BREAK-UP OF AGGREGATES IN TURBULENT CHANNEL FLOW

1Università degli Studi di UdineCentro Interdipartimentale di Fluidodinamica e Idraulica

2Università di Roma “Tor Vergata”Dipartimento di Fisica

3Eindhoven University of TechnologyDept. Applied Physics

Eros Pecile1, Cristian Marchioli1, Luca Biferale2,Federico Toschi3, Alfredo Soldati1

Session TS036-1 on “Multi-phase Flows”

ECCOMAS 2012

September 10-14, 2012, University of Vienna, Austria

PremiseAggregate Break-up in Turbulence

What kind of application?

Processing of industrial colloids• Polymer, paint, and paper industry

PremiseAggregate Break-up in Turbulence

What kind of application?

Processing of industrial colloids• Polymer, paint, and paper industryEnvironmental systems• Marine snow as part of the oceanic carbon sink

PremiseAggregate Break-up in Turbulence

What kind of application?

Processing of industrial colloids• Polymer, paint, and paper industryEnvironmental systems• Marine snow as part of the oceanic carbon sinkAerosols and dust particles• Flame synthesis of powders, soot, and nano-particles• Dust dispersion in explosions and equipment breakdown

PremiseAggregate Break-up in Turbulence

What kind of aggregate?

Aggregates consisting ofcolloidal primary particles

Schematic of an aggregate

What kind of aggregate?

Aggregates consisting ofcolloidal primary particlesBreak-up due toHydrodynamics stress

Schematic of break-up

PremiseAggregate Break-up in Turbulence

Problem DefinitionDescription of the Break-up Process

Focus of this work!

SIMPLIFIEDSMOLUCHOWSKIEQUATION (NOAGGREGATIONTERM IN IT!)

• Turbulent flow laden with few aggregates (one-way coupling)• Aggregate size < O(h) with h the Kolmogorov length scale• Aggregates break due to hydrodynamic stress, s• Tracer-like aggregates: s ~ m(e/n)1/2

with

• scr = scr(x)

• Instantaneous binary break-up once s > scr(x)

Problem DefinitionFurther Assumptions

2

21

=i

j

j

i

xu

xune

Problem DefinitionStrategy for Numerical Experiments

• Consider a fully-developed statistically-steady flow• Seed the flow randomly with aggregates of mass x at a given location• Neglect aggregates released at locations where s > scr(x)

• Follow the trajectory of remaining aggregates until break-up occurs• Compute the exit time, t= tscr

(time from release to break-up)

Problem DefinitionStrategy for Numerical Experiments

• Consider a fully-developed statistically-steady flow• Seed the flow randomly with aggregates of mass x at a given location• Neglect aggregates released at locations where s > scr(x)

• Follow the trajectory of remaining aggregates until break-up occurs• Compute the exit time, t= tscr

(time from release to break-up)

Problem DefinitionStrategy for Numerical Experiments

• Consider a fully-developed statistically-steady flow• Seed the flow randomly with aggregates of mass x at a given location• Neglect aggregates released at locations where s > scr(x)

• Follow the trajectory of remaining aggregates until break-up occurs• Compute the exit time, t= tscr

(time from release to break-up)

• Consider a fully-developed statistically-steady flow• Seed the flow randomly with aggregates of mass x at a given location• Neglect aggregates released at locations where s > scr(x)

• Follow the trajectory of remaining aggregates until break-up occurs• Compute the exit time, t= tscr

(time from release to break-up)

Problem DefinitionStrategy for Numerical Experiments

Problem DefinitionStrategy for Numerical Experiments

• Consider a fully-developed statistically-steady flow• Seed the flow randomly with aggregates of mass x at a given location• Neglect aggregates released at locations where s > scr(x)

• Follow the trajectory of remaining aggregates until break-up occurs• Compute the exit time, t= tscr

(time from release to break-up)

t

For jth aggregatebreaking afterNj

time steps:

x0=x(0)

xt =x(tcr)

dtn n+1

tj=tcr,j=Nj·dt

t

sscr

Problem DefinitionStrategy for Numerical Experiments

• The break-up rate is the inverse of the ensemble-averaged exit time:

For jth aggregatebreaking afterNj

time steps:

x0=x(0)

xt =x(tcr)

dtn n+1

tj=tcr,j=Nj·dt

Characterization of thelocal energy dissipationin bounded flow:

Wall-normal behavior of mean energy dissipation

RMS

Flow Instances and Numerical MethodologyChannel Flow

• Pseudospectral DNS of 3D time- dependent turbulent gas flow• Shear Reynolds number: Ret = uth/n = 150

• Tracer-like aggregates:

2

21

=i

j

j

i

xu

xune

Wall Center

• Wall-normal behavior of mean energy dissipation

Whole Channel

Channel FlowChoice of Critical Energy Dissipation

• PDF of local energy dissipation

PDFs are strongly affected by flow anisotropy (skewed shape)

• Wall-normal behavior of mean energy dissipation

Whole Channel Bulk

Channel FlowChoice of Critical Energy Dissipation

• PDF of local energy dissipation

PDFs are strongly affected by flow anisotropy (skewed shape)

Bulk ecr

• Wall-normal behavior of mean energy dissipation

Whole Channel Bulk Intermediate

Channel FlowChoice of Critical Energy Dissipation

• PDF of local energy dissipation

PDFs are strongly affected by flow anisotropy (skewed shape)

Bulk ecr

Intermediate ecr

• Wall-normal behavior of mean energy dissipation

Whole Channel Bulk Intermediate Wall

Channel FlowChoice of Critical Energy Dissipation

• PDF of local energy dissipation

PDFs are strongly affected by flow anisotropy (skewed shape)

Wall ecr

Bulk ecr

Intermediate ecr

Different values of the critical energy dissipation level requiredto break-up the aggregate lead to different break-up dynamics

• PDF of the location of break-up when ecr = Bulk ecr

• Wall-normal behavior of mean energy dissipation

errorbar = RMS

Channel FlowChoice of Critical Energy Dissipation

For small values of ecr break-up events occur preferentially in the bulk

Bulk ecr

Wall Center Wall

errorbar = RMS

Channel FlowChoice of Critical Energy Dissipation

Wall ecrWall Center Wall

Different values of the critical energy dissipation level requiredto break-up the aggregate lead to different break-up dynamics

• PDF of the location of break-up when ecr = Wall ecr

• Wall-normal behavior of mean energy dissipation

For large values of ecr break-up events occur preferentially near the wall

Evaluation of the Break-up RateResults for Different Critical Dissipation

Measured Expon. Fitcr

crff cr

ss t

e 1)(0|== x

00

/)(ln)(

])(exp[)(

NtNf

tfNtN

cr

cr

=

e

e

Exp. Fit

Exponential fit works reasonably for small values of the critical energy dissipation…

Measuredf(ecr) fromDNS

Evaluation of the Break-up RateResults for Different Critical Dissipation

-c=-0.52

cee crcrf )( Exp. Fit

Measuredf(ecr) fromDNS

Measured Expon. Fitcr

crff cr

ss t

e 1)(0|== x

00

/)(ln)(

])(exp[)(

NtNf

tfNtN

cr

cr

=

e

e

Exponential fit works reasonably for small values of the critical energy dissipation… and a power-law scaling is observed!

Evaluation of the Break-up RateResults for Different Critical Dissipation

-c=-0.52

cee crcrf )( Exp. Fit

Measuredf(ecr) fromDNS

Measured Expon. Fitcr

crff cr

ss t

e 1)(0|== x

00

/)(ln)(

])(exp[)(

NtNf

tfNtN

cr

cr

=

e

e

Exponential fit works reasonably for small values of the critical energy dissipation… and away from the near-wall region!

How far do aggregates reach before break-up?Analysis of “Break-up Length”

Consider aggregates released in regions of the flow where s > scr(x) with scr(x) ~ m(ewall/n)1/2

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

Num

ber o

f bre

ak-u

ps

Channel lengths covered in streamwise direction

Consider aggregates released in regions of the flow where s > scr(x) with scr(x) ~ m(ewall/n)1/2

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

How far do aggregates reach before break-up?Analysis of “Break-up Length”

Num

ber o

f bre

ak-u

ps

Channel lengths covered in streamwise direction

How far do aggregates reach before break-up?Analysis of “Break-up Length”

Consider aggregates released in regions of the flow where s > scr(x) with scr(x) ~ m(ewall/n)1/2

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

Num

ber o

f bre

ak-u

ps

Channel lengths covered 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 is c ~ 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. Babler et al. (2012)

Thank you for your kind attention!

• Wall-normal behavior of mean energy dissipation

errorbar = RMS

Whole Channel Intermediate Bulk Wall

Channel FlowChoice of Critical Energy Dissipation

• PDF of local energy dissipation

PDFs are strongly affected by flow anisotropy (skewed shape)

Wall ecr

Bulk ecr

Intermediate ecr

Estimate of Fragmentation RateTwo possible (and simple…) approaches

Fit

Exponential fit works reasonably away from the near-wall region and for small values of the critical energy dissipation

Measuredf(ecr) fromDNS

Consider aggregates released in regions of the flow where s > scr(x) with scr(x) ~ m(ewall/n)1/2

-0.52 (slope)

Problem DefinitionStrategy 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 DefinitionStrategy 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 DefinitionStrategy 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 DefinitionStrategy 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 DefinitionStrategy 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.