Effects of turbulence modulation and gravity on particle collision statistics

Dynamics of inertial particles in homogeneous isotropic turbulence is investigated by means of numerical simulations that incorporate the effect of two-way interphase momentum transfer. The continuous phase is solved in the Eulerian approach employing Direct Numerical Simulations (DNS). The dispersed phase is treated using the Lagrangian approach along with the point-particle assumption. The main focus is on computing collision statistics of inertial particles relevant to cloud droplets in typical atmospheric conditions. The vast majority of previous DNS were performed assuming one-way momentum coupling between continuous and dispersed phases. Such simplified approach is adequate only for dilute systems with relatively low mass loading. In this study we investigate the effect of two-way momentum coupling on the kinematic and dynamic collision statistics of the dispersed phase. A number of simulations have been performed at different droplet radii (inertia), mass loading, viscosity and energy dissipation rate. To assess the accuracy of numerical approach the coupling force (exerted by particles on the fluid) was computed using two different techniques, namely particle in cell and projection onto neighboring node. To address the effect of gravity, the simulations have been carried out simultaneously both with and without gravitational acceleration. It has been found that the effect of two-way coupling is significant both for droplet clustering and the radial relative velocity. It turns out that the collision kernel is more sensitive to the particle mass loading when the gravitational acceleration is considered. The collision kernel of settling droplets increases as the droplet mass loading increases. This is direct consequence of larger radial relative velocity. For non-settling droplets the effect of mass loading is opposite, namely, we observe a minor reduction of the collision kernel as the number of droplets increases.