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Discrete Element Modeling:
Modeling of bulk solid flows
Tamoghna Mitra,
Thermal & flow Engineering laboratory,
Abo Akademi University, Turku
Bulk solids
An assembly of solid particles
that is large enough for the
statistical mean of any
property to be independent of
number of particles.
Bulk solids Behave different from
liquids
– Fluid pressure =
ℎ ∙ 𝑑 ∙ 𝑔
– Solid pressure is not
linear
Part of the pressure is
carried by the walls
because of the shear
stresses (termed wall
support)
Resulting in non fluid like
behaviors like dead zone
formation and bridge
formation
Dead zone
formation
Bridge
formation
resulting in
no flow
Modeling of flows
Eulerian models
– Reference frame outside
the motion of the
constituents
– The fluid/particles are
treated as continuum
– Bulk properties are required
– Boundary conditions are
difficult to formulate
– Need to solve Navier stokes
equation
Lagrangian models
– Reference frame moves
along with the constituent
– The fluid/particles are
treated individually
– Properties of individual
particles are needed
– Boundary conditions are
relatively easier
– Need to solve Newton’s
second law
𝑖
𝑖
𝑣𝑖, 𝑝𝑖
𝑣𝑖, 𝜔𝑖
Fluids
Granular
particles
Single phase
Multi
phase
Fluid -
fluid
Fluid -
particle
Granular
Granular and fluid
Lagrangian
Eulerian
Eulerian-
Eulerian
Eulerian-
Lagrangian
Lagrangian -
Lagrangian
Eulerian -
Eulerian
Lagrangian
Eulerian M
od
elin
g o
f F
low
s
CFD
SPH, MPX
CFD
SPH, MPX
CFD-DEM
CFD-KT
KT, Plasticity
DEM, MC
Main principles of DEM
Each particle in a system is tracked
Particles are represented by spheres
usually (not necessary)
Newton’s second law is solved
F = 𝑚 ∙ a
Example of forces
– Contact forces
– Gravitational force
– Electrostatic or Magnetic force
– Fluid drag force
The effect of the forces are
integrated over time
B
Main steps
Generate the particles
(position, linear and
angular velocity)
Generate the geometry
Contact detection
Calculate the net forces
and torques on particles
Calculate the new position
and velocity after time Δt
using Newton’s second law
Do more
particles
need to be
created?
Does the
geometry
needs to
change?
Reached
the end of
simulation
time?
Change geometry
Start Stop
Yes
Yes
Yes
No
No
No
Contact detection
Checking for each
pair could be tedious
The simulation area
is divided into grids
Contact detection
Checking for each
pair could be tedious
The simulation area
is divided into grids
Particles lying in a
particular grid are
checked with
particles in the
neighboring grid
The grid thickness
doesn’t effect the
simulation results
but the simulation
time is affected
Calculation of forces: Contact
force
Various models are available to
evaluate the contact forces
The most common contact force
model is given by Hertz (1882)
𝐹𝑁 = 𝐾𝛿𝑛
𝑛 = 3/2 for parabolic stress at
contact region
𝐾 =4
3 𝜎𝑖+𝜎𝑗
𝑅𝑖𝑅𝑗
𝑅𝑖+𝑅𝑗
𝐹𝑇 = 0, ok as long as 𝛿 is small
𝛿
Cattaneo (1938) and Mindlin (1949)
added tangential forces for slip
conditions
Spring dashpot contact model
Calculation of forces: Contact
force
𝐹Ns,𝑖𝑗 −𝑘𝑛𝛿𝑛32 𝑛
𝐹Nd,𝑖𝑗 −𝜂𝑛v𝑛,𝑖𝑗
𝐹Ts,𝑖𝑗 −𝑘𝑡𝛿𝑡
𝐹Td,𝑖𝑗 −𝑘𝑡v𝑡,𝑖𝑗
Time integration: Verlet
integration
Most commonly used algorithm
originally developed by Carl Størmer.
It is used for calculating trajectories.
Steps:
Time integration: Timestep
The disturbance flow through the particle
in Rayleigh time.
The timestep should be smaller than this,
typically 20%
This depends on the material property and
size of the particles
𝑇𝑅 =𝜋
𝜌
𝐺
12
0.1631𝜈+0.8766, 𝜌 is density, 𝐺 is
shear modulus and 𝜈 is Poisson’s ratio
Main DEM parameters
Particle properties
– Size
– Density
– Young’s modulus
– Shear modulus
Contact properties
– Coefficient of static friction
– Coefficient of rolling friction
External parameters
– Gravity
– Other long range forces (e.g. due to an electric field)
Modifications of DEM: Non-
spherical particles
Main drawback of traditional DEM is the reliance on
spherical particles. It is good for spherical or almost
spherical particles.
Most everyday particles are non-spherical, need special
consideration
Clumped spheres to somewhat mimic the actual situation.
The spheres are clumped rigidly to the shape original
particle shapes
9.5.2015 Åbo Akademi University | Domkyrkotorget 3 | 20500 Åbo | Finland 15
+
Parallel processing
DEM is extremely time consuming expecially due
to the very small timestep.
– With 10-7 s timestep simulating a 10 s condition would
require 108 iterations!!
DEM is easy to parallelize because of the explicit
implementation.
Different regions of the space are handled by
different processors and the results are then
combined at the end of the timestep.
This helps to simulate extremely large particulate
systems.
Example code: Newton’s
pendulum
Written in MATLAB
Slow
2 dimensional
Easy and fun
https://se.mathworks.com/matlabcentral/fileexchange/50786-
discrete-element-modeling-of-newton-s-pendulum
Simulation result (e = 0.5)
Simulation result (e = 0)
Simulation result (e = 1)
Software
Commercial
– EDEM
– Newton
Open-source
– LIGGGHTS
– dp3D
– YADE
Applications
Gummy bears
– https://www.youtube.com/watch?v=39ihvsGr-Do
Cutting concrete
– https://www.youtube.com/watch?v=ln7d74uxyBQ
Screw feeder
– https://www.youtube.com/watch?v=b0IK4JpwwCw&list=PL1487B
97F09156811&index=3
Compression test – https://www.youtube.com/watch?v=RwEOiGhobv8&index=1&list=
PL1487B97F09156811
Case study: Raw material
charging in an ironmaking
furnace
Raw material
charging
Layered structure
– slowly descending
burden
– rising reducing gas from
below
Rings of ore and coke
Charging program–material,
amounts, position
Effects gas distribution,
overall performance
Simple models have been
developed for simulating
burden and gas distribution.
C
O
Burden distribution effects
-2 0 2-8
-6
Radial coordinate (m)
Heig
ht
(m)
-2 0 2-8
-6
Radial coordinate (m)
Heig
ht
(m)
-2 0 2-8
-6
Radial coordinate (m)H
eig
ht
(m)
-2 0 2-8
-6
Radial coordinate (m)
Heig
ht
(m)
-2 0 2-8
-6
Radial coordinate (m)
Heig
ht
(m)
-2 0 2-8
-6
Radial coordinate (m)
Heig
ht
(m)
-2 0 2-8
-6
Radial coordinate (m)
Heig
ht
(m)
-2 0 2-8
-6
Radial coordinate (m)
Heig
ht
(m)
-2 0 2-8
-6
Radial coordinate (m)
Heig
ht
(m)
-2 0 2-8
-6
Radial coordinate (m)
Heig
ht
(m)
-2 0 2-8
-6
Radial coordinate (m)
Heig
ht
(m)
-2 0 2-8
-6
Radial coordinate (m)
Heig
ht
(m)
-4 -2 0 2 40
0.5
1
Radial coordinate (m)
Ore
/(O
re+
Cok
e)
-4 -2 0 2 40
0.5
1
Radial coordinate (m)
Ore
/(O
re+
Cok
e)
-4 -2 0 2 40
0.5
1
Radial coordinate (m)
Ore
/(O
re+
Cok
e)
-4 -2 0 2 40
0.5
1
Radial coordinate (m)
Ore
/(O
re+
Cok
e)
-4 -2 0 2 40
0.5
1
Radial coordinate (m)
Ore
/(O
re+
Cok
e)
-4 -2 0 2 40
0.5
1
Radial coordinate (m)
Ore
/(O
re+
Cok
e)
-4 -2 0 2 40
0.5
1
Radial coordinate (m)
Ore
/(O
re+
Coke)
-4 -2 0 2 40
0.5
1
Radial coordinate (m)
Ore
/(O
re+
Coke)
-4 -2 0 2 40
0.5
1
Radial coordinate (m)
Ore
/(O
re+
Coke)
-4 -2 0 2 40
0.5
1
Radial coordinate (m)
Ore
/(O
re+
Coke)
-4 -2 0 2 40
0.5
1
Radial coordinate (m)
Ore
/(O
re+
Coke)
-4 -2 0 2 40
0.5
1
Radial coordinate (m)
Ore
/(O
re+
Coke)
Radial coordinate (m)
Heig
ht
(m)
-2 0 2
0
5
10 200
400
600
800
Radial coordinate (m)
Heig
ht
(m)
-2 0 2
0
5
10200
400
600
800
Radial coordinate (m)
Heig
ht
(m)
-2 0 2
0
5
10 200
400
600
800
Radial coordinate (m)H
eig
ht
(m)
-2 0 2
0
5
10 200
400
600
800
Radial coordinate (m)
Heig
ht
(m)
-2 0 2
0
5
10 200
400
600
800
Radial coordinate (m)
Heig
ht
(m)
-2 0 2
0
5
10 200
400
600
800
Radial coordinate (m)
Heig
ht
(m)
-2 0 2
0
5
10 200
400
600
800
Radial coordinate (m)H
eig
ht
(m)
-2 0 2
0
5
10200
400
600
800
Radial coordinate (m)
Heig
ht
(m)
-2 0 2
0
5
10 200
400
600
800
Radial coordinate (m)
Heig
ht
(m)
-2 0 2
0
5
10 200
400
600
800
Radial coordinate (m)
Heig
ht
(m)
-2 0 2
0
5
10 200
400
600
800
Radial coordinate (m)
Heig
ht
(m)
-2 0 2
0
5
10 200
400
600
800
Gas temperature (deg C)
DEM simulation
9.5.2015 Åbo Akademi University | Domkyrkotorget 3 | 20500 Åbo | Finland 26
Green, Blue, Red – Coke of different size
Yellow - Pellets
Coke push experiment/full
scale simulation
*2 million particles
Coke shift full scale simulation/scaled experiment
before after
Conclusions
Discrete Element Modeling is a very powerful
technique to simulate granular materials.
But, they are computationally expensive.
As the computers become faster and more cores
can be added to a chip, DEM calculations would
become faster due to ease of parallelization.
Results provide incredible insight into the process
in a way neither experimentation or any eulerian
method can provide.
Thank you!!!