## 3 Results and Discussion
### Mechanical Subcooling System Performance  
The system with dedicated mechanical subcooling is investigated in this section. This system consumes extra work in the secondary refrigeration cycle which operates with R134a. The subcooling after the gas cooler gives two important advantages, the increase of the cooling capacity and the lower consumption in the CO\({}_{2}\) compressor, because of the reduction in the optimum pressure compared to the conventional system. Figure 8 gives the COP of the M-SC system and of the Ref system, while the  
Figure 6: The impact of the pressure ratio parameter of the reference system in exergy efficiency. The black solid points show the maximum exergy efficiency and the dotted line shows the geometric location of the maximum values (T\({}_{\rm e}\) = \(-\)15 \({}^{\circ}\)C). Figure 7: The impact of the pressure ratio parameter of the reference system exergy efficiency (T\({}_{\rm c}\) = 40 \({}^{\circ}\)C). energy efficiency of these systems is given in Figure 9. These cases are all optimized cases and so the comparison was able to be done. The curves of the M-SC system had similar trends compared to the Ref system, but they had higher values. In other words, the M-SC system presented increased COP and exergy efficiency; the facts that make it a promising choice for enhancing the performance of CO\({}_{2}\) transcritical refrigeration systems. It is important to state that the overall maximum exergy efficiency was 38.46% and it was obtained for (T\({}_{\rm e}\) = -15 \({}^{\circ}\)C and T\({}_{\rm c}\) = 35 \({}^{\circ}\)C), while for this case the COP was 2.482. Moreover, it has to be said that the optimum evaporating temperatures were equal to -15 \({}^{\circ}\)C for heat rejection temperatures up to 40 \({}^{\circ}\)C, while for higher heat rejection temperatures the optimum evaporating temperature was equal to -25 \({}^{\circ}\)C. It is remarkable to state that the optimum evaporating temperatures were lower in the M-SC system compared to the Ref system. This fact is based on the increased COP of the M-SC system, which makes the product of Equation (15) have different behaviors with the variation of the refrigeration temperature level. The optimization of the M-SC system was performed using two parameters; the pressure ratio parameter (a) and the temperature level in the evaporator of the secondary cycle (T\({}_{\rm e,m}\)). Figures 10 and 11 exhibit the optimization procedure results for the case (T\({}_{\rm e}\) = -15 \({}^{\circ}\)C and T\({}_{\rm c}\) = 40 \({}^{\circ}\)C). Figure 10 shows that the optimum values of the (T\({}_{\rm e,m}\)) were generally in the region from 5 \({}^{\circ}\)C up to 15 \({}^{\circ}\)C, while the global optimum case was found for (a = 1.05 and T\({}_{\rm e,m}\) = 14.38 \({}^{\circ}\)C). Figure 11 shows that the optimum pressure ratio parameters were for values close to (\(\alpha\) = 1) when the (T\({}_{\rm e,m}\)) was relatively high, and for values close to (\(\alpha\) = 1.25) when the (T\({}_{\rm e,m}\)) had lower values. The reason for the different trends between the curves is based on the non-linear character of the CO\({}_{2}\) saturation curve in the liquid phase, which leads to higher optimum pressure ratios when there were higher subcooling values after the gas cooler. These figures clearly prove the need for a detailed optimization procedure and this is the reason for its conduction in this work. The role of Figures 10 and 11 in this work is only to show the impact of the optimization parameters on the exergy efficiency for a typical operating scenario. Moreover, it is important to state that the results of Figure 11 indicate that the optimum pressure ratio was up to 1.25, while for the same operating conditions it was 1.35 for the conventional system (see Figure 7). So, it was obvious that the use of the mechanical subcooling system reduced the optimum high-pressure ratio and, consequently, the work of the main compressor.