Computation of the Inner Vortex Cut-Point

A very fundamental characteristic of any lightly-loaded cyclone is its cut-point diameter or cut size, X50, produced by the spin of the inner vortex. This is the particle diameter that has a 50% probability of capture. As discussed elsewhere in this book, the cut size is analogous to the screen openings of an ordinary sieve or screen although, with a cyclone, the separation is not as sharp as that of a sieve. 

In order to compute X50, we must first compute the tangential velocity of the gas at the inner core radius Res- (See Figs. 6.1.1 and 6.1.2) This velocity follows from the expression 

Upstream of any flow expansion that may occur within the vortex tube. 

Knowing Ar we are now in a position to compute vqcs from Eq. (6.2.1), which is needed in the computation of the cut-point diameter of the inner vortex  

This equation is a variation of Barth s famous expression for a cyclone s cut-size, Eq. (5.2.1). In fact, the two equations become identical if we neglect the roof leakage flow and the gas density (relative to that of the solids), and set the Xfact term equal to 1. This Xfact term is simply a correction factor that may be applied, if desired, to force the computed cut point to match that observed in practice. It normally falls within the range of about 0.9 to 1.4. No such factor, however, has been applied in the example problems reported later in this chapter. 

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