# Effect of Fuel Mass Flow at the End of Injection on Cavitation and Gas Ingestion in the Nozzle
## 4 Results and Discussion
### Analyzing the Cavitation Mechanism of Different Mass Fluxes  
Figure 12 shows the distribution of Q = 2 \(\times\) 10\({}^{9}\) iso-surface, streamline, and \(\alpha\) = 0.25 vapor iso-surface in the nozzle at different mass fluxes. From left to right are cloud pictures of Q = 2 \(\times\) 10\({}^{9}\) iso-surface, streamlines, and \(\alpha\) = 0.25 vapor iso-surface, respectively. As can be seen, regardless of whether the mass flux was 12 mg/str, 14 mg/str, or 18 mg/str, the orifice always occurred cavitation first, the cavitation in the nozzle had similar morphology, and the sac was dominated by annular cavitation, while the orifice was bulk. In addition, the annular cavitation in the sac was mainly concentrated at the fuel inlet, then developed from the inlet toward the sac downstream but never reached the bottom of the sac.  
At 0.069 ms, the streamline in the whole nozzle was relatively smooth, and cavitation occurred only in the orifice. Although there was a strong vortex movement in the sac at 0.08 ms, the vortex did not separate, and its structure was compact, i.e., at this temperature, the pressure in the sac did not drop to the saturated vapor pressure, therefore the sac was still turbulent. As the fuel continued to be injected, the strong vortex motion of the sac could be found in the streamline at three different mass flow rates. As previously shown, the core of the vortex had a higher velocity and was prone to form lower pressure zones, thus enhancing cavitation. The streamline separation in the nozzle corresponding to a mass flux of 18 mg/str was more obvious than the mass flow rates of 12 mg/str and 14 mg/str, and the vortex core morphology was larger. The vortex core morphology of the nozzle with a mass flow rate of 18 mg/str was more distorted than that of the other two. This is because the high mass flow nozzle sac corresponding velocity was higher, considering the viscous force between the fuel, therefore, the stretching effect was more obvious in the sac.  
As the fuel injection further continued, the area occupied by the vapor iso-surface in the sac and the orifice increased gradually, i.e., the cavitation increased. The number of vortex cores in the sac increased, which was reflected by the enlargement of the iso-surface area in the nozzle on the Q iso-surface, and the iso-surface passed through the vortex core. This indicated that the surrounding pressure was higher than the central pressure of the vortex core, and the existence of the Q iso-surface was attributed to the internal and external  
Figure 11: Effect of different mass fluxes on gas ingestion.  
pressure difference of the vortex core. At three different mass fluxes, the bulk cavitation was dominated in the orifice, and the annular cavitation caused by the end stretching was the major one in the conical nozzle sac.  
To sum up, annular cavitation was dominant in the conical nozzle sac, and the orifice was dominated by bulk cavitation at different mass flow fluxes. Under a certain Q isosurface, higher mass flow rates increased the stretching in the nozzle and subsequently the flow velocity, fuel inertial outflow, and cavitation.