Vortex end

Hoffman et al. (1995) studied the cyclone vortex length and found that separation efficiency was less for cyclones with their natural vortex ending in the cone instead of the barrel. They also reported that the vortex length (swirl intensity) deereased with increasing solids loading and was a strong function of the eyelone length. Akiyama and Marui (1989), in... 

The total loss shown above is that which occurs from inlet to (gas) overflow and represents also the loss in static pressme over the cyclone. As a rough estimate, the difference in static pressme between the inlet and the (solids) underflow, under the point at which the vortex ends, is the same as that computed by Eq (6.6.1) but without the core loss contribution. However, if the vortex core happens to extend or dip down to the underflow pipe, the difference in static pressure between inlet and imderflow can equal—or even exceed—the total pressure drop from inlet to overflow. 

Significant strides still need to be made, however. Cyclone efficiency depends to a large extent on the behaviour of dense particle strands where the interaction between the particles becomes important, and this is a field where much research still needs to be done and one in which the authors of this book are active. Also, although interesting progess is being made, phenomena such as the vortex end are still not successfully simulated. 

If, in a transparent cyclone, there is some mobile dust or liquid on the cyclone wall, the end of the vortex can clearly be seen as a ring. Until now, it has not been possible to ascertain the exact nature of the vortex end. Two possible explanations circulate in the literature and among cyclone experts. 

One is that the end of the vortex is an axisymmetric phenomenon, that the end represents a sort of recirculating gas bubble . Such a vortex end is observed in the research field of vortex breakdown in vortex tubes , tubes in which a flowing liquid is caused to swirl with swirl vanes. A difference between a vortex tube and a cyclone or swirl tube is that the flow reverses in the latter, while in the vortex tube it continues past the vortex end, and discharges from the bottom of the tube. Another difference is that this type of experiment is usually (but not always, see Sarpkaya, 1995) performed under laminar flow conditions, while the flow in a cyclone is turbulent. 

The following sections will show that the vortex end significantly influences the behavior of cyclones and swirl tubes. Its nature, and the factors governing its position, should therefore be well understood by anyone who designs such cyclonic type separators, and this topic should be given high priority in cyclone research at this time. 

If we perform a simplified analysis of the gas velocity near the wall in a cyclone operating with the vortex end precessing around the wall, an interesting result emerges with respect to the near-wall velocities. The illustration below attempts to show the vortex end precessing around the entire inner wall of a cyclone while, at the same time, displaying a snapshot of its characteristic rotational imprint ( eye of the hurricane) at any given point in time. 

Fig. 9.2.4. Vortex end in contact with, and precessing around, inner wall...

In light of what is reported above, if the end of the vortex is allowed to attach to, and process around, the inner walls of the cyclone, such action can lead to severe localized erosion in the form of an acute erosion ring. This ring effectively defines the path of the processing vortex end. 

Although this seems to be approximately true in swirl tubes with a cylindrical body, experimental results indicate that the separation performance of cylinder-on-cone cyclones is reduced more than would be expected from the reduction of their effective length when the vortex ends within the conical section. One example is the dramatic reduction in separation efficiency (corresponding to an increase in cut diameter) for the longest cyclone length... 

There are, as the discussion in the two previous sections indicate, reasons, other than efficiency considerations, for designing cyclones to avoid the vortex ending in the separation space. The collected dust that would normally experience an orderly downward transport along the wall will encoimter a gross disturbance at the point (actually a plane) where the vortex ends. This usually occurs near the lower cone wall. 

It has furthermore been claimed that the position of the vortex end is related to the sharpness of the cyclone cut (Abrahamsen and Allen, 1986). In support of this, the writers have observed considerable mixing of the solids originating in the plane where the precessing vortex tail attaches to the lower walls of model cyclones. This has been observed in both dedusting and demisting cyclones. 

In Fig. 9.2.7 we plot the velocity at which the vortex end or core trans-verses around the inside wall of the hopper (from Eq. 9.2.1) versus the estimated maximum tangential velocity of the vortex core (from Eq. 9.2.2). This plot strongly suggests that the precessional velocity is directly related to the maximum spin velocity. Thus, as stated earlier, precession frequency can be estimated by simply dividing the core s maximum spin velocity by the circumference of the inner wall to which it is attached. If this is true, then the end of the vortex acts much like a rubber wheel that rotates around the inner walls at a velocity equal to the maximum spin velocity of the vortex core. 

Where the vortex ends can have a significant bearing on cyclone performance. We ll try to illustrate this by examining two scenarios for vortex attachment, as shown in Fig. 9.2.8. The frame on the left has the vortex ending, and precessing around, the lower cone walls. Here, the pressure at the bottom of the cyclone (or top of the dipleg) can be expected to equal the inlet pressure minus the pressure loss due, primarily, to wall friction. (The latter typically... 

The position of the vortex end is difficult to model. The first and, by far, the best known relation for the natural vortex length i.e. the length from the lip of the vortex finder to the position of the end of the vortex) was proposed by Alexander (1949) ... 

Fig. 9.2.8. Vortex end terminating on cone wall (left) and at bottom of cyclone (right)...

The issue of overall cyclone length was already discussed in Chaps. 5 and 9 in connection with the effect of length on pressure drop/efficiency and the natural vortex end. 

In cyhnder-on-cone cyclones, indications are that the separation performance becomes erratic if the vortex terminates within the conical section. Our experience is that this is less so with cylindrical swirl tubes. It appears that the main effect of the vortex ending in the tube is simply to shorten the effective... 

If the body tube length is increased so that it is greater than the natural vortex length , the vortex end or tail will pop up into the tube body, and take up a position on the wall at some distance from the solids (or liquid) discharge opening. It is likely that a drop in efficiency and a rise in pressure drop will be observed at the length at which this first takes place, since the effective tube length will decrease quite considerably at this point. 

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