Particle Velocity Fluctuations Research Articles

Multi-scale analysis on particle fluctuation velocity near the minimum pressure drop in a horizontal pneumatic conveying

Multi-scale characteristics of particle fluctuation velocity at the MPD (minimum pressure drop) air velocity in the acceleration and fully-developed regimes are experimentally investigated. The high-speed particle image velocimetry (PIV) is first used to measure the fluctuating particle velocities at the MPD air velocity in a horizontal pneumatic conveying. Then the fluctuating particle velocities in the acceleration and fully-developed regimes are analyzed by the continuous wavelet transform and orthogonal wavelet multi-resolution technique. It is found that the wavelet components of low frequency dominate the fluctuating energy of axial particle velocity in the bottom part of the pipe, and contribute about 70% and 84% to the acceleration and fully-developed regimes, respectively. The more contribution to the fluctuating energy of vertical particle velocity, however, comes from the wavelet components of high frequency, accounting for about 82%. The low frequency component of auto-correlation suggests a large-scale particle flow in both acceleration regime and fully-developed regime. The low frequency wavelet component also makes a large contribution to spatial correlation of axial particle velocity, which increases from the acceleration regime to fully-developed regime. The PDF of low frequency components are asymmetrical near the bottom of the pipe, but the PDF of the relatively high frequency exhibits symmetry and the spread of the PDF evidently shrinks for increasing frequencies, implying a reducing fluctuation of high frequency component.

Experimental study on particle fluctuation velocity of a horizontal pneumatic conveying near the minimum conveying velocity

The high-speed particle image velocimetry (PIV) is employed to measure the distribution of particle fluctuation velocity near the minimum conveying velocity in the acceleration and fully developed regimes in a horizontal pneumatic conveying. The fluctuation characteristics of particle velocity are examined in terms of time-averaged particle velocity and concentration, power spectrum, auto-correlation coefficients, two-point correlation coefficients, intensity of particle fluctuation velocity, skewness factor and probability density function. It is revealed that the profile of the time-averaged particle velocity depends on the conveying velocity and solids loading ratio in the bottom part of the pipe in the fully developed regime. A quasi-periodical particle flow pattern with the lower frequency appears in this region and dominates the pressure drop of the pneumatic conveying. The intensities of particle fluctuation velocity of the sliding strand flows in the bottom part of pipe are smaller that of the suspension flows in the top part of pipe, revealing that the low intensity of particle fluctuation velocity can result in the low conveying pressure drop. The particle fluctuation velocity of the low or minimum conveying velocity follows the Gaussian probability distribution in the fully developed regime.

Wavelet analysis on particle dynamics in a horizontal air–solid two-phase pipe flow at low air velocity

High-speed particle image velocimetry (PIV) is first used to measure two components of the fluctuating particle velocities for different particle sizes and solid mass flow rates at low air velocity in a horizontal pipe. Then, the continuous wavelet transform and orthogonal wavelet multi-resolution techniques are employed to analyze and decompose the fluctuating particle velocities to provide both quantitative and qualitative information on the particle fluctuation velocity of various frequencies. It is revealed that the fluctuating energy of axial particle velocity is mainly contributed from the wavelet components of low frequency, accounting for about 84%, near the bottom part of the pipe cross-section. However, the contribution to the fluctuating energy of vertical particle velocity accounts for about 82% from the wavelet components of high frequency. The auto-correlation analysis suggests a quasi-periodical large-scale axial particle fluctuating velocity. On the other hand, the spatial correlation analysis indicates that the low-frequency components of the axial particle velocity exhibit a large correlation near the bottom part of the pipe cross-section. From the probability density function (PDF) distribution, it is found that the low-frequency components of the axial particle velocity exhibit larger fluctuation, and this fluctuation reduces as the frequencies increase near the bottom part of the pipe cross-section. Near the top part of the pipe cross-section, however, a larger fluctuating axial particle velocity appears in the high-frequency range.

Particle dynamics in the channel flow of a turbulent particle–gas suspension at high Stokes number. Part 2. Comparison of fluctuating force simulations and experiments

AbstractThe particle and fluid velocity fluctuations in a turbulent gas–particle suspension are studied experimentally using two-dimensional particle image velocimetry with the objective of comparing the experiments with the predictions of fluctuating force simulations. Since the fluctuating force simulations employ force distributions which do not incorporate the modification of fluid turbulence due to the particles, it is of importance to quantify the turbulence modification in the experiments. For experiments carried out at a low volume fraction of $9. 15\ensuremath{\times} 1{0}^{\ensuremath{-} 5} $ (mass loading is 0.19), where the viscous relaxation time is small compared with the time between collisions, it is found that the gas-phase turbulence is not significantly modified by the presence of particles. Owing to this, quantitative agreement is obtained between the results of experiments and fluctuating force simulations for the mean velocity and the root mean square of the fluctuating velocity, provided that the polydispersity in the particle size is incorporated in the simulations. This is because the polydispersity results in a variation in the terminal velocity of the particles which could induce collisions and generate fluctuations; this mechanism is absent if all of the particles are of equal size. It is found that there is some variation in the particle mean velocity very close to the wall depending on the wall-collision model used in the simulations, and agreement with experiments is obtained only when the tangential wall–particle coefficient of restitution is 0.7. The mean particle velocity is in quantitative agreement for locations more than 10 wall units from the wall of the channel. However, there are systematic differences between the simulations and theory for the particle concentrations, possibly due to inadequate control over the particle feeding at the entrance. The particle velocity distributions are compared both at the centre of the channel and near the wall, and the shape of the distribution function near the wall obtained in experiments is accurately predicted by the simulations. At the centre, there is some discrepancy between simulations and experiment for the distribution of the fluctuating velocity in the flow direction, where the simulations predict a bi-modal distribution whereas only a single maximum is observed in the experiments, although both distributions are skewed towards negative fluctuating velocities. At a much higher particle mass loading of 1.7, where the time between collisions is smaller than the viscous relaxation time, there is a significant increase in the turbulent velocity fluctuations by ${\ensuremath{\sim} }1$–2 orders of magnitude. Therefore, it becomes necessary to incorporate the modified fluid-phase intensity in the fluctuating force simulation; with this modification, the mean and mean-square fluctuating velocities are within 20–30 % of the experimental values.

Particle dynamics in the channel flow of a turbulent particle–gas suspension at high Stokes number. Part 1. DNS and fluctuating force model

AbstractThe fluctuating force model is developed and applied to the turbulent flow of a gas–particle suspension in a channel in the limit of high Stokes number, where the particle relaxation time is large compared to the fluid correlation time, and low particle Reynolds number where the Stokes drag law can be used to describe the interaction between the particles and fluid. In contrast to the Couette flow, the fluid velocity variances in the different directions in the channel are highly non-homogeneous, and they exhibit significant variation across the channel. First, we analyse the fluctuating particle velocity and acceleration distributions at different locations across the channel. The distributions are found to be non-Gaussian near the centre of the channel, and they exhibit significant skewness and flatness. However, acceleration distributions are closer to Gaussian at locations away from the channel centre, especially in regions where the variances of the fluid velocity fluctuations are at a maximum. The time correlations for the fluid velocity fluctuations and particle acceleration fluctuations are evaluated, and it is found that the time correlation of the particle acceleration fluctuations is close to the time correlations of the fluid velocity in a ‘moving Eulerian’ reference, moving with the mean fluid velocity. The variances of the fluctuating force distributions in the Langevin simulations are determined from the time correlations of the fluid velocity fluctuations and the results are compared with direct numerical simulations. Quantitative agreement between the two simulations are obtained provided the particle viscous relaxation time is at least five times larger than the fluid integral time.

Spherical particle Brownian motion in viscous medium as non-Markovian random process

The Brownian motion of a spherical particle in an infinite medium is described by the conventional methods and integral transforms considering the entrainment of surrounding particles of the medium by the Brownian particle. It is demonstrated that fluctuations of the Brownian particle velocity represent a non-Markovian random process. The features of Brownian motion in short time intervals and in small displacements are considered.

Simulation of Granular Transport of Geldart Type-A, -B, and -D Particles through a 90° Elbow

The flow behavior of three different classes of granular materials - pulverized coal particles (type-A), glass beads (type-B), and polypropylene beads (type-D) - is numerically investigated based on computational fluid dynamics. Three elbow geometries - square and circular (R/D = 1.5 and 3.0) - are employed to investigate turbulent gas-particulate flow in dilute and dilute-to-dense phase modes of pneumatic conveying. The unsteady Eulerian-Discrete phase approach with renormalized group (RNG) k-ε model is adopted, with the effects of particulate phase velocity on the gas flow, turbulent dispersion, lift forces, and particle-wall collisions incorporated in the model. The phenomenon of particle roping is well captured by the computations. Significant phase separation and particle segregation are observed in the vicinity of the lower wall of the pipe. Different classes of particles exhibit very distinct flow dynamics in terms of particle roping, particle segregation, turbulent dispersion, and particle velocity fluctuations. Numerical predictions for pressure drop, particle, and gas velocity profiles are in satisfactory agreement with experimental data from the literature.

CFD simulation and experiments of dynamic parameters in gas–solid fluidized bed

Particle and bubble motion plays an important role in determining the hydrodynamic characteristics of a fluidized system. The dynamic parameters of a fluidized bed are reflection of the complex correlation between particle–particle and particle–bubble in a system. A two-dimensional Eulerian–Eulerian model integrating the kinetic theory of granular flow is used to simulate the bubble and linear low density polyethylene (LLDPE) particle dynamic behavior in a gas–solid fluidized bed. The simulated method is validated by pressure fluctuation experiment. The computed vertical turbulent energy spectrum of particles is applied to identify the particle motion intensity and the inhomogeneity of turbulent energy dissipation. The energy spectrum captures the Levy–Kolmogorov law in inertial range at high frequency. Furthermore, the flatness factors of wavelet decomposition coefficients of particle fluctuation velocity are for the first time introduced to analyze the intermittence caused by coherent structures in the flow field. The results show that the intermittence in dissipation range is much stronger than that in energy-containing and inertial range, and reinforces rapidly as the radial distance and the bed height increase. Moreover, the acoustic emission (AE) energy is found to be able to indicate the flow regimes. By combing granular temperature and AE energy, the relationship between the spatial distribution of granular temperature and the flow regimes is established. To get more detail of bubble motion behavior, the power spectrum of voidage fluctuation is analyzed. This work provides valuable insights into the dynamic characteristics and the flow field information of a gas–solid fluidized bed by CFD simulation.

Derivation and validation of a binary multi-fluid Eulerian model for fluidized beds

The paper presents a multi-fluid Eulerian model derived from binary kinetic theory of granular flows, free path theory and an empirical friction theory. The effects of the inter- and inner-particle collisions, particle translational motions and particle–particle friction are included. As the effects due to fluiddynamic particle velocity differences and particle–particle friction are considered, some unconventional terms are produced compared with the previous models. Model validation using the data from Mathiesen et al. (2000) shows that the coupling terms give a stronger and more realistic particle–particle coupling because the effects due to the fluiddynamic velocity differences are considered. The model gives reasonable predictions of the particle volume fraction, particle velocities and velocity fluctuations. The model analysis reveals that the basic particle velocity fluctuations constitute 2 terms: the velocity fluctuations of the discrete particles, and the velocity fluctuations of the continuous fluid flow. Furthermore, the simulation results show that the velocity fluctuations of the continuous fluid flow are dominant in a binary riser flow.

Prediction of turbulent gas‐solid flow in a duct with a 90° bend using an Eulerian‐Lagrangian approach

AbstractA dilute, particle‐laden turbulent flow in a square cross‐sectioned duct with a 90° bend is modeled using a three‐dimensional Eulerian‐Lagrangian approach. Predictions are based on a second‐moment turbulence closure, with particles simulated using a Lagrangian particle tracking technique, coupled to a particle‐wall interaction algorithm and a random Fourier series method used to model particle dispersion. The performance of the model is tested for a gas‐solid flow in a horizontal‐to‐vertical duct, with predictions showing good agreement with experimental data. In particular, the consistent use of anisotropic and fully three‐dimensional approaches throughout yields predictions that result in fluctuating particle velocities in acceptable agreement with data. © 2011 American Institute of Chemical Engineers AIChE J, 2012

An improved collision damping time for MP-PIC calculations of dense particle flows with applications to polydisperse sedimenting beds and colliding particle jets

This paper describes several improvements to a numerical model introduced by O’Rourke et al. (2009) for collisional exchange and damping in dense particle flows. O’Rourke et al. (2009) use a Bhatnagar, Gross, and Krook (BGK) approximation to the collision terms in a particle distribution function transport equation to model the effects of particle collisions on damping fluctuating particle velocities and, in gas/liquid/solid beds, fluctuating temperatures and compositions of liquid films on particle surfaces. In this paper we focus on particle flows in which the particles have no liquid films and report on an improved expression we have developed for the collision damping time of particle velocity fluctuations used in the BGK approximation. The improved expression includes the effects on the collision damping time of the particle material coefficient of restitution and of non-equilibrium particle velocity distributions. The collision model improvements are incorporated into the general-purpose computational-particle fluid dynamics (CPFD) numerical methodology for dense particle flows. Three computational examples show the benefits of using the new collision time in calculations of particle separation in polydisperse dense particle flows and calculations of colliding particle jets.

Hydrodynamic Modeling of Dense Gas-Particle Turbulence Flows Under Microgravity Space Environments

An Euler–Euler two-fluid model based on the second-order-moment closure approach and the granular kinetic theory of dense gas-particle flows was presented. Anisotropy of gas-solid two-phase stress and the interaction between two-phase stresses are fully considered by two-phase Reynolds stress model and the transport equation of two-phase stress correlation. Under the microgravity space environments, hydrodynamic characters and particle dispersion behaviors of dense gas-particle turbulence flows are numerically simulated. Simulation results of particle concentration and particle velocity are in good agreement with measurement data under earth gravity environment. Decreased gravity can decrease the particle dispersion and can weaken the particle–particle collision as well as it is in favor of producing isotropic flow structures. Moreover, axial–axial fluctuation velocity correlation of gas and particle in earth gravity is approximately 3.0 times greater than those of microgravity and it is smaller than axial particle velocity fluctuation due to larger particle inertia and the larger particle turbulence diffusions.

Fluid–particle correlated motion and turbulent energy transfer in a two-dimensional particle-laden shear flow

Discrete vortex simulations of a dilute two-dimensional particle-laden shear layer with one-way coupling were performed to study fluid–particle correlated motion and the transfer of turbulent kinetic energy between the phases. The resulting modification of carrier phase turbulence, estimated according to current computational models, was evaluated. Particle Stokes numbers were between 1.0 and 4.5, so that the particles showed considerable temporal concentration fluctuations due to centrifuging by the fluid flow structures, and the mass loading was 12% corresponding to a volume fraction of 6.0×10 −5. Fluid velocities and particle concentration and velocities and their covariances, which appear in a commonly used model equation for carrier phase turbulence modification, were evaluated. Additionally, the probability density functions of fluid velocity fluctuations viewed by the particles are presented and compared with their Eulerian counterparts. It was found that particles view reduced velocity fluctuations due to preferential clustering. The model for carrier-phase turbulence modification predicted turbulence reduction, depending on the particle Stokes number. The mechanism responsible for turbulence reduction was the correlated velocity fluctuations of fluid and particles and this reduction could reach values up to one third of the fluid flow dissipation. Preferential particle concentration together with a relative velocity between the phases could generate turbulent kinetic energy of the gas phase, however this production was nearly an order of magnitude smaller compared to reduction of turbulence due to the correlated motion. The findings were compared with experiments available in the literature and help to clarify the view when turbulence reduction or augmentation occurs.

Experiments and simulations of cohesionless particles with varying roughness in a bladed mixer

The kinematics of granular flow of cohesionless particles in a bladed mixer was studied experimentally using particle image velocimetry and computationally using the discrete element method. The discrete element simulations were able to reproduce the surface velocities, granular temperature profiles, and mixing kinetics observed experimentally. Procedures for roughening of glass bead surfaces via coating were developed and the effect of surface roughness was studied experimentally and computationally. Increasing particle surface roughness led to the development of less uniform flows inside the mixer and to increased dilation of the particle bed. Systems composed of rougher particles experienced increased radial and vertical velocities as well as higher particle diffusivities. Cylinder wall roughness was also shown to significantly influence particle velocities in bladed mixers. Rough cylinder walls led to more pronounced particle velocity fluctuations near the top surface and to an increase in granular temperature. The effect of increasing blade speed was also studied. Two distinct flow regimes were observed as blade speed was increased. At low rotational speed, the flow occurs in the bumping regime where particle surface velocities are linearly proportional to the tip speed of the blades. In this regime, the rotational speed of the blades provides the time scale for momentum transfer and for the mixing process. At higher rotational speed, the roping regime is encountered where particle surface velocities are no longer proportional to the tip speed of the blades. This regime is characterized by enhanced radial and vertical particle velocities as well as faster mixing kinetics.

Direct numerical simulation of gas–solid suspensions at moderate Reynolds number: Quantifying the coupling between hydrodynamic forces and particle velocity fluctuations

Predictive device-level computational fluid dynamics (CFD) simulation of gas–solid flow is dependent on accurate models for unclosed terms that appear in the averaged equations for mass, momentum and energy conservation. In the multifluid theory, the second moment of particle velocity represents the strength of particle velocity fluctuations and is known to play an important role in the prediction of core-annular flow structure in risers (Hrenya and Sinclair, AIChEJ, 43 (4) (1994) [5]). In homogeneous suspensions the evolution of the second velocity moment is governed by the particle acceleration–velocity covariance. Therefore, fluctuations in the hydrodynamic force experienced by particles in a gas–solid flow affect the evolution of particle velocity fluctuations, which in turn can affect the mean and variance of the hydrodynamic force. This coupling has been studied in the limit of Stokes flow by Koch and co-workers using a combination of kinetic theory and multipole expansion simulations. For Reynolds numbers beyond the Stokes limit, direct numerical simulation is a promising approach to quantify this coupling. Here we present direct numerical simulation (DNS) results for the evolution of particle granular temperature and particle acceleration variance in freely evolving homogeneous gas–solid suspensions. It is found that simple extension of a class of mean particle acceleration models to their corresponding instantaneous versions does not recover the correlation of particle acceleration with particle velocity. This study motivates the development of better instantaneous particle acceleration models that are able to accurately capture the coupling between particle acceleration and velocity.

Accuracy analysis of the window overlapping technique for velocity measurements using artificial and real signals

The feasibility of using window overlapping processing technique together with cross-correlation method was investigated for measuring instantaneous particle velocities using a fiber optic system. A pair of artificial signal pulses was generated to yield a known velocity field when they were cross-correlated. A parametric analysis was conducted to determine whether the window overlapping technique enhanced the velocity sampling frequency of the fiber optic probe system. The window overlapping technique was found to be effective in improving the accuracy of the instantaneous velocity calculations for relatively shorter data segments (windows). As the length of the window size increased, the efficiency of the window overlapping method diminished. The window overlapping technique was found to be effective only for window sizes up to four times longer than the minimum window size. The minimum window size contains sufficient number of data points that corresponds to the maximum velocity sampling frequency according to the Nyquist Theory. That is, the window overlapping technique could be beneficial for enhancing the velocity sampling frequency only if the velocity data (or the window size used in the cross-correlation function) were sampled at a frequency of four times lower (or better) than the highest frequency in the flow. Due to the hardware limitations, it is not possible to sample data at frequencies high enough to capture the highest frequency velocity fluctuations in a turbulent flow. Therefore, in this study, it was investigated that the velocity sampling frequency of a fiber optic probe could be enhanced by window overlapping technique using data collected from a highly turbulent particle laden pipe flow. The results indicated that the window overlapping technique slightly improved the accuracy of the instantaneous particle velocity measurements. This is believed to be due to the larger window sizes (or low sampling frequencies) relative to the high frequency velocity fluctuations in the flow. Therefore, the particle velocity fluctuations may not be computed accurately using a fiber optic probe due to the nature of the cross-correlation method which filters the velocity variations during the time period of Δ T . In order to obtain reasonably accurate results for measuring the particle velocity fluctuations in real life applications, the time interval (window size) must be sufficiently small such that it corresponds to the frequencies, at most, four times lower than the highest frequency occurring in the flow. The feasibility of using window overlapping processing technique together with cross-correlation method was investigated for measuring instantaneous particle velocities using a fiber optic system. The efficiency of window overlapping technique for enhancing the velocity sampling frequency was evaluated using artificial signals and data obtained from a fiber optic probe ( Fig. 1 ) in a highly turbulent particle laden pipe flow.

Particle dynamics in a turbulent particle–gas suspension at high Stokes number. Part 1. Velocity and acceleration distributions

The effect of fluid velocity fluctuations on the dynamics of the particles in a turbulent gas–solid suspension is analysed in the low-Reynolds-number and high Stokes number limits, where the particle relaxation time is long compared with the correlation time for the fluid velocity fluctuations, and the drag force on the particles due to the fluid can be expressed by the modified Stokes law. The direct numerical simulation procedure is used for solving the Navier–Stokes equations for the fluid, the particles are modelled as hard spheres which undergo elastic collisions and a one-way coupling algorithm is used where the force exerted by the fluid on the particles is incorporated, but not the reverse force exerted by the particles on the fluid. The particle mean and root-mean-square (RMS) fluctuating velocities, as well as the probability distribution function for the particle velocity fluctuations and the distribution of acceleration of the particles in the central region of the Couette (where the velocity profile is linear and the RMS velocities are nearly constant), are examined. It is found that the distribution of particle velocities is very different from a Gaussian, especially in the spanwise and wall-normal directions. However, the distribution of the acceleration fluctuation on the particles is found to be close to a Gaussian, though the distribution is highly anisotropic and there is a correlation between the fluctuations in the flow and gradient directions. The non-Gaussian nature of the particle velocity fluctuations is found to be due to inter-particle collisions induced by the large particle velocity fluctuations in the flow direction. It is also found that the acceleration distribution on the particles is in very good agreement with the distribution that is calculated from the velocity fluctuations in the fluid, using the Stokes drag law, indicating that there is very little correlation between the fluid velocity fluctuations and the particle velocity fluctuations in the presence of one-way coupling. All of these results indicate that the effect of the turbulent fluid velocity fluctuations can be accurately represented by an anisotropic Gaussian white noise.

Flow structures inside a large-scale turbulent fluidized bed of FCC particles: Eulerian simulation with an EMMS-based sub-grid scale model

Turbulent fluidized bed reactors are widely used in industry. However, CFD simulations of the hydrodynamic characteristics of these reactors are relatively sparse, despite the urgent demand from industry. To address this problem, Eulerian simulations with an EMMS-based sub-grid scale model, accounting for the effect of sub-grid scale structures on the inter-phase friction, are performed to study the hydrodynamics inside a large-scale turbulent fluidized bed of FCC particles. It is shown that the simulated axial and radial solid concentration profiles, entrained solid fluxes and standard deviation of the solid concentration fluctuation agreed well with experimental data available in the literature. In-depth analysis of time-averaged particle velocity and solid concentration shows that a dense-suspension upflow regime coexists with fast fluidization regime in this bed, which is reminiscent of the hydrodynamic characteristics in high-density circulating fluidized bed (CFB) risers, even though they are operated in different fluidization regimes. The Reynolds stresses in turbulent fluidized beds are anisotropic, but the degree of anisotropy is far less pronounced than the reported values in CFB risers. It was also found that the solid concentration fluctuation and axial particle velocity fluctuation are strongly correlated.

Numerical prediction of particle dispersions in downer under different gravity environments

Abstract Particle dispersion behavior of dense gas–particle flows in a downer affected by gravity environment is numerically simulated using an Euler–Euler two-fluid approach incorporating unified-second-order-moment two-phase turbulent models and kinetic theory of granular flows (USM-θ). Anisotropy of gas–solid two-phase stress and the interaction between two-phase stresses are fully considered by two-phase Reynolds stress model and the transport equation of two-phase stress correlation. The flow behavior of particles in a downer of Wang et al. (1992) [27] experiments is predicted under earth gravity, lunar gravity and microgravity environment. Simulation results of particle concentration and particle velocity are in good agreement with measurement data under earth gravity environment. Comparison earth gravity to lunar and microgravity condition, peak value of particle concentration is shifted to near center region and axial particle fluctuation velocity is larger than that of approximately 3.0 times. Particle temperature, particle heterogeneities dispersion and particle–particle collision are weakened due to decrease gravity. Furthermore, roles of particle and gas kinetic energy in particle–fluid system are alternated. Both particle kinetic energy and gas kinetic energy are greater than ones under earth gravity conditions.

Particle statistics in a gas–solid coaxial strongly swirling flow: A direct numerical simulation

A direct numerical simulation of a strongly coaxial swirling particle-laden flow is conducted with reference to a previous experiment. The carrier phase is simulated as a coaxial swirling flow through a short nozzle injecting into a large container. The particle phase is carried by the primary jet, and simulated in the Lagrangian approach. The drag force, slip-shear force and slip-rotation force experienced by particles are calculated. A partial validation of the results is followed. The results are analyzed in Eulerian approach focusing on the statistical behavior of particle motion. The relative importance of the drag, slip-shear and slip-rotation forces under different Stokes numbers is indicated quantitatively. The particle velocity profiles, fluctuations, Reynolds stress, and turbulence intensity are demonstrated and analyzed respectively. An important “choke” behavior for large particles within the mainstream is found and interpreted. Additionally, the patterns of particle distribution and the helical structures of particle motion under different Stokes numbers are demonstrated qualitatively and analyzed quantitatively.