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Flow of Granular Material through Rotating Cylinders: Modelling Transients

Published online by Cambridge University Press:  01 February 2011

Richard J. Spurling
Affiliation:
Department of Chemical Engineering, University of Cambridge, Pembroke Street, Cambridge, CB2 3RA, UK
John F. Davidson
Affiliation:
Department of Chemical Engineering, University of Cambridge, Pembroke Street, Cambridge, CB2 3RA, UK
David M. Scott
Affiliation:
Department of Chemical Engineering, University of Cambridge, Pembroke Street, Cambridge, CB2 3RA, UK
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Abstract

Granular material, fed continuously into the top of a slowly rotating, slightly inclined cylinder, forms a moving bed. Much of the bed rotates with the cylinder in solid body motion. When particles reach the surface of the bed, they move rapidly down it, and are absorbed once more into the solid body motion. Such cylinders are used in calcining, pharmaceutical manufacture, and drying. A steady state transport model, applicable when the bed depth varies slowly along the cylinder, has existed for around 50 years. The bed surface is considered locally flat, and particles in it fall along the line of steepest descent, inclined to the horizontal at the angle of repose. There is reasonable agreement with experiment.

We propose a quasi-steady state dynamical model, in which the steady state model is coupled with a volume balance across an axial element. The model takes the form of a nonlinear diffusion equation which was solved numerically. The parameters of the dynamic model are the dimensions of the cylinder and outlet dam, the inclination of the axis of the cylinder, its rotational speed, the angle of repose of the granular material and its feed volumetric flow rate: the dynamic model has no free parameters. Experiments were conducted using sand, mean particle size 490 μm, in a perspex tube of length 1 m, radius 0.0515 m, lined with sandpaper, with a feed end dam of height 0.029 m, and with no exit dam, or an exit dam of height 0.0105 m. With the system initially in steady state, step changes in feed flow rate, rotational speed or axis inclination were imposed, and the resulting discharge flow rate and bed depth axial profile measured as functions of time. Good agreement is found between model and experiment.

Type
Research Article
Copyright
Copyright © Materials Research Society 2000

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References

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