(493f) Numerical Study On Large Scale Discrete Element Modeling for Fine Particles in a Fluidized Bed

Numerical
Study on Large Scale Discrete Element Modeling for Fine Particles in a Fluidized
Bed

Mikio SAKAI¹, Naoto SEKIMURA¹,
Tatsuya ITOI¹

¹Department
of Nuclear Engineering and Management, School of Engineering, The University of Tokyo

7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656
Japan

Tel:
+81-3-5841-6977 Fax: +81-3-5841-6977

E-mail:
mikio_sakai@n.t.u-tokyo.ac.jp

Introduction

Fluidized beds
are widely employed in industrial operations, ranging from the pharmaceutical
and food industry, to processes such as catalytic cracking of petroleum,
combustion and biomass gasification. Fluidized beds are typical gas-solid flow
systems. The flow in the fluidized beds is too complicated to fully
characterize experimentally. Numerical simulation might contribute to understanding
the complex phenomena. The gas-solid flows have often been simulated by
combining the discrete element method (DEM) (Cundall
and Strack¹) with computational fluid dynamics (CFD) (Tsuji et al.²). The DEM is a Lagrangian
approach where each individual particle is calculated based on Newton's second
law of motion, and is used to compute the solid particle behavior, enabling the
granular flow characteristics to be investigated at the particle level. Since
the development of the DEM-CFD method, various gas-solid flows have been
computed so far.

Although the
numerical approach is promising for understanding granular flows, the DEM has a
critical problem, namely, the number of calculated is substantially restricted
because of the excessive calculation cost. The number of calculated particles
that could be handled in recent studies was at most a few hundreds of
thousands. This is because the DEM simulations using an excessive number of
particles cannot be completed within a practical time period. On the other
side, over billion particles were required in industries. Consequently, the
existing DEM is difficult to be applied to industrial systems.

A new
large-scale DEM simulation model, referred to as the coarse grain model (Sakai
and Koshizuka³; Sakai et al.^4,5)
was proposed to solve this issue. A coarse grain particle represents a group of
original particles. Therefore, a large scale simulation can be performed by
using a smaller number of calculated particles than is physically present. In
the present study, we address the coarse grain model to simulate fine particles
involving the van der Waals force. Verification of the coarse grain model was
made by comparing the simulation with the results obtained from the original
particle system.

The Coarse Grain Model

Solid phase

At first, we
briefly address the coarse grain model for non-cohesive particles which was
previously developed to model contact, drag and gravitational forces. The
details of the modeling are well addressed in the literature (Sakai and Koshizuka³;
Sakai et al.^4,5). There are l³ original particles in the
coarse grain particle whose size is l times larger than the original particle.
The translational motion of the coarse grain particle is assumed to be the same
as that of the group of original particles. Therefore, the velocity and
displacement of the coarse grain particle is assumed to be the average of those
of the original particles. As far as the rotational motion is concerned, the
original particles existing in the coarse grain particle are assumed to rotate
around each center of mass with equal angular velocity. The contact force
acting on the coarse grain particle was estimated under the assumption that the
kinetic energy of the coarse grain particle agrees with that of the original
particles. In addition, when a binary collision of the coarse grain particles
occurs, the binary collisions due to all the original particles (i.e., l³ binary collisions) are
assumed to occur simultaneously. The contact force acting on the coarse grain
particle is evaluated using springs, dash-pots and a friction slider, as for
the existing DEM. The displacement was estimated by the same manner as the
existing DEM. The drag and external gravitational forces are modeled by the
same manner as modeling of the contact force. The coarse grain model can take
into account the van der Waals force. The van der Waals force is modeled based
on the assumption that the potential energy of the coarse grain particle is the
same as that of the original particles. When coarse grain
particles i
and j interact, binary interaction of
all the original particles in the coarse grain particles is assumed to have
occurred. The original particles are assumed to be located at even
intervals according to the location of the coarse grain particles.

Gas phase

The
governing equations for the gas phase are given by the fluid continuity and Navier-Stokes equations for an incompressible fluid, where
the local volume average technique is introduced.

Numerical Simulation

In the current
study, 2D DEM-CFD simulations are performed to show that cohesive particles can
be simulated by the coarse grain model. The coarse grain model is shown to
reproduce the results obtained by simulations of the original particles.

Calculation
conditions

The domain was
rectangular with size 30 mmx360 mm. The spherical particles were initially
packed randomly. The cell size was chosen to be large relative to the particle
diameter. The number of grids was 10x120. The gas was injected from the bottom
side by changing the superficial velocity.

The particle density
was 800 kg/m³. The value of the spring constant was set to be softer
than that estimated for the actual material. Coefficients of restitution and
friction were 0.9 and 0.3, respectively. The gas density and viscosity were 1.0
kg/m³ and 1.8x10^-5 Pa sec. The same values of the
physical properties were used in all the simulations.

Four kinds of
simulations were performed in each case. Table 1 shows the calculation
conditions. We simulate cohesive particle behavior by setting the Hamaker number 1.0x10^-20 J. In each case, the
coarse graining ratio was set to be 2.0 or 3.0. The simulation results obtained
with/without the coarse grain model using the same calculated particle were
also compared, i.e., Case 3 and Case 4 in Table 2. In this study, the coarse grain
model is shown to simulate the original particles accurately, despite using a
smaller number of large-size modeled particles. It is also illustrated that the
original particle behavior cannot be simulated by the use of large-sized
particles without the coarse grain model.

Table
1 Calculation Conditions

Results and
Discussion

Figure 1 shows
typical snapshots of the simulation results, taken at 5, 10, 15 and 20 sec. The
bed height became lower as the superficial velocity decreased. The bubbles
became larger as they moved up the bed, and were also larger when the
superficial velocity was higher. A few particles stuck to the walls. The
particle behavior obtained using the coarse grain model was in quantitatively
agreement with the results obtained from the original particle system. On the
other hand, the solid particles barely moved in Case 4, implying that simply
using large particles cannot reproduce the behavior of small particles. Figure
2 illustrates the relationship between pressure drop and superficial velocity.
Very similar results were obtained for Cases 1 to 3, and the minimum
fluidization velocity was estimated to be 0.022 m/s. The original particle
behavior could be simulated by the coarse grain model because the drag,
contact, and van der Waals forces were modeled suitably. The coarse grain model
was shown to effectively model the cohesive particle system. Hence, adequacy of
the coarse grain model was proven by the comparison in the 2D systems.

(a) Case 1: Original system        (b) Case 2: l = 2.0         
(c) Case 3: l =  3.0

Fig.
1 Typical Snapshots of the Simulation Results

Fig.
2 Bed Pressure Drop versus Superficial Velocity

Conclusion

We show the
coarse grain model to simulate fine particles involving the van der Waals
force. Verification of the modified coarse grain model was made by comparing
the simulation with simulation results obtained from the original particle
system.

              This
model can contribute to the simulation of Geldart A
or C particles in a large-scale powder system. This approach can be extended to
simulate particles which are cohesive due to other forces, e.g., liquid bridge, electrostatic forces, etc.

Acknowledgement

This study was
financially supported by a Grant (22760579) from the Ministry of Education,
Culture, Sports, Science and Technology (MEXT), Japan.

References