Spatio-temporal analysis of sprays by using Phase Doppler Anemometry data

Spray characterization commonly relies on statistical quantities assuming quasi-steady behavior, although stochastic and instability-driven mechanisms govern atomization. Despite widespread application of Phase Doppler Anemometry (PDA), the temporal characteristics of sprays and their implications for modeling are unexplored. Deviations from Poisson arrival statistics indicate droplet clustering, i.e., time-dependent behavior. The present study investigates the spatio-temporal characteristics of an airblast atomizer using PDA datasets, including droplet size, velocity, and arrival time. Interparticle arrival time distributions are evaluated against theoretical Poisson statistics using chi-squared testing and effect size analysis. Multimodality is observed in specific spray regions, indicating pronounced clustering and temporal intermittency. K -means clustering combined with gap statistics quantifies droplet clusters across 10,800 datasets covering various atomizing pressures, temperatures, liquids, and spatial positions. Approximately 30% of datasets exhibit clustering, affecting up to 40% of droplets. Cluster occurrence depends on atomizing pressure and spatial position, while no clear dependence on preheating temperature was observed within the investigated range of conditions. After removing secondary clusters, the spray approaches quasi-steady behavior, indicating that clustering dominates unsteadiness in the core region, while mixing governs peripheral fluctuations. Despite the identified clustering in arrival times, the distributions of droplet size and velocity remain statistically similar across clusters, indicating that clustering reflects temporal intermittency rather than dynamic sorting of droplet populations. This supports a kinematic packing interpretation consistent with intermittency imposed by the carrier flow. The results demonstrate that neglecting clustering may bias spray statistics and modeling, emphasizing the need to incorporate temporal structures into advanced spray models.