Page 209 - Air pollution and greenhouse gases from basic concepts to engineering applications for air emission control

184 6 Separation of Particles from a Gas

64lLU 0 1:5 3
DP ¼ 2 a 1 þ 56a ð6:102Þ
d
f
where the pressure drop DP is in Pascal. It is thus directly proportional to thickness
2
of the filter L and inversely proportional to cross section area of the fiber d .
f
From the staggered array model, Yeh and Liu [38, 39] calculated the drag force
over the fibers as
4plU 0
F D ¼ ð6:103Þ
Y
and the corresponding pressure drop per unit thickness of the filter is

16laU 0
0
DP ¼ ð6:104Þ
Yd 2
f
Then the total pressure drop over the entire array is determined as
16LlaU 0
0
DP ¼ LDP ¼ 2 ð6:105Þ
Yd
f
The corresponding pressure drop coefficient can then be determined by com-
paring Eq. (6.105) with (6.100).

4a
C DP ¼ ð6:106Þ
Y
With Y in the denominator, Yeh’s equation is complicated in form. In addition,
as seen in Fig. 6.15, Yeh’s model gives greater pressure drops than Davies model.
Figure 6.15 is produced for a filter with d f =10 µm, U ∞ = 0.2 m/s for
α = 0.0–0.10 and L = 5, 10, 20 mm.
First of all, the pressure drop increases with filter solidity; the relationship based
on these equations is not linear, so the pressure drop begins to dramatically increase
as solidity increases. Increasing the thickness of the filter also causes the pressure
drop to increase, but this increase is linear as the factor for thickness is not raised to
any exponent and acts as a scalar quantity in the relationship (thus, this would also
be true for velocity). Both of these responses make intuitive sense, as logically one
would expect that the addition of filter material (whether by increasing solidity or
thickness) would increase the pressure drop.
When comparing these two different models, it is clear that, for the same filter
and operating conditions, Yeh’s equations predict a greater pressure drop. Yeh’s
equations predict pressure drops about 1.5 times higher than Davies’s. When
solidity is 1 (though, this may be outside of the equation’s domain), the result of