Simulation of Gas–Solid Flow in Rectangular Spouted Bed byCoupling CFD–DEM and LES

Chunhua Wang,1,2 Zhaoping Zhong,2* Xiaoyi Wang2 and Siti Aisyah Alting2

1. College of Energy & Power Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

2. Key Laboratory of Energy Thermal Conversion and Control of Ministry of Education, School of Energy and Environment,Southeast University, Nanjing 210096, China

For a better understanding of the dynamics of spouted beds, the gas–solid flow in a three‐dimensional rectangular spouted bed was simulated usingcoupled computational fluid dynamics (CFD) and the discrete element method (DEM), and the anisotropic turbulent flow was solved by large eddysimulation (LES). The distributions of gas velocity, particle velocity, subgrid‐scale eddy viscosity, gas turbulent intensity and particle turbulent intensityin the simulation results were analysed in detail. In comparisonwith particle trajectory velocimetry (PTV) analysis, it was found that the particle velocitydistributions in the simulation results agree well with those in the experimental results, which also verify the efficiency of the simulation model.

Keywords: computational fluid dynamics, fluid‐particle dynamics, turbulence, fluidisation, simulation

INTRODUCTION

Spouted beds are gas–solids granular contactors appropriatefor a large variety of chemical engineering and miningoperations that deal with the handling of heavy, coarse,

sticky and/or irregularly shaped solids through cyclic flowpatterns.[1,2] In spouted beds, particles are agitated by the gasesthrough a single nozzle, which causes the flow pattern of particlesin spouted beds to be more regular than that in conventionalfluidised beds. A spouted bed is divided into three different regionswith their own specific flow behaviour: the dilute phase core ofupward gas–solid flow called “spout”, the surrounding region ofdownward quasi‐static granular flow called “annular” and the topregion called “fountain”. Knowledge of the solids flow pattern inspouted beds is of great importance in their design. In addition,better understanding of the dynamics of spouted beds with asingle nozzle is crucial as a first step towards understanding themore complex, inhomogeneous convection of particles in multi‐nozzle bubbling bed.

Computational fluid dynamics–discrete element method (CFD–DEM) coupling method was firstly developed by Tsuji et al.[3]

and used to simulate the gas–solid flow in fluidised bed. In theCFD–DEM coupling method, the gas movement is governed bytraditional continuity equation and Navier–Stokes equations,while particle–wall and particle–particle contacting forces aredetermined by DEM, and the momentum exchange betweengas and solid phase is usually expressed by Ergun and Wen &Yu correlations in meso‐scale. The great advantage of CFD–DEMis that the trajectory of every particle in simulation process canbe traced. Because of this, CFD–DEM has been widely usedin the simulation of dense gas–solid flow.[4–7] In this paper,CFD–DEM was applied to simulate gas–solid flow in spouted bed.

In the spouted bed, the Reynolds number of gas phase in jetregion is high and, to a certain extent, the simulation accuracy ofgas–solid flow depends on the solution of turbulence. In theprevious researches, turbulence in spouted bed is solved by RANSequations.[8–10] There are many empirical parameters that need tobe determined in RANS equations (e.g. in k‐e equations, sixempirical parameters need to be determined), but there were no

widely acceptable values for these parameters in dense phase gas–solid flow until now. Compared with RANS equations, there arefewer empirical parameters in the large eddy simulation (LES)method. Additionally, the turbulence shows isotropic behaviourin RANS equations, which is different from the actual condition.In the LES method, the turbulence is anisotropic. By low‐passfiltering, LES resolves large scales of theflowfield solution by directnumerical simulation (DNS), which allows better fidelity thanRANS. LES also models the smallest scales of the solution, whichallows less computation time than DNS.[11]

In this paper, LES was coupled with CFD–DEM to simulate thegas–solid flow in the spouted bed. The simulation results werethen compared with particle trajectory velocimetry (PTV) results.Lastly, the velocity, sub‐grid scale (SGS) eddy viscosity andturbulent intensity distributions were analysed. To the best ofour knowledge, the research on the behaviour of anisotropicturbulence in rectangular spouted bed is novel, requiring a deepunderstanding of the subject.

GOVERNING EQUATIONS FOR GAS AND SOLID PHASE

Gas Phase

LES equations for gas flows are derived by filtering the N–Scontinuity and momentum equations in a 3‐D geometry. Itbecomes:

@ðarfÞ@t

þr � ðarf~ufÞ ¼ 0 ð1Þ

*Author to whom correspondence may be addressed.E‐mail address: zzhong@seu.edu.cnCan. J. Chem. Eng. 92:1488–1494, 2014© 2014 Canadian Society for Chemical EngineeringDOI 10.1002/cjce.21997Published online 24 June 2014 in Wiley Online Library(wileyonlinelibrary.com).

1488 THE CANADIAN JOURNAL OF CHEMICAL ENGINEERING VOLUME 92, AUGUST 2014

@ðarf~ufÞ@t

þr � ðarf~uf~ufÞ ¼ �ar~P þr � ~T þ fD þ fs þ fM þ arfg

ð2Þ

where an overbar ‘�’ denotes application of the filteringapplication, a is the void fraction, rf is the gas density, uf is thegas velocity, P is the gas pressure, fD is the gas–solid drag force, fs isthe Saffman force and fM is the Magnus force. T is the stress tensor,and can be modelled as:

~T ¼ ðmSGS þ mfÞ 2D� 23ðr � ~uÞE

� �ð3Þ

where mf is the gas viscosity, mSGS is SGS viscosity, D is thedeformation tensor rate, E is the unite matrix. In the Smagorisnkymodel,[12,13] mSGS can be modelled as:

mSGS ¼ ðCsDsÞ2rfð2trð~D � ~DÞÞ1=2 ð4Þ

where Cs is the Smagorinsky constant, Cs¼ 0.1. Ds is thecharacteristic length and can be modelled as:

Ds ¼dp=2 a ¼ 0:4

ðDxDyDzÞ1=3 a ¼ 1:0

(ð5Þ

where dp is the particle diameter, and Dx, Dy and Dz denotes thegrid size in the x, y and z directions, respectively. When a is lessthan 0.4, Ds is assumed as zero. When a is between 0.4 and 1.0,linear interpolation method can be used to calculate Ds.

Particle Phase

According to Newton’s equation of motion, the motion of particlescan be modelled as:

mpdupdt

¼ fc þ fD þ fs þ fM þ frp þmp g ð6Þ

Ipdvp

dt¼ Mp ð7Þ

where mp is the particle mass, fc is the contact force, Ip is theparticle moment of inertia and Mp is the torque.

The drag force can be calculated by:

fD ¼ bðup � ~ufÞ ð8Þ

where b denotes the drag coefficient. It can be modelled as:

b ¼

mfð1� aÞd2pa

150ð1� aÞ þ 1:75 ~ReÞ� �a � 0:8

34CD

mfð1� aÞd2p

a�2:7 ~Re a > 0:8

8>>>><>>>>:

ð9Þ

where CD is the drag coefficient of single particle. Given asfollows:

CD ¼24ð1þ 0:15 ~Re0:687Þ

~Re~Re � 1000

0:43 ~Re > 1000

8><>: ð10Þ

where Re is the particle Reynolds number, and defined as:

~Re ¼ a up � ~uf�� ��rf dp

mfð11Þ

The Saffman force can be modelled as:

f s ¼ 1:615ð~uf � upÞðrfmfÞ0:5d2pC1

ffiffiffiffiffiffiffiffiffiffiffiffi@~uf;i

@xi

��������

ssgn

@~uf;i

@xi

� ð12Þ

where C1 is the Saffman lift coefficient, and can be calculated by thecorrelation developed by Mei.[14]

The Magnus force can be modelled as:

fM ¼ 18rf ~uf � up�� ��2pd2pC2

vr � ð~uf � upÞð~uf � upÞ�� �� � vrj j ð13Þ

where vr is the relative angular velocity between gas and particle.C2 is the Magnus lift coefficient, and can be calculated by thecorrelation developed by Liu and Liu.[15]

In DEM,[16] the collision between particles is modelled bysprings, dashpots and sliders, and the contacting force fc can bemodelled as:

fcn ¼ �kdn � hvn ð14Þ

fct ¼ �kdt � hvt ð15Þ

where the subscript ‘n’ and ‘t’ is the normal and tangentialcomponent of the vector. k is the spring stiffness, h is the coefficientof viscous dissipation, v is the relative velocity and d is the particledisplacement. When |fct|>mf |fcn| is satisfied, fct should becalculated by following:

fct ¼ �mfrjfcnj ð16Þ

where mfr is the coefficient of friction. The coefficient of viscousdissipation, h, can be calculated by the following correlations:[17]

h ¼ 2gðmkÞ0:5 ð17Þ

g ¼ a

ð1þ a2Þ0:52 ð18Þ

a ¼ � 1p

� ln e ð19Þ

where e is the restitution coefficient of spring.

EXPERIMENTAL AND SIMULATION SYSTEM

The detailed schematic of the experimental set‐up is shown inFigure 1. The spouted bed is made of plexiglass; its geometryis shown in Figure 2. To facilitate the analysis, the x‐direction isdefined as the radial direction. The fluidisation air is supplied by aircompressor, and is measured by the Laminar flow measuringsystem, consisting of Laminar flowmeter, strain pressure recorder,dynamic stain amplifier and A/D converter. The flow of the solidphase is shot by a high‐speed camera, which is used to compare thesimulation results. The frames per second (FPS) of the camera is set

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to 500. To optimise the photo quality, a halogen lamp is used. Thegas temperature ismeasured by thermometer. A pressure samplingsystem consisting of pressure sensor, A/D converter and terminalcomputer is used to determine the minimum spouted velocity.Particles are made of aluminum and have a diameter of 3mm. Toreduce the reflection factor, the particles used in this research werecoated with a black body paint (THI‐1B, Tasco Japan Co., Osaka,Japan). The photos of particles before and after coating are shownin Figure 3.

To realize the particle tracking velocimetry, the nearest‐neighbour method based on image analysis is used. In thismethod, the particle displacement in continuous video imagesshould be restricted to be less than the particle radius whichensures that the particles having the closet coordinates insequential images are the same ones. To determine the particlecentre, four steps are applied:[18]

Step 1: Laplacian and smoothing filters are used to diminish thenoise in the original images.

Step 2: A particle is selected from a series of images, and itsbrightness distribution is stored as a standard particle image.

Step 3: The distributions of correlation function between thevideo image and the standard particle image is calculated.

Step 4: The pixel that shows the highest correlation value isexpected to contain the particle centre.

In a staggered grid, finite volume method (FVM) was applied fordiscretisation of the differential equations, and the semi‐implicit

method for pressure linked equations (SIMPLE) algorithmwas used to solve gas pressure and velocity. Non‐slip, pressureoutlet and velocity inlet boundary conditions were set to determinethe boundary parameters near the wall, outlet and inlet,respectively, in this research. The two‐way coupling methodwas used to couple particle and gas motion. The time step wasdetermined by the method proposed by Tsuji et al.[3] In CFD–DEM,the convergence of the solution for gas‐phase governing equationsshould be taken into account. If the gas‐phase mass change in thetime step DT is very small in the computational grid, we can saythat the solution for gas‐phase governing equations is converged.In addition, all codes used in this research were compiled withFORTRAN.The parameters of the simulation system are given in Table 1.

The particle in this research is similar to the one used in the Tsujiet al.[17] experiment, thus the spring stiffness, the restitution andthe friction coefficients in this paper are the same as those in theTsuji et al.[17] paper. In meso‐scale CFD–DEM, the grid size shouldbe at least 2.5 times the particle size. In this research, if the gridsize (in the x‐direction) meets the above requirement, there is onlyone grid in the x‐direction in the gas inlet, which may lead to aremarkable error. The authors reduced the grid size by comparingdifferent mesh sizes, andmade sure that there are at least two grids(in the x‐direction) in the jet region. By comparing different meshsizes, it is found that the simulation error with the grid size inTable 1 is the lowest.

Figure 1. The schematic of the experimental set‐up. 1. Halogen lamp, 2.High speed camera, 3. Spouted bed, 4. Pressure transducer, 5. A/Dconverter, 6. Terminal computer, 7. Dynamic strain amplifier, 8. Strainpressure recorder, 9. Laminar flowmeter, 10. Regulator, 11. Thermometer,12. Compressor.

Figure 2. Geometry of spouted bed in the experiment (unit: mm).

Figure 3. The photograph of particles before and after coated: (a) Particles before coating and (b) particles after coating.

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SIMULATION RESULTS

Flow Patterns

Figure 4 shows the flow snapshots in simulation results by LES–DEM. Figure 5 shows the flow snapshots in experimental results.At this working condition (H0¼ 50mm, us¼ 3.0m/s) the spoutingis stable, and the fountain height does not change with time.

The void fractions in simulation results appear higher than those

in the photographic images. This can be contributed by two factors:(1) the particle used in this paper was coated with the black bodypaint which makes the particle distribution in the photographicimage look very dense;[18] (2) the grid size (in the x‐direction) inthis paper does not strictly meet the requirement of meso‐scopicCFD–DEM, which may also lead to the error.

Particle Velocity

Figure 6(a) shows the particle vertical velocity distribution in thespouted bed. In the jet region, the gas–solid drag force is muchlarger than gravity, which makes particles move upward. As theheight from the vessel bottom increases, the particle velocityincreases, but the drag force decreases.[9] In the central region ofthe fountain, particles still move upward, but the particle velocitydecreases with the increase of height. As particle velocity reducesto zero, particles start to fall with acceleration of gravity. In theannular region, the profiles of vertical velocity are nearly flat, butbecause of the friction between particles and wall, the particlevertical velocity near the wall is less than its average value.[19] Theprofiles of vertical velocity in this research are similar to those inthe research of Roy et al.[20] Particle downward velocity in annularregion increases with height, He et al.[21] explains that this is due toparticle entrainment.

Table 1. Simulated system parameters in this research

Parameters Unit Value

Grid size (Dx�Dy�Dz) mm 5.5�10.5�10Particle size mm 3Particle density kg/m3 2700Gas density kg/m3 1.293Gas viscosity m2/s 14.8�10�6

Time step s 2�10�5

Static bed height mm 50Restitution coefficient 0.43Coefficient of particle–particle friction 0.88Coefficient of particle–wall friction 0.77Spring stiffness on normal direction N/m 800Spring stiffness on tangential direction N/m 200

Figure 4. Snapshots of solid flow in simulation results by LES–DEM (H0¼50mm, us¼3.0m/s). (a) t¼0.7 s, (b) t¼0.8 s, (c) t¼0.9 s.

Figure 5. Snapshots of solid flow in experimental results (H0¼50mm, us¼3.0m/s). (a) t¼0.7 s, (b) t¼0.8 s, (c) t¼0.9 s.

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Figure 6(b) shows the particle radial velocity distribution in thespouted bed. Compared with the particle vertical velocity, particleradial velocity is much lower. At the bottom of vessel, because ofthe entrainment effect,[9,10] particles move from annular region tojet region with high radial velocity. As the height increases, theentrainment becomes weak[22] and the particle radial velocity inthe jet region decreases. When particles enter the fountain region,their movement direction becomes opposite. The averaged radialvelocity of the particles in the fountain is higher than that at a lowerheight.

The radial profiles of vertical particle velocity in jet region areof near‐Gaussian distribution.[23] However, because the particlediameter in our research is large, the radial profiles of verticalparticle velocity in jet region cannot be shown.

The changing trend of particle velocity in the simulation resultsis similar to that in the experimental results; yet, it is a calculationerror (especially in the fountain region) between the simulationand experimental results. The relative velocity error is calculatedby Equation (20):

error ¼P

uexp � upre�� ��= uexp

�� ��n

ð20Þ

where uexp and upre denotes the velocity in the experiment andsimulation results, respectively, and n denotes the grid number inspouted bed. The mean velocity error in vertical direction is about10.3%, while the value is about 7.3% in x‐direction. The error maybe contributed to two factors: firstly, PTV only analyzes the particlevelocity near the front wall where the friction is very large;[18]

secondly, the grid size in x‐direction is not good enough for spatialaccuracy, thus the gas–solid force in simulation results is slightlyhigher than in the real situation.[3]

Gas Velocity

Figure 7(a) shows the gas vertical velocity distribution in thespouted bed. Because the void fraction in jet region is much largerthan that in annular region, and gas spreads from the jet regionto annular region,[10,19] the gas vertical velocity in the jet regiondecreases with the increase of height. At the same height, the gasvelocity in the central region is larger than that in the annularregion, but the velocity difference between these two regionsbecomes low as height increases.Figure 7(b) shows the gas radial velocity distribution in the

spouted bed. At the bottom of the vessel (H¼ 10mm), gas spreadsfrom the jet region to the annular region with high radial velocity.As height increases, the diffusion becomes weak,[10] and the gasvelocity decreases. When the gas reaches the fountain region(H¼ 70, 90mm) the diffusion is reinforced again. At the sameheight, the maximum velocity can be observed at the boundarybetween the jet region and annular region.The gas radial velocity distribution in this research is a little

different from that in the Wang et al.[24] research because thespouted bed used there was rectangular spouted with a cone‐bottom, and the gas–solid flow is influenced by the shape ofspouted bed.

SGS Eddy Viscosity

Figure 8 shows the SGS eddy viscosity distribution in thesimulation results. The value of eddy viscosity in the Smagorinskymodel reflects the effect of small‐scale eddy on the gas flow.[11] TheSGS eddy viscosity in the central region is higher than that in theannular region, which means the influence of small‐scale eddy inthe central region is greater;[12] it is because the gas Reynoldsnumber in the central region is higher. The viscosity difference

a b

Figure 6. Particle velocity distribution in rectangular spouted bed (a) Vertical direction (b) Radial direction.

a b

Figure 7. Gas velocity distribution in the simulation result: (a) Gas vertical velocity and (b) gas radial velocity.

1492 THE CANADIAN JOURNAL OF CHEMICAL ENGINEERING VOLUME 92, AUGUST 2014

between these two regions becomes weak as the height increases –this is because of the gas diffusion from the central region to theannular region which makes the Reynolds number in the centraland annular regions decrease and increase with the increase ofheight, respectively.

Particle Turbulent Intensity

Turbulent intensity is defined as:

Ii ¼ fmeanðDui2Þg0:5

�uið21Þ

where Dui denotes the velocity fluctuation in the i direction. Thevalue of turbulent intensity corresponds to the mutual interactionbetween the gas phase and the solid phase.[4,10]

Figure 9(a) shows the particle radial turbulent intensity insimulation results. At the bottom of the vessel (H¼ 10mm),particles move from the annular region to the jet region, and theradial velocity fluctuation is sharp, which makes the turbulentintensity high at the bottom.[4] As height increases, the entrain-ment effect becomes weak, and the turbulent intensity decreases.When particles enter the fountain region (H¼ 60, 80mm), theparticle movement direction becomes opposite, and turbulentintensity does not change with height. At the same height, theturbulent intensity increases first, and then decreases as the radialdistance to the centre of the base increases.

Figure 9(b) shows the particle vertical turbulent intensity insimulation results. The vertical gas–solid force in the jet dilutephase region is large, which makes the particle velocity fluctuationin vertical direction sharp, so the vertical turbulent intensity in this

region is high. On the contrary, vertical gas–solid force in theannular dense region is less, and the vertical turbulent intensity inthe annular dense phase region is low. The changing tendency ofturbulent intensity to radial distance in the fountain region issimilar to that below the fountain region.

Gas Turbulent Intensity

Figure 10(a) shows the gas radial turbulent intensity in simulationresults. The turbulent intensity increases first, and then decreasesas the radial distance increases. In the central region of the vessel,the interaction between the gas and solid phases in radial directionis low, so the radial turbulent intensity in the central region is nothigh. Conversely, in the annular region, particles and jet gas bothhave radial velocity, and the radial interaction is greater than thatin the central region, so the turbulent intensity in annular regionis higher.[13] In the region near x¼ 80mm, because of the wallresistance, the gas velocity reduces to zero, which makes the gasturbulence intensity very low. The radial turbulent intensity doesnot change with the height.

Figure 10(b) shows the gas vertical turbulent intensity insimulation results. At the low height, the gas turbulent intensityincreases first, and then decreases as the radial distance to thevessel centre increases. Although the gas–solid vertical interactionin the jet dilute phase region is great, the averaged vertical velocityof gas is too high, which makes the turbulent intensity low in thisregion.[4] As height increases, the gas‐averaged vertical velocity inthe jet region decreases, whichmakes the turbulent intensity in thejet region increase, but the velocity in the annular region alsoincreases, which makes the turbulent intensity in the annularregion decrease. In the fountain region, the changing tendency ofturbulent intensity to the radial distance becomes opposite.

The turbulent distribution in this research is different from thatin the Zhong et al. research.[10] It can be contributed to two factors:(1) the vessel there is a spout‐fluidised bed, yet no fluidised gas isintroduced in this research; (2) the turbulence in the other researchis solved by RANS equations.[10] The turbulent flow in RANSequations is isotropic which is different from the behaviour of theturbulent flow in LES.

CONCLUSIONS

A traditional RANS equations method can only solve the isotropicturbulence, which is different from the actual condition. Forsolving the anisotropic turbulence in a spouted bed, LES wascoupled with traditional CFD–DEM to simulate the gas–solid flowunder the Euler–Lagrange framework. The particle and gasvelocity distributions in this research are similar to those in

Figure 8. SGS eddy viscosity distribution in the simulation result.

a b

Figure 9. Particle turbulent distribution in the simulation result: (a) Radial direction and (b) vertical direction.

VOLUME 92, AUGUST 2014 THE CANADIAN JOURNAL OF CHEMICAL ENGINEERING 1493

some previous literature, and the research findings also verify theearlier literature. Some meaningful conclusions are summarized:

(1) The SGS eddy viscosity in the central region is larger than thatin the annular region. The viscosity difference between thesetwo regions becomes smaller while the height increases.

(2) As the height from the vessel bottom increases, particle radialturbulent intensity decreases first, and then remains stable.Particle radial turbulent increases first, and then decreaseswith the increasing of the radial distance. Particle verticalturbulent intensity in the central region of the vessel is largerthan that in the annular region.

(3) Gas radial turbulent intensity increases first, and thendecreases as the radial distance increases. At low height,the changing trend of gas vertical turbulent intensity to radialdistance is the same as that of the gas radial turbulentintensity, but nevertheless, at high height, it is in the oppositedirection.

The findings in this research will help researchers have a deeperunderstanding of the rectangular spouted bed.

ACKNOWLEDGEMENTS

The authors would like to thank the National Natural Science FundProgram of China (51276040), National Basic Research Program ofChina (2013CB228106) and the scientific innovation research ofcollege graduates in Jiangsu province (CX10B_065Z) for financialsupport.

The experimentswere carried out in Tanaka and Tsuji lab duringthe authors’ visit to Osaka University in Japan. Authors show oursincere thanks to Professor Toshitsugu Tanaka and Takuya Tsuji.

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Manuscript received August 3, 2013; revised manuscript receivedOctober 25, 2013; accepted for publication November 18, 2013.

a b

Figure 10. Gas turbulent distribution in the simulation result: (a) Radial direction and (b) vertical direction.

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