Hostname: page-component-848d4c4894-8kt4b Total loading time: 0 Render date: 2024-06-28T08:52:20.377Z Has data issue: false hasContentIssue false
  • English
  • Français

A scaling law for the length of granular jumps down smooth inclines

Published online by Cambridge University Press:  10 October 2023

Andrés Escobar Open the ORCID record for Andrés Escobar [Opens in a new window] ,
François Guillard ,
Itai Einav  and
Thierry Faug Open the ORCID record for Thierry Faug [Opens in a new window]
Andrés Escobar
Affiliation:
Université Grenoble Alpes, CNRS, INRAE, IRD, Grenoble INP‡, IGE, 38000 Grenoble, France School of Civil Engineering, The University of Sydney, Sydney, NSW 2006, Australia
François Guillard
Affiliation:
School of Civil Engineering, The University of Sydney, Sydney, NSW 2006, Australia
Itai Einav
Affiliation:
School of Civil Engineering, The University of Sydney, Sydney, NSW 2006, Australia
Thierry Faug*
Affiliation:
Université Grenoble Alpes, CNRS, INRAE, IRD, Grenoble INP‡, IGE, 38000 Grenoble, France
*
†Email address for correspondence: thierry.faug@inrae.fr
Get access Rights & Permissions [Opens in a new window]

Abstract

Granular jumps commonly develop during granular flows over complex topographies or when hitting retaining structures. While this process has been well-studied for hydraulic flows, in granular flows such jumps remain to be fully explored, given the role of interparticle friction. Predicting the length of granular jumps is a challenging question, relevant to the design of protection dams against avalanches. In this study, we investigate the canonical case of standing jumps formed in granular flows down smooth inclines using extensive numerical simulations based on the discrete element method. We consider both two- and three-dimensional configurations and vary the chute bottom friction to account for the crucial interplay between the sliding along the smooth bottom and the shearing across the granular bulk above. By doing so, we derived a robust scaling law for the jump length that is valid over a wide range of Froude numbers and takes into account the influence of the packing density. The findings have potential implications on a number of situations encountered in industry as well as problems associated with natural hazards.

JFM classification

Granular media: Dry granular material Non-Newtonian Flows: Rheology Waves/Free-surface Flows: Channel flow
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 973 , 25 October 2023 , R1
Check for updates
Copyright
© The Author(s), 2023. 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.)

Footnotes

‡

Institute of Engineering and Management Université Grenoble Alpes.

References

Albaba, A., Lambert, S. & Faug, T. 2018 Dry granular avalanche impact force on a rigid wall: analytic shock solution versus discrete element simulations. Phys. Rev. E 97, 052903.CrossRefGoogle ScholarPubMed
Brodu, N., Richard, P. & Delannay, R. 2013 Shallow granular flows down flat frictional channels: steady flows and longitudinal vortices. Phys. Rev. E 87 (2), 022202.CrossRefGoogle ScholarPubMed
Chanson, H. 2009 Development of the Bélanger equation and backwater equation by Jean-Baptiste Bélanger (1828). J. Hydraul. Engng 135 (3), 159–163.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
GDRMidi 2004 On dense granular flows. Eur. Phys. J. E 14 (4), 341–365.CrossRefGoogle Scholar
Gray, J.M.N.T. & Hutter, K. 1997 Pattern formation in granular avalanches. Contin. Mech. Thermodyn. 9, 341–345.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
Hoover, W.G. & Hoover, C.G. 2006 Smooth-particle phase stability with generalized density-dependent potentials. Phys. Rev. E 73 (1), 016702.CrossRefGoogle ScholarPubMed
Iverson, R.M., George, D.L. & Logan, M. 2016 Debris flow runup on vertical barriers and adverse slopes. J. Geophys. Res. 121 (12), 2333–2357.CrossRefGoogle Scholar
Jaworski, A.J. & Dyakowski, T. 2007 Observations of ‘granular jump’ in the pneumatic conveying system. Exp. Therm. Fluid Sci. 31 (8), 877–885.CrossRefGoogle Scholar
Johannesson, T., Gauer, P., Issler, P. & Lied, K. 2009 The design of avalanche protection dams. Recent practical and theoretical developments. European Commission Directorate-General.Google Scholar
Louge, M.Y. 2003 Model for dense granular flows down bumpy inclines. Phys. Rev. E 67 (6), 061303.CrossRefGoogle ScholarPubMed
Louge, M.Y. & Keast, S.C. 2001 On dense granular flows down flat frictional inclines. Phys. Fluids 13 (5), 1213–1233.CrossRefGoogle Scholar
Méjean, S., Faug, T. & Einav, I. 2017 A general relation for standing normal jumps in both hydraulic and dry granular flows. J. Fluid Mech. 816, 331–351.CrossRefGoogle Scholar
Méjean, S., Guillard, F., Faug, T. & Einav, I. 2020 Length of standing jumps along granular flows down smooth inclines. Phys. Rev. Fluids 5 (3), 034303.CrossRefGoogle Scholar
Méjean, S., Guillard, F., Faug, T. & Einav, I. 2022 X-ray study of fast and slow granular flows with transition jump in between. Granul. Matt. 24 (26), 1–15.CrossRefGoogle Scholar
O'Sullivan, C. & Bray, J.D. 2004 Selecting a suitable time step for discrete element simulations that use the central difference time integration scheme. Engng Comput. 21 (2/3/4), 278–303.CrossRefGoogle Scholar
Pournin, L., Liebling, T.M. & Mocellin, A. 2001 Molecular-dynamics force models for better control of energy dissipation in numerical simulations of dense granular media. Phys. Rev. E 65, 011302.CrossRefGoogle ScholarPubMed
Pudasaini, S.P., Hutter, K., Hsiau, S.-S., Tai, S.-C., Wang, Y. & Katzenbach, R. 2007 Rapid flow of dry granular materials down inclined chutes impinging on rigid walls. Phys. Fluids 19 (5), 053302.CrossRefGoogle Scholar
Samadani, A., Mahadevan, L. & Kudrolli, A. 2002 Shocks in sand flowing in a silo. J. Fluid Mech. 452, 293–301.CrossRefGoogle Scholar
Selesnick, I.W. & Burrus, C.S. 1998 Generalized digital butterworth filter design. IEEE Trans. Signal Process. 46 (6), 1688–1694.CrossRefGoogle Scholar
Smilauer, V., et al. 2021 Yade Documentation, 3rd edn. The Yade Project.Google Scholar
Sovilla, B., Sonatore, I., Bühler, Y. & Margreth, S. 2012 Wet-snow avalanche interaction with a deflecting dam: field observations and numerical simulations in a case study. Nat. Hazards Earth Syst. Sci. 12 (5), 1407–1423.CrossRefGoogle Scholar
Tai, Y.C. & Lin, Y.C. 2008 A focused view of the behavior of granular flows down a confined inclined chute into the horizontal run-out zone. Phys. Fluids 20 (12), 123302.CrossRefGoogle Scholar
Utili, S., Zhao, T. & Houlsby, G.T. 2015 3D DEM investigation of granular column collapse: evaluation of debris motion and its destructive power. Engng Geol. 186, 3–16.CrossRefGoogle Scholar
Viroulet, S., Baker, J.L., Edwards, A.N., Johnson, C.G., Gjaltema, C., Clavel, P. & Gray, J.M.N.T. 2017 Multiple solutions for granular flow over a smooth two-dimensional bump. J. Fluid Mech. 815, 77–116.CrossRefGoogle Scholar
Xiao, H., Hruska, J., Ottino, J.M., Lueptow, R.M. & Umbanhowar, P.B. 2018 Unsteady flows and inhomogeneous packing in damp granular heap flows. Phys. Rev. E 98, 032906.CrossRefGoogle Scholar
Zhu, Y., Delannay, R. & Valance, A. 2020 High-speed confined granular flows down smooth inclines: scaling and wall friction laws. Granul. Matt. 22, 1–12.CrossRefGoogle Scholar
Supplementary material: File

Escobar et al. supplementary material

Escobar et al. supplementary material 1

Download Escobar et al. supplementary material(File)
File 66.3 KB
Supplementary material: File

Escobar et al. supplementary material

Escobar et al. supplementary material 2

Download Escobar et al. supplementary material(File)
File 14.7 KB