Theory of the Cut-Size, The Fractional Collection Efficiency, and the Vortex Breakdown in the Axial Flow Hydro-Cyclone

From a practical point of view, it is important to be able to predict the collection efficiency of the axial flow hydro-cyclone. In order to perform such estimation, it is necessary to predict the cut-size for the various operating conditions. Up to this time, there were many papers that derived the cut-sizes theoretically based upon the effect of the centrifugal force on the suspended solid particles, and experimentally based upon the effect of the geometrical construction of the hydro-cyclone on particle size. However, there have been few, if any, papers that included the effects of gravitational settling on the suspended solid particles when estimating the cut-size for the hydro-cyclone. Therefore, this paper presents the theoretical equation of the cut-size, which includes the gravitational and centrifugal forces acting on the suspended solid particles in the axial flow hydro-cyclone. The equation is derived based on the mass balance. The characteristics of the predicted cut-size are divided into two regions, one of which is dominated by the gravitational force effect while the other is dominated by the centrifugal force effect. Therefore the maximum value of the cut-size will be located between these two regions. Comparison of the predicted cut-size with the cut-size that was determined experimentally using glass beads reveals that the cut-sizes agree well. The vortex breakdown phenomena that occur in the exit pipe are also presented in detail in this paper. The phenomena are predicted with the simplified flow model (Hallett), and experimentally confirmed through experimentation, the results of which are presented photographically.