A Design Tool for Aerodynamic Lens Systems - Department of ...

FIG. 10. Particle transmission efficiency as a function of the Stokes number
for various Reynolds numbers at three different subsonic Mach numbers.
(a) Ma = 0.03; (b) Ma = 0.10; (c) Ma = 0.32.
A DESIGN TOOL FOR AERODYNAMIC LENS SYSTEMS 329
FIG. 11. Cutoff Stokes numbers as a function of Reynolds number for three
different Mach numbers.
lens corresponding to the limiting trajectory of particle loss to
the downstream spacer is ri = ds,i/(2ηc,i). The transmission
efficiency can be estimated as the ratio of particle flux within ri
to the total flux in that stage. Therefore,
ηt, spacer, i =
⎧
⎪⎨
1 for dB,i ≤ ds,i
⎪⎩
for dB,i > ds,i
. [24]
� � d
2 � �
s,i
d
4
s,i
2 ds,i−1η −
c,i ds,i−1ηc,i � � dB,i−1
2 � � dB,i−1
4
2 d −
s,i−1 ds,i−1 Note that dB,i = dB,i−1 ×|ηc,i|, and the diffusion effect is
neglected.
Loss by diffusion at each stage can be estimated through the
Gormley-Kennedy equation (Gormley and Kennedy 1949):
ηt, GK, i =
⎧
⎨1
− 5.50 ξ
⎩
2/3 + 3.77ξ for ξ