Numerical modelling of non-Newtonian slurry in a mechanical flotation cell
Introduction
The mixing of non-Newtonian fluids, which are found in a wide range of industries, is poorly understood due to the often high apparent viscosities, complex changes in rheology during agitation, and the fact that many also exhibit a yield stress that needs to be overcome for the fluid to flow. Certain liquid–solid mineral slurry suspensions used in flotation cells in the minerals processing industry are one such example of these types of fluids. Various researchers have found that these slurries exhibit different rheological behaviours depending on their physical and chemical characteristics such as particle type, particle size, solids concentration and pulp chemistry (Prestidge, 1997, Tseng and Chen, 2003, He et al., 2006).
Due to the preferential use of high quality ores in the past, mining operations are having to process more complex, finely disseminated ore bodies, and in order to do this ores are having to be ground to ever finer particle sizes, and this therefore increases the non-Newtonian nature of the slurries. Solids concentrations are also being increased in order to reduce water consumption, further increasing the slurries’ non-Newtonian nature. Until recently, however, researchers have modelled all mineral slurries as Newtonian fluids when, in many cases, they may not be. One such case where this may have a large effect is in mechanical flotation cells, where the change in rheology affects the hydrodynamics within the cell. This in turn can affect the various subprocesses necessary for efficient flotation, such as gas dispersion, particle suspension, bubble–particle collision, attachment and detachment in the cell. In order to fully understand the effects of slurry rheology on the local hydrodynamics, a detailed knowledge of local variables in the flow field are required. Most experimental methods need optically clear fluids or low solid concentrations and low velocities (Boyer et al., 2002), however mineral slurries are inherently opaque with relatively high solid concentrations and high fluid velocities.
There have been various experimental studies conducted into the effects of non-Newtonian fluids on the hydrodynamics inside stirred tanks, but only using either optically clear fluids or low fluid velocities due to the constraints of most experimental techniques such as PIV or LDV. It has been found that stirred tanks containing yield stress fluids form a region of yielded fluid, or cavern, moving in a predominantly tangential direction around the impeller, while the rest of the fluid remains stagnant (Elson and Cheeseman, 1986, Moore et al., 1995, Wilkens et al., 2005). There has been little research into the numerical modelling of cavern formation in stirred tanks however (Adams and Barigou, 2007, Arratia et al., 2006), and although there has been research on modelling of mechanical flotation cells (Koh et al., 2003, Koh and Schwartz, 2006), no-one has modelled non-Newtonian fluids in mechanical flotation cells. This research has therefore been undertaken to study the effect of the rheology of slurries on the flow dynamics inside mechanical flotation cells, and the potential formation of caverns around the impeller. This was done using the commercial CFD package Fluent 6.3 as a peer methodology in the absence of suitable experimental techniques. In order to validate the modelling methodology, the flow inside a tank stirred by a pitch-blade turbine (PBT) was predicted and compared to published experimental results by Adams and Barigou, 2007. Adams and Barigou conducted experimental tests on the PBT at various impeller speeds, and visualised the flow using Planar Laser Induced Fluorescence (PLIF), presenting results of the cavern boundary position at each impeller speed. They also compared their experimental results to CFD simulations, but since only laminar simulations were conducted, accurate predictions were only obtained at low speeds where the flow was still in the laminar regime. The methodology developed was then used to model the more complex mechanical flotation cell. The predicted results were validated using experimental measurements. These were in the form of cavern boundary positions obtained using measurements of the magnitude of pressure fluctuations in an experimental pilot scale flotation cell containing mineral slurry, from which the the movement of the slurry, and therefore the size of the cavern, could be determined.
Section snippets
Experimental geometry
This study was conducted on a 100l pilot scale Bateman flotation cell (Fig. 1), with diameter, , and liquid depth, , which consists of a 6 bladed impeller of maximum diameter, , tapering down to 70 mm at the lower edge, and height . This was surrounded by a ring of 16 stator blades of by attached to a diameter stator disc. The impeller bottom clearance was .
The modelling methodology was first validated by modelling a simple impeller driven
PBT
A fully three-dimensional mesh was used to model half the PBT tank geometry, utilising the symmetry of the tank to reduce computational cost. Periodic boundary conditions were applied to the cut planes. The mesh used to model the PBT consisted of a hybrid tetrahedral/quadrilateral mesh of approximately 260 000 cells. An unsteady sliding mesh was used to model the rotation of the impeller, whereby a separate cell zone is defined around the impeller and this entire region is rotated. Although the
PBT
The results of the PBT simulations were validated by comparing the position of the predicted cavern boundary to experimentally measured cavern boundary positions obtained from literature (Adams and Barigou, 2007) using PLIF. It was found that the predicted flow was sensitive to the value of chosen until was less than approximately , after which there was no change in the cavern predictions. Since ranges from 1.29 to 1.97 Pa, μy was set to . Adams and Barigou (2007)
Conclusions
CFD simulations were conducted in order to investigate the effects of non-Newtonian mineral slurry rheology on the hydrodynamics inside a mechanical flotation cell. The modelling methodology used was first validated by modelling a pitch-blade turbine agitated tank and comparing results against published experimental cavern measurements. A pilot scale mechanical flotation cell containing a non-Newtonian Bindura nickel slurry was then modelled. The predicted flow in the flotation cell was also
Acknowledgement
The authors would like to thank the Minerals to Metals SARChI Chair for funding in this research.
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