A coupled Eulerian–Lagrangian approach with explicit volume diffusion subgrid closures for jet breakup and atomisation

A novel, coupled Eulerian–Lagrangian Large Eddy Simulation method is developed to model turbulent jet breakup, atomisation and droplet dispersion applicable to combusting sprays and other two-phase flows. The approach integrates an Eulerian single-fluid representation incorporating Explicit Volume Diffusion (EVD) subgrid closures for the continuous fluids, including the liquid core and interfacial region, which transitions to a two-fluid representation involving Lagrangian Particle Tracking (LPT) of inertial droplets. The Eulerian–Lagrangian transition utilises criteria based on liquid volume fraction thresholds and a critical droplet Weber number. The coupled model (EVD-LPT) is validated against new high-resolution Direct Numerical Simulation (DNS) data of a turbulent round liquid jet and existing experimental and numerical data for a turbulent jet in crossflow. Results demonstrate substantial improvements in droplet size prediction relative to Eulerian-only EVD simulations. In the round jet case, mesh convergence is achieved for droplets larger than $5\mu m$, with low sensitivity to transition parameters. The crossflow simulations also agree closely with DNS and previous Large Eddy Simulation (LES) results, particularly in capturing inertial droplet behaviour. The study reveals that the Lagrangian representation significantly enhances the prediction of droplet size distributions, addressing known limitations of Eulerian-only models in regions dominated by aerodynamic inertial effects. Overall, the coupled EVD-LPT method provides a computationally efficient, accurate approach for atomisation predictions in complex spray systems, laying a foundation for future developments incorporating droplet secondary breakup, non-spherical droplet shapes, and droplet interaction models.