BREAK-UP OF AGGREGATES IN TURBULENT CHANNEL FLOW

1. 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”

2. Premise Aggregate Break-up in Turbulence • Whatkind of application? • Processing of industrial colloids • Polymer, paint, and paper industry

3. 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

4. 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

5. Premise Aggregate Break-up in Turbulence Whatkind of aggregate? Aggregatesconsisting of colloidalprimaryparticles Schematic of an aggregate

6. Premise Aggregate Break-up in Turbulence Whatkind of aggregate? Aggregatesconsisting of colloidalprimary particles Break-up due to Hydrodynamicsstress Schematic of break-up

7. Problem Definition Description of the Break-up Process SIMPLIFIED SMOLUCHOWSKI EQUATION (NO AGGREGATION TERM IN IT!) Focus of this work!

8. 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)

9. 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)

10. 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)

11. 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)

12. 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)

13. 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)

14. 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

15. 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:

16. Channel Flow Choice of CriticalEnergy Dissipation • Wall-normalbehavior of • meanenergydissipation • PDF of localenergydissipation WholeChannel PDFs are stronglyaffectedby flow anisotropy (skewedshape)

17. Channel Flow Choice of CriticalEnergy Dissipation • Wall-normalbehavior of • meanenergydissipation • PDF of localenergydissipation WholeChannel Bulk Bulk ecr PDFs are stronglyaffectedby flow anisotropy (skewedshape)

18. 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)

19. 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)

20. 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

21. 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

22. 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…

23. 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!

24. 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!

25. 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<z+<10 Number of break-ups Channellengthscovered in streamwise direction

26. 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<z+<100 Number of break-ups Channellengthscovered in streamwise direction

27. 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<z+<150 Number of break-ups Channellengthscovered in streamwise direction

28. 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)

29. Thankyou for yourkindattention!

30. 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)

31. 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

32. 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.

33. 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.

34. 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.

35. 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.

36. 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.