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03_chap_wang.qxd 05/05/2004 12:48 pm Page 103
Cyclones 103

or
(
2
−
π D 2  π D  H h   B B  π DH S)
2
−
2
V = 4 c ( hS) +  c   3    1 + D + D   − e 4 (11)
−
2
H
 4
−
if ( HS) < Z c c c
The diameter of the cyclone central axis, d , is given by
c
h
d = D − ( D − B)   S + Z −   (12)
c
c
c
c
H −
h
The vortex natural length, Z , and the vortex exponent, n, can be estimated by the
c
following expressions (20):
1
 D  3
2
Z = 2.3D e  c  (13)
c
 ab 
[ D ( c )]  T  0.3
0.14
n = 1 − 1 − 0.67 (14)
 283 
with D given in meters and the gas temperature T in degrees Kelvin.
c
Equation (13), although often used, is not entirely satisfactory, because it does
not include the dependence of Z on the gas velocity at the entrance, which was
c
experimentally verified by Hoffmann et al. (21).
The relaxation time, τ , is given by
i
ρ D ( ) 2
τ = p i (15)
18µ
i
The parameter G is sometimes expressed in terms of K , K , and K , as
a b c
G = 8K c (16)
2
KK 2
a b
with
K = a (17)
a
D
c
K = b
b (18)
D
c
and
(2V s + V )
K = (19)
,
nl H
c
D 3
c
V is the annular volume between the central plane of the inlet duct and the bottom
s
of the exit duct, S, and is given by
c (
2
2
D − D )
V = ( π S − a ) 2 e (20)
s
4