275395 Numerical Study On Large Scale Discrete Element Modeling for Fine Particles in a Fluidized Bed

Wednesday, October 31, 2012: 2:10 PM
Conference C (Omni )
Mikio Sakai1, Naoto Sekimura2 and Tatsuya Itoi2, (1)School of Engineering, the University of Tokyo, Tokyo, Japan, (2)School of Engineering, The University of Tokyo, Tokyo, Japan

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

Case 1

Case 2

Case 3

Case 4

Solid phase

Coarse graining ratio

-

1.0

2.0

3.0

1.0

Original particle size

mm

200

200

200

600

Calculated particle size

mm

200

400

600

600

Number of particles

-

90000

22500

10000

10000

Hamaker number

J

1.0 x 10-20

Time step

sec

2.0 x 10-6

Gas phase

Number of grids

-

10 x 120

Grid size

mm

3.0 x 3.0

Time step

sec

1.0 x 10-5

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

1.

Cundall, P.A., Strack, O.D.L., Geotechnique 29 (1979) 47-65.

2.

Tsuji, Y., Kawaguchi, T., Tanaka, T., Powder Technol. 77 (1993) 79-87.

3.

Sakai, M., Koshizuka, S., Chem. Eng. Sci. 64 (2009) 533-539.

4.

Sakai, M., Yamada, Y., Shigeto, Y., Shibata, K., Kawasaki, V.M., Koshizuka, S., Int. J.

Num. Meth. Fluids 64 (2010) 1319-1335.

5.

Sakai, M., Takahashi, H., Pain, C.C., Latham, J-P., Xiang, J., Adv. Powder Technol. (in press)


Extended Abstract: File Uploaded