BREAK-UP OF AGGREGATES IN TURBULENT CHANNEL FLOW
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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
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PremiseAggregate Break-up in Turbulence
What kind of application?
Processing of industrial colloids• Polymer, paint, and paper industry
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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
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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
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PremiseAggregate Break-up in Turbulence
What kind of aggregate?
Aggregates consisting ofcolloidal primary particles
Schematic of an aggregate
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What kind of aggregate?
Aggregates consisting ofcolloidal primary particlesBreak-up due toHydrodynamics stress
Schematic of break-up
PremiseAggregate Break-up in Turbulence
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Problem DefinitionDescription of the Break-up Process
Focus of this work!
SIMPLIFIEDSMOLUCHOWSKIEQUATION (NOAGGREGATIONTERM IN IT!)
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• 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
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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)
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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)
![Page 11: BREAK-UP OF AGGREGATES IN TURBULENT CHANNEL FLOW](https://reader035.fdocuments.us/reader035/viewer/2022062410/56816337550346895dd3c556/html5/thumbnails/11.jpg)
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)
![Page 12: BREAK-UP OF AGGREGATES IN TURBULENT CHANNEL FLOW](https://reader035.fdocuments.us/reader035/viewer/2022062410/56816337550346895dd3c556/html5/thumbnails/12.jpg)
• 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
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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
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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
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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
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• 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)
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• 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
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• 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
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• 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
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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
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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
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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
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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!
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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!
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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
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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
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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
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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)
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Thank you for your kind attention!
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• 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
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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)
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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.
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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.
![Page 34: BREAK-UP OF AGGREGATES IN TURBULENT CHANNEL FLOW](https://reader035.fdocuments.us/reader035/viewer/2022062410/56816337550346895dd3c556/html5/thumbnails/34.jpg)
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.
![Page 35: BREAK-UP OF AGGREGATES IN TURBULENT CHANNEL FLOW](https://reader035.fdocuments.us/reader035/viewer/2022062410/56816337550346895dd3c556/html5/thumbnails/35.jpg)
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.
![Page 36: BREAK-UP OF AGGREGATES IN TURBULENT CHANNEL FLOW](https://reader035.fdocuments.us/reader035/viewer/2022062410/56816337550346895dd3c556/html5/thumbnails/36.jpg)
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.