Modeling of Gas‐Particle Turbulent Flow in Spout‐Fluid Bed by Computational Fluid Dynamics with Discrete Element Method

Gas and solid turbulent flow in a cylindrical spout‐fluid bed with conical base were investigated by incorporating various gas‐particle interaction models for two‐way coupling simulation of discrete particle dynamics. The gas flow field was computed by a k‐ϵ two‐equation turbulent model, the motion of solid particles was modeled by the discrete element method. Drag force, contact force, Saffman lift force, Magnus lift force and gravitational force acting on individual particles were considered in the mathematical models. Calculations on the cylindrical spout‐fluid bed with an inside diameter of 152 mm, a height of 700 mm, a conical base of 60° and the ratio of void area of 3.2 % were carried out. Based on the simulation, the gas‐solid flow patterns at various spouting gas velocities are presented. Besides, the changes in particle velocity, particle concentration, collision energy, particle and gas turbulent intensities at different proportions of fluidizing gas to total gas flow are discussed.     

Relative importance of the lift force on heavy particles due to turbulence driven secondary flows

Saffman lift forces on dense particles due to gradients in both streamwise and cross-stream velocities in a downward, fully developed turbulent square duct flow at Re_τ = 360 are studied using large eddy simulations. Volume fraction of the dispersed phase is low enough (≤ 10^− 5) that the one-way coupling approach is reasonable, i.e., two-way coupling and particle-particle collisions are not considered. Eulerian and Lagrangian approaches are used to treat the continuous and dispersed phases, respectively. Subgrid stresses are modeled with the dynamic subgrid kinetic energy model of Kim and Menon [W.W. Kim and S. Menon. Application of the localized dynamic subgrid-scale model to turbulent wall-bounded flows, AIAA 97-0210, 1997.]. The particle equation of motion includes drag, lift forces due to both the streamwise and cross-stream velocity gradients, gravity, and is integrated using the fourth-order accurate Runge-Kutta scheme. Dependence of particle drag and lift forces on duct cross-sectional location and particle response time is demonstrated using the mean value contours and probability density functions (PDFs) of particle forces. It is shown that the streamwise component of the mean drag force experienced by particles of all response times is a deceleration force, i.e. on average, fluid streamwise velocity lags the particle streamwise velocity. Secondly, the two wall-normal (or lateral) components of the mean drag force are oriented such that the particles experience a net mean force toward the duct corners. PDFs of particle drag force components show that smaller response time particles experience a wider range of drag force about the mean value, as compared to the more inertial particles. Contours of mean wall-normal lift forces due to streamwise velocity gradients show that this force predominantly acts toward the duct walls and that the maximum lift force occurs close to the walls. PDFs of lift force due to streamwise velocity gradients show that the range of fluctuations increases with particle response time, but the dependence on particle response time is weaker compared to drag force. Lift forces due to cross-stream velocity gradients are at least an order of magnitude smaller than lift forces due to streamwise velocity gradients and are found to decrease in their range of fluctuations with particle response time. It is demonstrated that lift forces due to secondary flow velocity gradients are not as important as those due to streamwise velocity gradients in a square duct flow.     

DEM simulation of particle mixing in flat-bottom spout-fluid bed

The particle mixing mechanism affects the rate of the process and the achievable homogeneity. This paper presents a numerical study of the particle motion and mixing in flat-bottom spout-fluid bed. In the numerical model, the particle motion is modeled by discrete element method (DEM) and the gas motion is modeled by κ–? two-equation turbulent model. Validation with experiments is first carried out by comparing solid flow pattern and bed pressure drop at various gas velocities. Then, particle velocities, obtained from DEM simulations, are presented to reveal the mixing mechanisms. On the basic, the dependence of mixing index on the time and the effect of gas velocity on mixing and dead zone (stagnant solid) are discussed, respectively. The results indicate that the spouting gas is the driving force for the formation of particle circulation roll, resulting in the mixing. The convective mixing caused by the motion of circulation roll, shear mixing induced by the relative move of circulation rolls and diffusive mixing generated by random walk of particle among circulation rolls are three different mixing mechanisms in spout-fluid bed. The increase of spouting gas velocity promotes the convective and shear mixing. While increasing the fluidizing gas velocity improves significantly the convective mixing and but weakens the shear mixing. Both of them yield a reduction in the dead zone.     

Numerical investigation of coarse powder and air flow in an electrostatic powder coating process

The work presented here reports on the numerical simulation of an electrostatic powder coating process that uses a commercial computational fluid dynamic code, FLUENT v6.1. The purpose of this study was to understand the gas and particle flow fields inside a coating booth under given operating conditions and the effect of particle sizes on its trajectories and the final coating quality. The air and powder particle flows in a coating booth were modeled as a three-dimensional turbulent continuous gas flow with solid particles as a discrete phase. The continuous gas flow was calculated by solving Navier-Stokes equations including the standard k − ε turbulence model with non-equilibrium wall function and the discrete phase was modeled based on the Langrangian approach. Since the solid phase volumetric fraction was less than 0.1%, the effect of particle-particle interaction on particle trajectories was not taken into account. In addition to drag force and gravity, the electrostatic force including the effect of space charge due to the free ions was considered in the equation of motion and implemented using user defined scalars and functions. The governing equations were solved using the second order upwind scheme. Information was provided on the particle trajectories with respect to the particle diameters that could be used to develop suitable operating conditions for the use of fine powders in a powder coating process.     

Numerical simulation of pulsed fluidized bed with immersed tubes using DEM-LES coupling method

The present work is a 2-D numerical simulation of pulsed fluidized bed with immersed tubes using DEM-LES coupling method. The pulsed inflow of gas phase is modeled as U₀(1+sin(2πft)), in which four pulsating frequencies of f=5, 10, 15 and 20 of velocity inflow are used. The discrete element method (DEM) simulation for particle motion coupled with the large eddy simulation (LES) for gas phase is used. The fluidized bed with five immersed tubes of staggered arrangement and six immersed tubes of in-line arrangement is simulated, respectively. It is found that the pressure drop, the mean drag force and the mean pressure gradient force experienced by particles are forced oscillated. The different effects of pulsed fluidization on the circumferential distribution of particle-tube collision on the outer surface of tubes at different pulse frequencies and modes of arrangement of immersed tubes are numerically analyzed. Finally, it is found that the pulsed motion of fluid with high frequency leads to suppression of particle fluctuating motion.     

SIMULATION OF PARTICLE TRANSPORT AND DEPOSITION IN A COMBUSTOR

A computational model for Lagrangian particle tracking for studying dispersion and deposition of particles in a combustor with swirling flow and chemical reaction is developed. The model accounts for the effect of thermophoretic force, as well as the drag and lift forces acting on particles, in addition to the Brownian motion and gravitational sedimentation effects. The mean turbulent gas flow, temperature fields and chemical species concentration in the combustor are evaluated using the stress transport turbulent model of the FLUENT code. The instantaneous fluctuation velocity field is generated by a Gaussian filtered white noise model.

The simulated axial, radial and tangential mean gas velocities are compared with the existing experimental data. Ensembles of particle trajectories are generated and statistically analyzed. The effects of size and initial distribution on particle dispersion and deposition are studied. The particle concentration at different sections are also evaluated and discussed. The results shows that the turbulence dispersion effect is quite important, while the thermophoresis effect is small.     

Discrete particle simulation of solids motion in a gas–solid fluidized bed

The solids motion in a gas–solid fluidized bed was investigated via discrete particle simulation. The motion of individual particles in a uniform particle system and a binary particle system was monitored by the solution of the Newton's second law of motion. The force acting on each particle consists of the contact force between particles and the force exerted by the surrounding fluid. The contact force is modeled by using the analogy of spring, dash-pot and friction slider. The flow field of gas was predicted by the Navier–Stokes equation. The solids distribution is non-uniform in the bed, which is very diluted near the center but high near the wall. It was also found that there is a single solids circulation cell in the fluidized bed with ascending at the center and descending near the wall. This finding agrees with the experimental results obtained by Moslemian. The effects of the operating conditions, such as superficial gas velocity, particle size, and column size on the solids movement, were investigated. In the fluidized bed containing uniform particles better solids mixing was found in the larger bed containing smaller size particles and operated at higher superficial gas velocity. In the system containing binary particles, it was shown that under suitable conditions the particles in a fluidized bed could be made mixable or non-mixable depending on the ratios of particle sizes and densities. Better mixing of binary particles was found in the system containing particles with less different densities and closer sizes. These results were found to follow the mixing and segregation criteria obtained experimentally by Tanaka et al.     

Aerosol Particle Removal and Re-entrainment in Turbulent Channel Flows – A Direct Numerical Simulation Approach

Aerosol particle removal and re-entrainment in turbulent channel flows are studied. The instantaneous fluid velocity field is generated by the direct numerical simulation (DNS) of the Navier – Stokes equation via a pseudospectral method. Particle removal mechanisms in turbulent channel flows are examined and the effects of hydrodynamic forces, torques and the near-wall coherent vorticity are discussed. The particle resuspension rates are evaluated, and the results are compared with the model of Reeks. The particle equation of motion used includes the hydrodynamic, the Brownian, the shearinduced lift and the gravitational forces. An ensemble of 8192 particles is used for particle resuspension and the subsequent trajectory analyses. It is found that large-size particles move away roughly perpendicular to the wall due to the action of the lift force. Small particles, however, follow the upward flows formed by the near-wall eddies in the low-speed streak regions. Thus, turbulent near-wall vortical structures play an important role in small particle resuspension, while the lift is an important factor for reentrainment of large particles. The simulation results suggests that small particles (with τ _p ⁺ ≤ 0.023) primarily move away from the wall in the low-speed streaks, while larger particles (with τ _p ⁺ ≥ 780) are mostly removed in the high-speed streaks.     

Modeling of particle deposition in a vertical turbulent pipe flow at a reduced probability of particle sticking to the wall

Particle deposition on the wall in a dilute turbulent vertical pipe flow is modeled. The different mechanisms of particle transport to the wall are considered, i.e., Brownian motion, turbulent diffusion and turbophoresis. The Saffman lift force, the electrostatic force, the virtual mass effect and wall surface roughness are taken into account in the model developed. A boundary condition that accounts for the probability of particle sticking to the wall is suggested. An analytical solution for deposition of small Brownian particles is obtained. A particle relaxation time range, where the model developed is reliably applicable, is evaluated. Computational results obtained at different particle-wall sticking probabilities in the wide particle relaxation time range are presented and discussed.     

Lift force on bubbles in a bubble column reactor: Experimental analysis

The lift force acting on bubbles in a swarm has been estimated by analyzing the instantaneous velocity-time data obtained using LDA in a cylindrical bubble column. Phase distinction was achieved through the multiresolution analysis of the velocity-time data. Several important issues related to the transverse motion of bubbles subjected to a shear field have been discussed quantitatively. The actually measured bubble sizes, the respective slip velocity values in transverse and axial directions and the local shear rates (γ) enabled the verification of known formulations for the lift coefficient (C_L) for bubbles. At many locations in the column the radial flux of the gas phase by turbulent dispersion and the radial slip were estimated. The radially inward movement of bubbles from low to high axial velocity (from column wall to center, i.e., C_L<0) was observed at most of the measurement locations. The local lift coefficient was estimated using the transverse drag force and the values support the results from the material balance approach. The estimated C_L values showed a wide variation over the column cross-section.     

Incipient motion of a small particle in the viscous boundary layer at a pipe wall

A force balance is derived for a hemispherical particle in the viscous boundary layer at the wall of a horizontal pipe conveying Newtonian fluid; the hemisphere, of radius much less than that of the pipe, rests on the bottom with its flat face against the wall. The drag on the hemisphere is calculated from the creeping flow field of Price (Q. J. Mech. Appl. Math. Pt. 1 (1993)). This yields a prediction of the maximum velocity gradient at the wall for equilibrium, with limiting friction between the hemisphere and the wall. It is shown that the flow field of Price predicts a zero lift force but the validity of this, for actual flows, is questioned. Use of a hemisphere formulates a relevant well-posed problem, capable of mathematical solution. However, the flow field around real particles, e.g. sand, is complex, because of their irregular shapes, but the hemisphere work gives a qualitative indication of the behaviour of irregular particles. For turbulent flow in a pipe it is pertinent to consider a particle wholly within the viscous sub-layer, because it is isolated from significant turbulence and therefore hard to move; for such flow, the theory gives Eq. (21) to predict the critical pipe velocity, v_C, for incipient motion of the hemisphere. For laminar flow, the wall shear rate is readily obtained from the parabolic velocity profile leading to Eq. (26) for v_C. The flow field of Price (and therefore the force acting on the hemisphere) is valid only for creeping flow (i.e. very low particle Reynolds number). Modifications to the force balance are tentatively suggested to account for inertial components to the drag force. The predictions of critical velocity are tested against our data for the incipient motion of small hemispheres at pipe walls in hydraulic conveying as well as new and previously published data for both hydraulic and pneumatic conveying. The new method of predicting incipient motion works well for both the pneumatic and hydraulic conveying of hemispheres and sand shaped particles but it overpredicts the critical velocity for more rounded particles. The dependency of critical velocity on particle shape is under-researched.     

RANS modeling of a particulate turbulent round jet

A complete and accurate model for the symmetric gas–solid turbulent round jet is accomplished using the Reynolds Averaged Navier–Stokes (RANS) equations. The two-fluid model was used to describe the averaged characteristics of the two phases, including the particle mass concentration, the turbulent kinetic energy and its dissipation in the mixture. Particle–turbulence interaction (turbulence modulation) is described by a two-way coupling model. The drag, lift and gravitation forces are incorporated into the system of equations using appropriate closure equations. A finite difference numerical scheme was used for the solution of the set of the governing equations and the results of the model were validated by comparison with data from several experiments. The influence of two types of particles, namely glass and electrocorundum, of different sizes and different loadings on the velocity and turbulence structure of the jet is examined. The computational results show the influence of the particulate phase on the velocity and turbulence structure of the jet.The significance of this study is that for the first time it presents explicitly the full RANS equations for a fluid jet with particles in an unabridged way and specifies the entire set of closure relations that are used for fluid–particle interactions including the equations for the extended k–ε model, the two-way particle–turbulence interactions and turbulence modulation as well as the inclusion of a lateral Saffman force.     

Particle dispersion in a turbulent natural convection channel flow

Direct numerical simulations of particle dispersion in the turbulent natural convection flow between two vertical walls kept at constant but different temperatures are reported. It is assumed that the particles do not affect the flow (i.e. the dilute phase approximation is adopted). Particles with different levels of inertia, or Stokes numbers (0.843≤St≤17.45), are tracked according to the drag force imposed by the fluid. The gravity force is included for two cases, St=0.843 and St=17.45. The different levels of turbulence near the wall and near the center of the channel produce, as in isothermal turbulent channel or pipe flow, a larger concentration of particles near the wall. This effect becomes more important, and the deposition velocity of particles on the wall increases, as the particle inertia is increased. The simulations at St=8.38 and St=17.45 predict similar concentration profiles and deposition velocities according to the large inertia of these particles. The deposition velocities, obtained when the gravity force is ignored in the particle equations, follow the trend observed and measured for isothermal turbulent channel flows in the diffusion impaction regime. For the conditions considered, the gravity vector imposes a strong descending motion on the particles and this produces the increase of the particle concentration near the wall and a reduction of the deposition velocities in comparison with the results without the gravity force.     

DEM-LES of coal combustion in a bubbling fluidized bed. Part I: gas-particle turbulent flow structure

The gas and particle motions in a bubbling fluidized bed both with and without chemical reactions are numerically simulated. The solid phase is modelled as Discrete Element Method (DEM) and the gas phase is modelled as 2-D Navier-Stokes equations for 2-phase flow with fluid turbulence calculated by large Eddy simulation (LES), in which the effect of particles on subgrid scale gas flow is taken into account. The gas/particle flow structure, the mean velocities and turbulent intensities can be predicted as a function of several operating parameters (particle size, bed temperature, and inlet gas velocity). The lower the inlet gas velocity, the higher the ratio of particle collision. The distributions of the particle anisotropic velocity show that the particles have no local equilibrium, and the distribution of gas kinetic energy corresponds to the distribution of gas-particle coupling moment in the fluidized bed. An intensive particle turbulent region exists near the wall, and the gas Reynolds stress is always much higher than the particle stress. The presence of the large reactive particles in the fluidized bed may affect significantly the gas and particle velocities and turbulent intensities. The effects of the bed temperature and inlet gas velocity on the gas particle flow structure, velocity, and turbulent intensity are also studied.     

Lift force in bubbly flow systems

From the significance of three-dimensional simulation of dispersed flow systems in many engineering fields, extensive study was conducted for lift force in a single particle system as well as a multiparticle system. In this study, the lift force in a single particle system was modeled by considering the effect of bubble deformation on the lift force. The model was finalized based on existing data obtained in the range of particle Reynolds number from 3.68 to 78.8, viscous number from 0.0435 to 0.203 and Eötvös number from 1.40 to 5.83. The viscous number is defined by where μ_f, ρ_f, σ, g and Δρ are, respectively, fluid viscosity, fluid density, surface tension, gravitational acceleration and density difference between phases. The applicability of the model to higher particle Reynolds number system such as an air-water system was qualitatively examined. The lift force model developed in a single particle system was extended to a multiparticle system. The applicability of the extended lift force model was qualitatively examined. The similarity between drag and lift forces were also discussed.     

Shear induced lift in the motion of small particles in rotating flows

A flow field constructed by the superposition of a rotation and a simple shear flow contains a small particle. A shear induced lift force acts on it. The equations of motion of the particle, which include this lift force, are solved using a singular asymptotic expansion. Conditions are obtained under which the effect of the lift force on the trajectory of the particle leads to instability. It is shown that even when the instability is not attained, and the lift coefficient is much smaller than the critical one, the effect of the shear induced lift may still be quite large. An example of turbulent flow in a pipe demonstrates the appreciable effect of the lift force on the path traced by the particle.     

Flow behaviors of a large spout-fluid bed at high pressure and temperature by 3D simulation with kinetic theory of granular flow

Flow behaviors of a large spout-fluid bed (I.D. 1.0 m) at high pressure and temperature were investigated by Eulerian simulation. The gas phase was modeled with k − ε turbulent model and the particle phase was modeled with kinetic theory of granular flow. The development of an internal jet, gas-solid flow patterns, particle concentrations, particle velocities and jet penetration depths at high pressure and temperature at different operating conditions were simulated. The results show that the bed operated at an initial bed height larger than the maximum spoutable bed height resembles the flow patterns of jetting fluidized beds. The radial profiles of particle velocities and concentrations at high temperature and pressure have the similar characteristic shapes to those at ambient pressure and temperature. The particle concentrations and velocities appear to depend on the bed heights when increasing pressure while keeping the gas velocities and temperature constant. The particle velocities in the lower region of the bed increase with increasing pressure, while they tend to decrease in the middle and upper regions of the bed. The particle concentrations have an opposite dependency with increasing pressure. They decrease in the lower region of the bed but increase in the middle and upper regions of the bed. Besides, the jet penetration depths are found to increase with increasing pressure.     

Influence of the lift force on the stability of a bubble column

This work investigates the role of the lift force for the stability of a homogeneous bubble column. Instabilities caused by the lift force may be one important reason for the transition from homogeneous to heterogeneous bubble column. On rising bubbles the lift force acts in a lateral direction, when gradients of the liquid velocity are present. Non-uniform liquid velocity fields may be induced if the gas fraction is not equally distributed, e.g. caused by local disturbances. This feedback mechanism is studied in the paper. It was found, that a positive lift coefficient (small bubbles) stabilizes the flow, while a negative coefficient (large bubbles) leads to unstable gas fraction distributions, and thus it favours the appearance of a heterogeneous bubble column regime. The turbulent dispersion force has always a stabilizing action, i.e., it partially compensates the destabilization induced by a negative lift coefficient. A stability analysis for a mono-dispersed system nevertheless showed, that influence of the lift force is much larger, compared to the influence of the turbulent dispersion force, if only bubble induced turbulence is considered. Thus, the stability condition is practically the positive sign of the lift force coefficient. The extension of the analysis to two bubbles classes, from which one being small enough to have a positive lift coefficient, results in a minimum fraction of small bubbles needed for stability. Finally a generalized criterion for N bubble classes and for a continuous bubble size distribution is given.     

Electrohydrodynamic Flow and Particle Transport Mechanism in Electrostatic Precipitators with Cavity Walls

The electrohydrodynamic (EHD) flow induced by the corona wind was observed in a model electrostatic precipitator (ESP) of the simple geometry composed of the plates with a cavity. And the influence of the EHD flow and the turbulence condition of inlet cross-flow on the particle behavior inside the ESP and its collection efficiency were elucidated through experimental and numerical analysis. The profiles of streamwise gas velocities and turbulence intensities were measured in the ESP with a laser Doppler anemometer.A laser beam sheet visualized particle trajectories. Collection efficiencies were measured with a particle counter. In addition, numerical computations were performed to compare with the experimental results. The numerical results showed good agreement with the experimental data. As the corona voltage increased, the gas velocities of the core flow and the circulating flow inside the cavity increased due to the corona wind and the turbulence intensity increased near the cavity region. As the corona voltage increased for the low bulk gas velocity, corona wind prevented the particle transport into the cavity. And the particle transport into the cavity by turbulent dispersion was observed as the bulk gas velocity increased. When the flow with high turbulence intensity entered the ESP, the turbulent dispersion enhanced the transport of particles into the cavity; hence, the collection efficiency was higher compared with the case of the relatively lower inlet turbulence intensity below a critical corona voltage. However, the collection efficiency was slightly lower for the high inlet turbulence than for the low inlet turbulence above the critical corona voltage due to the turbulent diffusion of particles toward the centerline downstream from the corona wire.     

DEM simulation of the particle dynamics in two-dimensional spouted beds

A Discrete Element Method (DEM) is used together with the continuum model of turbulent fluids to simulate the periodic spouting of granular solids in a two-dimensional spouted bed. The bed is contained in a rectangular column of 152 mm width and 15 mm depth with a tapered base. Glass beads with a diameter of 2 mm are used as bed material. Simulations using the DEM together with a low Reynolds number k-ε turbulence model for the fluid phase yield predictions of the unstable spout regime, characterized as a periodic upward-moving particle jet. The simulation results compare well to experimental data obtained using a particle image velocimetry (PIV) technique, including fluid flow fields, time-averaged particle velocity profiles, and spout shape. Finally, DEM predictions for distribution of drag and net force on the particles, particle concentration fields, gas velocity and turbulence field are discussed.