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102 José Renato Coury et al.

h m = H − S, for D ≤ B (3)
e
( H − )( D )
h D −
h m = c e + ( h − S), for D ≥ B (4)
c (
e
D − B)
According to Barth, the maximum tangential velocity, v , can be obtained by the
tmax
following correlation:
e (
 D 2)( D − b)π 
v = v  c  (5)
c (
α
tmax 0 ab + m D − b)πλ
  2 h  
where v is gas velocity at the cyclone exit, given by
0
v = 4Q (6)
π D 2
0
e
The parameter λ is the friction factor, for which the value 0.02 is suggested. The
parameter α can be related to the dimensions b and D by
c
−
α = 1 1.2(bD c ) (7)
2.2.2. The Leith and Licht Model
The Leith and Licht model (9,58) is based on the assumption that the noncollected
particles are fully mixed in the radial direction at a given point of the axial position,
because of turbulence. Therefore, the residence time of the particle inside the device can
be associated with the time it needs to move in the radial and axial directions in order
to reach the wall (1,19). This principle is semitheoretically treated in a number of equa-
tions and it results in the following expression for the particle collection efficiency:
 1 
τ
  GQ  2 n +2 
η = 1 − exp  −2  i ( n + ) 1   (8)
i
  D c 3  
 
where G is a dimensionless geometry parameter, n is the vortex exponent, and τ is the
i
relaxation time.
The geometry parameter G is expressed in terms of the dimensions of the cyclone
families and can be written as

G = D c 2 π ( [ { S − a )( D − D )] + 4 V nl H} (9)
2
2
2
c
e
,
22
ab
where V is an annular volume related to the vortex penetration inside the cyclone.
nl,H
Alexander (20) defines as “natural length” the distance below the bottom of the exit
duct where the vortex turns. Depending on the value of Z , the volume to be considered
c
in Eq. (9) is either V or V , as follows:
nl H
h 
2
π D 2  π D  Z + S −  d d  π DZ
2
2
V = c ( h − S) +  c  c 1 + c + c − e c


2
nl 4  4  3   D c D  4 (10)
c
if ( H − S) > Z
c