LINE-OF-SIGHT ABSORPTION OF H O VAPOR: GAS …hanson.stanford.edu/dissertations/Liu_2006.pdf ·...

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

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Copyright by Xiang Liu 2006 All Rights Reserved

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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)


__________________________________ Mark A. Cappelli


__________________________________ Jay B. Jeffries

Approved for the University Committee on Graduate Studies.

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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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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

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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

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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

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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

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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

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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

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)


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


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


Function Generator


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


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)


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


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)


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)


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)


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


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)


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


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]


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]


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


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)


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


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


100

50

0

-50Dev

. of L

ines

tren

gth

[%]

7320730072807260724072207200718071607140

(SMEAS-STOTH94)/STOTH94



(a)

(b)

T=297K

T=828K

Frequency [cm-1]


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)


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


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

]



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


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


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


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.


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


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


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]


(a) (b)

0.4

0.2

0.0

Abs

orb

ance

7453745274517450Frequency [cm

-1]


0.4

0.2

0.0

Abs

orb

ance

7427742674257424Frequency [cm

-1]


(c) (d)

Line C Line F

Line G Line D

Interference Line

InterferenceLine


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

.[%]


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

.[%]


(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]


0.015

0.010

0.005

0.000

Inte

grat

ed A

rea

[cm

-1]


(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


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


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)


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


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]


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


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


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

. (%

)


(a) (b)

8

6

4504030

It I0Line 1

1A

1B

1C Line 1

1B


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]



0.12

0.08

0.04

0.00Lore

ntzi

an F

WH

M [c

m-1

]



(a) (b)


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]



(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


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]


-0.03

-0.02

-0.01

δ CO

2 [cm

-1at

m-1

]


(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


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 .


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


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]


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


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)


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 --


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 --


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 -- --


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)


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


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


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)


( )

( )

( )

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



= ⋅

= ⋅

= ⋅

∫∫

∫

. (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


( )

( )

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]


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)


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


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


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)


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)


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)


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)


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)


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.


6.5.1.1 “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


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


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


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)


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.


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.


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.


6.6.1.1 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


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)


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]


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


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)


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)


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


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


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.


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)


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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