Investigation on the dynamic characteristics of a droplet subjected to a divergent shock wave

The present study numerically investigates the dynamic characteristics of a cylindrical droplet impinged by a divergent shock wave, focusing on deformation morphology, the onset of Kelvin–Helmholtz (K-H) instability, and global dynamics. Key features of droplet deformation, including general flattening, interface instabilities, and the formation and spanwise elongation of liquid ligaments, are captured and analyzed. Comparisons with the planar shock case indicate the significant role of shock wave curvature in droplet deformation. Ligaments form closer to the front stagnation point and experience further spanwise extension in the divergent shock case. Moreover, the inception location of the windward K-H instability is found to almost coincide with the windward fixed-point, which forms and migrates as a result of the combined effects of external and internal flows before resting. A theoretical analysis reveals that the initial location of the fixed-point coincides with the critical contact point of the transmitted shock. This location will move downstream with the increase in the shock curvature radius. This study is expected to provide new insights into the shock–droplet interaction problem, contributing to a better understanding of fuel atomization in supersonic propulsion systems.