## 3 Flow Distribution Characteristics of the Tapered Header
The backflow dead zone at the bottom of the header is eliminated to realize uniform distribution of the flow of the heat exchanger plate in each layer. Figure 8 shows the structure diagram of the tapered header. The magnitude of different taper angles \(\theta\) represents the rate at which pressure energy is converted into velocity energy along the flow direction of the tapered area. Limited by the structural characteristics of the model, the diameter of the top circle is constant at  
Figure 7: PCHE cold and hot side inlet and outlet header layout. \(d_{1}=10\) mm, and the distance between the first heat exchanger plate and the tenth heat exchanger plate is 29.8 mm. Assuming that the bottom circle diameter \(d_{2}\) is 0, the maximum value of the angle \(\theta\) is 18.55\({}^{\circ}\); that is, angle \(\theta\) ranges from 0\({}^{\circ}\) to 18.55\({}^{\circ}\). In this paper, 3\({}^{\circ}\) to 15\({}^{\circ}\) models which inlet mass flow is 0.05 kg/s are selected for numerical simulation to explore the influence of different structural parameters on the non-uniformity of the flow distribution in each layer. The \(d_{2}\) corresponding to specific angles is listed in the following Table 3.  
Figure 9 shows the proportion of the flow distribution in each layer of the models with different taper angles. The taper angle of the inlet header has a significant influence on the proportion of the flow distribution in each layer of the straight barrel inlet header PCHE. As mentioned above, \(\theta=0^{\circ}\) corresponds to the original configuration. The flow ratio gradually increases with the layer number. The deviation between the maximum and minimum values reaches 243%, significantly deviating from the state of uniform flow distribution in all layers. With the taper angle gradually increasing from 0, the flow distribution in each layer can be found to fundamentally follow a monotonic change law. In layer 1, the flow distribution of the heat exchanger plate gradually increases. In the 10 th heat exchanger plate layer, the flow distribution decreases, and in layers 5 and 6, the flow distribution of the heat exchanger plate remains around 10%, the closest to a uniform flow distribution state. This occurs because as the taper angle \(\theta\) gradually increases, the diameter d\({}_{2}\) of the bottom circle of the header slowly decreases, and the inclination degree of the tapered header slowly increases, leading to a more significant proportion of pressure energy being converted to velocity energy along the flow direction of the header. The larger the velocity energy is, the less flow is distributed to the layer. Therefore, as the taper angle \(\theta\) increases, the average slope of the flow distribution ratio curve of each layer of the straight barrel inlet header PCHE gradually decreases from positive to 0 and then negative. On the whole, when \(\theta=6^{\circ}\) and \(\theta=9^{\circ}\), the flow distribution in each layer is approximately 10%. Uniform flow distribution in each layer of the PCHE can be considered to be realized under these structural parameters. Figure 8: Structure diagram of a tapered header. (**a**) Schematic diagram, (**b**) local structure. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline Taper Angle \(\theta/^{\circ}\) & 3 & 6 & 9 & 12 & 15 \\ \hline d\({}_{2}\)/mm & 8.4 & 7.0 & 5.0 & 3.6 & 2.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Structural parameters of the tapered header. Figure 10 shows the non-uniformity of each layer of different taper angle models, and increasing the angle of the inlet header has a significant impact on the non-uniformity of the straight barrel inlet header PCHE. As previously mentioned, \(\theta=0\) corresponds to the original configuration, and the non-uniformity of the flow rate decreases with the gradual increase in the taper angle \(\theta\) when the taper angle \(\theta\) is 3-12\({}^{\circ}\) and the number of layers is 10.