Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: 13.1.2 - Comparison between DNS and DEM-CFD coupling mesoscopic simulation for 2-D spouted fluidized bed
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 Material Information
Title: 13.1.2 - Comparison between DNS and DEM-CFD coupling mesoscopic simulation for 2-D spouted fluidized bed Fluidized and Circulating Fluidized Beds
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: Tsuji, T.
Yada, H.
Yoshikawa, K.
Tanaka, T.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Subjects
Subject: gas-solid flow
fluidized bed
DNS
immersed boundary method
discrete element method
DEM-CFD coupling mesoscopic model
 Notes
Abstract: The direct simulation of flows including dense solid particles such as that in gas-fluidized beds is a challenging problem. A coupling method between discrete element method (DEM) and immersed boundary ( IB ) method is developed in this paper. In gas-fluidized beds, particles take complex arrangements by the interactions in-between particles, particles-wall in addition to particle-gas flows. Gas flows go through narrow gaps in-between particles and it is still difficult to capture these microscopic flows accurately while it has not been discussed well up to the present. In this paper, resolution-dependency studies are performed for several test problems in that hydrodynamic interactions between particles are important. Besides, a direct simulation of a two-dimensional gas-fluidized bed under a spouting condition is performed using IB-DEM method. To enable direct comparison, a DEM-CFD mesoscopic model simulation is also performed under the same condition and results are compared.
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: VID00318
Source Institution: University of Florida
Holding Location: University of Florida
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Resource Identifier: 1312-Tsuji-ICMF2010.pdf

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


Comparison between DNS and DEM-CFD coupling mesoscopic simulation
for 2-D spouted fluidized bed


Takuya Tsuji*, Hirotaka Yada, Kaoru Yoshikawa and Toshitsugu Tanaka

Department of Mechanical Engineering, Osaka University
2-1 Yamada-oka, Suita, Osaka 565-0871, Japan
tak @mech.eng.osaka-u.ac.jp


Keywords: Gas-Solid Flow, Fluidized Bed, Direct Numerical Simulation, Immersed Boundary Method, Discrete Element
Method, DEM-CFD coupling mesoscopic model

Abstract

The direct simulation of flows including dense solid particles such as that in gas-fluidized beds is a challenging problem. A
coupling method between discrete element method (DEM) and immersed boundary ( IB ) method is developed in this paper.
In gas-fluidized beds, particles take complex arrangements by the interactions in-between particles, particles-wall in addition
to particle-gas flows. Gas flows go through narrow gaps in-between particles and it is still difficult to capture these
microscopic flows accurately while it has not been discussed well up to the present. In this paper, resolution-dependency
studies are performed for several test problems in that hydrodynamic interactions between particles are important. Besides, a
direct simulation of a two-dimensional gas-fluidized bed under a spouting condition is performed using IB-DEM method. To
enable direct comparison, a DEM-CFD mesoscopic model simulation is also performed under the same condition and results
are compared.


Introduction

Gas-fluidized beds are widely used in industrial processes.
Flows in the beds have a multi-scale structure. The
concentration of solid particle is high and interactions
in-between dense particles, particle-wall and particle-gas
flow induce a spontaneous formation of internal
characteristic flow structures such as bubbles that are far
larger than the particle. These internal structures make the
flows unstable and complex and are influential for the entire
behavior of the flow. To enable advanced engineering
designs, it is important to know the behavior of internal
flow structures in the bed. The enhancement of our
knowledge on phenomena occurring in each scale under an
overall multi-scale structure shall help the essential
understanding of this type of flows. Due to the existence
of dense particles, however, it is still difficult to observe the
internal flows at each scale directly and a reliable numerical
model has been desired. The coupling method between
discrete element method and computational fluid dynamics
( DEM-CFD ) originally proposed by Tsuji et al. (1993) has
been applied to this type of flows successfully. From its
concept, this model can be regarded as a mesoscopic one.
The size of fluid calculation cell used in the model is larger
than particles and enough smaller than mesoscopic
characteristic structures such as bubbles. Hence, only flow
phenomena existing in meso and macro-scales are directly
resolved and microscopic flows occurring around each
particle are not. In the model, the effects due to
microscopic flows are taken into account indirectly by using
empirical equations.
The momentum, heat and mass transfers between gas-solid
phases are occurring through each particle's surface mainly.
In addition to meso and macroscopic behaviors, it is also


important to advance our understandings on microscopic
flow phenomena. A numerical technique which enables a
direct observation of phenomena occurring in a microscopic
scale is required.
Direct simulations of the flow including solid particles
become feasible (e.g., Kajishima et al., 2001; Pan et al.,
2002 and Uhlmann, 2005). The simulations of a
gas-fluidized bed including dense solid particles are tried by
several researchers recently (van der Hoef et al., 2008 and
Kuwagi et al., 2009), however, it is still a challenging
problem.
The purpose of our study is to establish a reliable direct
simulation technique which enables detailed observations of
the flow including microscopic phenomena. In the present
study, a coupling method between discrete element method
and immersed boundary method ( DEM-IB ) is developed.
In IB approaches, it is usual to use a fixed Cartesian grid
system and the accuracy of calculation heavily depends on
the resolution we adopted. In dense flows, particles are
interacting with each other and complex arrangements are
formed during a fluidization. It is usual that an
inter-particle distance is smaller than a particle diameter and
it is needed to resolve the flows existing in narrow gaps
in-between particles. The resolution requirement might be
more crucial comparing to dilute particle-laden flows,
however, it has not been discussed well up to the present.
In the present study, resolution-dependency studies are
performed for DEM-IB coupling method at first. In
addition to fluid drag forces working on a single particle,
resolution-dependency studies are performed for adjacent
paired particles and particles in randomly-packed bed.
Besides, by using DEM-IB method, a calculation of a
two-dimensional gas-fluidized bed under a spouting
condition is performed. For comparisons, a calculation





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


using DEM-CFD coupling mesoscopic model is also
performed.


Governing equations

The governing equations of particle-laden incompressible
Newtonian flow are the continuity and Navier-Stokes
equations.

V.uf = 0, (1)
Du,
P D = V-r+pfg (2)

where pf denotes the fluid density, ufthe fluid velocity, rthe
stress tensor:
T=- -plI+p Vu+ (Vu) (3)


where p the static pressure, p, the fluid viscosity. pf and yf
are assumed to be constant. The last term of the right-hand
side of Eq. (2) represents external forces such as the gravity.
The motion of a spherical solid particle is given by an
equation of momentum and angular momentum in a
Lagrangian frame of reference,

d(mpUp) Fc + Ff +G (4)
dt

dl( IM w, )
d(t = M +M +NP, (5)

where up is the translational velocity of the particle, mp is
the angular velocity of particle rotation, mp the mass, Ip the
inertia tensor given by Ip=(2/5)a2mj for the particle of
radius a. F, is a contact force with other particle and wall,
Ff a fluid force and Gp an external force. Me, Mf and Np
are the corresponding torques, respectively. The
summations in Eqs. (4), (5) are performed for all particles
and walls in contact.


Contact force by discrete element method

In the flows including dense solid particles, contact forces
in-between particles and particle-wall become important.
Cundall & Strack (1979) proposed a model in which a
contact force is modeled by the combination of simple
mechanical models such as a spring, a dashpot and a friction
slider as shown in Fig. 1.
The contact force is divided into the normal force Fc, and
tangential force Fc that are given by

Fen = -kdn rlv, (6)
v,n =(v, n)n, (7)


and tangential directions, respectively. k, and k, are the
stiffness of the spring for each direction, respectively. n is
the unit vector in the normal and outward direction at the
surface. v, is the relative velocity vector and 7 is the
coefficient of viscous dissipation. When the following
relation is satisfied,

IF, > f IFc,l (10)

where /tis the coefficient of friction, sliding takes place and
the tangential force is replaced by

Fc, = -f IFct. (11)

t is the unit vector defined by t = v/|vl.


Body-force type IB method by Kajishima et al.
(2001)

Kajishima et al. (2001) proposed a coupling method for a
moving particle-fluid system. In the method, cell size of
the calculation is smaller than particles. A system
consisted from particles and fluid flow is calculated
assuming the fluid occupies the entire flow field and the
effect of particles is expressed by introducing an additional
force which constrains the fluid velocity field to meet the
boundary condition at the particles surface. The following
particle volume-weighted velocity u is introduced.


u av +(1 a)uf


(12)


where a is the volumetric fraction of particle at a targeted
cell. It takes a =0 for a fluid-only cell, a =1 for a cell
contained in a particle and 0< a <1 for a cell across the
interface. v, is the velocity inside of the particle:


Vp = u, +rx %,p


(13)


where r represents the relative position from the center of
the particle to the particle surface. No-slip and
no-permeable conditions are imposed on its interface,
because the particle is rigid. Thus, the continuity
restriction is also assured on u in the whole domain,


Vu = 0.


Fc = -kd, rv,
Vt = Vr -Vn


(14)


Equation for u is introduced as


where d. and d, are the particle displacements in the normal


Paper No





Paper No


au 1
S Vp + H +fp,
at pf


H = -uVu +v f V.[Vu+(Vu)T]+g.


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

of continuity and momentum derived by Anderson &
Jackson (1967).


0 +V.(U,)=0 (23)


f is the kinematic viscosity of fluid. Eq. (15) is similar to
the Navier-Stokes equation (2) excepting for the last term.
fp is the force to constrain the predicted flow field to satisfy
the boundary condition on the particles' surface.
Time-marching calculation of Eq. (15) consists of two steps.
In the first step, we predict the velocity by using


= u" +At(-Vp /p+H)


regardless of a. The superscript represents the time and At
the time increment. The predicted velocity should be
modified byfp to meet the definition of u"+'. For the cells
inside the particles (a =1), fp =-(up u)/At gives u =vp.
For the cells occupied with fluid (a =0), on the other hand,
Eq. (15) is identical to Eq. (2) because fp vanishes. The
added termf, is modeled with a linear interpolation of a


Hence as the second step, the predicted velocity i is
constrained to the particle volume-weighted velocity u by
using Eq. (18).
Fluid force and torque working on a particle can be obtained
by integrating the fluid stress and torque on the particle
surface,


F,= frT-ndS+G,
Sp
Mf = frx(Tn)dS.


fp in Eq. (18) can be interpreted as the momentum exchange
term through the interface. In this method, fluid force
acting on the particle surface is replaced by the volume
integral of mutual interaction force, such as


F1 = -p, ffdV,
VP

V


C +
p +f
Pf


(24)


Quantities such as pressure p and velocity uf are averaged
in the cell using a weight function. In the meso and
macro scales directly treated in DEM-CFD approach, the
influence of viscosity is negligible and the inviscid
behavior is assumed in Eq. (24) (Tsuji et al., 1993). The
void fraction of each cell e can be defined by the number
of particles existing in the cell at each time step. The last
term in Eq. (24) denotes the effect of particles on fluid
motion which is given by


f=P Uf) (25)

where up is the particle velocity vector averaged in a cell.
When the void fraction is less than 0.8, the coefficient P is
deduced from the well-known Ergun equation (Ergun,
1952). When c 20.8, that from Wen & Yu equation is
used (Wen & Yu, 1966).


_U' }


1- (1-e) 1 p
I150 +1.75p UP
dp8 dp
(e <0.8)


3 Up-u p(1-0) 2
4 D d


(26)


(e > 0.8)

Drag coefficient CD is obtained by using Shiller &
Naumann and Newton equations depending on the particle
Reynolds number.


=24(l+0.15Re687)/IRe (Re < 1000) (27)
S 0.43 (Re > 1000)


where


Re= u -uf psEdp.p.


(28)


In DEM-IB coupling method, fluid and particle motions
are obtained by solving Eqs. (4), (5), (14), (15).

DEM-CFD coupling mesoscopic model by Tsuji et
al. (1993)

In DEM-CFD coupling mesoscopic model (Tsuji et al.,
1993), the cell size used in calculations is larger than
particles and enough smaller than characteristics
meso-scale characteristic structures. Fluid motion is
obtained by solving the locally-phase averaged equations


Fluid force working on a particle Ff can be obtained as a
combination of fluid drag and pressure gradient forces,


(29)


Ff,= (u-uf)- VP}m/pp


In DEM-CFD mesoscopic model, fluid and particle
motions are obtained by solving Eqs. (4), (5), (23), (24).


where


st u)+ V-.(su/U)


fp =c (v -fi)At.






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


inflow


Figure 2: Setup for drag force calculation of
an isolated particle


Fluid force working on a single particle

In the IB method adopted in this paper, a solid particle is
represented by its volume fraction distributions. The
reproducibility of particle's surface geometry and flow field
around the particle in calculation heavily depends on the
resolution. Resolution-dependency studies for a single
particle in flows have been extensively conducted such as
fluid drag force, Saffman and Magnus lift forces and viscous
torque (Kajishima et al., 2001; Tsuji et al., 2003; Kuwagi et
al., 2009 and Yada, 2010).
In this section, the results of steady drag force working on a
single spherical particle are shown. Hereafter, the size of
computational cell used in DEM-IB calculations is uniform
through the study. The setup of calculations is shown in
Fig. 2. A particle is fixed in the domain. Uniform inflow
and convective outflow conditions are imposed on the
upstream (x =0) and downstream (x =30d,) boundaries,
respectively. For side boundaries, a traction-free condition
is used. The resolution is varied as d/Ax = 4, 8, 16, 32 and
results are compared with following empirical equations;


Figure 3: Drag force of a single particle


White (1974):
24 6
CD = + +0.4,
Rep 1+ Rep


Shiller and Naumann (1933):
CD 24 (1+0.15Re.687)
Re
(Rep <800),


and

Morsi and Alexander (1972):

CD = C + C + C2
Re, Re2


(30)





(31)


(32)


where Co, cl and c2 are the model parameters.
Fig. 3 shows the relation between the particle Reynolds
number and drag coefficient. We can confirm that a
general tendency of all resolution cases agrees with the
empirical equations. Especially for Re, =10, 50, 100, a
resolution-dependency is not apparent and the results agree
well with empirical equations quantitatively. In the regime
100 < Rep < 1000, on the contrary, a dependency on the
resolution becomes apparent. From Fig. 3, it is confirmed
that a fluid drag force is estimated larger as the resolution
becomes lower. It is known that wake structures formed
behind the particle give large influences on the fluid drag
force working on a particle. Wake structures becomes
smaller as the particle Reynolds number becomes larger.
Hence, a higher resolution is required in high particle
Reynolds number cases. The empirical equation by White
(1974) shows larger values comparing to Shiller and
Naumann (1933) and Morsi and Alexandar (1972) in this
region. Excepting for d/Ax = 4 case, the results are
located in-between these empirical equations. When Rep
=1000, the result of d/Ax = 4 case is 76 and 33 % larger
comparing to Morsi and Alexandar (1972) and White (1974)
equations, respectively.


Fluid force working on paired two particles

In dense flows, many particles come close each other and
have contacts. In such situation, hydrodynamic
interactions due to the flows through the narrow gaps
existing in-between particles become important. In this
section, fluid drag forces working on paired two particles
are investigated. Particles are arranged in tandem and side
by side normal to the main stream. In addition to the
resolution of calculation, an inter-particle distance is varied
and its influence is investigated. In tandem arrangements,
the same domain size with the single particle case is used.
In side-by-side arrangements, a cross-sectional size of
calculation domain is enlarged to keep the distance between
a particle surface and side boundary to 5.75dp through the
cases.
Fig. 4 shows the relation between normalized inter-particle
distance and drag coefficient of the trailing particle in
tandem arrangements. The particle Reynolds number in
gas-fluidized beds can be O(103). Investigations in paired


Paper No


White (1991)
Schiller and Nauman (1933)
orsi and Alexander (1972)
x d/Ax 4
p
A d/Ax 8
p
d/Ax 16
p
d* /Ax 32

`VX






Paper No


0.7
0.6
0.5
0.4
0.3,
0.2
0.1 k


X d/Ax
P
p
A d/Ax
p
V d/Ax
P
* d/Ax
p


0 1 2 3
l/d

Figure 4: Drag force of the trailing particle for two
particles aligned streamwise

1.25


X d/Ax 4
p
A dAx 8
P
v d/Ax 16
* d/Ax 32
P


0 1 2 3
l/d
p


Figure 5: Drag force of particles aligned side by side

arrangements also should be conducted up to 0 (103),
however, the number of experimental results is restricted in
high Reynolds number regions and the results of Rep= 106
case is discussed in this section. Inter-particle distance 1 is
defined as a distance between particle surfaces. Drag
coefficient is normalized by that of a single particle under
the same Reynolds number condition. Experimental
results by Zhu et al. (1994) are also shown. A general
tendency of all resolution cases agrees with the experimental
result and the drag forces decrease when l/d, becomes
smaller. When two particles are touching (l/d,=O), the drag
coefficient becomes 23% of single particle in the case
d/Ax=32. In the case of /d, = 3, the hydrodynamic
interaction between two particle is still clearly observed.
When the inter-particle distance becomes larger than 2, a
resolution-dependency is not observed clearly. Excepting
for the case d/Ax=-4, a resolution-dependency is also not
clear in the region /d, < 1.
Fig. 5 shows the relation between inter-particle distance and
drag coefficient working on the particles placed side by side
normal to the main stream. The particle Reynolds number
is set to 102. An experimental result by Chen & Lu (1999)
is also shown. A general tendency of all resolution cases
also agrees with the experimental result in side-by-side
arrangements. Comparing to the tandem arrangements, the
effect of adjacent particle is not so intense even if the two
particles are almost touching (l/d,=0.3). In is confirmed
that the results of d,/Ax=16, 32 cases are almost converged
in the range l/d, >1. Similar to the single particle and two
particles in tandem arrangement, the result of d/Ax=-4 case
is largely deviated from others.


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


Table 1: Conditions for a packed bed
Case 1 2
Domain size
(L i siL 60 x 300 x 60
(Lx, L,, L,) [mm]
Number of mesh [-] 50 x 750x 150 300 x 1500 x 300
Particle diameter:
[mm] 3.20
d, [mm]
Number [-] 455
dAx [-] 8 16
Void fraction: e [-] 0.4261
Viscosity: u [Pa- s] 1.81x10-5
Density: pf[kg/m3] 1.205
Reynolds number:
1, 5, 10, 50, 100, 500
Re, (=uodJv)

Fluid force working on particles in a
randomly-packed bed

The fluid drag force working on particles in
randomly-packed bed is verified. Conditions of
calculation are shown in Table 1. Due to the
computational time limitation, only results of d/Ax=8 and
16 cases are compared. A packed bed including
randomly-distributed particles is obtained as follows.

(1) An arbitrary random velocity is given to all particles
arranged regularly at first.
(2) By imposing the gravity force, particles are settled
down from an appropriate height. During the settling,
routines for the fluid calculation are skipped and only
DEM calculation is performed.
(3) Due to the artificial random velocity, particles have
contacts with other particles. Potential and kinetic
energy particles obtained are dissipated gradually due
to the dashpot. After the steady state is reached,
positions of particles are fixed.

For inflow and outflow boundaries, an uniform inflow and
convective outflow condition are imposed, respectively.
Periodic boundary condition is used for horizontal (x, z)
directions. To avoid the effect of artificial forced inflow,
all particles are kept in 60 mm higher position from the
inflow boundary. The fluid drag forces working on all
particles in the domain are averaged and results are
compared with the drag force equation obtained from Ergun
equation.
Ergun (1952) shows that the pressure drop in a packed bed
consisted from spherical particles having the same diameter
dp is expressed as


-Ap 1- 150(1-p +1.75pu0
L d, dp


(33)


where L, uo are the dimension and superficial velocity of the
packed bed, respectively. The fluid drag force working on
a particle, FD, is expressed as


S(34)
F, = CDA 2p'fof (34)






Paper No


p
104 V v rd/Ax-16


102


101
10


100 10' 102 103


Figure 6: Drag force working on a particle in
randomly-packed bed (e =0.427).


where CD is the drag coefficient, A is the cross-sectional
area of the particle. When the pressure drop is balanced
with the fluid drag force working on N particles existing in
the domain V,


FD xN= xV.
L


(35)


From Eqs. (33), (34), (35), an empirical equation for the
drag force working on a particle in a packed bed is obtained.


CD = 150,-u 1 +1.75 1
3 d,u -' C3


Fig. 6 shows the relation between the particle Reynolds
number and the drag coefficient defined by Eq. (36). The
averaged void fraction of the packed bed we obtained by
the settling method is 0.4261. In the region 1_ Rep, 50,
a resolution-dependency is not apparent and the behavior
of both cases agrees with Eq. (35) in the qualitative sense.
Quantitatively, the values obtained by calculations are 2-3
times larger from Ergun equation. In the region Rep >
100, the results of d/Ax=8 become relatively large
comparing to the Eq. (35).


2-D Gas-fluidized bed under spouting condition

In this section, a calculation of flow inside of a fluidized
bed is performed by using DEM-IB method. For
comparisons, a calculation by using DEM-CFD
mesoscopic model is also performed. The conditions of
calculations are shown in Table 2. 3-D calculations are
performed for so-called 2-D fluidized bed in which the
depth of the bed is restricted comparing to other
dimensions. Initially, particles are packed randomly in
the bed using the same technique shown in the previous
section. The same initial condition is used for both
calculations. Calculations are performed under a
spouting condition where a gas jet is injected only from the
bottom center of the bed.
No-slip condition is used for side and bottom walls in the
DEM-IB approach. On the contrary, slip condition is
used in the DEM-CFD mesoscopic model approach
following Tsuji et al. (1993). For the upper boundary, the
convective outflow condition is used in both approaches.
In DEM-IB calculation, a numerical code is parallelized by


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

Table 2: Conditions for a fluidized bed under
a spouting condition
Container
Size of container (Lx, L, L,) [mm] 96 x 160 x 16
Number of mesh (DEM-IB) [-] 240 x 400 x 40
Number of mesh (DEM-CFD) [-] 12 x 16 x 2
Inflow cross-section size [mm] 16 x 16
Particle
Particle diameter: d, [mm] 3.20
Number [-] 3104
Density: p, [kg/m3] 910
Initial bed height [mm] 64
Gas
Superficial velocity: uo [m/s] 1.0
Minimum fluidization velocity: 1.037
Umf [m/s]
Viscosity: p [Pa- s] 1.81x10-5


Kinetic viscosity: v [m2/s]
Density: p [kg/m3]
Gravitational constant: g [m/s2]
DEM
Normal spring constant: k, [N/s]
Tangential spring constant: kt [N/s]
Coefficient of restitution: e [-]
Coefficient of friction
(particle particle): p, [-]
Coefficient of friction
(particle-wall): uli, [-]
Time
Time increment (IB-DEM): At [s]
Time increment (IB-CFD): At [s]
Total time: T [sl


1.45 10-5
1.205
9.8


800
200
0.43
0.88


Ixl0-6
2.0 x 105
1.8


using a standard 1-D domain decomposition technique.
For the data transfers between different domains, MPI
library is used. All calculations are performed using a
cluster computer consisted from 128 Intel Xeon Woodcrest
processors (3.0 GHz) in Cybermedia center, Osaka
University.
As we observed already, an accuracy of IB calculation
heavily depends on the resolution. In dense case, the
resolution requirement is depending on the inter-particle
distance (void fraction) in addition to the particle Reynolds
number. Void fraction and particle Reynolds number are
expected to vary depending on flow conditions and
positions in a gas-fluidized bed under a spouting condition.
In the DEM-IB calculation demonstrated in this section, a
resolution is set to d/Ax= 8. Under the conditions shown
in Table 2, the particle Reynolds number is expected to
exceed 103 in the vicinity of gas inlet section and the
averaged void fraction at the initial condition is less than
0.45. We admit that d/Ax 8 is not sufficient and higher
resolution is needed to enable quantitative observations
and predictions. Even in case of d,/Ax=8, however, it
requires more than 40 days to obtain 1.8 s results by using
16 cores. We restrict our discussions in this section to
qualitative observations using d,/Ax=8 only.

Fig. 7 shows the temporal development of the bed for 0.01
to 0.50 s. The results are obtained by using DEM-IB





Paper No


method. The position and velocity of the particles,
iso-surface of gas velocity and streamwise gas velocity
component at the bed center (z = 8 mm) and a plane near
the front wall (z = 0.2 mm) are shown.
From Fig. 7 (a), it is confirmed that a bubble is formed just
above the gas inlet and particles are start to fluidize. The
investigations are performed under a spouting condition
and we can confirm that fluidized and unfluidized regions
are clearly separated. As observed in previous
experimental studies, particles in the region just above the
gas inlet is well-fluidized and it is not in the region close to
the bottom covers of the bed. As Eq. (36) shows, the
fluid drag force working on a particle in a packed bed
changes drastically depending on the void fraction. In
actual gas-fluidized beds, the void fraction is not uniformly
distributed and can change drastically depending on the
time. Fig. 7 (b) shows the iso-surface of gas velocity
vector. The same value with inflow gas velocity is used
for the visualization. Fig. 8 show the fluid velocity
vectors and particle's volume fraction distributions. Only
the results at t = 0.01 and 0.50 s are shown. At the initial
stage (t = 0.01 s), void fraction distributions of the bed is
relatively uniform excepting for the regions near the side
walls. Gas flows are trying to find a route in which a
resistance due to particles is minimum. As can be seen
from Figs. 7 (b), (c) and 8 (a), gas flow paths spread over
the whole bed and result in a very complex structure. In a
plane near the front wall (Figs. 7 (d), 8 (b)), gas velocity
becomes larger comparing to the center because void
fraction is relatively high. Once the bubble is formed
(0.05 to 0.5 s), gas flows do not spread over the bed and
follow the bubble because the void fraction is large inside
of the bubble and fluid resistance is small.
As shown in the previous section, when the resolution is
not enough, the fluid drag force working on the particles in
packed bed is over-estimated especially in a high particle
Reynolds number region. It means that particles start to
fluidize under a smaller superficial velocity. In the
calculations performed here, the superficial velocity of the
calculations is set to 1.0 m/s which is smaller than the
minimum fluidization velocity 1.037 m/s. The result of
DEM-CFD mesoscopic model under the same conditions is
shown in Fig. 9. Particles in the region just above the gas
inlet are raised and high void fraction region is formed,
however, fluid drag force working on particles is estimated
from Ergun and Wen & Yu equations (Eq. (26)) in
DEM-CFD mesoscopic model and it does not start to
fluidize and reach a steady state as we expected. In case
of the DEMC mesoscopic model, it requires only 3 hours
to obtain the results by use a desktop PC.


Conclusions

Toward an establishment of reliable direct simulation
technique for the flows including dense solid particles such
as that in a gas-fluidized bed, DEM-IB coupling method
was presented in this paper. In addition to a standard
steady drag force problem, resolution-dependency studies
were conducted for the drag force problems in that
hydrodynamic interactions due to gas flows existing
in-between particles are important. Besides, by using
DEM-IB coupling method, a numerical simulation of a 2-D


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

gas-fluidized bed was performed. For comparison, a
simulation by DEM-CFD mesoscopic model under the same
condition was also performed.
If the resolution is not sufficient, fluid drag force is
over-estimated in IB calculations. The trend is common to
the problems investigated in this paper: drag forces working
on a single particle, paired particles in tandem and
side-by-side arrangements and particles in randomly-packed
bed. This becomes apparent when the particle Reynolds
number is high and inter-particle distance is small.
Due to the computational time restriction, the resolution
used in the calculation of a gas-fluidized bed under a
spouting condition is still insufficient for quantitative
observations and predictions of flows. Actually, it starts to
fluidize with the superficial velocity condition which is
smaller than the minimum fluidization velocity. By using
the direct simulation as we demonstrated in this paper, it is
possible to observe the microscopic flows in a particle-level.
It helps essential understandings of the behavior of flows
including dense solid particles. We expect that the results
obtained by DEM-IB method will approach to experimental
results when the resolution of calculation becomes higher.
In gas-fluidized beds, void fraction changes drastically and
has distributions in the bed. Resolution-requirement in
most dense region will be a criterion to enable quantitative
observations and predictions.


Acknowledgements

We would like to show our acknowledgements to New
Energy and Industrial. Technology Development
Organization (NEDO) and Grand-in-Aid for Young
Scientists (B), Japan Society for the Promotion of
Science. We also would like to show our
acknowledgement to Cybermedia center, Osaka University.


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


0.01 s















0.05 s















0.15 s


0.35 s


0.50 s


(a) Particles' position
and velocity
Figure 7:


Fluid Velocity
--Io- n 5 1n I52n














Fluid Velocity
[r/si















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Ims


Fluid Velocity
Fm/si


Fluid Velocity
-LlLL-JJU521L














(b) Iso-surface of gas (c) Streamwise gas
velocity (|lu=6.0m/s) velocity at z = 8 mm
Development of flow field by DEM-IB method


Fluid Velocity























Fluid Velocity I
Fluid Velocity







Fluid Velocity















Fluid Velocity l















(d) Streamwise gas
velocity at z = 0.2 mm


Paper No





Paper No







0.01 s














0.50 s


(a) Center (z = 8 mm) (b) In a plane close to the front wall (z = 0.2 mm)
Figure 8: Instantaneous fluid velocity distributions obtained by DEM-IB at z = 8 mm and t = 0.50 s.


Figure 9: Particles' position and velocity
obtained by DEM-CFD mesoscopic model


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



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