Thermodynamic analysis of the effect of internal heat exchanger on the dual-ejector transcritical CO2 cycle for low-temperature refrigeration

中文 / Bilingual · English version

ENERGY RESEARCH WILEY

Thermodynamic analysis of the effect of internal heat exchanger on the dual-ejector transcritical ${\mathrm{{CO}}}_{2}$ cycle for low-temperature refrigeration

Min-Qiang Zeng ${}^{1}\left| {{\text{ Xue-Lai Zhang }}^{1}{}^{ \odot }}\right| \;$ Fan-Yang Mo ${}^{2}\; \mid \;$ Xin-Rong Zhang ${}^{2,3}{}^{ \odot }$

${}^{1}$ Merchant Marine College, Shanghai Maritime University, Shanghai, China

${}^{2}$ Department of Energy and Resources Engineering, College of Engineering, Peking University, Beijing, China

${}^{3}$ Beijing Engineering Research Center of City Heat, Beijing, China

Correspondence

Xin-Rong Zhang, Department of Energy and Resources Engineering, College of Engineering, Peking University, Beijing 100871, China.

Funding information

National Key Research and Development Program, Grant/Award Number: 2018YFD0901002

Summary

The use of ${\mathrm{{CO}}}_{2}$ as a refrigerant has become a trend in the development of the refrigeration industry. Refinement of new layout and improvement of cycle performance remains a major research direction, which coupling ejector and internal heat exchanger with the transcritical ${\mathrm{{CO}}}_{2}$ cycle is a popular method. In this paper, the issue of the effect of different positions of the internal heat exchanger on the dual-ejector transcritical ${\mathrm{{CO}}}_{2}$ refrigeration cycle is discussed. The dual-ejector cycle is evaluated both thermodynamically and economically by means of multi-parameter optimization, which is compared with conventional two-stage transcritical ${\mathrm{{CO}}}_{2}$ refrigeration cycle. The obtained results show that the COP of the dual-ejector transcritical ${\mathrm{{CO}}}_{2}$ refrigeration cycle is on average about ${42}\%$ higher than that of the conventional two-stage tran-scritical ${\mathrm{{CO}}}_{2}$ refrigeration cycle. Adding internal heat exchanger at different locations cannot improve the performance of dual-ejector transcritical ${\mathrm{{CO}}}_{2}$ refrigeration cycle system in low-temperature refrigeration. In addition, the exergy and economic analysis shows that the dual-ejector transcritical ${\mathrm{{CO}}}_{2}$ refrigeration cycle has better exergy efficiency, and the increase of internal heat exchanger is an unfavorable exergy efficiency. The exergy destruction rate and the total cost of the dual-ejector system are on average ${58}\%$ and ${19}\%$ lower than that of the conventional cycle, respectively. At the same time, the addition of internal heat exchanger has very little impact on the total system cost.

KEYWORDS

${\mathrm{{CO}}}_{2}$ , comparative study, dual-ejector, internal heat exchanger, multi-parameter optimization, thermodynamic analysis

1 | INTRODUCTION

The refrigeration industry consumes a large amount of fluorinated refrigerants with high Global Warming Potential (GWP). ${}^{1,2}$ On October 15,2016, the Kigali Amendment to the Montreal Protocol reached an agreement on the reduction of HFCs and pointed out that HFCs’ consumption and production are to be phased down gradually by 80% to 85% from 2019 to the late 2040s, ${}^{3}$ 17 refrigerants are added to the restriction agreement. ${}^{4}$ In order to cope with the increasingly serious environmental warming problem in the world, seeking environmentally friendly refrigerants and improving the efficiency of the refrigeration cycle are an urgent need in the areas of refrigeration. ${}^{5}$ As a natural refrigerant, ${\mathrm{{CO}}}_{2}$ , which is increasingly used in cooling and heating systems, is expected to solve this problem, especially in the cryogenic realm. ${}^{6,7}$

Abbreviations: COP, coefficient of performance; CTRC, conventional two-stage refrigeration cycle; CR, compression ratio; CRF, capital recovery factor, dimensionless; DER, exergy destruction rate (kJ/kg); DERC, dual-ejector refrigeration cycle; Exp, experiment; IHX, internal heat exchanger; Pet, percentage (%); Sim, simulation.

For many years in the past, the traditional single-stage cycle has been widely used by commercial and industrial. ${}^{8,9}$ But with the threat of environmental and energy issues, the refrigeration system is required to be more efficient and environmentally friendly. ${}^{10}$ However, ${\mathrm{{CO}}}_{2}$ hinders its wide range of applications because of its low coefficient of performance (COP). This is mainly because when a single-stage evaporation at low temperatures is required, the transcritical ${\mathrm{{CO}}}_{2}$ circulation COP is low. In view of this, many improvements have been proposed in the paper to increase the COP of the ${\mathrm{{CO}}}_{2}$ system. ${}^{11}$ For the ${\mathrm{{CO}}}_{2}$ transcritical refrigeration cycle, the ejector shows good performance and has become a research hotspot. ${}^{{12},{13}}$ A 1-D model for ejector thermodynamic calculations was first developed by Keenan et al. ${}^{14}$ The authors proposed different approaches of constant area mixing and constant pressure mixing to solve the flow. Later, Keenan et ${\mathrm{{al}}}^{15}$ also verified through experiments that the constant pressure method is more accurate. Li and Groll ${}^{16}$ and Deng et ${\mathrm{{al}}}^{17}$ theoretically investigated injectors in the transcritical ${\mathrm{{CO}}}_{2}$ cycle: the results show that the ejector can improve the cycle performance. Ksayer et al ${}^{18}$ have demonstrated that, compared with conventional refrigeration cycle, the performance of cycle using ejectors has increased by more than 15%. In addition, there is also some research on the dual-ejector model. Xing et ${\mathrm{{al}}}^{19}$ proposed a two-stage transcritical ${\mathrm{{CO}}}_{2}$ heat pump cycle to enhance cycle performance. Banasiak et al ${}^{20}$ conducted experimental and numerical simulation studies on the optimal ejector structure of the ${\mathrm{{CO}}}_{2}$ heat pump and reported an $8\%$ increase in the COP compared with a conventional refrigeration system. Manjili and Cheraghi ${}^{21}$ proposed a two-stage transcritical ${\mathrm{{CO}}}_{2}$ refrigeration cycle with two ejectors, and found that the COP of the new cycle increased by 20% to 80% compared with the conventional refrigeration cycle.

On the other hand, the impact of adding an internal heat exchanger (IHX) to the ejector system also needs to be studied. Zhang et al2 ${}^{22}$ analyzed subcritical and tran-scritical ${\mathrm{{CO}}}_{2}$ cycles with and without IHX, and the results showed that increasing IHX makes subcritical ${\mathrm{{CO}}}_{2}$ systems have a negative effect, while it is beneficial in transcritical ${\mathrm{{CO}}}_{2}$ systems. Cao et al ${}^{23}$ experimentally studied the prototype of a transcritical ${\mathrm{{CO}}}_{2}$ heat pump water heater to study the influence of the IHX. Rigola et ${\mathrm{{al}}}^{24}$ conducted experimental and numerical comparative studies on ${\mathrm{{CO}}}_{2}$ vapor compression refrigeration cycles, and obtained relatively ideal results. Wang et al ${}^{25}$ conducted energy, exergy, and exergoeconomic analysis studies on transcritical ${\mathrm{{CO}}}_{2}$ heat pumps with and without IHX, and the results showed that IHX is beneficial for cycle performance. Purohit et ${\mathrm{{al}}}^{26}$ evaluated the experimental study of a ${\mathrm{{CO}}}_{2}$ transcritical system using IHX under warm climate conditions up to ${45}^{ \circ }\mathrm{C}$ , and the maximum COP and exergy efficiency increased by 5.71% and 5.05%, respectively. In addition to studying the impact of IHX on the performance of conventional refrigeration cycles, many scholars have also done research on the impact of IHX on ejector systems. Rodríguez-Muñoz et ${\mathrm{{al}}}^{27}$ did research on two IHX configurations with a single injector and found that IHX presence promotes a decrease in the COP in both cases. Nakagawa et al2 ${}^{18}$ used experiments to analyze the effect of IHX in a transcritical ${\mathrm{{CO}}}_{2}$ refrigeration cycle with a two-phase ejector: the results showed that IHX significantly increased the COP of the ejector system. Liu et ${\mathrm{{al}}}^{29}$ discussed the thermodynamic models of three supercharging systems using IHX: the results show that IHX can improve the COP value of pressurized systems when operating in a high-temperature environment.

In addition to the review of the ejector and IHX research, the thermodynamic evaluation method is also one of the topics discussed in this paper. To evaluate the effect of the ejector and IHX on the ${\mathrm{{CO}}}_{2}$ cycle, it is not complete to evaluate only from the energy point of view, and the exergy and economic analysis of the cycle must be carried out. ${}^{{30},{31}}$ Exergy analysis is considered to be a useful method for determining the thermodynamic losses of various components of a refrigeration system, and economy is considered to be an effective method to determine the cost of each component of the refrigeration system and optimize the economic performance of the environment.

The above literature reviews the related research contents of ejector and IHX, but the effect of IHX position on the cycle performance of dual-ejector cycle still lacks relevant research to support. In this study, the addition of IHX at three positions in a dual-ejector transcritical ${\mathrm{{CO}}}_{2}$ refrigeration cycle (DERC) is proposed to evaluate whether the combination of ejector and IHX is always increasing the cycle performance. In addition, because the DERC system involves many thermodynamic parameters, multiple parameters need to be optimized at the same time. The performance is evaluated in a refrigeration cycle using a one-dimensional constant pressure in the ejector. Meanwhile, the conventional two-stage tran-scritical ${\mathrm{{CO}}}_{2}$ refrigeration cycle (CTRC) is used as the reference cycle, and the simulation results of the newly proposed cycle will be comprehensively compared with the reference cycle in terms of energy, exergy, and economy.

In Section 2, the configurations of the aforementioned dual-ejector transcritical ${\mathrm{{CO}}}_{2}$ refrigeration systems as well as the form of IHX in three different positions are presented. In Section 3, the simulation model is established for system analysis and evaluation from the energetic, exergetic, and economic perspectives. In Section 4, validation of the ejector model is provided in this part, and the impact of IHX on the performance of the DERC system is discussed in terms of energetic, exe-rgetic, and economic aspects. The concluding remarks are finally given in Section 5.

2 | CYCLE DESCRIPTION

This paper analyses the impact of adding IHX at different locations in a transcritical ${\mathrm{{CO}}}_{2}$ refrigeration cycle with dual ejectors for low-temperature refrigeration. The CTRC is shown in Figure 1A. The P-h diagram of CTRC is shown in Figure 1B. It is composed of a compressor, intercooler, a gas cooler, an IHX, an expansion valve, and an evaporator. At the same time, CTRC is used as a reference cycle to discuss the effect of IHX on cycle performance.

The CTRC system performance can be further improved by adopting dual ejectors. Dual-ejector tran-scritical ${\mathrm{{CO}}}_{2}$ refrigeration cycle architecture is shown in Figure 2A. Figure 2B shows the P-h diagram of DERC. The high-temperature and high-pressure supercritical ${\mathrm{{CO}}}_{2}$ fluid from the gas cooler is used as the primary flow to enter ejector-1. Then, the stream leaving ejector-1 is divided into two phases in separator-1. To keep the compressor inlet mass flow constant, the vapor mass flow from separator-1 must be greater than the mass flow into the compressor-1. Therefore, a bypass line is provided at the gas outlet to allow excess gas to enter ejector-2. This bypassed fluid is mixed with the separated fluid, then is used as the primary flow to drive the ejector-2. The fluid from the evaporator enters the secondary nozzle of ejector-2, then the stream leaving the ejector-2 is divided into two phases of flow in separator-2. Same as separator-1, set a bypass line to ensure a constant flow of compressor-2, the vapor from separator-2 enters compressor-2 for boosting and enters the secondary nozzle of ejector-1 as a secondary flow. This bypassed fluid is mixed with the separated fluid and flows through the expansion valve into the evaporator inlet to complete the entire cycle.

FIGURE 1 CTRC: (A) Schematic of conventional two-stage transcritical ${\mathrm{{CO}}}_{2}$ refrigeration cycle; (B) P-h diagram of CTRC

DERC is considered to be the basis for comparing the impact of IHX position. The three configurations of adding IHX in DERC are shown in Figure 2. three types of IHX placement will be discussed:

1. IHX-1: the ${\mathrm{{CO}}}_{2}$ flows from the gas phase outlet of the separator-1 through the IHX and then enters compressor-1;

2. IHX-2: the ${\mathrm{{CO}}}_{2}$ flows from the gas phase outlet of the separator-2 through the IHX and then enters compressor-2;

3. IHX-3: the ${\mathrm{{CO}}}_{2}$ flows at the outlet of the evaporator outlet pass through IHX and then enters the secondary flow inlet of ejector-2. In the present study, the temperature range of the studied low-temperature refrigeration is set to (233.15, 263.15) K. In addition, the ambient temperature is set to 300.15 K, and the heat transfer temperature difference of all heat exchangers is set to ${\Delta T} = 5\mathrm{\;K}$ .

FIGURE 2 DERC: (A) Schematic of dual-ejector transcritical ${\mathrm{{CO}}}_{2}$ refrigeration cycle; (B) P-h diagram of DERC

3 | MODELING FOR SIMULATION AND EVALUATION

To analyze the thermal performance of DERC low-temperature refrigeration and the feasibility of adding IHX, in this section, based on typical assumptions, the above systems are modeled and evaluated from the energetic, exergetic, and economic perspectives.

3.1 | Modeling assumptions

This study will use the 1-D constant pressure model for the ejector calculation. ${}^{32}$ To simplify the theoretical model of the cycle, the following assumptions are made:

1. The flow through the ejector is regarded as a 1-D steady state flow.

2. The pressure loss at the connection of each component and the speed of the fluid at the inlet and outlet of the ejector are ignored.

3. The primary and the secondary flow are constant pressure mixed in the mixing section.

4. The liquid flow is saturated liquid and the vapor flow is saturated vapor in the gas-liquid separator.

5. The flow through the expansion valve is ideal isenthalpic expansion.

3.2 | Two-phase flow ejector modeling

The working flowchart of the ejector is shown in Figure 3. Entrainment ratio is an important parameter for the ejector performance. ${}^{33}$ The entrainment ratio, $\omega$ , is the ratio between the secondary flow mass flow rate, ${m}_{s}$ , and the primary flow mass flow rate, ${m}_{p}$ .

The ejector efficiency $\left( {\eta }_{ej}\right)$ is defined as the ratio of the actual recovered compression energy to the theoretical energy available in the primary flow. Equation (2) was proposed by Elbel et ${\mathrm{{al}}}^{34}$

Alternatively, in order to facilitate our theoretical analysis of the thermodynamic cycle, the theoretical performance of the ejector is usually characterized by an assumed value for each stage of efficiency. Table 1 collects hypothesized values of two-phase ejector efficiencies in transcritical ${\mathrm{{CO}}}_{2}$ systems in the literature. In this study, the smaller relative error between theoretical simulation and experimental data is considered. Therefore, primary and secondary nozzles efficiencies around ${\eta }_{p} = {\eta }_{s} = {0.75}$ , mixing section efficiency around ${\eta }_{m} = {0.85}$ , and diffuser efficiency around ${\eta }_{d} = {0.80}$ . The reasonableness of the above assumptions is verified in Section 4.1.

FIGURE 3 Schematic of ejector working process

3.2.1 | Primary and Secondary nozzle

In this study, the ejector was designed based on the thermodynamic model. The primary flow is accelerated as its pressure drops from ${P}_{pi}$ to ${P}_{b}$ before it enters the mixing section. In addition, the pressure drops of the secondary nozzle fluid pressure from ${P}_{si}$ to ${P}_{b}$ is called ${\Delta P}$ .

The primary nozzle efficiency value has been assumed; the enthalpy value of the outlet of the power nozzle can be obtained using the definition of efficiency

The outlet velocity ${u}_{pb}$ is determined by using the energy conservation equation between the inlet and outlet of the primary nozzle as follows:

The flow of the secondary nozzle is expanded due to the low pressure at the outlet of the primary nozzle. The calculation sequence for the secondary stream is analogous to the one for the primary flow. The secondary flow enthalpy and velocity at the outlet of the secondary nozzle are defined as:

TABLE 1 Ejector efficiencies in other studies

3.2.2 | Mixing section

The mixing part of the ejector starts at the outlet of the primary and secondary nozzles and ends in the intake gas to the constant area section. To simplify the model of the mixing section, we have assumed constant pressure mixing. Therefore, according to the following Equations (10) to (12), the velocity and enthalpy values after mixing the primary and secondary flow can be calculated.

(11)

(12)

3.2.3 | Constant area section

Considering that under transcritical cycle conditions, when the pressure difference is large, the fluid is likely to reach the speed of sound during the mixing process, and shock waves appear in the constant area section. Niguen et ${\mathrm{{al}}}^{44}$ presented a simple model for predicting the sonic velocity in two-phase systems.

The void fraction and sound velocity of two-phase flow are defined as:

If the speed of ${\mathrm{{CO}}}_{2}$ after the mixing process is greater than the speed of sound $\left( {{M}_{m} > 1}\right)$ , normal shocks will occur in the constant area chamber, otherwise all parameters of ${\mathrm{{CO}}}_{2}$ remain the same. The mass, momentum, and energy conservation of the constant area section are as follows:

Conventional formula for density using ideal gas:

In which $k$ for two-phase:

3.2.4 | Diffuser section

The mixed flow is decelerated in the diffusion section, converting kinetic energy into pressure flow work, the pressure of the mixed fluid is increased, and the pressure is higher than the pressure of the secondary fluid. The diffusion section is also an isentropic flow process, and the efficiency of the diffusion section is defined as follows:

According to the conservation of energy, the enthalpy value at the exit of the diffusion section can be calculated.

To keep the mass flow into the compressor constant, the vapor mass flow from the separator must be greater than the mass flow into the compressor. The vapor quality at the exit of the ejector diffuser must satisfy Equation (23).

TABLE 2 Thermodynamic equations for the components of the refrigeration system

3.3 | Energetic analysis

The general energy balance equation can be defined as:

By using Equation (24), the thermodynamic equations of each component of the above system are obtained, as shown in Table 2. Among them, the detailed model of the ejector and the energy equation are already given in Section 3.2.

For the CTRC cycle, the two-stage compression cycle has an intercooler to reduce compressor discharge temperature and increase efficiency, and ${\eta }_{ic}$ is assumed to be ${80}\% {.}^{45}$ The efficiency of an intercooler is defined as:

For compressors, pressure ratio is an important factor affecting compressor efficiency. In the thermodynamic calculation process of the transcritical ${\mathrm{{CO}}}_{2}$ cycle, the compressor discharge pressure has an optimal value, which is also one of the parameters of cycle optimization. ${\mathrm{{CO}}}_{2}$ compressor is expressed in the following equations ${}^{46}$ :

where ${CR}$ is the ratio of compressor discharge pressure to suction pressure. At the same time, motor efficiency ${\eta }_{m, c}$ and mechanical efficiency ${\eta }_{e, c}$ need to be considered. The total efficiency of the compressor is defined as:

where the value of combined motor and mechanical efficiency is ${0.93}^{47}$

The COP of the cycle is defined as:

(30)

3.4 | Exergetic analysis

Exergy analysis was used to evaluate irreversible exergy damage of CTRC and DERC components. The exergy of the refrigeration system at each state point can be defined ${\text{ as }}^{48}$ :

where the subscript 0 represents the reference state, which is selected as ${300.15}\mathrm{\;K}$ under the ambient atmospheric pressure of 101.325 kPa. Based on the second law of thermodynamics, the exergy loss of each component can be calculated by the following formula:

TABLE 3 The exergy destruction for the components of the refrigeration system

Based on the above two equations, the exergy destruction of each component of the CTRC and DERC systems is listed in Table 3.

In Table 3, ${T}_{sh}$ is superheat, which can also be called superheat; the temperature difference is taken as a constant ${T}_{sh} = 5\mathrm{\;K}$ .

The system exergy efficiency is expressed as follows ${}^{49}$ :

3.5 | Economic analysis

Before calculating the investment cost, the heat exchange area of the heat exchanger should be calculated. The heat transfer area can be calculated using the heat transfer equation. ${}^{50}$ The total heat transfer coefficient is assumed from values reported in the literature, as shown in Table 4.

Considering that cyclic DERC and CTRC are compared under the same conditions, and the total investment cost can be estimated by calculating the cost of each component. The cost equation of the overall system is given in Equation ${\left( {36}\right) }^{56}$ :

where the cost of capital rate is calculated as follows ${}^{56}$ :

where CRF is defined as the capital recovery factor, which can be used to calculate the annual capital cost within a year. CRF can be defined as ${}^{49}$ :

The costing equations for the major components of the system are shown in Table 5. Some of the parameters in the above model formula are shown in Table 6. In addition, the cost of equipment installation was outside the scope of this study; therefore, the cost of pipes and instruments is considered to be 28% of the total capital cost. ${}^{59}$ The evaluation parameter in terms of economic performance is given as cost per unit of exergy production. Therefore, the economic evaluation parameters of the system are expressed as ${}^{56}$ :

3.6 | Model procedure

We integrate each part to achieve the entire system model through the model calculation of the above components. The two-phase flow ejector model and system model are solved. Figure 4 shows the ejector model and the calculation process of the DERC system, where the ejector model is called a subroutine. In multi-parameter optimization process, compressor discharge pressure, inlet pressure of the secondary nozzle of ejector-2, entrainment rate of ejector-1, entrainment rate of ejector-2, secondary nozzle pressure drop of ejector-1, and secondary nozzle pressure drop of ejector-2 are taken as the constraints, and a certain range is given as follows:

TABLE 4 Heat transfer coefficient of heat exchanger considered

TABLE 5 The cost for the components of the refrigeration system

TABLE 6 Other constants for modeling parameters

NIST database REFPROP 9.1 is called by MATLAB R2017b for programming, and finally the required thermodynamic parameters are calculated. The specific optimization process is shown in Figure 5, where the constant value including the ambient temperature and the heat transfer coefficient of the heat exchanger has been given above, and the outlet temperature of the gas cooler is set to ${308.15}\mathrm{\;K}$ .

4 | RESULTS AND DISCUSSION

4.1 | Model validation

To validate the accuracy of the model of ejector and efficiency assumptions. Experimental operating data on ${\mathrm{{CO}}}_{2}$ ejectors from open literature ${}^{{60} - {62}}$ are used for comparative research. Specifically, in the experimental data mentioned in the literature, 36 sets of data of the step span are selected, and the results obtained by the model calculation are compared with the experimental data in the literature. The collected results are shown in Table A1 in Appendix. The experimental data give the pressure and temperature of the ejector’s primary and secondary flow, as well as the ejector outlet pressure and the entrainment rate. Figure 6 shows the comparison result of the prediction error bandwidth. It is found that the error is between -8% and +5%. Considering the constant efficiency assumption is to simplify the model, therefore, the error range can be acceptable, and the mathematical model is considered accurate enough for this investigation.

FIGURE 4 The flow chart of the program

FIGURE 5 The flow chart of multi-parameter optimization process

EXTERNAL OPERATING CONDITIONS

FIGURE 6 Comparison of simulated and experimental values of ejector model

FIGURE 7 COP of the DERC system: (A) under different $\omega$ of ejectors 1 and 2; (B) under different ${\Delta P}$ of ejectors 1 and 2

4.2 | Parametric analysis on the COP of the CTRC and DERC systems

4.2.1 | Ejector entrainment rate $\mathbf{\omega }$ and secondary nozzle pressure drop $\Delta \mathbf{P}$

The graph of COP of DERC vs ejector entrainment rate can be observed in Figure 7A, when fixing gas cooler pressure ${P}_{gc}$ of 9.0 MPa and the pressure drop of the two ejectors ${\Delta P}$ are both ${100.0}\mathrm{{kPa}}$ . It should be noted that in this simulation, in the case that the cyclic simulation model can run, as the entrainment rate increases, the COP will gradually decrease. It can be observed from Figure 7A that as the entrainment rate ${\omega }_{1}$ and ${\omega }_{2}$ increases, the COP decreases as expected. From the perspective of the relationship between the entrainment rate $\omega$ of a single ejector and the COP, the law is consistent with the previous results. ${}^{{16},{17}}$ It is worth noting that the change trend of the relationship between ${\omega }_{1}$ and COP will not be affected by ${\omega }_{2}$ as shown in Figure 7A, and vice versa. This conclusion can provide reason for the hypothesis of the content discussed next.

Figure 7B shows the relationship between COP and secondary nozzle pressure drop, when fixing gas cooler pressure ${P}_{gc}$ of ${9.0}\mathrm{{MPa}}$ and the pressure drop of the two ejectors $\omega$ are both 0.50 . With the increase of the secondary nozzle pressure drop $\Delta {P}_{ej1}$ and $\Delta {P}_{ej2}$ , the system COP showed a sharp increase. After reaching the optimal secondary nozzle pressure drop, the COP slowly decreased again. This trend is similar to R134a, R290, and R1234ze (E) studied by Rodríguez-Muñoz et al. ${}^{27}$ The difference is that the optimal pressure drop of ${\mathrm{{CO}}}_{2}$ is larger. The reason is that in the supercritical operation of ${\mathrm{{CO}}}_{2}$ , the pressure difference between the ejector primary flow and the secondary flow is large, which makes the optimal pressure drop larger than R134a, R290, and R1234ze(E). In addition, as shown in Figure 7B, the changing trend of the relationship between $\Delta {P}_{1}$ and COP will not be affected by $\Delta {P}_{2}$ , and vice versa.

4.2.2 | COP and ejector efficiency ${\eta }_{ej}$

To evaluate the impact of IHX on system performance, we compared the changes in COP after IHX is added to the CTRC and DERC systems under the same operating conditions in Figure 8. Where Figure 8A shows the change in COP under the condition of ${T}_{e}$ as a single variable, which is a common analysis method before optimization; Figure 8B shows the change of COP with ${T}_{e}$ after multi-parameter optimization in this study. It can be seen that the COP value decreases as the evaporation temperature decreases.

FIGURE 8 COP: (A) Comparison of COP before optimization; (B) Comparison of COP after optimization

The result of univariate analysis before optimization is shown in Figure 8A. Other setting conditions for comparison are: ${\omega }_{1} = {0.65},{\omega }_{2} = {0.55},{P}_{gc} = {9.0}\mathrm{{MPa}}$ , $\Delta {P}_{ej1} = {80.0}\mathrm{{kPa}},\;\Delta {P}_{ej2} = {140.0}\mathrm{{kPa}},\;{P}_{{ej1},{si}} = {5.5}\mathrm{{MPa}}.$ Compared without IHX in the temperature range (233.15, 263.15) K studied, the COP with IHX increased by 8.8% to 13.5% for CTRC. In the DERC system, it can be seen that the COP is significantly improved compared with the CTRC system under the above conditions. The impact of IHX on the cycle performance is the focus of attention. The DERC with IHX-1 is profitable compared without IHX, and the COP is increased by about 10 to 28%, while adding IHX-2 and IHX-3 is harmful to improve system performance.

The results of the multivariate analysis are shown in Figure 8B. The difference from the univariate research method is that the optimization calculation does not set the above parameters to a fixed value, but sets the range value (Section 3.6) to obtain the optimal solution. It can be seen from Figure 8B that the COP of the DERC system after the optimization solution is about ${42}\%$ higher than that of the CTRC system, and the COP of DERC at ${T}_{e} = {263.15}\mathrm{\;K}$ reaches 3.052, even reaching a COP improvement of ${51}\%$ when ${T}_{e} = {233.15}\mathrm{\;K}$ . At the same time, we need to pay attention to whether IHX is beneficial to the improvement of COP, which is different from the phenomenon observed before the optimization calculation. After multi-parameter optimization, it is obvious that adding three positions of IHX in the DERC system will have an adverse effect on system performance. When ${T}_{e} = {233.15}\mathrm{\;K}$ , IHX-1 reduces COP by 11.9%, IHX-2 reduces COP by 26.8%, and IHX-3 reduces COP by 14.1%. The results show that adding IHX to the three positions studied in this paper in the dual-ejector transcritical ${\mathrm{{CO}}}_{2}$ cycle is not beneficial to the system performance.

FIGURE 9 Variation of the ejection efficiency with different evaporation temperature

FIGURE 10 Exergy: (A) system total exergy destruction $E{x}_{D, T}$ ; (B) exergy efficiency ${\eta }_{Ex}$

The ejector efficiency vs evaporation temperature is shown in Figure 9. Ejector-1 efficiency varies from 0.4 to 0.43 without IHX, and the efficiency value of ejector-2 varies from 0.22 to 0.18 . It can be seen that regardless of whether IHX is added or not, the efficiency of the ejector-1 gradually increases as the evaporation temperature decreases, which is due to the increased pressure difference between primary and secondary nozzles. Conversely, the higher the evaporation temperature the higher the efficiency of ejector-2: the reason is the decrease of pressure difference between primary and secondary nozzles as the evaporation temperature decreases. In addition, it is also shown in Figure 9, the positions of IHX-1 and IHX-2 mainly affect ejector-1, so it can be seen that the efficiency improvement of ejector-1 is the most obvious; IHX-3 mainly affects the secondary nozzle inlet of ejector-2, so it can also be seen that the efficiency improvement of ejector-2 is the most obvious. It can be concluded that higher ejection efficiency does not mean higher COP of the system.

4.3 | Parametric analysis of the exergy of the CTRC and DERC systems

As shown in Figure 10A, when ${T}_{e}$ increased from 233.15K to ${263.15}\mathrm{\;K}$ , the total exergy destruction decreased. The main reason for this phenomenon is that the compressor suction pressure increased with ${T}_{e}$ , which reduces the exergy destruction at the compressor and the ejector, thereby reducing the total exergy destruction. It can be seen from Figure 10A that the exergy destruction of the DERC system is 51% to 63% lower than that of the CTRC system. At the same time, the addition of IHX to the CTRC and DERC systems will increase exergy destruction.

The relationship between the system exergy efficiency and the evaporation temperature is shown in Figure 10B. It can be seen that the exergy efficiency of the DERC system is higher than that of the CTRC. The exergy efficiency of the DERC system is on average 43% and 13% higher than that of CTRC and CTRC IHX, and 4.67%, 6.13%, 2.14% higher than the use of IHX-1/2/3 system, respectively. This is mainly due to the greatly reduced throttling loss of the expansion valve due to the use of ejectors. At the same time, the use of dual ejectors and dual compressors reduces the compression ratio, and the exergy loss is also reduced, thereby the total exergy efficiency of the system is improved. In addition, the addition of IHX improves the efficiency of the CTRC cycle, and presents a trend of first rising and then dropping with the increase of ${T}_{e}$ .

FIGURE 11 Exergy destruction ratios of each component for CTRC and DERC systems $\left( {{T}_{e} = {253.15}\mathrm{\;K}}\right)$

Figure 11 shows the exergy destruction for each component of the CTRC and DERC systems. In Table 7, the values and percentages of exergy destruction for each component of CTRC and DERC systems are presented when ${T}_{e} = {253.15}\mathrm{\;K}$ . It can be noticed that the gas cooler and expansion valve are the main exergy destruction in CTRC and CTRC IHX systems. The heat transfer occurs in gas cooler, resulting in larger irreversibility, the large pressure difference during throttling also leads to greater irreversibility. It is worth noting that the addition of IHX reduces the throttling loss of the CTRC system and increases the exergy destruction ratio of the gas cooler. Besides, the exergy destruction of the gas cooler and ejector in the DERC system is higher, the addition of IHX mainly affects the proportion of the ejector, and other components have less impact. However, it can be seen from Table 7 that the exergy destruction of each component of the DERC system has decreased compared with that of CTRC, which reflects the high COP and high exergy efficiency of the system, and the exergy loss of the throttling process is reduced.

TABLE 7 Exergy destruction in cycles $\left( {{T}_{e} = {253.15}\mathrm{\;K}}\right)$

FIGURE 12 Normalized cost of each component for CTRC and DERC systems $\left( {{T}_{e} = {253.15}\mathrm{\;K}}\right)$

4.4 | Parametric analysis of the economy of the CTRC and DERC systems

To clearly compare the costs of each component of the system, the cost of each component is shown in Figure 12. When ${T}_{e} = {253.15}\mathrm{\;K}$ , the addition of IHX increased the cost of the CTRC system by 20.4%; the cost of the DERC system is 14.8% and 29.3% lower than that of CTRC and CTRC IHX, respectively. This is because the dual ejectors are introduced in the system. However, the cost of the ejector contributes very little to the cost of the total investment. At the same time, the DERC system has relatively high COP and higher exergy efficiency help overcome the shortcomings of high investment costs, making the total system cost lower than the CTRC system. The addition of IHX did not significantly increase the total cost of the DERC system. In addition, it is also found from Figure 12 that the cost of compressors in different systems is similar, and the compressor and gas cooler account for a larger proportion of the system cost.

The comparison of the ${c}_{P}$ values of the CTRC and DERC systems is displayed in Figure 13. It can be seen that the curve trends of CTRC and CTRC IHX are basically the same, the ${c}_{P}$ of the CTRC IHX system is ${10}\%$ to 14% lower than that of CTRC, the increment of the total exergy efficiency of the system is an important reason. In addition, the addition of IHX has relatively little impact on the DERC system; the DERC system shows a smaller ${c}_{P}$ when the evaporation temperature is low, which means that it has a greater cost advantage under low-evaporation temperature conditions. It also means that the DERC system is suitable for applications in the field of low-temperature refrigeration.

FIGURE 13 Variation of ${c}_{P}$ with different evaporation temperatures for CTRC and DERC systems

5 | CONCLUSIONS

This present paper has analyzed the thermodynamic and economic performances of the DERC system for low-temperature refrigeration, The DERC system is also compared with the CTRC system under the same operating conditions. A thermoeconomic model has been developed, considering a two-phase ejector model, a two-stage ejector expansion, double compressor, and an IHX for superheating-subcooling. A two-phase ejector model was validated using operating data from ${\mathrm{{CO}}}_{2}$ ejector experimental for transcritical conditions. Multi-parameter optimization of DERC system based on thermodynamic modeling. A parametric and comparative study was conducted to discuss the impact of different positions of IHX on the performance of DERC systems. The concluding remarks are obtained as follows.

1. The DERC system has higher values of COP, on average, about 42% higher than that of CTRC system. In particular, after multi-parameter optimization calculation, it is found that the addition of IHX at different positions under the studied conditions did not improve the performance of the DERC system in low-temperature refrigeration. This also provides theoretical guidance for practical applications.

2. The DERC system has higher exergy efficiency and lower exergy destruction. The exergy efficiency of the DERC system is about 43% and 13% higher than that of CTRC and CTRC IHX on average, respectively. The difference is that the addition of IHX reduces the exergy efficiency of the DERC system, and the total exergy destruction increases. This phenomenon becomes more prominent at low-evaporation temperatures.

3. The total investment cost of the DERC system was the lowest in the range investigated. When ${T}_{e} = {253.15}\mathrm{\;K}$ , the cost of the DERC system is 14.8% and 29.3% lower than that of CTRC and CTRC IHX, respectively. The addition of IHX in different positions did not significantly increase the cost of the DERC system, on average, about 3% higher than that of DERC system. Cost per unit of exergy production of the DERC system is the lowest when the evaporation temperature is low.

Based on these obtained conclusions, DERC system is not suitable for adding IHX under low-temperature refrigeration conditions. The combination of ejector and IHX does not always mean the improvement of system performance, so it cannot be superimposed blindly in practical applications. The current work results provide a theoretical basis for future experimental work and design work with the coupling of ejector and IHX. At present, the ejector has not yet been widely used. The specific application of the ejector still needs further research.

NOMENCLATURE

English Letters

$C$ speed of sound $\left( {\mathrm{m}/\mathrm{s}}\right)$

$\dot{C}$ cost rate ($/s)

cost rate of electricity $/(kW·h)

isobaric specific heat capacity $\left( {\mathrm{{kJ}}/\mathrm{{kg}} \cdot \mathrm{K}}\right)$

isochoric specific heat capacity $\left( {\mathrm{{kJ}}/\mathrm{{kg}} \cdot \mathrm{K}}\right)$

${c}_{P}$ cost per unit of exergy $\left( {\$ /\mathrm{{kJ}}}\right)$

ex specific exergy $\left( {\mathrm{{kJ}}/\mathrm{{kg}}}\right)$

$\dot{E}{x}_{D}$ exergy destruction rate (kW)

$h$ specific enthalpy $\left( {\mathrm{{kJ}}/\mathrm{{kg}}}\right)$

$i$ annual interest rate (%)

$\dot{m}$ mass flow rate $\left( {\mathrm{{kg}}/\mathrm{s}}\right)$

$M$ Mach number

$n$ operating period (y)

$N$ annual operating hours (h)

$P$ pressure (MPa)

Q rate of net heat (kW)

$S$ specific entropy $\left( {\mathrm{{kJ}}/\mathrm{{kg}} \cdot \mathrm{K}}\right)$

$T$ temperature $\left( {\mathrm{K},{}^{ \circ }\mathrm{C}}\right)$

$u$ velocity $\left( {\mathrm{m}/\mathrm{s}}\right)$

$U$ overall heat transfer coefficient $\left( {\mathrm{{kW}}/{\mathrm{m}}^{2} \cdot \mathrm{K}}\right)$

$\dot{W}$ work rate (kW)

$X$ quality $\left( {\mathrm{{kg}}/\mathrm{{kg}}}\right)$

$Z$ capital cost ($)

$\dot{Z}$ capital cost rate ($/s)

Greek Letters

void fraction $\left( {{\mathrm{m}}^{3}/{\mathrm{m}}^{3}}\right)$

efficiency

specific heats ratio

density $\left( {\mathrm{{kg}}/{\mathrm{m}}^{3}}\right)$

maintenance factor, dimensionless

entrainment ratio of the ejector

difference

Subscripts

$b$ receiving chamber

C compressor, constant area section

$d$ outlet of diffuser

$e$ evaporator

${ev}$ expansion valve

ej ejector

gc gas cooler

$G$ gas

$i$ inlet of the component

is isentropic process

in in

$L$ liquid

$m$ mixing section

0 outlet of the component

out out

0 reference state

$p$ primary

pi primary flow at nozzle inlet

pb primary flow at receiving chamber

$S$ secondary

si secondary flow at nozzle inlet

sb secondary flow at receiving chamber

sh super heat

$T$ total

$- 1, - 2,\ldots$ component number

1, 2, 1a, 1b, .. cycle locations

ACKNOWLEDGEMENTS

The support from the National Key Research and Development Program (2018YFD0901002) is gratefully acknowledged.

DATA AVAILABILITY STATEMENT

The data that support the findings of this study are available from the corresponding author upon reasonable request.

ORCID

Xue-Lai Zhang https://orcid.org/0000-0002-8084-4654 Xin-Rong Zhang D https://orcid.org/0000-0002-6689-5754

REFERENCES

1. Nair V. HFO refrigerants: a review of present status and future prospects. Int J Refrig. 2021;122:156-170.

2. Abas N, Kalair AR, Khan N, Haider A, Saleem Z, Saleem MS. Natural and synthetic refrigerants, global warming: a review. Renew Sust Energ Rev. 2018;90:557-569.

3. Birmpili T. Montreal protocol at 30: the governance structure, the evolution, and the Kigali amendment. Compt Rendus Geosci. 2018;350(7):425-431.

4. Polonara F, Kuijpers L, Peixoto R. Potential impacts of the Montreal protocol Kigali amendment to the choice of refrigerant alternatives. Int J Heat Technol. 2017;35(Special Issue1): S1-S8.

5. Goldstein EA, Raman AP, Fan S. Sub-ambient non-evaporative fluid cooling with the sky. Nat Energy. 2017;2(9):17143.

6. Dilshad S, Kalair AR, Khan N. Review of carbon dioxide $\left( {\mathrm{{CO}}}_{2}\right)$ based heating and cooling technologies: past, present, and future outlook. Int J Energy Res. 2019;44(3):1408-1463.

7. Ma Y, Liu Z, Tian H. A review of transcritical carbon dioxide heat pump and refrigeration cycles. Energy. 2013;55:156-172.

8. Park C, Lee H, Hwang Y, Radermacher R. Recent advances in vapor compression cycle technologies. Int J Refrig. 2015;60: 118-134.

9. Zhao L, Cai W, Ding X, Chang W. Model-based optimization for vapor compression refrigeration cycle. Energy. 2013;55: 392-402.

10. Ciconkov R. Refrigerants: there is still no vision for sustainable solutions. Int J Refrig. 2018;86:441-448.

11. Yu B, Yang J, Wang D, Shi J, Chen J. An updated review of recent advances on modified technologies in transcritical ${\mathrm{{CO}}}_{2}$ refrigeration cycle. Energy. 2019;189:116147.

12. Little AB, Garimella S. A review of ejector technology for refrigeration applications. Int J Air-Cond Refrig. 2011;19(1): 1-15.

13. Sarkar J. Ejector enhanced vapor compression refrigeration and heat pump systems-a review. Renew Sust Energ Rev. 2012; 16(9):6647-6659.

14. Keenan J, Neumann E. A simple air ejector. 1942.

15. Keenan JH, Neumann EP, Lustwerk F. An Investigation of Ejector Design by Analysis and Experiment. 1950.

16. Li D, Groll EA. Transcritical ${\mathrm{{CO}}}_{2}$ refrigeration cycle with ejector-expansion device. Int J Refrig. 2005;28(5):766-773.

17. Deng J-q, Jiang P-x, Lu T, Lu W. Particular characteristics of transcritical ${\mathrm{{CO}}}_{2}$ refrigeration cycle with an ejector. Appl Therm Eng. 2007;27(2-3):381-388.

18. Ksayer EBL, Clodic D. Enhancement of ${\mathrm{{CO}}}_{2}$ Refrigeration Cycle Using an Ejector: 1D Analysis. Paper presented at: Eleventh International Refrigeration Engineering Conference. 2006.

19. Xing M, Yu J, Liu X. Thermodynamic analysis on a two-stage transcritical ${\mathrm{{CO}}}_{2}$ heat pump cycle with double ejectors. Energy Convers Manage. 2014;88:677-683.

20. Banasiak K, Hafner A, Andresen T. Experimental and numerical investigation of the influence of the two-phase ejector geometry on the performance of the R744 heat pump. Int J Refrig. 2012;35(6):1617-1625.

21. Eskandari Manjili F, Cheraghi M. Performance of a new two-stage transcritical ${\mathrm{{CO}}}_{2}$ refrigeration cycle with two ejectors. Appl Therm Eng. 2019;156:402-409.

22. Zhang FZ, Jiang PX, Lin YS, Zhang YW. Efficiencies of subcritical and transcritical ${\mathrm{{CO}}}_{2}$ inverse cycles with and without an internal heat exchanger. Appl Therm Eng. 2011;31(4):432-438.

23. Cao F, Ye Z, Wang Y. Experimental investigation on the influence of internal heat exchanger in a transcritical ${\mathrm{{CO}}}_{2}$ heat pump water heater. Appl Therm Eng. 2020;168:114855.

24. Rigola J, Ablanque N, Pérez-Segarra CD, Oliva A. Numerical simulation and experimental validation of internal heat exchanger influence on ${\mathrm{{CO}}}_{2}$ trans-critical cycle performance. Int J Refrig. 2010;33(4):664-674.

25. Wang Y, Ye Z, Yin X, Song Y, Cao F. Energy, exergy and exer-goeconomic evaluation of the air source transcritical ${\mathrm{{CO}}}_{2}$ heat pump with internal heat exchanger for space heating. Int J Refrig. 2021;130:14-26.

26. Purohit N, Gupta DK, Dasgupta MS. Experimental investigation of a ${\mathrm{{CO}}}_{2}$ trans-critical cycle with IHX for chiller application and its energetic and exergetic evaluation in warm climate. Appl Therm Eng. 2018;136:617-632.

27. Rodríguez-Muñoz JL, Pérez-García V, Belman-Flores JM, Ituna-Yudonago JF, Gallegos-Muñoz A. Energy and exergy performance of the IHX position in ejector expansion refrigeration systems. Int J Refrig. 2018;93:122-131.

28. Nakagawa M, Marasigan AR, Matsukawa T. Experimental analysis on the effect of internal heat exchanger in transcritical ${\mathrm{{CO}}}_{2}$ refrigeration cycle with two-phase ejector. Int $J$ Refrig. 2011;34(7):1577-1586.

29. Liu S, Wang J, Dai B, et al. Alternative positions of internal heat exchanger for ${\mathrm{{CO}}}_{2}$ booster refrigeration system: thermodynamic analysis and annual thermal performance evaluation. Int J Refrig. 2021;131:1016-1028.

30. Tashtoush B, Megdouli K, Elakhdar M, Nehdi E, Kairouani L. A comprehensive energy and Exergoeconomic analysis of a novel Transcritical refrigeration cycle. Processes. 2020;8(7):758.

31. Megdouli K, Sahli H, Tashtoush BM, Nahdi E, Kairouani L. Theoretical research of the performance of a novel enhanced transcritical ${\mathrm{{CO}}}_{2}$ refrigeration cycle for power and cold generation. Energy Convers Manage. 2019;201:112139.

32. Keenan JH. An investigation of ejector design by analysis and experiment. J Appl Mech. 1950;17:299-309.

33. Besagni G, Mereu R, Inzoli F. Ejector refrigeration: a comprehensive review. Renew Sust Energ Rev. 2016;53:373-407.

34. Elbel S, Hrnjak P. Experimental validation of a prototype ejector designed to reduce throttling losses encountered in transcritical R744 system operation. Int J Refrig. 2008;31(3): 411-422.

35. Sarkar J. Optimization of ejector-expansion transcritical ${\mathrm{{CO}}}_{2}$ heat pump cycle. Energy. 2008;33(9):1399-1406.

36. Fangtian S, Yitai M. Thermodynamic analysis of transcritical ${\mathrm{{CO}}}_{2}$ refrigeration cycle with an ejector. Appl Therm Eng. 2011; 31(6-7):1184-1189.

37. Manjili FE, Yavari MA. Performance of a new two-stage multi-intercooling transcritical ${\mathrm{{CO}}}_{2}$ ejector refrigeration cycle. Appl Therm Eng. 2012;40:202-209.

38. Liu F, Groll EA. Study of ejector efficiencies in refrigeration cycles. Appl Therm Eng. 2013;52(2):360-370.

39. Zheng L, Deng J, Zhang Z. Dynamic simulation of an improved transcritical ${\mathrm{{CO}}}_{2}$ ejector expansion refrigeration cycle. Energy Convers Manage. 2016;114:278-289.

40. Zheng L, Deng J. Research on ${\mathrm{{CO}}}_{2}$ ejector component efficiencies by experiment measurement and distributed-parameter modeling. Energy Convers Manage. 2017;142:244-256.

41. Taslimi Taleghani S, Sorin M, Poncet S. Modeling of two-phase transcritical ${\mathrm{{CO}}}_{2}$ ejectors for on-design and off-design conditions. Int J Refrig. 2018;87:91-105.

42. Zare V, Rostamnejad TH. Novel geothermal driven CCHP systems integrating ejector transcritical ${\mathrm{{CO}}}_{2}$ and Rankine cycles: thermodynamic modeling and parametric study. Energy Con-vers Manage. 2020;205:112396.

43. Tashtoush B, Nayfeh Y. Energy and economic analysis of a variable-geometry ejector in solar cooling systems for residential buildings. J Energy Storage. 2020;27:101061.

44. Nguyen D, Winter E, Greiner M. Sonic velocity in two-phase systems. Int J Multiphase Flow. 1981;7(3):311-320.

45. Yari M. Performance analysis and optimization of a new two-stage ejector-expansion transcritical ${\mathrm{{CO}}}_{2}$ refrigeration cycle. Int J Therm Sci. 2009;48(10):1997-2005.

46. Robinson DM, Groll EA. Efficiencies of transcritical ${\mathrm{{CO}}}_{2}$ cycles with and without an expansion turbine: rendement de cycles transcritiques au ${\mathrm{{CO}}}_{2}$ avec et sans turbine d’expansion. Int J Refrig. 1998;21(7):577-589.

47. Rezayan O, Behbahaninia A. Thermoeconomic optimization and exergy analysis of ${\mathrm{{CO}}}_{2}/{\mathrm{{NH}}}_{3}$ cascade refrigeration systems. Energy. 2011;36(2):888-895.

48. Ahamed JU, Saidur R, Masjuki HH. A review on exergy analysis of vapor compression refrigeration system. Renew Sust Energ Rev. 2011;15(3):1593-1600.

49. Liu J, Lin Z. A novel dual-temperature ejector-compression heat pump cycle - exergetic and economic analyses. Int J Refrig. 2021;126:155-167.

50. Bergman TL, Incropera FP, DeWitt DP, Lavine AS. Fundamentals of Heat and Mass Transfer. USA: John Wiley & Sons; 2011.

51. Peris Pérez B, Expósito Carrillo JA, Sánchez de La Flor FJ, Salmerón Lissén JM, Morillo NA. Thermoeconomic analysis of ${\mathrm{{CO}}}_{2}$ ejector-expansion refrigeration cycle (EERC) for low-temperature refrigeration in warm climates. Appl Therm Eng. 2021;188:116613.

52. Kemp IC. Chemical process dand integration. Chem Eng Res Des. 2005;83(9):1155-1156.

53. Peris PB Thermo-economic assessment of small-scale organic Rankine cycle for low-grade industrial waste heat recovery based on an experimental application, Universitat Jaume I. 2017.

54. Xu Y, Guo F, Song M, Jiang N, Wang Q, Chen G. Exergetic and economic analyses of a novel modified solar-heat-powered ejection-compression refrigeration cycle comparing with conventional cycle. Energy Convers Manage. 2018;168:107-118.

55. Mohammed RH, Qasem NAA, Zubair SM. Enhancing the thermal and economic performance of supercritical ${\mathrm{{CO}}}_{2}$ plant by waste heat recovery using an ejector refrigeration cycle. Energy Convers Manage. 2020;224:113340.

56. Wang G-B, Zhang X-R. Thermoeconomic optimization and comparison of the simple single-stage transcritical carbon dioxide vapor compression cycle with different subcooling methods for district heating and cooling. Energy Convers Manage. 2019; 185:740-757.

57. Nasruddin N, Sholahudin S, Giannetti N, Arnas L. Optimization of a cascade refrigeration system using refrigerant ${\mathrm{C}}_{3}{\mathrm{H}}_{8}$ in high temperature circuits (HTC) and a mixture of ${\mathrm{C}}_{2}{\mathrm{H}}_{6}/{\mathrm{{CO}}}_{2}$ in low temperature circuits (LTC). Appl Therm Eng. 2016;104: 96-103.

58. Mosaffa AH, Farshi LG, Infante Ferreira CA, Rosen MA. Exergoeconomic and environmental analyses of ${\mathrm{{CO}}}_{2}/{\mathrm{{NH}}}_{3}$ cascade refrigeration systems equipped with different types of flash tank intercoolers. Energy Convers Manage. 2016;117: 442-453.

59. Eini S, Shahhosseini H, Delgarm N, Lee M, Bahadori A. Multi-objective optimization of a cascade refrigeration system: exe-rgetic, economic, environmental, and inherent safety analysis. Appl Therm Eng. 2016;107:804-817.

60. Zhu Y, Li C, Zhang F, Jiang P-X. Comprehensive experimental study on a transcritical ${\mathrm{{CO}}}_{2}$ ejector-expansion refrigeration system. Energy Convers Manage. 2017;151:98-106.

61. Palacz M, Haida M, Smolka J, Nowak AJ, Banasiak K, Hafner A. HEM and HRM accuracy comparison for the simulation of ${\mathrm{{CO}}}_{2}$ expansion in two-phase ejectors for supermarket refrigeration systems. Appl Therm Eng. 2017;115: 160-169.

62. Giacomelli F, Mazzelli F, Banasiak K, Hafner A, Milazzo A. Experimental and computational analysis of a R744 flashing ejector. Int J Refrig. 2019;107:326-343.

How to cite this article: Zeng M-Q, Zhang X-L, Mo F-Y, Zhang X-R. Thermodynamic analysis of the effect of internal heat exchanger on the dual-ejector transcritical ${\mathrm{{CO}}}_{2}$ cycle for low-temperature refrigeration. Int J Energy Res. 2022;46(9):12702-12721. doi:10.1002/er.8038

APPENDIX

TABLE A1 Experimental data and results of the model validation