BREAK-UP OF AGGREGATES IN TURBULENT CHANNEL FLOW 1 Università degli Studi di Udine Centro...
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Transcript of BREAK-UP OF AGGREGATES IN TURBULENT CHANNEL FLOW 1 Università degli Studi di Udine Centro...
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
Premise
Aggregate Break-up in Turbulence
What kind of application?
Processing of industrial colloids• Polymer, paint, and paper industry
Premise
Aggregate Break-up in Turbulence
What kind of application?
Processing of industrial colloids• Polymer, paint, and paper industry
Environmental systems• Marine snow as part of the oceanic carbon sink
Premise
Aggregate Break-up in Turbulence
What kind of application?
Processing of industrial colloids• Polymer, paint, and paper industry
Environmental systems• Marine snow as part of the oceanic carbon sink
Aerosols and dust particles• Flame synthesis of powders, soot, and nano-particles• Dust dispersion in explosions and equipment breakdown
Premise
Aggregate 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 particles
Break-up due toHydrodynamics stress
Schematic of break-up
Premise
Aggregate Break-up in Turbulence
Problem Definition
Description 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 Definition
Further Assumptions
2
2
1
i
j
j
i
x
u
x
u
Problem Definition
Strategy 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 Definition
Strategy 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 Definition
Strategy 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 Definition
Strategy for Numerical Experiments
Problem Definition
Strategy 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)
x t =x(tcr)
dtn n+1
tj=tcr,j=Nj·dt
t
sscr
Problem Definition
Strategy 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)
x t =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 Methodology
Channel Flow
• Pseudospectral DNS of 3D time- dependent turbulent gas flow
• Shear Reynolds number:
Ret = uth/n = 150
• Tracer-like aggregates:
2
2
1
i
j
j
i
x
u
x
u
Wall Center
• Wall-normal behavior of mean energy dissipation
Whole Channel
Channel Flow
Choice 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 Flow
Choice 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 Flow
Choice 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 Flow
Choice 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 Flow
Choice 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 Flow
Choice 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 Rate
Results for Different Critical Dissipation
Measured Expon. Fitcr
crff cr
1)(
0| x
00
/)(ln)(
])(exp[)(
NtNf
tfNtN
cr
cr
Exp. Fit
Exponential fit works reasonably for small values of the critical energy dissipation…
Measuredf(ecr) fromDNS
Evaluation of the Break-up Rate
Results for Different Critical Dissipation
-c=-0.52
crcrf )( Exp. Fit
Measuredf(ecr) fromDNS
Measured Expon. Fitcr
crff cr
1)(
0| x
00
/)(ln)(
])(exp[)(
NtNf
tfNtN
cr
cr
Exponential fit works reasonably for small values of the critical energy dissipation… and a power-law scaling is observed!
Evaluation of the Break-up Rate
Results for Different Critical Dissipation
-c=-0.52
crcrf )( Exp. Fit
Measuredf(ecr) fromDNS
Measured Expon. Fitcr
crff cr
1)(
0| x
00
/)(ln)(
])(exp[)(
NtNf
tfNtN
cr
cr
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
of
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
of
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
of
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 < < 0.9c ).
• 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 Flow
Choice 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 Rate
Two 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 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.
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.