Thermodynamic Comparative Analysis of Cascade Refrigeration System Pairing R744 with R404A, R448A and R449A with Internal Heat Exchanger: Part 2—Exergy Characteristics

Abstract

The cascade refrigeration systems (CRS) used in hypermarkets and supermarkets, which are used by many people, have been employing R744 for the low-temperature cycle (LTC) and R404A for the high-temperature cycle (HTC) due to environmental and public safety issues. However, the use of R404A is limited due to its high GWP, and therefore research on alternative refrigerants is necessary. Nevertheless, there is no detailed study in the literature that compares and analyzes the three refrigerants for practical design by applying R744 for LTC and R404A, R448A, and R449A for HTC in CRS. Therefore, this study aims to provide data for the practical detailed design of an alternative system to R744/R404A CRS. Under standard conditions, we analyzed how the exergy destruction rate (EDR) and exergy efficiency (EE) of the system and the EDR of each component change when the important factors affecting CRS (degree of superheating (DSH), degree of subcooling (DSC), and internal heat exchanger (IHX) efficiency of HTC, DSH of LTC, condensation temperature (CT), evaporation temperature (ET), cascade evaporation temperature (CET), and temperature difference of CHX) are varied over a wide range. The main conclusions are as follows. (1) Under the given constant conditions, the smallest change in system EDR based on R448A is DSH of HTC (decreased by 0.07–0.1 kW), followed by IHX of HTC (decreased by 0.12–0.3 kW), DSH of LTC (increased by 0.19–0.25 kW), DSC of HTC (decreased by 0.59–0.69 kW), temperature difference of CHX (increased by 1.57–1.83 kW), CET (decreased and then increased by 0.67–4.43 kW), CT (increased by 1.49–3.9 kW), ET (decreased by 2.39–4.61 kW). (2) The highest change rate of system EE based on R448A is CET (increased and then decreased by 1.38–8.28%), followed by temperature difference of CHX (decreased by 2.96–3.16%), ET (increased and then decreased by 0.63–2.75%), DSC of HTC (increased by 1.26–1.34%), CT (increased and then decreased by 0.24–1.12%), IHX of HTC (increased by 0.11–1.02%), DSH of LTC (decreased by 0.35–0.49%), and DSH of HTC (increased by 0.14–0.19%).

1. Introduction

The cascade refrigeration system (CRS) [1,2,3,4] and indirect refrigeration system (IRS) [5,6] are used in hypermarkets and supermarkets to freeze and chill various food products. Due to the large number of people and the leakage of refrigerants, there are restrictions on the use of non-toxic and non-flammable refrigerants [7,8,9,10,11]. Therefore, R404A has been widely applied for safety reasons, such as R744/R404A CRS and R404A IRS using R744 as secondary fluid [7,12].

However, R404A is limited by its high GWP (GWP 3922), and therefore research into alternative refrigerants is needed. For this reason, research is being conducted on R448A (GWP 1387) and R449A (GWP 1397), which are well-known alternatives to R404A (below GWP 1500). These studies include refrigerant properties [13,14], evaporative heat transfer [15,16,17], and condensation heat transfer [18,19]. In particular, the studies related to refrigeration systems are as follows.

Jörgen Rogstam et al. [20] confirmed the feasibility of R449A as an alternative refrigerant to R404A in two different supermarket stores. In case study 1 (CS1—large fully IRS), the coefficient of performances (COPs) were similar. In this test, there was basically no difference and the cooling capacity was about 10% lower for R449A. In case study 2 (CS2—small DX system), the energy use of R449A was about 2% higher than R404A. In conclusion, the efficiency of the two refrigerants is very similar, but the capacity of R449A is slightly lower, which generally corresponds to a 0–10% reduction.

Makhnatch et al. [21] proposed retrofitting R404A indirect supermarket refrigeration systems with R449A. They confirmed that R449A can be used in refrigeration systems designed for R404A with minor expansion unit adjustments and a 4% increase in refrigerant charge. Ghanbarpour et al. [22] performed modeling to analyze the replacement of R404A with the low GWP alternative R449A in indirect supermarket refrigeration systems.

Mota-Babiloni et al. [23] proposed a semi-empirical analysis of R404A MT and LT with subcoolers by experimenting on a real supermarket refrigeration system. The goal was to predict the energy and, environmental and economic impacts and determine the main factors affecting the feasibility of a system redesign utilizing the R449A advanced vapor compression configuration. Giménez-Prades et al. [24] evaluated the impact of R449A subcooling in commercial refrigeration systems and proposed R449A as an environmentally friendly alternative refrigerant.

Moto-Babiloni et al. [25] conducted an experimental comparison of R404A and R448A, a non-flammable alternative with a GWP of 1390. The main findings were that the cooling capacity of R448A is slightly lower than that of R404A, but the energy consumption of R448A is lower, and the COP of R448A is higher than that of R404A. Therefore, R448A can be an energy-efficient alternative to R404A with a 70% reduction in GWP [25].

Deng et al. [26] experimentally compared non-inverter and inverter refrigeration units using R404A and R448A as refrigerants. The performance of the cold storage units was investigated at four different ambient temperatures with six performance parameters included in the analysis, including cooling capacity, energy efficiency ratio, evaporation temperature, condensation temperature, superheat degree, and subcooling degree. The results show that inverter units perform better. The year-round energy efficiency ratio increases by about 13% compared to the non-inverter unit. In addition, the cold room performed better using R448A as a refrigerant. The parameters of the device when charged with R448A are reduced by 2.94%, 2.68%, and 33.3% compared to when charged with R404A, respectively.

The results of a drop-in replacement test using R448A refrigerant by Vaitkus and Dagilis [27] show a significant performance degradation. At an ambient temperature of 25 °C, pull-down time increased by 24% and power consumption increased by 9%. In addition, due to glide and low evaporating pressure, the retrofitted system was unable to reach the required evaporating temperature.

In the study by Ustaoglu et al. [28], TOPSIS analysis was applied to determine the optimal refrigerant by considering cost, safety, environmental and eco-economic considerations along with thermophysical properties. The performance of the vapor compression refrigeration cycle was investigated by statistical and thermodynamic approaches. COP, exergy efficiency, and total, avoidable, and unavoidable exergy destruction rates were calculated for different experimental designs. Based on their relative proximity to the ideal solution, the best refrigerants for the system were determined to be R513A, R134a, and R448A, respectively.

In the study by Altinkaynk [29], an energetic and energetic performance evaluation of a theoretical refrigeration system was performed for R404 refrigerant and its substitutes. The analysis was carried out for R448A, R449A, R452A, and R404A, and a parametric analysis was performed to investigate the effect of evaporator and condenser temperatures.

As mentioned earlier, many researchers have studied R448A and R449A as alternatives to R404A. However, while there are some studies on R448A and R449A individually, there are no studies comparing R404A, R448A, and R449A, except for Altinkaynk [29]. Furthermore, there is no study that compares the three refrigerants by applying R744 to a low-temperature cycle (LTC) and R404A, R448A, and R449A to a high-temperature cycle (HTC) in a CRS. Also, in Altinkaynk [29], an exergy comparison analysis of R404A, R448A, and R449A in a basic refrigeration system was performed, but the parameters were limited to evaporation and condensation temperatures. Therefore, in this paper, we analyze the exergy destruction rate (EDR) and exergy efficiency (EE) of the CRS and EE of each component according to various parameters (degree of superheating (DSH), degree of subcooling (DSC) and internal heat exchanger (IHX) efficiency in the HTC and LTC, condensation temperature (CT), evaporation temperature (ET), cascade evaporation temperature (CET) and temperature difference of cascade heat exchanger (CHX)) of CRS using R744 for LTC and R404A, R448A, R449A for HTC, providing the optimal design data for each refrigerant.

2. Mathematical Model

2.1. System Description

Figure 1 is a conceptual diagram for comparative analysis of the exergy characteristics of CRS pairing R744 with R404A, R448A, and R449A applying IHX. In the existing R744/R404A CRS, which is widely used in hypermarkets and supermarkets, R404A refrigerant is regulated and restricted due to its high GWP (above GWP 1500), and therefore we would like to analyze R448A and R449A, which are well-known alternative refrigerants for R404A, by comparing them with R404A. In addition, in order to investigate the performance improvement and energy saving of CRS, IHX is applied to analyze the effect of detailed IHX efficiency. Therefore, in this study, the parameters that affect CRS, such as DSC, DSH and IHX efficiency of HTC, DSH of LTC, CT, ET, CET, and temperature difference of CHX, are varied widely to reveal the changes in the EDR, EE of the system, and EDR of each component.

As in Jeon and Lee [30], the DSC of LTC in CRS is not set as a variable in CRS because it is determined by the efficiency and temperature difference of CHX, and the evaporation capacity (EC) is fixed at 50 kW to compare R404A, R448A, and R449A under the same conditions to find out the changes according to R404A, R448A, and R449A. In addition, the system EE and COP decrease as the IHX efficiency of the LTC increases, and therefore the analysis based on the efficiency of the IHX is meaningless. Therefore, the analysis based on the IHX efficiency of the LTC is omitted [30].

2.2. Thermodynamic Analysis

The thermophysical properties such as enthalpy and entropy of R404A, R448A, and R449A, as well as the exergy analysis (EDR and EE of the system, and EDR of each component) were calculated using the Engineering Equation Solver (EES) software (version Professional V10.561). The exergy analysis of the cascade refrigeration system with an internal heat exchanger was performed with the same general assumptions as in the previous paper [30].

2.2.1. Compressor Modelling and Validation

In this study, the efficiencies of R404A and R449A compressors were analyzed using the formulas in

Table 1. Polynomial formulas for compressor efficiencies of R404A and R449A [23].

System	R404A	R449A
HTC	${\mathsf{\eta }}_{\mathrm{V}\mathrm{O}\mathrm{L}}$ = −0.0379CR + 0.9944 ${\mathsf{\eta }}_{\mathrm{I}\mathrm{S}\mathrm{O}}$ = −0.0213CR2 + 0.2293CR + 0.0045	${\mathsf{\eta }}_{\mathrm{V}\mathrm{O}\mathrm{L}}$ = −0.0412CR + 0.9865 ${\mathsf{\eta }}_{\mathrm{I}\mathrm{S}\mathrm{O}}$ = −0.0079CR2 + 0.105CR + 0.2718
LTC	${\mathsf{\eta }}_{\mathrm{I}\mathrm{S}\mathrm{O}}$ = −0.0046CR2 − 0.0073CR + 0.7253

, which were obtained from experimental data of commercial compressors (high-temperature compressor: Bitzer 6FE-50Y [Bitzer, Sindelfingen, Germany], low-temperature compressor: Bitzer 4ESL-9K-40S [Bitzer, Sindelfingen, Germany]) as in the previous paper [30], to obtain values close to actual experimental values rather than simple analysis, and the compression efficiency of R448A was used as the same as that of R449A because R448A has refrigerant properties that are much different from R404A but very similar to R449A, as shown in

Table 2. The characteristics summary for R404A, R448A and R449A [32,33,34,35,36].

Refrigerant	R404A	R448A	R449A
Molar mass (kg/kmol)	97.6	86.3	87.2
Boiling point (°C)	−46.2	−46.0	−46.0
Critical temperature (°C)	72	83.7	81.5
Critical pressure (kPa)	3730	4660	4450
GWP (100 yr)	3922	1387	1397
k (W/mK)	0.067	0.088	0.080
Chemical formula [37]	R125/143a/134a	R32/R125/R134a/R1234yf/R1234ze	R32/R125/R134a/R1234yf
	(44%/52%/4%)	(26%/26%/21%/20%/7%)	(24.3%/24.7%/25.7%/25.3%)

. Furthermore, the electromechanical efficiency of the compressor was assumed to be 0.94 as in references [23,24,31].

2.2.2. Performance Analysis of CRS

The exergy of the CRS pairing R744 with R404A, R448A and R449A applying IHX is analyzed by calculating the EDR of each component according to the formulas listed in

Table 3. Exergy balance equation for each component of the CRS pairing R744 with R404A, R448A and R449A applying IHX [39,40,41].

Cycle	Component	${\dot{\mathbf{E}\mathbf{x}}}_{\mathbf{F},\mathbf{k}}$, kW	${\dot{\mathbf{E}\mathbf{x}}}_{\mathbf{P},\mathbf{k}}$, kW	${\dot{\mathbf{E}\mathbf{x}}}_{\mathbf{D},\mathbf{k}}$, kW
HTC(R404A/R448A/R449A)	Compressor (1→2)	${\mathrm{W}}_{\mathrm{C}\mathrm{O}\mathrm{M},\mathrm{R}404\mathrm{A}}$	${\dot{\mathrm{E}\mathrm{x}}}_2-{\dot{\mathrm{E}\mathrm{x}}}_1$	${\mathrm{W}}_{\mathrm{C}\mathrm{O}\mathrm{M},\mathrm{R}404\mathrm{A}}$ $-$ (${\dot{\mathrm{E}\mathrm{x}}}_2$-${\dot{\mathrm{E}\mathrm{x}}}_1)$
	Condenser (2→4)	${\dot{\mathrm{E}\mathrm{x}}}_2-{\dot{\mathrm{E}\mathrm{x}}}_4$	${\mathrm{Q}}_{\mathrm{c}}\left[1-{\displaystyle \frac{{\mathrm{T}}_0}{{\mathrm{T}}_{\mathrm{C}}}}\right]$	(${\dot{\mathrm{E}\mathrm{x}}}_2-{\dot{\mathrm{E}\mathrm{x}}}_4$) $-$ ${\mathrm{Q}}_{\mathrm{c}}\left[1-{\displaystyle \frac{{\mathrm{T}}_0}{{\mathrm{T}}_{\mathrm{C}}}}\right]$
	Internal heat exchanger (4→5, 8→1)	${\dot{\mathrm{E}\mathrm{x}}}_8-{\dot{\mathrm{E}\mathrm{x}}}_1$	${\dot{\mathrm{E}\mathrm{x}}}_4-{\dot{\mathrm{E}\mathrm{x}}}_5$	(${\dot{\mathrm{E}\mathrm{x}}}_8-{\dot{\mathrm{E}\mathrm{x}}}_1$) $-$ (${\dot{\mathrm{E}\mathrm{x}}}_4-{\dot{\mathrm{E}\mathrm{x}}}_5$)
	Expansion valve (5→6)	${{\dot{\mathrm{E}\mathrm{x}}}_5}^{\mathrm{M}}-{{\dot{\mathrm{E}\mathrm{x}}}_6}^{\mathrm{M}}$	${{\dot{\mathrm{E}\mathrm{x}}}_6}^{\mathrm{T}}-{{\dot{\mathrm{E}\mathrm{x}}}_5}^{\mathrm{T}}$	(${{\dot{\mathrm{E}\mathrm{x}}}_5}^{\mathrm{M}}-{{\dot{\mathrm{E}\mathrm{x}}}_6}^{\mathrm{M}}$) $-$ (${{\dot{\mathrm{E}\mathrm{x}}}_6}^{\mathrm{T}}-{{\dot{\mathrm{E}\mathrm{x}}}_5}^{\mathrm{T}}$)
	Cascade heat exchanger (6→8, 12→14)	${\dot{\mathrm{E}\mathrm{x}}}_6-{\dot{\mathrm{E}\mathrm{x}}}_8$	${\dot{\mathrm{E}\mathrm{x}}}_{14}-{\dot{\mathrm{E}\mathrm{x}}}_{12}$	(${\dot{\mathrm{E}\mathrm{x}}}_6-{\dot{\mathrm{E}\mathrm{x}}}_8$) $-$ (${\dot{\mathrm{E}\mathrm{x}}}_{14}-{\dot{\mathrm{E}\mathrm{x}}}_{12}$)
LTC (R744)
	Compressor (11→12)	${\mathrm{W}}_{\mathrm{C}\mathrm{O}\mathrm{M},\mathrm{R}744}$	${\dot{\mathrm{E}\mathrm{x}}}_{12}-{\dot{\mathrm{E}\mathrm{x}}}_{11}$	${\mathrm{W}}_{\mathrm{C}\mathrm{O}\mathrm{M},\mathrm{R}744}-$ (${\dot{\mathrm{E}\mathrm{x}}}_{12}-{\dot{\mathrm{E}\mathrm{x}}}_{11})$
	Expansion valve (14→15)	${{\dot{\mathrm{E}\mathrm{x}}}_{14}}^{\mathrm{M}}-{{\dot{\mathrm{E}\mathrm{x}}}_{15}}^{\mathrm{M}}$	${{\dot{\mathrm{E}\mathrm{x}}}_{15}}^{\mathrm{T}}-{{\dot{\mathrm{E}\mathrm{x}}}_{14}}^{\mathrm{T}}$	(${{\dot{\mathrm{E}\mathrm{x}}}_{14}}^{\mathrm{M}}-{{\dot{\mathrm{E}\mathrm{x}}}_{15}}^{\mathrm{M}}$) $-$ (${{\dot{\mathrm{E}\mathrm{x}}}_{15}}^{\mathrm{T}}-{{\dot{\mathrm{E}\mathrm{x}}}_{14}}^{\mathrm{T}}$)
	Evaporator (15→11)	${\dot{\mathrm{E}\mathrm{x}}}_{15}-{\dot{\mathrm{E}\mathrm{x}}}_{11}$	${\mathrm{Q}}_{\mathrm{E}}[{\displaystyle \frac{{\mathrm{T}}_0}{\left({\mathrm{T}}_{\mathrm{E}}+∆{\mathrm{T}}_{\mathrm{E}}\right)}}-1]$	(${\dot{\mathrm{E}\mathrm{x}}}_{15}-{\dot{\mathrm{E}\mathrm{x}}}_{11}$) $-$ ${\mathrm{Q}}_{\mathrm{E}}[{\displaystyle \frac{{\mathrm{T}}_0}{\left({\mathrm{T}}_{\mathrm{E}}+∆{\mathrm{T}}_{\mathrm{E}}\right)}}-1]$

, the same as in the reference [38].

The exergy is calculated by the following Formulas (1) and (2): [39,42].

$${\dot{\mathrm{E}\mathrm{x}}}_{\mathrm{k}}=\dot{\mathrm{m}}[\left({\mathrm{h}}_{\mathrm{k}}-{\mathrm{h}}_0\right)-{\mathrm{T}}_0({\mathrm{s}}_{\mathrm{k}}-{\mathrm{s}}_0\left)\right]$$

(1)

$${\dot{\mathrm{E}\mathrm{x}}}_{\mathrm{k}}-{\dot{\mathrm{E}\mathrm{x}}}_{\mathrm{m}}=\dot{\mathrm{m}}[\left({\mathrm{h}}_{\mathrm{k}}-{\mathrm{h}}_{\mathrm{m}}\right)-{\mathrm{T}}_0({\mathrm{s}}_{\mathrm{k}}-{\mathrm{s}}_{\mathrm{m}}\left)\right]$$

(2)

The system EE is calculated by Formula (3) following Sun et al. [40]

$${\mathsf{\eta }}_{\mathrm{E}\mathrm{x},\mathrm{S}\mathrm{Y}\mathrm{S}}={\displaystyle \frac{{\dot{\mathrm{E}\mathrm{x}}}_{\mathrm{F},\mathrm{S}\mathrm{Y}\mathrm{S}}-{\dot{\mathrm{E}\mathrm{x}}}_{\mathrm{D},\mathrm{S}\mathrm{Y}\mathrm{S}}}{{\dot{\mathrm{E}\mathrm{x}}}_{\mathrm{F},\mathrm{S}\mathrm{Y}\mathrm{S}}}}$$

(3)

Here, ${\dot{\mathrm{E}\mathrm{x}}}_{\mathrm{F},\mathrm{S}\mathrm{Y}\mathrm{S}}$ is the sum of compressor power consumption in the HTC and LTC.

And the IHX efficiency can be expressed as shown in Formula (4) and Figure 1.

$${\mathsf{\eta }}_{\mathrm{H},\mathrm{I}\mathrm{H}\mathrm{X}}={\displaystyle \frac{({\mathrm{T}}_1-{\mathrm{T}}_8)}{({\mathrm{T}}_4-{\mathrm{T}}_8)}}$$

(4)

2.2.3. Analysis Conditions

The analysis ranges of the various variables used in this study are summarized in

Table 4. Analysis conditions of CRS pairing R744 with R404A, R448A and R449A applying IHX [30].

Division	Parameter	Range	Unit
HTC (R404A/R448A/R449A)	${\mathrm{T}}_{\mathrm{C}}$	30, 35, 40 *, 45, 50	°C
	${\mathsf{\eta }}_{\mathrm{H},\mathrm{C}\mathrm{O}\mathrm{M},\mathrm{E}}$	0.94 *	-
	${\mathsf{\eta }}_{\mathrm{H},\mathrm{I}\mathrm{H}\mathrm{X}}$	0 *, 0.2, 0.4, 0.6, 0.8	–
	${∆\mathrm{T}}_{\mathrm{H},\mathrm{S}\mathrm{U}\mathrm{C}}$	1 *, 3, 5, 7, 9	°C
	${∆\mathrm{T}}_{\mathrm{H},\mathrm{S}\mathrm{U}\mathrm{H}}$	0, 5, 10 *, 15, 20	°C
	${\mathrm{T}}_{\mathrm{C}\mathrm{A}\mathrm{S},\mathrm{E}}$	−25, −20, −15 *, −10, −5	°C
	${∆\mathrm{T}}_{\mathrm{C}\mathrm{A}\mathrm{S}}$	1, 3, 5 *, 7, 9	°C
LTC (R744)
	${\mathsf{\eta }}_{\mathrm{L},\mathrm{C}\mathrm{O}\mathrm{M},\mathrm{E}}$	0.94 *	-
	${∆\mathrm{T}}_{\mathrm{L},\mathrm{S}\mathrm{U}\mathrm{C}}$	1 *	°C
	${∆\mathrm{T}}_{\mathrm{L},\mathrm{S}\mathrm{U}\mathrm{H}}$	0, 5, 10 *, 15, 20	°C
	${\mathrm{T}}_{\mathrm{E}}$	−50, −45, −40 *, −35, −30	°C
	${\mathrm{Q}}_{\mathrm{E}}$	50 *	kW
Atmospheric conditions	${\mathrm{T}}_0$	25 *	°C
	${\mathrm{P}}_0$	101.325 *	kPa

*: Standard conditions.

.

The analysis range of various variables (${\mathrm{T}}_{\mathrm{C}}$, ${\mathsf{\eta }}_{\mathrm{H},\mathrm{C}\mathrm{O}\mathrm{M},\mathrm{E}}$, ${\mathsf{\eta }}_{\mathrm{H},\mathrm{I}\mathrm{H}\mathrm{X}}$, ${∆\mathrm{T}}_{\mathrm{H},\mathrm{S}\mathrm{U}\mathrm{C}}$, ${∆\mathrm{T}}_{\mathrm{H},\mathrm{S}\mathrm{U}\mathrm{H}}$, ${\mathrm{T}}_{\mathrm{C}\mathrm{A}\mathrm{S},\mathrm{E}}$, ${∆\mathrm{T}}_{\mathrm{C}\mathrm{A}\mathrm{S}}$, ${\mathsf{\eta }}_{\mathrm{L},\mathrm{C}\mathrm{O}\mathrm{M},\mathrm{E}}$, ${∆\mathrm{T}}_{\mathrm{L},\mathrm{S}\mathrm{U}\mathrm{C}}$, ${∆\mathrm{T}}_{\mathrm{L},\mathrm{S}\mathrm{U}\mathrm{H}}$, ${\mathrm{T}}_{\mathrm{E}}$, ${\mathrm{Q}}_{\mathrm{E}}$, ${\mathrm{T}}_0$, ${\mathrm{P}}_0$) used in this study is shown in Table 4.

Figure 2 and Figure 3 are P-h and T-s diagrams when the standard conditions of Table 4 and HTC’s IHX efficiency of 0.8 are applied [30].

3. Analysis Results and Discussion

In this paper, we analyze the EDR and EE of IHX-mounted CRS with R744 as the refrigerant of LTC and R404A, R448A, and R449A as the refrigerant of HTC, respectively, to provide a basis for designing the CRS. Therefore, we will analyze the EDR and EE of the system, the EDR of each component according to the wide variation of various parameters affecting the CRS. In order to compare the COP of the system with the EE of the system and to utilize MFR for cause analysis, the results of a previous paper [30] were used.

3.1. Effect of DSC and DSH

3.1.1. Effect of DSC in the HTC

We can see how the EDR and EE of the system and the EDR of each component change as ${∆\mathrm{T}}_{\mathrm{H},\mathrm{S}\mathrm{U}\mathrm{C}}$ increases under standard conditions (${\mathrm{Q}}_{\mathrm{E}}$ = 50 kW, ${\mathrm{T}}_{\mathrm{E}}$ = −40 °C, ${\mathrm{T}}_{\mathrm{C}\mathrm{A}\mathrm{S},\mathrm{E}}$ = −15 °C, ${\mathrm{T}}_{\mathrm{C}}$ = 40 °C, ${∆\mathrm{T}}_{\mathrm{H},\mathrm{S}\mathrm{U}\mathrm{H}}$ = 10 °C, ${∆\mathrm{T}}_{\mathrm{L},\mathrm{S}\mathrm{U}\mathrm{H}}$ = 10 °C, ${∆\mathrm{T}}_{\mathrm{L},\mathrm{S}\mathrm{U}\mathrm{C}}$ = 1 °C, ${∆\mathrm{T}}_{\mathrm{C}\mathrm{A}\mathrm{S}}$ = 5 °C, ${\mathsf{\eta }}_{\mathrm{H},\mathrm{I}\mathrm{H}\mathrm{X}}$ = ${\mathsf{\eta }}_{\mathrm{L},\mathrm{I}\mathrm{H}\mathrm{X}}$ = 0) in Table 4.

As can be seen in Figure 4, as ${∆\mathrm{T}}_{\mathrm{H},\mathrm{S}\mathrm{U}\mathrm{C}}$ increases by 2 °C from 1 °C to 9 °C, when R404A, R448A, and R449A are applied to HTC, the system EDR decreases by 0.8–1 kW, 0.59–0.69 kW, and 0.65–0.77 kW, respectively, while the system EE increased by 1.74–1.96%, 1.26–1.34%, and 1.36–1.47%, respectively, and the system COP increased by 2.0–2.19%, 1.42–1.52%, and 1.63–1.73%, respectively.

For the R448A and R449A alternatives to R404A refrigerant, all the trends were the same as R404A. The reason for these results is that as ${∆\mathrm{T}}_{\mathrm{H},\mathrm{S}\mathrm{U}\mathrm{C}}$ increases, the MFR of LTC and all conditions remain unchanged, but the MFR of HTC decreases by 2.4–3%, 1.8–2.1%, and 1.9–2.3%, respectively, which is believed to reduce the EDR of the system. The reason why the MFR of HTC decreases is that all the conditions of LTC are constant, and therefore the outlet enthalpy (OE) of CEC and cascade evaporator (CE) are constant by the energy equilibrium of CHX, but the inlet enthalpy (IE) (h₆) of CE decreases by 3.2–3.3 kJ/kg, 3.1–3.2 kJ/kg, and 3.2–3.3 kJ/kg, respectively, which increases the difference (h₆–h₈) between IE and OE of CE.

As a result of comparing the three refrigerants according to the increase in ${∆\mathrm{T}}_{\mathrm{H},\mathrm{S}\mathrm{U}\mathrm{C}}$ under certain conditions, R404A has the largest decrease in system EDR and R448A has the smallest. And the system EDR is the largest for R449A and the smallest for R448A below approximately 2.4 °C, and the smallest for R404A above approximately 2.4 °C. With the increase in ${∆\mathrm{T}}_{\mathrm{H},\mathrm{S}\mathrm{U}\mathrm{C}}$, the increase in system EE was the largest for R404A and the smallest for R448A, and the system EE was the smallest for R449A and the largest for R448A below approximately 2.4 °C and the smallest for R404A above approximately 2.4 °C. Here, when the decrease rate of system EDR was largest, the increase rate of system EE was largest, and when the decrease rate of system EDR was smallest, the increase rate of system EE was the smallest. And when the system EDR was the largest, the system EE was the smallest, and when the system EDR was the smallest, the system EE was the largest. In addition, the EDR and EE of the system, like the system COP, were reversed between R404A and R448A around 2.4 °C. In other words, the trend of the system EDR is the opposite of the trend of the system EE and COP.

Also, according to Figure 5, with the increase in ${∆\mathrm{T}}_{\mathrm{H},\mathrm{S}\mathrm{U}\mathrm{C}}$, the EDR of the expansion valve, compressor, and evaporator of LTC does not change, and the EDR of CHX increases by 0.003–0.004 kW, 0.002–0.003 kW, and 0.002–0.003 kW, respectively, while that of condenser decreases by 0.053–0.073 kW, 0.054–0.089 kW, and 0.063–0.09 kW, respectively, that of the HTC compressor decreases by 0.31–0.39 kW, 0.21–0.25 kW, and 0.23–0.29 kW, respectively, and that of the HTC expansion valve decreases by 0.41–0.55 kW, 0.29–0.39 kW, and 0.32–0.43 kW, respectively. Here, when analyzing the EDR of CHX, according to Table 3 and Formula (2), the EDR of the cascade condenser and the OE (h₈) and outlet entropy (s₈) of the CE do not change, but the IE (h₆) of the CE decreases. The inlet entropy (s₆) decreased by 0.012–0.013 kJ/(kg·K), and the enthalpy difference (h₆–h₈) and entropy difference (s₆–s₈) at the inlet and outlet of the CE increased. In other words, despite the increase in the enthalpy difference at the inlet and outlet of the CE and the decrease in the MFR of HTC, the EDR of CHX is judged to have increased because the effect of the increase in the entropy difference due to ${\mathrm{T}}_0$ applied as an absolute temperature is dominated. And the decrease in EDR of HTC compressor, HTC expansion valve and condenser is believed to be due to the decrease in MFR of HTC. In particular, the expansion valve and compressor of HTC had the largest EDR for R404A and the smallest EDR for R448A, the condenser had the smallest EDR for R404A and the largest EDR for R448A, and the CHX had the smallest EDR for R404A and the largest EDR for R449A. These results are consistent with Altinkaynak [29], and the reason for this is due to the characteristics of each refrigerant.

3.1.2. Effect of DSH in the HTC

We analyzed how the EDR and EE of the system and the EDR of each component change as ${∆\mathrm{T}}_{\mathrm{H},\mathrm{S}\mathrm{U}\mathrm{H}}$ increases under standard conditions.

As shown in Figure 6, as ${∆\mathrm{T}}_{\mathrm{H},\mathrm{S}\mathrm{U}\mathrm{H}}$ increases by 5 °C from 0 °C to 20 °C when R404A, R448A, and R449A are applied to HTC, the system EDR decreases by 0.38–0.39 kW, 0.07–0.1 kW, and 0.13–0.16 kW, respectively, but the system EE increases by 0.76%, 0.14–0.19%, and 0.22–031%, respectively, and the system COP increases by 0.87%, 0.19%, and 0.29–0.39%, respectively. In other words, in this analysis, the system EDR decreased with the increase in ${∆\mathrm{T}}_{\mathrm{H},\mathrm{S}\mathrm{U}\mathrm{H}}$, which resulted in an increase in system EE. It is also believed that the system COP increased due to the increase in system EE. R448A and R449A, which are alternatives to R404A refrigerant, showed the same trend as R404A. The reason for these results is that as ${∆\mathrm{T}}_{\mathrm{H},\mathrm{S}\mathrm{U}\mathrm{H}}$ increases, there is no change in EDR because there is no change in MFR and all conditions in LTC, but the system EDR decreases because the MFR of HTC decreases by 3.4–4.4%, 2.5–3%, and 2.6–3.1%, respectively. The reason for the decrease in MFR of HTC is that, similar to ${∆\mathrm{T}}_{\mathrm{S}\mathrm{U}\mathrm{C},\mathrm{H}\mathrm{T}\mathrm{C}}$, the CEC is constant, but the OE of the CE (h₈) increases by 4.5–4.6 kJ/kg, 4.3–4.4 kJ/kg, and 4.2–4.4 kJ/kg, respectively, which increases the enthalpy difference (h₈–h₆) of the CE inlet and outlet.

The comparison of the three refrigerants with increasing ${∆\mathrm{T}}_{\mathrm{S}\mathrm{U}\mathrm{H},\mathrm{H}\mathrm{T}\mathrm{C}}$ under constant conditions shows that, as with the trend with ${∆\mathrm{T}}_{\mathrm{H},\mathrm{S}\mathrm{U}\mathrm{C}}$, the decrease rate of system EDR is the largest for R404A and the smallest for R448A. And the system EDR is the largest for R404A below approximately 2 °C and the largest for R449A above approximately 2 °C, while the system EDR is the smallest for R448A below approximately 13.5 °C and the smallest for R404A above approximately 13.5 °C. As ${∆\mathrm{T}}_{\mathrm{S}\mathrm{U}\mathrm{H},\mathrm{H}\mathrm{T}\mathrm{C}}$ increases, the increase rate of system EE is the largest for R404A and the smallest for R448A, and the system EE is the smallest for R404A below approximately 2 °C and the smallest for R449A above approximately 2 °C, and the largest for R448A below approximately 13.5 °C and the largest for R404A above approximately 13.5 °C. Here, when the decrease rate of system EDR is the smallest, the increase rate of system EE is the smallest, and when the decrease rate of system EDR is the largest, the increase rate of system EE is the largest. Also, when the system EDR is the largest, the system EE is the smallest, and when the system EDR is the smallest, the system EE is the largest. Furthermore, the system EDR and EE are the same as the system COP, with R404A and R449A inverting around approximately 2 °C and R404A and R448A inverting around 13.5 °C.

Also, according to Figure 7, as ${∆\mathrm{T}}_{\mathrm{H},\mathrm{S}\mathrm{U}\mathrm{H}}$ increase, the EDR of evaporator, expansion valve, and compressor of LTC is constant and the EDR of condenser increases by 0.28–0.34 kJ/(kg∙K), 0.34–0.38 kJ/(kg∙K), and 0.31–0.35 kJ/(kg∙K), respectively, but the EDR of CHX decreases by 0.03–0.17 kJ/(kg∙K), 0.04–0.14 kJ/(kg∙K), and 0.04–0.15 kJ/(kg∙K), respectively, the EDR of HTC compressor decreases by 0.33–0.35 kJ/(kg∙K), 0.22–0.23 kJ/(kg∙K), and 0.23 kJ/(kg∙K), respectively, and the EDR of the HTC expansion valve decreased by 0.22–0.28 kJ/(kg∙K), 0.12–0.15 kJ/(kg∙K), and 0.14–0.16 kJ/(kg∙K), respectively. Here, when analyzing the reason why the EDR of the condenser increases using the formulas in Table 3, it is because ${\dot{\mathrm{E}\mathrm{x}}}_{\mathrm{F},\mathrm{C}}$ increases by 0.26–0.32 kW, 0.34–0.37 kW, and 0.31–0.34 kW, respectively, and ${\dot{\mathrm{E}\mathrm{x}}}_{\mathrm{P},\mathrm{C}}$ decreases by 0.019–0.02 kW, 0.004–0.005 kW, and 0.007–0.008 kW, respectively, as ${∆\mathrm{T}}_{\mathrm{S}\mathrm{U}\mathrm{H},\mathrm{H}\mathrm{T}\mathrm{C}}$ increases. Furthermore, the reason why ${\dot{\mathrm{E}\mathrm{x}}}_{\mathrm{F},\mathrm{C}}$ increases is because the increase in enthalpy at the condenser inlet dominates despite the decrease in MFR of the HTC and the increase in entropy at the condenser inlet, while the reason why ${\dot{\mathrm{E}\mathrm{x}}}_{\mathrm{P},\mathrm{C}}$ decreases is because the MFR of the HTC decreases even though ${\mathrm{T}}_0$ and ${\mathrm{T}}_{\mathrm{C}}$ are constant. And the reason for the decrease in EDR of CHX, HTC compressor, and HTC expansion valve is due to the dominant effect of the decrease in MFR of HTC.

Furthermore, when comparing the EDRs of each component for R404A, R448A, and R449A with each other as ${∆\mathrm{T}}_{\mathrm{H},\mathrm{S}\mathrm{U}\mathrm{H}}$ increases, it can be seen that the condenser has the smallest EDR for R404A and the largest EDR for R448A, the expansion valve and compressor of HTC have the smallest EDR for R404A and the largest for R449A, and the CHX have the smallest EDR for R404A and the largest EDR for R449A, the same as the results of increasing ${∆\mathrm{T}}_{\mathrm{S}\mathrm{U}\mathrm{C},\mathrm{H}\mathrm{T}\mathrm{C}}$.

3.1.3. Effect of DSH in the LTC

Under standard conditions, we analyzed how the EDR and EE of the system and the EDR of each component change as ${∆\mathrm{T}}_{\mathrm{L},\mathrm{S}\mathrm{U}\mathrm{H}}$ increases.

As shown in Figure 8, as ${∆\mathrm{T}}_{\mathrm{L},\mathrm{S}\mathrm{U}\mathrm{H}}$ increases by 5 °C from 0 °C to 20 °C, the system EDR with R404A, R448A, and R449A applied to HTC increases by 0.2–0.25 kW, 0.19–0.25 kW, and 0.2–0.25 kW, respectively, the system EE decreases by 0.36–0.49%, 0.35–0.49%, and 0.36–0.47%, respectively, and the system COP decreases by 0.38–0.57%, 0.47–0.56%, and 0.38–0.57%, respectively. The reason for this is analyzed in Figure 9, which shows that with the increase in ${∆\mathrm{T}}_{\mathrm{L},\mathrm{S}\mathrm{U}\mathrm{H}}$, the EC (${\mathrm{Q}}_{\mathrm{E}}=50\mathrm{k}\mathrm{W}$), IE of evaporator (h₁₆), and all conditions of HTC are constant, but the OE of evaporator (h₁₈) increases by 4.82–5.11 kJ/kg, the MFR of LTC decreased by 1.62–1.93% depending on the energy equilibrium in the evaporator, and the MFR of HTC also increases by 0.23–0.28%, 0.21–0.26%, and 0.23–0.25%, respectively, because the cascade EC increases by 0.21–0.27% as ${∆\mathrm{T}}_{\mathrm{L},\mathrm{S}\mathrm{U}\mathrm{H}}$ increases.

Here, the EDR of the evaporator decreases by 0.013–0.075 kW, the EDR of the LTC expansion valve decreases by 0.02–0.024 kW, the EDR of the LTC compressor decreases by 0.032–0.037 kW, the EDR of the condenser increases slightly by 0.003–0.004 kW, 0.007–0.009 kW, and 0.007–0.008 kW, respectively, the EDR of the HTC expansion valve increases by 0.012–0.016 kW, 0.01–0.012 kW, and 0.01–0.013 kW, respectively, and the EDR of the HTC compressor increases by 0.02–0.04 kW, 0.02–0.03 kW, 0.02–0.04 kW, respectively. In other words, the EDRs of the evaporator, expansion valve, and compressor in LTC decreases slightly as the MFR of the LTC decreases, and the EDRs of the condenser, expansion valve, and compressor in HTC increases as the MFR of the HTC increases.

In particular, the EDR of CHX is obtained from Table 3 as the difference between the EDR of the CE (${\dot{\mathrm{E}\mathrm{x}}}_{\mathrm{F},\mathrm{C}\mathrm{A}\mathrm{S}})$ and the EDR of the cascade condenser (${\dot{\mathrm{E}\mathrm{x}}}_{\mathrm{P},\mathrm{C}\mathrm{A}\mathrm{S}}$). That is, as ${∆\mathrm{T}}_{\mathrm{L},\mathrm{S}\mathrm{U}\mathrm{H}}$ increases, ${\dot{\mathrm{E}\mathrm{x}}}_{\mathrm{F},\mathrm{C}\mathrm{A}\mathrm{S}}$ increases by 0.021–0.026 kW, 0.02–0.03 kW, and 0.02–0.03 kW, respectively, and ${\dot{\mathrm{E}\mathrm{x}}}_{\mathrm{P},\mathrm{C}\mathrm{A}\mathrm{S}}$ decreases by 0.237–0.267 kW, and therefore ${\dot{\mathrm{E}\mathrm{x}}}_{\mathrm{D},\mathrm{C}\mathrm{A}\mathrm{S}}$ increases by 0.264–0.287 kW, 0.264–0.288 kW, and 0.265–0.288 kW, respectively. Therefore, it is concluded that the system EDR increases because the CHX increases more than the EDR change of other components due to the increase in ${∆\mathrm{T}}_{\mathrm{S}\mathrm{U}\mathrm{H},\mathrm{L}\mathrm{T}\mathrm{C}}$.

And as shown in Figure 8, under constant conditions, when the three refrigerants are compared with each other with increasing ${∆\mathrm{T}}_{\mathrm{L},\mathrm{S}\mathrm{U}\mathrm{H}}$, the increase rate of system EDR and the decrease rate of system EE and COP are almost similar because the change is small for each refrigerant. Furthermore, as ${∆\mathrm{T}}_{\mathrm{L},\mathrm{S}\mathrm{U}\mathrm{H}}$ increases, the system EDR is the largest for R449A and the smallest for R448A, while the system EE and COP are the highest for R448A and the smallest for R449A. Looking at Figure 9, the expansion valve and compressor of HTC have the largest EDR for R404A and the smallest for R448A, while the condenser has the largest EDR for R448A and the smallest for R404A. In addition, CHX has the smallest EDR for R404A and the largest for R449A.

3.2. Effect of CT and ET

3.2.1. Effect of CT

This was analyzed to determine how the EDR and EE of the system and the EDR of each component change as ${\mathrm{T}}_{\mathrm{C}}$ increases under standard conditions.

As shown in Figure 10, as the ${\mathrm{T}}_{\mathrm{C}}$ increases by 5 °C from 30 °C to 50 °C, the system EDR increases by 1.57–6.15 kW, 1.49–3.9 kW, and 1.61–4.15 kW, respectively, and the system EE with R404A increases by 0.36–1.06% with ${\mathrm{T}}_{\mathrm{C}}$ up to 40 °C and then decreases by 0.39–1.37% thereafter, but the system EE with R448A and R449A increases by 0.24–1.12% and 0.15–1.07%, respectively, with ${\mathrm{T}}_{\mathrm{C}}$ up to 45 °C and then decreases by 0.37% and 0.41%, respectively. In addition, the system COP decreases by 7.19–10.24%, 6.93–7.95%, and 7.15–8.11%, respectively. The reason for the peculiar trend of the system EE is that as ${\mathrm{T}}_{\mathrm{C}}$ increases, the numerator of Formula (3) increases by 1.55–2.13 kW, 1.54–1.92 kW, and 1.56–1.97 kW, respectively, and the denominator increases by 3.12–8.28 kW, 3.03–5.82 kW, and 3.17–6.12 kW, respectively, and therefore the increase rate of the system EE gradually decreases and then the system EE decreases. Also, the inflection point of R404A occurs when ${\mathrm{T}}_{\mathrm{C}}$ is 40 °C, while the inflection point of R448A and R449A occurs when ${\mathrm{T}}_{\mathrm{C}}$ is 45 °C, and these differences are due to the refrigerant characteristics such as molar mass, critical temperature and critical pressure in Table 2.

Under constant conditions, a comparison of the three refrigerants with increasing ${\mathrm{T}}_{\mathrm{C}}$ shows that the increase rate in system EDR is the greatest for R404A and smallest for R448A, and that the system EDR is the smallest for R404A below approximately 38 °C and smallest for R448A above approximately 38 °C, largest for R449A below approximately 43 °C and largest for R404A above approximately 43 °C. Furthermore, with the increase in ${\mathrm{T}}_{\mathrm{C}}$, the system EE shows that R404A is the largest below approximately 38 °C and R448A is the largest above approximately 38 °C, and R449A is the smallest below approximately 43 °C and R404A is the smallest above approximately 43 °C. In other words, the system EDR shows the opposite trend to that of the system EE and COP.

As shown in Figure 11, since the conditions of the LTC are constant, the EDRs of the evaporator, compressor and expansion valve of the LTC are constant, and the EDR of the CHX decreases slightly by 0.07–0.013 kW, 0.005–0.007 kW, and 0.006–0.009 kW, respectively, while the EDR of the condenser, the expansion valve and compressor of the HTC increases. The reason for the decrease in EDR of CHX is that the OE (h₁₈) and outlet entropy (s₁₈) of the CE are constant, but the IE (h₁₆) and inlet entropy (s₁₆) of the CE increase, and the enthalpy and entropy difference between the inlet and outlet of the CE decreases accordingly. In addition, the MFR of HTC increases by 6.75–11.92%, 4.89–7.39%, and 5.33–8.26%, respectively, but the EDR of CHX decreases because the effect of the decrease in enthalpy and entropy difference of the CE inlet and outlet is slightly larger. The EDRs of the condenser, compressor and expansion valve of HTC increase significantly with the increase in the MFR of HTC. In particular, the expansion valve and compressor of HTC have the largest EDR magnitude and increase rate for R404A and the smallest EDR magnitude and increase rate for R448A, the condenser has the smallest EDR for R404A and the largest EDR for R448A, and CHX has the smallest EDR for R404A and the largest EDR for R449A.

3.2.2. Effect of ET

Under standard conditions, the EDR, EE, and EDR of the system and each component change were analyzed as ${\mathrm{T}}_{\mathrm{E}}$ increases.

As shown in Figure 12, as ${\mathrm{T}}_{\mathrm{E}}$ increases from −50 °C to −30 °C in 5 °C increments, the system EDR decreases by 2.4–4.63 kW, 2.39–4.61 kW, and 2.42–4.65 kW, respectively, and the system EE increases by 0.6–2.73%, 0.63–2.75%, and 0.55–2.66% to −35 °C and then decrease by 0.17%, 0.17%, and 0.23%, respectively, while the system COP increases by 12–13.23%, 12.02–13.29%, and 11.96–13.1%, respectively. The reason why the system EE shows a tendency to increase and then decrease is that as ${\mathrm{T}}_{\mathrm{E}}$ increases, the values of the numerator in Formula (3) become smaller by 1.43–1.7 kW, 1.43–1.7 kW, and 1.43–1.71 kW, respectively, and the values of the denominator become smaller by 3.83–6.33 kW, 3.82–6.31 kW, and 3.85–6.36 kW, respectively. So, as ${\mathrm{T}}_{\mathrm{E}}$ increases, the rate of increase decreases until around −35 °C and then decreases at −30 °C.

The comparison of the three refrigerants as ${\mathrm{T}}_{\mathrm{E}}$ increases under constant conditions is shown below. The rate of decrease in system EDR varies little between refrigerants, with the magnitude of the system EDR being largest for R449A and smallest for R448A. The system EE and COP reverse the trend of the system EDR, with R448A being the largest and R449A being the smallest.

As can be seen in Figure 13, the EDR of the evaporator, condenser, CHX, and the compressor and expansion valve of HTC and LTC all show a decreasing trend as ${\mathrm{T}}_{\mathrm{E}}$ increases. Analyzing the reasons for this, it can be concluded that as ${\mathrm{T}}_{\mathrm{E}}$ increases, the enthalpy at the inlet of the evaporator (h₁₆) is constant, but the enthalpy at the outlet of the evaporator (h₁₈) increases, and therefore the MFR of the LTC decreases due to the thermal equilibrium of the evaporator with the EC, and the compressor power consumption of the LTC also decreases. Accordingly, the cascade EC is also reduced, and the MFR of the HTC is also reduced by the thermal equilibrium of the HTC and CHX under the constant condition of the HTC. In other words, it is judged that the EDR of all components is reduced by the reduction in MFR and compressor power of the HTC and LTC. In addition, when comparing R404A, R448A, and R449A refrigerants, it is confirmed that the refrigerant with the maximum value and the refrigerant with the minimum value are the same in the EDR of each component device according to the increase in DSC, DSH, and CT of HTC and LTC in the previous section.

3.3. Effect of CET and Temperature Difference of CHX

3.3.1. Effect of CET

Under standard conditions, the EDR and EE of the system and the EDR of each component change were analyzed as ${\mathrm{T}}_{\mathrm{C}\mathrm{A}\mathrm{S},\mathrm{E}}$ increases.

As shown in Figure 14, as ${\mathrm{T}}_{\mathrm{C}\mathrm{A}\mathrm{S},\mathrm{E}}$ increases by 5 °C from −25 °C to −5 °C, the system EDR decreases by 1.22–7.03 kW, 0.67–4.43 kW, and 0.62–4.16 kW, respectively, and then increases by 1.15–2.55 kW, 1.03–2.07 kW, and 1.02–2.04 kW, respectively, around the inflection point (approximately −15.6 °C, −15.9 °C, and −16 °C). And the system EE increases by 2.64–12.78%, 1.38–8.28%, and 1.27–7.65%, respectively, and then decreases by 2.48–5.09%, 2.14–4%, and 2.09–3.84%, respectively, at the inflection point. The system COP increases by 3.15–15.07%, 1.69–9.66%, and 1.49–8.94%, respectively, and then decreases by 2.92–6%, 2.53–4.68%, and 2.44–4.48%, respectively, at the inflection point.

The reason for this inflection point with increasing ${\mathrm{T}}_{\mathrm{C}\mathrm{A}\mathrm{S},\mathrm{E}}$ is that the sum of the EDRs of the components of the LTC increases by a small amount, but the sum of the EDRs of the components of the HTC decreases significantly compared to the LTC, as shown in Figure 15. Specifically, as A increases, the evaporator decreases slightly by 0.002–0.003 kW, but the LTC expansion valve and LTC compressor increase by 0.29–0.59 kW and 0.78–1.21 kW, respectively, and the EDR of CHX increases by 0.38–0.75 kW, 0.36–0.73 kW, and 0.38–0.74 kW for R404A, R448A, and R449A, respectively. On the other hand, the HTC expansion valve, which is a component of HTC, gradually decreases by 0.8–1.15 kW, 0.59–0.83 kW, and 0.64–0.89 kW, respectively, depending on the refrigerant, and the HTC compressor gradually decreases by 1.66–6.27 kW for R404A and 0.03–0.75 kW for R448A and 0.2–3.84 kW for R449A, respectively, and 0.19–3.7 kW for R448A and 0.19–3.7 kW for R449A, respectively, before increasing by 0.2 kW at −5 °C. And the condenser decreases by 0.05–1.06 kW for R404A, then increases by 0.03 kW at −5 °C, and decreases by 0.07–1.19 kW and 0.07–1.03 kW for R448A and R449A, respectively. In other words, as ${\mathrm{T}}_{\mathrm{C}\mathrm{A}\mathrm{S},\mathrm{E}}$ increases, the system EDR decreases due to the dominant effect of the decrease in HTC EDR at the beginning, but there is an inflection point because the decrease in HTC EDR becomes smaller and the increase in LTC EDR becomes larger. The trend of EDR in the condenser and HTC compressor decreases and then increases as ${\mathrm{T}}_{\mathrm{C}\mathrm{A}\mathrm{S},\mathrm{E}}$ increases, which is believed to be due to the fact that ${\dot{\mathrm{E}\mathrm{x}}}_{\mathrm{F},\mathrm{C}}$, ${\dot{\mathrm{E}\mathrm{x}}}_{\mathrm{P},\mathrm{C}}$, ${\dot{\mathrm{E}\mathrm{x}}}_{\mathrm{F},\mathrm{C}\mathrm{O}\mathrm{M}}$, and ${\dot{\mathrm{E}\mathrm{x}}}_{\mathrm{P},\mathrm{C}\mathrm{O}\mathrm{M}}$ decrease as ${\mathrm{T}}_{\mathrm{C}\mathrm{A}\mathrm{S},\mathrm{E}}$ increases, but the decrease in ${\dot{\mathrm{E}\mathrm{x}}}_{\mathrm{F},\mathrm{C}}$ and ${\dot{\mathrm{E}\mathrm{x}}}_{\mathrm{F},\mathrm{C}\mathrm{O}\mathrm{M}}$ is initially larger than the decrease in ${\dot{\mathrm{E}\mathrm{x}}}_{\mathrm{P},\mathrm{C}}$ and ${\dot{\mathrm{E}\mathrm{x}}}_{\mathrm{P},\mathrm{C}\mathrm{O}\mathrm{M}}$, but later the decrease in ${\dot{\mathrm{E}\mathrm{x}}}_{\mathrm{F},\mathrm{C}}$ and ${\dot{\mathrm{E}\mathrm{x}}}_{\mathrm{F},\mathrm{C}\mathrm{O}\mathrm{M}}$ is smaller than the decrease in ${\dot{\mathrm{E}\mathrm{x}}}_{\mathrm{P},\mathrm{C}}$ and ${\dot{\mathrm{E}\mathrm{x}}}_{\mathrm{P},\mathrm{C}\mathrm{O}\mathrm{M}}$, which reverses.

In Figure 14, comparing the three refrigerants as ${\mathrm{T}}_{\mathrm{C}\mathrm{A}\mathrm{S},\mathrm{E}}$ increases under constant conditions, the largest change in system EDR is for R404A and the smallest for R449A. In addition, the system EDR is greatest for R404A when ${\mathrm{T}}_{\mathrm{C}\mathrm{A}\mathrm{S},\mathrm{E}}$ is below approximately −19 °C and greatest for R449A thereafter, and the smallest system EDR is for R448A. It can be seen that the system EE and COP have the opposite trend to that of the system EDR. Furthermore, in Figure 13, the comparison of the three refrigerants with increasing ${\mathrm{T}}_{\mathrm{C}\mathrm{A}\mathrm{S},\mathrm{E}}$ under constant conditions shows that R404A has the largest EDR and R448A has the smallest EDR in HTC’s expansion valve and compressor. In the condenser, R448A has the highest EDR and R404A has the lowest EDR, and in CHX, R449A has the highest EDR and R404A has the lowest EDR.

3.3.2. Effect of Temperature Difference of CHX

Under standard conditions, the EDR and EE of the system and the EDR of each component change were analyzed as ${∆\mathrm{T}}_{\mathrm{C}\mathrm{A}\mathrm{S}}$ increases.

As shown in Figure 16, as ${∆\mathrm{T}}_{\mathrm{C}\mathrm{A}\mathrm{S}}$ increases by 2 °C from 1 °C to 9 °C, the system EDR increases by 1.58–1.84 kW, 1.57–1.83 kW, and 1.58–1.85 kW, system EE decreases by 2.95–3.15%, 2.96–3.16%, and 2.92–3.15%, respectively, and system COP decreases by 3.34–3.54%, 3.4–3.61%, and 3.36–3.57%, respectively. The reason for the increase in system EDR with increasing ${∆\mathrm{T}}_{\mathrm{C}\mathrm{A}\mathrm{S}}$ is as follows. As ${∆\mathrm{T}}_{\mathrm{C}\mathrm{A}\mathrm{S}}$ increases, the cascade condensation temperature increases while other conditions remain constant, and the cascade EC also increases, which is affected by the increase in LTC compressor power consumption. Therefore, while the operating conditions of HTC remain constant, ${\dot{\mathrm{m}}}_{\mathrm{H}\mathrm{T}\mathrm{C}}$ increases by 1.75–2.06%, 1.76–2.05%, and 1.75–2.06%, respectively, and ${\dot{\mathrm{m}}}_{\mathrm{L}\mathrm{T}\mathrm{C}}$ increases by 1.63–1.85% depending on the energy equilibrium in the evaporator due to the increase in the evaporator inlet enthalpy, although the evaporator outlet enthalpy and EC are constant. In other words, the EDR of each component of the CRS increases due to the dominant effect of the increase in MFR of HTC and LTC, which leads to an increase in the system EDR. In addition, the system EE and COP are considered to decrease due to the increase in system EDR.

Here, for each of the three refrigerants, R449A has the largest system EDR and R448A has the smallest. It can be seen that the system EE and COP follow the opposite trend of the system EDR.

As shown in Figure 17, under standard conditions, with the increase in ${∆\mathrm{T}}_{\mathrm{C}\mathrm{A}\mathrm{S}}$, the EDR of evaporator remains constant at 1.29 kW, the expansion valve and compressor of LTC increase by 0.15–0.19 kW and 0.34–0.41 kW, respectively, while the EDR of CHX increases by 0.74–0.83 kW, 0.75–0.84 kW, and 0.75–0.84 kW, respectively, depending on the refrigerant. In addition, the EDR of the condenser increases by 0.023–0.027 kW, 0.056–0.064 kW, and 0.05–0.059 kW, respectively, and the EDR of the HTC compressor increases by 0.22–0.25 kW, 0.2–0.23 kW, 0.21–0.24 kW, respectively. Finally, the EDR of the HTC expansion valve increases by 0.099–0.12 kW, 0.076–0.088 kW, 0.083–0.097 kW, respectively. And when comparing R404A, R448A, and R449A refrigerants according to the increase in ${∆\mathrm{T}}_{\mathrm{C}\mathrm{A}\mathrm{S}}$ under constant conditions, it is confirmed that the refrigerant with the maximum value and the refrigerant with the minimum value are the same in the EDR of each component according to the increase in DSC and DSH, CT and ET, and CET of HTC and LTC in the previous section.

3.4. Effect of IHX Efficiency of the HTC

Under standard conditions, the EDR and EE of the system and the EDR of each component change were analyzed as ${\mathsf{\eta }}_{\mathrm{H},\mathrm{I}\mathrm{H}\mathrm{X}}$ increases.

As shown in Figure 18, the system EDR decreased by 0.48–0.81 kW, 0.12–0.3 kW, and 0.26–0.43 kW for each 0.2 increment of ${\mathsf{\eta }}_{\mathrm{H},\mathrm{I}\mathrm{H}\mathrm{X}}$ in CRS from 0.2 to 0.8, respectively. The reason for the decrease in system EDR can be seen in Figure 19. While the EDR of the evaporator, expansion valve of LTC, and compressor are constant, the EDR of the condenser increases by 0.62–0.67 kW, 0.68–0.71 kW, and 0.63–0.67 kW for the three refrigerants, respectively, while the EDR of CHX increases by 0.006–0.007 kW, 0.004–0.005 kW, and 0.005–0.006 kW, respectively, and the EDR of the HTC IHX increases by 0.012–0.137 kW, 0.011–0.103 kW, and 0.006–0.105 kW, respectively. On the other hand, the EDR of the HTC expansion valve decreases by 0.68–1.02 kW, 0.5–0.71 kW, and 0.56–0.77 kW, respectively, and the EDR of the HTC compressor decreases by 0.49–0.56 kW, 0.35–0.38 kW, and 0.37–0.39 kW, respectively. Therefore, the system EDR is found to decrease because the sum of the components with increasing EDR is greater than the sum of the components with decreasing EDR. The reason for the decrease in EDR of HTC expansion valve and compressor is dominated by the effect of decreasing MFR of HTC by 5.06–6.43%, 3.86–4.63%, and 4.11–4.89%, respectively, and the reason for the increase in EDR of the condenser is that in the formula of Table 3, ${\dot{\mathrm{E}\mathrm{x}}}_{\mathrm{F},\mathrm{C}}$ is 0.62–0.67 kW, 0.68–0.71 kW, and 0.62–0.65 kW, respectively, and ${\dot{\mathrm{E}\mathrm{x}}}_{\mathrm{P},\mathrm{C}}$ decreases by 0.031–0.033 kW, 0.009–0.01 kW, and 0.015–0.017 kW, respectively. The EDR of HTC IHX is found to increase because the higher the IHX efficiency, the larger the heat capacity, and the EDR of CHX is found to increase because ${\dot{\mathrm{E}\mathrm{x}}}_{\mathrm{P},\mathrm{C}\mathrm{A}\mathrm{S}}$ is constant at 6.583 kW because the conditions of LTC are constant, but ${\dot{\mathrm{E}\mathrm{x}}}_{\mathrm{F},\mathrm{C}\mathrm{A}\mathrm{S}}$ increases by 0.006–0.007 kW, 0.001 kW, and 0.01 kW due to the effect of HTC subcooling.

Accordingly, the system EE increases by 0.56–2.19%, 0.11–1.02%, and 0.22–1.33%, respectively, and the system COP increases by 1.41–1.5%, 0.38–0.47%, and 0.67–0.76%, respectively. From these results, it can be concluded that even with a large heat capacity IHX, the system EE increases by approximately 4%, 2%, and 2.4%, respectively, and the system COP increases by approximately 4.4%, 1.2%, and 2.2%, respectively. This shows that applying IHX increases the system EE and COP, but the effect is marginal.

Furthermore, a comparative analysis of the three refrigerants as the ${\mathsf{\eta }}_{\mathrm{H},\mathrm{I}\mathrm{H}\mathrm{X}}$ of the CRS increases is shown in Figure 18. Figure 18 shows that the percentage decrease in system EDR is the largest for R404A and the smallest for R448A, and the largest system EDR is for R449A and the smallest for R404A. As shown in Figure 19, the EDRs of the evaporator, LTC expansion valve, and compressor are constant, but the EDRs of the HTC expansion valve, compressor, and IHX are the largest for R404A and the smallest for R448A, the EDRs of the condenser are the largest for R448A and the smallest for R404A, and the EDRs of the CHX are the largest for R449A and the smallest for R404A. Finally, the EDRs of the HTC IHX and CHX are not significant because the changes are minimal.

4. Conclusions

In this study, the performance characteristics of a CRS pairing R744 with R404A, R448A and R449A with an IHX are evaluated for supermarkets and hypermarkets. Under standard conditions, we analyzed how the EDR and EE of the system and the EDR of each component change when the important factors affecting CRS (DSH, DSC, and IHX efficiency of HTC, DSH of LTC, CT, ET, CET, and temperature difference of CHX) are varied over a wide range. The main conclusions are as follows.

• To minimize system EDR, the DSC, DSH, IHX efficiency, ET of HTC should be increased to the maximum, and the DSH, CT, and temperature difference of CHX of LTC should be reduced to the minimum.
• In terms of system EDR and EE, R448A is more favorable than R449A when comparing R448A and R449A as a replacement refrigerant for R404A. Therefore, R744/R448A CRS is recommended to replace R744/R404A CRS.
• Under the given standard conditions, the highest change in system EDR based on R448A is the ET, followed by the CT, CET, and temperature difference of CHX, and the change due to other variables was less than 1 kW. Therefore, it is recommended to proceed with the design by considering the ET, CT, CET, and temperature difference of CHX in that order.
• In addition, the highest change rate of system EE due to R448A is the CET, followed by the temperature difference of CHX, ET, and DSC of HTC, and the change rate due to other variables is about 1% and can be ignored. Therefore, it is recommended to consider it when designing according to the order of the highest change rate.
• In particular, in the case of CHX, the system EDR is the smallest and the system EE is the largest at the inflection point (approximately −15.6 °C, −15.9 °C, −16 °C) depending on R404A, R448A, and R449A.
• When R448A is used in CRS’s HTC, for every 0.2 increase in HTC IHX efficiency, the EE of the system increases by 0.11–1.02% and the COP of system increases by 0.38–0.47%. Therefore, IHX is not recommended when applying R448A for economic and efficiency reasons.
• In the EDR of CRS components, the HTC compressor is the largest component, followed by the HTC expansion valve, LTC compressor, CHX, condenser, and evaporator, with the LTC expansion valve being the smallest.