## 3 Flow Distribution Characteristics of the Tapered Header
This indicates that the structure of the original configuration is optimized for the taper angle, which is advantageous for uniform distribution of the flow rate in the straight barrel inlet header PCHE to each heat exchanger plate layer. With an increase in the taper angle \(\theta\), the results indicate that the optimum taper angle \(\theta\) can make the flow uniformly distribute to each layer in the straight barrel inlet header PCHE. When the taper angle \(\theta\) is 6\({}^{\circ}\) and 9\({}^{\circ}\), the non-uniformity is less than 0.5, indicating that these two structural parameters of the header can significantly reduce the non-uniformity of the internal flow distribution of the straight barrel inlet header PCHE and realize uniform flow rate in each heat exchanger plate layer. When the taper angle \(\theta\) is increased to 12\({}^{\circ}\) and 15\({}^{\circ}\), compared to 6\({}^{\circ}\) and 9\({}^{\circ}\), it is not conducive to uniform distribution in each heat exchanger plate layer of the straight barrel inlet header PCHE. The distribution results indicate that to achieve uniform distribution in each heat exchanger plate layer, the taper angle \(\theta\) of the inlet header should be taken to be between 6\({}^{\circ}\) and 9\({}^{\circ}\). Figure 10: Non-uniformity of each layer. Figure 9: Flow distribution uniformity ratio of each layer. For taper angles \(\theta\) from \(0^{\circ}\) to \(15^{\circ}\), Figure 11 shows the mass flow rate flow diagram and mass flow rate cloud diagram, which reflect the velocity distribution in the inlet header and each heat exchanger plate layer, and fluid streamlines showing the flow field can be observed. The existence of a backflow area can be found, and analysis of the content indicates that with increasing taper angle, the backflow dead zone decreases. When \(\theta=12^{\circ}\), the backflow dead zone disappears completely. The maximum local value of the mass flow rate tends to appear on the heat exchanger plate near the lower part of the header. With increasing taper angle, the red area at the entrance of the bottom heat exchanger plate gradually becomes smaller, indicating that the pointed tip of the tapered header can regulate the flow distribution ratio in each heat exchanger plate layer. Figure 12 shows the statistical results of the standard deviation (\(\sigma_{p}\)) of the non-uniformity of each layer. According to the analysis of the trend in the figure of \(\sigma_{p}\), when the taper angle \(\theta\) is 3-15\({}^{\circ}\), \(\sigma_{p}\) is less than that when the taper angle \(\theta\) is 0\({}^{\circ}\), which indicates that optimization of the original configuration of the inlet header into a tapered header is conducive to evenly distributing the flow in the straight barrel inlet header PCHE to each heat exchanger plate layer. \(\sigma_{p}\) first decreases and then increases with decreasing angle \(\theta\), indicating an optimal taper angle \(\theta\) for evenly distributing the flow in the straight barrel inlet header PCHE among all the layers. When the taper angle \(\theta\) is 6\({}^{\circ}\) and 9\({}^{\circ}\), \(\sigma_{p}\) is less than 0.05, indicating that the header with these two structural parameters can significantly reduce the non-uniformity of the flow distribution in the straight barrel inlet header PCHE and realize uniform flow distribution in each heat exchanger plate layer. When the taper angle \(\theta\) increases to 12\({}^{\circ}\) and 15\({}^{\circ}\), \(\sigma_{p}\) is greater than the corresponding value when the taper angle is 6\({}^{\circ}\) and 9\({}^{\circ}\), which is not conducive to uniform distribution of the flow rate in each heat exchanger plate layer in the straight barrel inlet header PCHE. The distribution results show that to realize uniform flow distribution in each heat exchanger plate layer, the inlet header taper angle \(\theta\) should be between 6\({}^{\circ}\) and 9\({}^{\circ}\).