An engineering method for predicting shock-driven droplet cloud dynamics

The evolution of droplet clouds from shock-driven breakup is a critical multiphase flow process with significant implications for applications such as raindrop impacts on hypersonic vehicles, explosive dispersal of chemical agents, and liquid-fueled detonations. This study develops an engineering prediction method that advances traditional Lagrangian Particle Tracking (LPT) by explicitly simulating the trajectory of each physically shed child droplet, rather than grouping them into computational parcels. To accurately capture the coupled physics underlying the long-term cloud evolution, from the parent droplet's deformation and persistent mass shedding to the subsequent entrainment of child droplets, the method integrates an experimentally validated breakup model, a General Neural Operator Transformer (GNOT)-based drag model for the deforming parent, and a GNOT surrogate for the transient wake flow. This combination resolves the shielded aerodynamic environment of child droplets within the parent's wake, an effect neglected in conventional simulations. Validation across the shear-induced entrainment (SIE) regime (Weber numbers We ∼10²–10⁴) demonstrates the method's quantitative accuracy. It simultaneously reproduces macroscopic cloud transport and morphology (with a time-averaged Hausdorff distance ≈ 0.115) and the microscopic internal mass concentration field (achieving a mean structural similarity SSIM ≈ 0.903). By accurately reproducing the observed cloud development from initial breakup to final equilibrium, the presented framework provides a robust tool for fundamental study. The quantitative agreements confirm its utility for predicting both global cloud metrics and local concentration gradients, making it readily extensible for integration with CFD simulations of complex flows.