# 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 Large-Charge Underwater Explosion near Free Surface  
To further investigate the impact of the charge size and the presence of a rigid wall on cavitation evolution, we conducted simulations of explosions involving a large quantity of explosive in deeper water. Specifically, we selected a TNT charge weighing 100 kg and detonated it at a depth of 2 m underwater. Figures 14 and 15 depict the distribution of the free-field environment and the calculation model area under the influence of a rigid wall, respectively. Figure 12: Comparison of the volume evolvement in cavitation domain under two cases. Figure 13: Pressure–time history curve of the measurement point at distances of 0.5 m (**a**) and 1.0 m (**b**) from the symmetry axis, at a depth of 0.2 m from the free surface. Figure 14: 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 15: Schematic of underwater explosion near a free surface with a rigid wall (**a**) and mesh strategy of the fluid domain (**b**). Every 1 in 10 lines is plotted in the right figure. In Figure 14, except for the left boundary, which is assigned a symmetrical boundary condition, all other boundaries are set as non-reflective boundary conditions. This configuration allows for the accurate representation of the explosion dynamics and the resulting cavitation evolution in an unrestricted environment. Figure 15, on the other hand, incorporates the presence of a rigid wall. In this case, the left boundary is a symmetrical boundary, the right boundary represents the rigid wall condition, and the upper and lower boundaries are the non-reflective boundary conditions. This setup allows for the examination of the interaction between the explosion, cavitation, and the rigid wall. The initial fluid state of the explosive gas, water, and air within the calculation domain remains consistent with the conditions described earlier. These simulations provide valuable insights into the behavior of cavitation under the influence of larger explosive charges and the presence of rigid boundaries, contributing to a deeper understanding of underwater explosion-induced cavitation phenomena. Such knowledge can inform the development of safety measures and protective strategies in various marine and underwater engineering applications. Figures 16 and 17 depict the evolution of the flow field density, pressure, and cavitation domain under two different operating conditions. The selected flow field size and position are identical in both cases. Prior to \(t=14\) ms, it can be observed that the cavitation domain is similar under the two operating conditions. However, at \(t=14\) ms, the reflected wave from the solid wall boundary is fully reflected into the cavitation domain. From this point onwards, due to the propagation of reflected waves within the cavitation domain, the boundary of the cavitation domain with the wall appears smoother and more rounded compared to the sharper boundary shape observed in the free-field condition. At \(t=26\) ms and \(30\) ms, a noteworthy observation is the emergence of a new cavitation region beneath the explosion bubble in the case with the wall. Additionally, the cavitation domain above the bubble is larger compared to the free-field condition. At \(t=36\) ms, the cavitation domain vanishes under both operating conditions, yet there is a noticeable difference in the pressure distribution within the flow field. In the case of a free-field explosion, a high-pressure zone emerges in the area above the bubble. Conversely, in the case with a rigid wall, high-pressure zones appear on both sides below the bubble. This discrepancy arises primarily from the contrasting effects of the reflected wave on the wall and the cavitation collapse load. Figure 18 illustrates the evolution of the cavitation domain volume over time under the aforementioned operating conditions.