Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-25T13:57:11.106Z Has data issue: false hasContentIssue false
  • English
  • Français

On the dynamics of unconfined and confined vortex rings in dense suspensions

Published online by Cambridge University Press:  03 September 2020

Kai Zhang Open the ORCID record for Kai Zhang [Opens in a new window]  and
David E. Rival
Kai Zhang*
Affiliation:
Department of Mechanical and Materials Engineering, Queen's University, Kingston, ONK7L 3N6, Canada
David E. Rival
Affiliation:
Department of Mechanical and Materials Engineering, Queen's University, Kingston, ONK7L 3N6, Canada
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

An experimental study of particle–vortex interactions has been undertaken in suspensions with volume fractions up to $\Phi =20\,\%$. Time-resolved particle image velocimetry measurements using a refractive index matching technique were performed to characterize the formation and evolution of vortex rings in both unconfined and confined configurations. It is shown that vortex rings in dense suspensions are more diffuse, which results in larger vortex cores and lower maximum vorticity. Furthermore, these vortex rings remain stable during their evolution, whereby the primary vortex breakdown and the formation of secondary vortices are inhibited. Although similar to vortex rings generated at lower Reynolds numbers in pure water, further results demonstrate that the vortex-ring circulation and non-dimensional vortex-core radius in dense suspensions remain higher than those in pure water at the same equivalent Reynolds number. Thus, the modification of vortex-ring behaviour in dense suspensions cannot be described solely through a variation in the effective viscosity. Finally, unlike in pure water, the confinement does not impact the non-dimensional vortex-core radius, vortex-ring circulation and maximum vorticity in dense suspensions. This unusual result demonstrates that the dynamics of vortex rings in dense suspensions are strongly insensitive to the effect of confinement.

JFM classification

Vortex Flows: Vortex dynamics Multiphase and Particle-laden Flows: Particle/fluid flow Complex Fluids: Suspensions
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 902 , 10 November 2020 , A6
Check for updates
Copyright
© The Author(s), 2020. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Auerbach, D. 1987 Experiments on the trajectory and circulation of the starting vortex. J. Fluid Mech. 183, 185–198.CrossRefGoogle Scholar
Bagnold, R. A. 1954 Experiments on a gravity-free dispersion of large solid spheres in a Newtonian fluid under shear. Proc. R. Soc. Lond. A 225 (1160), 49–63.Google Scholar
Baker, L. J. & Coletti, F. 2019 Experimental study of negatively buoyant finite-size particles in a turbulent boundary layer up to dense regimes. J. Fluid Mech. 866, 598–629.CrossRefGoogle Scholar
Chang, C. & Powell, R. L. 1994 Effect of particle size distributions on the rheology of concentrated bimodal suspensions. J. Rheol. 38 (1), 85–98.CrossRefGoogle Scholar
Costa, P., Picano, F., Brandt, L. & Breugem, W. P. 2016 Universal scaling laws for dense particle suspensions in turbulent wall-bounded flows. Phys. Rev. Lett. 117 (13), 134501.CrossRefGoogle ScholarPubMed
Dabiri, J. O. 2009 Optimal vortex formation as a unifying principle in biological propulsion. Annu. Rev. Fluid Mech. 41, 17–33.CrossRefGoogle Scholar
Danaila, I. & Helie, J. 2008 Numerical simulation of the postformation evolution of a laminar vortex ring. Phys. Fluids 20 (7), 073602.CrossRefGoogle Scholar
Danaila, I., Luddens, F., Kaplanski, F., Papoutsakis, A. & Sazhin, S. S. 2018 Formation number of confined vortex rings. Phys. Rev. Fluids 3 (9), 094701.CrossRefGoogle Scholar
Gharib, M., Rambod, E. & Shariff, K. 1998 A universal time scale for vortex ring formation. J. Fluid Mech. 360, 121–140.CrossRefGoogle Scholar
Gillies, R. G. & Shook, C. A. 2000 Modelling high concentration settling slurry flows. Can. J. Chem. Engng 78 (4), 709–716.CrossRefGoogle Scholar
Guazzelli, E. & Pouliquen, O. 2018 Rheology of dense granular suspensions. J. Fluid Mech. 852, P1.CrossRefGoogle Scholar
Joseph, G. G., Zenit, R., Hunt, M. L. & Rosenwinkel, A. M. 2001 Particle–wall collisions in a viscous fluid. J. Fluid Mech. 433, 329–346.CrossRefGoogle Scholar
Kaplanski, F., Fukumoto, Y. & Rudi, Y. 2012 Reynolds-number effect on vortex ring evolution in a viscous fluid. Phys. Fluids 24 (3), 033101.CrossRefGoogle Scholar
Kheradvar, A. & Gharib, M. 2009 On mitral valve dynamics and its connection to early diastolic flow. Ann. Biomed. Engng 37 (1), 1–13.CrossRefGoogle ScholarPubMed
Krueger, P. S. & Gharib, M. 2003 The significance of vortex ring formation to the impulse and thrust of a starting jet. Phys. Fluids 15 (5), 1271–1281.CrossRefGoogle Scholar
Kulkarni, P. M. & Morris, J. F. 2008 Suspension properties at finite reynolds number from simulated shear flow. Phys. Fluids 20 (4), 040602.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
Linares-Guerrero, E., Hunt, M. L. & Zenit, R. 2017 Effects of inertia and turbulence on rheological measurements of neutrally buoyant suspensions. J. Fluid Mech. 811, 525–543.CrossRefGoogle Scholar
Linden, P. F. & Turner, J. S. 2001 The formation of ‘optimal’ vortex rings, and the efficiency of propulsion devices. J. Fluid Mech. 427, 61–72.CrossRefGoogle Scholar
Mohseni, K., Ran, H. & Colonius, T. 2001 Numerical experiments on vortex ring formation. J. Fluid Mech. 430, 267–282.CrossRefGoogle Scholar
Norbury, J. 1973 A family of steady vortex rings. J. Fluid Mech. 57 (3), 417–431.CrossRefGoogle Scholar
Palacios-Morales, C. & Zenit, R. 2013 Vortex ring formation for low Re numbers. Acta Mech. 224 (2), 383–397.CrossRefGoogle Scholar
Picano, F., Breugem, W. P. & Brandt, L. 2015 Turbulent channel flow of dense suspensions of neutrally buoyant spheres. J. Fluid Mech. 764, 463–487.CrossRefGoogle Scholar
Picano, F., Breugem, W. P., Mitra, D. & Brandt, L. 2013 Shear thickening in non-Brownian suspensions: an excluded volume effect. Phys. Rev. Lett. 111 (9), 098302.CrossRefGoogle Scholar
Pierrakos, O. & Vlachos, P. P. 2006 The effect of vortex formation on left ventricular filling and mitral valve efficiency. Trans. ASME: J. Biomech. Engng 128 (4), 527–539.Google ScholarPubMed
Raffel, M., Willert, C. E., Scarano, F., Kähler, C. J., Wereley, S. T. & Kompenhans, J. 2018 Particle Image Velocimetry: A Practical Guide. Springer.CrossRefGoogle Scholar
Rahmani, M., Hammouti, A. & Wachs, A. 2018 Momentum balance and stresses in a suspension of spherical particles in a plane Couette flow. Phys. Fluids 30 (4), 043301.CrossRefGoogle Scholar
Stewart, K. C., Niebel, C. L., Jung, S. & Vlachos, P. P. 2012 The decay of confined vortex rings. Exp. Fluids 53 (1), 163–171.CrossRefGoogle Scholar
Stewart, K. C. & Vlachos, P. P. 2012 Vortex rings in radially confined domains. Exp. Fluids 53 (4), 1033–1044.CrossRefGoogle Scholar
Stickel, J. J. & Powell, R. L. 2005 Fluid mechanics and rheology of dense suspensions. Annu. Rev. Fluid Mech. 37, 129–149.CrossRefGoogle Scholar
Tinaikar, A., Advaith, S. & Basu, S. 2018 Understanding evolution of vortex rings in viscous fluids. J. Fluid Mech. 836, 873–909.CrossRefGoogle Scholar
Töger, J., Kanski, M., Carlsson, M., Kovács, S. J., Söderlind, G., Arheden, H. & Heiberg, E. 2012 Vortex ring formation in the left ventricle of the heart: analysis by 4D flow MRI and Lagrangian coherent structures. Ann. Biomed. Engng 40 (12), 2652–2662.CrossRefGoogle ScholarPubMed
Vlachopoulos, C., O'Rourke, M. & Nichols, W. W. 2011 McDonald's Blood Flow in Arteries: Theoretical, Experimental and Clinical Principles. CRC.CrossRefGoogle Scholar
Weigand, A. & Gharib, M. 1997 On the evolution of laminar vortex rings. Exp. Fluids 22 (6), 447–457.CrossRefGoogle Scholar
Zade, S., Costa, P., Fornari, W., Lundell, F. & Brandt, L. 2018 Experimental investigation of turbulent suspensions of spherical particles in a square duct. J. Fluid Mech. 857, 748–783.CrossRefGoogle Scholar
Zhang, K., Jeronimo, M. D. & Rival, D. E. 2019 Lagrangian method to simultaneously characterize transport behaviour of liquid and solid phases: a feasibility study in a confined vortex ring. Exp. Fluids 60 (11), 160.CrossRefGoogle Scholar
Zhang, K. & Rival, D. E. 2018 Experimental study of turbulence decay in dense suspensions using index-matched hydrogel particles. Phys. Fluids 30 (7), 073301.CrossRefGoogle Scholar
Zhou, J., Adrian, R. J., Balachandar, S. & Kendall, T. M. 1999 Mechanisms for generating coherent packets of hairpin vortices in channel flow. J. Fluid Mech. 387, 353–396.CrossRefGoogle Scholar