# A Theoretical Comparative Study of CO\({}_{2}\) Cascade Refrigeration Systems
## 1 Introduction
However, the environmental analysis indicates that the cascade system is not an attractive choice compared to the systems with parallel compression and mechanical subcooling. The use of R404a/CO\({}_{2}\) has been studied by [PERSON] et al. [35] and they found it to be more efficient than the system with the only R404a with a difference of 25%. [PERSON] et al. [36] examined the use of R407C/CO\({}_{2}\) and they found it more efficient than the conventional heat pump and with a lower global warming impact. [PERSON] et al. [19] suggested the use of R513A/CO\({}_{2}\) as a highly effective choice for refrigeration systems in supermarkets. [PERSON] et al. [37] found the CO\({}_{2}\)/CO\({}_{2}\) to be a less efficient choice than designs with parallel compression and by-pass compressor. Other examined refrigerants in the high-temperature circuit are ethane [38], N40 [39], as well as CO\({}_{2}\) blends [40]. The last part of the literature is devoted to comparative studies for cascade systems with CO\({}_{2}\) in the low-temperature circuit. [PERSON] et al. [41] found that the R600 is more efficient than R290 which has similar performance with R134a, while NH\({}_{3}\) is the less efficient choice. On the other hand, [PERSON] et al. [42] found the use of NH\({}_{3}\) to be more efficient than R290 in various cascade configurations. Moreover, [PERSON] and [PERSON] [43] found the NH\({}_{3}\) to be more efficient than R290, R1270 and R404a with the respective efficiency order. Recently, [PERSON] et al. [44] found that the NH\({}_{3}\)/CO\({}_{2}\) is more efficient than the all CO\({}_{2}\) system in the warmer climates, while both cases are more efficient than the conventional system with R404a in all circuits. The previous analysis clearly indicates the high interest in the CO\({}_{2}\)-based cascade systems. To our knowledge, there is no study which compares many refrigerants under the same examined conditions and there are no established results about the most efficient and the most environmentally friendly systems. In this direction, this study comes to complete the existing literature review by presenting a systematic comparative analysis of 18 different cascade refrigeration systems for different operating conditions. Practically, the novelty of this work is based on the clear and systematic investigation of numerous cascade configurations in steady-state conditions, as well as on a yearly basis. The results of this work can be used for the proper selection of the working fluids in CO\({}_{2}\)-based cascade systems using energetic and environmental criteria. More specifically, 17 different refrigerants examined in the high-temperature circuit and they compared with the CO\({}_{2}\)/CO\({}_{2}\) case in subcritical or transcritical mode (depending on the ambient temperature). The evaporator temperature is studied parametrically for the values of \(-35\), \(-25\), \(-15\) and \(-5\)\({}^{\circ}\)C, while the condenser temperature is studied from 10 to 45 \({}^{\circ}\)C. The yearly evaluation of the system is performed for the climate conditions of Athens (Greece) which is a relatively warm climate, ideal for cascade systems with CO\({}_{2}\). The most important indexes of the present work are the COP and the total equivalent warming impact (TEWI) which are evaluated separately and together. The analysis is conducted with a developed theoretical model in Engineering Equation Solver (EES) which is validated using literature data.