# Numerical Simulation Study on the Volumetric Efficiency Loss of CO2 Swash Plate Axial Piston Pumps
## 3 Verification of Mesh Generation and Mesh Independence  
The mesh of the piston pump fluid domain model with a fluid film on the mating pair, piston pair, and slide shoe pair is shown in Figure 2. As can be seen in the figure, the unstructured tetrahedral mesh and structured hexahedral mesh composite meshing technique was used to mesh the piston pump's fluid domain. As the inlet and outlet pipes had a complex structure, a tetrahedral mesh was chosen; meanwhile, as the plunger  
\begin{table}
\begin{tabular}{l c} \hline \hline
**Parametric** & **Design Value** \\ \hline Plunger diameter d (mm) & 35 \\ Plunger distribution circle diameter D (mm) & 116 \\ Inclination angle of swashplate \(\beta\) (\({}^{\circ}\)) & 20 \\ Inside diameter of distributor disc waist groove r1 (mm) & 48 \\ Outer diameter of distributor waist groove r2 (mm) & 62 \\ Opening angle of distributor waist slot \(\theta\) (\({}^{\circ}\)) & 65 \\ Inlet pipe diameter di (mm) & 50 \\ Outlet pipe diameter do (mm) & 50 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Geometric parameters of the fluid domain and liquid film of a friction pair of a swashplate axial piston pump.  
Figure 1: Schematic diagram of geometric structure of fluid domain of plunger pump.  
cavity had a regular structure, the multi-area mesh division method was chosen. The structured meshing method was adopted for the fluid domain of the liquid film on the flow distribution vice, plunger vice, and sliding shoe vice, with five layers of meshing along the thickness direction. The liquid film could be enlarged by 1000 times along the thickness direction during the modeling of the flow distribution vice and then proportionally scaled down to the micrometer-level thickness of the liquid film in the numerical simulation analysis.  
Considering the balance between calculation accuracy and calculation cost, numerical simulations with various grid numbers were carried out with the objective function being the compression retention volume loss in the fluid domain of the piston pump and the leakage volume loss of the port pair. The calculation results are shown in Figures 3 and 4. It can be seen from the figure that for the plunger pump fluid domain, when the grid number was greater than 700,000, the calculation results for the compression retention volume loss tended to be stable. In the plunger pump fluid domain, 76.79% of the tetrahedral grid cells had a mesh quality of more than 0.8, and the hexahedral grid cells all had a quality greater than 0.8. It can be seen from this that the mesh quality was high, indicating that the mesh was suitable for the subsequent numerical simulation. As such, about 700,000 grid cells were used for the numerical simulation. For the secondary liquid film structure, when the number of grid cells was greater than 60,000, the calculation results for the leakage volume loss were stable, and the grid quality of all cells was greater than 0.8, meeting the calculation accuracy requirements.  
Figure 3: Grid-independent validation of compression hold-up volume loss.  
Figure 2: Grid model of the fluid domain, fluid film of the distribution pair, fluid film of the plunger pair, and fluid film of the slipper pair of the plunger pump. (**a**) Piston pump fluid domain. (**b**) Port auxiliary liquid film. (**c**) Piston auxiliary liquid film. (**d**) Slipper auxiliary liquid film.