## 5 Simulation Results and Analysis  
### Pressure Field  
The pressure distribution in the same compression chamber is basically uniform both radially and axially. Figure 7 shows the pressure field cloud distribution at different rotational angles after the working fluid in the working chamber stabilizes. For both the combined profile and uniform wall thickness vortex compressors, the pressure increases from the suction chamber to the central exhaust chamber and is symmetrically distributed around the center, conforming to the theoretical cycle pressure variation. The pressure in the central exhaust chamber slightly decreases when reaching the exhaust angle due to the outward exhaust, with a clear pressure difference between adjacent compression chambers. The pressure distribution within the same compression chamber is uniform in both radial and axial directions. The maximum pressure in the working chamber of both the combined profile and uniform wall thickness vortex compressors increases and then decreases as the main shaft rotates, with the optimized combined profile working chamber having a higher flow pressure compared to the uniform wall thickness vortex compressor. Figure 6: Mark point pressure curve. Figure 7a shows an enlarged view of the radial engagement gap area between the dynamic and static vortex teeth. The radial gap of the vortex compressor acts as a channel that is narrow in the middle and wider on both sides. As the eccentric main shaft performs rotary translational motion, the engagement points of the dynamic and static vortex teeth continuously move towards the central chamber. Simultaneously, the pressure difference on both sides of the engagement point gradually increases, showing a decreasing gradient change in pressure from the high-pressure chamber to the low-pressure chamber at the radial gap engagement point. Leakage in the working chamber of vortex compressors leading to unstable pressure fluctuations further affects the smooth operation and performance stability of the compressor. Figure 8 shows the trend of the total pressure at the inlet and outlet as the main shaft angle changes during five cycles of operation of the vortex compressor. The total pressure at the outlet of both the combined profile and uniform wall thickness vortex compressors shows periodic changes during the second cycle of the main shaft's rotation, with the trend gradually stabilizing. When the main shaft angle approaches 290\({}^{\circ}\), the flow cross-sectional area of the exhaust port is at its maximum, and the total pressure at the outlet reaches its maximum value. The maximum total pressure at the outlet of the combined profile vortex compressor is 4.34% higher than that of the uniform wall thickness vortex compressor, and the average total pressure is 2.38% higher. The average total pressures at the inlet of both the combined profile and uniform wall thickness vortex compressors are almost equal and stabilize at 107,380 Mpa. A comparison of the related pressure values is shown in Table 4. Compared to the uniform wall thickness vortex compressor, the maximum outlet pressure of the combined profile vortex compressor is increased by 4.34%, and the average total outlet pressure is increased by 2.38%. Additionally, the total outlet pressure of the variable  
Figure 7: Pressure could map distribution at different corners. (**a**) Pressure nephogram of combined profile; (**b**) pressure nephogram of uniform wall thickness profile. diameter vortex compressor is always higher than the outlet pressure, indicating the absence of backflow at the exhaust port, thereby reducing leakage losses during operation of the compressor. Figure 9 shows the trend of mass flow rate at the inlet and outlet over five cycles of the main shaft's operation in the vortex compressor. The mass flow rates at the inlet and outlet exhibit regular changes during the second cycle of operation. As the total pressure at the outlet reaches its maximum value, the mass flow rate at the outlet also reaches its peak.