# Numerical Simulation Study on the Volumetric Efficiency Loss of CO2 Swash Plate Axial Piston Pumps
## 1 Introduction
Their results showed that the liquid film temperature increased with increases in the working pressure and inclination angle of the swashplate. Prior performance research on the plunger pair includes that by [PERSON] et al. [16], who set grooves on a plunger surface and studied the influence of the number of grooves and their position on the plunger surface on the lubrication characteristics of a plunger pair. Using the finite volume method, a mathematical model of the liquid film of a plunger pair was established. The results showed that a plunger pair can work more stably when the grooves are positioned on the plunger surface. [PERSON] et al. [17] established a mathematical model of a plunger pair based on mixed lubrication theory, which considers parameters such as the plunger inclination, thermal effect, and surface roughness. Their results showed that when the inlet pressure is high, the liquid film thickness of the plunger pair increases, and the liquid film thickness decreases with an increase in working speed. [PERSON] et al. [18] found that under harsh environments, the friction and corrosion between the plunger surface and the cylinder block are considerable, resulting in damage to the outer surface of the plunger and eventually leading to failure. According to bionic theory, two kinds of bionic plunger with friction-reducing performance were designed. The results showed that the bionic plunger reduced the plunger wear. [PERSON] j et al. [19] established a leakage model of a plunger pair and used a genetic algorithm and the finite volume method to numerically simulate the liquid film gap and pressure distribution of the plunger pair. Their results showed that the model had high accuracy, and they discussed the influence of the plunger diameter, initial plunger clearance, and plunger movement speed on the liquid film leakage. Prior performance research on the slipper pair includes that by [PERSON] et al. [20], who conducted a numerical simulation of a slipper pair. Their results showed that with an increase in working pressure, the pressure field of the liquid film increased, while the velocity field and temperature field remained basically unchanged. With an increase in working speed, the velocity field and temperature field were greatly improved, and the pressure field was almost unchanged. [PERSON] et al. [21; 22] proposed a new analysis model for a slipper pair based on the Reynolds equation. Compared with an experimental analysis, their theoretical model was able to more accurately predict the leakage loss and pressure distribution of a slipper pair. [PERSON] et al. [23] designed a new test scheme for a slipper pair and used test methods to analyze the influence of different slipper surface roughnesses on the lubrication characteristics of the slipper pair. [PERSON] et al. [24] established a dynamic liquid film model to determine the critical pressure of a shell according to the influence of the plunger pump's shell pressure on a slipper pair. Their results showed that the thickness of the liquid film and the overturning angle of the slipper increased with an increase in the shell pressure. With an increase in shell pressure, the support stiffness of the slipper pair's high- and low-pressure transition zone decreased. [PERSON] et al. [25] used computational fluid dynamics numerical simulation methods based on N-S equations and the Lagrange method to analyze the performance of a slipper pair. Their numerical simulation results showed that a higher slipper rotation speed led to an uneven pressure distribution of the liquid film along the radial direction, along with greater friction of the slipper pair. At present, there are no relevant studies in the literature analyzing the volumetric efficiency loss of swashplate axial piston pumps with a CO\({}_{2}\) medium.