U.S. Department
ot Transportation
Federal Aviation
Administration
Nitric Oxide
Measurement Study
Office of Environment
and Energy
Washington, D.C. 20591
Optical Calibration
Volume I
Report Numbers:
FAA-EE-80-28
USAF ESL TR-80-12
NASA CR-159861
USN NAPC-PE-37C
EPA-460/3-80-013
MAY 1980
L.G. Dodge
M.B. Colket, III
M.F. Zabielski
J. Dusek
D.J. Seery
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This document is disseminated under the joint sponsorship
of the Federal Aviation Administration, U.S. Air Force,
U.S. Navy, National Aeronautics and Space Administration,
and the Environmental Protection Agency in the interest of
information exchange. The United States Government assumes
no liability for the contents or use thereof.
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Technical Report Documentation Page
1. Report No.
FAA-EE-80-28
2. Government Accession No.
3. Recipient's Catalog No.
4. Title and Subtitle
Nitric Oxide Measurement Study: Optical Calibration -
Volume I
5. Report Date
October 18, 1979
6. Performing Organization Code
7. Author's) L> G_ Dodge> M_ B> Colket> m> M< F. Zabielski
J. Dusek, D. J. Seery
8. Performing Orgonizotion Report No.
R79-994150-1
' P erformi ng Organ i zo* ion N ome and Addre s s
United Technologies Research Center
Silver Lane
East Hartford, CT 06108
10. Work Unit No. (TRAIS)
11. ControcT or Gront No.
DOT FA77WA-4081
13. Type of Report ond Period Covered
12. Sponsoring Agency Nome and Address
U.S. Department of Transportation
Federal Aviation Administration
Office of Environment and Energy
Washington, DC 20591
14. Sponsoring Agency Code
15. SuppiementoryNo.es Funding for this study was provided by an Interagency Committee.
Contributing agencies and report nos. are: DOT-FAA (FAA-EE-80-28); USAF (ESL TR-80-
12); NASA (CR-159861); USN (NAPC-PE-37C); and EPA (EPA-460/3-80-013).
16 Abstroct
Calibration devices suitable for providing known amounts of nitic oxide (NO) at
temperatures ranging from 300 K to 2000 K and pressures of 0.5 atm (50.7kPa) to 2.0
atin (203kPa) are described with their design considerations. Methods for confirming
nitric oxide concentrations are given. The spectroscopic theory for the absorption
of ultraviolet radiation in the y(0,0) band of nitric oxide is reviewed. Experi-
incntal values for oscillator strengths and broadening parameters for NO with various
collision partners are provided. Experimental results confirming the adequacy of a
..umputer spectral model and, hence, the calibration are presented along with the
details of the model. Finally, the results of an empirical calibration of an
infrared gas correlation spectrometer are given.
The Nitric Oxide Measurement Study is in three volumes:
Optical Calibration - Volume I;
Probe Methods - Volume II;
Comparison of Optical and Probe Methods - Volume III.
17. Keywords Citric oxide, ultraviolet
spectroscopy, high temperature calibra-
tion, broadening parameters, oscillator
strengths, spectroscopic model, infrared
gas correlation spectrometer.
18. Distribution Stotement
Document is available to public through
the National Technical Information
Service, Springfield, VA 22161
19. Security Clossif. (of this report)
Unclassified
20. Security Clossif. (of this poge)
Unclassified
21. No. of Poges 22. Price
222
Form DOT F 1700.7 (8-72)
Reproduction of completed poge authorized
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ABSTRACT
Calibration devices suitable for providing known amounts of nitric oxide
(NO) at temperatures ranging from 300 K to 2000 K and pressures of 0.5 atm
(50.7kPa) to 2.0 atm (203kPa) are described with their design considerations.
Methods for confirming nitric oxide concentrations are given. The spectro-
scopic theory for the absorption of ultraviolet radiation in the y(0,0) band
of nitric oxide is reviewed. Experimental values for oscillator strengths
and broadening parameters for NO with various collision partners are provided.
Experimental results confirming the adequacy of a computer spectral model and,
hence, the calibration are presented along with the details of the model.
Finally, the results of an empirical calibration of an infrared gas correlation
spectrometer are given.
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ACKNOWLEDGMENTS
This contract was administered by the Federal Aviation Administration.
Funding for this work was provided by an Interagency Committee representing
the Federal Aviation Administration (FAA), Air Force, Navy, National Aeronautics
and Space Administration (NASA), and the Environmental Protection Agency (EPA).
The assistance of Mr. D. Kocum, Mr. R. P. Smus, Mr. D. Santos, and Mr. R. L.
Poitras during the experimental portions of this study is gratefully acknowledged.
The authors also would like to acknowledge the contributions of the following
UTRC staff: Dr. P. J. Marteney for his kinetics analysis during the calibration
source design phase; Mr. L. Chiappetta, Jr. and Dr. R. N. Guile for aerodynamic
analyses of the tnicroprobes; Mr. M. D. Page and R. E. LeBarre for programming;
Mr. R. Thornton and Mr. C. Ekstrom for electronic instrumentation and Mrs.
Barbara Johnson for data reduction and report preparation. Our thanks are extended
to A. Kondracki of the Standards Laboratory of Pratt and Whitney Aircraft for
certifying gas mixtures used in this study.
In addition, we extend our thanks to Mr. J. Few and his colleagues at Arnold
Research Organization for providing us with their spectral computer model and
for their cooperation during their measurements made at UTRC. Finally, thanks are
given to Dr. D. Gryvnak of Ford Aerospace for his infrared gas correlation measure-
ments.
ii
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Nitric Oxide Measurement Study:
Task__I
Optical Calibration
TABLE OF CONTENTS
Page
ABSTRACT i
ACKNOWLEDGEMENTS ii
LIST OF FIGURES iv
LIST OF TABLES vi
I. INTRODUCTION 1-1
II. CALIBRATION DEVICES H-l
A. Design Considerations II-l
B. Description of Devices and Performance II-8
III. ULTRAVIOLET ABSORPTION III-l
A. Apparatus III-l
B. Theoretical Development of Ultraviolet Absorption 111-10
C. Experimental Results - Spectroscopic Measurements 111-28
IV. DISCUSSION IV-1
V. SUMMARY AND CONCLUSIONS V
REFERENCES R~1
APPENDIX A - Measuring NO in Aircraft Jet Exhausts by Gas-Filter
Correlation Techniques, Task I A-l
APPENDIX B - Comments on the Problems in The Previously Reported
Spectral Model B-l
APPENDIX C - Comments on the Experimental Technique of Wise and
Freeh C-l
APPENDIX D - UTRC Spectral Computer Program Description and Listing . . D-l
iii
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LIST OF FIGURES
Figure No. Page
1 Equilibrium Values of NO at Various Initial Concentrations
and Temperatures II-2
2 Time for 5% of Initial NO Concentration to Decompose. . . . H-4
3 Schematic of Gas Handling System II-9
4 Typical Calibration Curves for Critical Orifices 11-10
5 Stainless Steel Shroud and Assembly 11-12
6 Calibration Assembly (Top View) 11-13
7 Flowing Gas Heater 11-15
8 Normalized Concentration Profiles Along Optical Axis Over
Flowing Gas Heater 11-18
9 NO Profiles Over Flowing Gas Heater at Different
Temperatures 11-20
10 Typical Temperature Profiles Over Flowing Gas Heater at
Elevated Temperature and Along Optical Axis 11-21
11 Flat Flame Burner 11-22
12 Water-Cooled Quartz Microprobe 11-24
13 Tip of Quartz Microprobe 11-25
14 Thermocouple and Traverse Mechanism 11-26
15 Ir/Ir-40% Rh Thermocouple and Support Wire 11-27
16 Normalized Concentration Profiles Over Flat Flame Burner. . 11-36
17 Horizontal Temperature Profiles Over Flat Flame Burner. . . 11-37
18 Arrangement of Apparatus For Optical Measurements III-2
19 Water-Cooled Hollow-Cathode Lamp IIT-5
20 Intensity Distribution in Narrow-Line Lamp - . . . . III-6
21 Narrow-Line Lamp Emission III-7
22 Emission from Fig. 21 After Absorption by 5 Torr 10% NO/Ar
Over Path Length of 18.6 cm III-8
23 Doppler Broadening (0.0005 nm) and Slit Function (0.0015 nm) 111-30
24 NO Absorption Spectrum 111-31
25 NO Absorption Spectrum 111-32
26 NO Absorption Spectrum 111-33
27 NO Absorption Spectrum 111-34
28 NO Absorption Spectrum 111-35
29 Computer Spectrum 111-36
30 Computer Spectrum 111-37
31 Computer Spectrum 111-38
32 Absorption by CO Coincident with ^(0,0) Band of NO 111-41
33 Spectrum Near PJ_J_ Bandhead 111-42
34 Computer Spectrum Near P^ Bandhead 111-43
35 Measured NO Broadening Parameter in Flames 111-48
36 Nitric Oxide Profiles Over Flowing Gas Heater at Elevated
Temperatures 111-53
iv
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LIST OF FIGURES (Cont'd)
Figure No. Page
37 Horizontal Temperature Profiles Over Flat Flame Burner. . . 111-55
38 Horizontal Temperature Profiles Over Flat Flame Burner. . . 111-56
39 Horizontal Temperature Profiles Over Flat Flame Burner. . . 111-57
40 Horizontal Profiles of Major Species Over Flat Flame
Burner 111-58
41 Horizontal Profiles of Major Species Over Flat Flame
Burner 111-59
42 NO Horizontal Profile Over Flat Flame Burner (Cold Flow). . 111-60
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LIST OF TABLES
Table No.
II-A
II-B
III-A
III-B
III-C
III-D
III-E
III-F
III-G
III-H
III-I
III-J
III-K
III-L
III-M
III-N
III-O
IV-A
Description of Sampling Probes Used Over The Flowing
Gas Heater and the Flat Flame Burner
Flow Conditions For Optical Measurements Over Flat
Flame Burner
Specifications For Gases
Bandheads in the y -System of Nitric Oxide
2
X TT State Constants for NO
2
A Z State Constants for NO
Notation for Transitions of NO
Spectral Lines Used For Broadening Measurements
2 2
Broadening Parameters for NO y(0,0) (A Z-X TT) Transitions .
Comparison of Collision Diameters for Broadening of NO
y(0,0) Lines
f\ f\
Oscillator Strengths for the NO y(0,0) (A I+-X IT) Band
For Different Gases
Oscillator Strengths (fQ Q) for the NO y(0,0) Band:
Literature Summary
Oscillator Strengths (fQ Q) for NO y(0,0) Band:
A Comparison
Static Cell Calibration Data (NO in N2)
Flowing Gas Heater (FGH) Optical Measurements
Continuum Lamp Transmissions for ^/Oo/Ar/NO Flat Flames. .
Flat Flame Burner Results
Comparison of Transmission Data ARO Lamp Versus UTRC Lamp .
Page
11-17
11-34
III-3
111-20
III-2A
111-26
111-27
111-40
111-44
111-46
111-49
111-50
111-52
111-62
111-63
111-65
111-66
IV-6
vi
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I. INTRODUCTION
Since Johnston (1971) and Crutzen (1970, 1972) independently suggested that the
injection of nitric oxide (NO) into the upper atmosphere could significantly diminish
the ozone (0-j) concentration, an accurate knowledge of the amount of NO emitted by
jet aircraft has been a serious concern to those involved in environmental studies.
This concern intensified when McGregor, Seiber, and Few (1972) reported that NO con-
centration measured by ultraviolet resonant spectroscopy were factors of 1.5 to 5.0
larger than those measured by extractive probe sampling with subsequent chemilumine-
scent analysis. These initial measurements were made on a YJ93-GE-3 engine as part
of the Climatic Impact Assessment Program (CIAP) which was one of four studies (CIAP,
NAS, COMASA, COVOS (see References)) commissioned to determine the possible environ-
mental consequences of high altitude aircraft operation, especially supersonic air-
craft. After those studies were initiated, economic factors strongly favored the
production and operation of subsonic aircraft. Nevertheless, since the subsonic air-
craft fleet is large and does operate as high as the lower stratosphere, interest in
the causes of the discrepancies between the two NO measurement methods continued.
Few, Bryson, McGregor, and Davis (1975, 1976, 1977) reported a second set of measure-
ments on an experimental jet combustor (AVCO-Lycoming) where the spectroscopically
determined NO concentrations were factors of 3.5 to 6.0 higher than those determined
by the probe method. In this set of measurements, optical data were obtained not only
across the exhaust plume but also in the sample line connecting the probe with the
chemiluminescent analyzer. The sample line optical data seemed to agree with the chemi-
luminescent analyzer data; hence, it was suggested that the discrepancies were due to
phenomena occurring in the probe. These results stimulated a third set of measurements
involving ultraviolet spectroscopy (Few et al, 1976a, 1976b), infrared gas correlation
spectroscopy (D. Gryvnak, 1976a, 1976b) and probe sampling on an Allison T-56 combustor,
The measured ratios of the ultraviolet to the probe values typically ranged between
1.5 and 1.9 depending on the data reduction procedure. The ratios of the infrared to
the probe values varied between 1.1 to 1.5 also depending on the method of data reduc-
tion. In addition to these engine and combustor data, evidence supportive of the ac-
curacy of the ultraviolet spectroscopic method, i.e., calibration data and model pre-
dications, was presented by McGregor, Few, and Litton (1973); Davis, Few, McGregor
and Classman (1976); and Davis, McGregor, and Few (1976). Nevertheless, it was still
not possible to make a judgment on the relative accuracy of the spectroscopic and
probe methods. The most significant reasons for this were: the complexity of the
spectroscopic theory and computer model required to infer concentration from optical
transmission; the inadequate treatment of probe use; and the incomplete exhaust tem-
perature and pressure data which are necessary for a valid comparison of the methods.
Recently, Oliver et al (1977, 1978) as part of the High Altitude Pollution Program
has ranked these discrepancies as a major and a continuing source of uncertainty in
atmospheric model predictions.
The purpose of this investigation was to identify and determine the magnitude of
1-1
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the systematic errors associated with both the optical and probe sampling techniques
for measuring NO. To accomplish this, the study was divided into three parts. The
first was devoted to calibrating the ultraviolet and infrared spectroscopic methods.
This entailed developing procedures which could provide known concentrations of NO
over a wide range of temperatures and pressures, and also reviewing and correcting
the ultraviolet spectroscopic theory used in the engine and combustor measurements
cited above. The second part of this study was focused on sample extraction, transfer,
and analysis by chemiluminescent instrumentation. The sampling methods were used on
three successively more complicated combustion systems starting with a flat flame
burner and culminating with a jet combustor. The results are presented in TASK II
Report: Probe Methods . In the third part of this study, optical measurements were
made on the same three combustion systems operated at the same conditions used for
the probe measurements. The results of the optical and probe measurements were com-
pared and are given in TASK III Report: Comparison of Optical and Probe Methods.
This report, i.e, TASK I, covers the results of the first part of this study.
As indicated above, the optical calibration entailed several steps which will be
briefly described below.
The first was the selection and development of devices which would provide known
concentrations of NO from room temperature to approximately 2000 K. Known concentra-
tions at pressures from subatmosphere to two atmospheres were also required but not
over the above temperature range. The selection of the devices was governed by the fol-
lowing criteria. NO decomposition through either hetero- or homogeneous processess was
to be minimal (£ 10%) relative to the discrepancies cited above. Temperature and con-
centration distributions were to be known along the optical path and stable during
the measurement. The optical path and the concentrations were to be such that unam-
biguous optical data would be obtained.
The second part of the calibration process started with the translation of a
spectroscopic computer model developed and used at Arnold Research Organization
(ARO) by the authors cited above (McGregor, Davis, Few. Classman). This model was
generously provided by J. D. Few and H. N. Classman. After encountering serious
deficiencies in that model (see Appendix B), a new model was developed which was used
to process both resonant line and continuum source, ultravilet, spectroscopic data. In
addition, broadening parameters and oscillator strengths were experimentally determined.
The third part of the calibration process was the actual verification of the new
model over the temperature range given above using a hollow cathode resonant lamp.
Measurements were also performed by ARO personnel with a capillary discharge lamp.
These results are described in an internal report by Few, Lowry, McGregor and Keefer
(1979). A review of that report is included in Section IV.
Finally, an empirical calibration of an infrared gas correlation spectrometer
was performed. The results of that calibration are presented by D. Gryvnak of Ford
Aerospace in Appendix A.
1-2
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II. CALIBRATION DEVICES
A. Design Considerations
II.A.I NO Decomposition, Equilibrium and Kinetic Considerations
The complexity of the problem of providing known concentrations of nitric
oxide at elevated temperatures and given pressures may be demonstrated by the
paradoxical predictions of equilibrium theory for the reaction
2NO ± N2 + 02 (1)
Assuming infinite time is available and an initial mixture of NO in nitrogen,
equilibrium values of NO may be calculated using mass balance and the equilib-
rium constant K^ = PN x pQ /p2m = 5.06 x 10~2 exp(+21,700/T) (determined
from JANAF tables). In Figure 1, where ratios of equilibrium to initial values
are plotted, it is shown that as temperature decreases from 2000K, the amount
of decomposition becomes greater. Equilibrium data, in fact, predict that NO
in N2 mixtures successfully used in calibrating analytical instruments should
not be useful. Clearly equilibrium information, by itself, is inadequate since
kinetics play the dominant role. Indeed, the problem of decomposition is most
severe at elevated temperatures.
Nevertheless, Figure 1 suggests that calibration procedures and apparatus
must be selected carefully if problems caused by equilibrium conditions are to be
avoided. Fortunately, the rate of destruction of NO is limited by chemical
kinetics, which in turn is dependent on local temperature, pressure, and the
presence of other reactive species and/or surfaces. In fact, at room tempera-
ture the homogeneous reaction rate is so slow that pure NO can be stored under
pressure for indef initeperiods with negligible conversion to N20, N02 and 02-
Alternatively, much NO can be lost in short periods of time in the presence
of a catalyst or a reactive surface such as copper or even other gaseous
species such as oxygen where NO may be lost via the reaction.
NO + NO + 02 + 2N02 (2)
Furthermore, it is clear that only through careful consideration of the rate
of chemical kinetics (both homo- and heterogeneous) can wide variations of
temperature and concentration conditions be provided for NO calibration. A
literature review of both the homogeneous and heterogeneous reactions (e.g.,
Wise and Freeh (1952), Yuan et al. (1959), McCullough (1975X Kaufman and Kelso
(1955), Winter (1971), Shelef and Kummer (1969), and Fraser and Daniels (1958)),
suggests three temperature regimes for the decomposition of NO at atmospheric
pressure: (1) below 1000K, heterogeneous kinetics dominate, (2) above 1400K
homogeneous reactions dominate, and (3) between 1000 and 1400K a transition
region exists. The size, i.e., temperature window of the transition region
for a given experiment depends, of course, on the reactivity and surface area
of exposed walls, the concentration of NO, and the identity of any third body
(diluent) if present.
II-l
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FIG. 1
EQUILIBRIUM VALUES OF NO AT VARIOUS INITIAL CONCENTRATIONS AND TEMPERATURES
TEMPERATURE (K)
2000
700
D
O
LU
O
100 ppm NO IN N2
1000 ppm NO IN N2
5000 ppm NO IN N,
10
-4
79-O4-54-1
II-2
-------
Of the several reports on the homogeneous (thermal) decomposition of NO,
perhaps the most comprehensive is the recent work by McCullough (McCullough
(1975), McCullough et al. (1977)). In this work, mixtures of NO in Ar (100
ppm - 5%) were passed through a packed ceramic flow reactor at temperatures
between 1500 and 2100K at atmospheric pressure. In addition to presenting
a detailed chain mechanism for the decomposition of NO, this work provides
experimental data for NO thermal decomposition at the concentration levels of
interest in the present study, i.e., 100-5000 ppm. Assuming that the effective
dead volume in McCullough's reactor is 2.75 cm^ (estimated from this published
data and using McCullough1s decomposition data), the time for 5% loss of the
initial NO can be computed. The results are shown in Fig. 2 for several
temperatures and concentration levels. A reduction of _<^ 10% during test time
is considered to be the objective of the calibration system.
II.A.2. High Temperature Calibration
These data suggest that an apparatus capable of providing a calibrated
source of nitric oxide up to 2000K must be able to heat the NO within several
milliseconds and continually replace the decomposing NO with freshly heated
NO. Otherwise, the stationary nitric oxide would undergo thermal decomposition
during the period of calibration, which for the infrared (IR) system nay
be 5 to 10 minutes. Even for the ultraviolet (UV) measurements, a minute or
so is required. Since a flow system appears necessary in order to continually
replace the heated NO, a static heated cell would clearly be impractical.
Several other calibration devices can immediately be eliminated for high
temperature use. For example, NO can be premixed with an inert carrier and
then heated by flowing it through a hot furnace or heat exchanger. This
technique, unfortunately, is not feasible since the time required for heating
of the gas will be on the order of seconds. Several methods of preheating the
carrier gas and then injecting cold NO prior to the optical measurement were
also considered, e.g., a plasma torch. However, in these cases characteristic
times of diffusion, i. e. , mixing, were found to be limiting. A shock tube has
the advantage of elevating the gas temperature nearly instantaneously (micro-
seconds) but insufficient time is available (only several hundred milliseconds)
for calibration before a reflected or rarefraction wave changes the gas
temperature and pressure.
The most viable alternative which would both heat the NO within several milli-
seconds and continually supply freshly heated NO is a lean H2/02/Ar flame seeded
with NO. Argon rather than nitrogen is selected as the diluent since it would
prevent additional formation of NO via the Zeldovich (1947) reactions.
This technique has, in fact, been used successfully at UTRC (Seery, et al
(1979)) in l/10th atmosphere flames using molecular beam sampling and by Kaskan
and Hughes (1973). This previous work indicated that NO would not be lost in
the reaction zone of a lean H2/Oo flame. To investigate the conservation of NO
II-3
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FIG. 2
TIME FOR 5% OF INITIAL NO CONCENTRATION TO DECOMPOSE
CURVES ESTIMATED FROM MCCULLOUGH (1975) DATA
1.0
0.8
0.6
0.4
0.2
0.0
100 ppm NO IN Ar
1000 ppm
10,000 ppm
1600 1700
1800 1900
T(K)
2000 2100
79-04-54-2
-------
In a post flame region where optical measurements would be made, decomposition
reactions and their rates were examined. These calculations predict that NO
decomposition should be small immediately above a lean H2/02/Ar flame at
atmospheric pressure. Due to the very wide flammability limits of a hydrogen/
oxygen flame, it is expected that a flat flame burner could be used as a
calibration device over the temperature range 1000-2000K. In addition, this
device is particularly suitable since in Tasks II and III of this program, a
flat flame burner using methane for fuel is needed.
II. A. 3. Low Temperature Calibration
Given that a I^/On/Ar flat flame can be employed for NO calibration from
1000-2000K, the lower temperature range, 300-1000K with possibly some tempera-
ture overlap remains to be considered. A literature review indicates that
heterogeneous reactions in the absence of high concentrations of reactive
radicals dominate below HOOK. Unfortunately agreement on overall reaction
rates and heterogeneous mechanisms is generally so poor that Shelef and Kummer
(1969) remarked in their summary of catalytic reduction of NO,
"It is truly so that catalysis is an art rather than a
science and although those working in catalysis are
impelled to offer plausible mechanisms for the catalytic
process based on kinetic and other data, these attempts
often fall very short of exact mechanistic descriptions
of surface processes involved. We can indicate broadly
those solid surfaces that will be of use in the catalytic
reactions of NO but it will require many more experiments
before we can hope to formulate the theory that will
enable us to predict in advance the catalytic behavior
of a given surface for these important reactions."
Conclusions generally differ, for example, with regard to the experimental
reaction order for which values of zero (Yuan, et al (1959), and Eraser and
Daniels (1958)), one (Winter (1971)), and two (Wise and Freeh, (1952)) have
been obtained. Here, the reaction order, n, is defined by the overall rate law.
' =-k[NO]n (3)
dt
where k is the effective rate constant which in general depends on temperature,
reaction order, surface material, and active or available surface sites. The
reaction order, in turn, may depend on NO concentration, temperature, surface
material, and available surface sites. For example, Wise and Freeh (1952)
show that, by doubling the surface to volume ratio, the overall decomposition
rate doubles at 900K. [NO], in Eq. 3, represents the concentration of nitric oxide.
II-5
-------
To reduce reaction rates, it is clear that total surface area should be
minimized and that a relatively inactive surface should be used. Porous
surfaces should be avoided due to relatively high total surface areas. One
measurement (Fraser and Daniels, (1958) using nitrogen absorption and the
Brunauer, Emmett anJ Teller (BET) theory (Brunauer, et al (1938)), indicates
that the total surface area of typical metal oxides are approximately thirty
times their macroscopic surface areas. Polished quartz or glazed ceramic,
of course, would provide ideal surfaces due to their smooth surfaces and
well-known low catalytic activity. Considerable experimental data are
available on ceramic materials such as alumina (AJ^Os) or zirconia (Zr02)l
however, the surfaces are not glazed and NO pressures are typically much
higher (approximately 10-500 torr) than the pressures of interest in this work
(1000 ppm of NO in one atmosphere of N2 is equivalent to .76 torr) . Extra-
polation of this decomposition data to the desired conditions of the present
work, i.e., low initial NO concentrations and small surface areas must be
questionable, especially in light of the comments by Shelef and Kummer. In
fact, direct application of their equations
-------
If Wise and Freeh's conclusions are accepted, then a static quartz cell
could be used up to 1100 K only, of course, if extreme care is taken so as to
avoid exposure to any other materials within the heated cell and no gaseous
impurities such as oxygen are present. Since the previously published report
is in question, a simple alternative might be to construct a heated quartz cell
and flow mixtures of NO in a carrier through the cell. Although this approach
was considered, it was decided that uncertainties in temperature profiles
(radial and axial) .and difficulties in probing together make this approach
undesirable.
Several other systems were considered where the carrier gas is preheated
and then the NO injected in a mixing zone just upstream of the optical measure-
ment. All of these designs, however, were subject to limitations by characteris-
tic diffusional rates and, therefore, could not be recommended. An alternative
system was conceived in which the nitric oxide and carrier gas is premixed and
then heated prior to the optical measurement up to the temperatures of interest.
The gas is heated using a quartz bed heat exchanger. Quartz is used to mini-
mize catalytic activity. This concept appeared to have several advantages.
First, uniform mixing of NO with the carrier would not be a problem. Second,
a design could be selected to be compatible with the flat flame burner and,
consequently, much of their support facilities would be identical and could
be used for either configuration. Furthermore, the flowing gas would be easily
accessible to probe measurements of concentration, and temperature. This cali-
bration device, entitled the flowing gas heater (FGH), seemed to be most practical
for the lower temperature range (300-1000 K) . Details of design and operating
characteristics are described in a following section.
At room temperature, a static cell should also be used. With this device,
concentration and temperature profiles are well-defined and a variety of experi-
ments can be performed including broadening measurements using several different
gases, and comparison of results from certified gas mixtures and from mixtures
made on site. This device is described in Section III.A.I.
In summary, the approach for calibration of the optical measurement for
nitric oxide includes the use of three devices: 1) a static cell at room tem-
perature, 2) a flowing gas heater for the temperature range 300-1000 K, and 3)
a flat flame burner with a H2/02/Ar flame useful in the temperature range
1000-2000 K. Items two and three were constructed with similar geometry so
that either could be installed in a central facility which allows for optical,
thermocouple, and probe access. This facility is provided with a gas handling
system.
II-7
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B. Description of Devices and Performance
II.B.I. Central Gas Facility
The central facility includes a gas-handling system and a water-cooled shroud
to contain the gas flow. The former consists of necessary plumbing that blends
various mixtures of gases for feeding both the flat flames and the flowing gas
heater. Separate blending facilities were constructed for the main and buffer
gas flows. The stainless steel shroud has mounts for thermocouple and gas
sampling probes and provides for optical access.
A diagram of the gas handling system is depicted in Fig. 3. The gases used
in these experiments were argon (Ar) , nitrogen C^) , oxygen (02) , methane (CH^) ,
hydrogen (H2), carbon dioxide (C02), nitric oxide (NO), and two mixtures of
nitric oxide and argon. The mixtures were approximately 10 percent NO, 90 per-
cent Ar, and 25 percent NO, 75 percent Ar. For each mix ratio, several bottles
were purchased and, for each bottle, the vendor (Scientific Gas Co.) specified
the ratio and certified the percentages to within jf 2 percent of their stated
values. The concentrations were verified to within approximately 3 percent, using
both mass spectrometric (MS) and chemiluminescent analysis (CA). In the latter
case, since NO concentrations of 10 percent and 25 percent cannot be easily
measured using a standard CA, the mix ratios were verified by diluting the gas
using the gas-handling system and comparing results using the same analysis
techniques with gravimetrically-prepared mixtures of NO in Ar (Scott) and with
mixtures prepared from pure NO and Ar.
Flow rates of gases were controlled by using orifices, metering valves, and
0-150 psig pressure gauges. The gauges are 8V diameter gauges-from Wallace
and Tiernan and are accurate to within + 0.15 psi. The orifices were all
operated at critical flow and ranged in diameter from 0.0015" to .050". The
combination of orifices, pressure gauges, and metering valves allowed the
accurate control of flows ranging from 8xlO~ to 3.5 grams/sec of ^2- The
stability of the flow system was enhanced by using two stage regulators upstream
of the metering valves. Although pressures and temperatures were continuously
monitored,only occasional adjustment of the metering valves was required.
»
Orifices less than .025" size were all jeweled orifices (Swiss Jewel Co. and
Brockton Jewel Co.), mounted in brass and aluminum discs and the discs were
mounted in 1/2-in. stainless steel fittings. Larger orifices were machined and
placed in fittings. Flow calibrations were made using a 3-liter wet test meter
(CGA/Precision Scientific) for flows less than 0.3 grams/sec (N~) . A calibrated
volume was used for larger flow rates and for hazardous gases. Typical calibra-
tion curves are shown in Fig. 4. Although most of the calibrations were performed
using nitrogen, several measurements were made using each of the other gases in
II-R
-------
FIG. 3
SCHEMATIC OF GAS HANDLING SYSTEM
CARRIER (N2OR Ar)
TOGGLE VALVES
METERING VALVES
CRITICALORIFICE
CARRIER (N2 OR Ar)
METHANE
OXYGEN
T/C
T/C
-o-
BUFFER GAS FLOW
T/C
79-04-54-18
II-9
-------
TYPICAL CALIBRATION CURVES FOR CRITICAL ORIFICES
O.:io
o
u
LU
cr
LU
i-
cr
5
o
CO
co
0.08 —
0.06 —
ORIFICE DIAMETER
O 0.008 IN.
D 0.050 IN.
0.04
0.02 —
i
g
60 80 100
ABSOLUTE PRESSURE (PSIA)
120
140
CM
z
u.
o
o
LU
CO
e/5
en
160
-------
these experiments. Correction factors between N2 and other gases for a given
orifice were within 3 percent of those predicted by the equation (derived from
Shapiro, 1953),
2 N2
where the subscripts x and N2 refer to the two gases of interest; m is the mass
flow rate; y is the ratio of specific heats; and MW is the molecular weight. This
equation was used when experimental data for a given gas and orifice were unavail-
able. Discharge coefficients were assumed to be similar.
Pressures downstream of the orifices were continually monitored to ensure that
the orifices, indeed, were choked. Pressure ratios (P . /P, . ) were
' upstream downstream
always 3.0 or greater while approximately 2.0 is required to maintain choked flow.
Calibration curves were repeatable to within 2% (usually to within less than
1%) for measurements using either the wet test meter or the calibrated volume.
Measurements using both techniques for the same orifice were within 3%. The un-
certainty associated with blending a mixture was primarily dependent on the
uncertanties in the orifice calibrations (-3%), pressure readings (-0.5%) and the
vendor certified and cross-checked Ar/NO mixture (<3%).
For the nitric oxide feed lines, the tubing, fittings, and valves were con-
structed of stainless steel to minimize corrosion of the lines and loss of NO to
surface reactions.
Once the gases mixed, their transit time to the test rigs was less than one-
half second. Oxygen was added just prior to the flat flame burner to minimize the
total volume of a combustible gas mixture and to reduce the effect of the reaction.
NO+NO+02 -2N02 (2)
The shroud and other support facilities are depicted in Fig. 5. Its purpose
is to contain the gas flow and to prevent outside air currents from disturbing
the flow. It is essentially a rectangular box constructed of stainless steel, is
open at both ends, and has internal dimensions of 22 cm long, 14 cm wide, and 26 cm
high. Copper tubing is silver soldered on the outside for water cooling. A large
(12.5 x 5 cm) port covered by quartz is installed on one side to view the quartz
bed and flames. A top view is shown in Fig. 6.
11-11
-------
STAINLESS STEEL SHROUD AND ASSEMBLY
FIG. 5
SAMPLE
LINE
PRESSURE
SAMPLE PROBE TRAVERSE
GENERAL VIEWING PORT
THERMOCOUPLE TRAVERSE
OPTICAL VIEWING POFH
79-04-64-20
11-12
-------
CALIBRATION ASSEMBLY (TOP VIEW)
BUFFER ZONE-
• S.S. SHROUD
INE
GAS P
1
RT
URGE
1
MAIN GAS FLOW —^
(SEEDED W/NO)
\
X
r
X
;<
/
1
>
QUARTZ WINDOWS— V
" !
1
1
^^s— DEAD SPACE
SCALE
I
g
I
u
5 cm
-------
Tubes (3.4 cm i.d.) are welded on opposite ends of the shroud to mount the
optical windows and to protect the optical grade quartz or salts flats from the
flame environment. Purge ports were attached to these tubes to flush out any
residual nitric oxide and to prevent gaseous diffusion of NO into these colder
regions. The gas exit from these tubes was 1.3 cm in diameter.
A thermocouple mount and traversing mechanism were attached to the outside
wall of the shroud directly above one of the tubes. The thermocouple bead could
be placed at the same height as the optical beam. The traversing mechanism allowed
for free movement (x + y translation) throughout a given horizantal plane.
Accuracy of positioning in both the x and y directions was approximately + 1 mm
relative and 4- 4 mm absolute.
The probe mount and traversing mechanism for the gas sample probes were mounted
outside the shroud. The probe mount could be adjusted vertically approximately
1 cm. This movement was sufficient to position the probe tip at the height of
the optical axis. A traversing mechanism was purchased which allowed for x-y move-
ment throughout a given vertical plane and with a relative accuracy of + 0.1 mm.
Probes were positioned with 4- 3 mm absolute accuracy.
II.B.2. Flowing Gas Heater
A cut-away view of the flowing gas heater is shown in Fig. 7. As previously
mentioned, the FGH was designed to be a low temperature calibration device with
a quartz heat exchanger. Ceramic heaters (Electro-Applications), which are capa-
ble of reaching 1480 K, heat the quartz bed primarily by radiative heat trans-
fer. The quartz bed is contained by a long, rectangular quartz tube (17.4 x 9.2
x 255 cm) open at the top and necked down to a 2.5 cm diameter tube at the bottom.
Inside are cylindrical quartz tubes ranging in diameter from 5 to 15 mm o.d. with
the largest at the bottom and with their sizes gradually decreasing to the top.
From the bottom of the heat exchanger, two chromel-alumel thermocouples in alumina
sleeves were inserted to monitor internal bed temperatures. Several other Cr-Al
thermocouples were mounted on the outside of the quartz wall using a ceramic paste.
The buffer zone was between the quartz wall and the internal sides of the
ceramic heaters. Its equivalent area was 84 crn^. A buffer zone was designed to
provide a region that would have similar gas temperature as the main flow yet be
void of nitric oxide. The gas flowing through the buffer zone was always the
same as the carrier gas in the main stream. The buffer region was sealed on the
bottom by a horizontal quartz plate. Four vertical ceramic lieaters were cemented
in place and were surrounded by a stainless steel heat shield (reflector) and
approximately 10 cm of insulation.
Due to its bulk and to material constraints the flowing gas heater could not
be raised or lowered once in position. All profiles (temperature and concentration)
11-14
-------
FLOWING GAS HEATER
FIG. 7
BUFFER
ZONE
QUARTZ
MAIN FLOW
\r OR N2 ]
•NO
STAINLESS
STEEL
HEAT SHIELD
79-04-54-4
11-15
-------
were obtained at a fixed location above the gas exit of the quartz heat
exchanger. This distance (6.5 cm) was at the height of the optical axis.
1 1 . B . 2 . a . P.robe_ Mea surement_s_
Several probes of differing design were made in order to access various
portions of the optical path above the flowing gas heater. These uncooled probes
are described briefly in Table II -A; where applicable, figures that show profiles
of NO concentrations also indicate the probe(s) used to obtain the data.
The extracted gas samples were analyzed either with a mass spectrometer or
a chemiluminescence analyzer. Details of these analyses systems and the corres-
ponding sampling trains are given at the end of this section.
1 1 . B . 2 . b . _T emp_er a_ t u_r^ Mea suremen _t_s_
Gas temperatures above the flowing gas heater were measured using a chromel-
alumel thermocouple. Wires were 0.010 inches in diameter while the diameter of the
junction is approximately 0.015 inches. Lead wires pass through an alumina rod
approximately 30 cm long mounted on the traversing mechanism at the side wall of
the shroud. The thermocouple bead was supported 3.0 cm below the ceramic rod.
Millivolt outputs were measured using a Data Precision Model 3500 DVM with a
room temperature junction. Radiation corrections were calculated and found to
be insignificant.
1 1 . B . 2 . c . j£x£e£iinen. tal_Resu_ l_t s_
Tests were made to investigate NO conservation at room temperature and NO pro-
files across the length of the optical axis. A typical profile is shown in Fig. 8.
The loss of approximately 8 percent NO from the seed value, which is calculated
from relative flow rates, is apparently due to a small percentage of intermixing of
the buffer and main flows. For these profiles and for all data presented in this
report, the window purge was on at a flow rate of .0109 moles/sec (.0043 moles/
sec/cm ) of nitrogen. For all calibration experiments, the molar flow rate of
the carrier and buffer zones were held constant at .109 and .0164 moles/sec
/ _/ 2
(6.8 x 10 and 1.95 x 10 moles/sec/cm ) respectively. These values are in-
dependent of molecular weight of the carrier gas or exit temperature of the
quartz bed. Under these conditions, the gas residence time within the quartz
heat exchanger is approximately three seconds.
Elevated gas temperatures were achieved by applying power to the ceramic
heaters. Periodically, the flow rate of the carrier would be increased to the
desired flow conditions for comparison of the actual gas temperatures to the
desired test conditions. Two hours were generally required to reach peak
operating temperatures due to the large riass and, therefore, large thermal
11-16
-------
TABLE II-A
Description of Sampling Probes Used Over
The Flowing Gas Heater and The Flat Flame Burner
Probe
A
B(D
C
D
E(2)
F(3)
Material
Quartz
Quartz
Quartz
Quartz
Stainless
Steel
Stainless
Steel
Internal
Diameter
(mm)
5
5
4
5
1.2
1.2
Water Cooled
Yes
Yes
No
No
No
No
Orifice
inches
.025
.006
.012
.035
.047
.047
Diameter
(microns)
(635)
(150)
(305)
(890)
(1200)
(1200)
(1) Photographs in Figs. 12 and 13.
(2) Probe inserted horizontally into the sampling region through the
optical ports which had their windows replaced with aluminum plates
with a small hole for the probe.
(3) Probe inserted vertically down the center of the shroud but had a
right angle bend at the height of the optical axis.
11-17
-------
NORMALIZED CONCENTRATION PROFILES ALONG OPTICAL AXIS OVER FLOWING GAS HEATER
00
I
g
I
2
Q
IXI
z
o
z
1.0
0.8
0.6
LU
J 0.4
CM
Z
O
0.2
0.0 _
-10
AVG TEMP = 300K
PROBE DESIGN
D
3/31/78
4/3/78
10/11/78
CHEMI
E
F
D
D'
_L
_L
-8-6-4-20 2 4 6
DISTANCE FROM CENTERLINE (cm)
10
12
14
16
P
oo
-------
inertia of the heaters and surrounding insulation. Peak gas temperatures that
were achieved were slightly above 850 K. Higher temperatures were prevented
primarily by local hot spots in the ceramic heaters which underwent thermal
runaway before other portions of the heaters had reached their peak temperatures.
The cause of the runaway was most likely due to nonuniformities (bends or
connections) in the alloy heating wires.
Normalized concentration profiles of nitric oxide at low and at elevated
temperatures are compared in Fig. 9. Two prominent features are apparent. First
of all, nitric oxide is conserved within the quartz heat exchanger. Although
these data were obtained using the chemiluminescence analysis system, similar
results were obtained with the mass spectrometer and its sampling system. Secondly,
the wings (8.5 to 11 cm from the centerline) contain noticeably less nitric oxide
at elevated temperature than at room temperature. This difference appears to be
real since profiles obtained at many different dates exhibit this phenomena. It
is believed that the difference in the wings is due primarily to a reduction in
the available time for mixing of the main and buffer flows at elevated temperatures.
The reduction is due to a velocity increase that is proportional to temperature.
When heated to gas temperatures above 500 K, it was found that power input to
the quartz bed was insufficient to maintain constant temperatures. This problem
existed in spite of the fact that even at 1/2 power (2.4 kW), the ceramic heaters
provided sufficient power, in theory, to elevate the gas from room temperature to
800 K. Consequently stable temperature profiles above 500 K could only be main-
tained for 10-15 minutes. Furthermore, "temperature waves" could be observed
within the quartz bed itself, depending on the immediate history of heating and/or
cooling cycles. Consequently, temperature profiles were obtained for each set of
experiments performed at elevated temperatures. A typical profile is shown in
Fig. 10.
II.B.3. Flat Flame Burner
A photograph of the flat flame burner is shown in Fig. 11. Its surface is
sintered copper constructed by Thermit, Inc. Otherwise the burner is made of
sheet copper with two separate zones: the main, NO-seeded zone and the buffer
zone. Imbedded in the 5/8" thick sintered surface are copper coils for water
cooling. The inside dimensions for the region of the main gas flow was 17.5 x
<^
9.2 cm or 161 cm. The buffer zone is slightly smaller than for the flowing
gas heater with an effective area of 76 cm . The flow systems feeding both the
buffer and main zones at the bottom of the burner were described earlier.
11. B . 3 . a. Pr obj2 Mea^sur_emen_t^
For gas sampling over the flat flame, water cooled quartz probes were used.
Similar designs were used both for the MS analysis and for detection via CA.
11-19
-------
FIG. 9
NO PROFILES OVER FLOWING GAS HEATER
AT DIFFERENT TEMPERATURES
O 753K
O 293K
PROBE D
CHEMI
468
DISTANCE FROM CENTERLINE (cm)
12
79-04-54-5
11-20
-------
TYPICAL TEMPERATURE PROFILES OVER FLOWING GAS HEATER AT ELEVATED TEMPERATURE
AND ALONG OPTICAL AXIS
O RUN NO 36
A RUN NO 43
(D
I
g
I
ID
800
700 -
600 -
a:
LLI
500 -
400 -
300
-12 -10
-6
-4-20 2 4
POSITION FROM CENTERLINE (CM)
8 10
12
P
o
-------
FLAT FLAME BURNER
MAIN ZONE
BUFFER ZONE
4
-------
The primary difference was the orifice size. To feed the mass spectrometer, both
low sampling pressure and very little sample volume are required. For mass
spectrometric analysis, probe tips were small, approximately 150 microns in
diameter (several tips were made due to occasional breakage and/or devitrification)
A typical probe and tip (probe B in Table II-A) are shown in Figs. 12 and 13,
respectively. (Although Figure 13 presents an illusion, the water-in tube is
indeed placed to one side of the gas sample tube). The CA required much larger
flow rates and a tip opening of 635 microns in diameter was used.
The large diameter of the water cooled probes prevented sampling of the
flame closer than 1.5 cm from the wall of the shroud. To sample the gas in this
region close to the wall an uncooled quartz probe (C) of 6 mm o.d. was constructed.
This probe was only used on a low temperature flame so that catalytic activity on
the hot quartz wall and divitrification of the quartz would both be minimized.
It should be pointed out that calculations using the UTRC probe deck were
performed for the quartz probes. Although details of the program will be described
in the Task II report, it is worthwhile mentioning an important prediction. For
the microprobes, of approximately 150 microns in diameter, aerodynamic quenching
of the gas sample is impossible, even at back pressures of '^ 10 torr used in this
work. The limiting factor is the growth of the boundary layer which prevents the
flow from accelerating supersonically. [Although plans are being made to test this
prediction on an atmospheric pressure flame, limited measurements made in a flame
at 76 torr (Seery, unpublished, 1978) suggest that the mass flow rate varies with
back pressure even down to a pressure ratio of 10]. This pressure ratio should
be compared with the ratio of 2 to 1, which is normally believed to be sufficient
to choke the flow. These conclusions may have practical implications to many
flame researchers who have believed previously that their microprobes were aero-
dynamically quenched even with pressure ratios as low as 2 or 3 to 1.
11. B. 3. b. ^T emperatlire N_ea. svaremeivt s_
For the flat flame burner, temperatures were monitored with a buttwelded
Ir/60% Ir-40% Rh thermocouple (.003" wires) coated with a mixture of 10% beryllium
oxide and 90% yttrium oxide. Kent (1970), has found that a mixture of these
metal oxides provides a good non-catalytic coating for thermocouples above
2000 K. The bead with its coating had a total diameter of .0035" - .0005"
and was approximately 1.2 cm away from either lead/support wire (.010" diameter).
Photographs of the thermocouple assembly and a close up of the yoke are shown
in Figs. 14 and 15. Millivolt output was measured using a DVM and converted to
temperatures uncorrected for radiation using published tables (Blackburn and
Caldwell, 1962).
Estimates of radiation corrections were calculated by equating the heat
transfer from the gas stream to total radiation
11-23
-------
WATER-COOLED QUARTZ MICROPROBE
GAS SAMPLE EXIT-
i
NJ
t
u
M
P
rsj
-------
TIP OF QUARTZ MICROPROBE
WATER OUT
g
2
-------
THERMOCOUPLE AND TRAVERSE MECHANISM
THERMOCOUPLE-
2
K>
-------
lr/lr-40%Rh THERMOCOUPLE AND SUPPORT WIRE
i
ro
-------
h (Tg - TT.C.> = e 0 .,.,. The
molar fractions of gas (X) obtained from the flow calculations were used in the
above determinations.
11-28
-------
Properties of the individual gases were obtained from JANAF tables (C ),
Hanley (1973) (y and A for Ar) and Svehla (1962) (y and X for all other gases).
Due to the uncertainties in the emissivity calculation of transport properties
of mixtures, and bead diameter, it is estimated that the calculation of AT
(= T - T ) is accurate to within 20-25 percent.
O 1 • Li •
11. B. 3 . c. j£xhau_s t^ _AnaJL%_zer__
The Scott Model 119 Exhaust Analyzer used in this present investigation pro-
vides for the simultaneous analysis of CO, C02, NO or N02, Q^ and total hydrocarbons
(THC). The analyzer is an integrated system, with flow controls for sample, zero
and calibration gases conveniently located on the control panel. The incoming gas
sample passes through a refrigeration condenser (^275K), to remove residual
water vapor. As the sample passes from the condenser, it is filtered to remove
particulate matter. The system is comprised of five different analytical instru-
ments. Beckman Model 315B Non-Dispersive Infrared (NDIR) Analyzers are used to
measure the CO and C02 concentrations in the gas sample. Concentration ranges
available on the CO analyzer were from 0-200 ppm to 0-15% on several scales.
Concentration ranges available on the C0? analyzer were 0-4% and 0-16%. The
accuracy of the NDIR analyzers is nominally +_ 1% of full scale. A Scott Model 125
Chemiluminescence Analyzer is used to measure the NO and N0~ concentrations in the
gas sample. Concentration ranges available with this instrument were from 0-1 ppm
to 0-10,000 ppm on several scales, with a nominal + 1% of full scale accuracy. The
thermal converter used in the chemiluminescent analyzer was stainless steel, and
was operated at a temperature of approximately 1000 K. A Scott Model 150 Para-
magnetic Analyzer is used to measure the 02 concentration in the gas sample. Con-
centration ranges available with this instrument were from 0-1% to 0-25% on
several scales, with a nominal accuracy of + 1% of full scale. A Scott Model 116
Total Hydrocarbon Analyzer is used to measure the hydrocarbon concentration in
the gas sample. This analyzer utilizes an unheated flame ionization detection
system to provide for measurement of hydrocarbons (as carbon) in concentration
ranges from 0-1 ppm to 0-10%, with a nominal accuracy of +_ 1% of full scale.
Output signals from the various analyzers are displayed on chart recorders and
a digital display.
For those flows in which Ar was the bulk or carrier gas, the chemiluminescent
analyzer was calibrated with a gravimetrically prepared NO in Ar standard..
This instrument can also be calibrated with NO in N2 standards; however a correc-
tion factor of 1.20 must be applied to the indicated reading. This difference
in calibration is primarily due to viscous effects in the instrument sample
capillary and varying quenching efficiencies between Ar and N2. These effects
have been recently analyzed (Dodge, et al. 1979).
II-29
-------
Gas samples were transferred to the SCOTT analysis instruments through a
four meter (13 feet) sampling line purchased from Technical Heaters, Inc.
This sampling line was constructed with an electrical heater including thermo-
couple and had a TFE teflon core of .48 cm (3/16 in.) internal diameter- For
measurements over the flowing gas heater, samples were extracted using an un-
cooled quartz probe (D) with an orifice diameter of 890 microns (0.035 in.).
Typical sampling line pressures and temperatures were 500 torr (^2/3 atm)
and 300 K respectively. Under these conditions, the calculated residence time
in the sampling line is approximately 3/4 seconds (mass flow is assumed to be
50 percent of choked flow). For sampling from the flame, probe A was used with
an orifice of 635 microns (0.025 in.). Using lower pressures and elevated
temperatures of 380 torr (1/2 atm) and 110°C in the sampling line, respectively,
the calculated residence time is similar, approximately one second. Although
these times are well within the required residence times required by the
Federal Register (1976), it should be pointed out that a gas sample typically
undergoes much longer transit times as it passes through the remainder of the
sampling train prior to analysis. For example, after the heated sample
line, the sample travels through refrigerators, metal bellows pumps, filters,
sample bypass, flow valves, all connecting lines and finally the chemilumenescence
detector. Altogether these components increase the sample transit time (from
probe tip to detector) by a factor of 15 to 20 from what is calculated in the
sample line alone. The increase is due not only to an increase in total line
length but also to a pressure rise (via the pumps) and the sample bypass, both
of which act to drastically reduce the gas velocity. The overall effect of the
sample bypass is favorable, since it provides a technique to continually flush
the sample lines and to increase the flow rate and velocity through the first
part of the sampling train. Ideally, the bypass should be located immediately
upstream of the analytical instruments. These comments are particularly per-
tinent to analysis of gas samples containing high concentrations of nitric oxide
due to the reaction
NO + NO + 0- -> 2N02 (2)
which is second order in NO and third order in total pressure. In the case of
the gas correlation measurements, NO concentrations of nearly 10,000 ppm were
required. With an oxygen rich environment, measurements in this laboratory
demonstrated that as much as 7 percent of the NO was converted to N02 via
Reaction 2. Indeed, kinetic measurements performed in this sampling system pro-
duced an evaluation of the rate constant k2 which was within 25 percent of the
accepted value (Hampsonand Garvin, 1978).and were consistent with the fractional
conversion to N02 observed during the IR measurements. Therefore, any N02
(NOX minus NO) was assumed to be formed in the sampling line (and are reported
as NO) for these series of tests where nitric oxide concentrations were
exceptionally high.
11-30
-------
II. B. 3. d Mass_S£ectr£LL Analy_sjLs
The calibration was conducted with mixtures of NO in Ar for the lower
temperatures (T < 900 K) and by seeding NO into lean H2/02/Ar flame at the higher
temperatures (900 K < T < 2000 K) . Standard instrumentation used for emission
measurements is not suitable for determining H2 and Ar. In addition, since the
calibration of the chemiluminescent analyzer is dependent on the bulk or carrier
gas,, interpreting NO measurements in the region of the buffer and shroud is not
straightforward.
Mass spectrometry is a method that with proper sampling technique can readily
measure homonuclear molecules (H2, 02, N~), inert gases, and nitric oxide. More-
over, proper sampling is more easily achieved since the mass spectrometer inlet
and sampling line can be operated at pressures of 10 torr (1.3 kPa). This ensures
a rapid reduction of the sampled gas temperature and pressure and minimizes sample
transfer time. Since only small mass flows are required to make a measurement,
the probe orifice can be made smaller than that used if a standard analytical
instrument train is employed.
The instrument used in these measurements is a one-meter, time-of-flight mass
spectrometer operated at a source pressure of 5 x 10~" torr (6.6 x 10 Pa).
Residual gas pressure is typically less than 1 x 10~^ torr (1.33 x 10~^ Pa). The
master clock for the instrument is crystal controlled at 10 kHz; hence, 10^ spectra
per second are obtained. Through the use of ion sampling, the high frequency real-
time output is converted into a lower frequency suitable for a data acquisition
system. This acquisition system was a Northern Scientific NS 575 signal averager
and NS 408 F tape interface with a Wang Mod 7 digital tape transport. For the
data reported here, 8 to 32 low frequency spectra were averaged to improve the
precision of the data. The mass spectrometer inlet was maintained at 8 torr
(1.06 kPa). The sample line was heated 3/8" stainless steel which was held at
a temperature no greater than 390 K. The terminal pressure of the sample line
when capped was 1.5 x 10"^ torr (2.0 Pa). Sample transfer time was less than 0.5
sec for He.
The procedure used to reduce the data depended on the calibration device.
For the flowing gas heater, the procedure consisted of measuring the intensities
at masses 28 (N2) , 30 (NO), 36 (Ar), 40 (Ar). 36Ar isotope was used as a monitor
on instrument performance. The sensitivity factors for these constituents were
empirically determined from gas standards and from mixes of gases prepared with
the critical flow gas system. These sensitivity factors are used to take into
account viscous effects in the mass spectrometer gas inlet, ion source pumping
speed, ionization cross section, ion gate transmission, and ion detector mass
11-31
-------
Ar
discrimination. The sensitivity factors used relative to Ar, i.e., S
were SfH; =1.16 and SAr = 1.03. Mole fraction of NO was obtained from
1.0,
''NO
= S**. I(30)/{SAr. 1(28)
NO
.. 1(30) + 1(40)}
(12)
For the flat flame burner, the procedure is made complicated by the difficulty
in making an accurate H~0 measurement. The standard method employed in emission
measurements is to dry the sample in a low temperature trap. Such a drying pro-
cedure is not required for these mass spectral measurements since the total molar
flow rate of Ar is known. A further complication is introduced by the mixing of
gas from the three zones of the apparatus. This latter problem can be treated by
using the knowledge that the N2 originates only from the window purge and the CO
comes only from the buffer zone flame.
The composition of the flow at any point can be described by
XM + *B + V = X
(13)
where X is the fraction from the main burner flow, X,, is the fraction from the
buffer flow, and X^ is the fraction from the window purge. Using N2 and C02 as
tracers, the local intensity ratios of N2 and C02 to Ar are
1(28) = 1
1(40) sF
^Ar
(14)
and
1(44)
1(40)
= 1
sAr
co?
V R
BCOo
/
XM MAr +
V "D
Xfi BAr
(15)
where M is the mole fraction of Ar in the main burner flow; B. is the mole
fraction in the buffer flow; 1(44) is the C02 intensity; S^ is the C02 sensi-
tivity; and BCQ is the mole fraction of C02 produced in the buffer flame. M.
and B. are known from the calibrated flow system. BCQ_ is known from the
Solving for XM and XT. yields
CQ 2
are known from the calibrated flow system.
equilibrium value of C02 for the buffer flame.
*N2
,Ar
3 CO-
1(44)
N2
1(28)
1 -
M
Ar
"CO,
+ 1
M
Ar
K40) \ +
1(28)
-1
(16)
11-32
-------
Bco2
The results of equations (16) and (17) can be inserted into equation (13) which
then can be solved for X,,.
Given these expressions, the local water to argon expression can be
calculated from
K18)
XM
where Bu and >L. n are known from the equilibrium value of H90 for the buffer and
n.-jUrl^u z
main flames, respectively. The mole fraction at any point for a given ith molecule
is
where .
T = 1 + TT40) ) S^ .1(44) + S^. 1(28) + S^. 1(30) + S^. (32) + 1(18)) (20)
*22 2,
All terms are measured values with the exception of the 1(18)/I(40) ratio which is
calculated. Also, for the buffer region and a small region on either side of
it, corrections are made for the contributions of C0(30) isotope to the nitric
oxide intensity and for the contributions of C0(28) from the flame and ion
fragmentation of C02 to the nitrogen intensity.
11. B. 3 . e. Ex£er_:ijneii t a.l_R£su_l_t s_
Initial tests of several flame conditions indicated a flow instability
several centimeters above the burner surface. To dampen these flow fluctuations
a three level tier of screens was constructed and hung from the side walls of the
shroud. The lowest screen was 7 cm above the optical axis. Slots were cut at
appropriate positions for movement of the probes along the optical axis. Although
not mentioned previously, this set of screens was used in all measurements above
the flat flame burner and flowing gas heater.
11-33
-------
TABLE II-B
FLOW CONDITIONS FOR OPTICAL MEASUREMENTS
OVER FLAT FLAME BURNER
Uncorrected
Thermocouple
Mole Fraction
Distance of Total
optical axis Molar
Temperature
(K)
950
1220
14 00
1600
^- —
H2
0.073
0.116
0.169
0.330
•» ^^__j>—
°2
0.102
0.114
0.116
0.170
-^
Ar
0.825
0.770
0.715
0.491
Equivalence
Ratio
0.36
0.51
0.73
0.92
above burner
(cm)
2.0
1.5
1.5
1.0
flow rate
(moles/sec)
0.128
0.134
0.145
0.194
11-34
-------
After selecting several flame conditions (listed in Table II-B), initial
gas sampling was made with probe B (Table II-A) and analysis was made with the
mass spectrometer. Typical profiles of nitric oxide along the optical axis are
shown in Fig. 16. Flow conditions for the l^/C^/Ar flames are given in
Table II-B. The observed scatter is characteristic of a statistical analysis
for the operating conditions of the mass spectrometer. This scatter could be
reduced by additional averaging of spectra. It is apparent that nitric oxide
is conserved through the flame front at least for the low temperature flames.
Similar data demonstrates conservation at higher temperatures.
A typical thermocouple profile with radiation corrections is reproduced in
Fig. 17. The profile shows near symmetry around the centerline. The slight
temperature rise near the edges (around 8 cm from the center) is probably due to
a separation by the sintered copper and the copper plate between the main and the
buffer flows. Resultant gas velocities are higher which push the flame away from
the burner and decrease the local heat loss to the burner.
At approximately 8.5 centimeters from the center of the burner, the tempera-
ture drops drastically. This fall-off seems surprising considering the existence
of the buffer flame out to 10.2 centimeters and is caused by the strong nitrogen
purge exiting from the window tubes. The effect of the purge at the selected
flow rates is quite noticeable on both the temperature and NO profiles. Although
this perturbation is undesirable, its presence does not affect the ability to
make the optical measurements since probe measurements provide sufficient data to
reduce results using multiple zones. Probe measurements indicated that lower flow
rates were ineffective in flushing out cold NO from the optical arms. Additional
experimental data on both the flowing gas heater and flat flame burner are
presented in the following chapter.
11-35
-------
FIG. 16
NO HORIZONTAL PROFILES OVER FLAT FLAME BURNER
H2/O2/Ar
THERMOCOUPLE NO SEED
TEMPERATURES LEVELS (WET)
(K)
ppm
MASS
SPEC
CHEMI
1220
950
950
950
1995 \
2030 > PROBE B
2030 )
2030 PROBE C
1.2
1.0
Q
01
LU
00
O
z
O
z
4 6 8 -1- 10
DISTANCE FROM CENTERLINE (cm)
12
79-04-54-8
11-36
-------
HORIZONTAL TEMPERATURE PROFILES OVER FLAT FLAME BURNER
H2/O2/Ar
UNCORRECTED TEMPERATURE = 1400K
1800
1600
1400
1200
i. 1000
800
600
400
ID
I
O
200
Hi
j_
-8-
UNCORRECTED
TEMPERATURES
O 5/1/78
D 5/5/78
A RADIATION CORRECTION
I
-12 -10 -8 -6 -4-20 2
DISTANCE FROM CENTERLINE (cm)
10
12
-------
III. ULTRAVIOLET ABSORPTION
A. Apparatus
III.A.I. Gas Mixing System for Static Cell Optical Measurement
The majority of static cell calibration data were obtained by mixing gases
using the system shown in Fig. 18. The system was evacuated below 25 x 10 torr
(3.3 Pa.) and then filled with a calibration gas to the desired pressure. If it
was desired to raise the pressure of the diluent gas further without adding more
NO, the valve to the static cell was closed, the system evacuated, and then filled
with the diluent gas by slowly raising the regulator pressure until the final
desired pressure was reached. The valve to the static cell was opened so that
the pressure in the rest of the system dropped and then quickly recovered via the
regulator to the desired final pressure and the valve was closed.
Pressures were monitored with three gauges. A thermocouple gauge was used
to verify the vacuum integrity of the system. A Barocell Datametrics capacitance
manometer (model 570 A sensor and model 1173 readout) with full scale ranges from
0 - 0.1 torr (0 - 13.3 Pa.) to 0 - 1000 torr (0 - 133.3 kPa.) was used along with
a Wallace and Tiernan 0 - 150 psia (0 - 1.034 MPa.) pressure gauge to determine
pressures.
For the broadening and oscillator strength study, cylinders of NO diluted to
about 2000 ppm in N2, Ar, C^, and CH/ were obtained from Scott Environmental
Technology along with the highest purity diluent gases commercially available.
The specifications for these gases are given in Table III-A. The NO/ No con-
centration was independently verified; but, the other cylinders were accepted
as labeled based on gravimetric blending by the vendor and vendor analysis.
III.A.2. Light Sources
Two distinct types of light sources were used. One lamp was a low pressure
hollow cathode lamp which produced discrete emission lines in the y (0,0), y (1,1),
and y (2,2) bands of NO. The other lamp was a high pressure Xe lamp which pro-
duced continuum radiation in the region of interest.
III.A.2.a. Na£Tow-Line Lamp
The hollow cathode lamp was operated with a dc discharge in flowing air and
produced emission lines from principally NO molecules, N2 molecules and ions, and
Ar atoms. The spectral lines used in this study were in the y (0,0), y (1,1), and
y (2,2) bands (A2I+ - X2ir) of NO.
III-I
-------
ARRANGEMENT OF APPARATUS FOR OPTICAL MEASUREMENTS
0-1.32 ATM
—>
P
HOLLOW CATHODE LAMP
OR
HIGH PRESS. Xe LAMP
10%NO/Ar
2000PPM NO/X
LIGHT SOURCE QUARTZ LENS
ABSORPTION CELL
MIRROR (OR TEST SECTION)
FILTER 226nm
PHOTOMULTIPLIER
J-Y 1.5M
SPECTROMETER
COOLED PHOTOMULTIPLIER
RATIOMETER
CHART RECORDER
P
03
-------
TABLE III-A
Specifications for Gases
Gas Blends of NO
Diluent Gas
Ar
C02
CH4
No
Concentration
of NO
(pptn)
1980
2030
2000
2080
Vendor Analysis
Accuracy
±1%
±1%
±1%
±2%
Pure Gases
Diluent Gas
N2
co2
CO
CH4
Ar
Purity
99.998%
99.99%
99.99%
99 . 99%
99.999%
Maximum (
5 ppm
5 ppm
5 ppm
5 ppm
2 ppm
III-3
-------
The design of the water-cooled hollow cathode lamp is shown in Fig. 19 and
followed that of Meinel (1975), who generously provided a drawing. of his lamp.
The operating characteristics are similar to those described by Meinel (1975) .
The lamp was operated on flowing air at a pressure of 2 torr and a current of
25 mA (0.1% electronic stability over eight hours). The ballast resistors were
combined for a net resistance of 1.67K and the operating voltage was about 600V.
At constant pressure, the intensity stability of the lamp was excellent (<.5%
drift) over several hours.
The possible steps leading to the production of NO in an excited state from
air in the discharge are discussed by Meinel (1975) . It is clear from the emission
spectra that the excited NO molecules are not in rotational or vibrational thermal
equilibrium. The population distribution of the 2j;(v'=0) level is shown in Fig.
20, where the points represent resolved spectral lines. The lines drawn through
the points were used as an input to the computer program to determine the
strengths of unresolved lines, as explained in the description of the computer
program.
There is a small amount of light in the NO y (0.0) band which appears to be
from some molecule(s) other than NO. The NO lines may be readily located, but there
are some weaker spectral features between the lines which have not been identified,
as shown in Fig. 21. These extra lines are not absorbed like the other NO lines
as shown in Fig. 22. The effect that this "extra-light" has on the measured f-
values is discussed in the section describing the oscillator strength measurements.
1 1 1 . A . 2 . b Ck> ri t jLnuum Lamp
The lamp used to obtain a continuum output was a 1000 watt- high pressure Xe
arc lamp (Canrad-Hanovia 976C-0010) mounted in an Oriel housing and using an Oriel
power supply. The lamp exhibited a moderate amount of intensity drift (3% over
10 min) , and the lamp housing had to be vented to the outside because of the
significant quantity of ozone produced.
1 1 1 . A . 2 . c S£e£t£ome_t er_ a_n<^ Assp£ia_t £d_E ^e£t ran ic s
A 1.5-m focal length J-Y spectrometer in a temperature controlled box with a
2400 g/mm holographic grating (110 x 110 mm), aperture of f/12, and Fastie curved
slits was employed for all measurements. Typical slit function, full width at
half maximum (FWHM), was observed to be .0018 run with 7 um slit settings for the
226 nm NO lines observed in the 2nd order of the grating. Most of the spectra
were recorded with a Hamamatsu R166 solar blind (Cs-Te photocathode) photo-
multiplier tube cooled to -30°C in a Products for Research TE-177 thermoelectrically
cooled housing. Some measurements were also made with an EMI 9659QB photo-
multiplier (extended S-20 photocathode) cooled to -78°C with dry ice.
III-4
-------
WATER COOLED HOLLOW CATHODE LAMP
T\
P
—.
CO
-------
FIG. 20
7.0
6.0
5.0
4.0
3.0
2.0
INTENSITY DISTRIBUTION IN NARROW-LINE LAMP
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
1*1 (I/S) = -0.002563 Eu + 117.23
•CORRELATION = -0.841
T = 561 K
AH (I/S) = -0.00084107 Eu + 38.939
. CORRELATION = -0.986
T= 1711 K
I I I
I I 1 I I I
I I
I
I
45.000
I I i i i
46,000 47,000
TOTAL ENERGY, Eu, CM~1
i i I i I i i i i I i i i I I
48,000
I
I
I
500
1000 1500 2000
ROTATIONAL ENERGY, CM"1
2500
3000
79-04-93-9
J.II-6
-------
FIG. 21
NARROW-LINE LAMP EMISSION
1- Pn (6.5) + PI, (11.5)
2. Pn (7.5) + P^dO.5) + P22 (22.5) + Q12 (22.5)
3. PH (8.5) +• Pn (9.5)
4. Q22 (14.5) + R-|2 H4.5) + R22 (9.5) + P12 (31.5)
5. P22 (21.5) + Q12 (21.5)
CO
•z.
LU
ZERO
I
226.36
I I
226.38 226.40
WAVELENGTH, nm
ZERO
79-02-155-1
III-7
-------
EMISSION FROM FIG. 21 AFTER ABSORPTION BY 5 TORR 10% NO/AR
OVER PATH LENGTH OF 18.6 cm
FIG. 22
1. Pn (6.5) + P^ (11.5)
2. P1 1 (7.5) + P.| ., (1 0.5) + P22 (22.5) + (X, 2 (22.5)
3. Pn (8.5) -f Pn (9.5)
4. Q22 (14.5) + R12 (14.5) + R22 (9.5)
(21.5)
5. P22 (21.5)
oo
WAVELENGTH
79-02-1 S5-2
-------
The signal from the photomultiplier was amplified with an Analog Devices
AD310K used in the electrometer mode with feedback components of Rf = 100 M
and G£ = SOOOpf. The scan rate was 3.95 • 10~4 nm/sec. The resulting spectra
were recorded with a Hewlett-Packard 7100B strip chart recorder. In the case
of the continuum lamp, some of the spectra were corrected for lamp drift by a
ratiometric technique. This involved a reference measurement of the source lamp
prior to any absorption, and was accomplished by placing a flat mirror slightly
off the beam directed through the calibration apparatus which reflected light
through a 226 run filter and onto an EMI 9601B photomultiplier tube. The signal
from the spectrometer was divided by this reference signal in an Ithaco model
3512 ratiometer and this resultant ratio was recorded on the strip chart recorder.
This ratiometric technique reduced but did not eliminate baseline drift in the
recorded spectra while using the continuum lamp.
The ultraviolet radiation from the source lamp was collimated and directed
through the 12.7 mm diameter apertures in the FGH/FFB shroud, across the FGH/FFB,
and then imaged on the spectrometer slit using fused silica lenses.
The spectrometer was operated in high resolution and low resolution. The
slits were set at about 5 to 10 ym for the high resolution work, corresponding
to slit functions with FWHM of about .0015 nm to .0025 nm. The slits were set
at 1380 pm for the low resolution studies, with a FWHM value of 0.146 nm.
III.A.3 Static Cell
The static cell is a room temperature absorption cell made of stainless steel
with valves toward each end and UV grade fused silica windows. The cell was
leaked checked at 10~6 torr (1.33'10~4 Pa.) and 115 psig (791 kPa.). The cell
i.d. is 22 mm and the optical path is 18.6 cm.
III-9
-------
B. Theoretical Development of Ultraviolet Absorption
III.B.I. Necessity fc>r Theoretical Model
A detailed theoretical model has been developed to describe the absorption
of ultraviolet radiation by nitric oxide in the (0,0) band. It would not be
unreasonable to question the necessity for such a first principles model, when
the possibility exists for an empirical calibration technique. But how well can
known concentrations of NO be generated over a temperature range of 300 K to
2000 K and a pressure range of 0.5 to 1.5 atm? The answer is that it is diffi-
cult and expensive to generate a complete range of conditions necessary for
repetitive empirical calibration. The approach adopted in this work was to start
with a theoretical model and then verify that model by testing it over a range of
conditions, similar to the approach used by Davis et al. (1976a) but with addi-
tional information from high resolution continuum absorption data.
An additional problem with empirical models is that they are often instru-
ment dependent and quite difficult to transfer from a given instrument at one
laboratory to instruments in general. An example for this particular experiment
would be that a strictly empirical calibration would depend on the characteristics
of the narrow-line source (rotational distribution) and the spectrometer (PM tube
response and slit function) which would make duplication of results at various
laboratories difficult. The theoretical model does include some empirical
"adjustments," as will be discussed, and several experimentally determined input
parameters, but the absorption process is modeled from basic principles.
III.B.2. Transmission Formulas, Narrow-Line Source
The general problem of relating measured absorptions in the y(0,0) band to
molecular densities of NO may be summarized as follows. In order to predict low
resolution absorption profiles in the y(0,0) band, it is necessary to model on
the order of 500 lines whose relative intensities change with temperature, and
whose shape changes with temperature, pressure, and gas composition. These
lines are so closely spaced that even when recorded with a high resolution
instrument, many of the lines overlap.
The theory for the transmission of a group of Doppler broadened NO source
lines through an absorbing gas with both Doppler and collision broadened lines
has been developed by Davis et al. (1976). We will use the results of Eqs. (1)
through (14) of Davis et al. (1976), which can be summarized as follows. The
total transmitted intensity for the j th emission line (T^) due to absorption by
many lines is related to the line center source intensity of the jth line (1° ?) ,
the Doppler'width of the source (Agv.) the line center Doppler absorption
coefficient of tne gas (kv-), the broadening parameter (a1), and the path length
U) by,
111-10
-------
° f
exp
J'D
(20)
exp
dy
+ (0). -
dv
where a' is related to the Lorentz full width at half maximum (FWHM) in the
absorbing gas (A v^) and the corresponding FWHM of the Doppler component
(AaVDby
L
(21)
and where
(22)
The DopDler widths (FWHM) of the source and absorbing line are given by
.A
(A
= v.
2(ln 2)k T _
--
m
2 (In 2) RT
M
(23)
where v^ is the wavenumber of line center, c is the speed of light, k is
Boltzmann's constant, T is the appropriate temperature (either source or
absorber), m is the molecular mass in grams of the emitting or absorbing
molecule, R is the universal gas constant, and M is the molecular weight in
grams per mole. The Lorentz FWHM due to collisions is given by,
L •
IT T C
(24)
where Z is the frequency of collisions between an absorbing molecule and the
perturbing molecules, and T is 1/Z or the mean time between collisions.
LJ
It should be noted that this development assumes that the collision process
and line broadening can be accurately explained by the Lorentz collision theory,
an assumption which is discussed in detail later in this report. The use of the
Lorentz theory to examine experimental results is certainly the usual assumption,
but deviations from Lorentz-theory behavior have been observed in numerous
instances (see Section III.B.5 on broadening theory).
III-ll
-------
It is worthwhile considering the factors in Eq. (20) which must be known
or determined in order to predict the transmission. The relative .intensities
of the source lines at line center must be measured for the narrow-line lamp,
and intensities of lines that cannot be measured directly must be interpolated
from a Boltzmann plot such as shown in Fig. 20. The Doppler FWHM ((Avj)D) may
easily be calculated from Eq. (23). The path length (£) is easily determined.
The broadening parameter (a1) must be determined experimentally because
theoretical computation of the Lorentz FWHM (^Aavi^L^ wnich is necessary to
determine a' through Eq. (21) is not feasible. The experimental technique
used to determine a' is described in a later section. The final parameter
which must be determined to solve Eq. (20) for the transmission is the absorption
coefficient at line center for a Doppler broadened line (k) . The relation
between ^v^ and the density of molecules in the initial state and the oscillator
strength is described below.
II.B.3 Computation of Doppler Absorption Coefficient
The line center absorption coefficient for a Doppler broadened line
(kv°) is given by Mitchell and Zemansky (1971),
2
k o = 2 e yA ln 2 M(n"y" I "J" p") f y*y" j'j" (25)
Vl ^ C (Vl>D
where e is the electron charge, me is the electron mass, c is the speed of
light, f , IIT,,,, is the oscillator strength of the line, and N(n"v"£"J"p")
is the population of the initial energy state. The single and double primes
refer to upper and lower electronic state parameters, respectively.
The Doppler FWHM (C^v.^)-) can be calculated from Eq. (23). The
oscillator strength for a line (f 'v"j'J"K'K"P"^ "*"s relatec' to the oscillator
strength for a band (fvivi.) by (Thorne (1974)5,
f S
v'v"J'J"K'K"p" _ J'J"K'K"p" ^ f )( (26)
2J" + 1
where Sj i J"K'K"P" ^-s ^e Honl-London factor and J" is the rotational quantum number
in the lower electronic state. The band oscillator strength (fin) for the
NO y(0,0) band has been measured previously and another determination is
reported in this work (see experimental results section). The Honl-London
factors may be computed from equations given by Earls (1935), but with an
adjustment factor for proper normalization (multiply Earls values by A). It
is important to note that the summation convention for the Honl-London factors
suggested by Tatum (1967) has been adopted here, that is:
111-12
-------
Z L s
•L-. ., . JJ — \^-—Or>ft!!)(jLD~!~_L)lZJ ~r J_ ) (27)
sub-levels J ^''^ ^
where the summation over sub-levels includes both spin splitting levels
(the 2S + 1 factor) and A doubling levels (the 2-<$0 A factor) . The value
6o'Ais unity for A = 0, but zero otherwise. For the NO y(0,0) band, the
summation convention for the Honl-London factor becomes
Z Z S = 4 (2J" + 1) (28)
sub-levels J'
from the fact that (2S + 1) = 2, and (2-6^,,) = 2 (see later section on the
spectroscopy of NO for an explanation ol quantum numbers;.
The remaining factor in Eq. (25) which must be determined in order to
solve for ^v^ is represented by the somewhat awkward but definitive notation
N(n"v" Z"J"p"), which is the population of the energy level of interest for a
molecule obeying Hund's case (a). The more often used symbol N,.,, is sometimes
ambiguous in that it may or may not include the factor of 1/2 for the A doubled
levels. Thus N(n"v"Z"J"p") represents the number of molecules in the electronic
state n", vibrational state v", spin state Z", rotational level J", and with
specified parity p" (+ or -). The fraction of the total number of molecules
which are in a given level is represented by N(n"v"Z"J"p")/N, and can be
determined for the NO 2ir-^/2 and 2:13/2 sublevels of the ground state as follows.
The ground state of the NO molecule is intermediate between Hund's cases
(a) and (b), but to a close approximation follows Hund's case (a). Following
Tatum's (1967) convention and notation for Hund's case (a) for the 2ir-,/2 state
(all terms are for the lower electronic state and, hence, should have double
primes),
w, -T * f 2(2S + 1) exp ((-hc/kT) To) ] fexp ((-hc/kT) G(v))
IN y. nvL j p) _ | i x|
I 2(2S+1) exp ((-hc/kT) T0)J [Zv exp ((-hc/kT) G(v))
all states
(29)
I exp ((-hc/kT) (-A/2)) 1
[exp ((-hc/kT) (-A/2)) + exp ((-hc/kT) (A/2))J
(2J + 1) exp ((-hc/kT) F(J))
x
E (2J + 1) exp ((-hc/kT) F(J))
111-13
-------
where S is the electron spin quantum number, h is Planck's constant, TQ is the
electronic term value when spin is neglected, G(v) is the vibratianal term
value, A is the spin splitting constant, and F(J) is the rotational term value.
The equivalent expression for the 2ir . state is identical except that the
numerator in the third term in brackets becomes exp ((-hc/kT)(A/2)).
The first term in brackets in Eq. (29) is the fractional population of a
given electronic level, N(n)/N, and differs from that given by Tatum in that
we have used the "average" electronic term value T (or electronic term value
when spin is ignored) rather than Tatum's Te where Te = Tn + AAZ (for ^1/2'
Te = TQ-(A/2); for 2*3/2> Te = To + (A/2)). The use of Te in place of TQ
would produce (for the N0y(0,0) band), a term essentially* identical to the
third term in brackets in Eq. (29), but following Tatum's guidelines, the
fractional populations of the spin-split levels are to be calculated separately
and explicitly as N(nvZ)/N(nv), the third term in brackets. Thus, it would
appear that Tatum has accounted for the fractional populations of the spin-
split levels twice, which we have avoided by using T in Eq. (29). For the
electronic term value, as expressed in Eq. (29), the first term in brackets
is unity.
The second term in brackets in Eq. (29) is the fractional population of a
given vibrational level, N(nv)/N(n), which for the v" = 0 level is close to
unity at 300 K but decreases to about 0.74 at 2000 K. The third term in
brackets in Eq. (29) determines the fractional population N(nvE)/N(nv) of the
spin-split T]/2 an^ ^3/2 J-ev£ls. The fourth term in brackets represents the
fractional population of a given rotational level N(nvZJ)/N(nvZ). By
employing the usual approximations (Herzberg (I95o))> the sum in the denom-
inator of the fourth term in brackets may be written as kT/hcB. • The fifth term,
symbolically written N(nvZJp)/N(nvZJ) , accounts for the A-type doubling of
the rotational levels of the ^ state into two sublevels of parity + and -.
Because the upper electronic state being considered is a 2£ state, only one of
the two sublevels is active for a transition to a specified upper state
rotational level (Herzberg (1950)).
* This assumes that exp ((-hc/kT)Te) « 1 for all electronic states higher
than the ground state (IT), which is true for the NO molecule even at high
temperature.
III-1A
-------
rj
Thus, Eq. (29) for the o state may be rewritten:
N(nvEJp) ^ exp((-hc/kT)G(v))
N Ev exp((-hc/kT)G(v))
exp ((-hc/kT) (-,
x|h_cB_ (2J + 1) exp ((-hc/kT) F (J))
£ K i.
exp((-hc/kT)(-A/2)) + exp((-hc/kT)(A/2))|
(30)
The equivalent expression for the ^3/0 state is:
N(nvEJp)
N
exp((-hc/kT)G(v))
Ev exp((-hc/kT)G(v))
exp((-hc/kT) (A/2))
exp((-hc/kT) (-A/2)) + exp((-hc/kT)(A/2))
hcB (2J + 1) exp ((-hc/kT) F (J)) |
2kT
(31)
These expressions may be modified intermediate to Hund's case (a) and (b) by
absorbing the spin-splitting term into the expression for F(J) (Hill and Van
Vleck (1928)) and dropping the third term in brackets on the right-hand side of
Eq. (29). When this is done, however, the rotational partition function may no
longer (in general) be approximated as kT/hcB. Assuming that the spin-splitting
energy is absorbed into F(J) and the resultant is labeled Fi(J), with i = 1 for
the 2Tr state and i = 2 for the 2__ ,„ state, then instead of Eqs. (30) and (31),
1/2
one gets,
N(nv(EJ)p) = [exp((-hc/kT)
N
2 state, then instead of Eqs.
exp((-hc/kT) G(v))
x (2J + 1) exp ((-hc/kT) Fn. (J)
(32)
V=l,
E (2J+1) exp ((-hc/kT) F± (J))
For the NO molecule, we have determined that the rotational partition function
can be approximated with high accuracy (± 0.3% for 300 K < T < 2000 K) as
almost Hund's case (a),
111-15
-------
Ei . 1 2^ (2J+l)exp((-hc/kT)Fi (J)) =(kT/hcB) fexp((-hc/kT)(-A+2B)/2)
J I i (33)
+ exp(-hc/kT)(A-2B)/2)
for the energy equations and constants as given by Engleman, et al (1970). This
approximation was subsequently verified by D. Keefer. Thus, Eq. (32) for the
intermediate Hund's case between (a) and (b) becomes,
N(nv(ZJ)p) ^ [ exp((-hc/kT)G(v))
N J Zv exp((-hc/kT)G(v))
(34)
exp( (-hc/kT) (-A+2B)/2) -I- exp( (-hc/kT) (A-2B)/2
hcB (2J+1) exp ((-hc/kT) F± (J)
2kT
If Eqs. 23, 26, and 34 are substituted into Eq. (25), the result is
V V J'J"
(35)
x /exp((-hc/kTa) G(v")) \ x / 1
:v,, exp((-hc/kTa)G(v"))/ \exp((-hc/kTa)(-A+2B)/2)+exp((-hc/kTa)(A-2B)/2)j
x exp((-hc/kTa) F.(J"))
or, substituting for the constants,
k - = 1.755-10"10 f , „ s N /exp(-1.4388G(v")/Ta) ,
Vi T3/2 vv J'J" lzv,, exp(-1.4388G(v")/Ta)J
3 (36)
(exp(-1.4388F F,(J")/T))
J-. d
exp(86.18/Ta)+exp(-86.18/Ta)
With Eq. (36) for kv?, all terms necessary to calculate the transmission
(Tj) using Eq. (20) have been determined except for the broadening parameter a'
and a confirmation of the band oscillator strength f ' ".
III.B.4, Transmission Formulas, Continuum Source
The development of the transmission formulas for continuum radiation is very
similar to that used for the narrow-line case given in Eq. (20). The source func-
tion is much simplified to just I(v), which is a very slowly varying and easily
measured function. The transmitted intensities must be recorded continuously as
111-16
-------
a function of wavenumber rather than as discrete intensities at the line center
of emission lines, as is done for the narrow-line source. The transmission at any
wavenumber v is,
T(v) = I(v)exp|-_l 2 k°A'e-y2dy I (37)
|-_l S k ° A'g y ^
I TT i vij a'2+(wi-
where the symbols are the same as explained previously for Eq. (20).
III.B.5 Broadening Theory
There is no lack of theoretical models available to treat pressure broaden-
ing. The theories of pressure broadening are discussed in some detail by
Breene (1957), Hindmarsh and Farr (1972), and Mitchell and Zemansky (1971).
Thorne (1974) discusses the subject with less depth but good clarity. An
often quoted work for microwave and infra-red regions is the paper by
Anderson (1949).
In spite of the number of theoretical models available, experimentalists
tend to use the standard Lorentz theory and label discrepancies as deviations
from the Lorentz theory, rather than attempting to use other models. In this
report, results from the Lorentz theory and Weisskopf theory are used, but
the reader is referred to the previous references for the details of these
theories.
The Lorentz model assumes that the optical collision diameter is indepen-
dent of the relative velocities of the two colliding molecules (or atoms).
From the Lorentz theory the FWHM due to collisions, AvL, is given by Mitchell
and Zemansky (1971),
ZT
AvL = -i (38)
TTC
where Z^ is the collision frequency of a single molecule, c is the velocity
of light, and Av^ is in wavenumbers. It should be noted that this is true
only for collisions between molecules of different types. If the molecules
are all of the same type then Fq. (38) is multiplied by a factor of 2. This
is due to the fact that each collision terminates one mean free path if the
collision is between the gas being studied and a foreign gas, but it termi-
nates two mean free paths if the collision is between two molecules of the
same type. The interest here is in collisions between a minor species and
foreign gases, so Eq. (38) applies.
The total number of collisions per second between molecules of type 1
and type 2 with number densities n, and n2 and molecular weights (molar) M-i
and M2 is given by Mitchell and Zemansky (1971) as,
2 I 11
Y = 2n1n2d1_2 ^2uRT (— + -±) (39)
Ml M2
111-17
-------
where d is the hard sphere collision diameter (d = r1+r2, where r is the radius), R
is the universal gas constant, and T the absolute temperature. The collision fre-
quency per molecule of a given type is,
ZL = — = 2nX o V 2"*T (— + —) (*<>)
n-i ^ 1—2 ' Mi M2
Combining Eqs. (38), (40), (21)
Ml (41)
where v is the wavenumber. Expressing n2 in terms of the partial pressure (atm)
of the foreign gas and temperature (K) , d in cm, and v in cir^l
a, = 4.14-1021 2 + % £2 (42)
2 1-2 > M T
(43)
If more than one foreign gas is active in broadening, Z is summed over all
Lt
the species and a! for each species is,
a! = C. I± (45)
1 1 T
where P. is the partial pressure of the ith species. The total' a' is the
sum of the a's.
i
An important point must be made regarding the collision diameter and the
effective collision cross-section. The effective optical collision diameter
is given by d in the equations above. References in the field of kinetic
theory, such as Reif (1965), and Hirschf elder et al (1954), call ird the
effective cross-section, while Mitchell and Zemansky, Davis et al (1976), and
9
others drop the IT and refer to d as the effective cross-section. Thus,
caution must be exercised in comparing effective cross-sections given by
different authors. We define cross-section as frd in this report.
According to the Lorentz theory, at constant pressure, AVT is proportional
to x~0-5 and a' is proportional to T. . There is a significant amount of
evidence to indicate that the temperature dependence is stronger than this.
Hence, the temperature dependence of Av should be between T and T and
that of a' between T~ >u and T . Among the evidence for a stronger temp-
erature dependence for neutral atoms or molecules is work by Hansen (1978).
Townes and Schawlow (1955), Engleman (1969), Cann et al (1979), Planet et al (1978),
and Breene (1967) .
111-18
-------
The Weisskopf theory gives a stronger temperature dependence in agree-
ment with a significant amount of experimental work (Thome (1974)).
Weisskopf developed a collision theory which includes the effect of collision
time in computation of the cross-section. For collisions between neutral
atoms or molecules, the Weisskopf theory, for a constant pressure, gives the
collision width as Avw proportional to T~ '7 and a' proportional to T."1*2
This is in almost exact agreement with the result reported by Hansen (1978)
of Av proportional to T~°4'^ for CO broadening over a wide range of temperatures.
The evidence from the flame measurements reported here indicates that the
temperature dependence of the Weisskopf theory seems to fit the experimental
data for NO broadening better than the Lorentz theory.
III.B.6. Spectroscopic Details of the Nitric Oxide Ultraviolet Y (0,0) Band
III. B . 6 . a . Band_Sv_st_ems_of_ N0_
The electronic transitions of the NO molecule are observed in the ultraviolet
and vacuum ultraviolet spectral regions. The lower energy transitions involving
the ground (X TT^ state are labeled as follows (Pearse and Gaydon (1965)).
Transition Type Label
A E+ - X TT Y system
2 9
B TT - X TT 3 system
2 ?
C TT - X~TT 6 system
D2I+ - X2Tr E bands
The excited electronic states are labeled in order of increasing energy by A, B,
C, etc., and therefore the lowest energy (longest wavelength) transitions are in
the Y system, which makes that system the most easily accessible for absorption
measurement of NO.
The bandheads for some of the lower vibrational levels are shown in Table
III-B. For determining NO concentrations from spectroscopic absorption measure-
ments at temperatures below 1000 K, it is only necessary to consider those states
originating from a ground vibrational level (v" = 0). The longest wavelength
transition of this type is the Y (v'=0, v"=0) band at -226 nm. A number of exper-
imental problems become more severe at wavelengths shorter than this: (1) the
transmission of quartz decreases, (2) hot C02 and 02 bands absorb more strongly
at flame temperatures (3) the chance of interfering absorptions by other species
increases, (4) intense continuum sources such as high pressure Xe and Hg-Xe
lamps decrease rapidly in intensity, and (5) scattering by soot particles gen-
erally increases. Thus, the Y (0,0) band is the most reasonable band selection
for the measurement of NO over the temperature range from 300 K to 2000 K.
111-19
-------
TABLE III-B
Bandheads in the Y -System of Nitric Oxide v
(Pearse and Gaydon (1965))
Double bandheads are given for each band
I „!!
(nm) v'.v
247.87 0,2
247.11
244.70 1,3
244.00
237.02 0,1
236.33
231.63 2,3
230.95
228.98 3,4
228.41
226.94 0,0
226.28
224.54 1,1
223.94
222.24 2,2
221.63
219.96 3,3
219.40
215.49 1,0
214.91
111-20
-------
The y (0,0) band represents transitions between the zeroth vibrational levels
of the excited state A^T.+ and the ground state X TT . The ground electronic energy
level of the NO molecule is split into two sub-levels, the lower energy ^TT^ state
and the higher energy 2^^/2 state> which are widely split in energy (-120 cm"1).
Because of the considerable difference in energy of the two sublevels, the TT
state of NO is usually treated as following Hund's case (a), but is actually
intermediate to cases (a) and (b), approximating case (a) for small rotational
velocities, but undergoing some spin uncoupling at higher rotational rates. The
upper A2T+ electronic state belongs strictly to case (b) coupling, as do all I,
states.
111. B. 6 . b. E_ner_g_y Levels
The equations and constants used here to determine the energy for various
rotational levels in both upper and lower electronic states are almost exclusively
from Engleman, et al. (1970). Energy levels of a molecule (exclusive of trans-
lation) may be approximated as the sum of the rotational (Er), vibrational (Fv),
and electronic energies (Ee),
E = Ee + Ev + Er (46)
It is common practice to express the molecular energies as term values, which
are energy values divided by he, and have units of cm . Using the term value
notation, Eq. (46) becomes,
T = Te + G(v) + F(J) (47)
In an electronic transition the wave number (cm"1) of a spectral line is given by
the difference of the term value in the upper electronic state (T!) and the lower
electronic state (T") ,
u = T' - T" = (Tef - Te") + (G'(v') - G" (v11)) + (Fv. (J') -Fv" (J")) (48)
III. B . 6 . c E_n^r^y_L£V£l_E^u£t_ion_s_f£r_th.e_X^_Tr_S_tat_e__oJ_ N0_
For the ^rr state of NO, the electronic energy and rotational energy are
slightly coupled so that Te and F(J) are not independent. The term value energy
equation is modified so that Fi(J) contains not only the rotational energy, but
also the energy associated with the spin splitting in the ^TT state, and T con-
tains the electronic energy exclusive of spin-splitting,
•T" = T " + G"(v") + F."(J") (49)
o i
where the vibrational term value G(v) is,
111-21
-------
G(v) = u (v+0.5) - u X_ (v+0.5)2 (50)
and the rotational term F.(J) is,
F±(J) = BV((J+0.5)2-l)-Dv((J+0.5)A-(J+0.5)2+l)+Bv Ja (51)
a = (Yv-2)2+ ((j+0.5)2-!) l+2y(2(J+0.5)2-X)+y2f(2(J+0.5)2-l)2-l)j (52)
Yv = [A + C(J-0.5)2J /Bv (53)
y = DV/BV (54)
The minus (-) sign is for the 2u^ state in which J = K + 0.5 and 1=1, while the
plus (+) sign is for the ^3/2 state in which J = K - 0.5 and 1=2. It should be
noted that our equation for F.(J) includes a term "-Bv" not found in Engleman,
et al. (1970), but which should be included following the derivations from the
original papers cited by Engleman. We have adjusted the upper state electronic
energy given by Engleman, et al. accordingly. We have likewise added to the
equation for a a term "y2," but this is numerically inconsequential. There also
appears to be a typographical error in the sign convention given by Engleman,
et al.
r\
In addition to the spin-orbit splitting of the ir state, each of the levels
is subject to a slight perturbation by A-type doubling due to the interaction
between the rotation of the nuclei and the electronic orbital angular momentum
L (Herzberg (1950)). The magnitude of this shift is given by , where,
= 0.5 (J+O.
.5) /2-Y^ + lWl+ Q }+ Q ((J+0.5)2-l) (55)
vr/— '\z ' TV
L 2VoT v^ J
and the sign convention is the same as above. Because of A-type doubling, each
rotational level is split into two components, but for a given transition only
one of the components is active. The reason for this is that the two components
are of opposite parity (+ and -). Because of the selection rule 4- —> -, only one
of the components may interact with an upper state with specified parity (the
upper state is not A-type doubled). The A-type doubling has an influence on the
spectral line locations as follows,
F. = F. -
1C X (56)
Fid = Fi + *
2
where F. is the energy of the TT state (exclusive of vibrational energy) for the
transitions ?•,-,> P22' ^12' ^21' ^11' anc* R22' anc* F'd *s fc^e state energy for
transitions P12> P21> QI;L, Q22> R.^, and R21.
111-22
-------
The zero-point energy of a molecule is arbitrary in that only energy differ-
ances have significance. For the constants given by Engleman et al. , if the
vibrational and rotational (but not spin-splitting) energies are set to zero, the
level of zero electronic energy is midway between the energies of the two spin
split states ( TT^ and ^3/2^' If> in addition, the spin splitting term A approached
zero, the two spin split states would collapse into one energy level defined as
the zero electronic energy for this system. However, we have shifted this zero
point energy by A/2 to correspond approximately to the zero level energy of the
lower 2TT^ state. Thus TQ = A/2, and Eq. (49) becomes
T" = - + G"(v") +
2
F'.1 (J")
1C
F" (J")
id
(57)
and the upper electronic state energy given by Engleman et al. is increased by
A/2.
The constants which describe the lower electronic state are given in Table
III-C. The A doubling constant P has a different sign in Engleman et al.'s
Tables VII and XI. We have chosen the negative sign because it gives better
agreement between the experimental and theoretical line locations.
Ill. B. 6. d ^ne_r^y_L£yel_E^u£t^:o_ns_f£r_th1e_A_E_ _Sta_te o_f_NO
2 +
The energy levels of the upper electronic state (A E ) are described by
the general Eq. (47)
T' = T + G(v') + F'(J') (58)
where T is a constant, G(v) is given by Eq. (50), and F(J) is given by Engleman
et al. as,
F^J) = BV(J+0.5)(J-0.5)-DV(J+0.5)2(J-0.5)2+0.5Y(J-0.5) (59a)
F2(J) = BV(J+0.5)(J+1.5)-DV(J+0.5)2(J+1.5)2-0.5Y(J+1.5) (59b)
where F-,(J) is for states with J = K + 1/2 and F2(J) is for states with J = K - 1/2,
Of course, all values of J, K, and v are for the upper electronic state and would
have single primes if any were indicated. The y is a small spin splitting constant
and the value used was determined by Bergeman and Zare (1972) from an rf resonance
study. The constants used to describe the upper state are given in Table III-D.
111-23
-------
TABLE III-C
o
X IT State Constants for NO
(from Engleman, et al. (1970))
T = 61.595 cm~1*(=A/2)
o
A = 123.19 cm'1
C = -5.8.10"4 cirT1
toe = 1904.405 cm"1
o)exe= 14.1870 cnT1
B = 1.69568 cm"1
D,T = 4.5-10"6 cnT1
v
P = -1.17-10 2 cm'1*
Q = 7.8-10'5 cm'1
*see text
111-24
-------
TABLE III-D
A2S State Constants for NO
(from Engleman, et al. (1970) except as noted)
Te = 43966.2643 cnT1+
u>e = 2374.307 cm
oigX e = 16.106 cm •*-
Bv = 1.98576 cm'1
Dv = 4. 6-ID"6 cm"1
Y = .00276 cm"1*
+adjusted for different zero references
from Engleman, et al.
from Bergeman and Zare (1972).
111-25
-------
111. B. 6 . e. NO_Y_( 0_, 0) _Band Structure_
o o
For cases where the TT^ and ^^/2 energy levels are noticeably separated
(Hund's case (a)) the band structure of a 2Z - 2-rr transition is usually considered
as two sub-bands, Z - 2^ and 2£ - 2l]3/2, which are separated from each other by
the amount of doublet splitting of the 2Tr state. There are six branches possible
for each of two sub-bands, making a total of twelve branches. Because of the
small spin splitting in the 2Z state of NO, only eight distinct branches are re-
solved, but in this study the spin splitting in the 2Z state has been included
based on the value given by Bergeman and Zare (1972).
The selection rules which determine which upper and lower electronic states
are involved in transitions are explained in detail by Herzberg (1950), and may
be summarized as follows. For changes in vibrational energy, Av = v' -v"= 0, - 1,
± 2, - 3..., with the relative strengths determined by the overlap of the potential
energy curves. These relative strengths are given by the Franck-Condon factors.
Concerning rotational levels, only states of opposite parity may interact, + *-* -
+ */•+, -*/•-. This has an effect on which of the A-type doubled levels in the IT
state may interact with given upper state levels. The total angular momentum J
is restricted such that AJ = J1 - J" = 0, ± 1. Since the 2u state is intermediate
between Hund's cases (a) and (b), the selection rule AN = N'-N" = 0, ± 1 (older
notation AK = K'-K") applies, but AN = ± 2 can appear subject to AJ = ± 1, although
the intensity is much reduced. Branches for which AJ ? AN will generally be weaker.
These selection rules imply that there are twelve branches and the labeling
of those branches is shown in Table III-E. The notation is the same as that used
by McGregor et al. (1973), and there are additional diagrams in that report ex-
plaining the notation. The following line pairs are overlapped due to the small
spin splitting in the upper state: P22 and Q12; Qn and P21; Q22 and R • and R
and Qoi-
111-26
-------
TABLE III-E
Notation for Transitions of NO
Rotational Rotational AN=N'-N"
Transition Upper State Lower State AJ=J'-J" (or AK=K'-K")+
P12(J") = F'(J"-1) - F" (J") -1 -2
*- 2d
P( I'M — T? ' ( T" i '\ T?" (i"\ i i
i i ^J / — t (J -i) - r \j ) -i -±
•L± 1 Ic
Pf T" \ _ TT ! f T11 1 \ T?"/'T!^ 1 1
ooW ; - ^0^.J ~L) - r (J ) -i -1
•" 2 ^c
P21(J") = F2(J"-1) - F" (J") -1 0
Ql.2(J") = F|(J") - F2'c (J"> 0 -I
Q-j^-LCJ") = F'(J") - F" (J") 0 0
Q99(J") = FMJ") - F" (J") 0 0
z z 2. ^u
Q21(J") = F2(J") - F^(J") 0 +1
Rno(J") = FMJ'M-l) - F" (J") +1
1^ J- ?j
Rn(J")
ROO(J") = F;(J"+D - F" (j") +1 +1
2.L *- 2c
R01(J") = Fl(J"+l) - F" (J") +1 +2
21 L Id
+the newer notation replaces K with N.
HI-27
-------
C Experimental Results - Spectroscopic Measurements
III.C.I. Determination of Broadening Parameters
111. C. 1. a. IJa£kground_
In the discussion of the development of transmission formulas, it was shovm
that all quantities necessary to calculate the transmission have been determined
except for the broadening parameter a' and the oscillator strength v'v"* Reas-
onable literature values exist for the oscillator strength, but there is no
concensus for the broadening parameters.
There are several techniques for studying pressure broadening. When the
rotational lines are closely spaced, as is the case for the NO Y (0,0) band,
direct line shape measurements are difficult. A curve of growth technique may
be used at various pressures and, with a knowledge of the oscillator strength,
the broadening may be determined. This technique was used by Thorson and Badger
(1957) to determine a collision diameter for NO broadening in the Y (0,0) band
by N2. A similar analysis was performed more recently by Tajime et al. (1978),
but serious deficiencies in their theoretical model were pointed out by Dodge and
Dusek (1979). Davis et al. (1976) utilized a narrow-line absorption technique
to study NO broadening by ^ but, again, serious problems in their theoretical
model were pointed out by Dodge and Dusek (1978) . Hadeishi et al. (1976) used
a Zeeman tuned Cd lamp to determine the profile of a single NO line in the Y
(1,0) band. (They report measurements of the 0-1 vibrational band of NO at
214.438 nm, but the Y (0,1) band is at about 236 nm, so we assume the measure-
ments were for the Y (1,0) band.) The results of Tajime et al. (1978) and
Davis et al. (1976) are in question because of the theoretical problems, but the
measurements by Thorson and Badger (1957) and Hadeishi et al. (1976) may be in
reasonable agreement. Unfortunately (or significantly), the results reported
here are substantially different than in those two papers.
A number of measurements of the NO Y (0,0) band oscillator strength have
been made, and, in contrast with the broadening measurements, there is reasonable
agreement for most of the literature values. The results reported here are
similar to published values. The problems associated with different techniques
used to measure oscillator strengths are discussed by Thome (1974) .
Ill. C. 1. b. jPr£c.£d_ure_
The technique used in this study for the oscillator strength and broadening
measurements of the NO Y (0,0) band was unique in that the rotational structure
of the band was resolved and actual individual line shapes and strengths were
determined photometrically. This requires a resolution of about 130,000 at
225 nm. With the additional ability to scan a spectrum with photoelectric de-
tection, it is possible to avoid the nonlinear response of photographic plates.
III-2P
-------
Commercial instruments with these specifications have only recently become
available. In addition, a sophisticated computer model developed jointly at
Arnold Engineering Development Center (AEDC) and this laboratory was required
for reducing the data.
The individual line profiles were recorded mostly in the spectral region
between the P^ and P22 bandheads where the lines were separated most clearly.
All of these lines originated in the ^3/0 ground state. A few measurements
were recorded in the P-Q bandhead region to examine lines originating in the
in the ^1/2 ground state.
All room temperature broadening measurements were made with the high pressure
Xe DC arc lamp (continuum source), the static cell and associated gas mixing
apparatus, and the high resolution spectrometer which were previously described.
The ratiometric electronics were used for recording some spectra while others
were recorded directly (Fig. 18).
The cell was first filled with about 5 torr (6.7 Pa) of 10% NO diluted in Ar
and a scan was taken to determine the slit function of the instrument, along with
a small contribution from the Doppler broadened gas. The slit function varied
slightly in shape and width over several hours while data were being recorded,
but the best fit to the experimental values could be obtained with a Gaussian.
Our slit function was slightly wider near the base than a Gaussian, but it did
not possess the wings characteristic of a Lorentzian. A more complicated slit
function such as given by Kusch et al. (1977) did not seem warranted. The effect
of convolving a slit function with the actual spectral shape is discussed by
Thorne (1974), Kusch et al. (1977), and Sulzmann et al (1976). The convolution
technique used here is described in the computer program description (Appendix D)
The measured FWHM for the slit function was typically 0.0018 nm while the Doppler
FWHM was 0.00051 nm. This slit function was monitored several times during
each data set. For Gaussians, the half widths combine as (Av) = (Av^)" +
(Av2)2 + . . . (Thorne (1974)), and since both the slit function and Doppler
shape are Gaussians, the actual slit function FWHM was typically .00173 nm. In
comparison, the range of FWHM for N2 for which broadening data were reduced was
0.00562 to 0.00965 nm, so slight variations in the slit function (±0.0002 nm)
had negligible effect on the measured profiles. An example spectrum at low pres-
sures is shown in Fig. 23.
After the slit function was determined, the gases were blended to arrive at a
constant NO number density for a given final pressure, independent of diluent gas.
Spectra were recorded at total pressures of 0.50 atm (50.7 kPa), 0.75 atm (76.0
kPa), 1.00 atm (101 kPa), 1.50 atm (152 kPa), and 2.00 atm (203 kPa). Experi-
mentally recorded spectra for NO broadening by N2 over this range of pressures are
shown in Figs. 24-28. Similar spectra were obtained for NO diluted in C02,
CO Ar, and CH^. These experimental spectra were compared with computer generated
spectra such as those shown in Figs. 29-31, which correspond to N2 broadening at
111-29
-------
FIG. 23
DOPPLER BROADENING (O.OOOSnm) AND SLIT FUNCTION (0.0015nm)
PT = 0.0076 ATM
Pwn£s3.5 1017CM~2
C/J
Z
Q
111
CO
ZERO
111-30
79-04-93-15
-------
FIG. 24
NO ABSORPTION SPECTRUM
PT = 0.50 ATM
PJ2-= 2.59 • 10
17 ~2
H
w
z
Q
LU
CO
2
<
-------
NO ABSORPTION SPECTRUM
PT = 0.75 ATM
PN£= 3.89 • 1017 CM~2
FIG. 25
ZERO
111-32
79-04-93-17
-------
NO ABSORPTION SPECTRUM
PT - 1.00 ATM
Pojrr£= 5.18 • 1017 CM~2
FIG. 26
Q
LLJ
H
co
Z
<
EC
ZERO
79-04-93-18
111-33
-------
NO ABSORPTION SPECTRUM
PT = 1.50 ATM
PN^= 5.18 • 1017 CM~2
FIG. 27
c/5
z
LU
Q
LU
in
z
ZERO1 L
79-04-93-19
111-34
-------
NO ABSORPTION SPECTRUM
FIG. 28
2.00 ATM
= 5.18 • 10 CM
17 ~2
co
z
LJJ
H
Q
LU
CO
ZERO
79-04-93-20
111-35
-------
1.25-,
1.00 —
0.75-
0.58 —
0.25-H
0 00
COMPUTER SPECTRUM
PT = 0.75ATM
TA = 295. K
L = 18.6 CM
A = 4.38609
DLAM= .0183
F=3.57, 3 75
GAUSSIAN LNSHPTHEOR
NO
.0000
2039+17
LINES
I
I
I
I
I
I
I
I
10
I
o
c.
I
ID
U
I
2265.2 2265.6 2266.8 2266.4 2266 8
2265.4 2265 8 2266.2 2266.6
WAVELENGTH, A
(nm x 10)
-------
(D
I
O
I
1C
u
1.25-1
1.80-
8.75-
8.50-
0.25-
8 80
COMPUTER SPECTRUM
PT = 1.00ATM
TE = 690. K
TA = 295. K NO
L = 18.6 CM 8000
A = 5 84700 2784+17
DLAM= .0183
3 57, 3 75
GAUSSIAN LNSHPTHEOR. LINES
T
I
I ' I ' I
2266.0
I
2265.2 2265.6 2266.0 2266 4 2266 8
2265.4 2265 8 2266 2 2266 6
WAVELENGTH, A
(nm x 10)
Tl
C>
CO
o
-------
COMPUTER SPECTRUM
1 00 —
0.75-
0 59-
0.25 —
0 80
PT = 1 .50ATM
IE = 680. K
TA = 295. K
L = 13.6 CM
A = 8 77189
DLAM= .0183
3 57 3 75
GAUSSIAN LNSHPTHEOR
HO
.0900
.2734*17
LINES
I
1C
I
o
to
u
' I 7
2265.2 2265.6
2265.4 2265 8
r 7 r
2266 0
r 1 i r
2266.4
1 I
2266 8
2266.2
2266 6
WAVELENGTH, A
(nm x 10)
P
u
-------
pressures of 0.75 a tin (76.0 kPa) . 1.00 atm (101 kPa) , and 1.50 atm (152 kPa) .
The spectral lines in Figs. 24-28 are identified in Table III-F.
At these NO densities, there is significant absorption between even the most
widely spaced lines over most of the pressure range studied. Thus the zero ab-
sorption baseline must be determined. Even with the dual-beam ratiometric
electronics small amounts of drift occurred in the zero absorption signal. The
baseline was determined in two ways. First, the zero absorption signals before
and after the runs were averaged and called the estimated baseline (EST. BASE, in
Figs. 24-28) . Second, for the higher pressure cases, the computer spectra were
used to estimate a baseline and called computer baseline (COMPUTER BASE, in Figs.
24-28). These agreed very well for the N2 and Ar data. The C02 and CH^ generally
showed somewhat more absorption in the wings than predicted by the computer model,
and thus, the estimated baseline was as much as 5 percent higher than the computer
baseline relative to zero transmission for the worst case at 2 atm (203 kPa) con-
dition. Such a comparison for CO could not be made easily because pure CO gas
absorbed significantly in the region of interest as shown in Fig. 32. None of the
other gases showed any absorption in this region. All data were reduced relative
to the computer baseline.
Reported data are only for the Q22 (9.5) + R,2 (9.5) line pair and the Q22
(10.5) + R12 (10.5) line pair and for the pressure range of 1.00 atm (101 kPa)
to 2.00 atm (203 kPa) . This pressure was selected to reduce uncertainties from
changes in the slit function. However, at the lower pressures where half widths
could be measured for all lines, the widths were consistent, and independent
of J value within experimental precision. At all pressures there was excellent
agreement between the computer predicted spectral shape and the observed profiles.
The same pressure broadening value gave an excellent match between experimental
and computed spectra for transitions originating in the ^2 state f°r the
pressures 0.75 atm (76.0 kPa) , 1.00 atm (101 kPa) , and 1.32 atm (133 kPa) , as
shown in Figs. 33 and 34.
III.C.l.c Low Temperature j5ro^ieriing_Data_ ami r^iscu_s^ion_
A listing of the typical experimental results for the broadening of NO by N~ ,
C02 , CO, CH/ , and Ar is given in Table III-G. This table gives an indication of
scatter in the data. All error bands in Table III-G are la of the experimental
data and do not reflect systematic errors. It is estimated that the broadening
parameters C and K are accurate to within 15 percent.
As discussed in the section on broadening theory, the Lorentz theory gives the
temperature dependence of a' as a' = CP/T, while the Weisskopf theory results in
a' = KP/T (Thorne (1974)). The optical collision diameter d is also shown.
2
As discussed previously, collision cross-sections are defined as either d or
Trd2.
111-39
-------
TABLE III-F
SPECTRAL LINES USED FOR BROADENING MEASUREMENTS
Group
Number
1
2
Line
Identification
P22(15.5)
Q12(15.5)
Q22(8-5)
R12(8.5)
F (26.5)
Wavelength
(ran) or (X/10)
226.66669
226.66647
226.652A7
226.65234
226.65156
Wavenumber
(cm-1)
44117.642
44117.685
44120.410
44120.436
44120.587
3
4
6
7
.(4.5)
R22(5.5)
P22(17.5)
Q22(17.5)
Q22(10.5)
R12(10.5)
226.64758
226.60194
226.59325
226.59300
226.57724
226.57708
44121.363
P22(16.5)
Q12(16.5)
Q22(9.5)
R19(9.5)
226.63137
226.63113
226.61623
226.61608
44124.519
44124.564
44127.466
44127.496
44130.248
44131.941
44131.989
44135.060
44135.091
+Theoretically determined (difference in upper and lower energies)
These are slightly different if experimental line locations by
Engleman et al. (1970) or Deezsi (1958) are used.
111-40
-------
ABSORPTION BY CO COINCIDENT WITH 7(0,0) BAND OF NO
a = —LOGe (l°/ll
pi
p... PARTIAL PRESSURE, ATM
!L... PATH LENGTH, CM
l°/l... 1/TRANSMISSION
T = 296K
5x10
-3r
ESTIMATED STANDARD DEVIATION
O
7
. 2
1C
I
o
I
u
I
I
I
220
22?
222 223 224
WAVELENGTH, nm
225
226
227
P
w
to
-------
FIG, 33
SPECTRUM NEAR PH BANDHEAD
PT = 1 ATM
PNO£=1.82-1017 CM"2
to
Z
LLJ
H
Z
Q
LLJ
CO
Z
DC
ZERO
111-42
79-04-93-22
-------
COMPUTER SPECTRUM NEAR P-|-| BANDHEAD
PT = 1ATM,
= 1.82 • 1017 CM 2
1.25-n
1.00-
0.75-
0.50-
0.60
TA « 296. K NO
L « 18.6 CM .0000
A « 5 82600 .9780*16
DLAM= 0170
F=3 5^ 3 78
GAUSSIAN LNSHP THEOR LINES
. i . . I . , , . I . . . . I . . . . , . . . . I . . . T !
2262.25 2262.50 2262 75 2263 00 2263.25 2263.50 2263.75
u
NAUELENGTH>
(nm x 10)
p
CO
-------
TABLE III-G
BROADENING PARAMETERS FOR NO y(0,0)
(A2Z-X2ir) TRANSITIONS (ALL TOLERANCES ARE + la OF MEASURED DATA)
Gas
N2
N2
N2
N2
co2
CO 2
CO 2
co2
CO
CO
CO
CO
CH4
CH4
CH4
CH4
Ar
Ar
Ar
Ar
Pressure
(atm)
1.00
1.50
2.00
AVG
1.00
1.50
2.00
AVG.
1.00
1.50
2.00
AVG.
1.00
1.50
2.00
AVG
1.00
1.50
2.00
AVG
FWHM
(nm)
.00562
.00743
.00965
.00565
.00720
+.00040
.00961
+.00035
.00580
+.00013
.00747
+.00050
.01038
+.00010
.00635
+.00033
.G0836
+.00013
.01041
.00490
+.00029
.00638
+.00016
.00803
+.00040
Slit
Function a'
(nm)
.00176 6.04
8.50
11.31
.00191 5.75
8.12
11.17
.00148 6.02
8.47
12.10
.00160 6.90
9.63
10.41
.00181 4.25
6.95
9.22
C K
atm"1 K atm"1 K1'2
1800
1689
1685
1725 5383
1705
1605
1656
1655 5165
1782
1671
1791
1748 5455
2046
1904
1803
1918 5986
1258
1371
1365
1331 4154
d
(nm)
1.13
1.17
1.15
1.10
1.04
111-44
-------
There are two items of note in Table III-G. First, the collision para-
meters for the gases shown are very nearly the same with the exception of
argon which is only a minor constituent of air fed combustion except in some
research- type flames. This implies that the calibration for NO absorption
will be relatively unaffected for various proportions of the gases shown
assuming the gases have the same relative collision efficiency at elevated
temperatures. Absent from Table III-G are two major species, H20 and 02.
Water vapor measurements could not be made with a room temperature cell,
although data were extracted from broadening measurements in l^/C^/Ar flames
as will be discussed. An effort was made to measure broadening by 02, but
the oxidation of NO to N02 in the presence of strong ultraviolet light was
too rapid to make precise measurements. However, it was estimated from the
recorded spectra that the broadening parameter for 02 was not significantly
different from the other gases tested and that its value was between that
of Ar and N2. Because of the similarity in molecular size, calculations for
flames were made assuming that N2 and 02 have the same collision parameter.
The convenience of a calibration almost independent of the gas composition should
be contrasted with the extreme dependence shown for NO measurements by fluore-
scence (Schwarz, 1975). it should be noted that the data in Table III-G are
for a constant NO density independent of pressure, so anomalously large self-
broadening by NO cannot explain the relative independence of molecular type on
the broadening parameter.
The magnitude of the collision cross-sections shown in Table III-G are much
larger than previously reported, and may revive an argument that has existed in
literature for some time. It was reported by Lambrey (1929, 1930) and by Naude
(1930) that the y system of NO showed abnormally large pressure broadening. An
explanation offered by Moore, Wulf , and Badger (1953) was that. this might be due
to induced predisssociation. The suggestion of abnormally large broadening was
opposed by Gaydon and Fairbairn (1954) and Thorson and Badger (1957) . All of
these measurements were made with photographic plates, which present a much more
difficult problem for reducing line widths than the photometric data recorded in
this study. It is not clear what constitutes abnormally large broadening,
but our results are in conflict with those of the latter two references. For
a partial pressure of NO (PNQ) of 2 torr (267 Pa) and a path length ££) of 15 cm,
and a total pressure with N2 of 1 atm (101 kPa) , Gaydon and Fairbairn (1954)
estimate the true half-breadth or -width of a line is less than .025 A (.0025
nm) . In this study, the corresponding value is .00562 run including the slit
function and ~. 0050 nm after deconvolving the slit function. Here, the optical
depth was less, i.e., P^Q =.85 torr (113 Pa) and & =18.6 cm. Since the total
pressure was the same, narrower lines rather than broader lines should have been
observed. Similarly, collision cross-sections of this study are significantly
greater than those of Thorson and Badger (1957) for T (0,0) lines and those of
Hadeishi et al. (1976) for y (1,0) lines as shown in Table III-H. Included in
the table are collision diameters from viscosity data, although it is not
111-45
-------
TABLE III-H
Comparison of Collision Diameters for
Broadening of NO y (0,0) Lines
Foreign Optical Collision Diameter (nm) Diameter
Gas This Thorson & Hadeishi Tajime from Viscosity
Study Badger et al et al (nm)
N2 1.13 .38 .32+ .66* .37
C02 1.17 .39
CO 1.15 .36
CH, 1.10 .38
4
Ar 1.04 .34
Assuming their collision cross-section of 1.0-10~15 cm is defined as d in agreement with
their references of Mitchell and Zemansky (1961).
*Based on incorrect theoretical model (see Dodge and Dusek (1979)), but Tajime et al. maintain
that results will probably not drastically change.
*Hirschfelder, Curtiss, and Bird (1954)
-------
unusual for optical collision diameters to be larger than those from viscosity
data (Engleman (1969), Townes and Schawlow (1955), Mitchell and Zemansky (1971)).
1 1 1 . C . 1 . d . _H ijjh_Temp_e r_a_t^£e_B^ojid j;n_ing_ I) a_t a_an.d_DjL S^US_SJL ori
The same procedure was used to measure the actual line profiles in the
H2/C>2/Ar flames. However, the relative precision of these measurements was less
than that for the room temperature static cell data because the line widths were
much narrower. A FWHM of about 0.0031 nm was typical with a slit function FWHM
of about 0.0018 nm. Thus, the actual line width without the instrument function
was about 0.0024 nm which is not significantly larger than the slit function.
The measured a' values are shown in Fig. 35 for four H2/02/Ar flames. Data are
also shown for three CH4/02/N2 flames, which are quite similar. The solid line
is for an a' given by the Weisskopf theory and the dotted line for the Lorentz
theory. However, values of the broadening parameters C and K were estimated for
both H20 and 02- Oxygen was assumed to be as efficient as N2 as a broadener,
which is probably reasonable. Water vapor is not similar to any of the molecules
tested, but was assumed to be an efficient broadener slightly stronger than CH^,
which has a similar molecular weight. For these assumptions, the Weiskopf model
fit the measured data within experimental precision. Perhaps more significantly,
actual line profiles were determined at flame temperatures independent of any
extrapolations from room temperature, albeit with some uncertainty.
III.C.2. Determination of Oscillator Strength
III. C. 2. a. CoritjLnuum Lamp_,_ Prp_cedu_r£ _and_ _Resu_lt_s
The oscillator strength was determined from the same experimental data used
for the broadening measurements. The procedure was to measure the peak absorp-
tions on the same line pairs over the same pressure range and to compare that
data with results from the computer model. Peak heights rather than areas were
used to reduce the errors due to baseline uncertainty, and to simplify data
reduction. For the region between the P,-, and P ~o bandheads used for the
broadening measurements, all absorption lines are due to transitions connected with
the ^3/2 level. Since Spindler et al . (1970) suggested that the strengths of the
transitions connected with the T]_/2 state are about 6 percent larger than those for
the TT3/2 state, separate measurement of the oscillator strength was made near
the PU bandhead region for transitions originating in the ^3/2 state, as shown
in Fig 33. The results are given in Table III-I. Data are shown for NO
mixtures in various diluent gases, but, of course, the oscillator strength must
be independent of the diluent gas. Since the NO/^ mixture was confirmed indep-
endently of the gas vendor, the oscillator strength values for that mixture were
used. The uncertainty in these values is estimated to be + 10 percent.
111-47
-------
MEASURED NO BROADENING PARAMETER IN FLAMES
£••
00
ID
I
O
1.5
1.4
1.3
1.2
1.1
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
WEISSKOPF THEORY
2° ' U2
SOLID LINE a' = a'Ar + a'H o + a'o
_P
- 1.2
KAr=4154, K
1000
1200
LORENTZ THEORY
DASHED LINE a'= a Ar + a u.n + a n
a = CP/T
CAr = 1331, C = 2000
=1725
O H2/02/Ar
A CH4/O2/N2 0= 0.8
D CH4/02/N2 0=1.0
0 CH4/O2/N2 0= 1.2
1400
TEMPERATURE, K
1600
1800
2000
O
(O
en
-------
TABLE III-I
OSCILLATOR STRENGTHS FOR THE NO y(0,0) (A2£+-X TT) BAND
FOR DIFFERENT GASES*
fo,o
NO Diluted In A2Z+-X2Tr3/2 A^-X2
N2 3.57 + 0.06f 3.72 + .23
C02 3.54 + O.OOA
CH4 3.51+0.02
Ar 3.27+0.06
The oscillator strength must be independent of diluent gas, so the
variation in values is indicative of the experimental error.
111-49
-------
TABLE III-J
OSCILLATOR STRENGTHS (f ) FOR THE NO y(0,0) BAND:
LITERATURE SUMMARY
Author
i
w
o
Weber & Penner (1957)
Bethke (1959)
Antropov, et al. (1964)
Pery-Thorne & Banfield (1970)
Jeunehomme (1966)
Jeunehotmne (1966)
Farmer, Hasson, Nicholls
(1972)
Hasson, Farmer, Nicholls,
Anketell (1972)
Average
Huber and Herzberg (1979) Recommended Value
This Study (
Interpreted By
Pery-Thorne & Banfield (1970)
Pery-Thorne & Banfield (1970)
Pery-Thorne & Banfield (1970)
Pery-Thorne & Banfield (1970)
Pery-Thorne & Banfield (1970)
Jeunehomme (1966)
Farmer, et al. (1972)
Hasson, et al. (1972)
O.O
4.1 + 0.8
3.99 + 0.4
3.9 + 0.8
3.64 + .05
3.0
3.8 + 0.3
4.01 + .2
4.09 + .1
4.33 + .2
3.87
3.8
3.72 + 0.4
-------
These results are compared with some previous values in Table III-J. The
value for the TTI/O state was chosen for comparison as it is the more heavily
populated state (by a factor of 1.8) at room temperature. The oscillator
strength determined in this study agrees well with the previous results, but appears
to be slightly lower than the most reliable values. However, this study is
unique in that the oscillator strength has been measured directly from individual
lines in high resolution. We are not familiar with any previous work which
provides such a direct measure of individual line strengths.
Ill. C . 2 . b. Narrow--LjLne_ l^amp^ P_rocedu_re^ and_ Resu_lt_s_
The broadening data determined by the continuum lamp were used in the model
to predict transmission by the narrow-line lamp. The oscillator strengths were
adjusted from those determined by the continuum lamp in order to match experimental
data obtained with the narrow-line lamp. The oscillator strength should be same
for both models, but several sources of error can cause small differences.
The narrow-line lamp contains a small amount of radiation not accounted
for in the model. This can be seen by comparing Figs. 21 and 22 which display
output from the narrow-line lamp before and after absorption by a low pressure
NO sample. The major peaks denoted 1-5 show absorption as predicted by the
model, but the low level light between the peaks is not absorbed by the NO. This
tends to decrease the f value required to fit experimental data. An estimate of
the effect of the "extra-light" on f value is shown in Table III-K along with the
values determined for the narrow-line lamp before correction. There may be other
factors associated with this difference in f values, such as a shift in frequency
for the emission lines due to the strong electric fields in the lamp, but these
have not been investigated.
III.C.3 Summary of Hot Calibration Device Data
111.C. 3. a F_lowing_ Gas_ Hea.ter_:_ _Summa_ry_o_f_ ^onj^ntrj^tjixm and_ T_emperature_ Dat_a_
The carrier flow rate through the flowing gas heater was held constant
at 0.109 moles/sec for all temperatures and gases. Typical concentration and
temperature profiles are depicted in Figs. 8-10 and 36. Various concentrations
of nitric oxide were added to the main gas flow at each temperature, and for
each condition gas samples were extracted from the center of the optical axis
and analyzed using the chemiluminescence detector. Although measured values
were nearly always lower than the calculated seed level, the two values were
usually within 7%. Predicted nitric oxide concentrations from the optical
measurements are compared to the average of the seed and measured values.
111-51
-------
TABLE III-K
OSCILLATOR STRENGTHS (fQ Q) FOR NO y(0,0) BAND:
A COMPARISON
104
Narrow-Line Lamp
Continuum Narrow-Line With "Extra-Light"
Transition Lamp Lamp Correction
3.72 3.53 3.76
3.57 3.20 3.43
IH-52
-------
FIG. 36
NITRIC OXIDE PROFILES OVER FLOWING GAS HEATER
AT ELEVATED TEMPERATURES
O CENTERLINE TEMPERATURE = 560K
Q CENTERLINE TEMPERATURE = 640K
£ CENTER LINE TEMPERATURE = 753K
CHEMI
1.0r
0.8
LLJ
IS)
0.6
CO
<
LU
-? 0.4
CM
0.2
0.0
t
El
468
DISTANCE FROM CENTERLINE (cm)
10
12
79-04-54-6
111-53
-------
II I.C. 3. b
Flat Flame Burner :_ j[ummary_ o^f jCon£en_t£at^ion_and_T«n£e£a_txi£e_D£ta^
For the optical measurements of NO, four flame conditions were selected.
The thermocouple temperatures (uncorrected for radiation) at the centerline
were 950, 1220, 1400 and 1600 K. The flow conditions for these flames are
listed in Table II-B. Profiles of thermocouple temperatures and radiation
corrections are shown in Figs. 17 and 37-39. Various NO concentrations were
introduced into the unburned gas for all four flame conditions. Concentration
profiles (normalized) are shown in Fig. 16. Except for a few high seed levels
of NO during the gas correlation experiments, all nitric oxide was introduced
using the 10% NO and 90% Ar mixtures. The excess argon associated with the
added NO is not included in the tables and typically amounts to 1 to 2% of the
total gas flow. For several of the gas correlation experiments, the 25% NO,
75% Ar mixtures were used to reduce the effect of the added argon. Once con-
servation of nitric oxide had been confirmed using mass spectrometric analysis,
it was not necessary to repeat these measurements for all tests. During the
UTRC optical measurements, therefore, only cold flow measurements of NO in Ar
were made before and after each set of experiments. These measurements were
made to verify orifice calibrations and to ensure that leaks or other problems
did not develop in the gas handling system. Concentrations of nitric oxide
during flame conditions were determined using calculated flow rates and assuming
complete combustion to water. Since the total concentration of other species
such as H2 , I^O? and radicals is rather small, this later assumption provides
a good and simple approximation. According to techniques outlined in
Section II.B.3.d, the mass spectrometric data were reduced to provide the
profiles of other species within the flame. These data are reproduced in
Figs. 40 and 41 for two flame conditions.
Profiles of nitric oxide and optical measurements over the burner assembly
were also made at room temperature for comparison with the FGH and the static
cell. The profile data is reproduced in Fig. 42.
III.C.4 Narrow-Line Calibration Study
As previously mentioned, one of the principal goals of the first phase of
this contract was the development of a model for predicting the transmission
of narrow-line NO radiation through a gas containing NO molecules at temperature
range from 300K to 2000K. The validity of the model would be certainly estab-
lished if an agreement of approximately ^ 10% in NO concentration between theo-
retical prediction and measurement was achieved. The bulk of the data presented
in this section are within the specified tolerance. Those data that are not
within this tolerance reflect some of the experimental difficulties associated
with NO chemistry and measurement.
IH-54
-------
FIG. 37
HORIZONTAL TEMPERATURE PROFILES OVER FLAT FLAME BURNER
H2/02/Ar
UNCORRECTED TEMPERATURE = 950K
O UNCORRECTED (THERMOCOUPLE)
TEMPERATURES
A RADIATION CORRECTION
1200
1000
800
^ 600
400
200
A
I
I
I
468
DISTANCE FROM CENTERLINE (cm)
ifl B
10
12
79-04-54-12
111-55
-------
FIG. 38
HORIZONTAL TEMPERATURE PROFILES OVER FLAT FLAME BURNER
H2/O2/Ar
UNCORRECTED TEMPERATURE = 1220K
5/1/78
5/5/78
UNCORRECTED
TEMPERATURE
RADIATION CORRECTION
1600
1400
0 —
—3—5——<
— -0-0
1200
1000
800
600
400
200 -
-a-
-fi 8-
_L
.
m n
468
DISTANCE FROM CENTERLINE (cm)
10
12
79-04-64-13
111-56
-------
FIG. 39
HORIZONTAL TEMPERATURE PROFILES OVER FLAT FLAME BURNER
H2/02/Ar
UNCORRECTED TEMPERATURE = 1600K
2200
2000
1800
1600
1400
1200
1000
800
600
400
5/8/78
O UNCORRECTED (THERMOCOUPLE)
TEMPERATURES
A RADIATION CORRECTION
2001
I
I H
468
DISTANCE FROM CENTERLINE (cm)
10
12
79-04-54-15
111-57
-------
FIG. 40
HORIZONTAL PROFILES OF MAJOR SPECIES OVER FLAT FLAME BURNER
H2/O2/Ar
UNCORRECTED TEMPERATURE = 950 K
MASS SPEC ANALYSIS
T = 950K(UNCORRECTED)
PROBE B
2
g
o
<
cc
u.
LU
_J
O
1.0
0.6
0.4
0.2
D Ar
0.10
<
0.08
0.06
0.04
0.02
\
0.00
_L
0/0
O 02
0 H20
V co,
JE B_
0.0 2.0 4.0 6.0 8.0
DISTANCE FROM CENTERLINE (cm)
10.0
12.0
79-04-54-
10
111-58
-------
FIG. 41
HORIZONTAL PROFILES OF MAJOR SPECIES OVER FLAT FLAME BURNER
H2/02/Ar
UNCORRECTED TEMPERATURE = 1220K
MASS SPEC ANALYSIS
T = 1220K (UNCORRECTED)
PROBE B
1.00
0.80
CJ
<
cr
LL
LLJ
0.60
0.40
0.20
0.0
D Ar
A N-,
0.12
0.10
0.08
0.06
0.04
0.02
0.0
I
I
O 02
0 H2o
j H
IB
0.0 2.0 4.0 6.0 8.0
DISTANCE FROM CENTERLINE (cm)
10.0
12.0
79-04-54-11
111-59
-------
FIG. 42
NO HORIZONTAL PROFILE OVER FLAT FLAME BURNER (COLD FLOW)
1.0*
0.8
UJ
J/5
< 0.6
O
z
<
LLJ
~ 0.4
O
0.2
0.0
O PROBE D
NOSEED-314ppm
CHEMILUMINESCENT ANALYZER
ROOM TEMPERATURE
J_
J.
'
468
DISTANCE FROM CENTERLINE (cm)
a.
10
12
79-04-
111-60
-------
Ill. C. 4. a Sta.tjLc_Cel_l Opt_ica_l Mea.su_rement_s_
A number of tests were performed in an 18.6 cm long static cell at room
temperature. Tests were performed in high resolution on single line pairs
and in low resolution (.146 nm FWHM) using gases blended with the gas mixing
system and gas mixtures obtained from vendors. Data were obtained for a pres-
sure range of .0627 atm (6.35 kPa) to 1.32 atm (134 kPa). Some of these data
for low resolution scans with gases (NO diluted in N2) checked against National
Bureau of Standards reference gases and used without dilution are shown in
Table III-L. The table lists the cylinder concentration (NO in M2 by volume),
total pressure, optical depth, and the measured transmission for the two band-
heads which are displayed for a spectra at this resolution in Fig. D-8. The
first bandhead is located at about 226.8 nm and the second is located at
about 226.15 nm. Also given in Table III-L is the transmission as predicted
by the computer model, and an estimate of the error that would be incurred in
predicting the NO concentration in the static cell from the measured trans-
mission and the computer model. Since the NO concentration is approximately
proportional to In T, where T is the transmission, the error E is defined by
E=l - (In TPRED/ln TMEAS _) , which is multiplied by 100 to convert a percent
error. Thus, if the known NO concentration is multiplied by the factor (1 + E) ,
the predicted and measured transmission values will agree. This same definition
is used for the flowing gas heater and flat flame burner, except than the factor
(1 + E) is multiplied by the probe determined NO profile for agreement between
predicted and measured transmissions.
These tests were used to obtain an estimate of the apparent line width of
the narrow-line source, and the effective oscillator strength. The line width in
the source could not be measured directly, but could be inferred, from measurements
in the static cell over a range of pressures. At the higher pressures, the ab-
sorption is almost independent of the source line width, and the absorption data
at these pressures were used to determine the effective oscillator strength when
using the narrow-line lamp. The oscillator strength determined in this manner
resulted in a slightly smaller value than that determined with the continuum source
as shown in Table III-K, with the difference attributable (at least partly) to the
"extra light" in the narrow-line lamp, as discussed previously. At the lower
pressures, the emission line width from the lamp becomes comparable with the ab-
sorption line width, and the transmittance at these pressures depends on the
value assumed for the source line width. The best fit to the static cell data
were obtained for a source Doppler width with a temperature of 600 K. This
compares favorably with the value of 561 K for the lower temperature part of the
Boltzmann plot for the line strengths in the narrow-line lamp (Fig. 20). Meinel
(1975) has suggested that this low temperature part of the Boltzmann plot should
give a measure of the translational temperature of the lamp, which, in turn,
determines the Doppler width of the emitted lines. This agreement may be
fortuitous, because the "extra light" phenomena should also affect the apparent
lamp line width.
111-61
-------
TABLE III-L
Static Cell Calibration Data (NO in N2)
Cylinder
Concen-
tration
(ppm)
93.3
93.3
93.3
93.3
93.3
93.3
93.3
470
470
470
470
470
470
Total
Pressure
(atm)
1.315
1.000
.751
.500
.474
.250
.125
1.001
.751
.503
.249
.125
.0627
Optical
Depth
(cm- 2)
5.679-1016
4.317-1016
3. 240-10^
2.159-10
2.044-10
1.079-1016
5.405-1015
2.176-1017
1.633-1017
1.093-1017
5.426-1016
2.721-1016
1.363-1016
1st
Bandhead
Trans .
Meas.
.896
.900
.912
.917
.918
.934
.956
.627
.646
.674
.738
.816
.887
1st
Bandhead
Trans .
Pred.
.890
.900
.909
.920
.921
.939
.959
.625
.633
.666
.734
.812
.882
Error
in Pred.
NO Cone.
(%)f
-6.5
-0.2
-3.2
+3.1
+4.4
+9.2
+5.7
-0.7
-4.5
-2.9
-1.5
-2,4
-4.2
2nd
Bandhead
Trans .
Meas.
.824
.843
.864
.879
.880
.906
.938
.465
.513
.568
.668
.762
.846
2nd
Bandhead
Trans .
Pred.
.821
.842
.859
.879
.881
.909
.938
.469
.498
.555
.651
.748
.835
Error
in Pred
NO Cone
(%)f
-1.9
-0.8
-3.5
-0.1
+0.9
+3.1
+1.3
+1.2
-4.6
-4.2
-6.2
-6.8
-7.5
These errors are based on more significant figures than shown in this table.
sion in Section III.C.4.a for definition of error.
See discus-
111-62
-------
Ill.C.4. b £lowing_ Gas_ ]le£t£r_(FGH)_Op_ticaJL_M£asurement£
Calibration tests were performed with the flowing gas heater for NO diluted
in pure N2 and pure Ar at a total pressure of 1 atm (101 kPa) and over a tempera-
ture range from 295K to 825K. All of these absorption spectra were obtained in
low resolution (FWHM = .146 nm = 1.46 &) , and transmission data were reduced for
the first bandhead, located at about 226.8 nm and the second bandhead, located
at about 226.15 nm. A comparison of the computer model prediction versus measured
transmission is shown in Table III-M. The values from the computer model were
based on an NO concentration which was the average of the measured value (chemi-
luminescent analyzer) and the value computed from flow calculations for the
critical orifices. The ratio of the measured NO concentration to that preducted
by the flow system was ^ 0.96, which was less than unity because of diffusion of
purge gas into the main stream and, possibly, calibration errors. The actual
temperature and NO concentration profiles were approximated as two or three zones
of constant temperature for computer predicted transmissions. The data were
reduced assuming Lorentz broadening, that is a1 = CP/T. For comparison with the
data reduction procedure used for the flat flame burner, the Weisskopf dependence
(a* = KP/T ' ) could have been employed for the FGH. At room temperature the
Weisskopf theory would give the same result as the Lorentz theory, but, at the
highest temperatures in the FGH, the Weisskopf theory would systematically reduce
the predicted transmissions as shown for Run 43 in Table III-M. At these tem-
peratures the predicted absorptance (-In T) is increased about 11 percent, so
that the numbers in column "Error in Pred. NO Cone." would be reduced by about
11 percent. The overall errors would probably be slightly reduced by this pro-
cedure .
III.C.4.C Flat Flame Burner (rU/O^/Ar/NO) Optical Measurements
Optical calibration for NO absorption was performed for H2/02/Ar/NO flames at
1 atm (101 kPa) over a temperature range from 1000K to 1860K. Data were obtained
independently for the continuum lamp and the narrow-line lamp.
The continuum lamp data were used principally to determine the line widths in
the flames, but the transmission information was also available, and since this
high resolution technique was used on some of the CH^/N /O /NO flames of Task III,
data were reduced for the H2/02/Ar/NO flames to determine its applicability. Trans-
mission data for three flames at 1000K, 1360K and 1610K are compared with computer
model predicted transmissions in Table III-N. These were reduced based on NO
centerline levels computed from flow calculations for the critical orifices,
which were checked in cold flow, and profile data as shown in Fig. 16. Two or
three zones of constant temperature were assumed.
The narrow-line lamp data were obtained for four different flame temperatures
with at least two MO concentrations at each temperature. The computed and actual
transmissions for the two bandheads observed in the low resolution spectra are
111-63
-------
TABLE III-M
Flowing Gas Heater (FGH) Optical Measurements
1st 1st Error in 2nd 2nd Error in
Run Temp NO Cone. Diluent Bandhead Bandhead Pred. NO Bandhead Bandhead Pred. NO
Number (Centerline) (Centerline) Gas Trans. Trans. Cone. Trans. Trans. Cone.
(K) (ppmV) Meas. Pred. (%)f Meas. Pred. (%)
31
32
33
34
35
36
37
38
39
40
41
42
43
44
43*
295.8
295.8
295.8
295.8
4°3.
453.
524.
452.
825.
788.
768.
793.
756.
738.
756
287
112
108
280
112
293
111
280
110
287
284
109
430
521
430
Ar
Ar
N2
N2
Ar
Ar
N2
N2
Ar
Ar
N2
N2
N2
Ar
NO
.735
.882
.904
.779
.926
.793
.945
.823
.962
.891
.907
.962
.856
.791
.856
.752
.895
.912
.790
.930
.815
.944
.843
.961
.896
.908
.965
.862
.809
.847
+7.9
+13.3
+9.1
+6.2
+6.4
+13.3
-2.6
+14.4
-2.6
+5.0
+1.9
+11 . 8
+5.2
+10.7
- 6.8
.609
.818
.848
.661
.899
.726
.920
.764
.947
.854
.869
.949
.805
.733
.805
.643
.841
.861
.684
.903
.750
.920
.783
.946
.859
.873
.951
.811
.747
.794
+12.3
+16.3
+9.9
+9.2
+4.7
+11.4
+0.4
+10.1
-0.6
+3.5
+3.1
+4.9
+3.6
+6.2
-6.1
-1- These errors are based on more significant figures than shown in this table. See discus-
sion in Section III.C.4.a for definition of error.
§Test case for a'determined from Weisskopf theory. See text.
111-64
-------
TABLE III-N
CONTINUUM LAMP TRANSMISSIONS FOR
H2/02/Ar/NO FLAT FLAMES
l_n
Spectral
Lines
P22(15.5)+Q12(15.5)
Q22(8.5)+R12(8.5)
+P12(26.5)
P22(16.5)+Q12(16.5)
Q22(9.5)+R12(9.5)
R22(5.5)
P22(17.5)+Q12(17.5)
Q22(10.5)+R12(10.5)
AVG. ERROR IN
1000K
Flame
Meas. Computer
Model
(a'=1.10)
.643 .628
.597 .599
.607 .634
.620 .598
.879 .886
.666 .647
.554 .586
+1.2
1360K 1610K
Flame Flame
Meas. Computer Meas.
Model
(a'=0.8)
.694 .702 .751
.702 .709 .744
.690 .688 .738
.695 .702 .754
.920 .924 .940
.688 .700 .748
.672 .705 .751
+4.7
Computer
Model
(a'=0.8)
.759
.760
.757
.764
.941
.761
.753
+4.9
PREDICTING
NO FROM MODEL (%)
ACTUAL NO
CONCENTRATION
(PPMV)
t
1466
1690
1867
See discussion in Section III.C.4.a for definition of error,
-------
shown in Table III-O. The computed transmissions were based on a centerline value
which was the average of calculated levels for the critical orifices and cherai-
luminescent measurements (corrected for Ar response), and profile data as shown
in Fig. 16. Two or three zones of constant temperature were assumed. The a' values
used to generate the computer spectra were taken from the solid line in Fig. 35.
An estimate of the error in predicted transmission due to the uncertainty in the
a' values is also shown in Table III-O for the highest temperature flame. The
uncertainty in a' of 0.6 + 0.2 results in a variation of predicted NO of + 9.7
percent.
The overall agreement between predicted and measured values was within - 16
percent for the flame data, which was slightly greater than the original goal of
- 10%, but was reasonable given the experimental uncertainties and relative to the
previously reported discrepancies. It should be noted that the overall errors
result from the summation of errors in the model, scatter in the experimental
spectra, uncertainties in the broadening parameter a', uncertainties in the flame
profiles for temperature and NO, and errors in the gas blending procedure.
111-66
-------
TABLE III-O
Temp
(K)
1000
1000
1360
1360
1610
1610
1610
1870
1870
§1870
Cone.
(Centerline)
(ppmV)
653
1027
999
1194
1092
1575
1988
1231
2324
2324
FLAT FLAME BURNER RESULTS
(H2/02/Ar/NO FLAMF.S)
1st 1st Error In
Bandhead Bandhead Pred. NO
a' Trans. Trans. Cone.
Run* (Centerline) Meas. Pred.
2 1.14 .824 .811 -8.2
1 1.14 .743 .720 -10.6
3 0.80 .822 .835 + 8.0
6 0.80 .790 .809 +10.1
4 0.67 .852 .864 + 8.7
5 0.67 .793 .811 + 9.7
11 0.67 .740 .768 +12.3
7 0.60 .866 .889 +18.2
9 0.60 .769 .802 +16.0
9 0.40 .769 .781 + 6.2
2nd
Bandhead
Trans.
Meas.
.790
.690
.777
.729
.807
.734
.672
.824
.718
.718
2nd
Bandhead
Trans.
Pred.
.750
.635
.776
.738
.811
.741
.687
.842
.726
.702
Error In
Pred. NO
Cone .
(%)f
-22.0
-22.3
- 0.5
+ 3.9
+ 2.3
+ 3.1
+ 5.5
+11.2
+ 3.3
- 6.4
Avg.
Error
(%)t
-15.1
-16.4
+ 3.6
+ 7.0
+ 5.5
+ 6.4
+ 8.9
+14.7
+ 9.6
- 0.1
tsee discussion in Section III.C.4a for definition of error.
§Test case for sensitivity to a'. See text.
-------
IV. DISCUSSION
A. Introduction
The computer model that was developed by W. K. McGregor, M. Davis, J. D. Few and
their colleagues at Arnold Research Organization (ARO) was one of the starting points
of this study. Initially, it was thought that the model rested on a sound theoretical
basis and was supported by strong experimental evidence. However, experimental data
obtained with the static cell, i.e., under the most ideal conditions, were not in
agreement with the predictions of the model. A thorough examination of the program
for errors in translation onto the UTRC UNIVAC 1110 computer revealed no such errors.
Additional verification of proper translation was obtained when the results of test
computations made at both UTRC and ARO were in agreement. An intense review of gas
standards, mixing procedure, optical and electronic instrumentation did not yield the
cause of the disagreement. Consequently, the theoretical basis of the model was studied
and found deficient. The errors that were discovered are reported in Appendix B.
These errors appear in reports published since 1973; however, a precise knowledge of
the various forms of the model from 1973 through 1977 is not known. Suggested refine-
ments to the model delivered to UTRC are also noted in Appendix B. A new model was
developed on the theory presented in Section III of this report. A description of
the new model is given in Appendix D. A major subroutine entitled NO-Spect (Appendix
D) was also provided to ARO in July 1978. This subroutine can be used to interpret
only resonant lamp data.
B. Comments on ARO AEDC TMR-79-P7
As part of this study, measurements were made on the UTRC calibration devices by
ARO personnel using a capillary discharge lamp. The results of those measurements are
contained in an internal ARO Report (AEDC TMR-79-P7) by Few , McGregor, and Keefer
(1979). This report will be published externally at a later date.
In order to prevent further confusion in the literature stemming from the errors
contained in the reports listed in Appendix B and problems contained in AEDC TMR-79-P7,
it seemed necessary and was requested by the FAA that the content of this latest :t
report be discussed here. That report has four major sections each of which will be
considered below.
IV.B.I. TMR Introduction
The last part of this section should be expanded to include a statement that the
agreement of the optical measurements with the calculated input of NO concentration in
conjunction with the probe profiles are generally within the uncertainties of the probe
and optical measurements. As written it could be inferred that the uncertainties rest
only in the probe measurements. Such an interpretation would not be accurate as will
be indicated later in this review.
IV-1
-------
IV.B.2 TMR Review of Model
In subsection A which is on the spectroscopic theory, it is stated that the
Hbnl-London factors are those of Earls as previously defined in a report by Davis,
McGregor, and Few (AEDC-TR-76-12, February 1976). Unfortunately some of the Honl-
London factors included in that report are in error. In subsection B on model
parameters, the authors state that the oscillator strength value of 4.09 ± 0.1 x
ID"4 Hasson et al) appears to be the most reliable. The author's judgment is neither
in agreement with Huber and Herzberg (1979) who prefer 3.8 x 10"4 nor with 3.7 x 10~
determined by UTRC. With regard to source temperature, it should be remembered
that 950 ± 25 K is a factor of 3 higher than that previously reported (e.g. McGregor,
Few. Litton (1973), Few Bryson and McGregor (1976)). Moreover, the broadening
parameters reported are a function of both the oscillator strength that was selected
from the literature and the source temperature, and, hence, are inferred and not
directly determined.
IV.B.3 TMR Optical Results
In the description of the calibration facility, it is incorrectly stated that the
majority of the sampling measurements on the flowing gas heater weremadewith the mass
spectrometer. In fact, the bulk of these measurements was made with the chemilumine-
scent analyzer. It is also incorrectly stated that the buffer flame of the flat flame
burner was lean burning H2/02/Ar. The buffer flame was actually a lean Clfy/^/Ar
flame. Figures 5 and 6 give respectively concentration and temperature profiles over
the flowing gas heater. In these figures, the uncertainty is listed as unknown.
These uncertainties are given in Figures 9 and 10 in the main body of the Task I Report.
Similarly, Figures 7 and 8 of the ARO report give concentration profiles with "unknown"
uncertainties. See Figures 42 and 16 of the Task I Report. Also, in Figure 11 of the
ARO report, the 40% uncertainty refers only to the radiation correction factor and is
not the uncertainty of the temperature measurement itself. It is not clear why, as
in the Introduction, the implication is given that the uncertainties in the experimen-
tal data reside only in probe, thermocouple, and calibration device performance. In-
deed, this is an incomplete assessment of the uncertainties. A complete assessment
of the errors should also include variations in lamp intensity, drift in system elec-
tronics, trigger and grating scan uncertainties and their influence on the signal
averaging process used by ARO. These experimental uncertainties were readily identi-
fiable during the ARO measurements made at UTRC.
With regard to data treatment, the new model developed by ARO is briefly described.
This new model does not employ a Beer's Law zonal treatment of temperature and con-
centration inhomogeneities encountered in combustion systems. Instead, the new model
keeps a detailed knowledge of the emission line shape from zone to zone. Figure 17
illustrates in an exaggerated manner the importance of a problem which can occur when
the absorber line is narrower than the source line. Such a situation, it is stated,
would be encountered for a jet engine exhaust under altitude conditions. This state-
ment is extremely vague and in the context of this study is misleading. No information
is given on what altitude such a condition may occur. Moreover, no data were obtained
IV-2
-------
in this study that required consideration of this phenomena. In addition, if the ICAO
standard atmosphere is used to provide temperature and pressure as a function of alti-
tude and if 600 K is assumed to be a typical static temperature of a jet exhaust, then
the absorbing lines at 35,000 feet are still considerably wider than the emission lines.
Even at 65,000 feet, significant transmitted line center "burnout" is not expected.
Equation (17) [Ac = {(j?n Tmeas/£n Tcal)-l}. 100] that was used to compute the per-
cent error in concentration given in Tables 3, 4, and 5 is not the same expression
used in Task I Report Tables III-L, III-M, and III-O. The expression used in Task I
Report was
Ac = l - ^ . 100
V *" Tmeas /
Using equation (17), the root-mean square average departures of the calculated
NO concentration is reported in the TMR as ± 9% for the absorption cell, ±18% for the
flowing gas heater, and ±21% for the flat flame burner. This method of summarizing
the errors obscures the fact that the errors indicated in Tables 4 and 5, which res-
pectively contain data from the flowing gas heater and flat flame burner are not really
random but systematic. In fact, for the bulk of the data reported in those Tables,
the error is positive and, generally, increases with temperature. The average error
for all the ARO tests from room temperature to the highest temperatures was equiv-
alent to an overprediction of NO using the optical technique by + 15%, but at the
highest temperature the overprediction was + 29%. This systematic error is most
likely due to deviations from Lorentz broadening theory. This deviation is dis-
cussed in Section III of Task I Report. Moreover, the errors (-15% to +4.8) listed
in Table III for the absorption cell give an indication of the errorsv associated
with the optical measurement system used by ARO.
IV. B. 4 TMR Summary
With regard to the broadening study results, it is suggested that the broadening
due to HoO is the same as that of N2 , Ar, and C02- The basis for this suggestion is
that the broadening cross sections for N2, Ar, and C02 are similar. This suggestion
cannot be accepted because of the evidence presented in Figure of Task I Report.
Furthermore, H20 is a polar molecule while N2 , Ar, and C02 are not.
It is restated in this summary that the ARO procedure avoids the incorrect assump-
tion of Beer's law which is reasonable for this data where the absorber lines are con-
siderably wider than the source lines. Furthermore, serious difficulty with Beer's law
would be expected during measurement on turbine engine exhausts at simulated altitudes.
However, there is no evidence presented in this ARO report that supports these state-
ments. In fact, for all the measurements made in this study, the Beer's law assump-
tion is valid. Moreover, it is also a valid assumption for those altitudes in which
the majority of the jet aircraft fleets operate.
Finally, the ARO report concludes with a statement that a 20% projected uncer-
tainty can be expected by the use of the ARO UV resonance line absorption technique
based on the results obtained with uncertain temperature and concentration profiles
IV- 3
-------
in the calibration devices. It must be reiterated that uncertainties also arise from
the performance of the optical systems as indicated by errors in the static cell measure-
ments which were obtained under the most ideal conditions.
C. Comparison of Hollow Cathode and Capillary Discharge Performance
Although these lamps are very different in design, the emission characteristics
are quite similar as opposed to the statement made in TMR-79-P7- Overall, the trans-
mission characteristics through media containing NO at various temperatures can be
seen to be comparable from the data in Table IV-A.
D. Comparison of the UTRC and ARO Computer Programs
Except for input data, e.g., lamp temperature,broadening coefficients, etc., the
main body of the present ARO computer program appears to be substantially similar to
the version developed by UTRC from the 1977 ARO model (Davis et al (1976a)). At room
temperature, the predictions of the ARO model agree with those of the UTRC model.
However, the predictions diverge significantly at elevated temperature due to the
different temperature dependence for the broadening parameter a'. The ARO model em-
ploys Lorentz theory while the UTRC model employs Weisskopf theory. The ARO model
will systematically predict more nitric oxide than the UTRC model for a given trans-
mission, pressure, and elevated temperature distribution. As stated in Section IV.B.3,
the different broadening dependence is the probable cause for the systematic overpre-
diction of NO by the ARO model at the high temperatures in the flat flame burner tests
at UTRC.
Moreover, it should be noted that the data reported in Table III-N on the con-
tinuum lamp transmissions for the flat flames was reduced using a -model which stored
the line shape for each zone. For a continuum lamp measurement, this procedure is
necessary. However, for a resonant lamp, such a procedure was not necessary for this
study. At typical commercial jet exhaust temperatures and operating altitudes (H ^
40,000 ft) this procedure is not necessary. Moreover, even at 65,000 ft, the resonant
line sources will have lines which are narrower than the exhaust absorber lines.
E. Comment on Gas Correlation Measurements
As stated in Appendix A, this instrument was designed to measure several pollu-
tant molecules emitted from smokestacks, NO being one of those molecules. For that
application, this instrument has considerable merit. However, for measurements in
this study, this instrument in its present configuration was not well suited for
several reasons. The first was related to the failure of the detector that was used
in the Wright-Patterson measurements. The active area of the original detector was
circular (1.3 mm dia) while the replacement has a rectangular area (4 mm x 0.4 mm).
This geometric mismatch is considerable. The second was that the intrinsic noise
of the replacement detector was higher than that of the original detector. These
two items alone were most likely responsible for a factor of four increase in the
noise equivalent NO. A third reason was due to the lines chosen for correlation.
IV-4
-------
For temperatures up to 900K, this selection of lines was such to produce a temperature
independent calibration curve. Above 900K, however, the selection is no longer
optimum; hence, the sensitivity decreases by almost a factor of three at the highest
temperatures of this study.
The center-line concentrations necessary for adequate signal-noise ratios for
the infrared measurements were typically factors of 2 to 10 greater than those used
in the ultraviolet measurements. Because of the loss in sensitivity, a side-by-side
comparison data is not possible.
IV-5
-------
TABLE IV-A
COMPARISON OF TRANSMISSION DATA
ARO LAMP VERSUS UTRC LAMP
TRANSMISSION
1st BH
ARO UTRC
ARO
2nd BH
UTRC
STATIC CELL
93.3 ppm
470 ppm
.892
-901
.621
.905
.899
.628
.627
.835
.849
.482
.850
.843
.504
.497
FGH
280,ppm 452 K
288ppm, 448 K
.817
.823
.753
.764
FFB
999 ppm, 1360 K
1066 ppm, 1360 K .811
(a=1.97-10-4)
.822
.777
(a-2.53.10~4)
.747
(a=2.74-10-4)
IV-6
-------
V. SUMMARY AND CONCLUSIONS
Methods for providing known amounts of NO from room temperature to 2000 K were
developed. At room temperature, a stainless steel, static cell was used. This cell,
which was 18.6 cm long and 2.2 cm in diameter, was leak checked at 1 x 10~6 torr
(1.33 x 10~4 pa) an(j could be pressurized to 115 psia (792 kPa). Its windows were
ultraviolet grade fused silica. The cell was attached to a precision mixing apparatus
and used in obtaining the majority of the broadening and oscillator strength informa-
tion presented in this report. For temperatures up to 850 K, a quartz-bed heat ex-
changer, through which mixtures of NO in N2 and Ar were flowed, served as a calibra-
tion device. NO decomposition in the bed was not significant (<10%). NO concentra-
tions, measured with both uncooled quartz and metallic probes at and near the center-
line, were in close agreement with NO concentrations calculated for a gas mixing
apparatus which employed critical flow orifices. The NO determinations were made
with both chemiluminescent analysis and mass spectrometry. For those cases where Ar
was the bulk gas, proper account of viscosity and quenching phenomena was taken in
the calibration of the chemiluminescent analyzer. Kinetic analysis indicated that
substantial decomposition would not occur in this exchanger up to 1000 K. Thermal
runaway of the electrical heating elements, however, prevented its use at that tem-
perature. For temperatures of 1000 K to 2000 K, a lean H2/02/Ar flat flame seeded
with NO was used. The burner surface was constructed of water-cooled, sintered
copper with two zones: a main, NO-seeded zone and an unseeded buffer zone. Measure-
ments made with water-cooled quartz probes indicated downstream conservation of NO
in flames whose stoichiometries were varied from 0.36 to 0.92. Ar was used as a
bulk gas instead of N~ to preclude the formation of thermal NO. The data confirm
that water-cooled quartz probes can be used in measuring NO in lean l^/^/Ar flames.
Detailed concentration and temperature distributions were obtained along the optical
path for both high temperature devices. These distributions had-to be available for
the reduction of the optical data and their comparison with probe results. The
temperature measurements were made with thermocouples. For the quartz-bed heat ex-
changer measurements, uncoated chromel-alumel was used. In the flame measurements,
Ir/60%Ir-40%Rh wires (76(jm) coated with 10% beryllium oxide and 90% yttrium oxide
were employed. The purpose for the coating was to minimize catalysis on the wires.
Corrections for radiation losses were applied to the data obtained on the flames.
Two distinct ultraviolet sources were used in this study. The first was a
hollow cathode lamp. A dc discharge in air at low pressure (2 Torr; 266 Pa) pro-
duced emission lines mainly from NO molecules, N£ molecules and ions, and Ar atoms.
The spectral lines used in this study were in the Y(0,0), Y(l,l) and Y(2,2) bands
(A^E"1" - X^rr) of NO. The second source was a high pressure Xe lamp which produced
radiation of the continuum type through the above spectral region.
V-l
-------
A detailed review of the previously developed spectroscopic 'theory and computer
model, which was supplied to these authors at the beginning of this study by ARO,
Inc., revealed several significant errors (Appendix B). The accuracy of the optical
results published by the originators of that theory and model is, hence, in doubt.
Due to the complex history of the computer model, inconsistencies in calibration data
and the unavailability of the original raw data, it is not possible to comment with
certainty on the accuracy of the optical data existing in the literature. Where
possible, some reanalysis of the original data will be included in TASK III Report.
Because of these difficulties, the spectral theory used in the previously
published model was corrected, and the computer model was expanded so that not only
data from resonant line sources can be analyzed but also that from continuum sources
(Appendix D). Experimental data were obtained at low and elevated temperatures
using these significantly different spectral sources. A comparison of these data
showed excellent agreement; hence, the validity of the theory and model were estab-
lished.
In order to use this model, a knowledge of the broadening of NO spectral lines
in foreign gases was necessary. Data on broadening in Ar, N2, C02, CO and CH^ were
obtained by the direct observation in high resolution of isolated lines using the con-
tinuum source. If Lorentz theory is assumed, i.e., a'=CP/T, the following values
of C were obtained: C(Ar) = 1331 atnT1 K; C(N2) = 1725 atm~l K; C(C02) = 1655 atm"1 K;
C(CO) = 1748 atm"1 K; and C(CH-) = 1918 atm"1 K. If Weisskopf theory is assumed,
i.e., a' = K'P/T1-2, then the same experimental data yield: K' (Ar) = 4154 atm~1K1'2;
K' (N2) = 5383 atm-l-K1-2; K' (C02) = 5165 atm'1^-2; K'(CO) = 5455 atnT^-K1-2; and
K (CH^) = 5986 atm^K1'2. These data were also reduced to determine the following
collision diameters: d(Ar) = 1.04 nm; d(N2) = 1.13 nm; d(C02) = 1.17 nm; d(CO) -
1.15 nm; and d(CH4) = 1.10 nm. Because of the oxidation of NO to N02 by 02, precise
measurement of the broadening parameter for 02 was not possible. However, for the
data obtained, it was estimated that the broadening parameter for 02 has a value
which lies between that of Ar and N2. Data taken on the flames indicated that at
elevated temperature Weisskopf theory seemed to provide a better fit to the data.
If that theory is used and if it is assumed that 02 is as efficient a broadener as
N2, then the broadening parameter for H20 is 6260 atm~l K^--2.
Oscillator strengths were determined from data obtained with both radiation
sources. From the continuum lamp data, the oscillator strengths for the NO Y(0,0)
A2£+ - X2n3/2 band when NO is diluted in N2, C02, CH^, and Ar were 3.57 ± 0.06 x 10~\
3.54 ± 0.004 x 10~4. 3.51 ± 0.02 x 10~4, 3.27 ± 0.06 x 10~4, respectively. A measure-
7-4-2
ment of the A £ - X TT]/2 band with N2 as the diluent yielded an oscillator strength
of 3.72 ± 0.23 x 10~^. This value was chosen for comparison with values in'the liter-
ature because the TT^/2 state is more heavily populated at room temperature than the
3/2 state- The agreement is good but slightly lower that those considered to be
the most reliable. However, it should be noted that this study is unique since the
oscillator strengths were measured directly from individual lines in high resolution.
V-2
-------
With the use of the broadening data obtained with the continuum lamp, the oscillator
strengths in the model were adjusted so that transmissions predicted by the model
agreed with the experimental data obtained with the hollow cathode lamp. The values
for the "1/2 an^ n3/2 were 3.53 x 10~^ and 3.20 x 10"^ respectively. These values
were low relative to the continuum values because of the presence of radiation in
the hollow cathode lamp due to species other than NO. If an estimate is made of the
effect of this excess radiation, the oscillator strengths for these transitions are
3.76 x 10~^ ( ^1/2) and 3.43 x 10~^ (^3/2) • The source temperature used in this
and all calculations involving the hollow cathode lamp was 600 K.
Sufficient measurements were conducted and compared with model predictions of
transmission that the optical system, based on a hollow cathode lamp and associated
spectral model, can be considered calibrated to measure NO. If accurate temperature
and pressure data are available and if the NO absorption is large relative to the
noise, then measurements with accuracies of at least - 20% are possible.
Similarly, if a proper model is used, the capillary discharge lamp (see Section
IV.D.) can also be considered calibrated.
In order to reach this conclusion for the hollow cathode lamp, data were ob-
tained and processed in the following manner. Two concentrations of NO in N~ (93.3
ppm and 470 ppm, independently certified) were introduced into the static cell at
pressures ranging from 47 Torr (6.3 kPa) to 1000 Torr (133 kPa). The first and
second bandhead transmissions of the Y(0,0) transitions were measured and compared
with model predictions. The averaged errors in concentration between predicted and
measured were -0.3% and -2.23% for the first and second bandhead data sets, respect-
ively. For the quartz-bed heat exchanger and the flat flame, the temperature and
concentration profiles were divided into zones, and the transmissions through each
zone were calculated using the average temperature and concentration in each zone.
For the quartz-bed heat exchanger, the averaged errors in concentration for the total
data set based on first and second bandhead transmissions were +7.14% and +6.79%,
respectively. Similarly, for the flat flame data, the averaged errors for the data
sets were +7.04% and -2.19%, respectively. The maximum error encountered for any
single measurements was 22.3%. Finally, for the high resolution continuum measure-
ments, the averaged error of the set was +3.6% in concentration. It must be noted
that these errors reflect the errors associated with the optical measurements, model
predictions, and the temperature and probe concentration measurements.
Finally, an empirical calibration of the infrared gas correlation spectrometer
was performed (Appendix A). Because this instrument was originally designed for stack
monitoring, i.e., low temperatures and high densities, it was not well-suited for the
measurements of interest here. The low temperature data indicated that the instru-
ment was 20% more sensitive relative to the calibration previously used in jet com-
bustor measurements. This variation is attributed to changes in grating alignment.
A dependence of the calibration on broadening gas was observed and determined. For
temperatures up to 900 K, the calibration, within the scatter of the instrument output,
V-3
-------
remained constant. Above 900 K, a significant decrease in sensitivity was observed.
This dependence is most likely due to significant changes in the populations of the
lines selected by the grating assembly. However, sufficient data were obtained to
allow measurements to be made at high temperatures if high NO seeding of the media
is used.
V-4
-------
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R-5
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APPENDIX A
MEASURING NO IN AIRCRAFT JET
EXHAUSTS BY GAS-FILTER CORRELATION
TECHNIQUES, TASK I.
David A. Gryvnak
Ford Aerospace and Communications Corp,
Aeronutronic Division
Ford Road
Newport Beach, California 92663
November 1978*
Submitted to:
United Technologies Research Center P.O. 82126
FINAL REPORT TASK I
*Revised Version Received 4/12/79
-------
INTRODUCTION AND SUMMARY
As a result of tests performed at Wright Patterson Air Force Base^ ' the
EPA Smokestack Instrument was requested to be used on additional jet exhaust
tests under controlled conditions. Tests were performed using a flat flame
burner, flowing gas heater and in the future, will be made on a jet burner
and a modified combustor can from a Pratt and Whitney FT12 combustor. This
phase of the tests deals with the calibration procedures used for the flat
flame burner and flowing gas heater conducted at United Technology Research
Center (UTRC).
The EPA Instrument is a laboratory instrument designed to detect S02, CO,
HCL, HF or NO contaminants being emitted from a smokestack. The details of the
(1 2)
instruments are well documented ' and are not repeated here. The instrument
uses the principle of gas correlation to detect small amounts of contaminant
gases and reduce or eliminate -the effect of other gases such as H.O, C02 etc.
For this series of tests it is being used to detect NO in the exhaust aircraft
jet engines for temperatures up to approximately 2000K.
Three different types of tests were performed. Static cell tests were
performed using a sample cell to contain the gas at room temperature. At UTRC
a glass cell 10 cm long with NaCl windows was filled with NO premixed with either
Ar or N2. At Ford two cells were used, each with a 20 cm path length. One cell
with A1203 window, the other a glass cell with A1203 windows. The samples were
NO premixed with N2. The Flowing Gas Heater tests at UTRC consisted of flowing a
carrier gas of either N2 or Ar through a heater unit into a sample area that is
17 by 9.2 cm. Known amounts of NO were seeded into the carrier gas at tempera-
tures up to 800K. Buffer gases surrounded and contained the sample gases and
flooded the remainder of the sample area. NaCl windows allowed the light beam
A-l
-------
to traverse the sample area while confining the gases. The Flat Flame Burner
tests at UTRC consisted of flowing an argon carrier gas containing H2 and
02- The H2 + 02 was burned at the proper ratio and flow rates to create
the desired temperatures from 1000K up to 1600K. The argon was seeded with
known amounts of NO. The same buffering system and external housing used
for the flowing gas heater were used for the flat flame burner.
Because of the versatility designed into the EPA instrument, it is not
optimized for any particular gas contaminant, physical pathlength, particular
environment or temperature. It was designed to be relatively insensitive to
NO sample temperature changes up to 900K. This was achieved by selecting a
spectral bandpass that contains NO absorption lines that will increase in
strength and some that will decrease as the sample temperature increases. This
results in the sum of the strengths of the lines remaining relatively constant
for the temperature range from 300 to 900K. Above 900K the response of the
instrument decreases with increasing temperature. The present tests were
performed to calibrate the instrument and to determine if an empirical relation-
ship could be formulated to account for the temperature effect. A curve has
been determined to relate the original calibration to the higher temperatures.
The instrument was found to be more responsive by 15 to 207« to samples pressurized
with N2 under static conditions at room temperature than when used at Wright
Patterson Air Force Base. This is due primarily to a shift in the bandpasses
of the grating box. The instrument was also found to be more responsive to
samples diluted with Ar than to samples pressurized with N2.
Differences of as much as 287,, occurs for room temperature samples between
static cell tests and flowing gas heater tests. These differences are"most"
]Ikely'due to improper purge flow.
A-2
-------
INSTRUMENT REFURBISHING
The instrument was received from EPA with no apparent damage in shipment.
A few mirrors that were broken, previous to shipment, were replaced with
mirrors of similar optical quality. The instrument was originally designed
to be used on a smokestack, with an across-stack path using a retro-reflector
to doublepass the sample area. With the type of test conducted at United
Technology Research Center we could not doublepass the beam because of the
physical dimensions of the apparatus involved. Consequently, a source section
was built to be placed on the opposite side of the sample section to direct
the beam through the sample area to the main instrument. This is similar to
the technique used at Wright Patterson Air Force Base when the same instrument
was used for NO measurements on a simulated jet aircraft engine. The source
optics consisted of some focusing mirrors and an electronic reference that
was actuated by the 435 Hz chopper that also chopped the light beam from a.
Nernst source. The main instrument was checked for optical alignment. The
transfer optics had to be adjusted when the grating box was placed into the
instrument. The mask on the transfer optics was removed in order to increase
the throughput of the instrument.
The grating box is the same one used for the Air Force Wright Patterson
experiment. The grating box passes three spectral intervals where NO absorption
lines occur. Figure 1 shows three spectral curves over the spectral interval
of interest. The upper panel shows the water vapor absorption by laboratory
air at room temperature. The middle panel shows the spectral bandpasses of the
grating box, and the third panel shows the absorption by NO in those bandpasses.
As can be seen by the middle panel, the spectral bandpasses mask out the strongly
absorbing H20 lines. In the spectral interval between 1925 and 1940 cm~* the
A-3
-------
0.5-
05'-
co
o:
1.0'-
0.5 r
0
I.
Figure 1.
1950
GRID
.I
N
i
w
i
A
i*
!ii
III
1!
f]
1
(|
1
/
A
1
\\
A
1
1
''GRID
i
NO a mo
1900
WAVENUMBER (cm-l)
Spectral transmittance cxirves over the spectral interval passed
by the NO grid assembly. The upper panel shows the H20 absorption
by laboratory air at room temperature. The middle panel shows the
spectral bandpasses of the grid. The lower panel shows the absorp-
by NO in the bandpasses of the grid. The dotted lines indicate the
bandpass shift.
A-4
-------
the NO absorption lines increase in strength as the temperature increases.
In the spectral interval between 1895 and 1920 cm" the NO absorption lines
decrease in strength as the temperature increases. The total absorption
tends to remain constant as the temperature changes in the range from 300 to
900K. The grating box was placed into the instrument and optically checked.
The InSb detector was installed, however, the dewar had leaked causing
the window of the detector to frost with water condensation. Our detector
department attempted to reevacuate the dewar. The pins had epoxy deposited
around them to stop the leak that was created by the cracks in the glass near
the pins. The dewar was tubulated, evacuated and pumped for about four days,
then the tubulation was sealed. The dewar subsequently was tested and found
to hold liquid nitrogen for four hours. However, because the dewar was filled
with liguid N2 to the top the epoxy cracked and allowed the dewar to
leak again.
A replacement detector, that was not optically suited for the instrument
because of its element size, was installed in the instrument. The area of the
element of this detector is 4 mm x 0.4mm , whereas the area of the original
detector element was 1.3 mm in diameter. The original preamps of the instrument
were found to be defective in that two of the operational amplifiers had to be
replaced. A new preamp was used with the replacement detector. The rest of the
electronics were found to be functioning very well.
Because of the late arrival of the instrument and the length of time that
it took to resolve the electronic and detector problems, limited time was
A-5
-------
available to check out the instrument and make the needed repairs. The grating
box was installed in the instrument and the transmittance of the correlation
cell was checked. This was done by comparing the carrier signal when the
correlation cell was not in the beam to the carrier signal when the correla-
t ion cell was in the beam. We found that the transmittance of the correlation
cell was 577», which was the same as when used on the Wright Patterson Air Force
tests. This test seemed to be a good indicator that the correlation cell and
the grating box were in good spectral alignment and that the correlation cell
had probably not changed its spectral characteristics.
A calibration test was then performed to check the previous calibration.
The calibration curve used at Wright Patterson is shown in Figure 2. A sample
of 1000 ppm in a 20 cm sample cell produced a V of 68 x 10'^. From the pre-
f\
vious calibration this V would represent an absorber thickness of 2.1 x 10~*
f\
atm cm q—p . Whereas the sample in the sample cell was 1.8 x 10"^ atm cmg^p •
The instrument was indicating approximately 15% higher than the sample in the
sample cell. The short term noise-equivalent V1 was 4 x 10" , which gave a
noise-equivalent u of 1.1 x 10" ^ atm cm__.
A-6
-------
0.1
NO Calibration
0.01
0.001
-I- 296K
o 581K
D 873K
880K
0.0001
0.0001
0.001 0.01
u Absorber Thickness (atm cm
0.1
Figure 2.
Calibration curve for NO used at Wright Patterson
Air Force Base, instrument response V' vs absorber
thickness u.
-------
TEST AT UTRC
The instrument arrived at UTRC in Connecticut in very good shape, with
no damage during shipment. The optics were set up, and mirrors had to be
cut to accommodate some of the thermocouple connectors that were sticking out
of the chimney.
Figure 3. shows, an optical diagram of the equipment. Sodium chloride
windows were used on the flat flame burner, and an image of the Nernst was
formed in the center of the flat flame burner. Mirror M5 then focused the
image on to mirror XI of the EPA Instrument. A glass cell with sodium
chloride windows could be Inserted on the source side of the flat flame
burner in order to test the instrument under static sample conditions. A
burner with a sintered copper top produced a flat flame by burning H2 + 02
in an Ar carrier. The flat flame burner was replaced with a flowing gas
heater wherein hot gases as high as 900K could be introduced into the
infrared monitoring beam.
Tests using the static cell were done by first evacuating the cell In
order to record a zero and then filling it with a sample. Two types of
samples were used, one with argon gas as a broadener and the other with
nitrogen gas as a broadener. After the sample was introduced into the cell
and the signal recorded on the recorder, the cell was evacuated to record
another zero. The two zeros on the chart were used to determine the zero
position for the instrument when the gas was in the sample cell. If any
drift had occurred it could be compensated for by drawing a line through the
two zeros. Typical shifts were less than 1 x 10"^ for V and 0.3 x 10*3 atm cm
for u.
A-8
-------
Gas Filter
Correlation
Instrument
f
XI
450 Hz
chopper
Flat Flame Burner
Flowing Gas Heater
Ml
M5
Static
Cell
-\'
NaCl
Windows
M4
Nernst
Glower
Figure 3. Optical diagram of source optics and sample area.
The static cell was removed when the Flat Flame
Burner or the Flowing Gas Heater was used.
-------
A similar procedure was used for the flowing gas heater and the flat
flame burner. The flowing gas heater was heated up to the temperature
desired with either Ar or N2 as a carrier gas; the temperature of the center
of the flowing gas heater sample section was measured and recorded. A zero
level was recorded on the chart, then the sample was seeded with NO to a
predetermined amount and the NO concentration at the center of the sample
area was determined by TJTRC using quartz probe techniques. The signal was
recorded on the recorder chart paper and the NO gas was turned off. The
instrument then gave another zero level. The two zeros on either side of the
signal recorded for the sample were used in order to determine the zero when
the NO sample was in the sample section. A similar procedure was used for
the flat flame burner. The burner was brought up to temperature, heating the
argon carrier gas. Two zero levels were recorded, one before and one after
the carrier gas was seeded with NO. In the flowing gas heater and the static
cell tests both nitrogen and argon were used as a carrier gas. The nitrogen
was not used for the flat flame burner for fear of creating other NO or NO,.
A
products which would contaminate the sample area.
RESULTS
The techniques used to reduce the data are very similar to the one used
for the tests conducted at Wright Patterson Air Force Base. The details of
the data reduction can be found in their report (2). Only a brief description
will be given here.
The signal, V, from the EPA instrument is proportional to the NO absorber
thickness for small samples at constant temperature and concentrations. For
A-10
-------
the samples encountered in these tests, u - 2 x 10'^ atnn cm STP, the response
of the instrument is linear as can be seen from the calibration curve in Figure
2. When the sample has temperature and concentration gradients, the sample
path can be considered to be divided into small increments such that each
incremental path is at a constant temperature and concentration. The absorber
thicknesses for each increment can be determined and because of the linear
response of the instrument their sum will give the total absorber thickness
in the sample path. In order to compare the results of the instrument with
the actual sample, the temperature and concentration gradients must be known.
A computer program was created to calculate the absorber thicknessess of the
samples at the elevated temperatures.
To determine the absorber thickness, values of temperature and concentra-
tion were determined from gradient and mole fraction gradient curves supplied
by UTRC. For the flowing gas heater tests, four temperature profiles were
supplied and shown in Figure 4. Each curve is flat for a distance out to
approximately 4 or 5 cm from the centerline of the burner. The actual
centerline temperatures of the samples are listed above the curves for which
they were used. These profiles were determined within an hour from the tests
using the EPA instrument were performed. The profiles are a result of probe
measurements made by the T7TRC staff on samples whose temperatures and con-
centrations were similar to those used when making the measurements with the
EPA instrument. From the curves in Figure 4, the actual centerline temperatures
of the NO sample can be off as much as 10% from the centerline temperature
of the curve that was used to determine the sample absorber thickness. Figure 5
shows the mole fraction profile for three different temperatures. The 300K
A-ll
-------
800
750
700
01
id
s
J_l
a
£
V
H 650
600
500
800K/793K
25A/24A
- 723K/703K
24T/25T
678K/603K
22A/23A
608K/573K
22T/23T
T
Flowing Gas Heater
Temperature
Profiles
46 8 10
Distance from Centerline (cm)
'igure 4. Temperature Profiles for the Flowing Gas Heater.
The sample numbers for which the curves were used
are written below each curve. The temperature at
the center of the sample is listed above each curve.
A-12
-------
111
C
l-i
01
4J
c
01
rt
a
rH
o
^-x
If
o
T)
(U
-------
curve was used for the room temperature samples and the dotted curve was used
for the elevated temperatures.
The absorber thickness, u, for a sample of constant temperature and con-
centration can be determined from the UTRC data from
273
u(atm effi) • p(atm) L(cm) -
where
u « Absorber thickness in atm cm
p - Absorber pressure in atm - c(ppm) x 10"
c » Absorber concentration in ppm
L » Path length in cm
6 • Temperature in K (2)
However, if the concentration and temperature varys over the sample path, then
the absorber thickness for a small incremental path length ^L^ is given by
27
u±
Si
then the total absorber thickness for the path can be found by summing over the
entire path.
u - Z Ui - pi ALt (4a)
i i B±
and if the path is divided into equal increments,
u - £L 273 x 1CT6 Z
A-14
-------
The concentration can be found from the mole fraction normalized concentration
profile, M, and the centerline concentration, C, from the following expression.
Ci - MjC (5)
Therefore
uc - LC 273 x 10"6
where uc denotes the calculated absorber thickness. The values used in the
calculations were determined at 0.5 cm increments from Figures 4 and 5. In-
tegration was done from the center of the sample through 10 cm. The results
were doubled on the assumption that the profile is symmetrical about the
center line. Some of the representative curves of previous data indicate that
this might not be an accurate assumption. Asymmetry might cause errors as large
as 8%.
Because the calibration curve for the EPA instrument has been determined
for temperatures in the range of 300K to 900K it is not expected to give
absolute results for samples pressurized with Ar or for samples whose tempera-
tures are higher than 900K. In addition it has previously been shown that
the EPA instrument is giving values that are 157. higher than the original
calibration curve. The signal, V, from the EPA Instrument will be used to
determine a measured equivalent absorber thickness, urn, from the original
calibration curve. These measured equivalent absorber thicknesses will be
compared to the calculated absorber thicknesses to determine an empirical
temperature relationship between the instrument response and the calculated
values for samples diluted with Ar.
A-15
-------
Table 1 lists the results of the static cell tests. The first column
lists the broadening gas. The second columns lists the results of the EPA
instrument. The third column lists the calculated absorber thickness and
the fourth column lists the ratios of um/uc. The noise equivalent u is
approximately 2 x 10"3. The values obtained for the fifth and sixth samples
in Table 1 are for small samples diluted with N2- The noise equivalent
u represents a larger percentage error than for the samples for higher
concentrations. The first three samples listed on Table 1, consequently would
give the more accurate result. This indicates the EPA instrument is giving
values of about 207, higher which agrees with the results that we obtained at
Ford prior to the UTRC tests. The seventh and eighth samples are for the
calibration test performed at Ford prior to and after the UTRC tests, res-
pectively. The last two samples are for argon as a broadener gas and the
values of um/uc are larger by about 357.. It has been shown (3) that the
broadening abilities of Ar and fh on CO are different and a similar effect
on NO might explain the observed effect above.
The results from the flowing gas heater tests are shown 'in Table 2. The
upper portion of the table shows the nitrogen carrier data, the lower portion
the argon carrier data. The left hand column list the test number; some of
the tests were repeated at a later date and consequently given the same test
number. The third column lists the temperature at the centerline of the
sample. The next column lists the centerline temperature of the curve that
was used in the calculation. The next column lists the centerline concentra-
tions supplied by UTRC. The next column lists the measured equivalent absorber
thickness, urn, in atm cmgYp» as determined with the EPA instrument. Next column
gives the calculated absorber thickness based on the probe curves given by UTRC.
The last column gives the ratio of um/uc. The lower portion of the table lists
the results when argon is used as a carrier gas.
A-16
-------
TABLE 1
Static Cell Results
Broadener urn uc um/uc
Gas (atm cm STP (atm cm, STP
xlO3) xlO3)
N2
N2
N2
N2
N2
24.0
23.5
23.6
4.2
8.5
19.2
19.2
19.2
3.64
7.56
1.25
1.22
1.22
1.15
1.12
N2 21.2 18.5 1.15
N2 21.2 18.5 1.15
Ar 24.5 18.3 1.34
Ar 24.5 18.3 1.34
A-17
-------
TABLE 2
Flowing Gas Heater Results
Test
#
20T
21 T
22 T
23 T
24 T
25 T
20 T
20 T
22A
23A
24A
25A
20A
20A
Carrier
Gas
N2
N2
N2
N2
N2
N2
N2
N2
Ar
Ar
Ar
Ar
Ar
Ar
600
Measured
296
296
608
573
723
703
296
296
678
603
793
800
295
295
9(K)
Curve
611
611
746
746
667
667
796
796
C
ppm
669
1315
1025
1850
1580
2220
650
668
1018
2047
1585
2200
\mi
atm cm STP
x!03
12.0
24.5
7.5
16.6
8.9
14.6
11.8
12.1
7.4
18.0
8.8
13.9
15.6
15.2
uc
atm cm SYP
xlO3
9.22
18.1
6.69
13.3
8.53
11.9
8.97
8.97
6.11
12.3
8.06
11.2
9.07
9.07
um/uc
1.30
1.35
1.12
1.25
1.04
1.23
1.32
1.35
1.21
1.47
1.09
1.24
1.72*
1.68*
* Window purge was most likely improperly set.
A-18
-------
The last column indicates a tendency for the ratio to decrease as the
temperature increases. The ratio for the room temperature samples are
much larger than the ratio for the samples at the elevated temperatures. The
calculated results for sample 25T may be reduced if the temperature curve,
746K were corrected to the temperature of the centerline of the sample, 703K.
It would cause the ratio to decrease coming closer to the results of sample
24T. The values obtained for the nitrogen samples tend to be lower than the
samples with argon as the carrier gas in agreement with the tests on the
static cell. The ratio for the argon sample tests also tend to get smaller
as the temperature is increased.
For the flat flame burner tests, similar type calculations were carried
out. However, the temperatures given at the centerline of the sample are not
the true temperatures of gas but the temperature of the thermocouple. These
temperatures have to be corrected because the thermocouples are radiating
thereby decreasing their temperature giving a result that is lower then the
actual gas temperature. The temperatures that were used were determined from
curves given to us by DTRC. They are shown in Figure 6. Four different
temperature profiles are represented. Listed above each curve is the corrected
centerline temperature.
These curves were determined for similar sample conditions in the flat
flame burner. However they were obtained prior to May 1978, six months before
the tests with the EPA instrument. It was assumed that they would give a true
representation of the temperature profile of the sample conditions of the present
tests. The Centerline temperatures for the present samples were slightly
A-19
-------
2000
1800
1600
1820K
1400
0)
u
OJ
CO
I*
V
£
1200
1000
800
600
400
200
Flat Flame Burner
Temperature Profile
I
I
468
Distance from Centerline (cm)
10
12
Figure
Temperature profile for the Flat Flame Burner
The centerline radiation temperature is listed for each
curve
A-20
-------
different. However, corrections to these temperature curves were made to get
representative temperature profiles. We have interpolated between the curves
for the different samples using a linear interpolation from 2966K to the
calibration curve. The radiation correction was done in the following matter:
The correction was assumed to follow the centerline temperature of the sample
raised to some power, probably near the third power. The temperature
corrections for the four different curves shown were plotted against the re-
corded centerline temperature on log-log paper. The slope of the curve gave
the exponent for the following equation:
A-A6 =-^B +^»t(e)n. (6)
From the slope of the curve, n was found to be 2.94 and by using the values
that were used to determine the curve, B was found to be 1.24 x 10" . With
the use of this equation the intermediate temperatures were corrected. Then
with the use of the computer we determined the values of the integrated u, for
the different samples. Figure 7 shows the curve determined using probe techniques
prior to May 1978 that was used for the mole fraction profile for the flat flame
burner calculations.
Table 3 lists the results for the flat flame burner tests. The second
column in Table 3 shows the uncorrected centerline temperature; the third
column lists the corrected center line temperature. The fourth column lists
the value of the measured equivalent absorber thickness as measured by the
EPA instrument, the sixth list the calculated values and the seventh column
gives the ratio of um/uc. As can be seen from Table 3 the data are grouped
into three different temperatures regions. As the temperature increases,
the tendency for the ratio is to decrease, similar to the flowing gas heater
results.
A-21
-------
01
c
C
01
u
CO
o
r-l
CO
o
2
T:
01
0)
CO
D
X
1.0
0.5
Figure 7.
Flat Flame Burner
Mole Fraction Profile
I
I
2 46 8 10 12
Distance from Centerline (cm)
Mole fraction profile for the Flat Flame Burner
A-22
-------
TABLE 3
Flat Flame Burner Results
Test
2 OF
2 IF
20FA
21FA
20FB
21FB
21FC
22FA
23FA
26FA
27FA
27FA
22FA
23FA
24FA
25FA
24FA
25FA
25FA
25FB
eoo
Uncorrected
940
935
934
939
919
919
919
1189
1180
1227
1227
1189
1189
1189
1393
1396
1381
1381
1381
1381
e(K)
Corrected
1008
1002
1001
1007
983
983
983
1325
1313
1377
1377
1325
1325
1325
1600
1615
1593
1593
1593
1593
C
pprn
1389
1954
2392
3775
3248
2293
3606
3089
4246
4018
6074
6074
3089
4246
4136
6125
4136
6125
6125
6125
1TTT1
atm cm STP
xlO3
5.8
7.8
7.2
12.0
13.0
8.2
16.0
6.0
8.5
5.8
8.5
7.2
8.4
10.8
5.1
8.5
7.5
10.6
11.8
11.5
uc
3,tffl cm STP
xlO3
6.41
9.08
11.1
17.5
15.4
10.9
17.1
10.7
14.8
13.4
20.2
20.2
10.7
14.7
12.0
17.7
12.1
20.2
20.2
20.2
um/uc
0.905
0.859
0.647
0.688
0.846
0.756
0.937
0.562
0.574
0.434
0.420
0.356
0.787
0.736
0.425
0.480
0.618
0.524
0.584
0.569
A-23
-------
TESTS AT FORD
After the tests at UTRC, additional tests were performed at Ford
that were not done prior because of tine limitations. Also tests were
performed to help explain some of the effects that were observed.
The grating box was tested by directing a beam of light through it and
into a grating spectrometer. The spectral transmittance curve of the grating
box was displayed on a chart recorder. The spectral bandpasses of the grating
box were compared to the previous spectral bandpasses and found to have been
displaced approximately 2 cm toward lower wavenumber. The displacement of
the spectral bandpasses probably resulted in the calibration shift. It
c ould have changed the response of the instrument to 1^0; however, during
our tests at TTTRC, when the H2 + Q^ burner was fired creating 1^0, no change
in signal was observed, indicating that the instrument still had good 1^0
rejection. Additional calibration tests were performed at the Ford facility
confirming the previous shift of 157. in the calibration curve from the earlier
data. The spectral transmittance curve of the correlation cell was obtained
and compared to its previous transmittance curve, and no observable difference
was noted.
There is a noticeable effect when Ar is used as a carrier or broadening
gas as compared to ^. We have observed a similar effect between Ar and
N2 with CO as an absorbing gas. N2 broadens the CO lines more than Ar. The
wings of the broadened lines would have more absorption that the wings of
less broadened lines. Because cylinders of Ar were not available to check
the effect of the broadening ability of Ar on NO, a test was performed to
A-24
-------
determine the effect of broadening the NO lines with fy- A sample of NO
at two different pressures near 1 atm was tested. A 1000 ppm NO in N2
sample at 0.7 atm in a 20 cm cell was pressurized with N2 to 1.0 atm and
the signal, V, decreased from 55 x 10~^ to 51.5 x 10"^. A decrease would
be expected because the wings of the absorption lines contribute to V as a
negative correlation, when the lines are broadened the wing absorption is
increased, thereby reducing the signal. Because Ar is not expected to
broaden as much as N2, the wings of the lines will absorb less for Ar-broadening
thereby increasing the signal.
A-25
-------
CONCLUSIONS
There is a calibration shift of approximately 15 to 20% higher from the
calibration used for the Wright Patterson Air Force tests in 1975. This is
probably due to the spectral shift of the gratin g box bandpasses of 2 cm"
toward lower wavenumber. The N2-broadened NO lines are broadened more than the
Ar-broadened NO lines and consequently absorb more in the wings of the lines.
However more absorption in the wings of the lines will cause a decrease in
the signal, therefore the samples diluted by Ar give larger signals than
samples pressurized by N2.
The ratio um/uc for the flowing gas heater tests are considerably higher
than for the static cell tests when Ar is used as the broadening gas. This is
very clear when the ratio um/uc is compared in Table 1 and Table 2 for room
temperature samples. The ratio is 1.34 for the static cell tests and 1.7
for the flowing gas heater. Personnel at UTRC indicate that the window purge
was improperly set. The difference is not as great for the samples pressurized
with N2. The N2 results are within experimental error.
Figure 8 shows a plot of the results for samples that are pressurized with
Ar. The ratio um/uc is plotted against temperature. The large difference in the
static cell tests and the flowing gas heater results is obvious. There is a
large amount of scatter in the data. The noise-equivalent u was approximately
1 x 10 atm cmgTp, 5 to 10% of the observed signal, and accounts for some
of the scatter. The use of standardized temperature and concentration profiles
rather than using a profile for each sample could add 5 to 10% to the scatter.
As can be seen from Tables 2 and 3 the centerline temperatures varied by as much
A-26
-------
2.0
i i I r
1 I I T
um
— vs temperature.
for Ar-broadened Samples.
4
1.0
• Flat Flame Burner
-J- Flowing Gas Heater
Static Cell Test at UTRC
1 I
I I
Figure 8.
looo"2000
Temperature (K)
Plot of um/uc vs Temperature for Ar-broadened samples,
A-27
-------
as 107. from the center-line temperatures of the profile curves used in the
calculation. Another source of error that could add up to 7 to 10% is
the assumption that the profiles are symmetrical. Previous data supplied
by UTRC indicate that the profiles may not be symmetrical.
A smooth curve was drawn through the points in Figure 8. The curve
shows the decrease in um/uc as the temperature increases. This apparent
change in calibration was not observed for temperatures below 900K in the
previous tests done in 1975. As can be seen in Figure 2 for temperatures
up to 900K, under static conditions, a single calibration curve could be
used. The absorption lines used in the detection of NO tend to account for
temperature changes because some of the absorption lines increase in strength and
and some decrease in strength with increasing temperature. The total strength
of the sum of the lines would then tend to remain constant over the temperature
range of interest. However as the temperature increases above 1000K the
strengths of the lines all start to decrease and the response of the instru-
ment falls off. For the subsequent tests on this contract the calibration
curve should be modified by a factor determined from the curve from Figure 8.
A similar plot for N2-broadened samples is shown in Figure 9. The
differences between the static cell tests and the flat flame burner are
not as great as for the Ar-broadened samples. In addition the difference
between the static cell tests and the flowing gas heater tests not as
apparent for ^-broadened samples.
A-23
-------
2.0
1 1 1 T
u
>e i.o
E
Figure 9.
um
— vs Temperature
uc r
for N2-broadened samples
f
-p Flowing Gas Heater
D Static Cell Tests at UTOC
Static Cell Test at Ford
I
I
I
I
1000 2000
Temperature (K)
Plot of um/uc vs Temperature for »9-broadened samples.
A-29
-------
REFERENCES:
(1) Gryvnak, D.A. and Burch, D.E., "Monitoring NO and CO in
Aircraft Jet Exhausts by Gas-filter Correlation Technique"
prepared by Ford Aerospace and Communications Corp for the
Air Force Aero-Propulsion Laboratory under contract F33615-
75-C-2038, Air Force report AFAPL-TR-75-101, January 1976.
(2) Burch, D. E. and Gryvnak, D.A./'Infrared Gas Filter Corre-
lation Instrument for Insitu Measurement of Gaseous Polutants,"
prepared Ford Aerospace and Communications Corp. for EPA under
contract No. 68-02-0575, EPA Report No. 650/2-74-094,December
1974.
(3) Burch D. E. and Williams D., "Infrared Absorption by Minor
Atmospheric Constituents" Sci. Report 1, Contract No. AF
19(604)-2633 the Ohio State Univ. Res. Fn.(1960)
A-30
-------
APPENDIX B
COMMENTS ON THE PROBLEMS IN THE PREVIOUSLY REPORTED SPECTRAL MODEL
The review of the spectroscopic model developed by ARO/AEDC revealed the
following major problems:
1. There is an error in equation 18 of Ref. B3 (the same error is reflected in
Refs. B3-B8) relating f^ " to f^ ".which is off by a factor of 4.
2. There is an error in equation 17 of Ref. B3 (and the other reports) giving
the ratio N "/NO7 which is off by a factor of about 2.
? 2
3. In Ref. Bl there was no distinction in population between the TT^ and ^3/2
states (i.e., Hund's case (b) was assumed) although this was partially cor-
rected in Ref. B3 and the computer program delivered to UTRC, but without the
correct normalization in the denominator.
4. An error exists in the equation for the Honl-London factor for Q;Q lines.
This error can be found in the text of a 1973 report (Bl) , the text of a
1976 report (Ref. B3), and the computer program delivered to UTRC in 1978.
ARO personnel have stated that this error was not always present, but they
are uncertain as to when it first appeared. The error results in a mis-
calculation of NO concentration by about 15% when considered alone, and an
incorrect temperature dependence for the absorption.
5. An error exists in Eq. 24 of Ref. B3 which relates the measured broadening
parameter to the collision cross section. This error does not affect the
predicted NO values from the model, but does result in a factor of 10 error
in the collision cross section reported in Ref. B7.
In addition to the major problems listed above, a number of minor problems
were discovered in the model delivered to UTRC which do not have much numerical
significance, but which should be corrected.
6. The Q22 (30.5) and R12 (30.5) lines were incorrectly labeled.
7. The lines Q12 (3.5), R21 (36.5), P12 (31.5) and P12 (34.5) through P12
(40.5) should be added.
8. There is an error in the equation for BV in subroutine HONNUM (Honl-London
factor computation).
B-l
-------
Finally UTRC has shown that the use of theoretically generated line locations
offers an improvement in the model when compared with the experimental line
locations as given by Deezsi (Ref. B9). This does not represent an error in the
earlier model, but does represent a considerable improvement, particularly at
low pressures or elevated temperatures.
References:
Bl McGregor, W. K., J. D. Few, and C. D. Litton, Resonance Line Absorption
Method for Determination of Nitric Oxide Concentration, Report AEDC-TR-73-
182, December, 1973.
B2 Davis, M. G., W. K. McGregor, and J. D. Few, Spectral Simulation of Resonance
Band Transmission Profiles for Species Concentration Measurements: NO y-bands
as an Example, Report AEDC-74-124, January 1975.
B3 Davis, M. G., W. K. McGregor, J. D. Few,.and H. N. Classman, Transmission of
Doppler Broadened Resonance Radiation Through Absorbing Media with Combined
Doppler and Pressure Broadening (Nitric Oxide y~Bands as an Example), Report
AEDC-TR-76-12, February 1976.
B4 Few, J. D., R. J. Bryson, and W. K. McGregor, Evaluation of Probe Sampling
Versus Optical in Situ Measurements of Nitric Oxide Concentrations in a Jet
Engine Combustor Exhaust, Report AEDC-TR-76-180, January 1977.
B5 Few, J. D., R. J. Bryson, W. K. McGregor, and M. G. Davis, Evaluation of
Probe Sampling Versus an In Situ Optical Technique for Nitric Oxide Concen-
tration Measurement in Combustion Gas Streams, Proceedings 'of the International
Conference on Environmental Sensing and Assessment, Las Vegas, Nevada, September
1975.
B6 Few, J. D., W. K. McGregor, and H. N. Classman, Ultraviolet Spectral Absorption
Measurements of Nitric Oxide Concentration in T-56 Combustor Exhaust, AIAA
Paper No. 76-109, AIAA 14th Aerospace Sciences Meeting, Washington, DC,
January 26-28, 1976.
B7 Davis, M. G., W. K. McGregor, and J. D. Few, J. Quant. Spectrosc. Radiat.
Transfer, 16, 1109 (1976).
B8 Few, J. D., W. K. McGregor, and H. N. Classman, Resonance Absorption Measure-
ments of NO Concentration in Combustor Exhaust, in Experimental Diagnostics
in Gas Phase Combustion Systems, edited by B. T. Zinn, p. 187, published by
AIAA, 1977.
B9 Deezsi, I., ActaPhysica, 9, 125 (1958).
B-2
-------
APPENDIX C
COMMENTS ON THE EXPERIMENTAL TECHNIQUE OF WISE AND FRECH
Wise and Freeh observed the amount of NO decomposition by measuring the
formation of the assumed products, N2 and 02- Molecular nitrogen was measured
by trapping the remaining NO in liquid nitrogen and using 'manometric' tech-
niques. Oxygen was allowed to react according to
NO + NO + 02 ->• 2 N02 (Ic)
The nitrogen dioxide was measured via optical absorption techniques. Several
problems with their paper and experimental procedure may be found. First of
all, no comparison is made between the No and N02 data. Secondly, no allowance
is made for alternative reactions or their products. For example, consider the
overall reactions
4NO ->• 2 Nn + 2 N02 (2c)
or
2ND ->- M20 4 1/2 02 (3c)
for which experimental data must be interpreted differently. Finally, and quite
importantly, their pressure measurement of the product N2 appears to be at
best extremely difficult. Since very low levels of conversion were examined
(usually about 0.5 percent), very small pressures of N2 are expected, typically
about one torr. In order for their technique to be useful, the nitrogen pres-
sure must be measured accurately in a background of approximately one torr nitric
oxide (vapor pressure at liquid nitrogen temperatures), one torr of oxygen (if
a product), and about 1/4 torr impurity (likely to be nitrogen). Certainly, a
measurement of one torr nitrogen with these other gases present would not be an
easy task. If the dominant impurity in the initial NO is N02 rather than N2 or
N-0 (stated purity is 99.93 percent NO), then a measurement of 0.5 percent de-
composition would be in error by (.07 percent) x 2/.5 percent = 28 percent when
the N02 data is interpreted.
C-l
-------
APPENDIX D
UTRC SPECTRAL COMPUTER PROGRAM DESCRIPTION AND LISTING
D.I. Program Description of NO Absorption of Continuum Radiation
D.I.a. Introduction
Several different versions of the NO spectral model have been developed.
All of these are based on the model developed by Davis et al (1976)a and sup-
plied to us, with corrections and additions made by us as noted in Appendix B.
The plot routines are substantially different. The corrections made to the
original program developed by Davis et al (1976a) make a significant differ-
ence in the amount of NO necessary to produce a given amount of absorption -
about a factor of 2 at room temperature and atmospheric pressure.
The different versions of the NO spectral model may be summarized as
follows. The absorption of continuum radiation by a homogeneous, isothermal
layer of NO diluted in a foreign gas is modeled by the program (DUSEK*)NO-ABS
(described in D.I.), in conjunction with the plot routine (DUSEK*)PLOT.
PLOT5 (detailed in D.IV.) and the data file (DUSEK*)DATA-2. or (DUSEK*)DATAENG.
The similar problem for absorption of continuum radiation by multiple zones,
each of which is homogeneous and isothermal, is treated with two programs not
described here, (PAGE*)NO-ABS. and (PAGE*)PLOT., along with the data file (PAGE*)
DATA-2. The multiple zone includes the proper accounting of the complete line
profile through the different absorbing layers before convolving the resultant
with the slit function. The model describing the absorption of narrow-line
radiation is called (DUSEK*) NO-SPECT. (described in D.II.), with the same plot
routine and data files as for (DUSEK*)NO-ABS.
The program NO-ABS. predicts the transmission as a function of wavelength
of incident continuum radiation by a known optical depth of nitric oxide at a
given temperature and pressure. This program was written specifically for pre-
dicting transmission in high resolution over a narrow wavelength region. An
additional program, PLOT., convolves this predicted transmission with a spectro-
meter slit function and displays the results graphically for comparison with
experimental spectra.
The program NO-ABS. is composed of a main program, four subroutines, and
a block data file. The program elements for the main body and the block data
are NO-ABS.MAIN and NO-ABS.BLOCK-DATA, respectively. The element names of
the subroutines are FUPPER, FLOWER, HONNUN, AND WFUNC. Each of these names
is preceded by the file name NO-ABS, as before. A definition of variables
for each element of NO-ABS. and a listing of the elements are included at the
end of the program description section.
D-l
-------
D.I.b. Main
The main program is divided into four parts. A description of the function
of each part follows.
Part One reads parameters such as the optical depth, temperature, pressure,
broadening information, options for line location, region of interest and a
code that describes the version of the program presently in use. The options
available for line location include either a theoretical calculation of line
center or the use of experimentally determined line center wavenumbers. The
experimental values for the line center wavenumbers were obtained from Engleman
et al (1970). Theoretical line locations using spectroscopic equations and
constants for NO (Engleman) yield predicted locations that differ from experi-
mental observation by less than the room temperature Doppler width of NO
(.005 & or .0005 nm) for almost all lines. The wavenumber region of interest
is defined by the first and last line numbers of that region. The present
version of the program reads 474 lines. Normally. 1 to 30 of these lines
are examined in a given run. Also contained in Part One of the main program is
the assignment routine for the f -number of the transition. Since experimental
evidence indicates that transitions originating in the ^T]/2 state have a larger
f-number than those originating in the ^3/2 state, provision has been made for
a spin dependent f number.
_D.I_.b._2._Main,_Part 2
Part Two of the main program reads and decodes the input line designation.
The line designation consists of the branch of the transition (P, Q, R for
J'-J" = -1, 0, +1), upper spin state, lower spin state, and the rotational
level in the lower state. The upper electronic state is slightly split (spin
split) into two levels by a weak interaction of the electron spin with the
magnetic field generated by the spinning molecule (and other effects, Ref .
Herzberg 1939) . Absorption transitions terminating in the J = K - 1/2 level
are designated with a 2, while those terminating in the J = K + 1/2 level are
assigned a 1. A similar system is used to define the level of the lower elec-
tronic state in which a transition originates. The lower state ( TT) is strongly
split by spin-orbit coupling. The separation of the spin 1/2 and spin 3/2
* 1 7
levels is ^120 cm . Transitions originating in the lower energy T]/2 state
are assigned the value 1, while those originating in the higher energy ^
state are assigned a 2.
Thus a line with J = 10.5 and K = 11 in the upper electronic state and
with J = 11.5 in the lower spin energy level of the lower electronic state
(i.e. ^1/2) would be labelled P21 (11.5). From the above discussion it can
be seen that' in general an absorption transition originating from a given J
value can terminate in any one of twelve possible systems, since there are
three branches and four possible combinations of levels for each branch.
D-2
-------
Also found in Part Two is the calculation for the line center absorption
coefficient, KO(I). The variable I is incremented by 1 as each line center
absorption coefficient is calculated. (At this stage, KO(I) does not contain
the path length over which the absorption takes place). In determining this
coefficient the three subroutines FUPPER, FLOWER, and HONNUM are accessed to
determine the upper state energy, lower state energy, and the Honl-London
factors, respectively, for the transition. Also at this time, the line location
option is queried. If the theoretical line option was selected, the line
center transition wavenumber (WO(I)) will be given by the difference of the
upper and lower state energies resulting from FUPPER and FLOWER. If the experi-
mental line location option was requested, then the wavenumber read with the
line designation is used for WO(I) .
Part Three of the program establishes the wavenumber region in which the
transmission calculations are done. The wavenumber region will begin 2.0 Lorentz
widths and 2.4 Doppler widths (DELTAW) before the line center wavenumber of
the first line selected and will end an equal amount, DELTAW, after the line
center wavenumber of the last line selected. The region defined by these
start and stop wavenumbers is divided into 499 panels. The transmission is
calculated at the wavenumber of each of these panels. The transmission is
obtained for a panel from Beer's Law, I = IQe v The absorption coefficient
kv is determined by summing the absorption coefficients at the panel from all
spectral lines which contribute significantly to the transmission at that
panel's wavenumber. To determine if the absorption at a panel from a given line
is significant, its contributrion to kv is divided by the total absorption coef-
ficient determined from all lines previously examined at that panel. If this
quotient is less than a value given to the variable ALLOW, a counter (NHOLDER, NHOLDL)
is indexed. This counter is reset to zero if the quotient becomes greater
than allow. When the counter value increases to three (indicating that the
Allow condition has been met three times consecutively) the transmission cal-
culation will advance to the next panel. The consecutive stipulation reduces
the chances of exiting the coefficient loop when encountering an isolated weak
line. In addition to the ALLOW check for the absorption contribution, the
loop cannot be terminated if the absorbing line's center wavenumber is within
DELTAW from the, panel being examined. The absorption coefficient must frequently
be evaluated at some distance from line center. For the Voight profile used,
this value (k . ) is related to the line center absorption coefficient kv . by the
vi 1
expression
kvi = kv° Re
,2>
exp(-(ui + ia'r) erfc(-\)i + a') j Dl
D-3
-------
where
Re = Real Part
o,
D2
AvD
o
v. = line center wavenumber
v. = wavenumber
Av_ = Doppler width of the line
= Lorentz width of the line
erfc = complementary error function
The expression for 1^. is evaluated in the subroutine WFUNC.
When the transmission calculation has been completed for all 499 panels
the program advances to Part Four.
The function of Part Four of the main program is to record the inputs of
Part One and each panel transmission and wavenumber on a temporary file for
later use by another program (PLOT.). The entire program MAIN will be repeated
for each NO concentration. When an end-of-file is detected in the input data
file DATA-2, the main program will terminate.
D.I.c. Input File DATA-2
In order to facilitate changes in the input parameters such as path-
length, gas temperature, and NO concentration, these values are placed in a
data file named DATA-2. This file also contains the spectral line information and
selections for the various options. Since DATA-2. is also used as an input to
a resonance absorption program (NO-SPECT.), some of the entries in DATA-2. do
not apply to NO-ABS. A partial list of DATA-2. with appropriate definitions
follows in Table D-I.
More concentrations can be added to the end of DATA-2 if desired. The
numbers appearing after the spectral line designation are the center wavenumber
of the transition as reported by Deezsi (1958). Many of these lines were not
-------
TABLE D-I
O
1234567
045
100
001
45100
45478
48500
9 10 11 12 13 14 15 16 17 18
column
A
6
1
2
F = 3
' 6
5 9 5
800
600
1 8 .
1 0 .
0
3 0 5 + H +
0
4
4
Variable
LINST
LINEND
NWOTHE
HEADS
APRIME
TA
EL
Comments
Integer
Integer
1, Theoretical Lines
0, Experimental Lines
Does Not Apply
Blank line
Version Code
Does Not Apply
Function of pressure,
temperature, broadening
constant
Degrees K
Does Not Apply
Path Length (cm)
Does Not Apply
0
0
4
1
2
3
4
5
P
P
P
P
P
1
1
1
1
1
2
2
2
2
2
( 1
( 1
(
( I
<
0 .
1 .
9 .
2 .
8 .
5 )
5 )
5 )
5 )
5 )
4
4
4
- 4
4
4
4
4
4
4
0
0
0
0
0
5
5
5
5
5
2
2
2
2
2
0
0
. • 0
7
7
3
3
3
8
8
7 4 R 2 1 ( 3 9
5 )
6953
1 5
First Spectral Line
Second Spectral Line
Third Spectral Line
Fourth Spectral Line
Fifth Spectral Line
474th Spectral Line
Blank line
No Nitric Oxide
1st Nitric Oxide
Concentration
-------
resolved by the instrument used; hence several different lines may appear at an
identical wavenumber. More highly resolved values for the line center wave-
numbers are available in Engleman et al (1970). Another input data file with
Engleman's experimental line locations exists in file DATAENG. This list
does not contain nearly as many lines as DATA-2. am' is only a partial tabulation
of all the lines listed in Engleman et al. Choosing the theoretical line
locations (i.e. placing 001 in line 3 of DATA-2.), while using DATA-2. will very
nearly reproduce all of the experimental values available in Engleman, et al.
A partial list of the difference between Engleman's experimentally measured
line center values and those derived theoretically can be found in Fig. Dl.
The differences are generally less than the room temperature Doppler width of
o
NO (.055 A or .0005 nm). At high rotational values, the theoretical locations
for the ?22 lines systematically diverged from the experimentally measured values.
For highest accuracy, lines should be arranged from lowest to highest energy
(increasing wavenumber).
D.I.d. NO-ABS. FUPPER
The purpose of this subroutine is to calculate the upper state energy
of the Y(0,0) transition. The equations and constants used are the same
as those described in the text see Section III-B.6.d.
D.I.e. NO-ABS. FLOWER
This subroutine calculates the lower state energy for a y(0,0) transition.
The equations and constants used are the same as those described in the text
see Section II-B.6.C.
D.I.f. NO-ABS.WFUNC
Subroutine WFUNC calculates the off-line center fractional absorption
coefficient (kv./ky9) for a particular spectral line. This is accomplished by
determining the real part (Wl) of the function.
W(z) = exp (-z2) erfc (-iz)
where i = \/-l
z = ^j + ia' (See NO-ABS Main, Part 3).
The technique for evaluating this function is taken from Abramowitz et al. MBS
Handbook of Mathematical Functions. There are basically two methods used to
determine Wl. If either ujj or a' are in the intervals
0 * wj ± 3.9
or
0 < a' < 3.0,
D-6
-------
THEORETICAL (EUPPER-ELOWER) VERSUS EXPERIMENTAL LINE LOCATIONS
i
o
ft.
to
' U
I
o
oc
LU
Q_
X
LU
3
I
o
H
LU
CE
O
e.4-1
e.2H
8.8-i
jE -8.2
3
-6.4
DOPPLER
WIDTH
18 15
(J-0.5)
26
25
38
p
o
-------
,
the value Wl is obtained by a two-dimensional linear interpolation from the
nearest Wj and a' values found in the block data table BLOCK-DATA (see Davis
et al (1976) for listing). This table consists of a 31 by 40 by 2- array whose
elements are labeled by z(Al, Bl, Cl) where Al corresponds to a1, Bl corres
sponds to UK,, and Cl corresponds to the real or imaginery part of W(z) i.e.,
Wl or W2.
The element z(ll, 3, 1) is the real part of the function w(z) evaluated
f or z= 0.2+1. 01, while the element z(ll, 3, 2) is the imaginery part of
the same function and argument. Conversion of the arguments of z to a table
element is accomplished by taking the integer portion of ten times the argu-
ment value plus one. This procedure yields 31 real values for a', and 40
real values for w^ since each is evaluated in increments of 0.1 over the
regions previously defined. For example, to locate the real part of u(z)
for z = 0.2 + 1.0 i, the element Al is found by multiplying 1.0 by ten,
adding 1 and taking the integer portion of this sum. Thus Al for a' equal to
1.0 is 11, and similarly Bl for to. equal to 0.2 is 3. Therefore the real
part of W(z) will be found in the table element z(ll, 3, 1). When the argu-
ments of z = tOj + a'i are nonzero beyond the first decimal place, this tech-
nique automatically results in the nearest table element less than the desired
value. The nearest table element greater than the desired value is obtained
by adding one to the values Al and Bl just found. From the table elements
found at these element locations, the two-dimension linear interpolation
approximates the desired value of W(z) .
For values of u-j and a' greater than 3.9 and 3.0 respectively, polynomial
approximations for W(z) are used. For tU and a' in the intervals
3.9 < 0)^ < 6.0
or
3.0 < a1 < 6.0
W(z) is given by
W(z) = iz (T1+T2+T3) + e(z)
where TX = .4613135/(z2 - .1901635)
T2 = .09999216/(z2 - 1.7844927)
T3 = .002883894/(z2 - 5.5253437)
and
|e(z) I < 2 x 10~6.
D-8
-------
When either w- or a' is greater than 6.0, W(z) is given by
W(z) = iz (Tl 4- T2) + n(z)
where Tl = .5124242/(z2 - .2752551)
T2 = .05176536/(z2 - 2.724745)
and
n(z) | < 10~6.
The last part of this subroutine is devoted to evaluating W(z) when
either or both arguments of z are negative. In practice, the evaluation for
negative argument is not needed. Likewise, for this application all the ele-
ments of the block data table labeled z(Al, Bl, 2) are never used since these
correspond to the imaginary part of W(z).
D.I.g. NO-ABS. HONKUM
Subroutine HONNUM calculates the normalized Honl-London factor for deter-
mining the intensity of a given transition. The equations are normalized such
that the summation of the Honl-London factors over all the upper state J values
(JT) for a given lower state J value (J") equals 4(2J"+1). In general, inten-
sities of absorption transitions originating in the J = 1/2 rotational level
must be considered separately (Earls (1935))- These intensities are
Q21 = Qn = 4/3
R21 = Rn = 2/3
All other branches are identically zero. In nitric oxide, the spin-orbit
coupling constant is so large that the intensities of lines connected to
the J = 1/2 level are correctly predicted to at least eight significant digits
by the general expressions given.
D.II. Program Description of Resonant Absorption of NO Radiation
The program NO-SPECT.predicts the fractional transmission of radiation
through a gas mixture containing a known amount of nitric oxide. The inci-
dent radiation is obtained from excited nitric oxide molecules at low pres-
sure. The program construction and description of NO-SPECT.is very similar
to the program NO-ABS.previously discussed. The differences are contained
D-9
-------
mainly in defining the spectral distribution of the incident radiation. For
NO-SPECT. the incident intensity is obtained from an experimental measurement
of individual spectral lines emitted by the source and from an assumed Doppler
broadened line shape. The transmission is calculated on a line by line basis.
Each source spectral line in the selected wavelength region is divided into
100 panels starting 2.3 Doppler widths (DELTAW) before line center and ending
an equal amount beyond line center. The incident intensity at a given panel
is found by assuming a Gaussian lineshape of known full width at half maxi-
mum (FWHM) centered on the center wavenumber of the transition. The relative
maximum intensity of the source line is obtained by linear interpolation from
a table of experimentally derived intensities that have been normalized by
the respective Hbnl-London factor of the measured line. This table is con-
tained in the data file DATA-2 in lines 4, 5, and 6. See discussion of FUNC
for more information on source line strength. The absorbing line's strength at
each panel is determined in a manner identical to that described in the discus-
sion of NO-ABS.
At the completion of NO-SPECT., the integrated intensity of each lime
leaving the absorbing gas is recorded on a temporary data file. The line
intensities are recorded with each line's center wavenumber in groups for each
concentration of NO listed at the end of the data input file DATA-2. This
information is read into another program, PLOT, that convolves these lines
with a spectrometer slit function and displays the results graphically.
An additional section exists at the end of NO-SPECT.MAIN Part Three that
outputs the integrated fractional transmission of very closely spaced line
groups. This option cannot be accessed by the input data file DATA-2. To
obtain output from this option the mandatory GO TO statement (GO TO 560) must
be removed from the program. These cluster transmissions are required for
determining source characteristics.
All subroutines used for NO-SPECT. are identical with those described in
NO-ABS. An additional subroutine (NO-SPECT. FUNC) is required for source line
intensities (see D.II.a below).
Additional variable definitions for variables found only in NO-SPECT. and
a figure (Fig. D-2) further describing the model's operation are found in the
variable definition section.
D-10
-------
D.I.f. NO-ABS FUNC
To predict the amount of transmission of resonant radiation through a gas,
the relative source intensity at each line must be known. Many times there
are overlapped lines or lines which cannot be resolved by the spectremeter and
whose intensities are not directly measurable. This subroutine linearly inter-
polates all line intensities from a least squares fit of normalized resolved
lines whose intensities can be directly measured. For electrical discharge
lamps, a log-linear plot of the measured spectral line intensities divided by
their respective Honl-London factors versus the line's upper state energy will
typically result in a curve shown in Fig. 20. For our purposes this curve
was fit with two straight lines. The intensity of any spectral line can now
be approximated from these two straight lines once the upper state energy and
the Honl-London factor for the trasition are known.
D-ll
-------
CONVOLUTION SYMBOL DEFINITIONS
(-•
S3
u
01
-RESONANT LAMP LINES
4 ' (DLAM-|XLAM-\1/DLAM)
5
-H
PI ANG(5)
I-[((XLAM-X)/DLAM]-1.66512)2)
t
10
ANG(6) P1
XLAM
DLAM
P2 ANG(10)
1
11
•
12
1—
3
NOTE: LINE NUMBERS
ARE ARBITRARY
•WIDE-
(GAUSSIAN)
•WIDE-
(TRIANGULAR)
SLIT FUNCTION
GAUSSIAN ( )
ISTART = 5
NOPTS= 8
P2 WAVELENGTH(X)
TRIANGULAR (
ISTART = 7
NOPTS = 3
Tl
P
O
to
-------
D.III. List of Symbols
MAIN (NO-ABS)
G(n)
QVIB
ALLOW
LINST
LINEND
NWOTHE
XDATA(I)
YDATA(I)
NP
HEADS
AP
TA
TE
EL
YHGT
BVEQ0
AFL
C1S12
- Vibrational energy of nth vibrational level
- Vibrational partition function
- Ratio of absorption coefficient for a given line to total
absorption coefficient from all previous lines at a parti-
cular wavenumber
V
- Line number of first spectral line defining start of interval
to be examined
- Line number of last spectral line to be examined
- Conditional branch variable to select theoretically-computed
line locations (=1), or use experimentally-determined line
locations (=0)
o
- Wavenumber array of resolved upper level (I) source spectral
lines
- Normalized logarithmic intensity array of resolved source
spectral lines
- Number of source lines used to characterize source output
- Version label
- Broadening parameter (a1)
- Absorber temperature
- Emitter temperature (applies only to NO-SPECT.)
- Path length of absorption
- Records option taken for variable NWOTHE
- Spectroscopic constant for the zero vibrational state
- Spin orbit coupling constant for lower level
- f number for transitions connected to the ^
1/2
D-13
-------
C1S32
- f number for transitions connected to the ^3/2 level
C2 - hc/kTA
CONST1 - -2>/£n(2)
CONST2 - Doppler width of source divided by line wavenumber
(2/2(£n2) kTU/inC2)
LJ S
CONST3 - Doppler width of absorber divided by line wavenumber
(/ITInT) kTA/msC2)
CONST4 - 2.3 • (CONST2)
J - Spectral line position in array of spectral lines input, (not
the rotational level)
RJPP - Rotational level (truncated integer)
JPP - Rotational level (truncated integer)
BRANCH - Rotational branch (P,Q,R)
ICODE - Rotational branch (=1, P, branch, = 2 Q branch, = 3 R branch)
NUP - Spin split state in upper level (2£)
•j
NLO - Spin state in lower level ( TT)
WO(J) - Line center wavenumber of line number J
ISPIN(J) - Array of lower spin states for all spectral lines in input list
S(J) - Honl-London factor of the Jth line
NLINES - Total number of spectral lines read from input list
ENO - Nitric oxide concentration (molecules/cm )
KO(I) - Line center absorption coefficient of Ith lines
NINT - Wavenumber range of interest is divided into this many panels
(max. 499)
DWJ - Doppler width of source
D-14
-------
DWL
DELTAW
WST
•WND
AZJ
BZJ
DEL
JLEFT
SUML
SUMR
NHOLDR
NHOLDL
NLESR
NLESL
BETA
WFUNC
Doppler width of absorber
2 Lorentz widths + 2.4 Doppler widths absorber (cm"1)
Wavenumber at beginning interval of interest
Wavenumber at ending interval of interest
Lower wavenumber limit of mandatory computation for
given spectral line
Upper wavenumber limit of mandatory computation for a given
spectral line
Incremental wavenumber of panels in region of interest
Center wavenumber of Ith panel
Source intensity of Ith panel (constant)
4> when examining lines of larger wavenumber than present
panel; = 1 when examining smaller
Total absorption coefficient from all lines of wavenumber
greater than, or equal to, nearest spectral line
Total absorption coefficient from all lines of wavenumber
less than, or equal to, nearest spectral line
Number of consecutive lines whose contribution to the total
absorption coefficient is less than minimum required
Number of consecutive lines whose contribution to the total
absorption coefficient is less than minimum required
Number of consecutive lines whose contribution to the total
absorption coefficient is less than minimum required
Number of consecutive lines whose contribution to the total
absorption coefficient is less than minimum required
- 2/£n2 (v•-v! V(Doppler width of absorber)
Complex complementary error function to determine absorption
coefficient at arbitrary distance from given spectral line
(fraction of line center absorption coefficient)
D-15
-------
TERM
TNEW
II
CAY(I)
DAT(I)
TAUTOP
TAUBOT
TAU
ALPHA
W02(I)
TJ2(I)
FUPPER
V
J
M
T
G
WE
WEXE
BE
ALPHAE
DV
- Absorption coefficient at arbitrary distance from given spectral
line (fraction of line center absorption coefficient)
- Absorption coefficient at arbitrary distance from given
spectral line
- Rotational level
- Total absorption coefficient for the Ith panel from all
spectral lines considered
- Intensity of Ith panel after passing thru absorbing gas
- Total transmitted intensity
- Total incident intensity
- Ratio of transmitted intensity incident intensity
- Ratio of absorbed intensity to incident intensity
- Reordered panel wavenumber, largest to smallest
- Reordered panel transmissions (see W02(I))
- Vibrational level
- Rotational level
2
_ Spin split level in upper state ( E level)
- Term value of electronic level
- Term value of vibrational level
'Ve
- D
D-16
-------
BV
- B,
GAMA - y
FN - Term value of rotational level
F - Term value of upper state ( Z level)
FLOWER
V
J
M
USS
T
G
DV
A
BE
BV
WE
WEXE
IB
NSIGN
LMDADB
F
- Vibrational level
Rotational level
Lower spin state ( TT level)
i-\
Spin split level of upper state (ZL level)
- Term value of electronic level
- Term value of vibrational level
- DT
- Lower state spin-splitting constant
- BT
level)
- B.
v
WFUNC
XF
- W
- Rotational branch
- Direction of lambda doubling shift
f~\
- Magnitude of lambda doubling term in lower state ( IT level)
n
- Term value of lower level ( IT)
- Same as BETA (MAIN .NO-ABS)
D-17
-------
YF - a' (Broadening parameter)
Wl - Interpolated real part of the complex function W(z) where z = XF + YF i
WZ - Interpolated imaginary part of the complex function W(z)
Z(DUM1,DUM2, 1) - Real part (W(DUM2 + (DUMl)i))
Z(DUM1,DUM2, 2) - Imaginary part (W(DUM2 + (DUMl)i))
X(DUM) - Real Tart of W(z) (Table Value)
Y(DUM) - Imaginary part of W(z) (Table Value)
IFLAG - Conditional branch variable whose value is
<(> -».when - XF > YF >
I when XF < $, YF >
4 when XF < <£, YF <
II - Converts YF into an integer - 1 (Lower bound in table look-up
for YF)
JJ - Converts XF into an integer - 1 (Lower bound in table look-up
for XF)
III - II+l upper bound in table look-up for YF interpolation
JJ1 - JJ+1 upper bound in table look-up for YF interpolation
Zl - Linearly interpolated value for XF with Y=CONST=II
Z2 - Linearly interpolated value for XF with Y=CONST=II1
W(l) - Interpolated real value of W(XF+YF i)
W(2) - Interpolated imaginary value of W(XF+YF i)
ZC - z - XF+ YFi (complex) = argument of W function
HONNUM
NUP
NUPP
MEGAN
- Upper vibrational state (v1)
- Lower vibrational state (v")
- Upper spin state
D-18
-------
MEGAM - Lower spin state
IB - Rotational branch
J - Lower rotational level
A - Lower state spin-splitting constant
BE - Be
ALPHAE - ae
BV - Bv
RNUM - Numerator of Honl-London factor
DENOM - Denominator of Honl-London factor
HONL - Honl-London factor for transition
MAIN (NO-SPECT)
XDATA(I)
YDATA(I)
TE
CONST2
CONST4
EO(J)
NINT
W(I)
E(I)
DIST
- Lower state wavenumber of source spectral line
- Natural logarithm of resolved source spectral line
intensity normalized by the Honl-London factor of
the transition
- Source Temperature
- Doppler width of source divided by line wavenumber
- 2.3 times CONST2
- Line intensity of Jth source spectral line
- Number of calculations (panels) performed over a single
source spectral line
- Wavenumber of Ith panel of a given source spectral line
- Intensity of Ith panel of a given source spectral line
(Gaussian shape assumed)
- 4.6 Source Doppler widths FWHM
D-19
-------
TAUTOP - Integrated intensity of lines passing through the
absorbing gas
TAUBOT - Integrated intensity of lines incident on absorbing gas
FUNC
X - Wavenumber of upper level transition of line of interest
XDATA - Wavenumber array of resolved upper level transitions for source
YDATA - Natural logarithm array of normalized resolved source
line intensities
NP - Number of points used to characterize source line intensities
NP1 - NP minus 1
FUNC - Linearly interpolated normalized natural logarithm of the
intensity of unresolved source line
D-20
-------
D.IV. Program Description PLOT.PLOT5
D.IV.a. Introduction
The program PLOT. PLOTS convolves the spectral transmission calculated in
programs NO-SPECT. and NO-ABS. with a spectrometer slit function to aid in
reducing experimental data. Results of the convolution are presented graphi-
cally.
The program is divided into four parts. A discussion of the function
of each part is presented in the following section.
D.IV.b. Discussion
(hie
Part One of the program reads the transmitted intensity and wavenumber
at each wavelength present in the radiation source. For resonant radiation
(NO-SPECT.), these wavenumbers are the center wavenumbers of each line.
The transmissions at these wavenumbers are the integrated intensities of
individual lines (i.e., the transmission verses wavenumber is nonzero only
at the center wavenumber of the transition; no direct information on line
shape is contained in these transmissions) . For absorption from a continuum
source (NO-ABS.), the wavenumbers read are uniformly spaced throughout the
region of interest. In this case, the original lineshape of the absorbing
line is retained. Original input parameters for NO-SPECT. or NO-ABS. are
read for documentation purposes on the plots. Options are presented for
plotting the data as read (zero slit plots) in addition to the -convolution
plots generated by PLOT. PLOTS. At this time, the user is also queried for
the slit width of the convolution. The slit width is defined as the apparent
full width at half maximum transmission (FWHM) of a resolved line in the
experimental spectra. The slit width must have units of angstroms (A). Part
One continues with a conversion of the original wavenumbers to wavelengths.
Since line order (increasing wavelength) is assumed in the construction of
later parts of the program, Part One contains a sorting loop (ISORT) which
looks twenty lines ahead of the present line location to resort lines
and intensities for continually increasing wavelength.
Tw
Part Two produces plots of the data as received after the line sort
operation described in Part One. A vertical line is drawn at the location
of each wavelength initially read. The relative heights of these vertical
lines are proportional to the spectral intensity read at each wavelength.
These plots are referred to as zero slit plots, since no instrument broaden-
ing has been included. It should be reemphasized that plots for resonant
absorption (NO-SPECT.) do not retain line shape information. Zero slit
D-21
-------
plots for resonant absorption, and absorption of continuum radiation are
shown in Figs. D3 and D4, respectively. Part Two also sets the convolution
interval (T,'IDE) for Part Three.
D-RM^S JPart Three
Part Three computes the resultant intensity verses wavelength when the
individual intensities are examined by a measuring intrument (spectrometer)
of finite resolution. The transfer function of the spectrometer can be
determined by scanning and examining the resultant profile of a spectral line
whose bandwidth is very narrow relative to the spectrometer's bandpass. For
the spectrometer used in our measurements, the transfer function can be
approximated as a triangular function for bandpasses greater than 0.5 A and
by a Gaussian function for bandpasses less than 0.5 A (Figs. D5 and D6) . To
produce the convolved spectral plots, a wavelength region starting twice the
convolution interval (2'WIDE) before the wavelength of the first spectral
line and ending an equal amount after the last spectral line is divided into
2499 panels. At each panel, a convolution interval is defined (WIDE) whose
width is twice the spectrometer slit function for the triangular case and
six times the slit function for the Gaussian case. This convolution interval
is centered on the panel at which the calculation is being performed. Beyond
this interval, the contribution to the convolution is considered to be zero.
A loop is set up to determine the first spectral line number (ISAVE) and
total number of spectral lines (NOPTS) within the convolution interval.
Starting at spectral line number ISAVE, the intensity of each of the next
NOPTS lines is weighted with a Gaussian or triangular function according to
the relation.
TRIADD = HT(JBL) exp (- [(XLAM-ANG(JBL))/DLAM • 1.66512]2)
or
TRIADD = HT(JBL) [DLAM- | xLAM-ANG(JBL)|] /DLAM
where TRIADD is the weighted intensity, HT(JBL) is the original line inten-
sity, DLAM is the FWHM of the spectrometer in angstroms, XLAM is the panel
wavelength at which the convolution is taking plare and ANG(JBL) is the
wavelength of the spectral line being weighted. Figure D2 presents symbol
definitions graphically. Weighted intensities at the edge of the convolu-
tion interval for the Gaussian case are down by more than 10" relative
to the same intensity at the center of the interval. The weighted intensities
over the entire convolution interval are summed under the variable name
SUMMER. When the sum is completed, the value of SUMMER is placed in the
array PLOTY (KKOUNT) and the center wavelength of the convolution interval
is placed in the array PLOTX (KKOUNT) where KKOUNT is the panel number at
D-22
-------
ZERO SLIT WIDTH PLOT FOR RESONANT LINE SOURCE
ID
O
t.
I
JO
END = .000
ZERO SLIT WIDTH
02 LIN X2+F=4 T
TE
TA
A
399. K
1000,. K
18.6 CM
seeee
2210 2220 2230 2246 2250
>260 2270 2280"
(nmx 10)
O
CO
-------
ZERO SLIT WIDTH FOR CONTINUUM SOURCE
o
I
t J
NQ = 8909+16
ERO SLIT WIDTH
F=3.395+H+C
Tft = 295. K
8.6 CM
84799
«..
¥
-------
SPECTROMETER TRANSFER FUNCTION, 1000/um SLITS
TRIANGLE, FWHM = l.uA (0.114nm) (USED IN COMPUTER)
EXPERIMENTALLY OBSERVED
GAUSSIAN, FWHM= 1.225A (0.1225nm) (FOR COMPARISON)
o
NJ
(D
!
o
I
10
D
01
-------
SPECTROMETER TRANSFER FUNCTION, 100jum SLITS
o
i
EXPERIMENTALLY OBSERVED
GAUSSIAN, FWHM = 0.174 A (0.0174nn
P
O
at
-------
which the calculation was performed. The weighting and summing process is
repeated for all 2499 panels. The maximum value in PLOTY (KKOUNT) is
assigned to the variable SPM&X and the first value of SPMAX (no nitric
oxide) is assigned to the variable DIV. The variable DIV is divided into the
intensities of each panel for each concentration to normalize the maximum
peak height to unity for plotting purposes. The remaining sections of Part
Three write the values of PLOTX and PLOTY into a temporary storage file and
reread this file for display purposes when all spectra for each nitric oxide
concentration have been calculated. This file is also used for wavelength
scale expansions; no new calculations are done when a scale expansion is
requested. Sample convolved outputs for a continuum and a resonant absorption
case are shown in Figs. D7 and D8. Numerical values for features in the con-
volved spectra can be obtained utilizing Part Four of PLOT. PLOTS.
Part Four produces the numerical value of extrema on each concentration
curve for a given wavelength range. This option is accessed by a carriage
return after the completion of the convolution plots. The wavelength of
the start of the extrema interval is assigned to the variable XSTR and the
end to XSTP. The minimum and maximum values and their wavelengths within
this interval are determined. The extrema of the first case (no nitric
oxide) are used to normalize the extrema of following cases. This results in
the fractional value of the extrema for each curve in the specified interval.
The extrema, fractional extrema, extrema wavelengths, and concentrations are
presented followed by a request to determine if another region is to be
examined. A response of ' NO1 (include blank before word NO) will terminate
the program. A sample of this option is included in Fig. D9.
D-27
-------
CONVOLUTED SPECTRUM FOR CONTINUUM LAMP, SLIT FUNCTION FWHM = 0.020A
o
I
oo
1.25-n
1 09-
0.75-
0.50-
0.25-
0 00
TA = 295. K
L = 18.6 CM
A = 5.84700
DLAM= .0200
* F=3.305+H+C
GAUSSIAN LNSHPTHEOR. LINES
+16
T
T
I
I
I
T
10
u
I
01
1 I ' I
2265.2 2265.6 2266.0 2266.4 2266.8
2265.4 2265.8 2266.2 2266.6
WAVELENGTH, A
(nm x 10)
P
O
-------
CONVOLUTED SPECTRUM FOR RESONANT LINE SOURCE, SLIT FUNCTION FWHM = 1.60A (0.16nm)
o
in
I
o
u
I
199 -i
88 —
66 —
?!
« 306. K
= 1800. K
= 18 6 CM
50900
DZ LIN X2*F=4 ,T
TRIANG
MAXIMUM
NO HEIGHT, IN
.000 1.00
900>16 44
WAUELENG.TH, A
(nm x 10)
TAU
1 080
512
O
CO
-------
EXTREMA DISPLAY
DO VOU UAHT EXTREHA?
>YES
DEFINE INTERVAL.
>8865.7,2865.85
H8/08/A 3F A-1.1
o
o
WIN- .9992 AT 8865.764
RAX- !.•••• AT 2265.?••
NIN- .5853 AT 8865.763 RAX- .9858 AT 8865.699
HIN RATIO- .5858 RAX RATIO- .9858
DO VOU UAHT EXTRENA?
> YES
DEFINE INTERVAL.
>3265.85,8266.
H8/08/A 3F A-1.1
CNOD • NONE
CN03 • CORB
NIN- .9991 AT 8865.881
HAX- .9998 AT 8865.983
NIN- .6464 AT 2265.926 NAX- .9859 AT 8865.849
NIN RATIO- .647t NAX RATIO- .9858
CN03 - NONE
• com
8
o
u
I
DO VOU UANT EXTRENA?
>NO
H2/02/A 3F A-1.1
P
a
(O
-------
D.IV.d. List of Symbols
PLOT.PLOT 5
NCASE
ISTART
DATE1
TIME1
STMAX
XMIN
XMAX
DLAM2
IPLT1I
PLTMIN
PLTMAX
YHGT
NLINES
ENO
TE
TA
EL
APRIME
TAU
HEADS
counter for concentration case
flag for no NO concentration (equals 1 for NO = 0.s
0 for NO + 0.
date of run
time of run
maximum line intensity
minimum wavelength to be plotted
maximum wavelength to be plotted
slit function of spectrometer in angstroms (FWHM)
option for plots, 1 for zero slit plots
0 to delete zero slit plots
same as LINST
same as LINEND
indicates method of obtaining line locations for data
(YHGT equals 1 for theoretically computed line locations
and 0 for experimentally measured line locations)
total number of spectral locations read
2
NO concentration (molecules/cm )
Source temperature (Kelvin)
absorber temperature (Kelvin)
path length of absorption (cm)
gas broadening constant
integrated fractional transmission
program version code
D-31
-------
IPLOT1
DLAM
LINST
LINEND
LINT
ANG(I)
HT(I)
IS1
IS2
WIDE
II
XPLT(l)
XPLT(2)
YPLT(l)
YPLT(2)
ISAVE
KKOUNT
DELLAM
PP1
same as IPLT1I
same as DLAM2
starting spectral line number
final spectral line number
total number of spectral lines read
wavenumber of Ith spectral line (later converted to
wavelength)
intensity of Ith spectral line
line number of start of wavelength sort
line number of end of wavelength sort (IS1 + 20)
width in angstroms of spectral region to be convolved
at a given wavelength
same as LINT
line center wavelength
same as XPLT(l)
0
integrated intensity of line at XPLT(2)
line number of first spectral line in convolution
interval
panel counter (1-2499)
total wavelength interval divided by 2499
wavelength of first panel
D-32
-------
SPMAX
maximum convolved intensity for a given concentration
PI
P2
XLAM
I
NOPTS
IPN1
JBL
SUMMER
TRIADD
wavelength of start of individual convolution interval
wavelength of end of individual convolution interval
center wavelength of convolution interval
counter to determine which spectral lines lie within the
convolution interval
same as KOUNT
line number of last spectral line in convolution interval
counter for lines within convolution interval
integrated intensity of all lines within the convolution
interval
line intensity weighted by slit function
PLOTX(I) wavelength of convolved line transmissions (Ith panel)
PLOTY(I) intensity of convolved line transmissions (Ith panel)
DIV maximum convolved intensity for no NO present
TRNCAS (NCASE,!) array of intensities for each concentration (NCASE) at Ith panel
DECIS option for extrema in wavelength region specified
XSTR starting wavelength for extrema option
XSTP ending wavelength for extrema option
Jl counter for concentration case
STLOOK
XSTR minus one percent of extrema interval
D-33
-------
SMALL
BIG
DIF1
DIF2
LAMIN
LATIAX
MI NSAY
MAXSAV
MINRAT
MAXRAT
minimum transmission over extrema interval
maximum transmission over extrema interval
minima check
maxima check
wavelength of minimum transmission
wavelength of maximum transmission
minimum transmission with no NO present
maximum transmission with no NO present
minimum fractional transmission
maximum fractional transmission
D-34
-------
NO-ABS.MAIN
KC
ZlCtttmXXXXXtXXXXXXXXXXXXXXXXXXUIXXXIXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXfX
3lC PARTI PARTI PARTI PARTI PARTI PARTI PARTI PARTI
4lCXXXtXX«XXXXttIXXXXXX*XX*XXXXt*«*XXX*(***XXXXXX*SI*XXXX*X*»t*SXXXXt**»(
5«C
6> REAU4 KO
7i INTEGERX4 P.O,R.ltANIC
81 INTEGERX4 BRANCH
9> DIMENSION S(SM),n.,UO(5M)
10: DIMENSION U02(5
11 « DIMENSION HEADS<2«>
12i DIMENSION KO
16t DIMENSION U(5M),E(5M),CAY(5««).DAT(S««)
17» G(LEU)-19«4.4«5X(LEW+.5>-14.187X(LEU+.5)XX2
181 AUOU'.Ol
19> READ(5,4) LINST
Ml READ(5,4) LINENO
211 READ(5,4) HOOTHE
E2l 4 FORT1AT(I3)
23 » 8 DO 12 I«1,1M«
241 READ (5.1« )XDATA(I),VDATA(I)
2S« !• FORnAT(8>l«.«)
86 1 IF (XDATA(I).EO.t.M) GO TO 14
27t 12 CONTINUE
21« 14 CONTINUE
391 NP-I-1
3»t NP1-NP-1
3H L1R2-2
32 « IUU-9
33 « IVL-t
34 1 READ (S.WHCAW
351 2» FORTMT(Z«M)
36 « READ (5,14«)DELFIT
37 » READ (S.14*>SUT
38t DLAfl-SLIT
39< READ <5.14«>AP
44 « READ (5.14«)TA
411 READ (S.14«)TE
421 READ (5,14«>El
43 « READ (5,14t)VH6T
441 READ <5,4«)IPIOT1
4«i READ (5,4«)IPLOTZ
4CI 4« FORNATCail)
471 M FORnAT(Il.aflt.»>
4ft URITE (6,SM)TA,TC.D«).CUTAU,ALPHA
MiC BVCM 1C TIC SPECTROSCOPIC CONSTANT FOR THE ZERO VII. STATE
fit lUEM-l.raSM
SI>C
S3IC ATI IS THE LOUOt STATE SPIN SPt-ITTINC
541 AR.-lZ3.li
54I>
-------
NO-ABS.MAIN (CONT'D)
S«»C INCLUDE TEHP. CORRECTION TO POP. DIST. FOR PARTITION FUNCTION
57> Cl>3.T796E-14XlUEOe/(TASt (3. Oe/2.D«)S(l>EXP( -1.43836*
58 « X
S9iC
60 COflSTl— 2.D»»DSORTlDLOC<2.I»)>
65 « CONST2-1.3«7D-7» SORT(TE)
661 CONST3-1.3«7D-7« SORT(TA)
67i CONST4-3.E-7*SORT(TE)
681 WRITE <6,80>HEAD$,AP
69t W FORI1AT(1H1,2«X,2«A4.1«X.3MA'«.F7.4)
71tC«St«tSt>tSfSSSS*t*SSS»SS»S»S>ttSXSSS»S»SSS>S«>SHtSttISSIS*SS«SttSS
74IC
751 J-l
76i 1M READ (5,12*>BRANCH,NUP,NIO.RJPP,UO(J>
771 ISPIN(J)-NLO
78< 12« FO»»flAT(3X.Al.Il,Il,lX,M.»,lX,Fll.»)
79< IF (WJANCH.Ed.lLANK) CO TO 24*
8«i JPP-RJPP
81t IF (MARCH. EO.P) GO TO 18*
82 « ICODE-3
83i IF (MANCH.EQ.Q) GO TO 16*
84t CALL FUPPEW(IUU.NUP.JPP*i.FU)
8St CALL MONNUmiyU.IUL.NUP.NLO,JPP+l,JPP,3,S(JM
86> GO TO 2t«
87t 14» FOR«AT(4F1«.»)
88 1 !€• CALL FUPPER(IUU.NUP.JPf» ,FU)
89 « CALL HONHUn(IUU.lUL,NUP.NLO,JPP.JPP,2,S(J))
9ti ICODE-2
9H CO TO 2t«
92> 1M CALL FUPPER(IUU.NUP,JPP-1.FU)
93i CALL MOMHUn(IUU,IWL.NUP.NLO,JPP-l.JPP.l,S(J))
941 I CODE* 1
95< 2t* CALL FLOgEU(IUL.MLO,ICODE,NUP,JPP,FL(J))
96 t IF (NUOTNE.E0.9) GOTO 2l«
97i UO(J)-FU-FL(J)
98* 21« CONTINUE
991 J-J«1
!«•> GO TO 1M
!•!« 24« CONTINUE
itf> NLINES-J-1
i«5« 2C* READ (5,14«,ENt-«t»)EHO
1*41 OUII-».
l*Ci IZ-«
DO 28* IUCE-XZ.C
CM OUI8-OVI|4EXP<6i*0(IUCC»
DO 3M I-l.NLINES
1991 C1-C1S12
ll*i IF (ISPIN(I).EO.a) C1-C1S3E
-------
NO-ABS.MA1N (CONT'D)
lilt l-Cl«StttXS»*t»t>S*S«»SSStlSS*ttt**»*tt*SS*S*lt*B**«*St*tt*
116 1C PART3 PART3 PART3 PART3 PAUT3 PART3 PART3 PART3
n?tCtii>ttttttttstiitsiiii«tsisittitttsts!tsst(tistxi«tsitsx*sstsisitist>is
118IC
1191 UHOLD-UO(LINST-l)
UNTOT-e
1241 TAUTOP-8.D6
125i TAUIOT-e.W
126: J-LINST
127i DO 5W I-1.NP2
128t DUJ*CONST2
13«« UST.UO(LINST)-CONST3»UO(LINST)I2.39t(«P*l)
13H UND-UO(LINEND)*COHST3*UO(LINENO)t2.39t(«P*l)
133t A2J*UOU)-DCLTAU
1331 BZJ*UO(J)^DCLTAU
134J DIST-1ZJ-AZJ
13Si DeL-(UHD-UST)/NINT
136i U.GT.(UO(J>+DCITMJ» J-J+1
139: IF (ENO.EO.t.) GO TO 4M
14«i IF (J.GT.LINENO) GOTO 5««
1411 JLEFT-*
1421 SUHL-t.
143t SUnR««.
1441 II. J
1451 NHOLDR-*
14€« NHOLDL-t
1471 NUSR*«
148i NLESL**
149i 32* DUL>COHST3XUO(II>
!S«i IF (AP.EO.t.) GO TO 349
ISH iCTA— COHSTlS(U(I)-yO(II))/DM.
15Z« CALL UFUNC(irrA,AP.TERfl,DUm>
153t GO TO 36«
1541 344 TEWl.EXP<-((U(I)-UO(II»tCOMSTl/DUL>«2)
155t 36» CONTINUE
ISC! TtCU-KO(II)«TEJW
1571 IF (JLEFT.EO.l) GO TO 42*
15tt SUHR-SUm+THEU
159t IF (UO(II).GT.U.LE. ALLOW) NLESR-MLESR*!
1631 IF(NHOLW.EO.MLES«) NLESR**
1641 NHOLOR-NLESR
ISSt IF(NLESR.E0.3) GOTO
16£t 3M CONTINUE
16*0
-------
NO-ABS.MAIN (CONT'D)
It7 i 11-11*1
in i co TO 3Z9
169> 4M JLEFT-1
17»i II-J-1
1711 If iJ.EO.l) 60 TO 469
1721 GO TO 32«
1731 4ZC CONTINUE
174! SUHl-SUNUTNEU
ITS i IF (UOUn.lT.um.AND.TNEU.EO.e.) GOTO 46*
17fit IF (II.CQ.l) GO TO 46t
irrt ir NLESL-NLESUl
179< IF(NHOLDL.eO.NLCSL) NLESL-9
180i NMOtDL-NLESL
181! IF (NLESL.E0.3) GOTO 46t
1821 44« CONTINUE
I83i II-II-l
184! GO TO 32«
ISSi 469 CONTINUE
186 1 CO TO
187i 48* 5UNL-e.
188! sum-e.
1891 S99 C«V(
19*1 SUfll-t.M
„ 192! DCL2-DCI/2.D9
Y 193t 00 S2t I-I.NP2
^ 1941 5» D*T( I )•£* EXP(-CAV(I)»EL)
00 1 95 1 URITE(21.1t«9)(MT(I),U(I),I-l.NP2)
19C< IMtFOWMTC ',2(616. 8. 3X) >
1971 DO 54* I-l.NIHT
1981 Sum-Aim *K12«IMT< I HDATUM))
199!
2*1 i
2«2tC
2M»C PART4 PART4 PMTT4 PAAT4 PART4 PART 4 PART4 PART4
2«5tCXXtTA{Tt.E*0,El1TAU,ALPMA
21«t Stt FOWIAT(//.5X,'TA-',Elfi.t,5X,'TE-'1ElS.8,5X,'NO-'.E16.8,5X.'L-'
211t 1E16.8.5X./.5X,'TAU-',E16.8,5X,'AI>MA.',E16.8)
2121 PLTHIN-1.
1131 PLTIMX-5M.
2141 VN6T-NUOTNE
Cifi UtITE(2«)SLIT,PLTNIN1PLTmx,DCLPl.T.DLAN,VMOT,NLINE$>EHO,
tlCt lTE.TA,EL,IPLOTl.IPtOt2
t!7t 2.L1W.AP
:18> 3.TAU
t9i 4.HEMW
22«i LINT-NINT*!
-------
NO-ABS.MAIN (CONT'D)
ttli DO
222« UT-LINT*!-!
223t U02(I»-U-DAT(UCT>
22St 999 COMTINUC
226> UfflTE (2«) (U02(I).TJ2(I),I-1,LINT)
227< GO TO 260
228< 62* CONTINUC
239« STOP
23«> END
23«»
o
i
UJ
vD
-------
NO-ABS.hWPRK
H SUtROUTINE FUPPER(U,n,JINDEX,F>
3«C SUWOUTINE FUPPER CALCULATES THE ROTATIONAL ENERGY OF THE UPPER
4iC ELECTRON STATE FOR A GIUEN UI1RATIONAL STATE(U). A GIWEN SPIN
5tC STATE(H), AMD A GIUEN ROTATIONAL STATE(J)
6iC
7: INTEGER U
8< REAL*4 J
9i J-JINDEX*.S
lOi T- 43966. 8643
111 UE'8374.307
12i WEXE- 16.1*6
13> IE -1.9977
141 ALPHAE-.»198
15i DU-4.6D-6
16> IU-1.98S76
17i GAI1A-.W276
18i GO TO (3e,4*),n
19! 29 FN-IU*(J«.5»(J-.5H.SSGMMS(J-.S>-DU«(J+.S>SI£*(J-.S»S2
2*< GO TO 6«
2H 49 FN-»Ut(J*.5)t(J»1.5)-.5*G<«A«(J»1.5)-DVt(J*.5)«8*(J*1.5)t«a
aat 6« CONTINUE
34« F-T+C*FN
ZSi RETURN
26i END
EOT t 26
-------
NO-ABS .FLOWER
It SUIROUTINE FLOUeR REAL*4 J.NU.JBAR.LUDADB
9: J-JINDEX+.S
l«"t JBAR-J+.5
11: P--1.17E-a
13« 0-*7.8E-5
13« T-e.
14t G*0.
15« D04.5E-*
16t A-123.19
18: ALPHAE-.ei728
19! By-BE-ALPHA€*(U*.S)
8«t BU-1.69S68
ai« C— 5.8E-4
32 i YU-(A+C»(J-.5)»t2)/BU
33: UE*1M4.4«5
34: UEXE-14.187
as: nu-ixi/Bv
as i
39« G-UE*(VH.S)-UEXE»(y*.5)*»a
3«t NSIGN-1
31 : IMUSS.EO.H) GOTO 5
32: IF(IB.NE.8) GOTO 19
33: NSIGN--1
34: GOTO !•
35 : 5 IF(IB.EO.a>GOTO !•
36: NSIGN--1
37: 16 CONTINUE
38: GO TO <2«.4«).H
39:C
4«:C SPIN 1/2 STATE
41: 29 FN-FN-SORT( ALPHA )»BV
42: LflDAI>B-(((a.-YV)/(a.«SORT(ALPHA))-l. )t(.5tP*0)+0/S«rr(ALPHA)
43 : XX JBARtta- 1 . ) )t JBAft/2 .
441 CO TO 6*
45:C
46 1C SPIN 3/2 STATE
471 44 FN-FmSORT( ALPHA )tBV
4f: LTOAOB-C ( (2. -W)/(8.tSOirr( ALPHA ) )*1. )»(.5tP*0)*a/S«rr( ALPHA)
49:
51< RETURN
52t END
EOF i 52
• O
-------
NO-ABS.FUNG
II FUNCTION FUNC(X.XDATA,YDATA.NP,NP1)
2« DincNSiON xDATAciee>.vDATA CO TO 4«
6> a» CONTINUE
7t FUNC-(VDATA(NP)-VOATA(NPl))t(X-XDATA(NP))/(XDATA(NP)-XDATA(NPl))+V
8> IDATA(NP)
91 RETURN
10« 4« FUNC-(VDATA(I*l)-VOATA(I))/(XBATA(I*n-XDATA(I))t(X-XDATA(I))
111 1+VDATA(I>
13l RETURN
13) 6« FUNC>(VDATA(Z)-VDATA(1))X(X-XDATA(1))/(XDATA(£)-XOATA(1))4VDATA(1)
HI RETURN
151 END
EOF«15
-------
NO-ABS.WFUNC
It SUtROUTlNE UFUNC
a-EXP(-ZtS2>E*FC<-IZ> (SEE NATIONAL IUREAU OF STANDARDS
6«C HANDBOOK OF MATHEMATICAL FUNCTIONS, PACE 287)
7tC
8« IMPLICIT REAU8(A-H,0-Z>
9i REAL XF.Yf.gi.ua
let COMPLEX ZC,UC,J.ZS,TltT2,T3
11» COMMON/-TAILE/Z<31,44,2>,X<44),Y<31 )
12t DIMENSION U<2>
13« IFLAG-e
14t IF(XF.LT.«.)IFLAC-IFLAC*1
15« IF(YF.LT.«.)IFLAC-IFLA6*3
16< Xl-AtS(XF)
17» YI-A»S 60 TO (M,l«f.lM.ia«),IFUM
381 44 IF (Xl.CT.fi.M.OR.YI.CT.e.M) 00 TO «•
33i J*(«.*«,1.M)
34t ZC-CMPLX(XI.YI)
35t ZS'ZOZC
37t T2-.»9999216M/(ZS-1.7t44927««)
3tt T3-.f«e8838944«/(Z
39t UC-J«2CKT1*T2*T3)
44t Ul-(OC*COnJG(UC))t.S*«
4H U3-(CONJC(UC)-WC)«Jt.
421 IF(IFLAC.EO.f)RETURN
43 » GO TO (8«,lM,lM.12t>,IFLAC
441 €• J-(«.M,1.M>
461 ZC-C«PU«XI.YI)
461 ZS-ZC«C
471 T1
49i UC-J»ZC*(T1*T2)
Ml Ul>(UC+CONJ6 IFUFLAC.CO.t>«CTURN
S3 1 00 TO (M,l«t,lM,18«).IFLM
54 1 74 FORMAT (// 'ft IFLAG IN UFUMC-'I3//>
ssi w ue— us
SCO
-------
o
NO-ACS.WFUNC (CONT'D)
S9O
MI
f7t
MI
59 1
Ml
6U
681
631
641
65i
661
67i
68i
69i
1W
RCTURN
Ul-CtCOSfCO-Ul
WRITE (6,791
RtTURN
G-a.MXCXP(VISVI-XISXI)
U1*G>COS(GG)-U1
URITE(6,7*> IFLM
RETURN
END
-------
NO-ABS.1IONNUM
ll SUBROUTINE HONNUH,HONL)
2lC SUBROUTINE HONNUfl CALCULATES THE HONL-LONDON FACTOR UHERE
3lC NUP-UPPER UIBRATIONAL STATE
4»C NUPP-LOUER UIBRATIONAL STATE
StC HESAN-UPPER SPIN STATE
6iC HEOAfl-LOUER SPIN STATE
7iC J«J"
8«C IB-1 FOR P BRANCH, -2 FOR Q BRANCH, -3 FOR R BRANCH
9iC
1*: REALM J
tl» J-JPP+.S
12: AM23.18
13: BE- 1. 7*437
14t ALPHAE-.ei72S
15« B<.i-BE-ALPHA£*(NUPP *.S)
16t YU-A/BU
17« Tl-Z.Ol.
18« T2-TUT1
19« T3-l./SQRT CO TO 44»
29t W RNUfl-T2-Tirr»(4.»JM2+4.«J+l.-2.tYU)
31 t CO TO 44«
321 l*t CONTINUE
33i CO TO (l2*,14«),NE6Afl
34t 129 RNUn-T2-TltT3«(4.*J«t244.«J-7.*a.»VV)
35i OENOn-«.*J
36: CO TO 44*
37« 14t RNUn-T2*Tl«T3«(4.tJ««e*4.«J-7.+2.»W)
381 D€NOfl-8.«J
39 « CO TO 44«
4«i 160 CONTINUE
41t CO TO (184,24«),fCGAN
42: 184 CONTINUE
43 « CO TO (2*O.ZZ«),nEQM1
44t 2M RNUn-Tl»((4.«Jt»a+4.»J-l
4S» DCMOn-8.«J»(J*l.)
46 1 CO TO 44«
471 229 RNU«-Tl*(4.»J«2»4.tJ-l.-T3«(l.*Jt*3412.tJS»2-2.JJ-7.*2.rA;))
4ft DENOfl>8.SJt(J+l.)
49 > CO TO 44«
6«t 24« CONTINUE
Sit 60 TO (2M,tM),rCQM
SZt BSO RNUH-TU((4.«J««2*4.«J-l.)-T3t(«.«J$I>t2.tJ»t2-2.»J+l.-2.»YU»
sat DENon-s.«j«
-------
NO-AUS.HONNUM (CONT'D)
M<
571 GO TO 44«
Sflt 3tt CONTINUE
59« 00 TO (32«,3M>.fCGAN
M> 32* CONTINUE
6H GO TO (34«,3t«>,HEGAn
621 346 RNUn«TZ*TUT3»<4.«JU+4.tJ-7.+2.*YV)
63< DENOH-».» 3C* RNU««Te-TlIT3t<4.tJMa+4.tJ-7.»a.tYV)
66> 0€HOfl-8.» 449 CONTINUE
TCI IF 00 TO 4M
77t
Ttt RETURN
79i 4C« HONI-*.
Ml RETURN
•It END
•1O
-------
NO-SPKCT.MAIN
nc
2iCtst>si*s**tt«sts*ssssts*>ttt*ss«s»*«s>«»tsi**s
3«C PARTI PARTI PARTI PARTI PARTI PARTI PARTI PARTI
4:Ct*t«*tSS«t«t(*tSS*t*t*tV«*S*>»t«**SS**SS*t*t*******tSSS*«SS**fS***SSSSt
S:C
6 1 REALM KO
7t INTECER*4 P.O. R, BLANK
8t INTEOERM BRANCH
9: DIMENSION S(S0«>,Fl(5«6>,UO(5««),EO
1«: D I HENS I ON U02(S««),TJ2(5«e>
111 DIMENSION HEADS(2ei
12: DIMENSION KO,ISPIN
13: DATA BLANK/' '/, P/'P'/.0/'0'/,R/'RV
14 « COrWON/PAREn/CONSTl,COMSTa,CONST3,UO,EO,KO,NLIKS
IS" DIHENSION XDATA(iee).YDATA(ie«)
16t DIMENSION U(5«« ),E(5«« ),CAY(5W ),DAT(5»9 ),EJ(5ee),TJ(5«« )
17s G(LEy)-19e4.4e5I(LEU+.5)-H.187*(LEU+.5)**2
18! ALLOU-.ftl
19: READ(5,4) LINST
2«: READ(5.4) LIMEND
311 READ(5.4) NUOTHE
33: 4 FORfWT(I3)
23i 8 DO 12 1-1. IMt
241 READ (5.19 )XDATA(I),YDATA(I)
25: 10 FORIWT(8F1«.«)
36: IF (XDATA(I).EQ.e.M) CO TO 14
27: \Z CONTINUE
O 28: 14 CONTINUE
' 29: NP-I-1
•^ 3«« NP1-NP-1
31: L1R2-2
32: lw«
33: IUL-9
34 « READ (S.atttCADS
35: 2« FORnAT(2«M)
36: READ (5,14»)DCLPLT
37: READ (5.14«)SLIT
3«: DLAfl-SLIT
39t READ (5,14«)AP
4«t READ IPLOT1
45 « READ (5.4«)IPLOT2
46 : 4« FORMAT (211)
471 6« FORMAT(I1.2F1».«)
48 : URITE (6,SM)TA,TE.ENO,EL,TAU,ALPHA
49>C
5«>C BVCO* IS THE SPECTROSCOPIC CONSTANT FOR THE ZERO VII. STATE
Sit tUECt*1.69SC2
53 :C ff\. IS THE LOWER STATE SPIN SPLITTING
54t AFL-1S3.S8
558C
-------
00
NO-SPECT.MAIN (CONT'D)
Sic TOP COUKCTION rod POPULATION DISTWIWTION
i ClO.7799D-14ttUE09/XU*EXP(-1.4393CX
Si X(ATL-2.t»UE09)/TA»>
iC _ _
MIC iNtcrr 9PiN DEPENDENT F NUHKR
Cli C1S32-CI/3. 94X3.89
Ut ClSia-Cl/3, 64*3.53
63i C2— 1.43939DO/TA
661 CONST2-1.397D-7X WTfCTf )
6€i COWST3-1.307D-7t SOTT(TA)
67i COMST4-3.E-7»SOirr(Tt)
ifi MITE (C.M>HCAD$,<*
69 > M FO(mAT(tHt,Z«X,2«M,l«X,3HA'-,r7.4)
7«iC
7iic»tn**ssssmxm»smmsss«tmsmstsusnstssnss*mssx«smstti
72iC FAm PMTT2 PMTT2 PMTTC PMTT2 PMTT2 PMTT2 PMTT2
73tcmttsmsxxsmtmmsxmmmmmssnmxsstxssm<*sssmssms
74IC
TSi
76i
771
7«i
791
991
•it
•21
•31
941
•Si
96i
•71
•91
99i
91i
92t
93i
941
9Si
96 1
97t
99i
99i
199IC
191 1C
totic
1931
1941
19fi
199i
197i
1991
1991
1191
1190
J*l
199 READ 9RANCM,NUP,NLO.RJPP,UO<.I)
129 FWmATC3X.Al.Il.Il.lX.F4.9,lX.Fll.f)
IF (MMNCH.E6.9LANK) GO TO 249
IF (IftANCM.EO.P) GO TO 199
IF (MANCH.EO.O) GO TO 1C9
ICODC-3
CALL HONNUmiMMUL'NUP,Nto.JPP+l.JPP,3.$>
GO TO 299
149 FORNAT(4F19.9>
1C9 CALL FUPPER(IUU,NUP,JPP ,FU)
CALL MONNUmiUU,IWL.NUP,NLO.JPF.JPP,2.S
CALL MONNUmiUU.IVL.NUP.NlO.JPP-l.JPP,l,S)
ICOK*1
299 CALL FLOUER(IUL.NU>iIC09E,NUP,JPP,FL(.m
IF (NMOTHC.E0.9) GOTO 219
UO(J>-FU-FL(J>
•19 CONTINUE
E0( J )-$( J >9EXP
-------
NO- SP
(CONT'D)
UK NlINES-J-l
llZi 269 READ <5,14«,END-62«)ENO
1131
115t DO 284 IUEE-IZ.5
116t 23* OUIB-OXill*EXP(C2*C C1-C1S33
130: B-Cl*S(I)'OVIB*EXPSS**I
12? :C PftRT3 PART3 PART3 PART3 PftRT3 PART3 PART3 PART3
127:C
128: UHOLD-UO(LINST-l)
129i LINTOT-e
130t IS«U€«1
13lt NINT-1W
132t NP2-NINT+1
133« TrtUTOP-e.M
134t TAUBOT-e.De
135: DO 5€« J-LINST.LIf€ND
136: DWJ-COMST2*UO(J)
137: DELTfty-COMST4*UO(J)
138: ftZJ-yO(J)-D€LTAU
139: IZJ-UO(JHD£LTAU
14«: DIST-»ZJ-A2J
Hit DEL-DIST/MINT
142: DO 5W I-1.NP2
143: U(I)-AZJ*(I-1)*DEL
144: E(I)-EO(J)I EXP(-( (U( I )-UO< J ) )«COHST1/
14S: IF (EMO.EO.e.) GO TO 48«
146: JLEFT-*
147: SUHL-e.
148: SUTR.*.
149: II-J
154: NHOU**t
151: NHOLDU-*
152: NLESft**
153: HLESL-*
154: 38* DUL-CONST3WOUI)
155: IF (AP.E0.0.) GO TO 344
156: 1CTA— COHSTlt(U< I )-»»( II ) )/DUU
157t CALL UFUMC(KTA.AP.TERn.IXjnS)
158> GO TO X9
159i 34» TERfl*EXP(-((U(I)-UO(II))*COMSTl/DUL)tt2>
l£«i X9 COHTINUe
16H TNCU'tCOdDSTEim
162> IF (JLEFT.EO.l) 00 TO 4M
1641 IF (UO(II).GT.U(I).AHD.TNEU.EQ.«.) GO TO 4M
1651 IF (II.EO.NUNES) CO TO 4M
1650
-------
NO-SPECT.MAIN (CONT'D)
16€> IF (UO(II).LT.IZJ) CO TO 3M
1«7« IF .LE. ALLOW) NLES»-NLESR*1
1681 IF (NHOLDR.EO.NLESR) NLESR-e
1601 NMOLDR-NLESR
1701 IF (NLESR.E0.3) GOTO 4««
171« 380 CONTINUE
172i 11-11*1
l?3i CO TO 329
1741 400 JLEFT-l
I75t II-J-1
17ei IF (J.EO.l) GO TO 460
177f GO TO 320
ITS* 420 CONTINUE
179i SUHL-SUHL*TNEU
180» IF iUO(II>.LT.U.AND.TNEU.EO.*.> CO TO 46*
181 < IF (II.EO.l) GO TO 460
1821 IF (UO(II).GT.AZJ) CO TO 44*
1831 IF (AISCTNEU/SUflD.LE.ALLOU) NLESL-NLESL*!
184t IF (NHOLDL.EO.NLESL) NLESL-*
18S: NHOLOL-NLESL
I8fii IF (NLESL.E0.3) GOTO 4€«
187: 444 CONTINUE
188* II-II-l
189> GO TO 32t
19«i 46« CONTINUE
191 < GO TO 5«t
192t 48» SUm.-«.
193i SUHR-*.
194t 5M CAV(I)-SUm.*SUW
19St SUH1-9.M
19S» SUN8-9.M
197! DEL2-DELX2.M
191i DO SZ« I-I.NP2
199t 52* MT( I )-£(!)» EXP(-CAV(I )tEL)
DO 54« I- 1, MINT
SUni-SUni«DCL2X(DAT(IHMT(I*l»
2*3 « EJ(J)-SUN2
2»4i TJ(J)-SUN1
2*5i TAUTOP-TAUTOf*TJ(J)
£•€ i TMJtOT-TMJtOT^EJ ( J )
2«7iC _
2MIC MCNOUC IMNMTORV GOTO 5€« TO OBTAIN INDIVIDUAL
2*9 «C LINE BUNOLC TRANSMISSIONS
21*tC
•ill GOTO 5§*
tilt IF (CNO.EO.*. ) GOTO SC*
«13i SUm-Sl*!T*TJ(J)
2141 SUHE-$unE*€J(J)
tlSt LINTOT-LINTOT*!
etc i TRNSLM-sunr/sunc
tl7i DOPCK*(UNOUMM>(J><(l.-t.5«CONST3))t(UHOLD-UO(J)*(l.*l.S«CONST3))
Sift IF (DOPCK.LT.*.) QOTO Sf7
219i IF (LINTOT.NE.l) GOTO 542
22*1 URITE (6,555) LINTOT.TRNSLN
23*0
-------
NO-SI'KI'.T.MAIN (OONT'D)
881t GOTO 544
8881 5-42 CONTINUE
223t URITt(6,55S) lINTOT.TRm.N2
2241 544 CONTINUE
225« LINTOT-0
226* sunr-e.
227« sune-e.
228> GOTO SS9
229« 557 CONTINUE
23«> 555 FORfWT uex,I2,2X,El6.6)
231» TRNLN2-TRNSLN
232* 559 CONTINUE
2331 UOINU-1.E+W/UO(J>
234t WRITE (6,550) J,TJ(J>,EJ(J).UO,WOINU
23S< UHOLD-UO(J)
3361 559 FO*HAT(1X.I3,2X,4E16.6>
237« 56« CONTINUE
238 «C
239icsmt*sss*>«smsxs*st*ts*ttts*i*ss«»»*ssst>«s>»sism*ass»sstsfttt
240JC P««T4 PART4 PART4 P«RT4 PART4 PART4 PART4 PrtRT4
241SCttS>lXttS*St«XSSlS»tttXStt««tSt*tS*fSS**ttSSSt(S**S»StS«SSSttS*St*S
242tC
243: TAU-TAUTOP/TrtUIOT
2441 ALPHA* l.M-TAU
2451 URITE (6,5W)TA,TE,ENO,EL,TAO,ALPHA
246: 5W FOWMT(//,5X,'TA-',E16.8,5X,'TE-',E16.8,5X.'NO-',E16.8.5X.a-',
247« lEie.S.SX./^SX.'TAU-'.Eie.S.SX.'ALPHA-'.Eie.S)
2481 Pl/rniN-UNST
0 249 J PLTHAX-LINENI)
i 25«i VHGT-NUOTHE
*£ Kit U»UTE(2«>SLIT,PlTmN,PVn*W,l«U»LT,DU*,VHGT. KLINES, ENO.
2S2« 1TE.TA,EL,IPLOT1,IPLOT2
2531 2.UR2.AP
2S4J 3.TAU
2551 4,HEADS
2S6i LINT-LINEND-LINST+1
2S7i DO 6M I-l.LINT
258: UT-LINEWD-I*!
259: U02(I)*UO(UT)
2€«« TJ2CI) • TJ(UCT)
2€1> CM COWTINUE
262: WRITS <2«) (U02(I),TJ2(I).!•!,LINT)
263: CO TO 26*
264t 62* CONTINUE
265i STOP
266t END
-------
PLOT.PLOT5
H REALt4 LAniN,LANAX,NINSAU,nAXSAy,HINRAT,NAXRAT
HI DATA NO''NO ••'
3> DINENSION HEADS(20>,HDURt2«>,TRNCAS(3,2S99>
41 DINENSION HTSTOR<39>.ENSTOR(39>.TAUSTR(3«)
Si PINENSION ANC(2S*e>,HT(25e«>.Pl.OTXl2See>,PLOTYC2S99)
6> X ,XPLT(4),YPLTl4)
71 DINENSION ENSTUR(a>,APUR(2>
8IC
91C tt*S*IS«tt*tStt*t***tSS««(St
1*»C PART 1 PART 1 PARTI
11*C ti»t**»ttl*»ttt**»»tl»t»t»»i«
12>C
13> NCASE-e
14: ISTART-1
15! CALL DATE (DATED
16t CALL TINE(TINEl)
18iC
19tC READ IN CONTROL PARAMETERS
29«C
21« CALL INITT(24«)
22t URITE (6,25)
23« 25 FORNAT (' FOR DEFAULT SCALES INPUT 9.,9.' /
24t X ' TO ILOU UP SCALE, INPUT HIM AND NAX FOR AISCISSA'/)
25< READ (5,39) XNIN.XNAX
26i 39 FORNAT( )
„ 27< IF(XniN.NE.XNAX) GOTO 36
i 28i URITE(6.32>
^ 2«: 32 FORNATC INPUT FUHN'/)
ro 391 READ(5,39) DLAH2
3H URITE (6,34)
32« 34 FORNATC TYPE 1 FOR ZERO UIDTN PLOTS'/
33« X ' TYPE 9 TO DELETE ZERO UIDTH PLOTS'/)
34t READ (5,39) IPLT1I
35: 36 CONTINUE
36> CALL ERASE
37tC IF VALUES NOT tOTH ZERO WANT TO ILOU UP SECTION OF PLOT FROM XNIN TO XNAX.
38iC VALUES UILL K AVAILABLE ON 28 SO UILL NOT REDO CALC.
391 IF (XfllN .NE. XNAX) GO TO 415
49t ISKIP-8
4H 49 READ (29.END-499)SLIT,PLTNIN,PLTNAX,DELPLT.DLAN.YHCT,NLINES.ENO,TE
42« l.TA,EL.IPLOT1,IPLOT2.L1R2,APRINE.TAU.HEADS
43« IPLOTi- IPLTII
441 LINST-PLTNIN
45i LINEND-PLTNAX
46I DLAN-DLAN2
471 IF (ISKIP .EO. 8> 00 TO 45
48i NUNPLT • IPLOT2
49i IF (NUNPLT .NE. 9) NUNPLT -1
59> ISKIP • 8
Kit 4V CONTINUE
58IC
53tC READ IN UAV€NUN9ER, TRANSMISSION PAIRS. CONVERT UAVENUNBERS
54tC TO UAVELENGTH AND DETERMINE NAXINUN TRANSMISSION
SSiC
550
-------
PLOT.PLtm (CONT'D)
56 1 LINT-LINEND-LINST+1
571 READ <2«) ,HT IF(HT(ICARD>.LT.e. >HT< ICARD >•«.
6d> STftAX-AnAXl(STHAX.HT >
6H ANG< ICARD >-U.E+e8>/ANG( ICARD)
62« 60 CONTINUE
63 1 DO 65 I CARD- 1. LINT
64« IS1-ICARD+1
65« IS2-ICARD+21
6€i DO 65 ISORT-IS1.IS2
6T« IF (ISORT.CT.LINT) GOTO 65
£81 IF (AHG(ICARD).LE.ANC(ISORT)) GOTO 65
69i TEHPl-AMG(ICARD)
78 t TEW»a-HT(ICARD)
7U
72t
73«
74i HT(ISORT)-TEHPa
7S» 65 CONTINUE
76:C
77: C t**SSS«S(SSt*StStS»tSSSSSSI*
78:C PART 3 PART 2 PART 2
79 tC *»**It»t«*»tt«*tt«»It«I»»*t*»
O 8H NCASE-NCASE*!
' 82: II-LINT
Co 83: PLTniN-AHCU)
84t PLTHAX-AMC
85 1 IF GOTO 79
86tC SET COfWOUmOM INTERVAL FOR GAUSSIAM SLIT FUNCTION
87: UIDE>6.*DLAfl
88 < GOTO 74
OTiC SET CONVOLUTION INTERVAL FOR TRIANGULAR SLIT FUNCTION
9«: 70 UIDE'2.«DLAfl
91» 74 PLTHIN-PLTNIN-2.WIDE
92 < PLTT1AX 'PLTnAX42.su IDE
93» DELTA-STHAX
941 80 CONTINUE
95 IF (IPLOT1.EQ.0) GO TO 120
99t XPLT(3)-PLTHIN
1000.
107t CALL IINITT
1M«C SUPPRESS X GRID
1091 CALL XFRfl(2>
110« CALL DLIUXJPLTmN.PtTHAX)
110O
-------
PLOT.FLOT5 (CONT'D
lilt CALL DLIWYce., DELTA)
ll«i CALL CHECK (XPLT.YPLT)
II3« CALL DSPLAY (XPLT.VPLT)
1141 LAIPRT • 18
11S> IX-SS4
1161 IV-765
117) ENCODE (481.HDUR) HEADS
118i 421 FORNAT (SA4)
U9i ENCODE ( 436. ENSTUR)ENO
i2«i CALL nouAis CALL NOVAISU8*,725>
12€< CALL AOUTST(20,HDUR>
1271 GO TO 429
128i 88 CONTINUE
129i DO 199 1*1,11
IMt RLAfUANCm
131> IF (I .CT. 5M) GO TO 95
1321 95 CONTINUE
133> IF (PLTniN.CT.RLAn.OR.PLTnAX.LT.RLAfl) CO TO 1M
134«C DfMU INDIUIDUAL LINES
135i YPLT(2)-AftINl(HT(I),iOOZE)
136: XPLT(l)-RLAfl
137i Xf»LT<2)-Xf»LT
138< CALL NOUEA (XPLTd ).VPLT( 1 ) )
139t CALL DAAUA (XPLT(2),VPLT(2) >
14«i 1M CONTINUE
141t CALL TSCNO
1421 CALL riNPUT(l)
143i CALL ERASE
1441 12* CONTINUE
145»C
14CIC M«M«t«t»ttt»»WMM«M«t
147iC PART 3 PART 3 PART 3
148 1C ttttSSSSSSSXSItStSStSSttStSSS
149IC
15«iC PRODUCE THE ACTUAL SPECTRA PLOT
151>C
1521 ISAUE-1
153t KKOUNT-1
lC4t DClLAfl-(PLT»IAX-FLTNIN)/2499
I55t PPl-PLTPIN-DElLAfl
15CI SPWAX— 1M.
1571 14« LOOK-ISAUC-1
10> IF(LOOK.LE.«)LOOK-1
159 iC
IMtC CHOOSE A POINT ALONG THE PLOT AXIS AND SET AN INTERVAL OF WIDTH
1«HC EQUAL TO HALF THE CONVOLUTION WIDTH ON EITHER SIDE
Pl-PPl««OUNT*D£tLAfl
1641 P2-P1*«IDC
KSi XLAN-(Pl+Pe>t.5
1CSO
-------
PI.OT.IM.OT) (CONT'D)
I
l_n
Ln
167 «C
16S»C
1S9IC
1701
1711
1721
1731
17m
1751
176i
177IC
1781C
1791C
181:
183:
18-41
185«
186 iC
187«
IBS:
189:C
191:
192 =
193:
195:
196:
1971
198<
299*
2*5:
2*6:
218t
219«
KOUHT-l
THIS LOOP DETERT1INES WHICH LINES LIE IN THE CHOSEN INTERVAL
DO 16« 1-1,11
IF (ANG(I).GT.P2> GO TO 180
IF (AHC(I).LT.Pl) GO TO 16«
21HC
KOUNT-KOUNT+1
16« CONTINUE
ISO NOPTS-KOUNT-1
THE FOLLOWING STATEMENTS SIMULATE THE SLIT FUNCTION
BY SUmiNC THE CONTRIBUTIONS OF ALL THE LINES IN THE INTERVAL
IF (NOPTS.EQ.e) GO TO 229
sunnER-0.
IPNl-ISAVE+NOPTS-l
DO 299 JiL-ISAVE.IPNl
IF (DLAH.GT..5) GO TO 19«
UCIGHTINC FACTOR FOR GAUSSIAN SLIT FUNCTION
TRIADD-HT(JBL)IEXP(-(ABS(XLAH-ANG(JBL))/DLAf1tl. 66512 )«2>
GOTO 299
WEIGHTING FACTOR FOR TRIANGULAR SLIT FUNCTION
19* TRIADD*HT(JBL>*(DLAfl-ABS(XLAn-ANG(JBL)))/DLAn
PLOTxdCKOUND-XLAfl
PLOTV(KKOUNT ) •SUHHER
IF (PLOTY(ICKOUNT) .GT. SPflAX) SPflAX-PLOTV(KKOUNT)
218 CONTINUE
ICICOUNT-ICICOUNT*!
IF UKOUNT.EQ.2S«1> GO TO 24«
GO TO 14«
22« PLOTX(lcrOUNT).XLAH
PLOTV(ICICOUNT)-«.
KICOUNT-KICOUNT-H
IF (ANG(II).LT.Pl) GO TO 24«
IF (KICOUNT.E0.25*!) GO TO
GO TO 14«
24« II-KKOUNT-1
N-II
IF(ISTART.EO.l) DIV«SPfMX
DO 26* I-l.N
PLOTY(I)-PLOTY(I)/DIV
269 CONTINUE
213>C
214IC
DETERflINC THE WWIIM! UALUE OF THE SPECTRAL CURVE AND IF THIS
IS THE FIRST CURVE COMPUTED, THE V AXIS SCALE FACTOR IS CALCULATED
IF( ISTART.EO. 1 )DELYP-SPmx
PLOTY (*+!>••.
PLOTY(N*2)-D€LVf
PLOTX(N»1)-PLTHIN
PLOTX(N*2)-DELPLT
-------
PLOT.PLOTS (CONT'D)
2211 ISTART-e
2221 TAUSTR-TAU
223i HT5TO««SPMAX/DELVP
2241 ENSTORiNCASEI-ENO
2251 URITE(28>NP2,ENSTOR.HTSTOR(NCASE).TAUSTR.
236i X TA.TE.EL.APRINE.DELYP,HEADS,VMGT.(PtOTXCL),PLOTYa>.L-l.NP2>.
227t X PLAH2
ZZ9i GO TO 4«
2291 369 CONTINUE
23«»C
231 »C PRODUCE THE FINAL SPECTRA PLOT
232'C
2331 3W FORMATCSX, 'N-'.E16.8.5X,'HT-'.E16.8>
2341 4A« CONTINUE
2351 END PILE 28
236t LABPRT-e
23?i REWIND 28
2381 415 CONTINUE
239> NCASE'9
24«t 42« CONTINUE
24K NCAS€-NCASE*1
2421 RCAD(28,END*4««)NP2,ENSTOR(NCASE),HTSTOR(NCASE),TAUSTR(NCASE>.
243t X TA.TE.EL.APRIfC.DELVP.HEADS.VHCT.CPLOTXtD.PLOTVCDA'l.NPa),
2441 X DLAH2
2451 418 CONTINUE
24€t N-NP2-2
2471 DO 419 J2-1.N
248* TRHCAS(NCASE,J2)-PLOTV(J2)
249t 419 CONTINUE
2S«t If (NUnPLT .EO. 8) CO TO 43*
25H CALL IINITT
2S2> IF (XfllN .NE. XHAX) CALL DLIKX (XHIN.XmX)
253i CALL DLinv (•.,!.•«)
2541 IF(XniN.EO.xnAX) CALL DLIKX(PLOTX(1).PLOTX(N)>
2551C HO V LAIELS
25fiiC CALL VLAI(«)
2S7iC SUPPRESS V AXIS
2581 CALL YfW1<2>
259tC PUT IN X TICS WT NOT X GRID
26*> CALL XFRf1(2>
2C1I CALL CMECIC(PLOTX,PLOTY)
2C2t IF (NUHPLT .NE. 1) NUHPLT-8
2*31C PUT IN LAKLS FOR SCALE AND OTHER GENERAL ONES HERE
2C4t 422 FORMAT (FE.t)
2CS< 423 FORMAT (F5.1)
£CC> 424 FORMAT (FS.5)
2<7i 42C FORMAT (E8.4)
2*8I 427 FORMAT(F7.4)
2C9i 42t FORMAT(AC)
I7«i IX-2M
B7tt IV-7S5
272t 429 COHTIHUE
t73i ENCODE (421.H8UR) HEAM
274t ENCODE (4tt,TCUI) TC
2751 ENCODE (422.TAUR) TA
I7CO
-------
PLOT. l'LOTr) (CONT'D)
2761 ENCODE (423,ELU*n EL
377i ENCODE (424,APW*> AP9INE
278> ENCODE (428, DATUfM DATE1
8791 ENCODED 428. T I HUH) TINE1
2Se: CALL nOVA§S(4S0,S>
281 « CALL AOUTST < 13, 'UAUE LENGTH, A')
282 1 CALL fKK)AISl7Se,25>
283t CALL AOUTST ( 6, DATUfM
284t CALL mX*ABS(7SetS>
28S: CALL AOUTST<6.T1NUR>
286« CALL «OVABSUX,IY>
287 1 CALL AOUTST ( 5. 'TE • ')
283 t CALL ACUTST (S,TEUR>
289 t CALL AOUTST (2,' K' >
29«: IY-IY-2*
291 1 CALL ItOUABS (IX, IV)
292t CALL AOUTST (5, 'TA • ')
293« CALL AOUTST
294 J CALL AOUTST (2, ' (C ' )
29S: IY-IY-2«
29€» CALL fWyAISdX.IY)
297t CALL AOUTST (5,'L • ')
298: CALL AOUTST (5,ELUR)
299 J CALL AOUTST (3,' CH' )
3»6i IY-IY-26
381: CALL HOWAtSC IX, IV )
39Zt CALL AOUTST(5,'A • ')
3*3 « CALL AOUTST (8.APOR)
304: IF (LAIPRT .EO. 88 ) GO TO 88
39BI IY -IV - 2«
396i ENCODE (457.DLUR )DLAH2
3*7i CALL NOMAtSdX.IY)
3*8: CALL AOUTST 16,' DLAfl- ')
3*9> CALL AOUTST ( 7. DLUR)
31»t IY-IY-2*
31 It CALL nOUAft$(IX,IY)
312i CALL AOUTST (2«, HOUR)
3131 IY-lV-Zt
314: CALL «XM1S( IX. IY)
3151 IF (DLAM2.GT..S) GOTO 429*
316: CALL AOUTSTf 14, 'GAUSSIAN LNSHPM
317: GOTO 43M
318: 489* CALL AOUTST ( 12, 'TRIANC LNSHP' )
319: 43M CONTINUE
32*: CALL nOUAtS(4«5,IV)
381: IF (YHCT.EO.l) GOTO 431*
3aa> CALL AOUTST (12,'EXPCT. LINES')
323 « GOTO 432*
324: 431* CALL AOUTST (12, 'THEM. LINES')
325: 438* CONTINUE
3871 IV- 765
32*: CALL WXMiS(69»,IV)
389» CALL AOUTST (7, '
33«« IY • IV -»
33* :>
-------
PLOT.PLOTS (CONT'D)
33H CALL n
332i CALL AOUTST(26.'NO HEIGHT TAU'>
3331 CALL NPTS (N)
3341 CALL DSPLAY iPLOTX.PLOTV)
33Si CO TO 431
3361 439 CONTINUE
3371 CALL NPTS (N)
338i CALL CPLOT (PLOTX,PLOTY)
339i 431 CONTINUE
34*1C PUT IN LAiELS FOB PARTICULAR CURUC
34is ENCODE<426.ENSTUR)ENSTOR(NCASE>
342s 432 FORMAT (F6.3)
343t 433 FORTWT
3441 ENCODE(432.HTSTUR)HTSTOR
345i ENCODE(433.TAUUR)TAUSTR(NCASE>
346i IY-IY-29
34?s CALL HOVA1S(S39,IY)
348s CALL AOUTSTU2.ENSTUR)
349s CALL AOUTST(6.HTSTUR)
3S*« CALL AOUTST(6,' ')
3511 CALL AOUTSm.TAUUR)
3521 GO TO 429
3S3i 460 CONTINUE
354 SC
3551C StS«St»*t*»»tSStISS
356SC PART 4 PART 4 PART 4
357«C »II««««ttt****t*t«tt»«t*t«»»»
35itC
359t NCASC-NCASE-1
36*i CALL TSEND
3€1> CALL TINPUT(l)
362s CALL ERASE
363i CALL rtOWAtS (9,7M)
3641 479 CONTINUE
36Si WRITE (6,419)
36£S 489 FORftAT (' DO YOU UAHT EXTRE5A?'/)
367s READ (5,495) DECIS
3681 495 FORTMT(1X,A2)
369t IF (DECIS.EO.'NO') GOTO 569
379t WRITE (6.599)
37lt 599 FORflAT (' DEFINE INTCKUAL.'/)
372t READ (5.39) XSTR.XSTP
373t STLOOr-XSTR-(XSTF-XSTR)*.91
3741 DO 539 Jl-l.NCASE
375t SIMLL-1.
3761 BIG-9.
377t DO 529 IDUM-l.N
3781 IF (PLOTX(IDUR).lT.SnOOK.Off.PlOTX(IDun).GT.XSTP) GOTO 529
3791 DIFl-S«ALL-T»NCA«(Jl.IDUn)
3Mt DIF2-TRNCA*(J1.IDUH)-IIC
3811 IF (DIF1.LE.9.) GOTO 595
382t S«ALL.TRHCA$(Jl,IDUn)
3831 UWIN-PLOTXdDUH)
3841 59S IF (DIF2.LC.9.) GOTO SM
385t flC-TRMCAS(Jl.IDUN)
t>
-------
PLOT. PLOT'S (CONT'D)
3Mt LMMX»PLOTX(IDUn)
3T7t 520 CONTINUE
381t WRITE (6,540)SHALL,LAHIN,IIG,LAI1AX,ENSTOa
391> IF (Jl.NC.l) GOTO 527
393<
3941 GOTO 53«
39St 587 CONTINUE
396 1
39? i
398 t URITE (6.539) .
399« 529 FORWATddX,' HIM RATIO- ' ,F7.4, ,5X, ' MAX RATIO- '.F7.4// )
4001 53« CONTINUE
40 It GOTO 470
40£( 560 CONTINUE
403: CALL ERASE
404: CALL FINITT (0.700)
405 « STOP
406 I END
406 «>
IT)
•0.S. GOVEENHEHT PRINTING OFFICE 1981 0-725-V>li/1113
------- |