21
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 not very efficient for collecting small particles because small particles have little mass that can generate a centrifugal force. Cyclones are very simple devices that use centrifugal force to separate particles from a gas stream. They commonly are constructed of sheet metal, although other materials can be used. They have a low capital cost, 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 hightemperature gas streams. Sometimes they are lined with castable refractory material to resist abrasion and to insulate the metal body from high-temperature gas. A typical cyclone is illustrated in Figure 21.1. 21.1. It has a tangential inlet to a cylindrical body, causing the gas stream to be swirled around. Particles are thrown toward the wall of the cyclone body. As the particles reach the stagnant boundary layer at the wall, they leave the flowing gas stream and presumably slide down the wall, although some particles may be re-entrained as they bounce off of the wall back into the gas stream. As the gas loses energy in the swirling vortex, it starts spinning inside the vortex and exits at the top. The vortex finder tube does not create the vortex or the swirling flow. flow. Its function is to prevent short-circuiting from the inlet directly to the outlet. Cyclones will work without a vortex finder, although the efficiency will be reduced.
21.1 21 .1 COLL COLLEC ECTI TION ON EFF EFFIC ICIE IENC NCY Y When a particle moves at a constant speed in a circular direction, the velocity vector changes continuously in direction, although not in magnitude. This creates acceleration resulting from a change in direction of the velocity, which is just as real and just as much an acceleration as that arising from the change in the magnitude of velocity. By definition, acceleration is the time rate of change of velocity, and velocity, being a vector, can change in direction as well as magnitude. Force, of course, is defined by Newton’s Second Law (F = ma). Centrifugal force is given by: F where F = m = V = r =
=
mV 2 r
centri cent rifu fuga gall forc forcee mas masss of of par parti ticl clee velocity velocity of of particle, particle, assumed assumed to to equal inlet inlet gas gas velocity velocity rad radiu iuss of of cyc cyclo lone ne body body
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(21.1)
FIGURE 21.1 Schematic of standard cyclone. Because the operating principle of a cyclone is based on using centrifugal force to move particles to the cyclone wall, a simple mistake in the piping con figuration, shown in Figure 21.2a, reduces ef ficiency. Ensure that particles are given a head start in the right direction by using the con figuration shown in Figure 21.2b.
21.1.1 FACTORS AFFECTING COLLECTION EFFICIENCY Several factors that affect collection ef ficiency can be predicted. Increasing the inlet velocity increases the centrifugal force, and therefore the ef ficiency, but it also increases the pressure drop. Decreasing the cyclone diameter also increases centrifugal force, ef ficiency, and pressure drop. Increasing the gas flow rate through a given cyclone has the effect of ef ficiency shown in Equation 21.2: Pt 2 Pt 1 where Pt = penetration (Pt = 1 – η) η = particle removal ef ficiency Q = volumetric gas flow
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0.5
Q1 = Q 2
(21.2)
FIGURE 21.2 Inlet piping configuration.
Interestingly, decreasing the gas viscosity improves ef ficiency, because drag force 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 toward the wall is the result of the force balance between the centrifugal and drag forces. Increasing gas to particle density difference affects penetration as shown in Equation 21.3: Pt 2 Pt1
0.5
µ 2 = µ1
(21.3)
where: µ = gas viscosity. Note that decreasing the gas temperature increases the gas density, but contrary to intuition, decreases the gas viscosity, which reduces drag force and results in a small ef ficiency improvement. However, decreasing the gas temperature also decreases the volumetric flow rate, which affects ef ficiency as described above in Equation 21.2. Finally, particle loading also affects ef ficiency. High dust loading causes particles to bounce into each other as they move toward the wall, driving more particles toward the wall and their removal. Pt 2 Pt1
0.18
L = 1 L2
where L = inlet particle concentration (loading).
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(21.4)
FIGURE 21.3 Generalized ef ficiency relationships. Figure 21.3 shows generalized ef ficiency relationships for high-ef ficiency conventional and high-throughput cyclones. It simply demonstrates that the dimensions of the cyclones can be tuned to the application. Figure 21.4 and Table 21.1 illustrate typical cyclone dimensions. Relative dimensions are based upon the diameter of the body of the cyclones. High-ef ficiency cyclones tend to have long, narrow bodies, while high-throughput cyclones generate less pressure drop with fat bodies.
21.1.2 THEORETICAL COLLECTION EFFICIENCY The force balance between centrifugal and drag forces determines the velocity of the particles toward the wall. Resident time of particles in the cyclone, which allows time for particles to move toward the wall, is determined by the number of effective turns that the gas path makes within the cyclone body. An empirical relationship for the number of effective turns is provided in Equation 21.5:
Ne where Ne = H = Lb = Lc =
=
L 1 Lb + c H 2
(21.5)
number of effective turns height of the tangential inlet length of cyclone body length of cyclone lower cone
The theoretical ef ficiency of a cyclone can be calculated by balancing the terminal velocity with the residence time resulting from a distance traveled in the cyclone. This force and time balance results in Equation 21.6: © 2002 by CRC Press LLC
FIGURE 21.4 Cyclone dimensions.
TABLE 21.1 Typical Cyclone Dimensions High Efficiency
Standard
Inlet height
H/D
0.44
0.5
0.8
Inlet width
W/D
0.21
0.25
0.35
Gas exit diameter
De /D
0.4
0.5
0.75
Body length
Lb /D
1.4
1.75
1.7
Cone length
Lc /D
2.5
2.0
2.0
Vortex finder
S/D
0.5
0.6
0.85
Dust outlet diameter
Dd /D
0.4
0.4
0.4
x 9µW d px = 100 π N e Vi (ρp − ρg )
0.5
where dpx = diameter of a particle with x% removal ef ficiency
µ
High Throughput
= viscosity
© 2002 by CRC Press LLC
(21.6)
FIGURE 21.5 Lapple’s ef ficiency curve.
W = inlet width Ne = number of effective turns Vi = inlet velocity ρp = density of particle ρg = density of gas
21.1.3 LAPPLE’S EFFICIENCY CORRELATION Unfortunately, the theoretical ef ficiency relationship derived above does not correlate well with real data. The relationship works reasonably well for determining the 50% cut diameter (the diameter of the particle that is collected with 50% ef ficiency). To better match data with reasonable accuracy, the ef ficiency of other particle diameters can be determined from Lapple’s empirical ef ficiency correlation,1 which is shown in Figure 21.5. This correlation can be set up for automated calculations using the algebraic fit given by Equation 21.7:
η j =
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1 2
d p50 1+ d pj
(21.7)
FIGURE 21.6 Effect of slope parameter, B. where
η j dp50 dpj
= collection ef ficiency of particle with diameter j = diameter of particles with 50% collection ef ficiency = diameter of particle j
Lapple’s ef ficiency curve was developed from measured data for cyclones with the “standard” dimensions shown in Table 21.1. The ef ficiency curve can be tailored for different industrial cyclone dimensions by adding a slope parameter, B, to the correlation:
η j =
1 B
d p50 1+ d pj
(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 larger particles, the sharper cut results in higher overall mass removal ef ficiency.
21.1.4 LEITH
AND
LICHT EFFICIENCY MODEL
Other models have been developed to predict cyclone performance. One is the Leith and Licht model2 shown in Equation 21.9: © 2002 by CRC Press LLC
η = 1 − exp(− Ψ d Mp ) M=
(21.9)
1 m +1
(21.9a)
0.3 T 0.14 m = 1 − (1 − 0.67Dc ) 283
K Qρp C′ (m + 1) Ψ = 2 3 µ 18 D C where dp DC T K Q
ρp C′ µ
= = = = = = = =
(21.9b)
M 2
(21.9c)
particle diameter in meters cyclone body diameter in meters gas temperature, °K dimensional geometric configuration parameter volumetric gas flow particle density cunningham slip correction factor gas viscosity
The geometric configuration parameter is estimated based on the cyclone configuration. Table 21.2 shows relative dimensions for three types of cyclones: the standard cyclone, the Stairmand design,3 and the Swift design.4 Note that the Stairmand 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 more centrifugal force and increased ef ficiency. In the Leith and Licht model, a larger geometric configuration parameter results in a higher predicted ef ficiency.
TABLE 21.2 Geometric Configuration Parameter Standard
Stairmand
Swift
Inlet height
H/D
0.5
0.5
0.44
Inlet width
W/D
0.25
0.2
0.21
Gas exit diameter
De /D
0.5
0.5
0.4
Body length
Lb /D
2.0
1.5
1.4
Cone length
Lc /D
2.0
2.5
2.5
Vortex finder
S/D
0.625
0.5
0.5
Dust outlet diameter
Dd /D
0.25
0.375
0.4
Geometric configuration paramater
K
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402.9
551.3
699.2
FIGURE 21.7 Cyclone ef ficiency curves.
21.1.5 COMPARISON
OF
EFFICIENCY MODEL RESULTS
Ef ficiency models are adequate for getting a fair idea of performance, but there can be a rather wide variation in model predictions. Part, but not all, of the variation can be explained by empirical factors for the cyclone con figuration. Figure 21.7 shows cyclone ef ficiency curves as a function of particle diameter based on several sources. Each curve is based upon the same gas flow and gas and particle conditions. The lowest ef ficiency is predicted by Lapple ’s curve for a standard cyclone. Interestingly, the Leith and Licht model for the same standard cyclone predicts a significantly higher ef ficiency. The Leith and Licht model for the higher ef ficiency Stairmand and Swift cyclone designs shows incremental improvement over the standard design. Vendor data also were collected for the same set of gas and particle conditions, with significant predicted performance improvement. Perhaps the vendors were being overoptimistic about their designs, or perhaps there have been significant improvements in cyclone design over the years. It does point out that performance guarantees for cyclones must be written with speci fic information about the gas and particle properties, including the particle size distribution, to ensure that vendor guarantees can be measured and substantiated after installation.
21.2 PRESSURE DROP Pressure drop provides the driving force that generates gas velocity and centrifugal force within a cyclone. Several attempts have been made to calculate pressure drop from fundamentals, but none of them has been very satisfying. Most correlations are based on the number of inlet velocity heads as shown in Equation 21.10:
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∆P = where ∆P = ρg = Vi = NH =
1 2g c
ρg Vi 2 N H
(21.10)
pressure drop gas density inlet gas velocity pressure drop expressed as number of the inlet velocity heads
One of the correlations for number of inlet velocity heads is by Miller and Lissman:5 2
D N H = K ∆P1 De
(21.11)
where K∆P1 = constant based on the cyclone configuration and operating conditions D = diameter of the cyclone body De = diameter of the exit tube A typical value for K∆P in the Miller and Lissman correlation is 3.2. For the standard cyclone configuration described above, the Miller and Lissman correlation results in 12.8 inlet velocity heads. Another correlation for number of inlet velocity heads is by Shepherd and Lapple:6
NH where K∆P2 H W De
= = = =
= K ∆P 2 HW2 De
(21.12)
constant for cyclone configuration and operating conditions height of the inlet opening width of the inlet opening diameter of the exit tube
The value for K∆P in the Shepherd and Lapple correlation is different, typically ranging from 12 to 18. The Shepherd and Lapple correlation results in 8 inlet velocity heads for the standard cyclone dimensions, 6.4 inlet velocity heads for the Stairmand cyclone design, and 9.24 inlet velocity heads for the Swift cyclone design. As can be seen, there is a substantial difference among the correlations. Again, it is best to rely upon vendors’ experience when your own experience is lacking; however, to enforce a performance guarantee, ensure that the specification is well-written and can be documented for the expected conditions.
© 2002 by CRC Press LLC
21.3 SALTATION The previous discussion of ef ficiency and pressure drop leaves the impression that continually increasing the inlet gas velocity can give incrementally increasing ef ficiency. However, the concept of “saltation” by Kalen and Zenz7 indicates that, more than just diminishing return with increased velocity, collection ef ficiency actually decreases with excess velocity. At velocities greater than the saltation velocity, particles are not removed when they reach the cyclone wall, but are kept in suspension as the high velocity causes the fluid boundary layer to be very thin. A correlation for the saltation velocity was given by Koch and Licht:8
Vs
= 2.055D
0.067
0.667 i
V
(ρp − ρg ) 4gµ 2 3ρg
0.333
W 0.4 D 0.333 W 1 − D
(21.13)
where Vs = saltation velocity, ft/s D = cyclone diameter, ft Vi = inlet Velocity, ft/s g = acceleration of gravity, 32.2 ft/s2 µ = gas viscosity, lbm/ft-sec ρp = particle density, lbm/ft3 ρg = gas density, lbm/ft3 W = width of inlet opening, ft The maximum collection ef ficiency occurs at Vi = 1.25Vs, which typically is between 50 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 ef ficiency 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 ef ficiency, Chem. Eng., 84(24), 1977.
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