Collisions of Small Drops in a Turbulent Flow. Part II: Effects of Flow Accelerations

Abstract

The effects of Lagrangian acceleration on collision efficiency and collision kernels of small cloud droplets in a turbulent flow are investigated using the results of the recent laboratory experiments by La Porta et al., conducted under high Re? flow of pronounced intermittency. The effect of Lagrangian accelerations on drop collisions has been found to be significant, namely, for drop pairs, containing a drop collector exceeding 10 ?m in radius, collision efficiency, and collision kernels increase by up to 25% and 40%, respectively, at dissipation rates of 200 cm2 s?3 typical of weak cumulus clouds. In well-developed deep cumulus clouds, the increase attains the factor of 2.5 and 5, respectively, at typical dissipation rates of 1000 cm2 s?3. The effect of Lagrangian accelerations is mainly caused by the increase in the collision efficiency that is highly sensitive even to weak variations of interdrop relative velocity. The increase in the swept volume is responsible only for a fraction of the overall increase in the collision kernel. The effect of intermittency of a turbulent flow manifests itself in two aspects: (i) an increase in variance of Lagrangian accelerations with an increase in Re?, and (ii) the formation of a specific shape of the probability distribution function (PDF) characterized by a sharp maximum and elongated tail. The increase in variance of Lagrangian accelerations leads to an increase in the collision rate between droplets. The effect of the PDF shape on the collision rate is studied by comparing the magnitudes of collision efficiencies (and kernels) obtained in case of the non-Gaussian PDF with those obtained using the Gaussian PDF of the same acceleration variation. The utilization of the Gaussian PDF leads to a slight (about 10%?15%) overestimation of the values of the collision efficiency and collision kernel. Thus, the effect of intermittency on drop collisions related to high values of PDF flatness has been found to be insignificant and is not responsible for the acceleration of the collision rate. Thus, the only information needed in practice for the evaluation of acceleration effects on collisions is the magnitude of acceleration variation at high Re?. The analysis also suggests that the problem of drop collisions remains incomplete in cases where only accelerations are taken into account. Effects of turbulent shears should be taken into account as well, which, supposedly, will lead to an additional increase in the collision rate in a turbulent flow.