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Problem DefinitionProblem Definition

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

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

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

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)

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.

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.

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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