Chemical Engineering Science 59 (2004) 41934203www.elsevier.com/locate/ces

DEM-LES of coal combustion in a bubbling &uidized bed. Part I:gas-particle turbulent &ow structure

Haosheng Zhou, Gilles Flamant, Daniel GauthierInstitut de Science et de Genie des Materiaux et Procedes, CNRS-IMP, BP.5 66125 Odeillo, Font-Romeu Cedex, France

Received 5 February 2003; received in revised form 1 December 2003; accepted 9 January 2004

Available online 18 August 2004

Abstract

The gas and particle motions in a bubbling &uidized bed both with and without chemical reactions are numerically simulated. The solidphase is modelled as Discrete Element Method (DEM) and the gas phase is modelled as 2-D NavierStokes equations for 2-phase &owwith &uid turbulence calculated by large Eddy simulation (LES), in which the e

4194 H. Zhou et al. / Chemical Engineering Science 59 (2004) 41934203

useful and versatile tools to study the hydrodynamic be-haviour of particulate &ows. They oltered equations represent the evolutionof time-dependent resolved scale motions. Due to the scaletruncation by >ltering, subgrid models are required to in-corporate the unresolved scale eltering the 2-phase NS continuity and momen-tum equations in a 2-D geometry, it comes:

@(f)@t

+@(fuf; i)

@xi= ; (1)

@(fuf; i)@t

+@(fuf; iu f; j)

@xj

= @p@xi

+@@xj

(ij) +@@xj

(ij)

+fg+ +; (2)

where an overbar denotes application of the >ltering op-eration, is the porosity, f is the gas density, uf is the gas

H. Zhou et al. / Chemical Engineering Science 59 (2004) 41934203 4195

velocity, i; j=1; 2, which represent x and y directions, p isthe gas pressure, g is the gravitational acceleration vector,t is the time, is the volumetric particlegas interaction,

is the rate of particle-to-gas phase mass transfer, is theened as follows:

Rep =f|

*uf *vp| Mdpf

: (7)

2.2. Particle phase hydrodynamics

2.2.1. Particleparticle interactionCundall and Stracks (1979) DEM model opened new

possibilities for using discrete particle simulation to calcu-late the dense phase &ows in &uidized beds (Tsuji et al.,1993). Contact forces are described in terms of a mechanicalmodel involving a spring, dashpot and friction. The contactforce Fc is divided into the normal force fcn and the tangen-tial force fc. Fig. 1 shows Cundall and Stracks model forthe forces, which they modelled by*fcn =kst

*dn -*vpn; (8)

Mvpn = (*vpr *n) *n; (9)

*fcr =kst

*d -*vp; (10)

*vp =

*vpr *vpn; (11)

where dn and d are the particle displacements in the normaland tangential directions, respectively, vpr is the relative ve-locity, and vpn and vp are the normal and tangential relative

4196 H. Zhou et al. / Chemical Engineering Science 59 (2004) 41934203

velocities, respectively. kst is the spring stied

|fc||fcn|; (12)where is the friction coePcient, then sliding occurs, andthe tangential force is given by

fc =|fcn|*t ; (13)

where t is the unit vector de>ned by*t =

*v =|*v |. In dense

phase &ows, a particle usually touches several other oneswhatever the time. In such circumstances, the total contactforce is obtained by summing all contacts. - is determinedby the restitution coePcient e

-= 2/mpkst ; (14)

where / = 1c=1 + 12c and 1c = (1=)ln e, and mp is the

particle mass. In the particle-to- wall collisions, one particlemass is in>nitely large and the velocity vectors are all setequal to zero.

2.2.2. Drag forceThe drag force on a suspended particle is given by

*Ff= 18 d

2p C

df

2|u f *vp|(u f *vp); (15)

where Cd is the e

H. Zhou et al. / Chemical Engineering Science 59 (2004) 41934203 4197

energies (Donskoi and McElwain, 1999). Buring char par-ticle evolves according to the shrinking core model. Thechemistry of the formation and destruction of NO and N2Ois complex. So, the heterogeneous reactions of char withCO, CO2, NO and N2O and the homogeneous reactions in-volving CO, O2, NO and N2O in the boundary layer aresimpli>ed according to the theory of Amand and Andersson(1989), Johnsson (1994), and De Soete et al. (1999). Thecolliding particle-particle heat transfers are modeled on thebasis of the analysis of the elastic deformation of collidingspheres (Sun and Chen, 1988). The equations of conserva-tion of species mass fraction and of energy for a &uid celldescribe the transportation of species (NO, CO, CO2, H2O,NO, N2O, and N2) and of energy in the gas, accounting forthe e

4198 H. Zhou et al. / Chemical Engineering Science 59 (2004) 41934203

Table 1Physical and numerical simulation parameters

Properties Value

Bed height, H 4:84 cmBed width, W 7:26 cmInlet gas (wall) temperature, 1123.15, 1173:15 KTf0

Minimum &uidization velocity, umf = 7:01 104d2pg(p f)=fumf (Lin et al., 2002) (for sand at 850:0C, umf = 0:4 m s1)

Inlet gas velocity, uf0 0.4 and 0:6 m s1Density,

Coal, pc 1100 kg m3

Sand, ps 2600 kg m3

Particle diameter, dpSand, ds 1:0 mmCoal, dc 0.8, 1.5 and 2:0 mm

np value 4.7Stiles of both particle

and gas velocities in the bed (height = 0:016 m) and at itssurface (height = 0:031 m). For both phases, the pro>lesare unsymmetrical along the bed width inside the bed, themean particle velocity is positive in the center and it isnegative near the walls. This means that a circulation patternexists, with particles rising in the bed center and fallingdown near the walls. Then, when particles reach the bed

Table 2Parameters of the simulated cases

Inlet gas velocity Inlet gas temperature Coal number Coal particle diameter Number of sand(m s1) (C) (mm) particles

Case 1 0.6 850 0 1480Case 2 0.6 900 20 0.8 1460Case 3 0.6 850 20 1.5 1460Case 4 0.6 850 20 2.0 1460Case 5 0.6 850 20 0.8 1460Case 6 0.4 850 20 0.8 1460

t = 0.00 s t = 0.20 s t = 0.50 s t = 0.75 s t = 0.90 s

t = 1.0 s t = 1.30 s t = 1.45 s t = 1.70 s t = 2.0 s

Fig. 3. Time series of the particle &ow structure (case 1).

0.0 0.5 1.0 1.5 2.0

0

10

20

30

40

50

Averaged value = 0.38 %

Averaged value = 5.4 %

Rat

io o

f col

lided

par

ticle

s / %

Time / s

0

2

4

6

8

R

atio

of p

artic

le- w

all c

ollis

ion

part

icle

/%

Fig. 4. Variation of percent of colliding particles with time (case 1).

surface, their mean velocity is always negative, which ischaracteristic of the bed free area. The mean gas velocity ishigher in the bed (where the particle concentration is rela-tively higher) than at the bed surface. Fig. 7 also shows thatthe particle mean velocity distribution is not correlated to thegas velocity distribution inside the bed, whereas they seemcorrelated at the bed surface. This indicates that the parti-cle motion in the dense zone is dominated by the particleparticle interactions.

H. Zhou et al. / Chemical Engineering Science 59 (2004) 41934203 4199

(a)

(b)

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.30

50

100

150

200 Pa

rticl

e nu

mbe

r

Particle velocity/ m. s-1

Mean = 0.0SD = 0.036

-0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4

0

20

40

60

80

100Mean = -0.003SD = 0.05

Mean = -0.07SD = 0.04

Pa

rticl

e nu

mbe

r

Particle velocity/ m. s-1

Fig. 5. Calculated particle velocity distribution at 1:45 s (case 1): (a)horizontal component, (b) vertical component.

The gas and the particle turbulent intensities pro>les (de->ned as (v2f(p)i)

1=2=uf0, where i represents x and y directions,respectively) inside the bed and at its surface are presentedin Fig. 8. Clearly, the intensity distributions along the bedwidth are dinedas ui;f(p)u

j:f(p)=u

2f0). The particle stress is always much

smaller than the gas stress, the di

4200 H. Zhou et al. / Chemical Engineering Science 59 (2004) 41934203

0.00 0.01 0.02 0.03 0.04 0.05-0.025

-0.020

-0.015

-0.010

-0.005

0.000

0.005

0.010Bed heights :

: 0.016 m : 0.031 m

Parti

cle

velo

city

/ m

. s-1

Bed width / m

0.8

0.9

1.0

1.1

1.2

1.3

G

as v

eloc

ity / m

. s-1

Fig. 7. Gas and particle velocity distributions along the width in the bedand at its surface (vertical component, case 1).

0.00 0.01 0.02 0.03 0.04 0.05

0.03

0.04

0.05

0.06

0.07

Parti

cle

turb

ulen

t int

ensit

y

0.3

0.4

0.5

0.6

0.7

0.8

0.9 G

as tu

rbul

ent i

nten

sity

0.016 m 0.031 m

Bed height

0.016 m 0.031 m

Bed height

0.00 0.01 0.02 0.03 0.04 0.05

0.12

0.15

0.18

0.21

0.24

0.27

0.30

Parti

cle

turb

ulen

t int

ensit

y

Bed width / m

Bed width / m

0.50

0.55

0.60

0.65

0.70

0.75

0.80

G

as tu

rbul

ent i

nten

sity

(a)

(b)

Fig. 8. Distributions of the gas and particle turbulent intensities along thewidth in the bed and at its surface (case 1): (a) horizontal component,(b) vertical component.

of colliding particles. The mean ratio is 7.4% (case 6) andit ranges from 5.4% to 5.9% (cases 25). The presence oflarge reactive particles (coal, dp = 1:5 or 2:0 mm, 1:35% ofthe total particles) in the &uidized bed acantlythe &ow structure. These large reactive particles inhibit thebubble formation even at very early stage (t 0:2 s). Thecoal particles tend to &oat at the bed surface (most coal par-ticles are at the bed surface after 1:5 s) at low gas velocity,because of density and diameter di

H. Zhou et al. / Chemical Engineering Science 59 (2004) 41934203 4201

the bed width (cases 15). For the particle phase, there ex-ists an intensive turbulent intensity region near the walls.At the bed center, the intensity is maximum or medium incases 1, 2, and 5 whereas it is minimum in cases 4 and5. The particle turbulent intensity is always low, in partic-ular at the bed center, in the presence of large particles.The simulation shows that the presence of large reactiveparticles in the &uidized bed may acantly theparticle turbulent intensity. The distributions of the verti-cal gas turbulent intensity are similar. The intensities arehigher in the center. The bed temperature (case 2) has nosigni>cant ecant role insidethe bed.The particle turbulent intensity increases with the inlet

gas velocity, whereas the gas turbulent intensity and theReynolds stress decrease. However, the simulation showsthat the higher the inlet velocity, the higher the absolutevalues of the gas and particle &uctuations (v2f(p); i) and the

higher the Reynolds stress (ui;f(p)uj;f(p)).

5. Conclusions

The turbulent gas and particle &ow both with and withoutchemical reactions in a bubbling &uidized bed was studied.The solid phase was modeled as discrete element method(DEM) and the gas phase was modeled as 2-D NavierStokes equations for 2-phase &ow with &uid turbulence cal-culated by large Eddy simulation (LES), in which the e

4202 H. Zhou et al. / Chemical Engineering Science 59 (2004) 41934203

vpr relative velocity, m s1

vpn normal relative velocity, m s1

vp tangential relative velocity, m s1

vp particle &uctuating velocity, m s1

vrel relative velocity, m s1

vrel relative &uctuating velocity, m s1

v mean velocity of the mass &ow covering the particlesurface, m s1

Vp particle volume, m3

Vgrid volume of a computational cell, m3

x, y x and y directions

Greek letters

/i Poisson ratioij Kronecker delta porosity in &uid cell characteristic length, = (Nx Ny)1=2, mNS area of computational cell, NS =Nx Ny, m2Nt time step, sNx x direction mesh spacing, mNy x direction mesh spacing, m- coePcient of viscous dissipation friction coePcientf gas viscosity, Pa sf kinematic gas viscosity, f = f=f, m2 s1

t SGS kinetic gas viscosity, m2 s1

f gas density, kg m3

p particle density, kg m3

turbulent Schmidt number, = 1:0

ij SGS stress, ij = fvf(Sf; ij 2=3Sf;kkij) tangential unit vectorij SGS stresses, ij =fuf; iuf;j volumetric particlegas interaction, N m3

! particle rotational velocity, s1

e

H. Zhou et al. / Chemical Engineering Science 59 (2004) 41934203 4203

Sun, J., Chen, M.M., 1988. A theoretical analysis of heat transfer toparticle impact. International Journal of Heat and Mass Transfer 31(3), 969975.

Tsuji, Y., Kawaguchi, T., Tanaka, T., 1993. Discrete particlesimulation of two-dimensional &uidized bed. Powder Technology 77,7987.

Van Wachem, B.G.M., Van der Scha