# Computational Evaluation of Shock Wave Interaction with a Liquid Droplet
## 3 Results
### Qualitative Analysis  
The early stages of the interaction process are illustrated in Figure 3, by considering the temporal evolution of the air-water interface, immediately after the SW impact. The snapshots correspond to twelve different time instants in the interval \(0<t^{*}\leq 0.72\), as they are indicated in the instantaneous pictures, where both front and back views are reported. Here and in the following, the instantaneous shape of the deforming droplet is determined as that one associated with the isosurface at \(\alpha=0.5\) for the volume fraction of water. Note that, to correctly visualize the deformation of the water body, the size and position of the zoomed images are exactly the same for each snapshot. Moreover, due to the adopted numerical resolution, the interface between the two immiscible fluids appears to be very slightly diffuse. As it is apparent from these pictures, initially, the passage of the SW does not produce appreciable droplet deformation. There exists a reaction time, which depends on both drop size and air stream velocity [35], during which the water body appears undistorted, with the air flow field practically resembling the flow past a rigid sphere. As the interaction process continues, after the reaction time has elapsed, small-scale instabilities on the liquid droplet surface appear. The droplet begins to be distorted due to the dominant action of the shock-induced pressure gradient along the axial direction, while still maintaining its coherence. The windward side of the water body remains practically spherical, while the leeward side is flattened into a planar surface, which corresponds to a decreasing axial width. At the same time, the droplet is dragged by the air stream moving at high velocity, while the liquid starts to be stripped at the droplet's equator. In fact, according to the sheet thinning mechanism proposed by [PERSON] and [PERSON] [36], the thin liquid sheet being drawn off at the droplet periphery is accelerated and stretched by the dominant action of shear forces due to the surrounding air flow. The liquid sheet becomes thinner and thinner until, eventually, flow instability leads to its incipient breakup into ligaments and the generation of small product droplets. As illustrated in the figure, the parent droplet is continually flattened in the streamwise direction and eroded at the periphery, with the entrainment of small droplets from the liquid sheet edge, near the equator of the main water body. Basically, these pictures confirm the qualitative characteristics of the shear-stripping breakup mechanism, as is expected at the present high Weber number [25]. During the successive stages, the droplet would disintegrate into fragments distributed widely in the flow field, which is out of the scope of this study. In order to illustrate the resolved mean flow, in Figures 4 and 5, the instantaneous contour maps for some variables of interest are reported. On the left column of these figures, the vertical plots show the speed that is the modulus of the velocity vector, while the horizontal plots show the pressure field, normalized by the corresponding post-shock values that are \(V_{2}\) and \(p_{2}\). On the right column, the vertical plots show the temperature field, normalized by \(T_{2}\), while the horizontal plots show the vorticity magnitude field, normalized by \(V_{2}/d_{0}\). All these two-dimensional slices are taken through the original center of the droplet, at the plane \(x=0\), while a rotation is performed for graphical purposes, with the positive \(z\)-axis direction being from the bottom left to top right corners. The different instantaneous pictures are ordered from top to bottom. Furthermore, the initial position of the droplet is represented in the vertical planes to highlight the movement and deformation induced by the SW interaction. Figure 3: Isosurfaces of liquid volume fraction at \(\alpha=0.5\), corresponding to twelve different time instants in the interval \(0<t^{*}\leq 0.72\).