# Study on the Interference Process of Liquid Radial Reflux on the Stability of a Shaped Charge Jet
## 3 Simulation Analysis
### Simulation Results  
The LFSCS 2D finite element models in the numerical research are shown in Figure 8. The LFCS was simplified into an LFSCS, and a side-wall thickness of 25 mm was given to the shell to reduce the deformation, which was consistent with assumption 4 in this study. The liquid cavity radius and depth of the LFSCS were 15 and 70 mm, respectively, and the thickness of the cover and bottom plates were 4 and 10 mm respectively. The liquid and the metal shell of the LFSCS were water and Q235, respectively. The shock EOS was adopted for water and Q235. The material parameters are shown in Tables 1-4. The sensitivity of the mesh size was studied through the application of 1, 0.5, and 0.25 mm meshes in the numerical calculation. The calculation shows that the results were significantly different with mesh size reduction from 1 mm to 0.5 mm, while the results stabilized when the mesh size reduced from 0.5 mm to 0.25 mm. Thus, the size of the Euler and Lagrange mesh in the second stage was set to be 0.25 mm \(\times\) 0.25 mm. A total of 14 follow-up gauge points were set to obtain the travel trajectory and velocity-time curve of liquid particles. Among these points, gauge points 1 to 8 were set on the jet surface, and gauge points 9 to 14 were set on the liquid material beside the jet penetration channel. Screenshots of 29, 35, 39, 43, and 47 \(\upmu\)s were selected from the simulation calculation results to observe the interaction between the jet and the LFSCS. We can see the propagation of the shock wave and the movement direction of the liquid particles by using the Vector option. Figure 9 shows the process of the initial shock wave generated in the liquid, the shock wave reflected on the side wall, and the radial reflux of the liquid driven by the reflection shock wave when the jet penetrated the LFSCS. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Material**} & **Density** & **Tensile** & \multirow{2}{*}{**Yield Strength (MPa)**} & \multirow{2}{*}{**Elongation (\%)**} \\  & **(g\(\cdot\)cm\({}^{-3}\))** & & & \\ \hline Q235 & 7.85 & 235 & 375 & 26 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Physical properties of steel Q235. Figure 9: Generation and propagation of the initial shock wave and side-wall reflection shock wave (the orange curve represents the shock wave front). Figure 9a demonstrates that the velocity direction of the liquid particle behind the shock wave front changes with the propagation direction of the shock wave, which is between the normal direction of the Mach angle and the radial direction. Figure 9b shows that the side-wall reflection shock wave propagated in the opposite direction, and the common points of the incident and reflection waves moved along the side-wall surface at a certain speed at 36 \(\upmu\)s. Figure 9c shows that the velocity direction of the liquid particles after the side-wall reflection shock wave front was vertical-inward at 39 \(\upmu\)s. This result is because the side-wall reflection shock wave propagates to the liquid crater wall and drives the liquid particles to radially converge to the SCJ surface. At 43 \(\upmu\)s, the jet penetrated the bottom plate of the LFSCS, and the shock wave was reflected on the bottom plate surface to produce the reflection shock wave (see Figure 10). At this point, the side-wall and the bottom plate reflection shock wave simultaneously propagate in the liquid. Under the influence of the bottom plate reflection shock wave and the pressure difference between inside and outside, the bottom liquid begins to converge in the radial direction. Thereafter, the reflux liquid impinges on the jet, which interferes with the stability of the tip of the jet. The bottom plate reflection wave is reflected from the side wall to form a secondary reflection wave. The secondary reflection wave propagates in the liquid until it reaches the liquid crater wall to drive the liquid to converge and disturb the jet.