## 4 Discussion  
In all the cases where water impacted on the melt surface, cavity development on the melt surface was observed, followed by the propagation of a radial surface wave at the later stage of interaction. It is interesting to compare the cavity growth features in the cases of droplet and impulse jet impacts. In Figure 9, the time dependencies of the cavern diameter are plotted for the cases J1 and J2, together with the data from Figure 2 for the free-falling droplet impact (Case D1). It can be seen that the data from Case J1 follow the three-stage sequence that was clearly seen in Figure 2. However, case J2 shows more irregular behavior, most probably due to the bubble formation under the melt surface caused by the evaporation of water captured by melt. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Case** & **D1** & **J1** \\ \hline \multicolumn{3}{c}{Stage 1} \\ \hline Time interval, ms & \(0\leq t\leq 2.745\) & \(0\leq t\leq 2\) \\ \(d_{0}\), mm & 4.519 & 8.297 \\ \(t_{0}\), ms & 0.073 & 0.1 \\ \(d_{1}\), mm & 0 & 0 \\ \hline \multicolumn{3}{c}{Stage 2} \\ \hline Time interval, ms & \(2.745\leq t\leq 9.65\) & \(2\leq t\leq 3.72\) \\ \(d_{0}\), mm & 1.769 & 5.626 \\ \(t_{0}\), ms & 2.745 & 2.0 \\ \(d_{1}\), mm & 7.112 & 10.862 \\ \hline \multicolumn{3}{c}{Stage 3} \\ \hline Time interval, ms & \(t>9.65\) & \(t>3.72\) \\ \(d_{0}\), mm & 26.750 & 25.611 \\ \(t_{0}\), ms & 9.65 & 3.72 \\ \(d_{1}\), mm & 8.163 & 12.366 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Best-fit approximation parameters (see Equation (1)). Figure 8: Melt–water jet interaction, Cases J4 (**a**) and J5 (**b**): shape of the cumulative jet at different times. The parameters of the best-fit approximation (1) for cases D1 and J1 are listed in Table 4. In Figure 9, the approximations (1) are plotted for each stage by the dashed (for J1) and dashed-dotted (for D1) lines; the line segments are deliberately extended beyond the limiting points of the stages to highlight the intersection points where the slope changes abruptly. It can be seen that Stage 3 (surface wave propagation) is only weakly dependent on the interaction details (the slope \(d_{0}\) coincides in Stage 3 in D1 and J1 within 4%, that is, 26.750 vs. 25.611, despite the significant differences in the water mass and velocity). However, the cavity edge velocity in Stages 1 is very different, and significant differences are observed in the duration of Stages 1 and 2. Generally, the data presented in Figure 9 suggests the idea of possible cavern growth regime similarity, but further experimental and theoretical studies are needed to find the governing similarity laws. A very interesting feature of the melt-water interaction that was observed experimentally is that not only water was scattered around the impact point in the form of small droplets, but noticeable amounts of melt particles (frozen droplets) also collected around the vessel after each test, see Figure 10. At this stage, no fractional analysis of the dispersed melt was performed because it was beyond the objectives of the current work. However, it can be said that the particles scattered by the interactions are in the mm, or sub-mm range. It remains to be seen how this dispersed fraction of melt depends on its superheat and properties, as well as how sensitive it is to the melt material and water impact characteristics. It is helpful to compare the results obtained with those available in the literature for droplets impinging on a liquid surface where both liquids are identical (i.e., the pool  
Figure 10: After-test photo of the heater and vessel with scattered frozen melt particles. Figure 9: Time history of the cavity diameters for cases D1, J1, and J2. The dashed lines show the approximations (1) for each stage, see parameters in Table 4.  
to droplet liquid density ratio is 1). As noted above, the non-dimensional parameters commonly used to analyze the regime boundaries are the Weber and Froude numbers (see review in [10]).