Air Classification : Computer Models and Experimental Results t

Computer simulations of the flow fields in centrifugal air classifiers have been undertaken in order to improve both the performance and efficiency of the commercially available Acucut air classifier. A !though the simulations have led to a much greater understanding of the nature of the flow likely to prevail in such systems, accurate predictions have been found to be strongly dependent on the assumption of correct inlet flow conditions during the initiation of the simulations. In spite of the fact that these simulations assumed axial symmetry (which is an oversimplification), they have enabled the identification of a number of engineering modifications which have contributed to reducing the cut size, and increasing the efficiency, of an A cucut Laboratory classifier.


Introduction and Program Objectives
The specifications for top sizes, especially for ceramics and fillers, have tended to become finer and finer-with a desire being expressed for top sizes around 1-3 ,urn and median sizes less than 0.5 ,um.If produced by mechanical means, this type of top size requirement can only be achieved either by repeated grinding in wet mills or by allowing very long residence times in batch mills.Alternatively, however, such sizes can be produced by air classification-a method that is particularly attractive if a market also exists for the coarse fraction from the classification process.An air classifier capable of achieving these specifications is the the Acucut classifier, shown in It consists of a rotor, made of two dished plates separated by a blade cage, which produces a forced vortex flow field.The air flow through the rotor is produced by a Rootes type blower located downstream of the classifier.The classifying zone is restricted to within the rotor.The air flow enters the classifying zone through a very narrow gap between the rotor periphery and the stator.The original design required the air velocity in this gap to be maintained at between 60 and II 0 m/s.This causes a highly turbulent dispersion zone through which the coarse particles and agglomerates must pass before reaching the coarse fraction exit.The air flow causes a high pressure loss in the gap, and the classifying zone is thus under negative pressure.This permits the feed to be sucked into the zone, via a converging/diverging nozzle, the throat of which is dimensioned to allow no more than I O%of the total air to enter the zone through this nozzle.
It is necessary that the entering feed material be accelerated to the rotational velocity of the air flow in order to prevent particles above a desired size from entering the blade cage.This is achieved in the expanding section of the rotor where the inward radial velocity is deliberately slowed down.The actual cut is intended to occur just outside the blade cage through which only those particles below the desired size are allowed to pass.Three sizes of these units were originally developed.The rotor diameters were 300 mm(AI2), 450 mm(BI8) and 600 mm(C24).The two smaller units were capable of very fine cuts, but the efficiency of the units was highly susceptible to feed rates, as shown in Attempts were made to improve on this situation by both changing the method by which the feed was introduced [I] , and/ or by increasing the air flow [2].The first attempt involved introducing the feed via the top rotor plate, as shown in This modification was considered likely at the time to lead to unacceptably high rotor wear, although variations of it have been used in at least two new systems [ 4,5] .Furthermore, it nullified what was though to be one of the classifier's major innovations-the highly turbulent dispersion zone.The sharpness of cut results, however, were clearly better than in the standard version, as seen in Figure 4. Y 1 is the fines yield, and K,s 75 is the ratio of the sizes at which T(x)has the values 0.25 and 0.75.
De silva (2] demonstracted that it was also possible to maintain high sharpness of cut values at high loadings if the air flow was increaed.see  It is, however, clear that fine fraction recovery is reduced at these loadings, although the rate of production was increased four-fold.Increasing air flow also leads to very high pressure losses in the rotor stator gap-and simultaneously leads to coarser cuts as shown in Figure 6.Thus the rotor speed has to be increased to compensate-leading to still higher pressure losses.This then was the point of departure for the development program.The aim was two-fold.First, to determine whether computer modelling could be applied to improving our understanding of the flow fields in the classifying zone, and secondly to determine whether engineeing modifications could be carried out to obtain improved efficiencies and lower cuts predicted by the model.It was always realized that simulations and experiments must be carried out sequentially, the results from the one to be used to improve those from the other on an on-going basis.

Preliminary Simulations
The preliminary simulations used the model geometry shown in Figure 7, and the turbulent modelling program Fluent (TM).The mathematical model used solves the Navier-Stokes equation using the well known K-c: model.The particulate phase IS described by continuity equations for five simultaneous size classes where the particle velocities are calculated from the gas velocity and their settling velocity in the centrifugal field.The model entirely neglects interparticle collisions and agglomeration effects.Furthermore, one has to make an assumption regarding what happens to particles which reach the system boundaries (the rotor plates).Either one can assume that these particles leave the system as the coarse fraction, or we can assume that no deposition occurs.The reality is likely to be somewhere in-between with particles reaching the rotor plates gliding along them inside a wall boundary layer as a result of the strong centrifugal forces.The existence of relatively large particle concentrations will alter the mean flow and dampen the turbulence in the classifier.These effects can only be allowed for by guess work.Full details of the assumptions made in the modelling are found elsewhere [3] .The grade efficiency curves are calculated by calculating the particle concentrations for a sufficiently large number of particle sizes.The grade efficiency for each size class is then calculated from the mass flow of particles reaching the fines exit.The equations were solved using standard finite difference techniques, and the geometry of the classifier was represented by a polar coordinate system.This causes some inaccuracies at the walls where the grid lines are not parallel to the wall and yield irregularities where none, in fact, exist.Figure 9 shows that they do, but that they are unable to reach the outlet.The reason lies in the nature of the vortices in the rotor.These simulations indicate that a forced vortex(Vj r=const.)onlyexists within the rotor blade cage, whereas free vortices(Y._,,r"=const.)exist outside.Thus V-increases from the inside diameter of the blade cage to the exit thus increasing the centrifugal force (V//r) acting on the particles and preventing them from moving inwards.

Modified Rotor Design
The simulations led to certain modifications being carried out to the rotor.One of these was the extension of the blade cage all the way to the outlet.This was intended to ensure that no free vortex was set up inside the blades.Secondly, a set of studs were machined on to the outer periphery of the two rotor plates on the outside.These, it was hoped, would ensure that the flow fields of Figure 8b) rather than those of Figure 8a) would be obtained.Third, the cross section of the rotor was reduced from the point where the original blades ended towards the centre.This would further help the rapid removal of fines by increasing the inward velocity of the air flow to a greater extent than in the previous rotor.
Diameter (micron) Fig. 11 Fine fraction recovery against rotor speed for the old and new rotors These results indicated one of two things.Either the simulations were not really reflecting reality, or the conditions necessary to produce the desired flow fields were not achieved.Further simulations were therefore performed.

New Simulations/Results
The new simulations used the geometry of the modified rotor as shown in Figure 12.The critical points for which answers were sought were a) does the flow actually rotate at the rotor periphery, and b) is there really a build up of particles within the rotor blades when the blades do not extend to the centre.The simulations and experiments lasted nearly a whole year.Many conflicting results were obtained which led to a thorough inves-tigation of the experimental procedures.Gradually, the experiments and simulations began to show increasingly good agreement.Some special modifications were carried out to ensure that the most promising boundary conditions were in fact also being obtained in practice.
Figure 13 and 14 show the decay of the rotation as the air flow passes through rotor/ stator gaps of 200,um and IOOO,um, respectively.The figures demonstrate that the rotational velocity imparted to the air on the outside of the rotor is significantly reduced in the rotor /stator gap.On the Inside of the rotor the actual tip speed of 47.8 m/s decays to Figure 15 confirms that the width of the gap does not play any significant role in determining the top size in the fines, while the actual tangential velocity at the periphery very certainly does.These results demonstrate that, somehow, the peripheral velocity of the rotor must be transmitted to the air flow, well inside the rotor, in order to maintain top size control.The next question was the effect of the rotor blades on the flow field.As mentioned earlier, it was found that if the inner diameter of the blade cage was 150 mm, then the forced vortex produced within the blades degenerates into a free vortex and prevents particles, which pass the blades, from leaving the classifier.
Extending the blades to the centre outlet (inner diameter of the blade cage is 40 mm) was expensive in terms of rotor manufac-turing and it did not appear to give any improvements in performance.Figure 16 shows the concentration profiles of 2pm particles for inner blade cage diameters of 40, 60, 80 and 150 mm.The figures show no build up expect in the last of the above.This figure is noc strictly comparable with Figure 9 since in that case the simulated rotor speed was 2000 rpm( size penetrating 4,um), whereas in Figure 16 the penetrating size is 2pm(rotor speed is 3000 rpm).
Thus, it appears that some leeway is available in designing the blade cage.It was also calculated that the pressure loss over the rotor increased from 5.7 kPa to 13.7 kPa when the inner diameter of the blades was increased from 40mm to 150mm.Experimental results confirm that there is a reduction in the pressure loss with the new rotor -but mainly at high rotor speeds.We have obtained reductions of more than 50% under otherwise identical condition ( c.f. Figure 17 ).These savings are quite significant when operating at very fine cut sizes.The above simulations led to further rotor modifications which cannot yet be revealed but the results of which are presented in the next section.

Results after Second Rotor Modification
The results after second set of modifications are quite clearly better, as shown in Fig. 19 The effect of loading on the grade efficiency curves at 3000 rpm and II 0 -/h been achieved, and top sizes of 2,um appear well within reach.The problem of loading has, however, not yet been solved.The classifier still shows sensitivity to feed rate, and efficiencies deteriorate at loadings over about 0.05 kg/ kg (Figure 19).The reduction of the pressure loss over the classifier will, however, allow the use of higher air flows and higher rotor speeds.We are working on further modifications to improve the ability of the classifier to handle larger loads and will also try out external dispersion to effect further increases in performance.The predicted and experimental grade efficiency curves now show a reasonable agreement (Figure 20 ), and we expect complete agreement to be achieved when the simulations are extended to three dimensions, and the effect of particle loading on the flow is fully accounted for.

6.Conclusions and Future plans
Computer simulations are viable means of improving the performance of process equipment in which complex flow fields are encountered.It is, however, necessary to constantly compare model predictions with experimental results in order to ensure that the 138 boundary conditions used in the model are achieved in practice, either by modifications to the model or to the piece of equipment.This requires a close cooperation between the experimenter and the modeller, with each being required to acquire an insight into the possibilities and limitations of the other. of the other.It is expected that still better agreement between models and experiments will be obtained when the simulations are extended to three dimensions.We are also working on a curved coordinate system which will fit the boundaries of the classifier better than the grid used in these simulations.Finally, we expect to incorporate an improved model for particle momentum which will allow for particle-particle and particle-wall collisions.

Figure 2 .Fig. 2
Figure 2. Grade efficiency as used in this figure is given by,

Fig. 4 Fig. 5
Fig. 4 Improved sharpness of cut obtained by Leschonski and Boeck using the modified feed entry shown in Figure 3. [I J

Fig. 6
Fig. 6 Cut size as a function of rotor speed and air flow for an Acucut Bl8 air classifier

Fig. 7
Fig. 7 Model geometry used m the computer simulations of the flowfields in an Acucut A 12 classifier

Fig. 9
Fig. 8 Distribution of radial velocity contours (left)and tangential velocities( right) at 2000 rpm and 100 m 1 h.Main flow is from left to right.

Fig. 10 x
Fig. 10 x 95 versus rotor speed for the old and new rotors

Fig. 12
Fig. 12 Rotor geometry used in the new simulations

Fig. 13
Fig. 13 The contours of tangential velocity as a rotational air flow passes through a 20011m rotor stator gap.Rotor tip velocity is 47.8 m/ s(3000 rpm) Fig.15The effect of the assumed tangential velocity at the rotor periohery on the grade efficiency curve

Fig. 16
Fig. 16 Concentration of 2,um particles along a radius.Rotor speed is 3000 rpm, Air flow is 100m 1 h

eFig. 17 Fig. 18
Fig.17The influence of rotor speed on pressure drop across the classifier for old and new rotors after modification