## Abstract

In this paper, the performance of R744 and R744/R170 mixed refrigerants in refrigeration and air source heat pump systems is studied by the simulation method. The change trend of coefficient of performance (COP), refrigeration/heat capacity, power consumption with discharge pressure, and the ratio of R744 is analyzed. In addition, optimal parameters of the system are discussed in detail with the change of evaporation temperature, outlet temperature of the gas cooler, and different proportions of R744. The results show that when the discharge pressure is 8–12 MPa, there is a critical ratio of R744. When the ratio of R744 is less than the critical ratio, the optimal pressure of the system increases with the increase of the ratio of R744, and when the ratio of R744 is higher than critical ratio, the optimal pressure of the system decreases with the increase of the ratio of R744. The change trend of COP with the ratio of R744 is first decreasing and then increasing, the optimal discharge temperature of the system increases with the increase of the ratio of R744, and the change trend of optimal discharge pressure with the ratio of R744 is first increasing and then decreasing. In addition, when the evaporation temperature is 233–253 K and the gas cooler outlet temperature is 308–318 K, the average optimal pressure and temperature of R744/R170 (25/75) are 11.64% and 8.06% lower than R744, respectively. And it is the most suitable refrigerant to replace R744. Finally, the optimal performance parameter correlations of R744, R744/R170 (25/75), R744/R170 (50/50), and R744/R170 (77.6/22.4) under the given conditions are fitted through the simulation data.

## 1 Introduction

Traditional refrigerants have been phased out due to the destruction of the ozone layer and the greenhouse effect [1]. Working fluids that exist in nature, rather than artificially synthesized, and have lower greenhouse effect potential values; R744 is widely used in refrigeration and heat pump fields due to its environment-friendly (ozone depleting potential (ODP) is 0, GWP is 1) and heat transfer characteristics [2]. Brandt et al. [3] studied the structure improvement scheme of the transcritical R744 circulation system in the household drum dryer. The results showed that the use of ejector and internal heat exchanger components can effectively improve the efficiency of the dryer and greatly reduce the energy consumption under the same drying time. Subei and Schmitz [4] studied the pipeline pressure drop of transcritical CO_{2} heat pump air conditioning by CFD and a one-dimensional model. The results showed that the pipeline pressure drop should not be simply ignored in the system simulation. Memory and Vetter [5] conducted a cooling experiment on a BMW car. The results showed that the rapid cooling time of the transcritical R744 air conditioning system is nearly 15 min shorter than that of R134a. Wang et al. [6] studied the charging characteristics of the transcritical R744 heat pump air conditioning and divided the charging into undercharging area, platform period, and overcharging area. Sian and Wang [7] conducted the simulation model of household roller dryers and compared the drying effect of R744 and R134a. The results showed that the outlet temperature and barrel temperature of the R744 drying system were higher, which increased the water removal rate of unit energy consumption by 13%. Dai et al. [8] studied R744 and a mixed refrigerant heat pump system composed of different low GWP gases. The results showed that in addition to higher energy utilization efficiency than traditional heat pumps, its annual operating environment effect, nitrogen oxide emissions, inhalable particulate matter emissions, and other indicators are significantly improved than primary energy combustion drying system. Wang et al. [9] studied the transcritical R744 air source heat pump hot water system. The results showed that the system can stably prepare domestic hot water above 80 ℃ under almost all environmental conditions.

However, R744 is faced with two major problems. First, the discharge pressure is too high. Second, the efficiency of the cycle is low. These problems can be solved by improving the system and mixing other low GWP working fluids with R744. In terms of the system, the system performance can be improved by using multistage compression, mechanical undercooling/overheating, ejector, vortex tube, and expansion agent [10–14].

In terms of the R744 mixture, Zhang et al. [15] analyzed the system performance by using R744/R290 with different ratios. The results showed that when the mass fraction of R744 is greater than 0.78, the system achieves optimal coefficient of performance (COP) and discharge pressure. Dai et al. [16] studied the performance of a variety of R744 environment-friendly mixtures used in heat pumps. The results showed that R744/R41 has the best performance and the lowest pressure. Yu et al. [17] studied the performance of automobile air conditioners by using CO_{2}/R290 as the refrigerant. The results showed that by increasing the mass fraction of R41, the COP of pure R744 in heating and cooling modes can be increased by 14.5% and 25.7%, respectively, and the optimal pressure correlation of R744/R41 is fitted. Sun et al. [18] studied the performance of water–water heat pump by using CO_{2}/R32 as the refrigerant. The results showed that when the mass fraction of carbon dioxide reaches 60%, the heating COP and refrigeration COP of the system increased by 23.3% and 65.2%, respectively. Nicola et al. [19] analyzed the performance of the cascade refrigeration cycle with R744/R32 mixture. The results showed that the R744/R32 mixture could be considered as an attractive choice for the low-temperature loop of the cascade system. Fan et al. [20] studied the performance of heat pumps by using R744/R290 as the alternative working medium of R22. The results showed that the when mass ratio of R744 is 20%, the system performance is optimal, and its COP_{h} and Q_{h} (heating capacity) increased by 12.62% and 34.24%, respectively. Onaka et al. [21] analyzed the performance of the heat pump water heater with CO_{2}/RE170 azeotropic mixture; the mass fraction of CO_{2} ranged from 0% to 100%. The results showed that there was a corresponding maximum COP of the system for mixtures with different proportions under constant discharge pressure. Afroz et al. [22] studied the heat transfer coefficient and pressure drop of in-tube condensation of CO_{2}/DME mixture. The results showed that the heat transfer coefficient and pressure drop decreased with the increase of CO_{2} mass fraction in the mixture. Hakkaki-Fard et al. [23] found a numerical model to study the performance of air heat sources with different refrigerant mixtures under cold climate conditions. The results showed that the heat pump with CO_{2}/R32 (20/80) mixture has the best performance. Song et al. [24] analyzed the R134a/CO_{2} cascade refrigeration system at different condensing temperatures by experiment and using the energy consumption analysis. The results showed that when the high-temperature evaporation temperature decreases, the system energy consumption changes between 7.6% and 14.0%. Lee et al. [25] designed the NH_{3}/CO_{2} cascade refrigeration system through thermodynamic analysis and calculation. The results showed that with the increase of low-temperature evaporation temperature, the decrease of high-temperature condensation temperature, and intermediate heat exchange temperature difference, the coefficient of performance of the system is improved, the calculation results are in good agreement with the existing experimental data, and the best intermediate temperature fitting formula for the system is proposed. Zhu et al. [26] studied the flow boiling heat transfer characteristics of CO_{2}/R290 by experiment. The results showed that under the same conditions, the flow boiling heat transfer coefficient increased with the increase of CO_{2} concentration. Sengers and Jin [27] studied the physical properties of the mixture of CO_{2} and ethane. The results showed that ethane and CO_{2} have similar critical point properties, and the CO_{2}/ethane binary mixture is an azeotropic mixture at a specific ratio.

Because the refrigerant mixture of R744 can be divided into azeotropic and nonazeotropic. For the nonazeotropic working medium, if there is leakage, it will lead to a change in the ratio and then affect the overall system performance. If the azeotropic refrigerant mixture leaks, the impact on the system performance is very small [28].

At present, only R41 and R170 can be mixed with R744 to form azeotropic refrigerants. R41 is not suitable for large-scale promotion due to its high price, while R170 is low in price and easy to obtain. At the same time, the mixing of R744 and R170 provides a certain possibility for reducing system pressure. In addition, in order to promote the engineering application of refrigeration in cold storage and heating in extremely cold areas, research on low evaporation temperature should be emphasized. Therefore, this paper focuses on R744 and R744/R170 mixture in the transcritical cycle system under the condition of low evaporation temperature, and the refrigeration and heating performance of R744/R170 are compared and analyzed comprehensively. At the same time, the correlation formula of COP, optimal pressure, and discharge temperature of R744/R170 under different ratios is fitted.

## 2 Working Fluid Characteristics

In this paper, R744/R170 mixtures with different ratios were used in the refrigeration and air source heat pump system, in which R744 accounted for 25%, 50%, 77.6%, and 100%. The temperature and pressure at the critical point are obtained by NIST REFPROP9.0, as shown in Table 1. The GWP and ODP after mixing are calculated by Eq. (1) [29], as shown in Table 2.

## 3 System Introduction and Model Establishment

### 3.1 System Introduction.

Because the critical evaporation temperature of R744 and its mixture is low, the transcritical cycle is adopted in both refrigeration and heating systems. In Fig. 1, (a) is the system schematic diagram of refrigeration in the low-temperature environment, and (*b *) is the system schematic diagram of the air source heat pump. Figures 1 and 2 are the corresponding diagrams of *P*–*h* and *T–s*. The whole system consists of a compressor, gas cooler, a throttle valve, an evaporator, and an internal heat exchanger. In Fig. 2, “2S” and “2” represent the state points of the working medium after isentropic compression and actual compression, respectively.

### 3.2 Model Assumptions.

The analysis content of this paper is based on the following assumptions:

All systems are in steady-state operation.

Ignore the pressure drop and heat loss of the connecting pipe and heat exchanger.

The compressor is adiabatic compression but nonisentropic.

At the outlet of the evaporator, the refrigerant is saturated.

The refrigerant is free of lubricant oil.

### 3.3 Energy Thermodynamic Model.

The design conditions of the transcritical system used for refrigeration and air source heat pump are shown in Table 3.

Refrigeration system | Air source heat pump system |
---|---|

External/internal ambient temperature /K 303/274 | External and inlet/outlet of hot water temperature /K |

274/290/338 |

Refrigeration system | Air source heat pump system |
---|---|

External/internal ambient temperature /K 303/274 | External and inlet/outlet of hot water temperature /K |

274/290/338 |

Note: Energy thermodynamic model

_{h}is given by:

_{e}is given by:

### 3.4 Simulation Steps.

First, given a high-pressure range, the variation trend of COP, refrigeration/heat, and power consumption with high pressure is calculated. In addition, because there is an optimal high pressure in the transcritical cycle, which corresponds to the maximum COP of the system, it is very important to determine the optimal high pressure. For R744/R170 mixed refrigerant in the transcritical cycle, there is no correlation to calculate the optimal high pressure and other related system performance. Therefore, in this paper, the optimal upper operating pressure of R744/R170 mixed refrigerant systems was determined by using an iterative calculation method. All simulation processes are calculated by engineering software ees (Engineering Equation Solver). The calculation method is shown in Fig. 3: (a) the calculation process of system performance parameters corresponding to different high-pressure inputs and Fig. 3 (b) the calculation process of system optimal pressure and system performance parameters under optimal pressure.

## 4 Results

In this section, the performance of the refrigeration system and heat pump system using pure CO_{2} and CO_{2}/R170 mixture as a refrigerant is analyzed and compared under a wider range of conditions, e.g., *T*_{e} is 233–253 K, *T*_{g} is 308–318 K, and discharge pressure is 8–12 MPa. At the same time, the correlation formula of COP, optimal pressure, and discharge temperature of R744/R170 under different ratios is fitted (Fig. 4).

### 4.1 Variation of System Performance Parameters With High Pressure.

Figures 5–8 show the change of performance parameters (including COP, refrigeration/heat capacity, power consumption, and discharge temperature) of mixed refrigerant under the influence of different factors. It can be seen from Fig. 5 that there will be an optimal pressure (that is, the corresponding pressure of the high-pressure side when the COP of the system reaches the maximum value) in a certain pressure range. When R744 accounts for 25%, the optimal pressure is the lowest, and when R744 accounts for 77.6%, the optimal pressure is the highest. It is worth noting that when R744 accounts for 100%, the optimal pressure is less than that when R744 accounts for 77.6%. Therefore, under the same working conditions, the maximum optimal pressure does not increase monotonously with the increase of R744. In addition, it can be inferred that there is a critical ratio of R744; when the ratio of R744 is less than the critical ratio, the optimal pressure of the system increases with the increase of R744, and when the ratio of R744 is higher than the critical ratio, the optimal pressure of the system decreases with the increase of the ratio of R744. The reason for this phenomenon is that, at first, with the increase of the ratio of R744 in the mixture, the influence of R744 in the mixture on the optimal pressure is more and more dominant than that of R170, so the optimal pressure becomes larger and larger. When the ratio of R744 and R170 reaches a certain range, because of the interaction of their physical properties, the optimal pressure is even greater than that of pure R744. Then, with the increase of the ratio of R744, the overall properties of the mixture are closer to that of pure R744, and the optimal pressure gradually approaches to that of pure R744, which makes the optimal pressure decrease.

The COP of R744 is much higher than that of other mixed refrigerants when the pressure of high-pressure side is higher. The COP of R744 is much lower than that of other mixed refrigerants when the pressure of high-pressure side is lower. The COP of the R744 system is the highest when the ratio of R744 is 25%. Therefore, in order to solve the problem of the high-pressure side of pure R744, so that reducing the pressure will not reduce the system COP too much, R744/R170 can be selected to replace R744 with a ratio of 25/75. Due to the large temperature difference between high-temperature refrigerant on the exothermic side and external low-temperature working fluid in the transcritical cycle, the system is very suitable for heating hot water. COP of the air source heat pump system is significantly higher than that of the refrigeration system.

Figure 6 shows the change trend of power consumption with the increase of high-pressure side pressure. It can be found that the power consumption of all working fluids increases with the increase of high-pressure side pressure. Under the same working conditions, the power consumption does not change monotonously with the increase of the ratio of R744. It can be seen from Fig. 6 that the refrigeration/heat capacity (*q*_{e} and *q*_{h}) increases with the increase of high-pressure side pressure, and the heating capacity is significantly higher than the cooling capacity. In some high-pressure side pressure ranges, the increase of refrigeration/heat capacity of pure R744 is significantly higher than that of other mixed refrigerants. In addition, when R744 accounts for 25%, the refrigeration/heat capacity of the system is the largest, and the overall trend is more stable than other refrigerants. Figure 7 shows the change of discharge temperature with the pressure of high-pressure side. There is no doubt that the increase of pressure of the high-pressure side increases the discharge temperature. The discharge temperature of R744 is significantly higher than that of other refrigerants, and when the proportion of R744 is 50% and 77.6%, the discharge temperature is lower. However, when the pressure of the high-pressure side is low, the corresponding discharge temperature is not conducive to heating hot water with a high temperature compared with R744/R170 (25/75). Therefore, from the perspective of discharge temperature, R744/R170 (25/75) is the most appropriate, because compared with pure R744, it can not only reduce the discharge temperature but also ensure the heating of high-temperature hot water. From the above analysis, it can be seen that under the same working conditions, when the ratio of R744 is 25%, the optimal pressure is the lowest. At the same time, under the premise of low pressure on the high-pressure side, the COP is the highest and the discharge temperature is moderate. Therefore, compared with other mixed refrigerants, R744/R170 is more suitable to replace R744 at the ratio of (25/75).

### 4.2 Factors Affecting Optimal Performance Parameters of Systems.

Figure 8 shows the variation trend of performance parameters of each working medium used in the refrigeration system with evaporation temperature and outlet temperature of the gas cooler. It can be seen from the figure that COP increases with the increase of *T*_{e} and decreases with the increase of *T*_{g}. The optimal discharge temperature and optimal pressure decrease with the increase of evaporation temperature and increase with the increase of outlet temperature of the gas cooler. In the system, when the evaporation temperature reaches 253 K and the outlet temperature of the gas cooler reaches 308 K, the corresponding COP is the maximum, and the discharge temperature and the optimal discharge pressure are the minimum; therefore, *T*_{e} of 253 K and *T*_{g} of 308 K are the optimal operating conditions for the system. Tables 4 and 5 show the change of system performance parameters of each working medium with evaporation temperature and outlet temperature of the gas cooler.

Working medium | T_{g}/K | T_{e}/K | COP (increased) | T-Discharge/K (decreased) | P-Discharge (decreased) |
---|---|---|---|---|---|

R744 | 308 | 233–253 | 61.2% | 42.78 | 0.48 |

R744/R170 (25/75) | 308 | 233–253 | 59.3% | 23.85 | 0.82 |

R744/R170 (50/50) | 308 | 233–253 | 56.1% | 28.06 | 1.03 |

R744/R170 (77.6/22.4) | 308 | 233–253 | 58.1% | 34.65 | 0.97 |

Working medium | T_{g}/K | T_{e}/K | COP (increased) | T-Discharge/K (decreased) | P-Discharge (decreased) |
---|---|---|---|---|---|

R744 | 308 | 233–253 | 61.2% | 42.78 | 0.48 |

R744/R170 (25/75) | 308 | 233–253 | 59.3% | 23.85 | 0.82 |

R744/R170 (50/50) | 308 | 233–253 | 56.1% | 28.06 | 1.03 |

R744/R170 (77.6/22.4) | 308 | 233–253 | 58.1% | 34.65 | 0.97 |

Working medium | T_{g}/K | T_{e}/K | COP (decreased) | T-Discharge/K (increased) | P-Discharge/MPa (increased) |
---|---|---|---|---|---|

R744 | 308–318 | 233 | 24.2% | 34.55 | 3.72 |

R744/R170 (25/75) | 308–318 | 233 | 25.5% | 24.17 | 3.3 |

R744/R170 (50/50) | 308–318 | 233 | 24.3% | 22.99 | 3.61 |

R744/R170 (77.6/22.4) | 308–318 | 233 | 23.2% | 25.02 | 3.8 |

Working medium | T_{g}/K | T_{e}/K | COP (decreased) | T-Discharge/K (increased) | P-Discharge/MPa (increased) |
---|---|---|---|---|---|

R744 | 308–318 | 233 | 24.2% | 34.55 | 3.72 |

R744/R170 (25/75) | 308–318 | 233 | 25.5% | 24.17 | 3.3 |

R744/R170 (50/50) | 308–318 | 233 | 24.3% | 22.99 | 3.61 |

R744/R170 (77.6/22.4) | 308–318 | 233 | 23.2% | 25.02 | 3.8 |

It can be seen from Tables 4 and 5 that the influence of the outlet temperature of the gas cooler on discharge pressure is greater than that of evaporation temperature, while evaporation temperature has more obvious influence on COP and discharge temperature. In the same range of evaporation temperature and gas cooler outlet temperature, with the increase of the ratio of R744, the increased range of COP is basically consistent, and the increased range of the discharge temperature and the discharge pressure is more obvious than COP.

In addition, under the same evaporation temperature and outlet temperature of the gas cooler, the maximum COP first decreases and then increases with the increase of the ratio of R744, and when the ratio of R744 is 50%, the COP is the lowest. The optimal pressure of the system first increases and then decreases with the increase of the ratio of R744. With the increase of the ratio of R744, the optimal discharge temperature of the system increases gradually. It can be seen that the optimal pressure and optimal discharge temperature of the system exhibit extreme points as the ratio of R744 changes. However, overall, when the ratio of R744 is 25%, the system achieves the lowest optimal pressure and optimal discharge temperature, which makes the operation of the system safer and more stable.

The performance parameters of the air source heat pump system change with evaporation temperature, and gas cooler outlet temperature are shown in Figs. 9–11. According to Fig. 9, in the air source heat pump system, the COP of pure R744 is the highest; there is no significant difference in COP between R744 accounting for 25% and 77.6%, while the system COP is the smallest when the ratio of R744 is 50%. When the evaporation temperature is 233–253 K and the outlet temperature of the gas cooler is 308–318 K, the COP of the system increases with the increase of the evaporation temperature and decreases with the increase of the outlet temperature of the gas cooler. When the evaporation temperature is 253 K and the outlet temperature of the gas cooler is 308 K, the COP of the system reaches the maximum value. When the ratio of R744 is 25%, 50%, 77.6%, and 100%, the difference between maximum and minimum COP was 0.76, 0.69, 0.73 and 0.9, respectively. Therefore, under the premise of using the same refrigerant, the design of relatively higher evaporation temperature and lower outlet temperature of the gas cooler is the key factor to improve the COP of the system.

Figure 10 shows the variation of the optimal pressure (*P*_{opt}) with the evaporation temperature and the outlet temperature of the gas cooler. It can be seen that when the ratio of R744 is 25%, the optimal pressure of the system is obviously lower than that of the other three. When the evaporation temperature is 233–253 K and the outlet temperature of the gas cooler is 308–318 K, the optimal pressure of the system decreases with the increase of the evaporation temperature and increases with the increase of the outlet temperature of the gas cooler. When the evaporation temperature is 253 K and the outlet temperature of the gas cooler is 308 K, the optimal system pressure of each working medium reaches the minimum value. And when the ratio of R744 is 25%, 50%, 77.6%, and 100%, the difference between the maximum and minimum optimal pressure is 4.04 MPa, 4.77 MPa, 4.71 MPa, and 4.16 MPa, respectively. Therefore, under the same working medium, in order to reduce the optimal pressure of the system and avoid too high pressure on the high-pressure side, a higher evaporation temperature and a lower outlet temperature of the gas cooler should be designed.

Figure 11 shows the optimal discharge temperature changes with the *T*_{e} (evaporation temperature) and *T*_{g} (outlet temperature of the gas cooler). It can be seen that when the ratio of R744 is 25%, the optimal discharge temperature of the system is significantly lower than that of the other three. When the evaporation temperature is 253 K and the outlet temperature of the gas cooler is 308 K, the optimal discharge temperature of each working medium reaches the minimum value. When the ratio of R744 is 25%, 50%, 77.6%, and 100%, the difference between the maximum and minimum optimal discharge temperatures is 48.02 °C, 51.05 °C, 59.67 °C, and 77.33 °C, respectively. Therefore, under the same working medium, in order to reduce the optimal discharge temperature of the system, but at the same time, the discharge temperature should not be too low, it is necessary to design appropriate evaporation temperature and gas cooler outlet temperature.

### 4.3 Correlation Fitting of Optimal Performance Parameters.

*P*

_{opt}is given by Eq. (12). In the present study, because the same compression and internal heat exchanger are specified, the effects of the internal heat exchanger and isentropic efficiency of the compressor are ignored, hence ignoring effects of

*ε*

_{is}and

*β*; at the same time,

*P*

_{2}is determined by

*T*

_{0}and

*T*

_{3}, and the expression of optimum condition is as follows (Eq. (13)):

As shown in Table 6, when the evaporation temperature is 233–253 K, the outlet temperature of the gas cooler is 308–318 K. Based on the data calculated by the simulation software, the correlations of the optimal performance parameters of pure R744 and its mixture under the influence of *T*_{e} and *T*_{g} are fitted. The establishment of these correlations provides a certain reference value for system performance analysis or practice under different operating conditions in the future.

Refrigeration of R744 | Sum of the squared errors | ||
---|---|---|---|

COP | $COP=46.88\u22120.4151Tg+0.1769Te+0.001Tg2+0.0003Te2\u22120.001TgTe$ | (14) | 0.12% |

P_{opt} | $Popt=\u221248.59\u22120.4397Tg+0.6432Te+0.00218Tg2+0.00013Te2\u22120.0023TgTe$ | (15) | 0.14% |

Discharge temperature | $Td=\u22123237+23.38Tg\u22121.956Te\u22120.02359Tg2+0.01365Te2\u22120.02212TgTe$ | (16) | 1.48% |

Refrigeration of R744 (77.6/22.4) | |||

COP | $COP=1.58\u22120.1646Tg+0.1486Te+0.00054Tg2+0.00027Te2\u22120.00083TgTe$ | (17) | 0.15% |

P_{opt} | $Popt=55.05\u22120.9763Tg+0.5139Te+0.003Tg2+0.0003Te2\u22120.0023TgTe$ | (18) | 0.04% |

Discharge temperature | $Td=\u22121231+11.42Tg\u22122.565Te\u22120.01Tg2+0.008Te2\u22120.01TgTe$ | (19) | 4% |

Refrigeration of R744 (50/50) | |||

COP | $COP=13.01\u22120.181Tg+0.1494Te+0.0005Tg2+0.0002Te2\u22120.0007TgTe$ | (20) | 0.11% |

P_{opt} | $Popt=61.94\u2212Tg+0.5084Te+0.003Tg2+0.0004Te2\u22120.002TgTe$ | (21) | 0.08% |

Discharge temperature | $Td=\u22121273+10.85Tg\u22121.685Te\u22120.01Tg2+0.005Te2\u22120.007TgTe$ | (22) | 2.7% |

Refrigeration of R744 (25/75) | |||

COP | $COP=14.42\u22120.1871Tg+0.1476Te+0.0005Tg2+0.0002Te2\u22120.0008TgTe$ | (23) | 0.04% |

P_{opt} | $Popt=43.72\u22120.96Tg+0.6219Te+0.003Tg2+0.0003Te2\u22120.002TgTe$ | (24) | 0.05% |

Discharge temperature | $Td=\u22121692+12.55Tg\u22120.83Te\u22120.012Tg2+0.005Te2\u22120.009TgTe$ | (25) | 3.8% |

Heating of R744 | |||

COP | $COP=6.962\u22120.147Tg+0.167Te+0.0005Tg2+0.0002Te2\u22120.0008TgTe$ | (26) | 0.3% |

P_{opt} | $Popt=\u221242.16\u22120.4485Tg+0.6047Te+0.002Tg2+0.0001Te2\u22120.0023TgTe$ | (27) | 0.05% |

Discharge temperature | $Td=\u22123237+23.38Tg\u22121.956Te\u22120.02359Tg2+0.01365Te2\u22120.02212TgTe$ | (28) | 2.1% |

Heating of R744 (77.6/22.4) | |||

COP | $COP=8.186\u22120.14Tg+0.14Te\u22120.0005Tg2+0.0003Te2\u22120.0008TgTe$ | (29) | 0.6% |

P_{opt} | $Popt=55.05\u22120.9763Tg+0.5139Te+0.003Tg2+0.0003Te2\u22120.0023TgTe$ | (30) | 0.15% |

Discharge temperature | $Td=\u22121231+11.42Tg\u22122.565Te\u22120.01Tg2+0.008Te2\u22120.01TgTe$ | (31) | 3.8% |

Heating of R744 (50/50) | |||

COP | $COP=10.84\u22120.155Tg+0.142Te+0.0005Tg2+0.0002Te2\u22120.0008TgTe$ | (32) | 0.5% |

P_{opt} | $Popt=61.94\u2212Tg+0.5084Te+0.003Tg2+0.0004Te2\u22120.002TgTe$ | (33) | 0.19% |

Discharge temperature | $Td=\u22121273+10.85Tg\u22121.685Te\u22120.01Tg2+0.005Te2\u22120.007TgTe$ | (34) | 2.9% |

Heating of R744 (25/75) | |||

COP | $COP=11.48\u22120.1627Tg+0.1482Te+0.0005Tg2+0.0002Te2\u22120.0008TgTe$ | (35) | 0.7% |

P_{opt} | $Popt=43.72\u22120.96Tg+0.6219Te+0.003Tg2+0.0003Te2\u22120.002TgTe$ | (36) | 0.16% |

Discharge temperature | $Td=\u22121692+12.55Tg\u22120.83Te\u22120.012Tg2+0.005Te2\u22120.009TgTe$ | (37) | 4% |

Refrigeration of R744 | Sum of the squared errors | ||
---|---|---|---|

COP | $COP=46.88\u22120.4151Tg+0.1769Te+0.001Tg2+0.0003Te2\u22120.001TgTe$ | (14) | 0.12% |

P_{opt} | $Popt=\u221248.59\u22120.4397Tg+0.6432Te+0.00218Tg2+0.00013Te2\u22120.0023TgTe$ | (15) | 0.14% |

Discharge temperature | $Td=\u22123237+23.38Tg\u22121.956Te\u22120.02359Tg2+0.01365Te2\u22120.02212TgTe$ | (16) | 1.48% |

Refrigeration of R744 (77.6/22.4) | |||

COP | $COP=1.58\u22120.1646Tg+0.1486Te+0.00054Tg2+0.00027Te2\u22120.00083TgTe$ | (17) | 0.15% |

P_{opt} | $Popt=55.05\u22120.9763Tg+0.5139Te+0.003Tg2+0.0003Te2\u22120.0023TgTe$ | (18) | 0.04% |

Discharge temperature | $Td=\u22121231+11.42Tg\u22122.565Te\u22120.01Tg2+0.008Te2\u22120.01TgTe$ | (19) | 4% |

Refrigeration of R744 (50/50) | |||

COP | $COP=13.01\u22120.181Tg+0.1494Te+0.0005Tg2+0.0002Te2\u22120.0007TgTe$ | (20) | 0.11% |

P_{opt} | $Popt=61.94\u2212Tg+0.5084Te+0.003Tg2+0.0004Te2\u22120.002TgTe$ | (21) | 0.08% |

Discharge temperature | $Td=\u22121273+10.85Tg\u22121.685Te\u22120.01Tg2+0.005Te2\u22120.007TgTe$ | (22) | 2.7% |

Refrigeration of R744 (25/75) | |||

COP | $COP=14.42\u22120.1871Tg+0.1476Te+0.0005Tg2+0.0002Te2\u22120.0008TgTe$ | (23) | 0.04% |

P_{opt} | $Popt=43.72\u22120.96Tg+0.6219Te+0.003Tg2+0.0003Te2\u22120.002TgTe$ | (24) | 0.05% |

Discharge temperature | $Td=\u22121692+12.55Tg\u22120.83Te\u22120.012Tg2+0.005Te2\u22120.009TgTe$ | (25) | 3.8% |

Heating of R744 | |||

COP | $COP=6.962\u22120.147Tg+0.167Te+0.0005Tg2+0.0002Te2\u22120.0008TgTe$ | (26) | 0.3% |

P_{opt} | $Popt=\u221242.16\u22120.4485Tg+0.6047Te+0.002Tg2+0.0001Te2\u22120.0023TgTe$ | (27) | 0.05% |

Discharge temperature | $Td=\u22123237+23.38Tg\u22121.956Te\u22120.02359Tg2+0.01365Te2\u22120.02212TgTe$ | (28) | 2.1% |

Heating of R744 (77.6/22.4) | |||

COP | $COP=8.186\u22120.14Tg+0.14Te\u22120.0005Tg2+0.0003Te2\u22120.0008TgTe$ | (29) | 0.6% |

P_{opt} | $Popt=55.05\u22120.9763Tg+0.5139Te+0.003Tg2+0.0003Te2\u22120.0023TgTe$ | (30) | 0.15% |

Discharge temperature | $Td=\u22121231+11.42Tg\u22122.565Te\u22120.01Tg2+0.008Te2\u22120.01TgTe$ | (31) | 3.8% |

Heating of R744 (50/50) | |||

COP | $COP=10.84\u22120.155Tg+0.142Te+0.0005Tg2+0.0002Te2\u22120.0008TgTe$ | (32) | 0.5% |

P_{opt} | $Popt=61.94\u2212Tg+0.5084Te+0.003Tg2+0.0004Te2\u22120.002TgTe$ | (33) | 0.19% |

Discharge temperature | $Td=\u22121273+10.85Tg\u22121.685Te\u22120.01Tg2+0.005Te2\u22120.007TgTe$ | (34) | 2.9% |

Heating of R744 (25/75) | |||

COP | $COP=11.48\u22120.1627Tg+0.1482Te+0.0005Tg2+0.0002Te2\u22120.0008TgTe$ | (35) | 0.7% |

P_{opt} | $Popt=43.72\u22120.96Tg+0.6219Te+0.003Tg2+0.0003Te2\u22120.002TgTe$ | (36) | 0.16% |

Discharge temperature | $Td=\u22121692+12.55Tg\u22120.83Te\u22120.012Tg2+0.005Te2\u22120.009TgTe$ | (37) | 4% |

## 5 Conclusion

In this paper, the performance of R744 and R744/R170 mixed refrigerants in refrigeration and air source heat pump systems is studied by simulation method. The trends of COP, refrigeration/heat capacity, and power consumption at the high-pressure side and different proportions of R744 are analyzed. In addition, the changing trend of the optimal parameters of the system with different evaporation temperatures, gas cooler outlet temperatures, and the ratio of R744 is discussed in detail. Finally, the correlations of the optimal parameters of each refrigerant are fitted. The main conclusions are as follows:

There is an optimal pressure in a certain pressure range, and the optimal pressure is the lowest when R744 accounts for 25%.

There is a critical ratio of R744; when the ratio of R744 is less than the critical ratio, the optimal pressure of the system increases with the increase of R744, and when the ratio of R744 is higher than the critical ratio, optimal pressure of the system decreases with the increase of the ratio of R744.

The change trend of COP with the ratio of R744 is first decreasing and then increasing, and when the ratio of R744 is 50%, COP reaches the minimum.

COP increases with the increase of

*T*_{e}and decreases with the increase of*T*_{g}.In a given working condition, when R744 accounts for 25%, its average optimal pressure and temperature are 11.64% and 8.06% lower than R744, respectively.

The optimal discharge temperature of the system increases with the increase of the ratio of R744.

The influence of the outlet temperature of the gas cooler on discharge pressure is greater than that of evaporation temperature, and the influence of evaporation temperature on COP and discharge temperature is more obvious.

When the ratio of R744 is 25%, it is the most suitable refrigerant to replace R744.

This paper is mainly based on the simulation method, and compared with the experimental research, it is difficult to judge the problems and errors that may occur during the actual operation of the system. Therefore, in the future, the team will mainly study the system performance of R744 and its mixture by the experimental method and verify the simulation results of this paper, so as to further promote the development of R744 and its mixture in the field of refrigeration and heat pump.

## Author Contributions

Conceptualization, writing—review and editing: Dahan Sun; methodology: Zhongyan Liu; data curation: Hao Zhang; and investigation: Xin Zhang. All authors have read and agreed to the published version of the manuscript.

## Conflict of Interest

We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work. There is no professional or other personal interest of any nature or kind in any product, service, and/or company that could be construed as influencing the position presented in, or the review of, the manuscript entitled.

## Data Availability Statement

No data, models, or code were generated or used for this paper.

## Nomenclature

### Greek Symbols

### Subscripts

### Acronyms

## References

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