Inertial particle collisions in turbulent synthetic flows: quantifying the sling effect

Turbulent motion increases very significantly the collision rate between particles in dilute suspensions. In the case of heavy inertial particles, the collision rate enhancement results both from the intermittent concentration in the flow, and also from the large relative velocity between colliding particles. The latter effect is a consequence of the ejection of particles out of curved streamlines, denoted here as the "sling effect." Here, we quantitatively study the collision rate between heavy particles in the presence of gravity, with the simplified synthetic model of turbulent flow known as kinematic simulation. Monitoring the velocity of colliding particles and comparing it with the local velocity gradient of the flow of particles allowed us to identify the collision induced by the sling effect and to evaluate their contribution to the total collision rate. Our numerical results are then systematically compared with the estimates based on the properties of particle trajectories in the flow recently proposed by Falkovich and Pumir [G. Falkovich and A. Pumir, J. Atmos. Sci. 64, 4497 (2007)]. At moderate values of the Stokes numbers (St<1) , we demonstrate that the resulting parametrization describes quantitatively correctly the collision rate, and that the sling effect can be responsible for up to approximately 50% of the total collision rate.