Session GQ: Particle Laden Flows II

Effect of large-scale flow forcing scheme on turbulent collision statistics of inertial particles

Direct numerical simulations (DNS) of turbulent collision of small inertial particles such as cloud droplets rest on an implicit assumption that the collision statistics of inertial particles are mainly governed by turbulent motion in the dissipation-range. Because of the potential coupling between dissipation-range scales and the energy-containing scales (i.e., vortical structure and intermittency), the limited resolution or scale separation in DNS, and the likely response of an inertial particle to a range of fluid motion, the nature of large-scale forcing used to maintain the stationarity of fluid turbulence could have some impact on the collision statistics of inertial particles. Here we compare results obtained from two forcing schemes: a stochastic forcing scheme and a deterministic forcing scheme. We focus on statistics related to the geometric collision including preferential concentration, radial distribution function, radial relative velocity, and dynamic collision rate for a range of droplet sizes and flow dissipation rates relevant to atmospheric clouds. Using an MPI implementation of DNS of turbulent collisions, we can also examine the effect of forcing scheme at several different flow Reynolds numbers or scale separations.   

High-resolution direct numerical simulations (DNS) of turbulent collision of inertial particles

In this talk we discuss an MPI implementation of turbulent collision and high-resolution DNS results using this MPI code. DNS is limited to relatively small flow Reynolds number or equivalently a small physical domain size at a given flow dissipation rate in a turbulent cloud. Here we are aimed at systematically extending the computational domain size by increasing the grid resolution. The MPI implementation requires parallelization of fluid velocity interpolation at the particle position, Lagrangian particle tracking, and collision detection in addition to the flow parallelization. Domain decomposition has been previously utilized for efficient MPI implementation of FFT in the pseudo-spectral simulation of fluid turbulence. Such a strategy is not naturally in line with the Lagrangian particle dynamics. Two general MPI issues for particle dynamics must be efficiently solved: the gathering of information in a finite region surrounding a particle and travelling of a particle through the boundaries of a subdomain. Our MPI results are carefully validated against a previous OpenMP implementation. Finally, turbulent collision statistics of inertial particles at grid resolution up to 512$^{3}$ with O(10$^{6})$ particles will be presented.   

Lattice Boltzmann Simulations of Peristaltic Particle Transport

A peristaltic flow occurs when a tube or channel with flexible walls transports the contained fluid by progressing a series of contraction or expansion waves along the length of those walls. It is a mechanism used to transport fluid and immersed solid particles when it is ineffective or impossible to impose a favorable pressure gradient or desirous to avoid contact between the transported mixture and mechanical moving parts. Peristaltic transport occurs in many physiological situations and has myriad industrial applications. We focus our study on the peristaltic transport of a macroscopic particle in a two dimensional channel using the Lattice Boltzmann Method (LBM). We systematically investigate the effect of variation of the relevant non-dimensional parameters of the system on the particle transport. We examine the particle behavior when the system exhibits the peculiar phenomenon of fluid ``trapping.'' Finally, we analyze how the particle presence affects stress, pressure, and dissipation in the fluid in hopes of determining preferred working conditions for peristaltic transport of shear-sensitive particles.   

Direct Simulation of Particulate Flows with a 3D Explicit Finite-Difference Scheme

A 3D explicit finite difference scheme has been developed to simulate moderately dense particulate flows at intermediate Reynolds numbers. The scheme solves the compressible Navier-Stokes equations at small Mach numbers to approximate the solution at the incompressible limit. It explicitly marches the fluid velocity and density in time without inverting any matrices. The solid rigid particles are moved according to the hydrodynamic forces and moments acting on them by the fluid. A spectral expansion method is implemented to exactly satisfy the no-slip boundary condition on the particle surface, such that the scheme is able to achieve good accuracy on coarse grids. The method has been validated by comparison to an implicit finite element particle solver, and by direct comparison with experiments. Using this scheme, we calculate the effective viscosity of a sheared suspension as a function of the particle volume fraction.   

Inertial particle accelerations in near-wall turbulence: comparison of experiments and simulations

Recent experiments in a turbulent boundary layer (Gerashchenko et al. 2008) revealed surprising trends for inertial particle accelerations in the near-wall region. In particular, acceleration variance was seen to increase with increasing inertia, contrary to what is found in isotropic turbulence. They conjecture an explanation for this reversal in the trend based on the interaction of the inertial particle with the mean flow and gravity. To gain further insight into these findings, we perform direct numerical simulations (DNS) of channel flow with suspended inertial particles that are tracked in the Lagrangian frame of reference. The DNS parameters have been chosen to match those of the experiment, based on boundary layer scaling. Three swarms of particles with different Stokes numbers (0.88, 1.77 and 11.9) have been simulated. Results for the mean and RMS profiles of particle acceleration are in qualitative agreement with the earlier experiments.   

Lattice Boltzmann Model of Drop Dynamics on Patterned Substrates with Particle Suspensions

A lattice Boltzmann method (LBM) model has been developed for multi-phase flows with solid particles suspended in the liquid and/or vapor phases. While significant research has been devoted to study multi-phase flows and particle suspensions separately, it is only recently that these separate threads are being combined. For the multi-phase part, the particle-interaction model of Shan and Chen is used. The particle suspension model is modified to incorporate surface forces between the suspended particle and the surrounding fluid, similar to the adhesive forces used in the multi-phase model near solid walls. Several validation problems are presented to test both the separate sub-models and the combined model. The combined multi-phase particle suspension model is first used to study clustering of colloidal particles within a liquid drop and migration of suspended particles from the bulk fluid region to the liquid-vapor interface. The model is then used to predict the wetting, dewetting, contact line pinning, and particle self-assembly of a drop containing suspended particles as it spreads on various types of substrates. In conjunction with experiments, the LBM model will help optimize inkjet printing of electronic inks on patterned substrates for flexible electronics fabrications.   

Modeling Dense Liquid-Solid Flows

The transport of solid particles in a turbulent flow has many industrial applications, including the liquid-slurry flows encountered in the mining industry. For numerical simulation of particle-laden flows, the two-fluid model utilises an Eulerian formulation of the mean fields, which treats the liquid and solid phases as interpenetrating continua. For both gas and liquid flows, at high particle concentrations, the flow characteristics are strongly influenced by the particle-particle and particle-wall interactions. The present study looks at the extension of two-fluid models originally developed for dilute gas-particle flows (e.g. Bolio et al, 1995) to liquid-solid flows, with the prediction of dense slurry flows as the long-term objective. In the case of a liquid, the interstitial fluid layer can modify the particle-particle and particle-wall collisions. For high solids concentrations, the turbulence can be significantly suppressed by the presence of particles. Both the solid and liquid phases are also affected by surface roughness at the wall. The present numerical study investigates the implementation of two-fluid models for fully-developed liquid-solid flows in the context of the modeling issues identified above.   

Coupling Discrete and Continuum Mechanics in Low Concentration, Particle-Laden Flows

The study of particle-laden flow plays a critical role in pressure-driven membrane filtration such as microfiltration (MF), ultrafiltration (UF), nanofiltration (NF), and reverse osmosis (RO). Hydrodynamic and inter-particle interactions, coupled to the ambient crossflow field, are well documented in literature. Transport of particles is originated due to Brownian and shear-induced diffusion, and convection due to the axial crossflow and transverse permeate flow. These effects are modeled using Hydrodynamic Force Bias Monte Carlo (HFBMC) simulations to predict the deposition of the particles on the membrane surface. In addition, the particles in the simulation are also subject to electrostatic double layer repulsion and van der Waals attraction both between particles and between the particles and membrane surfaces. In conjunction with the hydrodynamics, the change in particle potential determines the transition probability that a proposed, random move of a particle will be accepted. In the current study, these discrete particle effects at the microscopic level are coupled to the continuum flow via an apparent local viscosity, yielding a quasi-steady-state velocity profile. This velocity profile is dynamically updated in order to refine the hydrodynamic interactions. The resulting simulation predicts the formation of a cake layer of deposited interacting particles on the membrane surface.   

Large-Eddy Simulation of Particle-Driven Gravity-Currents

A gravity current forms when a heavier fluid propagates into a lighter one. In the case of particle-driven gravity currents, the density difference is caused by a differential loading of the fluid with small suspended particles. The particle influence is described in an Eulerian framework, such that the particles are represented as a concentration field. Typical Reynolds and Schmidt numbers in reality are orders of magnitude larger than those which are within reach of direct numerical simulation (DNS). In large-eddy simulations (LES) only the largest scales of the turbulent fluid motion are resolved by the numerical procedure, while the small (subgrid) scales are modeled. The LES approach is applied to both the fluid equations and the particle concentration equation. In the present work, we compare LES to DNS results at moderate Reynolds and Schmidt numbers. In particular, we consider the energy budget of the flow, the mixing behavior and the sedimentation profiles in a lock exchange configuration.   

Interaction of a spherical particle with freestream turbulent flow: Effect of microscale Reynolds number

The interaction of an isolated rigid sphere with an isotropic turbulent ambient flow is considered using a direct numerical simulation. The turbulence field is obtained from one realization of a separate DNS calculation (Donzis et al, JFM (2005), vol. 532; Yeung et al, JFM (2007) vol. 582), and used as the inflow condition for the flow around the sphere. This study is an extension of an earlier work (Bagchi and Balachandar, Phys. Fluids (2003), vol. 15; Bagchi and Balachandar, JFM (2004), vol. 518), where the Taylor microscale Reynolds number, $R_\lambda$, of the turbulence field was kept constant at 164. In the present study, we consider the effect of varying $R_\lambda$ as 38, 90, 140 and 240. The sphere Reynolds number (based on the diameter and relative velocity) is in the range 63 to 400, and the sphere diameter varies from 1 to 8 times the Kolmogorov scale, and 0.18 to 0.0042 times the integral length scale, of the ambient turbulent flow. We present DNS results on the drag and lift forces, and added-mass and history forces on the sphere under varying $R_\lambda$, and compare them with the analytical results. Mean, RMS and PDF of these forces are analyzed. We also present transition in the sphere wake as $R_\lambda$ is varied. Mean wake, and the modulation of the freestream turbulence in the wake are also presented under varying $R_\lambda$ of the ambient flow.