Effects of gravity on the acceleration and pair statistics of inertial particles in homogeneous isotropic turbulence

Abstract

Within the context of heavy particles suspended in a turbulent airflow, we study the effects of gravity on acceleration statistics and radial relative velocity (RRV) of inertial particles. The turbulent flow is simulated by direct numerical simulation (DNS) on a 2563 grid and the dynamics of O(106) inertial particles by the point-particle approach. For particles/droplets with radius from 10 to 60 μm, we found that the gravity plays an important role in particle acceleration statistics: (a) a peak value of particle acceleration variance appears in both the horizontal and vertical directions at a particle Stokes number of about 1.2, at which the particle horizontal acceleration clearly exceeds the fluid-element acceleration; (b) gravity constantly disrupts quasi-equilibrium of a droplet’s response to local turbulent motion and amplifies extreme acceleration events both in the vertical and horizontal directions and thus effectively reduces the inertial filtering mechanism. By decomposing the RRV of the particles into three parts: (1) differential sedimentation, (2) local flow shear, and (3) particle differential acceleration, we evaluate and compare their separate contributions. For monodisperse particles, we show that the presence of gravity does not have a significant effect on the shear term. On the other hand, gravity suppresses the probability distribution function (pdf) tails of the differential acceleration term due to a lower particle-eddy interaction time in presence of gravity. For bidisperse cases, we find that gravity can decrease the shear term slightly by dispersing particles into vortices where fluid shear is relatively low. The differential acceleration term is found to be positively correlated with the gravity term, and this correlation is stronger when the difference in colliding particle radii becomes smaller. Finally, a theory is developed to explain the effects of gravity and turbulence on the horizontal and vertical acceleration variances of inertial particles at small Stokes numbers, showing analytically that gravity affects particle acceleration variance both in horizontal and vertical directions, resulting in an increase in particle acceleration variance in both directions. Furthermore, the effect of gravity on the horizontal acceleration variance is predicted to be stronger than that in the vertical direction, in agreement with our DNS results.