# Numerical Simulation Study on the Volumetric Efficiency Loss of CO2 Swash Plate Axial Piston Pumps
## 6 Calculations and Analyses  
Before the numerical simulation, it was necessary to initialize a reasonable flow field to provide good initial conditions and to monitor the loss of pump compression retention volume and leakage of the friction pairs to judge whether the calculation results converged. Taking two rotation cycles as an example, it was found that the outlet flow of the plunger pump was stable and the flow was conserved. The loss of compressed retained volume was the main factor affecting the volumetric efficiency of the plunger pump. Figure 10 shows the plunger pump's loss of compressed retained volume. The following can be seen from the figure: (1) In the pressure range of 3-12 MPa, the CO\({}_{2}\) medium underwent a change process from a liquid to a dense phase. The dense-phase CO\({}_{2}\) had the characteristics of high-density liquid and low-viscosity gas. From Figure 5, it can be seen that the density, viscosity, and other physical parameters of the CO\({}_{2}\) changed with changes in the pressure and temperature, and the actual compressed volume changed nonlinearly. This deviated from the theoretical geometric displacement of the plunger pump, resulting in dynamic compression volume loss. (2) The following dead center plunger was taken as an example. In order to avoid rigid collision between the plunger and the top of the plunger cavity, it was necessary to ensure that there was a certain matching bottom gap between them. The bottom gap area formed a bottom gap volume. CO\({}_{2}\) has high compressibility under high pressure, and this part of CO\({}_{2}\) cannot be discharged in the bottom gap volume. This retention phenomenon causes a loss of displacement and causes secondary compression of the working fluid when the plunger returns, resulting in a loss of retention volume. (3) The compression retention volume loss of the plunger pump was 81.2L/min. According to Formula (7), under the fixed working conditions applied in this study, the compression retention volume loss of the CO\({}_{2}\) plunger pump accounted for 28.6% of the volumetric efficiency. Figure 11 shows the relationship between the leakage volume loss of the flow distribution sub-film and the leakage volume loss of the three outlets. From the figure, the following can be seen: (1) After 0.02s, the leakage volume loss of the flow distribution sub-film was basically stable, and each leakage channel showed differentiation. The leakage to the side of the pump casing was the largest, accounting for 61.5% of the total leakage volume loss; the leakage to the side of the pump shaft was the second largest, accounting for 36.0% of the total leakage volume loss; and the leakage to the low-pressure area of the waist-shaped groove was the least, accounting for 3.5% of the total leakage volume loss. (2) The leakage volume loss on the piston pump flow side was 4.4L/min. According to Equation (7), the liquid film leakage volume loss on the flow side accounted for 1.5% of the volumetric efficiency. As the cylinder speed of the plunger pump was 1000 rpm, it took 0.06 s for the cylinder to complete one cycle. The plunger moved back and forth in the plunger cavity in each cycle, and the leakage volume loss of the secondary liquid film of the plunger under two motion cycles was obtained, as shown in Figure 12. The following can be seen from the figure: (1) In the range of 0-0.03 s, the leakage volume loss of the liquid film was basically zero. Thus, at this time, the plunger moved in the low-pressure area, the inlet pressure value of the liquid film was consistent with the outlet pressure value, and no leakage occurred. In the range of 0.03-0.06 s, the inlet pressure of the liquid film of the plunger pair increased gradually.