# Dynamic Analysis of Cavitation Tip Vortex of Pump-Jet Propeller Based on DES
## 4 Conclusions  
In the present work, on the basis of the DES turbulence model and Zwart-Gerber-Belamri cavitation model, the shape and dynamic characteristics of TLV and TSV of a pump-jet propeller under slight and severe cavitation conditions were studied. The vorticity equation and two vortex recognition methods were employed in this study and through comparative analysis, it found that:  
1. At \(J=1.02\), the vortices at cavitation extend towards the trailing edge of the blade compared with the vortices at non-cavitation, and the integration time of TLV and TSV is delayed. The main frequency of the TLV vortex core is nine times the shaft frequency and the secondary frequency is 4 times the shaft frequency when the cavitation is mild. However, low-frequency and high-frequency pulsations occur at the severe cavitation. By using the stretching term in the vorticity equation to analyze the dynamic characteristics of TLV, it is found that cavitation will intensify the stretching and bending of the tip vortices. 2. At \(J=0.73\), the main frequency of the vortex core is still nine times the shaft frequency, but the secondary main frequency is almost all replaced by 0.1 times the shaft frequency. After cavitation occurs, a third type of vortex appears near the trailing edge of the blade, which is located between TLV and TSV while generated by the tip and moved towards TLV. The stretch term contour shows that the TLV and TSV are independent at the leading and middle parts of the blades. Figure 23: Frequency domain diagram of pressure fluctuation before and after cavitation at TSV monitoring points (**a**) \(J=1.02\) non-cavitation (**b**) \(J=1.02\) cavitation (**c**) \(J=0.73\) non-cavitation (**d**) \(J=0.73\) cavitation. When cavitation occurs, there are red ribbon vortexes at the trailing edge of the tip that connect the TLV and TSV. 3. When slight cavitation occurs, the cavitation promotes the intensity of the tip vortices and the Q is much higher. Furthermore, bubbles promote the strength of tip vortices and the Q at cavitation is much larger than that at non-cavitation. As the rotational speed increases, the cavitation area on the blade surface will increase further than at low rotational speeds, since the increase in velocity will lead to a decrease in local pressure. 4. After cavitation, the position of the TLV vortex core will deviate from that before cavitation. When slight cavitation occurs, the position of the vortex core hardly changes in the upper and middle reaches of the tip. However, along the stream-wise direction, the vortex core first moves towards the suction side of blade and then moves away from it. When severe cavitation occurs, the position of the vortex core deviates considerably from that before cavitation, and the trend of deviation is opposed to that of slight cavitation. 5. The pressure fluctuation of the TSV vortex core shows that, at \(J=1.02\), the pulsation intensity of the cavitation TSV near the middle of the tip is much lower than that near the leading edge of the suction side of the blade. This indicates that although cavitation only occurs near the suction side, its influence on the flow field extends to the middle area of the tip. At \(J=0.73\), the amplitude of the main frequency at all monitoring points of the TSV is increased and the entire TSV is affected by cavitation. In addition, the turbulent instability of TSV is more severe. For future work, similar optimization as in references [52; 53] for the pump-jet impeller can be performed to enhance the general propulsion efficiency of the device and to save power. Conceptualization, J.Y. and L.W. ; methodology, Y.C. ; software, Y.C. and Y.Z. ; investigation, Y.F. and J.X. ; writing-original draft preparation, Y.C. and L.W. ; writing--review and editing, L.W. and R.L. All authors have read and agreed to the published version of the manuscript. This research was funded by Institute of Fluid Engineering Equipment, Natural Science Foundation of Jiangsu Province (Grant No.