## 4 Flow Characteristics and Optimization of the Coupler
### Results and Discussion  
In order to more intuitively evaluate the flow characteristics of the NFFCS, they are compared with the simulation results of the CFFCS. The pressure drops of the CFFCS (50.76 kPa) and the NFFCS (49.49 kPa) were obtained through calculation of the average pressures at both sides of the inlet and outlet. It can be seen that although the internal geometry of the NFFCS is more complicated due to the inclusion of the instantaneous pressure relief device, its pressure drop is about 2.5% less than that of the CFFCS. Figure 12 shows the pressure distribution of the two flat-face type coupling systems. It can be seen that the pressure gradient distribution in the two systems in the steady state is uniform, and the pressure remains high at the inlet. The pressure drop around the guide pin of the valve at the inlet side of the CFFCS is more obvious, which is caused by the sudden decrease in the flow cross-sectional area and the increase in velocity. This is the main reason why the pressure drop of the CFFCS is higher than that of the NFFCS.  
Figure 11: Meshing and inlet boundary conditions, (**a**) The CFFCS, (**b**) Initial design of the NFFCS, (**c**) Optimal design of the NFFCS and (**d**) Internal view of the poly-hexcore mesh.  
Figure 13 shows the velocity and streamline distribution results of the two flat-face coupling systems. By comparing the velocity distributions, it can be seen that there is a sharp increase in the velocity at the guide pin position near the inlet of the CFFCS. As mentioned before, due to the sudden reduction of the geometrical cross-sectional area, the surge in the flow rate of the hydraulic oil flowing through it leads to greater energy consumption, which results in the greater pressure drop in the CFFCS. The initial model of the NFFCS was designed with changes included mainly inside the plug while the socket was the same as that used in the CFFCS. It can be seen from Figure 13 that the streamlines in the sockets of the two coupling systems show obvious vortex phenomena near the outlet. This is due to the sudden increase in the flow cross-sectional area, which causes the flow rate to reduce and the pressure to increase sharply.  
Figure 12: Pressure distribution results for the two flat-face coupling systems, (**a**) The CFFCS and (**b**) Initial design of the NFFCS.  
Figure 13: Velocity and streamline distributions for the two flat-face coupling systems, (**a**) The CFFCS and (**b**) Initial design of the NFFCS.  
It can be observed that there is a large unevenness in position 1 where the plug valve and the socket pin make contact, which can be assumed to be the reason for the large energy loss. The unevenness of position 1 was smoothed as shown in Table 1 without changing the structural reliability of the parts. From the result of turbulent kinetic energy distribution at position 1 shown in Table 2, it can be seen that the maximum value for the optimized design is 4.27 m\({}^{2}\)s\({}^{-2}\), which is 28.9% less than the 6.01 m\({}^{2}\)s\({}^{-2}\) value observed for the initial design.  
Similar to position 1, position 2 also has micro-geometric unevenness due to the improper chamfering of the component, which causes considerable energy loss at this position. By modifying the improper chamfer, the maximum value of the turbulent kinetic energy is reduced from 10.67 m\({}^{2}\)s\({}^{-2}\) to 7.50 m\({}^{2}\)s\({}^{-2}\), which is a reduction of 29.7%. A comparison of the results at position 2 is shown in  
inlet and the outlet, the pressure drop was found to be 42.79 kPa, which is 13.5% less than the pressure drop of the initial design (49.49 kPa). It can be seen from the pressure distribution that the overall pressure drop gradient distribution from inlet to outlet is uniform. By comparing Figure 15b with Figure 13b (initial design), it can be seen that the vortex phenomenon occurring at the outlet has also been significantly improved.