## 5 Conclusions  
In this study, the effects of viscous flux vectors on cavitation flow, and its radiated flow noise, of the Clark Y hydrofoil were numerically examined using computational fluid dynamics techniques  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Viscous Flux Treatment** & **Viscous Lagging** & **Full Viscous** & **Thin-Layer** \\ \hline PWL (dB) & 168.8 & 177.1 & 177.4 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Estimated acoustic power levels (dB) for three different viscous flux models according to source types. PWL: predicted acoustic power level.  
Figure 20: Predicted hydro-acoustic pressure due to dipole source: (**a**) directivity, spectrum at three azimuth angles of (**b**) 350\({}^{\circ}\); (**c**) 40\({}^{\circ}\); and (**d**) 80\({}^{\circ}\).  
and the Ffowcs Williams-Hawkings acoustic analogy. For the flow field analysis, the full 3D unsteady compressible RANS equations, coupled with the homogeneous mixture model, was applied. The hydro-acoustic field was predicted by solving the FW-H equation based on the information of monopole and dipole sources from the predicted flow field results, under the assumption of compact sources. The time-variation of cavity volume changes, and the hydro-dynamic forces on the hydrofoil surfaces, were used to determine the monopole and dipole source strength. The effects of viscous flux were examined by modeling the viscous flux terms in three different approximation approaches: the viscous lagging, the thin-layer, and the full viscous approaches. All three models exhibited similar periodic behaviors of generation, development, and extinction of cavitation, at the same 20 Hz fundamental frequency. However, the detailed unsteady behaviors differed significantly, especially between the viscous lagging method and the other two methods. The viscous lagging approach exhibited a tendency to over-predict the cavity structure and re-entrant jet, and to predict lower fluctuating hydro-dynamic forces. This resulted in larger SPLs for the monopolar noise components, but smaller SPLs for the dipolar noise components, than the other two cases. However, the thin-layer approach results were the closest to those of the full viscous model, in terms of the time-variation of hydro-dynamic loading and liquid volume fraction as characteristics of the predicted flow field, and the directivities and spectrum of the radiated acoustic field. However, it marginally under-predicted the leading-edge cavitation, and over-predicted the dissipation of shed cavities, and thus exhibited smaller SPLs because of monopolar noise. Based on these results, the thin layer approach can be proposed as an effective and efficient method for investigating the two-phase flow noise of hydrofoils as an alternative to the full viscous approach.  
This work was supported by the Ministry of Trade, Industry and Energy, MOTIE (project code: 10045337).  
[PERSON] developed the original CFD code. [PERSON] proposed the original idea motivating the present research. [PERSON] upgraded the original code by adding the filter-based turbulence models and additional viscous flux treatments (full viscous and thin-layer models), carried out the numerical simulations and prepared all of data. The relevant numerical analysis was carried out by both of [PERSON] and [PERSON].  
The authors declare no conflict of interest.