Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-18T23:51:42.607Z Has data issue: false hasContentIssue false
  • English
  • Français

Local measurements of velocity fluctuations and diffusion coefficients for a granular material flow

Published online by Cambridge University Press:  26 April 2006

V. V. R. Natarajan ,
M. L. Hunt  and
E. D. Taylor
V. V. R. Natarajan
Affiliation:
Division of Engineering and Applied Sciences, California Institute of Technology, Pasadena, CA 91125, USA
M. L. Hunt
Affiliation:
Division of Engineering and Applied Sciences, California Institute of Technology, Pasadena, CA 91125, USA
E. D. Taylor
Affiliation:
Division of Engineering and Applied Sciences, California Institute of Technology, Pasadena, CA 91125, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

Measurements were made of two components of the average and fluctuating velocities, and of the local self-diffusion coefficients in a flow of granular material. The experiments were performed in a 1 m-high vertical channel with roughened sidewalls and with polished glass plates at the front and the back to create a two-dimensional flow. The particles used were glass spheres with a nominal diameter of 3 mm. The flows were high density and were characterized by the presence of long-duration frictional contacts between particles. The velocity measurements indicated that the flows consisted of a central uniform regime and a shear regime close to the walls. The fluctuating velocities in the transverse direction increased in magnitude from the centre towards the walls. A similar variation was not observed for the streamwise fluctuations. The self-diffusion coefficients showed a significant dependence on the fluctuating velocities and the shear rate. The velocity fluctuations were highly anistropic with the streamwise components being 2 to 2.5 times the transverse components. The self-diffusion coefficients for the streamwise direction were an order-of-magnitude higher than those for the transverse direction. The surface roughness of the particles led to a decrease in the self-diffusion coefficients.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 304 , 10 December 1995 , pp. 1 - 25
Copyright
© 1995 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

Ahn, H., Brennen, C. E. & Sabersky, R. H. 1991 Measurements of velocity, velocity fluctuations, density and stresses in chute flows of granular materials. Trans. ASME E: J. Appl. Mech. 58, 792–803.Google Scholar
Brennen, C. & Pearce, J. C. 1978 Granular material flow in two-dimensional hoppers. Trans. ASME E: J. Appl. Mech. 45, 43–50.Google Scholar
Bridgewater, J. 1980 Self diffusion coefficients in deforming powders. Powder Technol. 25, 129–131.Google Scholar
Buggish, H. & Loffelmann, G. 1989 Theoretical and experimental investigation into local granular mixing mechanisms. Chem. Engng. Proc. 26, 193–200.Google Scholar
Campbell, C. S. 1989 The stress tensor for simple shear flow of a granular material. J. Fluid Mech. 203, 449–473.Google Scholar
Campbell, C. S. 1993 Self-diffusion in granular shear flows. J. Fluid Mech. (Submitted).Google Scholar
Chapman, S. & Cowling, T. G. 1971 The Mathematical Theory of Non-uniform Gases. 3rd edn. Cambridge University Press.
Dai, R. 1993 Granular flow studies through kinetic theory and numerical simulation approaches. PhD thesis, McGill University, Montreal.
Drake, T. G. 1991 Granular flow: physical experiments and their implications for microstructural theories. J. Fluid Mech. 225, 121–152.Google Scholar
Einstein, A. 1956 In Albert Einstein, Investigations on the theory of the Brownian movement (ed. R. Furth), chap. 1, §4, pp. 12–17. Dover.
Goodman, M. A. & Cowin, S. C. 1971 Two problems in the gravity flow of granular materials. J. Fluid Mech. 45, 321–339.Google Scholar
Haff, P. K. 1983 Grain flow as a fluid mechanical phenomenon. J. Fluid Mech. 134, 401–430.Google Scholar
Hsiau, S. S. & Hunt, M. L. 1993 Shear-induced particle diffusion and longitudinal velocity fluctuations in a granular-flow mixing layer. J. Fluid Mech. 251, 299–313.Google Scholar
Hsiau, S. S. & Hunt, M. L. 1993 Kinetic theory analysis of flow-induced particle diffusion and thermal conduction in granular material flows. Trans. ASMEC: J. Heat Transfer 115, 541–548.Google Scholar
Hui, K. & Haff, P. K. 1986 Kinetic grain flow in a vertical channel. Intl J. Multiphase Flow 12, 289–298.Google Scholar
Hunt, M. L., Hsiau, S. S. & Hong, K. T. 1994 Particle mixing and volumetric expansion in a vibrated granular bed. Trans. ASMEl: J. Fluids Engng 116, 785–791.Google Scholar
Hwang, C. L. & Hogg, R. 1980 Diffusive mixing in flowing powders. Powder Technol. 26, 93–101.Google Scholar
Jenkins, J. T. & Savage, S. B. 1983 A theory for the rapid flow of identical, smooth, nearly elastic, spherical particles. J. Fluid Mech. 130, 187–202.Google Scholar
Johnson, P. C. & Jackson, R. 1987 Frictional-collisional constitutive relations for granular materials, with application to plane shearing. J. Fluid Mech. 176, 67–93.Google Scholar
Liu, K. S., Kalos, M. H. & Chester, G. V. 1974 Quantum hard spheres in a channel. Phvs. Rev. A 10, 303–308.Google Scholar
Louge, M. Y. 1994 Computer simulations of rapid granular flows of spheres interacting with a flat, frictional boundary. Phys. Fluid. 6, 2253–2269.Google Scholar
Lun, C. K. K. & Savage, S. B. 1986 The effects of an impact velocity dependent coefficient of restitution on stresses developed by sheared granular materials. Ada Mech. 63, 15–44.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
Nedderman, R. M. & Laohakul, C. 1980 The thickness of the shear zone of flowing granular materials. Powder Technol. 25, 91–100.Google Scholar
Nguyen, T. V., Brennen, C. & Sabersky, R. H. 1979 Gravity flow of granular materials in conical hoppers. Trans. ASMEE: J. Appl. Mech. 46, 529–535.Google Scholar
Nunziato, J. W., Passman, S. L. & Thomas, J. P. 1980 Gravitational flows of granular materials with incompressible grains. J. Rheol. 24, 395–420.Google Scholar
Richman, M. W. & Marciniec, R. P. 1991 Granular chute flows. In Recent Advances in Mechanics of Structured Continua, AMD-Vol. 117. ASME.
Savage, S. B. 1979 Gravity flow of cohesionless granular materials in chutes and channels. J. Fluid Mech. 92, 53–96.Google Scholar
Savage, S. B. & Dai, R. 1993 Studies of shear flows. Wall slip velocities, ‘layering’ and self-diffusion. Mech. Mater. 16, 225–238.Google Scholar
Savage, S. B. & Jeffrey, D. J. 1981 The stress tensor in a granular flow at high shear rates. J. Fluid Mech. 110, 255–272.Google Scholar
Scott, A. M. & Bridgewater, J. 1976 Self-diffusion of spherical particles in a simple shear apparatus. Powder Technol. 14, 177–183.Google Scholar
Sherwood, T. K., Pigford, R. L. & Wilke, C. R. 1975 Mass Transfer. McGraw Hill.
Takahashi, H. & Yanai, H. 1973 Flow profiles and void fraction of granular solids in a moving bed. Powder Technol. 7, 205–214.Google Scholar
Taylor, E. D. & Hunt, M. L. 1993 Measurements of velocity fluctuations in a granular flow. In Powders & Grains 93 (ed. C. Thornton). Balkema.
Taylor, G. I. 1953 Dispersion of soluble matter in solvent flowing slowly through a tube. Proc. R. Soc. Land. A 219, 186–203.Google Scholar
Taylor, G. I. 1954 The dispersion of matter in turbulent flow through a pipe. Proc. R. Soc. Land. A 223, 446–468.Google Scholar
Walton, O. R. & Braun, R. L. 1986 Viscosity, granular temperature and stress calculations for shearing assemblies of inelastic, frictional disks. J. Rheol. 30, 949–980.Google Scholar
Zik, O. & Stavans, J. 1991 Self-diffusion in granular flows. Europhys. Lett. 16, 255–258.Google Scholar