## 2 Numerical Methods  
In this section, the numerical methods presented in this study are described in detail. The sequential one-way coupled Eulerian-Lagrangian method is applied to simulate the tip-vortex cavitation inception and noise of a NACA16-020 blade. It consists of six steps, as shown in Figure 1.  
In the first stage, the hydrodynamic steady flow field around the wing is obtained using a single-phase RANS solver. However, the accuracy of the numerical solution in resolving tip-vortex flow depends on the dissipation of numerical schemes, grid-resolution, and turbulence models. Therefore, a grid-refinement study is performed using four types of grids. Subsequently, the influence of turbulence models is quantified by comparing the tip-vortex structure predicted using each turbulence model.  
The vortex formed at the wing-tip is physically dependent on the Reynolds number and is convected in a long line-shape along with the downstream. Typically, the vortex core is located on the lowest pressure region, such that the wing-tip vortex cavitation occurs along the vortex core line, starting from the wing-tip and stretching to downstream. Therefore, the center of the vortex core is  
Figure 1: Numerical procedure using the sequential one-way coupled application of Eulerian and Lagrangian methods.  
identified in the flow field obtained from the RANS result and used as the central axis of the vortex regenerated using the vortex model.  
From a macroscopic point of view, cavitation is a phase change phenomenon from liquid to vapor that occurs at a pressure lower than vapor pressure. However, from a microscopic view, nude grow and form cavitation bubbles when the ambient pressure is lower than the critical pressure. Nuclei distribution depends on water quality, which varies according to temperature, seawater or freshwater, seasons, and regions.  
Experimental studies were performed to find the relationship between water quality and nuclei distribution. [PERSON] et al. [30] investigated water susceptibility and background nuclei content in a water tunnel using a cavitation susceptibility meter and showed that the cumulative histogram of nuclei concentration against critical pressure followed a power-law dependence over a large range of concentrations and pressures. [PERSON] et al. [31] measured the distribution of the number concentration density of nuclei in the Pacific Ocean and suggested the number density as a function of the initial nuclei radius. In this study, initial nuclei distributions are determined using this data as the standard seawater condition.  
The initial nuclei are distributed upstream of the wing. The subsequent behavior of nuclei (or cavitation bubble), such as bubble radius variation and bubble trajectory in the flow field, is predicted by solving the bubble dynamics equations. A single bubble is assumed as spherically symmetric and is treated as a point monopole source. Subsequently, the flow noise due to cavitation is predicted using the acceleration in bubble volume, which is a function of the radius of a spherical bubble. A detailed description of each step of numerical methods is provided in the following sections.