Spatio-Temporal Data Analysis of Single Droplet Breakup by High Velocity Gas Flow

Singular value decomposition (SVD), a data-driven fluid informatics method, was used to extract features of flow-induced single droplet breakup. The behavior of single droplet breakup induced by shockwave backflow was captured with high spatio-temporal resolution, and a large dataset was constructed by organizing the time and spatial luminance values according to the Weber number and its variations. SVD was performed on the dataset for space and variation, extracting spatial and variation features. Spatial modes indicating the upstream and downstream sides of the gas-liquid interface, as well as modes indicating planes perpendicular and parallel to the flow, were obtained. The sharp drop in the contribution rate of the second mode corresponds to the induction time of single droplet breakup. SVD was then applied to the dataset for space and time to extract spatial and temporal features. The first-order mode revealed features of the parent droplet and fragments with opposite signs, while higher-order modes captured detailed changes during the breakup process. The second mode, which shows the transition of the parent droplet, ligament, and fine fragment configurations, was emphasized. The moment when the time-mode feature becomes zero coincides with the induction time of droplet breakup. These results demonstrate that applying SVD to single droplet breakup provides a consistent and accurate determination of the breakup induction time.