M E 433
Professor John M. Cimbala
Lecture 31
Today, we will:
•
Do more examples of air cleaners in series and parallel; particle histograms
•
Discuss cascade impactors
Discussion: Does the order matter for these two air cleaners in series?
OR
Larger Dp,cut first
Sµaller Dp,cut first
In
Out
In
Out
cin
Cleaner A
cA Cleaner B cout
E(Dp)A
E(Dp)B
Q
Dp,cut = 10 µµ
Dp,cut = 1 µµ Q
cin
Cleaner A c
Cleaner B
cout
A
E(Dp)A
E(Dp)B
Q
Dp,cut = 1 µµ
Dp,cut = 10 µµ Q
Q
Q
Discussion: Which is better, series or parallel for these two air cleaners?
OR
Series
Out
In
cin
Q
Cleaner A
cA
E(Dp)A
Q
Dp,cut = 10 µµ
Cleaner B
E(Dp)B
Dp,cut = 1 µµ
Parallel
In
cout
cin
Q
Q
Cleaner A
E(Dp)A
Dp,cut = 10 µµ
Cleaner B
E(Dp)B
Dp,cut = 1 µµ
Out
cout
Q
Example: Histograms of particle number fraction through air cleaners in series
Given: Two particle cleaners in series as sketched below, with different values of Dp,cut.
To do: Sketch the particle number fraction histograms at each of the three locations.
Solution:
In cin
Q
Cleaner 1
E(Dp)1
Q
Dp,cut = 10 µµ
nj
nt
Cleaner 2
E(Dp)2
c1
Dp,cut = 1 µµ
nj
nt
nj
nt
cin
Dp
c1
cout Out
Dp
cout
Q
Dp
Example: Air Cleaners in Series or Parallel
Given: Two identical air cleaners are available to clean a polluted air stream. We want to
know which is better – to connect them in series or in parallel. At a particular Dp,
•
E(Dp)A = 90%
•
E(Dp)B = 85%
In
Cleaner A
E(Dp)A
cA
Series
Cleaner B
E(Dp)B
Out
In
Cleaner A
E(Dp)A
Out
Cleaner B
E(Dp)B
Parallel
To do: Compare the overall removal efficiency in series and for the best case in parallel.
What is the best overall removal efficiency you can get from these two cleaners? Give your
answer as a percentage to 3 significant digits. Equations:
Series:
Parallel:
m
m
Q
E ( Dp )
1 − ∑ f j 1 − E ( D p )  , f j = j
E ( Dp )
=
1 − ∏ 1 − E ( D p ) 
=
overall
overall
j
j


Qtotal
j =1
j =1
Solution:
Cascade Impactor:
(a)
(b)
Figure 9.7 of Heinsohn & Cimbala. Cascade impactor: (a) schematic diagram, showing
trajectories of particles of three different diameters (adapted from Willeke and
Baron, 1993); (b) Andersen eight-stage, non-viable, 1 ACFM ambient air sampler
(from Andersen Instruments Inc.).
100
90
stage 7
6
5
4
3
2 1
0
80
70
60
impaction
probability 50
(%)
40
preimpactor
30
20
10
0
0.1
1
10
aerodynamic particle diameter, Dp,aero (mm)
100
Figure 9.8 of Heinsohn & Cimbala. Particle collection efficiency for each stage of an
Andersen eight-stage, 1 ACFM ambient air sampler with preimpactor (redrawn
from Andersen Instruments, Inc.).
Computational fluid dynamics (CFD) simulations of a cascade impactor (by J. Cimbala):
(a) air streamlines
(b) 1-micron particles
(c) 2-micron particles
(d) 5-micron particles
(e) 10-micron particles
(f) 15-micron particles
Figure 10.17 of Heinsohn & Cimbala. CFD simulation of flow in a 3-stage cascade
impactor; (a) streamlines, (b)-(f): trajectories of unit density particles of diameter Dp = (b) 1,
(c) 2, (d) 5, (e) 10, and (f) 15 µm.