## 3 Setting and Verification of Numerical Simulation Strategy
### Open Water Simulation Settings  
As shown in Figure 4, the diameter of the propeller is D, the diameter of the stationary domain is 8D, and the length of the stationary domain is 10D; that is, the distance between the velocity inlet and the pressure outlet is 10D, the distance between the velocity inlet is 4D from the propeller disc surface, the pressure outlet is 6D from the propeller disc surface, the propeller disc surface is located in the center of the rotation domain, and the diameter of the rotation domain is 1.08D and the length is 0.24D. In this paper, STARCCM+ 2021.3 commercial software is selected for CFD simulation calculation, which adopts the numerical technology of continuum mechanics, which has significant advantages in dealing with complex geometric models and reducing meshing time. In the auto-meshing function of STAR CCM+, the Trimmed Mesher type was selected. The stationary domain and the rotation domain are independently set up with the same mesh base size, and the interface mesh settings of the stationary domain and the rotation domain are completely consistent. The number of prismatic layers is set to 10 and the total thickness of the prismatic layers is set to 2% of the grid base size. At the same time, some areas in the computing domain are encrypted. Taking the meshing of the propeller Kap509 when the grid base size is 0.01 m (0.04D, D is the propeller diameter) as an example, the meshing effect is shown in Figure 5.  
The propeller speed is set \(n=12\) rps, and the advance speed coefficient \(J=0.62\); that is, the incoming velocity of the set speed inlet is 1.862 m/s. The SST k-\(\omega\)+\(\gamma\) transition turbulence model was selected with the Schnerr-Sauer cavitation model and the Volume of Fluid (VOF) two-phase flow for CFD simulation. The parameters for the cavitation simulation are set as follows: the density of the liquid phase (water) is set to a constant of 998 kg/m\({}^{3}\), and the dynamic viscosity of the water should be set to 0.001008 Pa-s and the saturated vapor pressure should be set to 2338 Pa, assuming a temperature of 20 \({}^{\circ}\)C. The gas phase is water vapor, the density at 20 \({}^{\circ}\)C is 0.01719 kg/m\({}^{3}\), and the dynamic viscosity is 1.26765 \(\times\) 10\({}^{-5}\) Pa-s. The volume fraction of the gas-liquid phase is \(\alpha\) set to 0.1 to capture the water vapor surface. The seed density was set to 1.0 \(\times\) 10\({}^{12}\)/m\({}^{3}\) and the seed \begin{table}
\begin{tabular}{c c c c} \hline
**Geometric Scale Parameters** & **Symbols** & **Numerical Value** & **Units** \\ \hline Effective maximum length & L & 2.00 & m \\ Maximum body diameter & D & 0.22 & m \\ Bow length & L\({}_{1}\) & 0.23 & m \\ Length of stern & L\({}_{2}\) & 0.46 & m \\ Long hydrofoil span & B & 0.60 & m \\ Wingtip chord length & Ct & 0.05 & m \\ Wing root chord length & Cr & 0.10 & m \\ Hydrofoil wet surface area & S & 0.18 & m\({}^{2}\) \\ \hline \end{tabular}
\end{table} 
Table 2: Main geometry parameters of diamond wing underwater glider [31]. Figure 4: Calculation domain division of open water simulation. diameter was set to 1.0 \(\times\) 10\({}^{-6}\) m. As shown in Figure 6, the calculation accuracy of the SST k-\(\omega\)+\(\gamma\) transition turbulence model in the Kappel propeller Kap509 simulation is verified, and the SST k-\(\omega\)+\(\gamma\) transition turbulence model is used to calculate, which can control the calculation error of the open water propulsion efficiency within 3%, and the calculation error is small. The calculation results of the propeller Kap509 are shown in Figure 7, and the correspondence between the total number of meshes and the size of the grid foundation is shown in Table 3. Through the mesh independence verification of the propeller Kap509, the grid foundation size of the open water case simulation is determined to be 0.04D. The y+ distribution of the propeller Kap509, as shown in Figure 8, can be limited to a value of 0 to 3.1 on the propeller surface.