## 3 Numerical Simulation
### Internal Explosion Flow Field at the End Cover of the Vessel
#### 3.2.2 Influence of Scaled Distance on Internal Explosion Flow Field  
Observing Figure 2, it can be found that with a small amount of charge, the interval time between the convergence wave peak and the secondary shock wave peak is smaller, as shown in Figure 2a. To investigate this phenomenon, an explosion containment vessel model with a same aspect ratio of 2.025 and a smaller charge of 8 g was used for numerical simulation. In conversion, the scaled distance between the charge and the pole was 4.05 m\(\cdot\)kg\({}^{-1/3}\). Figure 6 shows the pressure nephogram at the critical moment.  
At 1400 \(\upmu\)s after the TNT explosion, the primary explosion wave reached near the end cover pole and caused a small pressure jump, while the secondary shock wave formed by the torus reflection wave convergence was already propagating to the pole. During the propagation process, the secondary wave and the shock wave propagating along the end cover converged toward the pole at the same time. For example, at 2000 \(\upmu\)s the two shock waves are almost equal to the wave at pole. At 2105 \(\upmu\)s, the impact of the secondary shock wave is encountered at the pole, and the shock wave propagating along the inner wall of the end cover is also about to reach the pole. Subsequently, only at 2130 \(\upmu\)s was the convergence wave at the pole compressed inward to the extreme, at which point the pressure reached the maximum. Of particular note was that, compared with the typical pressure flow field evolution, which was described in the previous section, it merely took about 25 \(\upmu\)s from the rising edge of the secondary shock wave to reach the peak of the convergence wave, instead of about 160 \(\upmu\)s. It was obvious that during the charge of 8 g TNT, the secondary wave and the convergence wave arrived at the pole almost at the same time, so they almost merged into one peak in the pressure curve. In other words, it can be called a superposition wave of the convergence wave and the secondary shock wave. From the pressure curve of the amplified superimposed wave, it can also be seen that, in fact, the two waves were not completely merged, but when the pressure was not unloaded after the secondary shock wave, the convergence wave reached the pole as shown in Figure 7a.  
Figure 5: Internal explosion nephogram under the 2.025 vessel aspect ratio.  
Figure 6: Internal explosion nephogram under the 8 g charge.  
In order to explore the changing law of the interval time between the convergence wave and the secondary shock wave at different scaled distances, the charge was set between 8 g to 155 g, and the corresponding scaled distance ranged from 1.51-4.05 m\(\cdot\)kg\({}^{-1/3}\). The simulation results are shown in Figure 7b. When the scaled distance was small, the interval time between the convergence wave and the secondary shock wave was large, therefore three dominating peaks at the initial stage could be observed in the pressure curve, and the maximum value appeared in the third peak--the convergence wave peak. As the scaled distance grew, the interval between the convergence wave and the secondary shock wave decreased gradually, until the convergence wave was superimposed on the secondary shock wave. When the scaled distance reached 4.05 m\(\cdot\)kg\({}^{-1/3}\), there were only two obvious wave peaks in the pressure curve and the maximum pressure appeared on the second peak--the superimposed wave peak.