Introduction to Discrete Element Modeling (DEM) simulation

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Debanga Nandan Mondal

Process and systems technology Laboratory, Åbo Akademi University, Biskopsgatan 8, FI-20500 Åbo, Finland

There are two kind of modeling approaches….Continuum 

Constitutive Laws Substance is continuous &

fills the space it occupies Behavior of individual

particles is ignored constitutive equations are

solved numerically (e.g.Finite Element Method).

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Discrete Model each single particle Bulk = assembly of particles Individual particle ‐ particle

interaction investigating phenomena

occurring at the length scaleof particle diameter

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Continuum  Discrete

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 Navierstokes equation

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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

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Eulerian models  Lagrangian models 

Modeling of flows

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Fluids

Granular particles

Single phase

Multi phase

fluid - fluid

fluid - particles

eulerian

lagrangian

Eulerian -eulerian

lagrangian -lagrangian

granular and fluid

granular

eulerian -eulerian

eulerian

lagrangian

eulerian -lagrangian

CFD

SPH, MPX

CFD

SPH, MPX

CFD-DEM

CFD-KT

KT, plasticity

DEM, MC

History

• 1956 : Alder and Wainwright: Theory of Discrete Element Model was 

introduced : for Molecular dynamics

• 1970 : Cundall and Strack: The principles of discrete element 

method : distinct element method 

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Main principles of DEM

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1. Contact detection algorithms

2. Suitable contact models2.1. Accelerations2.2. Velocities2.3. Positions

Application of DEM Each particle in a system is tracked. Direct particle‐particle contact. Other contact forces can be implemented. 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 

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Main DEM parameters

Particle properties• Diameter• Density• Young’s modulus• Shear Modulus

Contact Properties• Coefficient of static friction• Coefficient of rolling friction

External Parameters• Gravity• Other forces (attraction & repulsion)

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Åbo Akademi University | Domkyrkotorget 3 | 20500 Åbo 11

Accelerations  Velocities  Positions Newton’s Laws

Contacts Forces Contact Mechanics

Discrete simulation approaches

Hard-sphere Interaction forces :

impulsiveMomentum exchange:

only particle collisions

18.10.2019Åbo Akademi University | Domkyrkotorget 3 | 20500 Åbo 12

Soft-sphereParticles are rigidSmall overlaps:

deformation duringcontact

Soft-sphere method is the mostcommonand accurate approach. It isused in most DEM packages, includingEDEM

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v1 v2

overlap

V1’ V2’

The soft‐sphere approach allows for small overlaps which are used to calculate magnitudes of the forces acting on particles.

Each particle within a granular flow has 6 degrees of freedom : Rotational and Translational motion

Newton’s second law is used to calculate the translational and rotational accelerations

Those are are then numerically integrated over a time step to update particle velocities and positions.

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Particle Motion Calculations

Particle Motion CalculationsRotation 

I ω  𝑀

𝐼 : moment of inertia𝜔 : angular velocity𝑀 : resultant contact torque acting on the particle𝑡 : time

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mg

v

Fnc

Fc

M

ω

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Particle Motion Calculations

mg

v

Fnc

Fc

M

ω

Translation m   𝐹 𝐹 𝐹

v : translational velocity of the particlem : mass of the particle𝐹 : resultant gravitational force acting on the particle 𝐹 and 𝐹 : resultant contact and noncontact forces between the particle and surrounding particles or walls

Contact detection

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For spherical particles, a contact is detected if the distance between two spheres is less than summation of their radii 

Computationally expensive

Borrowed from EDEM tutorial

Contact force models

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Borrowed from EDEM tutorial

There are few contact force models

The contact models are based on theories of contact mechanics and are mostly developed for spherical contacts. 

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Spring dashpot contact model.

Cattaneo (1938) and Mindlin(1949) added tangential forces for slip conditions 

Contact force models

Bubbling fluidized bed

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Fluent Discrete Phase Model with…

DEM collisions enabled

Macroscopic particle model

Particles are treated in a Lagrangian frame of reference.

Each particle is assumed to span several computational cells.

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Macroscopic particle model

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Fluid cells touched by particle and patching of particlevelocity

Borrowed from Macroscopic Particle ModelTracking Big Particles in CFD, Madhusuden Agrawal

Gas flow through coke bed

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CFD – DEM coupled

To study particle behavior in fluid phase.

Solid and fluid motions are solved through Newton’s equation of motion for discrete particles

Navier‐Stokes equation for continuum particles

Different drag models are applicable for particle‐fluid interaction

Coke bed descend: Different diameters

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How to simulate?

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Set: Particle properties

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Macroscopic Particle Model: ANSYS

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EDEM

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Particle dimension

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Build geometry

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Coke‐pellet descend

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Conclusions

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Discrete element modeling is becoming very powerful tools.

Computational limitations are disappearing everyday.

Parallel processing are making DEM calculations faster: by handling different particle motions at different processors.

Large particles are being simulated in CFD‐DEM coupled solvers.

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Heat transfer through particle bed can be calculated.

Forces acting on the containers and equipment can be calculated.

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References

Check any material about EDEM

Search google.

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