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: mbayati@radix-ic.com

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%

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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

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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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