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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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BREAK-UP OF AGGREGATES IN TURBULENT CHANNEL FLOW

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Break up of aggregates in turbulent channel flow

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”


Break up of aggregates in turbulent channel flow

Premise

Aggregate Break-up in Turbulence

  • Whatkind of application?

  • Processing of industrial colloids

  • Polymer, paint, and paper industry


Break up of aggregates in turbulent channel flow

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


Break up of aggregates in turbulent channel flow

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


Break up of aggregates in turbulent channel flow

Premise

Aggregate Break-up in Turbulence

Whatkind of aggregate?

Aggregatesconsisting of

colloidalprimaryparticles

Schematic of an aggregate


Break up of aggregates in turbulent channel flow

Premise

Aggregate Break-up in Turbulence

Whatkind of aggregate?

Aggregatesconsisting of

colloidalprimary particles

Break-up due to

Hydrodynamicsstress

Schematic of break-up


Break up of aggregates in turbulent channel flow

Problem Definition

Description of the Break-up Process

SIMPLIFIED

SMOLUCHOWSKI

EQUATION (NO

AGGREGATION

TERM IN IT!)

Focus of this work!


Break up of aggregates in turbulent channel flow

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)


Break up of aggregates in turbulent channel flow

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)


Break up of aggregates in turbulent channel flow

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)


Break up of aggregates in turbulent channel flow

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)


Break up of aggregates in turbulent channel flow

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)


Break up of aggregates in turbulent channel flow

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)


Break up of aggregates in turbulent channel flow

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


Break up of aggregates in turbulent channel flow

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:


Break up of aggregates in turbulent channel flow

Channel Flow

Choice of CriticalEnergy Dissipation

  • Wall-normalbehavior of

  • meanenergydissipation

  • PDF of localenergydissipation

WholeChannel

PDFs are stronglyaffectedby flow anisotropy (skewedshape)


Break up of aggregates in turbulent channel flow

Channel Flow

Choice of CriticalEnergy Dissipation

  • Wall-normalbehavior of

  • meanenergydissipation

  • PDF of localenergydissipation

WholeChannel

Bulk

Bulk ecr

PDFs are stronglyaffectedby flow anisotropy (skewedshape)


Break up of aggregates in turbulent channel flow

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)


Break up of aggregates in turbulent channel flow

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)


Break up of aggregates in turbulent channel flow

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


Break up of aggregates in turbulent channel flow

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


Break up of aggregates in turbulent channel flow

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…


Break up of aggregates in turbulent channel flow

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!


Break up of aggregates in turbulent channel flow

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!


Break up of aggregates in turbulent channel flow

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


Break up of aggregates in turbulent channel flow

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


Break up of aggregates in turbulent channel flow

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


Break up of aggregates in turbulent channel flow

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)


Break up of aggregates in turbulent channel flow

Thankyou for yourkindattention!


Break up of aggregates in turbulent channel flow

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)


Break up of aggregates in turbulent channel flow

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


Break up of aggregates in turbulent channel flow

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.


Break up of aggregates in turbulent channel flow

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.


Break up of aggregates in turbulent channel flow

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.


Break up of aggregates in turbulent channel flow

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.


Break up of aggregates in turbulent channel flow

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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