In this paper, the interaction characteristics between the gaseous detonation and the water droplet are numerically investigated, utilizing a modified compressible two-phase flow model coupling with detailed hydrogen-oxygen chemistry. Firstly, an analysis is conducted on the propagation behaviors of the cellular detonation obstructed by the droplet. It is found that the cellular detonation undergoes reflection, diffraction, local extinction, and re-ignition upon the obstruction, and these behaviors vary with the droplet relative positioning with multi-dimensional structures of the cellular detonation, particularly in terms of the extinction degree caused by the diffraction and the relative positioning of the re-ignition region. Further, the droplet deformation characteristics are detailly analyzed. It has been revealed that the deformation behavior of the shocked droplet under planar detonation is consistent with that under high-speed airflow. However, for the droplet shocked by the cellular detonation, several windward surface pits are induced due to impaction from transverse shocks and direct hitting of the triple-point. The emergence of these pits notably precedes the onset of surface instabilities caused by high-speed airflow erosion. Further investigation has revealed that post-detonation flow, through the entrainment effect of the central pit, progressively penetrates and segregates the droplet into upper and lower segments, and this penetrating effect heavily depends on the droplet relative positioning. Moreover, the side pit, whose presence is significantly determined by whether there is direct impaction of the triple-point on the droplet windward side, is crucial for the deformation around the droplet equator and the subsequent shedding of smaller droplets.
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