## 5 Conclusions  
A one-way coupled method between Eulerian and Lagrangian approaches was developed to efficiently and accurately predict the tip vortex cavitation (TVC) inception and noise of submarine propellers. Notably, the two propellers of the same specifications except for sweep angle were considered to investigate its effects on the TVC inception and noise. Moreover, the realistic incident hydrodynamic flow field to the propeller was realized by including the entire submarine body to investigate the effects of incident disturbance on the TVC inception and noise. The Eulerian approach based on the sequential application of the RANS solver and the vortex model was employed to predict the highly resolved tip vortex flow of the submarine propellers. The RANS results were validated by comparing the predicted hydrodynamic performances with the measured ones. The computed axial velocity distribution revealed the structure of incident wake flow to the propeller, which matched the layout of the rudders and the sail location. This incident wake flow affected the cavitating flow of the propeller by increasing the local angle of attack. However, the tip vortex structure obtained from the RANS results showed inadequate agreements with the measured ones due to excessive numerical damping. The vortex model is applied to improve the predicted resolution of the tip vortex flow field. The vortex core trajectory was first identified by tracing the \(\lambda_{2}\)-distribution of the RANS results and defining the core center as the minimum \(\lambda_{2}\). Then, the Scully vortex model with the DVM was applied to reproduce a well-organized vortex structure. The tip vortex flow regenerated by using the vortex model also showed good agreement with the recorded snapshot of the tip vortex. Additionally, through the comparison of the minimum \(\lambda_{2}\) values for all blades of the Model-A and Model-B propellers, it was found that the larger sweep angle leads to tip vortex of less strength. The Lagrangian method based on the sequential application of bubble dynamics and trajectory equations for nuclei and of the acoustic equation for the bubbles was applied to predict the TVC inception and noise. The tip vortex cavitation inception of the propellers was predicted by numerically solving the bubble dynamics and bubble trajectory equations for initial nuclei in association with the regenerated tip vortex flow fields. The freshwater quality was reflected by adjusting the number density concentration (NDC) of nuclei to the 1/10 of the NDC reported for Santa Catalina Island. Finally, the acoustic pressure due to tip vortex cavitation was predicted by assuming each bubble as a point monopole source. The predicted spectral density of the acoustic pressure was compared with the measured one. There is good agreement between the predicted and measured ones in terms of spectral slopes in the high-frequency range. Furthermore, the predictions reveal that the TVC noise of Model-B was less than that of Model-A, which also matched the measured result. It was seen that the underwater propeller with a higher sweep angle reduces the TVC noise by decreasing tip vortex strength. Further computations were carried out to investigate the effects of the number concentration density of nuclei. Irrespective of the NCD, the predicted spectral levels for Model-A were higher than those for Model-B. It was found that there was a noticeable difference in the large structure of TVC between the predicted and measured results. This seems to be due to the restriction of bubble dynamic equations