## 3 Simulation Results and Impact Analysis
### Relationship between Backflow Clearance and Cylinder Pressure  
In order to study the relationship between backflow clearance and pressure rise during backflow, the CFD model of the reciprocating compressor was used for simulation. To ensure that the pressure curve peaks during backflow, the valve plate is fully open. There is a peak cylinder pressure at the end of the compression process (at a certain crank angle). By modifying the udf (user defined function) of the valve plate movement, the backflow clearance of the valve plate starts from 0.25 mm, and the interval is 0.25 mm. When the clearance of the valve plate reaches the maximum value of 2 mm, the actuator does not interfere with the closure of the valve plate, and the reciprocating compressor is under full load, so the simulation is stopped. The simulation results are shown in Figures 6-8.  
In the traditional design, the effect of the gas resultant force of valve plate on the actuator during the backflow is ignored. However, due to the machining error or small hydraulic force, the backflow clearance will inevitably exist and gradually increase, and the effect of the gas resultant force of the valve plate on the actuator will also gradually increase. As can be seen from Figure 6 and Table 4, when the clearance value is less than or equal to 1.25 mm, the maximum gas pressure increase in the backflow process is small. By increasing the hydraulic force, the backflow clearance can be kept from increasing, and the pressure rise can be controlled so that the unit can still run stably. When the clearance reaches 1.5 mm, the increase is close to 50%. Even if the further increase of the cylinder  
Figure 6: Cylinder pressure at different backflow clearances.  
pressure is controlled by increasing the hydraulic force, the backflow pressure and temperature are too high at this time, and the unit is in poor operation state. Therefore, the machine should be stopped for troubleshooting.  
Figure 7 shows the gas resultant force curve of different backflow clearances, and the trend is the same as the curve of the cylinder pressure. Figure 8 shows the comparison between the experimental curve and the simulation curve. It can be seen that the error is small, which verifies the correctness of the model. Figure 9 shows the maximum gas resultant force and corresponding angle of the valve plate with different backflow clearances. When the backflow clearance is 0.25-1.25 mm, the maximum gas resultant force and corresponding angle change little, indicating that stable operation of the capacity control system can still be achieved when the backflow is small. The relationship between backflow  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Gap Value (mm)** & **0.25** & **0.5** & **0.75** & **1** & **1.25** & **1.5** & **1.75** \\ \hline Maximum pressure in backflow (Pa) & \(1.37\times 10^{4}\) & \(1.49\times 10^{4}\) & \(1.63\times 10^{4}\) & \(1.96\times 10^{4}\) & \(2.61\times 10^{4}\) & \(4.37\times 10^{4}\) & \(1.07\times 10^{5}\) \\ Pressure increase amplitude & 13.67\% & 14.88\% & 16.26\% & 19.58\% & 26.10\% & 43.72\% & 107.19\% \\ \hline \hline \end{tabular}
\end{table}
Table 4: Increase amplitude of cylinder pressure in different backflow clearance.  
Figure 8: Experimental and simulation curves.  
Figure 7: The gas resultant force curve of different backflow clearances.  
clearance and the maximum gas resultant force and the corresponding angle shows exponential growth. By fitting the exponential function, the following can be obtained:  
\[F_{cy}=9.32e^{1.33h_{2}}+0.01329e^{5.822h_{2}} \tag{21}\]