1. BREAK-UP OF AGGREGATES IN TURBULENT CHANNEL FLOW 1 Università degli Studi di Udine Centro Interdipartimentale di Fluidodinamica e Idraulica 2 Università di Roma “Tor Vergata” Dipartimento di Fisica 3 Eindhoven University of Technology Dept. Applied Physics Eros Pecile 1, Cristian Marchioli 1, Luca Biferale 2, Federico Toschi 3, Alfredo Soldati 1 Session TS036-1 on “Multi-phase Flows” ECCOMAS 2012 September 10-14, 2012, University of Vienna, Austria

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

3. 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

4. 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

5. Premise Aggregate Break-up in Turbulence What kind of aggregate? Aggregates consisting of colloidal primary particles Schematic of an aggregate

6. What kind of aggregate? Aggregates consisting of colloidal primary particles Break-up due to Hydrodynamics stress Schematic of break-up Premise Aggregate Break-up in Turbulence

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

8. Turbulent flow laden with few aggregates (one-way coupling) Aggregate size < O() with  the Kolmogorov length scale Aggregates break due to hydrodynamic stress,  Tracer-like aggregates:  ~     with  cr  cr  Instantaneous binary break-up once cr  Problem Definition Further Assumptions

9. Problem Definition Strategy for Numerical Experiments Consider a fully-developed statistically-steady flow Seed the flow randomly with aggregates of mass  at a given location Neglect aggregates released at locations where  cr  Follow the trajectory of remaining aggregates until break-up occurs Compute the exit time,     cr (time from release to break-up)

10. Problem Definition Strategy for Numerical Experiments Consider a fully-developed statistically-steady flow Seed the flow randomly with aggregates of mass  at a given location Neglect aggregates released at locations where  cr  Follow the trajectory of remaining aggregates until break-up occurs Compute the exit time,     cr (time from release to break-up)

11. Problem Definition Strategy for Numerical Experiments Consider a fully-developed statistically-steady flow Seed the flow randomly with aggregates of mass  at a given location Neglect aggregates released at locations where  cr  Follow the trajectory of remaining aggregates until break-up occurs Compute the exit time,     cr (time from release to break-up)

12. Consider a fully-developed statistically-steady flow Seed the flow randomly with aggregates of mass  at a given location Neglect aggregates released at locations where  cr  Follow the trajectory of remaining aggregates until break-up occurs Compute the exit time,     cr (time from release to break-up) Problem Definition Strategy for Numerical Experiments

13. Problem Definition Strategy for Numerical Experiments Consider a fully-developed statistically-steady flow Seed the flow randomly with aggregates of mass  at a given location Neglect aggregates released at locations where  cr  Follow the trajectory of remaining aggregates until break-up occurs Compute the exit time,     cr (time from release to break-up)  For j th aggregate breaking after N j time steps: x 0 =x(0) x   x  cr  tt nn+1  j  cr,j  N j · t

14.    cr Problem Definition Strategy for Numerical Experiments The break-up rate is the inverse of the ensemble-averaged exit time: For j th aggregate breaking after N j time steps: x 0 =x(0) x   x  cr  tt nn+1  j  cr,j  N j · t

15. Characterization of the local energy dissipation in 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: Re  = u  h/ = 150 Tracer-like aggregates: Wall Center

16. 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)

17. 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  cr

18. 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  cr Intermediate  cr

19. 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  cr Bulk  cr Intermediate  cr

20. Different values of the critical energy dissipation level required to break-up the aggregate lead to different break-up dynamics PDF of the location of break-up when  cr = Bulk  cr Wall-normal behavior of mean energy dissipation errorbar = RMS Channel Flow Choice of Critical Energy Dissipation  For small values of  cr break-up events occur preferentially in the bulk Bulk  cr Wall Center Wall

21. errorbar = RMS Channel Flow Choice of Critical Energy Dissipation Wall  cr Wall Center Wall Different values of the critical energy dissipation level required to break-up the aggregate lead to different break-up dynamics PDF of the location of break-up when  cr = Wall  cr Wall-normal behavior of mean energy dissipation  For large values of  cr break-up events occur preferentially near the wall

22. Evaluation of the Break-up Rate Results for Different Critical Dissipation Measured Expon. Fit Exp. Fit Exponential fit works reasonably for small values of the critical energy dissipation… Measured f( cr ) from DNS

23. Evaluation of the Break-up Rate Results for Different Critical Dissipation -  =-0.52 Exp. Fit Measured f( cr ) from DNS Measured Expon. Fit Exponential fit works reasonably for small values of the critical energy dissipation… and a power-law scaling is observed!

24. Evaluation of the Break-up Rate Results for Different Critical Dissipation -  =-0.52 Exp. Fit Measured f( cr ) from DNS Measured Expon. Fit Exponential fit works reasonably for small values of the critical energy dissipation… and away from the near-wall region!

25. How far do aggregates reach before break-up? Analysis of “Break-up Length” Consider aggregates released in regions of the flow where  cr with cr  ~  wall   Wall distance of aggregate’s release location: 0<z + <10 Number of break-ups Channel lengths covered in streamwise direction

26. Consider aggregates released in regions of the flow where  cr with cr  ~  wall   Wall distance of aggregate’s release location: 50<z + <100 How far do aggregates reach before break-up? Analysis of “Break-up Length” Number of break-ups Channel lengths covered in streamwise direction

27. How far do aggregates reach before break-up? Analysis of “Break-up Length” Consider aggregates released in regions of the flow where  cr with cr  ~  wall   Wall distance of aggregate’s release location: 100<z + <150 Number of break-ups Channel lengths covered 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 is  a value lower than in homogeneous isotropic turbulence (where ). 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)

29. Thank you for your kind attention!

30. 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  cr Bulk  cr Intermediate  cr

31. 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 Measured f( cr ) from DNS Consider aggregates released in regions of the flow where  cr with cr  ~  wall    -0.52 (slope)

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.