Flow of Granular Material through Rotating Cylinders: Modelling Transients
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Flow of Granular Material through Rotating Cylinders: Modelling Transients Richard J. Spurling, John F. Davidson and David M. Scott Department of Chemical Engineering, University of Cambridge, Pembroke Street, Cambridge, CB2 3RA, UK 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. INTRODUCTION Rotary kilns are widely used in the processing of granular materials in the chemical and metallurgical industries, as mixers, dryers and reactors. A typical kiln used in the sulphate process for the manufacture of TiO2 is a cylinder 50 m long and 3 m in diameter, with axis inclined at a few degrees to the horizontal, and rotating about its axis at one revolution every 510 minutes. Granular material is fed to the upper end of the kiln, and forms a continuously rotating bed resting on the bottom of the kiln, filling each cross section to a level generally less than 30% by volume. The granular material is slowly conveyed along the kiln as a result of the continuous rotation, and the force of gravity down the slope. Some kilns have lifters in the wall, but here attention will be directed to smooth-walled kilns without lifters. Heating can be carried out by flow of hot gas countercurrent to the flow of solids, but this will not be considered here. The transverse motion of the bed of granular material in such a kiln has been classified by Henein et al. [1]. At very low r
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