Eulerian-lagrangian Modelling with Stochastic Approach for Droplet-droplet Collisions

In recent years, there has been growing interest to use computational fluid dynamics (CFD) for exploring dropletparticles interaction under the turbulent flow of air inside spray dryer systems. The final goal is to predict the dried solid particle size and mass flux distributions under the conditions of collision, coalescence and agglomeration of the droplets and particles. The coarse-grained simulation tool will be used to design more efficient spray dryers that can produce higher throughputs. We are developing an Euler-Lagrange model with stochastic treatment of collision, coalescence and agglomeration of droplet-droplet, droplet-particle, and particle-particle combinations in the spray dryer. In this approach, the gas phase is treated as continuum solved by an Eulerian equation and the solid phase is treated as a dispersed phase solved by a Lagrangian equation, with conventional gas-solid coupling. Inside the spray chamber, turbulent gas flow has an effect on the droplet-particle interactions. To take this into consideration we use a subgrid scale turbulence (SGS) model. In the spray dryer process, the number density of droplets at the nozzle is more than 10 m, which is why we employ a Direct Simulation Monte Carlo (DSMC) stochastic approach. In traditional DSMC the system volume is divided into cells and particles collide within a single cell. In this paper we study collisions in a spray of fine water droplets. To avoid lattice artifacts in our work we use a spherical searching scope, in which one droplet searches for another during a droplet time step. Droplet collisions under turbulent flow are calculated on the basis of a collision probability based on droplet concentration and relative velocity. Depending on values of characteristic dimensionless numbers, outcomes of the collisions are assumed to fall in one post-collision regime or another. In this paper we present the model and first validating steps.