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Shock–shock interactions in granular flows

Published online by Cambridge University Press:  17 December 2019

Aqib Khan ,
Shivam Verma Open the ORCID record for Shivam Verma [Opens in a new window] ,
Priyanka Hankare ,
Rakesh Kumar  and
Sanjay Kumar Open the ORCID record for Sanjay Kumar [Opens in a new window]
Aqib Khan
Affiliation:
Department of Aerospace Engineering, Indian Institute of Technology Kanpur, Kanpur, Uttar Pradesh - 208016, India
Shivam Verma
Affiliation:
Department of Aerospace Engineering, Indian Institute of Technology Kanpur, Kanpur, Uttar Pradesh - 208016, India
Priyanka Hankare
Affiliation:
Department of Aerospace Engineering, Indian Institute of Technology Kanpur, Kanpur, Uttar Pradesh - 208016, India
Rakesh Kumar
Affiliation:
Department of Aerospace Engineering, Indian Institute of Technology Kanpur, Kanpur, Uttar Pradesh - 208016, India
Sanjay Kumar*
Affiliation:
Department of Aerospace Engineering, Indian Institute of Technology Kanpur, Kanpur, Uttar Pradesh - 208016, India
*
†Email address for correspondence: [email protected]
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Abstract

Shock–shock interaction structures and a newly discovered dynamic instability in granular streams resulting from such interactions are presented. Shock waves are generated by placing two similar triangular wedges in a gravity-driven granular stream. When the shock waves interact, grains collapse near the centre region of the wedges and a slow-moving concentrated diamond-shaped streak of grains is formed that grows as the inclination of the channel is increased. The diamond streak, under certain geometric conditions, is found to become unstable and start oscillating in the direction transverse to the mainstream. When the wedges are placed too close to each other, the granular flux of the incoming stream is unable to pass through the small gap, resulting in the formation of a single bow shock enveloping both the wedges. Experiments are performed for a wide range of flow speeds, wedge angles and wedge separations to investigate the interaction zone. We discuss a possible mechanism for the formation of the central streak and the associated dynamic instability observed for specific physical parameters.

JFM classification

Granular media: Granular media Compressible Flows: Shock waves
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 884 , 10 February 2020 , R4
Copyright
© 2019 Cambridge University Press

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References

Amarouchene, Y., Boudet, J. F. & Kellay, H. 2001 Dynamic sand dunes. Phys. Rev. Lett. 86 (19), 4286–4289.CrossRefGoogle ScholarPubMed
Amarouchene, Y. & Kellay, H. 2006 Speed of sound from shock fronts in granular flows. Phys. Fluids 18 (3), 031707.CrossRefGoogle Scholar
Aranson, I. S. & Tsimring, L. S. 2006 Patterns and collective behavior in granular media: theoretical concepts. Rev. Mod. Phys. 78 (2), 641–692.CrossRefGoogle Scholar
Boudet, J.-F., Amarouchene, Y. & Kellay, H. 2008 Shock front width and structure in supersonic granular flows. Phys. Rev. Lett. 101 (25), 254503.CrossRefGoogle ScholarPubMed
Brennen, C. E., Sieck, K. & Paslaski, J. 1983 Hydraulic jumps in granular material flow. Powder Technol. 35 (1), 31–37.CrossRefGoogle Scholar
Brey, J. J., Cubero, D. & Ruiz-Montero, M. J. 1999 High energy tail in the velocity distribution of a granular gas. Phys. Rev. E 59 (1), 1256–1258.Google Scholar
Buchholtz, V. & Pöschel, T. 1998 Interaction of a granular stream with an obstacle. Granul. Matt. 1 (1), 33–41.CrossRefGoogle Scholar
Cui, X. & Gray, J. M. N. T. 2013 Gravity-driven granular free-surface flow around a circular cylinder. J. Fluid Mech. 720, 314–337.CrossRefGoogle Scholar
Delannay, R., Valance, A., Mangeney, A., Roche, O. & Richard, P. 2017 Granular and particle-laden flows: from laboratory experiments to field observations. J. Phys. D: Appl. Phys. 50 (5), 053001.CrossRefGoogle Scholar
Faug, T., Childs, P., Wyburn, E. & Einav, I. 2015 Standing jumps in shallow granular flows down smooth inclines. Phys. Fluids 27 (7), 073304.CrossRefGoogle Scholar
Forterre, Y. & Pouliquen, O. 2001 Longitudinal vortices in granular flows. Phys. Rev. Lett. 86 (26), 5886–5889.CrossRefGoogle ScholarPubMed
Forterre, Y. & Pouliquen, O. 2003 Long-surface-wave instability in dense granular flows. J. Fluid Mech. 486, 21–50.CrossRefGoogle Scholar
Garai, P., Verma, S. & Kumar, S. 2019 Visualization of shocks in granular media. J. Vis. 22 (4), 729–739.CrossRefGoogle Scholar
Goldhirsch, I. 2003 Rapid granular flows. Annu. Rev. Fluid Mech. 35 (1), 267–293.CrossRefGoogle Scholar
Goldshtein, A., Shapiro, M., Moldavsky, L. & Fichman, M. 1995 Mechanics of collisional motion of granular materials. Part 2. Wave propagation through vibrofluidized granular layers. J. Fluid Mech. 287, 349–382.CrossRefGoogle Scholar
Gray, J. M. N. T. & Cui, X. 2007 Weak, strong and detached oblique shocks in gravity-driven granular free-surface flows. J. Fluid Mech. 579, 113–136.CrossRefGoogle Scholar
Gray, J. M. N. T., Tai, Y.-C. & Noelle, S. 2003 Shock waves, dead zones and particle-free regions in rapid granular free-surface flows. J. Fluid Mech. 491, 161–181.CrossRefGoogle Scholar
Gray, J. M. N. T. 2018 Particle segregation in dense granular flows. Annu. Rev. Fluid Mech. 50, 407–433.CrossRefGoogle Scholar
Heil, P., Rericha, E. C., Goldman, D. I. & Swinney, H. L. 2004 Mach cone in a shallow granular fluid. Phys. Rev. E 70 (6), 060301.Google Scholar
Jaeger, H. M., Nagel, S. R. & Behringer, R. P. 1996 Granular solids, liquids, and gases. Rev. Mod. Phys. 68 (4), 1259–1273.CrossRefGoogle Scholar
Johnson, C. G. & Gray, J. M. N. T. 2011 Granular jets and hydraulic jumps on an inclined plane. J. Fluid Mech. 675, 87–116.CrossRefGoogle Scholar
Ottino, J. M. & Khakhar, D. V. 2000 Mixing and segregation of granular materials. Annu. Rev. Fluid Mech. 32 (1), 55–91.CrossRefGoogle Scholar
Padgett, D. A., Mazzoleni, A. P. & Faw, S. D. 2015 Survey of shock-wave structures of smooth-particle granular flows. Phys. Rev. E 92 (6), 062209.Google ScholarPubMed
Pouliquen, O., Delour, J. & Savage, S. B. 1997 Fingering in granular flows. Nature 386 (6627), 816–817.CrossRefGoogle Scholar
Pudasaini, S. P. & Kröner, C. 2008 Shock waves in rapid flows of dense granular materials: Theoretical predictions and experimental results. Phys. Rev. E 78 (4), 041308.Google ScholarPubMed
Rericha, E. C., Bizon, C., Shattuck, M. D. & Swinney, H. L. 2001 Shocks in supersonic sand. Phys. Rev. Lett. 88 (1), 014302.CrossRefGoogle ScholarPubMed
Savage, S. B. 1992 Instability of unbounded uniform granular shear flow. J. Fluid Mech. 241, 109–123.CrossRefGoogle Scholar
Savage, S. B. 1984 The mechanics of rapid granular flows. In Advances in Applied Mechanics, vol. 24, pp. 289–366. Elsevier.Google Scholar
Umbanhowar, P. B., Melo, F. & Swinney, H. L. 1996 Localized excitations in a vertically vibrated granular layer. Nature 382 (6594), 793–796.CrossRefGoogle Scholar
Vilquin, A., Boudet, J. F. & Kellay, H. 2016 Structure of velocity distributions in shock waves in granular gases with extension to molecular gases. Phys. Rev. E 94 (2), 022905.Google ScholarPubMed
Viroulet, S., Baker, J. L., Rocha, F. M., Johnson, C. G., Kokelaar, B. P. & Gray, J. M. N. T. 2018 The kinematics of bidisperse granular roll waves. J. Fluid Mech. 848, 836–875.CrossRefGoogle Scholar
Vreman, A. W., Al-Tarazi, M., Kuipers, J. A. M., Annaland, M. V. S. & Bokhove, O. 2007 Supercritical shallow granular flow through a contraction: experiment, theory and simulation. J. Fluid Mech. 578, 233–269.CrossRefGoogle Scholar

Khan et al. supplementary movie 1

Shock-shock interactions for Wedge angle = 60 degrees, Wedge spacing = 1d and channel inclination = 55 degrees at frame rate = 60 fps.

Download Khan et al. supplementary movie 1(Video)
Video 11.1 MB

Khan et al. supplementary movie 2

Shock-shock interactions for Wedge angle = 60 degrees, Wedge spacing = 1d and channel inclination = 60 degrees at frame rate = 60 fps.

Download Khan et al. supplementary movie 2(Video)
Video 11.8 MB

Khan et al. supplementary movie 3

Shock-shock interactions for Wedge angle = 60 degrees, Wedge spacing = 1d and channel inclination = 60 degrees at frame rate = 6 fps (slow motion).

Download Khan et al. supplementary movie 3(Video)
Video 4.2 MB

Khan et al. supplementary movie 4

Shock-shock interactions for Wedge angle = 60 degrees, Wedge spacing = 1d and channel inclination = 75 degrees at frame rate = 60 fps.

Download Khan et al. supplementary movie 4(Video)
Video 12.7 MB