Experiments in Fluids

, 59:30 | Cite as

Particle-pair relative velocity measurement in high-Reynolds-number homogeneous and isotropic turbulence using 4-frame particle tracking velocimetry

  • Zhongwang Dou
  • Peter J. Ireland
  • Andrew D. Bragg
  • Zach Liang
  • Lance R. Collins
  • Hui Meng
Research Article
  • 102 Downloads

Abstract

The radial relative velocity (RV) between particles suspended in turbulent flow plays a critical role in droplet collision and growth. We present a simple and accurate approach to RV measurement in isotropic turbulence—planar 4-frame particle tracking velocimetry—using routine PIV hardware. It improves particle positioning and pairing accuracy over the 2-frame holographic approach by de Jong et al. (Int J Multiphas Flow 36:324–332; de Jong et al., Int J Multiphas Flow 36:324–332, 2010) without using high-speed cameras and lasers as in Saw et al. (Phys Fluids 26:111702, 2014). Homogeneous and isotropic turbulent flow (\({R_\lambda }=357\)) in a new, fan-driven, truncated iscosahedron chamber was laden with either low-Stokes (mean \(St=0.09\), standard deviation 0.05) or high-Stokes aerosols (mean \(St=3.46\), standard deviation 0.57). For comparison, DNS was conducted under similar conditions (\({R_\lambda }=398\); \(St=0.10\) and 3.00, respectively). Experimental RV probability density functions (PDF) and mean inward RV agree well with DNS. Mean inward RV increases with \(St\) at small particle separations, \(r\), and decreases with \(St\) at large \(r\), indicating the dominance of “path-history” and “inertial filtering” effects, respectively. However, at small \(r\), the experimental mean inward RV trends higher than DNS, possibly due to the slight polydispersity of particles and finite light sheet thickness in experiments. To confirm this interpretation, we performed numerical experiments and found that particle polydispersity increases mean inward RV at small \(r\), while finite laser thickness also overestimates mean inward RV at small \(r\), This study demonstrates the feasibility of accurately measuring RV using routine hardware, and verifies, for the first time, the path-history and inertial filtering effects on particle-pair RV at large particle separations experimentally.

Notes

Acknowledgements

This work was supported by the National Science Foundation through Collaborative Research Grants CBET-0967407 (HM) and CBET-0967349 (LRC) and through a graduate research fellowship awarded to PJI. We would also like to acknowledge high-performance computing support from Yellowstone (ark:/85065/d7wd3xhc) provided by NCAR’s Computational and Information Systems Laboratory through Grants ACOR0001 and P35091057, sponsored by the National Science Foundation. We thank Adam L. Hammond for highly valuable technical and editorial assistance. We also thank Dr. Lujie Cao in Ocean University of China for initiating and helping in the implementation of the planar 4-frame PTV technique.

Supplementary material

348_2017_2481_MOESM1_ESM.pdf (1.1 mb)
Supplementary material 1 (PDF 1116 KB)

References

  1. Adrian RJ, Westerweel J (2010) Particle image velocimetry. Cambridge University Press, CambridgeGoogle Scholar
  2. Ayyalasomayajula S, Warhaft Z, Collins LR (2008) Modeling inertial particle acceleration statistics in isotropic turbulence. Phys Fluids 20:Artn 095104.  https://doi.org/10.1063/1.2976174 MATHGoogle Scholar
  3. Bragg AD, Collins LR (2014) New insights from comparing statistical theories for inertial particles in turbulence: II. Relative velocities. New J Phys 16:Artn 055014.  https://doi.org/10.1088/1367-2630/16/5/055014 Google Scholar
  4. Bragg AD, Ireland PJ, Collins LR (2015) Mechanisms for the clustering of inertial particles in the inertial range of isotropic turbulence. Phys Rev E 92:023029CrossRefGoogle Scholar
  5. Bragg AD, Ireland PJ, Collins LR (2016) Forward and backward in time dispersion of fluid and inertial particles in isotropic turbulence. Phys Fluids (1994–present) 28:013305Google Scholar
  6. Cao L, Pan G, de Jong J, Woodward S, Meng H (2008) Hybrid digital holographic imaging system for three-dimensional dense particle field measurement. Appl Optics 47:4501–4508.  https://doi.org/10.1364/Ao.47.004501 CrossRefGoogle Scholar
  7. Chun JH, Koch DL, Rani SL, Ahluwalia A, Collins LR (2005) Clustering of aerosol particles in isotropic turbulence. J Fluid Mech 536:219–251.  https://doi.org/10.1017/S0022112005004568 MathSciNetCrossRefMATHGoogle Scholar
  8. Cierpka C, Lutke B, Kahler CJ (2013) Higher order multi-frame particle tracking velocimetry. Exp Fluids 54:Artn 1533.  https://doi.org/10.1007/S00348-013-1533-3 Google Scholar
  9. Crowder TM, Rosati JA, Schroeter JD, Hickey AJ, Martonen TB (2002) Fundamental effects of particle morphology on lung delivery: predictions of Stokes’ law and the particular relevance to dry powder inhaler formulation and development. Pharmaceut Res 19:239–245CrossRefGoogle Scholar
  10. Daitche A (2015) On the role of the history force for inertial particles in turbulence. J Fluid Mech 782:567–593MathSciNetCrossRefGoogle Scholar
  11. Daitche A, Tél T (2011) Memory effects are relevant for chaotic advection of inertial particles. Phys Rev Lett 107:244501CrossRefGoogle Scholar
  12. de Jong J, Cao L, Woodward SH, Salazar JPLC, Collins LR, Meng H (2008) Dissipation rate estimation from PIV in zero-mean isotropic turbulence. Exp Fluids 46:499–515.  https://doi.org/10.1007/s00348-008-0576-3 CrossRefGoogle Scholar
  13. de Jong J, Salazar JPLC, Woodward SH, Collins LR, Meng H (2010) Measurement of inertial particle clustering and relative velocity statistics in isotropic turbulence using holographic imaging. Int J Multiphas Flow 36:324–332.  https://doi.org/10.1016/j.ijmultiphaseflow.2009.11.008 DOICrossRefGoogle Scholar
  14. Dou Z (2017) Experimental study of inertial particle-pair relative velocity in isotropic turbulence (Order No. 10255106. In: Mechanical and aerospace engineering. University at Buffalo—SUNY, Buffalo, NYGoogle Scholar
  15. Dou Z, Pecenak ZK, Cao L, Woodward SH, Liang Z, Meng H (2016) PIV measurement of high-Reynolds-number homogeneous and isotropic turbulence in an enclosed flow apparatus with fan agitation. Measure Sci Technol 27:035305CrossRefGoogle Scholar
  16. Dou Z, Bragg AD, Hammond AL, Liang Z, Collins LR, Meng H (2017) Effects of Reynolds number and Stokes number on particle-pair relative velocity in isotropic turbulence: a systematic experimental study. arXiv preprint. arXiv:1711.02050
  17. Dullemond C, Dominik C (2005) Dust coagulation in protoplanetary disks: A rapid depletion of small grains. Astron Astrophys 434:971–986CrossRefMATHGoogle Scholar
  18. Eaton JK, Fessler JR (1994) Preferential Concentration of Particles by Turbulence. Int J Multiphas Flow 20:169–209.  https://doi.org/10.1016/0301-9322(94)90072-8 CrossRefMATHGoogle Scholar
  19. Faeth GM (1987) Mixing, transport and combustion in sprays. Prog Energy Combust Sci 13:293–345CrossRefGoogle Scholar
  20. Falkovich G, Pumir A (2007) Sling effect in collisions of water droplets in turbulent clouds. J Atmos Sci 64:4497–4505.  https://doi.org/10.1175/2007jas2371.1 DOICrossRefGoogle Scholar
  21. Hearst RJ, Buxton ORH, Ganapathisubramani B, Lavoie P (2012) Experimental estimation of fluctuating velocity and scalar gradients in turbulence. Exp Fluids 53:925–942CrossRefGoogle Scholar
  22. Ireland PJ, Bragg AD, Collins LR (2016) The effect of Reynolds number on inertial particle dynamics in isotropic turbulence. Part 1. Simulations without gravitational effects. J Fluid Mech 796Google Scholar
  23. Kähler CJ, Kompenhans J (2000) Fundamentals of multiple plane stereo particle image velocimetry. Exp Fluids 29:S070-S077.  https://doi.org/10.1007/s003480070009 Google Scholar
  24. Lai WT, Bjorkquist DC, Abbott MP, Naqwi AA (1998) Video systems for PIV recording. Measure Sci Technol 9:297CrossRefGoogle Scholar
  25. Liu XF, Katz J (2006) Instantaneous pressure and material acceleration measurements using a four-exposure PIV system. Exp Fluids 41:227–240.  https://doi.org/10.1007/s00348-006-0152-7 DOICrossRefGoogle Scholar
  26. Lu J, Shaw RA (2015) Charged particle dynamics in turbulence: Theory and direct numerical simulations. Phys Fluids (1994–present) 27:065111Google Scholar
  27. Lu J, Nordsiek H, Saw EW, Shaw RA (2010) Clustering of Charged Inertial Particles in Turbulence. Phys Rev Lett 104.  https://doi.org/10.1103/Physrevlett.104.184505
  28. Lüthi B, Tsinober A, Kinzelbach W (2005) Lagrangian measurement of vorticity dynamics in turbulent flow. J Fluid Mech 528:87–118CrossRefMATHGoogle Scholar
  29. Malik N, Dracos T, Papantoniou D (1993) Particle tracking velocimetry in three-dimensional flows. Exp Fluids 15:279–294CrossRefGoogle Scholar
  30. Maxey MR, Riley JJ (1983) Equation of motion for a small rigid sphere in a nonuniform flow. Phys Fluids 26:883–889.  https://doi.org/10.1063/1.864230 CrossRefMATHGoogle Scholar
  31. Meng H, Pan G, Pu Y, Woodward SH (2004) Holographic particle image velocimetry: from film to digital recording. Measure Sci Technol 15:673–685CrossRefGoogle Scholar
  32. Novara M, Scarano F (2013) A particle-tracking approach for accurate material derivative measurements with tomographic PIV. Exp Fluids 54:Artn 1584.  https://doi.org/10.1007/S00348-013-1584-5
  33. Ouellette NT, Xu H, Bodenschatz E (2006a) A quantitative study of three-dimensional Lagrangian particle tracking algorithms. Exp Fluids 40:301–313CrossRefGoogle Scholar
  34. Ouellette NT, Xu HT, Bodenschatz E (2006b) A quantitative study of three-dimensional Lagrangian particle tracking algorithms. Exp Fluids 40:301–313.  https://doi.org/10.1007/s00348-005-0068-7 CrossRefGoogle Scholar
  35. Pan L, Padoan P, Scalo J (2014) Turbulence-induced relative velocity of dust particles. II. The bidisperse case. Astrophys J 791:48CrossRefGoogle Scholar
  36. Parishani H, Ayala O, Rosa B, Wang LP, Grabowski WW (2015) Effects of gravity on the acceleration and pair statistics of inertial particles in homogeneous isotropic turbulence. Phys Fluids 27:Artn 033304.  https://doi.org/10.1063/1.4915121 Google Scholar
  37. Saffman P, Turner J (1956) On the collision of drops in turbulent clouds. J Fluid Mech 1:16–30CrossRefMATHGoogle Scholar
  38. Salazar JPLC, Collins LR (2012a) Inertial particle relative velocity statistics in homogeneous isotropic turbulence. J Fluid Mech 696:45–66.  https://doi.org/10.1017/Jfm.2012.2 MathSciNetCrossRefMATHGoogle Scholar
  39. Salazar JPLC, Collins LR (2012b) Inertial particle acceleration statistics in turbulence: Effects of filtering, biased sampling, and flow topology. Phys Fluids 24:Artn 083302.  https://doi.org/10.1063/1.4744993
  40. Salazar JPLC., De Jong J, Cao LJ, Woodward SH, Meng H, Collins LR (2008) Experimental and numerical investigation of inertial particle clustering in isotropic turbulence. J Fluid Mech 600:245–256.  https://doi.org/10.1017/S0022112008000372 CrossRefMATHGoogle Scholar
  41. Saw E-W, Bewley GP, Bodenschatz E, Ray SS, Bec J (2014) Extreme fluctuations of the relative velocities between droplets in turbulent airflow. Phys Fluids (1994–present) 26:111702Google Scholar
  42. Shaw RA (2003) Particle-turbulence interactions in atmospheric clouds. Annu Rev Fluid Mech 35:183–227.  https://doi.org/10.1146/annurev.fluid.35.101101.161125 MathSciNetCrossRefMATHGoogle Scholar
  43. Smith OI (1981) Fundamentals of Soot Formation in Flames with Application to Diesel-Engine Particulate-Emissions. Prog Energy Combust Sci 7:275–291.  https://doi.org/10.1016/0360-1285(81)90002-2 CrossRefGoogle Scholar
  44. Sundaram S, Collins LR (1997) Collision statistics in an isotropic particle-laden turbulent suspension. 1. Direct numerical simulations. J Fluid Mech 335:75–109.  https://doi.org/10.1017/S0022112096004454 CrossRefMATHGoogle Scholar
  45. Tavoularis S, Corrsin S, Bennett J (1978) Velocity-derivative skewness in small Reynolds number, nearly isotropic turbulence. J Fluid Mech 88:63–69CrossRefGoogle Scholar
  46. Voth GA, La Porta A, Crawford AM, Alexander J, Bodenschatz E (2002) Measurement of particle accelerations in fully developed turbulence. J Fluid Mech 469:121–160.  https://doi.org/10.1017/S0022112002001842 CrossRefMATHGoogle Scholar
  47. Wang LP, Wexler AS, Zhou Y (2000) Statistical mechanical description and modelling of turbulent collision of inertial particles. J Fluid Mech 415:117–153.  https://doi.org/10.1017/S0022112000008661 MathSciNetCrossRefMATHGoogle Scholar
  48. Wilkinson M, Mehlig B (2005) Caustics in turbulent aerosols. Europhys Lett 71:186–192.  https://doi.org/10.1209/epl/i2004-10532-7 MathSciNetCrossRefGoogle Scholar
  49. Xu HT, Ouellette NT, Bodenschatz E (2008) Evolution of geometric structures in intense turbulence. New J Phys 10:Artn 013012.  https://doi.org/10.1088/1367-2630/10/1/013012
  50. Yang F (2014) Study on effect of charge on inertial particle motion in turbulence by using holographic particle tracking velocimetry. State University of New York at BuffaloGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Zhongwang Dou
    • 1
  • Peter J. Ireland
    • 2
  • Andrew D. Bragg
    • 3
  • Zach Liang
    • 1
  • Lance R. Collins
    • 2
  • Hui Meng
    • 1
  1. 1.Department of Mechanical and Aerospace EngineeringUniversity at BuffaloBuffaloUSA
  2. 2.Sibley School of Mechanical and Aerospace EngineeringCornell UniversityIthacaUSA
  3. 3.Department of Civil and Environmental EngineeringDuke UniversityDurhamUSA

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