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.

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.

Modelling Approaches and Computational Methods for Particle-laden Turbulent Flows introduces the principal phenomena observed in applications where turbulence in particle-laden flow is encountered while also analyzing the main methods for analyzing numerically. The book takes a practical approach, providing advice on how to select and apply the correct model or tool by drawing on the latest research. Sections provide scales of particle-laden turbulence and the principal analytical frameworks and computational approaches used to simulate particles in turbulent flow. Each chapter opens with a section on fundamental concepts and theory before describing the applications of the modelling approach or numerical method. Featuring explanations of key concepts, definitions, and fundamental physics and equations, as well as recent research advances and detailed simulation methods, this book is the ideal starting point for students new to this subject, as well as an essential reference for experienced researchers. - Provides a comprehensive introduction to the phenomena of particle laden turbulent flow - Explains a wide range of numerical methods, including Eulerian-Eulerian, Eulerian-Lagrange, and volume-filtered computation - Describes a wide range of innovative applications of these models

This book provides state-of-the-art results and theories in homogeneous turbulence, including anisotropy and compressibility effects with extension to quantum turbulence, magneto-hydodynamic turbulence and turbulence in non-newtonian fluids. Each chapter is devoted to a given type of interaction (strain, rotation, shear, etc.), and presents and compares experimental data, numerical results, analysis of the Reynolds stress budget equations and advanced multipoint spectral theories. The role of both linear and non-linear mechanisms is emphasized. The link between the statistical properties and the dynamics of coherent structures is also addressed. Despite its restriction to homogeneous turbulence, the book is of interest to all people working in turbulence, since the basic physical mechanisms which are present in all turbulent flows are explained. The reader will find a unified presentation of the results and a clear presentation of existing controversies. Special attention is given to bridge the results obtained in different research communities. Mathematical tools and advanced physical models are detailed in dedicated chapters.

This book contains contributions by former students, colleagues and friends of Professor John L. Lumley, on the occasion of his 60th birthday, in recognition of his enormous impact on the advancement of turbulence research. A variety of experimental, computational and theoretical topics, including turbulence modeling, direct numerical simulations, compressible turbulence, turbulent shear flows, coherent structures and the Proper Orthogonal Decomposition are contained herein. The diversity and scope of these contributions are further acknowledgment of John Lumley's wide ranging influence in the field of turbulence. The large number of contributions by the authors, many of whom were participants in The Lumley Symposium: Recent Developments in Turbulence (held at ICASE, NASA Langley Research Center on November 12 & 13, 1990), has presented us with the unique opportu nity to select a few numerical and theoretical papers for inclusion in the journal Theoretical and Computational Fluid Dynamics for which Professor Lumley serves as Editor. Extended Abstracts of these pa pers are included in this volume and are appropriately marked. The special issue of TCFD will appear this year and will serve as an additional tribute to John Lumley. As is usually the case, the efforts of others have significantly eased our tasks. We would like to express our deep appreciation to Drs. R.

In various branches of fluid mechanics, our understanding is inhibited by the presence of turbulence. Although many experimental and theoretical studies have significantly helped to increase our physical understanding, a comp- hensive and predictive theory of turbulent flows has not yet been established. Therefore, the prediction of turbulent flow relies heavily on simulation stra- gies. The development of reliable methods for turbulent flow computation will have a significant impact on a variety of technological advancements. These range from aircraft and car design, to turbomachinery, combustors, and process engineering. Moreover, simulation approaches are important in materials - sign, prediction of biologically relevant flows, and also significantly contribute to the understanding of environmental processes including weather and climate forecasting. The material that is compiled in this book presents a coherent account of contemporary computational approaches for turbulent flows. It aims to p- vide the reader with information about the current state of the art as well as to stimulate directions for future research and development. The book puts part- ular emphasis on computational methods for incompressible and compressible turbulent flows as well as on methods for analysing and quantifying nume- cal errors in turbulent flow computations. In addition, it presents turbulence modelling approaches in the context of large eddy simulation, and unfolds the challenges in the field of simulations for multiphase flows and computational fluid dynamics (CFD) of engineering flows in complex geometries. Apart from reviewing main research developments, new material is also included in many of the chapters.

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.