P. Bowen, EPFL. 20/09/2019 1 ÉCOLE POLYTECHNIQUE FÉDÉRALE DE LAUSANNE Technologie des poudres Des glissements de terrain au béton et des avalanches au chocolat Prof. P. Bowen, Dr. P. Derlet (PSI) Week 2 – Lecture no. 3 - on website PTG • BOOKS • The Colloidal Domain – D. F. Evans & H. Wennerström, Wiley, 1999, • Principles of Ceramic Processing – J.S.Reed , Wiley, 1995. English • T. A. Ring - Fundamentals of Ceramic Powder Processing and Synthesis. Academic Press,1996 • Les Céramiques, J. Barton, P. Bowen, C. Carry & J.M. Haussonne, Les Traité des Matériaux, Volume 16, PPUR, 2005
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P. Bowen, EPFL. 20/09/2019 1
ÉCOLE POLYTECHNIQUE FÉDÉRALE DE LAUSANNE
Technologie des poudres
Des glissements de terrain au béton et des
avalanches au chocolat
Prof. P. Bowen, Dr. P. Derlet (PSI)
Week 2 – Lecture no. 3 - on website
PTG
•BOOKS
•The Colloidal Domain – D. F. Evans & H. Wennerström, Wiley, 1999,
• Principles of Ceramic Processing – J.S.Reed , Wiley, 1995. English
• T. A. Ring - Fundamentals of Ceramic Powder Processing and Synthesis. Academic Press,1996
• Les Céramiques, J. Barton, P. Bowen, C. Carry & J.M. Haussonne, Les Traité des Matériaux, Volume 16, PPUR, 2005
– Broad size distribution – positive improves packing fraction
– Need good dispersion and colloidal stability with low degree or no aggregates or agglomerates
– The dispersion also influences the rheology – important for spraying
– We need a minimum viscosity but with a maximum of solids loading to create dense granules via spray drying – optimum with respect to above parameters
Useful tool for prediction of ceramic green body densities (and sintered see thesis (Violaine Guerin – EPFL No. 3021 (2004))
Allows insight into behaviour of powder during compaction and sintering from standard powder characteristics
Useful for optimisation in industry – evaluation of new powder lots
Should also be applicable to metallic powders
Can in fact use the programme in reverse – machine learning approach – i.ewe have optimised an algorithm for a given range of powder characteristics –now we can create virtual powder needed to create certain green or sintered density or microstructure – or find which powder needed for desired sintered density
Modelling
Modelling of materials processing and microstructures – numerical modelling methods
e.g. Finite Element Methods (FEM)– Discrete Element Methods (DEM) –
Variation of clay - Evolution of effective-viscosity
Sample SCR [g/g] Swelling clay proportion in
the bulk [g/g]
Md 1 0 0 ( only kaolinite)
Md 2 0.27 0.005
Md 3 0.54 0.01
Md 4 0.8 0.02
Relation between water content (%wt) (W) and
effective viscosity(K) for 4 mixtures
1:1 clay - Kaolinite China Clay™ (commercial)
2:1 clay - Smectite - extracted from watershed
soils (SCR swelling clay ratio = 2:1 / 1:1)
K
w
P. Bowen, EPFL. 20/09/2019 39
Comparaison with Natural Debris Flows
swelling
Non
-swelling
MD1
Model
Mixture
MD4
Model
Mixture
P. Bowen, EPFL. 20/09/2019 40
Future …….
• Theory : harmonise the classification (fluid-grains) and flow regimes….
• Lab : better understand the effects of the different clays and particles (size
and disitribution)
• Observations in-situ : modes of release – the trigger….
• Modelling : try and relate to regional parameters – clay content, soluble
ions, degree of aggregation, interparticle forces….
Submitted project failed maybe another project… some day….
P. Bowen, EPFL. 20/09/2019 41
Can you answer these questions? (1)
Give a field of application or an everyday example of Powder Technology
How is particle packing important for rheology?
How do aggregates influence the microstructure of a ceramic?
How can this effect the optical properties of polycrystalline alumina ceramics?
What are the different types of models used to describe the packing of particles?
Describe an example of a model in detail.
What is the difference between Random loose packed (RLP) and Random close packed (RCP) ?
For monodispersed spherical particles what is the maximum packing fraction for random close packing RCP? For an ordered array of monodispersed spheres ?
How is the packing of particle modified
- when the particle size has a log-normal distribution?
- if the particles are not spherical ?
- for dry powder as a function of size e.g when the size is reduced?
P. Bowen, EPFL. 20/09/2019 42
Can you answer these questions? (2)
What are the different forces that can act on particles and influence their packing .
-which forces dominate for particles < 1 micron
- which force dominates for particles > 100 microns
What is the effect of agglomeration on the particle packing – how can one describe quantitatively the degree of agglomeration ?
For a bimodal distribution of two monodispersed powders what is the maximum packing fraction that can be attained?
For a multimodal distribution of powders what is the maximum packing fraction that can be attained – give an example of where this is used in practice.
What are the limitations of using a multimodal packing method for ceramic fabrication?
What type of packing is found for ultrafine alumina powders produced by precipitation and how could this be improved ? What is its significance for the dry pressing of ceramic pieces?
Describe DEM modeling and give an example of its application to Particle Technology
P. Bowen, EPFL. 20/09/2019 43
BIBLIOGRAPHIE
BAR05 J. Barton, P. Bowen, C. Carry & J.M. Haussonne, Les Céramiques, Les Traité des Matériaux, Volume 16, PPUR, 2005
BRO50 G. BROWN, Flow of fluids through porous media 1 - Single Fluid phase,1950, pp. 210-216
DEX72 A.R. DEXTER, D.W. TANNER, Packing densities of mixtures of spheres withlog-normal size distributions, Nature physical science, 1972, vol. 238, pp. 31-32
DIN00 D.R. DINGER, One-dimensional packing of spheres, Part I, American ceramic society bulletin, 2000, pp. 71-76
*FLA04aR.J. Flatt, ‘Towards a prediction of superplasticized concrete rheology’, Materials and structures 27 (269) (2004) 289-300
FLA04b R.J. Flatt, N. Martys, L.Bergström The Rheology of Cementitious Materials, MRS Bulletin, may 2004, pp. 314-318
GER89A R.M. GERMAN, Packing of monosized nonspherical particles, Book “Powder packing characteristics”, 1989, pp. 122-133
GER89B R.M. GERMAN, Introduction to particle packing, Book “Powder packing characteristics”, 1989, pp. 1-20
MIL78 J.V. MILEVSKI, Handbook of fillers and reinforcement plastics, Eds Van Nostrand, 1978
NAR85 M. NARDIN, E. PAPIRER, J. SCHULTZ, Powder Technology, 1985, 44, pp.131-140
NAV99 P. Navi, C. Pignat, Three - dimensional characterization of the pore structure of a simulated cement paste, Cement and Concrete Research 29 (1999) 507-514
*NOL93 G.T. NOLAN, P.E. KAVANAGH, Computer simulation of random packings of spheres with log-normal distributions, Powder technology, 1993, vol. 76, pp.
309-316
*NOL94 G.T. NOLAN, P.E. KAVANAGH, The size distribution of interstices in random packings of spheres, Powder technology, 1994, vol. 78, pp. 231-238
NOL95 G.T. NOLAN, P.E. KAVANAGH, Random packing of nonspherical particles, Powder technology, 1995, vol. 84, pp. 199-205
PHI96 A.P. PHILIPSE, The random contact equation and its implications for(colloidal) rods in packings, suspensions, and anisotropic powders, American chemical society, 1996, 12, n°5, pp. 1127-33
PHI97 A.P. PHILIPSE, A. VERBERKMOES, Statistical geometry of caging effects in random thin-rod structures, Physica A, 1997, 235, pp. 186-193
SOH68 H.Y. SOHN, C. MORELAND, The effect of particle size distribution on packing density, Canadian journal of chemical engineering, 1968, vol. 46, pp.162-167
P. Bowen, EPFL. 20/09/2019 44
BIBLIOGRAPHIE
SUZ01 M. SUZUKI, H. SATO, M. HASEGAWA, M. HIROTA, Effect of size distribution on taping properties of fine powders, Powder technology, 2001,118, pp. 53-57
SUZ83 M. SUZUKI, T. OSHIMA, Estimation of the coordination number in a multicomponent mixture of spheres, Powder technology, 1983, 35, pp. 159-166
SUZ85 M. SUZUKI, T. OSHIMA, Coordination number of a multicomponent randomly packed bed of spheres with size distribution, Powder technlogy,1985, 44, pp. 213-8
WAK75 R.J. WAKEMAN, Packing densities of particles with log-normal sizedistributions, Powder technology, 1975, 11, pp. 297-299
*YU93 A.B. YU, N. STANDISH, Characterisation of non-spherical particles from theirpacking behaviour, Powder technology, 1993, vol. 74, pp. 205-213
YU97 A.B. YU, J. BRIDGWATER, A. BURBIDGE, On the modelling of the packingof fine particles, Powder technology, 1997, 92, pp. 185-194
ZOK91 F. ZOK , F.F. LANGE , Packing density of composite powder mixtures,journal of American ceramic society , 1991, 74
n°8, pp. 1880-85
Mark L. Sawley
Maître d’enseignement et de recherche (MER)
SGM – STI – EPFL
Numerical simulation of granular dynamics
using the Discrete Element Method
SMX course - Powder Technology
Autumn semester 2018
2
General aspects
§ Motivation
§ Industrial applications
§ Numerical simulation
Implementation
§ DEM technology
§ DEM implementation
§ Basic examples
Applications
§ Particulate flows
§ Materials processing
§ Multiphase flows
General aspects Presentation overview
3
Why study granular dynamics?
• granular materials are omnipresent
• granular materials exhibit a wide range of interesting fundamental behaviour
• granular dynamics are important for numerous industrial processes
General aspects Motivation
Why use the Discrete Element Method?
• conceptually simple technique
• can be applied to a wide range of different cases
• provides very detailed information regarding granular processes
• can provide results in agreement with experimental observation
4
Physical characteristics
& behaviour
• shape
• microstructure
• dilatancy
• cohesion
• segregation
• clustering
• self-organization
• …
General aspects Motivation
5
Industrial applications
• food & agriculture
• mineral processing
• steel making
• chemical
• pharmaceutical
• plastic
• metal
• ceramic
• geophysical
• …
General aspects Motivation
Dry granulation of pharmaceutical tablets
milling active ingredientsblending with excipients
granulation
screening
blending with lubricant
tabletting
final product
General aspects Industrial applications
6
multiphase processes
Manufacturing of breakfast cereals
grain storage conveying
drying
flaking
extrudingfinal products
mixing
General aspects Industrial applications
7
8
Numerical simulation of granular dynamics
-0.1
0
0.1
0.2
0.3
0.4
0 1 2 3 4 5 6
number
verti
cal p
ositi
on, z
[m
]
10 - 80 mm
10 - 20 mm
20 - 40 mm
40 - 80 mm
vsi_4000
table ejecteurs
cylindre
Provides valuable information :
• both qualitative and quantitative
• increase basic understanding of process
• virtual prototyping tool
• reduce significantly production costs
• improve product performance
• minimize time-to-market for new products
• complementary to experimentation
General aspects Numerical simulation
9
Types of particulate materials to be simulated
• Free-flowing granular materials
- dry (inter-particle collisional forces, e.g. dry sand)
- moist (inter-particle attractive forces, e.g. wet sand, powder)
• Powders
- large cohesive assemblies
• Rheologically-complex flowing materials
- polymers, paste, sludge …
• Wet particulate materials
- suspensions, blood …
• Agglomerate solid materials
- natural materials (e.g. rocks)
- man-made materials (e.g. concrete)
General aspects Numerical simulation
10
Coupled multi-method applications for multiphase flows
solidsprocessing
fluidprocessing
dry
granular
moist
granular
wet
granular
particle-laden
fluid fluid
coupled DEM/CFDDEM CFD
• Complementary simulation technologies can be coupled
- Computational Fluid Dynamics (CFD)
- Discrete Element Method (DEM)
[ coupled DEM / Finite Element Method (FEM) is also employed ]
General aspects Numerical simulation
11
Discrete Element Method (DEM)
• Basic aspects
- particle-based (Lagrangian) method
- based on solving Newton equations for an ensemble of
particles and their neighbouring boundary objects
- track the position, velocity and spin of all the individual
particles
- detect all contacts between particles and with the
boundary objects
- model the contact forces & torques acting on the particles
(and boundary objects)
Implementation DEM technology
12
General approach
• “Soft particle” approach
- continuous interaction between “deformable” particles (particles can slightly overlap)
- calculate time-dependent collisional process
- “time driven” methodology
- most commonly employed approach
Implementation DEM technology
• Improved computational performance using a two-step contact detection process :
- spatial sorting (find near neighbours)
- individual contact testing
Goal is to reduce operation count from O(N2) to O(N) or O(N logN)
13
Implementation DEM technology
define geometry (boundary objects)
set initial positions and velocities
find near neighbours
calculate forces & torques on particles
calculate physical quantities of interest
move particles and objects due to forces
t2 >> t
1
t1
test for particle contacts
Basic DEM algorithm
• Soft particle approach
14
Modelling of inter-particle forces & torques
• “Physics” is incorporated in the inter-particle interaction model
• Different physical phenomena can be modelled :
- contact forces
- body forces (e.g. gravity)
- rolling resistance
- cohesion (due to moisture, electrostatics, van der Waals …)
- interstitial fluid
- breakage / agglomeration
- …
Implementation DEM technology
15
Implementation DEM technology
Modelling of inter-particle forces & torques
• Contact (collision)
• repulsive force between particles
• Cohesion
• attractive force between particles
• Cluster
• particles in cluster “glued” together
16
Implementation DEM technology
Modelling of inter-particle forces & torques (cont.)
• Bond
• force inhibits relative motion of particles
• Torsional beam
• repulsive force between particles
• Sintering
• overlapping particles “glued” together
17
Modelling of inter-particle contact : relationship between force and overlap
• Example : Cundall model
- based on a combination of linear springs & dashpots
Implementation DEM technology
18
Implementation DEM technology
• The normal contact force Fn (aligned with particle centres) is :
Fn = kn dn + Cnnn ,
where dn is the overlap between particles in the normal direction
nn is the relative velocity of the particles in the normal direction
kn is the normal spring constant (spring stiffness)
Cn is the normal damping coefficient
The damping constant Cn is related to the coefficient of restitution e :
Cn = 2 g [ mred kn ]½
; g = - ln(e) / [ p2+ ln
2(e) ] ½
where mred is the reduced mass = m1
m2
/ ( m1
+ m2
)
Modelling of inter-particle contact : Cundall model
19
Modelling of inter-particle contact : Cundall model
Implementation DEM technology
• The tangential contact force Ft (aligned normal to the particle centres) is :
Ft = kt dt + Ctnt ,
where dt is the overlap between particles in the tangential direction
nt is the relative velocity of the particles in the tangential direction
kt is the tangential spring constant (spring stiffness)
Ct is the tangential damping coefficient
The tangential contact force is limited by the Coulomb frictional limit
Þ particles slide over each other (surface contact shears)
Ft = min ( µ Ft , ò kt nt dt + Ct nt )
where µ is the coefficient of friction
20
Implementation DEM technology
Moving particles due to forces & torques
• Solve Newton equations of motion for particles (and boundary objects)
where
Fij is the total force on particle i due to contact with particle j
Mi j is the total torque on particle i due to contact with particle j
position xi = ui
velocity ui = S Fij / mi
orientation qi = wi
spin wi = S Mij / Iij
j
.
.
.
.
Time-dependent differential equations are solved using a explicit integration method