Skip to main content
×
Home

Three-dimensional Lagrangian Voronoï analysis for clustering of particles and bubbles in turbulence

  • Yoshiyuki Tagawa (a1) (a2), Julián Martínez Mercado (a1) (a2), Vivek N. Prakash (a1) (a2), Enrico Calzavarini (a3) (a2), Chao Sun (a1) (a2) and Detlef Lohse (a1) (a2)...
Abstract
Abstract

Three-dimensional Voronoï analysis is used to quantify the clustering of inertial particles in homogeneous isotropic turbulence using data sets from numerics in the point particle limit and one experimental data set. We study the clustering behaviour at different density ratios, particle response times (i.e. Stokes numbers ) and two Taylor–Reynolds numbers ( and 180). The probability density functions (p.d.f.s) of the Voronoï cell volumes of light and heavy particles show different behaviour from that of randomly distributed particles, i.e. fluid tracers, implying that clustering is present. The standard deviation of the p.d.f. normalized by that of randomly distributed particles is used to quantify the clustering. The clustering for both light and heavy particles is stronger for higher . Light particles show maximum clustering for around 1–2 for both Taylor–Reynolds numbers. The experimental data set shows reasonable agreement with the numerical results. The results are consistent with previous investigations employing other approaches to quantify the clustering. We also present the joint p.d.f.s of enstrophy and Voronoï volumes and their Lagrangian autocorrelations. The small Voronoï volumes of light particles correspond to regions of higher enstrophy than those of heavy particles, indicating that light particles cluster in higher vorticity regions. The Lagrangian temporal autocorrelation function of Voronoï volumes shows that the clustering of light particles lasts much longer than that of heavy or neutrally buoyant particles. Due to inertial effects arising from the density contrast with the surrounding liquid, light and heavy particles remain clustered for much longer times than the flow structures which cause the clustering.

Copyright
Corresponding author
Email addresses for correspondence: y.tagawa@tnw.utwente.nl, c.sun@utwente.nl, d.lohse@utwente.nl
References
Hide All
1. Aliseda A., Cartellier A., Hainaux F. & Lasheras J. C. 2002 Effect of preferential concentration on the settling velocity of heavy particles in homogeneous isotropic turbulence. J. Fluid Mech. 468, 77105.
2. Bec J., Biferale L., Boffetta G., Celani A., Cencini M., Lanotte A., Musacchio S. & Toschi F. 2006 Acceleration statistics of heavy particles in turbulence. J. Fluid Mech. 550, 349358.
3. Benzi R., Biferale L., Calzavarini E., Lohse D. & Toschi F. 2009 Velocity-gradient statistics along particle trajectories in turbulent flows: the refined similarity hypothesis in the Lagrangian frame. Phys. Rev. E 80 (6), 066318.
4. Biferale L., Scagliarini A. & Toschi F. 2010 On the measurement of vortex filament lifetime statistics in turbulence. Phys. Fluids 22, 065101.
5. Bodenschatz E., Malinowski S. P., Shaw R. A. & Stratmann F. 2010 Can we understand clouds without turbulence? Science 327, 970971.
6. Calzavarini E., van den Berg T. H., Toschi F. & Lohse D. 2008a Quantifying microbubble clustering in turbulent flow from single-point measurements. Phys. Fluids 20, 040702.
7. Calzavarini E., Cencini M., Lohse D. & Toschi F. 2008b Quantifying turbulence-induced segregation of inertial particles. Phys. Rev. Lett. 101, 084504.
8. Calzavarini E., Kerscher M., Lohse D. & Toschi F. 2008c Dimensionality and morphology of particle and bubble clusters in turbulent flow. J. Fluid Mech. 607, 1324.
9. Chen L., Goto S. & Vassilicos J. C. 2006 Turbulent clustering of stagnation points and inertial particles. J. Fluid Mech. 553, 143154.
10. Ferenc J. S. & Néda Z. 2007 On the size distribution of Poisson Voronoï cells. Physica A 385, 518526.
11. Fessler J. R., Kulick J. D. & Eaton J. K. 1994 Preferential concentration of heavy particles in a turbulent channel flow. Phys. Fluids 6, 37423749.
12. IJzermans R. H. A., Reeks M. W., Meneguz E., Picciotto M. & Soldati A. 2009 Measuring segregation of inertial particles in turbulence by a full Lagrangian approach. Phys. Rev. E 80, 015302(R).
13. Kerscher M., Mecke K., Schmalzing J., Beisbart C., Buchert T. & Wagner H. 2001 Morphological fluctuations of large-scale structure: the PSCz survey. Astron. Astrophys. 373, 111.
14. Martinez Mercado J., Chehata-Gomez D., van Gils D. P. M., Sun C. & Lohse D. 2010 On bubble clustering and energy spectra in pseudo-turbulence. J. Fluid Mech. 650, 287306.
15. Martinez Mercado J., Prakash V. N., Tagawa Y., Sun C. & Lohse D. 2011 Lagrangian statistics of light particles in turbulence. Phys. Fluids (submitted), arXiv:1109.0188v1.
16. Maxey M. R. & Riley J. J. 1983 Equation of motion for a small rigid sphere in a non-uniform flow. Phys. Fluids 26, 883889.
17. Mazzitelli I. M. & Lohse D. 2004 Lagrangian statistics for fluid particles and bubbles in turbulence. New J. Phys. 6, 203.
18. Mazzitelli I. M., Lohse D. & Toschi F. 2003 On the relevance of the lift force in bubbly turbulence. J. Fluid Mech. 488, 283313.
19. Monchaux R., Bourgoin M. & Cartellier A. 2010 Preferential concentration of heavy particles: a Voronoï analysis. Phys. Fluids 22, 103304.
20. Okabe A., Boots B., Sugihara K. & Chiu S. N. 2000 Spatial Tesselations. Wiley.
21. Pratsinis S. E. & Vemury S. 1996 Particle formation in gases: a review. Powder Technol. 88, 267273.
22. Saw E. W., Shaw R. A., Ayyalasomayajula S., Chuang P. Y. & Gylfason A. 2008 Inertial clustering of particles in high-Reynolds-number turbulence. Phys. Rev. Lett. 100, 214501.
23. Schmitt F. G. & Seuront L. 2008 Intermittent turbulence and copepod dynamics: increase in encounter rates through preferential concentration. J. Marine Syst. 70, 263272.
24. Toschi F., Biferale L., Calzavarini E., Scagliarini A. & Leveque E. 2009 Lagrangian modelling and properties of particles with inertia. In Advances in Turbulence, XII, Proceedings of the 12th European Turbulence Conference (ETC-12), Marburg (D), Springer Proceedings in Physics.
25. Toschi F. & Bodenschatz E. 2009 Lagrangian properties of particles in turbulence. Annu. Rev. Fluid Mech. 41, 375404.
26. van de Weygaert R. & Icke V. 1989 Fragmenting the universe. Part II. Voronoï vertices as Abell clusters. Astron. Astrophys. 213, 19.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Keywords:

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 68 *
Loading metrics...

Abstract views

Total abstract views: 209 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 19th November 2017. This data will be updated every 24 hours.