Discrete Elemente Method (DEM) · PDF file19.01.2011 Discrete Elemente Method (DEM) ......
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Lecture DEM19.01.2011
Discrete Elemente Method (DEM)
Matthias Börner – NaWiTec, Institute of Process Engineering
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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
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EinführungWhat is DEM
Problems in process engineering:
particle processes and particle
handling
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IntroductionWhat is DEM
Working examples of DEM
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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
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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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