# Instability and Atomization of Liquid Cylinders after Shock Wave's Impacting
## 3 Results and Discussion  
Figure 4 shows high-speed photographs of \(d_{0}=4.14\) mm diameter single row water column after interaction with a \(Ma=1.10\) shock wave. It is seen that from Figure 4(1-5), the cylinder is compressed and moves to the right after shock wave's impact. The compression duration is longer than that of \(d_{0}=2.76\) mm water cylinder [25]. It should be noted that compression of the liquid column, as mentioned in the introduction, is due to the high-pressure zone formed by the interaction between the diffracted shock wave and the transmitted shock wave [17, 18, 19]. From Figure 4(6), the liquid is stripped off and many thin ligament tails are formed on the leeward side of the column. From Figure 4(8) to Figure 4(12), the windward side of the column starts to deform and bend but the surface is still smooth. At the moment, the instability has not been developed obviously. From Figure 4(13-16), the spike and bubble structures appear on the windward side of the column. Then, they develop gradually and merge together. Figure 5 gives high-speed photographs of RM instability after a \(Ma=1.10\) shock wave impacts on \(d_{0}=3.38\) mm diameter in-line double rows water columns. We mark the first one as the left column (L) and the second one as the right column (R). As shown in Figure 5(1-6), after shock wave's impact, the two columns are compressed and move to the right direction. The motion of the right column lags behind the left one. From Figure 5(7), many thin ligament tails appear on the leeward side of the left column. Meanwhile, in Figure 5(7), the streamwise size of the right column is compressed to minimum. From Figure 5(8-11), as disintegration and atomization of the liquid develop further, the two columns expand gradually and the wakes on the leeward sides integrate with the surrounding air. The spike and bubble structures appear on the windward side of the left column from Figure 5(12) and similar phenomenon occurs on the right column from Figure 5(13). From Figure 5(14-24), the spike and bubble structures develop further and merge with each other; at the later stage, the two columns interact mutually and mix together to form a complicated turbulent cloud. Noticeably, the left column takes precedence to develop because it firstly meets the shock wave. In comparison with the single row water cylinder, the in-line double rows water columns deform and break up more slowly to some degree. This can be explained due to retardation of the left column to the shock wave. The measured spike height \(h_{s}\), bubble depth \(h_{b}\) and turbulent mixing zone \(h\) are presented in Figures 6-8. It is clear that at \(Ma=1.10\), the parameters are all linear with time in spite of the single row water column or in-line double rows water cylinders (see Figures 6 and 8). However, as the increase of Mach number to \(Ma=1.25\), \(h_{s}\), \(h_{b}\) and \(h\) all become nonlinear with time (see Figure 7). Figure 6: Evolution of spike height, bubble depth and turbulent mixing zone of single row water cylinder at \(Ma=1.10\). The measured spike height \(h_{s}\), bubble depth \(h_{b}\) and turbulent mixing zone \(h\) are presented in Figures 6-8. Next, we introduce the results of the shock wave interaction with alongside triple rows water columns with 2 mm space of \(d_{0}=2.0\) mm diameter at Mach number \(Ma=1.20\). The shadowgraphs and numerical schlieren pictures of cross-sectional view are given in Figure 9. It is known that the reflection and diffraction of shock wave from the neighbour cylinders cause a very complex wave system, so that this may bring a nonlinear RM instability. The measurement results of the spike height and bubble depth confirm this postulation (see Figure 10). The results of three dimensional numerical simulations based on Fluent software and VOF method [26, 27] give a similar trend.