Droplet collisions of water and milk in a spray with Langevin turbulence dispersion

Abstract

In this work we investigate droplet-droplet collision interactions in a spray system using an Eulerian-Lagrangian model with subgrid turbulence dispersion. The effect of different droplet viscosities on the type and frequency of droplet collision is investigated, knowledge of which is essential for industrial processes such as spray drying for production of milk powder. The dispersed phase is treated with Lagrangian transport of droplets and the turbulent self-induced gas flow using large eddy simulation (LES). A stochastic Direct Simulation Monte Carlo (DSMC) method is used to detect collisions between droplets. The outcome of a binary collision is described by a collision boundary models for water and milk concentrates. A turbulence dispersion model, based on the Langevin equation, accounts for the stochastic subgrid fluid velocity fluctuations along the droplet trajectory. We compare the spray dynamics with and without droplet interactions and turbulence dispersion. For a spray with typical droplet size of 50 µm, we find that the turbulence dispersion model enhances the total collision frequencies by approximately 25%. The performance of the turbulent dispersion model is tested by investigating the rate of collisions for different milk concentrates. The evolution of size distributions inside the spray is strongly influenced by the complementary effects of collision boundary models and turbulence dispersion.