## 2 Flow Distribution Characteristics of the Straight Bartel Inlet Header PCHE
### Physical and Numerical Models  
To explore the influence of the flow distribution law in the PCHE on the thermal hydraulic characteristics, the basic structure of the straight barrel inlet header PCHE must be analyzed. The single-side flow channel model of the straight-channel PCHE is shown in Figure 2, which includes five parts: inlet header, inlet diversion area, microchannel area, outlet confluence area, and outlet header. Given the complexity of the straight-channel PCHE structure, the simplified assumptions in this section are as follows:  
Figure 1: Structure of the PCHE. Figure 2: Single-side flow channel model and grid block division strategy of the straight-channel PCHE. (1) The junction between the semicircular microchannel area and the inlet diversion area is tangent at the bottom of the heat exchanger plate, and the quality of the mesh division in the diversion area is deficient. Therefore, the semicircular flow channel is simplified into a rectangular flow channel according to the hydraulic diameter, which is convenient for improving the mesh quality. (2) Ref. [30] shows that the primary thermal resistance in S-CO\({}_{2}\)-water heat transfer is on the S-CO\({}_{2}\) side, so only the S-CO\({}_{2}\) side flow channel needs to be calculated, and a constant wall temperature is given on the S-CO\({}_{2}\) side. The grid block partitioning strategy is shown in Figure 2, where the inlet and outlet headers are divided into O-grids to improve the grid quality. To ensure the accuracy of numerical simulation calculations, the fluid domain is divided by hexahedral grids. The thickness of the first layer grid at the interface is 0.01 mm, the growth rate is 1.2, and the final orthogonal value is above 0.55. Grid independence was verified and the number of grids finally was determined, about 12 million. In the single-side flow channel model of the straight-channel PCHE, the inlet boundary is a mass flow rate, and the outlet boundary sets a specific pressure. The upper and lower parts of each heat exchanger plate are closest to the fluid on the other side, and the temperature is set as constant. The other wall surfaces are simplified as adiabatic walls. The NIST real gas model in Fluent is used to simulate the flow properties of S-CO\({}_{2}\) in the PCHE. This model can consider the influence of temperature and pressure changes on the physical properties of S-CO\({}_{2}\). The \(SST\)\(k\)-\(\omega\) model is used for the turbulence model. SIMPLE is used for the discrete algorithm. The second-order discrete scheme is used for the pressure, the second-order upwind method is used for the momentum and density, and the second-order upwind scheme is used for the turbulent kinetic energy and turbulent dissipation rate. The convergence criterion is \(10^{-3}\). To verify that the numerical model in this section can be used to simulate the flow distribution uniformity in the PCHE, as a validation, the experimental data in Ref. [10] were selected to validate our model. Figure 3 shows that the Nusselt number of the simulation results and experimental data are essentially consistent. The average error is within 10%, and the maximum error is 12.5%. This shows that the numerical model can simulate the flow distribution uniformity in the PCHE. To explore the influence of the straight barrel inlet header PCHE on the flow rate, the working conditions listed in Table 1 are set for numerical simulation. Figure 3: Numerical model validation (Experimental Results [10]). The flow non-uniformity in the PCHE can be divided into three kinds according to different objects of attention: the non-uniformity in each layer, the non-uniformity in each flow channel, and the overall non-uniformity, which can be used to characterize the degree of flow distribution deviation from the uniform flow distribution in the PCHE.