Granular flow modelling of rotating drum flows using positron emission particle tracking

Doctoral Thesis


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University of Cape Town

Tumbling mills are characterized by a flowing granular mixture comprising slurry, ore and grinding media. Akin to fluid flow, a rheological description underpinning granular flow has long been expected and pursued by many researchers. Unfortunately, no single theory has hitherto been able to successfully describe all the peculiar features and flow phases of granular systems. Tumbling mills exhibit a rich coexistence of all known flow phases and is arguably the most complicated of the granular flow geometries. Not surprisingly, current comminution models are almost entirely empirical with limited predictive capability beyond their window of design. Using Positron Emission Particle Tracking (PEPT) data we recover the key ingredients (velocity, shear rate, volume concentration, bed depth) for developing, testing and calibrating granular flow models. In this regard, 5 mm and 8 mm glass beads are rotated within a 476 mm diameter mill, fitted with angled lifter bars along the inner azimuthal walls and operated in batch mode across a range of drum rotation speeds that span cascading and cataracting Froude regimes. After averaging the PEPT outputs into representative volume elements, subsequent continuum analysis of the flowing layer revealed a rich coexistence of flow regimes - (i) quasi-static, (ii) dense (liquid-like), and (iii) inertial - that are consistent with the measured volume concentrations spanning these regimes in rotating drums. Appropriately matched constitutive choices for the shear stresses then facilitated the derivation of a new granular rheology that is able to (smoothly) capture all phases of the tumbling mill flow at transition points that match leading experimental findings reported in the literature. Limiting our models to athermal boundary conditions, we then derive the power density for better understanding of flow dissipation that ultimately drives the comminution purpose of tumbling mills. The rheology and power density models were then applied to the 5 mm and 8 mm glass bead data to reveal that shear power density is an order of magnitude larger than the normal component. Notwithstanding, the effective friction coefficient - which is akin to viscosity in typical fluids - remains relatively constant across most of the flowing layer with notable exponential growth across the interface from dense-to-inertial that continued into the inertial regime.