## 3 Results and Discussion  
In an air refrigeration cycle, a counter-current flow heat-exchanger is commonly utilized as a recuperator. Considering the limitations of pressure loss and size, it is assumed that the minimum temperature difference in the heat exchanger is 5 K. The design parameters for the thermodynamic analysis of air refrigeration cycles are shown in Table 1. The working fluid in the closed cycle is dry air to avoid the energy loss due to condensation of water vapor in the moist air. The open-loop cycle intakes air from the ambient environment, which contains water vapor. When the outlet temperature of the expander is lower than the dew point, the water vapor is condensed, which has an impact on the outlet temperature of the expander. The influence of the latent heat of water condensation is considered in the calculation of the outlet temperature of the expander. Figure 4: Calculation process of thermodynamic performance for a practical TC cycle. For closed air refrigeration cycles with varied expander inlet pressure, Figure 5 shows the variations in COP and supplied-air temperature with the expansion ratio. It is apparent that the increase in operating pressure can improve cycle COP, but it has little effect on the supplied-air's temperature. As operating pressure increases, the enhancement of the cycle COP becomes less obvious. This is mainly because the system power consumption and cooling capacity mainly depend on the enthalpy difference when the pressure is beyond 0.3 MPa. Figure 5 shows that there is an optimal expansion ratio to maximize the cycle COP. When the inlet pressure of the expander is 506.625 kPa, the maximum COP of 0.652 can be reached at an expansion ratio of 2.25. Figure 6a shows the comparisons of the COP and supplied-air temperature for various air refrigeration cycles. The COP of open-loop cycles is greater than closed-loop cycles, and the two-stage compression open-loop cycles, including TC-C, C-TC, C-CT and CT-C cycles have higher COPs than the one-stage compression open-loop cycles. The greatest COP for the TC cycle and CT cycle are 0.728 and 0.747, respectively, for the optimal expansion ratios of 2.10 and 2.17. Figure 6b shows the p-H diagrams for the air cycles at the respective optimal expansion ratio. In an open-loop high-pressure cycle (CT cycle), the cold air from the expander can be supplied to the compartment directly, and there is no loss of cooling capacity caused by the temperature difference in the cold-side heat exchanger. The inlet temperature of the expander in an open-loop low-pressure cycle (TC cycle) is the ambient temperature, which is generally lower than that of the CT cycle, and the cooling capacity \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Work Fluid** & **Ambient Pressure** & **Dry Bubble** & **Wet Bubble** \\  & & **Temperature (Indoor)** & **Temperature (Indoor)** \\ \hline Moist Air & 101.325 kPa & 300.15 K & 292.15 K \\ \hline
**Dry Bubble** & **Wet Bubble** & **Isentropic** & **Isentropic Efficiency** \\
**Temperature (Outdoor)** & **Temperature (Outdoor)** & **Efficiency (Compressor)** & **(Expander)** \\ \hline
308.15 K & 297.15 K & 75\% & 80\% \\ \hline
**Pressure Drop** & **Pressure Drop** & **mechanical Efficiency** & **Temperature Difference** \\
**(Water Separator)** & **(Heat Exchanger)** & **mechanical Efficiency** & **(Heat Exchanger)** \\ \hline
1.0 kPa & 1.0 kPa & 99\% & \(\geq\)5 K \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Ambient conditions and design parameters of air refrigeration cycles. Figure 5: Comparisons of COP and supplied-air temperature for closed air-refrigeration cycles under different expander inlet pressures. can be increased effectively. However, the temperature difference in the cold-side heat exchanger of the TC cycle leads to a lower COP than that of the CT cycle, and the influence is more obvious when the expansion ratio is higher than the optimum value.