Large eddy simulation of turbulent gas-droplet flows using the fully Lagrangian approach

The fully Lagrangian approach (FLA) is a promising means of modelling gas-droplet flows, through its representation of the droplet phase as a continuum in combination with a seeding of Lagrangian trajectories which retain the mesoscopic detail of individual droplet motion. This provides a high resolution of the droplet number density field as it undergoes clustering and segregation in response to the structural behaviour of the carrier flow, and along with the advantages in both accuracy and computational economy that the FLA offers, makes it a suitable methodology for use within turbulent flows. The present work addresses this by developing a formulation of the FLA in the framework of large eddy simulation. In keeping with the continuum representation of the FLA, droplets are tracked in the filtered turbulent velocity field, and the sub-grid scale (SGS) fluid velocity is formally accounted for through the Lagrangian form of the droplet phase continuity equation. This contribution takes the form of an additional unclosed mass flux, and is modelled using a kinetic PDF approach, with the correlations between the droplet number density and SGS fluid velocity fluctuations being closed via a correlation splitting procedure that incorporates the non-local turbulent drift effects on the droplet phase. The evolution of the number density field calculated using this procedure is examined, and compared to the number density based on only the filtered fluid velocity field across a range of values of droplet inertia.