P. Bowen, EPFL. 04/10/2017 1

LTPÉCOLE 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 3

P. Bowen, EPFL. 04/10/2017 2

Course Contents - Plan

4 semaines

3 semaines

2 semaines

2 semaines

1 semaine1. Introduction – general introduction to course– example transparent ceramics

2. Particle Packing and Powder Compaction - Theoretical and empirical models (PB)- Powder compaction (PD)

3 Particle-Particle Interactions (PB)- Colloidal Dispersions- DLVO –theory and limitations- non-DLVO and steric forces

4. Introduction to Atomistic Scale Simulations (PD)- introduction to modeling of surfaces and interfaces at the atomic scale - defects in metals – towards sintering

5. Sintering mechanisms (PD)- metals, ceramics- influence of microstructure- simulation

6. New Powder Processing Technologies (PB)- rapid prototyping- laser sintering, Spark Plasma Sintering

2 semaines

•The Colloidal Domain – D. F. Evans & H. Wennerström, Wiley, 1999,

• Principles of Ceramic Processing – J.S.Reed , Wiley, 1995. English

• Les Céramiques, J. Barton, P. Bowen, C. Carry & J.M. Haussonne, Les Traité des Matériaux, Volume 16, PPUR, 2005

Réseau neurone - compaction

Laves Torrentielles – Debris Flow

Granular Dynamics – Modelling

Mark Sawley

P. Bowen, EPFL. 04/10/2017 3

Teaching plan 2017

• Files of lectures and notes to be found on LTP website : http://ltp.epfl.ch/Teaching

Week-DATE File.

no.

Powder Technology – Wednesday 10.15-12.00 – MXG 110

1- sept 20 1 Introduction - PB

2 – sept 27 2 Powder packing and compaction - 1- PB -

3 – oct 4 3 Powder packing and compaction - 2-PB- and guest lecturer - MS

4 – oct 11 4 Powder packing and compaction -3- PD

5 – oct 18 4 Powder packing and compaction - 4 – PD

6 – oct 25 5 Particle – Particle Interactions 1 - PB

7 – nov1 6 Particle – Particle Interactions 2- PB

8 – nov 8 7 Particle – Particle Interactions - 3-PB

9 – nov -15 8 Introduction to atomistic scale simulations PD

10 – nov 22 9 Compaction, Sintering & Defects in metals at atomistic scale - PD

11 -nov-29 10 Sintering Mechanisms& New Technologies - 1 – PB

12 - dec 6 11 Sintering Mechanisms & New Technologies - 2 - PD

13 – dec 13 11 Sintering Mechanisms &New Technologies -3 PD

14 – dec 20 10 Sintering Mechanisms & New Technologies- and exam 4 – PB

PB – Prof. Paul Bowen (EPFL), PD – Dr. Peter Derlet (PSI)

MS- Dr. Mark Sawley (EPFL)

P. Bowen, EPFL. 04/10/2017 4

Particle Packing - Last week

Literature Models

– Empirical Models

– Semi-empirical models - physics of particles

– Numerical and analytical (computer aided simulations)

Models evaluate packing or porosity in a packed powder as a function of 4

characteristics:

– Particle Shape - sphericity

– Modal Size differences in multimodal distributions

– Mean particle size

– Size distribution

Effect of agglomeration also plays an important role on particle packing

P. Bowen, EPFL. 04/10/2017 5

Aims of todays course

Two examples of powders in application or research where particle packing and

rheological behaviour linked to particle shape and dispersion (leading us to the next

section of the course colloidal dispersions)

Neural Network – applied to the particle packing of alumina particles in spray dried

granules - Thesis de Violaine Guerin – EPFL No. 3021 (2004)

Landslides or Alpine Debris Flow…..Eric Bardou (Thesis EPFL- 2479(2002))

Numerical simulation of Granular Dynamics using DEM - Dr. David Geissbühler

– LTP (MXC 320 ….14.15)

Typical Questions - Section Particle Packing

English Books for ceramic processing and powder dispersion

1. T. A. Ring - Fundamentals of Ceramic Powder Processing and Synthesis. Academic

Press,1996

2. J.S. Reed - Principles of ceramic processing – J. Wiley & sons, 2nd Edition (1995)

P. Bowen, EPFL. 04/10/2017 6

Comparaison de la prédiction théorique et des résultats

expérimentaux la densité verte de poudres Bayer et l’alumine

de haute pureté en utilisant un réseau neurone

Thèse de Violaine Guerin – EPFL No. 3021 (2004)

Comparison of theoretical prediction and experimental

green density of high purity and Bayer alumina powders

using a neural network

P. Bowen, EPFL. 04/10/2017 7

Introduction

Goals :

Predicting green and sintered density using a neural network

Better understanding of the densification behavior

Design and predict microstructure

Powder characteristicsDensification behaviour

?

P. Bowen, EPFL. 04/10/2017 8

Particle packing and Neural Network approach

Ceramic Manufacturing - Generalities

- Packing of particles

- Mathematical models

- Neural network

Characteristics of powders and densities of Green Bodies

Using the results of the neural network as a predictive tool

Conclusions and future development

P. Bowen, EPFL. 04/10/2017 9

Ceramic Fabrication - Generalities

Different manufacturing processes-from powders- Compaction of granulated powders – uni-axial – CIP*- Suspension - casting (slip, tape, pressure)

Compaction of spray-dried granules$

Effects of parameters of the powder on the green densities

Compaction 3 steps

–Re-arrangement

–Deformation of granules

–Fracture of granules (rarely achieved)

Consider two families of powders

1. Bayer aluminas - low agglomeration factor

2. Non-Bayer finer more agglomerated

Pores inside the granules between the primary particles

and between the granules

Pore distribution - bimodal (inter-granular, intra-granular)

Particule primaire (0.1 -1µm)

Granulée pour la compression

(50-300µm)

* CIP – Cold isostatic pressing $ - see BAR05 p. 204-219

P. Bowen, EPFL. 04/10/2017 10

Alpha alumina – effect of agglomerates – week 1 Intro

Particle size distribution shows small tail of agglomerates – leads to defects in

microstructure and low sintered densities (94%) – poor (hard) granules (50 mm)

and aggregates (2 mm)

0.1

1

.01 .1 1 5 10 2030 50 7080 9095 99 99.999.99

AKP50-non-broyéeAKP50-broyée

ES

Dia

mèt

re (

µm

)

% volume cumulés

P. Bowen, EPFL. 04/10/2017 11

Alpha alumina – effect of agglomerates

Attrition milling 1 hr agglomerates removed

Improved sintered density & microstructure

Attrition milled 1hr – slip cast – 99%As received – slip cast – 94 %

F-S. Shiau, T-T. Fang, T-H Leu, Materials Chemistry and Physics, 57, 33-40 (1998).

P. Bowen, EPFL. 04/10/2017 12

Neural Network Approach

Neural network- compaction

P. Bowen, EPFL. 04/10/2017 13

Réseau neurone – Neural Network

• IW – weighted

hidden layer

- non-linear

function

• LW – weighted

output layer

- linear function

• b- bias

• Adjust until target

value achieved

P. Bowen, EPFL. 04/10/2017 15

Powder Characteristics & Treatment

31 a-alumina commercial powders from different producers (Prof. Hofmann,

Alusuisse)

2 families Bayer* (18) and Non-Bayer*(precipitated) (13)

Characterised by:

– Chemical Composition (Na, Si, Ti, Fe, Mg)

– Particle size distributions (laser diffraction)

– Powder X-ray diffraction (XRD)

– Specific Surface Area (SSA, BET model)

– Particle shape (SEM)

Spray dried (atomisation-spray drying)$ after wet milling

Addition of PVA as binder and PEG as plasticizer

Cold Isostatic Pressing (CIP)

– 200 MPa

– Cylinders, 2cm de diameter and 10 cm long

Spray dried granules

* Voir BAR05 – pages 111-113 $- BAR05 pages 196-203

P. Bowen, EPFL. 04/10/2017 16

Log-normal - Bayer Aluminas

Neuron network compared with

Kavanagh and Nolan log-normal model &

Experimental values for coarse powders

Median diameter (Dv50) and standard deviation (sv)

– verified experimentally

22 of the 32 followed reasonably well a log-normal

distribution (see BAR05 pages 64-65)1 µm

0

5

10

15

20

25

30

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

% F

req

uen

cy

Equivalent spherical diameter (µm}

0

0.1

0.2

0.3

0.4

0.5

0 1 2 3 4 5 6

Fre

quen

cy

Diameter (µm)

Normal distribution Log Normal distribution

P. Bowen, EPFL. 04/10/2017 17

Neural Network (NN) - method

Program used NETS –

– Developed by NASA

Input Parameters – 5 neurons

– d10,d50 d90 volume based particle size

distribution

– Specific surface area

– Type of powder

- Bayer or Non-Bayer

NN – 10 intermediate neurons, 1 ouput

optimised with 28 powders then tested on 3

– Results predicted better than 5%

– Within the powder characteristics

« box » or set used to train the NN

Min (µm) Max (µm)

d90 0.60 20.0

d50 0.25 12.5

d10 0.15 4.0

• Can now use NN to predict behaviour

of powders within this range –

• Even if we do not have exact data for

particular Dv50 and s etc

• For clearer trends split Bayer and Non-

bayer into different Dv50 size ranges

P. Bowen, EPFL. 04/10/2017 18

Log-normal - Bayer Aluminas– fine particles (< 2mm)

For green (compact ) densities after CIP but before sintering

Predictions

RCP – Random Close

Packed

RLP - Random Loose

Packed

Particle packing model –

density of packing

increases with increasing

standard deviation(s)

Bayer Aluminas

corresponds to Random

Loose Packed when

s > 2.5

P. Bowen, EPFL. 04/10/2017 19

Log-normal - Bayer Aluminas

•Bayer aluminas (< 2mm) correspond

well to experimental data for the RLP

•after spray drying of granules

•Slight increase in the packing

fraction with the s of the original

PSD

•Compaction - 3 stages - re-

arrangement, deformation, fracture

•3rd stage rarely is reached with

typical technical conditions

•The packing fraction of the powder

within the granules dominates the

behavior

•Assuming that the binders* and

plasticizers* behave the same way for

all powders * See BAR05 – p.218-219

P. Bowen, EPFL. 04/10/2017 20

Log-normal - Bayer Aluminas

200 µm granule

Surface of

granule

1 µm

The density or packing in the granule depends on the following parameters

– Particle shape – non-spherical negative →lower packing fraction

– 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

P. Bowen, EPFL. 04/10/2017 21

Influence of PSD width and particle size dv50

Precipitated powders

Non-BayerBayer Powder

sg rv

1 2 3 4 50.3

0.4

0.5

0.6

0.7

0.8

De

nsi

té r

ela

tive

Déviation standard géométrique sg

RCP S&M

RLP N&K

RCP N&K

RLP D&T

d50

=0,75mm

d50

=1,6mm

d50

=3,75mm

sg et/ou dv50 rv

1 2 3 4 50.3

0.4

0.5

0.6

0.7

0.8

De

nsité

re

lative

Déviation standard géométrique sg

d50

=0.75mm

d50

=1.6mm

d50

=3mm

RCP N&K

RLP N&K

Application of Neural Network

P. Bowen, EPFL. 04/10/2017 22

Spray Dried Alumina Powders

* ' 1*0.6 0.6granules particules facteur d empilementr r

30mm

Primary Particles Bayer

Theoretical Density

(relative density =1)

Granules

Density RLP

(relative density =0.6)

BAYER

* ' 0.6*0.6 0.36granules agglomérats facteur d empilementr r

PrimaryAgglomerates

Density RLP

(relative density =0.6

)

Granules

DensityRLP

(relative density =0.6)

PRECIPITATED

Non-BAYER

Packing factor

Packing factor

= 𝜌𝑎𝑔𝑔𝑙𝑜𝑚é𝑟𝑎𝑡𝑠

P. Bowen, EPFL. 04/10/2017 23

Conclusions

Neural Networks

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 and 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) –

P. Bowen, EPFL. 04/10/2017 24

Les laves torrentielles en milieu alpin

Eric Bardou

eric.bardou@unil.ch

EPFL Thesis No. 2479 (2002)

Effect of the Clay Type on the Rheology of an Heterogeneous Dense

Granular Material.

Implication for the Study of Alpine Debris Flow

Eric Bardou, Paul Bowen, Pascal Boivin (EPFL), Phil Banfill (HWU, UK)

Powder Page – Landslide simulation - http://www.granular.com/

Earth Surface Processes and Landforms

Earth Surf. Process. Landforms 32, 698–710 (2007)

P. Bowen, EPFL. 04/10/2017 25

Scope of working length scale!!!

Du bassin versant – Alpine Watershed…..

Aux feuillets argileux

- Clay platelets

-Diameter Microns

--thickness 20-100nm

P. Bowen, EPFL. 04/10/2017 26

Exemple

P. Bowen, EPFL. 04/10/2017 27

Description du phénomène – Description of the phenomenon

Transport of bed load (charge de fond)

Debris (mud) flow

The transfer of sediment a problem

between geology and hydraulics

Bed load – saltation (hopping), rolling, sliding

P. Bowen, EPFL. 04/10/2017 28

Definition

front

tailbody

Lateral section

• Grains >400

microns

• Fluid – matrix

• < 400microns

• Model system for

sizes < 20mm

The debris or mudflows are granular flows - lubricated kinematically –

they are of a transient nature - simple model - two-phases

- grains and fluid

P. Bowen, EPFL. 04/10/2017 29

Particle sizes – (grains & matrix < 20mm)

ar g

il es silts

sabl e

sfi n

s

sabl e

sm

oye

ns

sabl e

sgr o

ssi e

r s

graviers

0.001 0.01 0.1 1 100

20

40

60

80

100

[mm]20

fracti

on

cu

mu

lée [

%]

viscoplastic

collisional-frictional

frictional-viscous

Bed load

Argiles

• Fluid – matrix < 400microns • Grains >400 microns

Clays Fine Medium CoarseSands

Gravels

P. Bowen, EPFL. 04/10/2017 30

Rheological Models Different types of fluid behaviour – Newtonian and non-Newtonian

Various models used to extract information e.g. yield stress – all give very similar results

M. Palacios. -Química del Cemento – Enero 2010

(Ferraris, C. F. , 1999)

• Yield Stress – t0 Minimum stress to make liquid or suspension flow

• Typical of systems with attractive network

• Yoghurt – Cement - Ceramic slurries – (see BAR05)

30

P. Bowen, EPFL. 04/10/2017 31

Influence of clays

Size

range

(mm)

Particle class Solids

weight

(%)

Solids

volume

(%)

0.0 - 0.02 clay size 4.1 11.4

0.02 - 0.05 silt size 13.0 12.0

0.05 - 0.1 fine sand 5.7 5.4

0.1 - 0.5 medium sand 26.4 24.4

0.5 - 1.0 coarse sand 13.1 12.1

1.0 - 2.0 very coarse sand 3.5 3.2

2.0-20.0 gravel 34.2 31.6

• Grains >400 microns

• Fluid – matrix

• < 400 microns

With clays

Without clays

P. Bowen, EPFL. 04/10/2017 32

Model system PSD – (grains & matrix < 20mm)

Argiles

Model PSD

P. Bowen, EPFL. 04/10/2017 33

2,8 mm

Why – plate –plate?

• easy to use

• No jamming of particles

• Roughened surfaces to

avoid wall-slip

• Low cost….

150 tests

Rheometer plate-plate

Rheology – Matrix (<400mm)

P. Bowen, EPFL. 04/10/2017 34

Rheology with model PSD up to 20 mm

Herriot Watt University (UK) – ciment expert – Prof. Phil Banfill

Sample wieghts for each test

30 kg !!! dry!!!

Measure torque – off-centre to

avoid moving through same area

of sample – effective viscosity

P. Bowen, EPFL. 04/10/2017 35

Clays – main industrial use – porcelain ceramics!

Kaolin

(50-55%)

Feldspath

(25%)

Quartz

(20-25%)

Porcelaine

(dure)

P. Bowen, EPFL. 04/10/2017 36

Structure of clays 1:1 & 2:1

Konan eta l J.Coll.Interf.Sci

307(1) 2007, 101–108

(a) Structure of 1:1 clay mineral e.g. kaolin

(b) Structure of 2:1 clay mineral, e.g montmorillonite

P. Bowen, EPFL. 04/10/2017 37

Argile (2:1) – swelling – Na Montmorillonite

Atomistic model of the one-layer

hydrate of sodium montmorillonite

O: red,

H: white,

Si: yellow,

Na: blue,

Al: purple,and

Mg: green

This simulation super cell consists of

two interlayer regions made up by 8

unit cells

Exchange of Na+ with Li+ - extra

water of hydration interlayer spacing

increased – pillared clays – catalysis

Mg2+ substitutes Al3+ ….Na+ in

interlayer charge compensation

Si

Si

Si

Si

Al(Mg)

Na

P. Bowen, EPFL. 04/10/2017 38

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 0.01

Md 3 0.54 0.01

Md 4 0.8 0.02

Relation between water content (%wt) (W) and

effective viscosity(K) for 4 samples

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. 04/10/2017 39

Comparaison with Natural Debris Flows

swelling

Non

-swelling

MD1

Model

Mixture

MD4

Model

Mixture

P. Bowen, EPFL. 04/10/2017 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. 04/10/2017 41

Can you answer these questions? (1)

Give a field of application or an everyday example of Powder Technology

What is the effect of adding a superplastifier to a concrete mix and what are the consequences on the concrete (cement) rheology and its properties in application?

What are the dispersing mechanisms of the superplasitifier (SP) – that is to say what forces are modified by the addition of the SP?

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. 04/10/2017 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. 04/10/2017 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. 04/10/2017 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 2017

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 ingredients blending 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

extruding final 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

solids processing

fluid processing

dry granular

moist granular

wet granular

particle-laden fluid fluid

coupled DEM/CFD DEM 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 >> t1

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

•  Bond •  force inhibits relative motion of particles

•  Cluster •  particles in cluster “glued” together

16

Modelling of inter-particle contact : relationship between force and overlap

•  Example : Cundall model -  based on a combination of linear springs & dashpots

Implementation DEM technology

17

Implementation DEM technology

•  The normal contact force Fn (aligned with particle centres) is :

Fn = kn δn + Cn νn ,

where δn is the overlap between particles in the normal direction νn 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 ε :

Cn = 2 γ [ mred kn ] ½ ; γ = - ln(ε) / [ π2 + ln2(ε) ] ½

where mred is the reduced mass = m1 m2 / ( m1 + m2 )

Modelling of inter-particle contact : Cundall model

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Modelling of inter-particle contact : Cundall model

Implementation DEM technology

•  The tangential contact force Ft (aligned normal to the particle centres) is :

Ft = kt δt + Ct νt ,

where δt is the overlap between particles in the tangential direction νt 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 ⇒ particles slide over each other (surface contact shears)

Ft = min ( µ Ft , ∫ kt νt dt + Ct νt )

where µ is the coefficient of friction

19

Implementation DEM technology

Moving particles due to forces & torques

•  Solve Newton equations of motion for particles (and boundary objects)

where

Fi j 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 = Σ Fi j / mi

orientation θi = ωi

spin ωi = Σ Mi j / Ii j

j

.

. .

.

Time-dependent differential equations are solved using a explicit integration method

20

Basic features of an “advanced” DEM code

•  Geometry

-  any 2D / 3D geometry (composed of different objects, defined by CAD tools) -  different objects can have relative motion (e.g. translation, rotation, vibration)

•  Particle characteristics

-  basic spherical shaped particles -  any (reasonable) size & density distributions

•  Interactions between particles (and with objects) : -  collisions (repulsive force between particles) -  cohesion (attractive force between particles) -  bonds (force inhibits relative motion of bonded particles) -  clusters (particles in cluster “glued” together)

Implementation DEM implementation

21

Schematic diagram of DEM implementation

Implementation DEM implementation

geometry design & surface meshing

Newton solver

visualization

quantitative analysis

Pre-processing Computation Post-processing

particle initialization modelling

improvement

22

Influence of model choice

•  Rectangular hourglass containing 400 identical particles

standard cohesive particles agglomerate material

Implementation Basic examples

23

Influence of particle shape

•  Different basic approaches :

•  composite particles (e.g. form cluster by joining spheres)

•  non-spherical primitives - ellipsoids - spherocylinders - superquadrics …

•  polygonal assemblies

Implementation Basic examples

non-spherical particles (5-particle cluster)

24

Influence of interstitial fluid

•  Three basic approaches :

•  solve Navier-Stokes equations for interstitial region (coupled DEM/CFD)

•  solve Navier-Stokes equations for porous medium (coupled DEM/CFD)

•  add empirical drag force to each particle (DEM only)

Implementation Basic examples

spherical particles (empirical drag force)

25

Agglomerate solid materials

•  Three basic steps :

•  creation of agglomerate material sample

•  creation of inter-particle bonds

•  testing of material structural properties

Implementation Basic examples

26

Agglomerate solid materials

•  Growing particle technique for constructing material :

Implementation Basic examples

3D rectangular slab (160 mm x 40 mm x 20 mm)

11,009 spherical particles particle diameter - initial : 0.8 - 2.0 mm final : 1.1 - 3.4 mm

27

Different types of simulations involving particulate flows and materials processing of industrial interest have been computed

•  industrial flow processing (e.g. mixing, transport)

•  geological flows (e.g. avalanches, landslides)

•  industrial materials processing (e.g. drilling)

Applications Overview

28

Ball mill for crushing and grinding

of mineral ore

courtesy Magotteaux SA

Comparison of computed and experimental power draw

800 mm x 400 mm cylindrical mill rotational speed : 70% critical

19,116 spherical balls particle diameter : 15 mm

Applications Particulate flows

29

Landslides, rockfalls & debris flow

courtesy of CSIRO, Australia

2.5 x 4 km2 rectangular section

165,000 spherical particles particle diameter : 2 - 10 m total mass : 10 million tonnes (2.5 million m3)

S. Wiederseiner – EPFL semester project

Applications Particulate flows

30

Ribbon blender

Applications Particulate flows

influence of inter-particle cohesion on mixing

contact

ri + rj

compression tension Fn

dij

cohesion

Fn

ri + rj

compression tension

dij

contact + cohesion

ri + rj

compression tension Fn

dij

31

Ribbon blender

Applications Particulate flows

high cohesion low cohesion

500 mm x 300 mm container dual ribbons rotating at 30 rpm

100,000 spherical particles particle diameter : 6 mm

particles coloured according to initial position

influence of inter-particle cohesion on mixing

32

Ribbon blender

Applications Particulate flows

computed mixing in lateral direction : GMMI(x,y,z) =

0.0

0.5

1.0

1.5

2.0

2.5

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0time [s]

Mix

ing

(GM

MI x

)

no cohesion

low inter-particle cohesion

high inter-particle cohesion

fully mixed

v = 30 rpmd = 6 mm

e = 0.3µ = 0.75

Δ t = 5 msMixing rates

γ  no = -0.300

γ low = -0.143

γ high = -0.044

centre of mass of one colour particle centre of mass of all particles

33

Applications Particulate flows

34

Applications Particulate flows

35

Applications Particulate flows

36

Applications Materials processing

37

Applications Materials processing

38

Agglomerate solid materials

•  Flexion testing :

Implementation Materials processing

2D rectangular slab (160 mm x 40 mm)

21,243 circular particles particle diameter : 0.3 - 1.0 mm inter-particle cohesion

39

Sprouted bed

S. Wiederseiner – SGM Master project

Applications Multiphase flows

forced air flow

vertical silo containing glass beads

Coupled DEM-CFD simulation

for advanced drying of granular material

40

Coupled fluid-particle simulation

•  Pouring beer - “the ultimate multiphase flow” -  liquid (simulated by CFD - Smoothed Particle Hydrodynamics) -  bubbles (simulated by DEM)

Applications Multiphase flows

courtesy of CSIRO, Australia

41

General aspects Further information

Basic DEM textbooks are not common •  A. Munjiza “The combined finite discrete element method” (Wiley 2004) •  book chapters / review articles (e.g. by P.A. Cundall, J.R. Williams or P.W. Cleary) •  SGM Master course “Numerical flow simulation” (Autumn semester) •  CSE Master course “Particle-based methods” at EPFL-SMA (Spring semester)

Conference proceedings •  e.g. International conference on discrete element methods, Powder & Grains,

ECCOMAS Particles conference •  general engineering conferences

Rapidly growing number of scientific papers •  e.g. Granular Materials, Powder Technology •  many other engineering journals

EPFL – SGM ; Master / Minor in Computational Science & Engineering •  “Particle-based methods” course