High resolution simulation of turbulent collision-coalescence of cloud droplets
University of Delaware
In this dissertation we investigate the effects of turbulence, inertia and gravitational settling on the dynamics of colliding cloud droplets. This study is motivated by the open question in cloud microphysics concerning the fast growth of droplets in warm clouds through the size range from 10 to 50 micrometer in radius, for which neither the diffusional growth nor the gravitational collision-coalescence is effective. In order to simultaneously compute the turbulent flow field and the droplet dynamics with a sufficient domain size, we developed a massively parallel direct numerical simulation (DNS) code using 2D domain decomposition (2D DD). We simulate the flow using a pseudo spectral DNS code and track individual droplets whose motion is affected by Stokes drag, gravity and local droplet-droplet hydrodynamic interactions. The hydrodynamic interactions are represented analytically by Stokes disturbance flows that are coupled to the background air turbulence. To better understand the scalability of this parallel hybrid DNS code, we measured the wall clock time of the code under different simulation conditions and developed a theoretical complexity analysis to predict the execution time for any problem size and any number of processors. The resulting analysis is found to be in good agreement with the measured timing data for all the problem sizes and numbers of processors tested. The execution time scales with the number of processors almost linearly before the performance saturates due to excessive communication latency. The complexity analysis is used to estimate the maximum number of processors below which the linear scalability could be sustained, demonstrating that our code is likely to perform well on Petascale machines for large problem sizes. In the second part of the dissertation, the newly developed 2D DD code is used to study the dynamics of droplets in a turbulent flow up to flow Taylor Reynolds number of 143. The effects of gravity on the inertial particle acceleration was studied. We found that the gravity plays a very important role in particle acceleration statistics: a) A peak value of particle acceleration variance appears in both the horizontal and vertical directions at a particle Stokes number of about 1.2, at which the particle horizontal acceleration clearly exceeds the fluid-element acceleration; b) Gravity suppresses extreme acceleration events both in the vertical and horizontal directions by reducing the particle-eddy interaction time, and thus effectively enhances the inertial filtering mechanism. A theory was developed to explain the effects of gravity and turbulence on the horizontal and vertical acceleration variance of droplets at small particle Stokes numbers. We found analytically that gravity affects particle acceleration variance both in horizontal and vertical directions, resulting in an increase in particle acceleration variance in both directions. Furthermore, the effect of gravity on the horizontal acceleration variance is found to be stronger than that in the vertical direction, in agreement with our DNS results. By decomposing the radial relative velocity of the particles into three parts: the gravitational term, the shear term and the differential acceleration term, we were able to evaluate separately their contributions. For monodisperse particles, our results show that the presence of gravity does not have a significant effect on the shear term. On the other hand, gravity broadens the pdf tails of the acceleration term due to both the inertial bias and the preferential sweeping effect when encountering a vortical structure. For bidisperse cases, we found that gravity can decrease the shear term slightly by dispersing particles into vortices where fluid shear is relatively low. We also found that the differential acceleration term is positively correlated with the gravity term, and this correlation is stronger when the difference in colliding particle radii becomes smaller. Through DNS data, we found that the ratio of the differential acceleration to the gravity term is between 30% to 60%. This implies that the enhancement factor due to turbulence relative to the gravity term, is 1.04 to 1.17, consistent with the results in previous studies. In the third part, the size distribution of the growing cloud droplets under cloud conditions was studied. Two average radii were measured for the droplets: the average of droplet radii over whole domain (the average radius) and the average radius for the 1024 largest droplets in the domain (the lucky-droplet average radius). For an initially bidisperse system, the turbulence contributes significantly via acceleration and coupling mechanisms. The growth rate of lucky droplets was found to be significantly affected by turbulence. Finally, we study the effect of turbulent Reynolds number on the growth rate of the droplets. We found that the flow Reynolds number has a negligible effect on the growth rate of average droplet radius. However, the growth rate of the lucky-droplet average radius is significantly affected indicating that the lucky droplets interact with the large-scales flow. A Froude number based on the Taylor scale is introduced to help interpret this interaction. We found that this interaction is stronger when the particle Froude number is of order unity. In summary, the results obtained in this dissertation provide insights into the contributions of the different scales of turbulent air motion on the initiation and development of rain droplets from cloud droplets through the collision-coalescence mechanism.