In this work, we examine the motion of particles which are subjected to varying levels of turbulence, inertia, and gravity, in both homogeneous and inhomogeneous turbulence. These investigations are performed through direct numerical simulation (DNS) of the Eulerian fluid velocity field combined with Lagrangian particle tracking. The primary motivation of these investigations is to better understand and model the dynamics and growth of water droplets in warm, cumulus clouds. In the first part of this work, we discuss the code we developed for these simulations, Highly Parallel Particle-laden flow Solver for Turbulence Research (HiPPSTR). HiPPSTR uses efficient parallelization strategies, timeintegration techniques, and interpolation methods to enable massively parallel simulations of three-dimensional, particle-laden turbulence. In the second, third, and fourth sections of this work, we analyze simulations of particle-laden flows which are representative of those at the edges and cores of clouds. In the second section, we consider the mixing of droplets near interfaces with varying turbulence intensities and gravitational orientations, to provide insight into the dynamics near cloud edges. The simulations are parameterized to match windtunnel experiments of particle mixing which were conducted at Cornell, and the DNS and experimental results are compared and contrasted. Mixing is suppressed when turbulence intensities differ across the interface, and in all cases, the particle concentrations are subject to large fluctuations. In the third and fourth sections, we use HiPPSTR to analyze droplet motion in isotropic turbulence, which we take to be representative of adiabatic cloud cores. The third section examines the Reynolds-number scaling of single-particle and particle-pair statistics without gravity, while the fourth section shows results when gravity is included. While weakly inertial particles preferentially sample certain regions of the flow, gravity reduces the degree of preferential sampling by limiting the time particles can spend interacting the underlying turbulence. We find that when particle inertia is small, the particle relative velocities and radial distribution functions (RDFs) are almost entirely insensitive to the flow Reynolds number, both with and without gravity. The relative velocities and RDFs for larger particles tend to weakly depend on the Reynolds number and to strongly depend on the degree of gravity. While non-local, path-history interactions significantly affect the relative velocities of moderate and large particles without gravity, these interactions are suppressed by gravity, reducing the relative velocities. We provide a physical explanation for the trends in the relative velocities with Reynolds number and gravity, and use the model of [198] to understand and predict how the trends in the relative velocities will affect the RDFs. The collision kernels for particles representative of those in atmospheric clouds are generally seen to be independent of Reynolds number, both with and without gravity, indicating relatively low Reynolds-number simulations are able to capture much of the physics responsible for droplet collisions in clouds. We conclude by discussing practical implications of this work for the cloud physics and turbulence communities and suggesting areas for future research.

Particle-laden turbulent shear flows are ubiquitous in environmental and industrial flow-systems, and their analysis is thus of prime importance. In this work, we study the motion of a dilute suspension of particles in a non-stationary homogeneous turbulent shear flow (HTSF), subject to varying levels of imposed mean-shear, gravity, and inertia. We use direct numerical simulations (DNS) of the fluid velocity field (coupled with Lagrangian particle tracking), to assess the influence of flow-anisotropy and gravity on the motion of the particles. We first discuss numerical challenges encountered while performing DNS of HTSF at higher Reynolds numbers. The presence of sharp velocity gradients in the HTSF flow field is found to cause premature loss of resolution at the small scales, leading to shortened simulation-times. To counter this, the existing pseudo-spectral DNS setup is augmented with a Weighted Essentially Non-Oscillatory (WENO) scheme, enabling numerically-stable HTSF simulations at higher Reynolds numbers. We then consider the motion of individual particles as they interact with the anisotropic topology of the turbulence. In contrast to isotropic turbulence, particles are found to collect within vortex layers, regions where strong vorticity and strain are coupled with low streamline curvature. Shear-induced anisotropy in the turbulence also leads to reduced gravitational settling speeds for intermediate-inertia particles, though stronger gravity overcomes this effect. Particle velocity variances are found to be highly anisotropic at stronger shear, while gravity now tends to diminish this effect by limiting the interaction-time between particles and turbulence. Shear and gravity acting together cause particle acceleration variances to exceed those of the underlying fluid, corroborating findings from past turbulent boundary layer experiments. Analytical expressions are derived for the mean velocities and accelerations of the particles, and are in agreement with the DNS results. Finally, we analyze the relative velocities and clustering characteristics of particle pairs, and find that stronger shear and gravity suppress path-history effects for particles with stronger inertia. Shear-induced anisotropy in pair-statistics is affected by both inertia and gravity, with stronger gravity seen to oppose the action of shear. Changes in the relative-velocity anisotropy are correlated to the trends shown by single-particle velocity variances. Particle collision rates increase with stronger shear, and are found to scale in proportion to the underlying turbulence timescales.

Turbulence is well known for its ability to efficiently disperse matter, whether it be atmospheric pollutants or gasoline in combustion motors. Two considerations are fundamental when considering such situations. First, the underlying flow may have a strong influence of the behavior of the dispersed particles. Second, the local concentration of particles may enhance or impede the transport properties of turbulence. This dissertation addresses these points separately through the experimental study of two different turbulent flows. The first experimental device used is the so-called von K\'arm\'an flow which consists of an enclosed vessel filled with water that is forced by two counter rotating disks creating a strongly inhomogeneous and anisotropic turbulence. Two high-speed cameras permitted the creation a trajectory data base particles that were both isodense and heavier than water but were smaller than the smallest turbulent scales. The trajectories of this data base permitted a study of the turbulent kinetic energy budget which was shown to directly related to the transport properties of the turbulent flow. The heavy particles illustrate the role of flow anisotropy in the dispersive dynamics of particles dominated by effects related to their inertia. The second flow studied was a wind tunnel seeded with micrometer sized water droplets which was used to study the effects of local concentration of the settling velocities of these particles. A model based on theoretical multi-phase methods was developed in order to take into account the role of collective effects on sedimentation in a turbulent flow. The theoretical results emphasize the role of coupling between the underlying flow and the dispersed phase.

The only work available to treat the theory of turbulent flow with suspended particles, this book also includes a section on simulation methods, comparing the model results obtained with the PDF method to those obtained with other techniques, such as DNS, LES and RANS. Written by experienced scientists with background in oil and gas processing, this book is applicable to a wide range of industries -- from the petrol industry and industrial chemistry to food and water processing.

Publisher Description

Microhydrodynamics: Principles and Selected Applications presents analytical and numerical methods for describing motion of small particles suspended in viscous fluids. The text first covers the fundamental principles of low-Reynolds-number flow, including the governing equations and fundamental theorems; the dynamics of a single particle in a flow field; and hydrodynamic interactions between suspended particles. Next, the book deals with the advances in the mathematical and computational aspects of viscous particulate flows that point to innovations for large-scale simulations on parallel computers. The book will be of great use to students in engineering and applied mathematics. Students and practitioners of chemistry will also benefit from this book.