efficiency of the compressor is estimated by employing the following correlation for the semi-hermetic compressor [27]: where η is the compressor efficiency, P c,o is the CO 2 pressure at the outlet of the compressor (MPa), and P c,i is the CO 2 pressure at the inlet of the compressor (MPa). For the split cycle, the temperatures for the high-pressure IHX could be given by [25]: The outlet enthalpy of the expansion valve could be calculated using: where h outlet is the CO 2 enthalpy at the outlet of the expansion valve (kJ/kg) and h inlet is the CO 2 enthalpy at the inlet of the expansion valve (kJ/kg). Llopis et al. [28] tested a CO 2 transcritical refrigeration plant, where the difference between the gas cooler outlet CO 2 temperature and inlet water temperature was reported to be less than 5 • C. Hence, the temperature difference between the inlet water and outlet CO 2 was taken as 5 • C in this study.
In practical applications, the superheat is controlled at a constant to adjust the refrigerant mass flow rate to meet the various demands. In simulated analyses, the constant is usually selected to be a small value, like 0 • C, 5 • C, or 10 • C. The superheat assumption will affect the optimization results, but a similar trend will be found for different superheat assumptions. In this study, the superheat at the inlet of the first stage compressor was assumed to be 0 • C. Compared to the high operating pressure of the CO 2 cycle, the pressure drop in the pipes and heat exchanger is very small. Hence, the pressure drop in the pipes and heat exchangers were considered to be negligible. This assumption has little influence on the thermodynamic state parameters and thus the optimization results.

Optimization Conditions
In this paper, each cycle was optimized regarding the maximum heating COP using the conjugate directions method in EES. The discharge pressure and the intermediate pressure were simultaneously optimized. Because the critical temperature and critical pressure of CO 2 are 31.1 • C and 7.39 MPa, this means the heat is rejected in a supercritical process in residential heating applications. Hence, the lower bound of the P D for the second stage compressor was taken to be 7.4 MPa and the upper bound of the P M , namely the discharge pressure of the first stage compressor, was taken to be 6.8 MPa.
The manufacturer could provide a CO 2 compressor capable of operating at the maximum of 14 MPa; therefore, the upper bound of the P D was taken to be 14 MPa.
For the two sub-cycles with heat recovery and the sub-cycle without heat recovery, civil water was used as a coolant for the intercooler. If the temperature in the intercooler is lower than that of civil water, the civil water neither has an effect on cooling down the intercooler nor has the capability of recovering the heat rejected from the intercooler. With the assumption of the 5 • C temperature difference between the civil water temperature and the CO 2 temperature (discussed in Section 3.1), the lower bound of P M for these two sub-cycles was set to be 5.1 MPa, where 5.1 MPa is the corresponding saturated pressure of CO 2 at 15 • C. Table 2 presents the optimization conditions.

Results and Discussion
The cycle performance was evaluated on the basis of a maximum heating COP to obtain optimum values for P D and P M . The performance was evaluated over an evaporator temperature range of −20 • C to 0 • C. The heat rejected from gas cooler was used for space heating, so the gas cooler outlet temperature of CO 2 was fixed at 40 • C to meet the requirements of space heating. This temperature could be achieved by adjusting the inlet water flow rate according to the heat demand. The performance parameters and their optimum values are displayed graphically and elucidated below. Figure 4 shows the variation of the optimum P D and P M for each sub-cycle with the change of T ev from −20 • C to 0 • C for the intercooler cycle. It was found that for the sub-cycle without heat recovery, the optimum P M was calculated to have an optimum value of 5.1 MPa for all operating conditions. This means the that sub-cycle without heat recovery had a maximum COP when P M was operating at its minimum limit. The sub-cycle without intercooling had an optimum P M of 5.1 MPa when the T ev was less than −15 • C. It was also observed that the optimum P D of each sub-cycle decreased linearly with T ev . For the sub-cycle with heat recovery, the optimal P D decreased linearly with T ev , while P M increased with T ev . the optimum PM was calculated to have an optimum value of 5.1 MPa for all operating conditions. This means the that sub-cycle without heat recovery had a maximum COP when PM was operating at its minimum limit. The sub-cycle without intercooling had an optimum PM of 5.1 MPa when the Tev was less than −15 °C. It was also observed that the optimum PD of each sub-cycle decreased linearly with Tev. For the sub-cycle with heat recovery, the optimal PD decreased linearly with Tev, while PM increased with Tev.   Figure 5 shows the variation of the optimum P D and P M for each sub-cycle with the change of T ev from −20 • C to 0 • C for the flash cycle. With the similarity of the intercooler cycle, the sub-cycle without heat recovery had an optimum P M of 5.1 MPa. The sub-cycle without intercooling had an optimum P M of 5.1 MPa at T ev equals −20 • C. It was also observed that the optimum P D decreased almost linearly with T ev for all the sub-cycles while P M increased with T ev for the sub-cycle with heat recovery. The optimum P D of the sub-cycle without HR showed a significant decrease, while the optimum P D had a slight decrease for the other two sub-cycles. almost linearly with Tev for all the sub-cycles while PM increased with Tev for the sub-cycle with heat recovery. The optimum PD of the sub-cycle without HR showed a significant decrease, while the optimum PD had a slight decrease for the other two sub-cycles.  Figure 6 shows the variation of the optimum PD and PM for each sub-cycle with the change of Tev from −20 °C to 0 °C for the split cycle. It can be observed that, regarding the optimal PM of the subcycle without heat recovery, the split cycle resembled the other two cycles investigated above. The sub-cycle without heat recovery had an optimum PM of 5.1 MPa until Tev was around −5 °C. Like the flash cycle, the optimum PD decreased almost linearly with the increase of the Tev for all the sub-cycles and the PM increased with the increase of the Tev for the sub-cycle with heat recovery and the subcycle without intercooling. This might be because the sub-cycle without heat recovery had the maximum COP at the lower bound of the PM when the Tev was less than −5 °C. Therefore, the PD without HR was larger than the PD with HR when the Tev was less than −5 °C and lower than the PD with HR when Tev was 0 °C and −5 °C.  Figure 6 shows the variation of the optimum P D and P M for each sub-cycle with the change of T ev from −20 • C to 0 • C for the split cycle. It can be observed that, regarding the optimal P M of the sub-cycle without heat recovery, the split cycle resembled the other two cycles investigated above. The sub-cycle without heat recovery had an optimum P M of 5.1 MPa until T ev was around −5 • C. Like the flash cycle, the optimum P D decreased almost linearly with the increase of the T ev for all the sub-cycles and the P M increased with the increase of the T ev for the sub-cycle with heat recovery and the sub-cycle without intercooling. This might be because the sub-cycle without heat recovery had the maximum COP at the lower bound of the P M when the T ev was less than −5 • C. Therefore, the P D without HR was larger than the P D with HR when the T ev was less than −5 • C and lower than the P D with HR when T ev was 0 • C and −5 • C. flash cycle, the optimum PD decreased almost linearly with the increase of the Tev for all the sub-cycles and the PM increased with the increase of the Tev for the sub-cycle with heat recovery and the subcycle without intercooling. This might be because the sub-cycle without heat recovery had the maximum COP at the lower bound of the PM when the Tev was less than −5 °C. Therefore, the PD without HR was larger than the PD with HR when the Tev was less than −5 °C and lower than the PD with HR when Tev was 0 °C and −5 °C. From the optimal PD and PM values of the three cycle types, it can be concluded that the optimal PD decreased with Tev and the optimal PM increased with Tev for two-stage heating operations. These findings agree with the results of Agrawal et al. [10] for cooling operations. From the optimal P D and P M values of the three cycle types, it can be concluded that the optimal P D decreased with T ev and the optimal P M increased with T ev for two-stage heating operations. These findings agree with the results of Agrawal et al. [10] for cooling operations. Figure 7 illustrates the comparison of the COP for all sub-cycles operating at optimum conditions for the intercooler cycle. It can be seen that the sub-cycle with heat recovery had the highest COP and the sub-cycle without heat recovery had the lowest COP. As T ev varied from −20 • C to 0 • C, the sub-cycle with heat recovery experienced an increase in COP from 2.4 to 3.3. The COP of the sub-cycle with heat recovery was greater than that of the sub-cycle without intercooling by 11.2% to 14.1%, and greater than that of the sub-cycle without heat recovery by 24.2% to 50.3%.  Figure 7 illustrates the comparison of the COP for all sub-cycles operating at optimum conditions for the intercooler cycle. It can be seen that the sub-cycle with heat recovery had the highest COP and the sub-cycle without heat recovery had the lowest COP. As Tev varied from −20 °C to 0 °C, the sub-cycle with heat recovery experienced an increase in COP from 2.4 to 3.3. The COP of the sub-cycle with heat recovery was greater than that of the sub-cycle without intercooling by 11.2% to 14.1%, and greater than that of the sub-cycle without heat recovery by 24.2% to 50.3%.

Intercooler Cycle
The results show that the recovery of heat from the intercooler yielded the highest COP among the sub-cycles. The COP of the sub-cycle with heat recovery was even greater than the COP of the sub-cycle without intercooling, with an advantage of about 13.1%. It had a 37.5% advantage over the sub-cycle without heat recovery. However, installing an intercooler without heat recovery after the first-stage compression led to a COP about 17.4% lower than that of the sub-cycle with no intercooler at all. The COP trends for the intercooler cycle is explained via the differing compression work and heating capacity of the sub-cycles. Figure 8 illustrates the heating capacity and compression work per unit of CO2 mass for the sub-cycles operating at optimum conditions in the intercooler cycle. The results show that the recovery of heat from the intercooler yielded the highest COP among the sub-cycles. The COP of the sub-cycle with heat recovery was even greater than the COP of the sub-cycle without intercooling, with an advantage of about 13.1%. It had a 37.5% advantage over the sub-cycle without heat recovery. However, installing an intercooler without heat recovery after the first-stage compression led to a COP about 17.4% lower than that of the sub-cycle with no intercooler at all.
The COP trends for the intercooler cycle is explained via the differing compression work and heating capacity of the sub-cycles. Figure 8 illustrates the heating capacity and compression work per unit of CO 2 mass for the sub-cycles operating at optimum conditions in the intercooler cycle. The COP trends for the intercooler cycle is explained via the differing compression work and heating capacity of the sub-cycles. Figure 8 illustrates the heating capacity and compression work per unit of CO2 mass for the sub-cycles operating at optimum conditions in the intercooler cycle. It can be observed that both the heating capacity and compression work of the sub-cycle without intercooling were greater than those of the sub-cycle with heat recovery. Although both the heating capacity and work values of the sub-cycle without intercooler were greater than those of the subcycle with heat recovery, the higher COP of the sub-cycle with heat recovery was attributed to the compression work having a more significant influence on COP than heating capacity. For example, when Tev = −20 °C, the heating capacity of the sub-cycle without intercooling was greater than that of It can be observed that both the heating capacity and compression work of the sub-cycle without intercooling were greater than those of the sub-cycle with heat recovery. Although both the heating capacity and work values of the sub-cycle without intercooler were greater than those of the sub-cycle with heat recovery, the higher COP of the sub-cycle with heat recovery was attributed to the compression work having a more significant influence on COP than heating capacity. For example, when T ev = −20 • C, the heating capacity of the sub-cycle without intercooling was greater than that of the sub-cycle with heat recovery by 5.3%. Meanwhile, the compression work of the sub-cycle without intercooling was greater than that of the sub-cycle with heat recovery by 17.3%. As a result, the sub-cycle with heat recovery outperformed the sub-cycle without intercooling.
Regarding the COP comparison of the sub-cycle without intercooling and the sub-cycle without heat recovery, both the heating capacity and compression work of the sub-cycle without intercooling were greater than those of the sub-cycle without heat recovery. The difference in heating capacity ranged between 37.6% and 22.2%, and the difference in work ranged between 9.5% and 8.5% as the evaporator temperature rose. It can be concluded that the decrease in the heating capacity was proportionally greater. Therefore, the sub-cycle without heat recovery had a lower COP compared to the sub-cycle without intercooling.
Regarding the COP comparison of the sub-cycle with heat recovery and the sub-cycle without heat recovery, the situation was different. The sub-cycle with heat recovery had a higher heat capacity and a lower compression work, leading to a better COP. Figure 9 illustrates the comparison of the COP for all sub-cycles at optimum conditions for the flash cycle. The COP of the sub-cycle with heat recovery increased with T ev from 2.7 to 3.7, and was greater than that of the sub-cycle without intercooling by 9.8% to 10.4%. It was also greater than that of the sub-cycle without heat recovery by 34.3% to 19.7% as the evaporator temperature increased. In addition, the COP of the sub-cycle without heat recovery was less than that of the sub-cycle without intercooling by 17.7% to 7.8% as T ev increased.

Flash Cycle
The results show that for the flash cycle, the recovery of heat from the intercooler was also beneficial to the performance. The COP of the sub-cycle with heat recovery was greater than the COP of the sub-cycle without intercooling by about 10.2%, and greater than the COP of the sub-cycle without heat recovery by about 26.0%. Additionally, installing an intercooler after the first-stage compression without heat recovery led to a lower COP than having no intercooler; the COP of the sub-cycle without heat recovery was less than that of the sub-cycle without intercooling by around 12.4%.
beneficial to the performance. The COP of the sub-cycle with heat recovery was greater than the COP of the sub-cycle without intercooling by about 10.2%, and greater than the COP of the sub-cycle without heat recovery by about 26.0%. Additionally, installing an intercooler after the first-stage compression without heat recovery led to a lower COP than having no intercooler; the COP of the sub-cycle without heat recovery was less than that of the sub-cycle without intercooling by around 12.4%.  Figure 10 illustrates the heating capacity and compression work values of all sub-cycles at optimum conditions for the flash cycle. Regarding the COP comparison of the sub-cycle with heat recovery and the sub-cycle without intercooling, similar to the intercooler cycle, both the heating capacity and compression work of the sub-cycle without intercooling were greater. The difference in heating capacity ranged between 7.9% and 7.7%, and the difference in work ranged between 19.9% and 18.9% with increasing evaporator temperature. Since the higher compression work was a more significant factor than the higher heating capacity, the sub-cycle with heat recovery outperformed the sub-cycle without intercooling.  Figure 10 illustrates the heating capacity and compression work values of all sub-cycles at optimum conditions for the flash cycle. Regarding the COP comparison of the sub-cycle with heat recovery and the sub-cycle without intercooling, similar to the intercooler cycle, both the heating capacity and compression work of the sub-cycle without intercooling were greater. The difference in heating capacity ranged between 7.9% and 7.7%, and the difference in work ranged between 19.9% and 18.9% with increasing evaporator temperature. Since the higher compression work was a more significant factor than the higher heating capacity, the sub-cycle with heat recovery outperformed the sub-cycle without intercooling. In terms of the COP comparison of the sub-cycle without intercooling and the sub-cycle without heat recovery, the heating capacity of the sub-cycle without intercooling was greater than that of the sub-cycle without heat recovery by 34.4% to 17.9% when Tev increased. The compression work of the sub-cycle without intercooling was more than that of the sub-cycle without heat recovery by 11.3% to 8.7% as Tev increased. Obviously, the greater heating capacity of the sub-cycle without intercooling was a more significant factor that its better performance. Hence, the sub-cycle without intercooling yielded a higher COP than the sub-cycle without heat recovery.
Regarding the COP comparison of the sub-cycle with heat recovery and the sub-cycle without heat recovery, the compression work of the sub-cycle with heat recovery was lower and its heating capacity was higher compared to the sub-cycle without heat recovery. Hence, the sub-cycle with heat recovery yielded a higher COP than the sub-cycle without heat recovery.
From the above discussion, it can be concluded that the reasons for the differing COPs among the flash sub-cycles was the same as for the intercooler cycle. Figure 11 illustrates the COP of all sub-cycles at optimum conditions for the split cycle. It can be seen that the COPs of this cycle had the same behavior as in the intercooler and flash cycles. The COP of the sub-cycle with heat recovery increased from 2.9 to 4.0 in the range investigated. The COP of the sub-cycle with heat recovery was greater than that of the sub-cycle without intercooling by In terms of the COP comparison of the sub-cycle without intercooling and the sub-cycle without heat recovery, the heating capacity of the sub-cycle without intercooling was greater than that of the sub-cycle without heat recovery by 34.4% to 17.9% when T ev increased. The compression work of the sub-cycle without intercooling was more than that of the sub-cycle without heat recovery by 11.3% to 8.7% as T ev increased. Obviously, the greater heating capacity of the sub-cycle without intercooling was a more significant factor that its better performance. Hence, the sub-cycle without intercooling yielded a higher COP than the sub-cycle without heat recovery.

Split Cycle
Regarding the COP comparison of the sub-cycle with heat recovery and the sub-cycle without heat recovery, the compression work of the sub-cycle with heat recovery was lower and its heating capacity was higher compared to the sub-cycle without heat recovery. Hence, the sub-cycle with heat recovery yielded a higher COP than the sub-cycle without heat recovery.
From the above discussion, it can be concluded that the reasons for the differing COPs among the flash sub-cycles was the same as for the intercooler cycle. Figure 11 illustrates the COP of all sub-cycles at optimum conditions for the split cycle. It can be seen that the COPs of this cycle had the same behavior as in the intercooler and flash cycles. The COP of the sub-cycle with heat recovery increased from 2.9 to 4.0 in the range investigated. The COP of the sub-cycle with heat recovery was greater than that of the sub-cycle without intercooling by between 10.8% and 11.4%. The COP of the sub-cycle with heat recovery was greater than that of the sub-cycle without heat recovery by 28.2% to 23.7%. The COP of the sub-cycle without heat recovery was less than that of the sub-cycle without intercooling by a value ranging from 13.6% to 9.9% with rising T ev .

Split Cycle
heat recovery, the compression work of the sub-cycle with heat recovery was lower and its heating capacity was higher compared to the sub-cycle without heat recovery. Hence, the sub-cycle with heat recovery yielded a higher COP than the sub-cycle without heat recovery.
From the above discussion, it can be concluded that the reasons for the differing COPs among the flash sub-cycles was the same as for the intercooler cycle. Figure 11 illustrates the COP of all sub-cycles at optimum conditions for the split cycle. It can be seen that the COPs of this cycle had the same behavior as in the intercooler and flash cycles. The COP of the sub-cycle with heat recovery increased from 2.9 to 4.0 in the range investigated. The COP of the sub-cycle with heat recovery was greater than that of the sub-cycle without intercooling by between 10.8% and 11.4%. The COP of the sub-cycle with heat recovery was greater than that of the sub-cycle without heat recovery by 28.2% to 23.7%. The COP of the sub-cycle without heat recovery was less than that of the sub-cycle without intercooling by a value ranging from 13.6% to 9.9% with rising Tev. Figure 11. Heating COP for split cycle at optimum discharge and intermediate pressure. Figure 11. Heating COP for split cycle at optimum discharge and intermediate pressure.

Split Cycle
The results show that for the split cycle, the recovery of heat from the intercooler still resulted in the highest COP, while the installation of an intercooler without heat recovery after the first-stage compression still resulted in the lowest COP. The COP of the sub-cycle with heat recovery was greater than the COP of the sub-cycle without intercooling by about 10.9%, and greater than the COP of the sub-cycle without heat recovery by about 25.4%. Installation of an intercooler after the first-stage compression reduced the COP compared to the sub-cycle without intercooling by around 11.4%. Figure 12 illustrates the heating capacity and compression work comparison at optimal conditions for the split cycle. The results may be due to the sub-cycle without heat recovery having an optimum P M at the lower bound until T ev was around −5 • C. Consequently, the heating capacity slope of the sub-cycle without HR changed at around −5 • C. This led to the heating capacity of the sub-cycle without HR being greater than the sub-cycle with HR when T ev was more than −5 • C. The results show that for the split cycle, the recovery of heat from the intercooler still resulted in the highest COP, while the installation of an intercooler without heat recovery after the first-stage compression still resulted in the lowest COP. The COP of the sub-cycle with heat recovery was greater than the COP of the sub-cycle without intercooling by about 10.9%, and greater than the COP of the sub-cycle without heat recovery by about 25.4%. Installation of an intercooler after the first-stage compression reduced the COP compared to the sub-cycle without intercooling by around 11.4%. Figure 12 illustrates the heating capacity and compression work comparison at optimal conditions for the split cycle. The results may be due to the sub-cycle without heat recovery having an optimum PM at the lower bound until Tev was around −5 °C. Consequently, the heating capacity slope of the sub-cycle without HR changed at around −5 °C. This led to the heating capacity of the sub-cycle without HR being greater than the sub-cycle with HR when Tev was more than −5 °C. The heating capacity and compression work of the sub-cycle without intercooling were greater than those of the sub-cycle with heat recovery. The difference in heating capacity ranged from 4.1% to 3.7% and the difference in work ranged from 16.5% to 15.2% with rising evaporator temperature. This was due to the fact that the higher compression work appeared to be more significant than the difference in heating capacity. The sub-cycle with heat recovery had a higher COP than the sub-cycle without intercooling.
Regarding the COP comparison of the sub-cycle with heat recovery and the sub-cycle without The heating capacity and compression work of the sub-cycle without intercooling were greater than those of the sub-cycle with heat recovery. The difference in heating capacity ranged from 4.1% Energies 2019, 12, 4763 13 of 15 to 3.7% and the difference in work ranged from 16.5% to 15.2% with rising evaporator temperature. This was due to the fact that the higher compression work appeared to be more significant than the difference in heating capacity. The sub-cycle with heat recovery had a higher COP than the sub-cycle without intercooling.
Regarding the COP comparison of the sub-cycle with heat recovery and the sub-cycle without heat recovery, the higher heating capacity and lower compression work of the sub-cycle with heat recovery yielded a relatively higher COP. The sub-cycle without intercooling yielded a higher COP than the sub-cycle without heat recovery for the same reason: lower compression work and higher heating capacity.
The reasons for the differing COPs among the sub-cycles of the split cycle was different from the above two cycles. Regarding the effect of intercooling on performance, the sub-cycle without intercooling yielded a higher COP than the sub-cycle without heat recovery because of its lower compression work and higher heating capacity.

Conclusions
In this study, the effects of intercooling on the heating performance of the two stage transcritical CO 2 cycle and inter-stage heat rejection recovery potential were explored for three commonly used two-stage cycles-intercooler, flash, and split cycles-through a performance comparison of three sub-cycles. When the sub-cycles operated at optimal conditions, the main findings were as follows: 1.
There was a great potential for performance improvement via the recovery of heat from the intercooler. The COP of the sub-cycle with heat recovery was greater than that of the sub-cycle without intercooling by around 13.1% for the basic intercooler cycle, 10.2% for the flash cycle, and 10.9% for the split cycle; furthermore, it was greater than that of the sub-cycle without heat recovery by around 37.5% for the basic intercooler cycle, 26.0% for the flash cycle, and 25.4% for the split cycle.

2.
Incorporating an intercooler without heat recovery reduced the COP compared to the sub-cycle without intercooling for all cycle types. The COP of the sub-cycle without heat recovery was less than that of the sub-cycle without intercooling by around 17.4% for the basic intercooler cycle, 12.4% for the flash cycle, and 11.4% for the split cycle.

3.
The sub-cycle with heat recovery had a better COP than the sub-cycle without intercooling for all three cycle types examined; this was because the sub-cycle with heat recovery had lower compression work and lower heating capacity. However, the lowered compression work was a more significant factor, which led to a better performance. Similarly, the lower COP of the sub-cycle without heat recovery compared to the sub-cycle without intercooling was attributed to the fact that the decrease in heating capacity was more significant than the difference in compression work.

4.
It was found that the optimum discharge pressure, P D , decreased with the evaporating temperature, T ev , and the optimum intermediate pressure, P M , increased with T ev . This result was consistent with the results for cooling operations in the literature.

Conflicts of Interest:
The authors declare no conflict of interest.