Three-dimensional numerical simulation method for gas–solid injector

A three-dimensional turbulent gas–solid two-phase flow model for a gas–solid injector is developed in the present study. Time-averaged conservation equation for mass and momentum and a two-equation k– closure are used to model the carried fluid phase. The solid phase is simulated by using a Lagrangian approach. In this model, the drag and lift forces on particles, the multi-body collisions among particles and the mutual interaction between gas and particles were taken into account. Interparticle interactions and particle–wall collisions are emulated by using the three-dimensional distinct element method (DEM). A new correlation, which represents the transfer of kinetic energy of the particle motion to kinetic energy of the carrier fluid, is introduced in the additional source term S_d of the transport equation of turbulence kinetic energy, K. The calculated pressure distributions along the axis in the different parts of gas–solid injectors using pressured pneumatic conveying system under different driving jet velocities, pressures and values of angle of convergent section () are found to be in agreement with the experimental results. The axial mean velocity of particles and the behavior of gas and particles in the gas–solid injector are calculated, their results reasonably explaining actual phenomenon observed in experiment.     

Effect of cohesive forces on fluidized and spouted beds of wet particles

Fluid beds are now being used for processing pasty materials including production of fine powders through drying suspensions in beds of inert particles; coating of tablets or pellets; granulation, etc. In such processes, the fluid bed operation becomes more complex due to the development of cohesive forces resulting from liquid bridges between particles. Such forces can affect gas and solids flow leading to uncontrollable particle agglomeration and to poor gas–solid contact. This work is aimed at analyzing and quantifying the differences of flow behavior in fluidized and spouted beds of wet and dry particles. Experimentally, surface stickiness is induced by application of metered amounts of glycerol. Based on pressure drop vs. fluid flow rate curves, solids circulation rates and bed porosity variations, two types of particle–particle interaction forces are identified and their effect on air–solid flow is quantified as a function of glycerol concentration. Implications of these results in coating, granulation and drying of suspensions in these beds are also discussed.     

Lateral migration of spherical particles in porous flow channels: application to membrane filtration

Lateral migration of spherical rigid neutrally buoyant particles moving in a laminar flow field in a porous channel is induced by an inertial lift force (tubular-pinch effect) and by a permeation drag force due to convection into the porous walls. The analysis of Cox and Brenner [7], for the particle motion in a nonporous duct is extended to include the effect of the wall porosity. Criteria are established under which the inertial and permeation drag force in the lateral direction can be vectorially added. Particle trajectories and concentrations profiles are calculated for a plane Poiseuille flow with one porous wall. For particles with radius of 1 μm, inertial and permeation drag forces are of comparable size under flow conditions often met in ultra- and hyperfiltration of dilute suspensions. For smaller particles the permeation drag force dominates.     

The mechanism model of gas–liquid mass transfer enhancement by fine catalyst particles

In order to present the enhancement of gas–liquid mass transfer by heterogeneous chemical reaction near interface, the mechanism model has been proposed to describe the mass transfer rate for a gas–liquid–solid system containing fine catalyst particles. The composite grid technique has been used to solve the model equations. With this model the effect of particle size, first-order reaction rate constant, distance of particle to gas–liquid interface and residence time of particle near gas–liquid interface on the mass transfer enhancement have been discussed. The particle–particle interaction and slurry apparent viscosity can be considered in the model. The experimental data have been used to verify the model, and the agreement has been found to be satisfied.     

Drag force in discrete particle models—Continuum scale or single particle scale?

Unresolved discrete particle (DP) models, where a Lagrangian method is used for the solid phase, and a Eulerian method for the fluid phase, have become increasingly popular. The fluctuations of the drag force on individual particles in a homogeneous random array obtained from fully resolved simulations using a lattice Boltzmann method were analysed; such fluctuations are by construction ignored in the unresolved DP model. The drag on individual particles in the array can differ up to 40% with the drag that would be used in DP type simulations was found. A detailed analysis shows that the drag on an individual particle depends strongly on all its surrounding neighbors within a distance of at least two particle diameters. As in DP models, the local flow field is unresolved, the conclusion is that this root mean square (RMS) deviation in the drag force is inherent to the model. © 2012 American Institute of Chemical Engineers AIChE J, 59: 316–324, 2013     

Numerical simulations of ultrafine powder coating systems

Numerical simulations for gas–solid two-phase flows were conducted for an experimental coating booth and an industrial coating booth to study the effect of the coating powder size on the performance of the coating process. To optimize coating parameters, simulations were conducted for different coating parameters, such as the size of the coating part, the distance between the coating part and the spray gun, the air flow rate and particle flow rate from the spray gun, the position of the pattern adjust sleeve of the spray gun, and the electrostatic field, in order to increase the coating process efficiency and coating quality.

In numerical simulations, the air flow field is obtained by solving three-dimensional Navier–Stokes equations with standard κ– turbulence model and non-equilibrium wall function. The second phase, the coating powder, consists of spherical particles and is dispersed in the continuous phase, the air. In addition to solving transport equations for the air, the trajectories of the particles are calculated by solving the particle motion equations using Lagrangian method. It is assumed that the particle–particle interaction can be neglected due to low particle volume fraction in coating systems. The electrostatic field is predicted by solving the Laplace equation.     

Numerical evaluation of virtual mass force coefficient of single solid particles in acceleration

Virtual mass force is an indispensable component in the momentum balance involved with dispersed particles in a multiphase system.In this work the accelerating motion of a single solid particle is math-ematically formulated and solved using the vorticity-stream function formulation in an orthogonal curvi-linear coordinate system.The total drag coefficient was evaluated from the numerical simulation in a range of the Reynolds number (Re) from 10 to 200 and the dimensionless acceleration (A) between-2.0 to 2.0.The simulation demonstrates that the total drag is heavily correlated with A,and large decel-eration even drops the drag force to a negative value.It is found that the value of virtual mass force coef-ficient (Cv) of a spherical particle is a variable in a wide range and difficult to be correlated with A and Re.However,the total drag coefficient (Coy) is successfully correlated as a function of Re and A,and it increases as A is increased.The proposed correlation of total drag coefficient may be used for simulation of solid-liquid flow with better accuracy.     

Mixing and segregation in a bidisperse gas–solid fluidised bed: a numerical and experimental study

In many industrial applications of dense gas–solid fluidised beds, mixing and segregation phenomena play a very important role. The extent of mixing and segregation is strongly influenced by the bubble characteristics. Therefore, the extent of mixing and segregation, induced by a single bubble injected in a monodisperse and bidisperse fluidised bed at incipient fluidisation conditions and in freely bubbling fluidised beds has been studied both with well-defined experiments and with a 3D Euler–Lagrangian model. Particle image velocimetry (PIV) was successfully applied to obtain the ensemble averaged particle velocity profile in the vicinity of the bubble in dense gas–solid fluidised systems.

The bubble size of a single injected bubble in a fluidised bed at minimum fluidisation conditions calculated with a 3D discrete particle model (DPM) depended strongly on the selected gas-particle drag model. The widely used Ergun equation combined with the Wen and Yu [Powder Technol. 98 (1998) 38; Chem. Eng. Sci. 47 (1992) 1913] relations overpredicted the bubble size due to an overprediction of the drag force. The DPM with the drag model proposed by Koch and Hill [Annu. Rev. Fluid Mech. 33 (2001) 619], based on Lattice–Boltzmann simulations, gave much better agreement with the experimental findings.

The segregation rates in a bidisperse freely bubbling fluidised bed predicted by the DPM agreed very well with the experimentally measured segregation rates by Goldschmidt [M.J.V. Goldschmidt, Hydrodynamic modelling of fluidised bed spray granulation, PhD thesis, Twente University, 2001].     

Effect of particle orientation on the drag force in random arrays of prolate ellipsoids in low-Reynolds-number flows

Direct numerical simulations are performed to study the effect of particle orientation on flows through fixed random arrays of prolate ellipsoids at low Reynolds numbers. The Hermans orientation factor and Beta distribution are introduced to quantify the mean orientation and orientation deviation of the particles. The simulation results show that the effect of particle orientation is profound especially when the solid volume fraction and the aspect ratio are large. With the increase of Hermans orientation factors, the drag force decreases when the flow follows a reference direction defined by the average direction of all particles' semi-major axes, while increases when the flow is perpendicular to the reference direction. Comparisons show that the traditional drag force correlations for ellipsoidal particles significantly under-predict the drag force. Based on current simulation results, new drag relations are proposed for prolate ellipsoidal particles at arbitrary aspect ratios, Hermans orientation factors and solid volume fractions.     

Measurement of the Aerodynamic Drag Force on Single Aerosol Particles

The “picobalance” (quadrupole) was used to measure the aerodynamic drag force on individual solid particles and droplets by suspending the object in a laminar jet of gas introduced through the bottom electrode. Particles ranging in diameters from about 1 to 150 μm can be studied in this manner. The DC voltage required to maintain the particle position against the opposing forces of aerodynamic drag and gravity was measured to determine the drag force. The flow velocity at which the aerodynamic drag force balances the gravitational force yields information on the aerodynamic size, and the DC voltage required to suspend the particle against gravity with no flow provides a measure of the particle mass. Particle mobilities for spherical and irregularly shaped solids are presented. Light-scattering measurements for spherical particles provide an independent determination of size; the results are generally in good agreement with the aerodynamic size. It is shown that the electrodynamic balance can be used to measure drag forces much larger than the particle weight.     

Particle‐resolved direct numerical simulation of gas–solid dynamics in experimental fluidized beds

Particle‐resolved direct numerical simulations (PR‐DNS) of a simplified experimental shallow fluidized bed and a laboratory bubbling fluidized bed are performed by using immersed boundary method coupled with a soft‐sphere model. Detailed information on gas flow and individual particles’ motion are obtained and analyzed to study the gas–solid dynamics. For the shallow bed, the successful predictions of particle coherent oscillation and bed expansion and contraction indicate all scales of motion in the flow are well captured by the PD‐DNS. For the bubbling bed, the PR‐DNS predicted time averaged particle velocities show a better agreement with experimental measurements than those of the computational fluid dynamics coupled with discrete element models (CFD‐DEM), which further validates the predictive capability of the developed PR‐DNS. Analysis of the PR‐DNS drag force shows that the prevailing CFD‐DEM drag correlations underestimate the particle drag force in fluidized beds. The particle mobility effect on drag correlation needs further investigation. © 2016 American Institute of Chemical Engineers AIChE J, 62: 1917–1932, 2016     

Direct numerical simulations of dynamic gas‐solid suspensions

Direct numerical simulation results for gas flow through dynamic suspensions of spherical particles is reported. The simulations are performed using an immersed boundary method, with careful correction for the grid resolution effect. The flow systems we have studied vary with mean flow Reynolds number, solids volume fraction, as well as particle/gas density ratio. On the basis of the simulation results, the effect of particle mobility on the gas‐solid drag force is analyzed and introduced into the existing drag correlation that was derived from simulations of stationary particles. This mobility effect is characterized by the granular temperature, which is a result of the particle velocity fluctuation. The modified drag correlation is considered so‐far the most accurate expression for the interphase momentum exchange in computational fluid dynamics models, in which the gas‐solid interactions are not directly resolved. © 2016 American Institute of Chemical Engineers AIChE J, 62: 1958–1969, 2016     

Discrete particle simulation of gas fluidization of ellipsoidal particles

Fluidization is widely used in industries and has been extensively studied, either experimentally or theoretically, in the past decades. In recent years, a coupled simulation approach of discrete element method (DEM) and computational fluid dynamics (CFD) has been successfully developed to study the gas–solid flow and heat transfer in fluidization at a particle scale. However, to date, such studies mainly deal with spherical particles. The effect of particle shape on fluidization is recognized but not properly quantified. In this paper, the CFD–DEM approach is extended to consider the fluidization of ellipsoidal particles. In the simulation, particles used are either oblate or prolate, with aspect ratios varying from very flat (aspect ratio=0.25) to elongated (aspect ratio=3.5), representing cylinder-type and disk-type shaped particles, respectively. The commonly used correlations to determine the fluid drag force acting on a non-spherical particle are compared first. Then the model is verified in terms of solid flow patterns. The effect of aspect ratio on the flow pattern, the relationship between pressure drop and gas superficial velocity, and microscopic parameters such as coordination number, particle orientation and force structure are investigated. It is shown that particle shape affects bed permeability and the minimum fluidization velocity significantly. The coordination number generally increases with aspect ratio deviating from 1.0. The analysis of particle orientations shows that the bed structures for ellipsoids are not random as that for spheres. Oblate particles prefer facing upward or downward while prolate particles prefer horizontal orientation. Spheres have the largest particle–particle contact force and fluid drag force under the comparable conditions. With aspect ratio deviating from 1.0, particle–particle interaction and fluid drag become relatively weak. The proposed model shows a promising method in examining the effect of particle shape on different flow behaviour in gas fluidization.     

颗粒特性对撞击分离器性能影响的实验与数值研究

颗粒-壁面撞击行为和气固相间作用对撞击分离器的性能具有重要影响。基于玻璃珠及煤粉的单颗粒撞击实验数据建立平均撞击恢复系数模型,采用非球形颗粒曳力模型对平板式撞击分离器的分离性能和气固流动开展数值研究。结果表明,采用基于实验的平均恢复系数模型以及考虑颗粒形状的曳力模型,能够准确地预测撞击式分离器的总分离效率和分级分离效率。颗粒分离过程中,Stokes数较大的颗粒对颗粒-壁面撞击模型比较敏感,Stokes数较小的颗粒对气固曳力模型比较敏感。     

Measurement and analysis of particle—particle interaction in a cocurrent flow of particles in a dilute gas—solid system

The experimental apparatus of Arastoopour et al.[3] was modified to measure pressure drop and solid velocities for cocurrent flow of particles in a pneumatic conveying line. The data were translated into particle—particle interaction expression using a force balance over the particles. The particle interaction is a combination of collision and drag force in a particles low relative velocity region. A correlation for particle—particle interaction with relative velocity between the particles of 0.3–4.6 m/s has been developed. The correlation describes our experimental data within the 10% deviation.     

Computational investigation of the mechanisms of particle separation and “fish‐hook” phenomenon in hydrocyclones

The motion of solid particles and the “fish‐hook” phenomenon in an industrial classifying hydrocyclone of body diameter 355 mm is studied by a computational fluid dynamics model. In the model, the turbulent flow of gas and liquid is modeled using the Reynolds Stress Model, and the interface between the liquid and air core is modeled using the volume of fluid multiphase model. The outcomes are then applied in the simulation of particle flow described by the stochastic Lagrangian model. The results are analyzed in terms of velocity and force field in the cyclone. It is shown that the pressure gradient force plays an important role in particle separation, and it balances the centrifugal force on particles in the radial direction in hydrocyclones. As particle size decreases, the effect of drag force whose direction varies increases sharply. As a result, particles have an apparent fluctuating velocity. Some particles pass the locus of zero vertical velocity (LZVV) and join the upward flow and have a certain moving orbit. The moving orbit of particles in the upward flow becomes wider as their size decreases. When the size is below a critical value, the moving orbit is even beyond the LZVV. Some fine particles would recircuit between the downward and upward flows, resulting in a relatively high separation efficiency and the “fish‐hook” effect. Numerical experiments were also extended to study the effects of cyclone size and liquid viscosity. The results suggest that the mechanisms identified are valid, although they are quantitatively different. © 2009 American Institute of Chemical Engineers AIChE J, 2010     

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.     

Experimental and computational study of gas–solid fluidized bed hydrodynamics

The hydrodynamics of a two-dimensional gas–solid fluidized bed reactor were studied experimentally and computationally. Computational fluid dynamics (CFD) simulation results from a commercial CFD software package, Fluent, were compared to those obtained by experiments conducted in a fluidized bed containing spherical glass beads of 250– in diameter. A multifluid Eulerian model incorporating the kinetic theory for solid particles was applied in order to simulate the gas–solid flow. Momentum exchange coefficients were calculated using the Syamlal–O’Brien, Gidaspow, and Wen–Yu drag functions. The solid-phase kinetic energy fluctuation was characterized by varying the restitution coefficient values from 0.9 to 0.99. The modeling predictions compared reasonably well with experimental bed expansion ratio measurements and qualitative gas–solid flow patterns. Pressure drops predicted by the simulations were in relatively close agreement with experimental measurements at superficial gas velocities higher than the minimum fluidization velocity, U_mf. Furthermore, the predicted instantaneous and time-average local voidage profiles showed similarities with the experimental results. Further experimental and modeling efforts are required in a comparable time and space resolutions for the validation of CFD models for fluidized bed reactors.     

Use of numerical modeling in design for co-firing biomass in wall-fired burners

Co-firing biomass with coal or gas in the existing units has gained increasing interest in the recent past to increase the production of environmentally friendly, renewable green power. This paper presents design considerations for co-firing biomass with natural gas in wall-fired burners by use of numerical modeling. The models currently used to predict solid fuel combustion rely on a spherical particle shape assumption, which may deviate a lot from reality for big biomass particles. A sphere gives a minimum in terms of the surface-area-to-volume ratio, which impacts significantly both motion and reaction of a particle. To better understand the biomass combustion and thus improve the design for co-firing biomass in wall-fired burners, non-sphericity of biomass particles is considered. To ease comparison, two cases are numerically studied in a long gas/biomass co-fired burner model. (1) The biomass particles are assumed as solid or hollow cylinders in shape, depending on the particle group. To model accurately the motion of biomass particles, the forces that could be important are all considered in the particle force balance, which includes a drag for non-spherical particles, an additional lift due to particle non-sphericity, and a “virtual-mass” force due to relatively light biomass particles, as well as gravity and a pressure-gradient force. Since the drag and lift forces are both shape factor- and orientation-dependent, coupled particle rotation equations are resolved to update particle orientation. To better model the reaction of biomass particles, the actual particle surface area available and the average oxygen mass flux at particle surface are considered, both of which are shape factor-dependent. (2) The non-spherical biomass particles are simplified as equal-volume spheres, without any modification to the motion and reaction due to their non-sphericity. The simulation results show a big difference between the two cases and indicate it is very significant to take into account the non-sphericity of biomass particles in order to model biomass combustion more accurately. Methods to improve the design for co-firing biomass in wall-fired burners are finally suggested.