# Dynamic Analysis of Cavitation Tip Vortex of Pump-Jet Propeller Based on DES
## 3 Cavitation and Vortex Dynamics Analysis of Pump-Jet Propeller
### Comparison of J = 1.02 and J = 0.73 Results  
In order to investigate the mechanism by which cavitation bubbles affect the tip vortex, it is necessary to compare the results of different rotational speeds. As shown in Figure 21, the TLV trajectory changes as the rotational speed increases from \(J=1.02\) to \(J=0.73\). When cavitation occurs at \(J=1.02\), the trend of TLV trajectory almost coincides with that of non-cavitation in the upper and middle part of the tip. However, as it moves towards the outlet of the rotor, the cavitation vortex core firstly approaches the suction side of the blade and then shifts away from it. It is obvious that the track of the TLV will be far away from the suction side of the blade when the rotational speed is high, so it can be inferred that the starting point of the TLV will move towards the leading edge of the tip as the rotational speed increases. Differing from the TLV vortex core track at \(J=1.02\), there is little coincidence of TLV vortex core before and after cavitation at high rotational speed. In addition, when cavitation occurs, the vortex core first moves away from the blade in the downstream area near the tip, which then shifts towards it. In order to investigate the intensity changes of TLV under different cavitation levels, the vortex cores of TLV are extracted from 8 axial sections along the axial heights of 6 mm, 4 mm, 2 mm, 0 mm, \(-2\) mm, \(-4\) mm, \(-6\) mm and \(-8\) mm, named P1\(\cdot\)P8 respectively, and their vorticity changes (represented  
Figure 21: Variation of TLV core trajectory with rotational speed and cavitation. Figure 20: Z-direction component contour of stretching term at \(J=0.73\), (**a**) non-cavitation (**b**) cavitation. by \(Q\) value) are shown in Figure 22. It can be found that \(Q\) decreases gradually in the stream-wise direction at \(J=1.02\) without cavitation and then hardly changes at the trailing edge of the tip due to the dissipated tip vortices. Then, when the pump-jet propeller cavitates at this rotational speed, the vorticity strength of P1 and P2 increases sharply, and the \(Q\) is almost twice as much as that of non-cavitation. It indicates that under slight cavitation, bubbles promote the strength of tip vortices. The \(Q\) value under cavitation is much larger than that under non-cavitation up to the trailing edge of the blade, showing that the influence of cavitation bubbles on the tip vortices always exists along the tip clearance near the blade tip. As the rotational speed increases to 1750 rpm, the TLV intensity without cavitation becomes more intense. That can be explained as the faster the rotor rotates, the bigger the speed gradient in the tip vortex region and the higher the curl. At \(J=0.73\), the bubbles cover almost the entire suction side of the blade, so that the fluid near the tip is replaced by bubbles. In severe cavitation condition, \(Q\) rises from P5 due to the bubbles filling the surrounding water. Bubbles appear because of the low-pressure zone, and the range of the low-pressure area around the vortex core is larger than that without cavitation, which promotes the generation of the tip vortex. Since the driving force of tip vortices comes from the pressure gradient, the cavitation will increase the pressure gradient around the vortices core, which makes TLV develop for a second time. From Figure 23, it can be found that the main frequency of TSV is 9 times the shaft frequency regardless of the cavitation situation. When there is no cavitation, the sub-main frequency of SP1-SP5 is 4 times the shaft frequency. The amplitude of 4 times the shaft frequency in SP6 and SP7 decreases, which is almost negligible compared with the amplitude of the main frequency. When cavitation occurs, except that the amplitude corresponding to the main frequency of SP1 is higher than that of non-cavitation, the most obvious difference is that many low frequency pulsations occur in the cavitation TSV, which is most evident in SP5 and SP6.