| Description |
A mathematical model of the hydrocyclone based on the physics of fluid flow has been developed. The model itself is a large computer code that solves the governing Navier-Stokes equations in the vorticity-stream function formulation numerically. Turbulent closure is effected by employing a modified Prandtl mixing-length model, and an algebraic slip approach is used to model the movement of particles in the hydrocyclone. The input of the computer program will be the geometry of the hydrocyclone, the properties of the slurry, and the volumetric flow rate; while the output is the velocity profiles of the fluid and the slip velocities of the particles with respect to the fluid, which in turn yield the particle trajectories and eventually separation efficiency. In order to validate the model, a laser-Doppler velocimeter (LDV) has been used to measure the velocity profiles inside a 75-mm glass hydrocyclone. Pure water and glycerol-water mixtures to simulate the increase of viscosity of the slurry in the presence of solid particles were the working media. The predicted velocity profiles agreed well with the experimental measurements. Two dilute limestone slurry systems were also examined with the same 75-mm glass hydrocyclone, and the separation efficiency curves analyzed by a Microtrac Particle Size Analyzer showed good agreement with the model predictions. Because the design geometry of the hydrocyclone is already incorporated and the basic fluid-dynamic equations are also solved, the phenomenological model has no reliance on empirical information except at a fairly deep level, e.g., associated with particle motion and turbulent structure. As a result, the model can be used in industrial applications to predict and optimize the performance of the existing hydrocyclones as well as to investigate other novel designs. However, the model should account for non-Newtonian behavior of concentrated slurries and transport of particles by turbulent eddies. Therefore, future work is needed before all the limitations are revealed and accounted for in the model. |
