Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: 14.5.5 - 3D Unsteady Numerical Simulation of the Hydrodynamic of a Gas Phase Polymerization Pilot Reactor
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 Material Information
Title: 14.5.5 - 3D Unsteady Numerical Simulation of the Hydrodynamic of a Gas Phase Polymerization Pilot Reactor Fluidized and Circulating Fluidized Beds
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: Fede, P.
Neau, H.
Simonin, O.
Ghouila, I.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Subjects
Subject: fluidized bed
two-phase flow
CFD
Euler multi-fluid approach
 Notes
Abstract: Three-dimensional numerical simulations of polymerization reactor have been carried out. The mean pressure drop have been compared with experimental data from an existing industrial medium-scale pilot. The results show that a standard pure slip wall boundary condition for the mean particle velocity leads to an underestimation of the fluidized bed height. In contrast, a no-slip wall boundary condition gives better predictions and the mean pressure distribution is in better accordance with experimental data. The using of an existing model to account for non-spherical particle shape shows that the bed height is increasing when non-spherical particle shape are considered.
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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Volume ID: VID00358
Source Institution: University of Florida
Holding Location: University of Florida
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Resource Identifier: 1455-Fede-ICMF2010.pdf

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


3D Unsteady Numerical Simulation of the Hydrodynamic of a Gas Phase
Polymerization Pilot Reactor


P. Fede*i, H. Neau**, O. Simonin*i and I. Ghouilai

University de Toulouse : INPT, UPS : IMFT :AllCe Camille Soula, F-31400 Toulouse, France
SCNRS :Institut de M~canique des Fluides de Toulouse : F-31400 Toulouse, France
i:INEOS: Innov~ne: CTL/PRO Ecopolis Lardra, F-13117, Lardra, France
fedeiiimft.fr

Keywords: Fluidized bed, two-phase flow, CFD, Euler multi-fluid approach




Abstract

Three-dimensional numerical simulations of polymerization reactor have been carried out. The mean pressure drop
have been compared with experimental data from an existing industrial medium-scale pilot. The results show that a
standard pure slip wall boundary condition for the mean particle velocity leads to an underestimation of the fluidized
bed height. In contrast, a no-slip wall boundary condition gives better predictions and the mean pressure distribution
is in better accordance with experimental data. The using of an existing model to account for non-spherical particle
shape shows that the bed height is increasing when non-spherical particle shape are considered.


Nomenclature

Roman symbols
L'D drag coefficient (-)
g gravitational constant (i.s-2)
Hbell bed height (In)
P, mean gas pressure (N.mn-)
q~ mean particle agitation (mn-.s )
Re, particle Reynolds number (-) _
UK,; mean velocity of phase k (m.s )
u< fluctuating velocity of phase k (m.s-1)
Greek symbols
asvolume fraction of phase k (-)
p, gas viscosity (kg.mn-g -)
Pre density of phase k (kg.mn3)
,F, mean gas-particle relaxation timescale (s)


medical modeling of industrial fluidized bed is challeng-
ing because of many complex phenomena taking place:
particle-fluid interactions, particle-particle and particle-
wall collisions, heat and mass transfers and chemical re-
actions.
Since a few years the numerical modeling of flu-
idized bed hydrodynamic has been extensively devel-
oped. At the same time we have seen the strong de-
velopment of the high parallel computing permitting to
perform numerical simulations of practical application
with big meshes (more than ten millions of cells). Then
these both developments allow now 3-dimensional real-
istic numerical simulations of industrial configurations
by using unsteady Eulerian multi-fluid approach.
Numerical simulations of industrial and pilot-reactor
gas-solid pressurized fluidized beds were carried out
with such an approach and have shown a good agree-
ment with the qualitative knowledge of the flows but
further detailed experimental validations were needed
(Gobin et al. 2003). Indeed, such numerical approaches
are extensively used for circulating or dense gas-solid
fluidized bed predictions but their assessments are usu-
ally restricted to a comparison between the predicted and
the experimentally measured mean pressure drop at the
wall. Recently Fede et al. (2009) made a comparison be-
tween numerical simulation and experimental data ob-
tained by Positron Emission Particle Tracking (PEPT).


Subscripts
Y
p


gas
particle
ith component of a vector


Introduction

Gas-solid fluidized beds are used in a wide range of
industrial applications such as coal combustion, cat-
alytic polymerization or uranium fluoration. The nu-
















10,60m


0,222m













7m


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



Table 1: Powder properties and operating points.
RUN #1 #2 #3 #4
Particle properties
Solid mass (kg) 608.3 617.3 640.8 650.5
Density (kg/nl3) 825.6 825.6 825.6 825.6
Mean diameter (pm) 750 750 750 750
Gas properties
Density (kg/nt") 23.6 13.2 26.0 26.8
Viscositvx10" (Pa.s) 1.53 1.74 1.37 1.38
Pressure (bar) 20.4 12.6 21 21
Fluidiz. Vel. (nt/s) 0.48 0.48 0.40 0.56


Geometry and physical parameters

The pilot's geometry is shown by Fig. 1. The pilot re-
actor is composed of a cdlindrical column with a diam-
eter of 0.74ni and an height of 7nt. In the upper part
of the pilot we find an hemispherical dome of diameter
0.695ni following a widening of height 1.41ni with an
expansion angle of 12 Finally a chimney takes place
for gas outlet. We emphasized that in the real geome-
try the chimney is cylindrical but for meshing reasons
we have represented the chimney with a squared section
(see Fig. 2) with an equivalent area.
The powder properties and operating points are given
in Table 1 corresponding to measurement performed on
the experimental pilot. Two operating pressure (RUN#1
& RUN#2) and two fluidization velocities (RUN#3 &
RUN#4) have been considered. In the experiment the
particulate phase is polvdispersed however the numeri-
cal simulation have been carried out with monodisperse
particulate phase having a median diameter.

Mathematical Model

Three dimensional numerical simulations of dense flu-
idized bed flows have been carried out using an Eule-
rian n-fluid modeling approach for fluid-particle turbu-
lent polvdispersed flows developed and implemented by
IMFT (Institut de M~canique des Fluides de Toulouse)
in the NEPTUNE CFD V1.ll'c Ther version. NEP-
TUNE_CFD is a multiphase flow software developed
in the framework of the NEPTUNE project, financially
supported by CEA (Commissariat g l'Energie Atom-
ique), EDF (Electricit6 de France), IRSN (Institut de Ra-
dioprotection et de Stiret6 Nucl~aire) and AREVA-NP.
The multiphase Eulerian approach is derived from joint
fluid-particle PDF equation allowing to derive the trans-
port equations for the mass, momentum and agitation of
particle phases (Simonin 1996). In the proposed model-
ing approach, separate mean transport equations (mass,
momentum, and fluctuating kinetic energy) are solved
for each phase and coupled through inter-phase transfer


0,74m


Figure 1: Sketch of the polymerization pilot reactor.






The PEPT technique allows to measure the mean par-
ticle velocity inside a dense fluidized bed. Fede et al.
(2009) have shown that the wall boundary condition on
the particle velocity may have a strong influence on the
fluidized bed hydrodynamic. They showed that a no-slip
wall boundary condition improves the numerical predic-
tions of the mean particle vertical velocity component in
the near wall region. However the mean pressure drop
data was not experimentally measured and they cannot
investigate the effect of such a wall boundary condition
on the bed height


In the present study we consider the configuration and
operating conditions of an existing industrial medium-
scale pilot employed for ethylene catalytic polymeriza-
tion. Several pressure probes measure the gas wall-
pressure during the polymerization process, allowing to
estimate the bed height. Numerical simulations have
been carried out in order to analyze the dependence
of the pilot reactor fluidized bed hydrodynamic to the
fluidization velocity, operating gas density and particle
shape. Also a systematic analysis of the effect of the
particle wall-boundary condition is performed in order
to complete the analysis of Fede et al. (2009).









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


f


Z
X


Z


Figure 2: 3-dimensional mesh composed of 217,668 hexahedra.


According to a large particle to gas density ratio
only the drag force is accounted as acting on the parti-
cles. Hence the mean gas-particle interphase momentum
transfer is written:


terms.
In the following when subscript k = g we refer to
the gas and k = p to the particulate phase. The mass
balance equation is:
8 8
8tamcprc+8 agpgpU g,, =0 (1)
where as is the kth phase volume fraction, pa the den-
sity and Us~i the ith component of the velocity. In (1)the
right-hand-side is equal to zero because no mass transfer
takes place.
The mean momentum transport equation takes the fol-
lowing expression:


Vr7
Ip~i= Ig~i=appy


where the particle relaxation time scale writes


1 3 p, (|vT I) D
Sp 4 pp dp


For solid volume fraction 0, > 0.3 Gobin et al. (2003)
proposed to compute the drag coefficient, CD, with


as*+ acPpag (2)
8x4


Ill= in -d,WY, Cd,Erg)


+Ik,i + [-ag1pL (U;,.. ;) + ep,23


where the Ergun's drag coefficient is given by:


CD,Erg = 200np


where ..' is the fluctuating part of the instantaneous
velocity of phase k, P, the mean gas pressure, gi the
ith component of the gravity acceleration and la y the
mean gas-particle interphase momentum transfer with-
out the mean gas pressure contribution. Finally 8pc,ij is
for k g the molecular viscous tensor and for k p
the collisional particle stress tensor.


and Wen & Yu's correlation by
C ~~ (1+ 0.15Re .687) Q1.7 Re, < 1000
DWY 0.444Re, '> 1000
(7)


arPps dU,i + Us,3 d~i
81 8x,
















In case of al, < 0.3 the Wen & Yu's correlation (7) is
employed. The particle Reynolds number is defined by

Rel, = as" |, ) (8)

The mean gas-particle relative velocity, V,,;, is ex-
pressed in terms of the mean gas velocity, mean particle
velocity and a drift velocity. The drift velocity accounts
for the correlation between the particle distribution and
the turbulent velocity (Balzer et al. 1996). In (2) the col-
lisional particle stress tensor is derived in the frame of
the kinetic theory of granular media (Boelle et al. 1995).
For the turbulence modeling we use a standard k e
model extended to the multiphase flows accounting for
additional source terms due to the interfacial interac-
tions. For the dispersed phase, a coupled transport equa-
tions system is solved on particle fluctuating kinetic en-
ergy and fluid-particle fluctuating velocity covariance.

Mesh, boundary condition and numerical
parameters

The 3-dimensional mesh is shown by Fig. 2. The mesh'
based on O-grid technique, is composed of 217,668 hex-
ahedra with approximately AJ:r Ay = 13nin and
aZ = 40nun. The time step is typically at 10's.
At the bottom (2 = 0), the fluidization grid is an in-
let for the gas with imposed surfacic velocity (QSUS,S)
corresponding to the fluidization velocity 1 7. For the
particles this section is a wall. At the top of the flu-
idized bed, we defined a free outlet for both the gas
and the particles. The wall-type boundary condition is
friction for the gas. A recent study comparing 3D nu-
merical simulations and experimental data from dense
fluidized bed have shown that the particle wall bound-
ary condition is crucial for the numerical prediction of
the fluidized bed hydrodynamic (Fede et al. 2009). In
the present study two kinds of boundary condition for
the particulate phase have been tested. First a pure slip
boundary condition,

[U star l= o

wei~ l~l (9)


corresponding to particle-wall elastic rebounds on a flat
wall. In (9) U,,,, is the tangential to the wall component
of mean particle velocity and Up,,, the normal to the wall
component of mean particle velocity. Fede et al. (2009)
have shown that no-slip boundary'


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


gives numerical predictions in good accordance with ex-
perimental measurement obtained by Positron Emission
Particle Tracking. Their analysis has been accomplished
by comparing mean particle velocity profiles at several
heights of the fluidized bed. However, Fede et al. (2009)
were not able to compare the full bed height because
of lack of pressure measurements. We emphasized that
the no-slip boundary condition for the mean particle ve-
locity and zero flux for the particle fluctuating kinetic
energy is very questionable but could represent elastic
bouncing on the wall with an isotropic angle distribu-
tion. This situation could correspond to spherical par-
ticles bouncing on very rough wall or to very irregular
particles bouncing on a smooth wall (Konan et al. 2009).
A numerical simulation is carried out as following.
First, at t = 0 the fluidized bed is filled of uniform solid
volume fraction according to the solid mass of experi-
ment. A transitory phase takes place for t E [0, 20s]
corresponding to the destabilization of the fluidized bed.
The statistics are computed for t E [20s, 100s] in-
suring a statistical convergence. Because of the mesh
and the physical time needed, the numerical simulation
have been performed on parallel computer with 32 cores
(Neau et al. 2010).

Effect of the operating fluidization velocity

In this section we study the effect of the fluidization ve-
locity on the lwdrodynamic of the polymerization reac-
tor. The physical parameters are given in Table 1 and we
compare RUN#3 and RUN#4. The numerical simula-
tions have been performed with pure slip wall boundary
condition for the mean particle velocity and with no-slip
boundary condition.
The Fig. 3 shows the wall distribution of the mean gas
pressure, for two fluidization velocities and for the two
kinds of wall boundary conditions. As expected, in the
upper part of the fluidized bed, the pressure wall distri-
bution is linear corresponding to the hydrostatic pressure
of the gas. In the lower part (less than 4m) we observe
two different behaviors depending on the wall bound-
ary condition. When no-slip wall boundary condition is
used we have also a linear gas pressure distribution. In
contrast, for slip wall boundary condition the gas pres-
sure distribution is slightly curved.
In a general manner, the fluidized bed height is de-
fined as the height where the wall gas pressure distribu-
tion shifts. Here the fluidized bed height is determined
by the following expression used by the industrial oper-
ators
dP,
Hbed = *3 +(

where the pressure drops have been measured at several


[u~~art= 0














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


4 05






0 2


-03 -02 -0 101


05


-Co 4
w --~
k
c
03


I



r
t~-c~-
~--"4 ~i
- IC


I
I.





-bV 0 40m/s, shp
SV 0O 56m/s, shp
SV-0 40m/s, noshp
SV 0 56m/s, noshp
01 02 03


Vo 40m/s, shp
SVO 56m/s, shp
VO 40m/s, no shp
SVO 56m/s, no shp
0 01 02 03


0 2


-03 -02 -0 10


Figure 4: Effect of the fluidization velocity on the radial profile of the mean solid volume fraction (0, : Vf
0.40m/s and 0, #: Vf 0.56m/s). The empty symbols correspond to the slip wall boundary for the mean
particle velocity and black-filled symbols to the no-slip boundary.



heights: is in good accordance with experimental data.


The Fig. 4 shows the mean solid volume fraction pro-
files at different heights. As expected, we observe that
for Vf 0.56m/s the mean solid volume fraction is
lower than in case of Vf 0.40m/s. This effect leads
to higher bed expansion because in both case we have
nearly the same solid mass. Then increasing the fluidiza-
tion velocity leads to an expansion of the fluidized bed
and consequently the mean solid volume fraction in a
given section decreases. The Fig. 4 shows that the dis-
crepancies between both fluidization velocities are not
equivalent in a given section. Indeed, for pure slip wall
boundary condition, in the near wall region both flu-
idization velocities lead to particle accumulation up to
ap 0.6. In contrast, in the center of the fluidized bed
for Vf 0.40m/s we have up 0.4 and a, 0.32
with Vf 0.56m/s. This trend is also observed when


= P,(z
SPg(z
=Pg(z
= (


= 1.3m)
= 2.3m)
=3.3m)
9.03m)


P, (z
Pg(z
Pg(z
Pg(z


0.3m)
1.3m)
2.3m)
0.3m) .


dPI
dP,
dPs
dP,


The Table 2 shows the comparison between the mean
pressure drops measured on the experimental pilot and
the ones from numerical simulations. As previously
mentioned increasing fluidization velocity leads to a
higher expansion of the bed and consequently to larger
value of the bed height in the model if a fixed mass
of solid is considered. We observe that no-slip wall
boundary condition gives a linear pressure distribution
(dP1 dPi dPs) as observed experimentally. Also
the bed height, computed with (11), predicted by the nu-
merical simulation with no-slip wall boundary condition


z=0 )30m





1 -06



04



0 2 t VO 56m/s, shlp
SVO 56m/s, no shlp
-03 -02 -0 1 01 01 02 03











































































Table 2: Comparison of pressure drop measured in ex-
periments and in numerical simulations Effect
of fluidization velocity.
Vf Numerical Simulation
Ex. Slip No-slip

dP1 (mbar) 33.24 42.80 37.30
SdPA (mbar) 29.20 41.62 34.65
SdP3 (mbar) 29.80 32.18 36.43
dPt (mbar) 152.0 150.2 150.4
aHbed (m) 5.24 4.17 4.46

dP1 (mbar) 28.84 42.30 34.35
SdPA (mbar) 26.97 39.20 30.93
SdP3 (mbar) 29.51 30.01 32.84
usdPt (mbar) 140.0 153.5 153.4
aHbed (m) 5.22 4.43 4.99


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


0O 30m


;i~7


a~~0~
-C--*, ,

..
..


i- 1



-03 -02 -01 60


V ) 40m/s, shp
e-V ) 56m/s, shp
SV ) 40m/s, n sp
t ~ 6m/s, no shp
01 02 03


V,-0 40m/s, shp
V,-0 56m/s, shp
-5 V-0 40m/s, no
C0,- 56m/s, no si
-03 -02 -0 1 u0 01 02 03



z 330m


-3
-5






-03 -02 -01 -uO


*
**









t- ~ 6m/s, no shp
01 02 03


-,3

+- 2





-03 -02 -0 1 00


t~yP;B



SV,-0 40m/s, shp
SV,-0 56m/s, shp
- V, (M6m/s, nosh
01 02 03


Figure 5: Effect of the fluidization velocity on the radial profile of the mean axial gas velocity normalized by the
fluidization velocity (0, : Vf=0.40m/s and 0, #: Vf 0.56m/s). The empty symbols correspond to
the slip wall boundary for the mean particle velocity and black-filled symbols to the no-slip boundary.


no-slip wall boundary condition is used.

The Fig. 4 exhibits that the no-slip wall boundary con-
dition leads to lower mean solid volume fraction. This
point was expected because we have seen in Fig. 3 that
no-slip wall boundary condition leads to larger value of
bed height. More interesting we observe the modifica-
tion of the shape of mean solid volume fraction which
exhibits peaks localized in the near wall region. These
modifications can be explained by the modification of
the mass flux in near wall region by applying the no-slip
wall boundary condition.

The Fig. 5 shows the radial profiles of mean gas veloc-
ity normalized by the fluidization velocity. We observe
that the fluidization velocity does not modify the mean
gas velocity profile. In contrast, the wall boundary con-
dition noticeably changes the mean gas velocity profile
because of the modification of the mean solid volume














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


Om
Vpo 40m/s, shp
Vpo 56m/s, shp
VpO 40m/s, no shp
VpO 56m/s, no shp


V,-0 40m/s, shp
e V,-0 56m/s, shp
V-0 40m/sno shp
SV,0 56m/s, no shp


3 -


r -C~ t
o
r


-03 -02 -0 1 0 01 02 03
r (m)


z=2 30m
Vpo 40m/s, shp
e-Vp 56m/s, shp
3 Vp 40m/s, no p
SVpO 56m/s, no sp


-03 -02 -0 1 0 01 02 03
r (m)


z 330m
V,-0 40m/s, shp
3 V-0 40m/s, no sh
V,=0 5m/sno shp


-03 -02 -0 1 0 01 02 03
r (m)


Figure 6: Effect of the fluidization velocity on the radial profile of the mean axial particle velocity normalized by the
fluidization velocity (0, : Vf 0.40m/s and 0, #: Vf 0.56m/s). The empty symbols correspond to
the slip wall boundary for the mean particle velocity and black-filled symbols to the no-slip boundary.


fraction observed in Fig. 4. Indeed, in a dense fluidized
bed the near-wall region exhibits downward solid mass
flux. The particles entrain the gas at their own veloc-
ity and as the solid volume fraction is reduced, by no-
slip wall boundary condition, the solid mass flux in the
near-wall region decreases and consequently the inten-
sity of the downward gas velocity. The flow rate balance
implies that the gas velocity in the bulk is then also re-
duced.





The Fig. 6 shows the radial profiles of the mean axial
particle velocity normalized by the fluidization velocity.
For z < 3m the fluidization velocity has no effect on
the shape of the radial profile of the mean axial particle
velocity.


Effect of the operating gas density (pressure)



The present section is dedicated to the influence of the
operating gas density on the hydrodynamic of the flu-
idized bed. The modification of operating density corre-
sponds to the modification of the operating pressure that
can occurs in industrial facilities.

The Fig. 7 shows the wall pressure distribution mea-
sured for two operating gas densities. For p,=
2 : I l: /m3 the bed height is larger than in case of p,
13.2kg/m3 because the drag force is increased leading
to a fluidized bed expansion. We find also this trend in
Table 3 where the fluidized bed is computed with (11).
As previously, the numerical predictions are slightly im-
proved by the using of the no-slip wall boundary condi-
tion for the mean particle velocity.













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


10 -









S4-


SV,=0 40m/s, slip
SV,=0 56m/s, slip
V,=0 40m/s, no slip
SV,=0 56m/s, no slip


~~p,=23 6kg/m3
Sp,=13 2kg/ms
p,=23 6kg/ms
<=p13 2kg/ms


*

*:.


16000


12000 16000


4000 8000
p-po (Pa)


12000


4000 8000
p-po (Pa)


Figure 3: Effect of the fluidization velocity on the wall
distribution of the mean gas pressure (0:
Vf 0.40m/s and 0: Vf 0.56m/s).
The empty symbols correspond to a slip wall
boundary for the mean particle velocity and
black-filled symbols to the no-slip boundary.
The reference pressure po is taken at z =
8.5m.


Effect of particle shape

In this section we propose to analyze the effect of non-
spherical particle shape on the hydrodynamic of the
dense fluidized bed. According to Loth (2008), non-
spherical particle shape can be taken into account in
the drag law by introducing two parameters: fshape and
Shape. These two coefficients represent the asymptotic
behaviors of drag law for Re, < 1 and Re, > 1 re-
spectively. Following Loth (2008), the modified particle
Reynolds number writes

Re shape Re(12)
shape

where Re, is the particle Reynolds number of spheri-
cal particles and is given by (8). The drag coefficient is
modified according to
24 (+lie"g i (3
CD = shape E .5e067 17 1)

This drag coefficient is used instead of (7) in case of
Re* < 1000. To investigate the effect of non-spherical
particle shape two numerical simulations have been car-
ried out with the same operating condition correspond-
ing to RUN#1 but in one case Cshape = shape 1.
(spherical particle) and in other case Cshape 2.05 and


Figure 7: Effect of the operating gas density on the
wall distribution of the mean gas pressure
(0, : p, 2 : al: _/m3 and 0, #: p,
13.2kg/m3). The empty symbols correspond
to the slip wall boundary for the mean par-
ticle velocity and black-filled symbols to no-
slip boundary.




fshape 1.05 (non-spherical particle shape). These val-
ues have been chosen according to Loth (2008). Based
on the previous analysis no-slip wall boundary condi-
tions have been applied.

The Fig. 8 shows the axial mean gas pressure distribu-
tion measured at the wall. As expected the non-spherical
particle shape leads to a fluidized bed height larger than
in case of spherical particles. Table 4 summarizing the
pressure drop measured at the wall and the bed height
also exhibits this trends. This increasing of fluidized
bed results from increasing drag force by non-spherical
Shape.

The radial distribution of mean solid volume fraction
is shown by Fig. 9. In each section, the averaged solid
volume fraction is reduced because the bed height is in-
creased. However, we observe that, in all sections, the
shapes of the radial profiles are very similar. It means
that, in our particular case, the particle shape modifies
the bed height but not the hydrodynamic of the fluidized
bed. We also find this trend in Fig. 10 showing the ra-
dial profiles of mean axial velocity particle distribution.
The modification of the particle shape does not modify
the mean particle velocity distribution in a section of the
fluidized bed.








































































of gas density.

p E Numerical Simulation
x. Slip No-slip
dPI (mbar) 25.77 42.44 36.33
SdP, (mbar) 26.58 39.73 34.06
SdP (mbar) 24.01 29.00 35.19
dPt (mbar) 133.0 142.1 142.5
Hbed (m) 5.52 4.14 4.35
SdPI (mbar) 27.89 43.15 38.20
SdP, (mbar) 29.99 41.68 35.81
SdPs (mbar) 26.59 34.96 38.15
dPt (mbar) 128.4 136.3 136.3
Hbede (m) 4.86 3.71 3.94


Table 4: Comparison of pressure drop measured in ex-
periments and in numerical simulations Effect
of particle shape.
Numerical Simulation
Ex. Spherical Non-spherical
dPI (mbar) 25.77 36.33 32.61
dPi (mbar) 26.58 34.06 30.20
dP3 (mbar) 24.01 35.19 29.00
dPt (mbar) 133.0 142.5 143.2

Hbed (m) 5.52 4.35 4.98


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


0O 30m


z 130m
-----------~-----~- 07-~--------~-----


06+


,,


~.~..
,, I
X
Cc
etc,


`



r J
~A-Ct-C r
~utttt~x


0 2
SSpherical partcles
Non-spherical partcles
-03 -02 -0 1 00 01 02 03
r (m)


z=2 30m


0 2
SSpherical partcles
Non-sphericalpartles
-03 -02 -0 1 00 01 02 03
r (m)


z 330m
0 7


Figure 9: Effect of non-spherical particle shape on the radial profile of the mean solid volume fraction. The wall
boundary for the mean particle velocity is no-slip.





Table 3: Comparison of pressure drop measured in ex-
periments and in numerical simulations Effect













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


0O 30m


=130m


2




x
*- -I-
o
B




-03 -02 -O 1


SSpherical partcles
SNon-spherical partcles
01 02 03


Figure 10: Effect of non-spherical particle shape on the radial profile of the mean axial particle velocity. The wall
boundary for the mean particle velocity is no-slip.


Conclusions


Three-dimensional unsteady numerical simulations of
polymerization reactor have been performed. The mean
pressure distribution has been extracted in order to com-
pare with available experimental data. The results show
that a no-slip wall boundary condition improves the nu-
merical predictions of the hydrodynamic of the polymer-
ization reactor in terms of bed height. The influence of
operating conditions has been investigated. As expected,
it has been shown that increasing fluidization velocity
leads to higher fluidized bed height. However, the gas
velocity radial profiles are not strongly modified. In con-
trast the particle velocity radial distribution is affected
by the modification the solid volume fraction and then
the mass flux near the wall. The numerical simulations
have shown that increasing the operating gas density
leads to an expansion of the fluidized bed. The effect of


non-spherical particle shape has been investigated. The
results shows that non-spherical particle shapes lead to
higher bed because of larger drag coefficient. The gas
pressure distribution at the wall exhibit more linear pro-
file.


Acknowledgements

This work was granted access to the HPC resources
of CINES under the allocation 2010-026012 made by
GENCI (Grand Equipement National de Calcul Inten-
sif).


References

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


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Sphencal particles
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4000 8000 12000
P-Po (Pa)


Figure 8: Effect of non-spherical particle shape on the
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