Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: 9.2.2 - A Novel Multigrid Approach for Lagrangian Modeling of Fuel Mixing in Fluidized Beds
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 Material Information
Title: 9.2.2 - A Novel Multigrid Approach for Lagrangian Modeling of Fuel Mixing in Fluidized Beds Fluidized and Circulating Fluidized Beds
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: Farzaneh, M.
Sasic, S.
Almstedt, A.E.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Subjects
Subject: fluidized bed
fuel mixing
multigrid
Lagrangian simulations
 Notes
Abstract: This paper presents a novel Larangian approach to model fuel mixing in gas-solid fluidized beds. In the mixing process, fuel particles are considerably larger than the inert bed material and therefore, the commonly used Largangian particle algorithms are not able to simulate the phenomenon properly. In the proposed model two grids are used for simulations and the information between the two grids is exchanged using an algorithm presented in the paper. In addition, a statistical procedure is developed to analyze the results obtained from the simulations. The effects of initial distribution of bed material, inlet gas velocity and amount of the bed material on the fuel mixing are investigated. It is concluded that initial location of fuel particles affects their preferential positions. Also, increasing the fluidization velocity and the amount of the bed material influences the flow structure and configuration of the fuel particles.
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
 Record Information
Bibliographic ID: UF00102023
Volume ID: VID00219
Source Institution: University of Florida
Holding Location: University of Florida
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Resource Identifier: 922-Farzaneh-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 Novel Multigrid Approach for Lagrangian Modeling of Fuel Mixing in Fluidized Beds

M. Farzaneh, S. Sasic, A. E. Almstedt

Department of Applied Mechanics, Chalmers University of Technology, Gothenburg 41296, Sweden
meisam@chalmers.se, srdjan@chalmers.se and affe@chalmers.se
Keywords: fluidized bed, fuel mixing, multigrid, Lagrangian simulations



Abstract

This paper presents a novel Larangian approach to model fuel mixing in gas-solid fluidized beds. In the mixing process, fuel
particles are considerably larger than the inert bed material and therefore, the commonly used Largangian particle algorithms
are not able to simulate the phenomenon properly. In the proposed model two grids are used for simulations and the
information between the two grids is exchanged using an algorithm presented in the paper. In addition, a statistical procedure
is developed to analyze the results obtained from the simulations. The effects of initial distribution of bed material, inlet gas
velocity and amount of the bed material on the fuel mixing are investigated. It is concluded that initial location of fuel particles
affects their preferential positions. Also, increasing the fluidization velocity and the amount of the bed material influences the
flow structure and configuration of the fuel particles.


Introduction

The mixing of fuel particles with inert bed material in
gas-solid fluidized beds is an important phenomenon in
many industrial applications and has a significant effect on
the performance of a fluidized-bed unit. Achieving good
mixing of fuel and combustion air is crucial in order to
avoid hot spots due to highly exothermic chemical reactions
and consequently, to reach a uniform temperature
distribution in the bed. Industrial units for gas fluidization
usually involve particles of different size and density and
many models have been proposed to investigate the
hydrodynamics of polydisperse systems. Generally, there
are two approaches commonly used to model gas-solid
fluidized beds: two-fluid models, which regard the
particulate phase as a continuum (e.g. Enwald et al., 1996),
and Lagrangian or discrete particle methods (DPM), in
which solid particles are tracked individually through the
flow domain (Tsuji et al., 1993). In recent years, with a
rapid development of computing power, DPM has been
become a widely used tool in the field of gas-solid flows. A
comprehensive review of papers using DPM is given by
Zhu et al., (2008).
Despite the importance of fuel mixing, little work has been
done to study this phenomenon in fluidized beds.
Conventional DPM models are not adequate for simulating
the process of fuel mixing in fluidized beds, since the
process includes two types of particles with great difference
in size and density. In the majority of DPM models treating
polydispersed particulate systems, the different particle
classes are close in size. In such a case, using a single
computational mesh is reasonable (e.g. Hoomans et al.,
2000, Feng et al., 2004). Due to the size difference of the
particles treated here, such an approach is not possible in the
present work.
The purpose of this paper is to propose a Lagrangian model
to overcome the complication caused by the great difference
in size between the fuel and the inert particles. Note that,
both types of particles are of Group B type, according to


Geldart's classification, Geldart (1973). The approach
suggested here uses two grids for simulations, one coarse
and one fine. A computational cell of the coarse grid
contains a number of cells belonging to the fine grid. The
fine grid is used to resolve the gas flow field and track the
small particles, while the drag force on the large particles is
obtained in the coarse grid.


Nomenclature

CD drag coefficient (-)
F force (N)
g gravitational acceleration (ms-2)
I moment of inertia ikgun
M particle mass (kg)
P pressure (Nm2)
Re Reynolds number (-)
T torque (Nm)
U,, minimum fluidization velocity of the inert
particles (ms-1)
vg gas velocity (ms-1)
vsm mth solid phase velocity (ms-1)

Greek letters
pf inter-phase momentum transfer coefficient (-)
Eg volume fraction of gas phase (-)
Em volume fraction of mth solid phase (-)
w rotational velocity of particle (s-1)
p density (kgm 3)

Subsripts
G gas
m mth soild phase
P Particle
S Solid






Paper No


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


In the present work, solid flow patterns of a bi-disperse
fluidized bed are studied. The two-dimensional bed is a
mixture of small inert particles, dp,inert = 500pm ,
Pp,inert = 2600 kg/m3 and a limited number of large
particles representing the fuel particles in the bed with
different size and density, dp,juet = 5.0mm, Pp,fuet =
985 kg/m3 A schematic view of the fluidized bed
simulated in this paper is shown in Fig. 1.
gas outlet


gas inlet velocity
20 cm


Figure 1: Bed geometry. The static bed height is 5 cm for
40,000 particles and 7.5 cm for 60,000 particles


Pallares and Johnsson, (2006) experimentally studied the
mixing mechanisms of fuel particles in a two-dimensional
fluidized bed using a particle tracking technique. They
tracked a phosphorescent tracer particle by means of video
recording with a subsequent digital image analysis. The
procedure yielded, concentration, velocity and dispersion
fields of the tracer particle. If we wish to simulate the unit
with exactly the same geometry as in Pallares and Johnsson
(2006), we will end up with an intractable number of
particles with the presently available computational power.
Therefore, we have decided here to carry out simulations on
a geometrically-scaled unit, with a number and properties of
the particles chosen in such a way to secure both tractable
simulations and to obtain reliable information about the fuel
mixing. In order to understand the operating conditions that
affect the mixing process, four cases are designed in which
the effects of inlet gas velocity, initial distribution of fuel
particles and of the number of inert particles are
investigated. The information of the cases is summarized in
Table 1. Two types of initial distribution of the large
particles are tested. In the first one, shown in Fig. 2(a), the
large particles are uniformly positioned on the top of the bed,
and in the second one, the large particles are randomly
distributed within the inert bed material, Fig. 2(b).


Figure 2. Initial distribution of fuel particles; a) top-located
b) randomly-located

Air with a velocity higher than the minimum fluidization
velocity of the inert particles is introduced in the bed, as
presented in Fig. 1. Since the gas velocity is smaller than
the minimum fluidization velocity of the fuel particles, the
latter are not fluidized due to the gas drag force and
therefore, the particle-particle interaction is the most
important force in the fuel mixing process. The gas velocity
here cannot be increased to exceed the minimum
fluidization velocity of the fuel particles, since the fine
particles will then be blown out of the bed.

Table 1: Numerical cases analyzed in the present work

Number of
large
Case particles/Num Superficial Initial distribution
ber of small gas velocity of the large
particles particles

1 40000/15 1.5Uf randomly-located

2 40000/15 1.5U,, top-located

3 40000/15 2.0U,f top-located

4 60000/15 1.5U,f randomly-located


Computational Model


X(cm)
(a)


lU
X(cm)
(b)






Paper No


Multigrid Approach

Choosing the grid size is a challenging problem in
Lagrangian simulations of multiphase flows, especially,
when the particulate phase includes two types of particles
with great difference in size. If the selected mesh is based on
the size of the large particles, the cells will generally include
a large number of small particles and the detailed
information about the small particles will consequently be
lost. In addition, in such a situation the flow field of the
carrying phase will not be resolved properly. In this paper, a
procedure is suggested to overcome this problem. We use
here one coarse and one fine grid, where a computational
cell of the coarse grid contains a number of cells belonging
to the fine grid. The fine grid is used to resolve the gas flow
field and to obtain the interaction force between the gas
phase and the small particles. Fig. 3 shows a schematic view
of the approach. The drag force and the volume fraction of
the large particles are calculated in the coarse grid and the
corresponding source term is then equally distributed into
the small cells incorporated in the large cell. In order to
calculate the drag and buoyancy forces on the large particles,
the pressure and velocity need to be computed in the coarse
cells. These values are taken as the mean pressure and
velocity of the small cells included in each large cell. For
instance, for the large cell shown in Fig. 3, the pressure and
the velocity in the centre of the large cell are obtained as a
mean value of the pressure and the velocities of the 36 small
cells. The volume fraction of the large particles is calculated
in the large cell and then uniformly distributed into the small
cells. Using the mean values of the small cells in a large cell
and also equally distributing the values of the large cells into
the small cells is not the most accurate approach, but it is
simple and easy to implement. Moreover, there is no need to
interpolate and it makes the method computationally
reasonable.


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

phase (https://www.mfix.org). The developed multigrid
approach has been implemented into the MFIX code.
When using the Lagarangian approach, all the particles are
tracked individually and the equations of translational and
rotational motion of the particles are solved. The
fluid-particle interaction force, the gravitational force and
the particle-particle collisional force are taken into account.
The equations of motion of a particle are generally similar
to those given by Tsuji et al. (1993)


F
r =-+ g
m

-? T
) = -


where r is the particle position vector, m is the particle
mass, g is the gravity acceleration, a is rotational
velocity, I is moment of inertia, which for spherical
particles with radius R is equal to I = 2/5mR2, T is the
torque caused by contact forces, and F is the total force
acting on the particles including the fluid-particle
interaction force, the pressure gradient force, the
gravitational force and the particle-particle collision force.
There are two general approaches to model collisions in
Lagrangian modelling of solid particles: a hard-sphere and
a soft-sphere model. In the present work, the soft-sphere
method is used to calculate the contact forces, including
the normal, damping and tangential forces between
particles and between particles and the walls. The contact
forces are modelled using an analogy with a mechanical
system consisting of springs and dash pots. The gas phase
is treated as a continuous phase and the governing
equations are solved using the Finite Volume
Method(FVM). The continuous phase equations are given
by


Figure 3: A schematic view of large and small particles in a
coarse cell including a number of fine cells. The properties
of the large particles are distributed in the fine cells included
in the coarse cell


Governing Equations

In this work, we have used MFIX (Multiphase Flow with
Interphase eXchange), a general-purpose computer code
developed at the National Energy Technology Laboratory
(NETL), to resolve the flow field and model the particulate


a = 0
+(W)fv (EBP)=O


- (EgP, ) + V (CEpgg) = -EgVPg
M
+V S + gPggg Ig
m=1


where Sg is the gas phase stress tensor and I,, is the
interaction force between the gas phase and the mth solid
phase, given by


Igm = -P/gm((sm ig)


flm is the inter-phase momentum transfer coefficient
between the gas phase and the mth solid phase. Although
many correlations have been proposed to calculate this
coefficient, that by Wen and Yu (1966) is still one of the
most widely used, and this correlation has also been used
in the present study.





Paper No


3 PgEEgm\g -sm\ -26S
pgm = CD d- E-
4 dpm


The solution domain is discretized by a structured mesh
including 80 x 200 small and 20 x 50 large quadrilateral
cells. Thus, each big cell includes 16 small cells. The time
step of 10-4 s is used to resolve the motion of the
continuous phase. The time step of the Lagrangian part of
the simulations is calculated using the correlations given
by Deen et al. (2006). The time step is then a function of
mechanical properties of the colliding particles.


Statistical Analysis

In the present work, a statistical procedure is developed to
capture the preferential positions of the fuel particles. The
procedure consists of the following steps:
1. Relevant information of the fuel particles including
their positions and velocities is stored.
2. The computational domain is discretized by
quadrilateral elements. This discretization is
different from the one used for the simulations of
the flow field.
3. The number of times that particles enter each
element is counted.
4. The mean velocity of the particles belonging to
each element is calculated.
As a result, the preferential positions of the fuel
particles are acquired. Moreover, the particles mean
velocity is obtained.


Results and Discussion

Fig. 4 shows the particle configuration at different
times. In this case, the simulation is started with the
randomly-located distribution of fuel particles. The air
is uniformly introduced into the bottom of the bed
with the 1.5Uf. The injected air fluidizes the bed
material with bubbles rising through the bed and
bursting out at the bed surface. When the bubbles
grow and rise in the bed, they carry fuel particles and
then throw them by the energy released from their
bursting. Although the process seems random in
character and without a notable structure, statistical
analyses illustrate that it is not correct. The behaviour
of the fuel particles, displayed in Fig. 4, indicates that
they have a tendency to move towards the middle part
of the bed. This conclusion is proven by a statistical
study of the positions of the fuel particles over 14
seconds of the bed performance. The results of the
analysis are displayed in Fig. 5. The figure shows the
number of times that the fuel particles move to a
certain region of the bed. The middle of the bed with
darker color shows the preferred zone for the fuel
particles. Although the particles move to all parts of
the bed, they spend most of the time in the region in
the middle of the bed. To better understand the process,
the velocity vectors of the fuel particles are shown in
Fig. 5. As can be seen in the figure, there are two main
vortices in which the fuel particles move from the
near-wall regions towards the middle of the bed and


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

their velocity vectors point at this zone. In the pattern
observed here, after reaching the surface of the bed,
the fuel particles are thrown into the splash zone,
where they are less affected by the small inert particles.
Therefore, with a fast horizontal displacement, they
move to the centre and return to the dense zone.
Three parameters are changed to investigate their
effect on the fuel mixing process: the initial
distribution of the fuel particles, the fluidization
velocity and the amount of inert material. Fig. 6
displays the preferential positions of the fuel particles
for the case with the top-located initial condition and
the fluidization velocity of 1.5Umf. The fuel particles
are divided into two groups by the first rising bubbles
in the bed. In the first 7 seconds of the simulation,
there are two concentrated areas representing the fuel
particles in the right and left hand side regions of the
bed. However, after this period, they approach each
other and form a single zone that is spread over a
relatively wide part of the bed. In such a situation, the
number of vortices decreases from three in the first
seven seconds to two in the rest of the simulation. The
fuel particles at the top move to the centre of the bed
from the two sides with velocities significantly larger
than those in the dense bottom bed.
Fig. 7 shows the preferential positions and velocity
vectors of the fuel particles for the top-located initial
condition and 2.0 Umf fluidization velocity. Fig. 7 (b)
shows the fast horizontal displacement of the fuel
particles in the splash zone. In most of the cells, the
mean velocity vectors are directed towards the centre
of the bed. However, there is a big dark area in the
right hand side of the bed, shown in Fig. 7 (a)
revealing that the fuel particles spend most of time at
it. Looking at the bed pattern at different times
illustrates that a number of fuel particles are trapped in
that region in such a way that they are not able to
move to other parts of the bed.
In order to investigate the effect of the amount of the
bed material on mixing mechanism, the number of
inert particles is increased to 60,000. The number of
vortices forming the flow structure depends on the
amount of bed material, and increasing the bed
material lowers the number of vortices present in the
flow pattern (Pallares and Johnsson, (2006)). The
statistical analysis performed here agrees well with
these experimental observations. As shown in Fig. 8(a),
the fuel particles occupy all parts of the fluidized bed
and the configuration seen here is different from the
one observed in case 1 with 40,000 particles. In case 1,
a large preferred zone is obtained in the middle of the
bed, but adding the amount of the bed material
completely changes the structure of the flow. In such a
situation, no preferred zone is observed. Similar to the
other cases, the fuel particles can easily move
horizontally on the top of the dense bed and go back to
the dense bed. Fig. 8(b).






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


... .- .
10 -





Ill

5 10 15
X(cm)
(b)
Figure 5: preferential positions (a) and velocity vectors (b)
of the fuel particles for case 1


.. .. -,



X("II) X(cm)
T=10.0s T=14.0s

Figure 4: Configuration of solids particles at different times
for case 1


5 10 15
X(cm)


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1


5 10 15
X(cm)
(a)




15



10/i /
\ / o /


5


i iIi
5 10 15
X(cm)
(b)
Figure 6: preferential positions (a) and velocity vectors (b)
of the fuel particles for case 2


Paper No


Tc.Os
T=0.0s


T=2.0s


T=5.0s


T=8.0s


0 0.1 0.20.3 0.40.5 0.60.70.80.9 1


!


8'
1S`~


1i






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


0 01 0.2 03 0.4 0.5 0.6 0,7 0.8 0,9 1













5 10 1E
X(cm)


. /


I / / .. .


5 10 15
X(cm)


Figure 7: preferential positions (a) and velocity vectors (b)
of the fuel particles for case 3



30

0 0.1 0.2 03 0.4 0.5 0.6 0,7 0.6 0.9 1
25

20

15


10
X(cm)


25

20l

15



*'N
10


}i2 <


5 10 15
X(cm)


Figure 8: preferential positions (a) and velocity vectors (b)
of the fuel particles for case 4




Conclusions

A novel multigrid Lagrangian particle tracking is proposed
to study fuel mixing in fluidized beds. In the approach two
grids are used to treat small and large particles that are
significantly different in size. Motion of a limited number of
large particles, representing the fuel particles in a fluidized
bed, is studied numerically. In order to obtain the
preferential positions of the fuel particles in the bed, four
cases are modelled using the technique developed here. The
effects of the initial distribution of the fuel particles, the
inlet air velocity and the amount of the inert material are
investigated.
It is observed that the initial distribution of the fuel particles
has a significant effect on their final preferential locations.
For the case with randomly-located initial condition, there is
a single preferred region in the middle of the bed, but for the
initially top-located bed, the fuel particles are widely spread
in the bed. When increasing the fluidization velocity, there
is a change in the preferential positions of the fuel particles
and their velocity vectors. In addition, the effect of the
amount of the bed material is investigated. We have
demonstrated that the increase of the dense bottom bed
height enhances bubble coalescence and consequently,
decreases the number of vortices in the flow structure.
Therefore, increasing the amount of the bed material
changes the flow configuration and removes the preferred
zone observed in the centre of the fluidized bed seen in case
1.
The purpose of this study has been to obtain the general
pattern of the fuel particles in the beds experimentally
studied by Pallares and Johnsson, (2006). In order to reach a
tractable number of particles, it has been necessary to
decrease the size of the bed used for simulations and also, to
somewhat increase the size of the inert particles. In such a
situation, the computational cases will not be the same as
experimental ones. Nevertheless, even if it is not possible to
directly compare the numerical results with the
experimental data, the numerical method developed here
seems to be a useful tool for obtaining relevant information


Paper No






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

related to fuel mixing in gas-solid fluidized beds.

Acknowledgements

The authors are grateful to the Swedish Energy Agency for
the financial support of their work.


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Geldart D., Types of Fluidization, Powder Techno. Vol. 7, pp.
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Granular Dynamics Simulation of Segregation Phenomena
in Bubbling Gas-fluidised Beds, Vol. 109, pp. 41-48, 2000

Pallares D., Johnsson F., A Novel Technique for Particle
Tracking in Cold 2-dimensional Fluidized Beds-simulating
Fuel Dispersion, Chemical Engineering Science, Vol. 61, pp.
2710-2720, 2006.

Tsuji Y., Kawaguchi T. and Tanaka T., Discrete Particle
Simulation of Two-dimensional Fluidized Bed, Powder
Techno., Vol. 77, pp. 79-87, 1993

Wen C.Y. and Yu Y.H., Mechanics of Fluidization, AIChE
Symp. Ser., Vol. 62, pp. 100-111, 1966

Zhu H.P., Zhou Z.Y, Yang R.Y and Yu A.B.,Discrete
particle Simulation of Particulate Systems: A Review of
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pp. 5728-5770, 2008




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