# Effect of Fuel Mass Flow at the End of Injection on Cavitation and Gas Ingestion in the Nozzle
## 4 Results and Discussion
### After Injection (AI)  
The diesel volume fraction AI is presented in Figure 6. From 0.40 ms onward, it can be seen that the external air enters the nozzle through the orifice outlet and finally extends into the sac. In this process, cavitation gradually decreased, and the gas ingestion bubbles increased. As can be seen from Figure 6, the zone colored in blue shows that gas ingestion gradually increased, and the area occupied by bright black also increased at the corresponding moment, i.e., the gas ingestion bubbles increased in the nozzle. This phenomenon can be further explained like this: as the cavitation extended to the outlet of the nozzle, under the action of the pressure wave and aerodynamic force, a dynamic pressure imbalance occurred between the external environment and the cavitation. The environmental pressure was greater than the internal pressure of the cavitation bubble, this differential pressure imbalance led to cavitation rupture, and then a new pressure imbalance was created, which resulted in the cavitation collapse [4]. From the simulation result, cavitation reached its maximum at 0.35 ms.  
At 0.55 ms, the external air flowed back into the orifice inlet, and the cavitation in the orifice disappeared completely. At 0.8 ms, with the collapse of the cavitation in the sac, the external air also back-flowed into the sac. At 1.5 ms, the cavitation in the nozzle disappeared completely, the gas part in the nozzle was all ingestion gas. Due to surface tension, the gas ingestion bubbles began to fuse and became brighter, more transparent, and regular. When the nozzle was in the static state (2.0 ms), the gas ingestion bubbles were fully fused and occupied 3/4 of the length of the orifice.  
Figure 6: Volume fraction of diesel in the nozzle after injection (AI).  
In Figure 7, time-dependent changes in ingestion gas and cavitation in the nozzle are presented. Before 0.25 ms, the volume fraction of cavitation in the nozzle was mainly up to the orifice. After 0.25 ms, the total amount of cavitation in the nozzle depended on the sac, and the cavitation in the orifice began to collapse. However, at the initial stage of the EOI (0.2 ms), there was almost no cavitation in the sac. This indicated that cavitation more likely occurred in the orifice, instead of the sac, which further validated the analysis in Figures 6 and 7. The cavitation in the nozzle was almost zero in the later stage of the EOI, and the maximum volume fraction of cavitation in the sac was close to that of ingestion gas. It is noteworthy that the growth rate of the volume fraction of the ingestion gas is \(1.06\cdot\times 10^{-5}\cdot/\)ms, and the volume fraction reduction rate of cavitation is \(-1.05\cdot\times 10^{-5}\cdot/\)ms; it was concluded that gas ingestion was mainly caused by cavitation collapse.  
Figure 8 represents the time-dependent variations in fuel inertial outflow and in average pressure within the nozzle. At the beginning of the EOI, the pressure in the nozzle was high. As the fuel injection process progressed, the average pressure in the nozzle dropped rapidly and maintained a certain low pressure for a duration. Then the average pressure increased rapidly, which finally decreased slightly and remained constant. As seen from Figure 7, the duration in a lower pressure was the stage of cavitation development. The fuel inertia outflow increased in the cavitation development stage because there was a lower pressure in the nozzle and a strong pressure difference between the nozzle entrance and exit, thus increasing the fuel kinetic energy. It can be seen from Figures 7 and 8, although the fuel inertial outflow increased at the beginning of the EOI, as the pressure difference decreased, impelling a decrease in the kinetic energy and inertial outflow of fuel, the cavitation amount decreased.