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Lecture DEM19.01.2011

Discrete Elemente Method (DEM)

Matthias Börner – NaWiTec, Institute of Process Engineering

Matthias.Boerner@ovgu.de

Introduction DEM

- What is DEM?

- Basics

- Equations and models

Software solutions

Example 1

- Screw auger

Coupling to CFD

Example 2

- Fluidized bed

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OverviewContent

3

EinführungWhat is DEM

Problems in process engineering:

particle processes and particle

handling

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IntroductionWhat is DEM

Working examples of DEM

5

DEM – operational areas

Industry of bulk materials

- Mining

- Metallurgy

- Agriculture

Processes of particle formulation

- Pharmaceuticals

- Fertilizer industry

- Food industry

Mechanical + thermal process engineering

- Drying

- Breakage events

- Behavior of bulk materials and transport

properties

- Phase-coupled systems

solid

liquid

gas

IntroductionWhat is DEM

6

Diskrete Elemente Method

Observation and mathematical description of

single objects / particles / granules (discrete

calculation)

Investigation of mechanical attributes of discrete

separated structures and allocations

MeshIess method compared to FEM or FVM

Explicit numerical finding of solution (ODE

systems)

Interactions between objects only at contact points

First scientific reference 1978 and further

developments by Cundal et al. using the program

BALL

x,vx

z,vz

y,vy

F

x,vx

z,vz

y,vy

IntroductionWhat is DEM

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Advantages

Few equations which have to be solved for each object

Forces and motions can be investigated for each single object

in the middle of system, which are usually not measureable

Limits in usage

Real particle systems consists of billions of elements

All-embracing description not feasible

Compromises by system simplifications – partially difficult to get

conclusions about the system behavior of real, large production

plants

IntroductionWhat is DEM

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Newton„s

law of motion

(applied on every particle)

force + momentum

Force displacement law

(applied on every contact)

Relative motion

Constitutive laws

Current particle–paricle and

particle–wall position as well as

estabished connections

Contact forces

IntroductionWhat is DEM

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Newton‘s laws of motion

I. law

wenn

II. law

III. law

Superposition of forces

dI dmvF= =

dt dt

res 1 2 nF =F +F +...+F

v const 0i

i

F

A-B A-BF =-F

Discription of particle

motion

IntroductionWhat is DEM

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Force displacement law

Finding contact forces during interaction with resulting

displacement of elements

contact models

Fn

Ft

IntroductionWhat is DEM

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DEM - organization

Neighborhood search- Determination of interacting particle pairs

- Wall dependencies

Force calculation- Calculation of forces acting on particles

Integration- transient dependencies of particle dynamics

IntroductionBasics

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Neighbourhood search

Finding surfaces and volumes in contact with each other

If no contact exists – exceptionally Newton„s second law

At contact – solution of Newton and force displacement law

Basis: an efficient algorithm for contact search of polygonal

constructed particles – for identical particles “spatial

hashing”

Naive neighborhood search is time consuming due to complex

system structure

IntroductionBasics

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, , ,contact a ab n ab tF F Fab n ab t abI I n I n

Particle interactions

Description of single particles interactions with each other and with

their vicinity/wall

Description by so-called contact models

Basis is the force displacement law

Hard-Sphere and Soft-Sphere(momentum based exchange forces) (contact forces)

IntroductionBasics

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Contact models

At the contact of particles an overlap at the contact area is allowed

(Soft-sphere)

Choice of approach depends on particle velocities –

- low velocities: soft sphere

- high velocities: hard sphere

Hard-sphere approach fails in prediction at low particle velocities and

long contact times

At low contact times (high particle

velocities) the time step resolution

to handle particle contacts increases

for the Soft-sphere approach

- Correspondingly more time steps

and longer calculation time

FF

δ

A

IntroductionBasics

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Hertz-Mindlin contact modell(with and without slip)

- Hertz (Journal of Applied Mechanics 1949)

- Approximation of particle impact like a dash pot, non-linear

- Interconection of springs and dash pots in series

- only for sheres in contact

IntroductionBasics

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Linear-Spring contact modell

- Extention of Hertz-Model by Cundal 1979

- Simplified solution method – faster in calculation

- Partially based on non-physical models (spring stiffness)

IntroductionBasics

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Further contact models

For considering various system characteristics

Bond model – strong connection/bond between particle, breakage is

possible, extension of Hertz-Mindlin

Ductile model – Extension of bond model to consider brittle breakage

Cohesion model – Additional inter-particle forces (e.g. van der Waals)

Electrostatic model – Impact on particles in surrounding without direct

contact

Burger‘s model – Combination of Maxwell and Kelvin to investigate

creep processes

etc.

IntroductionBasics

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Time integration

Rayleigh time step

- transient description of particle impact

- tsim < 0.25 tR for sufficient accuracy

tR

δ1

2

3

1

2

3

Shear waves

through particle

IntroductionBasics

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SimulationParameter

Necessary material properties

Particulate properties to simulate the system of materials

Density ρ in [kg/m³]

Particle diameter d in [m]

Shear modul in [Pa]

Poisson„s ratio

Coefficient of restitution

Coefficent of static friction

Coefficent of rolling friction

Part

ikulä

r

Inte

r-

part

ikulä

r

Volume

Mass

Moment of inertia

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SimulationParameter

Values of a simulation

Calculated values as result of simulation

Positio

n

Zeitlic

he

Abhängig

keit

Krä

fte / E

nerg

ie

Inte

r-

part

ikulä

r

x-coordinate

y-coordinate

z-coordinate

Velocity (vx,vy,vz)

Angular velocity

Mass

Volume

Total energy

Potential energy

Kinetic energy

Rotational energie

Total force

Compression force

Momentum

Collisionfrequence

Forces in bonds

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SimulationSoftware

Commercial Software

- EDEM by DEM-Solutions

- PFC by Itasca

- Chute Maven by Hustrulid

Technologies

- Elven by Rockfield Software

- SimPARTIK by Frauenhofer Institut

Open Source

- LAMMPS

- LIGGGHTS (CFDEM)

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SimulationSoftware

EDEM – Software for applied particle processes

Short presentation about DEM-applications using the commerical

software EDEM

Product of DEM-Solutions Ltd.

Company founded in 2002

First EDEM version in 2005

Contineous developments in the software

Simple structure with graphical user interface

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SimulationSoftware

Scheme of a DEM-simulation

GeometryCAD-Program

Usual formats can be imported

Simple geometries can be

created within

CreatorGlobals

Particles

Geometry

Factory

SimulatorTime step

Cell size

Progress of

simulation

AnalyzerAnalyzes and graphical

output of results, export to

external programs (e.g.

EnSight)

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Example 1Screw auger

Transport of bulk materials

Simulation of transport phenomena of spherical particles in a

rotating screw auger

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Results of simulation

Elongated particle form

(contained of 6 particles)

Rotation of particles

+ transport of particles

Example 1Screw auger

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Coupled simulations between CFD and DEM

Dry powder inhaler

Pneumatic transport

Particle motions through constrictions

Coupling with CFDBasics

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CFD DEMUDF

Eulerian-Lagrange coupling between CFD and

DEM

Gas / fluid phase

- Calculation of fluid flow with the continuums approach,

Navier-Stokes equations

- FVM, mesh based

Solid phase

- Discrete calculation of single particles

- solid concentration below <10%

- e.g. DPM, Ansys

Momentum exchange

Coupling with CFDBasics

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CFD DEMUDF

Eulerian-Eulerian coupling between CFD and DEM

Gas / fluid phase

- Calculation of fluid flow with the continuums approach,

Navier-Stokes equations

- FVM, mesh based

Solid phase

- Discrete calculation of single particles

- facilitates the handling of high solid concentrations

- in EDEM

Momentum exchange

+ conservation of mass-

and momentum

Coupling with CFDBasics

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Field coupling between DEM und CFD

Gas / fluid phase

- Stationary calculation of fluid flow with the continuums

approach, Navier-Stokes equations

- FVM, mesh based

- Export of field data (CGNS-Format)

Solid phase

- Discrete calculation of single particles

- Lagrange or Eulerian

- Only applicable, if particles do not effect the fluid flow

- indirecte coupling scheme for both phases

Coupling with CFDBasics

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Scheme of coupled DEM-CFD-simulation

Geometryin CAD (Import to Ansys) or Design

Modeller

MeshingAnsys Meshing

ConfigurationFluent simulation adjustments for fluid

flow

Post-ProcessingCFD-Post or Ensight

Analysis and graphical output of both

results

EDEMAdjustments for

coupling

EDEMCreator

EDEMSimulator

Calculation

Coupling with CFDBasics

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Coupling with CFDBasics

Scheme of a coupled simulation

EDEM:

Time step of EDEM begins after the

converged solution isdelivered by Fluent

EDEM:

Drag and lift forcesdetermined by Fluent

are applied on particlesat the according position

EDEM:

Particle position isupdated

Fluent:

Particle forces calculated in EDEM are applied in Fluent

grid cells causing a momentum sink or an

energy source

Fluent:

Calculation until a converged solution

Particle

coordinates

are transfered

to Fluent

Transfer of fluid

field data to EDEM

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Solid volume fraction estimation

Estimation of solid fraction in CFD grid

- Sample points determine if a particle is contained in a grid cell

and how much volume it occupies

- the more sample points are used the more precise and accurate

the solution

4/9

3/9

2/9

5/9

6/9

1/9

DEM

m

i particle

i

sample fluidcell

SV

N V

Coupling with CFDBasics

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Drag force on particles

Fluid forces appealing on particles

- various relations are published e.g.:

- Kürten

- Clift

- Di Felice

- Ergun und Wen & Yu

FD FL

FG FA

0.5freestream D f p f p f pF c A v v v v

D freestreamF F

2

0.5

4.80.63

ReDc

Coupling with CFDBasics

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Example 2Fluidized bed

Particlde dynamic in fluidized beds

Simulation of mixing, heat and mass transfer processes

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Example 2Fluidized bed

Results of simulation

Bi-disperse particle system

d1 = 2mm

d2 = 5mm

ugas = 6 m/s

Facts of interest:

- Mixing effects of both particle

systems

- Discharge behavior

- Fluidization behavior

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