# Spatiotemporal Evolution of Gas in Transmission Fluid under Acoustic Cavitation Conditions
## 3 Results
### Transient Change of Air and Vapor Void Fraction  
Figure 4 shows the change in transmission fluid flow velocity. From the figure, the maximum forward flow velocity of transmission fluid is about 50 m/s, and the reverse flow velocity is almost 130 m/s. The pressure difference between the air cavitation and vapor cavitation stage is large, leading to the rapid increase in flow velocity, especially in the vapor cavitation stage. The cavitation process is divided into the cavitation formation stage, cavitation growth stage, and cavitation end stage. Figures 5-7 present the flow states at the various locations of the tube at \(t\) = 0.09-0.145 s. The air cavitation and vapor cavitation are expressed separately in the figures, showing the transient changes in flow velocity, pressure, and gas void fraction along the axial direction of the transmission tube at different times in the two cavitation zones. Figure 4: Variation of transmission fluid flow velocity. Figure 5: Cavitation formation stage. Figure 5 shows the variation of transmission fluid flow velocity, pressure, and gas void fraction with the tube axial distance in the cavitation formation stage. When \(t=0.09\) s, the situation before vapor cavitation is described in Figure 5a. At this time, the pressure wave propagates toward the outlet and does not influence the cavitation zone, so the gas void fraction does not change. Vapor cavitation occurs due to the pressure wave effect when \(t=0.1\) s. Because the local pressure is lower than the saturated vapor pressure, a rarefaction  
Figure 6: Cavitation growth stage. Figure 7: End of cavitation stage. wave is produced and passes through the cavitation zone, making the flow discontinuous. At the same time, the gas void fraction is dominated by air cavitation, and the maximum air void fraction is around 1.38%, while the maximum vapor void fraction is almost 0.008%. At \(t\) = 0.1-0.114 s, the vapor cavitation zone along the tube's axial direction moves toward the tube outlet and the interval increases from 0.05 m to 0.2 m. The trend of movement is consistent with the result by [PERSON] et al. [25]. Figure 5d indicates that the vapor void fraction gradually increases, reaching 0.012%. As the vapor cavitation increases, the reverse flow velocity increases rapidly, from 40 m/s to 130 m/s. At this stage, the vapor void fraction presents a trapezoidal distribution. Therefore, the vapor void fraction generated by cavitation rises slightly. The variation of transmission fluid flow velocity, pressure, and gas void fraction with tube axial distance in the cavitation growth stage is shown in Figure 6. When \(t\) = 0.122-0.128 s, the gas void fraction is still dominated by air cavitation. The maximum air void fraction increases from 1.38% to 1.387%. Along the tube's axial direction, the vapor cavitation zone continues to move towards the tube outlet, and the interval increases from 0.23 m to 0.293 m. Due to the short time history and small pressure change at this stage, cavitation needs time to grow. The distribution of vapor void fraction is similar to the M-shape distribution. The maximum vapor void fraction increases from 0.013% to 0.308%, so the vapor cavitation is more intensified. The reverse flow velocity continues to increase from 130 m/s to 140 m/s until the rarefaction wave leaves the vapor cavitation zone, and the pressure wave starts to propagate from the tube's outlet to the tube inlet. Figure 7 shows the variation of transmission fluid flow velocity, pressure, and gas void fraction with tube axial distance at the end of cavitation. The maximum vapor cavitation degree is attained at \(t\) = 0.134 s, and the maximum air void fraction is about 1.925%. The vapor void fraction presents an inverted V-shaped distribution, and the maximum vapor void fraction is approximately 0.5% in Figure 7a. This is close to the maximum vapor void fraction of 0.52%, reported by [PERSON] et al. [25].