# Spatiotemporal Evolution of Gas in Transmission Fluid under Acoustic Cavitation Conditions
## 3 Results
### Pressure Transmission Characteristics  
Figure 2 shows the transient pressure change of transmission fluid. The \(x\)-axis represents the axial position of the tube, and the y-axis represents the time. It can be seen from the figure that the initial pressure of transmission fluid is 6 bar, and the maximum pressure is about 500 bar. The pressure wave propagates in the transmission tube. At \(t\) = 0.1-0.14 s, \(x\) = 0-0.51 m, the transmission fluid pressure drops significantly, and its pressure is around the saturated vapor pressure. The local cavitation effect of vapor is generated near the inlet of the transmission tube, which leads to cavitation, and then the transmission fluid pressure starts to increase. From the perspective of pressure fluctuation, the changing trend of transmission fluid pressure is the same as that of the result by [PERSON] et al. (2015), including the zone where cavitation occurs and the propagation trend of the pressure wave, which illustrates the effectiveness of the conservative homogeneous flow model.  
Figure 3 shows the change of gas void fraction with pressure, including air and vapor. At the position of \(x\) = 0 m, when \(t\) = 0.04-0.07 s, the pressure rises and the gas in the transmission fluid dissolves. Within 5 us, the gas void fraction decreases from 1% to 0.1%. When \(t\) = 0.07-0.1 s, the pressure decreases, and the dissolved gas starts to evolve. Within 5 us, the gas void fraction increases from 0.05% to about 1%. When \(t\) = 0.1-0.14 s the pressure is lower than the saturated vapor pressure, a small part of the transmission fluid evaporates, and the maximum air void fraction reaches about 1.3%. Additionally, air cavitation occurs when t is around 0.16 s. The transmission fluid pressure peak value and the vapor cavitation start time are delayed in the tube axial direction. The vapor cavitation duration decreases along the tube axial direction, from 0.04 to 0 s, as found by [PERSON] et al. (2019). However, in the pseudo-cavitation zone, the difference is that the gas void fraction rises and drops rate obtained by the conservative solution is rapidly, while the non-conservative solution is slower. This is because the original variable depends  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Main Parameters** & **Unit** & **Value** \\ \hline Tube length & m & 1.1 \\ Tube diameter & mm & 2 \\ Air gas constant & J/(mol\(\cdot\)K) & 287 \\ Vapor gas constant & J/(mol\(\cdot\)K) & 87.34 \\ Atmospheric pressure & bar & 1 \\ Air separation pressure & bar & 10 \\ Saturated vapor pressure & bar & 0.65 \\ Specific heat capacity ratio & - & 1.2 \\ Initial gas-to-liquid mass flow rate ratio & \% & 0.13 \\ Constant-pressure-specific heat capacity & J/(kg\(\cdot\)K) & 2.06 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameters required for simulation calculation.  
Figure 2: Variation of transmission fluid pressure.  
on the bubble model to solve the gas void fraction, and the model does not consider the change in the speed of sound under vapor cavitation. The pressure wave propagates along the speed of sound line \(\gamma\) and changes slowly during the rising and falling of the pressure. The solution of the gas void fraction of the conservation variable depends on the conservation variable density \(\rho\) and momentum \(\rho u\). The pressure wave propagates along the characteristic line u \(\pm\)\(\gamma\), while the characteristics of the three cavitation zones have different slopes. At the turning point where air cavitation and pseudo-cavitation effects occur, the gas void fraction changes rapidly.  
Figure 3: Variation of gas void fraction with pressure ((**a**–**h**) represent the process from tube inlet to outlet).