## 2 Flow Distribution Characteristics of the Straight Bartel Inlet Header PCHE
### Flow Distribution Characteristics of the Straight Bartel Inlet Header PCHE  
The internal flow characteristic is analyzed under the conditions of pressure 9.5 MPa, flow rate 0.05 kg/s, inlet temperature 305 K, and wall temperature 333 K. Figure 4 shows the numbering rules for the layers and flow channels. Figure 5 shows the flow distribution at each channel. Based on an analysis of the flow characteristic, inside the straight-channel PCHE, a significant difference between the flow distributions in each layer can be found. The flow distribution within the flow channel in a particular layer exhibits relatively small differences. The single current flow gradually increases with increasing layer number, and the flow distribution on both sides is higher than that in the middle. In the whole straight barrel inlet header PCHE, the flows in _channels C1_ and _C10_ of the _plate10_ heat exchanger plate are the maximum. In contrast, the flow in _channel C6_ of the _plate1_ heat exchanger plate is the minimum, and the flow in _channel C1_ of the _plate5_ heat exchanger plate is closest to the uniform flow distribution state. Figure 4: Schematic diagram of the PCHE inner layer number and flow channel number. Because the direction of the inlet header is perpendicular to the direction of the heat exchanger plates, the flow is similar to that of a confined impact jet. When a flow impacts a disk, the velocity is evenly distributed in 360\({}^{\circ}\). When the disk shape is gradually reduced from 360\({}^{\circ}\) to 180\({}^{\circ}\), 90\({}^{\circ}\), and 60\({}^{\circ}\) by a wall, the existence of the wall prevents the flow on the disk from expanding in all directions, resulting in the velocity in the region near the border of the disk being much higher than that in the region away from the wall. The flow velocity distribution in the diversion area of the straight barrel inlet header PCHE is similar to that in the case with an angle of 60\({}^{\circ}\). Therefore, Figure 5 shows that the flow distribution on both sides of the straight barrel inlet header PCHE is higher than that in the central flow channel. Figure 6 shows the flow proportion curves of each heat exchanger plate layer under different inlet flow rate conditions. A higher inlet flow rate has almost no influence on the flow proportion of each layer. On the one hand, as the structure of the inlet header and heat exchanger plate is similar to that of an impact jet, according to the Bernoulli theory, the velocity energy is converted into pressure energy at the bottom of the inlet header. With increasing PCHE layer number, the pressure is greater at the entrance of the heat exchanger plate, and the more flow is distributed. On the other hand, each heat exchanger plate layer, in turn, leads to a gradual reduction in the average speed of the flow along the header, slowly resulting in a higher static pressure. In contrast, the velocity in the central part of the header is higher. As a result of the no-slip wall boundary conditions of each heat exchanger plate layer, near the entrance, the velocity is low, and the low-speed flow in the peripheral region of the header cannot protect against pressure gradient flow [31]. Therefore, flow separation leads to the formation of a backflow zone at the bottom of the header. Hence, the proportion of flow distribution in each layer increases with the PCHE layer number. Further statistics show that the standard deviation of the overall non-uniformity is 0.226. The standard deviation of the non-uniformity of each layer (\(\sigma_{p}\)) is 0.188 under the condition that the flow rate is 0.05 kg/s. The standard deviation of the non-uniformity of each flow channel of each heat exchanger plate layer (\(\sigma_{i,c}\)) is shown in Table 2. \(\sigma_{i,c}\) and \(\sigma_{p}\) are equivalent in order of magnitude. The flow distribution in the straight barrel inlet header PCHE is uneven between each heat exchanger plate layer and between the flow channels of a single-layer heat exchanger plate.