# Study on the Influence of a Rigid Wall on Cavitation in Underwater Explosions Near the Free Surface
## 3 Results and Discussions
### Effect of Rigid Wall on Medium-Charge Underwater Explosion near Free Surface  
The formation of cavitation during underwater explosions near the free surface is a complex phenomenon influenced by multiple factors, including the water depth and charge size. Understanding these factors is crucial for predicting and mitigating the potential effects of underwater explosions. When considering the charge size, it becomes evident that a larger charge generates a stronger shock wave. The increased amount of explosive material leads to a higher energy release upon detonation, resulting in a more intense initial compression wave. This amplified shock wave propagates through the water, interacting with the surrounding medium and causing the formation of cavitation bubbles. On the other hand, the water depth plays a significant role in the propagation of the shock wave and its impact on cavitation formation. As the water depth increases, the shock wave's strength diminishes as it travels towards the free surface. This attenuation occurs due to the energy dissipation and dispersion experienced by the shock wave as it interacts with the water column. Consequently, the intensity of cavitation near the free surface is somewhat mitigated compared to shallower depths. The interplay between the charge size and water depth creates an interesting dynamic in cavitation formation. While a larger charge generates a stronger shock wave, which would typically lead to more significant cavitation effects, the greater water depth weakens the shock wave's propagation towards the free surface. These counteractive effects result in a complex cavitation pattern that varies depending on the specific conditions of the underwater explosion. To delve deeper into the influence of charge size on cavitation, a simulation was conducted. Specifically, a 60 g TNT explosion at a depth of 1 m underwater was studied. By analyzing the evolution of cavitation in this scenario, we aimed to gain insights into the relationship between the charge size and cavitation dynamics near the free surface. Furthermore, we examined the impact of a rigid wall on the cavitation evolution process. By comparing scenarios with and without a rigid wall, we sought to understand how the presence of a boundary surface affects the cavitation characteristics. Important features, such as the cavitation duration, total volume, and collapse pressure, were scrutinized to assess the influence of the rigid wall on the cavitation behavior. The computational models for the two operating conditions are illustrated in Figures 8 and 9, respectively. The initial conditions, including the state parameters of the explosive gas, water, and air, remain the same as described previously. Figure 8: Schematic of underwater explosion near a free surface without a rigid wall (**a**) and mesh strategy of the fluid domain (**b**). Every 1 in 10 lines is plotted in the right figure. Figure 10 illustrates the evolution of the flow field density, pressure, and cavitation domain during the process of cavitation generation near the free surface in the absence of a rigid wall (i.e., a free-field environment) at eight typical moments. Similarly, Figure 11 shows the evolution of the flow field density, pressure, and cavitation domain at the same eight typical moments with the presence of a rigid wall. Comparing Figures 10 and 11 reveals that due to the presence of the rigid wall, the shock wave reflects and generates new compression waves at the wall. Prior to \(t=2\) ms, the two operating conditions are relatively similar. However, at \(t=2.6\) ms, the cavitation domain temporarily disappears in the case with the rigid wall, only to reappear near the water surface at \(t=3\) ms and \(4\) ms, which is a new phenomenon not observed in the other operating condition. These effects are primarily caused by the reflection of waves at the wall. Figure 12 presents the evolution of the cavitation volume over time for the two operating conditions.