NUMERICAL-CALCULATIONS OF FLOW IN A HYDROCYCLONE OPERATING WITHOUT AN AIR CORE

Abstract Steady flow in a hydrocyclone operating without an air core is modelled by a finite difference solution of the Navier-Stokes equations, following the approach of Pericleous and Rhodes, in which the shear stress due to tangential motion is derived from the familiar Prandtl momentum transport theory, applied to angular momentum. In this application, the Prandtl model breaks down very near the axis of symmetry and a boundary condition, corresponding to zero shear, must be imposed at a radius of about one mixing length to ensure realistic flow predictions. Calculations are based on a commonly used solution procedure for velocity and pressure which uses the SIMPLE algorithm of Patankar and Spalding. Hybrid first-order upwind/central differencing is used, and calculated flow velocities are obtained which agree with both published data and analytical predictions. The corresponding transport equation for the dispersed (particle) phase is solved similarly, and the predicted efficiency curve and distributions of particle concentration are shown. Finally, predicted velocity and particle distributions are compared with corresponding results based on quadratic upstream differencing of the governing equations; it is concluded that numerical diffusion on has little effect on the predicted fluid or particle movement in this case.