Preferential Concentration Of Particles Research Articles

Solid particle distribution in particle-laden turbulent channel flows

Large Eddy Simulation (LES) of fully developed particle-laden turbulent channel flows were performed at Reynolds number 180 and 644, respectively. The effects of Stokes numbers, turbulent flows SGS fluctuations and inter-particle collisions on the distributions of solid particles were discussed. It was verified that, regardless of the Reynolds number of fluid flows, the maximum departure from randomness is when the ratio of the particle's aerodynamic response time to the Kolmogorov time scale of flow was approximately one. In addition, the simulation results showed that the degrees of particle preferential concentration are selectively associated with the SGS fluctuations of fluid turbulence.

An Eulerian–Eulerian model for gravity currents driven by inertial particles

In this work we introduce an Eulerian–Eulerian formulation for gravity currents driven by inertial particles. The model is based on the equilibrium Eulerian approach and on an asymptotic expansion of the two-phase flow equations. The final model consists of conservation equations for the continuum phase (carrier fluid), an algebraic equation for the disperse phase (particles) velocity that accounts for settling and inertial effects, and a transport equation for the disperse phase volume fraction. We present highly resolved two-dimensional (2D) simulations of the flow for a Reynolds number of Re = 3450 (this particular choice corresponds to a value of Grashof number of Gr = Re 2 / 8 = 1.5 × 10 6 ) in order to address the effect of particle inertia on flow features. The simulations capture physical aspects of two-phase flows, such as particle preferential concentration and particle migration down turbulence gradients (turbophoresis), which modify substantially the structure and dynamics of the flow. We observe the migration of particles from the core of Kelvin–Helmholtz vortices shed from the front of the current as well as their accumulation in the current head. This redistribution of particles in the current affects the propagation speed of the front, bottom shear stress distribution, deposition rate and sedimentation. This knowledge is helpful for the interpretation of the geologic record.

Refinement of the probability density function model for preferential concentration of aerosol particles in isotropic turbulence

The purposes of the paper are threefold: (i) to refine the statistical model of preferential particle concentration in isotropic turbulence that was previously proposed by Zaichik and Alipchenkov [Phys. Fluids 15, 1776 (2003)], (ii) to investigate the effect of clustering of low-inertia particles using the refined model, and (iii) to advance a simple model for predicting the collision rate of aerosol particles. The model developed is based on a kinetic equation for the two-point probability density function of the relative velocity distribution of particle pairs. Improvements in predicting the preferential concentration of low-inertia particles are attained due to refining the description of the turbulent velocity field of the carrier fluid by including a difference between the time scales of the of strain and rotation rate correlations. The refined model results in a better agreement with direct numerical simulations for aerosol particles.

Self-similar clustering of inertial particles in homogeneous turbulence

It is shown by direct numerical simulation that the preferential concentration of small heavy particles in homogeneous isotropic developed turbulence has a self-similar multi-scale nature when the particle relaxation time is within the inertial time scales of the turbulence. This is shown by the pair correlation function of the particle distribution extending over the entire inertial range, and the probability density function of the volumes of particle voids taking a power-law form. This self-similar multi-scale nature of particle clustering cannot be explained only by the centrifugal effect of the smallest-scale (i.e. the Kolmogorov scale) eddies, but also by the effect of co-existing self-similar multi-scale coherent eddies in the turbulence at high Reynolds numbers. This explanation implies that the preferential concentration of particles takes place even when the relaxation time of particles is much larger than the Kolmogorov time, provided it is smaller than the longest time scale of the turbulence, since even the largest-scale eddies bring about particle clustering.

Heavy particles in incompressible flows: The large Stokes number asymptotics

The dynamics of very heavy particles suspended in incompressible flows is studied in the asymptotics in which their response time is much larger than any characteristic time of fluid motion. In this limit of very large Stokes numbers, particles behave as if suspended in a δ -correlated-in-time Gaussian flow. At those spatial scales where the fluid velocity field is smooth, following Piterbarg [L.I. Piterbarg, The top Lyapunov exponent for stochastic flow modeling the upper ocean turbulence, SIAM J. Appl. Math. 62 (2002) 777] and Mehlig et al. [B. Mehlig, M. Wilkinson, K. Duncan, T. Weber, M. Ljunggren, Aggregation of inertial particles in random flows, Phys. Rev. E 72 (2005) 051104], the two-particle dynamics is reduced to a nonlinear system of three stochastic differential equations with additive noise. This model is used to single out the mechanisms leading to the preferential concentration of particles. Scaling arguments are used to predict the large Stokes number behavior of the distribution of the stretching rate and of the probability distribution function of the longitudinal velocity difference between two particles. As for the fractal character of the particle distribution, strong numerical evidence is obtained in favor of saturation of the correlation dimension to the space dimension at large Stokes numbers. Numerical results at finite Stokes number values reveal that this model catches some important qualitative features of particle clustering observed in more realistic flows.

Acceleration statistics of heavy particles in turbulence

We present the results of direct numerical simulations of heavy particle transport in homogeneous, isotropic, fully developed turbulence, up to resolution decrease with St. Two concurrent mechanisms lead to the above results: preferential concentration of particles, very effective at small St, and filtering induced by the particle response time, that takes over at larger St.

Characterization of near-wall accumulation regions for inertial particles in turbulent boundary layers

In this paper, we examine particle distribution in the wall region of turbulent boundary layers, considering specific flow conditions (Reτ=150) and spanning two orders of magnitude of particle inertial parameter—the particle timescale. First, we identify the flow timescales that govern particle distribution, examining the degree of particle preferential concentration and determining the optimum in connection with particle timescale. Second, we identify which of the flow variables may be used to control particle distribution. These are the streamwise and spanwise shear stress components at the wall, which correspond to the only nonvanishing elements of the fluctuating fluid velocity gradient tensor.

Preferential concentration of particles in homogeneous and isotropic turbulence

Non-homogeneous particle concentrations resulting from the carrier fluid turbulence occur frequently in nature as well as in many industrial processes. For this reason, it is important to fully understand the mechanisms that lead to this occurrence in order to use them advantageously. Many experiments and numerical simulations have been conducted to explore this phenomenon, known as preferential concentration. Maxey (1987), Squires and Eaton (1991), and Fessler et al. (1994) have shown that particles subjected to specific turbulent conditions tend to concentrate non-uniformly into areas of low vorticity and high strain rate. The major parameter determining the degree of preferential concentration is the Stokes number, defined in Eq. (1.1).

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.

Preferential concentration of particles in isotropic turbulence: a comparison of the Lagrangian and the equilibrium Eulerian approaches

In this brief note, we present a study of the preferential concentration of particles in isotropic turbulence using the fast Eulerian method [Int. J. Multiph. Flow 27 (2001) 1199]. The advantage of the fast Eulerian method is that it obviates the need to solve additional governing equations for the particulate phase. For small particle response times, Ferry and Balachandar [Int. J. Multiph. Flow 27 (2001) 1199] show that a unique equilibrium Eulerian particle velocity field, v( x, t), independent of initial conditions can be obtained. The resultant expansion in τ p is an explicit function of the fluid velocity field, u( x, t), and its spatial and temporal derivatives. In the current work, a truncated expansion of the particle velocity field, accurate to O( τ p), is used to calculate statistics of particle dispersion and preferential accumulation in isotropic turbulence. These statistics are compared with those from the Lagrangian evolution of particles. There is good agreement for small τ p, where the theory is best applicable. Preferential concentration properties of dense particles as well as bubbles are studied. It is demonstrated that instantaneous velocities of exact Lagrangian particles agree well with those evaluated by interpolating the Eulerian particle velocity field to the particle positions. In addition, particles evolved using the Eulerian velocity field exhibit similar long-time spatial distribution as the exact particles, indicating that there is no accumulation of errors in time. Specifically, the concentration of dense particles in high strain-rate regions and of bubbles in high vorticity regions is accurately captured by the Eulerian method.

Preferential concentration of particles in a fully developed turbulent square duct flow

The preferential concentration of dense particles in a downward, fully developed turbulent square duct flow at Re τ =360, based on mean friction velocity and duct width, is studied using large eddy simulations. Due to the low volume fractions involved (maximum volume fraction <10 −5), one-way coupled simulations are performed, i.e., two-way coupling and particle–particle collisions are not considered. The continuous and the dispersed phases are treated using Eulerian and Lagrangian approaches, respectively. A finite volume based second-order accurate fractional step scheme is used to integrate the unsteady, three-dimensional Navier–Stokes equations. The subgrid stresses are modeled with a dynamic subgrid kinetic energy model, as reported previously. The particle equation of motion includes drag, lift and gravity forces and is integrated using the fourth-order accurate Runge–Kutta method. Four cross-sectional locations representative of the mean secondary flow patterns and six particle response times were chosen to study the effect of location and particle inertia on preferential concentration. To demonstrate preferential concentration, variation of vorticity magnitude, swirling strength, maximum compressional strain-rate, and ∇ u : ∇ u , and their probability distribution functions (PDF) conditioned on particle presence, with particle response time is presented. Since the square duct cross-section is inhomogeneous, we also study variation in preferential concentration with cross-sectional location. Particles are seen to accumulate in regions of high ∇ u : ∇ u and strain-rate and in regions of low swirling strength. In general, particles accumulate in regions of low vorticity magnitude. However, near the wall, the tendency of particles to accumulate in regions of high vorticity increases with response time.

Numerical simulation of gas-particle flow in a single-side backward-facing step flow

Particle-laden turbulent flow over a backward-facing step has been investigated by using large eddy simulation for the fluid phase while particle motion is traced by particle track model. Effects of both drag and gravitational forces on particle motion are considered. The simulation is carried out with the flow parameters and geometry of the test section is same as those in the experiment carried out by Fessler and Eaton (J. Fluid Mech. 314 (1999) 97), who measured the two-dimensional flow fields of both phases. Predicted statistical mean properties of the fluid phase with Reynolds number of 18,400 and particle phase with 70 μm copper spheres and 150 μm glass spheres respectively are in good agreement with the experimental results. Simulation also predicts detailed flow fields of both phases and their evolution. Further investigation has been carried out on the dispersion of particles with different Stokes numbers in the turbulent structure of the fluid field. Motion of glass spheres with diameters 2, 20, 50, 100 and 200 μm , respectively, introduced in the fluid field is simulated. The predicted patterns of instantaneous dispersion of particles reveal that the phenomenon of preferential concentration of particles occurs at a certain range of Stokes number. The effects of initial velocity slip between the two phases and the action of gravity on particle dispersion are also investigated.

Evaluation of the equilibrium Eulerian approach for the evolution of particle concentration in isotropic turbulence

In the current work, the accuracy of the equilibrium Eulerian approach in evolving the particulate concentration field is evaluated by comparing it against the Lagrangian approach, for varying particle response time and terminal velocity. In particular, we compare the statistics of preferential accumulation and gravitational settling of particles in a cubic box of isotropic turbulence. Twelve simulations corresponding to four values of nondimensional particle response time, τ p=0.05, 0.1, 0.2, 0.4, and three values of nondimensional terminal velocity, | V s |=0.5,2,4 are considered. The equilibrium Eulerian approach obviates the need to solve additional governing equations for the particle velocity field. It, however, involves evolution of the particle concentration field using the equilibrium Eulerian velocity field. A spectral diffusion term is included in the particle concentration equation to provide an essentially non-oscillatory behavior to the solution. There is good agreement between the equilibrium Eulerian and Lagrangian statistics for small particles. With increasing particle size, the equilibrium Eulerian approach tends to somewhat overestimate particle preferential concentration in regions of excess strain-rate over rotation-rate compared to the Lagrangian approach. Over the entire range of parameters considered, the equilibrium approach provides a good approximation to the actual mean and rms fluctuating settling velocities of the particle.

Pair dispersion and preferential concentration of particles in isotropic turbulence

The objective of the paper is to present a statistical model for predicting pair dispersion and preferential concentration of particles suspended in an isotropic homogeneous turbulent flow field. This model is based on a kinetic equation for the probability density function of the relative velocities of two particles. The model developed is applied to predict the pair relative velocity statistics and the accumulation effect of heavy particles in a steady-state suspension. The effect of particle inertia on the predicted Eulerian two-point particle velocity correlations is demonstrated and compared with known results of numerical simulation.

Transient airflow structures and particle transport in a sequentially branching lung airway model

Considering oscillatory laminar incompressible three-dimensional flow in triple planar and nonplanar bifurcations representing generations three to six of the human respiratory system, air flow fields and micron-particle transport have been simulated under normal breathing and high-frequency ventilation (HFV) conditions. A finite-volume code (CFX4.3 from AEA Technology, Pittsburgh, PA) and its user-enhanced FORTRAN programs were validated with experimental velocity data points for a single bifurcation. The airflow structures and micron-particle motion in the triple bifurcations were analyzed for a representative normal breathing cycle as well as HFV condition. While both the peak inspiratory and expiratory velocity profiles for the low Womersley case (α=0.93) agree well with those of instantaneously equivalent steady-state cases, some differences can be observed between flow acceleration and deceleration at off-peak periods or near flow reversal, especially during inspiratory flow. Similarly, the basic features of instantaneous particle motion closely resemble the steady-state case at equivalent inlet Reynolds numbers. The preferential concentration of particles caused by the coherent vortical structures was found in both inhalation and exhalation; however, it is more complicated during expiration. The effects of Womersley number and non-planar geometries as well as the variations in secondary flow intensity plus pressure drops across various bifurcations under normal breathing and HFV conditions were analyzed as well. This work may elucidate basic physical insight of aerosol transport relevant in dosimetry-and-health-effect studies as well as for drug aerosol delivery analyses.

Stokes and Reynolds number dependence of preferential particle concentration in simulated three-dimensional turbulence

An analysis of particle concentrations formed in direct numerical simulations of forced three-dimensional (3-D) turbulence is described. Up to 48 million particles responding passively to the flow with response times ranging from 0.2 to 6 times the dissipation time of the fluid were evolved together until the concentration field reached a statistical stationary state. The Stokes number (St), defined at the dissipation time scale, was the sole parameter used to characterize the particle–fluid coupling in the regime where particles preferentially concentrate. Concentrations resulting from three simulations equilibrating at the Taylor microscale Reynolds numbers (Reλ) 40, 80, and 140 were studied. We present several new results for concentration measures utilized in previous studies as well as measures introduced in this paper. The measures are compared and contrasted on a finer St grid than presented in previous work and are analyzed as functions of Reλ and spatial binning scale. The measures are based on (a) deviations of the concentration PDF (probability density function) from the PDF of a uniform particle field, (b) the correlation dimension (D2) for both 3-D and two-dimensional concentrations, and (c) the relative St-dependent concentrations contained in a localized region of space. Measure (c) is motivated by the observation that the total and St-dependent concentrations are linearly correlated. The concentration measures reveal St dependencies that are insensitive to the Reynolds number of the flow with each measure having its own characteristic shape. The widths and maxima of St functions for measures explicitly constructed on a single spatial binning scale showed a very weak dependence on bin sizes ranging from 2 to 6 times the Kolmogorov length scale. We conclude that the measures studied in this paper reveal a universality that may persist to much higher Reynolds numbers.

On the preferential concentration of solid particles in turbulent channel flow

We present results from a direct numerical simulation of the passive transport of solid particles by a fully developed turbulent channel flow with a Reynolds number of 180 based on the friction velocity and the channel half-width. Three particle sets are studied, ranging in diameter from 0.5 to 1.4 viscous wall units and in aerodynamic time constant from 0.6 to 56 centreline Kolmogorov time scales. We use particle number density histograms and fractal dimensions to show that the level of order in the particle spatial distribution peaks near a Stokes number of unity based on the Kolmogorov time scale. We then quantify the relationship between this spatial distribution and the instantaneous flow topology. The results indicate that the previously reported preferential concentration of particles in low-speed streaks leads to a suppression of particle velocities in the viscous sublayer and buffer region even in the presence of streamwise gravitational acceleration. In other regions of the flow, the particles' non-random spatial distribution is shown to be uncorrelated with the local flow topology. We compare our results with the experimental data of Kulick et al. (1994) and Fessler et al. (1994) and confirm that the latter authors' results were not influenced by turbulence modification.

Flow Structure and Particle Transport in a Triple Bifurcation Airway Model1

Considering steady laminar incompressible flow in a triple bifurcation, which represents generations three to six of the human respiratory system, air flow fields and micron-particle transport have been simulated for several combinations of relatively high and low inlet Reynolds and Stokes numbers. While the upstream bifurcations are hardly affected by the third bifurcation, complex air and particle flow fields occur in the daughter tubes leading to the third dividers. Variations in Reynolds number, 500⩽Re⩽2000, and Stokes number, 0.04⩽St⩽0.12, cause locally changing vortical air flows as well as irregular particle motions. Preferential concentration of particles can be induced by the secondary vortical flow in the tubes when the inlet Reynolds number is high enough. The air and particle velocity profiles in the third daughter tubes are still quite different from those in the upstream tubes, which indicates that additional downstream effects are possible. This work may contribute to respiratory dose estimation in health risk assessment studies, as well as the analyses of drug aerosol delivery.

Comparison of two-way coupling models for confined turbulent gas–particle jets in flash smelting

Flow predictions of confined particle-laden gas jets based on three different two-way coupling models of gas–particle turbulent interaction are compared for 50 and 200 μm particles at inlet particle/gas mass fractions from about 0.3–3.0. Attention is focused on the application to fluid dynamic models of flash smelting. Two confined jet experiments and a flash furnace double-entry jet are simulated. Three types of inlet flow are represented: (1) dominant primary (central) velocity; (2) primary and secondary velocities of similar strength; and (3) dominant secondary stream. Flow type 1 is conceptually similar to flow in a single entry flash furnace shaft, and type 3 is typical of a double-entry flash furnace shaft. All two-way coupling models were acceptable to a varying extent when compared with experimental data at low particle concentration for the dominant primary jet. However, differences increased with increasing particle loading, but were very much smaller for 200 μm particles than for 50 μm particles. Significantly, very large differences between the predictions were obtained for the flash furnace jet with the dominant secondary flow. The results highlight the need for more experimental velocity data at an elevated mass fraction and for type 3 flows. It is suggested that preferential concentration of particles will occur when the secondary inlet stream dominates and will consequently limit the validity of conventional two-way coupling models in double-entry flash furnace models.

Large eddy simulation of particle-laden turbulent channel flow

Particle transport in fully-developed turbulent channel flow has been investigated using large eddy simulation (LES) of the incompressible Navier–Stokes equations. Calculations were performed at channel flow Reynolds numbers, Reτ, of 180 and 644 (based on friction velocity and channel half width); subgrid-scale stresses were parametrized using the Lagrangian dynamic eddy viscosity model. Particle motion was governed by both drag and gravitational forces and the volume fraction of the dispersed phase was small enough such that particle collisions were negligible and properties of the carrier flow were not modified. Material properties of the particles used in the simulations were identical to those in the DNS calculations of Rouson and Eaton [Proceedings of the 7th Workshop on Two-Phase Flow Predictions (1994)] and experimental measurements of Kulick et al. [J. Fluid Mech. 277, 109 (1994)]. Statistical properties of the dispersed phase in the channel flow at Reτ=180 are in good agreement with the DNS; reasonable agreement is obtained between the LES at Reτ=644 and experimental measurements. It is shown that the LES correctly predicts the greater streamwise particle fluctuation level relative to the fluid and increasing anisotropy of velocity fluctuations in the dispersed phase with increasing values of the particle time constant. Analysis of particle fluctuation levels demonstrates the importance of production by mean gradients in the particle velocity as well as the fluid-particle velocity correlation. Preferential concentration of particles by turbulence is also investigated. Visualizations of the particle number density field near the wall and along the channel centerline are similar to those observed in DNS and the experiments of Fessler et al. [Phys. Fluids 6, 3742 (1994)]. Quantitative measures of preferential concentration are also in good agreement with Fessler et al. [Phys. Fluids 6, 3742 (1994)].