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Reynolds analogy for a shearing granular material

Published online by Cambridge University Press:  26 April 2006

David G. Wang  and
Charles S. Campbell
David G. Wang
Affiliation:
Department of Mechanical Engineering, University of Southern California, Los Angeles, CA 90089-1453, USA
Charles S. Campbell
Affiliation:
Department of Mechanical Engineering, University of Southern California, Los Angeles, CA 90089-1453, USA
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Abstract

The bulk motion of a granular material affects its apparent thermal as well as its apparent mechanical properties. This paper presents the simultaneous measurements of the apparent viscosity and thermal conductivity for a dry granular material undergoing shear in an annular shear cell. Both properties are seen to vary linearly with the shear rate. As such, it can be argued that both the apparent conductivity and viscosity are proportional to the square root of the granular temperature in exactly the same way as the kinetic theory of gases predicts that the conductivity and viscosity of a perfect gas vary as the square root of the thermodynamic temperature. Thus, analogies can be drawn between the mechanical and thermal behaviour of a granular flow that share much with similar — a.k.a. Reynolds — analogies for both laminar and turbulent flows of simple fluids. However, the results do indicate fundamental differences in the internal transport of heat and momentum. In particular, heat may only be transmitted by the streaming motion of the particles, while momentum may also be exchanged during interparticle collisions.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 244 , November 1992 , pp. 527 - 546
Copyright
© 1992 Cambridge University Press

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References

Bagnold R. A. 1954 Experiments on a gravity-free dispersion of large solid spheres in a Newtonian fluid under shear Proc. R. Soc. Lond. A 225, 49–63.Google Scholar
Campbell C. S. 1982 Shear flows of granular. Ph.D. thesis and Rep. E-200.7, California Institute of Technology.
Campbell C. S. 1986 Computer simulation of rapid granular flows In Proc. 10th Natl Congr. of Applied Mechanics, Austin Texas, June 1986, pp. 327–338. ASME.
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. 1990 Rapid granular flows. Ann. Rev, Fluid Mech. 22, 57–92.Google Scholar
Campbell, C. S. & Brennen C. E. 1985 Computer simulation of granular shear flows. J. Fluid Mech. 151, 167–188.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
Campbell, C. S. & Gong A. 1987 Boundary conditions for two-dimensional granular flows. Proc. Sino–US Intl Symp on Multiphase Flows, Hangzhou, China, August, 1987, vol. i, pp. 278–283. Zhejiang University Press, Hangzhou, China.
Campbell, C. S. & Wang G. D. 1986 The apparent conductivity of shearing particle flows. In Proc. 8th Intl Heat Transfer Conf., vol. 4, pp. 2567–2572. Hemisphere.
Chung, Y. C. & Leal L. G. 1982 An experimental study of the apparent thermal conductivity of a sheared suspension of rigid spheres. Intl J. Multiphase Flows 8, 605–625.Google Scholar
Craig K., Buckholtz, R. H. & Domoto G. 1987 The effects of shear surface boundaries on stresses for the rapid shear of dry powders. Trans. ASME: J. Tribology 109, 232–237.Google Scholar
Hanes D. M. 1983 Studies on the mechanics of rapidly flowing granular-fluid materials. Ph.D. thesis, University of California, San Diego.
Hanes, D. M. & Inman D. L. 1985 Observations of rapidly flowing granular-fluid materials. J. Fluid Mech. 150, 357–380.Google Scholar
Hunt, M. L. & Hsiau S. S. 1990 Thermal conductivity of granular flows. In Proc. Intl 9th Heat Transfer Conf., pp. 177–182. Hemisphere.
Leal L. G. 1973 On the apparent conductivity of a dilute suspension of spherical drops in the limit of low particle Peclet number. Chem. Engng Commun. 1, 21–31.Google Scholar
Lin C. J., Peery, J. H. & Schowalter W. R. 1970 Simple shear flow around a rigid sphere; inertial effects and suspension rheology. J. Fluid Mech. 4, 1–17.Google Scholar
Löffelmann G. 1989 Theoretische und experimentelle Untersuchungen zur Schüttgut-Wand-Wechselwirkung und zum Mischen un Entmischen von Granulaten. Dr.-Ing. thesis, Universitat Fridericiana Karlsruhe (Technische Hochschule).
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
Nir, A. & Acrivos A. 1976 The effective thermal conductivity of sheared suspensions. J. Fluid Mech. 78, 33–48.Google Scholar
Patton J. S., Sabersky, R. H. & Brennen C. E. 1986 Convective heat transfer to rapidly flowing granular materials. Intl J. Heat Mass Transfer 29, 1263–1269.Google Scholar
Reynolds O. 1874 On the extent and action of the heating surface of steam boilers. Proc. Lit. Phil. Soc. Manchester 14, 7–12. See also Papers on Mechanical and Physical Subjects, vol. 1, pp. 81–85. Cambridge University Press, 1900.Google Scholar
Savage, S. B. & Sayed M. 1983 Stresses developed by dry cohesionless granular materials in an annular shear cell. J. Fluid Mech. 142, 391–430.Google Scholar
Sun, J. & Chen M. M. 1988 A theoretical analysis of heat transfer due to particle impact. Intl J. Heat Mass Transfer 31, 969–975.Google Scholar
Walton, O. R. & Braun R. L. 1986a Viscosity and temperature calculations for shearing assemblies of inelastic, frictional disks. J. Rheol. 30, 949–980.Google Scholar
Walton, O. R. & Braun R. L. 1986b Stress calculations for assemblies of inelastic spheres in uniform shear. Acta Mechanica 63, 73–86.Google Scholar
Wang D. G. 1991 Mechanics and heat transfer for granular flows. Ph.D. thesis, University of Southern California, Los Angeles.
Wang D. G., Sadhal, S. S. & Campbell C. S. 1989 Particle rotation as a heat transfer mechanism. Intl J. Heat Mass Transfer 32, 1413.Google Scholar
Xavier, A. M. & Davidson J. F. 1985 Heat transfer in fluidized beds: convective heat transfer in fluidized beds. In Fluidization (ed. J. F. Davidson, R. Clift & D. Harrison). Academic.