# Numerical and Experimental Studies of the LK Type Shaped Charge
## 5 Results and Discussion  
The numerical simulations that we conducted enabled us to analyze cumulative jet formation. In the basic LK charge (see Figure 3a), the detonation wave reached the surface perpendicularly to the object. Cumulative jet formation occurred from the detonation wave, which reached the cumulative insert and generate a great number of small incidence angles. Such an arrangement resulted in too short a cumulative jet. The results of this simulation are shown in Figure 11.  
Figure 10: Models for the simulation analysis of the LK charge. Despite its shorter jet, its velocity distribution was linear (see Figure 11b). On the other hand, the phenomenon of liner collapse, determined by the Birkhoff effect, was slightly less favorable [58]. In a charge with an additional insert (see Figure 3b), the charge jet formation parameters improved slightly. The results of this analysis are shown in Figure 12. The numerical simulation results relating to the formation of jets (based on the model assumptions for charges used in the experimental tests) indicated different tendencies in these formations. The axial charge was more stable, but its jet was shorter (see Figure 11b). In the case of a peripheral charge, a lengthening of the jet (see Figure 12b) was caused by a significant difference in velocity between the head and tail of the jet, and in the case of the axial charge, these differences were smaller. They resulted from the different angles of incidence of the detonation wave on the liner. For an axial charge, this angle was smaller than for a peripheral charge. The reliability of the numerical results was verified by evaluating the entry and exit holes of the cumulative jet's passage in the armored plate. In the experiment, the entry hole average for the axial charge was 22.7 mm, and the exit hole was 15.7 mm. In the case of the peripheral charge, the entry hole average was 13 mm, and the exit hole was 12.5 mm. In the simulation, the entry was 21.8 mm, and the exit was 19.7 mm, but the peripheral charge had a 12.0 mm entry hole and 11.6 mm exit hole, which is a satisfactory result. Figure 11: Stages of formation jet of the axial charge for individual time steps: (**a**) process of propagation of explosion detonation wave; (**b**) stages of the jet’s formation in the liner. The jet formation times were also compared (see Figure 13). As can be seen, in the first phase of jet formation, the addition of an insert into the LK charge (see Figure 3b) caused a significant velocity difference, and the liner collapsed for the peripheral charge. It can be assumed that the stagnation point was more favorable for this type of charge. The effectiveness of such a charge is determined by the air gap between the charge and the obstacle. In this case, the gap was 60 mm. As can be seen, axial charges, due to the higher focusing, resulted in larger entry hole diameters in the pierced armor plate. The jets of these charges were shorter than those of the peripheral charges, and in two cases, no perforation was noted (see Table 2). In the peripheral charges, this jet had a lower focal length, which made it more effective, despite the fact that in the final phase, the jet lost its axisymmetric parameters. Ultimately, the jet velocities were 7.8 km/s for the axial charge and 7.58 km/s for the peripheral charge. Figure 12: Stages of jet formation of the peripheral charge for individual time steps: (**a**) the process of propagation of an explosion detonation wave onto an additional insert in order to increase the angles of incidence on the liner; (**b**) stages of the jet formation in main liner. In the following part, the explosive charge was modified in order to extend the range of incidence angles of the detonation wave on the insert and increase jet formation. The results from the studied numerical models are presented in the figure below (see Figure 14). Some differences can be seen among the stages of cumulative jet formation shown for individual types of charges.