ECT measurement and CFD–DEM simulation of particle distribution in adown-flow fluidized bed
Tong Zhao a,∗, Masahiro Takei a, Deog-Hee Doh b
a Department of Mechanical Engineering, College of Science and Technology, Nihon University, 1-8-14, Kanda Surugadai, Chiyoda-ku, Tokyo 101-8308, Japanb Division of Mechanical and Information Engineering, Korea Maritime University, #1, Dongsam-Dong, Yeongdo-Gu, Busan 606-791, Republic of Korea
a r t i c l e i n f o
Article history:
Received 12 July 2009
Received in revised form
25 December 2009
Accepted 29 December 2009
Keywords:
Electrical capacitance tomography
Discrete element method
Computational fluid dynamics
Down-flow fluidized bed
a b s t r a c t
Inthe present study,a combinedmodelof computational fluid dynamics andthe discrete element method(CFD–DEM) was used to simulate the particle distributions in a down-flow fluidized bed (DFB) with a
newly designed particle–air distributor. In the simulation model, particle motion is calculated by solvingNewton’s equations and the flow field of air is predicted by the Navier–Stokes equations. The calculation
was made for the same geometric and operating conditions as the experiment which was carried out forcomparisonwith thesimulationusing electricalcapacitance tomography (ECT). Thenumericalpredictions
for the axial and radial profiles of the particle distribution agreed well with the experimental results.
A circulating fluidized bed is an important device in variouschemical industrial processes. According to the flow direction, the
circulating fluidized bedcan be classified into twobasicmodes:up-flow system in which gas and particles flow concurrently upward;and down-flow system (down-flow fluidized bed) in which bothgas and solids flow in the direction of gravity. Previous investiga-tions have shown that the distribution of particles and the contact
timebetween gasand solids in a down-flowfluidized bed (DFB) aremuch more uniform than those in the riser [1,2]. Due to these sig-nificant advantages, the DFB hasbeen proposed forsome processessuch as the fluid catalytic cracking process, where extremely shortbut uniform contact between gas and solids is required to prevent
overreacting. DFBs have therefore attracted many investigations inthe past decade.
Various researches have been carried out in the past to studythe flow behaviours in DFBs using either experimental or simu-lation approaches. For example, Wang et al. [3] provided the de-tailed information of the axial air–solid velocity profiles using a
fiber-optic probe; Huang et al.[4] presented the mixingbehavioursof both air and solids in a DFB by a phosphor tracer technique;Zhang et al. [5] simulated the particle aggregation behaviours us-ing the combined computational fluid dynamics and discrete ele-ment method (CFD–DEM). However, the results from experiments
T. Zhao et al. / Flow Measurement and Instrumentation 21 (2010) 212–218 213
Nomenclature
mi Mass of particle i
v p,i Translational velocity of particle i
ωi Rotational velocity of particle i
I i Inertia moment of particle i
f a,i Fluid drag force acting on particle i
f c Contact forceGi Gravity
Ti Torque caused by the contact force and inertia
moment of particle i
kn Spring stiffness in the normal directionkt Spring stiffness in the tangential directionηn Coefficient of viscous dissipation in the normal
directionηt Coefficient of viscous dissipation in the tangential
direction xn Particle displacement in the normal direction xt Particle displacement in the tangential directionµ f Friction coefficientε Void fraction
u Velocity vector of fluid p Pressure of fluidµ Fluid viscosityδV Volume of a computational celld p Particle diameterρ p Particle density
the particle behaviour in the DFB was undertaken by the CFD–DEMmodel under the same parameter conditions. The simulation datawere then compared with the experimental results.
2. Governing equations of CFD–DEM simulation
2.1. Solid phase
In this mathematical model, the solid phase is treated as a dis-crete phase that is described by a conventional DEM. The move-ment of individual particles is evaluated by Newton’s equation of motion which includes the effects of gravitational force, contactforce, and fluid force. The translational and rotational motions of a particle i at any time t in the reactor are determined by momen-tum balance, given by
mi
d v p,i
dt = f a,i + f c + Gi (1)
I idωi
dt = Ti (2)
where mi is the mass of particle i; v p,i and ωi are the translationaland rotational velocity of particle i; I i is the inertia momentof parti-cle i; f a,i is the fluid drag force acting on particle i; f c is the contactforce; G is the gravity of particle i; Ti is the torque caused by thecontact force and the inertia moment of particle i.
Cundall and Strack [13] proposed a typical model to formulatethe particle–particle interaction. Based on their research, thecontact force between two spherical particles can be modelledby the simple concept of a spring, dash-pot and friction slider, asshown in Fig. 1. The contact force f c can be divided into a normalcontact force f cn and a tangential contact force f ct , as follows [14]:
f cn = kn xn − ηn
d xn
dt (3)
f ct = kt xt − ηt d xt
dt if | f ct | ≤ µ f | f cn| (4)
spring
dashpot
friction slider
Fig. 1. Models of contact force.
f ct = µ f | f cn| xt
| xt |if | f ct | > µ f | f cn| (5)
where kn and kt are the spring stiffnesses in the normal andtangential directions, respectively, ηn and ηt are the coefficientsof viscous dissipation in the normal and tangential directions,respectively, xn and xt are the particle displacements in the normaland tangential directions, respectively, and µ f is the frictioncoefficient. As seen in the above equations, it is clear that the
stiffness, coefficient of viscous dissipation and friction coefficient,which canbe obtained from the physical properties of the particles,must be determined before the calculation of the contact force.In the present work, these parameters were determined by themethod proposed in previous papers [14,15]. Moreover, the springstiffness in the tangential direction kt is assumed to be equal to kn,andthe coefficient of viscous dissipation in the tangential directionηt is also assumed to be equal to ηn. Here, the contact force modelis also used to simulate the interaction between a particle and thewall.
2.2. Gas phase
The gas phase is treated as a continuous phase and modelled ina way similar to the one used in the conventional two-fluid model.
The governing equations are the conservations of mass and mo-mentum in terms of the local mean variables over a computationalcell, given by
∂ε
∂t + · (εu) = 0 (6)
∂(ρ g εu)
∂t + · (ρ g εuu) = −ε p −
ni=1
f a,i
δV + εµ2u (7)
where ε is the void fraction; u is the velocity vector of thefluid; p isthe pressure of the fluid; µ is the fluid viscosity; δV is the volumeof a computational cell, and n is the number of particles inside thecell. The fluid drag force acting on each particle inside the compu-tational cell can be calculated by
f a,i = β( v p,i − u)δV . (8)
The coefficient β can be determined by Ergun’s equation (ε ≤0.8) [16] or Wen and Yu’s equation (ε > 0.8) [17]. In the presentsimulation, β was deduced based on the summarized equations inprevious works [15,18].
2.3. Simulation conditions
The simulated fluidized bed consists of a specially designeddistributor and a rectangular DFB container. Fig. 2 shows theconfiguration of the newly designed distributor. As shown in Fig. 2,this distributor consists of one annular particle inlet and four well-distributed side airnozzles.The insideand outsidediameters of the
annular particle inlet are 122mm and 212mm, respectively. In thepresent simulation, the geometrical parameters of the simulation
8/4/2019 ECT measurement and CFD¨CDEM simulation of particle distribution in a down-flow fluidized bed.
model are the same as the for the real experimental equipment.The flow of gas and particles is assumed to be two dimensionalsince the thickness of the bed is equal to the particle diameter,which is much less than thebed width. Fig. 3 shows the calculationdomain and the grid arrangements of the two-dimensional (2D)simulation model. In this 2D model, the particle motion whichis perpendicular to the paper was not considered. The annularparticle inlet was simplified into two particle inlets with a widthof 45 mm, and the distance between these two inlets is 122 mm,as shown in Fig. 3. The number of the air nozzles was reducedfrom four to two, as shown in Fig. 3. The widths of these twoair nozzles are 24 mm, which is the same as the diameter of thereal nozzles. The angle between the centre lines of the side nozzleand the centre line of the DFB container is 45◦. The bottom of thedistributor connects with a DFB container that is 1.98 m in heightand 0.27 m in width. The calculation domain is divided into smallcalculation cells. The cell size for the calculation of gas motion is
6.75 mm × 6.75 mm, and the total number of grid cells is 13,196.Each cell consists of thegas phase contacting with particles, andthevoid fraction of each cell can be defined by the number of particlesexisting in the cell. As is usual in many numerical calculationsfor flow fields, the differential equations of the gas phase weresolved by the finite difference method. The well-known numericalmethod, the semi-implicit method for the pressure-link equation(SIMPLE) scheme, was used. A no-slip condition is used for theair phase at the walls and particles are allowed to have frontalcollisions with the wall. The simulation is started with the randomgeneration of particles without overlaps at the top of the particleinlet. Then, after a gravitational settling, the particles will drop intothe calculation domain.
The parameter settings of the simulation are summarized
in Table 1. Because of the huge particle numbers and limitedcomputation capacity, the particle diameter is set as 350 µm,
Fig. 3. Calculation domain and grid arrangement.
which is around five times the real particle diameter. Then, in
order to keep the similarity of flow in the simulation, a correlationmodel proposed by Washino et al. [19] has been used to adjust the
simulation conditions, such as the superficial velocity, gas density,
gas viscosity and particle density. The time step for simulation is
calculated as follows [15]:
t =2
5π
π (d p)3ρ p
6kn
(9)
where d p is the particle diameter, kn is the spring stiffness and ρ p
is the particle density.
3. Experiments using ECT
In this study, the experimental equipment, which consists of a
hopper tank, a sender, an air–particle distributor,a circulatingpipe,
a cyclone separator, and a receiver tank, has been constructed, as
shown in Fig. 4. The DFB, which is connected to the bottom of the
distributor, has a diameter of 270 mm and lengths of 5.3 m. Three
capacitance tomography sensors each with a length of 0.66 m
were wrapped around the circumference of the DFB at different
vertical positions. Particles were supplied from the hopper tank
to the distributor inlet. The geometry of the distributor is the
same as in the simulation model, except that the particle inlet is
annular and four well-distributed side nozzleswere adopted. Fig. 5
shows the schematic diagram of the ECT sensor. The details of the
ECT sensor have been reported in the authors’ former research
paper [6]. The particulate solids used for this study were fluidcatalytic cracking (FCC) catalyst particles, which have a particle
8/4/2019 ECT measurement and CFD¨CDEM simulation of particle distribution in a down-flow fluidized bed.
T. Zhao et al. / Flow Measurement and Instrumentation 21 (2010) 212–218 215
Fig. 4. Experimental equipment.
(a) Frontal view. (b) Section view.
Fig. 5. Overview of the ECT sensor.
Table 2
Experimental conditions.
Case 1 Case 2
Particle circulation rate (kg/m2 s) 175 175
Air superficial velocity (m/s) 8.3 5.1
density of 1200 kg/m3, a mean diameter of 69.6µm and a relativepermittivity of 2.7.
The experimental conditions are shown in Table 2. The hopperwas adjusted to provide a 175 kg/m2 s particle flow rate. Theair flow rate at each air nozzle was set as 0 .118 m3/s for Case1 and 0.073 m3/s for Case 2. After a few seconds delay, in order
to allow the particle to flow in a stable manner, the capacitancemeasurements started at base times using a combined systemconsisting of a capacitance acquisition device and a high-speedmultiplexer. The time interval to acquire the 66 capacitancemeasurements from 12 electrodes in each cross-section was t =10.0 ms. The total measurement time is 5 s,and thetotal number of framesof the reconstructedimage N t is 500.The generalized vectorsampled pattern matching (GVSPM) method was used for imagereconstruction [20].
4. Results and discussion
4.1. Distribution image of particle volume fraction
Table 3 shows the distribution images of particle volume frac-tion obtained from experiment and simulation. In these images,
the red pixels indicate high solid concentration of 0.2. As the solidconcentration in an image pixel decreases, the image pixel turns
blue, which indicates air, as shown by the colour bar. In the ex-periment, the initial space resolution of the reconstructed parti-cle distribution image was 32 × 32 pixels, which was improvedto 120 × 120 pixels using the state transition matrix method [21].Based on the high-resolution images, a three-dimensional (3D)im-age of the particle distribution (time and 2D space image) was
established. Table 3 shows the results with a 3D resolution of 100 (time domain) × 120 × 120 (2D space domain). In Table 3,only a quarter of the 3D image is shown in order to indicate theparticle distribution at the centre region.
The experimental images in Table 3 show that, at a distance of 0.33 m from the entrance of the DFB, a high-solid-concentrationarea, which represents solid aggregation (cluster), always exists
in the near-wall region and at the centre of the DFB. As themeasurement position moves downstream, the clusters becomesmaller, or even disappear; thus, the particle distribution becomesuniform. Moreover, as the air superficial velocity decrease from8.3 m/s (Case 1) to 5.1 m/s (Case 2), the particle volume fractionbecomes higher.
On the other hand, qualitatively, the simulation images show
the same properties as the experimental result shown above. Afterdropping from the inlet, the particles concentrate together andthis results in cluster formation due to the geometric configurationof the particle inlet. Then, as the particles move downstream, ahigh-velocity air flow with relative high drag forces is applied inboth axial and radial directions. The force destroys the clusters
and disperses the particles. It was found that the air superficialvelocity strongly influences the cluster formation. Specifically, asthe airsuperficialvelocity decreases, the clusters near the entranceof the DFB become more noticeable and cause a non-uniform soliddistribution.
4.2. Axial and radial profiles of particle volume fraction
In the experiment, the average particle volume fraction can becalculated from the reconstructed images as follows:
α =1
N t (N xN y − N w)
N t t =1
N y y=1
N x x=1
E xyt (%) (10)
where N t is the total frame number of the reconstructed images,N w is the number of pixels positioned outside the pipe or in thethickness of the pipe wall, N x and N y are the cross-sectional spaceresolutions, and E xyt is the particle volume fraction value of pixel
( x, y) at time interval t .Fig. 6 reveals the axial profiles of the average particle volume
fraction obtained from the experiment and simulation for Case 1and Case 2. In Fig. 6, both the experiment and simulation results
show that the average particle volume fraction decreases as theaxial position goes downstream. The reason for this phenomenoncould be the slip velocity between the particles and the air phase.
Wang et al. [3] put forward that there are three sections of particlevelocity in solid–air two-phase down-flow: the first accelerationsection, the second acceleration section and the constant velocitysection. Following this theory, as the particles drop down, theparticle velocity will increase in the first and second accelerationsections. Then, as particles reach the constant velocity section in
which the air fluid drag becomes upward and equal to the particlegravity, the particle velocity will level off. During this process, theair velocity remains almost constant. Therefore, the slip velocitybetween the particles and the air phase decreases as the particlesdrop downstream, and this also causes the decrease of particle
volume fraction. However, a difference between the experimentaland simulation values can be observed, as shown in Fig. 6(a) and
8/4/2019 ECT measurement and CFD¨CDEM simulation of particle distribution in a down-flow fluidized bed.
T. Zhao et al. / Flow Measurement and Instrumentation 21 (2010) 212–218 217
P a r t i c l e v o l u m e f r a c t i o n [ - ]
Radial distance from the centre [mm]
0 15 30 45 60 75 90 105 120 135
h=0.33m (Simulation) h=0.99m (Simulation)
h=0.33m (Experiment) h=0.99m (Experiment)
h=1.65m (Simulation)
h=1.65m (Experiment)
0.1
0.08
0.06
0.04
0.02
0
P a r t i c l e v o l u m e f r a c t i o n [ - ]
Radial distance from the centre [mm]
0 15 30 45 60 75 90 105 120 135
h=0.33m (Simulation) h=0.99m (Simulation)
h=0.33m (Experiment) h=0.99m (Experiment)
h=1.65m (Simulation)
h=1.65m (Experiment)
0.1
0.08
0.06
0.04
0.02
0
(a) Case 1. (b) Case 2.
Fig. 7. Radial profiles of particle volume fraction.
agreement with the experiment. As shown in Fig. 7(a), for boththe experiment and the simulation, a low particle volume fractionalways occurs in the region between the centre and the wall of the
pipe, while the highest particle volume fraction can be observednear the wall. As the axial position goes downstream, the profilesof the particle radial distribution became increasingly flat, whichmeans that the particle distribution becomes uniform. In Case 2,the same feature of the radial particle distribution profiles can alsobe observed in Fig. 7(b), but the particle volume fraction value ishigher than that in Case 1.
The above radial profiles of particle volume fraction are veryreasonable. In the present work, particles were introduced from anannular particle inlet as shown above. By means of the distributor,the air velocity was inclined with respect to the gravity directionbecause of the side nozzle. After dropping from the inlet, particlesare accelerated not only in theaxial direction, but also in the radialdirection. Under the effect of this radial force, the particles move
away from theannular region towards the centre and the wall, andas a result, higher particle volume fraction regions were formedat the centre and near the wall. However, as the particles movedownstream, the high-velocity air at the centre imposed a radialfluid drag force on the particles, and caused the particles to moveaway from the centre. Andalso, because of the friction between theair–particle suspensions and the wall, particles near the wall alsomove away, which causes the clusters near the wall to disperse.
5. Conclusion
A numerical simulation for particle distribution in a down-flow fluidized bed was performed by combining the DEM and CFDin a two-dimensional domain. At the same time, an experiment
under the same parameter conditions using the ECT technique wascarried out for comparison with the simulation. The distributionimages of the particle volume fraction were obtained from boththe experiment and the simulation, and the axial and radialprofiles of the particle volume fraction were extracted from theseimages. Qualitatively, the comparison results between simulationand experiment are encouraging. The results are summarized asfollows.
In theaxialdirection, dueto theincreasing slip velocity betweenthe particles and air, the particle volume fraction decreases as theparticles descend, but a decrease in the air superficial velocitycauses an increase in the particle volume fraction value. In theradial direction, the highest particle volume fractions can beobserved near the wall, and a relatively low particle volume
fraction in an annular region always exists near the entrance of theDFB. However, the particles become well distributed as they move
further downstream. The reason for this could be the radial dragforce imposed by the air phase. In this study, it was also found thatthere are some differences in the particle volume fraction values
between the experiment and the simulation, and to resolve thesedifferences, further research should be devoted to improving thesimulation by using multi-sized particles and a 3D model.
Acknowledgements
The authors wish to acknowledge the financial support pro-vided by the Information Center of Powder Technology Japan, andthe Grant-in-aid for scientific research B (21360088) from JapanSociety for the Promotion of Science. The authors also wish to ac-knowledge the support provided by the Rflow Co. Ltd in the DEMsimulation. And this work was partly supported by the NRL PJT of Korea Research Foundation of Korea (R0A-2008-000-20069-0).
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