Lattice Boltzmann simulation of flow past a non-spherical particle

Lattice Boltzmann method was used to predict the fluid-particle interaction for arbitrary shaped particles. In order to validate the reliability of the present approach, simulation of flow past a single stationary spherical, cylindrical or cubic particle is conducted in a wide range of Reynolds number (0.1 < Re_p < 3000). The results indicate that the drag coefficient is closely related to the particle shape, especially at high Reynolds numbers. The voxel resolution of spherical particle plays a key role in accurately predicting the drag coefficient at high Reynolds numbers. For non-spherical particles, the drag coefficient is more influenced by the particle morphology at moderate or high Reynolds numbers than at low ones. The inclination angle has an important impact on the pressure drag force due to the change of projected area. The simulated drag coefficient agrees well with the experimental data or empirical correlation for both spherical and non-spherical particles.     

Numerical Simulation of Particle Saltation Process

A numerical model for simulation of particle single-step saltation was developed. The model includes drag force, shear lift force, rotational lift force, buoyancy force, added mass force, and torque. The governing equations were solved using the fourth-order Runge-Kutta scheme. The model was calibrated and verified using the experimental data. The computational results include particle trajectory, longitudinal velocity of particle and flow, relative velocity of particle and flow, dimensionless drag, and lift forces along the trajectory. Sensivity analysis was performed to determine the influence of various parameters. Saltation characteristics were also calculated for various Reynolds numbers in the range of 2.5 to 7.7. It was found that very close to the bed, drag force decreases as Reynolds number increases. An increase of about three times the Reynolds number has a decreasing effect of three times and two times on the drag and lift force, respectively. The influence of Reynolds number increase on the falling phase was less than that on the rising phase.     

Experimental investigation of bubble and particle motion behaviors in a gas-solid fluidized bed with side wall liquid spray

Bubble and particle motion behaviors are investigated experimentally in a gas solid fluidized bed with liquid spray on the side wall. The particles used in the experiment are classified as Geldart B particles. The results reveal that when the fluid drag force is less than the liquid bridge force between particles, liquid distribute all over the bed. Bubble size increases as the increase of inter-particle force, then decreases owing to the increase of particle weight with increasing liquid flow rate. When the fluid drag force is greater than the liquid bridge force, liquid mainly distribute in the upper part of the bed. And it is difficult for the wet particles to form agglomerates. Bubble size decreases with increasing liquid flow rate due to the increasing of minimum fluidization velocity. Besides, the acoustic emission (AE) measurements illustrate that the liquid adhesion and evaporation on particles could enhance the particles motion intensity. Consequently, the bubble and particle behaviors change due to the variation in fluidized gas velocity and liquid flow rate should be seriously considered when attempting to successfully design and operate the side wall liquid spray gas solid fluidized bed.     

Three-dimensional simulation of the particle distribution in a downer using CFD–DEM and comparison with the results of ECT experiments

A three-dimensional numerical model of the down-flow fluidized bed (Downer) with a newly designed distributor was applied to investigate the particle distribution profiles using combined computational fluid dynamics (CFD) and the discrete element method (DEM). A realistic model of DEM, which calculates the contact force acting on the individual particles, is used to monitor the movement of individual particles in the bed. The contact force is calculated using the concepts of the spring, dash-pot, and friction slider. The flow field of gas is predicted by the Navier–Stokes equation. This CFD–DEM model provides information regarding the particle movement and distribution, the particle velocity, and the gas velocity in the bed under different air-particle mixture conditions. The results demonstrate that the air supply conditions directly influence the particle distribution uniformity. Furthermore, the numerical predictions for the axial and radial profiles of the particle distribution were found to agree well with the experimental results obtained by electrical capacitance tomography (ECT).     

Determination of laminar and turbulent flow ranges through vertical packed beds in terms of particle friction factors

Despite the presence of a variety of studies dealing with the magnitude of particle Reynolds number, Re_p defining transition from laminar to turbulent regime for flow through packed beds, the manner is still one of the unknowns. An approach based on the experimental data concerning upward airflow through fixed cylindrical packed beds is presented in this paper. The utilized packed beds had the following ranges of; sphericity, Φ, 0.55 ? Φ ? 1.00, packing material diameter to bed length ratio, D_p/L, 0.04 ? D_p/L ? 0.72, and bed porosity, ε, 0.36 ? ε ? 0.56. The test cases covered the ranges of particle Reynolds number, Re_p 708 ? Re_p ? 7772 and particle Froude number; Fr_p 2.86 ? Fr_p ? 10.39. The measurements of pressure drop through packed bed; ΔP_Bed and superficial mean exit velocity; U are used to determine bed frictional effects in reference to the available literature on particle friction factors, f_p. The magnitude of Re_p defining transition is assumed to be 2000 with particular emphasis to the flow dynamics. The definitions of Bird et al. [R.B. Bird, W.E. Stewart, E.N. Lightfoot, Transport Phenomena, John Wiley and Sons, NY, 1960] are used to calculate f_p. The calculated f_p for the covered test cases are given as a function of pressure coefficient, ΔP* and Re_p, Fr_p, Φ, ε, D_p/L in the approximate ranges of laminar and turbulent flow for Re_p < 2000 and Re_p > 2000, respectively. The proposed separate equations of f_p = f_p(ΔP*, Re_p, Fr_p, Φ, ε, D_p/L) are satisfied for laminar and turbulent flows with corresponding average error margins of ±7.6% and ±18%. Furthermore ranges of transitional and fully rough flow through packed beds are estimated as 2000 ? Re_p ? 4000 and Re_p > 5000 with an analogy to the well-known Moody Chart in pipe flows.     

A modified drag model for power-law fluid-particle flow used in computational fluid dynamics simulation

A modified drag model for the power-law fluid-particle flow considering effects of rheological properties was proposed. At high particle concentrations (ε_s ≥ 0.2), based on the Ergun equation, the cross-sectional shape and the tortuosity of the pore channel are considered, and the apparent flow behavior index and consistency coefficient of the power-law fluid at the surface of the particles are corrected. At low particle concentrations (ε_s < 0.2), based on the Wen-Yu drag model, the modified Reynolds number for power-law fluid and the relational expression between drag coefficient for single particle and Reynolds number that considers the effect of the flow behavior index are adopted. Numerical simulations for the power-law fluid-particle flow in the fluidized bed were carried out using the non-Newtonian drag model. The effects of rheological parameters on the drag coefficient were analyzed. The comparisons of simulation and experiment show that the modified drag model predicts reasonable void fraction under different rheological parameters, particle diameters, and liquid velocities in both low particle concentrations and high particle concentrations. The increase in flow behavior index and consistency coefficient increases the drag coefficient between the two phases and decreases the average particle concentration within the bed.     

Numerical study to predict the particle deposition under the influence of operating forces on a tilted surface in the turbulent flow

This study uses a v2-f turbulence model with a two-phase Eulerian approach. The v2-f model can accurately calculate the near wall fluctuations in y-direction, which mainly represent the anisotropic nature of turbulent flow. The model performance is examined by comparing the rate of particle deposition on a vertical surface with the experimental and numerical data in a turbulent channel flow available in the literature. The effects of lift, turbophoretic, electrostatic and Brownian forces together with turbulent diffusion are examined on the particle deposition rate. The influence of the tilt angle and surface roughness on the particle deposition rate were investigated. The results show that, using the v2-f model predicts the rate of deposition with reasonable accuracy. It is observed that in high relaxation time the effect of lift force on the particle deposition is very important. It is also indicated that decreasing the tilt angle from 90° to 0° enhances the deposition rate especially for large size particles. Furthermore, the results show that increasing the Reynolds number at a specific tilt angle decreases the rate of particle deposition and the tilt angle has insignificant impact on the particle deposition rate in high shear velocity or high Reynolds number.     

Large eddy simulation of particle deposition and resuspension in turbulent duct flows

Particle deposition and resuspension in a horizontal, fully developed turbulent square duct flow at four flow bulk Reynolds numbers (10,320, 83k, 215k and 250k) is simulated by applying large eddy simulation coupled with Lagrangian particle tracking technique. Forces acting on particles includes drag, lift, buoyancy and gravity. Four particle sizes are considered with the diameters of 5?μm, 50?μm, 100?μm and 500?μm. Results obtained for the fluid phase are in good agreement with the available experimental and numerical data. Predictions for particles show that particle size, flow Reynolds number and the duct (celling, floor and vertical) walls play important roles in near-wall particle deposition and resuspension. For the smallest particle (5?μm), the particle deposition rates in duct ceiling, floor and vertical walls are found to be similar with each other and all increase with the flow Reynolds number, while the particle resuspension tends to occur in the middle wall regions and corners of the duct with less influenced by the flow Reynolds number. The ceiling deposition rate gradually decreases with particle size while the floor and vertical wall deposition rates both increase with particle size. The ceiling particle deposition rate increases with Reynolds number while the floor deposition rate decreases with it. The vertical deposition rate for the small particles (5–50?μm) increases with the flow Reynolds number obviously, while for the large particles (100–500?μm) that becomes insensitive. In addition, the flow Reynolds number is found to have an obvious effect on particle resuspension while the effect of particle size on particle resuspension decreases with Reynolds number. Eventually, a dynamic analysis was conducted for particles deposition and resuspension in turbulent duct flows.     

Influence of air velocity and powder bed height on local density and float–sink of spheres in a gas–solid fluidized bed

Depending on their density, large objects will either float or sink in a gas–solid fluidized bed due to the liquid–like properties and density of the fluidized bed. The float–sink technology has been applied to dry density separations in industry. It is important for optimized industrial application to understand how the air velocity and the powder bed height affect the float–sink as the key operating factors. In this study, we investigated the float–sink of spheres of various density by varying the air velocity and the powder bed height. Also, we obtained the local fluidized bed density and the buoyancy force working on the sphere at various heights. We used the weight of a stainless-steel sphere in the fluidized bed to estimate the local fluidized bed density and the buoyancy force based on Archimedes principle. We found that the spheres float–sink behavior changes dramatically with the air velocity and the powder bed height and that the spheres float–sink behavior is correlated to ΔF = F_b – F_g, where F_b is the buoyancy force and F_g is the gravity force acting on the sphere. We also found that the fluidized bed density is not constant as a function of height when the air velocity is relatively large; the local fluidized bed density is interestingly either minimal at approximately mid-height or surprisingly, gradually increases with height within the fluidized bed at higher air velocities. The possible reasons are discussed by considering the local variation of the motion of air bubbles and the fluidized medium which affect the fluid force acting on the sphere in the fluidized bed.     

Rate of CO2 adsorbent attrition induced by gas jets on perforated plate distributors in bubbling fluidized beds

Particle attrition is a major challenge when handling bulk solid materials with fluidized beds due to its ability to cause particle loss. Herein, the particle attrition induced by the gas jets on a perforated plate distributor in a bubbling fluidized bed was investigated for CO₂ adsorbent particles. An attrition tube, which used air as the fluidizing gas, was used as the fluidized bed. At a constant fluidizing velocity, the initial static bed height and orifice gas velocity were considered as variables. It was confirmed that abrasion dominated the particle attrition. The trend indicating the change in the maximum size of the particles (d_pm,a) formed by attrition followed that of the attrition rate (i.e., the formation rate of fine particles via attrition). A new stirring factor that combined the model developed by Werther and Xi with the original stirring factor adequately explained the effect of the static bed height on both the attrition rate and d_pm,a when the initial static bed height was greater than the length of the orifice gas jet that penetrated the bed. The attrition rate increased linearly with the new stirring factor. However, d_pm,a increased exponentially with the new stirring factor. Relationships were successfully proposed to enable the estimation of the attrition rate and d_pm,a for the CO₂ adsorbent particles. This study provided the evidence indicating the significance of the effect of bed height on particle attrition induced by the gas jet on the distributor. Moreover, proper models for correlating the attrition rate and the maximum size of the fine particles formed by attrition in the bubbling fluidized bed were provided.     

Time behavior of heat fluxes in thermally coupled turbulent dispersed particle flows

The effect on heat transfer produced by injection of solid microparticles with high thermal capacity in turbulent channel flow is analyzed. Convection is forced by letting the fluid flow between a hot plate and a cold plate under zero-gravity conditions. An Eulerian?CLagrangian approach based on direct numerical simulation of turbulence (shear Reynolds number Re*?=?150 and molecular Prandtl number Pr?=?3) and on point-particle tracking is used. Full momentum and energy coupling between fluid and particles is considered. Different particle sizes and different particle concentrations are examined.     

Experimental study on fluidization characteristics of different-sized particles in a U-type reduction chamber

A novel fluidized bed reactor, which is an improvement of the loop seal, was applied successfully to iron ore reduction roasting. For this U-type reduction chamber, the fluid dynamic behaviors of different-sized particles were investigated via a cold experimental apparatus using the pressure measurement method in this study. The results showed that the measured U_mf of 71, 101 and 147 μm-sized particles were 0.033, 0.040 and 0.059 m/s, while the U_c were 0.167, 0.190 and 0.223 m/s, respectively, demonstrating that the decrease of particle size caused a rapid transition from both the fixed to bubbling regime, and the bubbling to turbulent flow regime. Under stable operation, the pressure drop, average solids holdup and axial nonuniformity index across the FC increased when particle size increased, along with the solids height and pressure drop gradient in the SC, though the differential pressure fluctuation decreased. These consequences indicated that larger particle size promotes the opportunity for particle mixing and contacting, accordingly increasing the preferential formation of the particle aggregation and deteriorating the reduction performance. These can provide guidelines for the regulation and control of industrial iron ore fluidized bed roasting.     

Direct measurement of particle–particle interaction using micro particle interaction analyzer (MPIA)

Direct particle–particle contact force measurement was successfully conducted for realistic parameter determination to support discrete element method (DEM) simulation by using a newly developed force measurement of micro particle interaction analyzer (MPIA). In this system particle-to-particle distance and deformation can be controlled by nanometer accuracy. The system can be used for measuring not only short-distance deformation but also long-distance deformation that was validated by both elastic contact and liquid bridge interaction including rupture distance, respectively. Then, the system was applied to obtain plastic normal deformation characteristics such as coefficients of restitution of the spherical granules at low loading force less than 0.5 mN. Granules were prepared from two-stage pressure swing granulation (PSG) technique in a fluidized bed.     

Growth kinetics in particle coating by top-spray fluidized bed systems

The kinetics of growth for the coating of particles in top- spraying fluidized bed systems is reported. The results indicated that only a small amount of particles that visited the spraying region are coated at a time. It was also revealed that different particle sizes are not equally coated during the process. In a polydispersed particle distribution, smaller particles were found to receive more coating than their larger counterparts. This preferential coating, which was associated with a rapid decrease in the distribution variance, is more pronounced in the earlier parts of the process. When a narrower seed distribution was used, the preferential coating was reduced. A segregation factor, f_s, was introduced in the development of a growth kinetics model to represent the chance of each particle size visiting the coating region. The result for the distribution from the model clearly resembled the results obtained experimentally. For the top-spraying process, the segregation factor was found to be an exponentially decaying function of particle weight. For lactose particles coated with hydroxypropyl methyl cellulose, two different rates of growth were observed during the coating process.     

Influence of particle size on the exit effect of a full-scale rolling circulating fluidized bed

This paper investigated the influence of particle size on the exit effect of a full-scale rolling circulating fluidized bed (CFB) by using the Computational Fluid Dynamics-Discrete Element Method (CFD-DEM) method. The gas–solid two-phase flow of the full-scale rolling CFB was compared with that of a simplified rolling CFB. Thus, the exit effect of the full-scale rolling CFB was clarified. In the air phase, a peak of air axial velocity v_ya was observed when the full-scale rolling CFB reached the maximum angular displacement. The particle phase possessed back mixing and radial exchange phenomena at the top and bottom of the full-scale rolling CFB, respectively. However, those phenomena were not obvious at the top and bottom of the simplified rolling CFB. The mechanism of the above-mentioned exit effect was then clarified by analyzing the forces acting on the particles under different particle sizes. Finally, the increases in particle size lead to the intensification of the peak of v_ya, particle back mixing, and radial exchange phenomena. Therefore, the intensity of the exit effect of the gas–solid two-phase flow increased as the particle size increased_. The results suggested that the small particles had the potential to promote the purification rate of the full-scale rolling CFB on account of its small exit effect.     

Drag,lift and torque acting on a two-dimensional non-spherical particle near a wall

Gas-solid granular flows with non-spherical particles occur in many engineering applications such as fluidized beds. Such flows are usually contained by solid walls and always some particles move close to a wall. The proximity of a wall considerably affects the flow fields and changes the hydrodynamic forces and torque acting on particles moving near the wall. In this paper, we numerically investigate the drag, lift and torque acting on a non-spherical particle in the vicinity of a planar wall by means of lattice Boltzmann simulations. To gain an exhaustive understanding of the complex hydrodynamics and study the influence of various geometrical and flow parameters, a single 2D elliptical particle is selected as our case study. In the simulations, the effect of particle Reynolds number, distance to the wall, orientation angle and aspect ratio on drag, lift and torque is studied. Our study shows that the presence of a wall causes significant changes in hydrodynamic forces, with increasing or decreasing drag and lift forces, depending on the distance from the wall. Even the direction of lift and torque may change, depending on both the distance from the wall and particle orientation angle. Also, an ellipse with higher AR experiences larger hydrodynamic forces and torque whatever the gap size and orientation angle.     

The yield stress of jammed magnetofluidized beds

By means of a magnetic field externally imposed, fluidized beds of magnetizable particles may experience a transition from a fluidlike unstable to a solidlike stable state. In our work, measurements have been taken of the gas velocity and particle volume fraction at the jamming transition as well as of the tensile yield stress of the stabilized bed subjected to a small consolidation. The influence of diverse physical parameters such as initialization mode, magnetic field orientation, average particle size and size polydispersion, are analyzed. Noninvasive visualization of the bed structure has revealed that magnetic stabilization is determined by the formation of particle chains. Due to the enhancement of the interparticle attractive force with field strength and particle size, the transition to stability takes place at higher gas velocities as the magnitude of these parameters is increased. The magnetic yield stress of magnetofluidized beds of naturally aggregated particles because of a large presence of fines is significantly larger than that corresponding to naturally nonaggregated particles. Moreover, the jamming transition occurs at larger gas velocities (or smaller field strengths) in the former case since the agglomerates behave magnetically as large effective particles. The effect of the magnetic field on the yield stress ia only relevant when it is applied during initialization of the bed in the bubbling regime and particles are free to move and restructure in chains. Measurements of the yield stress are presented when the applied magnetic field is oriented either in the vertical or horizontal direction (B co-flow and B cross-flow modes, respectively). The variation of the magnetic yield stress with particle size was found to be dependent on the field direction. This can be justified by the dependence of the interparticle magnetic force on the chain average angle with the field, which is affected by particle size as the stabilized bed is subjected to small consolidations.     

Experimental study on the fluidization discharging characteristics of Geldart-C kaolin powders in a blow tank with pulsed gas

Kaolin powders have been suggested to be able to adsorb heavy metal vapor from coal-fired flue gas. However, due to the influence of inter particle forces, such as liquid bridge force, it is difficult to realize stable pneumatic conveying. In the present work, the fluidization characteristics of kaolin powders were investigated. A series of unstable flow phenomena such as agglomeration, channeling, and slugging occurred during the fluidization process. Also, the fluidization discharging characteristics of kaolin powder in an optimized blow tank were experimentally studied. The results indicated that the introduction of pulsed gas can effectively destroy agglomeration and thus improving the stability of discharging. Visual experiments in pseudo-2D fluidized bed were also confirmed the destructive effect of pulsed gas on agglomeration. With an increase in either fluidization gas velocity U_f or pulsed gas velocity v_pulsed, the mass flow rate of kaolin powder G first increased and then decreased. Finally, drying experiments demonstrated that there is free water on the surfaces of the kaolin powders. The analysis of forces indicated that the liquid bridge force F_lb between particles is much larger than the particle gravity F_g. The liquid bridge force might be one of key reasons for kaolin powder agglomerating.     

Dynamic forces on an immersed cylindrical tube and analysis of particle interaction in 2D-gas fluidized beds

The interactions of bubbles and particles with fixed cylindrical tubes in two-dimensional fluidized beds were investigated by experiments and by simulations, based on results for single bubbles impinging on a tube. The experimental results based on PIV analysis support our previous force origin model and indicate that the model is able to successfully model bubble behavior and particle motion around fixed objects. The simulation results give useful predictions, dynamic force induced on a tube consists of the force from pressure gradient, fluid viscous force and particle contact force. The predominant force component is from the pressure gradient. As bubbles directly interact with a tube, the particle contact force contribution briefly becomes predominant.Bubble behavior and particle motion are greatly affected by the state of the emulsion phase as the medium of the fluidized bed into which gas is injected. Hence the dynamic forces on immersed objects are directly affected by the state of the emulsion phase.     

Experimental and Simulation Studies of Dilute Horizontal Pneumatic Conveying

Dilute horizontal pneumatic conveying has been the subject of this experimental and numerical study. Experiments were performed utilising a 6.5 m long, 0.075 m diameter horizontal pipe in conjunction with a laser-Doppler anemometry (LDA) system. Spherical glass beads with three different sizes 0.8–1 mm, 1.5 mm, and 2 mm were used. Simulations were carried out using the commercial discrete element method (DEM) software, EDEM, coupled with the computational fluid dynamics (CFD) package, FLUENT. Experimental results illustrated that, for mass solid loading ratios (SLRs) ranging from 2.3 to 3.5, the higher the particle diameter and solid loading ratio, the lower the particle velocity. From the simulation investigations it was concluded that the inclusion of the Magnus lift force had a crucial influence, with observed particle distributions in the upper part of the conveying line reproducible in the simulation only by implementing the Magnus lift force terms in the model equations.