## 5 Conclusions  
In this work, we studied the flow distribution characteristics of the straight barrel inlet header PCHE by a numerical simulation method. We analyzed the flow mechanism of the extremely uneven flow distribution in each layer.  
In a single flow channel, the non-uniform flow distribution phenomenon in the heat exchanger plate layers is caused by the structure itself. If a guide plate is set up in the diversion area, then a higher flow can be obtained in the middle of the channel. Nevertheless, the additional guide plate structure is bound to cause a diversion area with increased pressure drop, leading to the deterioration of the PCHE hydraulic characteristics on the whole, thus affecting the turbine inlet pressure in the Brayton cycle, which is a pyrrhic gain. In addition, due to the high operating pressure of the system, the setting of the guide plate may cause local stress concentration, which is not conducive to the safe and stable operation of the system. Therefore, the design of the existing straight barrel inlet header PCHE must be optimized to improve the non-uniformity of the flow distribution in each layer of the PCHE so that the flow in the straight barrel inlet header PCHE can be approximately evenly distributed and the system can run under conditions close to the design point.  
The problem of flow matching on the cold and hot sides was analyzed according to two different layout modes of \"different in and different out\" and \"same in and same out\". Then, the inlet header was optimized as a tapered type to find the best range of taper angles and analyze the influence of different taper angles on the thermal hydraulic characteristics of the straight barrel inlet header PCHE. The results show that when the taper angle varies from \(6^{\circ}\) to \(9^{\circ}\), the standard deviation of the non-uniformity of the flow distribution in each layer of the straight barrel inlet header PCHE is less than 0.05, and the flow distribution in each layer is relatively uniform. The comprehensive heat transfer performance of the straight barrel inlet header PCHE can be improved by 17.3-19.7%. Finally, the response surface and a genetic algorithm were combined to optimize the inlet header. Compared with the standard structure, the heat transfer performance of the optimized system was improved by 19.7%, reaching 1.187. This study can provide theoretical guidance for the design of the PCHE inlet header.  
Writing--original draft preparation, K.Z.; writing--review and editing, W.W. and M.L.; software, K.Z. and Q.W.; investigation, Y.S. and M.T. All authors have read and agreed to the published version of the manuscript.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Number** & **Angle** & **Re** & **CP** & **Desirability** \\ \hline
**1** & **7.271** & **6200** & **1.187** & **0.98** & **Selected** \\
2 & 7.209 & 6199.993 & 1.187 & 0.979 & \\
3 & 7.152 & 6199.987 & 1.187 & 0.979 & \\
4 & 7.456 & 6199.999 & 1.187 & 0.979 & \\
5 & 7.047 & 6199.998 & 1.186 & 0.979 & \\
6 & 6.938 & 6199.991 & 1.186 & 0.977 & \\
7 & 6.374 & 6199.995 & 1.179 & 0.964 & \\
8 & 6.228 & 6200.000 & 1.176 & 0.959 & \\
9 & 0.000 & 6199.997 & 0.983 & 0.577 & \\
10 & 15.000 & 6199.998 & 0.979 & 0.570 & \\ \hline \hline \end{tabular}
\end{table}
Table 5: Optimization results for the inlet tapered header.  
**Funding:** This work was supported by the High-Tech Ship Research Project of the Ministry of Industry and Information Technology (no. MIIT [2017]614) and the Fundamental Research Funds for the Central Universities (WUT: 2021 IUA105).  
**Informed Consent Statement:** Informed consent was obtained from all subjects involved in the study.  
**Data Availability Statement:** Data are available upon reasonable request to the submitting author.  
**Conflicts of Interest:** The authors declare no conflict of interest.