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World Journal Of Engineering
Mixing Solid Particles in Fluidized Beds
Fan Haihong*, Xu Delong, Min Yong, Li Hui, Chen Yanxin, Fan Jinhe
Institute of Powder Engineering, Xi’an University of Architecture & Technology, PRC
1. Introduction:
The fluidized bed reactors are used in various industries,
such as the petrochemical, biological and chemical
industries. The mixing solid particles in fluidized bed
reactions has been recognized as an important factor
determining the heat and mass transfer rates as well as
the overall reaction rates. Many studies have been made
in the past in order to understand the underlying
mechanisms and predict the behavior of mixing and
segregation, including the investigation of factors
affecting the mixing/segregation. Results show that
segregation/mixing is strongly affected by gas velocity
[1]. Mixtures of different solid particles (difference in
density or size) tend to separate in fluidized beds.
According to the experimental results by Manfred
Wirsum etc., segregation of large flotsam particles is
apparent in bubbling fluidized bed systems even under
well-fluidized conditions. In addition, segregation strongly
depends on excess gas velocity, on particle size, particle
density [2]. Miryan CASSANELLO etc. investigated the
mixing in monosized particles and binary mixtures of
solids in three-phase fluidized beds [3]. Axial mixing
times are found to be specially influenced by the
velocities of the particles. To date, almost all the studies
in this area are concerned with monosized particles. Few
studies are reported for single-size particles. This paper
will extend the work of these work, aiming to establish a
comprehensive understanding of the mixing process of
single-size solids in relation to gas velocity and
temperature.
fluid field was two dimensions, and particles were threedimension ball.
2.2.2 The boundary conditions
The fluid velocity across the wall was set to zero. At the
six nozzles, the fluid velocity across the wall was set to
the given value. The pressure gradient and the velocity
gradient were set to zero in the top cells.
2.2.3 Computation conditions
While modeling fluidization bed, three beds at ambient
temperature 300K, 1000K and 1700K were used to
obtain the bed characteristics at different temperatures.
The particle diameter is 3mm. The simulation conditions
and the input parameters are listed in Table 2.
2. Simulation Method and Conditions
2.1 Governing equations
The gas phase is treated as a continuous phase and
calculated from the volume averaged gas phase
governing equations. The solid phase is treated as a
discrete phase that is described by a conventional
discrete element method. Newton’s second law of motion
determines the translational motions of a particle at any
time. The forces action on the particles is mainly from
the gas phase, gravity and impact elastic deformation.
The collisions between particles as well as between a
particle and a wall are simulated by Hooke’s linear
springs and dashpots.
h   hi n
3. Quantitative evaluation of the mixing degree
3.1 Mixing index
Various mixing indexes are applied to describing the
effectiveness of different mixers in the process industry.
Most of mixing indexes are based on statistical analysis
and on the definitions of standard deviations of a
specified property. In this article, the index can be
defined as
  (hi  h)2 n
Where
  (hi  h)2 n
is the standard deviation of tracer particle
n
h   hi n
height. n is the number of trace particles;
is i the
1
average height of tracer particles in the sampling cells,
and
n
i 1
Where hi is the height of the trace particle i.
In this simulation, two part of particles which located in
different locations are selected as tracers. Their location
and velocity are extracted at any time, which is the very
information for calculating the mixing indexes mentioned
above.
3.2 The minimal mixing time
In this paper, the minimal mixing time was defined as the
time to reach a macroscopically stable state. From the
moment that the minimal mixing time reaches, the value
2.2 Simulation condition
2.2.1 Simplifying assumptions
The fluid was assumed to be inviscid, expect for
calculating the drag force. The soft sphere model was
used to calculate the interaction both particle-particle and
particle –wall, and particles had the same diameter. The
  (hi  h)2 n
is almost constant, and it is named the maximal
mixing index. That is to say that the minimal mixing time
is the moment the homogenous distribution of the tracer
particles occurs.
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World Journal Of Engineering
4 Results and discussion
4.1 Solid flow pattern and mixing kinetics
The solid flow patterns are examined first to generate
some visual understanding of the mixing process. Fig. 1
shows the evolvement of solids mixing in the fluidized
bed. The fluidization number N is 1.33. For better
visualization, particles whose centre points are between
0.06 and 0.08 m from distributor in the height direction
are tracers 1, 0.56 and 0.58 m are tracers 2. Starting
from well-layered, bed expansion is observed as soon as
gas is injected. A bubble is initiated at the distributor and
gradually grows in size through the bed. Bubbles cause a
drift of particles drawn up as soon as gas is injected.
Tracers appear to be pulled upward, and some of them
moved into the wake and drift. Thus, mixing appears.
transfer coefficience，it is the better means that increase
gas velocity and decrease temperature.
Acknowledgement
This research was funded by National Natural Science
Foundation of China (NNSFC) under the project
No.50432040.
References
[1]Y.Q. Feng, A.B. Yu. Microdynamic modeling and
analysis of the mixing and segregation of binary mixtures
of particles in gas fluidization . Chemical Engineering
Science 62(2007)256-268.
[2]Manfred Wirsum, Franz Fett, Natalia Iwanowa,
Genadij Lukjanow. Particle mixing in bubbling fluidized
beds of binary particle systems. Powder Technology,
120(2001):63-69
[3]Miryan CASSANELLO, Faical LARACHI，Christophe
GUY, Jamal CHAOUKI. SOLIDS MIXING IN GASLIQUID-SOLID FLUIDIZED BEDS: EXPERIMENTS AND
MODELLING. Chemical Engineering Science, Vol.51
No.10, pp.2011-2020, 1996
[4]M.J. Rhodes, X.S. Wang, M. Nguyen, P. Stewart, P.
Srewart, K. Liffman. Study of mixing in gas-fluidized beds
using a DEM model. Chemical Engineering Science
56(2001)2859-2866
[5]Lacey, P. M. C. Developments in the theory of particle
mixing. Journal of Applied Chemistry, 4(1954).257.
Fig.2 exhibits the curves of the average heights and
standard deviations of tracer particles as functions of
mixing time. Starting at the well-mixing state, the mixing
index decreases as mixture develops.
4.2 Effect of gas temperature on mixing
The different minimal mixing time are showed in table 1
at three fluidized number and three gas temperature. At
high temperature of 1700K and low fluidized number of
1.1, it takes too long time to reach a macroscopically
stable state. With the increase of fluidized number and
the decrease of gas temperature, the time decreases.
5 Conclusions
At high temperature and low fluidized number, fluidized
bed can run at stable state, but particles move slowly
and the mixing degree is low. To improve the heat
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