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ECCOMAS 2012 September 10-14, 2012, University of Vienna, Austria . BREAK-UP OF AGGREGATES IN TURBULENT CHANNEL FLOW. Eros Pecile 1 , Cristian Marchioli 1 , Luca Biferale 2 , Federico Toschi 3 , Alfredo Soldati 1. 1 Università degli Studi di Udine

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ECCOMAS 2012

September10-14, 2012, University of Vienna, Austria

BREAK-UP OF AGGREGATES

IN TURBULENT CHANNEL FLOW

Eros Pecile1, Cristian Marchioli1, Luca Biferale2,

Federico Toschi3, Alfredo Soldati1

1Università degli Studi di Udine

Centro Interdipartimentale di Fluidodinamica e Idraulica

2Università di Roma “Tor Vergata”

Dipartimento di Fisica

3Eindhoven University of Technology

Dept. AppliedPhysics

SessionTS036-1 on “Multi-phase Flows”


Premise

Aggregate Break-up in Turbulence

  • Whatkind of application?

  • Processing of industrial colloids

  • Polymer, paint, and paper industry


Premise

Aggregate Break-up in Turbulence

  • Whatkind of application?

  • Processing of industrial colloids

  • Polymer, paint, and paper industry

  • Environmentalsystems

  • Marine snow as part of the oceanic

  • carbonsink


Premise

Aggregate Break-up in Turbulence

  • Whatkind of application?

  • Processing of industrial colloids

  • Polymer, paint, and paper industry

  • Environmentalsystems

  • Marine snow as part of the oceanic

  • carbonsink

  • Aerosols and dust particles

  • Flamesynthesis of powders, soot,

  • and nano-particles

  • Dustdispersion in explosionsand

  • equipmentbreakdown


Premise

Aggregate Break-up in Turbulence

Whatkind of aggregate?

Aggregatesconsisting of

colloidalprimaryparticles

Schematic of an aggregate


Premise

Aggregate Break-up in Turbulence

Whatkind of aggregate?

Aggregatesconsisting of

colloidalprimary particles

Break-up due to

Hydrodynamicsstress

Schematic of break-up


Problem Definition

Description of the Break-up Process

SIMPLIFIED

SMOLUCHOWSKI

EQUATION (NO

AGGREGATION

TERM IN IT!)

Focus of this work!


Problem Definition

Further Assumptions

  • Turbulent flow ladenwith fewaggregates (one-waycoupling)

  • Aggregate size< O(h) with h the Kolmogorovlength scale

  • Aggregates break due to hydrodynamic stress, s

  • Tracer-likeaggregates:

  • s ~ m(e/n)1/2

  • with

  • scr = scr(x)

  • Instantaneousbinary

  • break-up once s > scr(x)


Problem Definition

Strategy for Numerical Experiments

  • Consider a fully-developedstatistically-steadyflow

  • Seed the flow randomly with aggregates of mass x at a given location

  • Neglectaggregatesreleased at locationswheres > scr(x)

  • Follow the trajectory of remainingaggregatesuntil break-up occurs

  • Compute the exittime, t=tscr (timefromrelease to break-up)


Problem Definition

Strategy for Numerical Experiments

  • Consider a fully-developedstatistically-steadyflow

  • Seed the flow randomly with aggregates of mass x at a givenlocation

  • Neglectaggregatesreleased at locationswheres > scr(x)

  • Follow the trajectory of remainingaggregatesuntil break-up occurs

  • Compute the exittime, t=tscr (timefromrelease to break-up)


Problem Definition

Strategy for Numerical Experiments

  • Consider a fully-developedstatistically-steadyflow

  • Seed the flow randomly with aggregates of mass x at a given location

  • Neglectaggregatesreleased at locationswheres > scr(x)

  • Follow the trajectory of remainingaggregatesuntil break-up occurs

  • Compute the exittime, t=tscr (timefromrelease to break-up)


Problem Definition

Strategy for Numerical Experiments

  • Consider a fully-developedstatistically-steadyflow

  • Seed the flow randomly with aggregates of mass x at a given location

  • Neglectaggregatesreleased at locationswheres > scr(x)

  • Follow the trajectory of remainingaggregatesuntil break-up occurs

  • Compute the exittime, t=tscr (timefromrelease to break-up)


Problem Definition

Strategy for Numerical Experiments

For jth aggregate

breakingafterNj

timesteps:

xt=x(tcr)

x0=x(0)

t

dt

n

n+1

tj=tcr,j=Nj·dt

  • Consider a fully-developedstatistically-steadyflow

  • Seed the flow randomly with aggregates of mass x at a given location

  • Neglectaggregatesreleased at locationswheres > scr(x)

  • Follow the trajectory of remainingaggregatesuntil break-up occurs

  • Compute the exittime, t=tscr (timefromrelease to break-up)


Problem Definition

Strategy for Numerical Experiments

For jth aggregate

breakingafterNj

timesteps:

xt=x(tcr)

x0=x(0)

t

dt

n

n+1

tj=tcr,j=Nj·dt

  • The break-up rate is the inverse of

  • the ensemble-averagedexittime:

scr

s


Flow Instances and Numerical Methodology

Channel Flow

RMS

  • Characterization of the

  • localenergydissipation

  • in bounded flow:

  • Wall-normalbehavior of

  • meanenergydissipation

Wall Center

  • Pseudospectral DNS of 3D time-

  • dependent turbulent gas flow

  • Shear Reynolds number:

  • Ret = uth/n = 150

  • Tracer-likeaggregates:


Channel Flow

Choice of CriticalEnergy Dissipation

  • Wall-normalbehavior of

  • meanenergydissipation

  • PDF of localenergydissipation

WholeChannel

PDFs are stronglyaffectedby flow anisotropy (skewedshape)


Channel Flow

Choice of CriticalEnergy Dissipation

  • Wall-normalbehavior of

  • meanenergydissipation

  • PDF of localenergydissipation

WholeChannel

Bulk

Bulk ecr

PDFs are stronglyaffectedby flow anisotropy (skewedshape)


Channel Flow

Choice of CriticalEnergy Dissipation

  • Wall-normalbehavior of

  • meanenergydissipation

  • PDF of localenergydissipation

WholeChannel

Bulk

Intermediate

Intermediate ecr

Bulk ecr

PDFs are stronglyaffectedby flow anisotropy (skewedshape)


Channel Flow

Choice of CriticalEnergy Dissipation

  • Wall-normalbehavior of

  • meanenergydissipation

  • PDF of localenergydissipation

WholeChannel

Bulk

Intermediate

Wall

Wallecr

Intermediate ecr

Bulk ecr

PDFs are stronglyaffectedby flow anisotropy (skewedshape)


Channel Flow

Choice of CriticalEnergy Dissipation

  • Wall-normalbehavior of

  • meanenergydissipation

  • Differentvalues of the criticalenergydissipationlevelrequired

  • to break-up the aggregate lead to different break-up dynamics

    • PDF of the location of break-up

    • whenecr= Bulk ecr

  • For smallvalues of ecr break-up eventsoccurpreferentially in the bulk

errorbar = RMS

Wall Center Wall

Bulk ecr


Channel Flow

Choice of CriticalEnergy Dissipation

  • Wall-normalbehavior of

  • meanenergydissipation

  • Differentvalues of the criticalenergydissipationlevelrequired

  • to break-up the aggregate lead to different break-up dynamics

    • PDF of the location of break-up

    • whenecr= Wallecr

  • For largevalues of ecr break-up eventsoccurpreferentiallynear the wall

Wallecr

errorbar = RMS

Wall Center Wall


Evaluation of the Break-up Rate

Results for DifferentCriticalDissipation

MeasuredExpon. Fit

Measured

f(ecr) from

DNS

Exp. Fit

Exponentialfitworksreasonably for smallvalues of the critical

energydissipation…


Evaluation of the Break-up Rate

Results for DifferentCriticalDissipation

MeasuredExpon. Fit

Measured

f(ecr) from

DNS

-c=-0.52

Exp. Fit

Exponentialfitworksreasonably for smallvalues of the critical

energydissipation… and a power-lawscalingisobserved!


Evaluation of the Break-up Rate

Results for DifferentCriticalDissipation

MeasuredExpon. Fit

Measured

f(ecr) from

DNS

-c=-0.52

Exp. Fit

Exponentialfitworksreasonably for smallvalues of the critical

energydissipation… and awayfrom the near-wallregion!


How far do aggregatesreachbefore break-up?

Analysis of “Break-up Length”

Consideraggregatesreleased in regions of the flow where

s > scr(x) withscr(x) ~ m(ewall/n)1/2

Walldistance of aggregate’s release location: 0<z+<10

Number of break-ups

Channellengthscovered in streamwise direction


How far do aggregatesreachbefore break-up?

Analysis of “Break-up Length”

Consideraggregatesreleased in regions of the flow where

s > scr(x) withscr(x) ~ m(ewall/n)1/2

Walldistance of aggregate’s release location: 50<z+<100

Number of break-ups

Channellengthscovered in streamwise direction


How far do aggregatesreachbefore break-up?

Analysis of “Break-up Length”

Consideraggregatesreleased in regions of the flow where

s > scr(x) withscr(x) ~ m(ewall/n)1/2

Walldistance of aggregate’s release location: 100<z+<150

Number of break-ups

Channellengthscovered in streamwise direction


Conclusions and …

… Future Developments

  • A simple method for measuring the break-up of small (tracer-like)

  • aggregates driven by local hydrodynamic stress has been applied

  • to non-homogeneous anisotropic dilute turbulent flow.

  • The aggregates break-up rate shows power law behavior for small

  • stress (small energy dissipation events).

  • The scaling exponent isc ~ 0.5, a value lower than in homogeneous

  • isotropic turbulence (where 0.8 < c < 0.9).

  • For small stress, the break-up rate

  • can be estimated assuming an

  • exponential decay of the number

  • of aggregates in time.

  • For large stress the break-up rate

  • does not exhibit clear scaling.

  • Extend the current study to higher

  • Reynolds number flows and heavy

  • (inertial) aggregates.

Cfr. Bableret al. (2012)


Thankyou for yourkindattention!


Channel Flow

Choice of CriticalEnergy Dissipation

  • Wall-normalbehavior of

  • meanenergydissipation

  • PDF of localenergydissipation

WholeChannel

Intermediate

Bulk

Wall

Wallecr

errorbar = RMS

Intermediate ecr

Bulk ecr

PDFs are stronglyaffectedby flow anisotropy (skewedshape)


Estimate of Fragmentation Rate

Twopossible (and simple…) approaches

Consideraggregatesreleased in regions of the flow where

s > scr(x) withscr(x) ~ m(ewall/n)1/2

-0.52 (slope)

Measured

f(ecr) from

DNS

Fit

Exponentialfitworksreasonablyawayfromthe near-wall

region and for smallvalues of the criticalenergydissipation


Problem Definition

Strategy for Numerical Experiments

  • The break-up rate is the inverse of

  • the ensemble-averaged exit time:

  • In bounded flows, the break-up

  • rate is a function of the wall distance.


Problem Definition

Strategy for Numerical Experiments

  • The break-up rate is the inverse of

  • the ensemble-averaged exit time:

  • In bounded flows, the break-up

  • rate is a function of the wall distance.


Problem Definition

Strategy for Numerical Experiments

  • The break-up rate is the inverse of

  • the ensemble-averaged exit time:

  • In bounded flows, the break-up

  • rate is a function of the wall distance.


Problem Definition

Strategy for Numerical Experiments

  • The break-up rate is the inverse of

  • the ensemble-averaged exit time:

  • In bounded flows, the break-up

  • rate is a function of the wall distance.


Problem Definition

Strategy for Numerical Experiments

  • The break-up rate is the inverse of

  • the ensemble-averaged exit time:

  • In bounded flows, the break-up

  • rate is a function of the wall distance.


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