# A Theoretical Comparative Study of CO\({}_{2}\) Cascade Refrigeration Systems
## 3 Results and Discussion
### Energetic Analysis of Different Operating Scenarios  
Figure 4 illustrates the COP of the systems CO\({}_{2}\)/CO\({}_{2}\) (reference system for the comparison) and of the conventional system NH\({}_{3}\)/CO\({}_{2}\) (it is usually examined in the literature). The results are presents for different condenser temperatures and evaporator temperatures. It is important to state again that for (\(T_{c}>30\)\({}^{\circ}\)C), the condenser temperature regards the gas cooler outlet temperature and the CO\({}_{2}\)/CO\({}_{2}\) cycle is transcritical which operates at the respective optimum maximum pressure level in every case. It is obvious that the NH\({}_{3}\)/CO\({}_{2}\) system is more efficient than the CO\({}_{2}\)/CO\({}_{2}\) system for all the examined scenarios. The COP is decreased for higher condenser or gas cooler outlet temperatures and also it decreases for lower evaporate temperatures. These results are reasonable and they are in accordance with the Carnot efficiency [\(CO_{var}=T_{e}/(T_{c}-T_{e})\)]. Figure 5 depicts the values of the optimum medium temperature level (\(T_{m1}\)) of the low-temperature CO\({}_{2}\) cycle. The optimum values of the (\(T_{m1}\)) increase with the increase of the evaporator and the condenser temperature. So, it can be said that the optimum (\(T_{m1}\)) tries to follow temperatures levels of the (\(T_{e}\)) and the (\(T_{c}\)). The interesting result is that the optimum (\(T_{m1}\)) is higher for the CO\({}_{2}\)/CO\({}_{2}\) system compared to the NH\({}_{3}\)/CO\({}_{2}\) system. It is remarkable to state that the slope of the curves about CO\({}_{2}\)/CO\({}_{2}\) system changes after \(T_{c}=30\)\({}^{\circ}\)C because the cycle becomes transcritical for higher values of \(T_{c}\). This result indicates that the transcritical cycle does not need so high values for the (\(T_{m1}\)). Figure 4: Coefficient of performance (COP) at different operating conditions for CO\({}_{2}\)/CO\({}_{2}\) and CO\({}_{2}\)/NH\({}_{3}\) systems. The next step in this work is the comparison of the CO\({}_{2}\)/CO\({}_{2}\) system with other cascade configurations. Figure 6 includes the comparison results for different combinations of (\(T_{c}\)) and (\(T_{c}\)). The results are given for the systems NH\({}_{3}\)/CO\({}_{2}\), R152a/CO\({}_{2}\), R290/CO\({}_{2}\) and R1270/CO\({}_{2}\). The refrigerants R290 and R1270 are natural refrigerants, while R152a has a relatively low GWP. So, these candidates are promising choices for future cascade systems. Figure 6a,d indicate that the COP values are similar among the examined refrigerants. The enhancement values compared to the CO\({}_{2}\)/CO\({}_{2}\) system are higher for greater (\(T_{c}\)) and greater (\(T_{c}\)). The COP enhancement curves have a different slope for (\(T_{c}\) > 30 \({}^{\circ}\)C) because of the transcritical operation of the CO\({}_{2}\)/CO\({}_{2}\) system. Also, in low condenser temperatures, the COP enhancements are similar for all the evaporating temperatures, while for higher condenser temperatures the curves are not so close to each other. In low condenser temperatures, the COP enhancements are around 10%, while they can reach up to 80% in high condenser temperature levels. So, it can be said that the use of a refrigerant different from CO\({}_{2}\) in the high-temperature circuit can be beneficial, especially in warmer climates. This is something in accordance with the general opinion about the utilization of cascade systems in warm climates such as in Mediterranean countries (for example Greece, Spain, Italy) [19]. Figure 7 shows the enhancement with 8 different refrigerants for the case of (\(T_{c}\) = \(-\)35 \({}^{\circ}\)C). This evaporating temperature is typical, especially in refrigeration systems in supermarkets. This figure indicates that similar enhancements can be found with the examined refrigerants. The most promising choices seem to be R152a, NH\({}_{3}\), R1270, R290 and R600a. R404a is the less efficient case, with R1234 yf(E) and R1234 ze to be a bit more efficient.