A granular flow model of an annular shear cell

Doctoral Thesis


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University of Cape Town

Machinery such as an IsaMillTM used in communition to produce fine particle sizes that allow minerals to be extracted are best modelled using granular flows. A single rheological description that captures all the features of granular flows has not yet been realised, although considerable progress towards a complete theory has been made. Existing models of such horizontally stirred mills are empirical, tend to be extremely dependent on boundary conditions and do not allow for confident extrapolation beyond their window of design. As a first step to understanding the dynamics inside the IsaMillTM,a constitutive stress model of a horizontal annular shear cell is developed. This shear stress model was used in an athermal energy balance to develop a description of the power dissipation, which drives the communition purpose of the IsaMillTM. The key ingredients (velocity, shear rate and volume fraction distributions) to the granular ow model are extracted from experiments using Positron Emission Particle Tracking (PEPT), as well as Discrete Element Method (DEM) simulations. 5mm glass beads were used to fill an annulus 51mm wide. In the PEPT experiments, two different surfaces of the driving wall (the inner cylinder of the shear cell) were used, over two shearing velocities. The effect of two friction coefficients over a range of shearing wall velocities were examined in the DEM simulations. The data were examined over 3 selected radial lines and utilised to calculate the shear stress distribution and the power dissipation from the developed models. It was found that even the usually simple relations describing the dynamics within a vertical shear cell are greatly modified by changing the orientation of the rotation axis.