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

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Radial coordinate (m)

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(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

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Radial coordinate (m)

Ore

/(O

re+

Cok

e)

-4 -2 0 2 40

0.5

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Radial coordinate (m)

Ore

/(O

re+

Cok

e)

-4 -2 0 2 40

0.5

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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

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-2 0 2

0

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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!!!