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.

Numerical investigation of droplet-droplet collisions in a water and milk spray with coupled heat and mass transfer

“…Under equilibrium conditions the temperature of the surface of the droplets and hence the vapor pressure at the surface will be such that the heat transfer and mass transfer rates are balanced. Our previous work, [22] revealed that the inclusion of droplet interactions and a turbulent dispersion model strongly influence the size distribution along the spray as well as the rate of collisions. We will now investigate the influence of droplet drying, and the incorporation of two-way coupling of heat and mass transfer between droplet and gas, on the droplet spray characteristics.…”

“…A droplet turbulent dispersion model estimates the instantaneous fluid velocity along the droplet trajectory, accounting for subgrid-scale gas velocity which are not resolved in the simulations. For details on the turbulent dispersion model and its effect on dropletdroplet interactions the reader is referred to the work of Finotello et al [22] The single droplet drying model of the reaction engineering approach is adopted in our work.…”

“…Because the rate of evaporation is low in the section of the spray considered in this work, we assume that the vapor production does not significantly modify the fluid phase density. We use the Vreman [48] model to describe the subgrid-scale gas flow effects in Large Eddy Simulations (LES), see also Finotello et al [22] In LES of turbulent flow, the averaging operator is a linear filtering operator, i.e. a local weighted average over a small volume of fluid.…”

“…Finotello et al [22] studied droplet collision outcomes in a spray with a turbulent dispersion model accounting for stochastic subgrid fluid velocity fluctuations along the droplet trajectory. They affirmed that it is important to quantify the frequency of collisions in the spray, as well as the capability to predict the spatial region of the spray where a prevalence of a specific collision regime can be expected.…”

“…Indeed, in all the above-mentioned studies the distribution and frequency of droplet collision events such as coalescence, separation and bouncing were not presented. In this study we start from our previously developed Euler-Lagrange model [22] based on Direct Simulation Monte Carlo (DSMC), which includes turbulent dispersion of the droplets, and extends it to study droplet behavior in the presence of heat, mass and momentum transfer mechanisms. Moreover, we will conduct a parametric study of the air and droplet phase patterns by varying initial operating conditions in the spray dryer.…”