Evolution of the size distribution of drops settling in a non-continuum, turbulent gas
The evolution of droplets in clouds is studied with focus on the 'size-gap' regime of 15-40 μm radius, where condensation and differential sedimentation are least effective in promoting growth. This bottleneck leads to inaccurate growth models and turbulence can potentially rectify disagreement with in-situ cloud measurements. Turbulent shear and differential sedimentation will both drive collisional growth in the ‘size-gap’ and the resulting coupled configurational dynamics is rigorously studied. Droplet inertia will not significantly alter the local collision dynamics as it is weak in typical cloud conditions. However, weak inertia acting over a range of separation scales enhances the concentration of neighbouring drops available for collision. An inertial clustering model is developed which incorporates an inertia-induced drift velocity, relative diffusion due to turbulent shear and acceleration and differential sedimentation. This model is built upon available direct-numerical simulations and theoretical predictions in limiting conditions. It allows predictions over a broad range of particle separations, Stokes numbers, settling velocities and Taylor scale Reynolds numbers Reλ. The inertia-less local collision dynamics of sub-Kolmogorov droplets due to turbulence and gravity is studied for both a frozen linear flow approximation, in line with the classical work by Saffman & Turner, and for a stochastically fluctuating linear flow based on a Lagrangian velocity gradient model. It is found that the ideal collision rate has a significant dependence on Reλ that has not been recognized in previous work. Inclusion of interparticle interactions strongly retards the collision rate. Non-continuum hydrodynamic interactions of droplets in clouds dominates over colloidal forces, deformation, interface mobility, and medium compressibility but has not found extensive treatment in the previous literature. Hence, the collision efficiency, capturing retardation, is calculated over a large parameter space including Knudsen number (Kn), the ratio of mean free path to mean sphere radius, relative size of the interacting spheres, Reλ, and strength of differential sedimentation relative to turbulence. Analytical fits of the collision rate results facilitate their use in drop population models. The steady linear flow approximation facilitated a detailed examination of the complex trajectory evolution that results from the competition of gravity and shear in the presence of non-continuum hydrodynamic interactions. Utilising the collision rate results an evolution study is carried for cloud droplets from condensation controlled sizes of a few micron to differential sedimentation dominated sizes through the ‘size-gap’. For a complete description of cloud droplet dynamics non-collisional components of turbulence, mixing of droplets and water vapour fluctuations, are included. To resolve turbulent intermittency and retain a discrete drop distribution with manageable computational load a Monte Carlo scheme is used. Cloud packets are used to capture multiple realisations of the stochastic turbulent processes. The collection of droplets within each packet represents a unique history of turbulent intensity and water vapour concentration and so different packets represent different regions of the cloud. Turbulent mixing is modelled by moving droplets between different packets. The simulations reveal the strong effect of hydrodynamic interactions and the mean-free path on drop size evolution. Condensation in a uniform environment tends to create a nearly monodisperse drop size distribution making differential sedimentation weak. It is shown that turbulent shear and clustering as well as water vapour fluctuations play important roles in producing polydispersity and allowing droplet growth through the size gap.
Hydrodynamic interactions; Particle/fluid flow; Slender-body theory; Turbulence
Koch, Donald L.
Collins, Lance; Bewley, Gregory Paul
Ph. D., Mechanical Engineering
Doctor of Philosophy
dissertation or thesis