Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: 9.2.1 - A binary kinetic granular model for fluidized beds
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 Material Information
Title: 9.2.1 - A binary kinetic granular model for fluidized beds Fluidized and Circulating Fluidized Beds
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: Chao, Z.
Wang, Y.
Jakobsen, J.P.
Fernandino, M.
Jakobsen, H.A.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Subjects
Subject: kinetic theory of granular flow
fluidized bed
particle segregation
friction drag
 Notes
Abstract: The paper presents a multi-fluid Eulerian model derived from binary kinetic theory of granular flows and an empirical friction theory. In the process of deriving the constitutive equations, the exact discrete particle velocity differencec C v ik ik ik   is used in this work whereas in previous studies a simplification c C ik ik  is used. As the effects due to hydrodynamic velocity differences and particle-particle friction are considered, some unconventional terms are produced. Model validation by use of the data from Goldschmidt et al. (2003) shows that the particle-particle drag models play an important role and the friction drag must also be included in order to predict the particle segregation phenomena in dense binary fluidized beds.
General Note: The International Conference on Multiphase Flow (ICMF) first was held in Tsukuba, Japan in 1991 and the second ICMF took place in Kyoto, Japan in 1995. During this conference, it was decided to establish an International Governing Board which oversees the major aspects of the conference and makes decisions about future conference locations. Due to the great importance of the field, it was furthermore decided to hold the conference every three years successively in Asia including Australia, Europe including Africa, Russia and the Near East and America. Hence, ICMF 1998 was held in Lyon, France, ICMF 2001 in New Orleans, USA, ICMF 2004 in Yokohama, Japan, and ICMF 2007 in Leipzig, Germany. ICMF-2010 is devoted to all aspects of Multiphase Flow. Researchers from all over the world gathered in order to introduce their recent advances in the field and thereby promote the exchange of new ideas, results and techniques. The conference is a key event in Multiphase Flow and supports the advancement of science in this very important field. The major research topics relevant for the conference are as follows: Bio-Fluid Dynamics; Boiling; Bubbly Flows; Cavitation; Colloidal and Suspension Dynamics; Collision, Agglomeration and Breakup; Computational Techniques for Multiphase Flows; Droplet Flows; Environmental and Geophysical Flows; Experimental Methods for Multiphase Flows; Fluidized and Circulating Fluidized Beds; Fluid Structure Interactions; Granular Media; Industrial Applications; Instabilities; Interfacial Flows; Micro and Nano-Scale Multiphase Flows; Microgravity in Two-Phase Flow; Multiphase Flows with Heat and Mass Transfer; Non-Newtonian Multiphase Flows; Particle-Laden Flows; Particle, Bubble and Drop Dynamics; Reactive Multiphase Flows
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Bibliographic ID: UF00102023
Volume ID: VID00218
Source Institution: University of Florida
Holding Location: University of Florida
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Resource Identifier: 921-Chao-ICMF2010.pdf

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Paper No 7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


A binary kinetic theory of granular flow model for fluidized beds


Zhongxi Chao*,Yuefa Wang* ,Jana P. Jakobsen t,
Maria Fernandino# and Hugo A. Jakobsen*

Department of Chemical Engineering, NTNU, Trondheim, 7049,Norway
T SINTEF Energy AS, Trondheim,7049,Norway
#Department of Energy and Process Engineering, NTNU, Trondheim, 7049,Norway
E-mail: hugo.atle.j @chemeng.ntnu.no

Keywords: kinetic theory of granular flow, fluidized bed, particle segregation, friction drag


Abstract

The paper presents a multi-fluid Eulerian model derived from binary kinetic theory of granular flows and an empirical
friction theory. In the process of deriving the constitutive equations, the exact discrete particle velocity
difference c, = Ck + vk is used in this work whereas in previous studies a simplification c,k = Ck is used. As the effects
due to hydrodynamic velocity differences and particle-particle friction are considered, some unconventional terms are
produced. Model validation by use of the data from Goldschmidt et al. (2003) shows that the particle-particle drag models
play an important role and the friction drag must also be included in order to predict the particle segregation phenomena in
dense binary fluidized beds.


Introduction

Fluidized beds are widely used in many industrial processes.
In some applications, there exist 2 types of particles with
completely different physical properties (for example
particle density and size). The particles will segregate due to
the property differences. Previous investigations (Rowe and
Nienow, 1976; Hoffmann and Romp, 1991; Wang and Chou,
1995) show that the small, light particles called flotsam tend
to rise, and the large, heavy particles called jetsam tend to
sink. Some scholars put forth some mathematical models to
describe the flow behavior. Among them, the KTGF (kinetic
theory of granular flow) Eulerian-Eulerian models are often
used. The KTGF is based on an analogy to the classical
kinetic theory of gases. The basic particle billiard ball
collision theory and some statistical methods are adopted to
obtain continuity equations, Navier-Stokes-like momentum
equations and other transport equations. Lun et al. (1984)
and Gidaspow (1994) successfully applied the theory to a
mono-particle system. Jenkins and Mancini (1987) extended
a mono-KTGF model to a binary particle system. In the
model, it is assumed that both particle species share the
same local granular temperature. Gidaspow et al. (1996),
Manger (1996), Mathiesen et al. (2000), Lu et al. (2000,
2003 and 2007), Iddir et al. (2005) applied binary KTGF
models with unequal individual granular temperatures.
Lathouwers (2000) also derived a binary KTGF model with
unequal individual granular temperatures, but with different
constitutive equations. In these models only the transport
effects due to the peculiar particle-particle velocity
differences are considered, and the effects due to the
hydrodynamic particle-particle velocity differences are
neglected. This may be one reason why the model
under-predict the particle-particle momentum coupling. In
dense flows, in which the long term particle-particle sliding


and rolling contacts play important roles, the friction
stresses and friction drag should be considered. Fan and Fox
(2008) and Gera et al. (2'k14) used an empirical friction
stress and a particle-particle drag in order to make the
particle-particle drag sufficiently large. Neglecting these
particle-particle couping terms may be a second reason why
the previous models under-predict the particle-particle
coupling. Hence, in this paper, the authors present a model
considering the effects due to the hydrodynamic velocity
differences and the particle-particle friction. Furthermore,
the data from Goldschmidt et al. (2003) is used to validate
the model, and some discussions are given about the effects
of friction drag and the hydrodynamic particle-particle
velocity differences.

Nomenclature

Cfr, particle friction coeffcient
Ck peculiar particle velocity difference between
particle i and k, Clk= C1 Ck, (ms-1)
c,k discrete particle velocity difference between
particle i and k, Ck= C1 Ck, (ms-1)
d particle diameter (m)
d,k sum of the radii of particle i and k (m)
e,k coefficient of restitution for a collision between
particle i and k
g gravitational constant (m2s-)
g,k radial distribution function for a collision
between particle i and k
mo sum of the masses of particle i and particle k(kg)
h,m initial packed bed height (m)
Kf,, correction coefficient for frictional particle drag
N number of particle species
n particle number density (m3)
p pressure (Nm 2)





Paper No


k,
v
vA

Greek
a
P


At

P,

Eg


Subsripts
g gas phase
i particle i
k particle k
col collisional
fri frictional
kin kinetic
large large particle
small small particle
Supersripts
max maximum


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

some unconventional terms related to the hydrodynamic
velocity difference v,k and conventional terms related to the


gas turbulent kinetic energy (m2s-2)
velocity (ms-1)
particle hydrodynamic velocity difference
between particle i and k, vl= v, vk, (ms-1)
letters
volume fraction of a particle species or gas
density of the particles or gas (kgm 3)
granular temperature (m2s-2)
viscosity (Pas)
particle-particle drag coefficient between species
i and k (kgm'3s-)
gas-solid drag coefficient for particle i (kgm 3s-)
gas turbulent kinetic energy dissipation rate per
unit mass(m s 3)


similar to the

(4)


(5)


-Z(l+ek),k 5 k=1


The dilute viscosities are:
4p,0,
HAr,dilute N 1 1
Sk= I n di (I +0
k=1


Governing equations

The authors derived a binary kinetic theory of granular flow
model, in which the model equations for the particle phases
are as follows.
The continuity equations are:


(ap,)+V.(apv,) 0
at
The momentum equations are:

-(ap,,) + V (av,,)
at


(1)


-aVpg V (pk, +


PC, +Pf,)+(, +Pi,(Vg-v,)+a,p,g (2)
The granular temperature equations are:
38 3
3 (a,p0,)+ -V(a,p,v,0,) =-(PCO +P, +
2 at 2
pf,) :Vv V (qco + qk,,)- 3,,0, + (3)
In order to close the model equations, the KTGF is used to
obtain the kinetic pressure tensor pk ,collisional pressure
tensor po,, the momentum source term , the kinetic heat
flux vector q, ,the collisional heat flux vector qco, and the
dissipation term for the granular temperature equation In
a dense fluidized bed, the friction pressure tensor pf should
also be included as the particle-particle sliding and rolling
contacts become important.
In calculating the constitutive equations, the assumption
,k = Ck which was used by Manger (1996) is abandoned.
The exact expression for discrete particle velocity difference
c, = C, +v,, is used. So in the equations, there are


0.500, 025)


(7)


The collisional pressure tensor is:
N
Pool = ,kV,kV,k +a,Pcoll- a, (2,u,0S, +
k k=l
/,BV v,I+2/Uk,colSk + /k,BV Vk) (8)
Where the standard strains for particle i and k are

S, = I(Vv +Vv,)- V.v,I (9a)

Sk ((Vvk) + Vvk) VVkJ (9b)

The collisional pressure which contains both the effects of
hydrodynamic and peculiar velocity differences is:

P akPlPk (1 +ekdkk ( ,k) k
kl 3mo 5


The correction coefficients ,k are:
2 d 3 a,akp, pk (+ek)
7 dk g (1+er)
k 15 kg
The collisional viscosity for particle i is:

7 (1+ ek k akppk
,co 72


S 1 1
302 +402
k I


1.95504E)


The collisional viscosity for particle k is:
(r + ) 4 a^kP0Pk
kc 72 = (1+ ek) gkd m, ak
72 mO


1 1
302 +402
1 k


1 1
1.95504 )4


(12)






(13)


peculiar velocity difference C,k
The form of the kinetic pressure tensor is
expression used by Mathiesen et al. (2000).
Phkn =a, (p,k +2/,,,, S, )
The kinetic pressure for the particle i is:
P,kin = PO,
The kinetic viscosities are:





Paper No


The bulk viscosity for particle i is:

-J (l+ek)g", 4 ckP9Pk
,B =36 1+m e ,


1 15
1.95504E 4


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

The friction pressure for particle i is considered using a
similar method as used by Lindborg (2008).


ax -aCx


1 l


(14)


f Zx (25)
-l (25)


The bulk viscosity for particle k is:

k 36 e(1 )g,4 akp'Ok
36 m,


1 1+
302 +402


1.95504


(15)


The form of the kinetic heat flux is similar to the
expression used by Mathiesen et al. (2000).
qkn =ak ,kk,.V (16)
The kinetic heat conductivity for particle i is:
2k 6 N 12
kkn N ,-lute-- --ik
1 l ) 5 k=1
N k=-1
(17)
Where the dilute heat conductivity for particle i is:
15p,,


N
z d72 (0 + 02
k=l1


S) akco


The collisional flux term is:
N
q1 = k equ Vk V-
k=l


0.500;- ')

(18)


V0, (19)


The first term is the hydrodynamic heat correction flux and
the second term is the collisional diffusion heat flux. The
hydrodynamic correction coefficient uk is:
2
z- mm mnnk (1 32 (3
uk =- 1k ( k+)2 gd (20)
10 m,

The equivalent granular temperature Oequ is:

equ = ,k+30, +3k (21)
The collisional granular heat conductivity for particle i is:
2 2xz- ak P / k
kco 2 k (1+ ek)g zkd4 (22)
k=l 5 mo
The dissipation term for the granular temperature equation
is:

y, = /1T~1. mmknnk ( i
k k
k 1 8 Mo I I

1.98,8 + 1.98 k d 6 m nk (e (23)
k 1 J 60 WO k

(V .vk (98,+158k)+v.v (98k +158,))
For a dense system, the friction pressure tensor should also
be included.

Pfn= a(,, (p f+2/f~S,) (24)


N
0 if a, t=l
The friction viscosity for particle i is given by:

p,, 2 sin m
f -,_- (26)
2a, S, S + ,/ d
All the parameters in the model are purely empirical, in the
paper, the parameter values proposed by Ocone et al.
(1993) and Lindborg (2008) as listed in Table 1 are used.

Table 1. Empirical parameters for the friction stress and pressure
model proposed by Ocone et al. (1993) and Lindborg (2008)
9( angle of internal friction, 28
F constant, Nmn2 0.5
r constant 2
s constant 3
amm lower volume fraction limit
for friction 0

The gas particle drag for particle i is given by:
150pU(l-a )a, 1.75a pg v-v
a, d2 d .8

3C g, 165 >0.
4d a .8
(27)
Where the coefficient CD is:


if Re, <1000

if Rep, >1000


The particle Reynolds number for particle i is:


Rep,


ad pg v v -


The radial distribution function proposed
(2008) is used:


9k k



Sk ~d g, + ddk
dc +d,
The particle-particle drag force is:
N
k=, l(k -v,)
k=-


(29)

by Gao et al.



(30)



(31)


In a dense fluidized bed, the particle-particle drag


i,ddlute


1 1
302 +402





Paper No


coefficient includes 3 contributions which consist of the
two particle-particle collision effects due to hydrodynamic
and peculiar velocity differences respectively, and the
particle-particle friction effect.
A = fpec + hyd + (33)
The peculiar drag coefficient which is deduced from the
effects due to the particle peculiar velocity differences is:

,kec Mkmnnk d, (1+ ek )gk
mo

27 + 1 e7 2H0 25 0 25 (34)

The hydrodynamic drag coefficient which is deduced from
the effects due to the particle hydrodynamic velocity
differences is:
1hyd mm k 2 k
k k (1+ ek )gk (- k
mo 2
1.135v5( 025 025 0O.80 125 0125)) (35)
The empirical frictional drag coefficient used in the paper
is:

,fn m'mkn k d(1+el )gkkKfCf, n-v (36)
mo 2
For the gas phase, the turbulent k model is used
(Lindborg,2008). The governing equations and constitutive
relations for the gas phase are as follows.
The continuity equation is


a (p) + V .(agpgvg) =0
The momentum equation is

a(ugpgvg) + V- (apvv,)
at


(37)


-agVpg +


V -((ag a +agRe ) aggg (gk(Vk Vg)(38)
k
The turbulent kinetic energy equation is

(a (pkg)+V(agpgkgvg -V- ag Vk +
at O kg )

gr Re VVg +aSkg g-- gpg-g (39)
The turbulent energy dissipation rate equation is

0 i Vg +


agC1 Re VV g+ C Skg -agpgC2 (40)
k k k
g g g
The viscous stress tensor is modeled as

Tg 2pg1 (Vvg ) V *3 V-1 (41)
The turbulent stress tensor is modeled by using the
gradient-and Boussinesq hypotheses:

e 3 gkI+2P 1v ) + Vvg 3) I

(42)
The turbulent viscosity is given by:


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

k2
=g = gC (43)
g
The production of the kinetic energy due to the existence
of the particles is modeled by using the equation proposed
by Jakobsen (1993).

S~-ichj2 (44)
Skg Ck (Vk g) (44)
k=l
The empirical parameters are shown in Table 2
Table 2 Empirical parameters for the k E model
C kg cg C1 C2 b
0.09 1.00 1.30 1.44 1.92 0.25
Model validations and discussions

In order to validate the models, the experimental data from
Goldschmidt et al. (2003) is used. These experiments were
conducted in a 15cm-wide, 70cm-high, 1.5cm-deep pseudo
2D gas fluidized bed. Dynamic bed heights and segregation
rates were obtained by using digital image analysis
measurements. 2 types of spherical glass beads with the
properties shown in Table 3 were used. The fluidization gas
was mainly operated from Im/s to 1.3m/s. In the
experiments, the whole 2D domain was divided into many
small cells. Goldschmidt et al. (2003) defined the bed
heights for individual species as
C at,cellhcell
(h,) (45)
C a6eN
cell
where the summations are over all grid cells, a,,cei is the
average cell volume fraction for particle i, and hkez is the
cell height. A relative segregation rate is defined as
S-1
s = (46)

in which Smax and S are defined like:
S =(2 x,) / (1- Xm) (47)


S = hsma ) / largee


(48)


where xsmaii is the mass fraction of the small particles. The
value range of the relative segregation rate s is between 0
and 1 which means zero segregation and complete
segregation respectively.
Table 2 Properties of the particles
Small articles Large particles
Particle density, kg / m3 2526 2523
Particle diameter, mm 1.5 2.5
Minimum fluidization
0.78 1.25
velocity, m/s
Friction coefficient Cf 0.1 0.15
In order to implement the mathematical model, an in-house
code was developed. The finite volume method (Patankar,
1980) is applied to discretize the model equations. The
second order central differential scheme is used to discretize
the diffusion terms. A total variation diminishing (TVD)
scheme (Lindborg, 2008; van Leer, 1974, 1977) is applied to
discretize the convection terms. The SIMPLE algorithm for
multiphase flow (Jakobsen, 2008) is used for the






Paper No


pressure-velocity coupling. The Bi-conjugate gradient
method is used to solve the discretized algebraic equations
(Lindborg, 2008). A fully implicit coupled solver is used to
solve the coupled momentum equation in one dimension at
the time.
In the model the 2 types of particles are mainly coupled by
the particle-particle drag forces. Hence, the particle
segregation is closely related to the drag force models.
Figure 1-3 show comparisons of the particle segregation
rates and the particle bed heights predicted by the model
with different particle-particle drag force models. Drag
model 1 only includes the peculiar drag force, drag model 2
includes both the peculiar and hydrodynamic drag forces,
and drag model 3 includes the peuliar, hydrodynamic drag
forces and the friction drag force (in this paperKf, = 800,

the friction coefficient takes the average values for the 2
types of particles Cf = 0.125). Figure 1 shows that the final

particle segregation rates are similar using the 3 different
particle-particle drag forces. But the segregation rate is
over-predicted in the whole dynamic segregation process if
drag model 1 or drag model 2 is applied. Drag model 2 can
give a stronger particle-particle coupling than drag model 1
since an additional hydrodynamic velocity difference effect
is included. The simulation results fit well with the
experimental data if drag model 3 is used. Hence the friction
drag is important for calculating the particle segregation in a
binary dense bed. The bed heights for the small and large
particles calculated by using (45) are shown in Figure 2 and
Figure 3. These results show that the rise of the flotsam and
the sink of the jetsam can be well predicted if drag model 3
is used.


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

0,09 -------------------------
--Simulation,dragl
S--Siulaton,drag3
o 008 ExpenmentlGoldschmldt et al (2003)
a 0 Expenment2,Goldschmldt et al (2003)
0 07- H=15cm
Sv =1 lm/s

0 g
0 05

0 10 20 30 40 50 60
times]

Figure 3: Comparisons of the bed heights of the large

particles using different drag models


A qualitative comparison of the particle segregation using
different drag models is shown in Figure 4-Figure7. The
experiments (Goldschmidt et al., 2003) and the simulations
were run for 60 seconds. Some key snapshots are taken at
time 15s, 30s, 45s and 60s. In the experiments, the small
particles are yellow and the large particles are brown. The
variable used in the iso-profiles is the volume ratio of the

small particles aa,, / (asa,, + lr) All (b) Figures

show a similar segregation process to the experimental data
(shown in (a) Figures) as drag model 3 is used. The small
particles gradually rise to the top of the bed and the large
particles sink to the bottom. The (c) Figures and the (d)
Figures show that the particles are segregated more quickly
than the experimental data if drag model 1 or drag model 2
is used. There are no big differences in the trends for the
snapshots at time 30 s, 45s and 60s.


times]


Figure 1: Comparisons of the segregation rates using

different particle-particle drag models.


(a) Experiment


10



(b) Drag 3


H =15cm
8 v=8- 1m/s

Simulation,dragl
Smulaton,drag 2
Simulation, drag3
a Expenmentl,Goldschmidt et al (2003)
o Experment2,Goldschmldt et al (2003)

S10 20 30 40 50 60
time [s]


(c)Drag 2 (d)Dragl
Figure 4 Particle segregations at time 15s


Figure 2: Comparisons of the bed heights of the small

particles using different drag models







7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


(a) Experiment


10 ) D




(b) Drag 3


(c)Drag 2 (d)Dragl
Figure 5 Particle segregations at time 30s


(a) Experiment


(b) Drag 3


(c)Drag 2 (d)Dragl
Figure 6 Particle segregations at time 45s





25-

20




10


(c)Drag 2 (d)Dragl
Figure 7 Particle segregations at time 60s


The initial bed heights, gas velocities and the small particle

ratio xsmlare 3 important influential factors determining

the particle segregation. Figure 8-FigurelO show
comparisons between the experimental data and the
simulation results with a change of bed heights, gas
velocities and the small particle ratio. In these calculations,
the drag (33) is used. The broad range of comparisons
proves that the mathematical model can predict the
segregation behavior in a binary dense fluidized bed with
reasonable accuracy.


simulation
O Expenmentl,Goldschmidt,et al (2003)
28 Expenment2,Goldschmidt,et al (2003) / 8 0

2 h =30cm 0 O
v =1 m/s
0= 5
x 05
14 O


7 O O O
o


0 10 20 30 40 50 60
time [s]


Figure 8.a Comparisons of the segregation rate


o 0,18-
-

S0,17-
E
a)
0,16.

0,15-
-


0 10 20 30 40 50 60
time [sl

Figure 8.b Comparisons of the bed height of the small

particles


Paper No


0
D n


--sImulation
|O Expenmentl,Goldschmldt et al
S D Expenment2,Goldschmidt et al
h =30cm
v =1 1m/s
x ,,,=0 5







7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


10 20 30
time [s]


40 50


60


Figure 8.c Comparisons of the bed height of the large

particles


time [s]


Figure 10.a Comparisons of the segregation rate


^
-




E
S0,10-
-





0,08-
0)
(Dl

I


10 20 30 40
time [s]


I 10 20 30
time [s]


40 50 60


Figure 9.a Comparisons of the segregation rate


E




-
0,10-


E


08-
E 0,08

0)


10 20 30
time [s]


40 50 60


Figure 9.b Comparisons of the bed height of the small

particles


0,10-


0,09
oi-


v

S0,08-


S0,07-
S

E 0,06-


S0.05-


0 10 20 30 40 50 60
time [s]
Figure 9.c Comparisons of the bed height of the large
particles


A 0,085-


0,080-
-o

0.075-
'

0,070-


0) 0,065-


n non.


0 10 20 30
time [s]


Figure 10.c Comparisons of the bed height of the large
particles






Conclusions


A novel binary multi-fluid kinetic theory Eulerian
mathematical model has been presented. The validation and
a broad range of calculations show that the drag models play
an important role and the friction drag must be included for
predicting the particle segregation in a dense binary
fluidized bed.


Paper No



0,180
E

S0,165-


0,150-
--


0,135-


S0.120-


-- simulation
A experiment ,Goldschmidt,etal(2003)
S 0 experiment2,Goldschmidt,et a(2003)



o O



h =30cm
v =1 1 m/s
x =05


simulation E
O experiments Goldschmidt et al (2003) 0
5so. experiment 2,Goldschmldt et al (2003)



30- y^



20- ] h.n= 15cm
v=115m/s
S=0 5


h =15cm
v =1 15m/s
xsmL=0 25 O


0




-- simulation
O experimentl,Goldschmidtetal (2003)
O experiment 2,Goldschmidt et al (2003)


h,=15cm E B
S=1 15m/s O
0
x ,i =0 5 O
0O

O



-- simulation
O experiment ,Goldschmidt et al (2003)
O experiment 2,Goldschmidt et al (2003)


Figure 10.b Comparisons of the bed height of the small

particles


h =15cm
S=1 15m/s
E Xsr ,=0 25

\0
S0
O


O

--simulation
O experiment ,Goldschmidt et al (2003)
O experiment 2,Goldschmidt et al (2003)


40 50


60


--simulation
O experiment1,Goldschmidt et al (2003)
O experiment 2,Goldschmidt et al (2003)
j 0

o
0

B
h =15cm 0
O
v=1 15m/s
x =s05 0
s___________________


50 60






Paper No


Acknowledgements

The PhD fellowship (Chao, Z.) financed through the
GASSMAKS program (Advanced Reactor Modeling and
Simulation) and the PAFFrx project (Particle-Fluid Flow
with Chemical Reaction Multi level models for design
and optimization of fluidized bed processes) of the
Norwegian Research Council are gratefully appreciated.


References

Fan, R.& Fox, R.O. Segregation in polydisperse fluidized
beds: Validation of a multi-fluid model. Chemical
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