## 3 Numerical Modeling II  
Another important model created is the simulation of a LSC being shot without a target below. The model ran long enough for the tip of the jet to travel 12 inches (30.48 cm). The main purpose of this model is to simulate and analyze the jet break-up process over the surface of target when the LSC is subjected to large standoff distances. Because the large standoff distance in the operation of LSCs would significantly reduce the focusing of the elongated jet, the study of the jet behavior during the flight to the target is an important issue providing the essential information in determination of the effective standoff distance or optimum jet properties. A free shot LSC is simulated using the previously built template model of the 1,200 gr/ft LSC. Figures 5-7 show the jet after traveling 3, 6, and 12 inches (7.62, 15.24, 30.48 cm respectively). Two figures at each distance show the front and isometric views of the jet. The target is placed at the appropriate distance below the base of the LSC as a reference. Due to the extended model run time, a complete penetration profile is not able to be obtained for each of the four models. Instead, an analysis method is devised that consists of looking at the change in penetration into the target every microsecond over a 24 \(\upmu\)s period. The zero time is considered to be when a part of the jet initially makes contact with the target. The penetration profile is then analyzed at every microsecond afterward for 24 \(\upmu\)s to determine the penetration efficiency at the given standoff distance. Penetration profiles are analyzed for 0.75, 3, 6, and 12 inches (1.905, 7.62, 15.24, 30.48 cm respectively) standoff distances. The penetration into the target created by the jets formed by the different standoff distances can be seen in Figure 8. The points are recorded from the deepest point of penetration into the target viewed from a side penetration profile such as in Figure 2.  
This graph illustrates the penetration of the LSC jet into the mild steel target over a period of 24 \(\upmu\)s after the initial contact between the jet and the target. As shown, the penetration into the target decreases significantly as standoff distance increases. This is due to two different reasons. Firstly, break-up of the jet during the flight shortens the solid length of jet as it travels across the increased distance. This effect is one of the dominant factors that control the penetration capability in shaped  
Figure 8: Penetration effectiveness at different standoff distances. Figure 7: Front and isometric view after jet traveling 12 inches (30.48 cm). charges. The second reason for such penetration reduction is the jet spreading over a wide area during flight as shown in Figures 5-7. This effect of the jet spreading is not significant in the application of CSCs due to the single axis of jet production during the liner collapse. LSCs, however, are under the linear jet (two dimensional) focusing regime due to the linearly long shape during the liner collapse creating a less coherent jet. This mechanism acts as a drive of the jet spreading over a wide range at large standoff distances as it can be seen in Figures 5, 6, and 7. Table 2 and Figure 9 show the jet width at varying standoff distances. As is clearly shown in Figure 9, the LSC jet spreads widely apart as it travels long distances. This occurrence follows a linear fashion in the entire range of standoff distances. For an engineering application investigating the penetration capability of LSCs, the width of the LSCs jet does not generate valuable information and more related information is necessary. Figure 10 shows the jet velocity component variation collected from the simulation along the width of the spread jet.