## 4 Numerical Results
### Ventilated Cavitation  
For the supercavitation flow analysis, an alignment grid with three blocks is constructed. Figure 4 shows the entire grid system. The total number of cells is about 600,000. Many cells were placed around the cavitator and body to improve the stability and accuracy of the analysis. Figures 4 and 5 show length information and boundary conditions for the entire grid. In the case of the front grid of the cavitator, if sufficient length is ensured, the flow can develop well and stably. However, in this study, only 10 times the diameter of the cavitator was secured because the size of the cavitation tunnel to be compared was modeled. The rear grid also considered the size of the cavitation tunnel. The value of D/dc = 9.49 was chosen to be identical to the environment in which the blockage effect affecting the cavitation size was verified. The boundary conditions include velocity inlet conditions and pressure outlet conditions. As an experiment for ventilated cavitation, conditions that do not generate natural cavitation are required. Therefore, in the experiment and analysis, the low speed (6 m/s) and total pressure (40 kPa) conditions are maintained. In the analysis, a ventilated area with the same area as the experiment was modeled. The four ventilated areas are evenly distributed along the body diameter. The ventilated area is the velocity inlet condition equal to the inflow condition. At this time, the ventilated velocity was determined by the ventilated gas flux coefficient. Figure 6 shows the change of cavitation shape according to the change of Cq. In the experiment and analysis, the cavitation shape was confirmed after enough time had passed while Fn and Cq were kept constant. After enough time, the cavitation shape remains almost constant for a ventilated cavitation case [13]. Fn(\(=V_{\infty}/\sqrt{sd_{C}}\)) is the flow field characteristic (gravity effect) according to the inflow velocity. The results of the computational analysis indicate that Fn is 10.8, which means low-speed conditions (\(V_{\infty}\) = 6 m/s). At this time, the shape characteristic of ventilated cavitation is asymmetric due to the buoyancy effect due to low Fn. When Fn is 10.8, it can be seen that the area of the cavitation covering the body increases as the ventilated gas flux coefficient increases, and the experimental and computational results are in good agreement. Figure 7 shows that when Fn is maintained and Cq  
Figure 3: Analysis of changes in natural cavitation shape over time in two cavitation numbers. In this study, computational analysis was performed not only of the cavity shape, but also of the drag force in the injection cavity. The following Figure 9 models for drag analysis. The shapes of the cavitator, body, and ventilated areas are modeled with reference to the shape of the test [13]. Figure 10 is the result of computational analysis of the drag coefficient value according to the change in the injection cavitation number. The drag coefficient is given by  
\[C_{D}=\frac{Drag}{\frac{1}{2}\rho_{water}{V_{\infty}}^{2}A}, \tag{25}\]  
where A is the area of the cavitator facing the flow. Drag is the sum of both form drag by pressure and skin friction due to viscosity. It can be seen that the results of the cavitation tunnel test and computational analysis are in good agreement. As the injection amount increases, the cavitation number decreases and approaches the supercavitation. According to the cavitation shape change from the experimental and analysis results, it can be confirmed that the supercavitation occurs when the cavitation number is below 0.23. It can be confirmed by tests and computational analysis that the C\({}_{\text{D}}\) value is maintained at a certain level when it is supercavitation. In the case of the drag, there is no change after the supercavity is achieved, but the cavitation shape changes. In Figure 10, when the cavitation number is 0.19 and 0.21, the drag coefficient values are the same, but the cavitation length is different.