Colliding droplets in turbulent flows: A numerical study

Droplets and the way they collide are at the very base of the formation of clouds and the initiation of warm rain. The evolution of a cloud droplet into a rain droplet can be classi?ed into three stages. For each stage different growth mechanisms can be identi?ed. In the ?rst stage condensation is the only effective mechanism. In the second stage, neither condensation nor gravity induced coalescence are effective, and droplets have to grow past this condensation-coalescence bottleneck to reach the third stage. In the third stage droplets are large enough that they start to fall under the effect of gravity, and thereby collect smaller droplets which are still hovering. This increases greatly the collision chances and allows the droplets to grow very rapidly into raindrops. The most plausible mechanism to bridge this bottleneck in the second stage is turbulence-droplet interaction, which may signi?cantly alter droplet dynamics, increases the collision probability and therefore accelerates rain formation. In this thesis we have focused on better understanding the effect of turbulence on droplet (or more generally on particle) collisions using direct numerical simulation (DNS). DNS solves the ?ow ?eld up to the smallest Kolmogorov scales of the ?ow. Combing DNS with a Lagrangian particle tracking algorithm allows us to identify the trajectories of individual droplets, and to investigate the interaction between particles and ?ow structures. It also allows us the detect individual collisions to better understand the mechanisms behind a collision. One of the key mechanisms identi?ed in this thesis to favor collisions between same-sized particles is dissipation. Dissipation can be associated with velocity gradients in the ?ow. Turbulence tends to make particles preferentially concentrate in regions of low vorticity. This clustering brings particles closer to each other. Thereby they experience the same ?uid ?ow which reduces their relative velocities and collision rate. Dissipative events detach the particles from the underlying ?ow ?eld and decorrelate their motion. Large velocity differences can then be found at small separations which increases the collision rate. Dissipation is also associated with converging regions in the ?ow (i.e. negative eigenvalues of the velocity gradient tensor), which bring particles closer together and favors collisions. While dissipation does not seem to play a role as important as vorticity in in?uencing the spatial distribution of the particle ?eld, its role is prominent in initiating collisions. We have also shown that the full distribution of relative velocities between particles in turbulent ?ows can be accurately predicted using the theoretical model of Gustavsson and Mehlig. This model is based on two asymptotic regimes, one where pair diffusion dominates (i.e. large coherence between particle motion) and one where caustics dominate (i.e. large velocity differences between particles at small separations). Knowledge of the distribution of relative velocities between particles provides not only invaluable information on for example the collision rate but also on the article relative velocities at impact. In this thesis we have also investigated the dynamics of cloud droplets at the edge of a cloud, where substantial mixing occurs between moist and positively buoyant cloudy air and the unsaturated and neutrally buoyant environmental air. Droplets are detrained out of the cloud and evaporate, which cools the surrounding air. As a result, this evaporative cooling creates a descending cloud shell which increases the turbulent intensity at the cloud edge and results in even more mixing. Through a complex interplay between turbulence, evaporation and gravity, the cloud edge appears to be a very favorable location for a fast droplet growth through coalescence. Evaporation signi?cantly broadens the droplet size distribution and thereby increases the collision rate. Under the effect of gravity, droplets remain longer in unsaturated air at the cloud edge which allows evaporation to broaden the droplet size distribution even further and increases the collision rate even more