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Cyclones 107

Table 2
Grade efficiency (%) of a High-Efficiency Stairmand Cyclone
as a Function of the Gas Velocity at the Entrance, v
i
D (µm) v = 5 m/s 10 m/s 15 m/s 20 m/s 25 m/s
i i
1.4 0.0 2.2 4.4 8.9 16.7
2.1 0.0 6.7 22.2 50.0 75.6
2.9 0.0 5.6 24.4 61.1 80.0
3.7 2.2 37.8 77.8 93.3 97.8
4.4 3.3 57.8 86.7 94.4 96.6
5.1 12.2 84.4 96.7 95.6
5.8 33.3 93.3
6.6 70.0
7.4 77.8
Source: ref. 17.

2.4.4. Overall Efficiency
Once a designer has adopted a given collection efficiency model and decided upon a
given cyclone configuration, the designer is in a position to evaluate the response of that
arrangement as far as the process at hand.
The overall efficiency of the cyclone η (i.e., the collected fraction of the total mass
o
entering it) can be calculated from the grade efficiency η by
i
η = ∑ ( η x ) (41)
o
i i
where x is the mass fraction of particles with diameter D collected with efficiency η .
i i i
The overall concentration at the cyclone exit can therefore be obtained as:
c = (1 − η o c ) in (42)
o
where c is the overall concentration at the entrance.
in
2.5. Application Examples

The three models presented above will be used for the prediction of the grade effi-
ciency of a cyclone and the results will be compared to experimental measurements
from the literature.
Dirgo and Leith (17) utilized a high-efficiency Stairmand cyclone, with a 0.305-m
body diameter, at ambient temperature. They determined the grade efficiency and the
pressure drop as a function of the gas velocity at the entrance, for spherical oil droplets
3
with a density of 860 kg/m . Their results are shown in Tables 2 and 3.
Example 1
3
Design a high-efficiency Stairmand cyclone for a volumetric flow rate of 500.4 m /h and
determine the grade efficiency curves utilizing the models of Barth, and Iozia and Leith
for the entry gas velocities of 10, 15, and 20 m/s. Also, estimate the maximum power
consumption of a fan, neglecting the loss in the external ducts and assuming 55% effi-
3
ciency for the fan motor. The particle density is 860 kg/m and the temperature is 27°C.
3
The air density and viscosity at 27°C are 1.18 kg/m and 1.8×10 −5 kg/m s, respectively.