Extended model of bouncing boundary for droplet collisions considering numerous different liquids

Sprays are widely utilised in different technical and industrial applications. The produced droplet size spectrum is one of the most important parameters that determine the spray characteristics and performance. Depending on the operational conditions and the spray structure, the droplet size spectrum obtained after atomisation will be of course modified by collisions between droplets. In numerical calculations, the Euler/Lagrangian approach is a favourable method for obtaining relatively accurate predictions of spraying processes. However, for correctly modelling droplet collisions, reliable boundary line correlations are needed for distinguishing the different droplet collision outcomes, which are bouncing, coalescence, and separations. These boundary lines are summarised in so-called collision maps to demark the various outcome scenarios. The result of a binary droplet collision depends on numerous parameters, namely, the kinetic properties (droplet velocities, droplet diameter ratio, impact angle) and the physical properties of gas and droplets (droplet liquid, density and viscosity, surface tension, type of gas phase, gas phase pressure and temperature). The boundary line for bouncing, primarily used in numerical studies so far, was derived based on experiments with ethanol droplets by Estrade et al. (1999). However, this theoretical derivation, based on an energy balance, unfortunately neglects viscous dissipation effects. Therefore, the deviations of the predicted bouncing region are pretty large for liquids with higher viscosity or other physical properties. Hence, a data-driven model is proposed in this paper, with new assumptions and definitions, considering the dissipated energy during the collision and the shape changes (i.e., deformation) of the collision complex. For that purpose, two new parameters are introduced in the model, namely a shape factor and an energy conversion rate, both depending on the impact parameter B, which describes the lateral displacement of droplets at a collision. Therefore, the new bouncing model is related to the degree of droplet deformation. The dependence on B could be described by linear correlations with two parameters for slope and intercept. These parameters are correlated with the Ohnesorge number, and polynomial fitting functions were derived with the help of numerous available experiments for different liquids. The upper limit of Ohnesorge numbers in the present study was Oh<0.35. Due to the dependence on the Ohnesorge number, the proposed model very well captures the effect of liquid properties on the bouncing boundary, however, not necessarily the influences of environmental conditions and interface modifications. The model was validated by comparison with numerous available experimental results.