Page 138 - Air Pollution Control Engineering

03_chap_wang.qxd 05/05/2004 12:48 pm Page 117
Cyclones 117

Table 5
Results from the Calculation of the Overall Efficiency in the Cyclone
Range D x (in η η x η η x η η x
i i i i i i i i i i i
(µm) (µm) mass) (10 m/s) (10 m/s) (15 m/s) (15 m/s) (20 m/s) (20 m/s)
0–1 0.5 0.01 0.00467 0.0000467 0.00307 0.0000307 0.00226 0.0000226
1–2 1.5 0.02 0.06413 0.0012825 0.06854 0.0013709 0.07690 0.0015380
2–4 3 0.04 0.27104 0.0108417 0.35295 0.0141180 0.44728 0.0178910
4–6 5 0.06 0.56392 0.0338351 0.70479 0.0422872 0.81212 0.0487270
6–8 7 0.08 0.74613 0.0596903 0.86326 0.0690605 0.92874 0.0742990
8–10 9 0.10 0.84439 0.0844392 0.92883 0.0928833 0.96745 0.0967446
10–20 15 0.13 0.94968 0.1234582 0.98280 0.1277633 0.99374 0.1291862
20–30 25 0.15 0.98499 0.1477489 0.99602 0.1494024 0.99882 0.1498233
30–40 35 0.12 0.99334 0.1192009 0.99849 0.1198188 0.99961 0.1199531
40–50 45 0.10 0.99638 0.0996382 0.99927 0.0999269 0.99983 0.0999828
50–60 55 0.07 0.99778 0.0698446 0.99959 0.0699713 0.99991 0.0699938
60–70 65 0.05 0.99852 0.0499261 0.99975 0.0499874 0.99995 0.0499974
70–80 75 0.04 0.99896 0.0399583 0.99983 0.0399933 0.99997 0.0399987
80–90 85 0.02 0.99923 0.0199846 0.99988 0.0199977 0.99998 0.0199996
90–100 95 0.01 0.99941 0.0099941 0.99992 0.0099992 0.99998 0.0099999
Σ x =1.0 Ση x = 0.87 Ση x = 0.91 Ση x = 0.93
i i i i i i i

Solution

Table 5 can be easily constructed from Eq. (41) and the collection efficiencies calculated
from Eq. (23) for the velocities of 10, 15, and 20 m/s. Therefore, the overall collection
efficiencies are:

η = 87% for v = 10 m/s
o i
η = 91% for v = 15 m/s
o i
η = 93% for v = 20 m/s
o i
For v = 20 m/s the particle concentration in the cyclone exit [Eq. (42)] is calculated as
i
−
c = (10 93 )002. kg m 3
.
o
kg
c =1.4 ×10 −3 =1.4g m 3
o 3
m
The particle size distribution at the exit is obtained from Eqs. (39) and (40), utilizing the
results listed in Table 6.
The results show that there are few particles larger than 10 µm in the cyclone exit, where
particles below 4 µm predominate. This is very useful information for defining of a
downstream particle collector that might be needed.
The pressure drop in the cyclone operating with particle loaded gas can be estimated by
Eq. (35), where the entry concentration c in grains per cubic feet is needed:
in
c = 0.02 kg 1 gr ( 0.3048 m) 3
×
in 3 − 5 ( 1 ft) 3
m 6.48 10 kg
c = 8.7 gr ft 3
in