# Dynamic Analysis of Cavitation Tip Vortex of Pump-Jet Propeller Based on DES
## 1 Introduction
[PERSON], [PERSON] et al. [PERSON] et al. (2018) took the standard propeller DTMB-4119 as the test object, and analyzed the propeller wake field through the PIV test method. They found that there are positive and negative vortices in the propeller tail vortex, which are generated on the suction side and pressure side of the blade, respectively. [PERSON] et al. [PERSON] et al. (2019) simulated and tested the tip vortex of an axial pump at three different flow rates based on the SST \(k\)-\(\omega\) turbulence model. The results indicate that, as the flow rate increases, the tip vortex gradually moves toward the pressure side of the adjacent blade, and the initial point of the tip vortex will also move from the leading edge to the midpoint of the chord. Focused on symmetrical tip clearance and unsymmetrical tip clearance, [PERSON] et al. [PERSON] et al. (2019) applied an improved cavitation model on a mixed flow pump as turbine at pump mode and the results showed that unsymmetrical tip clearance has more influence on radial force than symmetrical tip clearance. [PERSON] et al. [PERSON] et al. (2019) simulated the tip leakage vortex cavitating flow based on improved SST \(k\)-\(\omega\) turbulence model and Rayleigh-Plesset cavitation model combined with the test data provided by a high-speed imaging system. They revealed the vortex dynamics of TLV cavitation, tip corner vortex cavitation, shear layer cavitation, and blowing cavitation. Furthermore, the TLV cavitation patterns are also demonstrated which clearly explain the spatial evolution of TLV cavitating flow. Four types of transition model are analyzed and compared by [PERSON] et al. [PERSON] et al. (2019), which make great contributions to transition research and modeling in the future. In summary, though there have been studies on the internal vortex structure and cavitation performance of the pump-jet propeller, the correlation analysis of the interaction between cavitation and the vortex dynamics has been few, especially for the study of vortex core pressure of the pump-jet propellers. Therefore, this paper aims to fill the research gap. The main focus is to investigate the shape and dynamic characteristics of the TLV and TSV that appears in the rotor tip clearance area before and after cavitation under different rotational speeds by DES turbulent model. The vorticity transport equations are applied for the first time to research the effect of cavitation occurrence on the tip vortex evolution mechanism in pump-jet. Furthermore, the \(Q\) criterion is used to identify the vortex core before and after cavitation, respectively. The numerical settings in this research are based on previous work [33; 34; 35; 36; 37; 38; 39]. For the purpose of verifying the accuracy and reliability of the numerical work in this study, two other researches focused on pump-jet thruster conducted with experiment have been referred. [PERSON] et al. [8] obtained numerical and experimental thrust and torque coefficients curves at Bollard pull condition at different rotor spins, and the numerical results agreed well with experimental results. [PERSON] et al. [7] could predict the cavitation inception point well compared with test data. Moreover, [PERSON] et al. [40; 41] simulated a post-rotor pump-jet propeller with the same turbulent model as this research and compared with test data acquired in a cavitation tunnel, the computational results have a good agreement with the experiment data. The difference between numerical results and experimental results is small, which indicates the feasibility of the numerical calculation. In this paper, the structure arrangement is as follows. Numerical method and computational setup are described in Section 2, including pump-jet model and grid independence analysis. In Section 3, the vortex dynamics and the interaction between cavitation and vortex are analyzed, in addition, the pressure propulsion of tip separation vortex is compared between different working conditions. Finally, a summary of the results overview is exhibited in Section 4.