## 1 Introduction  
At present, the supercritical carbon dioxide (S-CO\({}_{2}\)) Brayton cycle system, instead of the traditional steam Rankine cycle system, shows great potential in improving the photoelectric conversion efficiency of the system and reducing the power generation cost. S-CO\({}_{2}\) Brayton cycle power generation technology, with its significant technological and performance advantages, has considerable application potential in the utilization of ship flue gas waste heat, which is a critical way to improve the green level of ships and realize energy conservation and emission reduction in the shipping industry [1; 2; 3]. As one of the core components of the system, the S-CO\({}_{2}\) heat exchange precooler influences the system circulation efficiency. The printed circuit heat exchanger (PCHE) is considered the ideal S-CO\({}_{2}\) high-efficiency heat exchanger in the system due to its advantages of pressure reduction, large heat exchange area, good compactness, high heat exchange efficiency, and proper operation under high-intensity conditions [4]. The PCHE, which is a typical representative of a microchannel heat exchanger, contains hundreds of microchannels, and whether the flow in each microchannel is evenly distributed has a significant influence on the heat transfer characteristics of the PCHE. Inaddition, considering that the physical properties of S-CO\({}_{2}\) (density, specific heat, viscosity, thermal conductivity, etc.) change with temperature, the flow state of S-CO\({}_{2}\) in the flow channel will also be affected [5; 6]. Therefore, the study of flow allocation in microchannels of the PCHE is of great significance. Most of the existing literature on PCHEs assumes that the flow distribution in the flow channels is uniform and that the operating condition is the steady state, ignoring the difference in the flow in the cross-section of the different flow channels and the influence of the inlet and outlet types on the flow distribution. An uneven flow distribution may lead to a decrease in the PCHE heat transfer performance. [PERSON] [7] studied the influence of four different inlet header types on the flow non-uniformity of PCHEs. [PERSON] [8] applied computational fluid dynamics (CFD) to optimize the mass flow rate distribution at the PCHE inlet, improving this distribution by 7.5%, eliminating the separation area near the surface, and reducing the pressure drop. [PERSON] [9] studied the flow and temperature in homogeneities at the inlet end of the cross-flow heat exchanger. Multichannel plate heat exchangers are recommended for efficient power and propulsion systems. [PERSON] [10] used a numerical simulation method to analyze the uneven distribution of large flow in the inlet header structure of high-temperature heat exchangers. Four kinds of improved intake headers were proposed, including an inclined baffle, a segmental baffle, a spiral baffle, and an improved spiral baffle. The results showed that all the proposed designs more or less improve the uniform flow distribution between the channels. [PERSON] [11] analyzed four different inlet headers and proposed an improved header that significantly reduced flow inhomogeneity. [PERSON] [12] established a new prediction model to predict the uneven flow distribution in PCHEs and found that an increase in the channel length could improve the uneven flow distribution. [PERSON] [13] studied the local and global thermal hydraulic properties of different PCHEs using supercritical liquefied natural gas (LNG) and liquid nitrogen by numerical methods and found that flow separation and recirculation at corners inhibited heat transfer and increased the pressure drop. Smoothness of the corners facilitates heat transfer and leads to a reduction in hydraulic resistance. At constant mass flow, a sinusoidal channel can reduce the pressure drop by 8.3% and increase the heat transfer coefficient by 2.9% compared with a serrated channel with a sharp angle.