# Computational Evaluation of Shock Wave Interaction with a Cylindrical Water Column
## 3 Results
### Shock-Column Interaction
#### 3.2.1 Qualitative Analysis  
In this section, the qualitative analysis is presented for the solution with the finest resolution, that is CFD III. At the very early stages of the interaction process, the passage of the shock wave did not produce appreciable cylinder deformation. As observed in [31], there existed a reaction time, which depended on both the drop size and air stream velocity, during which the water column appeared undistorted, with the air flow field resembling the flow past a circular cylinder. This fact was clearly demonstrated by looking at the contours of the volume fraction of water depicted on the left side of Figure 4, where the time history of the interaction process corresponding to the non-dimensional time interval \(0<t^{*}<0.03\), immediately after the impact, is illustrated. For clarity, the different contour maps were drawn in the reduced spatial domain defined by \(-1<x/d_{0}<2\) and \(y/d_{0}<5/3\). Note that, due to the finite numerical resolution, the interface between the two immiscible fluids appeared to be slightly diffuse. Apparently, the column showed no change in shape after being struck by the air shock. Moreover, by looking at the mean pressure, temperature, and streamwise velocity contours, both original and reflected moving wave fronts were evident. The impacting wave reflection that was initially regular became a Mach reflection at a certain angle, as observed at the last time instants. The stagnation flow region behind the reflected wave was particularly evident by looking at the velocity contours, while the pressure contours clearly revealed the wave that was transmitted inside the water body. As was illustrated by the temperature contours, the liquid phase was practically maintained at the constant temperature of the driven section. Figure 4: Contour maps for volume fraction of water, pressure, temperature, and streamwise velocity fields (from **left to right**), corresponding to \(t^{*}=0\), 0.01, 0.016, and 0.03 (from **top to bottom**). As the interaction process continued, after the reaction time elapsed and interfacial instabilities appeared, the water column began to be distorted due to the dominant action of pressure forces, while still maintaining its coherence. Specifically, the water cylinder was flattened in the streamwise direction, which corresponded to a decreasing centerline width and an increasing cross-stream breadth. The deformation of the water column is illustrated in Figure 5, where the pressure and streamwise velocity contours are reported for a later time interval in the spatial domain \(-0.01<x<0.05\), \(y<0.015\). For clarity, the volume fraction field is illustrated in the limited range defined by \(-0.5<x/d_{0}<4\). By inspection of the volume fraction contours, the drift and distortion of the water column were evident. In fact, the streamwise flattening of the liquid body and the subsequent formation of a peripheral tip were clearly observed for the first temporal phase, say \(0.17<t^{*}<0.45\). Then, the deformation progresses and the incipient breakup of the  
Figure 5: Contour maps for volume fraction of water, pressure, and streamwise velocity fields (from **left to right**), corresponding to \(t^{*}=0.17,0.27,0.45,0.55,0.7\), and \(0.85\) (from **top to bottom**). water column were observed at later time instants, say \(0.55<t^{*}<0.85\). Specifically, as the peripheral tip was drawn downstream by the surrounding flow, due to the dominant action of shear forces, the liquid sheet became thinner and thinner until, finally, the breakup process began. The water column was continuously eroded at the periphery, with the appearance in the near wake of microdroplets stripped from the parent body. Basically, these pictures confirmed the qualitative features of the shear-stripping breakup mechanism, as was expected at high Weber numbers [7]. During the successive stage, the water column would disintegrate into fragments distributed widely in the flow field, which was out of the scope of this study.