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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 con-structed 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 high-temperature 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. 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. 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 COLLECTION EFFICIENCY
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 acceler-ation 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 = mV2 (21.1)
where
F = centrifugal force m = mass of particle
V = velocity of particle, assumed to equal inlet gas velocity r = radius of cyclone body
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 configuration, shown in Figure 21.2a, reduces efficiency. Ensure that particles are given a head start in the right direction by using the configuration shown in Figure 21.2b.
21.1.1 FACTORS AFFECTING COLLECTION EFFICIENCY
Several factors that affect collection efficiency can be predicted. Increasing the inlet velocity increases the centrifugal force, and therefore the efficiency, but it also increases the pressure drop. Decreasing the cyclone diameter also increases centrif-ugal force, efficiency, and pressure drop. Increasing the gas flow rate through a given cyclone has the effect of efficiency shown in Equation 21.2:
Pt2 Q1 0.5 Pt1 Q2
(21.2)
where
Pt = penetration (Pt = 1 – h)
h = particle removal efficiency Q = volumetric gas flow
FIGURE 21.2 Inlet piping configuration.
Interestingly, decreasing the gas viscosity improves efficiency, 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:
0.5
2 = 2 (21.3) 1 1
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 efficiency improvement. However, decreasing the gas temperature also decreases the volumetric flow rate, which affects efficiency as described above in Equation 21.2.
Finally, particle loading also affects efficiency. 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.
Pt2 L1 0.18 Pt1 L2
(21.4)
where L = inlet particle concentration (loading).
FIGURE 21.3 Generalized efficiency relationships.
Figure 21.3 shows generalized efficiency relationships for high-efficiency con-ventional 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-efficiency 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 = H Lb + 2 (21.5)
where
Ne = number of effective turns
H = height of the tangential inlet Lb = length of cyclone body
Lc = length of cyclone lower cone
The theoretical efficiency 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:
FIGURE 21.4 Cyclone dimensions.
TABLE 21.1
Typical Cyclone Dimensions
High Efficiency Standard High Throughput
Inlet height H/D 0.44 Inlet width W/D 0.21 Gas exit diameter De/D 0.4 Body length Lb/D 1.4 Cone length Lc/D 2.5 Vortex finder S/D 0.5
Dust outlet diameter Dd/D 0.4
0.5 0.8 0.25 0.35 0.5 0.75 1.75 1.7 2.0 2.0 0.6 0.85
0.4 0.4
0.5
x 9µW 100 πNeV rp −rg
(21.6)
where
dpx = diameter of a particle with x% removal efficiency µ = viscosity
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