## 3 Results and Discussion
### Results of 'Group A' Mixtures (Substances for Reducing the Critical Temperature)
\begin{table}
\begin{tabular}{c c c c c c c c} \hline  & **Molar** & **Density** & **Isobatic Heat** & **Kinetic** & **Thermal** & **Prandtl** & **Plant** \\  & **Mass** & **(kg/m3)** & **Capacity** & **Viscosity** & **Conductivity** & **Number** & **Efficiency** \\ \hline s-CO\({}_{2}\) pure & 44.01 & 565.43 & 49.62 & \(7.19\times 10^{-4}\) & \(1.03\times 10^{-1}\) & 19.61 & 0.49 \\ s-CO\({}_{2}\)/He (90.0/10.0) & 40.01 & 386.23 & 378.95 & \(6.68\times 10^{-4}\) & \(5.52\times 10^{-2}\) & 177.08 & 0.53 \\ s-CO\({}_{2}\)/Kr (68.0/32.0) & 56.74 & 740.15 & 7.95 & \(6.20\times 10^{-4}\) & \(5.94\times 10^{-2}\) & 6.13 & 0.53 \\ s-CO\({}_{2}\)/CH\({}_{4}\) (67.0/33.0) & 34.78 & 414.49 & 6.59 & \(7.42\times 10^{-4}\) & \(6.52\times 10^{-2}\) & 3.11 & 0.52 \\ s-CO\({}_{2}\)/C\({}_{2}\)H\({}_{6}\) (68.0/32.0) & 39.55 & 371.85 & 1830.20 & \(7.91\times 10^{-4}\) & \(9.13\times 10^{-2}\) & 597.86 & 0.52 \\ \hline \end{tabular}
\end{table} 
Table 2: Results summary for ‘group A’ mixtures with UA\({}_{\text{total}}\) = 15,000 kW/K, CIT and CIP optimized. Figure 5: Cycle thermal efficiency versus mole fraction. Group A mixtures with UA\({}_{\text{total}}\) of 5000, 10,000 and 15,000 kW/K. In the future, alternative refrigerants could also be utilized to vary the UHS temperature range. Cooling with cold storage system based on water ice could be proposed as the second technical solution. In this case, the helium mixture, with a critical temperature around 274.24 K, is the most suitable option. In conclusion, maximizing the working fluid density in turbomachines minimizes the equipment dimensions, but also has to be warranted the equipment manufacturability. Maximizing the Cp and density values and minimizing the kinetic viscosity value reduce the heat exchangers size, and finally, selecting a mixture with a critical temperature compatible with the UHS storage system. The optimum s-CO\({}_{2}\) mixtures could be obtained with helium or ethane. However, another constraint, which was not cited before, is the added substance's maximum operating temperature. Helium has a maximum working temperature of around 2000 K, and the maximum working temperature of ethane is around 675 K. Accordingly, for the purposes in this work, the optimum mixture is s-CO\({}_{2}\)/He (90.0/10.0). However, for future works, it would be advisable to continue researching on a mixture based on adding both helium and ethane, as this last fluid has a very beneficial impact on the heat exchanger and also simplifies the UHS storage system's economical and technical design, opening future research paths for studying diverse refrigeration thermodynamic cycles coupled with the main s-CO\({}_{2}\) Brayton power cycle. A schematic diagram of the pressure vs. enthalpy for the s-CO\({}_{2}\) Recompression Brayton cycle is shown in Figure 6, this cycle works with CIP and CIT optimal values, pure s-CO\({}_{2}\) as working fluid and U\(\Lambda\)total = 15,000 kW/K. The specific heat contributing to the cycle through the primary heat exchanger is represented by q\({}_{\text{PHX}}\). The specific work of the main compressor is \(w_{mc}\), the specific work of the recompressor is \(w_{rc}\), the specific work of the turbine is \(w_{t}\), the maximum achievable temperature in the high-pressure side from the low-pressure side is \(T_{t}\), and \(\Delta\)h\({}_{a}\) is the specific enthalpy increment between the entrance of the primary heat exchanger and the exit of the turbine. The thermal efficiency of the recompression Brayton cycle is properly defined as the net specific work divided by the net supply of heat [19]. The thermal efficiency can be expressed as  
\[\eta_{th}=\frac{1-(1-\gamma)\cdot\frac{w_{mc}}{w_{t}}-\gamma\cdot\frac{w_{rc}} {w_{t}}}{1+\frac{\Delta_{\text{h}_{rc}}}{w_{t}}} \tag{1}\]  
where \(\gamma\) is the split fraction of the flow of the plant.