Comparison of numerical simulations and experiments in conical gas-solid spouted

Shuyan Wang *,Baoli Shao 2,Rui Liu Jian Zhao Yang Liu Yikun Liu Shuren Yang

1 School of Petroleum Engineering,Northeast Petroleum University,Daqing 163318,China

2 Institute of Petroleum Chemical,Jilin University of Chemical Technology,Jilin 132022,China

Keywords:Fluidization Simulation Experiment Conical spouted bed Drag coef ficient model Computational fluid dynamics

ABSTRACT Flowbehavior ofgas and particles in conicalspouted beds is experimentally studied and simulated using the twofluid gas-solid model with the kinetic theory of granular flow.The bed pressure drop and fountain height are measured in a conicalspouted bed of 100 mm I.D.atdifferentgas velocities.The simulation results are compared with measurements of bed pressure drop and fountain height.The comparison shows that the drag coef ficient model used in cylindrical beds under-predicted bed pressure drop and fountain height in conical spouted beds due to the partial weight of particles supported by the inclined side walls.It is found that the numerical results using the drag coef ficient model proposed based on the conical spouted bed in this study are in good agreement with experimentaldata.The presentstudy provides a usefulbasis for further works on the CFDsimulation ofconical spouted bed.

1.Introduction

Spouted beds are often used in various industrial processes of gassolid contacting operations,such as drying,coating,granulation,pyrolysis and gasi fication.This is because the signi ficant advantage is their ef ficiency in contacting gas and coarse particles[1],for example,application ofspouted bed elutriation in the recycling of lithium ion batteries[2],superheated steam drying of sawdust in continuous feed spouted beds[3],bio-oil production from rice husk fast pyrolysis in a conical spouted bed reactor[4],and conical spouted bed combustor for clean valorization of sludge wastes from the paper industry to generate energy[5].Knowledge of gas and particle hydrodynamics in spouted bedsis importantforoptimizing the bed performance[6].Computational fluid dynamics(CFD)is a powerful tool for investigating the complex hydrodynamics and reaction kinetics,that is dif ficult to observe by experiments[7,8],in particular in spouted beds.

Now there are growing interests to use CFD to understand dense gas-solid two-phase flows in spouted beds[9].The Eulerian-Eulerian(two- fluid)model with kinetic theory of granular flow(KTGF)is the most applicable approach to compute gas-solid flow in spouted beds.This model is particularly appropriate when the particle loading is relatively high and can be applied with reasonable computational loads.In the two- fluid model,the particles are treated as a continuum as in the gas phase.Thus,there are two interpenetrating phases(gas and solid)where each phase is characterized by its own conservation equation of motion.The interactions between the two phases are expressed as additional source terms added to the conservation equations.The kinetic theory ofgranular flow is used to de fine the fluid properties of the solid phase through constitutive equations.Detailed discussion on the development of granular flow models is provided by Gidaspow[10].Lu etal.incorporated hydrodynamic modeling with a kinetic-frictionalconstitutive modelofsolids to simulate flow behaviorof gas and particles in spouted beds[11].Zhong et al.investigated flow behaviors of a large spout- fluid bed in a Eulerian-Eulerian frame.The gas phase was modeled with a k-ε turbulent model and the particle phase was modeled with KTGF[12,13].Wu and Mujumdar simulated gasparticle flow behavior in a cylindrical spouted bed and a threedimensional spout- fluid bed using the Eulerian-Eulerian two- fluid modeling approach,incorporating a kinetic-frictional constitutive model for dense assemblies of particulate solids[14].Du et al.investigated the in fluences of drag coef ficient correlations,frictional stress,maximum packing limit and restitution coef ficient on the CFD simulation of spouted beds based on a gas-solid two- fluid approach using FLUENT[15].Bettega et al.used the Eulerian-Eulerian 3D modeling to analyze the in fluence of the flat wall on the solid behavior inside a semi-cylindrical spouted bed by comparing numerical results with experimental data[16].Duarte et al.simulated the dynamic behavior of gas and particles in conical and conical-cylindrical spouted beds using KTGF[17].Gryczka et al.characterized the hydrodynamics of a prismatic spouted bed apparatus by applying the gas-solid two- fluid approach with KTGF[18].Wang et al.discussed the impact of frictional stresses on the gas-solid flow by using a two- fluid model with the kineticfrictional constitutive model of particles[19],and then simulated the flow behavior of gas and particles in spouted beds with a draft tube[20]and porous draft tube[21],respectively.An integrated granular phase source term was introduced into the momentum balance equation of the solid phase in the annulus region to simulate different flow patterns in the conical spouted bed[22].Simulations show that the pro files of local velocity and solid volume fraction are required to use the source term that was obtained from the measured overall pressure drop over the spouted bed.Simon etal.introduced a new closure for the solid stress tensor for KTGF based on a two- fluid model to predict the flow in multiple-spout beds[23].In their study,the impact of the solid shear stresses and the flux of fluctuation energy on boundary conditions were investigated.

Simulations mentioned above were compared to radialsolid volume fraction distributions measured in spouted beds.Also,the comparisons of bed pressure drop between simulation and experiment are also required in spouted beds.In the present work,the bed pressure drop is measured in the conical spouted bed,and compared to simulations at various inlet gas velocities.In a conical based spouted bed,the partial weight of particles is supported by the inclined side walls,which causes the interaction force between the inclined walls and gas-particle mixture to vary in the vertical direction.To include the additional interaction force exerted by the tapered side wall on the gas-solid flow,a modi fied drag coef ficient model is proposed based on the Ergun equation from the dynamic balance of forces exerted on particles in the conical spouted bed.The present drag coef ficient model is an extension from cylindrical bed to conical bed.Flow behavior of gas and particles is simulated using a two- fluid model based on KTGF.The model is validated experimentally with comparison to numerical simulations.

2.Experimental Setup

Experiments were conducted in a conical spouted bed,as shown in Fig.1.The spouted bed was a cylindricalcolumn with an inside diameter of 155 mm and a heightof 0.8 m,and with a tapering angle of 60°in the conical base with a height of 0.09 m.It was made of Perspex sheet to allow visual observation.The diameter of the conical base at the bottom was 15 mm.A 60-mesh screen at the bottom served as the support as well as the air distributor.Two pressure taps,one just above the distributor and the other at the top of the bed were provided to record the bed pressure drop.The bed pressure drop was measured by a manometer.Air at a temperature ofaround 28°C was used as the fluidizing medium.It was passed through a silica gel tower to remove the moisture and a valve to control the air flow before entering the spouted bed.Two rotameters,one for the lower range(0-10 m3·h-1)and the other for the higher range(10-120 m3·h-1),were used to measure the air flow rates.Fluid cracking catalyst(FCC)particles with a diameter of 175.0 μm and density of 1650 kg·m-3,belonging to group A of the Geldart powder classi fication.Particles were fluidized with air at atmospheric pressure.The flow regime diagram of gas-solid reactors covers the operation of fixed and moving beds,conventional fluidized beds,circulating beds,spouted beds,and pneumatically conveyed suspensions.Reh proposed the fluidized bed regime diagram between groups A and B and between groups B and D of the Geldart powder classi fication scheme[24].In our study,the velocity range of spouted beds is from 0.031 to 0.1869 m·s-1in the phase diagram.

Fig.1.Experimental set-up of spouted bed.

3.CFD Model for Spouted Beds

The two- fluid model(TFM)is applied to simulate the complex gassolid flow in conical spouted beds.By the TFM approach,the gas and solid phases are treated mathematically as continuous and mutually interpenetrating.For simplicity,it is further assumed that flow is isothermalwithoutreactions,the gas phase is incompressible,and particles are spherical and monosized.

The Eulerian approach is used for both gas and particle phases within the spouted bed,taking into account all possible intra-and inter-phase interactions.In this work,the governing equations for the conservation of mass and momentum for each phase and the constitutive relations are given in Table 1.The mass balance equation of the gas phase is expressed by Eq.(T-1).In the gas phase momentum equation Eq.(T-3),the gas-phase stress tensor is calculated according to Newton's expression of Eq.(T-6).For simplicity,the constant viscosity of the gas phase is used in the present simulations.

The continuity equation of the particles is Eq.(T-2).The momentum equation of particles is Eq.(T-4),where the second term on the righthand side(RHS)is the solid pressure which includes the collisional part ps,kand frictional part ps,f.The third term represents the solid stresses.The remaining terms on the RHS represent the in fluence of the forces acting on particles.As for the conical base,the momentum equation of mixture of particles and gas is expressed by Eq.(T-5)at the steady state,where the last term on the RHS is the stress frictions originated from the wall of conical base by the gas phase and particles.Dtin Eq.(T-5)is the equivalent diameter,de fined as Dt=D0-D1,where D0is the top diameter of the conical base,and D1is the bottom diameter.In addition to the mass and momentum conservation equations for the solid phase,a fluctuation kinetic energy equation,Eq.(T-6),is also solved to accountforthe conservation of the fluctuation energy of the particle phase,through the implementation of the kinetic theory of granular flow(KTGF)[10].In principle,KTGF derived from the kinetic theory of dense gas,where the thermodynamic temperature is replaced by the granular temperature,de fined as θ = ＜c2＞/3,where c is the particle fluctuating velocity.The granular temperature expresses the macroscopic kinetic energy ofrandomparticle motion.Amore complete discussion of the implemented kinetic theory model can be found in Gidaspow[10].

At high concentrations of particles,individual particles interact with multiple neighbors through sustained contact.Under such conditions,the normal forces and the associated tangential frictional forces of sliding contact are the major contributions to the particle stresses.Following Savage[25],the particulate stress tensor,τs,is simply the sum of the kinetic stress tensor and the frictional stress tensor.Therefore,an additional frictional solid pressure ps,fand viscosity μs,fare added to the solid pressure and solid viscosity[24].For the frictional pressure of particles,the semi-empirical model proposed by Johnson&Jackson[26]is used,as given in Eq.(T-10),where F,n and p are empirical material constants.The values of empirical parameters of εs,min,F,n and p are taken to be 0.5,0.05,2.0 and 5.0 for glass beads,respectively[26].

The frictional viscosity is related to frictional solid pressure in an expression proposed by Schaeffer[27],as given in Eq.(T-12),where ψ isthe angle of internal friction and I2Dis the second invariant of the strain rate tensor.The value of ψ is taken to be 28.5°for glass beads[19].

Table 1 Mathematical model of gas-solid flow in conical spouted beds

In a conical based spouted bed,there exist three distinct regions:a dilute core,a dense annular region between the core and the wall,and a dilute hump region above the bed surface.This means that the bed should be divided mainly into two regions:a fluidized region(including both the core and the hump)and a de fluidized region(annulus)with high volume fraction of particles in the numerical simulations.Thus,the partial weight of particles is supported by the inclined side wall.This,in turn,causes the interaction force between the inclined walls and gas-particle mixture to vary in the vertical direction.To include the additional interaction force exerted by the tapered side wall on the gas-solid flow,the source terms are introduced with the following form:

where ΔP is the bed pressure drop which is calculated by the Ergun equation[28].Kais the ratio of the pressure drop in a conical spouted bed to that in a column fluidized bed.The drag model plays an important role in gas-solid two phase flow[29].Thus,the drag force in the conical spouted bed is predicted by Eq.(T-19)at εg＜ 0.8.When the gas volume fraction is more than 0.8 in the dilute regime,the drag coef ficient is obtained from the correlation Eq.(T-20)of Wen and Yu[30],and the drag coef ficient is expressed by Eq.(T-18).

To solve the equations listed in Table 1,the boundary conditions for the velocities of gas and solids and the granular temperature are needed.At the inlet,all velocities and concentrations of gas are speci fied.At the outlet,the pressure is that of the ambient atmosphere.Initially,the concentration of particles in the conical spouted bed is given,and the gas velocity inside the conical spouted bed is set to zero.At an impenetrable wall,the gas tangential and normal velocities are set to zero(no slip condition).The normal velocity of particles is also set to zero at the wall.The boundary conditions for the tangential velocity and granular temperature of the solid phase at the wall are given in Eqs.(T-27)and(T-28),where ewis the coef ficient of restitution at the wall and assumed to be a value of 0.90.

The simulations of conical spouted beds have been carried out with the CFD package FLUENT 14[31].The governing equations mentioned above are solved by a finite control volume technique.The Phase Coupled SIMPLE algorithm,which is an extension of the SIMPLE algorithm for multiphase flow,has been used for the pressure-velocity coupling and correction.For conical spouted beds,the variation of parameters in the tangential direction is negligible compared to the variations in the axial and radial directions.Therefore,2D simulations are performed in this work.The computational domain is the same as the actualconicalspouted bed.Grids have been created in the CADprogram GAMBIT and imported into FLUENT 14.User De fined Functions(UDF)are written to incorporate the present drag coef ficient model into FLUENT.A transient simulation has been adopted,using a very small time step of 0.0001 s with approximately 20 iterations per time step.A convergence criterion of 10-3for each scaled residual component has been speci fied for the relative error between two successive iterations.The transient computation continues to 50 s of actual fluidization time.After 45 s,the flow behavior of particles tends to stabilize,therefore the time-averaged value is obtained by averaging results from 45 to 50 s.

4.Results and Discussions

4.1.Qualitative analysis

Sensitivity of computed gas volume fraction distributions along the bed height to the computational grid size is tested.Fig.2 shows the time-averaged pro files of gas volume fraction obtained with three different grid sizes at the inlet gas velocity of 2.3 m·s-1,where the bed height is measured from the bed bottom.In the conical region,the unstructured meshes are used for an accurate prediction of flow of the gas-particle mixture in FLUENT.The triangularfaces are used in the conical region,resulting in a hybrid mesh.They are designed to ensure that finer grids cover the conical region.The solutions obtained with the mid-grid sizes(i.e.,38456)are nearly identical to the finer grids(i.e.,50562).The mid-grids seem suf ficient to obtain gas volume fractions that are independent of the grid resolution.Thus,the medium grid sizes are used throughout computations to reduce the computation times.

Fig.2.Distribution of time-averaged porosity along axial direction at inlet gas velocity of 2.3 m·s-1.

Fig.3 shows the experimental and simulated flow behavior of particles at the inlet gas velocity of 1.95 m·s-1in the conical spouted bed,and Fig.4 shows that at an inlet gas velocity of 2.3 m·s-1.Simulations clearly show that the flow can be divided into three regions in the slice view:a central spout region,where a stream of particles rises fast upwards;a fountain zone,where particles rise to their highestpositions and then rain back onto the surface of the annulus;and an annular zone between the spout and the column wall,where particles move slowly downwards as a dense phase.Experimental observation indicates that when the injected gas velocity is not high enough(shown in Fig.3),a void is generated only in the lower region along the center axis.As the gas velocity is increased,the heightofthe void zone increases,and eventually reaches the freeboard at a certain threshold gas velocity to form a fountain at the bed top.From Fig.4,it is also visible that with the increase of gas velocity,more particles are conveyed vertically in the spoutregion,causing the fountain to shoot up higher.Many researchers obtained their phase diagrams by plotting the bed height vs.gas velocity to represent the flow transitions to the spouted bed regime[1].Grace gave a phase diagram by plotting dimensionless gas velocity vs.dimensionless particle diameter[32].The phase diagram showed that the spouted bed regime occurred only in a very limited region.From experiments,the fountain can be clearly visualized and the spouting is stably established.At the same time,the flow pattern of conical spouted beds including three regions is clearly observed from simulations.

Fig.3.Flow pattern in the spouted bed at inlet gas velocity of 1.95 m·s-1.

Fig.4.Flow pattern in the spouted bed at inlet gas velocity of 2.3 m·s-1.

4.2.Comparison with experiments

Fig.5 shows the measured bed pressure drops as a function ofinletgas velocity.When the inletgas velocity wasincreased,the bed pressure drop varied following the path typically described by the lines marked as increasing from fixed bed to fluidize bed,or decreasing from fluidized bed to fixed bed.The different regimes are discernable in this figure as described separately as follows:(I) fixed-bed regime—at a low inlet gas velocity,the bed is maintained at a constant solid volume fraction and bed height.The magnitude of bed pressure drop rises fairly steeply with an increase in the inletgas velocity as expected.(II)Partially spouted bed regime—the bed pressure drop reaches a maximum,afterthat,itdeceases with the increase of inlet gas velocity.At the maximum bed pressure drop,the particles in the immediate vicinity of the inlet are lifted since the gas flow rate is suf ficiently high,creating an almostempty cavity containing a relatively small number of particles next to the inlet,that leads to form a partially spouted bed inside the cavity.(III)Fully spouted bed regime—in this regime,the particles in the center ofthe bed accelerate upwards,thus forming a core region with low solid volume fraction,while particles outside the core move downwards at a lower speed,forming an annulus with high solid volume fraction.With a further increase in the flow rate,the fountain is formed,and the bed pressure drop remains essentially constant.(IV)Entrained spouted bed—as the inlet gas velocity increases further,the fountain above the core starts to oscillate horizontally,and particles will be entrained by gas,and carried out of the bed.Small wakes or vortices with solid volume fraction much smaller than that in the core begin to appear inside the core.The boundary between the core and annulus becomes increasingly indistinguishable,and the core gradually breaks up as the flow rate increases further.The magnitude of bed pressure drop decreases slightly.

Fig.5.Measured bed pressure drop in a spouted bed.

Alternatively,with reduction of inlet gas velocity,the flow pattern degenerates from the entrained spouted bed to fully spouted bed,then to partially spouted bed,and finally to the fixed bed,accompanied with the reduction ofthe bed pressure drop.Once again,the different flow regimes can be identi fied in the figure.When the flow rate becomes suf ficiently small,the motionless region continues to enlarge,thus leading to the fixed-bed regime.Also,the bed pressure drop decreases without exhibiting a signi ficant peak when the inlet gas velocity decreases from the spouted bed to the fixed bed.Comparison of the bed pressure dropinletgas velocity curves forspouted bed and partially spouted bed suggests thatthe operation ofa gas-solid conicalspouted bed is history dependent.

Fig.6 indicates that simulations and experiments show the anticipated trend that the bed pressure drop decreases with the increase of inlet gas velocity.The bed pressure drops from experiments and simulations using the drag coef ficient Eq.(T-18)decrease with the increase of inlet gas velocity.From simulations,we found that at the low inlet gas velocity the particles at the center of the bed are fluidized.In contrast,those particles near the inclined walls remain static.The partial masses of particles near the walls will be supported by the inclined wall.As the inlet gas velocity is increased,the fluidized region in the bed enlarges.The core is formed with low solid volume fraction.Particles detached from the walls in the fixed bed can move freely.Allthe particles in the core are considered to be completely suspended in the fluidizing gas.The drag force on the particles is suf ficient to support the weight of particles in the spout.Simulations using the drag coef ficient Eq.(T-18)show thatthe bed pressure drop decreases atthe higherinletgasvelocity.The pressure drop predicted by simulations is less than that observed by experiments possibly owing to the factthatthe friction force between the particles and walls is neglected in deriving Eq.(T-18).

Fig.6.Experimental and simulated bed pressure drops.

Differentcorrelations are available in the literature for drag coef ficient calculation.The drag coef ficient model proposed by Huilin-Gidaspow,Eq.(T-21),is also available in Fluent 14.0[31].This expression is based on combining the Ergun equation for a cylindrical fixed bed[11]and the Wen and Yu model for a dilute region[30].A switch function is used to give a smooth transition from the dilute regime to the dense regime.The simulated bed pressure drops using Eq.(T-21)are given in Fig.6.The simulated bed pressure drops with Eq.(T-21)are less than those from experiments.This discrepancy can be explained by the presence of a region in which particles are supported by inclined walls.Using Eq.(T-18),it indicates that the actual pressure gradient in a conical spouted bed is the combination of the gravity term and the additional solid phase source term in the annulus where the solid volume fraction is larger than 0.2.Different values of Ka(or different solid phase source terms)represent different values of the pressure gradient in a conical spouted bed.Comparing to simulations with Eq.(T-21),a better agreement between simulations with modi fied drag coef ficient model Eq.(T-18)and experiments is obtained.

Qualitatively,good agreement between simulations and experiments can also be observed from Fig.7.We found thatthe modelpredictions using Eq.(T-21)under-predicted bed pressure drops in the conical spouted bed.Compared to bed pressure drop in Fig.6,the bed pressure drop is large because the conical spouted bed has a high static bed height.The comparison between the experiments and simulations with Eq.(T-21)shows that the Huilin-Gidaspow model underpredicts bed pressure drop in conical spouted beds because it is derived from a cylindrical bed.It indicates that the particles near the inclined walls are with the help of the additional interaction force exerted by the tapered side walls,which is varied in the vertical direction.

Fig.7.Experimental and simulated bed pressure drops.

Fig.8 shows the lateraldistribution oftime-averaged gas volume fraction at three different heights at the inlet gas velocity of 2.2 m·s-1.The local gas volume fraction decreases with height and with radial distance in the spout region.This phenomenon,which was observed experimentally by He et al.[33],is probably caused by the forces acting upon the region,such as drag due to gas cross- flow,the weight of particles in the annulus,the shear stress caused by gas and upward moving particles in the spout,and shear stress due to downward moving particles in the annulus.The simulation results indicate that the solid volume fraction is higher in the annulus than that in the spout.It can also be observed that at the position just above the inlet,a higher gas volume fraction can be found.Roughly,the simulated gas volume fraction using Eq.(T-21)is smaller than that using Eq,(T-18).Eq.(T-21)gives a narrow spout compared to simulations using Eq.(T-18).This means thatthe drag coef ficient model proposed by Huilin-Gidaspow model gives a high solid volume fraction in the core,while the solid volume fractions in the annulus are nearly the same.This indicates that the difference of gas volume fraction predicted by both drag coef ficient models is not obvious in the conical spouted bed.

Fig.8.Distribution of time-averaged porosity in the spouted bed.

Fig.9 presents the radial pro files of axial velocity of particles in the conical spouted bed at different heights.It is noteworthy that the local particle velocities in the annulus region are negative,indicating that the particles move downwards.Conversely,the axial velocity of particles is positive thatmeans particles flowup in the core.There are noticeable differences in particle velocity both in the spout and annulus regions.Roughly,the simulated axial velocities using Eq.(T-21)are smaller than that using Eq.(T-18)in the core,while the axial velocity of particles in the annular region are nearly the same.The drag coef ficient model of Eq.(T-21)under-predicts the axial velocity of particles in the core.However,the trends are the same.

Fig.9.Pro files of particle velocity in the conical spouted bed.

Fig.10 shows the axial velocity and solid volume fraction in the fountain at an inlet gas velocity of 2.2 m·s-1.Simulations using modi fied drag coef ficient model Eq.(T-18)show that the solid volume fraction is decreased and the axial velocity of particles is from positive to negative along the lateral direction.It is also observed that near the top of the spout and in the center of the fountain,there exists a somewhat denser zone around the spout axis,which is in agreement with the flow pattern in the spouted bed,as shown in Fig.4.The axialvelocity of particles is positive in the core and negative in the periphery.This means thatparticles flow up in the core zone,and downwards in the peripheral zone.Both modi fied drag coef ficient model Eq.(T-18)and Huilin-Gidaspow model Eq.(T-21)predict a low solid volume fraction in the core,while the predicted solid volume fraction by Eq.(T-21)is even lower than that by Eq.(T-18),though the predicted trends are the same.

The fountain heights,de fined as the vertical distance between the top of the spout and the dense bed surface,at different experimental conditions were measured from a digital camera obtained.Fig.11 shows the simulated and experimental distributions of height of fountain as a function of inlet gas velocity.Increasing inlet gas velocity results in increasing gas momentum,which leads to a larger fountain height since the particles in the central spout region can be lifted much higher.The simulations using Eq.(T-18)is closer to experiments than Eq.(T-21),however,the trends are the same.Therefore,a modi fied drag coef ficient model,Eq.(T-18),considering the effect of the tapered side wall on the gas-solid flow,is more appropriate to predict flow behavior in conical spouted bed than that from cylindrical bed.

5.Conclusions

The bed pressure drop and fountain height were measured in a conical spouted bed.The different flow regimes,known as the fixed-bed,the partially spouted bed,the fully spouted bed and entrained spouted bed,were found in a conical spouted bed with the increase of inlet gas velocity.The measured heightof fountain is increased with the increase of inlet gas velocity in a conical spouted bed.

A gas-solid Eulerian-Eulerian model integrating the kinetic theory for particles and the drag coef ficientmodelconsidering additionalinteractions between the walls and gas-solid mixture exerted by the tapered side wallhave been used to predictbed dynamics and pressure drop ofa conical spouted bed.Comparison of the model predictions and experimental measurements on the bed pressure drop and height of fountain indicated reasonable agreement.Simulated bed pressure drop and fountain height using the Huilin-Gidaspow drag coef ficient model under-predicts in the conical spouted bed.It is suggested that the drag coef ficient model used in the cylindrical beds will become invalid in the conical spouted bed.After the present preliminary test of the proposed drag coef ficient model,further comparison with other drag models is required,and will thus be the subject of future study.fountain height using the Huilin-Gidaspow drag coef fi cient model under-predicts in the conical spouted bed.It is suggested that the drag coef fi cient model used in the cylindrical beds will become invalid in the conical spouted bed.After the present preliminary test of the proposed drag coef fi cient model,further comparison with other drag models is required,and will thus be the subject of future study.

Fig.10.Pro file of axial velocity and solid volume fraction in the fountain.

Fig.11.Comparison of experimental and simulated height of fountain.

Nomenclature

Subscripts