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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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slide1
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”

slide2
Premise

Aggregate Break-up in Turbulence

  • Whatkind of application?
  • Processing of industrial colloids
  • Polymer, paint, and paper industry
slide3
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
slide4
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
slide5
Premise

Aggregate Break-up in Turbulence

Whatkind of aggregate?

Aggregatesconsisting of

colloidalprimaryparticles

Schematic of an aggregate

slide6
Premise

Aggregate Break-up in Turbulence

Whatkind of aggregate?

Aggregatesconsisting of

colloidalprimary particles

Break-up due to

Hydrodynamicsstress

Schematic of break-up

slide7
Problem Definition

Description of the Break-up Process

SIMPLIFIED

SMOLUCHOWSKI

EQUATION (NO

AGGREGATION

TERM IN IT!)

Focus of this work!

slide8
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)
slide9
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)
slide10
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)
slide11
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)
slide12
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)
slide13
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)
slide14
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

slide15
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:
slide16
Channel Flow

Choice of CriticalEnergy Dissipation

  • Wall-normalbehavior of
  • meanenergydissipation
  • PDF of localenergydissipation

WholeChannel

PDFs are stronglyaffectedby flow anisotropy (skewedshape)

slide17
Channel Flow

Choice of CriticalEnergy Dissipation

  • Wall-normalbehavior of
  • meanenergydissipation
  • PDF of localenergydissipation

WholeChannel

Bulk

Bulk ecr

PDFs are stronglyaffectedby flow anisotropy (skewedshape)

slide18
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)

slide19
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)

slide20
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

slide21
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

slide22
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…

slide23
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!

slide24
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!

slide25
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

Number of break-ups

Channellengthscovered in streamwise direction

slide26
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

Number of break-ups

Channellengthscovered in streamwise direction

slide27
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

Number of break-ups

Channellengthscovered in streamwise direction

slide28
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)

slide30
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)

slide31
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

slide32
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.
slide33
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.
slide34
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.
slide35
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.
slide36
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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