Particle Velocity Fluctuations Research Articles

Transport property measurements in sheared granular flows

Experiments were performed in a shear cell device under four different solid fractions. The glass spheres with a mean diameter of 3 mm were used as granular materials. The motions of the granular materials were recorded by a high-speed camera. By using image processing technology and a particle tracking method, the average and fluctuation velocities in the streamwise and the transverse directions could be successfully measured and analyzed. Three bi-directional stress gages were used to measure the normal and shear stresses along the upper boundary. The effective viscosity of the granular material flow can be calculated. By tracking the movements of particles continually, the curves of the mean-square diffusive displacements versus time were plotted and were used to determine the self-diffusion coefficients from the slopes of the curves. The fluctuations and the self-diffusion coefficients in the streamwise direction were much higher than those in the transverse direction. The fluctuations were found to increase with the solid fraction, but the diffusion coefficients were greater in a more dilute flow system.

Mechanisms of particle vertical diffusion in sediment-laden flows

Diffusion coefficient of natural sediments and effects of lift force and gradient in particle velocity fluctuations were investigated through using a closed kinetic model. Comparison against experimental data of Einstein & Chien (1955) validated the model. The diffusion coefficient eyy of medium and large sediments distinctly exceeds fluid eddy viscosityv f t , while eyy of fine sediments approximately equalsv f t . In the measured region of0.03<y/H<0.4, e yy/v f t increases with the distance from the wall decreasing. Combined effects of lift force and gradient in particle velocity fluctuations change sediment gravitational settling remarkably belowy/H=0.2, and need to be accounted for describing sediment diffusion in this region.

A numerical study of fluidization behavior of Geldart A particles using a discrete particle model

This paper reports on a numerical study of fluidization behavior of Geldart A particles by use of a 2D soft-sphere discrete particle model (DPM). Some typical features, including the homogeneous expansion, gross particle circulation in the absence of bubbles, and fast bubbles, can be clearly displayed if the interparticle van der Waals forces are relatively weak. An anisotropy of the velocity fluctuation of particles is found in both the homogeneous fluidization regime and the bubbling regime. The homogeneous fluidization is shown to represent a transition phase resulting from the competition of three kinds of basic interactions: the fluid–particle interaction, the particle–particle collisions (and particle–wall collisions) and the interparticle van der Waals forces. In the bubbling regime, however, the effect of the interparticle van der Waals forces vanishes and the fluid–particle interaction becomes the dominant factor determining the fluidization behavior of Geldart A particles. This is also evidenced by the comparisons of the particulate pressure with other theoretical and experimental results.

Stability of uniform fluidization revisited

The marginal stability of uniform gas-fluidized beds is analyzed making use of ‘macroscopic’ conservation equations based on a recent version of the theory of random particulate motion in dense, collisional suspensions. This version of the theory, developed by Buyevich and Kapbasov, combines the standard correlation theory of stationary random processes, applied to stochastic equations for fluctuations of the flow properties, and the generalization, to dense suspensions, of the classical Smoluchowski's theory of fluctuations of the particle concentration. It is shown that, within the framework of the adopted approach, the stability of uniform fluidization can be explained without reference to the hypothetical solid-like state of the particulate phase. The criterion of stability is derived in the form of the critical particle volume fraction as a function of the non-dimensional parameter controlling the dissipation, on interparticle collisions, of the kinetic energy of particle velocity fluctuations. The wavenumbers of ‘macroscopic’ perturbations with the maximum growth rate in the unstable fluidized bed are analyzed. Such perturbations are usually associated with the initial sizes of emerging bubbles; these sizes are obtained as functions of the particle concentration and the above mentioned parameter of inelasticity of interparticle collisions. Recent theoretical studies led to the conclusion that the apparent stability of uniform fluidization cannot be explained without taking into account yield stress caused by direct interparticle contacts. The approach of this paper provides an explanation of the stability without invoking non-hydrodynamic phenomena (except for interparticle collisions).

The role of the space charge density in particulate processes in the example of the electrostatic precipitator

Numerical calculations and experimental investigations of gas-particle flows involving an electrical field, as they are found in the electrostatic precipitation process, are presented. A test facility was set up, which allows observation and optical measurement in the precipitation gap under realistic conditions as far as possible. The numerical part is based on the Euler–Lagrange approach. The gas flow is calculated by solving the Reynolds-averaged Navier–Stokes equations including the k– ε turbulence model. In order to solve the coupled equations for the electrostatic field, a finite-volume approach is applied. The particle phase is simulated by using a Lagrangian treatment where a large number of particles are tracked through the flow and the electrostatic field. In addition to the drag and gravity, the electric field force is considered in the equation of motion. Average properties of the particle phase are obtained by ensemble averaging. The experimental investigations were performed with a Laser Doppler Anemometer (LDA), in contrast to the majority of publications, where concentration profiles are detected, and used to validate the numerical results, which showed reasonable good agreement between calculations and measurements; however, this holds not for the particle's velocity fluctuations. It is a well-known fact that velocity fluctuations are strongly modified by electrostatic fields and often reported as part of the “ionic wind” phenomenon. Nevertheless, the increase of turbulent energy is not fully explained by that. A discussion of the probable origin of the turbulence modification are given, as well as some impulsive remarks on possible ways to proceed.

Fluctuations of particle concentration in a turbulent two-phase shear layer

Measurements and calculations of mean and rms of fluctuations of particle velocities and concentration and cross-correlation coefficients of two particle velocity components and concentration fluctuations in a horizontal plane shear layer laden with glass beads with mean diameters 55 and 90 μm are presented. The particles were injected at the low speed side of the flow, which is different from previous studies, and enhances the influence of gravity on particle dispersion. The ranges of Stokes numbers, based on the time scale of the large eddies, were 0.2–0.6 and 0.6–1.4 for 55 and 90 μm respectively. The particle gravitational settling parameter, due to gravity acting normal to the main flow direction at the low speed side of the shear layer, was for the mean flow 0.2 and 0.5 and for the turbulent flow 0.5 and 1 for 55 and 90 μm respectively. Velocity measurements were obtained by particle image velocimetry (PIV) and instantaneous particle concentration by counting the number of particles in each interrogation cell of the PIV images. The effect of interrogation cell size on instantaneous particle concentration was assessed and an appropriate interrogation cell size was chosen to quantify the non-random contribution of particle concentration fluctuations. The intensity of spatially-resolved non-random concentration fluctuations varied between 0.6 and 0.9 of the local mean concentration at the edge of the shear layer, where particles dispersed only due to centrifuging by fluid flow large scale structures and between 0.15 and 0.35 in the central region of the shear layer, where particles are convected by the flow or arrive due to centrifuging from the fluid eddies and gravitational effects and, as a consequence, random contributions on particle concentration become more important. The contribution of various fluid flow structures and gravity on concentration fluctuations was quantified and explained by quadrant analysis of the cross-correlation between measured particle streamwise velocity and concentration. The calculations of the fluid flow in the shear layer were based on the discrete vortex method and the discrete phase motion was calculated by Lagrangian particle tracking. The calculations showed fluid velocity fluctuations frequency spectra with −5/3 decay, as measured in the experiments, and the simulated particle mean and rms velocities and cross-correlation coefficients of particle concentration and velocity fluctuations agreed qualitatively with the measurements. Remaining discrepancies in the absolute values were due to the omission of gravity in the calculations and the resulting narrower range of fluid flow eddy sizes predicted by the calculations relative to experiments. The consequences of current findings on the operation of light detection and ranging (LIDAR) systems for measurements of atmospheric turbulence due to vortices of the wake of airplanes are discussed and improvements in the data processing are suggested.

Particle density stratification in transient sedimentation.

Theoretical predictions for the scaling of particle velocity fluctuations with container size in homogeneous Stokes suspensions are not consistent with experimental observations. Several explanations have been advanced, including the formation of stratification in bounded systems, such as those used in experiments. Numerical simulations of transient Stokes sedimentation in bounded cells are presented here for several cell sizes. The simulated cells have top and bottom wall boundaries and periodic boundaries in the horizontal. Throughout the course of the simulations the number and distribution of particles in the cell evolve, with impacts on the bulk mean particle velocity, velocity fluctuations, and particle density gradient. Initially the sedimentation follows the classical description, with a sharp front and uniform particle concentration below, but this is not sustained. A layer of higher particle concentration develops below the front. This is unstable and there is a large-scale overturning of the fluid. As a consequence, there is a redistribution of the particles, leaving behind a mass loading of the particles, which is stably stratified (subject to small density fluctuations between horizontal levels). The mean velocity and fluctuations of the particles initially grow and then decay once stable stratification has developed.

Novel multifunctional optical‐fiber probe: II. High‐density CFB measurements

AbstractThe novel parallel three‐fiber optical probe described in Part I of this article is applied to determine simultaneously local instantaneous solids volume concentration, velocity, and flux in multiphase suspensions. Radial distributions of local particle concentration, velocity, and flux and their fluctuations in a high‐density circulating fluidized bed (HDCFB) are presented. A strong correlation exists between fluctuations of local particle velocity and particle concentration. The optical probe is shown to provide a means of evaluating alternative measurement techniques that have commonly been employed in earlier studies.

Rheology of suspensions with high particle inertia and moderate fluid inertia

We consider the averaged flow properties of a suspension in which the Reynolds number based on the particle diameter is finite so that the inertia of the fluid phase is important. When the inertia of the particles is sufficiently large, their trajectories, between successive particle collisions, are only weakly affected by the interstitial fluid. If the particle collisions are nearly elastic the particle velocity distribution is close to an isotropic Maxwellian. The rheological properties of the suspension can then be determined using kinetic theory, provided that one knows the granular temperature (energy contained in the particle velocity fluctuations). This energy results from a balance of the shear work with the loss due to the viscous dissipation in the interstitial fluid and the dissipation due to inelastic collisions. We use lattice-Boltzmann simulations to calculate the viscous dissipation as a function of particle volume fraction and Reynolds number (based on the particle diameter and granular temperature). The Reynolds stress induced in the interstitial fluid by the random motion of the particles is also determined. We also consider the case where the interstitial fluid is moving relative to the particles, as would occur if the particles experienced an external body force. Owing to the nonlinearity of the equations of motion for the interstitial fluid, there is a coupling between the viscous dissipation caused by the fluctuating motion of the particles and the drag associated with a mean relative motion of the two phases, and this coupling is explored by computing the dissipation and mean drag for a range of values of the Reynolds numbers based on the mean relative velocity and the granular temperature.

Diffusivities and front propagation in sedimentation

Continuum models for particles sedimenting in a fluid often assume that the diffusivity is a local function of the particulate volume fraction. Since the hydrodynamically induced diffusivity is a result of the velocity fluctuations of particles, the recent identification [e.g., Tee et al., Phys. Rev. Lett. 89, 054501 (2002)] of particle density stratification as a controlling parameter for the velocity fluctuations also extends to the diffusivities. In particular, the stratification control strongly affects the diffusivity in the vicinity of the falling sediment front between particle-laden fluid below and clarified fluid above. The resulting scaling for stratification-controlled diffusivities in creeping flow sedimentation is presented and compares favorably with measurements from dilute-limit particle simulations. Steadily falling concentration profiles for dilute sedimentation with these diffusivities are then presented, and an extension of the model to higher volume fractions is discussed.

Velocity fluctuations in electrostatically driven granular media.

We study experimentally the particle velocity fluctuations in an electrostatically driven dilute granular gas. The velocity distributions have strong deviations from a Maxwellian form over a wide range of parameters. We have found that the tails of the distribution functions are consistent with a stretched exponential law with typical exponents of the order 3/2. Molecular dynamic simulations shows qualitative agreement with experimental data. Our results suggest that this non-Gaussian behavior is typical of most inelastic gases with both short- and long-range interactions.

Turbulentlike fluctuations in quasistatic flow of granular media.

We analyze particle velocity fluctuations in a simulated granular system subjected to homogeneous quasistatic shearing. We show that these fluctuations share the following scaling characteristics of fluid turbulence in spite of their different physical origins: (i) scale-dependent probability distribution with non-Gaussian broadening at small time scales; (ii) spatial power spectrum of the velocity field showing a power-law decay, reflecting long-range correlations and the self-affine nature of the fluctuations; and (iii) superdiffusion of particles with respect to the mean background flow.

Experimental studies on particle behaviour and turbulence modification in horizontal channel flow with different wall roughness

Detailed measurements in a developed particle-laden horizontal channel flow (length 6 m, height 35 mm, the length is about 170 channel heights) are presented using phase-Doppler anemometry for simultaneous determination of air and particle velocity. The particles were spherical glass beads with mean diameters in the range of 60 µm–1 mm. The conveying velocity could be varied between about 10 m/s and 25 m/s, and the particle mass loading could reach values of about 2 (the mass loading is defined as the ratio of particle to gas phase mass flow rates), depending on particle size. For the first time, the degree of wall roughness could be modified by exchanging the wall plates. The influence of these parameters and the effect of inter-particle collisions on the profiles of particle mean and fluctuating velocities and the normalised concentration in the developed flow were examined. It was shown that wall roughness decreases the particle mean velocity and enhances fluctuating velocities due to irregular wall bouncing and an increase in wall collision frequency, i.e. reduction in mean free path. Thereby, the larger particles are mainly more uniformly distributed across the channel, and gravitational settling is reduced. Both components of the particle velocity fluctuation were reduced with increasing mass loading due to inter-particle collisions and the momentum loss involved. Moreover, the effect of the particles on the air flow and the turbulent fluctuations was studied on the basis of profiles in the developed flow and turbulence spectra determined for the streamwise velocity component. In addition to the effect of particle size and mass loading on turbulence modulation, the influence of wall roughness was analysed. It was clearly shown that increasing wall roughness also results in a stronger turbulence dissipation due to two-way coupling.

In-Situ Measurement of Local Particle Flux Densities in a Complex Two-Phase Flow

An optical measuring technique is presented allowing the exact in-situ measurement of local particle flux densities in a confined channel flow by counting single particles penetrating an optically well defined measuring volume. This enables a precise flux determination up to the direct vicinity of planar walls. The measurement set-up and its calibration as well as the whole test facility are described in detail. This measurement technique is used to study the particle transport in electrostatic precipitators. Exemplarily, results of particle flux profiles as well as precipitation, as gained from balances of parts of the precipitator channel, are presented. Furthermore, the possibility to determine particle velocity fluctuations is demonstrated.

Particle velocity fluctuations and correlation lengths in dilute sedimenting suspensions

We measure the instantaneous velocity of particles sedimenting in a three-dimensional container at low particulate Reynolds numbers. We aim at characterizing the main specificities of the particle velocity fluctuations. We obtain the local and instantaneous Eulerian velocity field from particle image velocimetry: a thin Yag laser light sheet (about two diameters thick) illuminates the particles from one side of the cell to the other. Our measurements are therefore spatially localized and, together with the squared cross sections of the cells, these are the two main originalities of our instrumentation. Four different cells and three different particle sizes give access to aspect ratios (cell width W over particle radius a) ranging from about 50 up to 800. We confirm the existence of eddy-like structures for the velocity fluctuations. The structure size is found to be almost independent of the volume fraction Φ for 6.25×10−4&amp;lt;Φ&amp;lt;5×10−2 for a fixed aspect ratio W/a, in seeming contradiction with the results of Segrè et al. [Phys. Rev. Lett. 79, 2574 (1997)]. The velocity fluctuations’ profiles are close to parabolic for the smallest aspect ratios but display a plateau value in the central part of the cell for higher aspect ratios. The unexpected result of our experiments is the large distance of influence of the boundaries: in fact, the plateau values are observed to saturate for aspect ratios larger than a few hundreds for Φ=1×10−2, for example. Moreover, the saturated plateau values scale as φ0.45±0.05, in contrast with the φ1/3 scaling observed in most previous works.

Kinetics of growth process controlled by convective fluctuations.

A model of the spherical (compact) growth process controlled by a fluctuating local convective velocity field of the fluid particles is introduced. It is assumed that the particle velocity fluctuations are purely noisy, Gaussian, of zero mean, and of various correlations: Dirac delta, exponential, and algebraic (power law). It is shown that for a large class of the velocity fluctuations, the long-time asymptotics of the growth kinetics is universal (i.e., it does not depend on the details of the statistics of fluctuations) and displays the power-law time dependence with the classical exponent 1/2 resembling the diffusion limited growth. For very slow decay of algebraic correlations of fluctuations asymptotically like t(-gamma), gamma in (0,1]), kinetics is anomalous and depends strongly on the exponent gamma. For the averaged radius of the crystal <R(t)> approximately t(1-gamma/2) for 0<gamma<1 or <R(t)> approximately (t ln t)1/2 for gamma=1.

Laser Doppler velocimetry measurements of particle velocity fluctuations in a concentrated suspension

Recent statistical constitutive models of suspensions of neutrally buoyant, noncolloidal, solid spheres in Newtonian fluids suggest that the particles migrate in response to gradients in “suspension temperature,” defined as the average kinetic energy contained in the particle velocity fluctuations. These models have not yet been compared systematically with experimental data. In addition the “temperature'’ models assume isotropic particle velocity fluctuations, since the suspension temperature is given as a scalar. However, highly anisotropic particle velocity fluctuations have been observed experimentally, which suggests that a suspension temperature tensor is more realistic. We use laser Doppler velocimetry to measure particle velocity fluctuations arising from interparticle collisions in a concentrated suspension under nearly homogeneous shear flow in a narrow-gap concentric cylinder Couette device. We compare the relative sizes of the fluctuating velocity components and determine the variation of each component with particle volume fraction and shear rate. The data indicate that the suspension temperature is anisotropic. The flow direction component is overwhelmingly the largest at every concentration and shear rate, followed in order of magnitude by the neutral-direction and velocity-gradient-direction components. Additionally, over the region of the flow accessible to measurement, each fluctuating velocity component demonstrates a distinct variation with shear rate and particle volume fraction. Finally, we explain the observed anisotropy and variation of the suspension temperature in terms of the dynamics of interparticle interactions.

6061-T6アルミニウム中を伝播する塑性衝撃波面の立ち上がり形状計測

The present paper reports observation of rising particle velocity profile of shock wave front in 6061-T6 aluminum. The elastic and plastic shock waves are generated in the present material by planer impact experiments using the single stage light gas gun that has 40mm muzzle diameter. The impact angle is also checked on using 4-pin-sensor system, and the fluctuation of particle velocity at the rear surface of target material is measured by the velocity interferometer system (VISAR). High-resolution measurements on the plastic shock wave front are carried out, and detailed experimental data that are needed for evaluating the estimating simulation of the shock wave profile are obtained.

Numerical study of the near-wall behaviour of particles in turbulent pipe flows

The near-wall behaviour of particles is important in terms of predicting both the particle-deposition and the near-wall particle-concentration. In this paper, we study the near-wall behaviour of elastic-bouncing small heavy spheric particles in fully developed turbulent pipe flows without gravity, using direct numerical simulations (DNS) with a one-way point-particle approach. The particle-concentration is assumed to be small enough such that the influence of the particles on the fluid and interparticle interactions can be neglected. The focus of the paper is on: (i) the understanding of the differences between elastic-bouncing and absorbing walls, and (ii) the evaluation of simple “local-equilibrium” models. Our results show that the near-wall behaviour of elastic-bouncing walls is very different from absorbing walls. The absence of a mean radial particle-velocity leads to a much higher particle-concentration near the wall than in the case of absorbing walls. This can be explained by the absence of a “mean drag force”: the “turbophoretic effect”, due to the gradient in the particle-velocity fluctuation in the radial direction, is balanced only by the “drift-velocity”, due to a gradient in the particle-concentration. Our results indicate that, from a pragmatic perspective, simple “local-equilibrium” models for the “turbophoretic effect”, assuming a proportionality between the particle and fluid “Reynolds-stresses”, are adequate, except very close to the wall, where the reduction in the radial fluid-velocity fluctuation is not accompanied by an equivalent reduction in the radial particle-velocity fluctuation.

A second-order-moment–Monte-Carlo model for simulating swirling gas–particle flows

A second-order moment (SOM) gas-phase turbulence model, combined with a Monte-Carlo (MC) simulation of stochastic particle motion using Langevin equation to simulate the gas velocity seen by particles, is called an SOM–MC two-phase turbulence model. The SOM–MC model was applied to simulate swirling gas–particle flows with a swirl number of 0.47. The prediction results are compared with the PDPA measurement data and those predicted using the Langevin-closed unified second-order moment (LUSM) model. The comparison shows that both models give the predicted time-averaged flow field of particle phase in general agreement with those measured, and there is only slight difference between the prediction results using these two models. In the near-inlet region, the SOM-MC model gives a more reasonable distribution of particle axial velocity with reverse flows due to free of particle numerical diffusion, but it needs much longer computation time. Both models underpredict the gas and particle fluctuation velocities, compared with those measured. This is possibly caused by the particle–wall and particle–particle interaction in the near-wall region, and the effect of particles on dissipation of gas turbulence, which is not taken into account in both models.