Turbulent collision efficiency of heavy particles relevant to cloud droplets

The collision efficiency of sedimenting cloud droplets in a turbulent air flow is a key input parameter in predicting the growth of cloud droplets by collision-coalescence. In this study, turbulent collision efficiency was directly computed, using a hybrid direct numerical simulation (HDNS) approach (Ayala et al 2007 J. Comput. Phys. 225 51-73). The HDNS results show that air turbulence enhances the collision efficiency partly due to the fact that aerodynamic interactions (AIs) become less effective in reducing the relative motion of droplets in the presence of background air turbulence. The level of increase in the collision efficiency depends on the flow dissipation rate and the droplet size ratio. For example, the collision efficiency between droplets of 18 and 20 μm in radii is increased by air turbulence (relative to the stagnant air case) by a factor of 4 and 1.6 at dissipation rates of 400 and 100 cm² s⁻³, respectively. The collision efficiency for self-collisions in a bidisperse turbulent suspension can be larger than one. Such an increase in self-collisions is related to the far-field many-body AI and depends on the volumetric concentration of droplets. The total turbulent enhancement agrees qualitatively with previous results, but differs on a quantitative level. In the case of cross-size collisions between 18 and 20 μm droplets, the total turbulent enhancement can be a factor of 7 and 2 at dissipation rates of 400 and 100 cm² s⁻³, respectively. For intermediate size ratios (0.2<a₂/a₁<0.8), the overall enhancement typically falls below 2. Scaling arguments show that the overall enhancement factor tends to peak at the two limiting cases of a₂/a₁→1 and a₂/a₁→0.