Effects of Internal Heat Exchanger on Two-Stage Compression Trans-Critical CO₂ Refrigeration Cycle Combined with Expander and Intercooling

Abstract

Because of the limitations of traditional refrigerants, the application of trans-critical CO₂ technology in domestic gas conditioners and other fields is becoming increasingly popular. This paper proposes a new CO₂ trans-critical refrigeration system. Combining the internal heat exchanger and expander components, as well as the two-stage compression cycle, we analyzed the effectiveness of the expander, internal heat exchanger, and intercooling on system performance under various operating conditions in terms of energy, exergy analysis, and optimal discharge pressure. The system performance can be changed by changing the cycle conditions and internal heat exchanger effectiveness, which reduces system power consumption and the percentage of exergy losses of gas cooler components. Compared to the single-stage compression with expander cycle, the systems cycle power consumption is reduced by 2–15.7% and the maximum system COP is increased by 2.93–6.93%. From the view of energy effectiveness, the system’s maximum COP increases by 3.9% and the percentage of exergy losses of gas cooler decreases by 22.5% with the effectiveness of internal heat exchanger varying. The addition of an internal heat exchanger has resulted in improved system performance, which is important for providing a relevant cycle model for the application.

1. Introduction

Due to the widespread use of traditional hydrofluorocarbons (HCFCs) refrigerants, the global ozone layer is being destroyed and the greenhouse effect is gradually intensifying [1]. HFCs do not damage the ozone layer, but they usually have high GWP, so they are limited by the Vienna Convention for the Protection of the Ozone Layer and the Kigali Amendment to the Montreal Protocol on Substances that Deplete the Ozone Layer. The international community has explicitly included HFC134, HFC134a, HFC143 and 18 other HFCs in the controlled substances list and they are being phased out gradually. The search and development of new environmental-friendly refrigerants such as CO₂ (ODP = 0, GWP = 1) has become an urgent issue [2] and has received increasing attention from researchers. The trend of CO₂ refrigerants as the most important solution in various applications is almost irreversible [3]. As a major energy-consuming industry [4], refrigeration and air conditioning face both opportunities and challenges in the process. Trans-critical CO₂ is an important technological tool for global carbon neutrality and renewable energy structural transformation, with the advantages of environmental protection, economy, safety, high-temperature heating capacity, and high unit mass cooling capacity, which is widely used in automotive air conditioning [5], hot water supply [6], and supermarket refrigeration [7].

However, the system performance of the conventional CO₂ trans-critical cycle is lower than the subcritical cycle of common refrigerants [8]. An exergy analysis of the CO₂ trans-critical system components is another important aspect for exploring the improvement of the thermodynamic performance [9,10,11]; the exergy analysis of the components of the CO₂ trans-critical system in terms of the exergy loss is concentrated on the compression process and the cooling process, which is not conducive to the stable operation of the system or to performance improvement. Therefore, researchers have improved the performance of CO₂ refrigeration systems by adding expanders [12], internal heat exchangers [13], ejectors [14], and mechanical sub-cooling [6].

In recent years, the internal heat exchanger (IHX) has been widely used as an effective way to improve system performance, and many researchers have analyzed the performance of IHX for CO₂ trans-critical cycles. Pérez [15] and Torrella [16] analyzed the variation of the performance of systems with IHX and showed that the COP and unit mass cooling capacity increased compared to the system without IHX. Apreaet [17] analyzed the performance of each component of the system based on experimental data and found that the COP of the CO₂ trans-critical cycle had been improved with IHX, but the contribution of the exergy efficiency improvement was not significant. Zhang [18] compared the effect of IHX on system performance in CO₂ subcritical and trans-critical cycles and found, theoretically and experimentally, that IHX is not applied to subcritical cycles. Feng [19] experimentally analyzed the system with IHX at the optimal discharge pressure condition in a trans-critical CO₂ heat pump water heater system, finding that it has a small variation in COP and high system stability.

In the CO₂ trans-critical cycle, expanders [20,21,22,23] are an effective way to reduce system throttling losses and thus improve system performance. A variety of expander mechanisms, including a reciprocating piston, rolling piston, rotary vane, scroll, screw and turbine, have been reviewed together with their reported performance. She [20] believed that the expander can still have a certain isentropic efficiency in the two-phase expansion process. Subiantoro [24] conducted a review related to the study of the working mechanism of expanders. Yang [25] further found that the COP and exergy efficiency of the system with expander increased by 33% and 30%, respectively. Pérez [26] and Douglas [27] analyzed the effect of an expander on system performance in a CO₂ trans-critical system, finding a 25.74% increase in maximum system COP and a 35% reduction in system exergy loss. Purjam, M. et al. [28] experimented with the expander on a CO₂ subcritical heat pump system and verified the same results. Liu [29] analyzed the existence of optimal discharge pressure and the corresponding maximum COP of the use of expander in CO₂ trans-critical systems. Wang, H. et al. [30] obtained the maximum COP of 2.77 for a two-stage compression intercooling system cycle with an expander, at an intercooling pressure of 7.09 MPa for a given calculated condition. Yang, J.L. [31] analyzed the performance of a trans-critical CO₂ two-stage compression cycle combined with expander; the results showed that both the COP and the exergy efficiency of the two-stage compression cycle with the expander were 9% higher than that of the single-stage compression cycle with the expander.

Pérez [26] proposed to attach the expander, IHX, and ejectors, among other equipments, to a CO₂ trans-critical system. The use of IHX in a CO₂ trans-critical single-stage compression system with an expander, on the contrary, has a negative impact. Douglas [27] discovered an 8% reduction in COP for a trans-critical CO₂ cycle combined with an expander, while when combined with an expansion valve it resulted in a 7% increase in COP. Zhang [20] found that the use of IHX in a CO₂ trans-critical cycle with an expander is only applicable for lower expander isentropic efficiencies (η_Exp) or higher gas cooler outlet temperatures. For a trans-critical CO₂ cycle combined with an expander and an internal heat exchanger, the maximum system COP is about 12.3% to 16.1% lower compared to a system without IHX. Joneydi [32] examined how an internal heat exchanger might affect the performance of a CO₂ single-stage compression refrigeration cycle combined with an expander; the findings demonstrated that IHX decreased the exergy efficiency. Therefore, IHX are not applicable to CO₂ trans-critical single-stage cycles combined with an expander.

The application of IHX or expanders in CO₂ trans-critical systems has been well studied by previous authors, recognizing that their use is an effective way to improve performance. However, in CO₂ trans-critical single-stage cycles with expanders, IHX instead leads to a reduction in system performance. The impact of the IHX on the system is related to the η_Exp and the effectiveness of the intercooling (η_Inc), but there is no literature on the impact of using IHX on a system of CO₂ trans-critical two-stage compression with an expander, from η_Inc, η_IHX and η_Exp. Therefore, in this paper, we studied the impact of IHX on a CO₂ trans-critical two-stage compression system combined with an expander cycle refrigeration system and investigated the component effectiveness on the system in terms of energy and exergy analysis, completing the research gap of IHX in the cycle of a CO₂ trans-critical two-stage compression system with an expander to investigate the influence of operating parameters such as gas cooler outlet pressure, gas cooler outlet temperature, and evaporation temperature on the system performance.

2. Thermodynamic Model

2.1. Simulation Model

According to the basic laws of thermodynamics, the system assumes the following conditions:

• The equipment in the system is in steady-state operation, and the flow of refrigerant in the system is continuous, ignoring the pressure drop of refrigerant in the pipeline and the heat exchange loss;
• The evaporating temperature of the refrigeration system varies in the range of −5 to 10 °C, and the outlet temperature of the gas cooler varies in the range of 35 to 50 °C, with an ambient temperature of 35 °C;
• Two fixed values are employed to simulate the performance of the compressor and expander: the isentropic efficiency is 0.9 for both CO₂ low-pressure and high-pressure compressors, and 0.8 for expanders [33];
• The internal heat exchanger effectiveness and the intercooling effectiveness ranges from 0 to 1. When η_IHX is set to 0, the system does not reheat. When η_Inc is 0, a single-stage compression system is used.

2.2. Descriptions of Presented System

The CO₂ trans-critical two-stage compressor–expander system with an internal heat exchanger consists of a high-pressure stage compressor, a low-pressure stage compressor, intercooling, a gas cooler, an expander, and an evaporator. The system diagram is shown in Figure 1a, and the P-h diagram is shown in Figure 1b.

CO₂ refrigerant completes the heat absorption process at constant pressure in the evaporator (7–0 process), and the refrigerant completes heat exchange with the refrigerant exiting from the gas cooler through the internal heat exchanger before entering the inlet of the low-pressure stage compressor, which increases the inlet superheat of the compressor (0–1 process) on the one hand, and achieves the outlet cooling of the IHX (5–6 process) on the other hand. Through the compression process of the low-pressure compressor (1–2), the cooling process of intercooling (2–3), the compression process of the high-pressure compressor (3–4), the high temperature and the high-pressure state refrigerant in the gas cooler fixed pressure exothermic process (4–5), refrigerant in the expander parts to complete the throttling process (6–7), the refrigeration cycle is completed. According to the above conservation laws, MATLAB was applied for programming, and the parameters of each state point were obtained by the physical property database Refprop. The specific calculation flow chart is shown in Figure 2.

2.3. Entropy, and Exergy Model

The system components were simulated by the mass conservation, energy conservation equation, and exergy balance equation, which are calculated as: the mass conservation equation for the fluid inlet and outlet of each component of the system:

$${\displaystyle \sum _{in}{m}_i}={\displaystyle \sum _{out}{m}_i}.$$

(1)

The equation of energy conservation under the condition of stable constant flow in the control body is [34]:

$$Q_{in}-{\displaystyle \sum _{in}{m}_i\cdot h_i}={\displaystyle \sum _{out}{m}_{\mathrm{o}}\cdot h_{\mathrm{o}}}+W_{out}.$$

(2)

The equilibrium equation of the exergy [10]:

$$X_i={\displaystyle \sum _i(1-\frac{T_0}{T_i})}\cdot Q_i-W_{out}+{\displaystyle \sum _{in}{m}_i\cdot e_i}-{\displaystyle \sum _{out}{m}_o\cdot e_o}.$$

(3)

The intermediate pressures of the high and low pressure compressors are determined by the empirical formula [35]:

$$p_{\mathrm{m}}={(p_0\cdot p_{\mathrm{k}})}^{0.5}.$$

(4)

By discussing the effect of η_IHX and η_Inc on the system performance, Torrella [16] found experimentally that the η_IHX depends on the evaporating temperature and the gas cooler outlet temperature, which are defined by the ratio of the refrigerant temperature difference in and out of the heat exchanger to the theoretical maximum heat exchange temperature difference; η_IHX is given by Eq [36]:

$${\eta }_{IHX}=\frac{T_1-T_0}{T_5-T_0}.$$

(5)

CO₂ refrigerant is cooled by heat exchange with the environment through intercooling. The η_Inc is defined as [37]:

$${\eta }_{Inc}=\frac{T_2-T_3}{T_2-T_{\mathrm{a}}},$$

(6)

where the numerator indicates the temperature difference of the intercooling and the denominator indicates the maximum degree of cooling that can be achieved.

The refrigerant goes through a two-phase process from a gaseous state to a gas–liquid phase; it undergoes an expansion recovery work process through the expander. The ratio between the actual enthalpy difference between the expander input and outlet and the theoretical isentropic enthalpy difference determines the expander’s isentropic efficiency [38].

$${\eta }_{Exp}=\frac{h_6-h_7}{h_6-h_{7\mathrm{s}}}.$$

(7)

Isentropic efficiency of the compressor:

$${\eta }_{Lp}=\frac{h_{2\mathrm{s}}-h_1}{h_2-h_1}$$

(8)

$${\eta }_{Hp}=\frac{h_{4\mathrm{s}}-h_3}{h_4-h_3}.$$

(9)

The exergy analysis of the two-stage compression trans-critical CO₂ refrigeration cycle system includes the exergy loss in each component; the exergy at each state point of the refrigerant is defined as [39]:

$$e_{\mathrm{i}}=h_{\mathrm{i}}-h_{\mathrm{a}}-T_{\mathrm{a}}\cdot (s_{\mathrm{i}}-s_{\mathrm{a}}).$$

(10)

The specific formulas for each system component are summarized in

Table 1. Energy and exergy relations for the system.

Components	Energy Relations	Exergy Relations
Compressor1	$W_{Lp}=q_m\cdot (h_2-h_1)$	$X_{Lp}=q_m\cdot (e_1-e_2+W_{Lp})$
Compressor2	$W_{Hp}=q_m\cdot (h_4-h_3)$	$X_{Hp}=q_m\cdot (e_3-e_4+W_{Hp})$
Gas cooler	$Q_{gc}=q_m\cdot (h_4-h_5)$	$X_{Gc}=q_m\cdot (e_4-e_5)$
Internal heat exchanger	$h_1-h_0=h_6-h_5$	$X_{IHX}=q_m\cdot (e_0-e_1+e_5-e_6)$
Expander	$W_{Exp}=q_m\cdot (h_6-h_7)$	$X_{Exp}=q_m\cdot (e_6-e_7-W_{Exp})$
Evaporator	$Q_{Ev}=q_m\cdot (h_0-h_7)$	$T_f=T_e+5$ $X_{Ev}=q_m\cdot (e_0-e_7)+Q_e\cdot (1-\frac{T_{\mathrm{a}}}{T_{\mathrm{f}}})$
Intercooling	$Q_{Inc}=q_m\cdot (h_2-h_3)$	$X_{Inc}=q_m\cdot (e_2-e_3)$

.

Refrigeration systems measure system performance through COP, and the refrigeration system COP is defined as follows:

$$COP=\frac{Q_{\mathrm{Ev}}}{W_{Hp}+W_{Lp}-W_{Exp}}.$$

(11)

In the system, the sum of the of exergy loss of each cycle component is defined as the total exergy loss, and it is calculated as follows:

$$X_t{}_{ot}=X_{Lp}+X_{Hp}+X_{Inc}+X_{Gc}+X_{IHX}+X_{Exp}+X_E{}_v.$$

(12)

In order to evaluate the performance of an individual component, the exergy loss percentage of each system component is as follows:

$$E_i=(X_i/X_{\mathrm{tot}})\cdot 100\%.$$

(13)

The overall second law efficiency is expressed as follows:

$$Ex=(1-\frac{X_t{}_{ot}}{W_{Lp}+W_{Hp}-W_{Exp}})\cdot 100\%.$$

(14)

3. Discussion

The variation of the COP of both the system with the discharge pressure of the gas cooler at an evaporating temperature of −10 °C and the gas cooler temperature of 35 °C has an error of 1.79% with the results obtained from the original literature when the operating parameters and design conditions from Zhili S [40] are applied to the mathematical model developed in this paper, Figure 3 shows the comparison between the simulation results with the reported data in literature [40] and

Table 2. Comparison of the present model results with the experimentally validated results. (T_e = 5 °C, T_gc = 40 °C, T_a = 300 K).

Cycles	Parameters	Present Work	Reported by Zhang [41]	Relative Error (%)
Basic cycle	Pgc	10.1 MPa	9.8 MPa	3.06
	COP	2.25	2.26	0.44
With IHX	Pgc	9.7 MPa	9.5 MPa	2.10
	COP	2.38	2.42	1.65
With IHX and expander	Pgc	9.4 MPa	9.2 MPa	2.17
	COP	2.83	2.91	2.75

shows the comparison with reference [41]; so, the logical correctness of the procedure and the model can be verified.

3.1. Analysis of η_IHX for CO₂ Trans-Critical Single-Stage System with Expander

The value of discharge pressure varies between 8 and 13 MPa. When the evaporation temperature and gas cooler outlet temperatures are 0 °C and 40 °C, respectively, as shown in Figure 4, the effect of η_IHX on the performance of the CO₂ trans-critical single-stage compression refrigeration system with an expander is investigated.

Figure 4a,b show the variation of COP and exergy efficiency, respectively. At different η_IHX, the COP and the exergy efficiency show a trend of firstly increasing and then decreasing with the change of the discharge pressure. There exists an optimal discharge pressure with the corresponding max of COP and exergy efficiency, which is consistent with the results of Joneydi [32]. As η_IHX increases from 0 to 1, both the system maximum of COP and the exergy efficiency show a decreasing trend. When the system is without IHX, the maximum COP is 2.74, the maximum exergy efficiency is 40.96%, and the optimal discharge pressure is 9.61 MPa. When η_IHX is in the ideal condition (η_IHX = 1), the maximum COP is 2.41, the exergy efficiency is 34.25%, and the optimal discharge pressure is 9.52 MPa. Compared with the system without IHX, the maximum COP and the exergy efficiency of the system with IHX decreased by 12.04% and 16.38%, respectively.

Figure 5 depicts the change in system power consumption and unit mass cooling capacity with IHX; the η_Exp is 0.8. The unit mass cooling capacity rises from 123.56 kW to 171.66 kW—by 38.93%—the W_Exp rises from 45.12 kW to 71.26 kW—by 37.84%—and the expander recovery work falls from 12.87 kW to 8.0 kW—by 37.84%. This is due to the increase of work recovery in the compressor inlet temperature at the same time, which also leads to making the gas cooler outlet temperature cooler, so that the refrigerant in the evaporator inlet enthalpy was further reduced and the system unit mass cooling capacity increased. However, it is less than the increase in compressor power consumption; therefore, the system COP decreases.

3.2. Effect of η_IHX and η_Inc on a CO₂ Trans-Critical Two-Stage Compression System

By examining the consequences of the change of the η_IHX on the two-stage compression with the intercooling system’s performance under various conditions, the system was assessed. As shown in Figure 6, η_Inc is taken to be a constant value of 1, and the evaporating temperature and gas cooler outlet temperature are 0 °C and 40 °C, respectively. As shown in Figure 6a, as η_IHX increases, the system performance changes in the opposite direction of that shown in Figure 4. When the η_Exp is 0.8, the system’s maximum exergy efficiency increases as η_IHX increases, with a trend of firstly decreasing and then increasing, while the optimal discharge pressure decreases as shown in Figure 6b. The maximum COP is 2.82, and the exergy efficiency is 42.06%, with a maximum discharge pressure of 9.96 MPa and an η_IHX of 0. When η_IHX approaches the ideal value (η_IHX = 1), the optimal discharge pressure is 9.71 MPa, the system’s maximum COP is 2.93, and the exergy efficiency is 41.83%.

The system power consumption and unit mass cooling capacity change with η_IHX are shown in Figure 7; the η_Exp is 0.8. The expander recovery work decreases from 12.60 kW to 7.85 kW—by 37.7%—the W_tot increases from 46.01 kW to 60.1 kW—by 30.62%—the unit mass cooling capacity increases from 129.83 kW to 175.88 kW—by 35.47%. The system COP and the efficiency of the system are decreasing and then increasing, which is because the system increases the inlet temperature of the low-pressure compressor, which increases the power consumption of the low-pressure compressor and leads to the decrease of COP. However, due to the intercooling, the power consumption of the high-pressure compressor is reduced. The reheat leads to a lower internal heat exchanger outlet temperature, so the unit mass cooling capacity will increase, and the overall system efficiency makes the system performance improve.

3.3. Effect of η_Inc and η_Exp on the CO₂ Trans-Critical Two-Stage Compression Refrigeration System

It was found that η_IHX was not always unfavorable for the trans-critical two-stage compression with an expander system when η_Inc was taken as different constant values, so the effect of η_Inc on the performance of the present system was further investigated and the system performance was varied. Figure 8a shows the variation of COP and exergy efficiency and Figure 8b shows the variation of optimum discharge pressure. At a constant value of η_Exp, the optimal discharge pressure and the corresponding maximum COP and exergy efficiency tended to increase as η_Inc increased. At an η_Exp of 0.8, and without intercooling, the optimal discharge pressure is 9.46, the corresponding maximum COP is 2.41, and the exergy efficiency is 34.26%. When the system is completely intercooled by two-stage compression (η_Inc = 1), the optimal discharge pressure is 9.62 MPa, corresponding to a maximum COP of 2.93 and a maximum exergy efficiency of 41.84%. This is because when the refrigeration system is fully reheated, the unit mass cooling capacity is also constant. After all, the evaporating temperature and gas cooler outlet temperature are unchanged, but due to the existence of intercooling, the better the intercooling effect, the lower it will make the inlet temperature of the high pressure-stage compression, and the compressor power consumption saving will be more obvious, so the COP and other performance improvements are dramatic.

Figure 9a,b show the variation of COP and exergy efficiency under different effectiveness of internal heat exchanger and intercooler. The influence law of changing η_IHX and η_Inc on system performance is shown in three dimensions, and the influence of two heat exchangers on system performance is more thoroughly analyzed. The COP and exergy efficiency change effects with η_IHX and η_Inc are ideal conditions. When η_IHX has a fixed value, and as η_Inc increases, the system COP and exergy efficiency increase, which is consistent with Figure 8a. The system’s performance improves the most when it has been fully reheated. When the internal heat exchanger effectiveness is low or without η_IHX, the system COP increases slightly as η_Inc rises. When η_Inc takes a constant value, with the change in η_Exp, the system COP and the exergy efficiency do not always show a decreasing trend. While the intercooling effectiveness is below 0.8, the system performance COP decreases with the increase of η_IHX, and the lower η_Inc is, the more COP and the exergy efficiency decrease, and decrease most when the intercooling is not used. The conclusion is the same in Section 3.1.

3.4. Effect of Evaporation Temperatures on System Performance

With a gas cooler outlet temperature of 40 °C, and an evaporation temperature of different values, the performance of the trans-critical CO₂ refrigeration system changes as shown in Figure 10a, depicting the system without IHX as well as η_IHX = 1 conditions, the evaporation temperature on the system COP and the change in the exergy efficiency. Under the same conditions, with the change of evaporation temperature, the maximum COP is in an increasing trend. The maximum system COP was 4.04 and 3.87 for the evaporation temperature of 10 °C, and the COP increased by 4.39% when the system was without an internal heat exchanger and was fully reheated, respectively. On the contrary, the maximum exergy efficiency of the system with the increase of evaporation temperature showed a decreasing trend. With an evaporation temperature of −5 °C, the maximum exergy efficiency of the system is 37.41% and 37.51%.

The evaporation temperature is 0 °C. Figure 10b shows that the change of the gas cooler outlet temperature on the system COP and exergy efficiency under the condition of η_IHX is 0 as well as showing the complete η_IHX of the system. The gas cooler outlet temperature is 35 °C, and the maximum system COP is 3 and 3.1 for both systems without reheating and with full reheating, and the maximum exergy efficiency is 44.5% and 44.2%.

With a gas cooler outlet temperature of 40 °C, and an evaporation temperature of different values, the system COP and the exergy efficiency are as shown in Figure 11a. With intercooling as well as without, the maximum system COP is in an increasing trend. The maximum system COP was 4.04 and 3.31 at evaporation temperatures of 10 °C, respectively, and the COP rises by 18.07%. On the contrary, the maximum exergy efficiency of the system decreased as the evaporation temperature increased. With evaporation temperatures of 37.41% and 30.47%, the system’s maximum exergy efficiency increases by 22.78%. The temperature of evaporation is 0 °C. Figure 11b depicts the effect of changing the gas cooler output temperature on the system COP and exergy efficiency when η_Inc is 0 and full. The maximum system COP is 2.6 and 3.1 for both systems without reheating and with a full cooler, respectively, while the maximum exergy efficiency is 36.8% and 44.2%.

3.5. Effect of Gas Cooler Outlet Temperature on the Performance of the System

Figure 12 shows the three-dimensional images of the effect of the evaporating temperature and gas cooler outlet temperature on the performance of the system. Figure 12a,b descript the variations of COP and exergy efficiency, respectively. When the gas cooler outlet temperature is a constant value. As the evaporating temperature increases from −5 °C to 10 °C, the system COP increases and the exergy efficiency decreases. When the evaporation temperature is fixed, with the increase of the gas cooler outlet temperature from 35 °C to 50 °C, the maximum COP and exergy efficiency decrease. The system COP decreases by 21.56% and 27.77%, and the maximum exergy efficiency decreases by 21.33% and 27.51% for evaporation temperatures of −5 °C and 10 °C, respectively, and the gas cooler outlet temperature increases from 35 °C to 50 °C, respectively. The maximum COP of the system increases and the exergy efficiency decreases with the change in evaporation temperature. When the outlet temperature of the gas cooler is 35 °C and 50 °C, the evaporating temperature increases from −5 °C to 10 °C, the maximum COP increases by 67.28% and 54.07% respectively, and the exergy efficiency decreases by 8.72% and 15.89% respectively.

3.6. The Percentage of the Components That Lose Exergy

An extremely useful tool for evaluating the performance of a refrigeration system is the exergy loss percentage of each component in the system. It is possible to determine the exergy loss percentage of each component at the responding discharge pressure by changing the evaporation temperature and discharge temperature of the gas cooler. Figure 13a displays the relationship between the percentage of exergy loss of each component and the evaporation temperature, where the evaporation temperature ranges from −5 °C to 10 °C. Each component’s percentage of exergy loss varies slightly, and the changing trend is consistent with the papers that have already been published. Figure 13b shows the impact of the temperature of the gas cooler on system performance, and each component’s change is considerable due to the system’s complete internal heat exchanger condition. The influence of gas cooler temperature on the inlet temperature of the low pressure stage compressor is obvious, so the percentage of exergy loss of the intercooling grows to 26.31%.

A critical step in the system analysis is calculating the variation in the exergy loss percentage of each system component at various internal heat exchanger efficiencies as shown in Figure 14. Figure 14a shows the effect of η_IHX on the system’s components exergy loss when the system equipped with an intercooler. When the internal heat exchanger effectiveness of the system’s is increasing, the exergy loss percentage of the gas cooler gradually decreases and the intercooling tends to rise. Figure 14b depicts the effect of η_Inc on the system’s components exergy loss when the system equipped with an internal heat exchanger. The exergy loss percentage of intercooler increases and the gas cooler decreases as the increasing of intercooler effectiveness.

4. Conclusions

In this paper, the mathematical model of a CO₂ trans-critical two-stage compression system with expander and internal heat exchanger was constructed by the MATLAB program according to the law of thermodynamics and energy conservation, and the influence of an internal heat exchanger on this system was analyzed and discussed theoretically from the perspectives of internal heat exchanger effectiveness, intercooling effectiveness, evaporation temperature, gas cooler outlet temperature, and discharge pressure. The results of the analysis are as follows:

(1)

Performance of trans-critical CO₂ cycle without an intercooling (η_Inc = 0) system; the single-stage compression cycle is negatively impacted by the internal heat exchanger. The system’s COP and exergy efficiency both tend to decline as η_IHX increases. The maximum system COP and exergy efficiency are 2.41% and 34.26%, respectively, when the η_IHX is acting ideally. Reheating reduces the maximum system COP and exergy efficiency by 12.04% and 16.52%, respectively, as compared to no reheating.

(2)

It is discovered that when increasing the η_Inc through the two-stage compression combined with an internal heat exchanger, within a certain range, IHX is beneficial for this system COP enhancement. Increasing the η_Exp is an effective way to improve system performance, while the internal heat exchanger can also achieve system performance improvement when the η_Inc is greater, and the conclusion is verified in the three-dimensional diagram. When the intercooling is completely cooled, the system unit mass cooling capacity increases by 35.47%, the W_tot consumed by the system increases by 30.62%, the cooling capacity increases faster than the system’s network consumption, and the COP increases.

(3)

By analyzing the changes in system performance for systems with or without the IHX and intercooling, we found that where the impact of the η_IHX is small, while the intercooling affects the system performance to a greater extent, at the evaporation temperature of 10 °C, COP increases by 18.07%, with a 22.78% decrease in exergy efficiency.

(4)

The exergy loss percentage of each component in a system is an important way to evaluate the performance of a refrigeration system. In the ideal condition (η_IHX = 1), the evaporation temperature of the system components does not affect the components as much as the outlet temperature of the gas cooler does, and with the change of the outlet temperature of the gas cooler, the percentage of exergy losses of the intercooling increases from 13.72% to 26.31%. With the increase of internal heat exchanger effectiveness, the percentage of exergy loss of the gas cooler tends to decrease.