9
Other Factors Influencing Performance
In this chapter we will look at two special factors that strongly influence cyclone performance.The are solids loading and the‘natural turning length’, both of which affect cyclone paration performance,wear and pressure drop, especially in cyclones with a tangential inlet.The natural turning length may also correlate with clogging.
9.1The Effect of Solids Loading
Contrary to what one might expect intuitively,cyclone performance improves with increasing solids loading up to quite high loadings:the overall efficiency increas,and the pressure drop decreas with increasing solids loading. 9.1.1Effect on Separation Efficiency of Cyclones
Cyclone designers have long known that the paration efficiency of tangen-tial inlet cyclones improves with increasing solids loading.Even so,the exact mechanism for this improvement is still not established beyond doubt,in spite of many investigations of the topic.
Figure9.1.1shows the overall efficiency as a function of loading for a cy-clone with a tangential inlet.Th
e overall efficiency can be en to increa substantially with increasing solids loading.It increas so much that,at a moderate solids loading of40g solids per m3of air,the fractional emission from the cyclone is only about one third of what it is at low loading.Thus, the fraction,or percentage,of incoming solids that is lost decreas with in-creasing solids loading even though the absolute magnitude of the loss still increas1.This is clearly an effect to be aware of,since problems can ari with a plant cyclone design bad on testing in a model at an unknown(high) solids loading.
1For15m/s in Fig.9.1.1,the absolute emission at a loading of44g/m3is15times that at1g/m3.
1849Other Factors Influencing Performance
0.800.901.0
同位语从句O v e r -a l l e f f i c i e n c y 0.8 m Fig.9.1.1.Overall efficiency of a cyclone acting on a chalk powder with a median particle diameter of 3.7µm as a function of solids loading (Hoffmann et al.,1991).Dimensions of the cyclone:D =0.2m;D x =0.075m;S =0.1;a =0.1;b =0.04;H c =0.5m;H =0.8m;D d =0.075.Scale drawing of the cyclone also shown.
Figure 9.1.2a and b show grade-efficiency data and size distributions of the overhead fraction corresponding to some of the points shown in Fig.9.1.1.Three features in Fig.9.1.2are noteworthy:
•
Moving in the direction of decreasing particle size,the efficiency decreas,goes through a minimum,and again increas for the very small particles •
the increa in solids loading pushes the grade-efficiency curve upwards as a whole,and
•the size distribution of the overhead solids remains esntially unchanged with solids loading,despite the dramatic increa in paration efficiency.The two latter features are consistent with the following picture of the effect of solids loading on efficiency:an ‘extra’amount of solids (‘extra’com-pared to what would normally be parated in the cyclone body in accordance with the cyclone grade-efficiency curve)parates or ‘salts out’more or less unclassified in the cyclone inlet hat for each size class about the same weight or volume fraction parates out in the inlet.The remaining solids continue to the ‘inner’vortex,where they are classified roughly the same as they would be at low loading.We say “roughly the same”since the extra solids on the wall at high loading will attenuate the vortex somewhat.
We will be returning briefly to the topic of solids loading in swirl tube parators later.Here,we wish to note that a difference exists between the behavior of cyclones with tangential inlets and swirl tubes equipped with inlet vane asmblies,so that the results shown in the figures cannot be applied to swirl tubes.
9.1The Effect of Solids Loading 185
午市9.1.2Models for the Effect on Separation Efficiency of Cyclones The reason for the effect of loading on paration efficiency is not established beyond doubt,but the data and obrvations in the previous ction can help us evaluate the merits of the explanations forwarded in the literature.A number of mechanisms and models have been propod.
0.0
0.2
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10 C u m u l a t i v e f r a c t i o n u /s Particle size (µm) 0.0
0.2
0.40.60.81.01.20.1 1.0
10 F r a c t i o n a l e f f i c i e n c y Particle size (µm) a
b
Fig.9.1.2.a,b Grade-efficiency and overhead size distributions for some of the experiments in Fig.9.1.1.Inlet velocity:10m/s.The size distributions of the feed and overhead fractions were measured by an optical disc centrifuge using a line-start technique
One explanation for the effect is the critical loading concept of Muschelk-nautz.We refer to our discussion of the Muschelknautz method in Chap.6,and give here only a brief outline of the hypothesis.This concept sprang from a model for horizontal pneumatic conveying of powders.The idea is that the
iowa1869Other Factors Influencing Performance
turbulence in the carrier gas can support only so much powder(the‘critical load’)in a horizontal conveying tube against the force of gravity.The excess powder beyond this critical load will ttle out of the gas stream to the bottom of the tube spontaneously and,according to the early work of Muschelknautz, esntially unclassified(e below and Chap.6for more discussion of the issue of classification in the inlet region).The extension of this notion to cyclones is straight-forward:the solid-laden inlet jet is considered as a sort of conveying tube,and the centrifugal force is substituted for the gravitational force.
In his earlier papers,Muschelknautz arrived at the following expression for the critical load or‘limit load’in terms of kg dust(that the gas could keep in turbulent suspension)per kg of gas:软件就业
c oL=
fD mµ
2(1−D x/D)ρp x2
med
vθmavatar是什么意思
(9.1.1)
where D m=(DD x)1/2and vθm=(vθw vθx)1/2,and x med is the median size of the inlet dust.An example of how to u this equation is included in Appendix9.A.Another,more recently developed expression for the critical load is given in Eqs.(6.4.1)and(6.4.2).The expression in Chap.6is of a different type,and is not bad on a direct analogy with pneumatic conveying in a gravitationalfield.
As mentioned,the upwards shifting andflattening of the grade-efficiency curve with increasing solids loading en by Hoffmann et al.(1992),and also exhibited by the data in Fig.9.1.2strongly supports the idea that the‘extra’material parating out in the inlet due to the solids-loading effect is esntially unclassified.However,in the more recent work,Muschelknautz and Trefz in-troduced the notion of a cut size in the inlet region of a highly-loaded cyclone in addition to the cut size in the inne
r vortex.This was discusd in detail in Chap.6.We note that the obrved change in shape of the grade-efficiency curve with loading is not consistent with the notion of a sharp‘cut’in the inlet region.
The upward shifting andflattening of the curve may,however,be consis-tent with a certain classification in the inlet.Greif(1997)found that at high loadings the large particles are completely removed in the inlet region,while the smaller particles are parated in the inlet with a high(but<1),almost uniform,efficiency(e Fig.6.B.2).Greif looked at this as a very shallow‘cut’in the inlet,meaning that the‘s-shaped’GEC is rather‘flat’and reflects an efficiency which is significantly greater than zero for all particle sizes.In this way Greif could reconcile the change in shape of his grade-efficiency curves as a function of incread loading(Greif found much the same solids loading effect as Hoffmann et al.(1992))with the obrvation of his predecessors that the material continuing to the inner vortex at high loadings isfiner than the feed.
As an alternative to the critical loading concept,Mothes and L¨offler(1984) put forward the idea that the improvement of cyclone efficiency with solids初三化学方程式总结
9.1The Effect of Solids Loading187 loading is due to particle agglomeration.They propod a model for particle agglomeration,bad on calculating
•the impaction probability and
•the sticking probability
of a small particle moving toward a large one.As the size of the small particle increas,the impaction probability increas while the sticking probability decreas.They found that the product of the two probabilities,which gives the probability that the small particle will actually agglomerate with the larger‘cleaning’particle,is a maximum for a particle size of about2µm, if the large particle is15µm.In this concept the larger particles are thus held to‘sweep up’smaller particles as the large particles move to the wall in the cyclone inlet region.According to the Mothes and L¨offler model the paration of small particles due to solids loading should therefore increa with the concentration of larger‘cleaning’particles.We refer the reader to their paper for further information.
platypusEmpirical relations without any mechanistic explanation have also been propod.Smolik,as quoted by Svarovsky(1981),propod:
η(c2)=1−(1−η(c1))
c1
c2
0.18
(9.1.2)
where c1and c2denote two different solids loadings in the inlet stream ex-presd in any concentration unit.η(c i)is the corresponding overall,fractional efficiency.
Another purely empirical model was propod by Zenz.This is a graphical method.The chart of Zenz,which is bad on years of practical experience, is shown in Fig.9.1.3.
Both the models of Smolik and Zenz predict cyclone paration efficiency as a function of loading purely from knowledge of the efficiency at low loading and the loading itlf.Physical and operational factors,such as cyclone geometry and size,solids size distribution and density,inlet velocity and other operating conditions,are not included in the models,and the effect of the parameters is thus not thought to be of primary importance.In the Muschelknautz model, on the other hand,the inlet velocity,the cyclone dimensions,and the mean size and density of the inlet solids all feature.
When trying to weigh up the relative merits of the mechanistic explana-tions for the effect of loading
on cyclone paration,we obrve that the results in Figs.9.1.1and9.1.2are consistent with the notion of the extra material being largely unclassified,and they are in this n more consistent with the Muschelknautz concept than the concept of Mothes and L¨offler.However,the Muschelknautz concept,as given in Eq.(9.1.1),leads us to expect a range of low loadings—under the‘critical load’—where there is no effect of solids load-ing on the fractional paration.We,nonetheless,do not e such a range in Fig.9.1.1,the effect of solids loading starts from zero loading,as the models of
late是什么意思
1889Other Factors Influencing Performance
S o l i d s l o a d i n g (g r a i n /f t 3) 1000 100
10 1 20 40
60 80 90 95 98 99 99.8
起息99.9
99.99 η Fig.9.1.3.The graphical model of Zenz for estimating the effect of solids loading on cyclone paration efficiency.1grain/ft 3=2.29g/m 3
