## 2 Numerical Methods
### Eulerian Approach Based on Continuum Properties  
#### 2.1.1 Reynolds Averaged Navier-Stokes Solver  
The test propellers named Model-A and Model-B are designed to have the same specifications except for the sweep angle, which is often employed as a design parameter to delay CIS. Because the Model-A propeller has a lower sweep angle than the Model-B propeller, the latter is expected to have less cavitation and thus less cavitation noise than the former. One of the benchmarking points is whether the current numerical method can adequately describe the effects of the sweep angle on the cavitation inception and noise. Moreover, the propeller located at the stern of the submarine is exposed to wake-like disturbance produced by the boundary layer flow of the hull body. In this respect, the cavitation inception and noise of the propeller may be affected by flow disturbance caused by the submarine body. This is the second benchmarking point. To account for this, the entire body of the submarine is considered along with the propellers. Because the inflow disturbance to the propellers is caused by the upstream flow from the submarine body and appendages, the DARPA Suboff 5470 is used to model a submarine body. Geometry information for submarine body and propellers are presented in Figure 1. The dimensions of the submarine body and the propeller are listed in Table 1.  
The entire computation domain and boundary conditions for the computation of the hydrodynamic flow of the submarine body with the propeller are shown in Figure 2. The dimensions of the computation domain are set the same as those of the test section of LCT in KRISO. The applied boundary conditions are determined to reproduce the experimental conditions, which is described in detail in Section 3. Liquid density, \(\rho\), and kinematic viscosity, \(\
u\), are equal to 997.05 kg/m\({}^{3}\) and \(1.004\times 10^{-6}\) m\({}^{2}\)/s, respectively. The test-section sizes (L \(\times\) W \(\times\) H) of LCT are equal to \(12.5\times 2.8\times 1.8\) m. Inflow velocity is 5 m/s at the inlet, gauge pressure is 0 Pa at the outlet, and operating pressure is set to be 51 kPa to realize the experimental background pressure. The other four side planes are set to be a solid wall where the no-slip boundary condition is applied. The sliding mesh method is used to reproduce the \begin{table}
\begin{tabular}{c c c c} \hline  & **Geometry** & & **Dimension** \\ \hline \multirow{8}{*}{**DARPA Suboff 5470**} & Length overall & L\({}_{\text{oa}}\) & 4.356 m \\ \cline{2-3}  & Length between & \multirow{2}{*}{L\({}_{\text{PP}}\)} & \multirow{2}{*}{4.261 m} \\  & perpendiculars & & \\ \cline{2-3}  & Maximum hull radius & R\({}_{\text{max}}\) & 0.254 m \\ \cline{2-3}  & Center of buoyancy(aft & \multirow{2}{*}{FB} & \multirow{2}{*}{0.4621 L\({}_{\text{oa}}\)} \\  & of nose) & & \\ \cline{2-3}  & Volume of displacement & \(\
abla\) & 0.718 m\({}^{3}\) \\ \cline{2-3}  & Wetted surface area & S\({}_{\text{wa}}\) & 6.338 m\({}^{2}\) \\ \hline \multirow{4}{*}{**Modeled Propellers**} & Propeller Diameter & D & 0.293 m \\ \cline{2-3}  & Number of blades & Z & 7 \\ \cline{2-3}  & Sweep angle & \multirow{2}{*}{\(\theta\)} & \multirow{2}{*}{\(17^{\circ}/38^{\circ}\)} \\  & (Model-A/Model-B) & & \\ \hline \end{tabular}
\end{table} 
Table 1: Detailed dimensions of Suboff body and propeller model. Figure 1: Geometry of the submarine and propeller: (**a**) DARPA Suboff 5470 submarine; (**b**) Model-A; (**c**) Model-B. Figure 2: Entire computation domain and boundary conditions with Suboff body and propeller. rotation of the propeller. The rotating speed of the propellers is set to be 25.05 rps. The cavitation number for the rotating propeller is set to be 1.78, which is given in the form,  
\[\sigma=\frac{p_{\infty}-p_{v}}{\frac{1}{2}\rho\left(nD\right)^{2}} \tag{1}\]  
where \(p_{\infty}\) and \(p_{v}\) denote the freestream pressure and vapor pressure, respectively. \(\rho\), \(n\) and \(D\) denote liquid density, round per second, and propeller diameter.