Collision statistics and settling velocity of inertial particles in homogeneous turbulence from high-resolution DNS under two-way momentum coupling

Abstract

Statistical quantities related to the motion of low inertia particles in homogeneous isotropic turbulence are investigated by means of direct numerical simulations applying the Eulerian–Lagrangian approach and the point-particle approximation. The modelled systems imitate, among others, the microphysical processes relevant for cloud droplets in typical atmospheric flows. To complement former studies, the turbulent flow is simulated using high-resolution grids, covering a wide range of Reynolds numbers, up to Rλ≈500. The effect of mutual interaction of the carrier and dispersed phases, known as two-way momentum coupling, is considered, and the new results are compared with those obtained under one-way coupling. The droplet kinematic statistics, including the radial relative velocity and radial distribution functions, and dynamic properties, such as the collision kernel and settling velocity, are reported over a wide range of mass loadings. The results show that the radial distribution function of “nearly touching” droplets decreases as the mass loading increases when gravity is not considered. In the presence of gravity there is an enhancement in clustering for dilute systems while a reduction occurs when the two-way coupling effect becomes considerable. An opposite trend is observed for relative velocities due to transfer of momentum from droplets to the fluid, decorrelating the motion of neighbouring droplets. By increasing Rλ, or equivalently enlarging the domain size at fixed energy dissipation rate, the clustering weakens if gravity is considered, while relative velocities augment, ultimately leading to a higher collision kernel. The average settling velocity increases with Rλ. It also increases with mass loading, especially for low-inertia droplets. When performing simulations of small particles at considerable mass loadings a parameterisation is unavoidable to reduce the numerical cost. We use the super-droplet approach and demonstrate its impact on physical fidelity of the modelled systems. The effect of the large-scale forcing scheme, deterministic or stochastic, on the droplet dynamic statistics is also investigated.