Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-17T20:22:46.559Z Has data issue: false hasContentIssue false
  • English
  • Français

Granular surface flow on an asymmetric conical heap

Published online by Cambridge University Press:  18 February 2019

Sandip Mandal  and
D. V. Khakhar Open the ORCID record for D. V. Khakhar [Opens in a new window]
Sandip Mandal
Affiliation:
Department of Chemical Engineering, Indian Institute of Technology Bombay, Mumbai 400076, India
D. V. Khakhar*
Affiliation:
Department of Chemical Engineering, Indian Institute of Technology Bombay, Mumbai 400076, India
*
†Email address for correspondence: khakhar@iitb.ac.in
Get access Rights & Permissions [Opens in a new window]

Abstract

We carry out an experimental study of the granular surface flow of nearly monodisperse glass beads on a conical heap formed on a rough circular disc by a narrow stream of the particles from a hopper, with the pouring point displaced from the centre of the disc. During the growth phase, an axisymmetric heap is formed, which grows either by periodic avalanches or by non-periodic avalanches that occur randomly over the azimuthal location of the heap, depending on the operating conditions and system properties. The dynamics of heap growth is characterized by the variation of the heap height, angle of repose and the angular velocity of the periodic avalanche with time, for different mass flow rates from the hopper. When the base of the heap reaches the edge of the disc closest to the pouring point, the heap stops growing and a steady surface flow of particles is developed on the heap surface, with particles flowing over the edge of the disc into a collection tray. The geometry is a unique example of a granular flow on an erodible bed without any bounding side walls. The corresponding steady state geometry of the asymmetric heap is characterized by means of surface contours and angles of repose. The streamwise and transverse surface velocities are measured using high-speed video photography and image analysis for different mass flow rates. The flowing layer thickness is measured by immersing a coated needle in the flow at different positions on the mid-line of the flow. The surface angle of the flowing layer is found to be significantly smaller than the angle of repose and to be independent of the mass flow rate. The velocity profiles at different streamwise positions for different mass flow rates are found to be geometrically similar and are well described by Gaussian functions. The flowing layer thickness is calculated from a model using the measured surface velocities. The predicted values match the measured values quite well.

JFM classification

Granular media: Granular media
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 865 , 25 April 2019 , pp. 41 - 59
Copyright
© 2019 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

Altshuler, E., Ramos, O., Martínez, E., Batista-Leyva, A. J., Rivera, A. & Bassler, K. E. 2003 Sandpile formation by revolving rivers. Phys. Rev. Lett. 91 (1), 014501.10.1103/PhysRevLett.91.014501Google Scholar
Altshuler, E., Toussaint, R., Martínez, E., Sotolongo-Costa, O., Schmittbuhl, J. & Måløy, K. J. 2008 Revolving rivers in sandpiles: from continuous to intermittent flows. Phys. Rev. E 77 (3), 031305.Google Scholar
Andreotti, B., Claudin, P. & Douady, S. 2002a Selection of dune shapes and velocities part 1. Dynamics of sand, wind and barchans. Eur. Phys. J. B 28 (3), 321–339.10.1140/epjb/e2002-00236-4Google Scholar
Andreotti, B., Claudin, P. & Douady, S. 2002b Selection of dune shapes and velocities part 2. A two-dimensional modelling. Eur. Phys. J. B 28 (3), 341–352.10.1140/epjb/e2002-00237-3Google Scholar
Bouchaud, J. P., Cates, M. E., Prakash, J. R. & Edwards, S. F. 1994 A model for the dynamics of sandpile surfaces. J. Phys. Paris I 4 (10), 1383–1410.Google Scholar
Boutreux, T., Raphaël, E. & de Gennes, P.-G. 1998 Surface flows of granular materials. A modified picture for thick avalanches. Phys. Rev. E 58, 4692–4700.Google Scholar
Campbell, C. S., Cleary, P. W. & Hopkins, M. 1995 Large-scale landslide simulations: global deformation, velocities and basal friction. J. Geophys. Res. 100 (B5), 8267–8283.10.1029/94JB00937Google Scholar
Douady, S., Andreotti, B. & Daerr, A. 1999 On granular surface flow equations. Eur. Phys. J. B 11, 131–142.10.1007/s100510050924Google Scholar
Elbelrhiti, H., Claudin, P. & Andreotti, B. 2005 Field evidence for surface-wave-induced instability of sand dunes. Nature 437 (7059), 720–723.10.1038/nature04058Google Scholar
Fan, Y., Jacob, K. V., Freireich, B. & Lueptow, R. M. 2017 Segregation of granular materials in bounded heap flow: a review. Powder Technol. 312, 67–88.10.1016/j.powtec.2017.02.026Google Scholar
Fan, Y., Umbanhowar, P. B., Ottino, J. M. & Lueptow, R. M. 2013 Kinematics of monodisperse and bidisperse granular flows in quasi-two-dimensional bounded heaps. Proc. R. Soc. Lond. A 469 (2157), 20130235.10.1098/rspa.2013.0235Google Scholar
Forterre, Y. & Pouliquen, O. 2008 Flows of dense granular media. Annu. Rev. Fluid Mech. 40, 1–24.10.1146/annurev.fluid.40.111406.102142Google Scholar
Grasselli, Y. & Herrmann, H. J. 1999 Shapes of heaps and in silos. Eur. Phys. J. B 10 (4), 673–679.10.1007/s100510050899Google Scholar
Hersen, P., Andersen, K. H., Elbelrhiti, H., Andreotti, B., Claudin, P. & Douady, S. 2004 Corridors of barchan dunes: stability and size selection. Phys. Rev. E 69 (1), 011304.Google Scholar
Hersen, P., Douady, S. & Andreotti, B. 2002 Relevant length scale of barchan dunes. Phys. Rev. Lett. 89 (26), 264301.10.1103/PhysRevLett.89.264301Google Scholar
Hutter, K., Koch, T., Pluüss, C. & Savage, S. B. 1995 The dynamics of avalanches of granular materials from initiation to runout. Part ii. Experiments. Acta Mech. 109 (1–4), 127–165.10.1007/BF01176820Google Scholar
Jop, P., Forterre, Y. & Pouliquen, O. 2005 Crucial role of sidewalls in granular surface flows: consequences for the rheology. J. Fluid Mech. 541, 167–192.10.1017/S0022112005005987Google Scholar
Jop, P., Forterre, Y. & Pouliquen, O. 2006 A constitutive law for dense granular flows. Nature 441 (7094), 727–730.10.1038/nature04801Google Scholar
Khakhar, D. V., Orpe, A. V., Andresen, P. & Ottino, J. M. 2001 Surface flow of granular materials: model and experiments in heap formation. J. Fluid Mech. 441, 255–264.10.1017/S0022112001005201Google Scholar
Komatsu, T. S., Inagaki, S., Nakagawa, N. & Nasuno, S. 2001 Creep motion in a granular pile exhibiting steady surface flow. Phys. Rev. Lett. 86 (9), 1757–1760.10.1103/PhysRevLett.86.1757Google Scholar
Kong, X.-Z., Hu, M.-B., Wu, Q.-S. & Wu, Y.-H. 2006 Kinetic energy sandpile model for conical sandpile development by revolving rivers. Phys. Lett. A 348 (3–6), 77–81.10.1016/j.physleta.2005.08.068Google Scholar
Lemieux, P. A. & Durian, D. J. 2000 From avalanches to fluid flow: a continuous picture of grain dynamics down a heap. Phys. Rev. Lett. 85 (20), 4273.10.1103/PhysRevLett.85.4273Google Scholar
Mandal, S. & Khakhar, D. V. 2017 An experimental study of dense granular flow of non-spherical grains in a rotating cylinder. AIChE J. 63 (10), 4307–4315.10.1002/aic.15772Google Scholar
Martínez, E., González-Lezcano, A., Batista-Leyva, A. J. & Altshuler, E. 2016 Exponential velocity profile of granular flows down a confined heap. Phys. Rev. E 93 (6), 062906.Google Scholar
Midi, GDR. 2004 On dense granular flows. Eur. Phys. J. E 14, 341–365.Google Scholar
Orpe, A. V. & Khakhar, D. V. 2001 Scaling relations for granular flow in quasi-two-dimensional rotating cylinders. Phys. Rev. E 64, 031302.Google Scholar
Orpe, A. V. & Khakhar, D. V. 2007 Rheology of surface granular flows. J. Fluid Mech. 571, 1–32.10.1017/S002211200600320XGoogle Scholar
Perry, R. H. & Green, D. W. 1997 Perry’s Chemical Engineers’ Handbook, vol. 7. McGraw-hill.Google Scholar
Reffet, E., Du Pont, S. C., Hersen, P. & Douady, S. 2010 Formation and stability of transverse and longitudinal sand dunes. Geology 38 (6), 491–494.10.1130/G30894.1Google Scholar
de Ryck, A., Zhu, H. P., Wu, S. M., Yu, A. B. & Zulli, P. 2010 Numerical and theoretical investigation of the surface flows of granular materials on heaps. Powder Technol. 203 (2), 125–132.10.1016/j.powtec.2010.04.034Google Scholar
Savage, S. B. & Hutter, K. 1991 The dynamics of avalanches of granular materials from initiation to runout. Part i. Analysis. Acta Mech. 86 (1), 201–223.10.1007/BF01175958Google Scholar
Taberlet, N., Richard, P., Valance, A., Losert, W., Pasini, J. M., Jenkins, J. T. & Delannay, R. 2003 Superstable granular heap in a thin channel. Phys. Rev. Lett. 91 (26), 264301.10.1103/PhysRevLett.91.264301Google Scholar