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Computational study of granular shear flows of dry flexible fibres using the discrete element method

Published online by Cambridge University Press:  16 June 2015

Y. Guo ,
C. Wassgren ,
B. Hancock ,
W. Ketterhagen  and
J. Curtis
Y. Guo*
Affiliation:
Chemical Engineering Department, University of Florida, Gainesville, FL 32611, USA
C. Wassgren
Affiliation:
School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907, USA
B. Hancock
Affiliation:
Pfizer, Inc., Groton, CT 06340, USA
W. Ketterhagen
Affiliation:
Pfizer, Inc., Groton, CT 06340, USA
J. Curtis
Affiliation:
Chemical Engineering Department, University of Florida, Gainesville, FL 32611, USA
*
†Email address for correspondence: guoyu03@gmail.com
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Abstract

In this study, shear flows of dry flexible fibres are numerically modelled using the discrete element method (DEM), and the effects of fibre properties on the flow behaviour and solid-phase stresses are explored. In the DEM simulations, a fibre is formed by connecting a number of spheres in a straight line using deformable and elastic bonds. The forces and moments induced by the bond deformation resist the relative normal, tangential, bending and torsional movements between two bonded spheres. The bond or deforming stiffness determines the flexibility of the fibres and the bond damping accounts for the energy dissipation in the fibre vibration. The simulation results show that elastically bonded fibres have smaller effective coefficients of restitution than rigidly connected fibres. Thus, smaller solid-phase stresses are obtained for flexible fibres, particularly with bond damping, compared with rigid fibres. Frictionless fibres tend to align with a small angle from the flow direction as the solid volume fraction increases, and fibre deformation is minimized due to the alignment. However, jamming, with a corresponding sharp stress increase, large fibre deformation and dense contact force network, occurs for fibres with friction at high solid volume fractions. It is also found that jamming is more prevalent in dense flows with larger fibre friction coefficient, rougher surface, larger stiffness and larger aspect ratio.

JFM classification

Complex Fluids: Complex Fluids Granular media: Granular media
Type
Papers
Information
Journal of Fluid Mechanics , Volume 775 , 25 July 2015 , pp. 24 - 52
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Copyright
© 2015 Cambridge University Press 

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References

Acevedo, M., Zuriguel, I., Maza, D., Pagonabarraga, I., Alonso-Marroquin, F. & Hidalgo, R. C. 2014 Stress transmission in systems of faceted particles in a silo: the roles of filling rate and particle aspect ratio. Granul. Matt. 16, 411–420.Google Scholar
Azéma, E. & Radjaï, F. 2010 Stress–strain behavior and geometrical properties of packings of elongated particles. Phys. Rev. E 81, 051304.Google Scholar
Babic, M. 1997 Average balance equations for granular materials. Intl J. Engng Sci. 35 (5), 523–548.Google Scholar
Börzsönyi, T., Szabó, B., Törös, G., Wegner, S., Török, J., Somfai, E., Bien, T. & Stannarius, R. 2012a Orientational order and alignment of elongated particles induced by shear. Phys. Rev. Lett. 108, 228302.Google Scholar
Börzsönyi, T., Szabó, B., Wegner, S., Harth, K., Török, J., Somfai, E., Bien, T. & Stannarius, R. 2012b Shear induced alignment and dynamics of elongated granular particles. Phys. Rev. E 86, 051304.Google Scholar
Campbell, C. S. 2002 Granular shear flows at the elastic limit. J. Fluid Mech. 465, 261–291.Google Scholar
Campbell, C. S. 2005 Stress-controlled elastic granular shear flows. J. Fluid Mech. 539, 273–297.Google Scholar
Campbell, C. S. 2006 Granular material flows – an overview. Powder Technol. 162, 208–229.Google Scholar
Campbell, C. S. 2011 Elastic granular flows of ellipsoidal particles. Phys. Fluids 23, 013306.Google Scholar
Campbell, C. S. & Gong, A. 1986 The stress tensor in a two-dimensional granular shear flow. J. Fluid Mech. 164, 107–125.Google Scholar
Cleary, P. W. 2008 The effect of particle shape on simple shear flows. Powder Technol. 179, 144–163.Google Scholar
Goldhirsch, I. 2010 Stress, stress asymmetry and couple stress: from discrete particles to continuous fields. Granul. Matt. 12, 239–252.Google Scholar
Goldhirsch, I. 2003 Rapid granular flows. Annu. Rev. Fluid Mech. 35, 267–293.Google Scholar
Goldshtein, A. & Shapiro, M. 1995 Mechanics of collisional motion of granular materials. Part I. General hydrodynamic equations. J. Fluid Mech. 282, 75–114.Google Scholar
Guises, R., Xiang, J., Latham, J. P. & Munjiza, A. 2009 Granular packing: numerical simulation and the characterization of the effect of particle shape. Granul. Matt. 11, 281–292.Google Scholar
Guo, Y.2010 A coupled DEM/CFD analysis of die filling process. PhD thesis, The University of Birmingham, UK, pp. 40–41.Google Scholar
Guo, Y., Wassgren, C., Hancock, B., Ketterhagen, W. & Curtis, J. 2013a Granular shear flows of flat disks and elongated rods without and with friction. Phys. Fluids 25, 063304.Google Scholar
Guo, Y., Wassgren, C., Hancock, B., Ketterhagen, W. & Curtis, J. 2013b Validation and time step determination of discrete element modeling of flexible fibers. Powder Technol. 249, 386–395.Google Scholar
Guo, Y., Wassgren, C., Ketterhagen, W., Hancock, B., James, B. & Curtis, J. 2012 A numerical study of granular shear flows of rod-like particles using the discrete element method. J. Fluid Mech. 713, 1–26.Google Scholar
Hidalgo, R. C., Zuriguel, I., Maza, D. & Pagonabarraga, I. 2010 Granular packings of elongated faceted particles deposited under gravity. J. Stat. Mech. 2010, P06025.Google Scholar
Hua, X., Curtis, J., Hancock, B., Ketterhagen, W. & Wassgren, C. 2013 The kinematics of non-cohesive, sphero-cylindrical particles in a low-speed, vertical axis mixer. Chem. Engng Sci. 101, 144–164.Google Scholar
Huthmann, M., Aspelmeier, T. & Zippelius, A. 1999 Granular cooling of hard needles. Phys. Rev. E 60, 654–659.CrossRefGoogle ScholarPubMed
Jenkins, J. T. 2006 Dense shearing flows of inelastic disks. Phys. Fluids 18, 103307.Google Scholar
Johnson, K. L. 1985 Contact Mechanics. Cambridge University Press.Google Scholar
Johnson, P. C. & Jackson, R. 1987 Frictional-collisional constitutive relations for granular materials with applications to plane shearing. J. Fluid Mech. 176, 67–93.Google Scholar
Johnson, P. C., Nott, P. & Jackson, R. 1990 Frictional-collisional equations of motion for particulate flows and their applications to plane shearing. J. Fluid Mech. 210, 501–535.Google Scholar
Jop, P., Forterre, Y. & Pouliquen, O. 2006 A constitutive law for dense granular flows. Nature 441, 727–730.CrossRefGoogle ScholarPubMed
Ketterhagen, W., Curtis, J., Wassgren, C. & Hancock, B. 2009 Predicting the flow mode from hoppers using the discrete element method. Powder Technol. 195, 1–10.Google Scholar
Langston, P., Kennedy, A. R. & Constantin, H. 2015 Discrete element modeling of flexible fibre packing. Comput. Mater. Sci. 96, 108–116.Google Scholar
Lavenson, D. M., Tozzi, E. J., McCarthy, M. J. & Powell, R. L. 2011 Yield stress of pretreated corn stover suspensions using magnetic resonance imaging. Biotechnol. Bioengng 108, 2312–2319.Google Scholar
Lees, A. W. & Edwards, S. F. 1972 The computer study of transport processes under extreme conditions. J. Phys. C: Solid State Phys. 5, 1921–1929.Google Scholar
Lindstrom, S. B. & Uesaka, T. 2007 Simulation of the motion of flexible fibers in viscous fluid flow. Phys. Fluids 19, 113307.Google Scholar
Lumay, G. & Vandewalle, N. 2006 Experimental study of the compaction dynamics for two-dimensional anisotropic granular materials. Phys. Rev. E 74, 021301.Google Scholar
Lun, C. K. K., Savage, S. B., Jeffrey, D. J. & Chepurniy, N. 1984 Kinetic theories for granular flow: inelastic particles in Couette flow and slightly inelastic particles in a general flow field. J. Fluid Mech. 140, 223–256.Google Scholar
Montanero, J. M., Garzo, V., Santos, A. & Brey, J. J. 1999 Kinetic theory of simple granular shear flows of smooth hard spheres. J. Fluid Mech. 389, 391–411.Google Scholar
Ning, Z. & Melrose, J. R. 1999 A numerical model for simulating mechanical behavior of flexible fibers. J. Chem. Phys. 111, 10717–10726.Google Scholar
Peña, A. A., García-Rojo, R. & Herrmann, H. J. 2007 Influence of particle shape on sheared dense granular media. Granul. Matt. 9, 279–291.Google Scholar
Potyondy, D. O. & Cundall, P. A. 2004 A bonded-particle model for rock. Int. J. Rock Mech. Min. Sci. 41, 1329–1364.CrossRefGoogle Scholar
Pouliquen, O. & Forterre, Y. 2009 A non-local rheology for dense granular flows. Phil. Trans. R. Soc. Lond. A 367, 5091–5107.Google Scholar
Reddy, K. A., Kumaran, V. & Talbot, J. 2009 Orientational ordering in sheared inelastic dumbbells. Phys. Rev. E 80, 031304.Google Scholar
Ross, R. F. & Klingenberg, D. J. 1997 Dynamic simulation of flexible fibers composed of linked rigid bodies. J. Chem. Phys. 106, 2949–2960.CrossRefGoogle Scholar
Stickel, J. J., Knutsen, J. S., Liberatore, M. W., Luu, W., Bousfield, D. W., Klingenberg, D. J., Scott, C. T., Root, T. W., Ehrhardt, M. R. & Monz, T. O. 2009 Rheology measurements of a biomass slurry: an inter-laboratory study. Rheol. Acta 48, 1005–1015.Google Scholar
Suiker, A. S. & Fleck, N. A. 2004 Frictional collapse of granular assemblies. Trans. ASME J. Appl. Mech. 71, 350–358.CrossRefGoogle Scholar
Thornton, C. 2000 Numerical simulations of deviatoric shear deformation of granular media. Géotechnique 50, 43–53.Google Scholar
Thornton, C. & Yin, K. K. 1991 Impact of elastic spheres with and without adhesion. Powder Technol. 65, 153–165.Google Scholar
Wegner, S., Stannarius, R., Boese, A., Rose, G., Szabo, B., Somfai, E. & Borzsonyi, T. 2014 Effects of grain shape on packing and dilatancy of sheared granular materials. Soft Matt. 10, 5157–5167.Google Scholar
Weinhart, T., Hartkamp, R., Thornton, A. R. & Luding, S. 2013 Coarse-grained local and objective continuum description of three-dimensional granular flows down an inclined surface. Phys. Fluids 25, 070605.Google Scholar
Weinhart, T., Thornton, A. R., Luding, S. & Bokhove, O. 2012 From discrete particles to continuum fields near a boundary. Granul. Matt. 14, 289–294.Google Scholar
Wouterse, A., Luding, S. & Philipse, A. P. 2009 On contact numbers in random rod packings. Granul. Matt. 11, 169–177.Google Scholar
Wu, J. & Aidun, C. K. 2010 A method for direct simulation of flexible fiber suspensions using lattice Boltzmann equation with external boundary force. Intl J. Multiphase Flow 36, 202–209.Google Scholar
Yamamoto, S. & Matsuoka, T. 1993 A method for dynamic simulation of rigid and flexible fibers in a flow field. J. Chem. Phys. 98, 644–650.Google Scholar