## 4 Numerical Results
### Cavitation and Drag Change According to Speed Variation  
In this section, the computational analysis of the change of the cavitation shape according to the speed change was studied. For the underwater body to achieve a super cavitation only with a natural cavitation without the injection cavitation, it needs a speed higher than a certain speed. When supercavitation is achieved by these high speed conditions, the object can receive a large drag reduction effect.  
Figure 16 shows the natural cavitation shape as the velocity increases. V is the velocity of inflow, \(\mathrm{d_{S}}\) is the maximum diameter of the cavitation, \(\mathrm{d_{C}}\) is the diameter of the cavitator, and \(\mathrm{l_{S}}\) is the maximum length of the cavitation. In the case of a natural cavitation, it can be confirmed that the body speed is completely covered by the cavitation between 70 and 80 m/s. As the speed increased, the maximum diameter of the cavitation increased, and after 70 m/s, the cavitation generated from the front met the cavitation created in the tail, and the maximum length of the cavitation increased significantly. Figure 17 shows the total force of drag divided by the forces for pressure and viscous. The total drag is given by,  
\[Drag=\int p\cos\theta dA+\int\tau\sin\theta dA, \tag{26}\]  
where \(\theta\) is the angle to the flow direction and \(A\) is the microsurface area.  
Figures 18-20 show the results of time analysis of pressure and viscosity forces when the speed conditions are 50, 70, and 90 m/s, respectively. It can be assumed to be in a semi-equilibrium state from 0.05 s onward, starting from a stationary state, and then the average value is applied to Figure 16. The pressure force is a function of the magnitude of the pressure and the direction the surface acts on. In this case, since the cavitator is perpendicular to the flow, most of the pressure force occurs at the cavitator and the slope. The pressure force decreases in spite of increasing speed in the range of 40 to 60 m/s. The reason is that the cavitation develops completely covering the slope after the cavitator.  
Figure 18 shows the results of the partial cavitation computational analysis with a speed of 50 m/s. The reason for the oscillation of the graph results is that the wetted surface continuously changes due to the partial cavitation, which is the result of the unsteady state analysis. The oscillation is more severe due to the cavitation shape falling off of the tail. Figure 19 is the result of the computational  
Figure 15: Real scale underwater body cavitation formation at various cavitator angles of attack (angle of attack = \(-10^{\circ}\), \(0^{\circ}\), \(10^{\circ}\), \(20^{\circ}\)): (**a**) cavity shape and point of collapse (\(-10^{\circ}\), \(0^{\circ}\), \(10^{\circ}\), \(20^{\circ}\)), and (**b**) cavitator angle of attack (\(-10^{\circ}\), \(0^{\circ}\), \(10^{\circ}\), \(20^{\circ}\)).  
analysis of 70 m/s. This is the result of the computational analysis of the transition point from the partial cavitation to the supercavitation. Although not yet complete supercavitation, it can be seen that the viscous force is reduced compared to Figure 18 because it is close to the supercavitation state. Figure 20 shows the force in a complete super cavitation as a result of the computational analysis of 90 m/s. As the speed increases, the pressure force is increased by the exposed head, but it can be seen that the viscous force is completely removed due to the complete supercavitation. By the relationship between the supercavitation and the viscous force, the supercavitation contributes to lowering the level of the total force.  
Figure 16: Prediction of supercavitation shape according to velocity change.  
Figure 17: Prediction of drag change according to velocity change.  
Figure 19: Analysis of drag unsteady state pressure force and viscous force at 70 m/s.  
Figure 20: Analysis of drag unsteady state pressure force and viscous force at 90 m/s.  
Figure 18: Analysis of drag unsteady state pressure force and viscous force at 50 m/s.