An Eulerian–Lagrangian hybrid model for the coarse-grid simulation of turbulent liquid jet breakup

• Numerical simulation of turbulent liquid jet breakup is studied using coarse grids.
• An energy-based sub-gird breakup model is applied to picture droplet formation.
• Eulerian–Lagrangian coupling for jet core and dispersed droplets is established.
• The model predicts the effect of gas pressure on droplet size distribution and SMD.

In this paper we present a numerical model for the coarse-grid simulation of turbulent liquid jet breakup using an Eulerian–Lagrangian coupling. To picture the unresolved droplet formation near the liquid jet interface in the case of coarse grids we considered a theoretical model to describe the unresolved flow instabilities leading to turbulent breakup. These entrained droplets are then represented by an Eulerian–Lagrangian hybrid concept. On the one hand, we used a volume of fluid method (VOF) to characterize the global spreading and the initiation of droplet formation; one the other hand, Lagrangian droplets are released at the liquid–gas interface according to the theoretical model balancing consolidating and disruptive energies. Here, a numerical coupling was required between Eulerian liquid core and Lagrangian droplets using mass and momentum source terms. The presented methodology was tested for different liquid jets in Rayleigh, wind-induced and atomization regimes and validated against literature data. This comparison reveals fairly good qualitative agreement in the cases of jet spreading, jet instability and jet breakup as well as relatively accurate size distribution and Sauter mean diameter (SMD) of the droplets. Furthermore, the model was able to capture the regime transitions from Rayleigh instability to atomization appropriately. Finally, the presented sub-grid model predicts the effect of the gas-phase pressure on the droplet sizes very well.