# A Theoretical Comparative Study of CO\({}_{2}\) Cascade Refrigeration Systems
## 1 Introduction  
The last two decades, the use of CO\({}_{2}\) as refrigerant is a revisited idea in order to avoid the use of harmful working fluids [1; 2]. CO\({}_{2}\) is a working fluid with crucial advantages such as high thermal conductivity, density, latent heat, specific heat capacity, and low dynamic viscosity [3]. Moreover, CO\({}_{2}\) presents low toxicity, and flammability, while its global warming potential is equal to 1 (itself). After the EU F-Gas Regulation 517/2014 [4], the usual refrigerants have to be substituted with natural refrigerants such as CO\({}_{2}\), propane, and NH\({}_{3}\). Moreover, the use of refrigerants with GWP100 lowers than 150 (e.g. R152a) is a choice for designing environmentally friendly systems [5]. CO\({}_{2}\) is a refrigerant with low critical temperature (\(-\)31 \({}^{\circ}\)C), which leads to transcritical refrigeration cycles, especially in warm climates during the summer period. The transcritical operation is associated with a reduced coefficient of performance (COP) and thus the CO\({}_{2}\) faces limitations on this domain. The technology of the CO\({}_{2}\)--only systems has performed huge steps in the last years and numerous configurations have been suggested and optimized. Systems with internal heat exchangers [6; 7], two-stage compression [8; 9], parallel compression [10; 11], mechanical subcooling [12; 13; 14; 15], as well the use of ejectors [16; 17] and expanders [18] are some of the most-established techniques for increasing the performance of the CO\({}_{2}\) refrigeration systems. Another promising configuration is the cascade system with CO\({}_{2}\) in the low-temperature circuit and other refrigerants in the high-temperature circuit. This system seems to be more efficient than the others, especial for the warm climates [19]. The use of CO\({}_{2}\) in the low stage solves the problem of the low critical point which leads to the transcritical operation and also makes the system to operate with lower pressure levels. In the high-temperature circuit, usually, natural refrigerants are used with NH\({}_{3}\) to be the most usual selection, as well as R290 and R1270 to be also interesting cases. However,the NH3 has high toxicity (B2L ASHRAE safety group), while the other natural refrigerants present high flammability (A3 ASHRAE safety group). These facts make the investigation of more refrigerants as possible candidates for the high-temperature circuit. For instance, R152a is a refrigerant with GWP = 124, lower than the limit of 150 [4]; but this fluid is flammable (A2 ASHRAE safety group). R1234 yf and R1234 ze(E) are also promising fluids but they face limitations such as the high cost and the stability issues, while they have relatively low flammability (A2L ASHRAE safety group). So, it can be said that there is no established choice for the utilization of any superior refrigerant for the high-temperature circuit. Table 1 includes the main information about the previously discussed working fluids, as well as information about other working fluids (with higher GWP on a 100 years basis or GWP100) which are usually used in refrigeration systems. The used values of the GWP100 regard the 4 th assessment report [20]. In the literature, there is a significant part of studies that investigate the CO\({}_{2}\) cascade configurations. The majority of the studies investigate systems with CO\({}_{2}\) in the low-temperature circuit and NH\({}_{3}\) in the high-temperature circuit. [PERSON] et al. [23] compared the cascade NH\({}_{3}\)/CO\({}_{2}\) system with other NH\({}_{3}\) refrigeration systems (single stage, two-stage, with or without economizer) and they found the cascade system more efficient for evaporating temperatures lower than \(-40\)\({}^{\circ}\)C. [PERSON] et al. [24] examined a similar configuration and they developed equations about the optimum value of the medium CO\({}_{2}\) temperature which maximizes the system COP. [PERSON] and [PERSON] [25] performed a thermoeconomic optimization and they reduced the annual cost of about 9.34%.