xvEPA
United States Industrial Environmental Research EPA-600/7-78-132a
Environmental Protection Laboratory July 1978
Agency Research Triangle Park NC 27711
A Data Reduction
System for Cascade
I m pa c tors
Interagency
Energy/Environment
R&D Program Report
-------
RESEARCH REPORTING SERIES
Research reports of the Office of Research and Development, U.S. Environmental
Protection Agency, have been grouped into nine series. These nine broad cate-
gories were established to facilitate further development and application of en-
vironmental technology. Elimination of traditional grouping was consciously
planned to foster technology transfer and a maximum interface in related fields.
The nine series are:
1. Environmental Health Effects Research
2. Environmental Protection Technology
3. Ecological Research
4. Environmental Monitoring
5. Socioeconomic Environmental Studies
6. Scientific and Technical Assessment Reports (STAR)
7. Interagency Energy-Environment Research and Development
8. "Special" Reports
9. Miscellaneous Reports
This report has been assigned to the INTERAGENCY ENERGY-ENVIRONMENT
RESEARCH AND DEVELOPMENT series. Reports in this series result from the
effort funded under the 17-agency Federal Energy/Environment Research and
Development Program. These studies relate to EPA's mission to protect the public
health and welfare from adverse effects of pollutants associated with energy sys-
tems. The goal of the Program is to assure the rapid development of domestic
energy supplies in an environmentally-compatible manner by providing the nec-
essary environmental data and control technology. Investigations include analy-
ses of the transport of energy-related pollutants and their health and ecological
effects; assessments of, and development of, control technologies for energy
systems; and integrated assessments of a wide range of energy-related environ-
mental issues.
EPA REVIEW NOTICE
This report has been reviewed by the participating Federal Agencies, and approved
for publication. Approval does not signify that the contents necessarily reflect
the views and policies of the Government, nor does mention of trade names or
commercial products constitute endorsement or recommendation for use.
This document is available to the public through the National Technical Informa-
tion Service, Springfield, Virginia 22161.
-------
EPA-600/7-78-132a
July 1978
A Data Reduction System
for Cascade Impactors
by
J.D. McCain, G.I. Clinard, L.G. Felix, and J.W. Johnson
Southern Research Institute
2000 Ninth Avenue, South
Birmingham, Alabama 35205
Contract No. 68-02-2131
T.D. 10101
Program Element No. EHE624
EPA Project Officer: D. Bruce Harris
Industrial Environmental Research Laboratory
Office of Energy, Minerals, and Industry
Research Triangle Park, NC 27711
Prepared for
U.S. ENVIRONMENTAL PROTECTION AGENCY
Office of Research and Development
Washington, DC 20460
-------
ABSTRACT
A computer based data reduction system for cascade impactors
has been developed.1 The system utilizes impactor specific cali-
bration information together with operating conditions and other
pertinent information such as stage weights, sampling duration,
etc., to determine particle size distributions in several forms
for individual runs. A spline technique is applied to fit a curve
to the cumulative size distribution obtained from each individual
impactor run. These fitted curves have forced continuity in co-
ordinates and slopes. Averages of size distributions for multiple
runs are made using the fitted curves to provide interpolation
values at a consistent set of particle diameters, irrespective of
the diameters at which the data points fall in the original indi-
vidual run data sets. Statistical analyses are performed to
locate and remove outliers from the data being averaged, following
which averages, variances, standard deviations and confidence in-
tervals are calculated. The averages and statistical information
are available in tabular and graphical form in several size dis-
tribution formats (cumulative mass loading, cumulative percentage
by mass, differential mass, differential number). The averaged
data are stored in disk files for subsequent manipulation. Addi-
tional programs permit data sets from control device inlet and
outlet measurements to be combined to determine fractional collec-
tion efficiencies and confidence limits of the calculated effi-
ciencies.
These results are available in graphical form with a choice
of log-probability or log-log presentations and as tabular output.
The program is set up to handle all commercially available round
jet cascade impactors, including common modifications, which are
in current use in stack sampling. Other round jet impactors can
be easily substituted and slot type impactors could be accommo-
dated with slight program revision.
This report was submitted in partial fulfillment of Contract
No. 68-02-2131, Technical Directive No. 10101, by Southern
Research Institute under the sponsorship of the U.S. Environmental
Protection Agency. This report covers the period March 1, 1978,
to May 1, 1978, and work was completed as of May 12, 1978.
11
-------
CONTENTS
Abstract j_j.
Figures iv
Tables vi
Acknowledgements v'ii
1. Introduction 1
2. Summary and Conclusion 4
3. Indivudual Run Data Analysis 5
4. Analysis of Grouped Data 22
5. Test Cases and Examples of Results 25
References 35
111
-------
FIGURES
Number Paqe
la Cumulative size distribution from raw
impactor data 12
Ib Start of development of interpolated
points between first and last Dso 12
Ic Continued generation of interpolated
points 13
Id Continued generation of interpolated
points 13
le Generation of interpolated points on parabola
which includes DMAX 14
If Generation of interpolated points on hyperbola
through D5o(D and DMAX 14
2a Start of the curve fitting procedure 17
2b Second step in the curve fitting procedure. . 18
2c Third step in the curve fitting procedure . . 19
3 Approximate differential size distribution
based on stage weights and same distribu-
tion based on spline fitting are compared
to a true unimodal log normal distribution. . 26
4 Approximate differential size distribution
based on stage weights and same distribu-
tion based on spline fitting are compared
to a true bimodal log normal distribution . . 27
5 Percent error of approximate differential
size distributions based on stage weights
and the same distributions based on spline
fitting from a unimodal log normal distribu-
tion 28
6 Percent error of approximate differential
size distributions based on stage weights
and the same distributions based on spline
fitting from a bimodal log normal dis-
tribution 29
IV
-------
FIGURES (Cont'd)
Number Page
7 Single run cumulative mass distribution
with original data points based on stage
weights and fitted curve from SPLINl 30
8 Differential size distribution obtained
for the run in Figure 7 based on stage
weights and curve fitting 31
9 Cumulative mass distribution on a per-
centage basis with confidence limits
obtained from the average of several
runs similar to that shown in Figures
7 and 8 32
10 A control device penetration curve
with confidence limits obtained from
sets of averaged inlet and outlet runs. ... 33
v
-------
TABLES
Number Page
1 Program Flow 3
2 Input Data to MPPROG 6
3 Sample Calculations 8
VI
-------
AC KNOWLE DGEMENT S
This work was conducted under U.S. Environmental Protection
Agency contract number 63-02-2131. The continued support and
assistance of Mr. D. B. Harris, the EPA project officer on this
contract is gratefully acknowledged. Additional appreciation is
also expressed to Mr. B. Gaston and Ms. A. Henry for their assis-
tance with the programs; to Mr. K. Gushing whose earlier program
was used as a basis for program MPPROG; and Dr. W. B. Smith for
his assistance and guidance during the program development.
VI1
-------
SECTION 1
INTRODUCTION
Cascade impactors have gained wide acceptance as a practical
means of making particle size distribution measurements. These
devices are regularly used in a wide variety of environments,
ranging from ambient conditions to flue gas streams at 500°C
(950°F). Specially fabricated impactors can be used for more ex-
treme conditions.
Because of their usefulness, the U.S. Environmental Protec-
tion Agency has funded research which has explored the theoret-
ical and practical aspects of impactor operation. As part of
this research, an effort has been made to design a comprehensive
data reduction system which will make full use of cascade- impac-
tor measurements.
The cascade impactor data reduction system (CIDRS) described
here is designed to automatically reduce data taken with any one
of four commercially available round jet cascade impactors: the
Andersen Mark III Stack Sampler, the Brink Model BMS-11 (as sup-
plied and with extra stages), the University of Washington Mark
III Source Test Cascade Impactor, and the Meteorology Research
Incorporated Model 1502 Inertial Cascade Impactor. Provision is
not made in this system for reducing data taken with slotted jet
impactors. With modification the computer programs can accommo-
date any round jet impactor with an arbitrary number of stages,
and with more extensive revision, can be made to handle data from
slotted jet impactors.
The computer programs which comprise this data reduction sys-
tem are written in the FORTRAN IV language. The plotting sub-
routines used were written specifically for the Digital Equipment
Corporation (DEC) PDP-15/76 computer, and these programs are not
compatible with other plotting systems. However, these programs
can be used as a guide when revision is made for use with another
operating system.
A broad outline of the program fundamentals is given here
with sufficient detail for anyone without a specialized knowledge
of computers to understand the methods and rationale of the pro-
gram. The program comprises two major blocks. The first block
treats data from individual impactor runs while the second treats
1
-------
data from groups of runs, providing averages, statistical informa-
tion and fractional penetration (efficiency) results. The six
mainline programs which make up the data reduction system are des-
cribed in the overall program flow shown in Table 1.
-------
TABLE 1. PROGRAM FLOW
BLOCK 1. SINGLE RUN ANALYSIS
I. Impactor Program (MPPROG)
Takes testing conditions and stage weights to produce stage
DSO'S, cumulative and cumulative % mass concentrations
-------
SECTION 2
SUMMARY AND CONCLUSION
CIDRS represents a powerful, versatile tool for reducing
and managing data obtained with cascade impactors. It provides
the capability for single and multiple run data analysis with
varying degrees of smoothing of single run data available and
averaging and statistical analysis of multiple runs. Results
from the program are not biased by forced fits to arbitrary dis-
tribution forms. Finally, the program makes possible a very
significant time saving in handling and processing field data
obtained with cascade impactors.
-------
SECTION 3
INDIVIDUAL RUN DATA ANALYSIS
This portion of the impactor data reduction package utilizes
impactor hardware information, particulate catch information, and
sampling conditions from single impactor runs to calculate size
distributions. The overall distributions are available in sev-
eral forms. The run analysis and output presentation are accom-
plished by three main programs, MPPROG, SPLINl, and GRAPH.
MPPROG and SPLINl perform analysis and manipulation while GRAPH
is totally devoted to various forms of graphical presentation of
the calculated distributions. The routines used in GRAPH are
specifically for use on a PDP-15/76 computer and are not compat-
ible with most other computers without modification. However,
the general structure of GRAPH should serve as a useful base for
programming to achieve similar graphical output from other com-
puting systems.
PROGRAM MPPROG
In MPPROG, sampling hardware information, sampling condi-
tions and particulate catch information are used to determine
the effective cut sizes of the various impactor stages and the
concentrations of particles caught on these stages. The output
is organized into several tabular forms and stored on a disk
file for later use.
Input Data to MPPROG
Because individual impactors, even of the same type, do not
necessarily have precisely the same operational characteristics,
the program calculates stage cut diameters on an impactor spe-
cific basis. Hardware data are stored within the program which
include, for each impactor to be used, the number of stages, the
number of jets per stage, the jet diameters, the stage calibra-
tion constants, and flow-pressure drop relations for each stage.
Run specific input data to MPPROG are listed in Table 2.
The maximum particle diameter must be measured by microscopic
examination of the particles collected on the first stage. Gas
analysis must be made at the same time the impactor is run.
-------
TABLE 2. INPUT DATA TO MPPROG
1. Impactor identification (required to call up
hardware information)
2. Gas composition (C02, CO, N2, 02 , H20)
3. Impactor flow rate (ACFM at stack conditions)
4. Stack pressure
5. Stack temperature
6. Gas temperature within impactor
7. Duration of sampling
8. True density of particles
9. Maximum particle diameter present in sample
10. Masses of catches by stage
-------
Output from MPPROG
Both input information pertaining to individual impactor
runs and calculated results are listed on the line printer. A
sample of output from MPPROG generated to the line printer is
shown in Table 3.
Input information for each run is given in the first five
lines of the printout. (Impactor pressure drop in inches of
mercury is calculated within the program; gas composition is in-
put as dry fractions and output as wet gas composition by per-
cent.) The mass collected on each stage in milligrams is listed
in the tenth line of the Table.
The mass loading is calculated from the total mass of par-
ticles collected by the impactor and the total gas volume sam-
pled, and it is listed in four different units after the heading
CALC. MASS LOADING. The units are defined as:
GR/ACF - grains per actual cubic foot of gas at stack conditions
of temperature, pressure, and water content.
GR/DSCF - grains per dry standard cubic foot of gas at engineer-
ing standard conditions of gas. Engineering dry stand-
ard conditions in the English system are defined as 0%
water content, 70°F, and 29.92 inches of Hg.
MG/ACM - milligrams per actual cubic meter of gas at stack con-
ditions of temperature, pressure, and water content.
MG/DNCM - milligrams per dry normal cubic meter of gas at engi-
neering normal conditons of the gas. Engineering dry
normal conditions in the metric system are defined as
0% water content, 21°C and 760 mm of Hg (Torr).
Below the run condition data summary, the information per-
tinent to each stage is summarized in columnar form in order of
decreasing particle size from left to right. Thus Si is the
first stage, S8 is the last stage, and FILTER is the back-up
filter. If a precollector cyclone was used, a column labeled
CYC would appear to the left of the SI column and information
relevant to the cyclone would be listed in this column. Beneath
each impactor stage number is listed the corresponding stage
index number, which also serves as identification for the stage.
Directly beneath these listings are the effective stage cut
diameters. The effective stage cut diameter is assumed to be
equal to the particle diameter for which the stage collection
efficiency is 50%. This diameter, Dso, is calculated from an
equation of the form
-------
TABLE 3. SAMPLE CALCULATIONS
CO
HYPOTHETIC*!. ANDFRSF.N
IMPACTOR FLOuPAT|f a 0,50r> ACFM
IMPACTOB PRESSURE nRtjP = 0.3 T "J . uF HR
ASSUMED PARTICLE DENSITY e 1.55 GM/CU.C
GAS COMPOSITION (PERCENT) en?
CALC, MASS LOADING • 8.0711E-03 GR/ACF
IMPACTOR STAGE
STARE INDEX NI.IMPFP
050 (MICROMETERS)
| MASS (MILLIGRAMS)
IMPACTOR TEMPERATURE « 400,0 F
STACK TEMPERATURE n ano.o F n
M. STACK PRESSURE • 26, 5« IN, OF
2 I ,9« CO a 0.00
1.4746E-02 GR/DNCF
31 32 33 34
1 2 3 4
10.72 9.93 6.35 «,16
0.72 0.40 0.53 0,09
o 20(1, U C
?OU.u C
HG MAX. PARTICLE
N2 » 76,53
1.8U70Ef01 M6/
85 S6
5 6
2.21 1.28
0,38 1,43
SAMPLING
DIAMETER o
02 o 20,53
tCM
37
7
0,67
1,25
DURATION a 20,00 flu
100,0 MICHQMETERS
H20 a 1.00
3,J7«I8E»01 tfO/DNCM
O
u.
Z
H
a.
Z
88 FILTER
8 9
0,33
o,oa 0,39
,5o
10. U.
MG/DNCM/STAGE
<|.71E+00 2,62E»00 3.«7E+00 5.B9E-01 2.U9E+00 9.3SE+00 B,18E*00 2,62E»01 2,55E»00
CUM. PERCENT OF MASS SMALLER THAN D50 R6.23 7S.59 68.45 66.73 59,46 32,12 8,22 7.06
CUM. (MG/ACW) SMALLER THA'J D50 1.S9E+01 1.45F+01 1.26E+01 1.23E+01 1.10E+01 5.93E+00 1.52E+00 l,38EtOO
CUM, (MG/ONCM) SMALLER THAN 050 2,91E+01 2.65E+01 2.31E+01 2,25E*01 2.01F+01 1,08F.#01 2.77E+00 2.52E+00
CUM, (GR/ACF) SMALLER THAN 050 6,96E-f>3 6.3«E»03 5.52E-03 5.39E-03 0.80E-03 2.59C.03 6,6aE«04 6.02E-04
CUM. (f.R/nMcF) SCALIER THAN n50 1.27E-n2 1.16E-0? 1.01E-02 9.SUE-03 S.77E-03 4.74£-03 1.21E-03 1.10E-03
LU
>
<
GEO, MEAN DIA, (MICROMETERS)
3.27E+01 l,03Et01 7.9«E+On 5.15E+00 3,0«E+00 1,68£+00 9.JOF.-01 a,73E-01 2,36E«01
«,86E»00 7.93E + 01 1.7SE + 01 3,2«E + 00 8,<»6E + 00 3,95EtOl 2.9«Et01 8.56F.-01 8,«7E*00
1.96E+05 1.02E+08 5.03F*07 3.35E+07 «.52E*08 1.18E+10 S.I8E*10 1,13E*10 9,l2E»ll
u.
U.
NORMAL
G STA»nA9D)
ARf 21 PEG C AND 760MM
-------
where D50 = effective cut size,
ks = stage calibration constant,
y = gas viscosity,
d = jet diameter,
Pp = particle density,
c = Cunningham slip correction factor, and
v = jet velocity.
Because the particle diameter, D50, enters the equation for
C, the solution of Equation 1 is done by ah iterative process.
If the particle density, pp, is set equal to the true density of
the particles, as is the case in the sample output in Table 3,
the resulting diameter calculated from Equation 1 is the Stokes
diameter, Dg. If Pn is set equal to 1.0 the resulting diameter
is the aerodynamic diameter DA as defined by the Task Group on
Lung Dynamics.2 If both pp and C are set equal to 1.0, the
resulting diameter is the aerodynamic impaction diameter, DAI, as
defined by Mercer.3 Unless otherwise specified, MPPROG will auto-
matically provide parallel output in terms of DS and D^. Parallel
results in terms of DS and D&I or in terms of D^ and D^j are
available if called for.
The stage weights, in units of milligrams as input, are like-
wise listed for the respective stages on the line labeled MASS.
The mass loadings from each stage follow and are labeled MG/DNCM/
STAGE (milligrams per dry normal cubic meter per stage).
The percentage of the total mass sampled contained in par-
ticles with diameters smaller than a particular DS o is called the
CUMULATIVE PERCENT OF MASS SMALLER THAN D5o. It is the cumula-
tive percentage of total mass accumulated to the stage j.
The cumulative mass loading of particles smaller in diameter
than the corresponding D50 is listed in four different units:
milligrams per actual cubic meter, milligrams per dry normal
cubic meter, grains per actual cubic foot, and grains per dry
normal cubic foot. Note that these are the same units used for
calculating the total mass loading. They represent both metric
and English units and both stack conditions and engineering dry
standard conditions of temperature, pressure, and water content.
The geometric mean diameter for the particles collected on
each stage is then listed in micrometers. The geometric mean
diameter of a given stage may be expressed as the square root of
the product of the Dso of the given stage and the Dso of the
previous stage. In calculating the geometric mean diameter of
the first stage (or cyclone if applicable), the maximum particle
diameter is used instead of the "D5o of the previous stage." In
calculating the geometric mean diameter of the filter, one-half
the Dso of the last stage (stage eight, here) is used instead of
-------
the "Dso of the given stage." (There is no D5o for the back-up
filter since all remaining particles are captured by this filter.)
Finally, an approximate differential particle-size distribu-
tion is listed as DM/DLOGD, in milligrams per dry normal cubic
meter, and as number concentration, DN/DLOGD, in number of par-
ticles per dry normal cubic meter.
Differential size distributions may be derived two ways:
1. Finite difference methods may be used based on the DSO'S
(abscissa) and the particulate masses on each stage
(ordinate). This technique was used to generate the
differential size distribution data in Table 3.
2. Curves may be fitted to the cumulative mass distribution
from which the differential curves (slope) for each test
can be calculated. This method is preferred and is de-
scribed in the following paragraphs.
PROGRAM SPLIN1
In many, if not most, sampling programs; a number of impactor
runs will be made. Frequently, these runs will be made using
several impactors, having different performance characteristics.
The latter may be true even if the same type of impactor is used
throughout a sampling program. This behavior results both from
manufacturing variations which cause calibration differences and
run-to-run variations in sampling rates, which cause shifts in
the DSO'S. Averaging results from such testing to obtain a rep-
resentative composite size distribution requires that the distri-
butions be broken down into like size intervals for all the runs
to be averaged. The same requirement for like size intervals
also holds for using inlet and outlet data from control device
sampling programs to obtain fractional efficiencies. This re-
quires curves to be fit to the data for each run to permit inter-
polation to obtain values at common diameters for all runs to be
compared or averaged.
Before making the final selection of the spline technique
for fitting curves to the size distribution data, consideration
was given to a number of alternate fitting methods, and several
of them were tried. It was concluded that any attempt to fit a
predetermined functional form (e.g. log-normal) to the data was
generally not proper. Because the slope of the cumulative distri-
bution curve, the differential distribution, is the required
quantity for calculating fractional efficiencies, consideration
was also given to fitting curves to the AM/AlogD approximations
of the true differential distribution, which are estimated direct-
ly from the stage loadings and D50's However, the magnitude of
the steps in D50 are large enough in most impactors as to fre-
quently make AM/AlogD a poor approximation to dM/dlogD. More- .
over, the boundary conditions are more difficult to handle in
10
-------
fitting curves to AM/AlogD than in fitting to the cumulative dis-
tributions. It was ultimately concluded, after many trial fit-
ting methods were tested that the best use was made of the data
if the fitting was done to the cumulative distribution curve by
means of a "SPLINE" method.
^
SPLINl operates by fitting a curve which is continuous in
X and Y and the first derivative of Y with respect to X to the
cumulative mass concentration size distribution data. The re-
sulting fitted curve is similar to that which one would draw
through the data points using a "French curve" or mechanical
spline. This fitted curve invokes no a priori assumptions as to
the shape of the distribution (i.e., power law, log-normal, etc.).
The manner in which the spline fits are made is described below.
Initial attempts at using the spline technique on the set of
points defining the cumulative distribution curve obtained di-
rectly from the D50's were not satisfactory. The difficulty
occurred as a result of the inability of the method to generate
sufficiently rapid changes in curvature when the curve to be gen-
erated was defined by a small number of points. A satisfactory
fit could be obtained by adding a set of interpolated points be-
tween the original data points of the measured cumulative curve.
These points are generated by means of a series of parabolas
through consecutive sets of three adjacent data points of the
original cumulative curve defined by the impactor stage data.
The fitting is done using log (concentration) and log (particle
diameter) as variables and begins with the segment- containing
the smallest Dso in the data set.
The sequence of operations by which the interpolated points
are generated is shown in Figures 1. A series of parabolas are
fit through consecutive sets of three data points beginning at the
smallest D50 as shown in Figures la and Ib. In this description,
three interpolation points between each pair of Dso's will be
assumed. However, the program will accommodate up to five inter-
polation points. The use of more points will improve the accu-
racy of the fitting, but will require more storage capacity. The
interpolation points are located along the parabolas, between the
lower pair of the three Dso points used to generate the parabola. The
interpolated points are spaced evenly in log diameter between the
pair of original points. A similar process is used to generate
interpolated points between consecutive pairs of D50's up to the
segment which terminates at the Dso of the first collection stage
as illustrated in Figures Ic to le. A slightly different proce-
dure which will be described later, is used for segments which
include the first collection stage Dso.
Since the fitting is for a cumulative curve, negative
slopes are not allowed. Therefore, a check is made for negative
first derivatives of the interpolation parabola at the bounds of
11
-------
z
Q
co
CO
uj
>
U
I I I III III I I I I I I I I I I I I I 1 I I I
H-1-
D50(6) D50(5) D50(4) D50(3) D50(2) D50(1) DMAX
PARTICLE DIAMETER
Figure 1a. Cumulative size distribution from raw impactor data.
z
5
ID
>
- FIRST INTERPLATION
- PARABOLA
©
D
5
CJ
CT/
INTERPOLATED POINTS
I i i i i i i i i i i i i i i i 11 i
D50<6) D50(5) D50(4) D50(3) D50(2) D50(1) DMAX
PARTICLE DIAMETER
Figure 1b. Start of development of interpolated points< between first and last
12
-------
o
z
o
<
o
s
uj
13
SECOND
INTERPOLATION
_ PARABOLA
INTERPOLATED POINTS
I i I i i i i i
I ' ' ','" ,—' 1 ' ' | ""
D50(6) D5Q(5) D50(4) D50(3) D5Q(2) D50(1) DM AX
PARTICLE DIAMETER
Figure 1c. Continued generation of interpolated points
(3
z
Q
1
ui
>
<
O
INTERPOLATED POINTS
Z
THIRD INTERPOLATION PARABOLA
o
O
O
o
o
e
i i i i i i i 11 i i i i i i i 11 i i i i i i i
i i i i i i I
D50(6) D50(5) D50(4) D50(3) D50(2) D50(1) DMAX
PARTICLE DIAMETER
Figure 1d. Continued generation of interpolated points
13
-------
z
5
<
o
_i
CO
1
D
CJ
INTERPOLATED POINTS ON
FINAL PARABOLA
FINAL INTERPOLATION
PARABOLA
00'
I
D50<5)D50(4) D50<3> D50<2> D50<1>
PARTICLE DIAMETER
Figure 1e. Generation of interpolated points on parabola
which includes DMAX.
DMAX
Z
5
>
P
o
SLOPE = O
HYPERBOLA AND
HYPERBOLIC
INTERPOLATION POINTS
BETWEEN
D50 (1) and DMAX
D50<6» D50<5> D50(4) D50(3) D50(2) D50(1)
PARTICLE DIAMETER
DMAX
Figure If. Generation of interpolated points on hyperbola through
D5Q(1) and DMAX
14
-------
each segment within which the interpolated points are to be gener-
ated. If a negative derivative is found in any segment other than
the first (the segment including the smallest Dso) a straight line
interpolation between the segment bounds is used rather than par-
abolic interpolation. If a negative first derivative is found in
the first segment to be fitted, a fictitious point is generated
and used to form a parabola which has no negative derivatives in
this segment. This fictitious point has the same concentration
value as that of the first point on the cumulative curve and has a
diameter defined by
(Dso of last stage)2
fictitious ~ TDof next to last stage)
Th6 interpolated values for the segment between the last two Dso's
on the cumulative curve are then generated from the parabola which
passes through this fictitious point, and the points for the last
two stages on the cumulative distribution curve.
In the region about the first stage DSO, three sets of inter-
polated points are generated. The first are generated by parabol-
ic interpolation using a parabola through DMAX, Dso (stage 1) and
DSO (stage 2) as was done in the case of the previous segments.
However, in addition to these, two more points are generated along
the parabola above the first stage DSO. These additional points
are spaced evenly in log (diameter) at the same intervals in log
(diameter) as the interpolated points between D50 (stage 1) and
DSO (stage 2) as shown in Figure.le. These points are used in
generating the final curve fit up to the point on the cumulative
distribution curve defined by the first stage D50. The third set
of points is illustrated in Figure If.
Note that the cumulative mass distribution used in the illus-
trations of Figures 1 is one in which a large step in concentra-
tion occurs between Dso (stage 1) and DMAX. This is typical of a
cumulative curve for a bimodal distribution in which one mode has
a median diameter substantially greater than first stage D5o.
The interpolation parabola through DMAX, Dso (stage 1) and DSO
(stage 2) does not properly represent the shape of the true dis-
tribution curve in this region. In particular, the true curve
must have zero slope at DMAX. It was empirically determined that
a hyperbolic interpolation equation fit in terms of linear concen-
tration and linear diameter between DMAX and Dso (stage 1) with
the hyperbola asymptotic to the total loading at infinite particle
size resulted in acceptable results for the final spline fits.
Therefore a seven point hyperbolic interpolation is used in addi-
tion to the previously described parabolic interpolation over
this segment of the curve. This hyperbolic interpolation
15
-------
is illustrated in Figure If. The use of the two sets of interpo-
lated points in the final interval will be discussed later.
Generation of the Final Spline Fit
The original data points, defined by the DSO'S, together with
the interpolated points just generated, form a set of points along
a continuous curve (if one disregards the two sets of points in
the final segment) which has no negative slopes. However, the
derivative of the curve in most cases will not be continuous at
the Dso points. The spline fit to be described is a smoothing
technique which generates a series of parabolic segments that ap-
proximates a continuous curve through the complete set of points
defining the cumulative distribution. The segments to be gener-
ated now will pass near or through those points and will have
forced continuity in both coordinates and first derivatives. The
technique is applied first to cover the interval between the first
and last stage DSO'S and then a second time to cover the interval
between the first stage D50 and DMAX. From this point on in the
discussion, no distinction is made between the original points de-
fined by the DSO'S and the interpolated values located between
them.
The spline fit is generated by joining successive parabolas
at locations determined by the x (or log diameter) coordinates of
the points which now represent the cumulative distribution curve
(original points at the DSO'S plus the interpolated points).
These parabolas have continuity in slope forced by the fitting pro-
cedure and are generated in such a fashion as to pass near or
through the points on the cumulative distribution curve.
The procedure is illustrated in Figures 2. The spline fit is
begun at the lowest point, 0, on the distribution curve (at the
DSO of the last stage). The parabola used to generate the inter-
polated points between the last two stages is assumed to be the
fitted curve up to the first interpolated point. (Point 1 in Fig-
ure 2a.) This parabola, a, is followed until the x-coordinate at
point 1 is reached. At the point A, located on this parabola by
the x-coordinate of point 1, a new parabola is fitted as shown in
Figure 2b. The parabola, b, is forced to pass through point A
with the same slope at A as the parabola used to define point A,
and is forced to pass through the third point above point 1 in
the set of points defining the cumulative curve, i.e. point 4.
The parabola, b, is followed to the point defined by the x-coordi-
nate of point 2, thus locating a point B. At B a new parabola is
fit with forced slope continuity with b passing through the third
point ahead of point 2, i.e., point 5, as shown in Figure 2c.
From C this process is repeated using point C and 6 to generate a
new parabola, d, and termination point D, e, and E, etc., until a
termination point at the Dso of the first collection stage is
reached. The last three points obtained by parabolic interpolation
are used in generating the spline fit parabolas up to the first
16
-------
6
O
5
O
o
z
a
V)
V)
4
•
5
O
I I I 1
I I I I
D50
(LAST STAGE) XA = X-|
D50
(LAST-1 STAGE)
PARTICLE DIAMETER
Figure 2a. Start of the curve fitting procedure. Cumulative mass loadings
derived from stage catches are represented by solid circles.
Interpolated values are shown with open circles.
17
-------
z
Q
GO
CO
D
5
D
U
5
O
I I I II I I
I
I I I I I
D50
(LAST STAGE)
D50
(LAST-1 STAGE)
PARTICLE DIAMETER
Figure 2b. Second step in the curve fitting procedure. Cumulative mass
loadings derived from stage catches are represented by solid
circles. Interpolated values are shown with open circles.
18
-------
O
2
Q
O
_i
CO
CO
5
LLJ
D
5
0
I
I I I I I I I
D50
(LAST STAGE)
xb xc DSQ
(LAST-1 STAGE)
PARTICLE DIAMETER
Figure 2c. Third step in the curve fitting procedure. Cumulative mass
loadings derived from stage catches are represented by solid
circles. Interpolated values are shown with open circles.
19
-------
collection stage Dso. The coefficients of the fitting spline fit
parabolas for the segments a, b, c, d, . . etc., are saved for
future use. These now represent the smoothed curve and will be
used henceforth to define the cumulative curve for that run.
The final spline fit starts by picking up at the point on
the fitting parabola which terminated at the Dso of the first stage,
The same procedure as before is followed, except that the third
point ahead determined by the hyperbolic interpolation is now used
for fitting, and the fitting parabolas are followed to x-coordin-
ates defined by the hyperbolic interpolation points. The curve
generated in this second zone of the spline fit [i.e., between D50
(stage l)and DMAX] is an extrapolation which has been found to be
reasonably good to diameters equal to about 2 to 3 times the first
stage D5Q. By using the second, third (as illustrated), fourth,
etc., point ahead in generating the final parabola segments, one
can influence the amount of smoothing provided by the program.
The cumulative concentration and slope of the cumulative
curve, dm/dlogD, can be calculated for any arbitrary particle size
by locating the fitting coefficients for the spline segment con-
taining that size. The boundary locations of each of the para-
bolic segments, 0, A, B, C, . ., and the fitting coefficients for
each segment are stored in a disk file for subsequent use by
other programs (e.g., GRAPH, STATIS, etc.).
Problems Resulting from Extremely Close Stage Cut Diameters (Dso's)
When two stages are used on an impactor which differ only
slightly in DS 0, the second of the two will collect too much
material because of the finite slope of real impactor stage col-
lection characteristics. The simplest example of this effect
would be obtained if two identical stages are used sequentially.
If that were the case, in an ideal impactor the second stage
should collect no material; however, because of the finite slope
of the real stage collection efficiency curve, it will collect
some particles. This would lead to the formation of a step in-
crease (infinite slope) in the cumulative concentration curve.
The severity of the effect is reduced as the spacing between the
Dso's increases but can be sufficiently severe so as to cause
significant errors in the size distribution curves if it is not
properly accounted for. Calibrations indicate that the effective
cut diameters,-or D50's, at the first two stages of several impac-
tors suffer from this problem. The program MPPROG, because of
this, ignores the presence of the second stage of Andersen, MRI,
and University of Washington impactors in generating the cumula-
tive mass concentration curve from which the fitted curves will
be made by SPLINl. This procedure effectively nullifies the
problem. However, if calibrations of future versions of these
impactors do not show the small spacing in DSO, MPPROG should be
modified appropriately so as not to lose good information when
the curve fits are made.
20
-------
PROGRAM GRAPH
Program GRAPH is dedicated entirely to presenting data from
single impactor runs. The output forms available on call are cum-
ulative mass loading versus D50, AM/AlogD versus geometric mean
diameter, and AN/AlogD versus geometric mean diameter as calcu-
lated in MPPROG. The latter are available on both Stokes, aero-
dynamic and aerodynamic impaction diameter bases. As an option,
up to ten runs can be superimposed on a single plot. Plots and
tabular output of the fitted curves from SPLINl are also available.
The fitted curves from SPLINl are plotted superimposed on the data
points from MPPROG, but only as single run plots. The plots are
all made on log-log grids.
The tabular output includes cumulative percent mass loading
less than particle diameter generated from the SPLINl fitted
curves, dM/dlogD versus particle diameter, and dN/dlogD versus
particle diameter generated by differentiation of the SPLINl fit-
ted curves.
21
-------
SECTION 4
ANALYSIS OF GROUPED DATA
PROGRAM STATIS
STATIS is a program for combining data from multiple impactor
runs under a common condition. The program tests data from a
series of runs (specified by the user) for outliers, flags and
removes outliers from the set, and then provides output in the
form of average size distributions with confidence intervals as
desired in both tabular and graphical form. The program is set
up to provide 50% confidence intervals; however, changes can be
made for the calculation of other confidence intervals as desired
(e.g. , 90% or 95%) .
The input data to STATIS are the fitted polynomial segments
generated from MPPROG by SPLIN1 which now define the cumulative
mass loadings for each run. The particle diameter basis for aver-
aging (i.e., aerodynamic, aerodynamic impaction, Stokes) is user
specified on control cards used to execute STATIS.
The fitting equations from SPLINl are differentiated at pre-
selected particle diameters to obtain the quantity (dM/dlogDjJj
where i refers to particle diameter and j refers to the sequence
number of a particular run in the set to be averaged. The values,
at each particle diameter, D-^, are subjected to an outlier analysis
based on the deviations of the values of dM/dlogD for individual
runs from the mean for all runs.
The outlier test used is that for the "Upper 5% Significance
Level".1* A curve fitted to the tabular list of critical values
for excluding an outlier is used to generate the table. The value
X. is excluded from statistical analysis based on the following
condition:
.
n
where Xi = individual value
X = mean of all values
S = standard deviation of the data set
Cn = critical value = function of number of values in the
data set, n.
22
-------
The application of this test requires that there be three
or more runs in the sequence to be averaged. This outlier test
is repeated after discarding any outliers already identified,
provided there are at least three runs remaining in the set of
retained points.
After discarding outliers, a final average, standard devia-
tion, and confidence interval are calcuated for each (dM/dlogDi).
These values are output on the line printer and are plotted on
call by the user.
Cumulative size distributions on a mass basis or percentage
basis are derived from the averaged dM/dlogD values by integra-
tion of these values. The choice of integrating the dM/dlogD
curve rather than direct computation of the cumulative averages
from the individual cumulative distributions is based on the
fact that an error in a single stage weight is propagated forward
throughout the cumulative curve for all stages subsequent to the
one on which the error occurred. This would cause substantial
quantities of good data from other stages to be discarded by the
outlier analysis. Integration of the averaged differential dis-
tribution, on the other hand, allows the data from the remaining,
error free, stages to have their proper influence on the averaged
cumulative distributions. These cumulative distributions are
again output in tabular form and, on call, in graphical form.
The cumulative distributions can be obtained either includ-
ing or excluding particles smaller than 0.25 ym in diameter.
The option of excluding the particles smaller than 0.25 ym is
made available because of the fact that in a significant percent-
age of sampling situations, impactor back up filter catches can
be dominated by oversize particles because of bounce and/or re-
entrainment. This results in a filter weight gain which can be
many times higher than the weight of the fine particles which,
ideally, should be the only material present. In those cases,
omission of the material which is nominally smaller than 0.25 ym
from the cumulative distributions will make the result a much
better representation of the true size distribution. This, of
course, is true only when the DSO of the last impactor stage is
about 0.25 to 0.5 ym as is usually the case with the commercially
available impactors.
Standard deviations and confidence limits for the cumulative
distributions are calculated from the approximation that the
variance (and square of a confidence interval) for a sum, A + B,
is given by the sums of the variances (and squares of the confi-
dence intervals) for A and B separately, i.e.,
Variance = variance + variance (3)
23
-------
and
(confidence interval)2 = (confidence interval)2 (4)
+ (confidence interval)2.
B
The averaged differential size distributions generated by
STATIS are stored in a disk file for use by the programs PENTRA
or PENLOG in calculating control device fractional efficiency
curves.
Tabular and graphical output from STATIS includes cumulative
mass loading versus diameter, cumulative percentage on a mass basis
versus diameter, dM/dlogD versus diameter, and dN/dlogD versus dia-
meter. The graphical presentations are made on log-log grids with
the exception of the cumulative percentage plot which is made on a
log-probability grid. All output forms, graphical and tabular,
include confidence limits. The choice of diameter definition used
is left to the user. An index of runs which were rejected through
the outlier analysis before averaging is also printed. Rejection
at any one particle size does not result in the run being excluded
at all particle sizes.
PROGRAMS PENTRA/PENLOG
These two programs are virtually identical and provide tab-
ular and graphical output of control device penetration and/or
efficiency versus particle size for a preselected series of par-
ticle sizes from about 0.25 to 20.0 ym. The only difference between
the two programs is in the form of the graphical output. In the
case of PENTRA, the fractional efficiency curves are presented on
a log-probability grid while in PENLOG they are presented on a
log-log grid.
The calculations are made from averaged sets of inlet and
outlet data developed by STATIS. The user identifies the pair of
averaged data sets from which the efficiency is to be calculated
together with the diameter basis required (i.e., Stokes, aero-
dynamic, aerodynamic impact ion) . The program retrieves the
appropriate averaged data sets and calculates the fractional effi-
ciency as
(dm/dlogD ) t
efficiency. (%) = 1.0 - _ x 100.
where i refers to the i particle diameter in the preselected
diameter sequence. Simultaneously, if both the inlet and outlet
data sets included two or more runs, confidence limits are cal-
culated based on a method described by Y. Beers.5 The confidence
level associated with the limits generated by the program as pro-
vided are 50% levels; however, other levels can be generated by
simply changing values of three constants used to generate the
appropriate t-table.
24
-------
SECTION 5
TEST CASES AND EXAMPLES OF RESULTS
Tests of the final fitting process were made by generating
fictitious impactor runs having known size distributions. These
runs were generated by calculating the D5o's associated with
several sets of sampling conditions. The stage weights required
to produce exact unimodal and bimodal log normal distributions
were then generated for these sets of particle diameters. The
program was exercised on these artificially constructed runs and
results obtained from the fitting procedure were then compared to
the original distributions. Figures 3 and 4 show examples of two
such tests in the form of differential size distributions. Fig-
ure 3 illustrates the input distribution and recovered distribu-
tion for an aerosol having a mass median diameter of 4.0 ym and
geometric standard deviation of 3.0. Recovered distributions
from the spline fit and the approximation results, AM/AlogD,
taken directly from the stage weights both show excellent agree-
ment with the input distribution. The fitted results for dia-
meters larger than 7.0 ym represent an extrapolation to sizes
larger than the first stage Dso. Figure 4 illustrates a similar
test for a bimodal distribution having equal amplitude modes,
mass median diameters of 2.0 ym and 10.0 ym^ and geometric stand-
ard deviations of 1.5. Again, beyond about 7.0 ym, the fitted
points represent extrapolations. Note that the AM/AlogD approxi-
mations derived directly from the stage weights lie very close to
the input curve in regions where the slopes are not large but fall
significantly above the true curve in regions of high slope. Er-
rors expressed as percentage deviations from true values are shown
for two cases each for unimodal MMD = 4.0, ag = 2.0, and bimodal
MMD = 2.0, ag = 1.5, and MMD = 10.0, ag = 1.5 distributions in Fig-
ures 5 and 6. Note that the results from the fitted curves gener-
ally fall within ±10% or better of the true values in the size inter-
val covered by the impactor stage Dso's and are for the most part
within ±50% of the true values in the extrapolation region above the
first stage DSO. Much larger errors occur with the AM/AlogD
approximations to the differential distributions obtained directly
from the stage weights. The errors shown in Figures 5 and 6
result only from the fitting procedure and do not include any
effects from non-ideal behavior in the impactors. Errors arising
from the latter can be much greater, as described by McCain and
McCormack (1978) ,6
Examples of some of the graphical output formats available
from the program are shown in Figures 7 through 10. Figure 7
25
-------
10*
103
2
o
z
Q
Q
O
_l
O
102
« UNI-MODAL LOG NORMAL DISTRIBUTION
D DM/DLOGD BASED ON CURVE FITTING
A AM/ALOGD BASED ON STAGE WEIGHTS
MMD = 4.0 jum; a = 3.0
10'1 10° 101
PARTICLE DIAMETER, micrometers
102
Figure 3. Approximate differential size distribution based on stage weights
and same distribution based on spline fitting are compared to a true
unimodal log normal distribution.
26
-------
102
o
g
o
10°
10"1
10
l-l
10
1-1
10-2
O
Q
O
3
Q
Q
10° 101
PARTICLE DIAMETER, micrometers
102
ID'3
-•- Bl-MODAL LOG NORMAL DISTRIBUTION
O dM/dlogD BASED ON CURVE FITTING
A AMMlogD BASED ON STAGE WEIGHTS
MMD'S = 2.0 j/m AND 10. Mm; a = 1.5
Figure 4. Approximate differential size distribution based on stage
weights and same distribution based on spline fitting are
compared to a true bimodal log normal distribution.
27
-------
30
20
10
M
CD
59
of
o
DC
DC
-10
-20
-30
•o—a-
— dM/dlogD BASED ON CURVE FITTING TO AN ANDERSEN RUN
& AM/AlogD BASED ON STAGE WEIGHTS OF SAME ANDERSEN RUN
. •• dM/dlogD BASED ON CURVE FITTING TO A BRINK RUN
D AM/AlogD BASED ON STAGE WEIGHTS OF SAME BRINK RUN
MMD = 4.0 pm; a = 3.0
I
I
o.i
1.0 10
PARTICLE DIAMETER, micrometers
Figure 5. Percent error of approximate differentia/ size distributions
based on stage weights and the same distributions based on
spline fitting from a unimodal log normal distribution.
100
-------
o
o
to
70
60
50
40
30
20
10
0
a? -10
cc
g -20
cc
LLJ
-30
-40
-50
-60
-70
0.1
— dM/dlogD BASED ON CURVE FITTING TO AN AN.DEB&EN RUN
A AM/AlogD BASED ON STAGE WEIGHTS OF SAME ANDERSEN
... dM/dlogD BASED ON CURVE FITTING TO A BRINK RUN
D AM/AlogD BASED ON STAGE WEIGHTS OF SAME BRINK RUN
MMD'S = 2.0 urn AND 10.0 nm; a = 1.5
I
I
I
I
1.0
10
PARTICLE DIAMETER, micrometers
Figure 6. Percent error of approximate differential size distributions
based on stage weights and the same distributions based on
spline fitting from a bimodal log normal distribution.
10
-------
UHO-7 H3-76 1544 ROWS 4,5,6
M = B.4D QMI
ID1-
M
Iff-.:
<, 1CT1,:
10'
O INPUT DATA
— CURVE FIT
Tier1
r3
10
1
I 1 I HIM 1—I I I Mill 1—I I I Mill
10°
PARTICLE DIAMETER (MICROMETERS)
Figure 7. Single run cumulative mass distribution with original
data points based on stage weights and fitted curve
from SPLIN1.
30
-------
10BJH7 1-13-76 1544 WTS 4,5,6
dfl = 2.4D
103!:
UOP,:
10
ri.
a •
•a
D AM/AlogD FROM STAGE WEIGHTS
• dM/dlogD FROM SPLINE FIT
10
1
i i iniH - 1 — i i i
101
1 — i i i imj
PARTICLE DIAMETER (MIO30METERS)
Figure 8. Differential size distribution obtained for the run in
Figure 7 based on stage weights and based on curve fitting.
31
-------
OB5 V8EHH1TEST HR/NBGBU
93.39
U
M
33.8^
33.5^
33^
3Bj
35:
soi
j
r
p>
•
»
•
R
»
•>
•
•
*
:
BO*
70\
BOi
SOi
4Oi
30i
m
i I
r i
f ,«
• a
• V
• ^ ^
= i1
X^
•» V
: m
EOf *
P *
10 i
si
E-«
i^
n.n-i J
: I
1 I
; i
i i
1 1
•r
r
r
F T
1 i i i i i ml i iiii nil i i i i i ml
10°
PARTICLE DIAMETER (MICRDKCTERS)
Figure 9. Cumulative mass distribution on a percentage basis with
confidence limits obtained from the average of several
runs similar to that shown in Figures 7 and 8.
32
-------
99.95:
99. 9^
> 99.8-
8 :
Q "'5:
L_J
t 99^
LJ ;
t oa •
§ ':
£
95-
90:
80^
1C
PEJSETRATIDN-EFFTCIBhCY
CD35 VQ5HM 1 TEST FIB redWTIffiH±f JUtftT. ffiNTM
^ •
• •
• m
m •
• •
• •
• «
• * ^ •
T I
II
" ^ "
• X j •
i i/5"' ;
• •
i ijijnit i iiiiini i iiiinf
J"1 10P 1O1 1C
rO.Ol
:O.O5
L0.1
-O.E
•0.5
:i
»
•
-5
^0
M
tf
u
PARTICLE DIAMETER (MICROMETERS)
Figure 10. A control device penetration curve with confidence limits
obtained from sets of averaged inlet and outlet runs.
33
-------
illustrates a single run cumulative mass distribution with the
original data points and fitted curve from SPLIN1. Figure 8
shows the differential distribution obtained for the run shown in
Figure 7. Figure 9 illustrates a cumulative mass distribution on
a percentage basis with confidence limits obtained from the aver-
age of several runs similar to that shown in Figures 7 and 8.
Figure 10 illustrates a control device penetration curve with con-
fidence limits obtained from sets at averaged inlet and outlet
runs.
34
-------
REFERENCES
Johnson, J. W., G. I. Clinard, L. G. Felix, and J. D. McCain.
A Computer-Based Cascade Impactor Data Reduction System.
EPA-600/7-78-042, March, 1978. 601 pp.
Morrow, P. E., (Chairman, Task Group on Lung Dynamics).
Deposition and Retention Models for Internal Dosimetry
of the Human Respiratory Tract. Health Physics, 12:173-
208. 1966.
Mercer, T. T., M. I. Tillery, and H. Y. Chow. Operating
Characteristics of Some Compressed Air Nebulizers. Am.
Ind. Hyg. Assoc. J. 29:66-78. 1968.
Quality Assurance Handbook for Air Pollution Measurement
Systems, Vol. 1. Principles. EPA-600/9-76-005, 1976.
Beers, Y. Introduction to the Theory of Error. 2nd
Edition. Addison-Wesley, Reading, Mass. 1957.
McCain, J. D., and J. E. McCormack. Non-Ideal Behavior
in Cascade Impactors. 70th Annual Meeting, APCA, Toronto,
1977. Paper 77-35.3.
35
-------
TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1. REPORT NO.
EPA -600/7 -7 8- 132 a
4. TITLE AND SUBTITLE
A Data Reduction System fo
2.
r Cascade Impactors
7. AUTHOR(S)
J.D. McCain, G.I. Clinard, L.G. Felix, and
J.W. Johnson
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Southern Research Institute
2000 Ninth Avenue, South
Birmingham, Alabama 35205
12. SPONSORING AGENCY NAME AND ADDRESS
EPA, Office of Research and Development
Industrial Environmental Research Laboratory
Research Triangle Park, NC 27711
3. RECIPIENT'S ACCESSION- NO.
5. REPORT DATE
July 1978
6. PERFORMING ORGANIZATION CODE
8. PERFORMING ORGANIZATION REPORT NO.
SoRI-EAS-78-331
10. PROGRAM ELEMENT NO.
EHE624
11. CONTRACT/GRANT NO.
68-02-2131, T.D. 10101
13. TYPE OF REPORT AND PERIOD COVERED
Task Final; 3-5/78
14. SPONSORING AGENCY CODE
EPA/600/13
15. SUPPLEMENTARY NOTES jERL-RTP project officer is D.Bruce Harris, Mail Drop 62,
919/541-2557.
16. ABSTRACT ip^ repOrt describes a computer-based data reduction system for cascade
impactors. The system utilizes impactor -specific calibration information, together
with operating conditions and other pertinent information (e.g. , stage weights, sam-
pling duration), to determine particle size distributions in several forms for indivi-
dual runs. The program can handle all commercial round-jet cascade impactors,
including common modifications , which are in current use in stack sampling. Other
round-jet impactors can be easily substituted. Slotted impactors could be accommo-
dated with slight program revision. A spline technique is applied to fit a curve in
the cumulative size distribution obtained from each individual impactor run. The
fitted curves have forced continuity in coordinates and slopes. Size distribution ave-
rages for multiple runs are made using the fitted curves for interpolation at consis-
tent particle diameters , regardless of the diameters at which the data points fall in
the original individual run data sets. After statistical analyses to locate and remove
outliers from the data being averaged, averages, variances, standard deviations,
and confidence intervals are calculated. The averages and statistical information
are available in tables and graphs in several size distribution formats. Averaged
data are stored on disks for subsequent use.
17.
a. DESCRIPTORS
KEY WORDS AND DOCUMENT ANALYSIS
b. IDENTIFIERS/OPEN ENDED TERMS
Air Pollution Sampling Air Pollution Control
Dust Stationary Sources
Impactors Particulate
Data Reduction Cascade Impactors
Size Separation Size Distribution
Flue Gases
13. DISTRIBUTION STATEMENT
Unlimited
19. SECURITY CLASS (This Report)
Unclassified
20. SECURITY CLASS (This page)
Unclassified
c. COSATI Field/Group
13B 14B
11G
131
09B
07A,13H
21B
21. NO. OF PAGES
44
22. PRICE
EPA Form 2220-1 (9-73)
------- |