Reynolds hydrocyclones

The Reynolds number defines flow features of the system and, in the case of hydrocyclones, the characteristic dimension may be taken as the cyclone body diameter D ... 

Whilst with larger hydrocyclones the resistance coefficient called the Euler number, Eu, depends on the Reynolds number, for very small hydrocyclones (such as the one used in this work) it is practically constant. We felt justified, therefore, in using such a combination of Eu with Stk (instead of a straight product of Stk-Eu as derived from first principles, equation 6.12), which would obviate the need to measure flow rates on the rig and, therefore, greatly simplify the testing procedure. 

Numerical calculations of the complete flowfield, using axially symmetric flow models and solving the full viscous equations of motion, have been carried out by Boyson, Ayers and Swithenbank and by Rhodes, Pericleous and Drake. These simulations are suitable for assessing parameters in design optimization provided they are based on realistic boundary conditions and a comprehensive flow model. Bloor, Ingham and Ferguson have also produced a numerical simulation for viscous flow in a hydrocyclone but at unrealistically low Reynolds numbers. Unlike the others they did not, however, ignore the three-dimensional character of the flow around the entry point and used three different models to simulate the entry flow. 

Despite the very different approaches and assumptions, the forms of correlations obtained by the equih-brium orbit theory and residence time theory are similar. For specific hydrocyclone designs, both theories provide their respective empirical equations for determining the cut size and pressure drop in terms of three dimensionless groups, the Stokes number at cut size, Stkso, the Euler number, Eu, and the Reynolds number, Re (see discussions in Sec. 5.4 below) ... 

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