## 1 Introduction
Typically, vapor pressure is assumed to be a function of only temperature, based on the assumption that the distance between vapor particles is sufficiently large. Hence, the molecular force can be ignored, which is valid for sheet cavitation. However, because the nuclei that are tiny seed particles causing tip-vortex cavitation are at a micro-scale, molecular forces cannot be ignored [28]. Given that the Eulerian method uses the volume fraction to quantify the cavitation flow, it is difficult to distinguish the interface between liquid and vapor precisely. Thus, it is difficult to determine the exact location and size of the cavitation. A Lagrangian approach based on bubble dynamics can be applied to evaluate the cavitation occurrence with more direct physical quantities. The bubble dynamics model aids in determining the time-varying position and size of the bubble that develops from each nucleus, and thus enables accurate prediction of the noise due to the bubble. [PERSON] et al. [29] predicted the cavitation inception in a line vortex flow using a Lagrangian approach combined with the single-phase RANS solvers. It was shown that that the size of nuclei plays an essential role in extrapolating the small-scale results to full-scale results. In this study, a systematic numerical methodology is developed to investigate the tip-vortex cavitation inception and noise of an elliptic NACA16-020 wing. The numerical method consists of sequential one-way coupled applications of Eulerian and Lagrangian approaches. First, the Eulerian method is applied to predict the hydrodynamic flow field around the wing with a focus on accurate simulation of the tip-vortex flow. The RANS solver is used to predict the single-phase hydrodynamic flow around the wing. Subsequently, the tip-vortex flow field is regenerated by employing the Scully vortex model. The model parameters, such as the circulation and core-radius, are determined using the information from the predicted hydrodynamic flow. Secondly, the Lagrangian approach is applied to predict the tip-vortex cavitation inception and noise of the wing. The initial nuclei are distributed upstream. The subsequent time-varying volume and location of the nucleus are computed by solving bubble dynamics equations in combination with the hydrodynamic flow field of the wing, especially the regenerated tip-vortex flow. Finally, the compressible acoustic pressure at a selected monitoring position is computed by modelling each bubble as a point monopole source. The validity of the present numerical methodology is confirmed by comparing its prediction results with the measured results. The overall procedure of the current numerical method is similar to that reported by [PERSON] et al. [29]. However, in the present study, the numerical methods used in each numerical step are investigated in more detail. Thus, the four main contributions of the present study are as follows. First, the effects of turbulence models and grid resolutions on the prediction of the tip-vortex flow are quantitatively compared, which can provide a guideline for performing an accurate numerical simulation of tip-vortex flow. Second, the systematic application of the vortex model is presented for regenerating high-resolved tip-vortex flow from the background flow obtained from the RANS solver. It includes the methods for tracing the tip-vortex core location and determining the vortex strength and core-radius of the vortex model. Third, the bubble dynamics equations are investigated in detail with a focus on the effects of each term of the equations on prediction accuracy. Fourth, the critical physical issues in predicting acoustic pressure due to tip-vortex cavitation are examined in detail. Notably, the effects of the number density of initial nuclei on the tip-vortex cavitation inception and noise are quantitatively analyzed. The results indicate the merit and constraints of the current numerical methods and their suitability as an analysis tool for investigating tip-vortex cavitation.