An Economical Model for Simulating Turbulence Enhancement of Droplet Collisions and Coalescence

Abstract

ClusColl, an economical simulation method for droplet motions and collisions in turbulent flows, has been developed, implemented, tested, and applied. In the Linear Eddy Model, permutations called triplet maps representing individual turbulent eddies implement turbulent advection of fluid in 1-D. This captures flow processes down to the smallest turbulent eddy (Kolmogorov microscale), but the inertial response of small Stokes number droplets to turbulence has important features at scales down to the droplet radius, notably sub-Kolmogorov-scale clustering of finite-inertia droplets that can increase collision rates significantly. Additionally, shear due to the smallest scales of turbulence increases collision rates of zero-inertia droplets. In ClusColl, a 3-D triplet map for droplets captures both effects. We implemented collision detection, enabling simulation of droplet collisions and coalescence, and a sedimentation treatment in ClusColl. Published direct numerical simulations (DNSs) of monodispersions were used to tune parameters. For sedimenting droplets in turbulence, ClusColl's turbulent enhancement of bidisperse collision kernels agrees reasonably well with published DNS results. We compared ClusColl and DNS coalescence growth results. For weak turbulence (ε≤100 cm2/s3), ClusColl's turbulent enhancement of coalescence growth closely matches that of the DNS. For ε≥200 cm2/s3, lack of accurate collision efficiencies precludes definitive quantitative evaluation of ClusColl's coalescence growth. In a comparison of coalescence growth dependence on the droplet size distribution width and on turbulent enhancement, ClusColl indicates that the latter dramatically accelerates cloud droplet conversion into raindrops, while the former has significantly less impact.