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Cyclones 131

Table 11
Empirical Constants of Eq. (64) for Four Commercial Sampling Cyclones
b
Cyclone D a (µm) Q (L/min) K n A B
pc
Aerotec 2 2.5–4.0 350–500 468.01 −0.80 2.02 −0.68
UNICO 240 1.0–5.0 65–350 123.68 −0.83 1.76 −0.82
Aerotec 3/4 1.0–5.0 22–65 214.17 −1.29 2.04 −0.77
10-rnm Nylon 1.8–7.0 0.9–5.0 6.17 −0.75 3.07 −0.93
1.0–1.8 5.8–9.2 16.10 −1.25 1.19 −0.59
0.1–1.0 18.5–29.6 178.52 −2.13 0.74 −0.07
a Range of cut diameters, D .
pc
b Range of operation flow rates, Q.
Source: ref. 46.

to sampling scale (1.9 < D <3.7 cm). Tables 12 and 13 list the dimensional characteris-
c
tics of the cyclones investigated. The dimensions are defined in Fig. 13.
Based on the work of Dring and Suo (50), a cutoff size parameter ψ is defined as:
50
FD
Ψ = s 50 (66)
50
D c
where D is the aerodynamic diameter of the particle corresponding to 50% collection
50
efficiency. The parameter F is the Cunningham slip factor, which accounts for the
s
reduced viscous drag on a particle whose size is comparable to the mean free path of
the gas. This correction factor is a strong function of particle size and becomes very
important in the submicron range, as can be seen in Fig. 14.
The cutoff size D was estimated by adjusting the efficiency curves to
50 θ ()

η = e f θ () (67)
1 + e f
where f(θ) is given by
f θ ( ) = a + a θ + a θ 2 (68)
1 2 3
The parameters a , a , and a were determined by fitting, and θ was the normalized
1 2 3
collection efficiency, defined as
(
FD ae )D ae
θ= − 1 (69)
s
(
FD ae )D 50
s
By examining the work of Moore and McFarland (51,52), it could be verified that the
cutoff size parameter ψ was highly correlated to the Reynolds number based on the
50
cyclone annular dimension, Re , defined as
ann
 D  vD
ρ
Re = 0.5 1− t  i c (70)

ann
 D c  µ
where D is the vortex finder external diameter (usually taken as D ), v is the gas veloc-
t e i
ity at the cyclone entrance, and ρ and µ are the gas density and viscosity, respectively.