## 3 Setting and Verification of Numerical Simulation Strategy
### Self-Propulsion Simulation Settings  
In this paper, the calculation domain of the horizontal propulsion and self-propulsion simulation was set as a cylindrical shape region and was divided into stationary domain and rotating domain so as to facilitate the adoption of the sliding grid motion simulation mode. The calculation domain was divided as shown in Figure 9.  
Figure 8: Y+ distribution of propeller Kap509.  
Figure 7: The calculation results of the propeller Kap509.  
Figure 9: Calculation domain division of self-propulsion simulation.  
The body length of the diamond wing underwater glider is represented by L, and the diameter of the propeller is represented by D. The diameter of the rotating field is 1.08D and the length is 0.24D. The diameter of the stationary domain is 4L and the length of the stationary domain is 7L; that is, the distance between the velocity inlet and the pressure outlet is 7L, the velocity inlet is 2L from the bow apex of the underwater glider, and the pressure outlet is 5L from the bow apex of the body. The propeller disk is the distance from the bow apex L of the underwater glider.  
In this paper, from the perspective of computational efficiency and the post-processing effect, the Trimmed Mesher type is selected in the automatic mesh function, the number of prismatic layers is set to 10, and the total thickness of the prismatic layer is set to 5% of the grid base size, as shown in the view in the enlarged box in Figure 10d. In the process of meshing, the line encryption is carried out at the guide edge and accompanying edge of the propeller blade, and at the wing tip and wing root edge of the hydrofoil, as shown in Figure 10c,d. Different surface encryption is adopted for the bow surface, the mid-section surface, the hydrofoil surface, the stern surface, the propeller blade surface, and the interface between the rotation domain and the stationary domain, as shown in Figure 10a-d. The propeller wake region in the rotating domain and the stationary domain were infilled separately to better capture the details of the wake field and the distribution structure of the wake vortex, as shown in Figure 10a,d. Figure 10 shows the meshing of the simulation example of propeller Kap01 and underwater glider when the grid base size is 0.01 m (0.04D, D is the propeller diameter).  
Due to the variation of the blade tip rake, the six types of Kappel propellers have significant differences in geometrical structure, which may affect the grid-independent analysis. Therefore, two representative Kappel propellers Kap01 and Kap04 (with smaller tip rake and larger tip rake, respectively) were selected to match with the underwater glider for the grid independence analysis of self-propelled examples.  
The Kappel propeller Kap01 and Kap04 were calculated by the SST \(k\)-\(\omega\)+\(\gamma\) transition turbulence model combined with the Schnerr-Sauer cavitation model and VOF gas-liquid two-phase method under \(J\) = 0.5 and \(n\) = 12 rps conditions. The overall force F, resistance D, propeller thrust T, and propeller torque Q of the propellers are shown in Figures 11 and 12, respectively, from which it can be seen that the total mesh tends to be stable when the total  
Figure 10: Meshing of the diamond wing UG + propeller Kap01 simulation example (grid base size is 0.04D): (**a**) overall view of meshing, (**b**) bow encryption view, (**c**) hydrofoil encryption view, (**d**) stern encryption and prismatic layer magnification view.