Particuology 12 (2014) 33–39
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Particuology
journal homepage: www.elsevier.com/locate/partic
Investigation of grain mass flow in a mixed flow dryer
Fabian Weigler ∗ , Jochen Mellmann
Department of Post-harvest Technology, Leibniz Institute for Agricultural Engineering Potsdam-Bornim, Potsdam 14469, Germany
a r t i c l e
i n f o
Article history:
Received 30 November 2012
Received in revised form 22 March 2013
Accepted 10 April 2013
Keywords:
Mixed-flow dryer
Grain mass flow
Discrete element method
a b s t r a c t
The numerical modeling of grain drying is a topic of great relevance to post-harvest engineering. The
required type of drying process depends on the quantity of grain to be dried and the required quality of
the grain. The choice of the drying system depends on the operating parameters of the drying process.
The granular flow pattern of the material exerts a significant influence on the drying process. Post-harvest
drying of grain is essential for better storage, handling, and processing. Therefore, it is important to know
the material behavior that controls the particle flow patterns of grain in the drying equipment to guarantee
the product quality and to optimize the drying process conditions. The discrete element method (DEM)
was applied to investigate the particle flow pattern of wheat through a mixed-flow dryer (MFD) without
airflow, and the findings were compared with experimental results in this work. The investigations were
performed using dry wheat with 14 wb% moisture content.
© 2013 Chinese Society of Particuology and Institute of Process Engineering, Chinese Academy of
Sciences. Published by Elsevier B.V. All rights reserved.
1. Introduction
Drying is widely applied in agriculture to preserve large mass
flows of grain, corn, and other coarse granular products. For continuous drying, mixed-flow dryers (MFDs) are widely used. MFDs
consist of a vertical drying shaft, inside which duct-shaped elements are arranged homogenously to distribute the drying air. The
drying air flow is controlled by the staggered inlet and outlet air
ducts. The humidified material is loaded from the top of the dryer
and flows vertically downwards by gravity. A discharge device at
the bottom of the dryer regulates the product mass flow rate.
Design elements that are unfavorably constructed or arranged
can cause broad residence time distributions, locally different
drying conditions, and inhomogeneous drying. Consequently, a
considerable part of the grain is over-dried in practice. This effect
was investigated by Mellmann et al. (2011), in which the authors
measured the grain moisture content and the temperature distributions at the dryer outlet. The measurements showed that the
grain moisture content and the grain temperature distributions significantly fluctuated at the cross-section, which resulted from the
effects of the air duct arrangement. This non-essential dehydration
caused high specific energy consumption, which led to quality and
economic losses.
Although the MFD has been studied by many researchers (Bruce,
1984; Cao, Yang, & Liu, 2007; Giner, Bruce, & Mortimore, 1998;
∗ Corresponding author. Tel.: +49 331 5699336; fax: +49 331 5699846.
E-mail address: fweigler@atb-potsdam.de (F. Weigler).
Klinger, 1977), the granular flow pattern in the vertical dryer shaft
has not been sufficiently considered in dryer modeling. In general,
relatively few works have studied and mathematically modeled the
individual processes. The grain flow through laboratory MFDs with
different forms of air ducts was studied by Klinger (1977) using
colored grains for visualization. However, only qualitative results
were obtained from these experiments.
Most research papers published on mixed-flow drying have
focused on the methods to increase the dryer performance and to
preserve product quality, e.g., by improving the dryer control. Bruce
(1984) modeled the MFD as a series of concurrent and countercurrent elements. This model was successfully employed to predict
the general dryer behavior and the influence of the operating variables on the dryer performance.
More recently, the number of papers related to basic research
on MFD has increased. Cao et al. (2007) used a simulation model
to investigate the effect of the structural and operating parameters
on the performance and the energy consumption of a mixed-flow
grain dryer. The conducted simulations were based on a twodimensional dryer model, which was previously developed by Liu
(1993). The authors emphasized the effect of the structural parameters such as the size and shape of the air ducts, the spacing between
the air ducts, the number of rows of air ducts, and the column
height. One of their observations was that the small air ducts were
more efficient than the large air ducts. Kocsis et al. (2008) reported
on experimental observations concerning the influence of air ducts
and side walls on the grain flow. The particle velocity and the
mass flow distributions were measured at an MFD test station,
which was equipped with a transparent acrylic glass front wall.
1674-2001/$ – see front matter © 2013 Chinese Society of Particuology and Institute of Process Engineering, Chinese Academy of Sciences. Published by Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.partic.2013.04.004
34
F. Weigler, J. Mellmann / Particuology 12 (2014) 33–39
As demonstrated, the particle flow through the center of the dryer
was faster than at the side walls. A two-dimensional model based
on the discrete element method (DEM) was developed to simulate the particle movement in MFDs (Iroba, Weigler, Mellmann,
Metzger, & Tsotsas, 2011). The obtained results showed that two
flow regions existed in the MFDs: the near-wall region with a low
particle velocity and the central region with a high particle velocity.
The comparison between the simulated results and the experimental results revealed that the DEM could adequately predict the main
features of particle flow. Based on the particle trajectory analysis,
Iroba, Mellmann, Weigler, Metzger, and Tsotsas (2011) demonstrated that the half air ducts positioned at the side walls of the
dryer created obstructions to the free flow of grains. However, all
of these simulations used a spherical particle structure.
The present paper aims to study the particle flow of dry wheat
through a MFD without airflow using experimental investigation
and numerical modeling. Therefore, the model of Iroba, Weigler,
et al. (2011) was advanced using a multi-sphere model to imitate
the real particle structure. Although the air flow through the bed
was not the focus of this work, this issue should be considered in
future works. Particle flow experiments were conducted to validate
the simulations.
Fig. 1. Simulated grain shape: ellipsoidal clump.
2. DEM and simulation conditions
In this work, the granular flow behavior of wheat in a conventionally designed MFD was investigated using the DEM. The
commercial software Particle Flow Code PFC2D was applied for this
purpose (Itasca Consulting Group, 2004). DEM was used to study
the mechanical behavior of discretely divided structures, and it
observed the bed not as a continuum but as individual particles
on both microscopic and macroscopic scales.
DEM was introduced by Cundall (1971) and was first applied
to soils by Cundall and Strack (1979) to compute the particle flow
numerically via an explicit time-stepping integration scheme with
suitable boundary and initial conditions. The calculation in PFC2D
consisted of repeated application of the law of motion to each
particle, of a force–displacement law to each contact, and constant updating of wall positions (Itasca Consulting Group, 2004).
The inter-particle force models were also applied to the interaction between a particle and the wall. The corresponding material
properties were used to describe the behavior of the wall. The
transaction in each time step was determined for each particle.
The particle equations of motion for translation and rotation were
solved numerically.
The equations of motion can be expressed as two vector equations: one equation relates the resultant force to the translational
motion; the other equation relates the resultant moment to the
rotational motion. The translational motion of the center of mass
is described in terms of its position xi , velocity ẋi , and acceleration
ẍi . The rotational motion of the particle is described in terms of its
angular velocity ωi and angular acceleration ω̇i . The equation for
translational motion can be written in the vector form
Fi = m(ẍi − gi ),
(1)
where Fi is the resultant force, m is the total mass of the particle,
and gi is the body force acceleration vector (e.g., gravity loading).
For either a spherical or a disk-shaped particle of radius R, Euler’s
equation of motion can be simplified and referred to in the globalaxis system as
M = Iω = ˇmR2 ω̇,
(2)
for a rotational motion with ˇ = 2/5 for spherical particles, where
I is the principal moment of inertia of the particle, and ω̇i is the
angular accelerations about the principal axes.
The equations of motion, represented by Eqs. (1) and (2),
were integrated using a centered finite-difference procedure that
involved a time step of t. The quantities ẋi and ωi were computed
at the mid-intervals of t ± nt/2, while the quantities xi , ẍi , ω̇i , Fi ,
and M3 were computed at the primary intervals of t ± nt.
Finally, the velocities were used to update the position of the
particle center as
xi (t + t) = xi (t) + ẋi (t + t/2)t.
(3)
The values of Fi (t + t) and M3 (t + t), which would be used in
the next cycle, were obtained using the force–displacement law.
After determining the forces, the moments and the resultant
displacements, the new positions of the particles were calculated.
The new contacts after the next time step followed from the new
positions. Hence, new particle forces and moments could be calculated.
To simulate the flow patterns of particles such as grains, the
particle bed can be simulated with a simplified particle structure
such as a sphere. In the commercial DEM software PFC2D , a sphere
is the commonly used geometric shape, but the actual shape of
wheat is nearly ellipsoidal. However, an ellipsoid is not possible
to generate in PFC2D . The main advantage of using spheres is the
lower computation time in comparison with the real structures; in
addition, the non-spherical particles require more advanced algorithms and are more difficult to model (Luding, 2008). The main
disadvantage of using spheres is that the flow patterns of the real
particle shape cannot be described. Therefore, the authors adopted
a multi-sphere model to compose ellipsoidal particles. To generate an ellipsoidal structure from the spheres, several spheres must
be symmetrically connected in a row. However, with an increasing
number of particles, the elliptical shape increases, the mechanical
time step of a discrete simulation decreases, and the computational time increases. Therefore, to replicate an ellipsoidal wheat
grain and to save computational time, different arrangements and
numbers of spheres were checked in the particle flow simulations
to find the optimal number of spheres, which were 5 spheres. To
describe the real particle behavior in our numerical model, clumps
of 5 connected spheres were formed. Each clump was 5.6 mm long
and 3.0 mm high (see Fig. 1). The clumps were assumed to have
F. Weigler, J. Mellmann / Particuology 12 (2014) 33–39
Table 1
Physical parameters of the bed material (wheat).
Table 2
Simulation parameters of the bed material used in the simulation.
Physical parameters
Particle density, p (kg/m )
Bulk density, b (kg/m3 )
Particle friction coefficient, p
Modulus of elasticity, E (N/m2 )
3
Particle size (ellipsoidal particle)
Particle moisture content (wb%)
35
l (m)
ı (m)
Value
Simulation parameters
1300
780
0.45
3.31 × 109
0.0056
0.003
14
Particle density, p (kg/m )
Particle friction coefficient, p
Wall friction coefficient, w
Particle contact stiffness in normal direction, kn (N/m)
Particle contact stiffness in shear direction, ks (N/m)
Wall contact stiffness in normal direction, kn (N/m)
Wall contact stiffness in shear direction, ks (N/m)
Viscous damping coefficient in normal direction
Viscous damping coefficient in shear direction
the same mechanical properties as real wheat grains. The physical
parameters of the wheat are shown in Table 1.
Calculations were conducted using a computer with an Intel®
CoreTM i7-950 Processor, 3.06 GHz and 18 GB RAM. All simulations were performed with 40,000 ellipsoidal particles, which
consisted of 200,000 spheres (see Fig. 2). The particle density
was set to p = 1300 kg/m3 . Regarding the mechanical behavior,
viscous contact damping and frictional slip were used to dissipate the energy. The simulations were conducted for dry wheat
with 14 wb% moisture content. Hence, friction coefficients of 0.45
and 0.35 were assumed among the particles and between the
particles and the wall, respectively. The elastic response of the
particles was assumed to obey a linear contact model, which was
represented by a spring with a defined stiffness. The particle contact stiffnesses in the normal direction and the shear direction
were approximated from the properties of the grain particles.
Value
3
1300
0.45
0.35
1.83 × 105
1.83 × 105
6.8 × 106
5.96 × 106
0.7
0.7
According to Mühlbauer (2009), the mechanical properties of the
clumps correspond to those of the grain. The contact stiffnesses of
the wall were approximated from the actual mechanical properties of the steel wall (Di Renzo & Di Maio, 2004). The displayed
values were: kn = 1.83 × 105 N/m and ks = 1.83 × 105 N/m for the
particles, and kn = 6.8 × 106 N/m and ks = 5.96 × 106 N/m for the
wall. All parameters of the bed material used in the simulation are
shown in Table 2. The program created the bed using gravitational
settling in a two-dimensional method (see Fig. 2), which means
that a single layer of spheres was fixed in one spatial coordinate
without any front and back wall. All simulations were performed
with a constant mechanical time step of 2.0 × 10−6 s. To observe
the mass flow behavior and the particle velocity in 2D, the particles were colored black and blue alternately after the gravitational
settling (see Fig. 2).
3. Experimental investigation
The experimental investigation of the particle flow was conducted using a laboratory test station (Mellmann, Richter, & Maltry,
2007). The MFD that formed the subject of this analysis consisted
of a vertical drying shaft, in which the inlet and outlet air ducts
were arranged horizontally. Although the cross-section of the dryer
was scaled down, the ducts were maintained in the industrial scale.
Therefore, the number of ducts was reduced. The dryer shaft, which
was approximately 2 m high and 0.6 m wide, consisted of 26 inlet
and outlet air ducts, which were horizontally aligned across the
dryer depth (Fig. 3(a)). In the pilot experiments, wheat with an
average moisture content of approximately 14 wb% and a bulk density of 780 kg/m3 was used as the bed material. The material was
loaded from the top of the dryer and flowed vertically downwards
by gravity. The test dryer was equipped with a pneumatically operated discharge gate (Fig. 3(a)), which provided an even grain flow
over the cross-section at the outlet. The discharge device at the bottom of the dryer operated on the principle of a rotary valve to allow
a constant product mass flow rate. The front wall of the grain flow
study equipment was made of transparent acrylic glass (Fig. 3(b))
to enable visual observation of the particle movement. After the
filling process, the bed was smoothed over the cross-section above
the last row of air ducts, and the colored wheat grains, which were
used as tracer particles, were filled on top. A digital video camera
was employed to observe the mass flow behavior and to illustrate
the particle velocity profiles.
4. Numerical investigation
Fig. 2. Part of the simulated dryer geometry after gravitational settling.
To compare the experimental and numerical results, the numerical models were calibrated using two independent experimental
methods.
First, the static angle of repose ˛s of the bed-material wheat was
measured and compared with the numerical results. The experimental values were determined according to DIN ISO 4324 and DIN
36
F. Weigler, J. Mellmann / Particuology 12 (2014) 33–39
Fig. 5. Bed angle ˚, the static (˛s ) and the dynamic () angles of repose formed
under the air ducts.
Fig. 3. Pilot-scale mixed-flow dryer: (a) schematic diagram, and (b) photograph.
Table 3
Comparison of the measured static angle of repose of wheat with numerical results
for different moisture contents.
Moisture content (%)
Static angle of repose (◦ )
(measured)
Static angle of repose (◦ )
(simulated)
13.4
15.1
19.5 ± 1.3
27.6 ± 1.7
19
28
EN 12047. In this method, wheat was piled up from a hopper onto
a plate, and the static angles of repose were measured for different
moisture contents (Table 3). The static angle of repose depended
on the humidity and the shape of the particles. Each measurement
was repeated ten times for statistical security. Table 3 shows ade-
quate agreements between the simulated angles of repose (Fig. 4)
and the measured values. Hence, the numerical model can predict
the real particle behavior of wheat.
In the second independent method, we measured the bed angle
˚, which was formed under the air ducts at the steady state during
the real particle flow experiments (see Fig. 5). These experiments
were performed at the MFD test station with the same portion of
wheat used in the static repose angle experiment. The physical
parameters of the wheat are shown in Table 1. The particle flow
experiments were conducted in both the continuous and the interrupted flow regimes (Mellmann & Teodorov, 2011). The continuous
flow regime is the theoretical mode of the dryer operation where
the discharge device is constantly open, and the grain flows out
unrestricted and continuously. This flow mode is of high theoretical value for particle flow investigations. Under continuous flow
conditions, the bed surface under the air ducts is inclined by the
dynamic angle of repose (Fig. 5). Industrial MFDs are operated
in the interrupted flow regime. In this case, the grain bed is at rest
almost throughout the entire drying time, and it only moves vertically during ticks of time when the discharge device is opened.
Under interrupted flow conditions, the static angle of repose ˛s is
formed under the air ducts.
Fig. 4. Simulation of the static angle of repose for different moisture contents according to DIN ISO 4324 and DIN EN 12047.
F. Weigler, J. Mellmann / Particuology 12 (2014) 33–39
37
Fig. 6. Superimposed pictures of the experimental and simulated particle flow pattern in MFD for (a) continuous flow, and (b) interrupted flow: comparison of the bed angle
˚ (wheat, 14 wb% moisture content).
To compare the measured and the simulated values of the bed
angles, the pictures from the respective DEM simulations were
superimposed over those taken from the particle flow experiments
at the steady state. Fig. 6 illustrates an example of the superimposed
images of wheat with 14 wb% moisture content. The measurements
were performed in the conventionally designed test dryer. For the
continuous flow, the pictures were produced after the steady state
of grain flow was attained. Using the experimental photo, a bed
angle ˚ of approximately 105◦ was measured, which resulted in a
dynamic angle of repose of = (2 − 105◦ )/2 = 37.5◦ . In the practically relevant interrupted flow mode, the grain bed was at repose
most of the time (the holding time) and moved only during ticks of
time when the discharge device was opened – the ‘discharge time’
(Mellmann & Teodorov, 2011). Therefore, the bed inclination angle
was measured at rest after the discharge device was closed and
the particle motion stopped (Fig. 5). This static angle of repose was
measured as ˛s = (2 − 120◦ )/2 = 30.0◦ . As expected, the dynamic
angle of repose was higher than the static angle of repose. All measured angles are shown in Table 4. The comparison showed that
the DEM model, which used ellipsoidal clumps, could effectively
predict the real particle flow pattern for both continuous flow and
interrupted flow (Fig. 6). The calibrated model was used to study
Fig. 7. Granular flow patterns in MFD: (a) DEM with spheres, (b) DEM with clumps, and (c) experimental result.
38
F. Weigler, J. Mellmann / Particuology 12 (2014) 33–39
Table 4
Comparison between measured and simulated angles of repose under the air ducts
for continuous flow and interrupted flow.
Flow regime
Bulk angle (◦ )
Experimental
Simulation
Continuous flow
Interrupted flow
115 ± 2
125 ± 2
110 ± 5
120 ± 5
the effect of different design elements with respect to the particle
flow behavior.
5. Results
The experimental investigation confirmed the results obtained
by Kocsis et al. (2008), which showed that the particles flowed
faster through the center of the dryer than at the side walls. Fig. 7
shows that the colored grain layer formed a cone-shaped profile
over the dryer width. It was also observed that the colored grain
layer at the acrylic glass wall deviated from that inside the dryer.
There was also a cone-shaped profile over the dryer cross-sectional
area. At the outlet, experimental investigations showed that this
velocity gradient resulted in a funnel flow that was comparable to
the funnel flow behavior in a silo. To measure the distribution of
tracer particles at the outlet, a set of sampling boxes was placed at
the discharge end.
To demonstrate the achieved progress in the DEM model development, the simulated results obtained for both particle structures
– ellipsoidal and spherical – are illustrated in Fig. 7. The simulations
were conducted for the continuous flow regimes. The comparison between the numerical simulation and the experimental result
(Fig. 7) shows that the DEM model based on the ellipsoidal particle
structure (Fig. 1) can effectively predict the real grain flow pattern.
The colored grain layer in the experiment showed the same profile as that in the numerical simulation. In contrast, when spherical
particles were used, the bed angle that was typically formed under
the air ducts did not occur (see Fig. 7).
By applying a discrete model, it is possible to track each individual particle trajectory in the dryer. The calculation of some particle
trajectories in the dryer (Fig. 8) illustrated that streaks of particles
existed between the ducts without any cross-mixing over the dryer
height.
6. Conclusions
The comparison between simulated and experimental results
showed that the DEM can adequately predict the main features
of a particle flow. Using the calibrated model, the general particle
flow patterns in MFDs with a conventional design (the horizontal
arrangement) were studied. As expected, the simulations confirmed the known flow behavior: the particles that flow through
the center of the dryer have higher velocities and lower friction
effects than those flowing through the regions near the dryer walls.
The tails at the side walls revealed the influence of the wall and the
half air ducts, which were positioned directly at the walls, on the
grain flow. These particles traveled with lower vertical velocities
due to the higher frictional effects. Consequently, the grains had
different residence times in the dryer (Iroba, Weigler, et al., 2011).
The particle channeling and the different residence times for
the actual air flow conditions between the center region and the
wall regions resulted in a non-uniform moisture distribution at
the dryer outlet (Mellmann et al., 2011). Hence, the dryer apparatus should still be optimized with respect to the particle flow. In
general, the analysis shows that the present MFD design does not
provide any amount of cross-mixing. Therefore, the future goal is to
develop a design that can properly capture all important flow patterns and velocity profiles for the product quality. However, a 2D
model does not accurately predict the absolute values of the solid
mass flow pattern and the particle velocity. Therefore, 3D simulations should be conducted for the dryer design studies mentioned.
Based on the results, the drying process in MFD can be modeled on
a realistic industrial scale.
Nomenclature
Symbols
F
g
I
k
m
R
t
t
ẋ
ẍi
force, N
gravity, m/s2
moment of inertia, kg m2
stiffness, N/m
mass, kg
radius of a spherical particle, m
time, s
time step, s
velocity, m/s
acceleration, m/s2
Greek symbols
ˇ
rotational motion coefficient
dynamic angle of repose, rad
angular velocity, s−1
ω
ω̇
angular acceleration, s−2
Indices
n
i
s
normal
particle number
shear
Acknowledgement
The authors wish to thank the Federal Ministry of Education and
Research (BMBF) for funding this work.
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