Analysis of the flow field between two eccentric rotating cylinders in the presence of a slotted sleeve.

Abstract

Overend et al [68] designed a viscometer to measure the viscosity of slurries that have a tendency to settle. This viscometer consists of a rotating ribbed rotor surrounded by a stationary slotted sleeve; this system is then placed eccentrically within an inclined rotating bowl. It, is claimed that this overcomes most of the difficulties encountered when attempting to obtain accurate measurements for these types of mixtures. If the mixture being sheared within the annulus does not represent the true composition of the slurry being, tested then the results are expected to be inaccurate. The presence of sediment at the bottom of the rotor or the formation of large masses of particles within the flow domain will affect the accuracy of the measurements obtained. This dissertation studies the amount of flow through the slotted sleeve and the region, or regions, of low shear rate within the flow domain. Assuming that end-effects are unimportant and that the slurries can be replaced by a single-phase fluid, three two-dimensional models are proposed. These models are designed to capture the large-slot construction of the sleeve and the, approximate, non-Newtonian behaviour of the slurries. The first two models solve analytically (using a regular perturbation scheme) and numerically (using a finite volume method) the moderate-and large-Reynolds-number flow, and the third model uses a finite volume method to study the flow patterns developed by pseudoplastic fluids. The results show that the mixing of the slurry is expected to be enhanced by moving the concentric system (i.e., the rotor and the slotted sleeve) close to the rotating bowl and using low to moderate speeds for the rotor and bowl. In addition, when the cylinders rotate in the same directions, two (counter-rotating) eddies are present within the flow domain; whereas, only one eddy (rotating counter-clockwise) is present when the cylinders rotate in opposite directions. The presence of eddies in the former situation inhibits the flow through the sleeve; while, for moderate rotorspeeds, the flow through the sleeve is enhanced in the latter. When the slurry assumed pseudoplastic, we observe a region of low shear rate located near the dividing streamline present within the flow field. The distribution of shear rate within the flow field is shown to be affected by factors such as the rate of diffusion of the apparent viscosity and the value of the power law index. Therefore, this study suggests that for certain types of slurries, concentrations of particles exist within the domain and that the mixing of slurries can be impeded by the presence of eddies within the main flow field.