Page 163 - Air Pollution Control Engineering

03_chap_wang.qxd 05/05/2004 12:48 pm Page 142
142 José Renato Coury et al.

Solution

The first step consists in calculating the gas flow rate that gives the desired cut diameter
for the SRI II cyclone, whose dimensions can be found in Table 13. For this, it is necessary
to calculate F , the Cunningham slip factor, which is given by
s
− (
F = 1 + (λ D )[ 2.514 + 0.8 exp 0.55 D ae λ )] (75)
ae
s
where λ is the gas mean free path. For air, at atmospheric pressure and 23°C, λ = 6.702×
10 −8 m. Thus,
FD (
s 50) = 1.0674
From Eq. (66), taking D = 3.1 cm, comes
c
×
×
−
6
×
ψ = 1.0674 2.5 10 m = 8.332 10 − 5
×
50 − 2
3.1 10 m
From Eq. (71) and Tables 13 and 14,
ψ = 0.0414Re − 0.713 ( 0.43) − 0.172 = 8.332 10 − 5
×
50 ann
Thus,
Re = 7412.73
ann
3
From Eq. (70) and Table 13, for ρ =1.17 kg/m and µ=1.80×10 −5 kg/ms,
g
×
−
3
2
(
−
Re = 0.5 1 0.286) 1.17kg m × 3.1 10 m v = 7412.73
×
ann − 5 i
1.8 10 kg ms
Thus:
v = 10.305 ms
i
Finally, the gas flow rate in the cyclone can be calculated as
π 2
=
−4
3
Q = (0.286 D ) v = 6.362 ×10 m s 38.2 L min −1
c
i
4
For this flow rate, the efficiency curve can be constructed as follows: For a given, D , the
ae
slip factor F is calculated as above. Then, the factor θ comes from Eq. (69) as
s
(
FD )D µ ( m )
θ = s ae ae
1.0674 × 2.5 µ ( m )
Next, f(θ) comes from Eq. (68) and Table 15 as
f θ ( ) = 8.196 θ − 3.239 θ 2
Finally, the efficiency η is calculated from Eq. (67). Table 22 lists the values of these steps
for a number of diameters. Figure 22 shows η as a function of D for the SRI II cyclone
ae
with a cut diameter of 2.5 µm (for which a flow rate of 38.2 L/min is necessary). The
PM curve is also plotted; some deviation can be seen in the larger-particle range. It is
2.5
worth noting that the predicted flow rate for the SRI cyclone (38.2 L/min) is somewhat
higher than the range reported by Smith et al. (54).