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Inertial effects in dusty Rayleigh–Taylor turbulence

Published online by Cambridge University Press:  07 September 2021

Marta Magnani Open the ORCID record for Marta Magnani [Opens in a new window] ,
Stefano Musacchio  and
Guido Boffetta
Marta Magnani*
Affiliation:
Dipartimento di Fisica and INFN, Università di Torino, Via P. Giuria 1, 10125Torino, Italy Istituto di Geoscienze e Georisorse, CNR, Via Valperga Caluso 35, 10125Torino, Italy
Stefano Musacchio
Affiliation:
Dipartimento di Fisica and INFN, Università di Torino, Via P. Giuria 1, 10125Torino, Italy
Guido Boffetta
Affiliation:
Dipartimento di Fisica and INFN, Università di Torino, Via P. Giuria 1, 10125Torino, Italy
*
†Email address for correspondence: [email protected]
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Abstract

We investigate the dynamics of a dilute suspension of small, heavy particles superposed on a reservoir of still, pure fluid. The study is performed by means of numerical simulations of the Saffman model for a dilute particle suspension (Saffman, J. Fluid Mech., vol. 13, issue 1, 1962, pp. 120–128). In the presence of gravity forces, the interface between the two phases is unstable and evolves in a turbulent mixing layer which broadens in time. In the case of negligible particle inertia, the particle-laden phase behaves as a denser fluid, and the dynamics of the system recovers to that of the incompressible Rayleigh–Taylor set-up. Conversely, particles with large inertia affect the evolution of turbulent flow, delaying the development of turbulent mixing and breaking the up–down symmetry within the mixing layer. The inertial dynamics also leads to particle clustering, characterised by regions with higher particle density than the initial uniform density, and by the increase of the local Atwood number.

JFM classification

Mixing: Turbulent mixing Multiphase and Particle-laden Flows: Particle/fluid flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 926 , 10 November 2021 , A23
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

Agrawal, N., Choueiri, G.H. & Hof, B. 2019 Transition to turbulence in particle laden flows. Phys. Rev. Lett. 122 (11), 114502.CrossRefGoogle ScholarPubMed
Ardekani, M.N., Costa, P., Breugem, W.-P., Picano, F. & Brandt, L. 2017 Drag reduction in turbulent channel flow laden with finite-size oblate spheroids. J. Fluid Mech. 816, 43–70.CrossRefGoogle Scholar
Balachandar, S. & Eaton, J.K. 2010 Turbulent dispersed multiphase flow. Annu. Rev. Fluid Mech. 42, 111–133.CrossRefGoogle Scholar
Balmforth, N.J. & Provenzale, A. 2001 Geomorphological Fluid Mechanics, vol. 582. Springer Science & Business Media.CrossRefGoogle Scholar
Bec, J., Biferale, L., Cencini, M., Lanotte, A., Musacchio, S. & Toschi, F. 2007 Heavy particle concentration in turbulence at dissipative and inertial scales. Phys. Rev. Lett. 98 (8), 084502.CrossRefGoogle ScholarPubMed
Bec, J., Biferale, L., Cencini, M., Lanotte, A. & Toschi, F. 2010 Intermittency in the velocity distribution of heavy particles in turbulence. J. Fluid Mech. 646, 527–536.CrossRefGoogle Scholar
Bercovici, D. & Michaut, C. 2010 Two-phase dynamics of volcanic eruptions: compaction, compression and the conditions for choking. Geophys. J. Intl 182 (2), 843–864.CrossRefGoogle Scholar
Boffetta, G., Celani, A., De Lillo, F. & Musacchio, S. 2007 The Eulerian description of dilute collisionless suspension. Europhys. Lett. 78 (1), 14001.CrossRefGoogle Scholar
Boffetta, G., De Lillo, F. & Musacchio, S. 2010 Nonlinear diffusion model for Rayleigh–Taylor mixing. Phys. Rev. Lett. 104 (3), 034505.CrossRefGoogle ScholarPubMed
Boffetta, G. & Mazzino, A. 2017 Incompressible Rayleigh–Taylor turbulence. Annu. Rev. Fluid Mech. 49, 119–143.CrossRefGoogle Scholar
Burns, P. & Meiburg, E. 2015 Sediment-laden fresh water above salt water: nonlinear simulations. J. Fluid Mech. 762, 156–195.CrossRefGoogle Scholar
Celani, A., Mazzino, A., Muratore-Ginanneschi, P. & Vozella, L. 2009 Phase-field model for the Rayleigh–Taylor instability of immiscible fluids. J. Fluid Mech. 622, 115–134.CrossRefGoogle Scholar
Chou, Y. & Shao, Y.-C. 2016 Numerical study of particle-induced Rayleigh–Taylor instability: effects of particle settling and entrainment. Phys. Fluids 28 (4), 043302.CrossRefGoogle Scholar
Falkovich, G., Fouxon, A. & Stepanov, M.G. 2002 Acceleration of rain initiation by cloud turbulence. Nature 419 (6903), 151–154.CrossRefGoogle ScholarPubMed
Fu, W., Li, H., Lubow, S., Li, S. & Liang, E. 2014 Effects of dust feedback on vortices in protoplanetary disks. Astrophys. J. Lett. 795 (2), L39.CrossRefGoogle Scholar
Gualtieri, P., Picano, F., Sardina, G. & Casciola, C.M. 2015 Exact regularized point particle method for multiphase flows in the two-way coupling regime. J. Fluid Mech. 773, 520–561.CrossRefGoogle Scholar
Guazzelli, E. & Morris, J.F. 2011 A Physical Introduction to Suspension Dynamics, vol. 45. Cambridge University Press.CrossRefGoogle Scholar
Homann, H., Guillot, T., Bec, J., Ormel, C.W., Ida, S. & Tanga, P. 2016 Effect of turbulence on collisions of dust particles with planetesimals in protoplanetary disks. Astron. Astrophys. 589, A129.CrossRefGoogle Scholar
Kasbaoui, M.H. 2019 Turbulence modulation by settling inertial aerosols in Eulerian–Eulerian and Eulerian–Lagrangian simulations of homogeneously sheared turbulence. Phys. Rev. Fluids 4 (12), 124308.CrossRefGoogle Scholar
Kull, H.-J. 1991 Theory of the Rayleigh–Taylor instability. Phys. Rep. 206 (5), 197–325.CrossRefGoogle Scholar
Lashgari, I., Picano, F., Breugem, W.-P. & Brandt, L. 2014 Laminar, turbulent, and inertial shear-thickening regimes in channel flow of neutrally buoyant particle suspensions. Phys. Rev. Lett. 113 (25), 254502.CrossRefGoogle ScholarPubMed
Matas, J.P., Morris, J.F. & Guazzelli, E. 2003 Transition to turbulence in particulate pipe flow. Phys. Rev. Lett. 90 (1), 014501.CrossRefGoogle ScholarPubMed
Mathai, V., Lohse, D. & Sun, C. 2020 Bubbly and buoyant particle–laden turbulent flows. Annu. Rev. Condens. Matter Phys. 11 (1), 529–559.CrossRefGoogle Scholar
Maxey, M.R. 1987 The motion of small spherical particles in a cellular flow field. Phys. Fluids 30 (7), 1915.CrossRefGoogle Scholar
Muramulla, P., Tyagi, A., Goswami, P.S. & Kumaran, V. 2020 Disruption of turbulence due to particle loading in a dilute gas–particle suspension. J. Fluid Mech. 889, A28.CrossRefGoogle Scholar
Nasab, S. & Garaud, P. 2020 Preferential concentration in the particle-induced convective instability. Phys. Rev. Fluids 5 (11), 114308.CrossRefGoogle Scholar
Necker, F., Härtel, C., Kleiser, L. & Meiburg, E. 2005 Mixing and dissipation in particle-driven gravity currents. J. Fluid Mech. 545, 339–372.CrossRefGoogle Scholar
Pan, T.-W., Joseph, D.D. & Glowinski, R. 2001 Modelling Rayleigh–Taylor instability of a sedimenting suspension of several thousand circular particles in a direct numerical simulation. J. Fluid Mech. 434, 23–37.CrossRefGoogle Scholar
Saffman, P.G. 1962 On the stability of laminar flow of a dusty gas. J. Fluid Mech. 13 (1), 120–128.CrossRefGoogle Scholar
Shaw, R.A. 2003 Particle-turbulence interactions in atmospheric clouds. Annu. Rev. Fluid Mech. 35 (1), 183–227.CrossRefGoogle Scholar
Sozza, A., Cencini, M., Musacchio, S. & Boffetta, G. 2020 Drag enhancement in a dusty Kolmogorov flow. Phys. Rev. Fluids 5, 094302.CrossRefGoogle Scholar
Völtz, C., Pesch, W. & Rehberg, I. 2001 Rayleigh–Taylor instability in a sedimenting suspension. Phys. Rev. E 65 (1), 011404.CrossRefGoogle Scholar
Wilkinson, M. & Mehlig, B. 2005 Caustics in turbulent aerosols. Europhys. Lett. 71 (2), 186–192.CrossRefGoogle Scholar
Youdin, A.N. & Goodman, J. 2005 Streaming instabilities in protoplanetary disks. Astrophys. J. 620 (1), 459.CrossRefGoogle Scholar
Yu, X., Hsu, T.-J. & Balachandar, S. 2014 Convective instability in sedimentation: 3-D numerical study. J. Geophys. Res.: Oceans 119 (11), 8141–8161.CrossRefGoogle Scholar
Zhao, L.H., Andersson, H.I. & Gillissen, J.J.J. 2010 Turbulence modulation and drag reduction by spherical particles. Phys. Fluids 22 (8), 081702.CrossRefGoogle Scholar