Hydrocyclones analytical flow models

The analytical mathematical models of the flow patterns inside the hydrocyclone and of the particle trajectories, including the boundary layer flow, the short circuit flow and the internal eddies but at low feed concentrations only. 

Theoretical representation of the behaviour of a hydrocyclone requires adequate analysis of three distinct physical phenomenon taking place in these devices, viz. the understanding of fluid flow, its interactions with the dispersed solid phase and the quantification of shear induced attrition of crystals. Simplified analytical solutions to conservation of mass and momentum equations derived from the Navier-Stokes equation can be used to quantify fluid flow in the hydrocyclone. For dilute slurries, once bulk flow has been quantified in terms of spatial components of velocity, crystal motion can then be traced by balancing forces on the crystals themselves to map out their trajectories. The trajectories for different sizes can then be used to develop a separation efficiency curve, which quantifies performance of the vessel (Bloor and Ingham, 1987). In principle, population balances can be included for crystal attrition in the above description for developing a thorough mathematical model. 

A more recent development by Concha et al makes use of the analytical model by Bloor and Ingham to predict the classification performance of the conventional hydrocyclone. They divide the flow inside a hydrocyclone into six zones and use previously derived or measured velocity profiles and air core correlations. The zones are linked by boundary conditions and resulting classification predictions are validated with experimental tests using copper ore and quartz on three different industrial hydrocyclones. 

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