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Density waves and coherent structures in granular Couette flows

Phys. Fluids 16, 509 (2004); doi:10.1063/1.1637348

Published 13 January 2004

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Stephen L. Conway and Benjamin J. Glasser
Department of Chemical and Biochemical Engineering, Rutgers, The State University of New Jersey, Piscataway, New Jersey 08854
Density inhomogeneities in granular flows can dramatically influence microscopic and macroscopic properties. Here, we numerically examine dilute rapid granular flows in the Couette geometry via large-scale particle-dynamic simulations, and characterize development of nonuniform particle distributions. For monodisperse grains we observe density waves in two- and three-dimensional computational domains of varying aspect ratios. Both fully developed and transient states are quantified using Fourier methods. For inelastic, planar (two-dimensional) flows exceeding a minimum solids fraction, one-dimensional, high-density clusters—well-known features of inelastic materials—align parallel to the walls. Above a critical streamwise length, these are destabilized by two-dimensional antisymmetric modes with wavelength ~100 particle diameters. We relate oscillatory behavior to an underlying physical mechanism of the slow drift of clusters towards walls and their subsequent bursting. Further streamwise or spanwise expansions permit additional wave numbers to be expressed in these directions. In "shallow" three-dimensional flows, the planar wave types initially survive. As depth is increased above a critical value, cross-stream invariance experiences symmetry preserving instabilities to form coherent structures resembling steady and wavy Taylor–Couette fluid vortices. Their presence strongly impacts macroscopic behavior, as regions of sustained vorticity develop, and stresses and granular temperatures deviate by up to an order of magnitude from mean values. The influence of solids fraction, particle size, material elasticity, surface friction, polydispersity, and gravity are considered, and instabilities are found to intensify as collisional dissipation rises. For planar flows, transient and fully developed density distributions share many parametric responses with previous continuum results using kinetic theory. ©2004 American Institute of Physics.
History: Received 3 June 2003; accepted 31 October 2003; published 13 January 2004
Permalink: http://link.aip.org/link/?PHFLE6/16/509/1
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KEYWORDS and PACS

Keywords
PACS
  • 45.70.Mg
    Granular flow; mixing, segregation and stratification
  • 47.60.+i
    Flows in ducts, channels, nozzles, and conduits
  • YEAR: 2004

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ISSN:
1070-6631 (print)   1089-7666 (online)
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REFERENCES (63)
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  1. D. J. Stephens and J. Bridgewater, "The mixing and segregation of cohesionless particulate materials. Part I. Failure zone formation," Powder Technol. 21, 17 (1977).
  2. H. M. Jaeger, S. R. Nagel, and R. P. Behringer, "Granular solids, liquids, and gases," Rev. Mod. Phys. 68, 1259 (1996).
  3. D. J. Goldfarb, B. J. Glasser, and T. Shinbrot, "Shear instabilities in granular flows," Nature (London) 415, 302 (2002).
  4. Y. Forterre and O. Pouliquen, "Longitudinal vortices in granular flows," Phys. Rev. Lett. 86, 5886 (2001).
  5. S. B. Savage, "Flow of granular materials," Theoretical and Applied Mechanics, edited by P. Germain, M. Piau, and D. Caillerie (Elsevier Science, North-Holland, 1989).
  6. O. Pouliquen, J. Delour, and S. B. Savage, "Fingering in granular flows," Nature (London) 386, 816 (1997).
  7. C. S. Campbell and C. E. Brennen, "Computer simulation of granular shear flows," J. Fluid Mech. 151, 167 (1985).
  8. O. R. Walton and R. L. Braun, "Viscosity, granular-temperature, and stress calculations for shearing assemblies of inelastic, frictional disks," J. Rheol. 30, 949 (1986).
  9. C. K. K. Lun, "Granular dynamics of inelastic spheres in Couette flow," Phys. Fluids 8, 2868 (1996).
  10. C. K. K. Lun, S. B. Savage, D. Jeffrey, and N. Chepurniy, "Kinetic theories for granular flow: Inelastic particles in Couette flow and slightly inelastic particles in a general flowfield," J. Fluid Mech. 140, 223 (1984).
  11. J. T. Jenkins and M. W. Richman, "Kinetic theory for plane flows of a dense gas of identical, rough, inelastic spheres," Phys. Fluids 28, 3485 (1985).
  12. M. Babic, "On the stability of rapid granular flows," J. Fluid Mech. 254, 127 (1993).
  13. C.-H. Wang, R. Jackson, and S. Sundaresan, "Stability of bounded rapid shear flows of a granular material," J. Fluid Mech. 308, 31 (1996).
  14. C. S. Campbell, "Rapid granular flows," Annu. Rev. Phys. Chem. 22, 57 (1990).
  15. I. Goldhirsch, "Rapid granular flows," Annu. Rev. Fluid Mech. 35, 267 (2003).
  16. M. A. Hopkins and M. Y. Louge, "Inelastic microstructure in rapid granular flows of smooth disks," Phys. Fluids A 3, 47 (1991).
  17. I. Goldhirsch and G. Zanetti, "Clustering instability in dissipative gases," Phys. Rev. Lett. 70, 1619 (1993).
  18. E. D. Liss and B. J. Glasser, "The influence of clusters on the stress in a sheared granular material," Powder Technol. 116, 116 (2001).
  19. M. C. Cross and P. C. Hohenburg, "Pattern formation outside of equilibrium," Rev. Mod. Phys. 65, 851 (1993).
  20. A. Akonur and R. M. Lueptow, "Three-dimensional velocity field for wavy Taylor–Couette flow," Phys. Fluids 15, 947 (2003).
  21. C. T. Veje, D. W. Howell, and R. P. Behringer, "Kinematics of two-dimensional granular Couette experiment at the transition to shearing," Phys. Rev. E 59, 739 (1999).
  22. A. W. Jenike, "Storage and Flow of Solids, Bulletin No. 123 of the Utah Engineering Experiment Station," Bulletin of the University of Utah, 1964, 53(26).
  23. S. B. Savage and M. Sayed, "Stresses developed by dry cohesionless granular materials sheared in an annular shear cell," J. Fluid Mech. 142, 391 (1984).
  24. E. Apicella, M. D'Amore, G. Tardos, and R. Mauri, "Onset of instability in sheared gas fluidized beds," AIChE J. 43, 1362 (1997).
  25. W. Losert, L. Bocquet, T. Lubensky, and J. Gollub, "Particle dynamics in sheared granular matter," Phys. Rev. Lett. 85, 1428 (2000).
  26. D. Mueth, G. F. Debregeas, G. S. Karczmar, P. J. Eng, S. R. Nagel, and H. M. Jaeger, "Signatures of granular microstructure in dense shear flows," Nature (London) 406, 385 (2000).
  27. A. Kudrolli, M. Wolpert, and J. P. Gollub, "Cluster formation due to collisions in granular material," Phys. Rev. Lett. 78, 1383 (1997).
  28. C. S. Campbell, "Shear flows of granular materials," Ph.D. thesis, Division of Engineering and Applied Science, California Institute of Technology, Pasedena, 1982.
  29. S. Luding and H. J. Herrmann, "Cluster-growth in freely cooling granular media," Chaos 9, 673 (1999).
  30. C. S. Campbell, "Granular shear flows at the elastic limit," J. Fluid Mech. 465, 261 (2002).
  31. S. McNamara and W. R. Young, "Kinetics of a one-dimensional granular medium in the quasielastic limit," Phys. Fluids A 5, 34 (1993).
  32. N. Sela and I. Goldhirsch, "Hydrodynamics of a one-dimensional granular medium," Phys. Fluids 7, 507 (1995).
  33. M.-L. Tan and I. Goldhirsch, "Intercluster interactions in rapid granular shear flows," Phys. Fluids 9, 856 (1997).
  34. S. B. Savage, "Numerical simulations of Couette flow of granular materials: Spatio-temporal coherence and 1/f noise," in Physics of Granular Media, edited by D. Bideau and J. Dodds (Nova Science, New York, 1991), pp. 343–362.
  35. S. B. Savage and R. Dai, "Some aspects of bounded and unbounded shear flows of granular material," in Advances in Micromechanics of Granular Materials, edited by H. H. Shen, M. Satake, M. Mehrabadi, C. S. Chang, and C. S. Campbell (Elsevier, Amsterdam, The Netherlands, 1992), pp. 151–161.
  36. P. Zamankhan, A. Mazouchi, and P. Sorkomaa, "Some qualitative features of the Couette flow of monodisperse, smooth, inelastic spherical particles," Appl. Phys. Lett. 71, 3790 (1997).
  37. A. Karion and M. L. Hunt, "Wall stresses in granular Couette flows of mono-sized particles and binary mixtures," Powder Technol. 109, 145 (2000).
  38. N. Sela, I. Goldhirsch, and S. H. Noskowicz, "Kinetic theoretical study of a simply sheared two-dimensional granular gas to Burnett order," Phys. Fluids 8, 2337 (1996).
  39. M. Alam and P. R. Nott, "Stability of plane Couette flow of a granular material," J. Fluid Mech. 377, 99 (1998).
  40. C.-H. Wang and Z. Tong, "Transient development of instabilities in bounded shear flow of granular materials," Chem. Eng. Sci. 53, 3803 (1998).
  41. M.-L. Tan, "Microstructures and macrostructures in rapid granular flows," Ph.D. thesis, Department of Chemical Engineering, Princeton University, 1995.
  42. P. R. Nott, M. Alam, K. Agrawal, R. Jackson, and S. Sundaresan, "The effect of boundaries on the plane Couette flow of granular materials: A bifurcation analysis," J. Fluid Mech. 397, 203 (1999).
  43. B. J. Glasser and I. Goldhirsch, "Scale dependence, correlations, and fluctuations of stresses in rapid granular flows," Phys. Fluids 13, 407 (2001).
  44. D. C. Rapaport, "The event scheduling problem in molecular dynamic simulation," J. Comput. Phys. 34, 184 (1980).
  45. C. K. K. Lun and S. B. Savage, "A simple kinetic theory for granular flow of rough, inelastic, spherical particles," J. Appl. Mech. 54, 47 (1987).
  46. C. S. Campbell and A. Gong, "The stress tensor in a two-dimensional granular shear flow," J. Fluid Mech. 164, 107 (1986).
  47. E. D. Liss, S. L. Conway, and B. J. Glasser, "Density waves in gravity-driven granular flow through a channel," Phys. Fluids 14, 3309 (2002).
  48. Care must be taken to set dimensions of X to avoid automatic truncation or addition of zero values by the MATLAB algorithm.
  49. Y. Du, H. Li, and L. P. Kadanoff, "Breakdown of hydrodynamics in a one-dimensional system of inelastic particles," Phys. Rev. Lett. 74, 1268 (1995).
  50. C. S. Campbell, "The stress tensor for simple shear flows of a granular material," J. Fluid Mech. 203, 449 (1989).
  51. M. A. Hopkins, J. T. Jenkins, and M. Y. Louge, "On the structure of 3D shear flows," in Advances in Micromechanics of Granular Materials, edited by H. H. Shen, M. Satake, M. Mehrabadi, C. S. Chang, and C. S. Campbell (Elsevier Science, New York, 1992), pp. 271–279.
  52. M. E. Lasinski, J. F. Pekny, and J. Sinclair, "Investigating the dependence of stress on the number of particles using an algorithm based on implicit representation of hard sphere collisions," presented at AIChE 2002 Annual Meeting, Session 202—Dynamics and Modeling of Particulate Systems, 2002, Indianapolis.
  53. B. P. B. Hoomans, J. A. M. Kuipers, W. J. Briels, and W. P. M. V. Swaaij, "Discrete particle simulation of bubble and slug formation in a two-dimensional gas-fluidised bed: A hard sphere approach," Chem. Eng. Sci. 51, 99 (1996).
  54. L. Popken and P. W. Cleary, "Comparison of kinetic theory and discrete element schemes for modelling granular Couette flows," J. Comput. Phys. 155, 1 (1999).
  55. E. Livne, B. Meerson, and P. V. Sasorov, "Symmetry breaking and coarsening of clusters in a prototypical driven granular gas," Phys. Rev. E 66, 050301 (2002).
  56. I. Volkov, M. Cieplak, J. Koplik, and J. R. Banavar, "Molecular dynamics simulations of crystallization of hard spheres," Phys. Rev. E 66, 061401 (2002).
  57. S. McNamara and W. R. Young, "Inelastic collapse in two dimensions," Phys. Rev. E 50, 28 (1994).
  58. M. Sasvári, J. Kertész, and D. E. Wolf, "Instability of symmetric Couette flow in a granular gas: Hydrodynamic field profiles and transport," Phys. Rev. E 62, 3817 (2000).
  59. M. Alam and P. R. Nott, "The influence of friction on the stability of unbounded granular shear flow," J. Fluid Mech. 343, 267 (1997).
  60. S. Luding, O. Strauss, and S. McNamara, "Segregation of polydisperse granular media in the presence of a temperature gradient," in IUTAM Symposium on Segregation in Granular Flows (Kluwer Academic, Dordrecht, The Netherlands, 1999).
  61. G. Kawahara and S. Kida, "Periodic motion embedded in plane Couette turbulence: Regeneration cycle and burst," J. Fluid Mech. 449, 291 (2001).
  62. S. R. Dahl, R. Clelland, and C. M. Hrenya, "The effects of continuous size distributions on the rapid flow of inelastic particles," Phys. Fluids 14, 1972 (2002).
  63. J. B. Knight, H. M. Jaeger, and S. R. Nagel, "Vibration-induced size separation in granular media: The convection connection," Phys. Rev. Lett. 70, 3728 (1993).

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