# Dynamic Analysis of Cavitation Tip Vortex of Pump-Jet Propeller Based on DES
## 1 Introduction
They found that the presence of blade tip vortices would lead to a further reduction in propulsion efficiency which is likely to cause cavitation. [PERSON] et al. [15] further studied the effect of tip clearance on pump cavitation performance. He pointed out that when the rotor tip clearance is large, the cavitation phenomenon is more obvious leading to a lower propulsion efficiency. However, it should also be noted that the size of the tip clearance cannot be too small, otherwise excessive viscous force in the tip area will hinder the flow of fluid which is unfavorable for the pump-jet propeller. [PERSON] et al. [16] also conducted a numerical simulation that focused on the influence of tip clearance size on pump-jet propeller, and concluded that the core of tip leakage vortex and tip separation vortex are closer as the tip gap size increases. [PERSON] et al. [17] used the DES (detached-eddy-simulation) method to study the uniform cavitation flow field of a pump-jet propeller. It was found that when the cavitation occurs, the range of TLV (tip leakage vortex) will increase in the circumferential direction. Furthermore, the intensity of TLV in the downstream non-cavitation area will also increase, while the intensity of TSV (tip separation vortex) will decrease. [PERSON] et al. [18] proposed a new tip vortex model based on the actual flow condition in the pump-jet, which made the pressure distribution in the tip clearance closer to the viscous flow results. [PERSON] et al. [PERSON] et al. (2019) analyzed the time domain curves and frequency domain curves and he found that the pulsation pressure is greater in the blade tip position. Because of the accurate prediction of flow separation at the separated region than URANS (unsteady Reynolds-averaged Navier-Stokes) method, more and more scholars employed a detached eddy simulation (DES) turbulence model in their studies. DES is a hybrid of the RANS (Reynolds-averaged Navier-Stokes) model and LES (large eddy simulation) model in which the model switches to a subgrid scale formulation in regions fine enough for LES calculations. [PERSON] et al. [PERSON] et al. (2018) used the DES method to simulate the blade tip vortex, hub vortex and secondary vortex in the duct propeller. [PERSON] et al. [PERSON] et al. (2018) achieved the accurate simulation of the three-dimensional dynamic vortex structure inside a turbine by using the DES turbulence model, and it shows a good agreement with the qualitative analysis of the turbine working under deviation from design conditions. [PERSON] et al. [PERSON] et al. (2018); [PERSON] et al. (2018) combined a finite volume method with IDDES (improved delayed detached eddy simulation) turbulence model to compute direct noise and compared with experimental results which showed good agreement. In the research of [PERSON] et al. [PERSON] et al. (2018), numerical simulation based on DES revealed that the strength of the tip vortices has an important influence on the onset of the instability of propeller wake. Through numerical simulation which used DES turbulence model, [PERSON] (2018) found a more aggressive vortex structure in the wake. In order to simulate the fluid flow accurately in a pump-jet propeller with a front-mounted stator, [PERSON] et al. [PERSON] et al. (2018) used the RANS and DES method to conduct the computation. It was found that DES can better simulate the turbulent characteristics than RANS solver. Compared with the RANS method, the RANS/LES hybrid method can capture a more detailed vortex structure, while the computing resources required are not as large as the LES. Hence, the hybrid model has now been adopted by more and more scholars. Cavitation is a pretty complex phenomenon that is easily appeared in turbo machinery operated at a high rotational speed. In addition, cavitation bubbles interacting with tip vortex will be more complicated which may deteriorate the fluency of flow field. Compared with pump-jet propellers, the research findings of cavitation and tip vortex of other axial flow machines are more abundant.