# Dynamic Analysis of Cavitation Tip Vortex of Pump-Jet Propeller Based on DES
## 1 Introduction  
Since the 1980s, pump-jet propellers have gradually attracted the attention of military industries in various countries due to their advantages of high propulsion efficiency, low radiation noise, and extraordinary anti-cavitation performance [1, 2]. In recent years, with the development of water transportation towards high speed, the application scope and demand of pump-jet propellers have beendrastically increasing. As is well known, when the rotational speed of the pump rotor is increasingly high, the pressure in the high-speed region is the lowest which, as a result, means the cavitation is most likely to occur. In most instances, e.g., propellers and pumps, the cavitation is an undesirable phenomenon causing intensive noise, component damage, vibration and loss of efficiency [3, 4]. The shock wave generated by the collapse of the bubble is the main source of noise, which particularly in the marine military field, poses a great threat to the art of stealth during underwater navigation. Above all, it is mandatory to study the cavitation characteristics of a pump-jet propeller for its wide applications. Recently, as more and more scholars have paid attention to new underwater propeller systems, the research of pump-jet propeller has become more and more abundant. Because of expensive cost of test rig, there are still only a few experimental researches about the pump-jet performance. [PERSON] et al. [5, 6, 7] studied the thrust and resistance of a pump-jet propeller. Through experiments in a cavitation water tunnel, it was found that at a higher inflow velocity coefficient, cavitation of the rotor first occurs at the blade tip and with the increase of the rotational speed, the cavitation bubbles shift to the suction side, while the stator and the duct do not exhibit cavitation. [PERSON] et al. [8] conducted ballard pull, self-propulsion point, and bare hull resistance tests in a towing tank on a full scale pump-jet model to research hydraulic performance, and he found that the variations of hydraulic coefficients are much smaller than conventional propellers as the advance coefficient varies. With the advantages of cost saving and more detailed flow field information, numerical simulation results are more plentiful than experiments researches. [PERSON] et al. [9] numerically analyzed the fluid flow of a high-speed underwater vehicle with a pump-jet propulsion system. [PERSON] et al. [10] used Fluent software to numerically simulate the underwater vehicle equipped with pump-jet propulsion based on the RNG \(k\)-\(\varepsilon\) turbulence model, which provides an important reference for pump-jet thruster optimization. A numerical study on a pump-jet propeller equipped with a ring at the blade tip was conducted by [PERSON] and [PERSON] [11], the results showed that the addition of the ring could help reduce the tip vortex strength which may prevent the generation of tip leakage cavitation. [PERSON] et al. [12] performed a steady analysis of the three-dimensional full-channel cavitation flow field of a pump-jet propeller based on the Rayleigh-Plesset equation and the \(k\)-\(\varepsilon\) turbulence model. Compared with the experimental test, it is found that, when cavitation occurs inside the pump-jet propeller, the open water efficiency can be reduced by more than 15%. [PERSON] et al. [13] simulated the unsteady characteristics of a pump-jet propeller based on the shear stress transport (SST) \(k\)-\(\omega\) turbulence model and the Z-G-B (Zwart-Gerber-Belamri) cavitation model. It was found that, among the rotor blade tip area, cavitation tip vortex will be formed due to the pressure difference between the pressure side and the suction side, which will cause local pressure to decrease, followed by the reduction of propulsion efficiency of the pump-jet. [PERSON] et al. [14] conducted a numerical simulation of a pump-jet propeller based on the RANS (Reynolds averaged Navier-Stokes) solver and the SST \(k\)-\(\omega\) turbulence model.