LINE-OF-SIGHT ABSORPTION OF H2O VAPOR: GAS
TEMPERATURE SENSING IN UNIFORM AND
NONUNIFORM FLOWS
A DISSERTATION
SUBMITTED TO THE DEPARTMENT OF MECHANICAL ENGINEERING
AND THE COMMITTEE ON GRADUATE STUDIES
OF STANFORD UNIVERSITY
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
Xiang Liu
June 2006
ii
Copyright by Xiang Liu 2006 All Rights Reserved
iii
I certify that I have read this dissertation and that, in my opinion, it is fully adequate, in scope and quality, as dissertation for the degree of Doctor of Philosophy.
__________________________________ Ronald K. Hanson (Principal Advisor)
I certify that I have read this dissertation and that, in my opinion, it is fully adequate, in scope and quality, as dissertation for the degree of Doctor of Philosophy.
__________________________________ Mark A. Cappelli
I certify that I have read this dissertation and that, in my opinion, it is fully adequate, in scope and quality, as dissertation for the degree of Doctor of Philosophy.
__________________________________ Jay B. Jeffries
Approved for the University Committee on Graduate Studies.
iv
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ABSTRACT
Gas temperature sensing is very important for combustion diagnostics. Line-of-
sight (LOS) laser absorption spectroscopy provides a non-intrusive, fast, sensitive and
reliable solution for quantitative gas temperature sensing, and H2O vapor is often the
target absorbing species used for this application. This thesis investigates gas temperature
sensing in uniform and non-uniform flows based on LOS absorption of H2O vapor.
The optimized design of tunable diode laser temperature sensors based on H2O
vapor absorption first requires a complete catalog of the H2O absorption transitions with
accurate spectroscopic parameters. Therefore, extensive experimental studies of H2O
spectroscopy were performed over the 1.3-1.5 µm near-infrared region for transitions
within the 2ν1, 2ν3, and ν1+ν3 bands, where diode laser and optical fiber technology has
been developed for the telecommunication industry. These new spectroscopy
measurements provide systematic examination of the sensor design capability of the
HITRAN spectroscopy database for combustion applications at elevated temperatures.
We found HITRAN2004 is sufficiently accurate for sensor design but quantitative sensor
calibration requires additional spectroscopic data of better accuracy. Thus, we used
HITRAN to select absorption transitions for a specific temperature sensing application
and then precisely measured the spectroscopic constants for the selected transitions.
Two-line thermometry, which yields a path-averaged temperature, provides a
simple but efficient solution for LOS absorption gas temperature sensing. It is most
appropriate for temperature sensing in near-uniform flows or over very short pathlengths
where the sampled gas can be assumed to be uniform. This thesis provides an illustration
for each case. One example is temperature sensing for gas turbine exhaust, which has
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relatively uniform temperature. A scanned-wavelength direct absorption spectroscopy
two-line thermometry method was designed and demonstrated for this application. The
other example is in-cylinder temperature sensing for the compression stroke of internal-
combustion engines, which has limited optical access with a very short sample path.
Two-line thermometry based on a fixed-wavelength scheme and wavelength modulation
spectroscopy with 2f detection was designed to address the challenges associated with the
weak absorption signals and the fast changing temperatures and pressures of this example
application. Several critical steps in the sensor design were investigated in this thesis,
including accurate measurements of spectroscopic parameters, selection of laser set-
points and construction of calibration databases. All of these steps have crucial
importance for achieving superior sensor performance.
Two-line thermometry is not appropriate for flow fields with significant
temperature gradients along the LOS. Thus, a large effort of this thesis research has been
devoted to the development of a novel multi-line thermometry strategy for temperature
sensing in non-uniform flows. The sensor concept is to measure the LOS absorptions for
multiple transitions with different temperature dependences, from which the non-uniform
temperature distribution along the LOS can be inferred using either of two strategies. The
first strategy, called profile fitting, fits a temperature distribution profile postulated in
advance using physical constraints; the second strategy, called temperature binning,
determines the temperature probability distribution function along the LOS using
prescribed temperature bins. The detailed mathematical models for both strategies were
established and the relevant algorithms were explored. Sensor design rules were
investigated to generate systematic line selection criteria. Both simulation calculations
and laboratory experiments were performed to provide proof-of-concept demonstrations
and investigate sensor performance. This work represents the first development of multi-
line thermometry based on H2O vapor absorption. The extensive theoretical, simulation
and experimental studies provide the background for future applications of multi-line
thermometry to practical combustion diagnostics.
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ACKNOWLEDGMENTS
I would like to express my most sincere gratitude to my advisor, Prof. Ronald K.
Hanson, for his guidance throughout my studies at Stanford. Although PhD study in
engineering is especially challenging for woman students, Prof. Hanson makes my PhD
journey an exciting and rewarding experience with his unwavering support and consistent
encouragement. His creative insights, desire for perfection and incredible industry
consistently inspired me to pursue higher goals in my work. And I significantly benefit
from the discussions with him on research, career, and even family and life.
I wish to forward my special thanks to Dr. Jay B. Jeffries for his valuable advice
and constant assistance with my research and thesis, as well as his great help in the
difficult times of my PhD journey.
I sincerely thank Prof. Mark A. Cappelli for serving on my reading committee, and
providing me with valuable feedbacks. I also thank Professor Michael D. Fayer and
Thomas W. Kenny for serving on my examination committee.
I also appreciate the support, assistance and friendship of my colleagues in
Hanson’s group, including Xin Zhou, Hejie Li, Greg Rieker, Adam Klingbeil, Jonathan
Liu, Kent Lyle, Dan Mattison, Lin Ma, Tonghun Lee, Ethan Barbour, Dave Rothamer,
Suhong Kim, Tom Hanson, Jon Koch, John Herbon, and many others.
Finally, I am sincerely grateful to my parents Jiuhong Liu and Xincheng Liu, and
my husband Xuejiao Hu. They have given me love and support beyond measure. This
thesis is dedicated to them and also to my daughter Gean.
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This research was supported by the Air Force Office of Scientific Research
(AFOSR), the Office of Naval Research (ONR), the Stanford Global Climate and Energy
Project (GCEP), the General Electric Global Research Center, Nissan Motor Company
and Zolo Technologies (via an Air Force STTR).
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TABLE OF CONTENTS
Abstract.............................................................................................................................. v
List of tables.................................................................................................................... xiii
List of figures................................................................................................................. xvii
Chapter 1 Introduction..................................................................................................... 1
1.1 Motivation and scope.............................................................................................. 1
1.2 Organization of thesis ............................................................................................. 3
1.3 Primary contribution ............................................................................................... 4
Chapter 2 Fundamentals of Laser Absorption Spectroscopy....................................... 7
2.1 Direct absorption spectroscopy............................................................................... 7
2.1.1 Beer-Lambert law .......................................................................................... 7
2.1.2 Spectral lineshapes....................................................................................... 10
2.2 Wavelength modulation spectroscopy .................................................................. 14
2.3 LOS absorption based temperature sensing techniques........................................ 21
2.3.1 DAS two-line thermometry.......................................................................... 22
2.3.2 WMS-2f two-line thermometry ................................................................... 24
2.3.3 Multi-line thermometry for non-uniform temperature measurement .......... 26
2.4 Multiplexing schemes ........................................................................................... 27
2.4.1 Time-division multiplexing ......................................................................... 28
2.4.2 Wavelength-division multiplexing............................................................... 29
2.4.3 Frequency-division multiplexing ................................................................. 30
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Chapter 3 Experimental Study of NIR H2O Spectroscopic Parameters ................... 33
3.1 Motivation and overview ...................................................................................... 33
3.2 Details of spectroscopy experiments .................................................................... 36
3.3 Spectroscopy results and discussions.................................................................... 39
3.3.1 Preliminary S(T) investigation within the ECDL scanning range ............... 39
3.3.2 Measurements of S(T) and γ(T) in five selected spectral regions ................ 43
3.4 Summary ............................................................................................................... 50
Chapter 4 Temperature Sensing Using DAS Two-line Thermometry....................... 53
4.1 Motivation and overview ...................................................................................... 53
4.2 Selection of spectral lines ..................................................................................... 55
4.3 Linestrength validation ......................................................................................... 59
4.3.1 Details of experiments ................................................................................. 59
4.3.2 Results of spectral survey and linestrength measurements.......................... 62
4.3.3 Uncertainty analysis in measured S(T) and two-line thermometry.............. 66
4.4 Laboratory demonstration measurements ............................................................. 68
4.5 Temperature sensing for gas turbine exhaust........................................................ 70
4.6 Summary ............................................................................................................... 73
Chapter 5 Temperature Sensing Using WMS-2f Two-line Thermometry ................ 75
5.1 Motivation............................................................................................................. 75
5.2 Overview of sensor concepts and design .............................................................. 77
5.3 Measurement of spectroscopic parameters ........................................................... 80
5.3.1 Motivation.................................................................................................... 80
5.3.2 Experimental details..................................................................................... 80
5.3.3 Raw data and data analysis .......................................................................... 82
5.3.4 Measurement results .................................................................................... 85
5.3.5 Construction of hybrid spectroscopic database............................................ 91
5.4 Selection of laser set-points .................................................................................. 92
5.4.1 Identification of candidate frequency pairs.................................................. 93
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5.4.2 Selection of eligible frequency pairs............................................................ 94
5.4.3 Selection of optimum frequency pairs ....................................................... 101
5.5 Construction of calibration databases ................................................................. 102
5.6 Summary ............................................................................................................. 106
Chapter 6 Non-uniform Temperature Sensing Using Multi-line Thermometry .... 107
6.1 Motivation and overview .................................................................................... 107
6.2 Theoretical principles.......................................................................................... 109
6.2.1 Profile fitting.............................................................................................. 109
6.2.2 Temperature binning.................................................................................. 112
6.3 Selection of absorption transitions...................................................................... 113
6.3.1 Three criteria for the initial screening........................................................ 113
6.3.2 Two criteria on E” for non-uniform temperature sensing ......................... 114
6.4 Simulation studies of the sensor performance .................................................... 118
6.4.1 Details of simulation studies...................................................................... 118
6.4.2 Profile fitting results .................................................................................. 120
6.4.2.1 “2-T” case ......................................................................................... 120
6.4.2.2 Parabolic case.................................................................................... 124
6.4.3 Temperature binning results ...................................................................... 126
6.4.3.1 “2-T” case ......................................................................................... 126
6.4.3.2 Parabolic case.................................................................................... 129
6.5 Demonstration measurements of a “2-zone” temperature distribution............... 131
6.5.1 Experimental details................................................................................... 131
6.5.1.1 “2-Zone” temperature distribution.................................................... 131
6.5.1.2 WDM setup....................................................................................... 133
6.5.1.3 Data reduction................................................................................... 135
6.5.2 Experimental results................................................................................... 137
6.5.2.1 Profile fitting results ......................................................................... 137
6.5.2.2 Temperature binning results ............................................................. 142
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6.6 Demonstration measurements of an inverse-trapezoid temperature distribution 143
6.6.1 Experimental details................................................................................... 143
6.6.1.1 Inverse-trapezoid temperature distribution ....................................... 143
6.6.1.2 ECDL and optical setup .................................................................... 146
6.6.1.3 Raw data and data reduction ............................................................. 147
6.6.2 Line selection ............................................................................................. 149
6.6.3 Experimental results................................................................................... 150
6.6.3.1 Profile fitting results ......................................................................... 151
6.6.3.2 Temperature binning results ............................................................. 154
6.7 Summary ............................................................................................................. 155
Chapter 7 Summary and Future Work ...................................................................... 157
7.1 Summary ............................................................................................................. 157
7.1.1 Experimental study of NIR H2O spectroscopic parameters....................... 157
7.1.2 Temperature sensing using DAS two-line thermometry ........................... 158
7.1.3 Temperature sensing using WMS-2f two-line thermometry ..................... 159
7.1.4 Non-uniform temperature sensing using multi-line thermometry ............. 160
7.2 Suggestions for Future Work .............................................................................. 161
7.2.1 Fundamental spectroscopy investigations.................................................. 161
7.2.2 Multi-line thermometry applications ......................................................... 163
Bibliography .................................................................................................................. 169
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LIST OF TABLES
Number Page
Table 3.1: Comparison of linestrength between measurements and databases for the
five candidate lines (shaded) and their strong neighbors. ............................ 46
Table 3.2: Comparison of air-broadening coefficients between measurements and
databases for the five candidate lines (shaded) and their strong
neighbors: (a) air-broadening coefficients at the reference temperature
γair(296 K); (b) the temperature exponents n. ............................................... 48
Table 4.1: Seven features which are the outcome of line selection steps 1-4................... 58
Table 4.2: Summary of the criteria and results for the line selection. .............................. 58
Table 4.3: Summary of measured linestrengths and comparisons with HITRAN2004
[Rothman et al. 2005] and Toth [Toth 1994] values. ................................... 65
Table 5.1: Line center frequencies and lower state energies of the ten transitions
measured in this study. Data are taken from HITRAN2004 [Rothman et
al. 2005]........................................................................................................ 81
Table 5.2: Summary of the measured linestrengths at the reference temperature S(296
K) and comparisons with HITRAN2004 and Toth [Toth 1994] values. ...... 88
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Table 5.3: Summary of (a) the measured air-broadening coefficients at the reference
temperature γair(296 K); (b) the temperature exponents nair, and
comparisons with HITRAN2004 values. ..................................................... 88
Table 5.4: Summary of the measured CO2-broadening coefficients at the reference
temperature γCO2(296 K) and the temperature exponents nCO2..................... 89
Table 5.5: Summary of the measured air-induced frequency shift coefficients at the
reference temperature δair(296 K) and the temperature exponents mair.
The measured δair(296 K) data are compared with HITRAN2004 values. .. 89
Table 5.6: Summary of the measured CO2-induced frequency shift coefficients at the
reference temperature δCO2(296 K) and the temperature exponents mCO2.... 90
Table 5.7: The expected SNR of the WMS-2f/WMS-1f signals at the candidate laser
set-points....................................................................................................... 95
Table 5.8: The estimated temperature measurement uncertainty arising from
measurement noises for the 13 candidate frequency pairs that pass
through the screening criteria of 1-2. ........................................................... 98
Table 5.9: The estimated temperature measurement uncertainty arising from the laser
set-point uncertainty for the 9 candidate frequency pairs that pass
through the screening criteria of 1-4. ......................................................... 100
Table 5.10: The estimated overall temperature measurement uncertainty for the 8
eligible frequency pairs that pass through all the five screening criteria. .. 101
Table 5.11: Illustration of the calibration databases at the prescribed pressure nodes. .. 104
Table 6.1: Transitions selected for the simulation studies discussed in section 6.4. ...... 117
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Table 6.2: Nine perturbation tests for investigating the influence on the profile fitting
results by the errors in the pre-estimated value for Lcs and the given
initial values for the two unknowns (Tm and Tcs)........................................ 123
Table 6.3: Expected properties of the “2-Zone” temperature distribution along the
LOS measurement path. ............................................................................. 133
Table 6.4: The seven water vapor transitions used in the demonstration measurements
of a “2-zone” temperature distribution. ...................................................... 134
Table 6.5: The average values of the profile fitting results with different number of
lines for cases 1 and 2................................................................................. 139
Table 6.6: The average values of the profile fitting results with different number of
lines for cases 3 and 4................................................................................. 141
Table 6.7: Comparison of the profile fitting results for all four cases with all 7 lines. .. 142
Table 6.8: The twelve H2O absorption transitions selected for the demonstration
measurements of an inverse-trapezoid temperature distribution................ 150
Table 6.9: The profile fitting results by using different number of lines........................ 153
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xvii
LIST OF FIGURES
Number Page
Figure 2.1: Schematic of direct absorption measurements. .............................................. 7
Figure 2.2: Illustration of the laser intensity transmission and the absorbance spectra.. 10
Figure 2.3: Illustration of the pressure-induced broadening and shifting (T = 296 K). .. 14
Figure 2.4: Schematic of the WMS based absorption measurements............................... 14
Figure 2.5: Illustration of DAS two-line thermometry. .................................................... 22
Figure 2.6: Illustration of WMS-2f two-line thermometry. .............................................. 24
Figure 2.7: Illustration of time-division multiplexing: (a) incident laser intensities; (b)
transmitted laser intensity recorded by the detector. .................................... 28
Figure 2.8: Schematic of wavelength-division multiplexing............................................ 29
Figure 2.9: Schematic of frequency-division multiplexing. ............................................. 30
Figure 3.1: Illustration of H2O vapor absorption transitions in the 1-8 µm region. ......... 33
Figure 3.2: Schematic of experimental arrangement used for the spectroscopy
measurements. .............................................................................................. 36
xviii
Figure 3.3: An example of (a) the raw data traces measured with the ECDL (solid
line: transmitted signal through the cell, dashed line: reference signal) for
neat H2O at T = 902 K, P = 14 Torr and L = 71.1 cm; (b) the reduced
absorption spectra. ........................................................................................ 38
Figure 3.4: Comparisons of peak absorbance between ECDL measurements and
HITRAN databases for neat H2O vapor: (a) at room temperature T = 297
K, P = 1 Torr, L = 35.6 cm; (b) at elevated temperature T = 828 K, P =
21 Torr, L = 35.6 cm..................................................................................... 40
Figure 3.5: Illustration of data analysis: (a) the measured spectra of neat H2O vapor at
T = 828 K, P = 21 Torr and L = 35.6 cm in the spectral region near
7185.60 cm-1; (b) the measured lineshape of transition 7185.60 cm-1
(solid line), its Voigt fit (dashed line) and the residual (top panel).............. 41
Figure 3.6: Comparison of linestrength between ECDL measurements and databases:
(a) at room temperature T = 297 K; (b) at elevated temperature T = 828
K. .................................................................................................................. 42
Figure 3.7: Comparison of measured spectra (top panels) of neat H2O vapor at T =
998 K, P = 16 Torr, L = 71.1 cm with simulations by HITRAN databases
(bottom panels, solid line: HITRAN 2004, dashed line: HITRAN 2000)
for: (a) line 1 region; (b) line 3 region; (c) line 4 region; (d) line 5 region. . 44
Figure 3.8: Illustration of linestrength data reduction for line 5 at 7435.62 cm-1: (a)
the measured integrated absorbance (symbol) versus pressure at T = 996
K, and the linear fit (line) used to infer the linestrength: S(996 K) =
1.697e-2 ± 9e-6 [cm-2atm-1]; (b) the measured linestrength (symbol)
versus temperature and the one-parameter best fit used to infer the
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linestrength at the reference temperature: S(296 K) = 1.932e-3 ± 4e-6
[cm-2atm-1]. ................................................................................................... 45
Figure 3.9: Illustration of air-broadening coefficient data reduction for line 2 at
7203.89 cm-1: (a) the measured collisional FWHM (symbol) versus
pressure at T = 447 K, and the linear fit (line) used to infer the γair(447
K) = 0.0410 ± 0.0001 [cm-1atm-1]; (b) the measured γair (symbol) versus
temperature, and the two-parameter best fit used to infer the γair(296 K) =
0.0537 ± 0.0001 [cm-1atm-1] and n = 0.646 ± 0.003..................................... 47
Figure 4.1: E(T) curve of H2O vapor in the temperature range of 300-3000 K................ 57
Figure 4.2: Experimental arrangement for the linestrength measurements. ..................... 59
Figure 4.3: Illustration of: (a) the measured raw data traces (solid line: transmission
through the cell, dotted line: transmission through the etalon) for the
linestrength validation of transition 7429.72 cm-1 at T = 894 K and P =
19.1 Torr; (b) the reduced lineshape of transition 7429.72 cm-1 (solid
line), its Voigt fit (dotted line) and the residual (top panel). ........................ 61
Figure 4.4: The measured spectra (solid line) of the selected four transitions and
comparisons with simulations (dotted line) by HITRAN2004 at the
experimental conditions of T = 894 K and P = 19.1 Torr: (a) line D at
7429.72 cm-1; (b) line G at 7454.45 cm-1; (c) line F at 7450.93 cm-1; (d)
line C at 7424.69 cm-1. ................................................................................. 62
Figure 4.5: Multiple-peak Voigt fit (dotted line) to the spectra (solid line) measured at
T = 894 K and P = 19.1 Torr: (a) two-peak Voigt fit for line F at 7450.93
cm-1; (b) six-peak Voigt fit for line C at 7424.69 cm-1................................. 63
xx
Figure 4.6: Determination of the linestrength from the slope of the linear fit (lines) to
the measured integrated absorbance (symbols) versus pressure at T = 894
K for: (a) line D: S(894 K) = 6.566e-3 ± 3e-6 [cm-2atm-1], line G: S(894
K) = 5.873e-3 ± 2e-6 [cm-2atm-1]; (b) line C: S(894 K) = 7.877e-3 ± 3e-6
[cm-2atm-1], line F: S(894 K) = 7.479e-3 ± 3e-6 [cm-2atm-1]. ...................... 63
Figure 4.7: Determination of the linestrength at the reference temperature Si(T0 = 296
K) from the one-parameter best fit (line) to the measured linestrength
(symbol) versus temperature with the known functional form of S(T) and
E” fixed at the HITRAN value for: (a) line D & G; (b) line C & F............. 64
Figure 4.8: Data analysis for line F’ (triangle & solid line) and a comparison with the
data analysis for line F only (circle & dotted line). Each triangle
represents the sum of linestrength values measured for line F and its
interfering neighbor. The effective linestrength at the reference
temperature Seff(296 K) = 4.818E-4 cm-2atm-1 and the effective lower
state energy "effE =1730.0 cm-1 for line F’ are inferred from a two-
parameter best fit (solid line) to the known functional form of S(T)............ 65
Figure 4.9: Calibration curves for inferring temperature from the measured ratio of
integrated areas. The dotted curves are calculated using the Si(T0) and E”
values from HITRAN. The solid curves are calculated using the
measured Si(T0) and the E” from HITRAN (using the measured "effE for
line F’). The ratio is defined as Ratio = AreaHighE”Line /AreaLowE”Line. (a)
line pair DG; (b) line pair DF’...................................................................... 66
Figure 4.10: The temperature measurement uncertainty for: (a) line pair DG; (b) line
pair DF’. The temperature measurement uncertainty is attributed to
uncertainties in spectroscopic parameters and integrated area
xxi
measurements. It will become dominated by area measurement
uncertainties for %32221
≥+= AAA σσσ ..................................................... 68
Figure 4.11: Temperatures measured by TDL sensor in the demonstration
experiments with a heated static cell and comparisons with thermocouple
readings: (a) line pair DG; (b) line pair DF’................................................. 69
Figure 4.12: Schematic of the sensor hardware for field test. .......................................... 70
Figure 4.13: Ten sample traces of line D taken consecutively in the field
measurements: (a) raw data traces with an average baseline fit; (b) the
corresponding absorbance spectra with an average Voigt fit. ...................... 71
Figure 4.14: Sample results of temperature measurements by the TDL sensor at 17
MW load in combined cycle mode. Each temperature is inferred from an
average of 20 sequential raw data scans. The solid line represents the
mean (724 K) of temperatures measured by the TDL sensor within five
and half minutes. The dotted line represents an average (730 K) of
temperatures measured by Type-K thermocouples within the same time
duration......................................................................................................... 72
Figure 5.1: Potential compression strokes of IC engines. The working conditions of
the TDL temperature sensor are confined by two extreme compression
strokes, the heavy exhaust gas recirculation (EGR) stroke which defines
the highest temperature at a certain pressure and the supercharging stroke
which defines the highest pressure at a certain temperature. A and B are
two extreme T/P conditions used for the selection of laser set-points. ........ 76
xxii
Figure 5.2: Absorption spectra of H2O vapor simulated at different pressures, T =
1000 K, XH2O = 1% and L = 1 cm. ................................................................ 76
Figure 5.3: Absorption spectra of the two target lines and their neighboring features
simulated for neat H2O vapor at T = 296 K, P = 18 Torr and L = 1 cm
with spectroscopic parameters from HITRAN2004: (a) line 1 and its
neighbors; (b) line 2 and its neighbors. ........................................................ 81
Figure 5.4: Illustration of raw data and data analysis: (a) the measured raw data traces
(solid line: transmission through the cell, dotted line: transmission
through the etalon) for line 1 region at T = 296 K, PH2O-air = 403 Torr and
XH2O = 1.56%. The inset shows the polynomial baseline fit (dash line)
for line 1 and 1B; (b) the reduced lineshape of line 1 and 1B (solid line),
the two-line Voigt fit (dotted line) and the residual (top panel)................... 82
Figure 5.5: Illustration of the determination of linestrength and broadening
coefficients at a selected temperature with the data measured for line 1 at
T = 296 K. With measurements for neat H2O vapor at various pressures,
(a) linestrength inferred from the linear fit to the integrated absorbance,
S1(296 K) = 6.927e-2 ± 2e-05 [cm-2atm-1]. With measurements for H2O-
air mixture at various pressures, (b) air-broadening coefficient inferred
from the linear fit to the collisional FWHM, γair(296 K) = 0.0539 ±
0.0001 [cm-1atm-1]. ....................................................................................... 84
Figure 5.6: Illustration of the determination of pressure-induced frequency shift
coefficients at a selected temperature. (a) raw data traces measured for
line 1 region with H2O-air mixture under two different pressures at T =
296 K; (b) expanded view of raw data traces for line 1; (c) reduced
spectra of line 1; (d) air-induced frequency shift coefficient inferred from
xxiii
the linear fit to the relative line-center frequencies at various pressures,
δair(296 K) = -0.0164 ± 0.0002 [cm-1atm-1].................................................. 85
Figure 5.7: The measured linestrength values (symbol) of line 1 and line 2 at various
temperatures and the one-parameter best fit (line) used to infer the
linestrength values at the reference temperature Si(T0 = 296 K). ................. 86
Figure 5.8: The measured pressure-broadening coefficients (symbol) of line 1 and line
2 at various temperatures and the two-parameter best fit (line) used to
infer: (a) the air-broadening coefficients at the reference temperature
γair(T0 = 296 K) and the temperature exponents nair; (b) the CO2-
broadening coefficients at the reference temperature γCO2(T0 = 296 K)
and the temperature exponents nCO2. ............................................................ 86
Figure 5.9: The measured pressure-induced frequency shift coefficients (symbol) of
line 1 and line 2 at various temperatures and the two-parameter best fit
(line) used to infer: (a) the air-shift coefficients at the reference
temperature δair(T0 = 296 K) and the temperature exponents mair; (b) the
CO2-shift coefficients at the reference temperature δCO2(T0 = 296 K) and
the temperature exponents mCO2. .................................................................. 87
Figure 5.10: Comparisons of calibration curves calculated based on the hybrid
spectroscopic database and HITRAN2004 at 25atm.................................... 92
Figure 5.11: WMS-2f spectra simulated at condition A (P = 5atm, T = 701 K) and B
(P = 25 atm, T = 610 K). (a) The low E” spectral region. (b) The high E”
spectral region. ............................................................................................. 93
Figure 5.12: The T/P nodes used for the evaluation of the sensor performance. ............. 94
xxiv
Figure 5.13: Illustration of the non-monotonic behavior in the ratio of the WMS-
2f/WMS-1f signals for the candidate frequency pair of 7203.9 cm-1 and
7435.5 cm-1. .................................................................................................. 96
Figure 5.14: Illustration of the sensor performance at the candidate laser set-points of
7203.5 cm-1 and 7435.7 cm-1 for P = 10 atm: (a) The WMS-1f
normalized WMS-2f signals; (b) the ratio of WMS-2f/WMS-1f signals
and the estimated temperature measurement uncertainty ∆T arising from
measurement noises...................................................................................... 98
Figure 5.15: Illustration of the sensor performance with laser set-point uncertainty for
the candidate frequency pair of 7203.8 cm-1 and 7435.7 cm-1 at pressure
of 25 atm. (a) A comparison of the WMS-2f/WMS-1f signal ratio at the
desired laser set-points with the ratios at the potential maximum offsets;
(b) A blowup of the boxed region in panel (a) to illustrate the
temperature measurement uncertainty arising from the laser set-point
uncertainty. ................................................................................................... 99
Figure 5.16: 3D illustrations of the calibration databases for the fixed-wavelength
WMS-2f two-line thermometry over the entire T/P region. (a) The ratio
of the WMS-2f/WMS-1f signals; (b, c) The WMS-2f/WMS-1f signals at
the low E” and high E” set-points. ............................................................. 102
Figure 5.17: Illustration of the polynomial fits to the simulated data over the 50
temperature nodes prescribed for the pressure of 25 atm. (a) The
temperature vs. ratio; (b) the WMS-2f/WMS-1f signals vs. the
temperature. ................................................................................................ 103
Figure 5.18: Illustration of calculating temperature from the measured ratio of WMS-
2f/WMS-1f signals for an intermediate pressure between 24 and 25 atm. 105
xxv
Figure 6.1: Postulated temperature distribution profiles for confined combustion gases
with cold walls............................................................................................ 110
Figure 6.2: Lower state energy E” vs. line center frequency for the selected 278
candidates after the initial screening described in section 6.3.1................. 114
Figure 6.3: Two generic (hypothetic) temperature distributions to be measured: (a) the
“2-T” distributions which are equivalent in terms of LOS absorption; (b)
the parabolic distribution............................................................................ 116
Figure 6.4: The ideal Boltzmann plot of absorption measurements along (a) the “2-T”
profiles; (b) the parabolic profile defined in Fig. 6.3. Uniform: T = 1900
K; ∆T = 800 K: Tm(Tc) = 1900K, Tcs(Tcb, Tw) = 1100K; ∆T = 1600K:
Tm(Tc) = 1900K, Tcs(Tcb, Tw) = 300K.......................................................... 116
Figure 6.5: The postulated “2-T” profile for measurements of the non-uniform
temperature distribution presented in the top panel of Fig. 6.3(a) using
the profile fitting strategy. .......................................................................... 120
Figure 6.6: Profile fitting results (three unknowns) for the “2-T” temperature
distribution (∆T = 800 K). .......................................................................... 121
Figure 6.7: Profile fitting results (two unknowns) for the “2-T” temperature
distribution (∆T = 200 K). .......................................................................... 122
Figure 6.8: Influence of the temperature non-uniformity ∆T on the profile fitting
results for the “2-T” temperature distribution. Only 4 lines are used. ....... 122
Figure 6.9: Profile fitting results for the nine perturbation tests listed in Table 6.2 for
the “2-T” temperature distribution (∆T = 200 K). Only 4 lines are used. .. 123
xxvi
Figure 6.10: The postulated parabolic profile for measurements of the non-uniform
temperature distribution shown in Fig. 6.3(b) using the profile fitting
strategy. ...................................................................................................... 125
Figure 6.11: Profile fitting results for the parabolic temperature distribution (∆T=400
K)................................................................................................................ 125
Figure 6.12: Influence of the temperature non-uniformity ∆T on the profile fitting
results for the parabolic temperature distribution. 8 lines are used. ........... 126
Figure 6.13: Temperature binning results for the “2-T” temperature distributions (∆T
= 800 K, 5 bins): (a) Illustration of the averaged PDF solution solved
with 6 lines; (b) the residual and STD of the PDF solutions solved with
different number of lines. ........................................................................... 127
Figure 6.14: Influence of number of bins on the temperature binning results for the
“2-T” temperature distributions (∆T = 800 K, 16 lines): (a) the averaged
PDF solutions; (b) the residual and STD for different number of bins. ..... 127
Figure 6.15: Influence of the temperature non-uniformity ∆T on the temperature
binning results for the “2-T” temperature distributions (3 bins and 16
lines): (a) the averaged PDF solutions; (b) the residual and STD for
different magnitude of ∆T. ......................................................................... 128
Figure 6.16: Temperature binning results for the parabolic temperature distribution
(∆T = 800 K, 4 bins): (a) the averaged PDF solution solved with 4 lines;
(b) the residual and STD of the PDF solutions solved with different
number of lines. .......................................................................................... 129
xxvii
Figure 6.17: Influence of number of bins on the temperature binning results for the
parabolic temperature distribution (∆T = 400 K, 16 lines): (a) the
averaged PDF solution; (b) the residual and STD for different number of
bins. ............................................................................................................ 130
Figure 6.18: Influence of the temperature non-uniformity ∆T on the temperature
binning results for the parabolic temperature distribution (3 bins and 4
lines): (a) the averaged PDF solution; (b) the residual and STD for
different magnitude of ∆T. ......................................................................... 130
Figure 6.19: Schematic of the experimental setup for a WDM absorption sensor. ........ 131
Figure 6.20: Thermocouple measurements of the non-uniform temperature
distribution along the laser beam path. The water mole fraction is ~10%
in the high temperature zone and ~1.75% in the room temperature zone
as listed in Table 6.3. .................................................................................. 131
Figure 6.21: Illustration of the absorption spectra for each of the five lasers measured
with the experimental setup shown in Fig. 6.19 and conditions listed in
Table 6.4. .................................................................................................... 134
Figure 6.22: Illustration of the hybrid Voigt fit for the measured lineshape of line 5.... 136
Figure 6.23: The “2-Zone” property distribution postulated for profile fitting
calculation................................................................................................... 137
Figure 6.24: Profile fitting results for case 1: T1, T2, X1 and X2 fit using (a) lines 1-5;
(b) lines 1-7................................................................................................. 138
xxviii
Figure 6.25: Profile fitting results for case 2: X1 fixed, T1, T2 and X2 fit using (a) lines
1-5; (b) lines 1-7. ........................................................................................ 139
Figure 6.26: Profile fitting results for case 3: X1 and X2 fixed, T1 and T2 fit using (a)
lines 1-3; (b) lines 1-5; (c) lines 1-7. .......................................................... 141
Figure 6.27: Profile fitting results for case 4: T1 and X1 fixed, T2 and X2 fit using (a)
lines 1-3; (b) lines 1-5; (c) lines 1-7. .......................................................... 141
Figure 6.28: Illustration of the temperature binning results solved using all 7
transitions. .................................................................................................. 143
Figure 6.29: The flat flame burner: (a) Photo illustration; (b) Schematic of the
configuration............................................................................................... 145
Figure 6.30: Thermocouple measurements of the flame temperature along (a) the
entire LOS laser beam path; (b) amplification of panel (a) to show the
inverse-trapezoid temperature distribution by neglecting the sharp
temperature drops at both ends................................................................... 146
Figure 6.31: Schematic of the experimental setup.......................................................... 147
Figure 6.32: The raw data measured by ECDL: (a) the full scanning range; (b)
illustration of the details of the raw data. ................................................... 148
Figure 6.33: The reduced absorption spectra measured by ECDL in the flame with
temperature distribution shown in Fig. 6.30............................................... 148
Figure 6.34: Lower state energy vs. line center frequency of the selected candidates. .. 149
Figure 6.35: The measured absorption spectra of the selected 12 transitions. ............... 150
xxix
Figure 6.36: The postulated inverse-trapezoid profile.................................................... 151
Figure 6.37: Profile fitting results (three unknowns) by using different number of
lines: (a) The entire path length; (b) Amplification of the two ends. ......... 152
Figure 6.38: Profile fitting results (two unknowns) by using different number of lines:
(a) The entire path length; (b) Amplification of the two ends.................... 153
Figure 6.39: Temperature binning results: (a) the PDF solution obtained by using all
12 lines; (b) the temperature distributions inferred from the PDF
solution. ...................................................................................................... 154
Figure 7.1: The temperature distributions along the measurement path of 10 cm at
three instantaneous times for a turbulent flow. .......................................... 164
Figure 7.2: The exact temperature binning result (PDF) for any of the temperature
distributions shown in Fig. 7.1. .................................................................. 165
Figure 7.3: The postulated PDF for the temperature distribution along the LOS
measurement path in a turbulent flow. ....................................................... 166
xxx
1
Chapter 1
INTRODUCTION
1.1 Motivation and scope
Gas temperature sensing is very important for combustion diagnostics since gas
temperature is a good indicator of combustion efficiency and it also affects the formation
of harmful emissions. Line-of-sight (LOS) laser absorption spectroscopy provides a non-
intrusive, fast, sensitive and reliable solution for quantitative sensing of multiple flow
field parameters including gas temperature. [Hanson and Falcone 1978, Demtroeder
1982, Allen 1998, Sanders et al. 2000, Ebert et al. 2000, Kohse-Höinghaus et al. 2005]
H2O vapor is often selected as the absorbing species for LOS absorption based gas
temperature sensing [Baer et al. 1994, Arroyo et al. 1994, Webber et al. 2000, Teichert et
al. 2003] since it is a major combustion product and it has strong rovibrational spectra
ranging from visible to middle-infrared (MIR) [Herzberg 1945]. This thesis investigates
gas temperature sensing in uniform and non-uniform flows based on LOS laser
absorption spectroscopy of H2O vapor.
The optimized design of any temperature sensors based on H2O vapor absorption
requires a complete catalog of the H2O transitions with accurate spectroscopic data. The
HITRAN spectroscopy database [Rothman et al. 2005] provides an extensive compilation
of fundamental spectroscopic parameters for many important small molecules including
H2O. However, HITRAN was originally designed for atmospheric monitoring
applications [McClatchey et al. 1973] that have a typical temperature range of 200-350
K. Therefore, the design capability of HITRAN for combustion or other applications at
2 CHAPTER ONE
elevated temperatures needs to be systematically examined. This need plus the release of
the latest version of HITRAN (HITRAN2004) motivate us to carry out an extensive
experimental survey of near-infrared (NIR) H2O spectroscopy. This survey is focused on
the 2ν1, 2ν3, and ν1+ν3 bands of H2O absorption spectra within the 1.3-1.5 µm region,
since they overlap with the most common telecommunication bands where diode lasers
and optical fibers are widely available [Allen 1998], and thus are often used for sensor
development [Furlong 1998, Nagali 1998, Liu 2004, Zhou 2005]. Based on this broad
survey, we found HITRAN2004 is sufficiently accurate for sensor design but still not
sufficient for quantitative sensor applications. The spectroscopic data of H2O vapor
transitions selected for high-temperature sensors generally require laboratory validation
or determination to enable accurate measurements of gas temperature. This conclusion
motivated us to measure the spectroscopic parameters for the specific H2O vapor
transitions we selected for specific temperature sensing applications.
Based on LOS absorption spectroscopy, two-line thermometry provides a simple
but efficient solution for gas temperature sensing [Hanson and Falcone 1978, Zhou et al.
2003, Liu et al. 2005]. Since two-line thermometry actually yields a path-averaged
temperature due to the implicit assumption of a uniform gas medium along the LOS
measurement path, it is most appropriate for temperature sensing in near-uniform flows
or over very short pathlengths where the sampled gas can be assumed to be uniform. This
thesis provides an example for each case.
The first example is temperature sensing for a gas turbine exhaust, which has
relatively uniform temperature, constant atmospheric pressure and substantial path
length. Since strong and isolated H2O transitions exist for this measurement condition, we
chose scanned-wavelength direct absorption spectroscopy (DAS) based two-line
thermometry for its simplicity in measurement execution and data reduction, as well as its
immunity to non-resonant transmission loss caused by beam steering, window
attenuation, scattering by droplets or soot, and other effects.
INTRODUCTION 3
The second application is in-cylinder temperature sensing for the compression
stroke of an internal-combustion (IC) engine, which has limited optical access with a very
short sample path, time-changing and widely varying temperature and pressure. At
elevated pressures, pressure-broadened spectral features, which lack non-absorbing
wings, present serious challenges for determining laser intensity baselines in DAS
measurements. Therefore, the two-line thermometry we designed for this IC engine
application is based on a fixed-wavelength scheme using wavelength modulation
spectroscopy with 2f detection (WMS-2f), which requires no baseline, allows for larger
measurement bandwidth over the scanned-wavelength scheme, and provides superior
signal to noise (SNR) over the DAS measurements.
However, in many practical flow fields, significant temperature gradients may exist
along the LOS measurement path due to chemical reactions, flow mixing, phase change,
heat transfer to the walls, and other effects. For such non-uniform flows, two-line
thermometry is no longer appropriate. A large portion of this thesis is devoted to the
development of a novel multi-line thermometry strategy which successfully extends LOS
absorption spectroscopy to temperature sensing in non-uniform flows.
1.2 Organization of thesis
The overall objective of this thesis is to investigate gas temperature sensing in
uniform and non-uniform flows based on LOS laser absorption spectroscopy of H2O
vapor. The present chapter discusses the motivation, organization, and primary
contribution of this thesis. Chapter 2 provides the theoretical spectroscopy background
necessary to understand the new research developments covered by the following
chapters. Chapter 3 provides a systematic experimental survey of NIR H2O spectroscopy
to evaluate the sensor design capability of HITRAN2004 for combustion applications.
Chapter 4 discusses the design and demonstration of DAS two-line thermometry for
uniform gases, and its application in the measurement of the path-averaged bulk
4 CHAPTER ONE
temperature of a gas turbine exhaust. Chapter 5 investigates several crucial steps for the
design of WMS-2f two-line thermometry for in-cylinder measurement of the time-
varying gas temperature during the compression stroke of IC engines. Chapter 6 is
devoted to the development of the novel multi-line thermometry for temperature sensing
in non-uniform flows. Chapter 7 summarizes the major achievements and conclusions of
this work, and suggests some future directions for continued research in relevant areas.
1.3 Primary contribution
The primary contributions of this thesis include: first, the sensor design capability
of the HITRAN spectroscopy database for combustion applications is evaluated by
extensive experimental survey of NIR H2O spectroscopy. We found that HITRAN2004 is
good enough for sensor design, but still not sufficient for quantitative sensor applications.
Second, the laboratory procedures for accurate and precise measurement of
spectroscopic parameters at atmospheric and sub-atmospheric pressures are developed,
improved and standardized. Based on the measured spectroscopy data, accurate two-line
thermometry in uniform gases is demonstrated. Simulation codes are also developed to
predict direct absorption and WMS-2f spectra for a variety of high temperature and high
pressure conditions.
Third, design rules for laser set-point selection are introduced to optimize the
WMS-2f two-line thermometry sensor over a wide range of temperature and pressure for
IC engine applications.
Finally, a novel multi-line thermometry strategy for temperature sensing in non-
uniform flows is developed. The first multi-line thermometry demonstration was
published by Sanders et al [Sanders et al. 2001], who used measurements of a few O2
absorption lines to infer the temperature distribution of an optical path through two static
cells at different temperatures. Here in this thesis, systematic and extensive investigations
INTRODUCTION 5
on the sensor concepts, mathematic models and design rules are presented. Both
simulation calculations and experiments are performed to illustrate sensor concepts and
investigate sensor performance. This work also represents the first use of H2O absorption
for multi-line thermometry, which has significant practical importance since H2O vapor is
a common target species for combustion diagnostics. The extensive theoretical,
simulation and experimental studies provide the ground work for future applications of
multi-line, non-uniform LOS thermometry as a practical combustion diagnostic.
6 CHAPTER ONE
7
Chapter 2
FUNDAMENTALS OF LASER ABSORPTION
SPECTROSCOPY
Laser absorption spectroscopy techniques can be roughly divided into two
categories in terms of laser operation and signal detection: direct absorption spectroscopy
and modulation spectroscopy. The theory of both techniques has been well documented
[Chou 2000, Webber 2001, Wang 2001, Zhou 2005]. In this chapter, the basic concepts
and principles for both techniques, which are necessary for the new research
developments covered by the following chapters, are briefly introduced in the first two
sections, followed by a summary of the temperature sensing techniques based on LOS
absorption spectroscopy. Wavelength multiplexing schemes which are often necessary to
exploit two-line or multi-line thermometries are presented in the last section.
2.1 Direct absorption spectroscopy
2.1.1 Beer-Lambert law
Figure 2.1: Schematic of direct absorption measurements.
L
ItI0
L
ItI0
P, T(x), Xabs(x)Ii
8 CHAPTER TWO
In direct absorption spectroscopy (DAS) measurements, a collimated laser beam
with an intensity of Ii is shone through the sample gas, and the transmitted laser intensity
It is measured with a detector, as shown by Fig. 2.1. When the laser frequency ν [cm-1] is
resonant with the frequency of a transition for the absorbing species in the gas, the laser
energy will be absorbed. The attenuation of the laser intensity along a differential path
length of dx can be predicted as follows by the Einstein theory of radiation [Banwell and
McCash 1994]
( )( ) ( )abs idI P X x S T x dxI
νν
ν
φ−= ⋅ ⋅ ⋅ ⋅ , (2.1)
where Iν is the laser intensity, P [atm] the total pressure, T(x) [K] the local temperature,
Xabs(x) the local mole fraction of the absorbing species, φν [cm] the lineshape function
which will be discussed in detail in the next subsection, and Si [cm-2atm-1] the
linestrength of the transition i. The linestrength is a function of the temperature
1"
0 0 0 00
0 0
( ) 1 1( ) ( ) exp 1 exp 1 exp( )
Q T T hcE hc hcS T S TQ T T k T T kT kT
ν ν−
− − = − − − − ,(2.2)
Where h [J⋅s] is Planck's constant, c [cm/s] is the speed of light, k [J/K] is Boltzmann’s
constant, Q(T) the partition function of the absorbing molecule, T0 [K] the reference
temperature (usually 296 K), ν0 [cm-1] the line-center frequency and E” [cm-1] the lower
state energy of the transition. The lower state energy E” determines the equilibrium
molecular population in the unabsorbing state as a function of temperature, and thus
controls how the linestrength of a particular transition varies with temperature.
The fractional transmission τν for a total path length of L [cm] can be inferred from
Eq. (2.1) as
( )( )00
exp ( ) ( )L
tabs i
I P X x S T x dxIν ν
ν
τ φ
= = −
∫ , (2.3)
FUNDAMENTALS OF LASER ABSORPTION SPECTROSCOPY 9
where I0 is the zero-absorption baseline intensity. In practical measurements, I0 is less
than the incident laser intensity Ii due to some non-resonant transmission losses caused by
beam steering, window attenuation, scattering by droplets or soot, and other effects. In a
fixed-wavelength direct absorption measurement, I0 can be approximated by the product
of the measured incident laser intensity Ii and the fractional transmission of the optical
elements which is measured with an off-resonant laser beam. This off-resonant beam is
multiplexed with the resonant laser beam as a transmission probe with the assumption
that all transmission losses except the gas absorption affect two lasers equally. In a
scanned-wavelength direct absorption measurement, I0 is usually fit from the non-
absorbing wings of the measured absorption feature to account for the laser intensity
variation, the detection gains, and the non-resonant transmission loss. In cases where no
zero-absorbing wings are available within the laser scanning range, owing for example to
pressure broadening (section 2.1.2) of the absorption feature or the interferences from
neighboring lines in a congested spectra, I0 can be approximated by measuring the
transmitted laser intensity when the sample gas region is purged with some non-
absorbing gas.
The absorbance αν is defined as
( )0
0
ln ( ) ( )L
tabs i
I P X x S T x dxIν ν
ν
α φ
≡ − =
∫ . (2.4)
Figure 2.2 illustrates the transmitted laser intensity It and baseline intensity I0 in the
frequency domain, and the resultant absorbance spectra. Since the lineshape function φ is
normalized such that ( ) 1dφ ν ν∞
−∞≡∫ , the spectrally-integrated absorbance A [cm-1], which
is the area underneath the absorption lineshape can be inferred from Eq. (2.4) as
( )0
( ) ( )L
abs iA d P X x S T x dxνα ν∞
−∞= =∫ ∫ . (2.5)
10 CHAPTER TWO
Figure 2.2: Illustration of the laser intensity transmission and the absorbance spectra.
When the gas medium is uniform (i.e. with uniform temperature T and species mole
fraction Xabs along the measurement path), Eq. (2.3) reduces to the Beer-Lambert’s law,
which is the most commonly used equation in DAS
( )0
exp ( )tabs i
I PX S T LIν ν
ν
τ φ
= = −
. (2.6)
The spectral absorbance is thus simplified as
( )abs iP X S T Lν να φ= ⋅ ⋅ ⋅ ⋅ , (2.7)
and the integrated absorbance is reduced to the product of the partial pressure of the
absorber, the linestrength at the gas temperature and the pathlength
( )abs iA P X S T L= ⋅ ⋅ ⋅ . (2.8)
2.1.2 Spectral lineshapes
The lineshape function φ(ν) of a particular absorption transition, which represents
the relative variation in the spectral absorbance with frequency, is determined by the
physical mechanisms that perturb the energy levels of the transition or the way in which
the absorbing molecules interact with the laser beam [Herzberg 1945, Yariv 1982,
Banwell and McCash 1994]. For the measurement conditions involved in the research for
Frequency
Inte
nsity
I0
It
Frequency
Inte
nsity
Frequency
Inte
nsity
I0
It
Frequency
Abs
orba
nce
A = area
Frequency
Abs
orba
nce
Frequency
Abs
orba
nce
A = area
(a) (b)
FUNDAMENTALS OF LASER ABSORPTION SPECTROSCOPY 11
this thesis, Doppler broadening, pressure (collisional) broadening and shifting are
important and thus will be summarized in this subsection. The discussion of other
mechanisms such as collisional line mixing [Levy et al. 1992, Eckbreth 1996, Nagali
1998] or Dicke narrowing [Dicke 1953, Murray and Javan 1972, Varghese and Hanson
1984a, Chou 2000], which are negligible for the current research but significant for some
other special cases (e.g. ultra high or ultra low pressures) can be found in the literature.
Doppler broadening of a spectral line is due to the random thermal motion of the
absorbing molecules. Once a molecule has a velocity component in the laser propagation
direction, the frequency at which the molecule absorbs photons will be changed. Since
the random thermal motion of molecules obeys a Maxwell velocity distribution, which
can be represented by a Gaussian function [Vincenti and Kruger 1965], the corresponding
Doppler lineshape function φD(ν) has a Gaussian form
2
02 ln 2( ) exp 4ln 2DD D
ν νφ νν π ν
−= − ∆ ∆
. (2.9)
The Doppler full-width at half maximum (FWHM) ∆νD [cm-1] is given by
70 02
8 ln 2 7.1623 10DkT Tmc M
ν ν ν−∆ = ≈ × , (2.10)
where M [g/mol] is the molecular weight of the absorbing species.
Pressure broadening and shifting of spectral lines are caused by the perturbation of
the energy levels due to molecular collisions. The measurement conditions for the current
research are well within the impact collision limit, which assumes that the collisions are
binary and the duration of collisions is negligibly short. In the impact theory, the
pressure-broadened lineshape takes a Lorentzian profile, which is symmetric about the
pressure-shifted line center ν0+∆νS
12 CHAPTER TWO
( ) ( )2 2
0
1 / 2( )/ 2
CC
S C
νφ νπ ν ν ν ν
∆=
− − ∆ + ∆, (2.11)
where ∆νC [cm-1] is the collisional FWHM and ∆νS [cm-1] the pressure-induced
frequency shift. With the binary collision assumption, both ∆νC and ∆νS should be
proportional to the system pressure
2C j jj
P Xν γ∆ = ∑ , (2.12)
S j jj
P Xν δ∆ = ∑ , (2.13)
where γj [cm-1atm-1] and δj [cm-1atm-1] are the broadening and shifting coefficients due to
the collisions between the absorbing molecules and the perturbing molecules j (called
foreign-gas broadening/shifting), or between the absorbing molecules themselves (called
self-broadening/shifting). γj and δj scale from the values at the reference temperature with
the temperature exponents nj and mj respectively
00( ) ( )
jn
j jTT TT
γ γ =
, (2.14)
00( ) ( )
jm
j jTT TT
δ δ =
. (2.15)
Note that although the pressure broadening coefficient γj is always positive, the pressure-
induced frequency shift coefficient δj can be either negative or positive, and can even
change its sign as the temperature increases [Gamache et al. 1998].
Doppler broadening usually dominates at low pressures, and collisional broadening
becomes dominant at high pressures. In many atmospheric applications, both mechanisms
are significant. If the collisional broadening is assumed statistically independent of the
FUNDAMENTALS OF LASER ABSORPTION SPECTROSCOPY 13
thermal motion, the overall lineshape will be a convolution of the Gaussian and
Lorentzian lineshapes, which is a Voigt profile
2 ln 2( ) ( ) ( ) ( , )V D C VD
u u du V a wφ ν φ φ νν π
+∞
−∞= − =
∆∫ . (2.16)
The normalized Voigt function V(aV,w) is characterized by two non-dimensional
parameters:
ln 2 CV
D
a νν
∆=
∆, (2.17)
which indicates the relative significance of the collisional and Doppler broadening
mechanisms, and
02 ln 2 S
D
w ν ν νν
− − ∆=
∆, (2.18)
which indicates the distance from the pressure-shifted line center. The Voigt profile,
which has been the basis for most quantitative absorption spectroscopy doesn’t have a
simple analytical form. It is either approximated by complex functions [Whiting 1968] or
most often calculated numerically [Humlicek 1982, Schreier 1992]. For very small or
very large values of aV, the Voigt profile reduces to the Doppler or Lorentzian lineshape
respectively.
As an example, the integrated absorbance A, the pressure-induced frequency shift
∆νS, as well as the overall linewidth which includes contributions from both the Doppler
FWHM ∆νD and collisional FWHM ∆νC are illustrated in Fig. 2.3 on the lineshapes of an
isolated H2O transition at a water vapor partial pressure of 15 Torr with/without a buffer
gas of dry air.
14 CHAPTER TWO
Figure 2.3: Illustration of the pressure-induced broadening and shifting (T = 296 K).
2.2 Wavelength modulation spectroscopy
Figure 2.4: Schematic of the WMS based absorption measurements.
In wavelength-modulation-spectroscopy (WMS) absorption measurements, the
wavelength of the diode laser is sinusoidally modulated at frequency f, and the
transmitted laser intensity It(t) is measured with a detector. Usually the second harmonic
(2f) component in the detected signal is isolated using a lock-in amplifier, as shown in
Fig. 2.4. Note at higher frequencies, radio frequency mixers are used for this task [Chou
2000]. WMS with 2f detection (WMS-2f) is a very sensitive technique since it shifts the
L
ItI0
T, P, Xabs
Function Generator
Lock-in Amplifierf 2f
L
ItI0
T, P, Xabs
L
ItI0
L
ItI0
T, P, Xabs
Function Generator
Lock-in Amplifierf 2f
Function Generator
Lock-in Amplifierf 2f
Ii
0.10
0.08
0.06
0.04
0.02
0.00
Abs
orba
nce
7203.27203.17203.07202.97202.87202.77202.6Frequency [cm
-1]
H2O-Air Mixture: P=1atm, PH2O=15torr, L=10cm Neat H2O: PH2O=15torr, L=1cm
A=PH2O·S·L
∆νs = Pair·δair
∆νC = Pair·2γair + PH2O·2γself FWHM
∆νD
FUNDAMENTALS OF LASER ABSORPTION SPECTROSCOPY 15
detection bandwidth to higher frequencies, which rejects many low frequency noise
sources present in practical measurements and thus significantly improves the signal-to-
noise ratio (SNR) over direct absorption measurements.
The theory of WMS-2f has been well documented in the literature [Reid and Labrie
1981, Philippe and Hanson 1993, Kluczynski and Axner 1999, Schilt et al. 2003], most
of which use small modulation depths. Li et al. [Li et al. 2006] have developed an
improved model for WMS-2f using current-tuned diode lasers with a large modulation
depth, which is required for optimal detection of broadened and blended absorption
spectra at elevated pressures [Liu et al. 2004b]. This section only presents the concepts
and relations needed to understand the design of a WMS-2f temperature sensor for the
compression cycles of an IC-engine (Chapter 5) where the wide pressure range dictates
wide modulation depths. A more detailed theoretical development and model validation
for wide-modulation-depth WMS-2f can be found in Li et al. [2006].
If the injection current of a diode laser is sinusoidally modulated at frequency f
[Hz], the instantaneous laser frequency can be well described by a linear frequency
modulation (FM)
( ) cos( )t a tν ν ω= + , (2.19)
where ω = 2πf is the angular frequency, ν [cm-1] is the center laser frequency (laser set-
point) and a [cm-1] the modulation depth. The corresponding laser intensity modulation
(IM) can be modeled by
[ ]0 0 0 1 2 2( ) 1 cos( ) cos(2 )I t I i t i tω ψ ω ψ= + + + + , (2.20)
where I0(t) is the instantaneous laser intensity, 0I is the average laser intensity at ν , i0 is
the linear and i2 the nonlinear IM amplitude (both are normalized by 0I ), ψ1 is the linear
and ψ2 the nonlinear FM/IM phase shift. For a particular laser, all of these parameters
16 CHAPTER TWO
have to be characterized at the desired modulation frequency and modulation depth. It has
been found [Li et al. 2006] that for commercial diode lasers with injection current
modulation, i0 increases linearly and i2 increases quadratically with the modulation depth,
and thus both the linear and 2nd-order nonlinear IM effects cannot be neglected for large
modulation depths. Higher-order harmonics in the nonlinear IM are negligibly small even
for large modulation depths, and thus are not included in Eq. (2.20).
The transmitted laser intensity, which is measured by the detector can be predicted
with the instantaneous incident laser intensity as
0( ) ( ) ( cos )tI t I t v a tτ ω= ⋅ + . (2.21)
Based on Beer’s law Eq. (2.6) and the definition of spectral absorbance Eq. (2.7), the
fractional transmission can be approximated by the following equation for small
absorptions (optically thin, α(ν) < 0.1)
( cos( )) 1 ( cos( ))v a t v a tτ ω α ω+ ≈ − + . (2.22)
The spectral absorbance is a periodic even function in ω t due to the FM, and thus can be
expanded into the following Fourier cosine series
0
( cos( )) ( , ) cos( )kk
v a t H v a k tα ω ω∞
=
+ = − ⋅∑ . (2.23)
By substituting Eq. (2.7) into Eq. (2.23), the coefficients for the Fourier harmonics can be
calculated as
0( , ) ( ) ( cos )2
absi i
i
PX LH v a S T v a dπ
π
φ θ θπ −
= − +∑∫ , (2.24)
( , ) ( ) ( cos )cosabsk i i
i
PX LH v a S T v a k dπ
π
φ θ θ θπ −
= − +∑∫ , (2.25)
FUNDAMENTALS OF LASER ABSORPTION SPECTROSCOPY 17
where θ = ω t. The summation accounts for the absorption contributions from
neighboring transitions, which are not negligible at elevated pressures due to pressure
broadening and blending. For low absorber concentrations, these Fourier coefficients can
be regarded as proportional to Xabs due to the negligible dependence of lineshape
functions φi(ν) on Xabs.
If a digital lock-in amplifier is used to isolate the 2f component of the transmitted
laser intensity, It(t) will be first multiplied with a cosine and a sine reference signal, both
of which are at twice of the laser modulation frequency, and then low-pass filtered to
obtain the X and Y component of the WMS-2f signal, which can be inferred [Li et al.
2006] from Eq. (2.21)-(2.23) as
( )0 0 42 2 1 3 1 2 0 2cos 1 cos
2 2 2fGI i HX H H H i Hψ ψ = + + + + +
, (2.26)
( )0 0 42 1 3 1 2 0 2sin 1 sin
2 2 2fGI i HY H H i Hψ ψ = − − + + −
, (2.27)
where G is the optical-electrical gain of the detection system and the detection phase shift
(i.e. the phase shift between the detector and the reference signal) has been assumed to be
zero. The final WMS-2f magnitude output from the digital lock-in amplifier, which is
actually independent of detection phase shift, can thus be predicted as
2 22 2 2f f fR X Y= + . (2.28)
Note that R2f is not proportional to the mole fraction of the absorbing species, since
when there is no absorption, the X and Y components reduce to non-zero values
0 02 2 2cos
2fGIX i ψ= , (2.29)
18 CHAPTER TWO
0 02 2 2sin
2fGIY i ψ= , (2.30)
which are not negligible for large modulation depth due to the quadratic dependence of
the nonlinear IM magnitude i2 on the modulation depth a. The amplitude of the zero-
absorption WMS-2f background signal can be inferred from Eq. (2.29)-(2.30) as
0 02 22f
GIR i= , (2.31)
which are usually referred to as residual amplitude modulation (RAM).
The WMS-2f background components 02 fX and 0
2 fY can be measured by purging
the sample gas region with non-absorbing gas and subtracted from X2f and Y2f
respectively to obtain the WMS-2f magnitude which is due only to the absorption
( )
( )
0 2 0 22 2 2 2 2
2
0 0 42 1 3 1 2 0 2
1 220 4
1 3 1 2 0 2
( ) ( )
cos cos2 2 2
sin sin2 2
f f f f fS X X Y Y
GI i HH H H i H
i HH H i H
ψ ψ
ψ ψ
= − + −
= + + + +
+ − + −
. (2.32)
Although this background subtracted WMS-2f magnitude S2f is proportional to the mole
fraction of absorbing species Xabs in optically thin conditions, it cannot be directly used to
infer Xabs without calibration due to its dependence on the detection gain G and the
average laser intensity 0I .
The amplitude modulation produced by the injection current modulation of a diode
laser incurs a signal at 1f. This WMS-1f harmonic component in the transmitted laser
intensity can be measured simultaneously with the WMS-2f signal to monitor the
detection gain, laser intensity variation, and non-resonant transmission loss due to beam
FUNDAMENTALS OF LASER ABSORPTION SPECTROSCOPY 19
steering, window attenuation, and scattering by droplets or soot. The principle to isolate
the WMS-1f signal by a digital lock-in amplifier is similar to that for the WMS-2f signal
detection except that the reference signals are at the modulation frequency. With similar
mathematics used to derive the WMS-2f magnitude R2f [Li et al. 2006], it can be inferred
that the WMS-1f magnitude output from a digital lock-in amplifier can be approximated
by the following equation for small absorptions
1 0 012fR GI i≈ . (2.33)
Normalization of the WMS-2f signal by the WMS-1f signal can eliminate the dependence
on the detection gain and laser intensity variation, as well as reject common mode noise
from the laser, detector and non-resonant transmission loss. The WMS-1f normalized
WMS-2f signal (WMS-2f/WMS-1f signal) can be calculated as follows using the
measured modulation parameters of the laser and the spectroscopy parameters of the
relevant absorption lines
( )
( )
22 /1
1
20 4
2 1 3 1 2 0 20
1/ 220 4
1 3 1 2 0 2
1 cos cos2 2
sin sin2 2
ff f
f
SC
R
i HH H H i Hi
i HH H i H
ψ ψ
ψ ψ
=
≈ + + + +
+ − + −
. (2.34)
For small absorber concentration, it can be directly compared with the measured C2f/1f
values to infer the Xabs once the T and P are known.
For atmospheric-pressure applications with small modulation depths, the nonlinear
IM can be neglected (i2 ≈ 0), and the FM/IM phase shift is usually approximated by ψ1 ≈
20 CHAPTER TWO
π without introducing big errors since the linear IM amplitude i0 is small. According to
Eq. (2.32), the WMS-2f magnitude can be approximated by
( )0 02 2 1 3[ ]
2 2fGI iS H H H≈ − + . (2.35)
For an isolated transition, the odd terms in the Fourier coefficients are zero at the
linecenter of this transition, thus the WMS-2f magnitude at the linecenter frequency,
which is usually called the WMS-2f peak height, reduces to
02 0 2 0
00
( ) ( )2
( ) ( cos ) cos22
f
abs
GIS H
GI PS T X L a dπ
π
ν ν
φ ν θ θ θπ −
≈
= − ⋅ + ⋅ ⋅∫. (2.36)
This WMS-2f peak height for an isolated transition will be maximized when the
modulation index
/ 2
amν
=∆
, (2.37)
takes a value of ~2.2. [Reid and Labrie, 1981, Liu et al. 2004a] At high pressures, the
linewidth ∆ν increases due to pressure broadening and thus large modulation depths are
required for WMS applications at elevated pressures. But it should be noted that at
elevated pressures, the linewidth will be ill-defined due to spectra blending, and thus the
modulation index m is no longer a useful concept.
Similar to the applications at elevated pressures, the WMS-2f peak height can also
be normalized by the WMS-1f signal
2 02 /1 2 0
1 0
( ) 1 ( )ff f
f
SC H
R iν
ν= = , (2.38)
FUNDAMENTALS OF LASER ABSORPTION SPECTROSCOPY 21
to eliminate the dependence on the detection gain and laser intensity variation, as well as
reject common mode noise from the laser, the detector and the non-resonant transmission
loss [Cassidy and Reid 1982].
In scanned-wavelength WMS measurements, the entire WMS-2f lineshape is
recorded, the WMS-2f peak height is obtained by subtracting the WMS-2f peak signal
with the background signal represented by the non-absorbing wings [Liu et al. 2004a,
Zhou et al. 2005]. In fixed-wavelength WMS measurements, only the WMS-2f signal at
the linecenter frequency is recorded, and the WMS-2f peak height can be obtained by
subtracting the recorded WMS-2f signal with the background signal measured with the
sample gas region purged with non-absorbing gas. [Rieker et al. 2006a]
2.3 LOS absorption based temperature sensing techniques
The temperature measurement techniques based on LOS laser absorption
spectroscopy can be categorized into one-line, two-line and multi-line thermometries
according to the number of absorption transitions used. The one-line and two-line
thermometries take the assumption that the temperature to be measured is uniform, and
thus yield “path-averaged” temperature values. The multi-line thermometry is used to
infer information on the non-uniform temperature distribution along the measurement
path. The one-line thermometry has to use the scanned-wavelength DAS technique. The
two-line thermometry can be based on either DAS or WMS, and for each case either the
scanned-wavelength or the fixed-wavelength scheme can be used. The multi-line
thermometry investigated in this thesis is based only on scanned-wavelength DAS.
The one-line thermometry is based on the fact that the Doppler broadening of a
particular transition is only temperature dependent. According to Eq. (2.10), once the
Doppler FWHM ∆νD is inferred from the measured direct absorption spectra, the
temperature can be calculated as
22 CHAPTER TWO
2
707.1623 10
DT M νν−
∆= ×
. (2.39)
This one-line thermometry has quite limited applications, essentially only to low pressure
cases where the Doppler width dominates the overall linewidth. At atmospheric pressure
or elevated pressures, the collisional broadening will dominate, thus it is very difficult to
measure accurate Doppler width and obtain accurate temperature values.
2.3.1 DAS two-line thermometry
Figure 2.5: Illustration of DAS two-line thermometry.
The basic concept for DAS two-line thermometry is illustrated in Fig. 2.5. In a
scanned-wavelength scheme, the integrated absorbances (areas) of two transitions are
measured simultaneously with the same pressure, same mole fraction and same
pathlength. Their ratio simply reduces to the ratio of linestrengths, which is a function of
temperature only
1 1
2 2
( ) ( )( )
A S TR f TA S T
= = = . (2.40)
Therefore, the gas temperature can be determined from the ratio of the measured
integrated absorbances (area ratio) for two isolated transitions with different temperature
dependence. The resulting terms in the area ratio due to the last two terms of Eq. (2.2)
Abso
rban
ce
Wavelength
λ1
λ2
Abso
rban
ce
Wavelength
λ1
λ2
Rat
io
Temperature
Rat
io
Temperature (a) (b)
FUNDAMENTALS OF LASER ABSORPTION SPECTROSCOPY 23
can usually be neglected if the linecenter frequencies of the two transitions are
sufficiently close to each other. The area ratio can thus be reduced to
( )" "1 1 01 2
2 2 0 0
( ) 1 1exp[ ]( )
A S T hcR E EA S T k T T
= ≈ − − −
, (2.41)
and the temperature can be analytically represented as
( )" "
2 1
" "1 2 0 2 1
2 1 0 0
( )ln ln( )
hc E EkT
A S T hc E EA S T k T
− = − + +
. (2.42)
Once the temperature is obtained, the mole fraction of the absorbing species can be
inferred from the measured integrated absorbance for either transition
( )
iabs
i
AXP S T L
=⋅ ⋅
. (2.43)
In a scanned-wavelength scheme, the entire absorption spectrum is obtained. The
zero-absorption baseline intensity can be inferred from the non-absorbing wings to
account for the laser intensity variation, detection gain and non-resonant transmission
loss. The interference absorption from neighboring lines can be differentiated by fitting
the recorded spectra with appropriate lineshape (usually Voigt). But it has the
disadvantage of limited sensor bandwidth due to the tradeoff between the laser scanning
speed and the scanning range, and the time consuming Voigt fit which is required to
obtain accurate integrated absorbance. In cases where a high sensor bandwidth is desired
or cases where no zero-absorbing wings are available within the laser scanning range due
to the spectral broadening and blending at elevated pressures, the fixed-wavelength
scheme can be used [Zhou et al. 2003, Nagali et al. 1997].
24 CHAPTER TWO
In fixed-wavelength two-line thermometry, usually the peak absorbances α(ν0) of
two transitions with different temperature dependence are measured. Note the peak
absorbance ratio is not only a function of temperature, but also a function of pressure and
absorber mole fraction since the lineshape functions are involved
1 01 1 1 01
2 02 2 2 02
( ) ( ) ( ) ( , )( ) ( ) ( )
S TR f T PS T
α ν φ να ν φ ν
⋅= = ≈
⋅. (2.44)
The line pair can be carefully selected to have similar lineshape functions so that their
peak absorbance ratio is insensitive to Xabs. [Zhou et al. 2003] In such cases, the
calibration database of the ratio versus temperature and pressure can be calculated in
advance using some typical value of Xabs, and the measured ratio will be compared with
the calibration database to infer the temperature once the pressure is independently
measured. Note that at elevated pressures, due to the spectral broadening and blending,
the calculation for the spectral absorbance at the laser set-point needs to include the
contributions from nearby lines
1
1 1 1
2 22
1
( ) ( )( )( ) ( ) ( )
n
i iim
j jj
S TR
S T
φ να να ν φ ν
=
=
⋅= =
⋅
∑
∑. (2.45)
2.3.2 WMS-2f two-line thermometry
Figure 2.6: Illustration of WMS-2f two-line thermometry.
2f S
igna
l
Wavelength
λ1
λ2 2f peak height
2f S
igna
l
Wavelength
λ1
λ2 2f peak height
2f P
eak
Rat
io
Temperature
2f P
eak
Rat
io
Temperature (a) (b)
FUNDAMENTALS OF LASER ABSORPTION SPECTROSCOPY 25
WMS-2f two-line thermometry strategies, for both scanned-wavelength schemes
and fixed-wavelength schemes, infer the temperature from the measured ratio of WMS-2f
peak heights for two transitions with different temperature dependence, as illustrated in
Fig. 2.6. Since the WMS-2f peak heights for the two transitions are measured at the same
pressure, mole fraction and pathlength, their ratio reduces as follows according to Eq.
(2.36) for atmospheric-pressure applications with small modulation depths
2 012
2 02
01 1 1 1 11 1
2 202 2 2 2 2
( )( )
( cos ) cos2( ) ( )( ) ( )( cos ) cos2
ff
f
SR
S
a dS T S TS T S Ta d
π
ππ
π
νν
φ ν θ θ θ
φ ν θ θ θ−
−
=
+ ⋅ ⋅∝ ⋅ ≈
+ ⋅ ⋅
∫∫
. (2.46)
Once the modulation depths are optimized for both transitions (m ≈ 2.2), the WMS-2f
peak ratio simply reduces to the linestrength ratio over a large temperature range [Liu et
al. 2004a]. Therefore, the linestrength ratio will be calculated in advance as a function of
temperature. The calibration curve of WMS-2f peak ratio versus temperature is assumed
to follow the trend of the linestrength ratio, and only a single-point calibration is needed
for the scaling. Otherwise the WMS-1f normalization can be used to eliminate the
calibration
2 /1 01 02 12 /1
2 /1 02 01 2
( ) ( )( ) ( )
f ff f
f f
C i S TRC i S T
νν
= ≈ ⋅ , (2.47)
if the linear IM amplitudes i01 and i02 for both lasers are measured in advance. The
measured WMS-2f peak ratio will be compared with the calibration curve to infer the
temperature.
For applications at elevated pressures with large modulation depths, the WMS-
2f/WMS-1f signals need to be calculated using the improved model as per Eq. (2.34), and
the contributions from nearby transitions need to be included as per Eq. (2.24)-(2.25).
26 CHAPTER TWO
The WMS-2f/WMS-1f signal ratio can no longer be reduced to the linestrength ratio, but
if the low concentration limit is warranted, the calibration database of WMS-2f/WMS-1f
ratio versus temperature and pressure can be calculated using some typical values of
absorber mole fraction (e.g. Xabs = 0.01)
2 /1 12 /1
2 /1 2
( )( , )
( )f f
f ff f
CR f T P
Cνν
= ≈ . (2.48)
The measured WMS-2f/WMS-1f ratio will be compared with the calibration database to
infer the temperature once the pressure is independently measured. The actual mole
fraction of the absorbing species can be inferred from the WMS-2f/WMS-1f signal for
either transition
2 /1 ,
2 /1 , @ 0.01
(0.01)abs
f f Measuredabs
f f Calculated X
CX
C =
= ⋅ . (2.49)
2.3.3 Multi-line thermometry for non-uniform temperature measurement
It is important to emphasize that two-line thermometry strategies, for both DAS and
WMS-2f, yield a path-averaged temperature due to the implicit assumption of uniform
gas medium along the LOS. Care should be taken during the line selection process to
minimize the impact of a thermal boundary layer on the measurement accuracy of a
relatively uniform temperature in the core flow, as will be discussed in section 4.2 of
Chapter 4. In cases where a significant temperature gradient exists along the beam path,
the two-line thermometry strategy is no longer appropriate. However, multiple lines with
different temperature dependence may be utilized to extract expanded information on the
temperature distribution.
The multi-line thermometry investigated in this thesis is based on the general
calculation equation for the integrated absorbance Eq. (2.5). If the integrated absorbances
FUNDAMENTALS OF LASER ABSORPTION SPECTROSCOPY 27
for m transitions are inferred from the direct absorption measurements, a nonlinear
equation set can be established
( )
( )
( )
1 10
2 20
0
( ) ( )
( ) ( )
( ) ( )
L
abs
L
abs
L
m abs m
A P X x S T x dx
A P X x S T x dx
A P X x S T x dx
=
=
=
∫∫
∫
. (2.50)
Two different strategies can be used to solve this equation set and infer some information
on the non-uniform temperature distribution T(x) (and even mole fraction distribution
Xabs(x)) along the measurement path. The first strategy, called profile fitting, solves the
characteristic properties of a temperature distribution profile postulated using physical
constraints. The second strategy, called temperature binning, determines the temperature
probability distribution (PDF) function along the LOS using prescribed temperature bins.
The detailed principles and mathematical representations for both strategies will be fully
addressed in Chapter 6.
2.4 Multiplexing schemes
In addition to fast wavelength scanning over multiple absorption features [Sanders
et al. 2001, Zhou 2005], two-line or multi-line thermometry can be accomplished by
combining multiple laser beams (multiplexing), passing this multiplexed beam through
the test region and then demultiplexing the beam into individual detectors for each laser.
Three types of multiplexing schemes are commonly used: time-division multiplexing
(TDM), wavelength-division multiplexing (WDM) and frequency-division multiplexing
(FDM). The principles, strengths and weakness of these schemes will be respectively
introduced in the following three sub-sections. And these three multiplexing schemes
have respectively been used in the design of the temperature sensing techniques covered
by Chapters 4, 6 and 5 of this thesis.
28 CHAPTER TWO
2.4.1 Time-division multiplexing
In a time-division multiplexing (TDM) scheme, the outputs of two or more lasers,
which are alternately scanned, are multiplexed together (usually using standard single-
mode fiber combiners) and pitched across the sample gas. The transmitted laser beam is
caught and sent to one detector. Figure 2.7(a) illustrates the time history of the incident
laser intensities from two alternately scanned lasers. Only one laser is active at a given
instant and the un-scanned laser is kept below lasing threshold without introducing extra
DC offset to the measured signal. The detected signal is shown in Fig. 2.7(b).
Figure 2.7: Illustration of time-division multiplexing: (a) incident laser intensities; (b) transmitted laser intensity recorded by the detector.
The virtue of the TDM scheme is that it allows for a simple optical setup. Only one
detector is needed to measure the transmitted laser intensities from two or more lasers.
One drawback of this scheme is the limited sensor bandwidth, since each laser is working
for only a fraction of the time. Another shortcoming is that the transmitted laser
intensities are not measured at exactly the same time, which will add extra measurement
uncertainties for applications in rapidly fluctuating flow fields. As will be discussed in
0 10 20 30 400
1
2
3
4
5
Sign
al [V
]
Time [ms]
Laser1 Laser2
0 10 20 30 400
1
2
3
4
5
Sign
al [V
]
Time [ms]
(a) (b)
FUNDAMENTALS OF LASER ABSORPTION SPECTROSCOPY 29
Chapter 4, this TDM scheme was used for the DAS two-line thermometry for gas turbine
exhaust temperature measurement.
2.4.2 Wavelength-division multiplexing
The schematic of a wavelength-division multiplexing (WDM) scheme is shown in
Fig. 2.8. The outputs from multiple DFB diode lasers operating at different frequencies
are multiplexed together (using standard single-mode fiber combiners or grating-based
multiplexers) and pitched across the sample gas. The transmitted laser beam is caught and
sent to a de-multiplexer where it is dispersed into the constituent wavelengths and fed to
multiple photo detectors.
Figure 2.8: Schematic of wavelength-division multiplexing.
The demultiplexer can be based on thin-film filters, arrayed waveguides, diffraction
gratings, or other alternatives. Most WDM-based absorption sensors reported in literature
[Baer et al. 1994, Furlong et al. 1996, Liu et al. 2004a, Mattison 2006] use free space,
conventional ruled gratings. They have the disadvantages of bulky hardware, problematic
polarization-dependent loss (PDL), and requirements for large spectral separation and
careful alignment. For water vapor measurements, this demultiplexing arrangement must
be purged of ambient water vapor. The WDM scheme has been used for the novel multi-
line thermometry discussed in Chapter 6 of this thesis. A fiber-coupled, echelle grating-
Single Mode Fiber
DFB Lasers Detectors
Pitch Lens
Catch Lens
Multiplexer De-multiplexer
Multi- Mode Fiber
30 CHAPTER TWO
based multiplexer and demultiplexer, which utilize higher diffraction orders for better
angular dispersion, are used since these compact devices allow dense wavelength
multiplexing and demultiplexing (up to tens of wavelengths) with high efficiency, pre-set
alignment and well-controlled PDL and thermal drift.
2.4.3 Frequency-division multiplexing
The frequency-division multiplexing (FDM) scheme can only be used in
modulation spectroscopy based applications. Usually the outputs of two lasers, which are
modulated at different frequencies (f1 and f2), are multiplexed together (usually using
standard single-mode fiber combiners), pitched across the sample gas and detected with
only one detector. The detector signal is sent to two lock-in amplifiers, as illustrated in
Fig. 2.9, to isolate the 2f1 and 2f2 signals respectively.
Figure 2.9: Schematic of frequency-division multiplexing.
Compared with TDM, the FDM scheme has the advantage of measuring the two
laser signals at exactly the same time. Compared with WDM, it has the merit of compact
sensor hardware, the use a single detector and obviates the requirement for wavelength
separation. But the modulation frequencies need to be separated enough to allow
Modulated @ f1
Single Mode Fiber
DFB Lasers
DetectorPitch Lens
Catch Lens
Multiplexer
Multi- Mode Fiber
Lock-in Amplifier
Lock-in Amplifier
Modulated @ f2
2f1 Signal
2f2 Signal
FUNDAMENTALS OF LASER ABSORPTION SPECTROSCOPY 31
sufficient suppression of the cross-talk harmonics by the available lock-in amplifiers [Liu
2004]. Therefore, FDM is usually difficult to be implemented with more than two lasers.
32 CHAPTER TWO
33
Chapter 3
EXPERIMENTAL STUDY OF NIR H2O
SPECTROSCOPIC PARAMETERS
3.1 Motivation and overview
Figure 3.1: Illustration of H2O vapor absorption transitions in the 1-8 µm region.
As discussed in Chapter 1, gas temperature sensors based on LOS absorption of
H2O vapor are attractive for a variety of practical applications including hydrocarbon-
fueled combustion systems. Water vapor, which is ubiquitous in combustion gases, has
strong rovibrational spectra ranging from the visible through the MIR, as illustrated in
Fig. 3.1. The 2ν1, 2ν3, and ν1+ν3 absorption bands in the NIR are especially attractive for
sensor development since they overlap with the spectral region of 1250-1650 nm where
10-4
10-3
10-2
10-1
100
101
102
S[cm
-2/a
tm]
87654321Wavelength [µm]
ν2ν1
2ν2
ν2+ν3ν1+ν2
2ν12ν3
ν1+ν3
ν3H2O at 300K
10-4
10-3
10-2
10-1
100
101
102
S[cm
-2/a
tm]
87654321Wavelength [µm]
ν2ν1
2ν2
ν2+ν3ν1+ν2
2ν12ν3
ν1+ν3
ν3
10-4
10-3
10-2
10-1
100
101
102
S[cm
-2/a
tm]
87654321Wavelength [µm]
ν2ν1
2ν2
ν2+ν3ν1+ν2
2ν12ν3
ν1+ν3
ν3ν2
ν1
2ν2
ν2+ν3ν1+ν2
2ν12ν3
ν1+ν3
ν3H2O at 300K ν2
34 CHAPTER THREE
robust, economical, fiber-coupled, mW, single-mode, telecommunication-grade tunable
diode lasers (TDL) are commercially available [NEL website]. Because there are several
thousands of water vapor absorption transitions in the 2ν1, 2ν3, and ν1+ν3 bands [Toth
1994], a design-rule-based line selection and optimization procedure has evolved to
identify lines with appropriate absorption strength, good temperature sensitivity, as well
as adequate immunity to the effects from cold boundary layers [Ouyang et al. 1989, Zhou
et al. 2003].
This design-rule approach to TDL absorption sensing, which is quite useful to
optimize sensor performance [Zhou et al. 2003, 2005a, 2005b, Liu et al. 2006a], assumes
that a complete and accurate catalog of the absorption transitions exists and that diode
lasers are available at any desired wavelength. It is anticipated [e.g., see the NEL
website] that lasers can be made available throughout the wavelength range where the
2ν1, 2ν3, and ν1+ν3 absorption bands of water vapor are located. The work discussed in
this chapter focuses on the measurements of NIR water spectroscopic parameters in these
bands and comparison of these results with the existing spectroscopic databases. The
purpose of these efforts is to evaluate (and improve where needed) the available
spectroscopic databases for quantitative water vapor absorption spectroscopy in these
bands and their potential of supporting the design-rule selection of optimum water vapor
absorption transitions for TDL sensors.
The HITRAN spectroscopy database has been developed over the past forty years
to provide a quantitative modeling tool for the transmission of light through the
atmosphere in the visible and infrared regions of the spectrum. This database provides an
extensive compilation of fundamental spectroscopic parameters for many important small
molecules using data compiled from experimental measurements, theoretical calculations
and estimations. Since the publication of the first HITRAN report [McClatchey et al.
1973], there have been several major revisions to the database; the three most recent
versions include HITRAN 1996 [Rothman et al. 1998], HITRAN 2000 [Rothman et al.
EXPERIMENTAL STUDY OF NIR H2O SPECTROSCOPY PARAMETERS 35
2003], and HITRAN 2004 [Rothman et al. 2005]. H2O is molecule number one in this
database as an indication of its importance for the HITRAN project. The HITRAN
database provides spectroscopic parameters of water vapor including line-center
frequency ν0, linestrength S, lower state energy E”, air-broadening coefficients γair and
their temperature-dependent exponents n, self-broadening coefficients γself and air-
induced frequency shift coefficients δair. HITRAN focuses on atmospheric conditions
where temperatures range from 200-350K. Hence, our desire to use this database for
combustion sensor design extends the temperature range well outside the HITRAN target
conditions. Not surprisingly, we have discovered discrepancies between our data and the
HITRAN values for the transitions we have studied for high temperature water vapor
sensing [Arroyo and Hanson 1993, Langlois et al. 1994a, 1994b, Nagali 1997b, Liu et al.
2005]. The latest edition of the database, HITRAN 2004 reports major changes to the
linestrength data for water vapor transitions in the 2ν1, 2ν3, and ν1+ν3 bands [Rothman et
al. 2005] based on the recent work of Toth [Toth 2005]. The purpose of the present study
is to systematically survey spectra of H2O vapor in portions of the NIR, to validate and
improve H2O spectroscopic parameters, and to experimentally investigate the reliability
of the HITRAN 2004 database at elevated temperatures.
Here we report fully resolved absorption measurements of H2O vapor in the
spectral range of 6940-7440 cm-1 (1344-1441 nm) as a function of temperature (296-1000
K) and pressure (1-600 Torr). Quantitative spectroscopic parameters inferred from these
spectra are compared to published data from Toth [Toth 1994], HITRAN 2000 [Rothman
et al. 2003], and HITRAN 2004 [Rothman et al. 2005]. Measurements of peak
absorbance are made for more than 100 strong transitions at room temperature and at 828
K, and linestrengths determined for 47 strong lines in this region. In addition to
linestrength S(296 K), the air-broadening coefficient γair(296 K) and its temperature
exponent n are inferred for strong transitions in five narrow regions, near 7185.60 cm-1,
7203.89 cm-1, 7405.11 cm-1, 7426.14 cm-1 and 7435.62 cm-1 that were targeted as
attractive [Zhou et al. 2005b] for the IC-engine diagnostics application discussed in
36 CHAPTER THREE
Chapter 5. These new spectroscopic data for H2O provide a useful test of the sensor
design capabilities of HITRAN 2004 for combustion and other applications at elevated
temperatures. We find that although HITRAN 2004 is a valuable tool for sensor design,
the spectroscopic data for transitions selected for high temperature sensors generally
require laboratory measurements to establish the uncertainty for accurate measurements
of gas temperature and water vapor concentration. Before examining our spectral data,
we first describe the experimental details.
3.2 Details of spectroscopy experiments
Figure 3.2: Schematic of experimental arrangement used for the spectroscopy measurements.
Figure 3.2 shows a schematic of the experimental arrangement used for the
quantitative measurements of spectroscopic parameters in a heated static cell. Neat H2O
vapor is extracted from a flask containing distilled liquid water which is pumped down
for 10 minutes prior to conducting the experiments to remove any gaseous impurities.
Controlled H2O-air mixtures are made by sequentially introducing H2O vapor and air into
a stainless steel tank with Teflon mixing balls. The tank is then shaken and allowed to
14” Sample Path
3-Zone Tube Furnace
Transmission Detector
DAQ Computer
ReferenceDetector
Etalon Detector
Quartz Cell
Mixing Tank
N2/Dry Air
Mullite Tube
Etalon
N2 Purge Region
Fiber Coupled ECDL or DFB Laser
H2O Flask
Vacuum Pump
45%
5%
50%
PPPP
N2 Purge Region
EXPERIMENTAL STUDY OF NIR H2O SPECTROSCOPY PARAMETERS 37
rest for several hours before the mixture is used for the absorption experiments. During
the experiments, gas samples are introduced into a 35.6 cm long static quartz cell placed
at the center of a three-zone tube furnace (MHI H14HT2.5x27). This furnace has three
independently adjustable heaters to maximize temperature uniformity in the cell. Three
K-type thermocouples (Omega) with an accuracy of ± 0.75% of reading are placed at the
middle and both ends of the heated cell to determine the temperature of gas samples. At
each temperature set-point in the range of 296-1000 K, the three heaters are adjusted to
guarantee that the measured deviation of the three thermocouple readings is no more than
3 K. The gas pressures are measured using pressure gauges (MKS Baratron) with a full
scale of 100 Torr or 1000 Torr and an accuracy of ± 0.12%.
In this study, an external-cavity diode laser (New Focus ECDL6327, 3-8 mW) with
a scanning range of 1355-1441 nm (6940-7380 cm-1) is used as the primary laser source
to investigate a large portion of H2O spectra in the 2ν1, 2ν3, and ν1+ν3 bands. The
spectral range is extended using three tunable distributed-feedback (DFB) diode lasers
(NEL NLK1B5E1AA, >10 mW) emitting near 1345 nm, 1347 nm and 1350 nm. The
narrow line widths of the lasers, which are less than 300 kHz for the ECDL and less than
2 MHz for the DFB diode lasers according to the specifications, guarantee negligible
instrument broadening. During the experiments, the ECDL is usually tuned with a speed
of 10 nm/s, requiring about 8.6 seconds to scan the tuning range of 86 nm (440 cm-1).
Although this is too slow to meet the requirements for real-time sensing applications, the
wide tuning range of the ECDL makes it an excellent tool for NIR spectroscopy studies.
The fiber-coupled output of the ECDL is split into three beams (0.45, 0.05, 0.50) as
shown in Fig. 3.2. The 45% intensity path is collimated in free space and transmitted
through the sample gas, focused by a spherical gold mirror and detected by an InGaAs
detector (Thorlabs PDA400). The optics, detector and the intermediate open paths are
enclosed by mullite tubes and plastic bags, which are purged with N2 to remove
interfering absorption by ambient H2O vapor in room air along the optical path. Wedged
(0.5º) windows are installed on the gas cell by a canted angle of 3º to reduce interference
38 CHAPTER THREE
effects as the laser wavelength is scanned. The 5% intensity path is fiber-coupled to a
similar detector to provide an intensity reference signal. The output power of the ECDL
varies with wavelength and must be normalized using the reference signal for quantitative
absorption measurements. The remaining 50% intensity path is collimated and
propagated through a solid etalon with a free spectral range (FSR) of 2.00 GHz to provide
a calibration of the laser wavelength.
Figure 3.3: An example of (a) the raw data traces measured with the ECDL (solid line: transmitted signal through the cell, dashed line: reference signal) for neat H2O at T = 902 K, P = 14 Torr and L = 71.1 cm; (b) the reduced absorption spectra.
Figure 3.3 shows an example of raw data traces and the reduced absorption spectra.
The transmitted and reference signals measured at the specified conditions are plotted as
10
8
6
4
2
Sig
nal[V
]
876543210Time [s]
ITrans IRef
(a)
1.0
0.5
0.0
Abs
orba
nce
735073007250720071507100705070006950Frequency [cm-1]
(b)
EXPERIMENTAL STUDY OF NIR H2O SPECTROSCOPY PARAMETERS 39
the solid and dashed lines respectively in Fig. 3.3(a). It should be noted that the ECDL
output power oscillates with output wavelength due to etalon effects (FSR = ~2 cm-1)
caused by the residual facet reflectivity during wavelength scanning. The absorption
spectra are calculated, where the transmitted laser intensity It is measured when the cell is
filled with neat H2O vapor, while the incident laser intensity I0 is approximated by the
measured transmission when the cell is evacuated. Both It and I0 are normalized by
reference signals measured at the same time with the transmission, in order to remove the
laser intensity fluctuations. Figure 3.3(b) shows the reduced absorption spectra over the
range of 440 cm-1 probed with a single laser scan, in which hundreds of H2O transitions
can be fully resolved. Figure 3.3 demonstrates that ECDL-based absorption spectroscopy
provides an efficient and effective method for surveys and validation of NIR H2O spectra.
Three fiber-coupled DFB diode lasers are used to probe regions near 7405.11 cm-1,
7426.14 cm-1 and 7435.62 cm-1, which are not covered by the ECDL scanning range but
have been selected for temperature sensing in propulsion applications [Zhou et al.
2005b]. The temperature and current of the DFB diode lasers are controlled by an ILX
Lightwave LDC-3900. The laser wavelength is tuned over a range of approximately 3
cm-1 across the desired absorption features by a linearly varying injection current. From
the transmitted laser intensity It, the unattenuated laser intensity I0 is determined by
fitting the part of the It trace without absorption with a 3rd order polynomial. The
absorption spectrum αν is then calculated with It and I0 .
3.3 Spectroscopy results and discussions
3.3.1 Preliminary S(T) investigation within the ECDL scanning range
The initial spectroscopy investigation starts with the ECDL measurements of
absorption spectra for neat H2O vapor at room temperature and an elevated temperature
40 CHAPTER THREE
of 828K in order to provide a preliminary overview on the linestrength accuracy of
available databases for strong transitions in the probed region.
Figure 3.4: Comparisons of peak absorbance between ECDL measurements and HITRAN databases for neat H2O vapor: (a) at room temperature T = 297 K, P = 1 Torr, L = 35.6 cm; (b) at elevated temperature T = 828 K, P = 21 Torr, L = 35.6 cm.
Peak absorbances for 87 strong lines are extracted from the spectra measured at
room temperature and the spectra simulated at the same conditions using the HITRAN
databases. The same procedures are performed for 141 strong lines at the elevated
temperature of 828 K. Figure 3.4 shows the peak absorbance comparisons between the
measurements and HITRAN databases. Both comparisons demonstrate that the ECDL
measurements agree much better with HITRAN 2004, which was released after these
experiments. We also find a larger discrepancy between measurements and simulations in
2.0
1.5
1.0
0.5
0.0Rat
ion
of P
eak
Abs
orba
nce
735073007250720071507100705070006950
αpeak,MEAS/αpeak,HITRAN04
αpeak,MEAS/αpeak,HITRAN00
2.0
1.5
1.0
0.5
0.0
Rat
io o
f Pea
k A
bsor
banc
e
735073007250720071507100705070006950Frequency, cm-1
αpeak, MEAS/αpeak, HITRAN04 αpeak, MEAS/αpeak, HITRAN00
(a)
(b)
T=297K
T=828K
EXPERIMENTAL STUDY OF NIR H2O SPECTROSCOPY PARAMETERS 41
the blue end of this spectral region (ν ≈ 7320-7380 cm-1), where the studied transitions all
have the same changes of rotational quantum numbers: ∆J = +1, ∆Ka = 0, and ∆Kc = +1.
Since the peak absorbance of neat H2O vapor transitions at low pressures is largely
determined by the linestrength of the transition, we draw an initial conclusion that
linestrengths of strong transitions in the probed region have been greatly improved in
HITRAN 2004, but there is evidence of some remaining systematic errors in this
database.
The linestrengths of strong lines in the region of 7130-7320 cm-1, which is a
primary target for sensor development, are determined from the initial ECDL
measurements. The data reduction is illustrated in Fig. 3.5. Figure 3.5(a) shows one
section of the spectra measured at T = 828 K to provide an expanded view of the ±3.5
cm-1 neighborhood of the transition at 7185.60 cm-1. As shown by Fig. 3.5(b), the
lineshape of transition 7185.60 cm-1 is well-fit by a Voigt profile. The Voigt fit provides
the integrated absorbance A, from which the linestrength can be calculated by Eq. (2.8).
Figure 3.5: Illustration of data analysis: (a) the measured spectra of neat H2O vapor at T = 828 K, P = 21 Torr and L = 35.6 cm in the spectral region near 7185.60 cm-1; (b) the measured lineshape of transition 7185.60 cm-1 (solid line), its Voigt fit (dashed line) and the residual (top panel).
0.8
0.6
0.4
0.2
0.0
Abso
rban
ce
7188718671847182Frequency, cm-1
0.6
0.4
0.2
0.0
Abs
orba
nce
0.80.60.40.2Relative Frequency, cm-1
2.0-2.0R
es.,
%
Measurement Voigt fit
(a) (b)
42 CHAPTER THREE
The inferred linestrengths of 47 strong lines within 7130-7320 cm-1 are compared
with the two most recent HITRAN databases [Rothman et al. 2003, 2005] and the room
temperature linestrength data measured by Toth [Toth 1994], as shown in Fig. 3.6. Lines
within 7250-7280 cm-1 are not studied since they are relatively weak and far from the
candidate transitions we selected for temperature sensing in propulsion applications
[Zhou et al. 2005b]. The measured linestrengths agree well with HITRAN 2004 (average
deviation of σavg = 6%) and Toth 1994 (σavg = 5%), but poorly with HITRAN 2000 (σavg =
23%). These comparisons confirm our conclusion that the linestrengths of strong
transitions in the probed region have been greatly improved in HITRAN 2004.
Figure 3.6: Comparison of linestrength between ECDL measurements and databases: (a) at room temperature T = 297 K; (b) at elevated temperature T = 828 K.
100
50
0
-50Dev
. of L
ines
tren
gth
[%]
7320730072807260724072207200718071607140
(SMEAS-STOTH94)/STOTH94
(SMEAS-SHITRAN00)/SHITRAN00
(SMEAS-SHITRAN04)/SHITRAN04
100
50
0
-50Dev
. of L
ines
tren
gth
[%]
7320730072807260724072207200718071607140
(SMEAS-STOTH94)/STOTH94
(SMEAS-SHITRAN00)/SHITRAN00
(SMEAS-SHITRAN04)/SHITRAN04
(a)
(b)
T=297K
T=828K
Frequency [cm-1]
EXPERIMENTAL STUDY OF NIR H2O SPECTROSCOPY PARAMETERS 43
3.3.2 Measurements of S(T) and γ(T) in five selected spectral regions
From the region of 7130-7320 cm-1, the transitions near 7185.60 cm-1 and 7203.89
cm-1 have been identified as attractive [Zhou et al. 2005b] for use in the temperature
sensing for IC engine application discussed in Chapter 5, owing to their appropriate
absorption strengths and isolation from neighboring lines. Three transitions outside of the
ECDL scanning range, at 7405.11 cm-1, 7426.14 cm-1 and 7435.62 cm-1, are also selected
[Zhou et al. 2005b]. Accurate spectroscopic parameters of these five candidate
transitions, including the linestrength S, air-broadening coefficient γair and its temperature
exponent n, are thus investigated here, to support the sensor applications at elevated
pressures. It is also important to establish accurate spectroscopic parameters for the
strong neighbors of the candidate features. Therefore, strong neighboring transitions of
the five candidate lines are identified and listed together with the five candidates by
ascending line-center frequencies in Table 3.1 and 3.2. The line-center frequencies ν0 and
lower state energies E” of all transitions are directly taken from HITRAN 2004. Note that
8 of the 35 transitions are spaced from their neighbors less than 0.02 cm-1 and hence are
not resolved in our measurements. They are thus studied as four single features in this
work and not compared with HITRAN databases for the measured spectroscopic
parameters.
To validate the line positions/spacings and infer the linestrength values for the
target transitions, the absorption spectra of neat H2O vapor at pressures of 1 to 20 Torr
are systematically measured at various temperatures between 296 and 1000 K by the
ECDL and the three DFB lasers. The measured spectra are first compared with
simulations at the same conditions using HITRAN databases.
Appreciable discrepancies are found for four of the five target regions as shown in
Fig. 3.7. Errors in HITRAN 2000 are illustrated by the extra feature near 7185.5 cm-1 in
Fig. 3.7(a), the missing feature near 7435.3 cm-1 in Fig. 3.7(d) and the incorrect line
positions/spacings near 7405.2 cm-1 in Fig. 3.7(b) and near 7426.1 cm-1 in Fig. 3.7(c).
44 CHAPTER THREE
Although HITRAN 2004 has been greatly improved from HITRAN 2000, it is still not
complete as revealed by the extra strong feature near 7404.9 cm-1 in Fig. 3.7(b).
Figure 3.7: Comparison of measured spectra (top panels) of neat H2O vapor at T = 998 K, P = 16 Torr, L = 71.1 cm with simulations by HITRAN databases (bottom panels, solid line: HITRAN 2004, dashed line: HITRAN 2000) for: (a) line 1 region; (b) line 3 region; (c) line 4 region; (d) line 5 region.
The linestrength data reduction procedure is illustrated in Fig. 3.8. At a selected
temperature, the integrated absorbances measured at various pressures of neat H2O vapor
are fit to a line, as shown in Fig. 3.8(a), to eliminate any systematic error in the zero of
the pressure gauge. The linestrength and its statistical precision at this temperature can be
inferred from the slope of the linear fit using Eq. (2.8). With the lower state energy Ei”
fixed at the HITRAN value, the linestrength at the reference temperature Si(T0 = 296 K)
can be inferred from a one-parameter best fit of the linestrength data measured at various
temperatures to the scaling relationship of Eq. (2.2), as shown by Fig. 3.8(b). In Fig. 3.8,
1.0
0.5
0.0
Abs
orba
nce
71877186718571847183Frequency [cm
-1]
1.0
0.5
0.0
Measurement
HITRAN2004 HITRAN2000
1.0
0.5
0.0A
bsor
banc
e7406740574047403
Frequency [cm-1
]
1.0
0.5
0.0
(a) (b)
0.5
0.0
Abs
orba
nce
742774267425Frequency [cm
-1]
0.5
0.0
0.5
0.0
Abs
orba
nce
7438743774367435Frequency [cm
-1]
0.5
0.0
(c) (d)
EXPERIMENTAL STUDY OF NIR H2O SPECTROSCOPY PARAMETERS 45
the error bar of each measured data point, which stands for the standard deviation of
multiple measurements at the same condition, is generally too small to be identified.
Figure 3.8: Illustration of linestrength data reduction for line 5 at 7435.62 cm-1: (a) the measured integrated absorbance (symbol) versus pressure at T = 996 K, and the linear fit (line) used to infer the linestrength: S(996 K) = 1.697e-2 ± 9e-6 [cm-2atm-1]; (b) the measured linestrength (symbol) versus temperature and the one-parameter best fit used to infer the linestrength at the reference temperature: S(296 K) = 1.932e-3 ± 4e-6 [cm-2atm-
1].
The measured linestrength values are compared with the HITRAN databases and
data from Toth [Toth 1994] in Table 3.1. For most transitions in the five spectral regions
studied, the agreement between measured and database linestrengths have been greatly
improved in the new edition of HITRAN. However, similar to what we observed for the
spectral region of 7320-7380 cm-1 in the ECDL peak absorbance measurements (section
3.3.1), large discrepancies (> 10%) still exist for some transitions in line 3 and line 4
regions, where all the studied transitions have the same changes of rotational quantum
numbers, i.e., ∆J = +1, ∆Ka = 0, and ∆Kc = +1. These large discrepancies, revealed by our
independent ECDL and DFB measurements, might result from some systematic errors in
the linestrength data source [Toth 2005] for these HITRAN values.
0.03
0.02
0.01
0.00Inte
grat
ed A
rea
[cm
-1]
20151050Pressure [Torr]
Measurements Linear Fit
0.02
0.01
0.00Line
Str
engt
h [c
m-2
atm
-1]
1000800600400Temperature [K]
Measurements Nonlinear Fit
(a) (b)
46 CHAPTER THREE
Table 3.1: Comparison of linestrength between measurements and databases for the five candidate lines (shaded) and their strong neighbors.
ν0 E” S(296 K) [cm-2atm-1] / Difference from database Diff. [%] Line [cm-1] [cm-1] Measured HITRAN04 Diff. HITRAN00 Diff. Toth94 Diff.
7182.21 42 3.48E-02 3.82E-02 -8.9 2.93E-02 18.8 3.40E-02 2.4 7182.95 142 7.70E-02 9.30E-02 -17.2 1.31E-01 -41.2 9.23E-02 -16.6 7183.27 1719 1.61E-04 1.65E-04 -2.4 2.13E-04 -24.4 1.90E-04 -15.3 7185.40 1475 2.66E-04 2.60E-04 2.3 2.73E-04 -2.6 2.60E-04 2.3 7185.60 1045 1.88E-02 1.97E-02 -4.6 1.76E-02 6.8 1.88E-02 0.0
1
7188.14 1256 8.07E-04 8.90E-04 -9.3 7.24E-04 11.5 7.65E-04 5.5 7202.26 447 2.52E-02 2.72E-02 -7.4 2.35E-02 7.2 2.55E-02 -1.2 7202.91 70 1.14E-01 1.15E-01 -0.9 8.31E-02 37.2 1.07E-01 6.5 7203.66 1742 1.49E-04 1.58E-04 -5.7 1.14E-04 30.7 7203.89 742 6.93E-02 7.38E-02 -6.1 8.28E-02 -16.3 7.05E-02 -1.7 7204.17 931 8.20E-03 7.85E-03 4.5 6.92E-03 18.5 7.50E-03 9.3
2
7205.25 79 2.29E-01 2.46E-01 -6.9 1.84E-01 24.5 2.32E-01 -1.3 7403.62 931 1.20E-02 1.39E-02 -13.7 1.20E-02 0.0 1.30E-02 -7.7 7404.40 1631 4.09E-04 4.48E-04 -8.7 3.60E-04 13.7 3.83E-04 6.8 7404.45 1631 1.40E-04 1.29E-04 1.45E-04 7404.47 1256 1.12E-03 9.80E-04 8.41E-04 9.00E-04 7405.11 920 2.47E-02 2.47E-02 0.0 2.48E-02 -0.4 2.57E-02 -3.9 7405.15 920 6.60E-03 8.30E-03 -20.5 8.68E-03 -24.0 8.10E-03 -18.5 7405.19 603 9.51E-03 1.57E-02 -39.4 2.73E-02 -65.1 1.40E-02 -32.1
3
7406.03 886 2.35E-02 2.35E-02 0.0 2.73E-02 -13.8 2.20E-02 6.8 7424.69 1477 1.03E-03 1.16E-03 -11.2 9.50E-04 8.5 1.03E-03 0.0 7426.11 1327 1.30E-03 1.36E-03 1.43E-03 7426.11 1216 3.08E-03 1.95E-03 1.86E-03 1.77E-03 7426.14 1327 4.20E-03 4.20E-03 0.0 3.87E-03 8.6 4.13E-03 1.7 7426.45 1293 1.30E-03 1.44E-03 1.27E-03 7426.46 1132 2.00E-03 2.00E-03 2.36E-03 1.93E-03
4
7426.60 1294 4.00E-03 4.00E-03 0.0 3.74E-03 6.8 3.85E-03 3.9 7435.35 2613 3.80E-06 3.80E-06 0.0 N/A 3.40E-06 11.8 7435.62 1558 1.93E-03 1.89E-03 2.1 2.18E-03 -11.5 1.77E-03 9.0 7435.73 1719 4.10E-04 4.21E-04 -2.6 3.42E-04 19.8 3.56E-04 15.2 7435.94 1525 1.40E-03 1.45E-03 -3.4 1.26E-03 10.7 1.34E-03 4.5 7436.00 1525 4.81E-04 4.93E-04 -2.4 4.02E-04 19.7 4.27E-04 12.6 7436.91 1446 2.18E-03 1.98E-03 2.07E-03 7436.92 1283 2.55E-03 8.50E-04 1.76E-04 6.10E-04
5
7437.19 1202 5.31E-03 5.20E-03 2.1 4.49E-03 18.3 4.88E-03 8.8
To infer the air-broadening coefficients for the target transitions in the selected five
spectral regions, the absorption spectra of H2O-air mixtures at pressures of 100 to 800
Torr are systematically measured at various temperatures between 296 and 1000 K by the
ECDL and the three DFB lasers. The Voigt fit of the measured absorption lineshape
EXPERIMENTAL STUDY OF NIR H2O SPECTROSCOPY PARAMETERS 47
provides the collisional (Lorentzian) FWHM. At a selected temperature, the collisional
FWHM measured at various pressures of H2O-air mixture are fit to a line, as shown by
Fig. 3.9(a). The air-broadening coefficient and its statistical precision at this temperature
can be inferred from the slope of the linear fit using Eq. (2.12). These plots of measured
collisional FWHM vs. pressure, as illustrated by Fig. 3.9(a), exhibit excellent linearity,
and thus suggest negligible Dicke narrowing [Dicke 1953] within the plotted pressure
range. [Langlois et al. 1994a, Nagali et al. 1997b, Chou et al. 1999]
Figure 3.9: Illustration of air-broadening coefficient data reduction for line 2 at 7203.89 cm-1: (a) the measured collisional FWHM (symbol) versus pressure at T = 447 K, and the linear fit (line) used to infer the γair(447 K) = 0.0410 ± 0.0001 [cm-1atm-1]; (b) the measured γair (symbol) versus temperature, and the two-parameter best fit used to infer the γair(296 K) = 0.0537 ± 0.0001 [cm-1atm-1] and n = 0.646 ± 0.003.
The air-broadening coefficient at the reference temperature γair(T0 = 296 K) and its
temperature exponent n can be inferred from a two-parameter best fit of the γair measured
at various temperatures to the scaling relation of Eq. (2.14), as shown by Fig. 3.9(b). The
measured results are compared with HITRAN databases in Table 3.2. Although for over
half of the studied transitions the γair(T0 = 296 K) have been greatly improved in HITRAN
2004, discrepancies (> 10%) between measurements and HITRAN 2004 are identified for
11 lines. For the temperature exponent n, the measured results feature large discrepancies
between HITRAN 2004 and our data for over half of the studied transitions. These
0.10
0.05
0.00Lore
ntzi
an F
WH
M [c
m-1
]
8006004002000Pressure [Torr]
Measurements Linear Fit
3x10-2
4
5
6
Air
Brd
. Coe
ff. [c
m-1
atm
-1]
2 3 4 5 6 7 8 91000
Temperature [K]
Measurements Nonlinear Fit
(a) (b)
48 CHAPTER THREE
discrepancies are not surprising since few of the air-broadening coefficients in HITRAN
come from measurements at elevated temperatures. The measured n for several
transitions are much smaller than the theoretical value of 0.5, which indicates the
intermolecular interactions are far off the hard-sphere model.
Table 3.2: Comparison of air-broadening coefficients between measurements and databases for the five candidate lines (shaded) and their strong neighbors: (a) air-broadening coefficients at the reference temperature γair(296 K); (b) the temperature exponents n.
(a)
ν0 E” γair(296 K) / Difference from database Diff. [%] Line [cm-1] [cm-1] Measured HITRAN04 Diff. HITRAN00 Diff.
7182.21 42 0.107 0.1104 -3.4 0.1099 -2.9 7182.95 142 0.096 0.0974 -2.0 0.0980 -2.6 7183.27 1719 0.076 0.0595 28.1 0.0617 23.5 7185.40 1475 0.078 0.0523 48.6 0.0870 -10.7 7185.60 1045 0.041 0.0421 -2.4 0.0505 -18.6
1
7188.14 1256 0.054 0.0587 -7.5 0.0758 -28.4 7202.26 447 0.086 0.0959 -10.7 0.0778 10.0 7202.91 70 0.103 0.1022 0.4 0.1089 -5.8 7203.66 1742 0.062 0.0884 -30.0 0.0908 -31.8 7203.89 742 0.054 0.0534 0.6 0.0778 -31.0 7204.17 931 0.087 0.0770 12.3 0.0750 15.3
2
7205.25 79 0.098 0.1015 -3.7 0.1000 -2.3 7403.62 931 0.080 0.0777 3.5 0.0644 24.8 7404.40 1631 0.038 0.0473 -20.3 0.0683 -44.8 7404.45 1631 0.0416 0.0683 7404.47 1256 0.070 0.0623 0.0758 7405.11 920 0.035 0.0336 5.4 0.0683 -48.2 7405.15 920 0.035 0.0337 4.5 0.0683 -48.5 7405.19 603 0.094 0.0830 13.0 0.0710 32.1
3
7406.03 886 0.053 0.0492 8.5 0.0577 -7.5 7424.69 1477 0.069 0.0673 2.5 0.0683 1.0 7426.11 1327 0.0232 0.0558 7426.11 1216 0.025 0.0522 0.0683 7426.14 1327 0.025 0.0220 13.6 0.0558 -55.2 7426.45 1293 0.0307 0.0617 7426.46 1132 0.054 0.0789 0.0758
4
7426.60 1294 0.035 0.0327 8.0 0.0617 -42.8 7435.35 2613 0.033 0.0330 -0.3 N/A 5 7435.62 1558 0.017 0.0179 -4.5 0.0504 -66.1
EXPERIMENTAL STUDY OF NIR H2O SPECTROSCOPY PARAMETERS 49
7435.73 1719 0.078 0.0547 41.9 0.0617 25.8 7435.94 1525 0.029 0.0278 3.6 0.0558 -48.4 7436.00 1525 0.023 0.0272 -14.0 0.0558 -58.1 7436.91 1446 0.0425 0.0617 7436.92 1283 0.057 0.0762 0.0963
7437.19 1202 0.070 0.0630 11.0 0.0683 2.3
(b)
ν0 E” n / Difference from database Diff. [%] Line [cm-1] [cm-1] Measured HITRAN04 Diff. HITRAN00 Diff.
7182.21 42 0.81 0.78 3.8 0.75 8.0 7182.95 142 0.91 0.77 18.2 0.76 19.7 7183.27 1719 0.81 0.45 80.0 0.68 19.1 7185.40 1475 0.89 0.49 81.6 0.68 30.9 7185.60 1045 0.65 0.64 1.6 0.68 -4.4
1
7188.14 1256 0.53 0.53 0.0 0.65 -18.5 7202.26 447 0.70 0.69 1.4 0.68 2.9 7202.91 70 0.73 0.78 -6.4 0.85 -14.1 7203.66 1742 0.50 0.78 -35.9 0.77 -35.1 7203.89 742 0.65 0.69 -5.8 0.68 -4.4 7204.17 931 0.94 0.59 59.3 0.68 38.2
2
7205.25 79 0.72 0.78 -7.7 0.79 -8.9 7403.62 931 0.81 0.53 52.8 0.68 19.1 7404.40 1631 0.38 0.45 -15.6 0.68 -44.1 7404.45 1631 0.45 0.68 7404.47 1256 0.68 0.49 0.68 7405.11 920 0.25 0.45 -44.4 0.68 -63.2 7405.15 920 0.27 0.45 -40.0 0.68 -60.3 7405.19 603 0.77 0.59 30.5 0.68 13.2
3
7406.03 886 0.48 0.49 -2.0 0.68 -29.4 7424.69 1477 0.66 0.45 46.7 0.68 -2.9 7426.11 1327 0.39 0.68 7426.11 1216 0.07 0.45 0.68 7426.14 1327 0.08 0.39 -79.5 0.68 -88.2 7426.45 1293 0.41 0.68 7426.46 1132 0.47 0.49 0.68
4
7426.60 1294 0.29 0.41 -29.3 0.68 -57.4 7435.35 2613 0.32 0.37 -13.5 N/A 7435.62 1558 0.18 0.37 -51.4 0.68 -73.5 7435.73 1719 0.80 0.41 95.1 0.68 17.6 7435.94 1525 0.32 0.39 -17.9 0.68 -52.9 7436.00 1525 0.33 0.39 -15.4 0.68 -51.5 7436.91 1446 0.41 0.68 7436.92 1283 0.64 0.45 0.68
5
7437.19 1202 0.67 0.45 48.9 0.68 -1.5
50 CHAPTER THREE
For most H2O vapor transitions in the HITRAN databases, the expected accuracies
of the linestrength values are generally within 5% [Rothman et al. 2003, 2005, Bernath
2002], and the expected accuracies of air-broadening coefficients range from 1-2% to 10-
20%, depending on the accuracies claimed by the data sources. The estimated
uncertainties of our measured linestrength and air-broadening coefficients are typically
less than 5%, resulting from the component measurement uncertainties of 0.5% in the
total pressure, 1% in the temperature, 0.5% in the total path length, 0.5% in the mole
fraction of H2O vapor, 2% in the area or FWHM for the Voigt fit, standard deviations of
less than 1% for multiple measurements, and a possible error of less than 2% introduced
to the measured FWHM by neglecting Dicke narrowing effect [Langlois et al. 1994a,
Nagali et al. 1997b]. For general applications requiring values for the spectroscopic
parameters of the studied transitions, we suggest adopting the existing HITRAN 2004
database values, when they agree with our measurements within ±5%. Use of our
measured values is recommended for those values where our measurements differ from
HITRAN 2004 by more than 5%. For combustion diagnostics applications, especially
those with temperature variations between 300-1000 K, we suggest using our
measurement results since the HITRAN databases are optimized for low temperature
applications.
3.4 Summary
This chapter addresses the measurement of fully resolved absorption spectra for
H2O vapor in the spectral range of 1344-1441 nm as a function of temperature and
pressure using a tunable ECDL and three DFB diode lasers. Spectroscopic parameters of
strong transitions in this spectral region are inferred from the measured spectra and
compared with existing databases. Most of the measured results, determined within an
accuracy of 5%, are found to be in better agreement with HITRAN 2004 than with earlier
editions of this database. Large discrepancies (> 10%) between measurements and
HITRAN 2004 database are identified for some of the probed transitions. These new
EXPERIMENTAL STUDY OF NIR H2O SPECTROSCOPY PARAMETERS 51
spectroscopic data for H2O provide a useful test of the sensor design capabilities of
HITRAN 2004 for combustion and other applications at elevated temperatures.
We find that HITRAN 2004 is sufficiently accurate for sensor design using the
absorption transitions in the 2ν1, 2ν3, and ν1+ν3 bands of water vapor. However, the
spectroscopic data for transitions selected for high temperature sensors generally require
laboratory validations to enable accurate quantitative measurements. This study provides
clear guidance for selection of the most accurate spectroscopic parameters for spectral
simulations, and thus will facilitate the design of quantitative NIR H2O sensors. The
validated spectroscopic data will enable prediction of absorption signals as a function of
temperature and pressure for a range of combustion applications. To the best of our
knowledge, this is the first study that measures the H2O absorption spectra over extensive
temperature and pressure conditions for large portions of the spectral region of 1.3-1.5
µm, where absorption of water vapor in the 2ν1, 2ν3, and ν1+ν3 bands is often used for
sensor applications.
52 CHAPTER THREE
53
Chapter 4
TEMPERATURE SENSING USING DAS TWO-
LINE THERMOMETRY
4.1 Motivation and overview
The design and demonstration of direct absorption spectroscopy (DAS) two-line
thermometry is motivated by the measurement of exhaust gas temperature in an industrial
gas turbine. The combustion efficiency of an industrial gas turbine can be inferred by
measuring the exhaust gas temperature. Thermocouples are traditionally used for this
application, but thermocouple probes provide only point measurements with typically
sub-Hz time response. This chapter investigates the design of a TDL sensor to monitor
exhaust gas temperature with improved temporal resolution and capability to provide
path-averaged temperature. Design rules are developed and used to select potential
optimal absorption transitions. Measurements are conducted to obtain precise
spectroscopic data, and validation experiments are used to choose the final sensor design.
As has been discussed in Chapter 1, LOS laser absorption spectroscopy can provide
a fast, non-intrusive, sensitive and reliable solution for in-situ gas temperature sensing.
The use of NIR TDLs for the sensor design is attractive since these lasers are compact,
robust, cost-effective and compatible with optical fiber technology. The ratio of
absorbance measurements for two transitions with different temperature dependence can
provide gas temperature. TDL temperature sensors based on two-line absorption
thermometry provide the path-averaged temperature along the laser beam, which may be
54 CHAPTER FOUR
a better indication of the bulk gas temperature than the point-temperature measured by
thermocouples typically near the wall. Wavelength scanning of the TDLs over the
absorption transitions provides immunity from noise and non-resonant transmission loss
with wavelength scan rates up to a few kHz. [Furlong et al. 1996, Hinckley et al. 2004,
Liu et al. 2005]
In this work, a TDL temperature sensor based on DAS two-line thermometry has
been designed, tested, constructed and utilized to measure the bulk exhaust gas
temperature in an industrial gas turbine. As has been discussed in Chapter 2, two-line
thermometry assumes a uniform temperature distribution along the measurement path.
Since these measurements are made in the exhaust annulus, downstream of both the
combustor and turbine, where spatial temperature gradients are minimized, the use of
two-line thermometry is appropriate to capture the path-averaged bulk exhaust gas
temperature. The sensor demonstrated here will allow the exhaust temperature to be
monitored and provide data to optimize engine performance and maintenance intervals.
H2O vapor is selected as the absorbing species to be probed since it is naturally
present in the combustion exhaust as a major combustion product, and its rovibrational
spectrum is strong and covers a wide wavelength range. The absorption transitions of
H2O vapor in the 1.3-1.5 µm region are systematically analyzed via spectral simulation,
and optimal spectral line pairs are selected with the criteria of appropriate absorption
strength, adequate immunity to the effects from cold boundary layers, good isolation
from neighboring transitions, and high temperature sensitivity over the expected exhaust
temperature range of 600-900 K. Since the measurement accuracy of the two-line
thermometry depends critically on the accuracy of linestrength values for the line pair, an
important element of this work is to provide suitable linestrength data for the selected
transitions. The temperature sensing accuracy of two potential line pairs is examined by
laboratory demonstration experiments with a heated cell and the optimal line pair selected
for field applications. Field measurements in a 20 MW industrial gas turbine demonstrate
the practical utility of TDL sensing in harsh industrial environments. Although multiple
TEMPERATURE SENSING USING DAS TWO-LINE THEMOMETRY 55
researchers have used water vapor absorption for gas temperature sensing [Furlong et al.
1996, Mihalcea et al. 1998, Ebert et al. 2000, Liu et al. 2005], to the best of our
knowledge, this is the first measurement in the exhaust of a commercial stationary gas
turbine.
4.2 Selection of spectral lines
The first step in the design of absorption two-line thermometry is to select the
optimal spectral line pair, and a significant effort has been devoted to develop systematic
line selection criteria. [Zhou et al. 2003, 2005b] In this section, the design rules for the
current line selection will be briefly discussed.
First, the selection of candidate H2O transitions is limited to the spectral region of
1.3-1.5 µm, where the ν1+ν3 combination and 2ν1 and 2ν3 overtone bands of H2O
absorption spectra overlap with the most common telecommunication bands, and thus
diode lasers and optical fibers are widely available. [Allen 1998] Within this region, there
are 6435 H2O transitions listed in the HITRAN 2004 database. [Rothman et al. 2005]
Second, the absorption strength of the candidates must be large enough to
guarantee a good SNR ratio but small enough to avoid optically-thick measurements over
the expected conditions in the gas turbine exhaust: T = 600-900 K, P = 1atm, XH2O = 10%
and L = 32 cm. Here we impose the upper and lower bounds on the peak absorbance as
follows
2, ,0.09 ( ) 1v peak H O i v peakPX S T Lα φ≤ = ≤ . (4.1)
A C++ program is developed to calculate the peak absorbance of each of the 6435 H2O
transitions with the spectroscopic parameters provided by HITRAN 2004. The criterion
in Eq. (4.1) reduces the possible transitions from 6435 to 188 potential candidates.
56 CHAPTER FOUR
Third, candidate lines are selected to reduce the influence of thermal boundary
layers. The boundary layer influence depends on the sensitivity of linestrength to
temperature, which can be derived from Eq. (2.2) as
[ ]" ( )//
E E TdS S hcdT T k T
−= ⋅ , (4.2)
where E(T) is a characteristic energy of the absorbing species and depends on
temperature [Ouyang and Varghese 1989]
[ ]( )( )
( )d T Q Tk TE T
hc Q T dT⋅
= ⋅ ⋅ . (4.3)
The E(T) curve of H2O vapor in the temperature range of 300-3000 K is plotted in Fig.
4.1. The impact of a cold boundary layer on the measurement accuracy of the core
(relatively uniform) temperature can be evaluated by the difference of integrated
absorbance along the beam path in the boundary layer [Ouyang and Varghese 1989]
[ ]0
2
[ ( ) ]
" ( )( )
c
b
c
b
S
c abs c abs S
T
abs T
A A A PX S T Sd PX dS
E E ThcPX S T dTk T
δδ ξ ξ
ξ
∆ = − = − =
−=
∫ ∫
∫, (4.4)
where A is the integrated absorbance due to boundary layer water vapor, δ is the
boundary layer thickness and ξ is the spatial integration variable. The subscript of c
denotes quantities evaluated at the uniform core temperature and b labels quantities
evaluated at the temperature on the boundary. Here the partial pressure of the absorbing
species PXabs is assumed to be uniform. When ∆A << A the boundary layer does not
influence the measurement. The cold boundary layer becomes significant for lines with
E”<<E(T). As shown by Fig. 4.1, EH2O(T) ranges from 1079 to 1727 cm-1 for the
temperature range of 600-900 K, therefore lines with E” < 500 cm-1 are rejected, reducing
the number of candidate transitions to 132.
TEMPERATURE SENSING USING DAS TWO-LINE THEMOMETRY 57
Figure 4.1: E(T) curve of H2O vapor in the temperature range of 300-3000 K.
Fourth, we simulate the absorbance spectra of the remaining 132 candidates at the
expected working conditions with the HITRAN2004 parameters, and screen the
candidates by spectral isolation from nearby H2O and CO2 features in order to minimize
the uncertainty in the analysis of the direct absorption. Only features free from strong
interferences within ± 0.5 cm-1 of their line center frequencies are retained. This screening
further reduces the number of candidate transitions to 7 as listed in Table 4.1. Features A
and B in the table are actually line pairs that are not resolved at 1 atm due to the pressure
broadening, but which will separate at low pressures. Because this might create
complexities in the linestrength validation and curve fitting at low pressures, these two
features are excluded from further consideration, leaving line D as the only low E”
transition among the 5 remaining candidates. Actually, feature A or B could be selected if
no better candidates are available. In order to be used for precise temperature sensing,
this would require an effective linestrength Seff(T0 = 296 K) and lower state energy "effE to
be established for the pair of overlapped lines in feature A or B by measuring the sum of
integrated absorbance for each line. [Gharavi and Buckley 2004]
1000 2000 3000
2000
4000
6000
8000
E(T)
[cm
-1]
T [K]
58 CHAPTER FOUR
Table 4.1: Seven features which are the outcome of line selection steps 1-4.
Line Index
Frequency [cm-1]
S@296K [cm-2/atm]
E” [cm-1]
7199.33 7.43E-03 888.63 A 7199.38 2.22E-02 888.60 7407.78 8.42E-03 882.89 B 7407.81 2.79E-04 224.84
C 7424.69 1.16E-03 1477.30 D 7429.72 4.54E-03 982.91 E 7447.48 2.22E-03 1360.24 F 7450.93 5.38E-04 1690.66 G 7454.45 1.83E-04 1962.51
Finally, we require the selected line pairs to have sufficient temperature sensitivity
to guarantee the accuracy of temperature measurements. It can be inferred from Eq.
(2.41) that
1 2
/ 1/ /
dT T TdR R hc k E E
= ⋅′′ ′′−
. (4.5)
Therefore, the general rule is the larger the difference of the lower state energy, the better
the temperature sensitivity of the absorbance ratio R. We predict line pair DG to be the
optimum for the 600-900 K temperature range expected for the gas turbine exhaust. The
line selection rules and results are summarized in Table 4.2.
Table 4.2: Summary of the criteria and results for the line selection.
Step Criteria # of Lines 1 1.3µm ≤Wavelength ≤1.5µm 6435 2 Appropriate absorption strength: 0.09 ≤ αν,peak ≤ 1 188 3 Immune to the effect of cold boundary layer 132 4 Good isolation from neighboring features 5 5 Sufficient temperature sensitivity 4
It has been shown in Chapter 3 that the NIR overtone/combination water vapor
spectra in HITRAN 2004 database are still not complete and although the linestrength
TEMPERATURE SENSING USING DAS TWO-LINE THEMOMETRY 59
data are sufficiently accurate for sensor design, the HITRAN data must be validated or
updated before using the selected lines for temperature measurements. Therefore, we
chose to experimentally examine the line pairs DG, DC, and DF as potential candidates
for the temperature sensor.
4.3 Linestrength validation
The next step in the design of the two-line thermometry sensor is to validate or
update the fundamental spectroscopic parameters of the selected transitions.
4.3.1 Details of experiments
Figure 4.2: Experimental arrangement for the linestrength measurements.
DAQ Computer
76 cm
127 cm
Vacuum Pump N2/Vacuum
Thermocouples
N2/Vacuum
N2 Purged
3-Zone Tube Furnace 3-Section Quartz Cell
Etalon
Fiber Coupled NEL DFB
Diode Laser
H2O Flask P
N2 Purged
Laser Controller
Function Generator
60 CHAPTER FOUR
Figure 4.2 shows the experimental arrangement used to determine the linestrengths
with a heated static cell. It is similar to the setup shown in Fig. 3.2 except that the static
quartz cell used here also has three zones. The 76 cm long center section is filled with gas
samples and located in the uniform temperature region (center zone) of the oven, while
the two outer regions are evacuated to avoid any undesired absorption by ambient
atmospheric constituents. These evacuated regions of the cell extend outside of the oven.
All three sections of the cell have an outer diameter of 4.45 cm. The ceramic heating tube
of the furnace has an inner diameter of 6.35 cm. The cavity between the cell and the
heating tube is shielded on both ends with aluminum foil to prevent convection and
reduce radiation loss. Three K-type thermocouples (Omega) are placed at the middle and
both ends of the center section of the heated cell to determine the temperature of gas
samples. At each temperature set-point in the range of 296-1000 K, the three heaters are
adjusted (so that the two outer heaters operate with higher power than the center heater)
to reduce the measured deviation of the three thermocouple readings to a maximum of 2
K. All these arrangements guarantee that when the system reaches equilibrium, there is
neither an axial nor a radial temperature gradient in the test gas. For thermocouple
measurements, the conduction loss is negligible since the thermocouple wires are aligned
with the isotherm, and there is no convection loss since the cavity between the heating
tube and the cell is fully enclosed. Additionally, the radiation losses from the
thermocouple beads, the center-section cell walls and the gas sample to the ambient ends
can be regarded as equivalent in terms of radiation flux, since their view factors to the
ambient ends are all very small. Therefore, we believe the thermocouple readings
(without any correction) sufficiently indicate the cell wall temperature and also the
temperature of the gas sample with the claimed thermocouple uncertainties (± 0.75% of
reading).
Two DFB InGaAsP lasers (NEL NLK1B5E1AA) are used, one at a time, as the
laser source with temperature and current controlled by an ILX Lightwave LDC-3900.
The laser wavelength is tuned over the desired absorption features by a linearly varying
TEMPERATURE SENSING USING DAS TWO-LINE THEMOMETRY 61
injection current. The fiber-coupled output of the laser in use is split into two beams as
shown in Fig. 4.2. One beam is collimated in free space and transmitted through the
sample gas, focused by a spherical gold mirror and detected by an InGaAs detector
(Thorlabs PDA400). The second beam is also collimated and propagated through a solid
etalon with a free spectral range (FSR) of 2.00 GHz to provide a wavelength calibration
of scan time to laser wavelength.
The laser wavelength is tuned over a range of ~3 cm-1 at a frequency of 100 Hz.
During data acquisition, 10 scans are averaged to remove stochastic noise from the laser
and detector, and the averages are the raw data traces plotted in Fig. 4.3(a). From the
transmitted signal It, the baseline laser intensity I0 is determined by fitting the part of the
trace without absorption with a 3rd order polynomial. The absorption spectrum is then
calculated as shown in Fig. 4.3(b). The lineshape of the target transition can be fit by a
Voigt profile with the Doppler FWHM fixed at the value calculated by Eq. (2.10). This
Voigt fit provides the integrated absorbance A, from which the linestrength at the
experimental conditions is calculated as per Eq. (2.8).
Figure 4.3: Illustration of: (a) the measured raw data traces (solid line: transmission through the cell, dotted line: transmission through the etalon) for the linestrength validation of transition 7429.72 cm-1 at T = 894 K and P = 19.1 Torr; (b) the reduced lineshape of transition 7429.72 cm-1 (solid line), its Voigt fit (dotted line) and the residual (top panel).
6
4
2
0
Sig
nal [
V]
0.100.080.060.040.020.00Time [s]
It IEtalon
0.2
0.1
0.0
Ab
sorb
anc
e
7430.07429.87429.67429.4Frequency [cm
-1]
-1.00.01.0
Res
.[%]
Measurement Voigt Fit
(a) (b)
62 CHAPTER FOUR
4.3.2 Results of spectral survey and linestrength measurements
Figure 4.4: The measured spectra (solid line) of the selected four transitions and comparisons with simulations (dotted line) by HITRAN2004 at the experimental conditions of T = 894 K and P = 19.1 Torr: (a) line D at 7429.72 cm-1; (b) line G at 7454.45 cm-1; (c) line F at 7450.93 cm-1; (d) line C at 7424.69 cm-1.
Figure 4.4 shows the measured spectra of the selected four transitions and a
comparison with simulations by HITRAN 2004 at the experimental conditions of T = 894
K and P = 19.1 Torr. Experiments confirm the good spectral isolation for lines D and G,
but reveal interference from transitions not present in the HITRAN database for lines F
and C. A two-line Voigt fit is used for line F and the observed interference, and a six-line
Voigt fit for line C and its neighbors in the data analysis, as shown in Fig. 4.5.
0.3
0.2
0.1
0.0
Abs
orba
nce
743174307429Frequency [cm
-1]
Measurement Simulation
0.3
0.2
0.1
0.0
Abs
orba
nce
7456745574547453Frequency [cm
-1]
Measurement Simulation
(a) (b)
0.4
0.2
0.0
Abs
orb
ance
7453745274517450Frequency [cm
-1]
Measurement Simulation
0.4
0.2
0.0
Abs
orb
ance
7427742674257424Frequency [cm
-1]
Measurement Simulation
(c) (d)
Line C Line F
Line G Line D
Interference Line
InterferenceLine
TEMPERATURE SENSING USING DAS TWO-LINE THEMOMETRY 63
Figure 4.5: Multiple-peak Voigt fit (dotted line) to the spectra (solid line) measured at T = 894 K and P = 19.1 Torr: (a) two-peak Voigt fit for line F at 7450.93 cm-1; (b) six-peak Voigt fit for line C at 7424.69 cm-1.
To determine linestrength at a selected temperature, the integrated absorbance of
each line is first measured at approximately 15 different pressures between 1 to 20 Torr.
At each pressure, 10 measurements are made, and the average of the integrated
absorbance and its statistical precision are extracted and plotted in Fig. 4.6 (the error bars
are generally too small to be identified on the figure). The linestrength and its statistical
precision at this temperature are inferred from the slope of a linear fit to the data. This
procedure eliminates systematic error in the zero of the pressure gauge, and stochastic
noise in the measured pressure values is reduced.
Figure 4.6: Determination of the linestrength from the slope of the linear fit (lines) to the measured integrated absorbance (symbols) versus pressure at T = 894 K for: (a) line D: S(894 K) = 6.566e-3 ± 3e-6 [cm-2atm-1], line G: S(894 K) = 5.873e-3 ± 2e-6 [cm-2atm-1]; (b) line C: S(894 K) = 7.877e-3 ± 3e-6 [cm-2atm-1], line F: S(894 K) = 7.479e-3 ± 3e-6 [cm-2atm-1].
0.3
0.2
0.1
0.0
Abs
orba
nce
7451.27451.07450.87450.6Frequency [cm
-1]
-1.00.01.0
Res
.[%]
Measurement Voigt Fit
0.3
0.2
0.1
0.0
Abs
orba
nce
7425.07424.87424.67424.47424.2
Frequency [cm-1
]
1.5-1.5
Res
.[%]
Measurement Voigt Fit
(a) (b)
Line C Line F
Interference Line
Interference Line Neighbor
Line
NeighborLines
0.015
0.010
0.005
0.000
Inte
grat
ed A
rea
[cm
-1]
20151050Pressure [Torr]
0.015
0.010
0.005
0.000
Inte
grat
ed A
rea
[cm
-1]
20151050Pressure [Torr]
(a) (b)
Line D
Line G
Line C
Line F
64 CHAPTER FOUR
These linestrength measurements are made at ten different temperatures between
300 and 900 K. The inferred linestrength and its statistical precision at each temperature
are plotted in Fig. 4.7 (the error bars are generally too small to be identified on the
figure). With the lower state energy Ei” fixed at the HITRAN value, the linestrength at
the reference temperature Si(T0 = 296 K) is obtained from a one-parameter best fit to the
known functional form of S(T) as in Eq. (2.2).
Figure 4.7: Determination of the linestrength at the reference temperature Si(T0 = 296 K) from the one-parameter best fit (line) to the measured linestrength (symbol) versus temperature with the known functional form of S(T) and E” fixed at the HITRAN value for: (a) line D & G; (b) line C & F.
The measured linestrengths for the four selected transitions are summarized in
Table 4.3 and compared with values from HITRAN2004 and Toth [Toth 1994].
However, for line F there is a small feature 0.08 cm-1 to the red side of the selected line.
This feature will be blended with line F at atmospheric pressure by pressure broadening.
Therefore we re-analyzed the total integrated area and calculated an effective
linestrength, Seff(T), for the blended pair. This blended pair is fit with a two parameter fit
to yield Seff(T0 = 296 K) = 4.818E-4 cm-2atm-1 and "effE = 1730.0 cm-1 as shown in Fig. 4.8.
This blended line pair is used as a single line F’ for the temperature sensor. Because the
E” for the interfering transition is not known, we caution the reader not to extrapolate
these effective spectroscopic constants for the blended line pair beyond the 300-1000 K
1.0x10-2
0.5
0.0
Line
stre
ngth
[cm
-2a
tm-1
]
12001000800600400Temperature [K]
1.0x10-2
0.5
0.0
Line
stre
ngth
[cm
-2at
m-1
]
12001000800600400Temperature [K]
(a) (b)
Line D
Line G
Line C
Line F
TEMPERATURE SENSING USING DAS TWO-LINE THEMOMETRY 65
range where the linestrength data is measured. The uncertainty analysis of our
linestrength measurements will be discussed in the next section together with the impact
of this uncertainty on the temperature measurement accuracy of our TDL sensor.
Figure 4.8: Data analysis for line F’ (triangle & solid line) and a comparison with the data analysis for line F only (circle & dotted line). Each triangle represents the sum of linestrength values measured for line F and its interfering neighbor. The effective linestrength at the reference temperature Seff(296 K) = 4.818E-4 cm-2atm-1 and the effective lower state energy "
effE =1730.0 cm-1 for line F’ are inferred from a two-parameter best fit (solid line) to the known functional form of S(T).
Table 4.3: Summary of measured linestrengths and comparisons with HITRAN2004 [Rothman et al. 2005] and Toth [Toth 1994] values.
Line Index Frequency E”
HITRAN S(296 K) Measured
Estimated Uncertainty
S(296 K) HITRAN04σS=5-10%
Dev. S(296 K)
Toth σS=2-7%
Dev.
[cm-1] [cm-1] [cm-2atm-1] [%] [cm-2atm-1] [%] [cm-2atm-1] [%] D 7429.72 982.9 4.588E-03 0.8 4.54E-03 0.9 4.17E-03 9.8 G 7454.45 1962.5 1.726E-04 1.8 1.83E-04 -6.0 1.40E-04 22.9 F 7450.93 1690.7 5.308E-04 1.4 5.38E-04 -1.7 4.82E-04 9.8 C 7424.69 1477.3 1.125E-03 1.1 1.16E-03 -3.4 1.03E-03 8.7
Using the linestrength Si(T0) from our measurements and HITRAN, and the lower
state energy E” from HITRAN (or "effE for line F’), the ratio of integrated areas for line
8x10-3
6
4
2
0Line
stre
ngth
[cm
-2at
m-1
]
12001000800600400Temperature [K]
Line F’ Line F
66 CHAPTER FOUR
pairs DG and DF’ are calculated and plotted in Fig. 4.9. The gas temperature can be
determined from measurements of the absorbance ratio using these calibration curves.
Although the linestrength values from our measurements and HITRAN differ by only a
few percent for line pair DG, this small deviation produces an error as large as 38 K, as
illustrated in Fig. 4.9(a). This demonstrates the importance of accurate linestrength data
as part of the design of a practical sensor. We should note that the line pair DC is
excluded from further consideration because of difficulties for baseline determination at
the working pressure of 1 atm owing to the multiple neighbor lines we discovered.
Figure 4.9: Calibration curves for inferring temperature from the measured ratio of integrated areas. The dotted curves are calculated using the Si(T0) and E” values from HITRAN. The solid curves are calculated using the measured Si(T0) and the E” from HITRAN (using the measured "
effE for line F’). The ratio is defined as Ratio = AreaHighE”Line /AreaLowE”Line. (a) line pair DG; (b) line pair DF’.
4.3.3 Uncertainty analysis in measured S(T) and two-line thermometry
The measurement uncertainty of the linestrength value can be determined from a
propagation of errors analysis. The measured linestrength is a function of the pressure,
temperature, species mole fraction, path length and integrated area according to Eq. (2.8).
Using the assumption that all independent variables are uncorrelated, we can determine
the uncertainty in the measured linestrength
1000
800
600
400Tem
pera
ture
[K]
1.21.00.80.60.40.20.0Ratio of Integrated Areas
HITRAN2004 Measurements 1000
800
600
400Te
mp
erat
ure
[K]
1.41.21.00.80.60.40.20.0Ratio of Integrated Areas
HITRAN2004 Measurements
(a) (b)
∆T=38K
TEMPERATURE SENSING USING DAS TWO-LINE THEMOMETRY 67
22 2 2 2
absabs
S S S S SS A X P L TA X P L T
∂ ∂ ∂ ∂ ∂ ∆ = ∆ + ∆ + ∆ + ∆ + ∆ ∂ ∂ ∂ ∂ ∂ . (4.6)
The partial derivatives in the first four terms are calculated by Eq. (2.8), and the
normalized linestrength uncertainty becomes
2
2 2 2 2 /abss A X P L
S S S TS T
σ σ σ σ σ∆ ∂ = = + + + + ∆ ∂ . (4.7)
The first four terms are the same for all four transitions with σA ≈ 0.4%, σXabs ≈ 0.1%, σP
≈ 0.1% and σL ≈ 0.2%. The final term is different for each line due to the temperature
dependence of the linestrength. The temperature measurement uncertainty ∆Τ is taken
from the thermocouple specifications provided by Omega. As listed in Table 4.3, the
uncertainty of the measured linestrength for the four lines is less than 2%. We believe
these data are among the most accurate for any published linestrength values for the NIR
overtone transitions of water vapor.
In two-line thermometry, the uncertainty of the integrated absorbance ratio R is
determined by the uncertainty of measured linestrengths and integrated areas, and can be
written
1 2 1 2
2 2 2 2S S A AR R σ σ σ σ∆ = + + + . (4.8)
Thus the temperature measurement uncertainty of our TDL sensor can be estimated by
1 2 1 2
2 2 2 2
/ / S S A AR RT
dR dT dR dTσ σ σ σ∆
∆ ≈ = ⋅ + + + . (4.9)
Figure 4.10 shows the variation of the temperature measurement uncertainty with
temperature for line pair DG and DF’. Temperature measurement uncertainties of 5-7 K
for line pair DG and 5-9 K for line pair DF’ are estimated for the expected working
68 CHAPTER FOUR
temperature of 600-900 K if the integrated areas can be perfectly measured. In practical
applications, the uncertainty in temperature measurements will become dominated by the
uncertainty in the measured absorbance area for %32221
≥+= AAA σσσ .
Figure 4.10: The temperature measurement uncertainty for: (a) line pair DG; (b) line pair DF’. The temperature measurement uncertainty is attributed to uncertainties in spectroscopic parameters and integrated area measurements. It will become dominated by area measurement uncertainties for %322
21≥+= AAA σσσ .
4.4 Laboratory demonstration measurements
Experiments to validate the TDL sensor are conducted on the same setup used for
linestrength validation except the gas sample is changed to a controlled H2O-air mixture
at atmospheric pressure. To prepare the gas sample, H2O vapor and air are sequentially
introduced into a stainless steel tank with Teflon mixing balls, producing a mixture with
XH2O ~ 2%. The tank is then shaken and allowed to rest for at least 5 hours before the
mixture is introduced into the static cell for the absorption experiments. The ratio of
integrated areas is measured for two candidate line pairs, and the temperature is obtained
by using the calibration curves plotted in Fig. 4.9 (a) and (b) respectively.
40
20
0
∆T [K
]
1000900800700600500T [K]
σA=0 σA=1% σA=3% σA=5%
40
20
0
∆T [K
]
1000900800700600500T [K]
σA=0 σA=1% σA=3% σA=5%
(a) (b)
TEMPERATURE SENSING USING DAS TWO-LINE THEMOMETRY 69
Figure 4.11 shows the comparison of the thermocouple readings with the
temperatures from the TDL measurements. The temperatures determined from the TDL
sensor are in excellent agreement with the thermocouple readings over the entire
temperature range of 350-1000 K. For the line pair DG, the average bias (∆Tbias = |TTC-
TTDL|) of the 21 measurements is 2.0 K and the largest deviation is 6.1 K. For line pair
DF’, the average deviation of the 19 measurements is 5.0 K and the largest deviation is
11.1 K.
Figure 4.11: Temperatures measured by TDL sensor in the demonstration experiments with a heated static cell and comparisons with thermocouple readings: (a) line pair DG; (b) line pair DF’.
These laboratory demonstration experiments lead to selection of line pair DG for
field applications due to its potential for more accurate temperature measurements. As a
backup candidate, line pair DF’ can be used in the 300-1000 K range if a sufficient SNR
is not obtained for line G during the field measurements (recall that Fig. 4.7 shows line F
has a larger absorbance than line G over the expected working conditions).
400 600 800 1000
400
600
800
1000
TDL
Mea
sure
men
ts [K
]
Thermocouple Readings [K]400 600 800 1000
400
600
800
1000
TDL
Mea
sure
men
ts [K
]
Thermocouple Readings [K](a) (b)
70 CHAPTER FOUR
4.5 Temperature sensing for gas turbine exhaust
The TDL sensor designed here using line pair DG is then successfully used by our
GE colleagues to measure the gas temperature in the exhaust of an industrial gas turbine
directly coupled to a 20 MW electric generator [Hinckley et al. 2005]. Figure 4.12 shows
a schematic of the sensor hardware. The laser sources and other optical and electrical
components are enclosed in an instrumentation shed near the gas turbine. The two lasers
are alternately scanned over a range of ~ 2 cm-1 at 100 Hz in a time-division multiplexed
approach. The fiber-coupled laser outputs are multiplexed and transmitted to the gas
turbine exhaust casing by a high-temperature single-mode fiber with 9 µm core diameter.
The output beam from the fiber is collimated by a small lens (d = 5 mm, f = 10 mm),
propagated across the exhaust annulus, collected by a larger lens (d = 25.4 mm, f = 38
mm), and focused into a high-temperature multi-mode fiber with a core diameter of 400
µm and a numerical aperture of 0.22. The larger collection lens and fiber on the reception
side provide tolerance to beam misalignment due to mechanical vibration, aero-optical
beam steering and thermal expansion of the optical assemblies. The multimode fiber
brings the transmitted signal to an InGaAs photodetector in the instrument shed. The
transmission data are sampled at 100 kHz, and the real-time data processing algorithms
allow temperature to be reported at 3 Hz.
Figure 4.12: Schematic of the sensor hardware for field test.
2x1 Multiplexer
Gas TurbineExhaust Casing(cross section)
Diode LaserController
InGaAsdetectorDSP
Laptopcomputer
High-temperaturesingle-modeoptical fiber
High-temperaturemulti-modeoptical fiber
Instrumentation Shed
Laser 1
Laser 2
Rotor
TEMPERATURE SENSING USING DAS TWO-LINE THEMOMETRY 71
Figure 4.13: Ten sample traces of line D taken consecutively in the field measurements: (a) raw data traces with an average baseline fit; (b) the corresponding absorbance spectra with an average Voigt fit.
Figure 4.13 presents ten sample absorbance spectra taken at a gas turbine part load
condition of 16 MW. In this figure, a significant stochastic noise is evident. The primary
source of this noise comes from losses in the multimode fiber connections in the
collection beam path. These losses produce significant mode noise on the scanned-
wavelength transmission and dominate the error in the measured absorbance. Since the
noise is stochastic, ensemble time-averaging is used to reduce the uncertainty in the
measured absorbance. A baseline is fit to the average of 20 sequential raw data scans
before the calculation of absorbance and the Voigt fit. Figure 4.14 shows the resulting
time-averaged temperature values at 17 MW load in a combined cycle mode. This
temporal averaging significantly reduces the uncertainty in the temperature measurement.
The mean temperature measured by the TDL sensor is 724 K, compared with an average
of 730 K measured by Type-K thermocouples within the same time duration. It is
important to note that the TDL sensor provides the path-averaged temperature along the
laser beam path while the thermocouple, inserted at the same axial location in the exhaust
7429.0 7429.5 7430.0 7430.5
0.00
0.05
0.10
0.15
Abso
rban
ce
Wavenumber [cm-1]
4.0
5.0
6.0
7.0
(b) Voigt fit
Baseline fit
Det
ecto
r Sig
nal [
V]
(a)
72 CHAPTER FOUR
flow, measures temperature at a distinct spatial location in the flow. Multiple transitions
could be probed to resolve the temperature non-uniformities along the LOS beam path,
though this is not considered necessary for the present uniform flow. The standard
deviation of the data in Fig. 4.14 is 11 K, which is a combination of statistical
measurement error and true physical variation in the gas temperature due to the turbulent
nature of the exhaust flow. Improved optical engineering is expected to significantly
suppress mode noises and allow substantial improvements in the sensor performance and
measurement accuracy.
Figure 4.14: Sample results of temperature measurements by the TDL sensor at 17 MW load in combined cycle mode. Each temperature is inferred from an average of 20 sequential raw data scans. The solid line represents the mean (724 K) of temperatures measured by the TDL sensor within five and half minutes. The dotted line represents an average (730 K) of temperatures measured by Type-K thermocouples within the same time duration.
0 60 120 180 240 300600
700
800
900
Exha
ust G
as T
empe
ratu
re [K
]
Time [s]
TEMPERATURE SENSING USING DAS TWO-LINE THEMOMETRY 73
4.6 Summary
A tunable diode laser sensor based on DAS two-line thermometry of H2O vapor has
been designed, constructed, validated in a controlled laboratory environment, and
demonstrated in a large-scale industrial gas turbine powering an electric generator.
Design rules are developed and used to select optimal spectral line pairs from the 1.3-1.5
µm spectral region of H2O vapor. The logic used to select the design rules is discussed
and considerations of appropriate absorption strength, adequate immunity to the effect of
cold boundary layers, good isolation from neighboring transitions and sufficient
temperature sensitivity over the expected exhaust temperature range of 600-900 K are
crucial to optimize the TDL sensor design. Experiments are performed to measure precise
linestrength values for four selected transitions. For two of the candidates, spectral
interferences not predicted by the HITRAN database are identified. Using our measured
linestrength values, calibration curves for two-line thermometry are created by
calculating the ratio of integrated absorbances as a function of temperature. The
uncertainties of our measured linestrengths are analyzed to be less than 2%. The impact
of this uncertainty on the temperature measurement accuracy of the two-line thermometry
is predicted to be less than ± 10 K. Laboratory validation experiments are conducted to
examine the temperature sensing capability of the TDL sensor. The transitions at 7429.72
cm-1 and 7454.45 cm-1 are identified as the best line pair for field applications due to their
superior accuracy for temperature measurements. Gas temperature measurements in the
exhaust stream of an industrial gas turbine show good agreement with conventional
thermocouple readings, and demonstrate the practical utility of TDL sensing in harsh
industrial environments. Future improvements in optical engineering are expected to
yield improved performance and accuracy of the TDL sensor.
74 CHAPTER FOUR
75
Chapter 5
TEMPERATURE SENSING USING WMS-2F
TWO-LINE THERMOMETRY
5.1 Motivation
The development of a TDL temperature sensor using WMS-2f two-line
thermometry is motivated by the requirement for in-cylinder gas temperature
measurement during the compression strokes of IC engines. This sensor is intended to be
mounted on a probe which is combined with a spark plug to provide optical access to the
combustion chamber. [Rieker et al. 2006a] Such a sensor system will enable non-
intrusive in-cylinder temperature measurements without any engine modifications, which
is a significant advantage over optical imaging techniques.
The working conditions of IC engines pose great challenges for developing a
temperature sensor using LOS absorption spectroscopy. First, the temperature and
pressure vary over wide ranges during the compression strokes of IC engines. Figure 5.1
shows the temperature and pressure traces of some potential compression strokes. The
TDL temperature sensor is required to work properly over a temperature range of 400-
1050 K and a pressure range of 5-25 atm. At elevated pressures, the absorption spectra
are broadened and blended as illustrated by Figure 5.2. The lack of non-absorbing wings
in the congested spectra imposes great difficulty on the determination of the zero-
absorption intensity baseline for the scanned-wavelength DAS strategy as discussed in
Chapter 4. Second, the LOS absorption by water vapor is weak due to the short optical
76 CHAPTER FIVE
path length (1.2 cm determined by the sensor probe tip) and the low water mole fraction
(~1% in the intake ambient air), thus a sensitive spectroscopy technique is demanded for
the sensor development. Third, the temperature and pressure change rapidly at a speed on
the order of ~1000 rpm, and thus the sensor needs to have a bandwidth on the order of
kHz.
Figure 5.1: Potential compression strokes of IC engines. The working conditions of the TDL temperature sensor are confined by two extreme compression strokes, the heavy exhaust gas recirculation (EGR) stroke which defines the highest temperature at a certain pressure and the supercharging stroke which defines the highest pressure at a certain temperature. A and B are two extreme T/P conditions used for the selection of laser set-points.
Figure 5.2: Absorption spectra of H2O vapor simulated at different pressures, T = 1000 K, XH2O = 1% and L = 1 cm.
300
400
500
600
700
800
900
1000
1100
0 1 2 3 4 5 6 7Pressure MPa
Tem
pera
ture
K
CR=15, EGR=50%
CR=15, SuperCharge(+50kPa)CR=15, SuperCharge(+100kPa)
CR=10, Stratified ChargeCR=10, Full load
CR=10, Partial loadCR=10, Idle
Heavy EGR
Supercharging
Working conditionsof TDL T sensor
Condition B
Condition A
7202 7204 72060.000
0.002
0.004
0.006
Abs
orba
nce
Frequency [cm-1]
1 atm 10 atm 20 atm 30 atm
TEMPERATURE SENSING USING WMS-2F TWO-LINE THERMOMETRY 77
A fixed-wavelength WMS-2f strategy is utilized to address these challenges since
the WMS technique is able to significantly improve the SNR over the DAS strategy
[Wang et al. 2000, Hovde et al. 2001, Aizawa 2001]. The fixed-wavelength scheme of
WMS requires no baseline and allows for larger measurement bandwidth over scanned-
wavelength WMS scheme [Liu et al. 2004b, Li et al. 2006].
The basic sensor concepts and design considerations will be briefly introduced in
section 5.1. The complete development of this sensor was a team effort. The following
sections will highlight the precision measurement of spectroscopic parameters, selection
of laser set-points and construction of calibration databases. Details of other work
including line selection [Zhou et al. 2005b] and laboratory validation [Rieker 2006a,
2006b] are reported separately by my colleagues.
5.2 Overview of sensor concepts and design
The spectroscopic fundamentals and mathematic representations for fixed-
wavelength WMS-2f two-line thermometry have been discussed in detail in Chapter 2. In
short, the WMS-2f and WMS-1f signals at the two selected laser set-points are measured.
A calibration curve is simulated in advance for the ratio R2f/1f as per Eq. (2.48) as a
function of temperature and pressure. Using the separately measured pressure, the
temperature is determined by the measured R2f/1f. The H2O mole fraction can be
calculated from the previously inferred temperature and the measured WMS-2f/WMS-1f
signal for either transition.
The sensor design begins with the selection of optimal absorption line pair using a
procedure similar to that discussed in Chapter 4.2. In short, a systematic search among
thousands of water vapor transitions tabulated in HITRAN 2004 within the NIR spectral
region of 1.25-1.65 µm is performed by following criteria: strong WMS-2f peak signal
over the entire T/P range, minimal interference from nearby transitions, good temperature
sensitivity and monotonic behavior of the WMS-2f peak ratio vs. temperature, as well as
78 CHAPTER FIVE
small temperature measurement uncertainty arising from relevant noise sources (σT).
[Zhou et al. 2005b] This screening combined with the availability of lasers leads to a
final line pair in the ν1+ν3 combinational vibration band of water vapor spectra: the low
E” line is selected as the (J = 5, Ka = 5, Kc = 0) → (5,5,1) transition located at 7203.9 cm-1
with E”=742 cm-1 and the high E” line as the (12,1,12) → (13,1,13) transition located at
7435.6 cm-1 with E”=1558 cm-1. For simplicity, the low E” line will be referred to as line
1, and the high E” line as line 2 throughout the rest of this chapter.
The spectroscopic parameters of both lines and their neighboring transitions are
measured in a high temperature static cell in order to accurately simulate the sensor
performance and construct the calibration databases. The details will be discussed in
section 5.3.
The laser modulation parameters are selected with the following considerations:
First, the modulation depths a1 and a2 should take the optimum values as determined by
Eq. (2.37) to maximize the WMS-2f signal strength for both lines. But at elevated
pressures, these optimum a values can be very large due to the pressure broadening of the
absorption features, usually far beyond the maximum modulation depths attainable by
DFB lasers. Of course the maximum a attainable by a specific laser is inversely related to
the modulation frequency [Liu et al. 2004b]. Therefore, to allow for as large modulation
depths as possible, the modulation frequencies f1 and f2 should take the minimum values,
which are determined by the acceptable sensor bandwidth. Last, a frequency-division
multiplexing (FDM) scheme is utilized to achieve compact and robust sensor
architecture. The spacing between f1 and f2 should be large enough to enable sufficient
suppression of the cross-talk harmonics by the available lock-in amplifiers. Therefore, the
modulation frequencies are selected as f1 = 70 kHz and f2 = 87.5 kHz to allow for an
acceptable sensor bandwidth of 7.5 kHz, which is capable of capturing the temperature
change with a resolution of two crank angle degrees at an engine speed of 2500 rpm. The
maximum modulation depths achievable by the specific lasers at the selected modulation
TEMPERATURE SENSING USING WMS-2F TWO-LINE THERMOMETRY 79
frequencies, which are measured to be a1 = 0.57 cm-1 and a2 = 0.69 cm-1 [Rieker et al.
2006b], are used for the sensor operation. At such large modulation depths, the nonlinear
intensity modulation and the phase shift between the frequency and intensity modulation
become prominent [Li et al. 2006] and are thus taken into account in the simulation of the
sensor performance and the calculation of the calibration databases.
The determination of the laser set-points is of great importance for this fixed-
wavelength WMS-2f scheme which is intended to work over a wide range of pressures.
Since the location of the WMS-2f signal peak shifts considerably over the entire pressure
range, the sensor performance will be significantly dependent upon the laser set-points.
The development of the design rules for the selection of optimal laser set-points will be
discussed in detail in section 5.4.
Finally, using the measured spectroscopic parameters for the selected transitions
and their neighboring features, and the selected laser set-points and modulation
parameters for both lasers, the calibration databases are constructed to infer the
temperature and water mole fraction from the measured WMS-2f/WMS-1f signals. The
procedures to build the databases, the content and usage of the databases will be
discussed in detail in section 5.5.
The integrated sensor is first tested using static cell and shock tube measurements
in the laboratory [Rieker et al. 2006b], and then used for crank angle-resolved
measurements in motored and fired IC-engine experiments [Rieker et al. 2006a]. The
architecture of the integrated sensor and the details of the laboratory validation and field
tests can be accessed in the referenced literature.
80 CHAPTER FIVE
5.3 Measurement of spectroscopic parameters
5.3.1 Motivation
Since the sensor accuracy depends critically on the accuracy of the spectroscopic
parameters for the selected H2O transitions, these parameters are measured carefully
before used to calculate the calibration databases. The HITRAN 2004 database provides
an excellent and convenient tool for selecting lines, but the tabulated spectroscopic
parameters contain a sufficient probability of errors and undesirable uncertainties, as
discussed in Chapter 3. Additionally, this database does not provide sufficient
spectroscopic parameters for simultaneous high-temperature and high-pressure
measurements.
The gas temperature and pressure vary over wide ranges during the compression
stroke of IC-engines, thus accurate calculation of the WMS-2f signal at the laser set-point
requires not only precise linestrength data, but also precise pressure-broadening and
pressure-shifting coefficients of the target transition. Additionally, at elevated pressures,
any strong absorption features spectrally close to the target transition will be pressure-
broadened and blended with the target transition, and thus contribute to the WMS-2f
signal at the laser set-point. Therefore, to make accurate gas temperature measurement
using fixed-wavelength WMS-2f two-line thermometry, spectroscopic parameters of the
target transitions and their neighbors, including linestrength S(T), pressure broadening
coefficients γj(T) and pressure-induced frequency shift coefficients δj(T), must be
established beforehand. This work is a critical step for the sensor development and is also
expected to contribute to the validation of the HITRAN 2004 database.
5.3.2 Experimental details
The direct absorption spectra in the spectral region near line 1 and 2 are simulated
in Fig. 5.3 using spectroscopic parameters from HITRAN 2004. Three strong
neighboring features for line 1 and five for line 2 are identified as the transitions that
TEMPERATURE SENSING USING WMS-2F TWO-LINE THERMOMETRY 81
must be measured in addition to lines 1 and 2, since they will contribute to the WMS-2f
signals at the laser set-points at elevated pressures. These ten transitions are indexed and
tabulated in Table 5.1 with their line center frequencies and lower state energies taken
from HITRAN 2004. Note that feature 2D is actually an unresolved doublet, and will be
considered as a single transition in this work.
Figure 5.3: Absorption spectra of the two target lines and their neighboring features simulated for neat H2O vapor at T = 296 K, P = 18 Torr and L = 1 cm with spectroscopic parameters from HITRAN2004: (a) line 1 and its neighbors; (b) line 2 and its neighbors.
Table 5.1: Line center frequencies and lower state energies of the ten transitions measured in this study. Data are taken from HITRAN2004 [Rothman et al. 2005].
Line Index Line Center Frequency ν0 [cm-1]
Lower State Energy E” [cm-1]
1A 7202.90921 70.0908 1 7203.89041 742.0763
1B 7204.16602 931.2371 1C 7205.24611 79.4964 2 7435.61542 1557.8478
2A 7435.73154 1718.7188 2B 7435.94006 1524.8479 2C 7435.99941 1525.1360
7436.90924 1446.1282 2D 7436.92469 1282.9191 2E 7437.19198 1201.9215
0.10
0.05
0.00
Abs
orba
nce
72087206720472027200Frequency [cm
-1]
0.002
0.001
0.000
Abs
orba
nce
7438743674347432Frequency [cm
-1]
(a) (b)
Line 1 1A
1B
1C Line 2
2A
2B
2C
2D 2E
82 CHAPTER FIVE
In this study, the absorption spectra of neat H2O vapor at pressures of 1 to 20 Torr
and temperatures of 296 to 1000 K are first measured to infer the linestrength S(T) of the
ten transitions. The absorption spectra of H2O-air and H2O-CO2 mixtures at pressures of
100 to 800 Torr and temperatures of 296 to 1000 K are measured to obtain the
corresponding pressure broadening coefficients γair(T) and γCO2(T), and pressure-induced
frequency shift coefficients δair(T) and δCO2(T).
These quantitative measurements of spectroscopic parameters are performed with
the same static cell and furnace as used in the NIR H2O spectroscopy survey in Chapter
3. Two DFB InGaAsP lasers (NEL NLK1B5E1AA) are used to probe the four lines near
7204 cm-1 and the six lines near 7436 cm-1, respectively. The optical layout, laser
operation and data acquisition are the same as discussed in section 4.3.1 of Chapter 4.
5.3.3 Raw data and data analysis
Figure 5.4: Illustration of raw data and data analysis: (a) the measured raw data traces (solid line: transmission through the cell, dotted line: transmission through the etalon) for line 1 region at T = 296 K, PH2O-air = 403 Torr and XH2O = 1.56%. The inset shows the polynomial baseline fit (dash line) for line 1 and 1B; (b) the reduced lineshape of line 1 and 1B (solid line), the two-line Voigt fit (dotted line) and the residual (top panel).
Figure 5.4(a) shows an example of the measured raw data traces. From the
transmitted signal It, the zero-absorption laser intensity baseline I0, is determined by
10
5
0
Sig
nal [
V]
100806040200Time [ms]
It IEtalon
0.4
0.2
0.0
Abs
orba
nce
1.21.00.80.60.4Relative Frequency [cm-1]
-1.00.01.0
Res
. (%
)
Measurement Voigt Fit
(a) (b)
8
6
4504030
It I0Line 1
1A
1B
1C Line 1
1B
TEMPERATURE SENSING USING WMS-2F TWO-LINE THERMOMETRY 83
fitting the part of the trace without absorption with a 3rd order polynomial, as illustrated
by the inset of Fig. 5.4(a). The absorption spectrum is then calculated with It and I0 using
Eq. (2.4). The reduced lineshape of the target transition is fit by a Voigt profile, as
illustrated in Fig. 5.4(b). This type of Voigt fit provides the integrated absorbance A,
collisional FWHM ∆νc and relative line-center frequency 0~ν , from which the linestrength
S(T), pressure-broadening coefficients γ(T) and pressure-shift coefficients δ(T) at the
experimental conditions are calculated.
At a specific temperature, the absorption spectra of neat H2O vapor are first
measured at over ten different pressures between 1 to 20 Torr. At each pressure, ten
measurements are made. The averages of the measured integrated absorbance A are
extracted together with their statistical precisions and plotted in Fig. 5.5(a). The error bars
are generally too small to be identified on the figures. The linestrength S(T) and its
statistical precision at this temperature are inferred from the slope of a linear fit to the
measured integrated absorbance at various pressures using Eq. (2.8). This procedure
eliminates systematic error in the zero of the pressure gauge, and stochastic noise in the
measured pressure values is reduced.
The absorption spectra of the H2O-air mixture at the same temperature are then
measured at nominally ten different pressures between 100 to 800 Torr. At each pressure,
ten measurements are made. The averages of the measured collisional FWHM ∆νc are
extracted together with their statistical precisions and plotted in Fig. 5.5(b). The air-
broadening coefficient at this temperature γair(T) and its statistical precision are inferred
from the slope of a linear fit to the measured collisional FWHM at various pressures
using Eq. (2.12). The CO2-broadening coefficient γCO2(T) and its statistical precision are
obtained in the same way.
84 CHAPTER FIVE
Figure 5.5: Illustration of the determination of linestrength and broadening coefficients at a selected temperature with the data measured for line 1 at T = 296 K. With measurements for neat H2O vapor at various pressures, (a) linestrength inferred from the linear fit to the integrated absorbance, S1(296 K) = 6.927e-2 ± 2e-05 [cm-2atm-1]. With measurements for H2O-air mixture at various pressures, (b) air-broadening coefficient inferred from the linear fit to the collisional FWHM, γair(296 K) = 0.0539 ± 0.0001 [cm-
1atm-1].
The pressure-induced frequency shift coefficients are also inferred from the
absorption spectra recorded under different pressures. Figure 5.6(a) shows an example of
the raw data traces measured with H2O-air mixture under two different pressures. The
shift of line-center is manifest in the expanded view of Fig. 5.6(b) and the reduced
absorption spectra of Fig. 5.6(c). It should also be noted in Fig. 5.6(b) that the drift of the
laser frequency, as shown by the shift of the etalon traces Ietalon measured simultaneously
with the transmitted laser intensity signals It, is not negligible compared to the pressure-
induced frequency shift. This drift of laser frequency has thus been included in the
wavelength calibration to correct the relative line-center frequencies at various pressures.
The air-induced frequency shift coefficient δair(T) at the experimental temperature and its
statistical precision are inferred from the slope of a linear fit to the measured relative line-
center frequencies at various pressures using Eq. (2.13). The CO2-induced frequency shift
coefficient δCO2(T) and its statistical precision are obtained in the same way.
0.10
0.05
0.00
Inte
grat
ed A
rea
[cm
-1]
20151050Pressure [Torr]
Measurements Linear Fit
0.12
0.08
0.04
0.00Lore
ntzi
an F
WH
M [c
m-1
]
8006004002000Pressure [Torr]
Measurements Linear Fit
(a) (b)
TEMPERATURE SENSING USING WMS-2F TWO-LINE THERMOMETRY 85
Figure 5.6: Illustration of the determination of pressure-induced frequency shift coefficients at a selected temperature. (a) raw data traces measured for line 1 region with H2O-air mixture under two different pressures at T = 296 K; (b) expanded view of raw data traces for line 1; (c) reduced spectra of line 1; (d) air-induced frequency shift coefficient inferred from the linear fit to the relative line-center frequencies at various pressures, δair(296 K) = -0.0164 ± 0.0002 [cm-1atm-1].
5.3.4 Measurement results
The absorption spectra of neat H2O vapor, H2O-air and H2O-CO2 mixtures are
measured at selected temperatures between 296 and 1000 K. The linestrength S(T) at each
temperature are inferred from the spectra of neat H2O vapor, while the pressure
broadening coefficients γair(T) and γCO2(T), and the pressure-induced frequency shift
coefficients δair(T) and δCO2(T) are inferred from the spectra of H2O-air and H2O-CO2
mixtures. These measured spectroscopic parameters and their statistical precision at each
temperature for line 1 and line 2 are illustrated by Fig. 5.7-5.9. The error bars are
10
5
0
Sig
nal [
V]
100806040200Time [ms]
It@763torr Ietalon@763torr It@104torr Ietalon@104torr
7
6
5
4
3
2
1
Sig
nal [
V]
4240383634Time [ms]
(a) (b)
0.4
0.2
0.0
Abs
orba
nce
-0.4 -0.2 0.0 0.2 0.4Relative Frequency [cm
-1]
P=763 torr P=104 torr
-1.5x10-2
-1.0
-0.5
0.0
Line
Cen
ter
[cm
-1]
8006004002000Pressure [Torr]
Measurements Linear Fit
(c) (d)
86 CHAPTER FIVE
generally too small to be clearly identified on these figures. Since the measured pressure-
induced frequency shift coefficients δair(T) and δCO2(T) for both lines are all negative,
they are plotted on a linear scale in Fig. 5.9.
Figure 5.7: The measured linestrength values (symbol) of line 1 and line 2 at various temperatures and the one-parameter best fit (line) used to infer the linestrength values at the reference temperature Si(T0 = 296 K).
Figure 5.8: The measured pressure-broadening coefficients (symbol) of line 1 and line 2 at various temperatures and the two-parameter best fit (line) used to infer: (a) the air-broadening coefficients at the reference temperature γair(T0 = 296 K) and the temperature exponents nair; (b) the CO2-broadening coefficients at the reference temperature γCO2(T0 = 296 K) and the temperature exponents nCO2.
8x10-2
6
4
2
0Line
stre
ngth
[cm
-2at
m-1
]
12001000800600400Temperature [K]
Line 1
Line 2
2x10-2
3
4
5
γ air [
cm-1
atm
-1]
3 4 5 6 7 8 91000
Temperature [K]
2
3
4
5
678
0.1
γ CO
2 [cm
-1at
m-1
]
3 4 5 6 7 8 91000
Temperature [K] (a) (b)
Line 1
Line 2
Line 1
Line 2
TEMPERATURE SENSING USING WMS-2F TWO-LINE THERMOMETRY 87
Figure 5.9: The measured pressure-induced frequency shift coefficients (symbol) of line 1 and line 2 at various temperatures and the two-parameter best fit (line) used to infer: (a) the air-shift coefficients at the reference temperature δair(T0 = 296 K) and the temperature exponents mair; (b) the CO2-shift coefficients at the reference temperature δCO2(T0 = 296 K) and the temperature exponents mCO2.
With the lower state energy E” fixed at the HITRAN value, the linestrength at the
reference temperature S(T0 = 296 K) is obtained from a one-parameter best fit of the
measured linestrength data at various temperatures to the known functional form of S(T)
as per Eq. (2.2). The pressure-broadening coefficients at the reference temperature
γair(296 K) and γCO2(296 K), and the corresponding temperature exponents n are inferred
by fitting the measured γ(T) at various temperatures to the scaling relation represented by
Eq. (2.14). Similarly, the pressure-induced frequency shift coefficients at the reference
temperature δair(296 K) and δCO2(296 K), and the corresponding temperature exponents m
are inferred by fitting the measured δ(T) to the scaling relation of Eq. (2.15). These
measured spectroscopic parameters at the reference temperature and the corresponding
temperature exponents for the ten transitions are summarized in Table 5.2-5.6 and
compared with values from HITRAN 2004 if available. The measured S(296 K) values
are also compared with the room temperature data reported by Toth [Toth 1994]. Table
5.2-5.6 show that the measured data differ from HITRAN 2004 by up to 16% for S(296
K), 23% for γself(296 K), 42% for γair(296 K), 95% for nair, and 62% for δair(296 K).
-0.03
-0.02
-0.01
δ air [
cm-1
atm
-1]
1000800600400Temperature [K]
-0.03
-0.02
-0.01
δ CO
2 [cm
-1at
m-1
]
1000800600400Temperature [K]
(a) (b)
Line 1
Line 2
Line 1
Line 2
88 CHAPTER FIVE
Table 5.2: Summary of the measured linestrengths at the reference temperature S(296 K) and comparisons with HITRAN2004 and Toth [Toth 1994] values.
Measurement HITRAN2004 Toth94 Line ν0 S(296 K) σ S(296 K) σ Diff. S(296 K) σ Diff.
[cm-1] [cm-2/atm] [%] [cm-2/atm] [%] [%] [cm-2/atm] [%] [%] 1A 7202.90921 1.14E-01 1.6 1.15E-1 -0.6 1.07E-01 3 6.9 1 7203.89041 6.93E-02 1.1 7.39E-2 -6.2 7.05E-02 3 -1.6
1B 7204.16602 8.20E-03 1.0 7.86E-3 4.3 7.50E-03 9 9.3 1C 7205.24611 2.29E-01 0.7 2.46E-1 -6.9 2.32E-01 3 -1.3 2 7435.61542 1.93E-03 0.2 1.89E-3 2.1 1.77E-03 3 9.2
2A 7435.73154 4.10E-04 0.7 4.22E-4 -2.7 3.56E-04 2 15.2 2B 7435.94006 1.40E-03 0.3 1.45E-3 -3.6 1.34E-03 4 4.4 2C 7435.99941 4.81E-04 0.2 4.94E-4 -2.6 4.27E-04 3 12.6
7436.90924 2.18E-3 2.07E-03 10 2D 7436.92469 2.55E-03 0.8 8.51E-4 -16.1 6.10E-04 15 -5.0
2E 7437.19198 5.31E-03 0.5 5.21E-3
5-10
1.9 4.88E-03 5 8.7
Table 5.3: Summary of (a) the measured air-broadening coefficients at the reference temperature γair(296 K); (b) the temperature exponents nair, and comparisons with HITRAN2004 values.
(a) Measurement HITRAN2004
Line ν0 γair(296 K) σ γair(296 K) σ Diff. [cm-1] [cm-1/atm] [%] [cm-1/atm] [%] [%]
1A 7202.90921 0.103 0.3 0.1022 1-2 0.4 1 7203.89041 0.054 0.2 0.0534 5-10 0.6
1B 7204.16602 0.087 0.2 0.0770 2-5 12.3 1C 7205.24611 0.098 0.4 0.1015 <1 -3.7 2 7435.61542 0.017 0.5 0.0179 5-10 -4.5
2A 7435.73154 0.078 0.6 0.0547 2-5 41.9 2B 7435.94006 0.029 0.7 0.0278 1-2 3.6 2C 7435.99941 0.023 0.8 0.0272 2-5 -14.0
7436.90924 0.0425 5-10 2D 7436.92469 0.057 1.3 0.0762 10-20 --
2E 7437.19198 0.070 0.6 0.0630 1-2 11.0
(b) Measurement HITRAN2004
Line ν0 nair σ nair σ Diff. [cm-1] [%] [%] [%]
1A 7202.90921 0.73 0.7 0.78 -6.4 1 7203.89041 0.65 0.4 0.69 -5.8
1B 7204.16602 0.94 0.3 0.59 59.3 1C 7205.24611 0.72 0.8 0.78
10-20
-7.7
TEMPERATURE SENSING USING WMS-2F TWO-LINE THERMOMETRY 89
2 7435.61542 0.18 3.2 0.37 -51.4 2A 7435.73154 0.80 1.1 0.41 95.1 2B 7435.94006 0.32 2.7 0.39 -17.9 2C 7435.99941 0.33 2.8 0.39 -15.4
7436.90924 0.41 2D 7436.92469 0.64 2.8 0.45 --
2E 7437.19198 0.67 1.3 0.45
48.9
Table 5.4: Summary of the measured CO2-broadening coefficients at the reference temperature γCO2(296 K) and the temperature exponents nCO2.
Measurement Line ν0 γCO2(296 K) σ nCO2 σ
[cm-1] [cm-1/atm] [%] [%] 1A 7202.90921 0.197 0.5 0.64 1.3 1 7203.89041 0.090 0.2 0.72 0.5
1B 7204.16602 0.104 0.8 0.70 1.7 1C 7205.24611 0.165 0.8 0.57 2.1 2 7435.61542 0.056 1.4 0.91 2.0
2A 7435.73154 0.074 1.1 0.47 2.9 2B 7435.94006 0.066 1.0 0.72 1.7 2C 7435.99941 0.049 1.9 0.60 3.9
7436.90924 2D 7436.92469 0.077 1.0 0.59 2.1
2E 7437.19198 0.083 0.7 0.43 1.8
Table 5.5: Summary of the measured air-induced frequency shift coefficients at the reference temperature δair(296 K) and the temperature exponents mair. The measured δair(296 K) data are compared with HITRAN2004 values.
Measurement HITRAN2004 MeasurementLine ν0 δair(296 K) σ δair(296 K) σ Diff. mair σ
[cm-1] [cm-1/atm] [cm-1/atm] [cm-1/atm] [cm-1/atm] [%] [%] 1A 7202.90921 -0.0156 0.0002 -0.01128 0.0001-0.001 -38.3 0.98 2.6 1 7203.89041 -0.0164 0.0002 -0.01176 -39.5 1.00 2.5
1B 7204.16602 -0.0234 0.0003 -0.01691 0.001-0.01 -38.4 1.09 2.5 1C 7205.24611 -0.0110 0.0002 -0.00691 -59.2 0.96 2.7 2 7435.61542 -0.0236 0.0004 -0.02126 11.0 0.94 3.0
2A 7435.73154 -0.0264 0.0006 -0.01626 62.4 0.91 3.9 2B 7435.94006 -0.0192 0.0004 -0.01809
0.0001-0.001
6.1 0.83 3.6 2C 7435.99941 -0.0199 0.0005 -0.01952 0.001-0.01 1.9 1.05 4.2
7436.90924 -0.01900 0.01-0.1 2D 7436.92469 -0.0203 0.0007 -0.01462 0.001-0.01 -- 0.88 6.0
2E 7437.19198 -0.0133 0.0003 -0.01023 0.0001-0.001 30.0 0.48 8.3
90 CHAPTER FIVE
Table 5.6: Summary of the measured CO2-induced frequency shift coefficients at the reference temperature δCO2(296 K) and the temperature exponents mCO2.
Measurement Line ν0 δCO2(296 K) σ mCO2 σ
[cm-1] [cm-1/atm] [cm-1/atm] [%] 1A 7202.90921 -0.0296 0.0008 1.10 4.7 1 7203.89041 -0.0115 0.0002 0.52 5.4
1B 7204.16602 -0.0313 0.0009 0.85 5.5 1C 7205.24611 -0.0110 0.0003 0.70 5.1 2 7435.61542 -0.0330 0.0019 0.97 8.2
2A 7435.73154 -0.0312 0.0011 0.85 5.6 2B 7435.94006 -0.0185 0.0012 0.84 9.9 2C 7435.99941 -0.0202 0.0018 1.18 10.9
7436.90924 2D 7436.92469 -0.0280 0.0019 0.88 10.2
2E 7437.19198 -0.0124 0.0010 0.99 11.0
In tables 5.2-5.6, the σ listed with the measured value is the statistical precision
(one-standard deviation) derived from the corresponding best fit to the measured data at
various temperatures. The uncertainty of the measured S(296 K) value is estimated by
propagation of errors [Liu et al. 2006] to be approximately 2% for the ten transitions
considering the statistical precision and the measurement uncertainties of temperature,
pressure, H2O mole fraction, path length and the integrated absorbance. The measurement
uncertainty is estimated to be ~ 2% for γair(296 K) and γCO2(296 K), and 2-5% for nair and
nCO2, using the measurement uncertainties of temperature, pressure and the collisional
FWHM ∆νc, and the corresponding statistical precisions. The uncertainties of the
measured δair(296 K), δCO2(296 K), mair and mCO2 values are estimated to be 5-25%
considering the statistical precision, the thermal drift of the etalon peaks, and the
measurement uncertainties of temperature, pressure and the relative line-center frequency
0~ν .
TEMPERATURE SENSING USING WMS-2F TWO-LINE THERMOMETRY 91
5.3.5 Construction of hybrid spectroscopic database
Since comparisons of the measurement results with HITRAN 2004 database reveal
some significant discrepancies, a hybrid spectroscopic database is constructed by
modifying HITRAN 2004 to incorporate these results. The S(296K), γair(296K), nair and
δair(296K) of the ten transitions in HITRAN 2004 are replaced with the corresponding
values measured in this work. The measured temperature exponents of air-shift mair are
also used for the ten transitions while 0.75 (an average of the theoretical value of 0.5
associated with the hard-sphere intermolecular interaction and 1.0 with the dipole-dipole
interaction [Murphy and Boggs 1967]) is used for all other transitions. The CO2-
broadening coefficients γCO2(296K) and CO2-shifting coefficients δCO2(296K) as well as
their temperature exponents nCO2 and mCO2 are not used in the current database since the
intake gases for compression strokes of IC engines are mainly composed of H2O vapor
and air except for the heavy EGR cycles. However, the CO2-collision parameters will be
used for the future applications in firing cases of IC-engines where the gas compositions
are significantly different from those of compression cycles and CO2 absorption is no
longer negligible.
This hybrid spectroscopic database has been used to simulate the sensor
performance and construct the calibration databases. The direct absorption and WMS-2f
spectra for both spectral regions at a variety of elevated pressures and temperatures were
measured in a controlled static cell by Rieker et al., and the results are found to agree
better with simulations using the hybrid database than with simulations using HITRAN
2004. [Rieker et al. 2006c] This work validates the improvement of the measured
spectroscopic parameters over HITRAN 2004 values, which is of great importance in
achieving the desired sensor accuracy. Figure 5.10 shows an example of the calibration
curves calculated with the hybrid database and HITRAN 2004 at the selected laser set-
points (see section 5.4.3) at the pressure of 25 atm. The temperatures inferred from these
two different calibration curves can differ by as much as ~ 80 K! Therefore, by using the
hybrid spectroscopic database, the measurement accuracy of the WMS-2f temperature
92 CHAPTER FIVE
sensor is expected to be greatly improved. The selection of laser set-points and the
calculation of the calibration curves will be discussed in the following sections.
Figure 5.10: Comparisons of calibration curves calculated based on the hybrid spectroscopic database and HITRAN2004 at 25atm.
5.4 Selection of laser set-points
For fixed-wavelength two-line thermometry with applications at constant pressures,
the lasers are typically parked at the peak frequencies of the selected absorption
transitions at the application pressure to achieve the best SNRs and thus minimize the
temperature measurement uncertainty. IC-engine applications are more complicated due
to the time-varying temperature and pressure. The location of the WMS-2f signal peak
shifts considerably as the pressure changes. The selected absorption transitions only
indicate the approximate wavelength ranges to park the lasers; the specific laser set-
points need to be refined against systematic design rules to optimize the sensor
performance over the entire range of conditions.
0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6600
700
800
900
1000
T [K
]
Ratio of (2f/1f)
HITRAN2004 Hybrid
∆T=80K
TEMPERATURE SENSING USING WMS-2F TWO-LINE THERMOMETRY 93
5.4.1 Identification of candidate frequency pairs
As discussed in section 5.2, the optimum absorption transitions have been selected
as line 1 at 7203.9 cm-1 and line 2 at 7435.6 cm-1. These are the line center (peak)
frequencies at vacuum, and the WMS-2f peak frequencies will shift from these vacuum
values at elevated pressures due to the pressure-induced frequency shifts and the blending
of the pressure-broadened absorption features.
The frequency ranges of the WMS-2f peak locations over the entire T/P conditions
must be determined to identify the candidate frequency pairs. Since the pressure-shifting
coefficients for both lines and their neighbors are all measured to be negative over the
entire temperature range of 400-1050 K, it can be predicted that the WMS-2f peak
locations of both lines will shift to the lower frequency side at higher pressures. And the
magnitude of this shifting is smaller at higher temperatures as suggested by the
temperature scaling relation Eq. (2.15) for the pressure-shifting coefficients. Therefore,
two extreme T/P conditions as shown in Fig. 5.1, i.e., condition A, which has the lowest
pressure of 5 atm and the highest temperature at this pressure (701 K), and condition B,
which has the highest pressure of 25 atm and the lowest temperature at this pressure (610
K), respectively define the minimum and maximum WMS-2f peak frequencies for either
absorption transition. And the WMS-2f peak frequencies at other T/P conditions are
confined within these frequency ranges.
Figure 5.11: WMS-2f spectra simulated at condition A (P = 5atm, T = 701 K) and B (P = 25 atm, T = 610 K). (a) The low E” spectral region. (b) The high E” spectral region.
3x10-3
2
1
0
2f M
agni
tud
e
7207720672057204720372027201Frequency [cm-1]
Low E" A B
3x10-3
2
1
0
2f M
agni
tude
743874377436743574347433Frequency [cm-1]
High E" A B
(a) (b)
94 CHAPTER FIVE
Figure 5.11 shows the WMS-2f spectra of both lines simulated at condition A and
B. The peak frequency range, as labeled by the arrows, is determined to be 7203.5-
7203.9 cm-1 for line 1 and 7435.4-7435.7 cm-1 for line 2. With a frequency grid resolution
(∆ν) of 0.1 cm-1, we examine five candidate laser frequencies for line 1 and four for line
2, which leads to 20 candidate set-point pairs as tabulated in Table 5.8-5.10. A finer
frequency grid, e.g. ∆ν = 0.01 cm-1, might be used in the further refinement of the sensor
design. The sensor performance, which includes the SNR and temperature measurement
uncertainties, was evaluated for each candidate frequency pair and the pair which enables
the best sensor performance was selected as the optimum laser set-points.
5.4.2 Selection of eligible frequency pairs
Figure 5.12: The T/P nodes used for the evaluation of the sensor performance.
The sensor performance needs to be evaluated over a wide range of temperature (T
= 400-1050 K) and pressure (P = 5-25 atm), as shown in Fig. 5.1. A practical approach is
to divide the entire T/P region into a limited number of T/P grids. The sensor
performance will be simulated at each T/P nodes, and their average (or minimum, or
maximum) values will be used for the evaluations. Figure 5.12 shows the set of T/P
5 10 15 20 25400
600
800
1000
T [K
]
P [atm]
TEMPERATURE SENSING USING WMS-2F TWO-LINE THERMOMETRY 95
nodes used in the simulations. The pressure nodes are set at 5, 10, 15, 20 and 25 atm. At
each pressure, 20 temperature nodes are equally spaced between the required minimum
and maximum temperatures at that pressure. The sensor performance for each candidate
frequency pair will be simulated over these 100 T/P nodes and evaluated against
following five criteria.
First, the WMS-2f/WMS-1f signal at each laser set-point should have sufficient
SNR. A computer simulation program has been developed to calculate the WMS-1f
normalized WMS-2f signal (C2f/1f) as per Eq. (2.34) and using the hybrid spectroscopic
databases introduced in 5.3.5. Here the WMS-1f normalization is included in the
simulation since it will be used to account for detection gain, laser intensity variation, and
transmission loss. A noise floor of 5x10-5 in the (C2f/1f) signal, which is inferred from
previous laboratory measurements [Liu 2004], is used for the SNR calculation. The
average and the minimum of the SNR values calculated at the 100 T/P nodes are
tabulated in Table 5.7 for each candidate frequency. If a minimum SNR ≥ 10 is imposed,
the frequency of 7435.4 cm-1 can be eliminated from the candidates for line 2, thus
leaving 15 candidate frequency pairs for further screening.
Table 5.7: The expected SNR of the WMS-2f/WMS-1f signals at the candidate laser set-points.
(a) Line 1 frequency ν1 [cm-1] SNR
7203.5 7203.6 7203.7 7203.8 7203.9 Avg 36 44 51 53 49 Min 20 31 35 30 23
(b)
Line 2 frequency ν2 [cm-1] SNR 7435.4 7435.5 7435.6 7435.7
Avg 42 47 47 42 Min 8 11 12 13
96 CHAPTER FIVE
Second, the ratio of the WMS-2f/WMS-1f signals should be single-valued with
temperature at any given pressure. Since this WMS-2f two-line thermometry infers the
temperature from the measured ratio of WMS-2f/WMS-1f signals (at the independently
measured pressure), any non-monotonic behavior in the ratio vs. temperature will incur
ambiguity in the temperature measurement. The ratio of the WMS-2f/WMS-1f signals for
each of the 15 candidate frequency pairs are calculated using the simulated WMS-
2f/WMS-1f signals obtained in the previous step. The ratio vs. temperature for two
frequency pairs, 7203.9 & 7435.5 cm-1 and 7203.9 & 7435.6 cm-1, are found to have
multi-valued behavior at the pressures of 20 and 25 atm, as illustrated by Fig. 5.13. These
two pairs are rejected and 13 candidate frequency pairs are left as tabulated in Table 5.8.
Figure 5.13: Illustration of the non-monotonic behavior in the ratio of the WMS-2f/WMS-1f signals for the candidate frequency pair of 7203.9 cm-1 and 7435.5 cm-1.
Third, the temperature measurement uncertainty arising from the measurement
noise should be small. Remember that the ratio of the WMS-2f/WMS-1f signals is
defined as
2 /1 "
2 /1 "
( )( )
f f HighE
f f LowE
C HRC L
= = . (5.1)
600 700 800 900 10001.4
1.5
1.6
1.7 P = 20 atm P = 25 atm
T [K]
Rat
io o
f 2f/1
f Sig
nal
1.9
2.0
2.1
2.2
Ratio of 2f/1f Signal
TEMPERATURE SENSING USING WMS-2F TWO-LINE THERMOMETRY 97
The uncertainty in this ratio resulting from the potential measurement uncertainties in the
WMS-2f/WMS-1f signals can be estimated by error propagation
2 2
2 2 2 2R H L HLR R R RH L H L
∂ ∂ ∂ ∂ ∆ = ∆ + ∆ + ∆ ∂ ∂ ∂ ∂ . (5.2)
If the WMS-2f/WMS-1f signals for both lines are assumed to be uncorrelated and have
the same noise floor, i.e. ∆H = ∆L = ∆N, the ratio uncertainty becomes
2
2 /1 "
1( )R N
f f LowE
RC
+∆ = ∆ . (5.3)
The uncertainty in the measured temperature can thus be estimated as
2 2
2 /1 " "
1 1 1( / ) ( ) ( / ) ( / )
NRT
P f f LowE P LowE P
R RR T C R T SNR R T
∆∆ + +∆ ≈ = ⋅ = ⋅
∂ ∂ ∂ ∂ ∂ ∂, (5.4)
which demonstrates the dependence of ∆T on the temperature sensitivity of the ratio
(∂R/∂T)P and the SNR of the measured signal.
The temperature measurement uncertainty ∆T at each of the 100 T/P nodes is
calculated as per Eq. (5.4) for the 13 candidate frequency pairs. Figure 5.14 shows an
example of the calculation results. Note that the temperature sensitivity of the ratio
(∂R/∂T)P is evaluated using the simulated trace of ratio vs. temperature at a given
pressure, as shown by the red-square trace in Fig. 5.14(b). The average ∆T and maximum
∆T for each of the 13 candidate frequency pairs are tabulated in Table 5.8. The four shade
pairs, which have their maximum ∆T larger than 100 K are eliminated, and thus 9
candidate frequency pairs remain for further screening.
98 CHAPTER FIVE
Figure 5.14: Illustration of the sensor performance at the candidate laser set-points of 7203.5 cm-1 and 7435.7 cm-1 for P = 10 atm: (a) The WMS-1f normalized WMS-2f signals; (b) the ratio of WMS-2f/WMS-1f signals and the estimated temperature measurement uncertainty ∆T arising from measurement noises.
Table 5.8: The estimated temperature measurement uncertainty arising from measurement noises for the 13 candidate frequency pairs that pass through the screening criteria of 1-2.
(a) the average values Line 1 frequency ν1 [cm-1] ∆T, AVG [K] 7203.5 7203.6 7203.7 7203.8 7203.9
7435.4 -- -- -- -- -- 7435.5 22 24 32 110 -- 7435.6 19 20 24 36 --
Line 2 frequency
ν2 [cm-1] 7435.7 17 17 20 25 40
(b) the maximum values
Line 1 frequency ν1 [cm-1] ∆T, MAX [K] 7203.5 7203.6 7203.7 7203.8 7203.9 7435.4 -- -- -- -- -- 7435.5 48 68 133 2798 -- 7435.6 40 51 78 181 --
Line 2 frequency
ν2 [cm-1] 7435.7 33 39 53 84 207
500 600 700 8001.0
1.5
2.0
2.5
3.0
(2f/1
f) S
igna
l
T [K]
Low E" High E"
500 600 700 800
0.8
1.2
1.6
2.0
Ratio ∆T
T [K]R
atio
of (
2f/1
f) S
igna
l
10
15
20
25
∆T [K]X10-3
(b)(a)
TEMPERATURE SENSING USING WMS-2F TWO-LINE THERMOMETRY 99
The fourth criterion arises from the uncertainties in the actual laser set-points. For
the fixed-wavelength scheme, the operating frequency of the laser is set by fine-tuning
the laser temperature and injection current until the measured (by wave-meter) laser
frequency reaches the desired set-point. The measurement uncertainty of the wave-meter
is ±0.005 cm-1.
The fourth criterion thus requires that the temperature sensor has sufficient
tolerance to the uncertainties in the actual laser set-points, i.e. the sensor performance
should not deteriorate too much even if both lasers are operated at frequencies ±0.005
cm-1 from the desired set-points. Therefore, for each of the remaining frequency pairs, the
WMS-2f/WMS-1f signals, their ratio, and the ∆T are simulated at four potential
maximum offset frequencies as illustrated by Fig. 5.15(a). A candidate pair is eliminated
if the sensor performance at any of the four offsets violates any of the previous three
criteria (SNRMIN > 10, monotonic for R vs. T, and ∆T,MAX < 100 K). All the remaining
frequency pairs satisfy this criterion.
Figure 5.15: Illustration of the sensor performance with laser set-point uncertainty for the candidate frequency pair of 7203.8 cm-1 and 7435.7 cm-1 at pressure of 25 atm. (a) A comparison of the WMS-2f/WMS-1f signal ratio at the desired laser set-points with the ratios at the potential maximum offsets; (b) A blowup of the boxed region in panel (a) to illustrate the temperature measurement uncertainty arising from the laser set-point uncertainty.
600 700 800 900 10000.8
0.9
1.0
1.1
1.2
1.3
1.4
Rat
io o
f 2f/1
f Sig
nal
T [K]
7203.80 & 7435.70 7203.795 & 7435.695 7203.795 & 7435.705 7203.805 & 7435.695 7203.805 & 7435.705
920 960 10001.24
1.28
1.32
1.36
1.40
7203.80 & 7435.70 7203.795 & 7435.705
Rat
io o
f 2f/1
f Sig
nal
T [K]
δT = 44 K
Tactual = 968 K Tinfer = 1012 K
(a) (b)
100 CHAPTER FIVE
The last criterion requires the temperature measurement uncertainty arising from
the laser set-point uncertainty to be small. Note that once the laser set-points are decided,
the calibration curve of ratio vs. temperature will be calculated at the desired laser set-
points. Any offset of the actual laser operating frequencies from the desired values will
incur an error δT in the measured temperature. For example, in the case illustrated by Fig.
5.15(b), if the measured ratio of WMS-2f/WMS-1f signals is 1.346, the temperature
inferred from the calibration curve calculated at the desired laser set-points (7203.8 and
7435.7 cm-1) will be 1012 K, compared to the actual temperature of 968 K if the lasers
are actually operated at 7203.795 and 7435.705 cm-1. This temperature measurement
uncertainty δT may be different at different T/P node. The average and maximum δT for
all the remaining 9 candidate frequency pairs are tabulated in Table 5.9. If a maximum δT
≤ 30 K is imposed, the shaded frequency pair can be eliminated, thus leaving altogether 8
eligible frequency pairs for the final selection.
Table 5.9: The estimated temperature measurement uncertainty arising from the laser set-point uncertainty for the 9 candidate frequency pairs that pass through the screening criteria of 1-4.
(a) the average values Line 1 frequency ν1 [cm-1] δT, AVG [K] 7203.5 7203.6 7203.7 7203.8 7203.9
7435.4 -- -- -- -- -- 7435.5 8 8 -- -- -- 7435.6 8 8 7 -- --
Line 2 frequency
ν2 [cm-1] 7435.7 9 9 9 12 --
(b) the maximum values
Line 1 frequency ν1 [cm-1] δT, MAX [K] 7203.5 7203.6 7203.7 7203.8 7203.9 7435.4 -- -- -- -- -- 7435.5 19 19 -- -- -- 7435.6 15 15 15 -- --
Line 2 frequency
ν2 [cm-1] 7435.7 18 19 21 44 --
TEMPERATURE SENSING USING WMS-2F TWO-LINE THERMOMETRY 101
5.4.3 Selection of optimum frequency pairs
An overall temperature measurement uncertainty σT is estimated as a root sum
square of the temperature uncertainty ∆T due to measurement noise and the temperature
uncertainty δT due to the laser set-point errors
2 2T T Tσ δ= ∆ + . (5.5)
The results are tabulated in Table 5.10. To select the optimum frequency pair that
provides the best sensor performance in terms of SNR and temperature measurement
accuracy, Table 5.7 and 5.10 must be considered simultaneously. Unfortunately, none of
the 8 eligible frequency pairs simultaneously enables the largest SNR and the smallest σT.
The frequency pair of 7203.6 cm-1 and 7435.7 cm-1 provides a good compromise and thus
is selected as the final laser set-points.
Table 5.10: The estimated overall temperature measurement uncertainty for the 8 eligible frequency pairs that pass through all the five screening criteria.
(a) the average values Line 1 frequency ν1 [cm-1] σT, AVG [K] 7203.5 7203.6 7203.7 7203.8 7203.9
7435.4 -- -- -- -- -- 7435.5 23 25 -- -- -- 7435.6 21 21 25 -- --
Line 2 frequency
ν2 [cm-1] 7435.7 19 20 22 -- --
(b) the maximum values
Line 1 frequency ν1 [cm-1] σT, MAX [K] 7203.5 7203.6 7203.7 7203.8 7203.9 7435.4 -- -- -- -- -- 7435.5 52 71 -- -- -- 7435.6 42 53 79 -- --
Line 2 frequency
ν2 [cm-1] 7435.7 37 44 57 -- --
102 CHAPTER FIVE
Note that the optimum laser set-points are different for different T/P requirements.
The design rules developed in this section provide useful guidelines for the determination
of laser set-points in temperature sensing using fixed-wavelength scheme, especially for
applications with widely varying T/P ranges.
5.5 Construction of calibration databases
Figure 5.16: 3D illustrations of the calibration databases for the fixed-wavelength WMS-2f two-line thermometry over the entire T/P region. (a) The ratio of the WMS-2f/WMS-1f signals; (b, c) The WMS-2f/WMS-1f signals at the low E” and high E” set-points.
(a) (b)
(c)
TEMPERATURE SENSING USING WMS-2F TWO-LINE THERMOMETRY 103
Now the calibration databases for the WMS-2f two-line thermometry can be
constructed with the hybrid spectroscopic database introduced in section 5.3.5 and the
laser set-points selected in section 5.4.3.
First, the normalized WMS-2f signals (i.e. 2f/1f) at the low E” and high E” laser
set-points as well as the ratio of these two WMS-2f/WMS-1f signals are simulated over a
limited number of T/P nodes using the WMS-2f mathematical representations discussed
in Chapter 2. Figure 5.16 shows the simulation results for the entire T/P region. The
discrete simulation data are represented by the black dots on these three-dimensional
(3D) surfaces. The projections of these 3D surfaces on the T/P planes are the T/P nodes
used in the simulation. There are 21 pressure nodes ranging from 5 to 25 atm with a
spacing of 1 atm. At each pressure, 50 temperature nodes are assigned to be equally
spaced between the prescribed minimum and maximum temperatures for that pressure.
Figure 5.17: Illustration of the polynomial fits to the simulated data over the 50 temperature nodes prescribed for the pressure of 25 atm. (a) The temperature vs. ratio; (b) the WMS-2f/WMS-1f signals vs. the temperature.
The actual calibration curves at each pressure are then calculated. At each pressure
node, the simulated 50 data points for the temperature vs. ratio are fit to a fifth-order
1.0 1.1 1.2 1.3 1.4 1.5600
700
800
900
1000
T [K
]
Ratio of (2f/1f)
Simulated Data Polynomial Fit
600 700 800 900 1000
2.0
2.5
3.0
Low E"
(2f/1
f) S
igna
l
T [K]
Simulated Data Polynomial Fit
High E"
X10-3
(a) (b)
104 CHAPTER FIVE
polynomial as illustrated by Fig. 5.17(a), and the WMS-2f/WMS-1f signals vs.
temperature at each laser set-point are fit to a third-order polynomial as illustrated by Fig.
5.17(b). The orders of the polynomials are selected to achieve desirable fitting accuracy
but minimize the potential computational costs. The calibration databases are embedded
into the data processing module of the sensor as the set of polynomial coefficients shown
in Table 5.11.
Table 5.11: Illustration of the calibration databases at the prescribed pressure nodes.
(a) The polynomial coefficients (x 10-3) for calculating temperature from the measured ratio of WMS-2f/WMS-1f signals.
P [atm] c0 c1 c2 c3 c4 c5 5 0.15 1.33 -2.21 3.63 -2.98 1.05
24 -2.17 11.56 -20.69 19.04 -8.82 1.68 25 -3.62 17.74 -31.10 27.77 -12.46 2.28
(b) The polynomial coefficients for calculating the WMS-2f/WMS-1f signal at the low E” laser set-point (7203.6 cm-1).
P [atm] a0 a1 a2 a3 5 -6.05E-03 4.14E-05 -6.34E-08 3.08E-11
24 -3.16E-03 1.66E-05 -1.63E-08 4.96E-12 25 -2.97E-03 1.54E-05 -1.49E-08 4.46E-12
(c) The polynomial coefficients for calculating the WMS-2f/WMS-1f signal at the high E” laser set-point (7435.7 cm-1).
P [atm] b0 b1 b2 b3 5 -1.42E-03 3.95E-06 5.58E-09 -6.99E-12
24 -8.31E-03 2.92E-05 -2.39E-08 6.04E-12 25 -8.34E-03 2.89E-05 -2.34E-08 5.89E-12
TEMPERATURE SENSING USING WMS-2F TWO-LINE THERMOMETRY 105
Once the ratio of the two WMS-2f/WMS-1f signals is obtained from the WMS-2f
measurements, the temperature will be calculated using the polynomial coefficients
shown in Table 5.11(a) at the pressure measured by the pressure transducer on the IC-
engine
2 3 4 50 1 2 3 4 5T c c R c R c R c R c R= + + + + + . (5.6)
If the measured pressure is at an intermediate value (e.g. 24.3 atm) between the
prescribed pressure nodes, the temperatures at the two relevant pressure nodes (24 atm
and 25 atm) will be calculated (referred to as T1 and T2) as illustrated by Fig. 5.18. The
temperature reported by the sensor is obtained from an interpolation of T1 and T2 against
the relevant pressure values.
Figure 5.18: Illustration of calculating temperature from the measured ratio of WMS-2f/WMS-1f signals for an intermediate pressure between 24 and 25 atm.
With the inferred temperature, the individual WMS-2f/WMS-1f signal for either
transition can be calculated using the polynomial coefficients shown in Table 5.11(b) or
5.11(c) at the measured pressure
1.0 1.1 1.2 1.3 1.4 1.5600
700
800
900
1000
T2
T [K
]
Ratio of (2f/1f)
P=24atm P=25atm
R
T1
106 CHAPTER FIVE
2 3
2 /1 , " 0 1 2 3
2 32 /1 , " 0 1 2 3
f f LowE
f f HighE
C a a T a T a T
C b b T b T b T
= + + +
= + + +. (5.7)
Similarly, the interpolation method will be used for calculations at an intermediate
pressure between any two prescribed pressure nodes. Since Eq. (5.7) yields the expected
WMS-2f/WMS-1f signal for unit path length (L = 1 cm) and unit H2O mole fraction
(XH2O = 0.01), the scaling factor between the measured WMS-2f/WMS-1f signal and the
expected value for either transition provides the H2O mole fraction once the path length is
corrected with the measured value.
5.6 Summary
In this chapter, development of a TDL temperature sensor based on fixed-
wavelength WMS-2f two-line thermometry for IC-engine applications has been
discussed. The emphasis is placed here on the precision measurements of spectroscopic
parameters, selection of laser set-points and construction of calibration databases, which
are of crucial importance for achieving optimal sensor performance.
The integrated sensor has demonstrated quite good performance in static tests in a
high T/P cell and dynamic tests in a shock tube. [Rieker et al. 2006b] It has also been
successfully used for crank angle-resolved measurements for both unfired and fired IC-
engine cylinders. [Rieker et al. 2006a] This new temperature-sensing technology is
expected to contribute towards developing future generation engines with improved fuel
efficiency and reduced emissions.
107
Chapter 6
NON-UNIFORM TEMPERATURE SENSING
USING MULTI-LINE THERMOMETRY
6.1 Motivation and overview
The two-line thermometry strategy, as illustrated by the applications discussed in
Chapter 4 and 5, is only appropriate for temperature sensing in near-uniform flows or
very short pathlength where the sampled gas can be assumed to be uniform. In many
practical flow fields, significant temperature and species concentration gradients may
exist along the optical diagnostics measurement path due to flow boundary layers, flow
mixing, chemical reactions, phase changes, heat transfer with the side walls, and other
effects. Tomographic reconstruction of laser absorptions along multiple LOS’s has been
demonstrated in laboratory experiments as a solution to resolve these non-uniformities
[Ravichandran and Gouldin 1986, Kauranen et al. 1994, Zhang et al. 2001, Dahm et al.
2002], but practical systems seldom have sufficient optical access and the sensor
redundancy necessary for tomographic techniques. Therefore, a significant part of this
thesis is devoted to extending LOS laser absorption spectroscopy to temperature sensing
in non-uniform flows.
Extension of LOS absorption measurements to non-uniform flow fields has been
previously explored including work to correct for boundary layer effects [Schoenung and
Hanson 1981, Ouyang and Varghese 1989, Zhou et al. 2003], to reduce sensitivities to
flow non-uniformities [Wang et al. 2000b], and to correlate pattern factor with the path-
108 CHAPTER SIX
averaged temperatures inferred from different line pairs [Seitzman and Scully 2000,
Palaghita and Seitzman 2005]. This chapter introduces a novel multi-line thermometry
strategy, which relies on simultaneous measurements of multiple absorption transitions
with different temperature dependence to extract the temperature distribution information
along the LOS. Sanders et al. introduced the concepts and made the first demonstration of
multi-line thermometry by measuring multiple O2 absorption lines to infer the
temperature distribution of an optical path through two static cells at different
temperatures. [Sanders et al. 2001] In this thesis, both theoretical and experimental
studies are performed to systematically investigate this multi-line thermometry strategy.
Simulation studies and laboratory experiments are carried out based on H2O vapor
absorption, since H2O vapor is commonly present in combustion gases and air. It is
straightforward to extend the conclusions drawn below to other absorbing species.
In this chapter, the sensor concepts and relevant mathematic models are explored in
detail in section 6.2. Two different strategies are investigated to interpret the
measurements for multiple absorption transitions and infer the temperature distribution
along the LOS. The first strategy, called profile fitting, fits a temperature distribution
profile postulated in advance using physical constraints. The second strategy, called
temperature binning, determines the temperature probability distribution function (PDF)
along the LOS using prescribed temperature bins. The design rules for line selection are
developed in section 6.3 to optimize the sensor performance and illustrated by the
selection of multiple H2O vapor transitions for measurements of potential non-uniform
combustion flow fields. Sensor performance is examined by simulation in section 6.4 for
two generic non-uniform temperature distributions: “2-T” and parabolic profiles.
Laboratory demonstration experiments with a wavelength-division multiplexing (WDM)
scheme and a wide-wavelength-scanning laser source are presented in section 6.5 to
illustrate the sensor concepts and investigate the sensor performance.
NON-UNIFORM T SENSING USING MULTI-LINE THERMOMETRY 109
6.2 Theoretical principles
The fundamental principles of LOS laser absorption spectroscopy and its
application to temperature sensing have been discussed in detail in Chapter 2. It has been
mentioned in section 2.3.3 that the information on a non-uniform temperature distribution
along the LOS can be extracted from the measurements of multiple absorption transitions
with different temperature dependence. Here we assume m (>2) transitions have been
selected (the line selection will be discussed in the next section) and the integrated
absorbance for each of the selected m transitions, Ai, has been obtained from the LOS
absorption measurements. Two different strategies, profile fitting and temperature
binning, can be used to interpret the LOS absorption data of multiple transitions for
inferring non-uniform temperature distributions along the measurement path.
6.2.1 Profile fitting
The profile fitting strategy first requires a postulated distribution of temperature
along the measurement path to constrain the temperature profile fitting. For example, in a
confined combustion flow, the gas temperature often has a cold boundary layer, and the
simplest representation would be a “2-T” profile with a core flow at an averaged
temperature of Tc and a boundary layer with an averaged temperature of Tb and a
thickness of Lb, as shown by Fig. 6.1(a). A more complex but common representation
would be a parabolic profile constrained by the center temperature of Tc and the wall
temperature of Tw, as shown by Fig. 6.1(b). Another somewhat more sophisticated model
would be a uniform core flow at a temperature of Tc and a boundary layer with parabolic
temperature distribution constrained by the wall temperature of Tw and the boundary layer
thickness of Lb, as shown by Fig. 6.1(c). These postulated temperature distribution
profiles can be represented by a general functional form as follows
( ) ( , , )char TcharT x f T L x= , (6.1)
110 CHAPTER SIX
where Tchar is the characteristic temperature such as Tc, Tw and Tb, and LTchar is the
characteristic length such as Lb. Similarly, the shape for the absorber mole fraction
distribution is also postulated using physical constraints
( ) ( , , )abs char XcharX x g X L x= , (6.2)
where Xchar is the characteristic mole fraction and LXchar the corresponding length.
Figure 6.1: Postulated temperature distribution profiles for confined combustion gases with cold walls.
Based on the presumed temperature and mole fraction profiles, the integrated
absorbance of any transition can be calculated by substituting Eq. (6.1) and (6.2) into Eq.
(2.50). For the selected m transitions, a nonlinear equation set can be established
1800
1600
1400
1200
1000
T [K
]
1086420x [cm]
Tb
Tc
Lb
(a) 1800
1600
1400
1200
1000
T [K
]
1086420x [cm]
Tw
Tc
(b)
1800
1600
1400
1200
1000
T [K
]
1086420x [cm]
Tw
Tc
Lb (c)
NON-UNIFORM T SENSING USING MULTI-LINE THERMOMETRY 111
( )
( )
( )
1 10
2 20
0
( , , ) ( , , )
( , , ) ( , , )
( , , ) ( , , )
L
char Xchar char Tchar
L
char Xchar char Tchar
L
m char Xchar m char Tchar
A P g X L x S f T L x dx
A P g X L x S f T L x dx
A P g X L x S f T L x dx
= ⋅
= ⋅
= ⋅
∫∫
∫
. (6.3)
Once the number of equations, i.e. the number of absorption transitions m, is larger than
the number of unknowns, Eq. set (6.3) can be solved by nonlinear least-square fitting
( )( )2
0, , , 1
min ( , , ) ( , , )char Tchar char Xchar
m L
char Xchar i char Tchar iT L X L i
P g X L x S f T L x dx A=
⋅ −∑ ∫ , (6.4)
to obtain the set of Tchar, LTchar, Xchar and LXchar that best describe the postulated
temperature and mole fraction profiles.
Expression (6.4) presents the most general mathematical model for the profile
fitting strategy. It can be simplified by using more physical constraints. For example, if
the temperature non-uniformity in a combustion flow results mainly from the non-
uniform local equivalence ratio, the mole fraction distribution of the absorber, e.g. water
vapor, can be assumed to be similar to the temperature distribution, i.e.
( , , ) ( , , )char Xchar char Tcharg X L x c f T L x= ⋅ , (6.5)
where c is a constant to be inferred from the fitting along with Tchar and LTchar. When such
relationship is utilized in the profile fitting, the number of unknowns will be greatly
reduced. As another example, the mole fraction can be assumed to be constant along the
measurement path in cases where the temperature non-uniformity is much more
significant than that of the mole fraction. Finally, measurements by other sensors, CFD
calculations, past knowledge on the target flow field or a similar system, etc., can be used
to constrain some of the variables and reduce the number of unknowns in the postulated
112 CHAPTER SIX
temperature profile. For example, thermocouples can be used to measure the gas
temperature near the wall Tw.
The profile fitting strategy obviously requires using physical understanding of the
flow fields to constrain the temperature and mole fraction distributions along the
measurement path. Simulation studies in section 6.4 will demonstrate that the
measurement results will be greatly improved by using as many physical constraints as
possible to reduce the number of unknowns in the postulated temperature profile.
6.2.2 Temperature binning
The temperature binning method is derived from a discretization of Eq. (2.5)
( ),1
( )n
j abs j jj
AA S T X LP =
= = ⋅ ⋅∑ , (6.6)
which implies decomposing the whole LOS measurement path with non-uniform
properties into n sections, each with a nearly uniform temperature of Tj, absorber mole
fraction of Xabs,j and path length of Lj. For the selected m absorption transitions, the
following linear equation set can be inferred from Eq. (2.50) as
1 1 1 2 1 11
2 1 2 2 2 22
1 2
( ) ( ) ( )( )
( ) ( ) ( )( )
( )( ) ( ) ( )
nabs
nabs
abs nm m m n m
S T S T S T AX L
S T S T S T AX L
X LS T S T S T A
⋅ =
, (6.7)
where the n temperature bins are prescribed based on a rough estimation of the possible
temperature range along the measurement path. Once the number of absorption
transitions is larger than the number of temperature bins, i.e. m > n, Eq. set (6.7) can be
solved by constrained linear least-square fitting
NON-UNIFORM T SENSING USING MULTI-LINE THERMOMETRY 113
( )
( )
2
( ) 1 1
min ( ) ( )
( ) 0 1,
abs j
m n
i j abs j iX L i j
abs j
S T X L A
X L j n= =
⋅ −
≥ =
∑ ∑ . (6.8)
The solution (XabsL)j, called column density, is actually the PDF of the absorbing species.
More physically meaningful results can be inferred from the PDF solution if other
physical constraints are available. For example, if the mole fraction of the absorbing
species can be assumed to be constant, the fraction of path length (fj) for each bin can be
calculated from the column density since
( )
1
( )
( )
abs j jj n
abs jj
X L Lf
LX L=
= =
∑. (6.9)
Simulation studies in section 6.4 will show that increasing the number of bins n (for fixed
number of transitions m) will deteriorate the measurement accuracy. Thus a moderate
number of bins, e.g. three or five, should be initially used and more bins justified only if
more transitions can be measured. In spite of the limited number of bins and the lack of
information on the spatial arrangement of the bins along the path, the PDF solution is
sufficient for many monitoring and control applications where the goal focuses on
minimizing or maximizing the non-uniformities. [Palaghita and Seitzman 2005]
6.3 Selection of absorption transitions
6.3.1 Three criteria for the initial screening
The systematic line selection criteria for temperature sensing in uniform flows have
been discussed in Chapter 4. Three of these criteria can be directly utilized here for the
initial screening of all H2O lines listed in the HITRAN 2004 database [Rothman et al.
2005]. First, the wavelength of the candidates is required to be within 1.3-1.5 µm (6667-
114 CHAPTER SIX
7692 cm-1), where the ν1+ν3 combination, 2ν1 and 2ν3 overtone bands of H2O absorption
spectra overlap with the most common telecommunication bands, and thus diode lasers
and optical fibers are widely available [Allen 1998]. In HITRAN 2004, there are 6435
H2O transitions within this spectral region. Second, we require the candidates have peak
absorbances of 0.02 < αpeak < 1 over conditions in typical combustion flows: 1000 K < T
< 2000 K, P = 1 atm, XH2O = 10%, L = 10 cm. This criterion, which guarantees a good
SNR and avoids optically-thick measurements, reduces the candidates to 316 lines. Third,
transitions with significant interferences from neighboring lines are eliminated and the
potential candidates are reduced to 278 lines as shown in Fig. 6.2. For this work,
neighboring strong lines with a line-center frequency spacing of <0.05 cm-1 have been
counted as one line since they can not be resolved at 1 atm.
Figure 6.2: Lower state energy E” vs. line center frequency for the selected 278 candidates after the initial screening described in section 6.3.1.
6.3.2 Two criteria on E” for non-uniform temperature sensing
A limited number of lines must be selected from these 278 candidates for practical
non-uniform temperature distribution measurements. The minimum number of lines,
mathematically speaking, must be no less than the number of unknowns to be solved
6800 7000 7200 74000
1000
2000
3000
E" [c
m-1]
ν0 [cm-1]
NON-UNIFORM T SENSING USING MULTI-LINE THERMOMETRY 115
from the least-square fitting problem (6.4) or (6.8): for the profile fitting strategy, the
number of lines must be no less than the number of quantities (Tchar, LTchar, Xchar and
LXchar) that describe the postulated profiles; for the temperature binning strategy, no less
than the number of bins. Using even more lines with appropriate E” will help to increase
the measurement accuracy, as will be shown in section 6.4. Although it is hard to develop
specific rules for the selection of multiple transitions, two general guidelines can be
proposed here.
First, the E” of the selected lines should be well distributed. This point can be
clarified by the ideal Boltzmann plot ( ln(A/S(T0)) vs. E” ) of the multiple absorption
measurements. The mathematics of profile fitting and temperature binning is equivalent
to curve fitting on the Boltzmann plot. Given the absorbing species (H2O vapor in this
case), the ideal shape of the Boltzmann plot is only determined by the temperature
distribution along the LOS measurement path if the H2O mole fraction can be assumed to
be uniform. Figure 6.4 presents the ideal Boltzmann plots for absorption measurements
along the two generic temperature distributions (see section 6.4.1) shown in Fig. 6.3.
When the temperature is uniform, the Boltzmann plot obeys a linear relationship as can
be derived from Eq. (2.2) and (2.8), and the uniform temperature can be inferred from the
slope of the Boltzmann plot [Li et al. 2005]. When the temperature is non-uniform, the
Boltzmann plot deviates from linearity and the curvature increases with the magnitude of
the temperature non-uniformity, as illustrated by the dash and dash-dot curves. As can be
seen on a Boltzmann plot, measurements isolated in one segment of the plot with a
narrow range of E” will not guarantee a good least square fitting. The requirement for
well-spread E” actually guarantees the selection of lines with different temperature
sensitivity so that different lines will be “turned on/off” at different temperatures and thus
different temperature components in a non-uniform temperature distribution can be
“detected” by different lines.
116 CHAPTER SIX
Figure 6.3: Two generic (hypothetic) temperature distributions to be measured: (a) the “2-T” distributions which are equivalent in terms of LOS absorption; (b) the parabolic distribution.
Figure 6.4: The ideal Boltzmann plot of absorption measurements along (a) the “2-T” profiles; (b) the parabolic profile defined in Fig. 6.3. Uniform: T = 1900 K; ∆T = 800 K: Tm(Tc) = 1900K, Tcs(Tcb, Tw) = 1100K; ∆T = 1600K: Tm(Tc) = 1900K, Tcs(Tcb, Tw) = 300K.
Second, given the number of transitions, more lines with good temperature
sensitivity in the target temperature range should be selected. It has been shown in
Chapter 4 that the temperature sensitivity of any absorption transition at a specific
temperature T is proportional to |E”-E(T)| as per Eq. (4.2), where E(T) is the
characteristic energy of the absorbing species. For a typical combustion temperature
0 1000 2000 3000 4000-5
0
5
10
ln(A
/S(T
0))
E"
Uniform ∆T = 800 K ∆T = 1600 K
0 1000 2000 3000 4000-5
0
5
10
ln(A
/S(T
0))
E"
Uniform ∆T = 800 K ∆T = 1600 K
(a) (b)
0 2 4 6 8 101600
1800
2000
T [K
]
x [cm]
1600
1800
2000
T [K
]
Tm = 1900 KLcs = 3 cmTcs = 1700 K
Tm = 1900 K
Lcb = 1.5 cm Tcb = 1700 K
0 2 4 6 8 101000
1500
2000
T [K
]x [cm]
Tc = 1900 K
Tw = 1500 K
(a) (b)
NON-UNIFORM T SENSING USING MULTI-LINE THERMOMETRY 117
range of 1000-2000 K, EH2O(T) ranges from 1966 to 4806 cm-1 as shown by Fig. 4.1, thus
H2O vapor transitions with E” << 1966 cm-1 or E” >> 4806 cm-1 are preferred for non-
uniform temperature sensing in a typical combustion environment. It is interesting to note
that using more H2O lines with E” << 1966 cm-1 will also help to capture the curvature of
the ideal Boltzmann plot for absorption measurements along the two generic temperature
distributions, as can been seen in Fig. 6.4.
For the purpose of example, these two guidelines are used to select 16 transitions
from the 278 candidates for the simulation studies discussed in section 6.4. First, their
E”s are spread over the entire E” range of the 278 candidates, which is 24-3536 cm-1 as
shown by Fig. 6.2; second, over half of the 16 lines have their E”s << 1966 cm-1. There
are multiple choices for such a set of 16 lines, and one such set is listed in Table 6.1(a).
For lines with similar E”, the ones with stronger linestrengths and better isolation from
their neighboring lines are selected. Also according to the two guidelines, subsets of the
16 lines are selected to investigate the dependence of the measurement accuracy on the
number of lines used, and these subsets are listed in Table 6.1(b).
Table 6.1: Transitions selected for the simulation studies discussed in section 6.4.
(a) Complete set of 16 transitions.
Line Index ν0 [cm-1] S(Tref) [cm-2atm-1] E" [cm-1] 1 7306.7521 4.453E-01 79.4964 2 7339.8342 3.684E-01 224.8384 3 7139.0891 2.452E-01 325.3479 4 7380.0105 9.476E-02 552.9114 5 7397.5746 5.083E-02 704.2140 6 7203.8904 7.385E-02 742.0763 7 7185.5973 1.971E-02 1045.0579 8 7417.8225 1.071E-02 1079.0796 9 7416.0465 1.441E-02 1114.5499
10 7179.7520 5.703E-03 1216.1945 11 6973.6650 1.961E-03 1446.1282 12 7444.3615 1.117E-03 1791.2281 13 6919.9475 2.141E-04 2073.5156 14 6892.7394 5.775E-05 2358.3015 15 7472.0560 5.254E-06 2952.3938 16 6854.1595 1.091E-06 3439.3066
118 CHAPTER SIX
(b) Subsets with different number of lines.
Number of Lines Line Index 4 2,6,7,16 6 (4 Lines) + 9,12 8 (6 Lines) + 1,4
12 (8 Lines) + 11,13,14,15 16 (12 Lines) + 3,5,8,10
For practical measurements, the selected candidates can be accessed either by wide-
wavelength-scanning laser sources such as the ECDL used for H2O spectroscopy survey
in Chapter 3, or by the WDM scheme as discussed in section 2.4.2.
6.4 Simulation studies of the sensor performance
The performances of both profile fitting and temperature binning strategies are
investigated via computational simulations. The details of simulation studies are
introduced in section 6.4.1 and the simulation results for profile fitting and temperature
binning are presented in section 6.4.2 and 6.4.3 respectively. Section 6.4.2 and 6.4.3 are
both divided into two parts, which address the measurements for the two generic
temperature distributions in Fig. 6.3 respectively. In each part, the variation of the
measurement accuracy is investigated with the number of lines used, the number of
unknowns to be solved and the magnitude of temperature non-uniformities.
6.4.1 Details of simulation studies
Two generic non-uniform temperature distributions as shown in Fig. 6.3 are
presumed as the flow fields to be measured by the LOS absorption sensors. The “2-T”
distribution consists of two constant temperature zones. It can be a uniform high
temperature region with a “cold” spot which has 30% of the total path length, as shown in
the top panel of Fig. 6.3(a). This is equivalent, in terms of LOS integrated absorbance for
any absorption transition, to a “cold” boundary layer on either end of the measurement
NON-UNIFORM T SENSING USING MULTI-LINE THERMOMETRY 119
path and each boundary layer is 15% of the total path length, as shown in the bottom
panel of Fig. 6.3(a). The parabolic distribution, as shown in Fig. 6.3(b), can be a simple
model of the temperature across the combustion gases inside a chamber with cold walls.
These hypothetic profiles are selected as the targets to be measured since they represent
the simplest case of very common non-uniform temperature distributions in practical
combustion flow fields. Additionally, the total path length L is assumed to be 10 cm, and
the water mole fraction XH2O is assumed to be constant throughout at 10%. For both
generic temperature distributions, the highest temperature TH, such as Tm or Tc, is always
fixed at 1900 K, while the lowest temperature TL, such as Tcs, Tcb or Tw, is set at 1100,
1500, 1700 or 1800 K to obtain a temperature non-uniformity (∆T = TH-TL) of 800, 400,
200 or 100 K, which facilitates studying the influence of the magnitude of the
temperature non-uniformity on the measurement accuracy.
The expected integrated absorbance Ai,true along the hypothetic temperature
distributions in Fig. 6.3 can be calculated as per Eq. (2.2) and (2.5). The measured
absorbance Ai, which is finally used in the profile fitting calculation (6.4) and the
temperature binning calculation (6.8), is simulated by imposing a random noise ξ on the
Ai,true
[ ], 1 (0, )i i trueA A ξ σ= ⋅ + . (6.10)
The random noise ξ is assumed to obey a normal distribution with a standard deviation σ
of 2-5%. It corresponds to a SNR of 20-50 which has been achieved in many of our
previous LOS absorption measurements.
For each case, 100 simulated measurements are calculated as if multiple absorption
experiments were conducted. The profile fitting and temperature binning calculations are
performed on each of the 100 simulated measurements. The mean values of the
calculated results are inferred and shown in panel (a) of each figure. These mean values
are represented by the symbols for profile fitting results shown in Fig. 6.6-6.12 and by the
120 CHAPTER SIX
bars for temperature binning results shown in Fig. 6.13-6.18. The dashed horizontal lines
indicate the expected values of the calculated results. In panel (b) of each figure, the
deviations of the calculated mean values from the expected values are plotted in the top
frame as residual (in percentage), while the standard deviations (STD) of the multiple
calculation results are plotted in the bottom frame. The STDs of the profile fitting results
are also represented by the error bars of the symbols in panel (a) of Fig. 6.6-6.12.
6.4.2 Profile fitting results
6.4.2.1 “2-T” case
To measure the “2-T” temperature distribution presented in the top panel of Fig.
6.3(a) by the profile fitting strategy, we first assume that our physical understanding of
the target flow field enables us to postulate a “2-T” profile as shown in Fig. 6.5 to model
the temperature distribution along the measurement path. The total path length L is
usually measured in experiments, so the unknowns in this postulated “2-T” profile are the
main temperature Tm, the cold spot temperature Tcs, and its length Lcs.
Figure 6.5: The postulated “2-T” profile for measurements of the non-uniform temperature distribution presented in the top panel of Fig. 6.3(a) using the profile fitting strategy.
0 2 4 6 8 101000
1500
2000
T [K
]
x [cm]
Tm
Tcs
Lcs
NON-UNIFORM T SENSING USING MULTI-LINE THERMOMETRY 121
These three unknowns can be solved by the nonlinear least square fitting (6.4)
using different number of transitions selected in section 6.3.2. The simulation results for
measuring a temperature non-uniformity of ∆T = 800 K are plotted in Fig. 6.6. It is
demonstrated that satisfactory measurements can be obtained by using a limited number
of lines with appropriate E”. For example, by using the 8 lines listed in Table 6.1(b), Tm
and Tcs can be measured within an accuracy of 1%, while Lcs within 3%. It should be
noted that these 8 lines may not be the best, i.e. another choice of 8 lines from the 278
candidates may lead to even better measurement accuracy. But this simulation case fully
demonstrates that by following the line selection guidelines proposed in section 6.3.2, we
are able to design LOS absorption sensors with a limited number of lines to achieve
desirable measurement accuracy. Figure 6.6 also reveals that the measurement accuracy
increases with the number of lines until reaches a limitation determined by the SNR of
the LOS absorption measurements.
Figure 6.6: Profile fitting results (three unknowns) for the “2-T” temperature distribution (∆T = 800 K).
More simulations suggest that the measurement errors rise when the temperature
non-uniformity of the target flow field decreases, i.e. it is more difficult to resolve a
smaller non-uniformity. However, the measurement results are greatly improved by
0 4 8 12 16 20 24800
1200
1600
2000
Tm Tcs
Number of Lines
T [K
]
0
4
8
Lcs
Lcs [cm]
0 4 8 12 16 20 240
20
40
Tm Tcs Lcs
STD
[%]
Number of Lines
0
10
Res
idua
l [%
]
(a) (b)
122 CHAPTER SIX
reducing the number of unknowns in the postulated temperature profile by adding more
physical constraints. For example, if Lcs can be pre-determined, Tm and Tcs can be solved
by profile fitting with desirable accuracy, even for a much smaller non-uniformity.
Figure 6.7: Profile fitting results (two unknowns) for the “2-T” temperature distribution (∆T = 200 K).
Figure 6.8: Influence of the temperature non-uniformity ∆T on the profile fitting results for the “2-T” temperature distribution. Only 4 lines are used.
Figure 6.7 shows the simulation results for the measurement of a small temperature
non-uniformity of ∆T = 200 K, where the cold spot temperature Tcs is only ~10% less
0 4 8 12 16 20 24800
1200
1600
2000
T [K
]
Number of Lines
Tm Tcs
0 4 8 12 16 20 240
5
10
Tm Tcs
STD
[%]
Number of Lines
0
2
Res
idua
l [%
]
(a) (b)
0 200 400 600 800 1000800
1200
1600
2000
T [K
]
∆T [K]
Tm Tcs
0 200 400 600 800 10000
5
10
STD
[%]
∆T [K]
0
5
10 Tm Tcs
Res
idua
l [%
]
(a) (b)
NON-UNIFORM T SENSING USING MULTI-LINE THERMOMETRY 123
than the main flow temperature Tm. Using only 4 lines, both Tcs and Tm can be determined
within an accuracy of 2%, and the errors can be further reduced by using more lines.
Even better accuracy is achievable if the temperature non-uniformity of the target flow is
larger, as suggested by the simulation results in Fig. 6.8.
Nine perturbation tests as listed in Table 6.2 are performed to investigate the
influences on the profile fitting results by the pre-estimated value for Lcs and the given
initial values for the two unknowns (Tm and Tcs). The corresponding simulation results are
plotted in Fig. 6.9.
Table 6.2: Nine perturbation tests for investigating the influence on the profile fitting results by the errors in the pre-estimated value for Lcs and the given initial values for the two unknowns (Tm and Tcs).
Postulated Lcs [cm] Initial Values [K] 3 3 X 0.8 3 X 1.2 Tm = 1900, Tcs = 1700 1 2 3 Tm = Tcs = 1800 4 6 8 Tm = 1900 X 1.2, Tcs = 1700 X 0.8 5 7 9
Figure 6.9: Profile fitting results for the nine perturbation tests listed in Table 6.2 for the “2-T” temperature distribution (∆T = 200 K). Only 4 lines are used.
0 1 2 3 4 5 6 7 8 9 10800
1200
1600
2000
T [K
]
Case Index
Tm Tcs
0 1 2 3 4 5 6 7 8 9 100
10
20
STD
[%]
Case Index
0
5
10 Tm Tcs
Res
idua
l [%
]
(a) (b)
124 CHAPTER SIX
In cases 1-3, the initial values for Tm and Tcs are accurate, while Lcs is postulated at
the exact value of 3 cm, under-estimated by 20% and over-estimated by 20%
respectively. A comparison of the results shows that a 20% deviation of the postulated Lcs
from the exact value will not cause significant errors in the results for Tcs and Tm, both of
which can still be determined within an accuracy of 4%. Therefore, the Lcs does not need
to be postulated accurately. This value may be roughly estimated (e.g., CFD) for the
measurement plane/path or taken from thermocouple rake measurements.
In cases 4 and 5, Lcs is postulated to be exact, while the initial values for Tm and Tcs
are varied so that the target temperature non-uniformity ∆T is far underestimated (∆Tinitial
= 0 K) and far overestimated (∆Tinitial ≈ 5∆Ttrue) respectively. The simulation results
demonstrate that the measurements are quite insensitive to the errors in the given initial
values for Tm and Tcs.
The combined perturbation effects of the errors in the postulated Lcs and the initial
values for Tm and Tcs are investigated by cases 6-9. The simulations results demonstrate
that the profile fitting measurements are quite robust to the postulated Lcs and the initial
values for Tm and Tcs. It should be pointed out that for all nine perturbation tests the target
temperature non-uniformity ∆T is 200 K and only 4 lines are used in the profile fitting
calculations, the measurement accuracy will be better when ∆T is larger or if more lines
are used, as has been suggested by Fig. 6.8 and 6.7.
6.4.2.2 Parabolic case
To measure the parabolic temperature distribution presented in Fig. 6.3(b) by
profile fitting strategy, we first assume that our physical understanding of the target flow
field enables us to postulate a parabolic profile as shown in Fig. 6.10 to model the
temperature distribution along the measurement path
22( ) ( )
( / 4) 2w c
cT T LT x T xL
−= + − . (6.11)
NON-UNIFORM T SENSING USING MULTI-LINE THERMOMETRY 125
The unknowns to be solved are the peak temperature at the center Tc and the temperature
at the wall/edge Tw.
Figure 6.10: The postulated parabolic profile for measurements of the non-uniform temperature distribution shown in Fig. 6.3(b) using the profile fitting strategy.
The simulation results for determination of a temperature non-uniformity of ∆T =
400 K with different number of lines are plotted in Fig. 6.11. Tc and Tw can be determined
within an accuracy of 2% by using 8 lines and increasing the number of lines helps to
improve the measurements further. But the measurement errors grow larger when the
temperature non-uniformity is smaller, as suggested by Fig. 6.12.
Figure 6.11: Profile fitting results for the parabolic temperature distribution (∆T=400 K).
0 2 4 6 8 101000
1500
2000
T [K
]
x [cm]
Tc
Tw
0 4 8 12 16 20 24800
1200
1600
2000
T [K
]
Number of Lines
Tc Tw
0 4 8 12 16 20 240
10
20
STD
[%]
Number of Lines
0
5
10 Tc Tw
Res
idua
l [%
]
(a) (b)
126 CHAPTER SIX
Figure 6.12: Influence of the temperature non-uniformity ∆T on the profile fitting results for the parabolic temperature distribution. 8 lines are used.
6.4.3 Temperature binning results
6.4.3.1 “2-T” case
Unlike the profile fitting strategy, which requires apriori knowledge of the target
temperature distribution, the temperature binning strategy only needs a rough estimation
of the temperature range possible along the LOS measurement path, which may be 1000-
2000 K for typical combustion flow fields. The initial example examines five temperature
bins, each of which has a span of 200 K. The “2-T” temperature distributions as
represented by both cases in Fig. 6.3(a) can be resolved in terms of the PDF, e.g. as
shown in Fig. 6.13(a) by using the absorption data of six lines. For a target temperature
non-uniformity of ∆T = 800 K (Tm = 1900 K, Tcs = 1100 K), the binning results reveal
that ~30% of the path length is in the 1st bin with T = 1000-1200 K, while ~70% in the 5th
bin with T = 1800-2000 K. The simulation results indicate that a desirable accuracy is
achieved with only 6 lines as selected in Table 6.1(b). The simulated results using
different number of lines are plotted in Fig. 6.13(b), and the same trend as that for profile
0 200 400 600 800 1000
1200
1600
2000
T [K
]
∆T [K]
Tc Tw
0 200 400 600 800 10000
10
20
STD
[%]
∆T [K]
0
5
10 Tc Tw
Res
idua
l [%
] (a) (b)
NON-UNIFORM T SENSING USING MULTI-LINE THERMOMETRY 127
fitting results is revealed, i.e. the measurement accuracy increases with the number of
lines until reaches a limitation set by the SNR of the LOS absorption measurements.
Figure 6.13: Temperature binning results for the “2-T” temperature distributions (∆T = 800 K, 5 bins): (a) Illustration of the averaged PDF solution solved with 6 lines; (b) the residual and STD of the PDF solutions solved with different number of lines.
Figure 6.14: Influence of number of bins on the temperature binning results for the “2-T” temperature distributions (∆T = 800 K, 16 lines): (a) the averaged PDF solutions; (b) the residual and STD for different number of bins.
0.0
0.2
0.4
0.6
0.8
1.0
1900170015001300
Frac
tion
of P
athl
engt
h
T [K]
Measured Expected
1100 6 8 10 12 14 164
6
8
10
RM
S_ST
D [%
]
Number of Lines
2
4
6
RM
S_R
es. [
%]
(a) (b)
0.0
0.2
0.4
0.6
0.8
1.0
Frac
tion
of P
athl
engt
h
1100
1500
1900
T [K]
Measured Expected
T [K] T [K]
1100
1500
1900
1300
1700
1100
1500
1900
1300
1700
2 3 4 5 6 7 8 9 100
5
10
RM
S_S
TD [%
]
Number of Bins
0
2
4
6
RM
S_R
es. [
%]
(a) (b)
128 CHAPTER SIX
It is desirable to use more bins to achieve a finer temperature resolution. However,
the measurement errors will increase with the number of bins, as suggested by the
simulation results shown in Fig. 6.14. Therefore, a small number of bins, e.g. 3-5, is
recommended to guarantee acceptable accuracy. In spite of this limited number of bins,
the PDF results are sufficient for many monitoring and control applications where
minimizing or maximizing the temperature non-uniformities is the final goal [Palaghita
and Seitzman 2005].
For a fixed number of bins and fixed number of lines, the measurement accuracy
will improve as the temperature non-uniformity of the target flow field increases, as
suggested by the simulation results shown in Fig. 6.15. When the cold spot temperature
Tcs (or cold boundary layer temperature Tcb) is only ~10% of the main flow temperature
Tm, the estimated error is ~ 11%, which drops to ~2% when the temperature non-
uniformity ∆T is four times larger.
Figure 6.15: Influence of the temperature non-uniformity ∆T on the temperature binning results for the “2-T” temperature distributions (3 bins and 16 lines): (a) the averaged PDF solutions; (b) the residual and STD for different magnitude of ∆T.
0.0
0.2
0.4
0.6
0.8
1.0
190015001100
Frac
tion
of P
athl
engt
h
T [K]
Measured Expected
T [K]1500 1700 1900 1700 1800 1900
T [K]
∆T=800K ∆T=400K ∆T=200K
200 400 600 8000
10
20
RM
S_S
TD [%
]
∆T [K]
0
5
10
RM
S_R
es. [
%]
(a) (b)
NON-UNIFORM T SENSING USING MULTI-LINE THERMOMETRY 129
6.4.3.2 Parabolic case
Temperature binning measurements of the parabolic temperature distribution as
illustrated by Fig. 6.3(b) are also investigated by varying the number of lines, the number
of bins and the magnitude of the temperature non-uniformity. The relevant simulation
results are shown in Fig. 6.16-6.18 respectively. The same conclusions as those obtained
in the “2-T” case are reached. By measuring the LOS absorption of a limited number of
lines, a parabolic temperature distribution can be accurately resolved in terms of PDF
with a moderate number of bins. The measurement accuracy will increase with the
number of lines and decrease with the number of bins; it remains more difficult to
accurately resolve smaller temperature non-uniformity.
Figure 6.16: Temperature binning results for the parabolic temperature distribution (∆T = 800 K, 4 bins): (a) the averaged PDF solution solved with 4 lines; (b) the residual and STD of the PDF solutions solved with different number of lines.
0.0
0.1
0.2
0.3
0.4
0.5
1400
Frac
tion
of P
athl
engt
h
T [K]
Measured Expected
1200 1600 1800 2 4 6 8 10 12 14 16 1865
70
75
RM
S_S
TD [%
]
Number of Lines
0
1
2
3
RM
S_R
es. [
%]
(a) (b)
130 CHAPTER SIX
Figure 6.17: Influence of number of bins on the temperature binning results for the parabolic temperature distribution (∆T = 400 K, 16 lines): (a) the averaged PDF solution; (b) the residual and STD for different number of bins.
Figure 6.18: Influence of the temperature non-uniformity ∆T on the temperature binning results for the parabolic temperature distribution (3 bins and 4 lines): (a) the averaged PDF solution; (b) the residual and STD for different magnitude of ∆T.
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Frac
tion
of P
athl
engt
h
T [K]1600 1800
T [K]18501650 1750
Measured Expected
T [K]1500 1700 1900 1550 2 3 4
0
50
100
RM
S_S
TD [%
]
Number of Bins
0
5
10
RM
S_R
es. [
%]
(a) (b)
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
19001500
Frac
tion
of P
athl
engt
h
T [K]1100
Measured Expected
T [K]
T [K]1500 1700 1900 1700 1800 1900
∆T=800K ∆T=400K ∆T=200K
200 400 600 8000
50
100
RM
S_S
TD [%
]
∆T [K]
0
5
10
RM
S_R
es. [
%]
(a) (b)
NON-UNIFORM T SENSING USING MULTI-LINE THERMOMETRY 131
6.5 Demonstration measurements of a “2-zone” temperature
distribution
Multi-line thermometry for temperature sensing in non-uniform flows is
demonstrated by laboratory measurements of a “2-Zone” temperature distribution with a
wavelength-division multiplexing (WDM) scheme.
6.5.1 Experimental details
6.5.1.1 “2-Zone” temperature distribution
Figure 6.19: Schematic of the experimental setup for a WDM absorption sensor.
Figure 6.20: Thermocouple measurements of the non-uniform temperature distribution along the laser beam path. The water mole fraction is ~10% in the high temperature zone and ~1.75% in the room temperature zone as listed in Table 6.3.
Single Mode Fiber Flat Flame Burner
DFB Lasers
25.4 cm
54.0 cm
Detectors
Pitch Lens
Catch Lens
ZMUXTM ZMUXTM
Multi- Mode Fiber
-15 -10 -5 0 5 10 15 20 25 30 35 40
400
800
1200
1600
T [K
]
x [cm]
132 CHAPTER SIX
The “2-zone” schematic is shown in Fig. 6.19. The free space laser beam has a total
path length of 54 cm set by the spacing between the pitch lens and the catch lens. A 25.4
cm long flat-flame burner is located at the center of the measurement path to create a
uniform hot section. Therefore, the entire LOS measurement path can be roughly divided
into two zones, one in the cold room air and the other in the hot flame gases. Figure 6.20
shows the thermocouple measurements of this steady, non-uniform temperature
distribution along the laser beam path.
The flat-flame burner is fueled by premixed ethylene and dry air. Due to its special
design [Mihalcea 1998], a stable laminar flame can be obtained over the equivalence ratio
range of 0.6-1.4. For the current demonstration experiments, the ethylene and air flow
rates are measured to be 1.8 l/min and 34.0 l/min respectively by calibrated rotameters.
The equivalence ratio is thus 0.76, which leads to an equilibrium water vapor mole
fraction of 10.0% with an uncertainty of ~3% due to the measurement uncertainty of the
fuel/air flow rates.
The flame temperature is measured at the height of the laser beam (~5 mm above
the burner surface) by a type S thermocouple with a bead size of 2 mil (~51 µm). The
radiation corrections for the thermocouple readings are ~55 K. [Shaddix 1999] As shown
by Fig. 6.20, the core part of the flame (1-24 cm) has a uniform temperature distribution.
The average is ~1534 K, with an uncertainty of ~3% estimated from the scatter of the
thermocouple readings and the uncertainty in the radiation correction. This measured
flame temperature is lower than the adiabatic flame temperature at the measured
equivalence ratio mainly due to the radiation loss to the surroundings and the heat
conduction to the water-cooled burner surface. At both edges of the flame, there is a
slight temperature rise and then a sharp drop to the room temperature, thus creating well-
defined high- and low- temperature zones along the LOS measurement path.
The thermocouple measurement of the room temperature is ~298 K, which agrees
with the readings of a mercury thermometer. The room air humidity is measured by a
NON-UNIFORM T SENSING USING MULTI-LINE THERMOMETRY 133
calibrated hygrometer to be ~56%, which indicates a water mole fraction of ~1.75%. The
temperature, water mole fraction and path length of the two zones are summarized in
Table 6.3.
Table 6.3: Expected properties of the “2-Zone” temperature distribution along the LOS measurement path.
Zone 1 Zone 2 T [K] 298 (±1) 1534 (±50)
XH2O [%] 1.75 (±0.05) 10.0 (±0.3) L [cm] 28.6 (±0.2) 25.4 (±0.2)
6.5.1.2 WDM setup
The layout of the WDM scheme is also shown in Fig. 6.19. The fiber-coupled
outputs from five DFB InGaAsP lasers (NEL NLK1B5E1AA, 10-30mW) are combined
together and coupled into one single-mode fiber by a multiplexer (Zolo Technologies,
ZMUXTM, ZD1549-A). The multiplexed laser beam is then collimated by the pitch lens
(Thorlabs F220FC-C) and propagates across the “2-Zone” measurement path. Another
lens (Thorlabs F220FC-C) installed in a five-axis mount is used to catch the free space
laser beam and focus it into a multi-mode fiber (50 µm core) which leads to a grating-
based de-multiplexer (Zolo Technologies, ZMUXTM, ZD1550-A). The wavelength-
multiplexed beam is then diffracted into the constituent five wavelengths collected on
fiber for each channel and delivered to five InGaAs detectors (Thorlabs PDA400).
The five DFB lasers emit near 1343, 1345, 1392, 1395 and 1398 nm. These
wavelengths are chosen to be compatible with five channels of the two Zolo ZMUXTM
products. The fiber-coupled, echelle grating based ZMUXTM multi/demultiplexers are
chosen over free space, conventionally ruled gratings because these compact devices
allow dense wavelength multiplexing and demultiplexing (up to 44 wavelengths) with
high efficiency, pre-set alignment and well-controlled polarization-dependent loss and
thermal drift.
134 CHAPTER SIX
Table 6.4: The seven water vapor transitions used in the demonstration measurements of a “2-zone” temperature distribution.
Line Index ν0 [cm-1] S(T0) [cm-2atm-1] E" [cm-1] 1 7154.35 3.670E-04 1789.04 2 7164.90 3.550E-03 1394.81 3 7185.60 1.960E-02 1045.06 4 7417.82 1.070E-02 1079.08 5 7444.36 1.100E-03 1786.00 6 7164.07 2.021E-02 300.36 7 7419.17 2.222E-02 842.36
Figure 6.21: Illustration of the absorption spectra for each of the five lasers measured with the experimental setup shown in Fig. 6.19 and conditions listed in Table 6.4.
0.4
0.2
0.0
Abs
orba
nce
7155.57155.07154.57154.07153.5Frequency [cm
-1]
0.4
0.2
0.0
Abs
orba
nce
7166.07165.57165.07164.57164.0Frequency [cm-1]
0.4
0.2
0.0
Abs
orba
nce
7186.07185.57185.0Frequency [cm-1]
0.4
0.2
0.0
Abs
orba
nce
7419.57419.07418.57418.07417.57417.0Frequency [cm-1]
0.4
0.2
0.0
Abs
orba
nce
7446.07445.57445.07444.57444.07443.5Frequency [cm-1]
1
2
6
3 4 7
5
NON-UNIFORM T SENSING USING MULTI-LINE THERMOMETRY 135
The DFB lasers can be scanned across 2-3 cm-1 by injection current variation,
enabling access to the seven strong water vapor transitions listed in Table 6.4 and
indicated in Fig. 6.21. These seven transitions are used for this experiment to illustrate
the proposed sensor concepts and demonstrate the feasibility. This set of wavelengths is
not the optimum choice for this temperature range. For future applications, improved
transitions can be selected according to the design rules proposed in section 6.3, and the
ZMUXTM multi/demultiplexer can be customized accordingly. Instead of using the WDM
scheme, wide-wavelength-scanning laser sources, such as ECDLs, could probe a larger
number of potential lines. A demonstration experiment using a ECDL will be presented
in section 6.6.
Each DFB laser (14-pin butterfly package) is installed in an ILX Lightwave mount
(LDM-4984) with its current and temperature controlled by one channel of an ILX
Lightwave diode-laser controller (LDC-3900). All five lasers are simultaneously scanned
at 1 kHz with a linear current ramp. The transmitted laser signals obtained by the five
detectors are simultaneously recorded at a 5 MHz sampling rate by two synchronized NI
DAQ cards using a Labview scope program. The wavelength of each laser scan has been
pre-calibrated using a solid etalon with a free spectral range (FSR) of 2.00 GHz.
6.5.1.3 Data reduction
The recorded raw-data scans from each of the five channels are corrected for
detector DC off-sets and background emission, although most of the emission from the
flame has been rejected by the ZMUXTM demultiplexer which acts as a band-pass filter
with a narrow bandwidth of ~1 nm for each channel. The corrected raw data for each
channel are then averaged for every ten sequential scans to reduce stochastic noise. From
each averaged laser scan (i.e. the transmitted signal It), the unattenuated laser intensity
(i.e. the baseline I0) is determined by fitting the part of the It trace without absorption
with a polynomial. The absorption spectrum is then calculated. Figure 6.21 shows an
example of the reduced absorption spectra for each of the five channels.
136 CHAPTER SIX
The integrated absorbances Ai for the seven lines are then calculated from the
measured absorption spectra. The data reduction is more complicated than that for
uniform cases since the lineshape measured along a non-uniform temperature distribution
can no longer be modeled by a single Voigt function. Instead of doing least-square fitting
using multiple Voigt functions, which will be computationally expensive, a hybrid Voigt
fit scheme similar to that proposed previously [Sanders et al. 2001] is employed in this
work, as illustrated in Fig. 6.22. First, the side wings of the target lineshape, excluding
the ~0.1 cm-1 center portion marked by the vertical dashed line, are Voigt fit to minimize
the residual shown on the top panel of Fig. 6.22. The area obtained is denoted as AVoigt,
and has excluded contributions from neighboring features. The width of the center
portion and the Doppler width of the Voigt function are free parameters of the least-
square fit. The difference between the Voigt fit and the measured lineshape, as shown by
the dash curve plotted in Fig. 6.22, is numerically integrated to obtain Aresidual. The total
integrated absorbance for the target line is thus the sum of AVoigt and Aresidual.
Figure 6.22: Illustration of the hybrid Voigt fit for the measured lineshape of line 5.
Once the integrated absorbances for the seven lines are obtained, either the profile
fitting strategy or the temperature binning strategy can be applied to characterize the non-
uniform temperature distribution using the models introduced in section 6.2.
0.4
0.2
0.0
Abs
orba
nce
7445.07444.57444.0Frequency [cm
-1]
-0.20.2
Res
.[%]
Measurement Voigt Fit Residual_Center
NON-UNIFORM T SENSING USING MULTI-LINE THERMOMETRY 137
6.5.2 Experimental results
If we assume that both the temperature and water mole fraction along the LOS
measurement path are uniform, this “uniform” temperature can be inferred from the
measured absorbances of any line pair as per Eq. (2.42). Here line pair 1 and 2 yields
1199 K, while line pair 1 and 3 produces 1122 K. This discrepancy suggests non-
negligible non-uniformities [Palaghita and Seitzman 2005] and thus value of interpreting
the multiple absorption measurements by the new strategies.
6.5.2.1 Profile fitting results
In the profile fitting calculation, the shape of the non-uniform property distribution
must be postulated in advance. The layout of the experimental setup (hot flame
temperature in the middle with cold room temperatures on both sides) enables us to
postulate a “2-Zone” profile as shown in Fig. 6.23 to model the temperature and mole
fraction distribution along the LOS measurement path. The unknowns (free parameters)
to be solved from the multiple absorption measurements are the temperature and mole
fraction for each zone, i.e. T1, T2, X1 and X2. We investigate four different interpretations
of the measured absorption data, each with different degree of constraints on the
postulated distributions. For each of these four cases, the influence of the number of lines
on the sensor performance is investigated.
Figure 6.23: The “2-Zone” property distribution postulated for profile fitting calculation.
-10 0 10 20 30 40
X H2O
[%]
T [K
]
x [cm]
T1, X1
T2, X2
138 CHAPTER SIX
In case 1, the measured absorbances are fit as per Eq. (6.4) with all four unknowns
T1, T2, X1 and X2 as free parameters. A time series of ten individual results are shown in
Fig. 6.24 and the average values are listed in Table 6.5. The results using lines 1-5 and
lines 1-7 are shown in Fig. 6.24 (a) and (b) respectively. The dash lines represent the
expected values. The error bars indicate the measurement uncertainty estimated based on
the uncertainties in the spectroscopic parameters, the measured integrated absorbance for
each line, and the solution of the nonlinear least square fit. Both the measurement
accuracy, as indicated by the difference between the measured and the expected values,
and the statistical precision, as indicated by the scatter of the fitting results over the 10
independent measurements, increase appreciably with the addition of data from lines 6
and 7. By using absorbance measured on lines 1-5, the temperature and mole-fraction
inferred deviate significantly from the expected values, which is partly due to the narrow
span of the lower state energy E” of these 5 transitions. By adding measurements from
lines 6 and 7 with lower E”, the results for T1, T2, X1 and X2 quickly converge to the
expected values within an accuracy of 2%, 3%, 3% and 6% respectively. This result
illustrates the importance of optimized selection of absorption transitions.
Figure 6.24: Profile fitting results for case 1: T1, T2, X1 and X2 fit using (a) lines 1-5; (b) lines 1-7.
0.00 0.02 0.04 0.06 0.08 0.10200
3001000
1200
1400
1600
T1 T2
X1 X2
Time [s]
T [K
]
0.010.02
0.08
0.10
0.12
0.14
X H2O
0.00 0.02 0.04 0.06 0.08 0.10200
3001000
1200
1400
1600
Time [s]
T [K
]
0.010.02
0.08
0.10
0.12
0.14
X H2O
(a)Time [s]
(b)
NON-UNIFORM T SENSING USING MULTI-LINE THERMOMETRY 139
Table 6.5: The average values of the profile fitting results with different number of lines for cases 1 and 2.
Case 1 Case 2 Lines
T1 [K] T2 [K] X1 [%] X2 [%] T1 [K] T2 [K] X2 [%] 1-5 309 1374 1.1 8.4 227 1264 7.8 1-7 292 1489 1.7 9.4 295 1524 9.7
Expected 298 1534 1.75 10.0 298 1534 10.0
In case 2, the H2O mole faction of the cold zone X1 is fixed at 1.75% which is
determined using the measured humidity and an estimated temperature (300 K) of the
room air. The three remaining unknowns T1, T2 and X2 are allowed to vary in the
nonlinear least square fit. A time series of ten individual results are shown in Fig. 6.25
and the average values are listed in Table 6.5. Again the measurement accuracy increases
with the addition of data from lines 6 and 7. By using all 7 transitions, the T1, T2 and X2
can be measured within an accuracy of 1%, 1% and 3% respectively. Compared with the
results for case 1, the accuracies of the fit values increase due to the addition of a physical
constraint on X1.
Figure 6.25: Profile fitting results for case 2: X1 fixed, T1, T2 and X2 fit using (a) lines 1-5; (b) lines 1-7.
0.00 0.02 0.04 0.06 0.08 0.10200
400
1200
1400
1600 T1 T2
X2
Time [s]
T [K
]
0.06
0.08
0.10
0.12
0.14
X H2O
0.00 0.02 0.04 0.06 0.08 0.10200
400
1200
1400
1600
Time [s]
T [K
]
0.06
0.08
0.10
0.12
0.14X
H2O
(a) (b)
140 CHAPTER SIX
In case 3, the H2O mole fractions for the two zones X1 and X2 are fixed at 1.75%
and 10% (the equilibrium value for the measured equivalence ratio) respectively. Since
there are only two remaining unknowns, T1 and T2, a minimum number of 3 lines are
required for the nonlinear least square fit. A time series of ten individual results are
shown in Fig. 6.26 and the average values are listed in Table 6.6. These fit results reveal
the same trend, namely an increasing of the accuracy of the fit values with an increased
number of lines. Even with the minimum number of lines, however, satisfactory results of
T1 and T2 can be obtained (with an accuracy of 4% and 1% respectively) by fixing the
H2O mole fraction values.
In case 4, the properties of the room air T1 and X1 are fixed in the fit, and only the
properties of the hot flame zone T2 and X2 are the free parameters. A time series of ten
individual solutions are shown in Fig. 6.27 and the average values are listed in Table 6.6.
Again, the accuracy increases with the number of lines, and particularly the inclusion of
data from lines 6 and 7. Using all 7 transitions, the T2 and X2 are determined within an
accuracy of 1% and 2% respectively. This measurement arrangement is clearly applicable
to cases with interference absorption by humid room air. Only the absorption by the
target gas is desired, but sometimes room air is inevitably enclosed in the LOS beam path
near the pitch or catch optics, since the laser sources or the measurement geometries
prohibit using fibers to deliver the laser beam directly to the edge of the flow fields to be
measured. Normally, in our laboratory, the open path in this boundary is purged with N2
to remove the interference absorption by the room air, but the purging efficiency can not
always be guaranteed, especially if the purging system is not well designed, installed and
maintained. By using more than two transitions as was done in case 4, the flow field
properties of interest can be inferred directly from the LOS absorption data without
installing complex purging systems.
NON-UNIFORM T SENSING USING MULTI-LINE THERMOMETRY 141
Table 6.6: The average values of the profile fitting results with different number of lines for cases 3 and 4.
Case 3 Case 4 Lines
T1 [K] T2 [K] T2 [K] X2 [%] 1-3 286 1516 1487 9.4 1-5 302 1554 1520 9.6 1-7 299 1552 1537 9.8
Expected 298 1534 1534 10.0
Figure 6.26: Profile fitting results for case 3: X1 and X2 fixed, T1 and T2 fit using (a) lines 1-3; (b) lines 1-5; (c) lines 1-7.
Figure 6.27: Profile fitting results for case 4: T1 and X1 fixed, T2 and X2 fit using (a) lines 1-3; (b) lines 1-5; (c) lines 1-7.
0.00 0.02 0.04 0.06 0.08 0.10280
300
320
T1 T2
Time [s]
T [K
]
1200
1400
1600
T [K
]
0.00 0.02 0.04 0.06 0.08 0.10280
300
320
T1 T2
Time [s]
T [K
]
1200
1400
1600
T [K
]
0.00 0.02 0.04 0.06 0.08 0.10280
300
320
T1 T2
Time [s]
T [K
]
1200
1400
1600
T [K
]
(a)
(b)
(c)
0.00 0.02 0.04 0.06 0.08 0.101200
1300
1400
1500
1600
T2 X2
Time [s]
T [K
]
0.08
0.09
0.10
0.11
0.12
XH
2O
0.00 0.02 0.04 0.06 0.08 0.101200
1300
1400
1500
1600
Time [s]
T [K
]
0.08
0.09
0.10
0.11
0.12
XH
2O
0.00 0.02 0.04 0.06 0.08 0.101200
1300
1400
1500
1600
Time [s]
T [K
]
0.08
0.09
0.10
0.11
0.12
XH
2O
(a)
(b)
(c)
142
Table 6.7 shows a comparison of the profile fitting results for all four cases when
data from all 7 transitions are used. It suggests that the fitting results improve when the
number of unknowns (free parameters) in the postulated distribution profiles is reduced
by using more physical constraints.
Table 6.7: Comparison of the profile fitting results for all four cases with all 7 lines.
Case T1 [K] T2 [K] X1 [%] X2 [%] 1 292 1489 1.7 9.4 2 295 1524 -- 9.7 3 299 1552 -- -- 4 -- 1537 -- 9.8
Expected 298 1534 1.75 10.0
6.5.2.2 Temperature binning results
Alternatively, we can interpret the measured absorption data using the temperature
binning strategy. An estimation of the possible temperature range along the LOS
measurement path allows the prescription of five temperature bins as shown in Fig. 6.28.
All 7 transitions are used in the analysis. The resultant column densities (XH2OL)j, as
indicated the solid bars, are very close to the expected PDF solutions, as indicated by the
dash-dot lines. Only the two side bins have non-zero solutions. They suggest that the
LOS measurement path can be approximately modeled as two zones, one at ~300 K and
the other at ~1500 K, which are very close to these used in the experiment. The
population of water vapor in the highest temperature bin is much larger than that in the
lowest temperature bin, which implies that the “2-T” distribution might result from a cold
spot somewhere along an otherwise uniform high temperature region or a cold boundary
layer on both sides of a uniform hot core temperature. Up to this point, no a priori
knowledge of the flow fields, except an estimation of the possible temperature range, has
been applied to extract the characteristic information on the LOS non-uniformities
discussed above.
NON-UNIFORM T SENSING USING MULTI-LINE THERMOMETRY 143
Figure 6.28: Illustration of the temperature binning results solved using all 7 transitions.
6.6 Demonstration measurements of an inverse-trapezoid temperature
distribution
The multi-line thermometry for temperature sensing in non-uniform flows is also
demonstrated by laboratory measurements of an inverse-trapezoid temperature
distribution with a wide-wavelength-scanning laser source. This laser is the ECDL we
used for the H2O vapor spectroscopy survey, and details of its capabilities have been
presented in Chapter 3. Even though the ECDL scan rate is far too slow for most
combustion sensing applications, its ability to tune over hundreds of H2O vapor
transitions provides a proof-of-concept experiment for the dense wavelength-division
multiplexing (DWDM) based multi-line thermometry.
6.6.1 Experimental details
6.6.1.1 Inverse-trapezoid temperature distribution
The flat flame burner as used earlier in the “2-Zone” measurements is modified to
generate a non-uniform temperature distribution in the flame. As illustrated by Fig. 6.29,
the premixed reactants (Ethylene and dry air) are introduced into the bottom chamber of
the burner through ten equally-spaced small holes drilled in a ¼” stainless steel tube. The
300 600 900 1200 15000.0
0.5
1.0
1.5
2.0
2.5
3.0
X H2O
L
T [K]
144 CHAPTER SIX
end of the tube is plugged and the holes are faced down. The mixture then passes through
a sintered wire mesh (TWP Inc., 0.000079” opening, 0.0223” thickness, stainless steel),
multiple layers of glass beads (1/8” diameter) and a porous stainless-steel matrix
(Kentucky Metals, 1 mm pore size, 0.2 mm wall thickness, 25.4 cm x 2.54 cm (10”x1”)).
A stable laminar flame is attached to the porous-matrix surface. When the glass beads are
filled uniformly inside the top chamber, a uniform flow and thus a uniform temperature
distribution in the central core of the flame can be generated.
The temperature at the flame boundary is ~40 K higher than that in the central core
for both dimensions, as can be seen in the photo of the flame in Fig. 6.29(a) as a brighter
edge. The hot boundary region has a length scale in the order of the diameter of the glass
beads. It may be due to the larger porosity of the glass beads close to the chamber wall as
happens at the boundary of any porous media [Kaviany 1995]. This larger porosity leads
to a higher flow rate and thus a greater heat release and a higher temperature at the flame
boundary. Similarly, this temperature non-uniformity can be amplified by artificially
reducing the thickness of the glass beads near the wall. In a 2.54 cm (1”) region at both
ends of the 25.4 cm (10”) long flame holder, the height of the glass beads is gradually
reduced as shown in Fig. 6.29(b). This results in an increased flow of fuel/air at the ends
of the burner and an inverse-trapezoid temperature distribution as illustrated by the
thermocouple measurements shown in Fig. 6.30. The flame temperature is measured at
the height of the laser beam (~5 mm above the burner surface) by a type S thermocouple
with a bead size of 2 mil (~51 µm). The radiation corrections for the thermocouple
readings are ~55 K. [Shaddix 1999] As shown by Fig. 6.30, the flame temperature drops
gradually from ~1640-1650 K down to ~1560 K within the ~2.54 cm boundary region,
then keeps uniform along the ~20.32 cm central core, thus presenting an inverse-
trapezoid-like temperature distribution along the LOS measurement path. A temperature
distribution with hot regions at the edges mimics the distribution in high-speed
supersonic flow fields which have boundary layers with increased static temperature near
NON-UNIFORM T SENSING USING MULTI-LINE THERMOMETRY 145
the wall. This distribution also presents the same LOS as a hot spot in a uniform high
temperature flow.
Figure 6.29: The flat flame burner: (a) Photo illustration; (b) Schematic of the configuration.
For the current experiments, the ethylene and air flow rates are set to be 1.8 l/min
and 34.0 l/min, respectively, as measured by calibrated rotameters. This corresponds to
an equivalence ratio of 0.76 and a water vapor mole fraction of 10.0% by equilibrium
(a)
Honeycomb
¼” s.s. tube with 10 equally-spaced holes
Glass Beads Metal Mesh
Premixed C2H4/Air
O-ring
Cooling Water Channel
Bottom Chamber
Flat flame25.4 cm
(b)
2.54 cm
25.4 cm
Cooling Water Inlet
Premixed C2H4/Air
Cooling Water Outlet
Top Chamber
146 CHAPTER SIX
calculation. Since the reactants have been well mixed before passing through the layers of
glass beads, we can assume that the manipulation of the height of the glass beads only
creates non-uniformity in the temperature and a constant water vapor mole fraction of
10% still exists everywhere in the flame.
Figure 6.30: Thermocouple measurements of the flame temperature along (a) the entire LOS laser beam path; (b) amplification of panel (a) to show the inverse-trapezoid temperature distribution by neglecting the sharp temperature drops at both ends.
6.6.1.2 ECDL and optical setup
Figure 6.31 shows the schematic of the experimental setup and the optical layout.
The laser source is the ECDL that we used for the H2O vapor spectroscopy investigation
in Chapter 3. It has a full scanning range of 1355-1441 nm (6940-7380 cm-1). During the
experiments, the ECDL is tuned with a speed of 10 nm/s, requiring about 8.6 seconds
scanning the full range of 86 nm (440 cm-1). Although this is too slow for real-time
sensing applications, the wide tuning range of the ECDL enables us to access hundreds of
H2O vapor transitions and use optimal transitions selected according to the design rules
proposed in section 6.3. Once the non-uniform temperature measurements with ECDL
are validated to be able to achieve desirable accuracy with the selected lines, a dense
wavelength-division multiplexing (DWDM) scheme, which possesses real time sensing
capabilities, could be constructed using the selected wavelengths.
0 5 10 15 20 25
1300
1400
1500
1600
1700
T [K
]
x [cm]0 5 10 15 20 25
1500
1550
1600
1650
1700
T [K
]
x [cm] (b)(a)
NON-UNIFORM T SENSING USING MULTI-LINE THERMOMETRY 147
Figure 6.31: Schematic of the experimental setup.
The fiber-coupled output of the ECDL is split into three beams (with intensity split
of 0.45, 0.05, 0.50) as shown in Fig. 6.31. The 45% intensity path is collimated in free
space, transmitted across the flame and detected by an InGaAs detector (Thorlabs
PDA400). The intermediate open paths along the laser beam are purged with N2 to
remove interfering absorption by ambient H2O vapor in room air. The 5% intensity path
is fiber-coupled to a similar detector to provide an intensity reference signal. The
remaining 50% intensity path is collimated and propagated through a solid etalon with a
free spectral range (FSR) of 2.00 GHz to provide a calibration of the laser wavelength.
6.6.1.3 Raw data and data reduction
Figure 6.32 shows the measured raw data traces. As mentioned in Chapter 3, the
ECDL output power oscillates with output wavelength due to etalon interference effects
caused by the residual facet reflectivity during wavelength scanning. The measured-
transmission is thus first normalized by the reference signal to remove the laser intensity
fluctuations. From this pre-conditioned transmission data It, the absorption features are
removed and the remaining sections are fit by spline interpolation to infer the baseline I0.
The absorbance can thus be calculated and the absorption spectra are plotted in Fig. 6.33.
Over the full range of 440 cm-1 probed with a single laser scan, hundreds of H2O
transitions can be fully resolved.
Single Mode Fiber
ECDL
25.4 cm
Reference Detector
Lens Flat Flame Burner
Etalon Detector
Lens
Transmission Detector
Purging Tube Purging Tube
Etalon
148 CHAPTER SIX
9
8
7
6
5
4
3
2
1
Sign
al [V
]
876543210Time [s]
ITrans IRef IEtalon
(a)
6
5
4
3
2
1
Sign
al [V
]
1.501.481.461.441.421.401.381.361.341.321.30Time [s]
ITrans IRef IEtalon
(b)
Figure 6.32: The raw data measured by ECDL: (a) the full scanning range; (b) illustration of the details of the raw data.
Figure 6.33: The reduced absorption spectra measured by ECDL in the flame with temperature distribution shown in Fig. 6.30.
0.4
0.2
0.0
Abs
orba
nce
7300720071007000Frequency [cm
-1]
NON-UNIFORM T SENSING USING MULTI-LINE THERMOMETRY 149
6.6.2 Line selection
A limited number of lines are selected for the non-uniform temperature
measurements using the criteria proposed in section 6.3. There are 3715 lines listed in
HITRAN 2004 within the ECDL tuning range of 6940-7380 cm-1. We first screen the
candidates by requiring a peak absorbance of 0.05 < αpeak < 1 over conditions in a typical
combustion flow field of 1000 K < T < 2000 K, P = 1 atm, XH2O = 10% and L = 25.4 cm
(10 inch). Second, we eliminate transitions with significant interferences from
neighboring lines. These criteria reduce the potential candidates to 57 lines as shown in
Fig. 6.34. Neighboring strong lines with a line-center frequency spacing of <0.05 cm-1
have been counted as one line since they can not be resolved at 1 atm.
Figure 6.34: Lower state energy vs. line center frequency of the selected candidates.
We finally select 12 transitions from the 57 candidates by applying the two criteria
on the lower state energy E”. First, the E” of the 12 transitions should be well distributed;
second, a majority of the 12 transitions should have their E”s << 1966 cm-1 to guarantee
a good temperature sensitivity in the possible temperature range of 1000-2000 K. There
are multiple choices for such a set of 12 lines, and one such set is shown in Table 6.8.
7000 7100 7200 73000
1000
2000
3000
E" [
cm-1]
ν0 [cm-1]
150 CHAPTER SIX
Table 6.8: The twelve H2O absorption transitions selected for the demonstration measurements of an inverse-trapezoid temperature distribution.
Line Index
ν0 [cm-1]
S(T0) [cm-2atm-1]
E" [cm-1]
1 7026.53 1.131E-02 1006.12 2 7070.78 5.544E-02 704.21 3 7075.60 2.352E-06 2972.83 4 7103.11 3.852E-05 2225.47 5 7105.85 1.011E-01 446.51 6 7154.35 3.670E-04 1789.04 7 7161.41 2.912E-01 224.84 8 7173.78 2.402E-03 1411.61 9 7179.75 5.703E-03 1216.19 10 7185.60 1.960E-02 1045.06 11 7215.48 6.405E-02 610.34 12 7230.91 1.341E-01 382.52
6.6.3 Experimental results
Figure 6.35: The measured absorption spectra of the selected 12 transitions.
0.4
0.2
0.0
Abs
orba
nce
71047103 71067105 7155715470277026
Frequency [cm-1
]
70717070 70767075.57075
1 2
3 45 6
0.4
0.2
0.0
Abs
orba
nce
71627161
Frequency [cm-1
]
71747173 71807179.57179 71867185 72167215 72317230
7 8 9
10
11 12
NON-UNIFORM T SENSING USING MULTI-LINE THERMOMETRY 151
The absorption spectra of the 12 transitions measured along the inverse-trapezoid
temperature distribution using ECDL are extracted from Fig. 6.33 and shown individually
in Fig. 6.35. The same hybrid Voigt fit procedures as used in the “2-zone” temperature
measurements are applied to infer the integrated absorbances of these 12 transitions from
the measured spectra. Both the profile fitting strategy and the temperature binning
strategy are applied to interpret the absorbance data and characterize the non-uniform
temperature distribution. Subsets of the 12 transitions (lines 1-3, 1-6 and 1-9) are also
used in the data analysis to investigate the fidelity of the measurement results with the
number of lines.
6.6.3.1 Profile fitting results
To begin with the profile fitting calculation, the profile of the measured non-
uniform temperature distribution has to be postulated in advance. Our previous
knowledge of the flat flame burner enables us to postulate an inverse-trapezoid profile as
shown in Fig. 6.36 to model the temperature distribution along the measurement path.
Figure 6.36: The postulated inverse-trapezoid profile.
( )
( )
1 , 0
( ) ,
1 ,
c w c bb
c b b
c w c bb
xT T T x LL
T x T L x L L
L xT T T L L x LL
+ − − ≤ ≤
= < < − − + − − − ≤ ≤
(6.12)
0 5 10 15 20 251000
1500
2000
T [K
]
x [cm]
L
Tb
Tc
Lb
152 CHAPTER SIX
The total path length L is measured to be equal to the long dimension (25.4 cm) of the
honeycomb, so the unknowns in this postulated trapezoid shape are the uniform core
temperature Tc, the highest temperature at the flame boundary Tb, and the length of the
non-uniform boundary Lb. At least 3 transitions should be used to solve these three
unknowns using the nonlinear least square fitting model (6.4). The results by using
different numbers of lines are listed in Table 6.9 and the corresponding temperature
distributions are plotted in Fig. 6.37. As can be seen, the use of more lines leads to
solutions that agree better with the thermocouple (TC) measurements. With only lines 1-
3, no meaningful results can be obtained. By adding 3 more lines, the solutions begin to
exhibit an inverse-trapezoid shape. Tc & Tb are actually very close to the thermocouple
measurements but Lb is far underestimated. When the number of lines increases further,
Tc & Tb improves a little, and Lb converges significantly to the expected length of ~2.54
cm as validated by the thermocouple measurements.
Figure 6.37: Profile fitting results (three unknowns) by using different number of lines: (a) The entire path length; (b) Amplification of the two ends.
If we impose another physical constraint on the postulated temperature profile that
the length of the non-uniform boundary should be 2.54 cm on both ends due to our
manipulation of the glass beads, only two unknowns (Tc & Tb) need to be solved by the
0 5 10 15 20 251550
1600
1650
T [K
]
x [cm]
TC 6 lines 9 lines 12 lines
0 5 20 251550
1600
1650
T [K
]
x [cm]
TC 6 lines 9 lines 12 lines
(a) (b)
NON-UNIFORM T SENSING USING MULTI-LINE THERMOMETRY 153
profile fitting strategy. The results by using different numbers of lines are listed in Table
6.9 and the corresponding temperature distributions are plotted in Fig. 6.38. Similar to the
3-unknown case, the solutions agree better with the thermocouple (TC) measurements by
using more lines. With only lines 1-3, the temperature non-uniformity cannot be resolved,
and the solution is a uniform temperature. By adding 3 more lines, the solutions begin to
exhibit an inverse-trapezoid shape and Tc is very close to the expected value. With even
more lines, Tc improves a little, and Tb improves significantly to agree better with the
thermocouple (TC) measurements.
Figure 6.38: Profile fitting results (two unknowns) by using different number of lines: (a) The entire path length; (b) Amplification of the two ends.
Table 6.9: The profile fitting results by using different number of lines.
2 Unknowns 3 Unknowns Lines Tc [K] Tb [K] Tc [K] Tb [K] Lb [cm] 1-3 1568 1568 -- -- -- 1-6 1565 1590 1567 1660 0.2 1-9 1561 1636 1564 1659 1.4 1-12 1560 1647 1561 1655 2.1 Expected ~1560 ~1640-1650 ~1560 ~1640-1650 ~2.54
0 5 10 15 20 251550
1600
1650
T [K
]
x [cm]
TC 3 lines 6 lines 9 lines 12 lines
0 5 20 251550
1600
1650
T
[K]
x [cm]
TC 3 lines 6 lines 9 lines 12 lines
(a) (b)
154 CHAPTER SIX
6.6.3.2 Temperature binning results
The possible temperature range along the LOS measurement path is estimated to be
1500-1700 K. Five temperature bins, each has a span of 40 K are prescribed to resolve
the PDF of the measured non-uniform temperature distribution. To obtain the column
density for each of the five bins, at least 5 transitions should be used to solve the relevant
linear least square fitting problem (6.8). Since the mole fraction of the H2O vapor can be
assumed to be uniform along the entire measurement path, the temperature binning
results indicate the fraction of path length for each temperature bin.
Figure 6.39: Temperature binning results: (a) the PDF solution obtained by using all 12 lines; (b) the temperature distributions inferred from the PDF solution.
The temperature binning results by using all 12 lines are shown in Fig. 6.39(a). The
PDF of the non-uniform temperature distribution is roughly recovered. Actually, the
measured temperature non-uniformity is so small that it is very difficult to recover the
exact temperature PDF by temperature binning strategy. The accuracy of the fitting
results will definitely be better if the target temperature non-uniformity is larger, as
demonstrated by the previous simulation studies discussed in section 6.4.3. The binning
results shown in Fig. 6.39(a) suggest that the LOS measurement path can be roughly
divided into two zones if we neglect the very small component in the highest-temperature
1500 1540 1580 1620 1660 17000.0
0.2
0.4
0.6
0.8
1.0
Frac
tion
of P
ath
Leng
th
T [K]
Expected Measured
0 5 10 15 20 251500
1600
1700
T [K
]
x [cm]
1500
1600
1700
T [K
]
Ths=~1600K, Lhs=~4.6 cm
Tm =~1560K
Tm =~1560K
Thb=~1600K, Lhb=~2.3 cm
(a) (b)
NON-UNIFORM T SENSING USING MULTI-LINE THERMOMETRY 155
bin. This “2-zone” temperature distribution might be a hot spot (or hot spots) at an
average temperature of ~1600 K with a (total) length of ~4.6 cm somewhere along the
otherwise uniform flow at ~1560 K, as illustrated by the top panel of Fig. 6.39(b).
Alternatively, the PDF reflects a hot boundary layer at an average temperature of ~1600
K with a thickness of ~2.3 cm on both sides of a uniform core flow at ~1560 K, as
illustrated by the bottom panel of Fig. 6.39(b).
6.7 Summary
In this chapter, the multi-line thermometry scheme for temperature sensing in non-
uniform flows is investigated systematically. It relies on LOS measurements of multiple
absorption transitions with different temperature dependence (lower-state energy E”).
Two strategies, called profile fitting and temperature binning, can be used to interpret the
measured absorption data and infer the non-uniform temperature distribution along the
measurement path. The profile fitting strategy fits a temperature distribution profile
which is postulated in advance using physical constraints, while the temperature binning
strategy determines the temperature probability distribution function (PDF) along the
LOS using prescribed temperature bins.
The sensor concepts are explored in detail. Both strategies are mathematically
modeled as least-square fitting problems. The design rules are proposed for the selection
of optimal absorption transitions. The most important guidelines are to select lines with
well-spread E” and good temperature sensitivity in the target temperature range. The
performance of both sensing strategies are first investigated by simulation studies with
selected H2O vapor transitions for two generic non-uniform temperature distributions (“2-
T” and parabolic profiles). Two experimental demonstrations are then presented to
illustrate the sensor concepts and further investigate the sensor performance. In the first
demonstration experiment, a “2-Zone” temperature distribution is measured with a WDM
156 CHAPTER SIX
scheme; in the second experiment, an inverse-trapezoid temperature distribution is
measured with a wide-wavelength-scanning ECDL as a proof-of-concept demonstration
of dense WDM. The measured absorption data are separately analyzed by profile fitting
and temperature binning strategies to extract information on the non-uniform temperature
distributions.
Both the simulation and experimental results demonstrate that a non-uniform
temperature distribution can be characterized with either strategy by measuring the LOS
absorption for a limited number of transitions with different temperature dependences.
The accuracies of the fit results will increase with the number of transitions, and the
choice of E” of the set of transitions should be optimized to the application. Use of
known physical constraints improve the interpretation of the measurement results and
thus improve the sensor performance.
157
Chapter 7
SUMMARY AND FUTURE WORK
The objective of this thesis was to investigate gas temperature sensing in uniform
and non-uniform flows based on the LOS laser absorption spectroscopy of H2O vapor.
We first performed a systematic survey of the spectroscopic parameters of H2O vapor in
the NIR spectral region to test and improve the capability of the HITRAN spectroscopy
database for temperature sensor design. Then we investigated three different LOS
absorption thermometries for gas temperature sensing in uniform and non-uniform flows.
First, we designed and demonstrated a precise DAS two-line thermometry for uniform
gases, which was applied to the measurement of the path-averaged bulk temperature of a
gas turbine exhaust. Second, we investigated several crucial steps in the design of a
WMS-2f two-line thermometry for in-cylinder measurement of the time-varying gas
temperature during the compression strokes of IC engines. Third, we systematically
investigated and developed DAS multi-line thermometry for temperature sensing in non-
uniform flows. The major achievements and conclusions in each of these areas are
summarized in the following section followed by the recommendations for the future
research efforts in these areas.
7.1 Summary
7.1.1 Experimental study of NIR H2O spectroscopic parameters
Optimized design of TDL temperature sensors based on H2O vapor absorption
spectroscopy requires a complete catalog of the assigned transitions with accurate
158 CHAPTER SEVEN
spectroscopic data. Our particular interest has been focused on the 2ν1, 2ν3, and ν1+ν3
bands in 1.3-1.5 µm NIR region, where telecommunications diode lasers are available. In
support of this need, the fully resolved absorption spectra of H2O vapor in the spectral
range of 1344-1441 nm are measured as a function of temperature (296-1000 K) and
pressure (1-800 Torr) using a tunable ECDL and three DFB diode lasers. Spectroscopic
parameters of strong transitions in this spectral region are inferred from the measured
spectra and compared with existing databases. Most of the measured results are found to
be in better agreement with HITRAN 2004 than with earlier editions of this database,
although large discrepancies between the measurements and HITRAN 2004 database are
still identified for some of the probed transitions. These new extensive spectroscopy
measurements provide useful tests of the sensor design capabilities of HITRAN 2004 for
combustion and other applications at elevated temperatures. Based on this study, we
conclude that HITRAN 2004 is sufficiently accurate and thus a valuable tool for sensor
design using the absorption transitions in the 2ν1, 2ν3, and ν1+ν3 bands of water vapor,
but the spectroscopic data for transitions selected for high temperature sensors require
laboratory validation or correction to enable accurate measurements of gas temperature.
7.1.2 Temperature sensing using DAS two-line thermometry
A TDL temperature sensor based on scanned-wavelength DAS two-line
thermometry is developed to measure the exhaust gas temperature of an industrial gas
turbine. Temperature is determined from the ratio of the measured absorbance for two
NIR water vapor transitions. Design rules, which are crucial to optimize the TDL sensor
design, are developed to select the optimal pair of transitions using spectral simulations
by systematically examining the absorption strength, spectral isolation, and temperature
sensitivity to maximize temperature accuracy in the core flow and minimize sensitivity to
water vapor in the cold boundary layer. Precise linestrength values for the selected
transitions, which are critical for the sensor accuracy, are measured with an estimated
uncertainty of less than 2%. Gas temperature measurements in a heated cell are
SUMMARY AND FUTURE WORK 159
performed to verify the TDL sensor accuracy. The TDL measurements agree with
thermocouple readings within 10 K over the temperature range of 300-1000 K. Field
measurements of exhaust gas temperature in an industrial gas turbine show good
agreement with conventional thermocouple readings, and demonstrate the practical utility
of TDL temperature sensing in harsh industrial environments.
DAS two-line thermometry is ideal for atmospheric (or sub-atm) pressure
conditions where strong and isolated absorption features of H2O vapor are available. As
with any two-line thermometry approach, it yields the path-averaged bulk gas
temperature due to the underlying assumption of uniform temperature along the LOS, and
thus is only appropriate for very short pathlengths where the sampled gas can be assumed
to be uniform or for near-uniform flows like gas turbine exhausts.
7.1.3 Temperature sensing using WMS-2f two-line thermometry
A TDL temperature sensor based on fixed-wavelength WMS-2f two-line
thermometry is developed for in-cylinder measurement of time-varying gas temperature
during the compression stroke of IC engines. This sensor samples, via a modified spark
plug, a short-path region of the in-cylinder gases which have rapid temperature variation
from 400 to 1050 K and pressure variation from 5 to 25 atm during the compression
stroke. The WMS-2f technique is used to achieve sufficient SNR for the small absorption
due to the short pathlength and low water concentration. The fixed-wavelength scheme is
used to enable real-time crank-angle-resolved measurement and address the lack of non-
absorbing wings at elevated pressures. Temperature is determined from the ratio of the
measured WMS-2f absorption signals for two NIR water vapor transitions. Several
critical steps in the sensor design are investigated in this thesis, including the precision
measurements of spectroscopic parameters, selection of laser set-points and construction
of calibration databases, which are of crucial importance for achieving optimal sensor
performance.
160 CHAPTER SEVEN
The integrated sensor has demonstrated very good performance in static tests in a
high T/P cell and dynamic tests in a shock tube. [Rieker et al. 2006b] It has also been
successfully used for crank angle-resolved measurements for both unfired and fired IC-
engine cylinders. [Rieker et al. 2006a] This new temperature sensing technology is
expected to contribute towards developing future generation engines with improved fuel
efficiency and reduced emissions.
7.1.4 Non-uniform temperature sensing using multi-line thermometry
Multi-line thermometry for temperature sensing in non-uniform flows has been
investigated systematically. The sensor concept is to measure the LOS absorptions for
multiple transitions with different temperature dependences, from which the non-uniform
temperature distribution along the LOS can be inferred using either of two strategies. The
first strategy, called profile fitting, fits a temperature distribution profile postulated in
advance using physical constraints; the second strategy, called temperature binning,
determines the temperature probability distribution function (PDF) along the LOS using
prescribed temperature bins. Design rules, which are crucial to optimize the sensor
design, are developed to select optimal absorption transitions of H2O vapor. The most
important guidelines are to select lines with widely spread E” and good temperature
sensitivity in the target temperature range.
Both simulation studies and laboratory experiments are performed to provide
proof-of-concept demonstrations, and investigate the sensor performance. The simulation
demonstrations are carried out to measure two generic non-uniform temperature
distributions (“2-T” and parabolic profiles). In the experimental demonstrations, a “2-
Zone” temperature distribution is measured with a WDM scheme, and an inverse-
trapezoid temperature distribution is measured with a wide-wavelength-scanning ECDL.
Both the simulation and experimental results demonstrate that a non-uniform temperature
distribution can be characterized with either strategy by measuring the LOS absorption
for a limited number of transitions with different temperature dependences. The accuracy
SUMMARY AND FUTURE WORK 161
of the fit results increases with the number of transitions and the use of optimally selected
transitions. Incorporation of known physical constraints to the fit improves the
interpretation of the measurement results and thus improves the sensor performance.
7.2 Suggestions for Future Work
7.2.1 Fundamental spectroscopy investigations
The importance of fundamental spectroscopy research to the development of TDL
absorption sensing techniques, including the two-line and multi-line thermometry
addressed in this thesis, cannot be over-emphasized. Several research directions are
recommended as follows.
First, more refined experiments and methodologies can be investigated to acquire
more precise spectroscopic data. Among the spectroscopic parameters measured in this
thesis work, the pressure-induced frequency shift coefficients δj and their temperature
exponents m have the largest uncertainties. The measurement accuracy could be
improved by using temperature-controlled etalons with a finer and better-calibrated FSR.
Alternative experimental methodologies might also be explored to find the best way to
determine line shifting data. For example, the absorption spectra at different pressures
can be measured simultaneously instead of subsequently by splitting the incident laser
beam into two branches, each passing through a cell containing the absorbing gas under
different pressures [Phelan et al. 2003]. Another method would be to make one laser
beam sequentially pass through two cells at different pressures, record the composite
absorption profile and extract the line shifting parameters [Chevillard et al. 1991, Mandin
et al. 1994]. WMS-2f technique may also be used for line shifting measurements in order
to obtain sharp absorption peaks and alleviate the peak frequency uncertainties caused by
the baseline fitting in DAS [Lyle 2005].
162 CHAPTER SEVEN
Second, more sophisticated lineshape profiles may have to be explored to model
the measured absorption spectra in some special cases. In this thesis work, all
spectroscopic parameters are extracted by fitting the measured lineshape with the Voigt
profile, which is the most commonly used profile mainly due to its computation
efficiency. The Voigt fit generally produces adequate results for the measurement
conditions involved in this thesis work, but more sophisticated lineshape profiles could
be used to model the absorption spectra measured at some special conditions. For
example, Galatry [Galatry 1961] or Rautian [Rautian and Sobel’man 1967] profiles,
which take into account the Dicke narrowing effects [Dicke 1953], might be used to fit
the absorption spectra measured at low pressures for molecules with large rotational level
spacing, such as HF [Pine 1980, Chou et al. 1999], HCN [Varghese and Hanson 1984b],
N2O [Chen et al. 1982] and etc.. A speed-dependent Voigt profile (SDVP) [Berman
1972, Ward et al. 1974], which assumes that absorbers of each velocity class from the
Maxwellian distribution have their own collision width and shifts, might be used for
cases where the perturber mass is much larger than the absorber mass, such as Xe
broadened CO spectra [Duggan et al. 1995].
Third, high-pressure H2O vapor spectroscopy might be investigated to improve
TDL sensor performance at elevated pressures. For the WMS-2f two-line thermometry
developed for high-pressure applications (Chapter 5), all the spectral simulations are
based on the impact and additive approximations, in which any isolated lineshape is
modeled by the Lorentzian profile, and the absorption at a particular frequency is a
simple linear addition of the contributions from all the transitions at that frequency.
Although these approximations generate adequate results over the target pressure range
(5-25 atm), they tend to break down at higher pressures [Rieker et al. 2006c]. Therefore,
to develop TDL sensor for applications at higher pressures, empirical or semi-empirical
corrections of the Lorentzian profile, such as the χ-function [Clough et al. 1989], that
take into account the finite duration of collisions [Hartmann et al. 1993, Nagali 1998]
might be investigated. The line mixing effect [Levy et al. 1992, Kochanov 2000], i.e. the
SUMMARY AND FUTURE WORK 163
blending and coupling of the rotational states resulting from the translation-rotation
relaxation at very high pressures, may also be explored. All these investigations will
require significant validation experiments at different pressures and temperatures.
7.2.2 Multi-line thermometry applications
The development of the multi-line thermometry discussed in Chapter 6 lays
groundwork for the temperature sensing in non-uniform flows using LOS absorption
spectroscopy. Although it will be unlikely that this new sensing technique will yield the
level of spatial resolution achievable with imaging methods such as planar laser induced
florescence (PLIF), the continuous-wavelength (CW) absorption allows for real-time and
continuous measurements, which is a significant advantage over pulsed imaging.
Therefore, continued research regarding this new technique might focus on realizing and
improving the real-time measurement capability. One research front might be to
investigate a more advanced dense wavelength-division multiplexing (DWDM) scheme.
Another direction might involve new laser sources to enable wide and rapid wavelength
scanning. Vertical cavity surface emitting lasers (VCSEL), which can be scanned across
tens of wavenumbers at hundreds of Hz, could be potential candidates although they are
currently commercially available only at limited wavelengths. For example, VCSELs
emitting near 1.3-1.5µm could enable fast multi-line thermometry based on H2O vapor
absorption spectroscopy.
Another advantage of LOS multi-line thermometry over imaging techniques is
minimum optical access requirements, and thus research efforts might be devoted to
application of this new technique to practical systems with non-uniform flow-fields,
including combustion and propulsion systems such as IC engines, gas turbine inlets,
scramjet combustors, power plant boilers, and various of systems in environmental
monitoring, semiconductor processing, and biomedical diagnostics.
164 CHAPTER SEVEN
The multi-line thermometry method also has great potential for turbulent flow
studies. The sensing concepts can be illustrated by the following example. Let’s assume
the temperature fluctuation of a turbulent flow follows a normal distribution with a mean
temperature of 1500 K and a standard deviation of 250 K. Figure 7.1 shows three
examples of the instantaneous temperature distributions along the LOS measurement path
of 10 cm.
0 2 4 6 8 100
1000
2000
30000
1000
2000
30000
1000
2000
3000
T [K
]T
[K]
T [K
]
x [cm]
t3
t2
t1
Figure 7.1: The temperature distributions along the measurement path of 10 cm at three instantaneous times for a turbulent flow.
Based on the measured LOS absorption data for multiple transitions, the
temperature binning analysis for a turbulent flow follows the same method as described
in section 6.2.2. If we prescribe 8 temperature bins within the temperature range of 500-
2500 K, the exact binning result for any of the above temperature distributions can be
represented by the PDF solution shown in Fig. 7.2.
SUMMARY AND FUTURE WORK 165
500 1000 1500 2000 25000.0
0.1
0.2
0.3
0.4
Pro
babi
lity
T [K]
Figure 7.2: The exact temperature binning result (PDF) for any of the temperature distributions shown in Fig. 7.1.
The profile fitting analysis for a turbulent flow first requires postulating a PDF,
P(T) for the unknown temperature distribution along the LOS measurement path. For
example, the PDF for the turbulent flow shows in Fig. 7.1 can be postulated to be a
Gaussian function as illustrated by Fig. 7.3. The analytical representation is
( )2
221( )2
T
P T eµ
σ
σ π
−−
= , (7.1)
where µ is the mean value and σ the standard deviation of the temperatures along the
measurement path. The standard deviation σ indicates the fluctuation level of the
turbulent flow. Both µ and σ are the unknowns to be solved from the measured LOS
absorption data for multiple transitions.
166 CHAPTER SEVEN
0 500 1000 1500 2000 2500 30000.0000
0.0005
0.0010
0.0015
0.0020
2σ
P
roba
bilit
y P
(T)
T [K]
µ
Figure 7.3: The postulated PDF for the temperature distribution along the LOS measurement path in a turbulent flow.
To facilitate the profile fitting analysis for turbulent flows, the calculation equation
for the integrated absorbance, Eq. (2.5) is modified as
0 0
( ) ( ) ( )L
abs absA PX S T dx PX L S T P T dT∞
= = ⋅ ⋅ ⋅∫ ∫ . (7.2)
Similar to the method described in section 6.2.1, once the postulated PDF, Eq. (7.1) is
substituted into Eq. (7.2), a nonlinear equation set can be established for m transitions as
1 10
2 20
0
( ) ( )
( ) ( )
( ) ( )
abs
abs
m abs m
A PX L S T P T dT
A PX L S T P T dT
A PX L S T P T dT
∞
∞
∞
= ⋅ ⋅ ⋅
= ⋅ ⋅ ⋅
= ⋅ ⋅ ⋅
∫∫
∫
. (7.3)
SUMMARY AND FUTURE WORK 167
This equation set can be solved by nonlinear least-square fitting
( )2
0, 1
min ( ) ( )m
abs i ii
PX L S T P T dT Aµ σ
∞
=
⋅ ⋅ ⋅ −∑ ∫ (7.4)
to obtain the set of µ and σ that best describe the postulated PDF for the temperatures
along the LOS measurement path in the target turbulent flow.
Research efforts for multi-line thermometry might also be devoted to combining
this new technique with traditional tomography. By applying multi-line thermometry
along each LOS of the tomographic arrangement, the non-uniform temperature
distributions might be reconstructed with improved spatial resolution.
168 CHAPTER SEVEN
169
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