## 3 Flow Distribution Characteristics of the Tapered Header  
Under the condition of countercurrent heat transfer, there are two arrangement modes, as shown in Figure 7. In the actual PCHE cold and hot side header arrangement, when the inlet headers of the cold and hot sides are on different sides and the outlet headers are also on different sides, this is simply referred to as \"different side in and different side out\"; when the cold and hot side inlet headers are on the same side and the outlet headers are also on the same side, this is termed \"same side in and same side out\". \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \(i\) & C 1 & C 2 & C 3 & C 4 & C 5 & C 6 & C 7 & C 8 & C 9 & C 10 \\ \hline \(\sigma_{ic}\) & 0.116 & 0.125 & 0.144 & 0.152 & 0.099 & 0.096 & 0.153 & 0.209 & 0.23 & 0.214 \\ \hline \end{tabular}
\end{table} 
Table 2: Statistics of the standard deviation of the non-uniformity of each flow channel of each heat exchanger plate layer. Figure 6: Flow distribution ratio of each layer. In this section, based on the simulation results, the flow distribution in the heat exchanger plate layer away from the entrance of the PCHE inlet header is found to be the highest, and that in the heat exchanger plate layer near the entrance of the PCHE inlet header is found to be the lowest. Under the different inlet and outlet configuration, the hot fluid has the highest flow distribution in the 10 th heat exchanger plate layer, while in the first layer, the hot fluid has a minor flow distribution. The flow distribution of the cold fluid is the highest in the first heat exchanger plate layer. The flow distribution is the lowest in the 10 th heat exchanger plate layer. For the same inlet and outlet configuration, the flow distribution of hot and cold fluids is the highest in the 10 th heat exchanger plate layer, and the flow distribution is the lowest in the first heat exchanger plate layer. For the \"different side in and different side out\" arrangement, the PCHE heat transfer unit in the first layer has less hot fluid flow and more cold fluid flow, which leads to a mismatch of the cold and hot side flows in the same heat transfer unit and excess cooling capacity of the cold fluid. However, in the PCHE heat transfer unit in the 10 th layer, there is more hot fluid flow and less cold fluid flow, which leads to insufficient cooling capacity of the cold fluid, similar to the situation of dry burning in a boiler with less flow distribution for the high heat load. (Note: Heat transfer unit here refers to a cold-side heat exchanger plate layer and a hot-side heat exchanger layer plate constituting a cold and heat transfer unit layer.) For the \"same side in and same side out\" arrangement, the flow distributions of both cold and hot fluids are small in the PCHE heat transfer unit in the first layer, while the flow distributions of both cold and hot fluids are enormous in the PCHE heat transfer unit in the 10 th layer. Matching of cold and hot flows is adequately realized, and matching of the flows corresponds to matching of the heat loads, which can give full play to the cooling capacity of the cold fluid. For the \"same side in and same side out\" arrangement, the flow rates and heat loads on the hot and cold sides match, but there is a significant asymmetry in the flow distribution from the first layer to the tenth layer. In the \"different side in and different side out\" arrangement, the flow rates and heat loads on the hot and cold sides are very different. Therefore, the uneven distribution of the flow rate must be improved to improve the comprehensive heat transfer performance of the PCHE. According to the analysis results, the lower the layer number is, the more flow rate is distributed by the heat exchanger plate. Therefore, optimizing the configuration of the header into a tapered type can be considered so that when S-CO\({}_{2}\) flows downward in the tapered area, the pressure energy and velocity energy at the entrance of the heat exchanger plate in each layer from top to bottom remain unchanged.