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1
CFD-DEM Investigation of Seed Clustering in an Air
Seeder with the Immersed Boundary Method
M. Bayati1 and C. Johnston1
1R&D Department, Radix Innovation Corporation
8401 113 St. Grande Prairie, AB, Canada, T8V 7B4
Email: [email protected]
ABSTRACT
Agricultural air seeders typically have uneven
distribution of seeds from their outlets, leading to
irregular planting patterns and inefficient farming.
When larger seeds are used, a clustering effect can also
occur where seeds emerge, not in steady streams, but
in clustered groups. This work investigates the causes
of these effects with a CFD-DEM approach to improve
future air seeder design. Two modelling approaches
are attempted.
In the first approach, small particles based on wheat
seeds are modelled with one-way coupling to validate
the numerical models and spatial discretization based
on experimental results for the outlet distribution. In
the second approach, the Immersed Boundary (IB)
method as modified by Hager (2014) is used in two-
way coupling to capture the effect of larger particles
(based on chickpeas) on the flow.
The first method finds a coefficient of variation (CV)
between the 11 different outlets of 12.5%, which is
within the accepted range of typical air seeder
performance, and matches the reported number by the
industry. For the second approach, the concept of a
“time CV” is introduced to describe the relative
amount of clustering in larger seeds based. The
clustering effect is found to be largely due to
obstructions in the flow causing the seeds to drop into
Geldart’s “spouted bed” fluidization regime (Geldart,
1973), resulting in periodic bursts of seeds after
localized pressure build-up.
Results of the simulations were compared to
experimental data, and are in good agreement.
NOMENCLATURE
CV Coefficient of variation
d Seed diameter
d*s Dimensionless particle diameter
fp,f Drag force on seeds
fp,w Collision force between walls and seeds
fp,p Collision force between different seeds
g Gravitational acceleration
k Turbulence kinetic energy
L Average path length of seeds
mp Seed mass
P Pressure
Re Reynolds number
St Stokes number
u* Dimensionless air velocity
U Air velocity
X Average value of sample
ε Turbulence kinetic energy dissipation rate
μ Air dynamic viscosity
φ Integral quantity for mesh dependency
ρc Air (carrier fluid) density
ρd Dispersed seed density
Πmom Momentum coupling factor
1. BACKGROUND
Agricultural air seeders are used in modern farming to
pneumatically convey seeds during the planting
process. An air seeder system begins at the primary
manifold, where a hopper introduces seeds in bulk into
the airstream. The primary manifold splits into several
secondary manifolds, which are long (2 m in length)
vertical pipes with 90° bends. Finally, each secondary
manifold exits into approximately 8 to 12 tertiary
hoses, which convey the seeds to the soil. Air seeder
systems are used while traveling in a field, and depend
on having constant and even distribution from each
tertiary outlet, to ensure regular planting patterns.
Unfortunately, the design of the secondary manifold in
particular often leads to irregular flow distribution,
and asymmetrical or clustered seeds.
2
In this work, Computational Fluid Dynamics (CFD)
and the Discrete Element Method (DEM) are used to
determine the features of the manifold contributing to
these effects. An Eulerian approach is used for the
fluid, and a Lagrangian approach for the particles.
Uncovering the causes of the asymmetrical seed
distribution and the clustering effect could lead to
more efficient air seeder designs, and ultimately to
improved crop yields.
Both of these effects are observed almost entirely in
the secondary air seeder manifold, with the primary
and tertiary systems introducing little to no variation
into the seed output. Therefore, the secondary
manifold system is isolated in this work, and modeled
separately from the remainder of the system, to
determine the features which cause these problematic
effects.
The asymmetrical seed distribution effect is observed
with seeds of all sizes, and is typically measured with
the coefficient of variation (CV) from the outlets,
defined here as:
�� � ������������
(1)
In Equation 1, SDseeds represents the standard
distribution of the seeds from the outlet, and Xseeds
represents the average of the seeds between all outlets.
The Prairie Agricultural Machinery Institute, for
example, has found that typical values for the CV from
seeding implements is between 10-15% [1].
The clustering effect, by contrast, has only been
experimentally observed by farmers for seeds greater
than 7.5 mm in diameter. Typical secondary air
seeder manifolds are close to 60 mm in diameter,
which is more than sufficient to avoid any clustering
for small seeds such as wheat. However, with pulse
crops (such as chickpeas and lentils) becoming more
popular in Canada, their large and brittle seeds are
being used more often in air seeder systems, with
poor results. Clustering in this context is where seeds
emerge, not in steady streams, but in clustered
groups. Uncovering the causes of the clustering effect
could lead to more efficient air seeds designs, and
ultimately to improved crop yields. However, as this
is a relatively unexplored phenomenon in agricultural
seeding,, there is not yet a standardized method to
measure the magnitude of clustering in the system.
This clustering effect is often replicated in the field,
during normal operation of the air seeders, as seen in
Figure 1, below. In this image, the shadows seen
moving through the tertiary hoses (exiting the ports
on top of the manifold) are groups of seeds. Ideally,
the operator would prefer the seeds to exit in a steady
stream, instead of emerging in bunches, which
disrupt seeding operations and controls. This
grouping and clustering occurs despite the lack of
any kind of cohesive forces acting on the particles; it
occurs even when the seeds are dried out.
Figure 1: Clustering effect replication on an
operating air seeder (one cluster called out for
reference)
2. PREVIOUS WORK
Some work has been done previously to model flow
through air seeders. One previous study by Bourges
and Medina (2012) [2] tested an air seeder with a small
number of particles (27) and found a propensity for the
seeds to exit through the front pipes of the distributor
head. Their main theorized cause was the seeds
bouncing against the top cover of the distributor head.
Other studies by Tashiro et al (1991 & 2001) [3] tested
horizontal pneumatic seed conveyances with
extremely small particles (55 to 468 microns), but did
not investigate larger seeds where more segregation or
clustering is expected to occur. A study by Raheman
(2003) [4] replicated these effects in lab experiments,
and focused on developing experimental correlation
factors or parameters for seeder design, rather than
looking at numerical solutions to determine the
features of the flow.
Little to no research has been done on the time
variance (clustering) phenomenon, and little
experimental data exists owing to the difficulty of
measuring the effect in the field. In this work, two
modelling methods are attempted, one for the
asymmetrical distribution effect, using wheat seeds in
one-way coupling, and one for the clustering
phenomenon, using chickpea seeds in two-way
coupling.
3
3. SIMULATION SETUP
The Navier-Stokes equations are used for the air flow
simulation, solved using a RANS method with a
standard k-ε turbulence model. For the first simulation
method, the flow was solved in steady state. In the
second simulation method, the momentum coupling
factor was greater than one, so two-way coupling was
implemented and the flow was solved in a transient
state [5]. Simulations were performed using the open
source CFD software OpenFOAM v1606+ [6], in
conjunction with the DEM software LIGGGHTS [7],
joined together using the coupling software CFDEM-
Coupling [8].
In the second approach, the Immersed Boundary (IB)
method is used in two-way coupling to capture the
effect of larger particles (based on chickpea seeds,
with a diameter d of 10 mm) on the flow. This method
adds a force source term to the Navier-Stokes
equations to treat the flowing seeds as surfaces inside
of the flow, as shown in Equation 2:
(�, �) � � �(�, �)��� − �(�, �)���
� (2)
In Equation 2, δ is the Dirac delta function, X is the
configuration in space of the particle, and F is the
Fréchet derivative of the elastic energy stored in the
particle at time t. By implementation of this
additional force source term, the IB method allows
the equations to be solved on a Cartesian mesh
without adjustments for the shape of the moving
bodies. This method allows the remeshing which
must be performed at every step as the large bodies
move in the flow to performed simply and
consistently. Each control volume containing a
particle is divided to a specified level of refinement,
and then the original cell is reconstructed after the
particle has passed.
The method was originally developed by Peskin
(2002) [9] to investigate flow inside of heart valves,
where the biological elastic surfaces are constantly in
motion, but it was adapted for use on large particles
in OpenFOAM by Hager (2014) [10]. Good
agreement with the IB method was found in the prior
work when control volumes along the immersed
surface were kept to be no larger than 1/8 the
diameter of the particle.
The secondary air seeder manifold used in this work
has 11 tertiary ports and an inner diameter of 0.060
m. A schematic of the manifold is presented below in
Figure 2, along with a view of the simplified model
for simulation in Figure 3.
Figure 2: Secondary manifold components
Figure 3: Simplified mesh for analysis
Boundary conditions were applied based on
simplified assumptions about the isolated manifold
system, shown in Table 1, below:
4
Table 1: Simulation Setup Parameters
Description Value Comment
Gas density
[kg m-3]
1.101 Air at 25°C
Gas viscosity
[kg m-1s-1]
1.85 x 10-5 Air at 25°C
Wheat density
[kg m-3]
1325 Guner (2006)
[11]
Wheat
diameter [mm]
4.35 Guner (2006)
[11]
Wheat
Young's
modulus
[N m-2]
2.2 x 107 Stasiak (2003)
[12]
Wheat
Poisson's ratio
0.22 Stasiak (2003)
[12]
Wheat
restitution
coefficient
0.35 Patwa (2014)
[13]
Wheat friction
coefficient
0.32 Cenkowski
(2006) [14]
Chickpea
density
[kg m-3]
1379 Ghamari
(2014) [15]
Chickpea
diameter
[mm]
8 - 10 Filtered in
experiments
Chickpea
Young's
modulus
[N m-2]
5.05 x 108 Tabar (2012)
[16]
Chickpea
Poisson's ratio
0.36 Kiani deh
Kiani (2009)
[17]
Chickpea
restitution
coefficient
0.48 Ozturk (2009)
[18]
Chickpea
friction
coefficient
0.302 Ghadge (2008)
[19]
Inlet
conditions
ug = 22.9 m s-1 Velocity inlet
condition
Outlet
conditions
Pgauge = 0 Pressure outlet
condition
Wall
conditions
ug = 0 No-slip wall
condition Reynolds
Number
9.0 x 104
Wheat drag
function
Schiller-
Naumann
Schiller &
Naumann
(1953) [20]
Chickpea drag
function
Shirgaonkar Shirgaonkar et
al (2009) [21]
The incompressible Navier-Stokes equations (as
modified by Peskin [9] and Hager [10]) and the
continuity equation were solved numerically for the
CFD, and Newton’s laws of motion were used for the
DEM. The simplified system of differential equations
is shown below in Equations 3, 4, and 5.
� ����� + (! ∙ �)�# − $!%� + !&
� �' + � �(�, �)��� − �(�, �)���
�
(3)
! ∙ � � 0 (4)
)*��+�� � )*, + *,- + *,. + *,*
(5)
4. MESH DEPENDENCY TEST
A baseline mesh size was determined based on a grid
independence study in the one-way coupling
simulation, to ensure that all relevant features of the
flow were adequately captured. In this case, the overall
force of the air on the distributor head, integrated
across the entire surface, was used as an integral
quantity φ to determine an adequate level of mesh
discretization. The results of this systematic mesh
refinement test are shown below in Figure 4:
Figure 4: Variation of integral quantity in mesh
dependency test
Here the mesh has been systematically refined by a
constant factor of 1.2 between each step, and a
Richardson extrapolation (shown as a straight line in
Figure 4) has been performed to determine the order
of truncation (here calculated as 2.5, appropriate for
the numerical schemes used).
5. RESULTS AND CONCLUSIONS
Using the numerical conditions and mesh sizing
described in Sections 3 and 4, two different sets of
simulations were performed. The first investigated the
5
unobstructed airflow through the manifold, and then
added wheat seeds in one-way coupling. This
simulation was in part to investigate the asymmetrical
airflow typically observed in operation, which has
been found in prior studies, and also to validate the
measured CV against typical values. The second
method used the same general discretization and
schemes validated in the first simulation to investigate
the clustering phenomenon.
5.1 Outlet Spread Simulation
In the first approach, smaller particles (based on wheat
seeds, d = 4.35 mm) are modelled with one-way
coupling for validation. The use of one-way coupling
is based on a calculation of the momentum coupling
factor of the air and wheat phases, as described by
Crowe (2011) [5]:
Π010 � �1 + ��010
��̅��̅4
1 + 5��������%18$7
�
6.67 ;<)=>?@
1.101 ;<)=>?@
1 + (22.9 )� )(1325 ;<)=)(0.0435 ))%
18(1.85 ∗ 10GH ;<) �)(0.6445 ))
� 2.26 ∗ 10G=
(6)
This momentum coupling factor represents the ratio of
the drag force on the particles to the total momentum
of the carrier fluid. It is the ratio of energy which is
extracted from the fluid to change the speed of the
particles, and is always less than unity. When it is close
to zero, as it is here, the effects of the particles on the
flow can be neglected. This indicates that one-way
coupling is appropriate for the simulation.
A great deal of experimental data was available for this
simulation, as the asymmetrical outlet distribution has
been extensively studied in lab tests. This study found
a CV in the outlets of 12.5%, which is perfectly within
the accepted range of typical air seeder performance
(10 to 15%), and which agrees well with experimental
data from the manifold manufacturer (who found a CV
of 10% for an analogous lab test). Figure 5, below,
shows the side flow profile, and Figure 6 shows the
observed front-to-back asymmetry. Both of these
profiles were also found in the prior work by Bourges
and Medina [2].
Figure 5: Side view of steady-state simulation of
unobstructed airflow in air seeder manifold
Figure 6: Top view of steady-state simulation of
unobstructed airflow in air seeder manifold
This asymmetrical airflow in the manifold head is
caused primarily by the jet of fast-moving air that
develops up the back of the vertical pipe. The section
of pipe above the elbow is not sufficiently long (for
space constraints) to allow the flow profile to fully
redevelop by the time it reaches the manifold head.
This leads to more air being pushed out of the back of
the manifold top compared to the front, as is expected
based on both the prior work and the manufacturer’s
lab results.
5.2 Clustering Simulation
Larger seeds lead to the clustering effect discussed
previously. In this work, chickpeas are used to produce
the effect, and are modeled with two-way coupling
based on a calculation of the momentum coupling
factor. Using the same method as in equation 6, the
momentum coupling factor was calculated as 0.0185
(using a dispersed seed density of 101.5 kg/m3 air, a
seed insertion velocity of 12.1 m/s (as per Raheman
6
[4]), and a minimum seed diameter of 8 mm). This
momentum coupling factor is an order of magnitude
greater than for the smaller wheat seeds. Owing to this,
it is likely that the clustering phenomenon is due
primarily to seeds obstructing the flow; therefore, two-
way coupling was used in this stage of the simulation.
To investigate the clustering effect which was the true
goal of this work, the concept of a “time CV” is
introduced to describe the relative amount of
clustering in large seeds. This time CV is calculated
based on the number of seeds released from the
manifold head over an interval of distribution ∆t
(being the fully-developed period of time when seeds
are actively leaving the manifold), as follows:
��IJ0� �K 1L����� ∑ N�J − L�����∆� P%∆I/IRSTU
JVWL�����
∆I
(7)
Based on this definition in Equation 7, the outlet
distribution for two different wheat seed simulations
and two different chickpea simulations were
compared, as shown in Figure 7 and Figure 8, below.
These figures show the full seed distribution from the
air seeds as a ‘parcel’ of ~600 seeds is released into the
manifold. The time CV is calculated over the steady
period after when the manifold head is fully saturated
with seeds; an ideal distribution with zero clustering
would ramp up to a flat distribution, and then drop
down again as the parcel passes.
Figure 7: Seed release over time of small wheat seeds in two air seeder simulations
Figure 8: Seed release over time of large chickpea seeds in two air seeder simulations
0.0
5.0
10.0
15.0
20.0
0.05 0.1 0.15 0.2 0.25
Am
ou
nt
of
seed
sa
mp
le
ejec
ted
in
10
ms
win
do
w [
%]
Time from seed release into manifold entrance [s]
One-Way Wheat Simulation (4 mm)
Time CV = 20.8%
Two-Way Wheat Simulation (4 mm)
Time CV = 25.1%
0.0
5.0
10.0
15.0
20.0
25.0
0.2 0.25 0.3 0.35 0.4 0.45Am
ou
nt
of
seed
sa
mp
le e
ject
ed
in 1
0 m
s w
ind
ow
[%
]
Time from seed release into manifold entrance [s]
Two-Way IB Chickpea Simulation (8 mm)
Time CV = 76.6%
Two-Way IB Chickpea Simulation (10 mm)
Time CV = 90.5%
7
5.3 Fluidization Analogy
As seen in these figures, the large seed simulations
demonstrated significantly more clustering than the
small seeds. The clustering effect was found to be
largely due to obstructions in the flow, causing the
seeds to drop into Geldart’s “spouted bed” fluidization
regime (Geldart, 1973) [22] and resulting in periodic
bursts of seeds after localized pressure build-up. The
baseline wheat simulation, operating in one-way
coupling, serves as a control for how much clustering
might typically be expected if the manifold is
operating primarily in a pneumatic conveying regime.
A second wheat simulation taking into account two-
way coupling (shown as a dashed line in Figure 7)
effects shows slight clustering, supporting the
hypothesis that the clustering is due to obstruction of
the flow.
This transition due to flow obstruction can be seen in
the Geldart fluidization regime map, presented below
in Figure 9:
Figure 9: Geldart fluidization regime transition
In Figure 9, the dimensionless coefficients have been
calculated as per the following equations:
��∗ = �� ����� �� − ��� ��
(7)
�∗ = � � ������ − ����
��
(8)
Based on an observed drop in average chickpea
velocity across the elbow from approximately 17 m/s
to approximately 5 m/s, this transition corresponds to
a change in u* from 27 to 8.1, at a dimensionless
diameter d* of 132. The observed pressure buildup
behind the seeds is clearly seen below, in Figure 10
and Figure 11.
Figure 10 shows the fully developed air pressure
profile prior to the introduction of the large seeds;
Figure 11 shows the obstruction caused by these seeds,
as the air pressure builds up behind them in stages and
segregates them into distinct waves.
Figure 10: Air pressure inside manifold prior to
introduction of large seeds
Figure 11: Air pressure inside manifold after
accumulation of large seeds
8
5.4 Conclusions
The asymmetrical airflow seen in the manifold in
Figure 5 and Figure 6 is primarily caused by the main
manifold elbow. Because of the high air velocity, the
short vertical section typically used in air drill seeders
following the elbow is not long enough to allow the
flow profile to become fully developed again. This
leads to an imbalanced airflow between the different
outlets, with more air exiting from the “back” outlets
(opposite the incoming pipe). Design changes which
discourage the back wall jet from forming, which
guide the air around the elbow more gently, or which
allow the flow profile to redevelop more quickly,
should reduce the airflow variation between the
outlets.
Larger seeds also tend to cluster, emerging from the
outlets in spurts which are analogous to the behaviour
of Geldart’s spouted bed characteristics. Pressure is
allowed to build up behind the seeds in the manifold
whenever the seeds come to rest inside of the pipe.
This occurs where the seeds are forced to suddenly
change direction, in the main elbow, and again in the
top of the manifold. In both cases, the seeds stagnate
inside the manifold, which causes the system to back
up with seeds. This build-up eventually results in a
spout of seeds being pushed out in a cluster. Design
changes which encourage a smooth transition of seeds
through the pipe, instead of hard collisions, should
reduce the amount of clustering observed in operation.
ACKNOWLEDGMENTS
The authors would like to thank Bourgault Industries
Ltd. for supporting this case study with data from
their air seeder design.
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