Developing a mechanistic model for flow through a perforated plate with application to screening of particulate materials

Doctoral Thesis


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University of Cape Town

Screening in mineral processing is the practice of separating granulated ore materials into multiple particle size fractions, and is employed in most mineral processing plants. Models of screening performance have been developed previously with the aim of improving process efficiency. Different methods have been used, such as physical modelling, empirical modelling, and mathematical modelling including the discrete element method (DEM). These methods have major limitations in practice, and experimental data to validate the models have been difficult to obtain. Currently, the design and scale-up of screens still relies on rules of thumb and empirical factor methods rather than a fundamentally based understanding of the behaviour of the granular system. To go beyond the current state-of-the-art in screen modelling requires a clear understanding of the particle motion along a dynamic (vibrating) inclined plane. Central to this understanding is the notion that granular systems exhibit a unique rheology that is not observed in fluids; i.e. neither Newtonian nor non-Newtonian. It is thus imperative to fully quantify the granular rheology, which is determined by the depth of the particle bed along the screen, the solids concentration, and the average velocity of the granular avalanche on the screen. The concept of granular rheology is important. Existing empirical models of vibrating screens tend to be extremely dependent on boundary conditions of a particular machine design. The concept of granular rheology is important because, akin to fluid flow, granular flow exhibits different flow regimes depending on the extent of energy input in the system. This work employed DEM to quantify the granular rheology of particles moving along a vibrating inclined screen in order to begin the development of a phenomenological model of screening. The model extends the visco-plastic rheology formation of Pouliquen et al. (2006) to capture the kinetic and turbulent stresses obtained in granular flow on an inclined vibrating screen. In general, DEM was employed to develop a mechanistic model of screening which includes a description of the rheology of granular flow on a vibrating screen. Microscopic properties of granular flow were used in DEM to simulate screening of particulate materials. Granular mixtures of two particle constituents (3 mm and 5 mm) were simulated on an inclined vibrating screen of 3.5 mm apertures. For the base case, frequency and amplitude are 4 Hz and 1 mm, respectively. While microscopic properties were employed for the simulation, the properties extracted from the simulations are macroscopic fields which are consistent with the continuum equations of mass, momentum and energy balance. From the continuum equations, a micro-macro transition method called the coarse-graining approach was employed to obtain the volume fraction and the tangential velocity as a function of the depth of flow along the inclined surface. This approach is suitable for this work because the produced fields satisfy the equations of continuum mechanics; even near the base of the flow. The continuum analysis of the flowing layer reveals a coexistence of flow regimes- (i) quasi-static, (ii) dense (liquid-like), and (iii) inertial. The regimes are consistent with the measured solids concentrations spanning these regimes on inclined vibrating screens. The quasi-static regime is dominated by frictional stress and corresponds to low inertial number (I). Beyond the quasi-static regime, the frictional stress chains break and the collisional-kinetic and turbulent stress begin to dominate. The variation of the effective frictional coefficient with the inertial number (I) characterises the flow. Finally, an effective frictional coefficient model that is based on frictional, collisionalkinetic and turbulent stress was developed. Data analyses for this model were done at a steady flow in the base case where a coexistence of three flow regimes were observed. It was observed that each regime of flow is dominated by corresponding shear stresses. While the quasi-static regime is dominated by frictional stress, the kinetic and the inertial regimes are dominated by kinetic and turbulent shear stresses, respectively. This model was tested by varying the intensity of vibration in the base case and it was observed that at higher frequencies and amplitudes, the quasi-static regime gradually disappeared. Furthermore, the inertial number at which transition occurs to different regimes varies in response to the intensity of vibration. This is an important step in developing a phenomenological model of screening. The model presents a fundamental understanding of the mechanisms governing transport of granular matter on an inclined vibrating screen.