## 3 Results and Discussion
### Water Entry of 3D Torpedo
#### 3.2.1 Effect of Entry Velocity
In general, when the entry velocity is low, the free surface of the cavity closes with the torpedo earlier at the front part of the torpedo. In addition, a small quantity of splashing droplets is also generated and they occupy a small space above the water domain. With increasing entry velocity, the cavity size increases significantly, and numerous droplets are simultaneously generated and splash above the water domain. Figure 11 summarizes the variations in the impact load projecting onto the \(y\)-axis \(F_{y}\), the velocity \(u_{y}\), and the vertical displacement of the center of mass \(y-y_{0}\) of the torpedo with time when the torpedo vertically enters the water at different speeds of 5, 10, and 15 m/s. As shown in Figure 11a, once the torpedo enters the water at a certain entry velocity, it is subjected to an instantaneous impact load along the positive \(y\)-direction, \(F_{y}\), which increases to two peak values in a short period and stabilizes afterward. In addition, it is also observed that a higher entry velocity results in a higher peak and stabilized impact loads. In addition, the gravity force \(G\) is calculated as 1.848 kN. Subsequently, the vertical resultant forces and the corresponding accelerations, that occur around the moment of the first peak impact loads, point to the positive direction of the \(y\)-axis. Therefore, the absolute values of the velocities decrease at the beginning, as shown in Figure 11b. Although the impact loads along the positive \(y\)-direction slightly fluctuate, the regions of \(F_{y}<G\) between two peak loads occur in a very short time. Therefore, the fluctuations in the velocities can be reasonably neglected during the corresponding period. Figure 11b also shows that different stabilized impact loads, induced by different entry velocities, induce different stabilized accelerations and variation trends of velocities. For a low entry velocity of 5 m/s, as the vertical stabilized impact load acting on the torpedo is less than the gravity force, the resultant force along the vertical direction is in the same direction as that of the velocity. Therefore, the torpedo accelerates and the absolute value of velocity of the torpedo linearly increases during the stabilization period. For an entry velocity of 10 m/s, as the vertical stabilized impact load is almost equal to the gravity force, the resultant force and the acceleration along the vertical direction are zeros and thus the corresponding velocity is maintained at a relatively stable value during the stabilization period. Contrary to the findings observed from the case of a low entry velocity of 5 m/s, the large entry velocity of 15 m/s induces a high stabilized impact load, which is greater than the gravity force. Thus, the corresponding resultant force is in the opposite direction from the directions of the gravity force and the velocity. Therefore, the absolute value of the velocity linearly decreases during the stabilization period. Although the variation trends of the velocities are opposite for different entry velocities of 5 and 15 m/s, the displacements of the center of mass are mainly dominated by the initial entry velocity. Therefore, the displacements of the center of mass at the initial entry velocities of 15 and 5 m/s increase the fastest and the slowest, respectively, as shown in Figure 11b.