## 4 Results and Discussion  
The Distribution of Air Phase Velocity Field and the Volume Fraction of Different Oil Droplet Diameter at Different Time  
According to the mechanism of oil droplet coalescence and breakup, the turbulence of air phase flow field has a great influence on the coalescence and breakup of oil droplet. Therefore, the velocity of air phase in the bearing chamber is firstly analyzed. Figure 5 shows the distribution of air phase velocity in the bearing chamber at different time when the air inflow is 12 g/s, oil inflow is 15 g/s, and the initial oil droplet diameter is 28 \(\upmu\)m. As can be seen from the figure, the velocity near the outlet of the bearing chamber is largest, and the other region is smaller. Because the seal air enters into the bearing chamber from the air inlet, it first moves along the axial direction. When the air is blocked by the wall surface, the velocity changes, which results in an uneven velocity distribution of the flow field. The air velocity in the middle region is significantly lower than that in the inner wall surface and the outer wall surface. Meanwhile, many vortices with different size existed in the bearing chamber. With the passage of time, the flow field structure tends to stable. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline Air mass inflow rate m\({}_{g}\) (g/s) & 8, 12, 14, 16 \\ Oil mass inflow rate m\({}_{L}\) (g/s) & 15, 20, 25, 30 \\ Initial diameter \(D_{0}\) (\(\upmu\)m) & 20, 28, 40, 56 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Operating condition. Figure 4: Comparison and verification of oil drop size distribution. Figures 6 and 7 show the volume fraction of oil diameter in the range of 56 to 80 \(\upmu\)m and 28 to 40 \(\upmu\)m when the air inflow is 12 g/s, oil inflow is 15 g/s, and initial oil droplet diameter is 28 \(\upmu\)m, respectively. In Figure 6, the volume fraction of the large diameter oil droplet on the outer wall surface of the bearing chamber is large, that near the inlet is relatively low, and gradually increases along the z axial direction. The volume fraction of large diameter oil droplet near the outer wall of the bearing chamber increases gradually with the passage of time. The reason is that the oil droplet flow with the air phase, and enter the bearing chamber from inlet. During the flow process, the oil droplets with smaller diameter constantly gather. When the air phase flow field reaches the wall that is opposite to the inlet, the flow direction of air phase changes and flows along the wall. During the movement of the oil droplet with the air phase flow field, the oil droplets constantly gather again. Therefore, the volume fraction of oil droplets at the external wall surface of the bearing chamber is large. It can also be seen from the figure that when the oil droplet with larger diameter runs to the entrance with larger velocity, the breakup will occur. The oil droplets are coalesced and broken in the bearing chamber, and finally reach a steady state. In Figure 7, the small diameter oil droplet is mainly distributed near the inlet, and this distribution gradually decreases along the axial direction. It can be seen that the size of the oil droplet in the bearing chamber is different because of the coalescence of oil droplets. The small diameter oil droplet is mainly concentrated near the inlet, while the large diameter oil droplet is mainly concentrated on the outer wall of the bearing chamber. Figure 5: The velocity (m/s) distribution of air at different time when the air inflow is 12 g/s, oil inflow is 15 g/s, and the initial oil droplet diameter is 28 \(\upmu\)m at z = 0 plane (the far left is vent; the far right is scavenge).