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Drag enhancement in a dusty Kolmogorov flow

A. Sozza1,*, M. Cencini1,†, S. Musacchio2, and G. Boffetta2

  • 1Istituto dei Sistemi Complessi, CNR and INFN sez. Roma2 “Tor Vergata”, via dei Taurini 19, 00185 Rome, Italy
  • 2Dipartimento di Fisica and INFN, Universitá di Torino, via P. Giuria 1, 10125 Torino, Italy

  • *Corresponding author: asozza.ph@gmail.com
  • †Corresponding author: massimo.cencini@cnr.it
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Phys. Rev. Fluids 5, 094302 – Published 17 September, 2020

DOI: https://doi.org/10.1103/PhysRevFluids.5.094302

Abstract

Particles suspended in a fluid exert feedback forces that can significantly impact the flow, altering the turbulent drag and velocity fluctuations. We study flow modulation induced by small spherical particles heavier than the carrier fluid in the framework of an Eulerian two-way coupled model, where particles are represented by a continuum density transported by a compressible velocity field, exchanging momentum with the fluid phase. We implement the model in direct numerical simulations of the turbulent Kolmogorov flow, a simplified setting allowing for studying the momentum balance and the turbulent drag in the absence of boundaries. We show that the amplitude of the mean flow and the turbulence intensity are reduced by increasing particle mass loading with the consequent enhancement of the friction coefficient. Surprisingly, turbulence suppression is stronger for particles of smaller inertia. We understand such a result by mapping the equations for dusty flow, in the limit of vanishing inertia, to a Newtonian flow with an effective forcing reduced by the increase in fluid density due to the presence of particles. We also discuss the negative feedback produced by turbophoresis, which mitigates the effects of particles, especially with larger inertia, on the turbulent flow.

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References (59)

  1. N. J. Balmforth and A. Provenzale, Geomorphological fluid mechanics (Springer Science & Business Media, Berlin, 2001), Vol. 582.
  2. R. A. Shaw, Particle-turbulence interactions in atmospheric clouds, Annu. Rev. Fluid Mech. 35, 183 (2003).
  3. A. Celani, G. Falkovich, A. Mazzino, and A. Seminara, Droplet condensation in turbulent flows, Europhys. Lett. 70, 775 (2005).
  4. F. Necker, C. Härtel, L. Kleiser, and E. Meiburg, Mixing and dissipation in particle-driven gravity currents, J. Fluid Mech. 545, 339 (2005).
  5. P. Burns and E. Meiburg, Sediment-laden fresh water above salt water: Nonlinear simulations, J. Fluid Mech. 762, 156 (2015).
  6. D. Bercovici and C. Michaut, Two-phase dynamics of volcanic eruptions: Compaction, compression and the conditions for choking, Geophys. J. Int. 182, 843 (2010).
  7. P. J. Armitage, Astrophysics of Planet Formation (Cambridge University Press, Cambridge, 2010).
  8. P. J. Armitage, Dynamics of protoplanetary disks, Annu. Rev. Astron. Astrophys. 49, 195 (2011).
  9. H. Homann, T. Guillot, J. Bec, C. W. Ormel, S. Ida, and P. Tanga, Effect of turbulence on collisions of dust particles with planetesimals in protoplanetary disks, Astron. Astrophys. 589, A129 (2016).
  10. I. Lashgari, F. Picano, W.-P. Breugem, and L. Brandt, Laminar, Turbulent, and Inertial Shear-Thickening Regimes in Channel Flow of Neutrally Buoyant Particle Suspensions, Phys. Rev. Lett. 113, 254502 (2014).
  11. H. T. Bi, N. Ellis, I. A. Abba, and J. R. Grace, A state-of-the-art review of gas–solid turbulent fluidization, Chem. Eng. Sci. 55, 4789 (2000).
  12. S. Balachandar and J. K. Eaton, Turbulent dispersed multiphase flow, Annu. Rev. Fluid Mech. 42, 111 (2010).
  13. R. A. Gore and C. T. Crowe, Effect of particle size on modulating turbulent intensity, Int. J. Multiphase Flow 15, 279 (1989).
  14. J. K. Eaton, Two-way coupled turbulence simulations of gas-particle flows using point-particle tracking, Int. J. Multiphase Flow 35, 792 (2009).
  15. J. D. Kulick, J. R. Fessler, and J. K. Eaton, Particle response and turbulence modification in fully developed channel flow, J. Fluid Mech. 277, 109 (1994).
  16. R. Monchaux and A. Dejoan, Settling velocity and preferential concentration of heavy particles under two-way coupling effects in homogeneous turbulence, Phys. Rev. Fluids 2, 104302 (2017).
  17. M. H. Kasbaoui, Turbulence modulation by settling inertial aerosols in Eulerian-Eulerian and Eulerian-Lagrangian simulations of homogeneously sheared turbulence, Phys. Rev. Fluids 4, 124308 (2019).
  18. P. Muramulla, A. Tyagi, P. S. Goswami, and V. Kumaran, Disruption of turbulence due to particle loading in a dilute gas–particle suspension, J. Fluid Mech. 889, A28 (2020).
  19. L. H. Zhao, H. I. Andersson, and J. J. J. Gillissen, Turbulence modulation and drag reduction by spherical particles, Phys. Fluids 22, 081702 (2010).
  20. D. Li, K. Luo, Z. Wang, W. Xiao, and J. Fan, Drag enhancement and turbulence attenuation by small solid particles in an unstably stratified turbulent boundary layer, Phys. Fluids 31, 063303 (2019).
  21. M. N. Ardekani, P. Costa, W-P. Breugem, F. Picano, and L. Brandt, Drag reduction in turbulent channel flow laden with finite-size oblate spheroids, J. Fluid Mech. 816, 43 (2017).
  22. W. Fornari, A. Formenti, F. Picano, and L. Brandt, The effect of particle density in turbulent channel flow laden with finite size particles in semi-dilute conditions, Phys. Fluids 28, 033301 (2016).
  23. P. Gualtieri, F. Battista, and C. M. Casciola, Turbulence modulation in heavy-loaded suspensions of tiny particles, Phys. Rev. Fluids 2, 034304 (2017).
  24. J. Bec, F. Laenen, and S. Musacchio, arXiv:1702.06773.
  25. V. Pandey, P. Perlekar, and D. Mitra, Clustering and energy spectra in two-dimensional dusty gas turbulence, Phys. Rev. E 100, 013114 (2019).
  26. E. Balkovsky, G. Falkovich, and A. Fouxon, Intermittent Distribution of Inertial Particles in Turbulent Flows, Phys. Rev. Lett. 86, 2790 (2001).
  27. J. Bec, Fractal clustering of inertial particles in random flows, Phys. Fluids 15, L81 (2003).
  28. J. Bec, L. Biferale, M. Cencini, A. Lanotte, S. Musacchio, and F. Toschi, Heavy Particle Concentration in Turbulence at Dissipative and Inertial Scales, Phys. Rev. Lett. 98, 084502 (2007).
  29. M. W. Reeks, The transport of discrete particles in inhomogeneous turbulence, J. Aerosol Sci. 14, 729 (1983).
  30. S. Belan, I. Fouxon, and G. Falkovich, Localization-Delocalization Transitions in Turbophoresis of Inertial Particles, Phys. Rev. Lett. 112, 234502 (2014).
  31. G. A. Sehmel, Particle deposition from turbulent air flow, J. Geophys. Res. 75, 1766 (1970).
  32. M. Caporaloni, F. Tampieri, F. Trombetti, and O. Vittori, Transfer of particles in nonisotropic air turbulence, J. Atmos. Sci. 32, 565 (1975).
  33. J. W. Brooke, K. Kontomaris, T. J. Hanratty, and J. B. McLaughlin, Turbulent deposition and trapping of aerosols at a wall, Phys. Fluids A 4, 825 (1992).
  34. C. Marchioli and A. Soldati, Mechanisms for particle transfer and segregation in a turbulent boundary layer, J. Fluid Mech. 468, 283 (2002).
  35. G. Sardina, P. Schlatter, L. Brandt, F. Picano, and C. M. Casciola, Wall accumulation and spatial localization in particle-laden wall flows, J. Fluid Mech. 699, 50 (2012).
  36. F. Picano, G. Sardina, and C. M. Casciola, Spatial development of particle-laden turbulent pipe flow, Phys. Fluids 21, 093305 (2009).
  37. D. WI. Rouson and J. K. Eaton, On the preferential concentration of solid particles in turbulent channel flow, J. Fluid Mech. 428, 149 (2001).
  38. J. Bec, H. Homann, and G. Krstulovic, Clustering, Fronts, and Heat Transfer in Turbulent Suspensions of Heavy Particles, Phys. Rev. Lett. 112, 234503 (2014).
  39. F. De Lillo, M. Cencini, S. Musacchio, and G. Boffetta, Clustering and turbophoresis in a shear flow without walls, Phys. Fluids 28, 035104 (2016).
  40. D. Mitra, N. E. L. Haugen, and I. Rogachevskii, Turbophoresis in forced inhomogeneous turbulence, Eur. Phys. J. Plus 133, 35 (2018).
  41. P. G. Saffman, On the stability of laminar flow of a dusty gas, J. Fluid Mech. 13, 120 (1962).
  42. G. I. Sivashinsky, Weak turbulence in periodic flows, Physica D 17, 243 (1985).
  43. H. Garg, E. Calzavarini, G. Mompean, and S. Berti, Particle-laden two-dimensional elastic turbulence, Eur. Phys. J. E 41, 115 (2018).
  44. S. Musacchio and G. Boffetta, Turbulent channel without boundaries: The periodic Kolmogorov flow, Phys. Rev. E 89, 023004 (2014).
  45. G. Boffetta, A. Celani, and A. Mazzino, Drag reduction in the turbulent Kolmogorov flow, Phys. Rev. E 71, 036307 (2005).
  46. E. L. C. Vim. Plan, S. Musacchio, and D. Vincenzi, Emergence of chaos in a viscous solution of rods, Phys. Rev. E 96, 053108 (2017).
  47. S. Olivieri, A. Akoush, L. Brandt, M. E. Rosti, and A. Mazzino, Turbulence in a network of rigid fibers, Phys. Rev. Fluids 5, 074502 (2020).
  48. D. G. E. Grigoriadis and B. J. Geurts, Reduced turbophoresis in two-way coupled particle-laden flows, in Direct and Large-Eddy Simulation VIII (Springer, Berlin, 2011), p. 207.
  49. A. N. Youdin and J. Goodman, Streaming instabilities in protoplanetary disks, Astrophys. J. 620, 459 (2005).
  50. D. Carrera, U. Gorti, A. Johansen, and M. B. Davies, Planetesimal formation by the streaming instability in a photoevaporating disk, Astrophys. J. 839, 16 (2017).
  51. S. Elghobashi, On predicting particle-laden turbulent flows, Appl. Sci. Res. 52, 309 (1994).
  52. J. Bec, L. Biferale, M. Cencini, A. Lanotte, and F. Toschi, Intermittency in the velocity distribution of heavy particles in turbulence, J. Fluid Mech. 646, 527 (2010).
  53. M. Wilkinson and B. Mehlig, Caustics in turbulent aerosols, Europhys. Lett. 71, 186 (2005).
  54. G. Falkovich, A. Fouxon, and M. G. Stepanov, Acceleration of rain initiation by cloud turbulence, Nature (London) 419, 151 (2002).
  55. M. Wilkinson, B. Mehlig, and V. Bezuglyy, Caustic Activation of Rain Showers, Phys. Rev. Lett. 97, 048501 (2006).
  56. G. Boffetta, A. Celani, F. De Lillo, and S. Musacchio, The Eulerian description of dilute collisionless suspension, Europhys. Lett. 78, 14001 (2007).
  57. L. D. Meshalkin and Ia. G. Sinai, Investigation of the stability of a stationary solution of a system of equations for the plane movement of an incompressible viscous liquid, J. Appl. Math. Mech. 25, 1700 (1961).
  58. Y. Chou and Y-C. Shao, Numerical study of particle-induced Rayleigh-Taylor instability: Effects of particle settling and entrainment, Phys. Fluids 28, 043302 (2016).
  59. U. Frisch, S. Kurien, R. Pandit, W. Pauls, S. S. Ray, A. Wirth, and J.-Z. Zhu, Hyperviscosity, Galerkin Truncation, and Bottlenecks in Turbulence, Phys. Rev. Lett. 101, 144501 (2008).

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Phys. Rev. Fluids 5, 094302– Published 17 September, 2020
  • Received 16 June 2020
  • Accepted 2 September 2020
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