Page 193 - Air pollution and greenhouse gases from basic concepts to engineering applications for air emission control

168 6 Separation of Particles from a Gas

Table 6.1 Design parameters for a Lapple cyclone
High efficiency Conventional High throughput
Height of inlet, H/D 0.5–0.44 0.5 0.75–0.8
Width of inlet, W/D 0.2–0.021 0.25 0.375–0.35
Diameter of gas exit, D e /D 0.4–0.5 0.5 0.75
Length of vortex finder, S/D 0.5 0.625–0.6 1.5–1.7
Length of body, L B /D 1.4 1.75 1.7
Cone length, L C /D 2.5 2 2.5–2
Diameter of dust outlet 0.375–0.4 0.25–0.4 0.375–0.4

The residence time of an involute cyclone is estimated by

Circumference of the vortex Number of turns of the air
t ¼ ð6:57Þ
Superficial gas speed
where the number of turns the gas flow makes before turning upward to the vortex
finder ðN e )is

L B þ 0:5L C
N e ¼ ð6:58Þ
H
where L B is the length of cyclone main body, and L C is the length of the cyclone
lower cone. Then the residence time can be calculated using

2prN e
t ¼ ð6:59Þ
u 0
Equation (6.56) then becomes

pN e q

p 2 2
g d p ¼ d v ð6:60Þ
p h
9lWu g
If the average tangential speeds are approximated as the same, v h u h u g ,
then Eq. (6.60) becomes
p u g N e q

p 2
g d p ¼ d p ð6:61Þ
9lW
Instead of using this equation for direct calculation of the particle fractional
efficiency, Lapple [19] presented a semi-empirical equation by introducing the cut
size into the analysis. The corresponding cut size is first determined using
Eq. (6.61) by letting g ¼ 0:5