## 3 Results and Discussion  
As the gear pump rotates, the rapid volume changes within the displacement chamber continuously compress and propel the liquid. This drastic change can easily lead to transition flow. Five moments are selected, as shown in Figure 5 (T1 = 0.1825 s, \(\Delta\)T = 365 \(\upmu\)s). The periodic evolution of cavitation at P2 (333.15 K) is shown in Figure 6. Comparing the volume of tooth tip gaps on the right, it can be seen from the pressure contour in Figure 6 at time T1 that pressure in the area where point P2 is located decreases due to the increase in cavity volume during rotation, leading to the occurrence of cavitation in the form of a vortex. It can be seen from Figure 6 at T1 and T2 that the volume of the cavitation area increases. Significant pressure fluctuations are evident on the contour at the meshing point, leading to leakage flow across these two narrow cross-sections. Additionally, as the gear pump continues to rotate at T3, T4, and T5, the two teeth disengage from the meshing area. Inlet hydraulic oil enters the cavitation area, resulting in increased pressure within this region and subsequent cavity collapse. Figure 7 shows the variations of temperature, velocity, and gas volume fraction at different positions at 303.15 K. The gas volume fraction and temperature change almost synchronously. Cavitation is a transition between liquid and gas, accompanied by the absorption and release of heat. When cavitation occurs, the gas volume fraction increases. The liquid absorbs heat from the surrounding fluid, resulting in a temperature increase. Conversely, when cavity collapse occurs, the gas volume fraction decreases, and the liquid releases heat to the surrounding fluid, causing a temperature drop. However, it can be seen in the curves that as the temperature approaches its lowest point, a small fluctuation consistently occurs, initially increasing and then decreasing. This phenomenon is particularly pronounced in Figure 7b,c. During the rotation of the gear pump, the volume and pressure inside the chamber continuously change. This rapid and vigorous fluctuation can readily induce cavitation and the rapid emergence of leakage flows within narrow gaps, ultimately resulting in the formation of a vortex. Figure 5: The selection of five time points at P3 (333.15 K). Figure 6: The evolution of cavitation at P2 (333.15 K). Figure 7: \(Cont\). Thermodynamic Effects of Cavitation at Different Temperatures  
The inlet cavitation number is maintained at a constant to analyze the influence of temperature on cavitation dynamics. The evolution of cavities at different temperatures is shown in Figure 8. The cavitation phenomena at each point exhibit significant fluctuations and generally display a diminishing trend with increasing temperature. Consequently, it is evident that higher temperatures inhibit cavitation development. The pressure coefficient, a dimensionless number, characterizes the relative pressure across the entire flow field, which is shown in Equation (13). \[C_{p}=\frac{p-p_{\infty}}{0.5\rho_{l}{\rm{U_{\infty}}}^{2}} \tag{13}\]  
\(p_{\infty}\) is the pressure of the flow field at infinity (referring to inlet pressure in this paper). \(p\) is the local pressure. \(\rho_{l}\) is the density of the fluid. \(U_{\infty}\) is the velocity of the incoming flow at infinity (refers to the gear top linear speed in this paper). Figure 7: Fluctuation of pressure, temperature, and gas volume fraction at P2 (**a**), P3 (**b**), and P4 (**c**). Pressure coefficients at P2, P3, and P4 at different temperatures are shown in Figure 9. The range of pressure coefficient fluctuation at each point increases with rising temperature. In other words, as the temperature increases, the influence of the thermodynamic effect on cavitation intensities.