Preferential Concentration Of Inertial Particles Research Articles

Case study on the influence of electrostatic charges on particle concentration in turbulent duct flows

Preferential concentration of inertial particles in wall-bounded turbulent flows is of paramount importance and, thus, subject of fundamental research. In practical applications of confined particle-laden flows the particles experience frequent collisions with the piping system which may result in an unwanted electric charge separation through triboelectric effects. The consequential occurrence of electrostatic forces alters the particle trajectories and their distribution. In this work the influence of charges on the averaged concentration of inertial particles in a fully developed turbulent duct flow was investigated by means of a combined numerical and experimental approach. The order of magnitude of the potential charge accumulation was estimated and imposed in a parametric study to the particulate phase in the simulations. Also, a new numerical approach based on the stochastic parcel method is introduced that allows to handle a large number of charged particles in a Lagrangian framework. This new approach extends standard formulations by including the effect of electrostatic forces on each parcel. The simulations demonstrate that the concentration profiles are for the most part independent of the prescribed charge except in the region close to the walls. The peaks of the particle number density at the walls caused by turbophoresis are strongly reduced through the local increase of repelling electrostatic forces. The comparison of numerical with experimental data indicates that the particles in the experimental setup could be affected by a surface charge density of the order of 100 C/m2. The presented results aim to elucidate the impact of electrostatic forces in the particle distribution in wall-bounded particle-laden flows.

Clustering in Euler–Euler and Euler–Lagrange simulations of unbounded homogeneous particle-laden shear

Particle-laden flows of sedimenting solid particles or droplets in a carrier gas have strong inter-phase coupling. Even at low particle volume fractions, the two-way coupling can be significant due to the large particle to gas density ratio. In this semi-dilute regime, the slip velocity between phases leads to sustained clustering that strongly modulates the overall flow. The analysis of perturbations in homogeneous shear reveals the process by which clusters form: (i) the preferential concentration of inertial particles in the stretching regions of the flow leads to the formation of highly concentrated particle sheets, (ii) the thickness of the latter is controlled by particle-trajectory crossing, which causes a local dispersion of particles, (iii) a transverse Rayleigh–Taylor instability, aided by the shear-induced rotation of the particle sheets towards the gravity normal direction, breaks the planar structure into smaller clusters. Simulations in the Euler–Lagrange formalism are compared to Euler–Euler simulations with the two-fluid and anisotropic-Gaussian methods. It is found that the two-fluid method is unable to capture the particle dispersion due to particle-trajectory crossing and leads instead to the formation of discontinuities. These are removed with the anisotropic-Gaussian method which derives from a kinetic approach with particle-trajectory crossing in mind.

Wavelet multiresolution analysis of particle-laden turbulence

The preferential concentration of inertial particles in isotropic turbulence is studied using wavelets, enabling the joint scale-space analysis of the flow field of the carrier phase, the concentration field of the dispersed phase, and interphase conditioned statistics.

Particle-to-fluid heat transfer in particle-laden turbulence

Preferential concentration of inertial particles by turbulence is a well recognized phenomenon. This study investigates how this phenomenon impacts the mean heat transfer between the fluid phase and the particle phase. Using direct numerical simulations of homogeneous and isotropic turbulent flows coupled with Lagrangian point particle tracking, we explore this phenomenon over wide range of input parameters. Among the nine independent dimensionless numbers defining this problem, we show that particle Stokes number, defined based on large eddy time, and a new identified number called heat mixing parameter have the most significant effect on particle to gas heat transfer, while variation in other non-dimensional numbers can be ignored. An investigation of regimes with significant particle mass loading, suggests that the mean heat transfer from particles to gas is hardly affected by momentum two-way coupling. Using our numerical results we propose an algebraic reduced order model for heat transfer in particle-laden turbulence.

Extreme Small-Scale Clustering of Droplets in Turbulence Driven by Hydrodynamic Interactions.

We perform three-dimensional particle tracking measurements on droplets in a turbulent airflow. The droplets display the well-known preferential concentration of inertial particles, with an additional extreme clustering at the smallest scales. We explain this additional clustering phenomenon theoretically based on a Stokes-flow description of two spheres including their mutual hydrodynamic interaction and a perturbative small-inertia expansion.

Explanation of differences in experimental and computational results for the preferential concentration of inertial particles

Using one-way coupled direct numerical simulations of inertial particles in homogeneous isotropic turbulence we investigate the non-linear dependence of local particle concentrations in particle clusters on the number density of particles used in the simulation per volume. We show that the Reynolds-number dependence of local concentrations in clusters can be predicted for sufficiently high Reynolds numbers by a scaling relation that depends on the average particle number density and the Kolmogorov length. Depending on the average particle number density and gravity, a maximum of preferential concentration does not necessarily occur at Stokes numbers around unity. This explains the differences observed between recent experimental and computational results.

Lagrangian coherent structures and inertial particle dynamics

In this work we investigate the dynamics of inertial particles using finite-time Lyapunov exponents (FTLE). In particular, we characterize the attractor and repeller structures underlying preferential concentration of inertial particles in terms of FTLE fields of the underlying carrier fluid. Inertial particles that are heavier than the ambient fluid (aerosols) attract onto ridges of the negative-time fluid FTLE. This negative-time FTLE ridge becomes a repeller for particles that are lighter than the carrier fluid (bubbles). We also examine the inertial FTLE (iFTLE) determined by the trajectories of inertial particles evolved using the Maxey-Riley equations with nonzero Stokes number and density ratio. Finally, we explore the low-pass filtering effect of Stokes number. These ideas are demonstrated on two-dimensional numerical simulations of the unsteady double-gyre flow.

Single-particle Lagrangian and structure statistics in kinematically simulated particle-laden turbulent flows

Kinematic simulation (KS) is a means of generating a turbulent-like velocity field, in a manner that enforces a desired input Eulerian energy spectrum. Such models have also been applied in particle-laden flows, due to their ability to enforce spatial organization of the fluid velocity field when simulating the trajectories of individual Lagrangian particles. A critical evaluation of KS is presented; in particular, we examine its ability to reproduce single-particle Lagrangian statistics. Also the ability of KS to reproduce the preferential concentration of inertial particles is examined. Some computational results are presented, in which particles are transported alternatively by (1) turbulence generated by direct numerical simulation (DNS) of the incompressible Navier-Stokes equations, and (2) KS. The effect of unsteadiness formulation in particular is examined. We find that even steady KS qualitatively reproduces the continuity effect, clustering of inertial particles, the elevated dispersion of inertial particles over fluid particles, and the intermittency of Lagrangian velocity signals, but generally not to the same extent as is seen in the DNS.

Experimental detection of superclusters of water droplets in homogeneous isotropic turbulence

We present a new technique to study preferential concentration of inertial particles in (active) grid generated turbulence. This method, based on the use of a Taylor hypothesis combined to high-speed imaging, allows to reconstruct unprecedentedly long fields of particles and therefore to analyse new large-scale features, not easily resolvable with standard high-speed imaging methods. We first show that the new approach robustly reproduces results on particles clustering previously reported from standard methods. We then extend the analysis to show the first evidence of superclustering (existence of clusters of clusters) of inertial particles in turbulence and present the first characterization of superclusters.

A Voronoï analysis of preferential concentration in a vertical channel flow

We use three-dimensional Voronoï analysis and results from a direct numerical simulation to study the preferential concentration of inertial particles in a vertical channel flow at Reynolds number 395. By comparing results in upward and downward flows with results from a channel flow without gravity, we are able to determine how gravity affects the particle clustering. Gravity increases the drift of particles towards the walls in an upward flow, while in the downward flow more particles are transported to the centre of the channel. For particles with Stokes number 100, the mean wall-normal particle velocity is positive in the entire core region. A significant increase in variance of the Voronoï probability distribution in the core region is observed in downward flow for Stokes numbers 30 and 100, indicating stronger particle clustering than in upward flow or flow without gravity. The increased clustering in the downward flow is believed to be partly caused by the reversed wall-normal drift assisting in bringing particles close together in the centre of the channel.

Measuring segregation of inertial particles in turbulence by a full Lagrangian approach

Preferential concentration of inertial particles in turbulence is studied numerically by evaluating the Lagrangian compressibility of the particle velocity field using the "full Lagrangian method." This is compared with the "mesoscopic Eulerian particle velocity field" both in a direct numerical simulation of turbulence and in a synthetic flow field. We demonstrate that the Lagrangian method, in contrast to the Eulerian, accurately predicts the compressibility of the particle velocity field even when the latter is characterized by singularities. In particular we use the method to evaluate the growth rates of spatial moments of the particle number density which reflect the fractal structure of segregation and the occurrence of singularities.

A spectral projection method for the analysis of autocorrelation functions and projection errors in discrete particle simulation

AbstractDiscrete particle simulation is a well‐established tool for the simulation of particles and droplets suspended in turbulent flows of academic and industrial applications. The study of some properties such as the preferential concentration of inertial particles in regions of high shear and low vorticity requires the computation of autocorrelation functions. This can be a tedious task as the discrete point particles need to be projected in some manner to obtain the continuous autocorrelation functions.Projection of particle properties on to a computational grid, for instance, the grid of the carrier phase, is furthermore an issue when quantities such as particle concentrations are to be computed or source terms between the carrier phase and the particles are exchanged. The errors committed by commonly used projection methods are often unknown and are difficult to analyse. Grid and sampling size limit the possibilities in terms of precision per computational cost.Here, we present a spectral projection method that is not affected by sampling issues and addresses all of the above issues. The technique is only limited by computational resources and is easy to parallelize. The only visible drawback is the limitation to simple geometries and therefore limited to academic applications.The spectral projection method consists of a discrete Fourier‐transform of the particle locations. The Fourier‐transformed particle number density and momentum fields can then be used to compute the autocorrelation functions and the continuous physical space fields for the evaluation of the projection methods error. The number of Fourier components used to discretize the projector kernel can be chosen such that the corresponding characteristic length scale is as small as needed. This allows to study the phenomena of particle motion, for example, in a region of preferential concentration that may be smaller than the cell size of the carrier phase grid.The precision of the spectral projection method depends, therefore, only on the number of Fourier modes considered. Copyright © 2008 John Wiley & Sons, Ltd.

Statistical models for predicting particle dispersion and preferential concentration in turbulent flows

The objective of the paper is to present a statistical approach to modelling dispersion and preferential concentration of inertial particles suspended in the turbulent fluid. This approach departs from kinetic equations for the one-point and two-point probability density functions of particle velocity distributions in turbulent Gaussian fluid flow fields. Preferential concentration of particles in sheared as well as in isotropic turbulent flows is analysed from a unified viewpoint, and an analogy between both phenomena is discussed.

Large scale inhomogeneity of inertial particles in turbulent flows

Preferential concentration of inertial particles in turbulent flow is studied by high resolution direct numerical simulations of two-dimensional turbulence. The formation of network-like regions of high particle density, characterized by a length scale which depends on the Stokes number of inertial particles, is observed. At smaller scales, the size of empty regions appears to be distributed according to a universal scaling law.

A model for preferential concentration

The preferential concentration of inertial particles in a turbulent velocity field occurs when the particle and fluid time constants are commensurate. We propose a straightforward mathematical model for this phenomenon and use the model to study various scaling limits of interest and to study numerically the effect of interparticle collisions. The model comprises Stokes’ law for the particle motions, and a Gaussian random field for the velocity. The primary advantages of the model are its amenability to mathematical analysis in various interesting scaling limits and the speed at which numerical simulations can be performed. The scaling limits corroborate experimental evidence about the lack of preferential concentration for a large and small Stokes number and make new predictions about the possibility of preferential concentration at large times and lead to stochastic differential equations governing this phenomenon. The effect of collisions is found to be negligible for the most part, although in some cases they have an interesting antidiffusive effect.