Modeling particle breakage inside rotating drums

(1)

HAL Id: hal-01906526

https://hal.archives-ouvertes.fr/hal-01906526

Submitted on 26 Oct 2018

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Modeling particle breakage inside rotating drums

Luisa Orozco, Duc Hanh Nguyen, Jean-Yves Delenne, Philippe Sornay,

Farhang Radjai

To cite this version:

Luisa Orozco, Duc Hanh Nguyen, Jean-Yves Delenne, Philippe Sornay, Farhang Radjai. Modeling

particle breakage inside rotating drums. 29th ALERT Geomaterials Workshop, Oct 2018, Aussois,

France. �hal-01906526�

(2)

Modeling particle breakage inside rotating drums

L. F. Orozco

1,4

, D.-H. Nguyen

4,5

, J.-Y. Delenne

2 , P. Sornay

4 ,

and F. Radjai

1,3

1 _{Laboratoire de Mécanique et Génie Civil (LMGC), Université de Montpellier, CNRS, Montpellier, France}

2 _{INRA, UMR IATE Montpellier, France}

3 _<MSE>

2 _{, MIT Energy Initiative, Massachusetts Institute of Technology, Cambridge CA 02139, USA}

4 _{CEA, DEN, DEC, SA3R, LCU, 13108 Saint Paul les Durance, France}

5 _{National University of Civil Engineering, Hanoi, Vietnam}

Crushable particle model (BCM)

Particle fragmentation in a rotating drum

Rotating drums are systems often used in industry for processes that require mixing and grinding of materials. Laboratory tests

show that the extrapolation of the observed behavior to the industrial scale does not produce the expected results in terms of

grinding performance (particle size distribution, specific surface, etc). It is difficult to measure experimentally the crushing

evolution, but, using numerical simulations, we are able to follow the breakage processes that take place at different scales. We use

the Contact Dynamics method (CD) and the Bonded Cell Method (BCM) in order to simulate breakable grains. The study of a

single grain impact enhances the understanding of the breakage process under dynamic conditions. Then, the evolution of material

properties is compared for different rotating drum configurations.

A particle is considered as an assembly of

independent cells generated using Voronoï

tessellation. The intercell cohesive behavior is

governed by two independent strength

thresholds: C

n

(preventing tensile failure) and C

t

(preventing shear failure). The effective contact

strength depends on the contact surface (s).

Once one of the thresholds is reached, the

contact can break irreversibly when the work

performed by the cells relative movement

reaches the fracture energy (G

f

= G

n

= G

t

). Then,

the non-cohesive interfaces follow a purely

frictional contact law.

Cohesive contact law between cells in (a) normal direction

(tension) (b) tangential direction (shearing)

Particle generated with 500 cells before and

after the impact, each color represents a cell

Tests of a single particle impacting

a rigid plane were performed for

different values of impact velocity,

cells configuration and values of

fracture energy G

f

.

Numerical simulations of breakable particles inside a rotating drum were performed for a set

of rotation speeds. As expected, this process is faster when higher rotation velocities are

applied. Also, we found that the specific surface increases during the grinding, while the

surface exhibits an unmonotonic evolution. In the beginning, the breakable particles have a

pentagonal shape visualized as bright green (A). As the breakage starts and proceeds,

rougher particles are produced that have lost few cells and therefore, the mean surface

increases (B). After the peak, the particles start losing their roughness and becoming rounder

and smaller, as presented with a dark green color (C).

A

B

C

A

B

C

Fragmentation efficiency ( ) as a function of the normalized

impact energy ( ). The error bars represent the standard

deviation of 10 independent tests

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Evolution of the mean particle surface S, for drums rotating

at different speeds. Inset: Development of mean particle

specific surface (SSA)

F r =

!

2 _R

g

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Evolution of the mean particle size normalized by the initial

grain diameter. Tests performed with different Froude

numbers (Fr), changing only the rotational speed ( )

!

<latexit sha1_base64="7kAwm7fXGFz1Za93aogZOtmFhP4=">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</latexit><latexit sha1_base64="7kAwm7fXGFz1Za93aogZOtmFhP4=">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</latexit><latexit sha1_base64="7kAwm7fXGFz1Za93aogZOtmFhP4=">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</latexit><latexit sha1_base64="7kAwm7fXGFz1Za93aogZOtmFhP4=">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</latexit>

Snapshot of an assembly of breakable particles modeled

with BCM inside a rotating drum. The color represents the

damage: bright green for intact particles, black for fully

crushed particles.

Single particle impact

!

⇤

<latexit sha1_base64="VsAa+7u2avRP3zUX8fVfumzN4Mc=">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</latexit><latexit sha1_base64="VsAa+7u2avRP3zUX8fVfumzN4Mc=">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</latexit><latexit sha1_base64="VsAa+7u2avRP3zUX8fVfumzN4Mc=">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</latexit><latexit sha1_base64="VsAa+7u2avRP3zUX8fVfumzN4Mc=">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</latexit>

⌘

!

<latexit sha1_base64="dt8Dzj7xkQtCfzCvIaUW+8TR2Hs=">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</latexit><latexit sha1_base64="dt8Dzj7xkQtCfzCvIaUW+8TR2Hs=">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</latexit><latexit sha1_base64="dt8Dzj7xkQtCfzCvIaUW+8TR2Hs=">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</latexit><latexit sha1_base64="dt8Dzj7xkQtCfzCvIaUW+8TR2Hs=">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</latexit>

The fragmentation efficiency

et

is defined as the ratio of fracture (

Wf

) and impact energy

(

Wk

).

W

is the impact energy normalized by the available fragmentation energy (

Wf

).

⌘

!

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W

_k

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W

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W

_f

T

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We find that all the data collapse when plotted as a function of

W

, the peak of maximum

efficiency coincides at

o*

for all the tested values of fracture energy G

f

. Further analysis show

that for

om <om

the injected energy is mainly used for surface generation, while for

om<om

it is mostly transformed on fragments kinetic energy.

! > !

⇤

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! < !

⇤

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