## 1 Introduction  
Cavitation typically occurs when the local pressure in a flow field drops below the vapor pressure of the liquid, and forms vapor cavities or gas bubbles. The generation, development, and extinction of cavitation involves subsequent pressure fluctuations, causing damage to neighboring bodies, and hydro-acoustic flow noise problems. Therefore, numerous experimental and numerical studies have been conducted to investigate the cavitation phenomena. Experimental studies were typically conducted using scale models in water-tunnels, with high-speed cameras used to visualize the cavitation with high-speed image processing techniques. [PERSON] and [PERSON] [1], [PERSON] et al. [2], and [PERSON] et al. [3] experimentally investigated cavitating flow around submerged hydrofoils. [PERSON] et al. [4] proposed noise source localization techniques for rotating propellers, by using source strength estimation methods in swallow water conditions. [PERSON] et al. [5] and [PERSON] et al. [6] studied the dynamics of ventilated cavitation with steady and periodic gust flows. However, the experimental approaches, based on scale models, typically suffer from an inability to apply the scaled results to the full-scale objects because of numerous non-dimensional parameters. As an alternative approach, numerical methods have been developed and used to investigate the cavitation phenomena. [PERSON] et al. [7] and [PERSON] et al. [8] proposed mass transfer models (also known as cavitation models) to deal with phase changes between liquid and vapor. [PERSON] et al. [9],[PERSON] [10], [PERSON] and [PERSON] [11], and [PERSON] and [PERSON] [12] proposed preconditioning methods to resolve numerical instability issues, that arise from large disparities between the acoustic and convective wave speeds. [PERSON] et al. [13] developed a filter-based turbulence model that was applied across a wide range of multi-phase problems [14; 15; 16]. However, as cavitation is highly unstable and sensitive to turbulent flow, it remains difficult to resolve the detailed features and mechanisms. To improve the understanding of the cavitation phenomena, the relevant numerical and physical issues need to be quantified. In addition, the International Maritime Organization (IMO) recently adopted guidelines to reduce underwater noise from commercial ships, recognizing that underwater-radiated noise from commercial ships has adverse effects on marine lift. This fact and the understanding that the propeller cavitation is one of most contributing factors to flow noise sources of commercial ships necessitates the improved understanding of numerical and physical issues related to cavitation flows and its radiated noise. For this purpose, in this study, the effects of viscous flux vectors on the generation, development, and extinction of cavitation from a hydrofoil, and the radiated hydro-acoustic flow noise, is numerically investigated with three different approaches to treating viscous flux vectors: viscous lagging, thin-layer, and full viscous models. Numerous numerical studies for cavitation phenomena can be classified into these three approaches. However, the effects of viscous flux vectors are not made clear. To reveal the effects of viscous flux vectors on the cavitation phenomena, the flow fields are predicted by solving the full three-dimensional (3D) unsteady compressible Reynolds-averaged Navier-Stokes (RANS) equations. The governing equations are numerically solved using the preconditioned implicit pseudo-time marching scheme, combined with the filter-based turbulence models. The homogeneous mixture model is applied to model the multi-phase fluid. When the phase of fluid is changed from water vapor to liquid water and vice versa, mass transfer is involved and its effects can be modelled with mass transfer models, also known as cavitation models. In this study, to model these phenomena, [PERSON]'s cavitation model [7] is applied.