Numerical and experimental investigation of induced flow and droplet–droplet interactions in a liquid spray

Abstract

An Euler–Lagrange model is presented that describes the dynamics of liquid droplets emerging from a high-pressure spray nozzle in a relatively large volume (of the order of almost a cubic meter). In the model, the gas phase is treated as continuum, solved on an Eulerian grid, and the liquid phase is treated as a dispersed phase, solved in a Lagrangian fashion, with interphase coupling through state-of-the-art drag relations obtained from direct numerical simulations. The droplets are introduced into the system at high velocities, leading to a turbulent self-induced gas flow which is solved using large eddy simulation. Despite the relatively low liquid volume fraction in the spray, the number density of droplets at the nozzle is still more than 1010m−3, which is why we employ a highly efficient stochastic Direct Simulation Monte Carlo approach to track collisions between droplets. The droplet collision frequency is calculated on the basis of local droplet number density, droplet size and relative velocities of neighbouring droplets within a dynamically adapting searching scope, as described in Pawar et al. (2014. Chem. Eng. Sci. 105, 132–142). We use known correlations from literature to determine the outcome of a binary droplet collision, which depending on characteristic dimensionless numbers can be coalescence, bouncing or, for high velocity impacts, stretching or reflexive separation leading to formation of satellite droplets. Our simulation model is compared with droplet velocities and size distributions obtained from phase Doppler interferometry experiments on an industrial scale hollow-cone pressure swirl nozzle spray. We find semi-quantitative agreement for spray characteristics such as the axial and radial spray velocity, spray jet width, and the dependence of the droplet size distribution on position within the spray. The simulation model enables us to study the relative importance of different droplet collision events occurring in the spray volume.