Cyclone Design

Cyclone Design

Cyclones are very common particulate control devices used in many applications,especially those where relatively large particles need to be collected. They are notvery efficient for collecting small particles because small particles have little massthat can generate a centrifugal force. Cyclones are very simple devices that usecentrifugal force to separate particles from a gas stream. They commonly are con-structed of sheet metal, although other materials can be used. They have a low capitalcost, small space requirement, and no moving parts. Of course, an external device,such as a blower or other source of pressure, is required to move the gas stream.Cyclones are able to handle very heavy dust loading, and they can be used in high-temperature gas streams. Sometimes they are lined with castable refractory materialto resist abrasion and to insulate the metal body from high-temperature gas.

A typical cyclone is illustrated in Figure 21.1. It has a tangential inlet to acylindrical body, causing the gas stream to be swirled around. Particles are throwntoward the wall of the cyclone body. As the particles reach the stagnant boundarylayer at the wall, they leave the flowing gas stream and presumably slide down thewall, although some particles may be re-entrained as they bounce off of the wallback into the gas stream. As the gas loses energy in the swirling vortex, it startsspinning inside the vortex and exits at the top.

The vortex finder tube does not create the vortex or the swirling flow. Its functionis to prevent short-circuiting from the inlet directly to the outlet. Cyclones will workwithout a vortex finder, although the efficiency will be reduced.

21.1 COLLECTION EFFICIENCY

When a particle moves at a constant speed in a circular direction, the velocity vectorchanges continuously in direction, although not in magnitude. This creates acceler-ation resulting from a change in direction of the velocity, which is just as real andjust as much an acceleration as that arising from the change in the magnitude ofvelocity. By definition, acceleration is the time rate of change of velocity, andvelocity, being a vector, can change in direction as well as magnitude. Force, ofcourse, is defined by Newton’s Second Law (F = ma). Centrifugal force is given by:

(21.1)

whereF = centrifugal forcem = mass of particleV = velocity of particle, assumed to equal inlet gas velocityr = radius of cyclone body

21

FmV

r=

2

9588ch21 frame Page 305 Wednesday, September 5, 2001 10:07 PM

Because the operating principle of a cyclone is based on using centrifugal forceto move particles to the cyclone wall, a simple mistake in the piping configuration,shown in Figure 21.2a, reduces efficiency. Ensure that particles are given a headstart in the right direction by using the configuration shown in Figure 21.2b.

21.1.1 F

ACTORS

A

FFECTING

C

OLLECTION

E

FFICIENCY

Several factors that affect collection efficiency can be predicted. Increasing the inletvelocity increases the centrifugal force, and therefore the efficiency, but it alsoincreases the pressure drop. Decreasing the cyclone diameter also increases centrif-ugal force, efficiency, and pressure drop. Increasing the gas flow rate through a givencyclone has the effect of efficiency shown in Equation 21.2:

(21.2)

wherePt = penetration (Pt = 1 –

η

)

η

= particle removal efficiencyQ = volumetric gas flow

FIGURE 21.1

Schematic of standard cyclone.

Pt

Pt

Q

Q2

1

1

2

0 5

=

.


Interestingly, decreasing the gas viscosity improves efficiency, because dragforce is reduced. Centrifugal force drives the particle toward the wall of the cyclone,while drag opposes the centrifugal force. The terminal velocity of the particle towardthe wall is the result of the force balance between the centrifugal and drag forces.Increasing gas to particle density difference affects penetration as shown inEquation 21.3:

(21.3)

where:

µ

= gas viscosity. Note that decreasing the gas temperature increases the gasdensity, but contrary to intuition, decreases the gas viscosity, which reduces dragforce and results in a small efficiency improvement. However, decreasing the gastemperature also decreases the volumetric flow rate, which affects efficiency asdescribed above in Equation 21.2.

Finally, particle loading also affects efficiency. High dust loading causes particlesto bounce into each other as they move toward the wall, driving more particlestoward the wall and their removal.

(21.4)

where L = inlet particle concentration (loading).

FIGURE 21.2

Inlet piping configuration.

Pt

Pt2

1

2

1

0 5

=

µµ

.

Pt

Pt

L

L2

1

1

2

0 18

=

.

9588ch21 frame 07 Wednesday, September 5, 2001 10:07 PM

Figure 21.3 shows generalized efficiency relationships for high-efficiency con-ventional and high-throughput cyclones. It simply demonstrates that the dimensionsof the cyclones can be tuned to the application. Figure 21.4 and Table 21.1 illustratetypical cyclone dimensions. Relative dimensions are based upon the diameter of thebody of the cyclones. High-efficiency cyclones tend to have long, narrow bodies,while high-throughput cyclones generate less pressure drop with fat bodies.

21.1.2 T

HEORETICAL

C

OLLECTION

E

FFICIENCY

The force balance between centrifugal and drag forces determines the velocity ofthe particles toward the wall. Resident time of particles in the cyclone, which allowstime for particles to move toward the wall, is determined by the number of effectiveturns that the gas path makes within the cyclone body. An empirical relationship forthe number of effective turns is provided in Equation 21.5:

(21.5)

whereN

e

= number of effective turnsH = height of the tangential inletL

b

= length of cyclone bodyL

c

= length of cyclone lower cone

The theoretical efficiency of a cyclone can be calculated by balancing theterminal velocity with the residence time resulting from a distance traveled in thecyclone. This force and time balance results in Equation 21.6:

FIGURE 21.3

Generalized efficiency relationships.

NH

LL

e bc= +

12


(21.6)

whered

px

= diameter of a particle with x% removal efficiency

µ

= viscosity

FIGURE 21.4

Cyclone dimensions.

TABLE 21.1Typical Cyclone Dimensions

High Efficiency Standard High Throughput

Inlet height H/D 0.44 0.5 0.8Inlet width W/D 0.21 0.25 0.35Gas exit diameter D

e

/D 0.4 0.5 0.75Body length L

b

/D 1.4 1.75 1.7Cone length L

c

/D 2.5 2.0 2.0Vortex finder S/D 0.5 0.6 0.85Dust outlet diameter D

d

/D 0.4 0.4 0.4

dx W

N Vpx

e i p g

=−( )

100

90 5

µπ ρ ρ

.


W = inlet widthN

e

= number of effective turnsV

i

= inlet velocity

ρ

p

= density of particle

ρ

g

= density of gas

21.1.3 L

APPLE

’

S

E

FFICIENCY

C

ORRELATION

Unfortunately, the theoretical efficiency relationship derived above does not correlatewell with real data. The relationship works reasonably well for determining the 50%cut diameter (the diameter of the particle that is collected with 50% efficiency). Tobetter match data with reasonable accuracy, the efficiency of other particle diameterscan be determined from Lapple’s empirical efficiency correlation,

1

which is shownin Figure 21.5. This correlation can be set up for automated calculations using thealgebraic fit given by Equation 21.7:

(21.7)

FIGURE 21.5

Lapple’s efficiency curve.

ηj

p

pj

d

d

=

+

1

1 50

2


where

η

j

= collection efficiency of particle with diameter jd

p50

= diameter of particles with 50% collection efficiencyd

pj

= diameter of particle j

Lapple’s efficiency curve was developed from measured data for cyclones withthe “standard” dimensions shown in Table 21.1. The efficiency curve can be tailoredfor different industrial cyclone dimensions by adding a slope parameter, B, to thecorrelation:

(21.8)

where B = slope parameter, typically ranging from 2 to 6.Figure 21.6 illustrates the effect of the slope parameter, B. Note that the larger

value for B results in a sharper cut. Since more mass is associated with largerparticles, the sharper cut results in higher overall mass removal efficiency.

21.1.4 L

EITH

AND

L

ICHT

E

FFICIENCY

M

ODEL

Other models have been developed to predict cyclone performance. One is the Leithand Licht model

2

shown in Equation 21.9:

FIGURE 21.6

Effect of slope parameter, B.

ηj

p

pj

Bd

d

=

+

1

1 50


(21.9)

(21.9a)

(21.9b)

(21.9c)

whered

p

= particle diameter in metersD

C

= cyclone body diameter in metersT = gas temperature, °KK = dimensional geometric configuration parameterQ = volumetric gas flow

ρ

p

= particle densityC

′

= cunningham slip correction factor

µ

= gas viscosity

The geometric configuration parameter is estimated based on the cyclone con-figuration. Table 21.2 shows relative dimensions for three types of cyclones: thestandard cyclone, the Stairmand design,

3

and the Swift design.

4

Note that the Stair-mand and the Swift cyclones have smaller inlet openings than the standard design,which means a higher inlet velocity for the same size body. This results in morecentrifugal force and increased efficiency. In the Leith and Licht model, a largergeometric configuration parameter results in a higher predicted efficiency.

TABLE 21.2Geometric Configuration Parameter

Standard Stairmand Swift

Inlet height H/D 0.5 0.5 0.44Inlet width W/D 0.25 0.2 0.21Gas exit diameter D

e

/D 0.5 0.5 0.4Body length L

b

/D 2.0 1.5 1.4Cone length L

c

/D 2.0 2.5 2.5Vortex finder S/D 0.625 0.5 0.5Dust outlet diameter D

d

/D 0.25 0.375 0.4Geometric configuration paramater K 402.9 551.3 699.2

η = − −( )1 exp Ψ dpM

Mm

=+1

1

m DT

c= − −( )

1 1 0 67

2830 14

0 3

. ..

Ψ =′ +( )

2

1

18 3

2K Q C m

Dp

C

M

ρµ


21.1.5 C

OMPARISON

OF

E

FFICIENCY

M

ODEL

R

ESULTS

Efficiency models are adequate for getting a fair idea of performance, but there canbe a rather wide variation in model predictions. Part, but not all, of the variationcan be explained by empirical factors for the cyclone configuration. Figure 21.7shows cyclone efficiency curves as a function of particle diameter based on severalsources. Each curve is based upon the same gas flow and gas and particle conditions.The lowest efficiency is predicted by Lapple’s curve for a standard cyclone. Inter-estingly, the Leith and Licht model for the same standard cyclone predicts a signif-icantly higher efficiency. The Leith and Licht model for the higher efficiency Stair-mand and Swift cyclone designs shows incremental improvement over the standarddesign. Vendor data also were collected for the same set of gas and particle condi-tions, with significant predicted performance improvement. Perhaps the vendorswere being overoptimistic about their designs, or perhaps there have been significantimprovements in cyclone design over the years. It does point out that performanceguarantees for cyclones must be written with specific information about the gas andparticle properties, including the particle size distribution, to ensure that vendorguarantees can be measured and substantiated after installation.

21.2 PRESSURE DROP

Pressure drop provides the driving force that generates gas velocity and centrifugalforce within a cyclone. Several attempts have been made to calculate pressure dropfrom fundamentals, but none of them has been very satisfying. Most correlationsare based on the number of inlet velocity heads as shown in Equation 21.10:

FIGURE 21.7

Cyclone efficiency curves.


(21.10)

where

∆

P = pressure drop

ρ

g

= gas densityV

i

= inlet gas velocityN

H

= pressure drop expressed as number of the inlet velocity heads

One of the correlations for number of inlet velocity heads is by Miller andLissman:

5

(21.11)

whereK

∆

P1

= constant based on the cyclone configuration and operating conditionsD = diameter of the cyclone bodyD

e

= diameter of the exit tube

A typical value for K

∆

P

in the Miller and Lissman correlation is 3.2. For thestandard cyclone configuration described above, the Miller and Lissman correlationresults in 12.8 inlet velocity heads.

Another correlation for number of inlet velocity heads is by Shepherd andLapple:

6

(21.12)

whereK

∆

P2

= constant for cyclone configuration and operating conditionsH = height of the inlet openingW = width of the inlet openingD

e

= diameter of the exit tube

The value for K

∆

P

in the Shepherd and Lapple correlation is different, typicallyranging from 12 to 18. The Shepherd and Lapple correlation results in 8 inlet velocityheads for the standard cyclone dimensions, 6.4 inlet velocity heads for the Stairmandcyclone design, and 9.24 inlet velocity heads for the Swift cyclone design. As canbe seen, there is a substantial difference among the correlations. Again, it is best torely upon vendors’ experience when your own experience is lacking; however, toenforce a performance guarantee, ensure that the specification is well-written andcan be documented for the expected conditions.

∆Pg

V Nc

g i H= 12

2ρ

N KDDH P

e

=

∆ 1

2

N KHWDH P

e

= ∆ 2 2


21.3 SALTATION

The previous discussion of efficiency and pressure drop leaves the impression thatcontinually increasing the inlet gas velocity can give incrementally increasing effi-ciency. However, the concept of “saltation” by Kalen and Zenz

7

indicates that, morethan just diminishing return with increased velocity, collection efficiency actuallydecreases with excess velocity. At velocities greater than the saltation velocity,particles are not removed when they reach the cyclone wall, but are kept in suspen-sion as the high velocity causes the fluid boundary layer to be very thin. A correlationfor the saltation velocity was given by Koch and Licht:

8

(21.13)

whereV

s

= saltation velocity, ft/sD = cyclone diameter, ftV

i

= inlet Velocity, ft/sg = acceleration of gravity, 32.2 ft/s

2

µ

= gas viscosity, lbm/ft-sec

ρ

p

= particle density, lbm/ft

3

ρg = gas density, lbm/ft3

W = width of inlet opening, ft

The maximum collection efficiency occurs at Vi = 1.25Vs, which typically is between50 and 100 ft/s.

REFERENCES

1. Lapple, C. E., Processes use many collector types, Chem. Eng., 58, 5, May 1951.2. Leith, D. and Licht, W., The collection efficiency of cyclone type particle collectors —

A new theoretical approach, AIChE Symp. Series, 126 (68), 1972.3. Stairmand, C. J., The design and performance of cyclone separators, Trans. Ind.

Chem. Eng., 29, 1951.4. Swift, P., Dust control in industry, Steam Heating Eng., 38, 1969.5. Miller and Lissman, Calculation of cyclone pressure drop, presented at meeting of

American Soc. of Mech. Eng., New York, December 1940.6. Shepherd, C. B. and Lapple, C. E., Flow pattern and pressure drop in cyclone dust

collectors, Ind. Eng. Chem., 32(9), 1940.7. Kalen, B., and Zenz, F., Theoretical empirical approach to saltation velocity in cyclone

design, AIChE Symp. Series, 70(137), 1974.8. Koch, W. H. and Licht, W., New design approach boosts cyclone efficiency, Chem.

Eng., 84(24), 1977.

V D V g

WDWD

s i

p g

g

=−( )

−

2 055 43

1

0 067 0 6672

0 3330 4

0 333. . .

..

.µρ ρ

ρ


Cyclone Design

Documents

Transcript of Cyclone Design