diode-laser absorption sensors for combustion...

DIODE-LASER ABSORPTION SENSORS FOR

COMBUSTION CONTROL

by

Xin Zhou

July 2005

TSD Report 161

High Temperature Gasdynamics Laboratory Mechanical Engineering Department

Stanford University Stanford, California 94305

ii

Copyright by Xin Zhou 2005

All Rights Reserved

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Abstract

Combustion is the most widely used energy conversion technique in the world. Measurements of

important combustion parameters are critical to understand combustion processes, improve

combustion efficiency and reduce the production of pollutants such as nitrogen oxides. Diode-

laser absorption sensors offer significant opportunities and advantages for in situ measurements

of multiple combustion parameters such as temperature and species concentration due to their

high sensitivity, high spectral resolution, fast time response, robustness and non-intrusive

character. The overall objective of this thesis is to design and develop time-resolved and real-time

tunable diode laser sensors with the potential for combustion control.

A crucial element in the design of a tunable-diode-laser optical-absorption-based sensor is the

selection of optimum transitions. Water vapor is present in ambient air as well as a primary

hydrocarbon combustion product, and thus provides a ubiquitous target for absorption-based

sensors. There are nearly half a million possible water vapor absorption transitions cataloged

between 1 and 2 µm, and an important part of this thesis is the development of a design-rule

approach for absorption transition selection. The strategy and spectroscopic criteria for selecting

optimum wavelength regions and absorption line combinations are developed for two-line

thermometry. The development of this design-rule approach establishes a new paradigm to

optimize tunable diode laser sensors for target applications.

The water vapor spectrum in the 1-2 µm near-infrared region is systematically analyzed to find

the best absorption transition pairs for sensitive measurement of temperature in the target

combustion environment using a single tunable diode laser. The use of a single laser capable of

tuning over two or more water lines can offer advantages over wavelength-multiplexing

techniques and make the system compact, rugged, low cost and simple to operate. Two sensors

are developed in this work. The first sensor is a 1.8 µm, single-laser temperature sensor based on

direct absorption scans. Successful time-resolved measurements in a variety of laboratory and

practical devices are presented and used to identify potential improvements, and design rules for a

second-generation sensor are developed based on the lessons learned. The second generation

sensor is a 1.4 µm, single-laser temperature sensor using water vapor absorption detected by

wavelength-modulation spectroscopy (WMS), which facilitates rapid data analysis and a 2 kHz

real-time data rate in the combustion experiments reported here. As part of the sensor

development, fundamental spectroscopic parameters for the selected transitions are measured to

iv

improve the available databases. Demonstration experiments in a heated cell and a forced

Hencken burner confirm the sensitivity and accuracy of the sensors. The first application of TDL

thermometry to a liquid-fuel swirl-stabilized spray combustor also is presented, illustrating the

potential for noninvasive temperature measurements in harsh, practical environments such as gas

turbine combustors.

The ability of the 1.4 µm temperature sensor to predict the approach to the lean blowout (LBO)

limit is investigated, and active control of thermoacoustic instabilities is successfully

demonstrated in a practical swirl-stabilized flame. These results illustrate the potential of this

sensor for active combustion control.

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Acknowledgements

I am deeply indebted to my advisor, Professor Ron Hanson, for his unwavering support. His

comments have been of greatest help at all times. Without his numerous encouragements,

inspiration, many insightful ideas and suggestions, this work would not be possible. I wish to give

special thanks to Dr. Jay Jeffries for his time, patience, help and great guidance in all the time of

research and writing of this thesis. I would also like to acknowledge the members of my

committee: Prof. Christopher F. Edwards, Prof. Craig T. Bowman and Prof. Piero Pianetta, for

their time and advice.

I would like to thank Prof. Ephraim Gutmark and Dr. Guoqiang Li from University of Cincinnati,

Dr. Tom Jenkins from MetroLaser for their cooperation and help in my research.

I would like to acknowledge the senior students and my colleagues who have provided help and

support during my research work: Micheael Webber, Jian Wang, Scott Sanders, Suhong Kim,

Jonathan Liu, Dan Mattison, Lin Ma, Kent Lyle, Xiang Liu, Ning Xu, Hejie Li, Adam Klingbeil,

Greg Rieker and all members of Hanson group. It is a pleasure to acknowledge the great moments

I spent with my wonderful friends: Liqiang, Xiaojun, Yue, Shuhuai, Xuejiao, Woo Kyung.

I would like to thank my wife, Yuhua, for her love, support, patience, and confidence in me. She

has made my life joyful even during difficult times. I am extremely grateful to my parents

Chunying Wang and Xuezhi Zhou for their constant support, understanding, encouragement and

love all through my life.

This work was supported by the ONR via the University of Cincinnati and the Global Climate

Energy Program at Stanford.

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Table of Contents

Abstract………………………………………………………………………….………….. iii

Acknowledgements..…………………………………………………………….………….. v

Table of Contents……………………………………………………………….………….. vii

List of Tables………………………………………………………………………………... x

List of Figures……………………………………………………………………………….. xi

Chapter 1. Introduction……………………………………………………………….. 1

1.1 Motivation and objectives………………………………………………….. 1

1.2 Scope of the current work………………………………………………….. 3

1.3 Organization of the thesis…………………………………………………... 4

Chapter 2. Theory of absorption spectroscopy…..…………………………………... 5

2.1 Beer-Lambert law…………………….. …………………………………… 5

2.2 Lineshape function…………………………………………….. ………….. 6

2.2.1 Gaussian lineshape function……………………………………. 6

2.2.2 Lorentzian lineshape function………………………………….. 7

2.2.3 Voigt lineshape function………………………………………... 9

2.3 Diode-laser absorption spectroscopy techniques…………………………… 11

2.3.1 Direct absorption spectroscopy…………………………………. 12

2.3.2 Modulation spectroscopy……………………………………...... 22

Chapter 3. Development of design rules for absorption-based sensors…………….. 30

3.1 Spectroscopic database (HITRAN) ………………………………………... 30

3.2 Design rules of selecting optimum transitions for 2-line T sensor…..……... 32

3.3 Selection of optimum transitions for high pressure T sensor…. ………….. 36

3.3.1 Motivation………………………………………………………. 38

3.3.2 Line selection criteria…………………………………………… 40

3.3.3 Summary……………………………………………………..…. 50

3.4 Multiplexing technique…………………………………………………….. 50

3.4.1 Wavelength Division Multiplexing (WDM) …………………… 51

3.4.2 Time Division Multiplexing (TDM) …………………………… 52

3.4.3 Frequency Division Multiplexing (FDM) ……………………… 53

viii

Chapter 4. Temperature sensing using H2O transitions near 1.8 µm……………… 55

4.1 Water, H2O…….…………………………………………………………... 55

4.2 Development of single-laser T sensor (direct absorption) ………………… 57

4.2.1 Selection of water line pairs…………………………………….. 57

4.2.2 Spectroscopy experiments, results and discussions……..……… 63

4.3 Combustion Demonstration………………………………………………… 69

4.3.1 Temperature and concentration measurements………………..… 69

4.3.2 Identification of acoustic instabilities…………………………… 73

4.3.3 Closed-loop control of mean temperature……………………….. 74

4.3.4 Time-resolved measurements in a swirl-spray combustor……... 77

4.4 Summary……………………………………………………………………. 82

Chapter 5. Temperature sensing using H2O transitions near 1.4 µm……….…….. 85

5.1 Motivation……………………………………………………………….… 85

5.2 Development of single-laser T sensor (2f) ………………………………… 87

5.2.1 Line selection……………………………………………………. 87

5.2.2 Spectroscopic verification……………………………………….. 94

5.2.3 2f temperature sensor validation..……………………………….. 103

5.2.4 Real-time capabilities…………...……………………………….. 107

5.3 Combustion Demonstration……………………………...…………………. 111

5.3.1 Identification of acoustic instabilities…………………………… 111

5.3.2 Real-time measurements in a swirl-spray combustor…………… 113

5.3.3 Comparison with 1.8 µm sensor…………………………..…….. 117

5.4 Summary……………………………………………………………………. 120

Chapter 6. Application of fast temperature sensor to combustion control….…….. 121

6.1 Motivation………………………...…….………………………………….. 121

6.2 Swirl-stabilized combustor…. ……………………………………………... 122

6.3 Lean blowout (LBO) prediction…………….……………...…….………… 124

6.3.1 Experimental setup………………………………………………. 124

6.3.2 Results and discussions…………………….……………………. 126

6.4 Combustion instability control………….………………………………….. 139

ix

6.4.1 Experimental setup……………………………………………… 139

6.4.2 Results and discussions….……...……………………………….. 140

6.5 Summary…………………………………………………………………… 145

Chapter 7. Conclusions and future work…………………………………………... 147

7.1

Summary of the use of design rules to identify the optimum transitions for

IC engine applications.……………………………………………………...147

7.2

Design of a single laser absorption sensor for temperature measurements

using direct absorption……………………..……………………………….147

7.3

Design of a single laser absorption sensor for temperature measurements

using WMS………………………………………………………………….149

7.4 Investigation of the 1.4 µm WMS T sensor for combustion control……….. 150

7.5 Potential Plan for future work……………………………………….. 151

Appendix Architecture of the real-time WMS sensor...…..……………………...… 153

References…………………………………………………………………………………… 161

x

List of Tables Chapter 3

Table 3.1 The 14 candidate lines………………………………………………………. 44

Table 3.2 The 16 attractive line pairs………………………………………………….. 46

Chapter 4

Table 4.1 Fundamental vibrations, frequencies, types and description for H2O………. 56

Table 4.2 Assignments of the NIR vibrational absorption spectrum of water………… 57

Table 4.3 Line selection result using the selection criteria in the near-infrared region

based on HITEMP…………………………………………………………... 60

Table 4.4 Candidate H2O line intensity pairs for measurements of temperature and

water concentration in the near-infrared region based on HITEMP………… 60

Table 4.5 Spectroscopic data for the selected H2O line pair…………………………… 67

Chapter 5


water concentration in the 1-2 µm region based on HITTRAN2004……….. 91

Table 5.2 Line selection result using the selection criteria in the near-infrared region

based on HITRAN2004……………………………………………………... 91

Table 5.3 Spectroscopic data for the selected H2O line pair…………………………… 103

Chapter 6

Table 6.1 Different inter, intermediate and outer swirler configurations……………… 124

xi

List of Figures Chapter 2

Figure 2.1 Schematic of typical absorption measurements…………................................ 5

Figure 2.2 Comparison of Gaussian, Lorentzian and Voigt lineshape on a normalized

frequency and intensity scale………..…………………………......................11

Figure 2.3 Schematic of typical scanned-wavelength direct-absorption measurements… 12

Figure 2.4 Schematic of typical direct-absorption measurements………………………. 13

Figure 2.5 Etalon signal vs. time………………………………………………………… 14

Figure 2.6 Calculated Doppler width as a function of temperature for one H2O

transition……………………………………………………………………...15

Figure 2.7 Two different temperature-dependent transitions……………………………. 17

Figure 2.8 Line strength as a function of temperature. Temperature is inferred from the

ratio of integrated areas for two different transitions……………………..….18

Figure 2.9 Line strength ratio sensitivity (E”1-E”2= 1500 cm-1) as a function of

temperature…………………………………………………………………...19

Figure 2.10 Schematic of typical fixed-wavelength direct-absorption measurements…… 21

Figure 2.11 Fixed-wavelength two line technique……………………………………….. 22

Figure 2.12 A typical arrangement for the WMS technique……………………………… 23

Figure 2.13 The Voigt profile and its first three harmonic signals vs. normalized

frequency……………………………………………………………………..25

Figure 2.14 Second harmonic line shape and line center peak height for different “m”… 26

Figure 2.15 Comparison of 2f line shape with and without intensity modulation…. 27

Figure 2.16 Temperature inferred from 2f peak ratio of two different temperature-

dependent transitions…………………………………………………………28

Chapter 3

Figure 3.1

Typical high EGR and Super-charged intake cycles in internal combustion

engine and representative water spectra under two limiting conditions

during the cycle………………………………………………………………

38

Figure 3.2 Survey spectra of H2O at 300 K in the 1~8 µm region based on the HITRAN

database………………………………………………………………………39

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Figure 3.3

The simulated 2f signals for nine of the fourteen lines (1, 2, 5, 8, 10, 11, 12,

13, and 14) for the compression portion of the high EGR (panels a and b)

and the supercharged (panels c and d) cycles using a modulation amplitude

of 0.8cm-1……………………………………………………………………..

43

Figure 3.4

High EGR compression cycle: (a) Simulated 2f ratio, (b) temperature

sensitivity, and (c) temperature uncertainty for the line pair 2 and 5 as a

function of pressure/temperature. (a=0.8cm-1)……………………………….

48

Figure 3.5

Super-charged intake compression cycle: (a) Simulated 2f ratio, (b)

temperature sensitivity, and (c) temperature uncertainty for the line pair 5,

11, 12, 13 and 15 as a function of pressure/temperature. (a=0.8cm-1)………..

49

Figure 3.6 Schematic of the wavelength division multiplexing…………………………. 51

Figure 3.7 Grating separates the colors in incident light………………………………... 51

Figure 3.8 Schematic of Time Division Multiplexing…………………………………... 52

Figure 3.9 Schematic of the Frequency Division Multiplexing…………………………. 53

Chapter 4

Figure 4.1 The structure of water molecule and its three fundamental vibrations……… 56

Figure 4.2 Survey spectra of H2O at 1000 K in the near-infrared region based on the

HITEMP database…………………………………………………………… 56

Figure 4.3

Expanded view of absorption spectra for the selected H2O line pairs in the

near-infrared region based on the HITEMP database; evaluated for P=1

atm, 10% H2O, 90% air……………………………………………………...

61

Figure 4.4 Calculated temperature sensitivity of line strength ratio as a function of

temperature for line pair 2, 5 and 10 based on the HITEMP database……… 62

Figure 4.5 Experimental schematic of the measurement system for determining

spectroscopic parameters……………………………………………………. 64

Figure 4.6 Reduced H2O line-shape (line pair #10) recorded in a static cell at T=944

K, PH2O=17.44 Torr………………………………………………………….. 66

Figure 4.7 Line strength of the transitions contributing to line pair #10 near 1.8 µm at

1000 K based on HITEMP parameters……………………………………… 66

Figure 4.8

Calculated and measured line strengths for the components of line pair #10

as a function of temperature. “Line 2” is the high temperature transition at

5553.86 cm-1; “Line 1” is the low temperature transition at 5554.18 cm-1….

67

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Figure 4.9

The ratio of peak absorbance coefficients, Rpeak(line pair #10), calculated as

a function of temperature for various values of water mole fraction at 1 atm

(based on HITEMP database [Rothman 1998])……………………………...

68

Figure 4.10 The ratio of line strength and peak absorbance coefficients and their

sensitivity to temperature versus temperature for the line pair #10………….69

Figure 4.11 Schematic diagram of the measurement system applied to the Hencken

burner……………………………………………………………………….. 70

Figure 4.12 Measured temperatures in the burned-gas region above a C2H4-air flame in

a 5 cm ×5 cm Hencken burner……………………………………………….71

Figure 4.13 Measured temperatures and its power spectrum in the burned region above

the C2H4-air flame……………………………………………………………73

Figure 4.14 Experimental schematic of the measurement system applied to the Hencken

burner………………………………………………………………………...74

Figure 4.15 Block diagram showing the strategy used for closed-loop control of the

mean temperature…………………………………………………………….75

Figure 4.16 The temperature response to a desired set-point temperature………………. 76

Figure 4.17 The response time of the closed-loop control system………………………. 76

Figure 4.18 Experimental schematic of the measurement system applied to the swirl

spray combustor…………………………………………………………….. 78

Figure 4.19 Reduced line-shapes for gas and liquid fuel………………………………… 79

Figure 4.20 Measured temperatures and its power spectrum in the burned region above

the Propane-air flame (unforced (a) and forced flow (b)).…………………..80

Figure 4.21 Four sensor positions investigated: 1. Top of flame 2. Under flame 3.

Above flame 4. Diagonal…………………………………………………… 81

Figure 4.22 Power spectrum at four sensor positions investigated (Propane)….………. 81

Chapter 5

Figure 5.1 Linestrength of H2O in the 1 to 2 µm spectral region at 1000 K (from

HITRAN 2004 database)…………………………………………………….87

Figure 5.2 Linestrength scaled by values at room temperature as a function of

temperature for H2O lines with various lower state energies………………..88

Figure 5.3

Expanded view of absorption spectra for the four selected H2O line pairs in

the 1.4 µm region based on the HITRAN2004 database; evaluated for P=1

atm, 10% H2O, 90% air……………………………………………………...

92

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Figure 5.4

Expanded view of absorption spectra for the selected H2O line pairs in the

1.8µm region based on the HITRAN2004 database; evaluated for P=1 atm,

10% H2O, 90% air…………………………………………………………...

93


spectroscopic parameters……………………………………………………. 95

Figure 5.6 Sample data (50-scan average) obtained from cell experiment at T = 951 K,

PH2O = 15.47 Torr……………………………………………………………. 96

Figure 5.7 Reduced H2O lineshape recorded in the cell at T = 951 K, PH2O = 15.47

Torr. The low T line is the line with the smaller value of lower-state E”…... 96

Figure 5.8 Line strength of the selected transitions at 1000 K based on HITRAN2004

parameters revealing that the high T line is composed of two lines………… 97

Figure 5.9

Measured integrated absorbance area vs. H2O pressure at T=951K for the

“Low T Line”, “High T Line 1” and “High T Line 2”. The line strength can

be calculated from the slope…………………………………………………

98

Figure 5.10

Measured collision width vs. H2O pressure at T=951K for the “Low T

Line”, “High T Line 1” and “High T Line 2”. The self-broadening

coefficient can be calculated from the slope…………………………………

98

Figure 5.11 Calculated and measured line strengths for the “Low T Line” as a function

of temperature……………………………………………………………….. 100

Figure 5.12 Calculated and measured line strengths for the “High T Line 1” and “High

T Line 2” as a function of temperature……………………………………… 100

Figure 5.13 Calculated and measured self-broadening coefficients for the “Low T Line”

as a function of temperature………………………………………………… 101

Figure 5.14 Calculated and measured self-broadening coefficients for the “High T

Line” as a function of temperature………………………………………….. 101

Figure 5.15 Calculated and measured air-broadening coefficients for the “Low T Line”


Figure 5.16 Calculated and measured air-broadening coefficients for the “High T Line”


Figure 5.17 Schematic of single-laser scanned-wavelength method…………………….. 103

Figure 5.18 Arrangement for the 2f sensor validation experiments……………………… 105

Figure 5.19

Comparison of measured 2f peak ratio with simulated 2f peak ratio (top);

Comparison of measured temperature with thermocouple temperature.

(bottom)……………………………………………………………………...

106

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Figure 5.20

Comparison of measured 2f peak ratio with simulated 2f peak ratio (top);

Comparison of measured temperature with thermocouple temperature.

(bottom)……………………………………………………………………...

107

Figure 5.21 Complete hardware-software framework…………………………………… 108

Figure 5.22 Diagram of the bias-tee……………………………………………………… 108

Figure 5.23 The trigger signal (top) and the laser transmission signal (bottom)………… 109

Figure 5.24 Timing diagram: timing trigger signal (Top), the second-harmonic signal

(Middle) and the acquired signal (Bottom)………………………………….110

Figure 5.25 Schematic diagram of the measurement system applied to a Hencken burner 111

Figure 5.26 Measured temperature and its power spectrum in the burned region above

the C2H4-air flame……………………………………………………………112

Figure 5.27 Schematic diagram of the measurement system applied to the swirl-

stabilized spray combustor…………………………………………………..113

Figure 5.28 Reduced H2O 2f line shapes (single scan) recorded in gas fuel (propane)

and liquid fuel (ethanol)……………………………………………………..114

Figure 5.29 Measured acoustic signal and its power spectrum in the burned region

above the propane-air flame…………………………………………………115


the propane-air flame……………………………………………………….. 115


above the ethanol-air flame………………………………………………….116


the ethanol-air flame…………………………………………………………116

Figure 5.33 Calculated spectroscopic features for water line pairs in the 1.4 µm and 1.8

µm sensors based on HITRAN; XH2O = 10%..................................................117

Figure 5.34 Comparison of the measurement strategy of the 1.4 µm sensor and 1.8 µm

sensor………………………………………………………………………...119

Chapter 6

Figure 6.1 Schematic of swirl-stabilized combustor……………………………………. 123

Figure 6.2 Scheme of the experimental setup…………………………………………... 124

Figure 6.3 Raw data with/without beam steering noise………………..……………….. 125

Figure 6.4 Reduced H2O 2f line shape (single scan) recorded in gas fuel (propane)…... 126

xvi

Figure 6.5 The blowout process for the first set of experiments (air flow rate = 27.3

SCFM)………………………………………………………………………. 127

Figure 6.6

Microphone and 2f sensor result during the lean blowout process for the

first set of experiments. (Air flow rate = 27.3 SCFM). (a) Laser beam:

20mm height from the injector (b) Laser beam: 50mm height from the

injector……………………………………………………………………….

129

Figure 6.7 The blowout process for the second set of experiments (air flow rate=38.7

SCFM)............................................................................................................. 132

Figure 6.8 The blowout process for the third set of experiments (air flow rate= 52.0

SCFM)………………………………………………………………………. 132

Figure 6.9 The blowout process for the fourth set of experiments (air flow rate=

63.9 SCFM) ……………………………………………………...…… 132

Figure 6.10


second set of experiments. (Air flow rate = 38.7 SCFM). (a) Laser beam:


injector……………………………………………………………………….

134

Figure 6.11


third set of experiments. (Air flow rate = 52.0 SCFM). (a) Laser beam:


injector……………………………………………………………………….

136

Figure 6.12


fourth set of experiments. (Air flow rate = 63.9 SCFM). (a) Laser beam:


injector……………………………………………………………………….

138

Figure 6.13 Scheme of the experimental setup…………………………………………... 139

Figure 6.14 2f peak ratio and its power spectra before and after control were applied on

the swirl-spray combustor (Propane/Air)…………………………………… 141

Figure 6.15 Microphone signal and its power spectra before and after control were

applied on the swirl-spray combustor……………………………………….. 142

Figure 6.16 Control performances versus controller time-delay………………………… 144

Figure 6.17 Control performances versus amplifier gain………………………………… 145

Appendix

Figure A.1 A simplified block diagram…………………………………………………. 153

xvii

Figure A.2 Flow chart for the data acquisition and analysis program…………………... 154

1

Chapter 1: Introduction 1.1 Motivation and objectives Combustion is the most widely used energy conversion technique in the world. Therefore

improvements in combustion efficiencies or reduction in harmful combustion emissions could

have an enormous impact on the world’s atmosphere. Measurements of important combustion

parameters are critical to understand the combustion process, improve combustion efficiency and

reduce the production of pollutants such as the nitrogen oxides. Numerous combustion diagnostic

techniques have been developed for measurements of temperature and species concentration, and

fall largely into two strategies: physical probing methods and optical methods. Compared with the

traditional physical probing methods, optical techniques offer significant advantages for non-

intrusive investigation of combustion process. The optical diagnostic methods include passive

emission measurements and active laser-based optical diagnostics. These methods include

traditional scattering techniques of Rayleigh, Mie, and Raman, as well as linear wavelength-

resonant processes such as absorption and laser-induced fluorescence, and non-linear techniques

such as wave-mixing, or coherent anti-strokes Raman scattering, etc. All of these laser-based

measurement schemes have contributed to modern combustion diagnostics. [Kohse-Höinghaus

2002] The continuous (or CW) laser measurement methods can be used for time-resolved

diagnostics and have the potential for real-time measurements. CW optical absorption can be

wavelength-tuned to provide a robust real-time measurement with sufficient data rate for the

potential use for combustion control. This thesis concentrates on the design of such time-resolved

and real-time tunable diode laser sensors with the potential for combustion control.

Modern combustion applications can be improved with real-time control. For many years, there

has been much concern about the reduction of NOx emissions from combustion [Martin 1990;

John 1997]. Such concern has led to the investigation of a number of schemes to reduce NOx

emissions. Lean premixed combustion is one of the effective approaches to reduce NOx

emissions because of lower flame temperatures [Martin 1990]. Unfortunately, this approach has

two major drawbacks: First, it is susceptible to lean blowout (LBO) of combustion, which could

lead to significant potential safety hazards, energy loss, and substantial costs of a power plant

shut-down [Muruganandam 2005], and it is thus important to precisely predict the lean blowout

limit. Second, it is susceptible to thermoacoustic combustion instabilities as a result of the

coupling of heat release to acoustic oscillations [Paschereit 1998; Mcmanus 1993; Docquier

Chapter 1

2

2002], which can lead to decreased combustion efficiency, increased noise pollution, and serious

system performance degradation.

Blowout and instability control are two major areas of concern. Temperature is a fundamental

parameter of combustion systems and a good physics-based control variable [Furlong 1996],

because it is a measure of combustion heat release and determines the overall thermal efficiency.

To meet the requirements of an active control strategy, the sensor system must be able to

determine the states of the combustion system rapidly and accurately [Docquier 2002]. Since

combustion instabilities usually occur with frequencies less than 500 Hz, a kHz real-time speed is

required to provide an effective feedback control signal. A traditional thermocouple sensor has

difficulty meeting such fast time response requirements. Sensor systems based on absorption

spectroscopy techniques are attractive for such applications due to their high sensitivity, high

spectral resolution, fast time response, robustness and non-intrusive character. Furthermore, the

line-of-sight measurements can provide an additional advantage by evaluating a flow-field-

averaged quantity. The present work is aimed at the design of a diode-laser absorption sensor

system for temperature that might be used for blowout and instability control in a practical

combustion control system, e.g., for gas turbine combustors.

There are many reasons that tunable semiconductor diode lasers (TDL) are nearly ideal sources

for CW absorption sensor applications including compact and rugged packaging, low cost,

compatibility with optical fiber and relative ease of use. Improvements in the performance,

reliability and wavelength availability of tunable diode lasers offer the potential to increase

detection sensitivity and accuracy of TDL sensors. Building upon the concepts of time-division

multiplexing (TDW) and wavelength-division multiplexing (WDM), sensors using multiple diode

lasers have been demonstrated in various environments [Allen 1998; Philippe 1993; Webber 2000;

Sanders 2000]. These multiplexing methods have some disadvantages with regard to system

complexity and cost, and chapters 4 and 5 will illustrate the design of a sensor with a single diode

laser.

A good sensor design can lead to remarkably improved sensor performance and accuracy. An

important step in the design of an absorption-based sensor is the line selection. The HITRAN

(High Resolution Transmission Molecular Absorption Database) database [Rothman 2003]

consists of important spectroscopic parameters of specific spectral lines, and has been widely

used to simulate absorption spectra and line selection for molecules present in the atmosphere.

Introduction

3

One goal of this work is to develop the strategy and spectroscopic criteria for selecting optimum

wavelength regions and absorption line combinations for sensor design. The development of such

design rules in this work makes it possible to produce absorption sensors that can achieve

accuracy and performance for a wide range of applications. Chapter 3 illustrates the use of

HITRAN for sensor design and chapter 4 and 5 extends these design rules for single-laser sensors.

The sensors developed in chapters 4 and 5 are then applied to real-time blowout prediction and

instability control. Chapter 4 introduces a 1.8 µm single-laser temperature sensor based on

wavelength-scanned direct-absorption measurement of two adjacent H2O lines. This sensor

system has the desired flexibility, sensitivity, speed and accuracy to be a useful tool for

fundamental and applied combustion monitoring. However, demonstration measurements show

this sensor has limitations; for example, it can not provide a kHz real-time rate due to its

relatively complex data reduction strategy. From the lessons learned with the 1.8 µm single-laser

temperature sensor, the design rules were modified leading to a new 1.4 µm single-laser

temperature sensor (chapter 5) based on a combination of scanned-wavelength and wavelength

modulation spectroscopy (WMS) with 2f detection. A real-time temperature readout rate of 2 kHz

was achieved for the 1.4 µm WMS sensor. This new sensor system offers significant

opportunities and advantages for in situ measurements of temperature for combustion control.

Finally, in chapter 6 a multiple-swirl spray combustor is used for sensor evaluation, leading to the

demonstration of TDL thermometry in a liquid-fuel swirl-stabilized spray flame. The 1.4 µm

WMS sensor is then successfully applied to lean blowout prediction and thermoacoustic

instability control in the swirl-stabilized combustor providing solid evidence that TDL sensing is

especially promising for use in combustion control applications.

1.2 Scope of the current work

The overall objective of this thesis is to develop strategies for sensor design and to extend the

application domains of absorption gas sensing to practical combustion environment e.g. a liquid-

fuel swirl-stabilized combustor. Specific objectives of this thesis are the following:

1. Investigate the water vapor spectrum in the 1~2 µm near-infrared region, develop the

strategy and spectroscopic criteria for selecting optimum wavelength regions and

absorption line combinations. The design rules developed in this work should prove

useful to those interested in temperature sensing using absorption spectroscopy.

Chapter 1

4

2. Explore the use of design rule TDL sensor development by using HITRAN to design and

choose two laser colors to monitor temperature during the compression stroke in an

internal combustion engine. This sensor design project illustrates the concept of design

rules for absorption sensor development.

3. Use the design rule concept to develop a robust temperature sensor for real-time

combustion sensing and control. Two generations of sensors have been investigated for

combustion diagnostics in practical combustion environments, e.g. a liquid-fuel swirl-

stabilized spray combustor. The first generation sensor near 1.8 µm is based on

wavelength-scanned direct absorption, and the second generation sensor near 1.4 µm uses

scanned wavelength modulation spectroscopy. Measurements of pertinent fundamental

spectroscopic parameters for both sensors were made using a heated cell. The

performance of each sensor has been investigated and validated in the laboratory and

demonstrated in liquid-fueled swirl-spray flames.

4. Demonstrate the utility of the second generation TDL sensor for use in a real-time closed-

loop control in a practical combustion system for lean blowout and acoustic instabilities

in a swirl-stabilized combustor.

1.3 Organization of the thesis The fundamentals of high-resolution absorption spectroscopy are introduced in Chapter 2, where

both direct absorption and wavelength-modulation spectroscopy are discussed. Chapter 3

introduces the characteristics of the HITRAN database, and then discusses the design-rule

strategy and spectroscopic criteria for selecting optimum wavelength regions and absorption line

combinations. The concepts developed in chapter 3 make it possible to design absorption sensors

that can achieve high accuracy and performance for a wide range of applications. Chapter 4

presents the development of a first-generation single-laser temperature sensor based on the direct

absorption technique. The sensor design, fundamental parameter measurements, and laboratory

spray combustor demonstrations are presented in detail. In Chapter 5, a second generation

wavelength-scanned WMS sensor is developed with design rules evolved from the lessons

learned from the investigations described in chapter 4, and a direct comparison of these two

sensors is made. Chapter 6 presents the application of the second-generation sensor to combustion

control in a swirl-stabilized spray combustor. Chapter 7 summarizes the thesis and suggests future

work. An appendix summarizes the hardware and software architecture of the real-time second-

generation wavelength-scanned WMS temperature sensor.

5

Chapter 2: Theory of absorption spectroscopy Diode-laser absorption spectroscopy techniques have become one of the most powerful tools for

gas sensing applications. [Arroyo 1993; Baer 1994; Nagali 1997; Kohse-Höinghaus 2002] Sensor

systems based on absorption spectroscopy techniques can offer significant opportunities and

advantages for in situ measurements of multiple flowfield parameters such as temperature,

pressure, velocity and density due to their high sensitivity, high spectral resolution, fast time

response, robustness and non-intrusive character. [Allen 1998; Philippe 1993] Diode-laser

absorption spectroscopy techniques usually fall into one of two categories: direct absorption

spectroscopy and modulation spectroscopy. This chapter will cover the theoretical aspects and the

fundamental principles of both techniques.

2.1 Beer-Lambert law

gas

I0(ν) I(ν)

L

Figure 2.1 Schematic of typical absorption measurements.

The fundamental theoretical principle of absorption spectroscopy is the Beer-Lambert law. This

law describes the relationship between transmitted and incident spectral intensities when the laser

beam passes through a uniform gaseous medium (Fig. 2.1). The equation of Beer-Lambert law is

simple and straightforward:

exp( )v vo v

IT k LI

≡ = ⋅

(2.1)

where Tν is the fractional transmission; I and Io are the transmitted and incident laser intensities;

kν [cm-1] is the spectral absorption coefficient; L[cm] is the path length. The product kν L

Chapter 2

6

represents the spectral absorbance, αν. The spectral absorption coefficient kν [cm-1] comprising Nj

overlapping transitions in a multi-component environment of K species can be expressed as

,, 0,1 1

( ) ( )jNK

j i jv i j ij i

P Tk SX Φ ν ν= =

= −∑ ∑ (2.2)

where P [atm] is the total pressure, Xj is the mole fraction of species j, Si,j [cm-2 atm-1] and Φi,j [cm]

are the linestrength and lineshape of a particular transition i of the species j, respectively.

The area underneath lineshape function Φi,j is normalized to unity so that

, ,0( ) ν 1i j iv v dΦν − ≡∫ (2.3)

2.2 Lineshape function

Broadening mechanisms can be grouped into homogeneous broadening which affects all

molecules in the same way, and inhomogeneous broadening which has different effects on some

groups of molecules. Due to different broadening mechanisms, a specific absorption transition

may be a convolution of multiple lineshape functions. The lineshape function provides important

information since it is a function of many parameters such as pressure, species concentration and

temperature. Three significant lineshape functions (Gaussian, Lorentzian and Voigt) and the

broadening mechanisms they describe are discussed in the following sections.

2.2.1 Gaussian lineshape function

The Gaussian lineshape function arises from inhomogeneous broadening mechanisms such as

Doppler broadening, which is caused by random thermal motion of the absorber molecules.

Statistical mechanics implies that the distribution of molecular speeds within a dilute gas is

Maxwellian; the Doppler lineshape is then described by a classical bell-shaped Gaussian curve:

∆−

−∆

=ΦDD

D ννν

πνν 0

2

2ln4exp2ln2)( (2.4)

Theory of absorption spectroscopy

7

where Dν∆ is the full width at half maximum (FWHM) of the lineshape, called the Doppler

width, and can be calculated using

70 02

8 ln 2 7.1623 10DkT Tmc M

ν ν ν−∆ = = × (2.5)

where 0ν [cm-1] is the linecenter frequency, T [K] is the temperature, and M [a.m.u] is the

molecular weight of the absorber species. The higher the temperature of the gas, the bigger the

Doppler width, thus the broader the line. Doppler width can provide a measure of gas temperature.

The peak height of the Gaussian lineshape function is

02 ln 2( )D

D

νν π

Φ =∆

(2.6)

2.2.2 Lorentzian lineshape function

Natural lifetime broadening and collisional broadening are the dominant homogeneous

broadening mechanisms and produce Lorentzian lineshapes. Natural broadening stems from the

uncertainty in energy of the states with finite lifetime involved in the absorption transition. As

described by the Heisenberg Uncertainty Principle

12

νπτ

∆ ≥ (2.7)

The energy of a photon can not be precisely known due to the finite lifetime of the excited state.

If the absorption line is damped only by the natural lifetime of the energy states, this is termed

“natural” broadening. Natural broadening leads to a Lorentzian lineshape function

( )2

20

1 2( )

2

n

nn

ν

νπ νν ν

∆

Φ =∆ − +

(2.8)

Chapter 2

8

where nν∆ [cm-1] is the “natural” width (FWHM) and 0ν [cm-1] is the linecenter frequency. In

most cases, natural broadening can be neglected due to the relatively long lifetime of the energy

levels.

Collisional broadening is another important homogeneous broadening mechanism. It is produced

by collisions of the emitting or absorbing particle with other particles. Based on two key

assumptions: a.) collisions are binary; b) collision duration is negligible compared to time

between the collisions, the collisional broadening lineshape takes the form of a Lorentzian profile,

( )2

20

1 2( )

2

c

cc

ν

νπ νν ν

∆

Φ =∆ − +

(2.9)

where cν∆ [cm-1] is the collisional width (FWHM) and 0ν [cm-1] is the linecenter frequency.

When collisions occur between different species, we call the process foreign-gas broadening.

When collisions take place between same species, we call it self-broadening. In the limit of

binary collisions, the collision width is proportional to pressure at constant temperature and the

total collision width in a multi-component environment is given by

2 )(C j jj

P Xν γ∆ = ∑ (2.10)

where Xj is the mole fraction of component j, and γj [cm-1 atm-1] is the collisional broadening

coefficient due to perturbation by the jth component. (Note, γj is the half-width at half maximum

per atm of pressure of the partner j) The temperature dependence of γj can be expressed as:

00( ) ( )

j

j j

nTT TT

γ γ =

(2.11)

where T0 is the reference temperature and nj represents the corresponding coefficient of

temperature dependence.


9

The peak height of the Lorentzian lineshape function is

02( )c

c

νν π

Φ =∆

(2.12)

2.2.3 Voigt lineshape function

Doppler broadening often dominates at low pressure, and collisional broadening becomes

predominant at high pressure. In general, the overall broadening is a combination of natural,

collisional and Doppler broadening. If the broadening mechanisms are independent, the lineshape

is given by the Voigt profile.

( ) ( ) ( )V D Cu u duν ν+∞

−∞

Φ = Φ Φ −∫ (2.13)

Defining the Voigt “a” parameter as

ln 2 C

D

a νν∆

=∆

(2.14)

with the nondimensional line position w as

02 ln 2( )

D

wν ν

ν−

=∆

(2.15)

and the integral variable y as

2 ln 2

D

uyν

=∆

(2.16)

then the Voigt function becomes

Chapter 2

10

2 2

02 2 2 2

2 ln 2 exp( ) exp( )( ) ( )( ) ( )V D

D

a y a ydy dya w y a w y

ν νν π π π

+∞ +∞

−∞ −∞

− −Φ = = Φ

∆ + − + −∫ ∫ (2.17)

The Voigt functional form has been the basis for most quantitative analysis in absorption

spectroscopy. Unfortunately, a simple analytic form is not available and so practical systems have

adopted different numerical approximations to the true Voigt function.

The line width (FWHM) of the Voigt lineshape can be estimated using: [Olivero 1977]

( )2 20.5346 0.2166V C C Dν ν ν ν∆ = ∆ + ∆ + ∆ (2.18)

The peak height of Voigt lineshape function can be expressed by: [Mayinger 2001]

01( )V

CED

β βνπ γγ π

−Φ = + ⋅

(2.19)

with( )

ED

C ED

γβγ γ

= +

and ln 2

DED

γγ = where γD and γC are the half-width at half maximum

line widths (HWHM) of the Gaussian and Lorentzian shapes respectively.


11

1.0

0.8

0.6

0.4

0.2

0.0

Φ(ν

)/Φ(ν

0)

-10 -5 0 5 10(ν−ν0)/∆ν

Gaussian profile Lorentzian profile Voigt profile (a=0.1) Voigt profile (a=1) Voigt profile (a=10)

Figure 2.2 Comparison of Gaussian, Lorentzian and Voigt lineshape on a normalized

frequency and intensity scale.

Figure 2.2 shows a comparison of Gaussian, Lorentzian and Voigt lineshape on a normalized

frequency and intensity scale. As can be observed in Figure 2.2, the Gaussian, Voigt (“a”=1) and

Lorentzian lineshape will reach 1% of the peak at 1.3 line widths, 3.9 line widths and 5.2 line

widths from the center, respectively. The Voigt profile shows a Lorentzian-like behavior in the

line wings and a Gaussian-like behavior in the line center. For small Voigt “a” parameter, a → 0,

the Voigt profile grows into the Gaussian profile. For large Voigt “a” parameter, a Lorentzian

profile is recovered.

2.3 Diode-laser absorption spectroscopy techniques

Many highly innovative spectroscopic techniques have been and continue to be demonstrated for

combustion using a wide variety of lasers [Kohse-Höinghaus 2002]. This section focused on two

of the most widely used absorption spectroscopy techniques based on tunable diode lasers: direct

absorption spectroscopy and wavelength modulation spectroscopy. Though somewhat different in

principle, these two techniques both can be used to measure important parameters such as

temperature and species concentration in practical combustion applications. This section will

Chapter 2

12

cover the principle, experimental methods, and the capabilities and limitations of these two

techniques. In addition, the relative merits of the direct absorption technique and the modulation

spectroscopy technique are discussed.

2.3.1 Direct absorption spectroscopy

Basically there are two different experimental methods which have been used for direct

absorption spectroscopy: scanned- and fixed-wavelength direct-absorption techniques. Details of

these two methods for temperature and species concentration measurement will be discussed in

the following subsection.

A. Scanned-wavelength direct absorption spectroscopy

Scanned-wavelength is the most common method in direct absorption spectroscopy. The laser

frequency is tuned over the selected absorption transition and the measured line shape is analyzed

to obtain important information such as absorption line strength and broadening coefficients.

From these spectroscopic measurements practical information can be inferred such as gas

temperature, species concentration, gas velocity, and gas pressure.

Figure 2.3 Schematic of typical scanned-wavelength direct-absorption measurements.


13

6

5

4

3

2

1

0

Sig

nal [

V]

1.00.80.60.40.20.0Time [ms]

Regions used to fit baseline

Transmitted signal Baseline

Region to monitor background signal

Figure 2.4 Schematic of typical direct-absorption measurements.

A typical experimental schematic of direct-absorption measurements is shown in Figure 2.3. The

laser controller, which includes temperature and current controllers, drives the diode laser. A

function generator is used to ramp the laser injection current and thus tune the wavelengths of the

laser over the desired absorption features. Figure 2.4 presents typical transmitted laser intensity

and corresponding absorbance. Note that laser current is intentionally tuned below laser threshold

to measure the background signal. The background signal comes from the detector background

signal, room lights, flame emission and interference signals. This signal should be relatively

constant and small, and is subtracted before we determine absorbance. The incident laser intensity

is obtained by fitting the regions without absorption to a low-order polynomial. As indicated

above, the wing of the Voigt line shape will decrease to 1% of the peak absorbance at 4 line

widths from center frequency. This can be used as “rule of thumb” to select the regions for

baseline fitting.

Chapter 2

14

0.6

0.5

0.4

0.3

0.2

0.1

0.0

Sig

nal [

V]

1.00.80.60.40.20.0Time [ms]

Etalon signal

FSR

Figure 2.5 Etalon signal vs. time.

To transform the transmitted intensity data from the time-domain into the laser wavelength-

domain, a solid etalon with a known free spectral range (FSR) is used (shown in figure 2.5). Such

an etalon is the simplest form of a Fabry-Perot interferometer, in which a beam of light undergoes

multiple reflections between two reflecting surfaces, and whose resulting optical transmission (or

reflection) is periodic in wavelength. The FSR is defined by the relation [Born 1975]

1 1( )2

FSR cmnd

− ≡ (2.20)

where n is the index of refraction of the material between the mirrors, and d is the distance

between the two parallel mirrors. Since the peak-to-peak separation in the etalon trace is constant

(the FSR), it allows a simple transformation between relative frequency and time.

Temperature Measurement

1. Doppler line width

As already mentioned above, the Doppler width can provide a measure of gas temperature.

Temperature is expressed as:


15

2

707.1623 10

DT M νν−

∆= ×

(2.21)

where Dν∆ is the Doppler width, 0ν [cm-1] is the linecenter frequency, and M [a.m.u] is the

molecular weight of the absorber species. Figure 2.6 shows the calculated Doppler width as a

function of temperature for a H2O transition near 1.4um, the resulting curves for other transitions

are similar to this one.

0.05

0.04

0.03

0.02

Dop

pler

Wid

th [c

m-1

]

200015001000500Temperature [K]

Figure 2.6 Calculated Doppler width as a function of temperature for one H2O transition.

The uncertainty of T, represented by the standard deviation σT, can be estimated using Equation

(2.22)

// / ( ) 2

/ / /D

D

TT D

D D D

T dT dT T

ν

ν

σ σσ νσ ν ν ν

∆

∆

∆= ≅ =

∆ ∆ ∆ (2.22)

According to Equation (2.22), the fractional uncertainty in T is twice that of the measured

Doppler width.

As discussed earlier, the line shape is dominated by collisional broadening at a pressure of one

atmosphere. From these Voigt and Lorentzian lineshape functions, it may be difficult in practice

Chapter 2

16

to extract the Doppler width accurately. Therefore, this method is applicable only in cases where

the Doppler width is dominant. For H2O in the NIR, where airγ ~0.05cm-1/atm at 296K, this

would require pressure less than 0.04 atm (30 Torr) for a Doppler width 5 times the collisional

width at 296K. The Doppler-width method works best for low pressure conditions. Hence, for the

applications addressed in this thesis (atmospheric pressure or above), the use of lineshape to infer

temperature is not discussed further.

2. Two-line technique

The two-line technique is the most widely used method for temperature measurement in scanned-

wavelength spectroscopy. The gas temperature is obtained by comparing the line strength of two

different transitions which have different temperature dependence.

The temperature-dependent linestrength [cm-2atm-1] can be expressed in terms of the known

linestrength at a reference temperature T0: 1"

0 0 00

0

0

0

( ) 1 1( ) ( ) exp 1 exp 1 exp( )

Q T T hchcE hcS T S TkTQ T T k T T kT

ν ν−

− − = − − − − (2.23)

where Q(T) is the molecular partition function, h [J sec] is Planck’s constant, c [cm/s] is the speed

of light, k [J/K] is Boltzmann’s constant, and E” [cm-1] is the lower-state energy.

The partition function is determined over a range of temperatures using the following polynomial,

which represents a best fit of a summation over all calculated energy levels:

2 3( )Q T a bT cT dT= + + + (2.24)

The coefficients of the polynomial expression for various species (including H2O) are included in

the HITRAN database. [Rothman 1998]

The temperature can be inferred from the measured ratio of integrated absorbance for two

different temperature-dependent transitions (shown in figure 2.7 and 2.8). Because the two

integrated absorbances are obtained with the same partial pressure of water and same path length,

the ratio of these two integrals reduces simply to the ratio of line strengths, which by Equation

(2.23) is given by


17

( )1

2

1 " "0 11 11 2

2 2 0 2 02

( ) ( , )( ) 1 1exp[ ]( ) ( , )( )

abs

abs

P L S T d S TA S T hcR E EA S T S T k T TP L S T d

ν

ν

ν ννν

Φ = = = = − − − Φ

∫∫

(2.25)

where Pabs [atm] is the partial pressure of the absorbing species, φν [cm] is the line-shape function

of a particular transition, S(T0, νi) is the line strength of the transition centered at νi (cm-1), for the

reference temperature T0; E” is the lower state energy (cm-1), and T is the gas temperature (K).

Note that if the two transitions are sufficiently close to each other in frequency, the last ratio term

of Equation (2.23) may be approximated by 1.

Abs

orba

nce

Frequency

A1

A2

S1(T)

S2(T)=

Integrated Area Ratio Line Strength Ratio

Figure 2.7 Two different temperature-dependent transitions

Chapter 2

18

12x10-3

10

8

6

4

2

0

Line

str

engt

h S

[cm

-2/a

tm]

30002500200015001000500Temperature [K]

5

4

3

2

1

0

Line Strength R

atioS1

S2

Ratio=S1/S2

Figure 2.8 Line strength as a function of temperature. Temperature is inferred from the ratio of

integrated areas for two different transitions

Thus, the temperature of the gas can be obtained using the relation

" "2 1

" "2 01 2 1

2 1 0 0

( )

( ) ( )ln ln( )

hc E EkTS TA hc E E

A S T k T

−=

−+ +

(2.26)

where T0 is the reference temperature for the line strengths. The quantity hc/k has a numerical

value of 1.438 cm K. A1 and A2 are the integrated areas of the absorption lines. E” is the lower

state energy for the given line.


19

8

7

6

5

4

3

2

1

0

Sen

sitiv

ity (

dR/R

)/(d

T/T

)

2500200015001000500Temperature [K]

T=1.44*(E"1-E"2)

Figure 2.9 Line strength ratio sensitivity (E”1-E”2= 1500 cm-1) as a function of temperature.

The relative sensitivity of this ratio to temperature can be obtained by differentiating Equation

(2.25): " "1 2( )/ ( )

/E EdR R hc

dT T k T−

=

(2.27)

It can also be seen from this equation that a line pair with a high lower state energy difference is

desired to have high temperature sensitivity. However, in practice this is limited by two practical

issues. First, because temperature is determined from the ratio of the measured absorbance on two

absorption lines, equal SNR is desired for both measurements. Lines with very high E” have very

small absorbance and the ability to measure the absorbance becomes the upper limit on E”.

Second, lines with small E” have large absorbance in cold boundary layers and this becomes a

practical lower limit on E”.

Line selection is a crucial step in the sensor design. The strategy and spectroscopic criteria for

selecting optimum absorption transitions will be discussed in chapter 3.

Chapter 2

20

Species Concentration Measurement

As mentioned above, the integrated absorbance is proportional to partial pressure; thus, species

concentration can be obtained:

( )( )A AX

P L S TPL S T dν ν= =

⋅ ⋅Φ∫ (2.28)

where P[atm] is the total pressure, L[cm] is the path length, S(T) [cm-2/atm] is the line strength

and A[cm-1] is the integrated area.

There are two important advantages to note regarding the scanned-wavelength method. The first

is that the entire line shape can be well resolved. This is important for four reasons. First, fitting

the entire line shape eliminates line broadening effects, so the ratio of integrated areas is reduced

to a ratio of line strengths which is only a function of temperature; this makes scanned-

wavelength thermometry more robust in hostile environments where gas composition and

pressure change rapidly with time. Second, many fundamental spectroscopic parameters such as

line strength and broadening coefficients can be inferred from the line shape. Thus the scanned-

wavelength method is usually employed to measure and validate the fundamental spectroscopic

parameters in a database. Third, the spectrally resolved line shape can distinguish the contributing

absorbance from nearby transitions. This method is not only applicable to isolated line conditions,

but also well suitable to the situation where overlap occurs. Therefore this method offers the

potential to measure multi-transitions using a single scan. In addition, the absolute species

concentration can be obtained without any calibration. Fourth, the baseline is obtained by fitting

the regions outside the absorption line (i.e., without absorption) to a low-order polynomial, thus

eliminating the need of an extra reference laser beam in the setup.

The second important advantage to note is that the scanned-wavelength method can distinguish

background noise and non-resonant attenuation from resonant gas absorption such as optical

window attenuation and beam steering. The signal interference from emission can be assessed by

scanning the laser below the current threshold. Etalon noise from optical components can be seen

by comparing the transmitted signal to the laser intensity.

However, the scanned-wavelength method also has disadvantages. First, the baseline fit may

become difficult at high pressure conditions where the line is broadened and blended with

neighbors and the limited laser scan range precludes collecting a precise baseline signal. Second,


21

the laser scan range decreases with scan rate, and the need to maintain an acceptable scan range

restricts the resulting frequency bandwidth. Furthermore, the time-consuming nonlinear Voigt fit

will limit the measurement bandwidth.

B. Fixed-wavelength direct absorption spectroscopy

Gas MediaCombiner

Demultiplexer Detector

Figure 2.10 Schematic of typical fixed-wavelength direct-absorption measurements.

A typical arrangement for the fixed-wavelength technique is shown in figure 2.10. Compared

with the scanned-wavelength method, an additional non-resonant reference laser beam is needed

to infer the baseline to account for non-resonant losses from beam steering and window fouling.

A combiner is used to multiplex two laser beams together, so they can pass through the same

measurement path. A demultiplexing technique is also needed to separate the multiplexed laser

beams. Such (de)multiplexing techniques including wavelength division (de)multiplexing, time-

division (de)multiplexing and frequency-division (de)multiplexing will be discussed in detail in

section 3.4.


In the fixed-wavelength technique, the laser wavelength is usually fixed at the transition’s center

frequency. The temperature can be inferred from the measured ratio of peak absorbance for two

different temperature-dependent transitions (shown in figure 2.12). The ratio of two peak

absorbances is given by

1 1

2 1

1 11

2 2 2

( ) ( )( ) ( )

abs

abs

P L S T S THRH P L S T S T

ν ν

ν ν

Φ Φ= = =

Φ Φ (2.29)

where φν [cm] is the line-shape function of a particular transition. The peak height ratio is not

only a function of temperature, but also pressure and mole fraction.

Chapter 2

22

Abs

orba

nce

Frequency

H1

H2

S1(T)Φν1(X, P, T)

S2(T)Φν2(X, P, T)

=

Peak Height Ratio Absorption Coefficient Ratio

H1

H2

=kν1

(T, X, P)

kν2(T, X, P)

Figure 2.11 Fixed-wavelength two line technique


( )HX

P L S Tν

=⋅ ⋅Φ ⋅

(2.30)

where H is the peak absorption. The peak height of Gaussian, Lorentzian and Voigt line shapes

are given by Eqn. (2.6), (2.12) and (2.19), respectively. Thus, the relationship between peak

height and species concentration is more complicated than using integrated absorption via the

scanned-wavelength method.

2.3.2 Modulation spectroscopy

Modulation spectroscopy is a widely used technique for sensitive trace-species detection

[Philippe 1993; Dharamsi 1996; Schilt 2003], and can be used to significantly reduce 1/f noise by

shifting detection to higher frequencies. Modulation spectroscopy is also classified into two


23

categories: wavelength-modulation spectroscopy (WMS) and frequency-modulation spectroscopy

(FMS), according to the relative magnitude of modulation frequency and transition half-width

frequency.

WMS utilizes a modulation frequency less than the half-width frequency of the transition

lineshape. FMS, on the contrary, uses a modulation frequency larger than the half-width

frequency of the transition lineshape. WMS and FMS provide a substantial sensitivity

enhancement compared to direct absorption methods previously discussed.

WMS with detection at 2f is chosen and discussed in this thesis. Numerous descriptions of FMS

can be found in the literature. [Cooper 1987; Trans 1984; Avetisov 1996; Reid 1981; Dharamsi

1996]

Wavelength-modulation spectroscopy (WMS)

Figure 2.12 A typical arrangement for the WMS technique.

A typical arrangement for the measurement by the WMS technique is shown in figure 2.12. A

combination of slow ramp and a fast sinusoidal modulation is used to drive the diode laser. The

laser output frequency can be expressed by:

( )ν( ) ν(t) cos 2 mt a f tπ= + (2.31)

Where ν (t) [cm-1] is the laser center frequency, a [cm-1] is the modulation amplitude and fm [Hz]

is the modulation frequency. The transmission coefficient can be expanded in a Fourier cosine

series:

0( cos(2 )) (ν, )cos( 2 )

n

m n mn

a f t H a n f tτ ν π π=+∞

=+ = ∑ (2.32)

Ramp

Measurement path length

Detector signals to lock-in

Diode laser Controller

Computer

Function generator

Diode Laser CollimatorModulate at f

Lock-in amplifier

Reference signalFunction generator

Harmonic Signal

+

Chapter 2

24

where (ν, )nH a is the nth Fourier coefficient of the transmission coefficient, and they are given by

01(ν, ) ( cos )

2H a a dπ

π τ ν θ θπ

+−= +∫ (2.33)

1(ν, ) ( cos ) cos( )nH a a n dππ τ ν θ θ θ

π+−= + ⋅ ⋅∫ (2.34)

For weak transitions,

( ) 0.05S P X Lφ ν⋅ ⋅ ⋅ ⋅ ≤ (2.35)

The transmission coefficient can be approximated thus:

( )

0

( )( ) [1 ( ) ]( )

LI e S P X LI

α νντ ν φ νν

−= = ≈ − ⋅ ⋅ ⋅ ⋅ (2.36)

And the nth harmonic Fourier coefficient simplifies as

(ν, ) ( cos ) cos( )nS P X LH a a n dπ

π φ ν θ θ θπ

+−

⋅ ⋅ ⋅= − + ⋅ ⋅∫ (2.37)

The analytical expression of the second Fourier coefficient of Gaussian and Lorentzian line shape

are given by [Reid 1981]

(ν, ) ( cos ) cos( )nS P X LH a a n dπ

π φ ν θ θ θπ

+−

⋅ ⋅ ⋅= − + ⋅ ⋅∫ (2.38)

2 (ν, ) ( cos ) cos(2 )S P X LH a a dππ φ ν θ θ θ

π+−

⋅ ⋅ ⋅= − + ⋅ ⋅∫ (2.39)

A Voigt profile and the corresponding 1f, 2f, 3f WMS line shapes are shown in figure 2.13 with a

relative ordinate scale. There are three important points to note: First, the Nth-harmonic line shape

has N+1 turning points; thus the existence of more than N+1 turning points will imply that there

are more than one transition in the spectral region scanned. [Dharamsi 1996] Second, the (N+1)th

harmonic signal has a smaller magnitude than Nth harmonic signal; hence lower harmonics are

usually employed in practice due to their relatively strong signal. Third, the line shapes of even-

numbered harmonics are symmetric about the line center, while the line shapes of odd-numbered

harmonics are asymmetric.


25

-10 -5 0 5 10Normalized Frequency (ν−ν0)/∆ν

Mag

nitu

de (

a.u.

)

-10 -5 0 5 10

Voigt Profile 1f Signal

2f Signal 3f Signal

Figure 2.13 The Voigt profile and its first three harmonic signals vs. normalized frequency

Detection using the signal at the second harmonic (2f) of the modulation frequency is the most

frequently applied method [Philippe 1993], for two reasons: first, the 2f line shape is symmetric

and peaks at line center due to the nature of even function. Second, as mentioned above, the 2f

provides the strongest signal of the even-numbered harmonics.

According to Eqn. (2.37), the second harmonic Fourier coefficient is given by

2 (ν, ) ( cos ) cos(2 )S P X LH a a dππ φ ν θ θ θ

π+−

⋅ ⋅ ⋅= − + ⋅ ⋅∫ (2.40)

The 2f signal depends not only on the transition parameters such as line strength but also depends

on the modulation amplitude “a”. Before further discussion, we first introduce the modulation

depth m, which is an important dimensionless parameter widely used in WMS.

/ 2am

ν=

∆ (2.41)

where a [cm-1] is the modulation amplitude and ∆ν/2 [cm-1] is the half width of the transition.

Chapter 2

26

20x10-3

15

10

5

0

-5

-10

-15

Sig

nal [

a.u.

]

-4 0 4Normalized Frequency (ν−ν0)/∆ν

54321m

m=1 m=2.2 m=3 m=4

Peak at m=2.2

Figure 2.14 Second harmonic line shape and line center peak height for different “m”.

2f line shapes of a Voigt profile are shown in figure 2.14 (left) for 1 4m≤ ≤ . The maximum

amplitude of the 2f signal occurs at line center. The line shape becomes wider as modulation

depth increases. The line center peak height as a function of modulation depth “m” is shown in

figure 2.14 (right). The peak height is maximum at m=2.2, which optimizes the signal-to-noise

ratio.

So far in this section it has been assumed that laser intensity is independent of frequency

modulation. However, for diode lasers it is convenient to modulate the laser wavelength by

modulating the inject current. Injection current modulation also modulates the laser intensity. For

small modulation amplitude, one can assume this intensity modulation is small, however at larger

modulation amplitude, a more detailed treatment is necessary. Philippe and Hanson [Philippe

1993] developed the first model to take into account intensity modulation of the emitted light. A

generalized and analytical theory of Lorentzian profile has been developed and can be found in

refs [Schilt 2003; Kluczynski 1999; Kluczynski 2001; Liu 2004]


27

Following the previous development of Eqn (2.32), the laser output intensity can be modified to

include intensity modulation

( )0 0 0I ( ) ( ) cos 2 mt I i f tν π φ= + + (2.42)

where I0(t) is the laser output intensity, Φ is the phase shift between intensity and frequency

modulation, and i0 is the intensity amplitude around the average laser intensity 0I at a given ν .

The final expression for 2f signal at ν is given by [Philippe 1993]

0 02 3 0 2 1S ( ) ( , ) ( ) ( , ) ( , )

2 2i iH I H Hν ν ν ν ν ν ν ν= − ∆ + ∆ − ∆ (2.43)

20x10-3

15

10

5

0

-5

-10

Sig

nal [

a.u.

]

-10 -5 0 5 10Normalized Frequency (ν−ν0)/∆ν

2f with IM 2f without IM

i0/I0=10%

Figure 2.15 Comparison of 2f line shape with and without intensity modulation.

Figure 2.15 shows a comparison of 2f line shape with and without intensity modulation. The 2f

line shape becomes asymmetric due to intensity modulation. Since 1f and 3f both are odd

functions, which are zero at line center, there is little difference of the 2f signal at line center from

intensity modulation. Thus, for an isolated transition at line center, these modulation effects are

Chapter 2

28

negligible. For this reason, in the experiments reported in this thesis, the line center peak height is

measured and the modulation effects are ignored.


2f P

eak

Rat

ioTemperature

2f S

igna

l

Wavelength

Ratio of 2f peak heightyields gas temperatureλ1

λ2 2f peak height

Figure 2.16 Temperature inferred from 2f peak ratio of two different temperature-dependent

transitions

Similar to the direct absorption technique, WMS uses a two-line signal ratio for temperature

measurements (figure 2.17).

1 11 2 1 1 12

2 2 2 2 2 2 2

( cos ) cos 2( ) ( ) ( ) ( )( , , , , )

( ) ( ) ( ) ( ) ( cos ) cos 2f

a dI H I S TR f T X P a laser

I H I S T a d

π

ππ

π

φ ν θ θ θν ν νν ν ν φ ν θ θ θ

+

−+

−

+ ⋅ ⋅= = =

+ ⋅ ⋅

∫∫

(2.44)

As can be seen in the above equation, the 2f peak height ratio is not only a function of

temperature, but also a function of species concentration, modulation amplitude and pressure

through the effects of line shape function. This obviously complicates the temperature

determination. A numerical simulation is used to provide the relationship between temperature

and 2f peak height ratio. This necessitates accurate knowledge of the spectroscopic parameters.

As pointed out earlier, a major limitation of temperature measurement by WMS is the

dependence of multiple parameters. In some cases, this can be eliminated by the use of suitable

modulation amplitude [Liu 2004] or an appropriate line pair. Line selection will be detailed in

chapter 3. In this section, we will discuss the selection of modulation amplitude. As indicated in

figure 2.14, the 2f peak height is most insensitive to modulation depth “m” (thus line width at


29

fixed modulation amplitude) when m is near 2.2. Therefore the 2f peak height ratio can be

accurately reduced to line strength ratio [Liu 2004] with the optimized modulation amplitudes

(where m~2.2).

It also should be noted that, for simplicity, many hardware-related parameters are not yet taken

into account. Values for a number of parameters related to the instrument hardware are required

in addition to measurements of the 2f signal itself, including the laser intensity, detector setting,

signal amplification, lock-in setting etc. The usual approach is to calibrate the WMS sensor at a

reference condition to eliminate the dependence of hardware-related parameters.


WMS with 2f detection is often used to measure trace species concentration. For precise work,

the 2f sensor may have to be calibrated by the user, which requires careful work. Calibration is

generally performed in either of two ways: from direct absorption, or, from a known gas

concentration.

If the measured species concentration is sufficiently low, the lineshape function become

insensitive to species concentration, and then the species concentration will be directly

proportional to 2f peak height:

2 (ν, )( cos ) cos(2 )

H aXS P L a dπ

π

πφ ν θ θ θ+

−

⋅= −

⋅ ⋅ ⋅ + ⋅ ⋅∫ (2.45)

If calibration and measurement are made at same temperature, the relationship between measured

and calibrated species concentrations is straightforward:

2

2

(ν, )(ν, )

measuremeasure Calib

calib

H aX XH a

= (2.46)

If they are different, numerical integration is necessary to correct for the difference:

2

2

( ) [ ( cos ) cos(2 ) ](ν, )(ν, ) ( ) [ ( cos ) cos(2 ) ]

calib

measure

calib Tmeasuremeasure Calib

calib measure T

S T a dH aX XH a S T a d

ππππ

φ ν θ θ θ

φ ν θ θ θ

+−+−

⋅ + ⋅ ⋅∫= ⋅

⋅ + ⋅ ⋅∫ (2.47)

As previously noted, the 2f peak height is used for the temperature and concentration

measurements. Thus, it is not always necessary to obtain the entire 2f line shape. Similar to the

Chapter 2

30

direct absorption technique, a fixed-wavelength technique can also be used with WMS.

Compared with scanned-wavelength WMS, fixed-wavelength WMS can achieve much faster

measurement response.

The fundamental principles for direct absorption spectroscopy and wavelength modulation

spectroscopy are described in this chapter. Sensor design for both techniques will be discussed in

chapter 3. The work in chapter 4 will illustrate the use of scanned-wavelength direct absorption

for temperature sensing in combustion flame, and the work in chapter 5 will incorporate scanned-

wavelength WMS to provide real-time temperature measurements. Chapter 6 will take advantage

of the real-time capability of this scanned-wavelength modulation spectroscopy sensor for

combustion control applications.

31

Chapter 3: Development of design rules for absorption-based

sensors

An important step in the sensor design is the line selection. A proper selection of the line can

optimize the accuracy and performance of the sensor. The HITRAN (High Resolution

Transmission Molecular Absorption Database) database consists of quantitative spectroscopic

parameters for many of the small molecular constituents of atmosphere, and provides an

important tool for sensor design. This chapter first introduces the characteristics of the HITRAN

database, and then discusses the general strategy and spectroscopic criteria for selecting optimum

wavelength regions and absorption line combinations for a two-line temperature sensor. The

concepts developed here make it possible to design an absorption sensor that can achieve

accuracy and performance goals for a wide range of applications. As an example, the optimum

transitions are selected for a high-pressure temperature (T) sensor using the ratio of two

absorption lines for practical application during compression in an internal combustion engine. In

the final section, several important multiplexing techniques are presented.

3.1 Spectroscopic database (HITRAN)

The HITRAN database [Rothman 2003] began in the 1960s as an effort to model atmospheric

transmission of light by the Air Force Cambridge Research Laboratories (AFCRL). This database

has grown over the past forty years, and the latest HITRAN EDITION 2004 includes 1,789,569

spectral lines and 34,001,811 spectroscopic parameters for 39 molecules. The most important

spectral parameters contained are line position, line intensity, lower state energy, air-broadened

halfwidth, self-broadened halfwidth, temperature-dependence coefficient for air-broadened

halfwidth, air-pressure shift and quantum numbers. These parameters are frequently used by

many researchers to perform spectroscopic theoretical modeling and simulate practical

experiments.

The following table describes the format of spectroscopic parameters in the HITRAN 2004

database: [Rothman 2003]

M I ν S A γ-air γ-self E” n δ 1 1 7154.354 1.55E-23 1.37E-03 .0321 .1770 1789.0428 .53 .01459

V’ V” Q’ Q” Ierr Iref * (flag) g’ g” 1 0 1 0 0 0 8 8 0 8 8 1 354543 311930 3 0.0 0.0

Chapter 3

32

Where:

M Molecule number (HITRAN chronological assignment) I Isotopologue number (Ordering by terrestrial abundance) ν Vacuum wavenumber [cm-1] S Intensity [cm-1/(molecule-cm-2)] at standard 296 K A Einstein-A coefficient [s-1]

γ-air Air-broadened halfwidth (HWHM at 296K) [cm-1/atm] γ-self Self-broadened halfwidth (HWHM at 296K) [cm-1/atm]

E” Lower-state energy [cm-1] n Temperature-dependence coefficient (for γ-air) δ Air-pressure shift [cm-1/atm]

V’ Upper-state “global” quanta V” Lower-state “global” quanta Q’ Upper-state “local” quanta Q” Lower-state “local” quanta Ierr Uncertainty indices (Accuracy for ν, S, γ-air, γ-self, N, δ) Iref Reference indices (References for ν, S, γ-air, γ-self, N, δ)

* (flag) Flag (Pointer to program and data for the case of line mixing) g’ Statistical weight of the upper state g” Statistical weight of the lower state

Note that the units for intensity in HITRAN are cm-1/(molecule-cm-2) at the standard HITRAN

temperature (296 K). This intensity unit [cm-1/(molecule-cm-2)= cm-2/(molecule-cm-3)] is the line

strength [in units of cm-2] normalized by concentration [in units of molecule-cm-3]. For many

applications, it is more convenient to use the unit cm-2/atm, which is the line strength [in units of

cm-2] normalized by pressure [in units of atm]. The relationship between these two units is

1 2 3

2 [ /( )] [ ][ / ][ ]

i

i

S cm molecule cm n molecule cmS cm atmp atm

− − −− − −

= (3.1)

This can be further simplified by the ideal gas equation to

21 3 1 2

2 7.339 10 [( ) / ] [ /( )][ / ][ ]

molecule cm K atm S cm molecule cmS cm atmT K

− − −− × − −

= (3.2)

This equation can be used to convert the HITRAN entry for S(296K) to S(cm-2/atm) at 296 K.

Calculations of S(T), cm-2/atm, are then done with Eqn. (2.23).

Development of design rules for absorption-based sensors

33

3.2 Design rules of selecting optimum transitions for 2-line T sensor

An important step in sensor design is the line selection. Senor performance can be greatly

improved by selecting optimum transitions. As mentioned above, the HITRAN database contains

1,789,569 transitions; it is a tedious and impractical process to pick a transition line-by-line using

a manual method. An efficient and systematic computer-based method is developed and used here

to select the appropriate transitions. The strategy and spectroscopic criteria for selecting optimum

absorption transitions are discussed in this section. To elucidate useful design rules and concepts,

this section will concentrate on the transition selections for absorption spectroscopy thermometry

based on the two-line absorption technique. The design rules discussed here should prove useful

to those interested in temperature sensing using absorption spectroscopy. However, it should be

pointed out that the selection of transitions for two-line ratio thermometry can be complicated by

many interrelated factors which determine the final sensor performance of a particular line pair.

Among the most important factors that must be considered in the selection of transitions are: (a)

absorption strength, (b) appropriate spectral separation, (c) temperature sensitivity, (d) lack of

interference from nearby transitions, and (e) effects of nonuniformities such as boundary layers. It

should be stressed that the interaction among all these factors has a considerable influence on the

selection process, and thus far no single figure of merit is derived to simplify this step. Thus, the

optimum transitions for the line pair are chosen case-by-case.

There are multiple different spectroscopic criteria one must consider to choose a line pair.

Understanding the definitions of the various spectroscopic parameters and how they affect the

sensor performance will greatly simplify the selection process. Because the two integrated

absorbances are obtained with the same partial pressure of water and same path length, the ratio

of these two integrals reduces simply to the ratio of line strengths, which is given by Equation

(2.25) The relative sensitivity of this ratio to temperature can be obtained by Equation (2.27):

The following selection criteria are developed:

Criterion 1: Both lines need sufficient absorption over the selected temperature

range.

The peak absorption of the transition is

Chapter 3

34

, ,( )v peak i abs v peakS T P x Lα φ= ⋅ ⋅ ⋅ ⋅ (3.3)

where P[atm] is the total static pressure, Si(T) [cm-2/atm] is the line strength, L [cm] is the path

length, φν,peak is the peak value of line-shape function, and xabs is the mole fraction of absorbers.

An empirical approximation to the Voigt profile [Whiting 1976] is used here to calculate the peak

value of the line-shape function.

We assume a noise level (NL), and a desired signal/noise ratio (SNR), which requires that the

peak absorption be greater than (NL)*(SNR). In addition, the peak absorption must be less than

about 0.8 to avoid experimental difficulties associated with “optically-thick” measurements.

For a path length of L (cm) and absorber concentration range between xabs,min and xabs,max at a

pressure of P (atm),

, ,min ,( ) ( ) ( )v peak i abs v peakS T P x L NL SNRα φ= ⋅ ⋅ ⋅ ⋅ ≥ ⋅ (3.4)

, ,max ,( ) 0.8v peak i abs v peakS T P x Lα φ= ⋅ ⋅ ⋅ ⋅ ≤ (3.5)

so that the constraint on the product of line strength and line-shape function becomes

,,min ,max

( ) ( ) 0.8( )i v peakabs abs

NL SNR S TP x L P x L

φ⋅≤ ⋅ ≤

⋅ ⋅ ⋅ ⋅ (3.6)

in the temperature range Tmin ~ Tmax K.

Criterion 2: The absorption ratio should be single-valued with temperature and the

line strengths of the two lines should be similar.

The absorption ratio is best determined if the measurement uncertainty is similar for the two

absorption transitions. A line strength ratio between R=0.2 and R=5 is thus imposed. Although

the limits of R are somewhat arbitrary, this criterion ensures that the measured absorbance using

the two transitions have similar signal-to-noise ratio (SNR).


35

Criterion 3: The two lines should have sufficiently different lower state energy E″ to

yield an absorption ratio that is sensitive to the probed temperature.

From Equation (2.25), the line strength ratio can be obtained from the ratio of the integrated

absorbance area for two transitions.

1 1

2 2

( )( )( )

S T AR TS T A

= =

(3.7)

This ratio is a function of two integrated absorbance areas A1 and A2, which are measured from

the best Voigt fit to the line-shape profile. The uncertainty of R, represented by the standard

deviation σR, is then calculated using the error propagation equation, [Bevington 1992]

1 2 1 2

2 22 2 2 2

1 2 1 2

2R A A A AR R R RA A A A

σ σ σ σ ∂ ∂ ∂ ∂

≅ + + ∂ ∂ ∂ ∂ (3.8)

The partial derivatives in Equation (3.8) are represented as follows:

11 AR

AR

=∂∂

22 AR

AR

−=∂

(3.9)

Assuming the integrated absorbance areas A1 and A2 are uncorrelated; dR/R can be estimated

using Equation (3.10),

1 2

2 2

1 2

A ARdRR R A A

σ σσ ≈ ≅ +

(3.10)

The sensitivity of line strength ratio to temperature is obtained from Equation (2.27). It is

generally desirable that the temperature sensitivity be as high as possible, resulting in a more

accurate sensor.

If the integrated absorbance can be determined within X%, the criteria to obtain a temperature

accuracy of Y% in the temperature range of Tmin - Tmax K, constrains the minimum lower state

energy difference

Chapter 3

36

" " "1 2 max

/ %* 2 1* */ % 1.4388i

dR R k XE E E T TdT T hc Y

∆ = − ≥ = (cm-1) (3.11)

It can also be seen from this equation that a line pair with a large lower state energy difference is

desired to have high temperature sensitivity.

Criterion 4: The two lines should be free of significant interference from nearby

transitions.

Some transitions will be rejected because of the appearance of adjacent features which can

produce interference. The remaining transitions are regarded as the promising features for

temperature measurement.

Recall that the HITRAN/HITEMP database contains 1,789,569 transitions for all gases, and thus

it is possible that numerous transitions can meet the selection criteria above. This has led to the

development of the following two criteria, either (or both) of which can be applied to find the

most promising line pair.

Criterion 5: The two lines are desired to have same lineshape function.

As was described in the previous chapter, lineshape function is a very important factor in

spectroscopy experiment. In the fixed-wavelength direct absorption and WMS schemes, the peak

ratio is not only the function of temperature, but also depends on pressure and mole fraction due

to the effect of the lineshape function. This leads to complications and potentially added

uncertainty for the measurements. To overcome this difficulty, two lines which have enarly

identical lineshape function can be selected. More specifically, we can examine

HITRAN/HITEMP database to select two lines which have nearly the same air-broadened

halfwidth, self-broadened halfwidth and temperature-dependence coefficients. Thus effects of the

lineshape function can be cancelled in Eqn. (2.29) and (2.44), and the ratio is simplified to a

function of temperature alone.


37

Criterion 6: The two lines are close enough to be scanned by a single laser.

Two-line absorption can be completed using two separate lasers multiplexed onto a single optical

path. Such multiplexing techniques will be discussed in the 3.4 section. However, these dual (or

multi)-laser methods have some disadvantages with regard to system complexity and cost. A

single-laser concept can offer a number of essential advantages. Using a single-laser allows a

much easier experimental setup and less cost with similar performance compared to the

multiplexing technique. For a single-laser sensor, the line selection process includes criteria to

insure the selected lines are close enough together in wavelength to be encompassed by a single-

laser scan, yet far enough apart to avoid overlap.

In this section, various criteria for line selection have been suggested. From this screening, the

transitions most applicable to temperature sensing emerge. It is clear that studies with different

criteria may yield different line pair choices, and it is hoped that presentation of the current

selection guideline logic will facilitate future investigations.

Chapter 4 and 5 will present the developments of single-laser temperature sensors using the

design rules developed here. In the following sections, the design rules are extended to high

pressure applications using a wavelength-multiplexed strategy.

3.3 Selection of optimum transitions for high pressure T sensor

Although the discussion in section 3.2 is based on direct absorption, the design rules can be easily

extended to other measurement strategies. In this section, the design rules are refined for the

selection of optimum H2O line pairs for a specific application, namely temperature measurements

in the compression phase of an IC engine (e.g., approximately 300-1100 K, 0.5atm-50atm). At

present we limit the selection to transitions in the 1.25-1.65 µm region where telecommunication

lasers and fibers are currently available. The water vapor spectrum in the 1.25-1.65 µm region is

systematically analyzed to find the best absorption transitions for sensitive measurement of in-

cylinder gas temperature over short path lengths for an internal combustion engine application.

The strategy and spectroscopic criteria are discussed for selection of optimum wavelength regions

and absorption line combinations for the time-varying pressures and temperatures expected

during the compression portion of an engine cycle. We have identified 14 water transitions in this

spectral region as promising for this target application. Based on these findings, 16 potential line

Chapter 3

38

pairs of H2O were considered for a wavelength-modulated absorption sensor for in-cylinder gas

temperature during the compression stroke. As part of the sensor development effort, the

expected performance is modeled for a variety of engine cycles.

3.3.1 Motivation

The IC engine is the most common source for vehicle power, and thus improvements in engine

performance to reduce pollutant emissions or increase fuel economy can have a tremendous

impact on the environment and the world’s energy resources. New engine concepts involve lower

temperature combustion to reduce NOx emissions and novel ignition processes to improve fuel

economy. Development of these new concepts would be facilitated by crank angle-resolved in-

cylinder temperature measurements made across a short path-length via an intrusive optical probe.

Spectroscopy-based sensors are attractive for this application, owing to their potentially fast time

response and species specificity, but must be designed to take into account the time-varying

pressure and temperature of typical IC engine cycles. For example, the variable pressure

broadening complicates absorption measurements and introduces varying degrees of overlap of

absorption transitions with neighboring transitions.

1200

1000

800

600

400

Tem

pera

ture

[K]

5040302010Pressure [atm]

72207210720071907180Frequency [cm

-1]

Super-charged intake High EGR

Abs

orba

nce

Figure 3.1 Typical high EGR and Super-charged intake cycles in internal combustion engine and

representative water spectra under two limiting conditions during the cycle.


39

Figure 3.1 presents two extreme examples of IC engine compression cycles, one with high

temperatures from large exhaust gas recirculation (High EGR) and one with very high pressure

from a super-charged intake. The inset in Figure 3.1 illustrates the pressure broadened spectrum

of a segment of the water vapor spectrum at the limiting pressure values of the super-charged

cycle, i.e. at 1 and 50 atm. The well-resolved water vapor spectrum at 1 atm becomes a blended,

highly overlapped spectrum at 50 atm without the ability to measure the zero-absorption base line

by scanning off-resonance. Second, the speed of an IC engine cycle can be very rapid (>2400

rpm), and a temperature measurement requires a sensor bandwidth of >15kHz to resolve one

degree of crank angle.

10-4

10-3

10-2

10-1

100

101

102

S[cm

-2/a

tm]

87654321Wavelength [µm]

H2O @ 300K

Telecommunications lasers available

1.25-1.65 µm(mature technology)

Quantum Cascade Lasers

QC lasers available5.0-5.4µm and near 7µm(developing technology)

ν2ν1

2ν2

ν2+ν3ν1+ν2

2ν12ν3

ν1+ν3

ν3ν2

ν1

2ν2

ν2+ν3ν1+ν2

2ν12ν3

ν1+ν3

ν3

Figure 3.2. Survey spectra of H2O at 300 K in the 1~8 µm region based on the HITRAN database.

Water is an attractive species for TDL thermometry, as it is naturally present in humid air, it is

one of the primary hydrocarbon combustion products, and it has a strong absorption spectrum.

Figure 3.2 graphically depicts the line strengths of water over a range of wavelengths from 1 to 8

µm at a temperature of 300 K. The many strong absorption transitions provide numerous options

for measurements in combustion environments. Although mid-infrared (MIR) transitions in the

fundamental vibration bands are 10 times stronger than the combination and overtone vibrational

transitions in the near infrared (NIR), laser and fiber technology is less mature in the MIR than in

the NIR. Accordingly, in the current work we limit the choice of transitions to the 1.25~1.65 µm

region (7788 H2O transitions in HITRAN 2004) where the telecommunication lasers and fiber

optics technology are well-developed and readily available. Telecommunication laser and fiber

technologies offer many attractive features, including advanced laser performance, simple

installation, easy laser beam alignment, improved ruggedness and flexibility, and reduced overall

system cost.

Chapter 3

40

There are two alternative strategies for fast time-resolved absorption measurements: a

wavelength-agile (wide-scan tuning at high speed) strategy and a wavelength-multiplexed

strategy. The wavelength-agile strategy is described in the literature (see papers 4-8), and Sanders

et al [Sanders 2003] have recently applied wavelength-agile strategy to IC engine compression

with some success. Here we examine the alternative strategy, wavelength-multiplexed absorption

for near-real-time temperature sensing.

The combination and overtone vibrational absorption transitions in the NIR have only a few

percent absorption across the diameter of a modern IC engine cylinder for intake air with a

natural range of humidity, and proportionally less absorption for measurements made over

reduced lengths (e.g. 1 cm) to provide spatially resolved results. Therefore, we examine the use of

wavelength modulation spectroscopy (WMS) to improve the signal-to-noise ratio (SNR) of the

NIR absorption measurements. WMS is an extremely sensitive technique which has been

successfully demonstrated in gas-sensing applications. [Liu 2004; Reid 1981; Silver 1999; Hovde

2001; Aizawa 2001; Bullock 1997] The time-varying pressure in an IC engine cycle produces a

time-varying absorption line width, and hence the WMS absorption measurements will have a

time-varying absorption modulation depth. The target transitions also will have time-varying

blending with their neighbors. Thus, a simulation computer program is developed to predict the

time-varying WMS signal as a function of crank angle for a specific variation of temperature and

pressure during the compression stroke. The WMS measurement principles needed for the

variable pressure IC engine application are examined in chapter 2.

3.3.2 Line selection criteria

The following selection criteria are developed:

Criterion 1: Both lines need sufficient absorption over the entire cycle.

The peak absorbance of a single H2O transition is

2, ,( )v peak i H O v peakS T P x Lα φ= ⋅ ⋅ ⋅ ⋅ (3.19) where , peakνφ is the peak value of line-shape function and XH2O is the mole fraction of water. An

empirical approximation to the Voigt profile [Whiting 1976] is used to calculate the peak value of

the line-shape function.


41

We assume a minimum detectable absorbance of 2 × 10-4, which together with a desired

signal/noise ratio of 10 requires that the peak absorbance be greater than 2×10-3. Anticipating the

need for spatially resolved measurements, we assume a typical desired path length of L = 1 cm

with intake air at 50% relative humidity, i.e.,

2

3, ,( ) 1 2 10peak i H o peakS T P x cmν να φ −= ⋅ ⋅ ⋅ ⋅ ≥ × (3.20)

in the entire compression cycle with a temperature range of about 300 – 1100 K and a pressure

range of about 0.5 atm – 50 atm. Measurements over longer path lengths have larger absorbance

and can be performed with the same transitions.

A search of the HITRAN2004 database [Rothman 2003] reveals a total of 139 H2O transitions

that provide sufficient absorption in the 1.25-1.65 µm NIR region, over the range of temperature

and pressure considered.

Criterion 2: The lines should be free of significant interference from nearby

transitions.

For applications such as the compression in IC-engines, the time varying pressure and

temperature produces time-varying absorption line strengths and line-shape functions. Thus, the

degree of interference from neighboring transitions varies with time (crank angle). Of the 139

candidate transitions, 107 are rejected because of significant interference from adjacent features.

For the P/T engine cycles shown in Fig. 3.1, collisional broadening dominates the line-shape. The

collisional broadening of a typical water vapor transition is airγ ~0.05cm-1/atm at 300K; thus, if

the candidate line has a neighboring transition within 2.5 cm-1, there will be significant overlap at

the highest pressures. The degree of interference depends on the relative line strengths during the

cycle. The simplest selection model would only retain lines which are completely isolated (no

neighbors within 2.5 cm-1; however this design rule is too restrictive. For example, it is possible

to have constructive interference. If the neighboring line has an E” nearly the same as the

candidate transition, the pressure broadening can increase the total absorption of the pressure-

blended lines. On the other hand, if the neighboring lines have quite different E” the pressure-

blended absorption feature has a very different temperature dependence. Therefore, we examined

simulated spectra for all of the candidate transitions at selected P/T points in the example engine

compression cycle and excluded candidates with significant interference from neighbor

Chapter 3

42

transitions, with one exception: 1) if the two lines are close enough together (~0.4 cm-1) that they

blend into a single feature at modest pressures and 2) if the lower state energy of the neighbor is

similar the candidate line is not eliminated for interference. An example of such blended lines

will be discussed in detail below. Criterion 2 reduces the potential number of candidates to 32

lines.

Criterion 3: The 2f signal of absorption lines should have high SNR over the

compression cycle.

The strongest 2f signal is obtained when modulation amplitude “a” is equal to 2.2 times the half-

width of the absorbance line. Since the modulation depth “m” will be much less than 2.2 for high

pressure applications, it is desirable to increase “a” to improve SNR. Our past laboratory

experiments [Liu 2004] determine that “a” values as large as 0.8 cm-1 can be achieved with

modern telecommunication diode lasers at the needed modulation frequency (~ 80 kHz). Hence

the simulations are based on fixed modulation amplitude “a” = 0.8 cm-1. For this value of “a”, the

2f signal strength is sacrificed at the low pressure end due to the over-modulation (m>2.2) in an

attempt to extract useful signal at the highest pressures due to under-modulation. Thus, a proper

choice of “a” is essential for the sensor performance and should be matched with the target engine

cycle.

The 2f signals of the 32 candidate lines are calculated over the high EGR and super-charged

intake compression cycle using a modulation amplitude a=0.8cm-1. From past laboratory

experiments [Liu 2004] we determine an optimistic detection limit to be about 5×10-5 in the units

of Equation (3.21) with a laser power of 5 mW, which is used in the simulation.

2(ν, ) cos(2 )( ) ( cos )i ii

P X LH a dS T a θ θ

πφ ν θ

ππ

⋅ ⋅=− ⋅ ⋅+∑

+−∫ (3.21)

A desired SNR ≥ 10 is imposed during the compression intake. There are 14 candidate lines

(listed in table 3.1) which satisfy criteria 1-3. Lines 1 and 2 (and lines 11 and 12) are only

separated by 0.33 cm-1 (0.18 cm-1). These two pairs of transitions are examples of the pressure-

blended lines with similar E” mentioned above. The other ten candidate transitions in Table 3.1

are all well-isolated individual transitions which could be used in pressure-broadened applications.

Figures 3.3 illustrate the simulated 2f signals for nine of the fourteen lines (1, 2, 5, 8, 10, 11, 12,

13, and 14) for the compression portion of the high EGR (panels a and b) and the super-charged


43

(panels c and d) cycles using a modulation amplitude of 0.8cm-1. Note that lines 1&2 in panels a

and c have the lowest internal energy, and thus have the largest signals at low temperature. The

highest temperatures in the compression stroke of the IC engine correspond to the largest

pressures, where these two lines have been collision-broadened into a single feature. Note that

without this broadening the signal size at the highest temperatures would be too small to retain

these low E” lines as potential candidates. The simulated signals from the collisional blending of

a pair of higher E” lines (11 and 12) is also illustrated in Fig 3.3 panels a and c. These lines do

not have significantly different signals than for the isolated line examples shown in Fig. 3.3

panels b and d.

25x10-3

20

15

10

5

0

2f p

eak

heig

ht


(1) 1405 nm (2) 1405 nm (11) 1429 nm (12) 1429 nm

High EGR

a = 0.8 cm-1

SNR = 10

25x10-3

20

15

10

5

0

2f p

eak

he

ight


(1) 1405 nm (2) 1405 nm (11) 1429 nm (12) 1429 nm

Super-charged intake

a = 0.8 cm-1

SNR = 10

25x10-3

20

15

10

5

0

2f p

eak

heig

ht


(5) 1388 nm (8) 1350 nm (10) 1392 nm (13) 1347 nm (14) 1345 nm

High EGR

a = 0.8 cm-1

SNR = 10

25x10-3

20

15

10

5

0

2f p

eak

heig

ht


(5) 1388 nm (8) 1350 nm (10) 1392 nm (13) 1347 nm (14) 1345 nm


a = 0.8 cm-1

SNR = 10

a

dc

b25x10

-3

20

15

10

5

0

2f p

eak

heig

ht


(1) 1405 nm (2) 1405 nm (11) 1429 nm (12) 1429 nm

High EGR

a = 0.8 cm-1

SNR = 10

25x10-3

20

15

10

5

0

2f p

eak

he

ight


(1) 1405 nm (2) 1405 nm (11) 1429 nm (12) 1429 nm


a = 0.8 cm-1

SNR = 10

25x10-3

20

15

10

5

0

2f p

eak

heig

ht


(5) 1388 nm (8) 1350 nm (10) 1392 nm (13) 1347 nm (14) 1345 nm

High EGR

a = 0.8 cm-1

SNR = 10

25x10-3

20

15

10

5

0

2f p

eak

heig

ht


(5) 1388 nm (8) 1350 nm (10) 1392 nm (13) 1347 nm (14) 1345 nm


a = 0.8 cm-1

SNR = 10

25x10-3

20

15

10

5

0

2f p

eak

heig

ht


(1) 1405 nm (2) 1405 nm (11) 1429 nm (12) 1429 nm

High EGR

a = 0.8 cm-1

SNR = 10

25x10-3

20

15

10

5

0

2f p

eak

he

ight


(1) 1405 nm (2) 1405 nm (11) 1429 nm (12) 1429 nm


a = 0.8 cm-1

SNR = 10

25x10-3

20

15

10

5

0

2f p

eak

heig

ht


(5) 1388 nm (8) 1350 nm (10) 1392 nm (13) 1347 nm (14) 1345 nm

High EGR

a = 0.8 cm-1

SNR = 10

25x10-3

20

15

10

5

0

2f p

eak

heig

ht


(5) 1388 nm (8) 1350 nm (10) 1392 nm (13) 1347 nm (14) 1345 nm


a = 0.8 cm-1

SNR = 10

a

dc

b

Figure 3.3 The simulated 2f signals for nine of the fourteen lines (1, 2, 5, 8, 10, 11, 12, 13, and 14)

for the compression portion of the high EGR (panels a and b) and the supercharged (panels c and

d) cycles using a modulation amplitude of 0.8cm-1.

Chapter 3

44

Criterion 4: Minimum temperature sensitivity of 2 line ratio.

The 14 candidate lines in Table 3.1 are combined into line pairs for two-line ratio thermometry as

shown in Eqn. (2.44). The temperature sensitivity is best for the largest difference

in " "1 2"E E E∆ = − . [Zhou 2003] The minimum "E∆ we accept is 300 cm-1. This reduces the

number of potential line pairs from 91 line pairs to 54 line pairs as indicated in Table 3.1. The

collisionally blended lines 1&2 and 11&12 are each considered as a single feature, reducing the

number of potential line pairs to 37.

Table 3.1 The 14 candidate lines.

Line E” [cm-1] λ [nm] f [cm-1] Potential line pairs

(involving this line as Low E” line)

1 399 1404.94 7117.75 9 2 447 1405.00 7117.42 3 586 1409.51 7094.68 6 4 649 1412.32 7080.57 4 5 742 1388.14 7203.89 4 6 744 1414.13 7071.48 4 7 782 1417.59 7054.23 3 8 920 1350.42 7405.11 3 9 920 1418.91 7047.68 3

10 1045 1391.67 7185.60 1 11 1294 1428.98 6997.99 12 1327 1428.95 6998.17 13 1327 1346.59 7426.14 14 1558 1344.88 7435.62

Criterion 5: The 2f signal ratio should be single-valued with temperature.

From Equation (2.44), the ratio of 2f signals is closely related to ratio of the individual line

strengths; note that this simple picture neglects blending of neighboring features, and thus a more

complex simulation is required for quantitative comparison. Simulations of the 2f signals were

calculated by our computer model including pressure broadening assuming air colliders. The

quantitative spectroscopy is taken from the 2004 version of the HITRAN database [Rothman


45

2003] for the candidate lines (and their neighbors) and calculated for the P & T expected in the

extreme compression cycles (high EGR and super-charged intake) shown in figure 3.1. Ratios of

these signals versus temperature (and pressure) during these candidate cycles were examined to

estimate performance as a temperature sensor. Based on these simulations, 2 line pairs are

rejected due to the multi-valued behavior with temperature. There remain a total of 35 line pairs

which satisfy criteria 1-5.

Criterion 6: The 2f signal ratio should have good temperature sensitivity and

measurement accuracy.

Using the spectroscopic parameters data in HITRAN, the 2f WMS signals were calculated for the

two compression cycles to evaluate the potential expected uncertainty of sensors based on the 35

line pairs. We estimate the temperature uncertainty as follows:

First, the 2f peak ratio can be obtained from

(2 ) "(2 ) "

peak

peak

f HHighE LineRf LLowE Line

= =

(3.22)

Second, the uncertainty of R, represented by the standard deviation Rσ , is then calculated

[Bevington 1992]:

2 22 2 2 22R H L HL

R R R RH L H L

σ σ σ σ∂ ∂ ∂ ∂ ≅ + + ∂ ∂ ∂ ∂ (3.23)

Where Hσ and Lσ are the estimates for potential measurement uncertainties of 2f peak heights

(high E” line & low E” line). We assume Hσ = Lσ = Mσ , where Mσ is the measured noise

floor (5×10-5 in units defined earlier). The partial derivatives in Equation (3.23) are represented

as follows:

R RH H

∂=

∂

R RL L

∂= −

∂ (3.24)

Assuming the 2f peak heights H and L are uncorrelated; The measurement uncertainty Rσ

becomes,

21 1 21 1H RR M ML L Lσ σ σ = + = +

(3.25)

Chapter 3

46

Thus the measured temperature uncertainty Tσ can be estimated

1 1 21/ / (2 ) "peak

R RT MdR dT dR dT f LowE Line

σσ σ≈ = +

(3.26)

The potential uncertainty of sensors based on the promising 35 line pairs are simulated using Eqn.

(3.26) for both high EGR and super-charged intake cycles. If we require the maximum

temperature uncertainty to be less than 30 K and average temperature uncertainty less than 10 K

during both high EGR and super-charged intake cycle, the potential line pairs are reduced to 16,

as summarized in table 3.2. These are regarded as the most promising water vapor features for

temperature measurement in the compression phase of the IC engine using the selection criteria

(1-6) noted above. Obviously, studies with different criteria may yield other line pair choices.

However, it is hoped that presentation of the current selection guidelines will facilitate future

investigations of other H2O transitions and other species.

Table 3.2 The 16 attractive line pairs.

Super-charged intake High EGR Line pair

Low E” Line

High E” Line Avg.

Tσ [K] Max Tσ [K] Avg. Tσ [K]

Max Tσ [K]

1 Line 1 Line 5 6.0 29.5 3.8 11.7 2 Line 1 Line 8 4.1 13.7 3.3 7.6 3 Line 1 Line 10 4.9 21.7 3.0 7.9 4 Line 1 Line 11 3.5 12.0 2.4 6.1 5 Line 1 Line 13 3.3 11.5 2.3 5.1 6 Line 3 Line 8 7.2 20.0 7.0 27.8 7 Line 3 Line 11 4.7 15.1 3.4 7.8 8 Line 3 Line 13 4.1 11.7 3.2 6.4 9 Line 4 Line 14 6.6 16.7 5.1 9.5 10 Line 5 Line 11 6.2 14.3 4.5 7.9 11 Line 5 Line 13 5.5 15.7 4.2 8.3 12 Line 5 Line 14 5.5 26.8 3.7 10.2 13 Line 8 Line 14 6.6 17.1 7.2 12.3 14 Line 9 Line 11 6.4 16.2 5.0 9.7 15 Line 9 Line 13 5.9 17.8 5.0 12.0 16 Line 9 Line 14 5.7 29.1 4.1 12.7


47

Based on the simulation results, these 16 line pairs have good temperature sensitivity and

accuracy for the entire compression cycle, and hence they show good potential for temperature

measurements during the compression phase of an internal combustion engine. Our results also

show that there is no single line pair which is best for all the conditions. Therefore, the optimum

line pair should be chosen case-by-case. For example, if we pick the high temperature end of high

EGR cycle (2 atm < P < 30 atm & 600 K < T <1050 K), the line pairs 5 and 12, are the most

promising candidates. Figure 3.4 shows in panel (a) the ratio of the 2f signals for these two line

pairs during compression for the high EGR cycle. The temperature sensitivity from this ratio is

nearly constant for the entire compression stroke as illustrated in panel (b) of Fig. 3.4. The

calculated uncertainty in temperature using the evaluation criteria above shows both line pairs are

quite promising for P and T values near the middle of the compression stroke. The uncertainty

becomes larger at the low T portion of the cycle where the high E” line has very low signals and

at the high P/T portion of the cycle where the low E” transition has low signal. As mentioned

above, the 2f signal at the low pressure end of the cycles is sacrificed by using large “a” (0.8 cm-1)

to achieve best performance at the high pressure portion of the compression cycles. Instead of the

fixed “a” method, other approaches such as the use of variable “a” or use of additional lines (e.g.

three rather than two) may be desired to improve sensor accuracy and performance during the

entire cycles. However, for the high EGR case, these two line pairs (5 and 12) have the optimum

performance.

If we pick the compression stroke for the super-charged intake cycle (10 atm < P < 50 atm & 600

K < T < 850 K), there are five lines pairs (5, 11, 12, 13, 15) which have nearly the same modeled

performance, as shown in figure 3.5. These line pairs have predicted temperature uncertainties

less than 10 K during compression. Here the simulations show quite similar behavior for the

signal ratio, temperature sensitivity, and predicted uncertainty, limited by signal for the over-

modulated low temperature portion of the cycle and similarly limited by signal at the under-

modulated high pressure portion of the cycle.

Chapter 3

48

3.0

2.5

2.0

1.5

1.0

0.5

0.0

Rat

io

1000900800700600500Temperature [K]

Line pair 5 Line pair 12

20x10-3

15

10

5

0

Sen

sitiv

ity (

dR/R

)/dT



20

15

10

5

0

σ T [K

]

1000900800700600500Temperature [K]


Figure 3.4. High EGR compression cycle: (a) Simulated 2f ratio, (b) temperature sensitivity, and (c) temperature uncertainty for the line pair 2 and 5 as a function of pressure/temperature. (a=0.8cm-1)

a

b

c


49

3.0

2.5

2.0

1.5

1.0

0.5

0.0

Rat

io



a = 0.8 cm-1 Line pair 5

Line pair 11 Line pair 12 Line pair 13 Line pair 15

20x10-3

15

10

5

0

Sen

sitiv

ity (d

R/R

)/dT



a = 0.8 cm-1

Line pair 5 Line pair 11 Line pair 12 Line pair 13 Line pair 15

40

30

20

10

0

σ T [K

]



a = 0.8 cm-1

Line pair 5 Line pair 11 Line pair 12 Line pair 13 Line pair 15

a

b

c

Figure 3.5. Super-charged intake compression cycle: (a) Simulated 2f ratio, (b) temperature sensitivity, and (c) temperature uncertainty for the line pair 5, 11, 12, 13 and 15 as a function of pressure/temperature. (a=0.8cm-1)

It is tempting to use simulations to further reduce the number potential line pairs in Table 3.2.

However, the quantitative uncertainty in the HITRAN database limits the value of further down-

selection. Even though HITRAN 2004 has significantly improved the quantitative spectroscopy

Chapter 3

50

for the 2ν1, 2ν3, and ν1+ν3 overtone and combination bands of H2O, important differences

between database and measured data for line strength and pressure broadening persist [Liu 2005].

Therefore further reduction of the number of candidate line pairs in Table 3.2 awaits confirmation

of the quantitative spectroscopic data for the candidate lines and their neighbors. It should also be

noted that intensity modulation effects, pressure shifts of line position, and optimum selection of

modulation depth, are not considered in the current study, and these may also impact selection of

optimum pairs for specific applications.

It is important to emphasize that this chapter concentrates on the temperature measurement

technology based on two-line water vapor, fixed “a” 2f spectroscopy. Building on this research,

however, temperature strategies based on more than two lines, variable “a” and other species can

be easily derived for other applications (such as fired engine cycles with higher T). The line

selection criteria and logic developed here should prove useful to those interested in temperature

sensing using absorption spectroscopy.

3.3.3 Summary

The optimum selection of the H2O lines for TDL absorption-based temperature measurements in

an internal combustion engine was investigated. The strategies and criteria to select optimum

water features in the 1.25-1.65 micron wavelength range have been detailed. Systematic

examination of models of the water vapor spectrum yield 14 candidate NIR water transitions

which can be combined into 16 attractive line pairs for in-cylinder gas temperature measurements

during compression for internal combustion engines. Simulations show that these line pairs have

good potential for TDL thermometry during the compression cycle for internal combustion

engines.

3.4 Multiplexing techniques

As discussed earlier, the two-line thermometry technique can be accomplished with the

combination of two laser beams along the same measurement path. There are three commonly

used techniques for such architecture: Wavelength Division Multiplexing (WDM), Time Division

Multiplexing (TDM) and Frequency Division Multiplexing (FDM), each with its individual

advantages and limitations. These techniques will be described briefly here, mainly to serve as a

guide for optimum selection for a given application.


51

3.4.1 Wavelength Division Multiplexing (WDM)

λ2

Measurementpath length

Diode Laser

Collimator

λ1 λ1

λ2

Grating

Combiner Detector

Figure 3.6 Schematic of the wavelength division multiplexing.

An arrangement quite frequently used for wavelength division multiplexing technique is shown in

figure 3.6. The system consists of two lasers operating at different wavelengths. They are

combined using a 1×2 single mode fiber coupler. The output beam is directed through the

measurement path by collimating lens. The two different wavelengths are spatially separated by a

diffraction grating.

m = -2 m = -1

m = -1 m = 0

m = 1

m = 1 m = 2

m = 2

α β

m = -2

m = 3 m = 3

Grating

Incident beam

Figure 3.7 Grating separates the colors in incident light.

A typical diffraction grating consists of a large number of parallel, closely spaced slits (or

grooves). The maximum of the laser intensity is obtained when the reflected beams from different

slits are in phase which occurs when

sin sind d mα β λ+ = (3.27)

Where α is the incident angle, β is the reflection angle, d is the slit separation, m is the order of

diffraction and λ is the wavelength. It can be seen that the output angle will depend on

wavelength. So the laser beams with different wavelength will propagate in different directions,

Chapter 3

52

as shown in figure 3.7. Order zero is the reflected beam. The first order (positive or negative) is

usually employed for detection.

With a given angle of incidence, the angle α, the change of diffraction angle β corresponding to a

small change in wavelength can be obtained by differentiating Eqn (3.27)

cosm

dδβδλ β

=⋅

(3.28)

Therefore, the wavelengths in WDM should be chosen based on the grating specifications and

distance between grating and detector. The main advantage of WDM is its simplicity. However,

WDM can not be used for a large number of wavelengths due to the possible overlap between

different orders reflection or when the wavelengths are too close. In principle this difficulty may

be overcome by Time Division Multiplexing (TDM) and Frequency Division Multiplexing

(FDM).

3.4.2 Time Division Multiplexing (TDM)

5

4

3

2

1

0

Sig

nal [

V]

20x103

151050Time [us]

5

4

3

2

1

0

Laser 2

Laser 1

Figure 3.8 Schematic of Time Division Multiplexing.


53

The concept of TDM is relatively simple; two signals are alternated in time, shown in figure 3.8

for two lasers. An asset of TDM is its flexibility and relative simple setup. The absorption signals

at two different wavelengths can be measured using one detector. At high repetition rate, however,

accurate timing circuits are usually required for TDM. Another limitation of TDM is that the two

absorption signals are not measured simultaneously; this could lead to measurement uncertainty if

the experimental conditions change rapidly. For WMS sensors, a different scheme, known as

frequency-division multiplexing, is preferred.

3.4.3 Frequency Division Multiplexing (FDM)

λ2

Measurement path length Diode Laser

Collimator

λ1 Combiner Detector

Modulate at f1

Lock-in amplifier Lock-in amplifier

Detector signals to lock-in

Modulate at f2

Figure 3.9 Schematic of the Frequency Division Multiplexing.

A typical setup using Frequency Division Multiplexing (FDM) is shown in figure 3.9. FDM is

commonly used in modulation spectroscopy where each laser signal can be modulated at a

different frequency. The optimum modulation frequencies are chosen based on the minimum

interference between different harmonic signals. The output signal from the detector is fed into a

pair of lock-in amplifiers set to detect 2f1 and 2f2 signal respectively.

FDM offers two advantages. The wavelength separation needed for WDM is not required for

FDM, and simultaneous measurements of two absorption signals can be made with a single

detector. The major limitation of FDM is that it is not applicable for direct absorption

spectroscopy.

Chapter 3

54

55

Chapter 4: Temperature sensing using H2O transitions near 1.8 µm

In this chapter, the water vapor spectrum in the 1-2 µm near-infrared (NIR) region is

systematically analyzed to find the best absorption transitions for sensitive measurement of H2O

concentration and temperature in combustion environments using a single tunable diode laser

with typical distributed feedback (DFB) single-mode scanning range (1 cm-1). The use of a single

laser, even with relatively narrow tuning range, can offer distinct advantages over wavelength-

multiplexing techniques. The strategy and spectroscopic criteria for selecting optimum

wavelength regions and absorption line combinations are then discussed. It should be stressed that

no single figure of merit has been derived to simplify the selection process, and the optimum line

pair is chosen case-by-case. Our investigation reveals that the 1.8 µm spectral region is especially

promising, and we have identified 10 of the best water line pairs in this spectral region for

temperature measurements in flames. Based on these findings, a pair of H2O transitions near 1.8

µm was selected as an example for the design and development of a single-laser sensor for

simultaneously measuring H2O concentration and temperature in atmospheric-pressure flames. As

part of the sensor development effort, fundamental spectroscopic parameters including the line

strength, line-center frequency, and lower state energies of the probed transitions were measured

experimentally to validate and improve the HITRAN database values. We conclude with

demonstration results in a steady and a forced atmospheric-pressure laboratory combustor.

4.1 Water, H2O

Water is an attractive combustion species to monitor, as it is one of the primary products of

hydrocarbon combustion and an excellent indicator of overall combustion efficiency, while

temperature, as a fundamental parameter of combustion systems, determines the overall thermal

efficiency. Simultaneous measurements of H2O concentration and temperature thus hold high

potential for combustion sensing and control.

H2O is a non-linear and triatomic molecule, which consists of two light hydrogen atoms attached

to a relative heavy oxygen atom. Although the structure of a water molecule is simple, its

absorption spectrum is relatively complicated. The structure of water molecule and its allowed

three fundamental vibration modes are shown in figure 4.1 and listed in table 4.1.

Chapter 4

56

H H

O

H H

O

H H

O

(a) Symmetric stretch, ν1(b) Symmetric bend, ν2 (c) Antisymmetric stretch, ν3

Figure 4.1 The structure of a water molecule and its three fundamental vibrations.

Table 4.1 Fundamental vibrations, frequencies, types and description for H2O.

[Banwell 1994]

Vibration Frequency [cm-1] Type Description

ν1 3651.7 || Symmetric stretch

ν 2 1595.0 || Symmetric bend

ν 3 3755.8 ⊥ Antisymmetric stretch

10-5

10-4

10-3

10-2

10-1

100

Line

Stre

ngth

[cm

-2/a

tm]

2.01.91.81.71.61.51.41.31.21.11.0Wavelength [µm]

2ν1, ν1+ν3, 2ν3

ν1+ν2, ν2+ν3

T=1000K HITRAN/HITEMP

2ν1+ν2, ν1+ν2+ν3, ν2+2ν3

Figure 4.2 Survey spectra of H2O at 1000 K in the near-infrared region based on the

HITEMP database.

Temperature sensing using H2O transitions near 1.8 µm

57

Figure 4.2 is the graphical depiction of the near-infrared line strengths of water over a range of

wavelengths from 1 to 2 µm at a temperature of 1000 K. The assignments of the NIR vibrational

absorption spectrum are given in table 4.2.

Table 4.2 Assignments of the NIR vibrational absorption spectrum of water

Wavelength

[nm]

Frequency

[cm-1] Assignment Note

1200 8330 aν1 + ν2 + bν3; a+b=2 1470 6800 aν1 + bν3; a+b=2

1900 5260 aν1 + ν2 + bν3; a+b=1

a and b are integers (0, 1, 2…)

4.2 Development of single-laser T sensor

The primary goal of this work is to elucidate useful design rules for the selection of the optimum

transitions for a robust, single-diode-laser sensor system for real-time measurements of

temperature and water vapor mole fraction in combustion gases at elevated temperature. (The

temperature range of interest is 1000 to 2500 K.) By analyzing the NIR water spectrum in the 1-2

micron range using the criteria we developed in the previous chapter, the 10 most promising (by

our criteria) NIR single-laser water transition pairs are suggested for temperature measurements

in flames; all these pairs lie near 1.8 micron. One of the optimum transition pairs, located near

1.8005 micron (5554 cm-1), is chosen and utilized to develop a prototype single-laser sensor

system. Fundamental spectroscopic measurements of the selected H2O transitions are used to

validate the HITRAN/HITEMP database. [Rothman 1998] The updated spectroscopic parameters

(line strengths, line-center positions, and lower state energies) form the theoretical basis for future

applications of this diode-laser sensor system. Subsequent to the spectroscopic efforts, the utility

of this new sensor is demonstrated in a small-scale laboratory combustor. We conclude that this

system has the desired flexibility, high speed and accuracy to be a useful tool for fundamental and

applied combustion monitoring.

4.2.1 Selection of water line pairs

There have been several previous studies that discuss the selection of transitions for absorption-

based thermometry. Chang et al. [Chang 1991] investigated candidate line pairs for NO

thermometry near 226 nm in the UV region, and Arroyo et al. [Arroyo 1994] identified a useful

Chapter 4

58

H2O line pair near 1.38 µm for H2O thermometry. Nagali and Hanson [Nagali 1997] investigated

a diode laser sensor for monitoring water vapor in high-pressure combustion gases in the 1.3~1.4

µm region. However, a systematic analysis of the broader NIR (1-2 µm) H2O spectrum aimed at

thermometry has not been reported. The design rules discussed here (and in chapter 3) should

prove useful to those interested in temperature sensing using absorption spectroscopy.

A primary objective of this chapter is to discuss the selection of optimum H2O line pairs for

absorption measurements of temperature and water mole fraction in representative combustion

environments (1000~2500 K, P≈1 atm). At present we limit the selection to transitions accessible

within the tuning range of single diode lasers currently available (380nm<λ<2400nm). Following

the selection criteria developed in chapter 3, the line selection process is as follows:


range.

We assume a minimum detectable absorbance of 10-4, which together with a desired signal-to-

noise ratio (SNR) of 10 requires that the peak absorption be greater than 10-3. In addition, the

peak absorption must be less than about 0.8 to avoid experimental difficulties associated with

“optically-thick” measurements.

For a pathlength of 5 cm and a combustion product water vapor mole fraction between 0.01 and

0.3 at a pressure of 1 atm,

3

,,, 105%11)()(2

−≥⋅⋅⋅⋅=⋅⋅⋅⋅= peakipeakoHipeak cmatmTSLxPTS ννν φφα (4.1)

8.05%301)()( ,,, 2≤⋅⋅⋅⋅=⋅⋅⋅⋅= peakipeakoHipeak cmatmTSLxPTS ννν φφα (4.2)

so that the constraint on the product of line strength and line-shape function becomes 11

,11 02.0)(53.0 −−−− ⋅≥⋅≥⋅ atmcmTSatmcm peaki νφ (4.3)

in the temperature range 1000 ~ 2500 K.

A total of 856 transitions in the HITEMP [Rothman 1998] database meet the absorption strength

criterion in the 1-2 µm NIR region.


59

Criterion 2: The absorption lines lie within a single laser scan, and do not overlap

significantly at atmosphere pressure.

A typical rapid-tuning range of a single-mode DFB diode laser is ~1 cm-1. Hence we require that

the spectral separation of the line pairs must lie between 0.1 and 0.6 cm-1. If line spacing is larger

than 0.6 cm-1, ambiguity in the baseline fit will result in unacceptable uncertainty in the

measurements. If line spacing is smaller than 0.1 cm-1, the two lines will overlap at atmosphere

pressure. Criterion 2 reduces the potential candidates to 339 line pairs.

Criterion 3: The absorption ratio should be single-valued with temperature and the

line strengths of the two lines should be similar.

The absorption ratio is best determined if the measurement uncertainty is similar for the two

absorption transitions. In addition, if one transition is much stronger, the wing of the strong

transition will have obvious influence on the measurement of the weak transition. A line strength

ratio between R=0.2 and R=5 is thus imposed. Although these limits of R are somewhat arbitrary,

this criterion ensures that these two transitions have similar SNR ratio [Nagali 1997]. There are

285 line pairs which satisfy criteria 1-3.


yield an absorption ratio that is sensitive to the probed temperature.

If the integrated absorbance can be determined within 4%, a temperature accuracy of 5% in the

temperature range of 1000 ~ 2500 K requires the lower state energy of the two transitions to

differ by at least 2000 cm-1.

1"2

"1

" 20004388.11*2500*

05.02*04.0

// −==≥−=∆ cm

hckT

TdTRdREEEi

(4.4)

There are total 24 line pairs that satisfy criteria 1-4, and they all have good temperature sensitivity

in temperature range 1000 ~ 2500 K.

Chapter 4

60


transitions.

Fourteen of the promising pairs of transitions are rejected because of the appearance of adjacent

interference features when the candidate line pairs are examined for 1000<T<2500K. The

remaining 10 line pairs are regarded as the most promising water vapor features for temperature

measurement in combustion environments using the selection criteria noted above, including a

single laser with a ~1 cm-1 scan range. Table 4.3 summarizes the line selection results.

Table 4.3. Line selection result using the selection criteria in the near-infrared region based on HITEMP.

Transitions between 1 µm and 2 µm 447207

Transitions, satisfying 1 856 Line pairs, satisfying 1,2 339

Line pairs, satisfying 1, 2, 3 285 Line pairs, satisfying 1, 2, 3, 4 24

Line pairs, satisfying 1, 2, 3, 4, 5 10


water concentration in the near-infrared region based on HITEMP.

Line pair λ [nm] ν [cm-1]

103 S @1000K

[cm-2atm-1] E” [cm-1] deltE”

[cm-1] Sensitivity

Rank Line

Spacing [cm-1]

Notes

1881.23 5315.670 2.1058 2552.881 1881.03 5316.238 3.7153 95.18 2457.70 3 0.568 A, B, C

1863.29 5366.847 1.9957 2433.802 1863.17 5367.196 3.2740 416.21 2017.59 10 0.349 B, C, D

1839.95 5434.922 42.2922 173.37 3 1839.88 5435.150 10.0224 2337.67 2164.31 5 0.228 A, C, D

1822.75 5486.214 10.2280 503.97 4 1822.60 5486.680 2.9274 2552.86 2048.89 7 0.466 B, C

1818.83 5498.025 2.8254 3391.175 1818.78 5498.203 6.4334 610.11 2781.06 1 0.178 A, C

1818.78 5498.203 6.4334 610.11 6 1818.70 5498.427 5.0516 2630.22 2020.11 8 0.224 C

1818.70 5498.427 5.0516 2630.227 1818.51 5498.997 19.2885 610.34 2019.88 9 0.570 B, C

1812.26 5517.987 3.4634 3135.808 1812.16 5518.291 8.1060 661.55 2474.25 2 0.304 A, B, C, D

1810.62 5522.964 4.6316 2818.429 1810.46 5523.455 7.3145 757.78 2060.64 6 0.491 B, C

1800.57 5553.797 2.6036 3314.8810 1800.45 5554.175 9.3542 982.91 2331.97 4 0.378 A, B,C, D, E

Notes: A: good sensitivity B: large separation, may be used at higher pressure


61

C: interfering absorption by room air, need purge D: isolated from nearby interference E: verified experimentally

14x10-3

12

10

8

6

4

2

0

Spec

tral a

bsor

ptio

n co

effic

ient

[cm

-1]

5316.85316.0

Frequency [cm-1]

1881.25 1881.00

5367.65367.0

1863.25 1863.00

5435.65435.05434.4 5486.85486.45486.0

1840.001839.75 1822.751822.50

Wavelength [nm]

T=296K T=1000K T=2000K

P=1atmX=0.1

1 2 3 4

14x10-3

12

10

8

6

4

2

0

Spec

tral a

bsor

ptio

n co

effic

ient

[cm

-1]

5499.05498.0

Frequency [cm-1]

1818.75 1818.50

5518.85518.0

1815.0 1812.0

5524.05523.0

1810.50 1810.25

Wavelength [nm]

5554.55554.05553.5

1800.50 1800.30

T=296K T=1000K T=2000K

P=1atmX=0.1

5,6,7 8 9 10This Work

Figure 4.3 Expanded view of absorption spectra for the selected H2O line pairs in the

near-infrared region based on the HITEMP database; evaluated for P=1 atm, 10%

H2O, 90% air.

Chapter 4

62

Figure 4.3 shows the calculated candidate H2O spectra (P=1 atm, 10% H2O and 90% air) based

on the HITEMP database [Rothman 1998]; spectroscopic constants are listed in Table 4.4. Figure

4.3 allows visual inspection of these candidate line pairs. First, note that typically one or both

transitions absorb strongly at room temperature, which makes these line pairs sensitive to

interference from absorption by ambient water vapor in room air. Consequently it may be

necessary to purge the optical path outside the target measurement zone.

6

5

4

3

2

1

0

Line

stre

ngth

Rat

io S

ensi

tivity

(dR

/R)/(

dT/T

)

30002500200015001000500Temperature [K]

Line pair 5 @ 1818.8nm [deltE"=2781.06cm-1] LIne pair10 @ 1800.5nm [deltE"=2331.97cm-1] Line pair 2 @ 1863.2nm [deltE"=2017.59cm-1] Desired minimum sensitivity

Figure 4.4. Calculated temperature sensitivity of line strength ratio as a function of

temperature for line pair 2, 5 and 10 based on the HITEMP database.

The line pairs are also ranked based on their temperature sensitivity in Table 4.4. Figure 4.4

shows the temperature sensitivities of the line strength ratio of line pair 2, 5 and 10 as a function

of temperature, using Equation (3.9) and data from HITEMP. Line pair 5 has the largest

temperature sensitivity because it has the largest difference of lower state energy for the two

candidate transitions. If the sensitivity is greater than 1.065, and if the integrated absorbance of

individual transitions can be determined within an accuracy of 4%, the subsequent error in the

temperature will be less than 5%.

All of the line pairs in Table 4.4 provide excellent time-resolved measurement of temperature

when the absorbance is fit with a set of Voigt lineshapes. However, real-time measurements


63

require a data reduction strategy sufficiently simple for rapid temperature computation, e.g. using

ratios of the peak absorption to avoid time consuming fits to the line-shape. Nearly half of our

candidate line pairs (5, 6, 7 and 9) have enough interferences from nearby lines that the direct use

of the peak absorption ratio is insufficient to determine temperature, and a correction scheme is

needed for real time applications. For this reason, we have excluded these line pairs from further

consideration, though it is certainly possible to develop correction algorithms or look-up table

strategies that would allow use of these line pairs for real time applications.

Ideally, the peak absorption ratio should also be insensitive to pressure. Since the HITEMP

database does not provide a value of self-broadening coefficient 2 2H O H Oγ − for most of the

transitions in Table 4.4, the sensitivities of the ratio of peak absorption to pressure and mole

fraction are not calculated here. Since pressure effects could become important for real-time

temperature measurements in practical systems, it is clear that experimental data for line-

broadening are critically needed in support of accurate temperature sensing.

From the above discussion, Figure 4.3, and Table 4.4, we see that some line pairs have good

temperature sensitivity but limited line spacing, thus they are unsuitable for high pressure

applications since the pressure-broadening mechanism will make them indistinguishable, while

others have large line spacing but moderate temperature sensitivity. In addition, interference

absorption by ambient water vapor should be minimized. Considering all these factors, more than

half of the line pairs in Table 4.4, namely line pairs 1, 2, 3, 4, 8 & 10, should be suitable for use

with a single-laser sensor for combustion applications at modest elevated pressures.

Line pairs 8 and 10 are the two most promising choices because of their large temperature range,

good temperature sensitivity, and relative isolation from other neighboring transitions. We have

selected line pair 10 for detailed investigation here due to laser availability. In order to proceed

with development of this potential temperature sensor, we must first validate the

HITRAN/HITEMP data base, as past work has revealed discrepancies in these data bases,

especially at high temperature.

4.2.2 Spectroscopy Experiments, Results and Discussions

Measurement strategies based on absorption spectroscopy techniques require the accurate

determination of important spectroscopic parameters of the probed species. Hence a primary

Chapter 4

64

focus of this initial work is to present survey spectra of H2O near 1.8 µm to validate available

spectroscopic data or obtain improved values for the needed spectroscopic parameters for the

target transitions and their neighbors. These spectroscopic measurements form the basis for the

design of a single diode-laser sensor system for non-intrusive measurements of H2O

concentrations and gas temperature.

To gas manifold andvacuum pump

DFB1800 nm

InGaAsDetector

Heated Quartz Cell

TransmittedIntensity

Wavemeter

InGaAsDetector

Solid Etalon

P 1-100 Torr MKS Baratron

20 cm

Flipper mirrors

FunctionGenerator

Water

LaserController

ParabolicMirror

N - Purged Area2


spectroscopic parameters.

Figure 4.5 illustrates the experimental arrangement of a diode laser, a heated quartz cell,

appropriate mirrors and lenses, and two InGaAsP detectors for measuring an etalon trace and the

transmitted intensities. One distributed-feedback InGaAsP laser emitting near 1.8 µm is used in

this study. The output from the laser is collimated using a parabolic mirror to reduce etalon

interference. The ILX Lightwave LDC-3900, which includes temperature and current controllers,

drives the diode laser. A function generator is used to ramp the laser injection current and thus

tune the wavelengths of the laser over the desired absorption features. The 20-cm long static cell

is made of quartz with 0.5°-wedged windows mounted at a 3° angle to minimize interference

effects in the transmission signal. The cell temperature is measured with four type-S

thermocouples that are equally spaced along the cell axis. The temperature deviations along the

cell are determined to be <2%. A pressure gauge (MKS Baratron with a full scale deflection of


65

100 Torr and accuracy of <1%) is used to measure the cell pressure, and a mechanical pump

evacuates the cell. A solid etalon with a known free spectral range (FSR=2.01 GHz) is used to

convert transmitted intensity data from the time domain to the frequency domain. Distilled liquid

water contained in a flask is used as a source of water vapor to measure spectroscopic parameters.

The flask is pumped down for an hour prior to measurements to remove all gaseous impurities.

The laser, detectors, and optics are enclosed in a nitrogen-purged area to prevent interfering

absorption by room air. The experimental profiles are best fit using Voigt profiles to get

fundamental spectroscopic parameters of the probed water transitions, and the temperature

dependence of the line pair’s intensity ratio.

The needed fundamental spectroscopic parameters, including line strengths, line-center

frequencies and lower state energies, are measured using low-pressure H2O in a heated cell.

Figure 4.6 shows the reduced pair of experimental profiles corresponding to the absorption

features at 944 K. Based on the HITEMP database [Rothman 1998], there are 4 transitions, as

shown in Figure 4.7. “Line 1” and “line 4” are low temperature lines, which are included in

HITRAN and HITEMP. “Line 2” and “line 3” are high temperature lines, which are included

only in HITEMP. The line strengths for these four transitions are plotted versus temperature in

Figure 4.8, as calculated using HITEMP and measured in our heated cell. The agreement between

the inferred E” and the HITEMP value confirms the spectroscopic assignment. For “lines 1, 2, 4”,

the general agreement between measured spectroscopic parameters and those published in the

HITEMP database is good, so we recommend adopting the values listed in the HITEMP database

for further use. Note “line 3” is a weak transition and ignored for this work.

Chapter 4

66

0.20

0.15

0.10

0.05

0.00

Abs

orba

nce

1.21.00.80.60.40.20.0Relative Frequency [cm-1]

-1.0

0.0

1.0R

esid

ual

(%)

Exp DataVoigt fit

T=944KPH2O=17.44 TorrL=40.8 cm

Figure 4.6 Reduced H2O line-shape (line pair #10) recorded in a static cell at T=944

K, PH2O=17.44 Torr.

10x10-3

9

8

7

6

5

4

3

2

1

0

Line

str

engt

h [c

m-2

/atm

]

5554.85554.65554.45554.25554.05553.85553.65553.4Frequency [cm

-1]

Line 1

Line 2

Line 3 Line 4

T=1000K

Line position

Line 2=5553.80 cm-1

(HITEMP)

Line 2=5553.86 cm-1

(Experiment)

Line 3=5553.99 cm-1

(HITEMP)

Line 3=5554.04 cm-1

(Experiment)

Figure 4.7 Line strength of the transitions contributing to line pair #10 near 1.8 µm at

1000 K based on HITEMP parameters.


67

24x10-3

22

20

18

16

14

12

10

8

6

4

2

0

Line

stre

ngth

S [c

m-2

/atm

]

30002800260024002200200018001600140012001000800600400

Temperature [K]

3.0x10-3

2.5

2.0

1.5

1.0

S [c

m-2

/atm

]

1000950900850800750Temperature [K]

4.0x10-3

3.5

3.0

2.5

2.0

1.5

1.0

S [c

m-2

/atm

]


Line 1 (HITEMP) Line 2 (HITEMP) Line 3 (HITEMP) Line 4 (HITEMP) Line 1 (Experiment) Line 2 (Experiment) Line 4 (Experiment)

Figure 4.8 Calculated and measured line strengths for the components of line pair

#10 as a function of temperature. “Line 2” is the high temperature transition at

5553.86 cm-1; “Line 1” is the low temperature transition at 5554.18 cm-1.

The line positions are also measured using a wavelength meter. The measured “line 1” and “line

4” position agree with HITEMP within the precision of the IR wavelength meter (0.01 cm-1), but

the measured positions agree less well for “line 2” and “line 3” near 5553.86 cm-1 and 5554.04

cm-1, respectively. We suggest using our measured positions in future work. The spectroscopic

parameters of the selected H2O transitions are listed in Table 4.5.

Table 4.5 Spectroscopic data for the selected H2O line pair.

Line # HITRAN Frequency

[cm-1]

Measured Frequency

[cm-1]

Line strength @ 296 K

[cm-2/atm]

Lower state energy [cm-1]

2 5553.80 5553.86 7.298E-7 3314.883 3 5553.99 5554.04 3.628E-7 3139.505 1 5554.18 5554.18 7.662E-3 982.912 4 5554.21 5554.21 9.200E-3 173.365

Chapter 4

68

At atmospheric pressure “line 1” and “line 4” are blended. The line strength of “line 4” is about

7% of “line 1” at 1000 K and 5% at 1500 K. The effect of “line 4” is included in the data analysis

to improve accuracy; therefore the peak ratio in this case is defined as “line 2”/(“line 1”+“line 4”).

2.8

2.4

2.0

1.6

1.2

0.8

0.4

0.0

Peak

Rat

io R

320028002400200016001200800400Temperature [K]

X=8% X=10% X=12%

Figure 4.9 The ratio of peak absorbance coefficients, Rpeak(line pair #10), calculated

as a function of temperature for various values of water mole fraction at 1 atm.

(based on HITEMP database [Rothman 1998])

The ratio of peak absorption is often used to infer temperature for real-time measurements.

Unlike the line strength ratio, the peak absorption ratio is also dependent on water mole fraction

and pressure via the line-shape function. To illustrate the relative insensitivity of these factors on

the peak absorption ratio of the selected line pair, Figure 4.9 shows the peak absorption ratio as a

function of temperature for values of water mole fraction in the range 8%~12% at a constant

pressure of 1atm. The result show that a 20% change in water mole fraction only leads to a 1%

change in the measured gas temperature. Hence, the peak absorption ratio of this line pair is

relatively independent of water mole fraction, which enables simplified data reduction for real-

time temperature measurements.


69

2.8

2.4

2.0

1.6

1.2

0.8

0.4

0.0

Ratio

320028002400200016001200800400Temperature [K]

6.0

5.5

5.0

4.5

4.0

3.5

3.0

2.5

2.0

1.5

1.0

Tem

pera

ture

sen

sitiv

ity (d

R/R

)/(dT

/T)

Peak Ratio Linestrength Ratio

Peak Ratio Sensitivity Linestrength Ratio Sensitivity

Figure 4.10 The ratio of line strength and peak absorbance coefficients and their

sensitivity to temperature versus temperature for the line pair #10.

Figure 4.10 presents the line strength ratio and peak absorption ratio for line pair #10 and their

corresponding temperature sensitivities as a function of temperature. At temperatures below 960

K, the line strength ratio is less than 0.2, which makes accurate measurements of the line strength

ratio difficult. At temperatures above 3300 K, although the sensitivity is still good, the absorption

coefficients of the two transitions becomes quite small. Thus, the selected H2O line pair for

temperature measurement is suitable for use in the temperature range 960~3300 K.

4.3 Combustion Demonstration

4.3.1 Temperature and Concentration Measurements

Figure 4.11 illustrates the arrangement employed for a demonstration measurement in a

laboratory burner. Light from a distributed-feedback InGaAsP diode laser emitting near 1.8 µm is

directed across a flat diffusion flame stabilized on a Hencken burner. The diode laser is

temperature and current controlled (ILX Lightwave LDC-3900), and injection current tuned (SRS

DS345) across the two absorption transitions. The beam path is purged to avoid interference from

Chapter 4

70

ambient water vapor. The flow rates of fuel (C2H4) and air are measured using calibrated flow

meters. Water vapor absorption is measured 1 cm above the 5 cm × 5 cm square flame.

DFB1800 nm

FunctionGenerator

LaserControllerMirror

InGaAsDetector


Computer

Sine wave

N - Purged Area2 N - Purged Area2

View looking down

Air

C H2 4

Figure 4.11 Schematic diagram of the measurement system applied to the Hencken

burner.

The laser is scanned at 500 Hz across the H2O line pair to record spectrally resolved absorption

line-shapes. The transmitted signal is sampled at 1 MHz, which corresponds to 2000 points in

each laser scan. The incident laser intensity I0 is determined by fitting the regions outside the

absorption lines to a low-order polynomial. Gas temperatures are inferred from the measured line

strength ratio, using Equation (2.26), for each scan (2 ms).


71

2600

2400

2200

2000

1800

1600

1400

1200

1000

800

Tem

pera

ture

[K]

5.04.03.02.01.00.0Position [cm]

Thermocouple Temperature distribution (trapezoid) Tpath-averaged (uniform)=1620 K Tpath-averaged (trapezoid)=1760 K

LcenterLedge Ledge

Figure 4.12 Measured temperatures in the burned-gas region above a C2H4-air flame

in a 5 cm ×5 cm Hencken burner.

Results are shown in Figure 4.12 for an air flow rate of 64 liter/min and fuel flow rate of 2.9

liter/min (overall equivalence ratio ~ 0.65). The thermocouple measurements (type S

thermocouples, 5-mil wires) are corrected for radiation loss. [Shaddix 1999] (The typical

correction is 50 K.) The thermocouple is traversed forward and backward to confirm stability of

the flame temperature. Since the boundary layer is not negligible in this case, it is clear that an

assumption of uniform temperature, implicit in the absorption ratio method, will lead to

systematic error. The temperature of primary interest is typically the temperature in the core

region, which is measured to be 1740 K using thermocouple. Under the assumption of uniform

temperature and mole fraction, the temperature inferred from laser absorption data is determined

to be 1620 ± 30 K along this path, i.e. 120 K (7.0%) below the true core temperature, and the

measured water mole fraction is determined to be 7.9 ± 0.3 %, i.e. 0.8% (9.2%) under the

corresponding calculated equilibrium mole fraction (8.7%).

It is of course not necessary to assume uniform conditions along the absorption path as long as

some spatial characteristics of the temperature and absorber concentration are prescribed. For

example, in the present case it is reasonable to assume a trapezoidal-shaped temperature

distribution with a boundary layer thickness estimated either from the observed thermocouple

data or simple mixing-layer analyses. A linear mixing model may be assumed for the water mole

Chapter 4

72

fraction between the combustion products value in the core region and room air humidity at the

edge of the flame so that the water mole fraction profile along the line-of-sight is also a

“trapezoid”.

Using such a simple model, the remaining unknowns, to be inferred from the peak ratio

absorption data are the core temperature (Tcore) and core water mole fraction (Xcore). We may

solve for Tcore and Xcore interactively, recognizing that the integrated absorbance is now given by:

dxTSXPAL

OHiOHi ∫=0 2,2 )(

(4.5)

We first assume an approximate core temperature from the uniform temperature assumption and

solve the integrated absorbance of one transition for the core water mole fraction Xcore. Using this

Xcore value, we solve the integrated absorbance of the other transition for Tcore; this Tcore value is

further used to solve for a new value of the core water mole fraction, and so on. For the flat flame

diffusion burner used here, we converge in 5 iterations to Tcore = 1760 K, only 20 K (1.2%) from

the radiation-corrected thermocouple value, and the water mole fraction in the core region is

about 9.0%, merely 0.3% (3.4%) from the theoretical calculated mole fraction.

This demonstration experiment confirms the sensitivity and potential accuracy of absorption-

based temperature sensing, while also illustrating the potential problems associated with

nonuniform properties along the line-of-sight. For combustion flows of the type studied here, it

may be sufficient to assume an approximate temperature distribution in reducing the data, or to

select line pairs immune to the effect of cold edges [Ouyang 1990]. Under other conditions where

temperature changes significantly along the absorption path and the relative temperature profile is

unknown, the 2-line absorption temperature technique may not yield useful results. In such cases,

it may be attractive to consider use of a larger number of absorption lines, as has been reported by

Sanders et al. [Sanders 2001] for oxygen, where multiple absorption lines were used to determine

the extent of the hot (or cold) regions in the optical path.


73

4.3.2 Identification of Acoustic Instabilities

2600

2400

2200

2000

1800

1600

1400

1200

Tem

pera

ture

[K]

3.02.52.01.51.00.50.0Time [s]

2400

2000

1600

1200

800

Tem

pera

ture

[K]

0.800.700.600.50

Time [s]

Hencken BurnerC2H4/AirSpeaker on

200

150

100

50

0

T rm

s [K

]

250200150100500Frequency [Hz]

Amplitude Spectrum

Figure 4.13 Measured temperatures and its power spectrum in the burned region

above the C2H4-air flame.

The laser absorption sensor offers fast time response for line-of-sight measurements making it

well-suited for the detection of combustion instabilities. To illustrate the use of the sensor to

identify acoustic combustion instabilities, a disturbance was introduced in the flame by

modulating the fuel flow with a speaker attached to the bottom of the Hencken burner (see Figure

4.11). The speaker is driven with a 50 Hz sine wave, thus producing an oscillating gas

temperature. Figure 4.13 shows a time series of gas temperature (top panel) and the Fourier

transform (lower panel). The dominant and harmonic modes of the temperature fluctuations are

clearly shown in the power spectrum. The width of each bar is around 0.33 Hz, which

corresponds to the frequency resolution in the determination of the discrete Fourier transform

Chapter 4

74

over a 3 sec sampling interval. Note the prominent acoustic fluctuation frequency of 50 Hz. These

results demonstrate the utility of this sensor for quantitative, accurate identification of acoustic

disturbances. The ability of this H2O absorption sensor to measure concentration and gas

temperature and track fluctuations illustrates the potential of this sensor for real-time monitoring

of combustion.

4.3.3 Closed-loop Control of Mean Temperature

DFB1800 nm

FunctionGenerator

LaserController

ParabolicMirror

InGaAsDetector


Computer

Fuel flow Controller

Control Signal

N - Purged Area2 N - Purged Area2

View looking down duct

Air

C H2 4

FilterFocusing mir ror

Figure 4.14 Experimental schematic of the measurement system applied to the Hencken burner.

The diode laser temperature sensor was used to control the mean temperature of a C2H4/Air

laboratory flame. Figure 4.14 shows the experimental arrangement: light from a distributed-

feedback InGaAsP diode laser emitting near 1.8 µm is directed across a Hencken burner, and the

transmitted light intensity is detected with an InGaAsP detector. The diode laser is driven with an

ILX Lightwave LDC-3900 module and appropriate temperature and current controllers; the

wavelength is injection current tuned with a ramp from an SRS DS345 function generator.

Reflective optics are used throughout, including the laser collimation, to minimize back

reflections into the laser and reduce etalon interference.


75

A uniform, 5-cm square flat-flame is produced with ethylene/air mixing at the surface of the

burner. The entire optical path except for the burner is purged with nitrogen to avoid absorption

from ambient water vapor. Apertures in the 7-cm diameter duct limit the laser beam to a 4 mm

diameter, which passes 2 cm above the burner surface on the diagonal of the square burner

resulting in an optical path length over the burner of 7 cm.

Figure 4.15 shows the strategy for closed-loop control of mean temperature in Hencken burner. A

proportional voltage-controlled solenoid valve is used to adjust the fuel flow rate in the current

experiment. With a constant air stream, adjusting the equivalence ratio varies the flame

temperature. The error signal fed to the control algorithm is obtained from the difference between

the measured temperature value and the desired set point value, Tdesired. The feedback control

signal Vcontrol is thus calculated from the product of the error signal (T-Tdesired) and an adjustable

gain factor G [Furlong 1996]. The gas temperature can be effectively adjusted to the desired

temperature by this closed-loop control system.

Tdesired HenckenBurner

Airm•

Fuelm•

Fuel Flow Controller

1.8 µm Single-laser Sensor

Vcontrol

Vbias

Control System

+ Vadjusted

Tmeasured

T∆

+ _

+

Figure 4.15 Block diagram showing the strategy used for closed-loop control of the mean

temperature.

Chapter 4

76

1800

1700

1600

1500

1400

Tem

pera

ture

[K]

6005004003002001000

Time [s]

Tdesired

Laser Scan=500HzSampling rate=1MHz300-scan (0.6 sec) average

Control On Control Off Control On

Figure 4.16 The temperature response to a desired set-point temperature.

1800

1700

1600

1500

1400

1300

Tem

pera

ture

[K]

1.00.80.60.40.20.0-0.2Time [s]

Tdesired 20-scan(40ms) averaged T 60-scan(120ms) averaged T 100-scan(200ms) averaged T

Laser scan rate=500HzSampling rate=1MHz

Figure 4.17 The response time of the closed-loop control system.


77

Figure 4.16 illustrates the measured temperature response to a desired set-point temperature. Note

when the control is turned off, the temperature fluctuation significantly increases, and when the

control is re-applied the temperature recovers its relatively stable state. The standard deviation in

the percentage temperature variation is less than 1% when the control is on (0~200 sec &

400~600 sec ), and nearly doubles when the control is off due to natural combustion instabilities.

Figure 4.17 demonstrates the system response to a step-change in the desired temperature using

different levels of scan averaging. The (1/e) response time of the closed-loop control system is

about 0.15 sec, owing primarily to the finite response time of the fuel flow control.

4.3.4 Time-resolved measurements in a swirl-spray combustor

The 1.8µm, wavelength-scanned, direct-absorption, one-laser temperature sensor was used for

time-resolved measurements in a swirl-spray combustor in the laboratory of Professor Ephraim

Gutmark at the University of Cincinnati. A detailed description of the swirl-stabilized spray

combustor utilized in the present experiment is given elsewhere [Li 2004]. The combustion

chamber has a 100 mm square cross section and is 450 mm long, with flat quartz windows to

provide optical access. The laser beam is angled ~10o horizontally to avoid the etalons from

multiple reflections within the quartz windows. The total path length is 102 mm. The laser is

scanned at 2 kHz across the H2O line pair to record spectrally resolved absorption line shapes.

The transmitted signal is sampled at 1MHz. A laboratory-code (written in LABVIEW) was used

for post-processing data. A 4-scan average is used to improve SNR, which reduces the

temperature data rate to 500 Hz. Temperature is measured for a single axial location at 50 mm

downstream of the nozzle for gaseous fuel (propane) and liquid fuel (ethanol).

Chapter 4

78

Diode laser controller

Functiongenerator

Computer

FilterN2 purge N2 purge

SpeakerSpeaker

Mirror

Mirror

HeNelaser

FlipMirror

1.8 µmDFB laser

Collimator

Detector


Functiongenerator

Computer

FilterN2 purge N2 purge

SpeakerSpeaker

Mirror

Mirror

HeNelaser

FlipMirror

1.8 µmDFB laser

Collimator

Detector

Figure 4.18 Experimental schematic of the measurement system applied to the swirl spray

combustor.

A schematic diagram of the experimental setup is shown in Figure 4.18. Light from a distributed-

feedback InGaAsP diode laser emitting near 1.8 µm is directed across a swirl spray combustor,

and the transmitted light intensity is detected with an InGaAsP detector. Although infrared-

sensitive cards are commercially available near 1.8 µm, the laser beam is not easily observed due

to the low power of the laser. The laser beam is coaligned with a “red” HeNe visible laser beam

for alignment purposes, via a flat flip mirror. The diode laser is driven with an ILX Lightwave

LDC-3900 module and appropriate temperature and current controllers; the wavelength is

injection current tuned with a ramp from an SRS DS345 function generator. In the experiment,

most of the laser beam is enclosed by a pipe with N2 flowing to eliminate ambient absorption in

the optical path. The transmitted signals are recorded by NI-6115 DAQ card installed in a PC for

post-processing of data. A bandpass optical filter is added so that the emission noise from flame

is attenuated. Reflective optics are used throughout, including the laser collimation, to minimize

back reflections into the laser and reduce etalon interference.


79

Gas Fuel (Propane) Liquid Fuel (Ethanol)

Figure 4.19 Reduced line-shapes for gas and liquid fuel.

Figure 4.19 shows the reduced pair of wavelength-scanned absorption measurements using gas

and liquid fuel in the combustor. Figure 4.19 (left panel) is for an air flow rate of 10 SCFM and

propane flow rate of 10 SLM. Figure 4.19 (right panel) is for an air flow rate of 57.5 SCFM and

ethanol flow rate of 0.1 kg/min. As expected, SNR is reduced in liquid fuel experiments due to

beamsteering effects and unburned liquid droplet interference. Although 4-scan averaging

provides sufficient precision for the current condition, additional averaging is required to improve

SNR under more noisy conditions for more practical flames.

200

150

100

50

0

T2 rm

s [K

2 ]

25020015010050

Frequency [Hz]

2400

2000

1600

1200

Tem

pera

ture

[K]

0.50.40.30.20.1Time [s]

Propane Speaker Off

Laser Scan Rate = 2000Hz4-scan average

(a) Unforced flow

40x10-3

30

20

10

0

Abs

orba

nce

(kL)

2.22.01.81.61.41.2Relative Frequency [cm-1]

Raw Data Voigt fit

40x10-3

30

20

10

0

Abs

orba

nce

(kL)

2.22.01.81.61.41.2Relative Frequency [cm-1]

Raw Data Voigt fit

Chapter 4

80

200

150

100

50

0

T2 rm

s [K

2 ]

250200150100500

Frequency [Hz]

2400

2000

1600

1200

Tem

pera

ture

[K]

0.50.40.30.20.1Time [s]

Speaker On: 100Hz

Laser Scan Rate = 2000Hz4-scan average

Propane

(b) Forced flow

Figure 4.20 Measured temperatures and its power spectrum in the burned region above the Propane-air flame (unforced (a) and forced flow (b)).

To illustrate the use of the sensor to identify acoustic combustion instabilities, a fluctuation was

introduced in the flame by modulating the air flow with two speakers attached to the fuel flow

line, as shown in figure 4.18. Measurements were made for an air flow rate of 10 SCFM and

propane flow rate of 10 SLM. With laser scan rates of 2000Hz and 4-scan averages, a time

resolution of 2ms is achievable. Figure 4.20(a) shows the measured temperature and its power

spectrum when the speaker is off. This unforced flame shows no dominant instability at this

condition. The speakers are driven with a 100 Hz sine wave, thus producing an oscillating gas

temperature. The dominant mode of the temperature fluctuations is clearly shown in figure

4.20(b), which demonstrates the utility of this sensor for quantitative characterization of acoustic

disturbances. It is concluded that fast-response of TDL T sensor allows direct measurement of

power spectrum which is not feasible with thermocouples. The time response of this sensor

suggests the potential for real-time combustion control.


81

Figure 4.21 Four sensor positions investigated: 1. Top of flame 2. Under flame 3. Above flame 4. Diagonal

Figure 4.22 Power spectrum at four sensor positions investigated (Propane).

1 2

3 4

1200800400

0

T2 rm

s [K

2 ]

250200150100500

Frequency [Hz]

80604020

0

600400

2000

80604020

0250200150100500

21

3 4

Chapter 4

82

It should be noted that the position of laser beam is quite critical for measurements. To

investigate the best location to observe the temperature fluctuations, four locations at 50 mm, 100

mm, 150 mm downstream of the nozzle and diagnostic direction are examined. As shown in

figure 4.21, location 1 is near the flame tip; location 2 is in the center of the flame; location 3 is

above the flame; and location 4 is diagonal through the flame and its tip. As indicated by the

power spectra in figure 4.22, position 1 (top of flame) is the most sensitive place to observe

temperature fluctuations from fuel modulation. The ability of the 1.8 µm sensor to measure gas

temperature and track fluctuations illustrates the potential of TDL temperature measurements for

combustion sensing and control.

4.4 Summary

A single-diode-laser sensor based on wavelength-scanned absorption was shown to provide rapid

and accurate temperature measurements in a combustion environment. The strategies and criteria

to select optimum water features in the 1-2 micron wavelength range have been detailed. The ten

best NIR water transitions for temperature measurements with a single DFB laser in atmospheric-

pressure flames were determined by systematically analyzing the water spectra in this spectral

region. These optimum line pairs are all in the 1.8~1.9 µm region. The greatest advantage of

these water line pairs is the potential to measure both with a single scan for one diode laser. Even

though different laser specifications may enable other (more widely spaced) line pairs, the line

selection criteria described here may be applied for a quantitative evaluation of potential

transitions. Discrepancies between the experimentally determined spectroscopic parameters and

HITRAN/HITEMP database are also found in this region. Thus, it is absolutely necessary to

verify or experimentally determine the fundamental spectroscopic parameters in the development

of a practical sensor.

A specific line pair (#10) was investigated experimentally, and the pertinent spectroscopic

parameters determined from cell experiments, yielding improvements in the spectroscopic

database. This line pair should be applicable for temperature measurements in the range from 960

to 3300 K. Demonstration experiments were conducted in a steady and a forced Hencken burner.

The presence of cold boundary layers was shown to impact the temperature inferred assuming

uniform conditions, but a simple assumption of a trapezoidal temperature distribution was shown

to recover very accurate values for the core temperature of the flow. Experiments with forced

flames confirmed the utility of the sensor to monitor temperature fluctuations. In addition, the


83

sensor is used for closed loop set-point temperature adjustment. Qualitative sensing of

temperature fluctuations and frequencies are also demonstrated in swirl spray combustor. The

results offer clear evidence that this sensor system has the flexibility, speed and accuracy to be a

useful tool for fundamental and applied combustion monitoring and control.

Chapter 4

84

85

Chapter 5: Temperature sensing using H2O transitions near 1.4 µm In this chapter, the development of a diode-laser sensor system is described for non-intrusive

measurements of gas temperature in combustion systems combining scanned-wavelength with

wavelength modulation and 2f detection. The sensor is based on a single diode laser (distributed-

feedback), operating near 1.4 µm and scanned over a spectral range targeting a pair of H2O

absorption transitions (7154.354cm-1 & 7153.748 cm-1) at a 2 kHz repetition rate. The wavelength

is modulated at a frequency f = 500 kHz with modulation amplitude a = 0.056 cm-1. Gas

temperature is inferred from the ratio of the second harmonic signals of the two selected H2O

transitions. The fiber-coupled-single-laser design makes the system compact, rugged, low cost

and simple to assemble. As part of the sensor development effort, fundamental spectroscopic

parameters of the probed transitions including the line strength, self-broadening coefficients, air-

broadening coefficients, and their temperature dependence were determined via laboratory

measurements. The sensor design includes considerations of hardware and software to enable fast

data acquisition and analysis; a temperature readout rate of 2 kHz has been demonstrated for

measurements in a laboratory flame at atmospheric pressure. The combination of scanned-

wavelength and wavelength-modulation minimizes interference from emission and provides a

robust temperature measurement that is useful for combustion control applications.

5.1 Motivation The previous chapter reported a 1.8 µm single-laser temperature sensor based on wavelength-

scanned direct absorption of two adjacent H2O lines. That sensor system has the desired

flexibility, sensitivity, speed and accuracy to be a useful tool for fundamental and applied

combustion monitoring. However, the specific sensor design was not without disadvantages. A

major limitation is that the strong absorption at room temperature of one of the lines employed

makes it sensitive to ambient air interference and subject to interference from cold boundary

layers in the combustor. Although this previous sensor could acquire temperature data at kHz

rates, the analysis of the direct absorption data required post-processing to extract accurate and

precise temperature, which significantly reduces the update rate for control applications.

These limitations are substantially mitigated in the approach reported here utilizing a wavelength-

scanned single-laser sensor architecture combined with wavelength modulation spectroscopy

(WMS) and 2f detection. By using wavelength modulation with 2f detection, the measurement

Chapter 5

86

sensitivity is improved by shifting the detection to higher frequencies where laser excess noise

and detector thermal noise are both much smaller; in addition flow-generated noise outside the

detection bandwidth is suppressed using phase-sensitive detection. [Liu 2004; Fernholz 2002;

Bullock 1997] Furthermore, the data analysis update rate is significantly increased because 2f

detection simplifies the computational analysis needed. The increased sensitivity enables the use

of relatively weak absorption transitions near 1.4 µm where fiber-coupled lasers and fiber

components are readily available from the mature telecommunication laser technology. We select

transitions that originate on energy levels with significant internal energy which have weak

absorption at room temperature, minimizing the interference from ambient air and cold boundary

layer. This new sensor system offers significant advantages for real-time, in situ measurements of

temperature for combustion control.

Water is a primary combustion product and its prevailing and relatively strong absorption spectra

in the near-infrared region make it an ideal species for temperature measurement. By suitable

choice of laser wavelength it is possible to measure temperature using a single diode laser [Zhou

2003]. The use of a single diode laser can greatly simplify the sensor system and reduce cost

compared with wavelength-multiplexing techniques.

Previous combustion control work [Furlong 1996; Furlong 1999] in our laboratory showed that

temperature is a good control variable for complete combustion and reduced emissions in a forced

vortex incinerator. Furlong et al. [Furlong 1999] multiplexed two diode lasers to infer

temperature at a 2 kHz rate from the ratio of two peak absorbances. Although this ratio was a

good control variable, it was contaminated by optical emission and other interference; thus the

absolute temperature determined by this sensor design can be subject to large uncertainty. This

problem generally limits fixed-wavelength sensors to flames without soot, fuel spray, or other

scattering interference. As shown in the previous chapter, a scanned-wavelength approach

utilizing ratios of integrated absorbance offers significant mitigation of these problems at the cost

of more complex data analysis. The laser wavelength is scanned across an absorption feature and

the zero absorption transmission baseline must be inferred. In this chapter we illustrate that this

data acquisition and processing can be significantly simplified by using a wavelength modulation

approach with 2f detection. A continuous temperature measurement readout rate of 2 kHz is

demonstrated for this scanned wavelength sensor.

Temperature Sensing using H2O transitions near 1.4 µm

87

5.2 Development of single-laser T sensor (2f) 5.2.1 Line selection

10-5

10-4

10-3

10-2

10-1

100

Line

Stre

ngth

[cm

-2/a

tm]

2.01.91.81.71.61.51.41.31.21.11.0Wavelength [µm]

2ν1, ν1+ν3, 2ν3

ν1+ν2, ν2+ν3

T=1000K HITRAN 2004

2ν1+ν2, ν1+ν2+ν3, ν2+2ν3

Figure 5.1 Linestrength of H2O in the 1 to 2 µm spectral region at 1000 K (from

HITRAN 2004 database)

Just as seen earlier for the direct absorption sensor, selection of water vapor absorption features is

an important part of the sensor design. Figure 5.1 graphically depicts the near-infrared (NIR) line

strengths of water over a range of wavelengths from 1 to 2 µm at a temperature of 1000K using

the HITRAN 2004 database [Rothman 2003], and the red bar illustrates the region where

telecommunication lasers are available. Transitions are chosen using the following requirements:


range.

We assume a minimum detectable absorbance of 10-4, and a desired SNR of 10, which requires a

peak absorption be greater than 10-3. In addition, the peak absorption should preferably be less

Chapter 5

88

than ~ 0.05 to meet the “weak transition” assumption in Eqn (2.35) associated with wavelength

modulation measurements.

For our laboratory experiment, with a pathlength of 5 cm and a combustion product water vapor

mole fraction between 0.05 and 0.2 at a pressure of 1 atm, we thus require

2

3, , ,( ) ( ) 1 5% 5 10peak i H o peak i peakS T P x L S T atm cmν ν να φ φ −= ⋅ ⋅ ⋅ ⋅ = ⋅ ⋅ ⋅ ⋅ ≥ (5.1)

2, , ,( ) ( ) 1 20% 5 0.05peak i H o peak i peakS T P x L S T atm cmν ν να φ φ= ⋅ ⋅ ⋅ ⋅ = ⋅ ⋅ ⋅ ⋅ ≤ (5.2)

Hence the constraint on the product of line strength and lineshape function becomes 1 1 1 1

,0.05 ( ) 0.004i peakcm atm S T cm atmνφ− − − −⋅ ≥ ⋅ ≥ ⋅ (5.3)

which we apply in the temperature range of current interest, 1000 - 2500 K.

A total of 963 transitions in the HITRAN 2004 database meet the absorption strength criterion in

the 1.0-2.0 µm NIR region.

Criterion 2: Transitions should be relatively free of ambient H2O interference

10-2

10-1

100

101

102

103

104

105

S(T

)/S

(296

)

4000300020001000Temperature [K]

E" = 500 cm-1

E" = 1500 cm-1

E" = 1700 cm-1

E" = 2500 cm-1

Figure 5.2 Linestrength scaled by values at room temperature as a function of

temperature for H2O lines with various lower state energies.


89

As previously mentioned, it is usually necessary to purge outside the target measurement zone

with nitrogen or dry air to eliminate interference from ambient water. The amount of purging

necessary to attain a desired low-humidity set-point depends not only on the ambient humidity

level, but also on the absorption strength of the transition. If a transition has a strong absorption

coefficient at room temperature, greater care has to be taken in the purging process. Even a short,

occasionally unpurged path may reduce accuracy and lead to greater measurement uncertainty.

This difficulty can be easily mitigated by choosing transitions with desirable lower state energies.

The temperature-dependent linestrength is given by Eqn. (2.23). The ratio of line strength at

temperature and line strength at room temperature is given by:

1"

0 0 0

0 0

0

0

( )( ) 1 1exp 1 exp 1 exp( ) ( )

Q T T hc hcS T hcEkTS T Q T T k T T kT

ν ν−

− − = − − − −

(5.4)

The curves in figure 5.2 show line strength scaled by values at room temperature vs. temperature

for H2O lines at various lower state energies. As the lower state energy is raised, the line strength

ratio at elevated temperature is increased. If we require the strength in the temperature range of

1000 - 2500 K to be at least 3 times stronger than its strength at room temperature, the constraint

on minimum lower state energy becomes

1" 1700E cm−≥ (5.5)

Criterion 2 reduces the number of potential candidates to 558 lines. For measurements with cold

thermal boundary layers, this criterion helps make the sensor immune to the effect of cold edges

and improve sensor accuracy. [Ouyang 1990]

Criterion 3: The absorption lines must lie within a single laser scan and not overlap

significantly at atmosphere pressure.

Currently the typical rapid-tuning range of a single-mode DFB diode laser near 1.4 µm is ~2 cm-1.

Hence we require that the spectral separation of the line pairs must lie between 0.3 and 1 cm-1. If

line spacing is larger than ~1 cm-1, modulation amplitude will be limited by the safe current limit

and threshold of the laser at the both ends of the laser scan, this limitation could decrease the

signal-to-noise ratio (SNR) in the measurements. If line spacing is smaller than 0.3 cm-1,

Chapter 5

90

interference on the 2f peak heights will be caused by the overlap of the two absorption features,

making analysis more complicated. Criterion 3 reduces the number of potential H2O line

candidates to 188 line pairs.


yield a 2f peak height ratio that is sensitive to the probed temperature.

It was previously mentioned that a line pair with a large difference in lower state energy is

desired to provide high temperature sensitivity [Zhou 2003]. A constraint on minimum lower

state energy difference of 700 cm-1 is proposed for the line selection " " " 1

1 2 700iE E E cm−∆ = − ≥ (5.6)

There are a total of 33 line pairs that satisfy criteria 1-4, and they all have good temperature

sensitivity in the temperature range 1000 ~ 2500 K.


transitions.

The 33 potential line pairs are examined for burnt gas conditions at 296K, 1000K and 2000K to

investigate the potential interference from neighbor transitions. In all, 21 of the promising

transition pairs are rejected because of interference from adjacent absorption features. The

remaining 12 line pairs are regarded as the most promising water vapor features for temperature

measurement in combustion environments using the selection criteria noted above. Table 5.1

summarizes the 12 line pair candidates.

Criterion 6: The wavelength should be in the 1.25-1.65 µm range.

In this work, we chose to limit the wavelength of the transitions to the 1.25-1.65 µm range, where

fiber-coupled telecommunication lasers are commercially available. Sensors built in this

wavelength range can also take advantage of extended fiber-optic component technology for

signal transmission and multiplexing. There are 4 line pairs (pairs 1-4 in Table 1) which satisfy

criteria 1-6. Table 5.2 summarizes the line selection result.


91

Table 5.1 Candidate H2O line intensity pairs for measurements of temperature and water concentration in the 1-2 µm region based on HITTRAN2004.

Line pair λ [nm] ν [cm-1]

103 S @1000K

[cm-2atm-1]

E” [cm-1]

∆E” [cm-1]

Max P [atm]

Line Spacing [cm-1]

Notes

1442.67 6931.592 4.604E-4 1813.22 1 1442.51 6932.352 4.604E-7 3072.73 1259.73 2.2 0.760 B

1397.87 7153.748 5.504E-6 2552.86 2 1397.75 7154.354 3.852E-4 1789.04 763.82 3.7 0.606 B, E

1337.44 7476.949 1.421E-4 1899.01 3 1337.37 7477.366 5.403E-7 3319.45 1420.44 5.0 0.417 A, C, D

1337.44 7476.949 1.421E-4 1899.01 4 1337.30 7477.743 3.954E-6 2746.02 847.01 5.0 0.794 A, C, D

1982.87 5043.193 9.927E-7 3058.40 5 1982.66 5043.738 9.267E-5 2246.88 811.52 2.8 0.545 B

1981.83 5045.831 2.242E-6 2915.89 6 1981.54 5046.576 5.554E-5 2105.87 810.02 8.0 0.745 B, C

1975.41 5062.250 6.234E-6 2904.43 7 1975.11 5063.017 1.141E-4 1960.21 944.22 5.9 0.767 B, C

1967.46 5082.697 5.504E-6 2690.59 8 1967.32 5083.058 1.611E-4 1843.03 847.56 3.7 0.361 B

1852.38 5398.473 3.041E-4 1908.02 9 1852.06 5399.396 1.531E-6 3032.69 1124.67 6.3 0.923 A, C

1764.78 5666.434 7.866E-7 3211.21 10 1764.57 5667.119 9.486E-6 2321.81 889.40 1.2 0.685 D

1764.78 5666.434 7.866E-7 3211.21 11 1764.51 5667.305 2.843E-5 2321.91 889.30 3.4 0.871 D

1764.57 5667.119 9.486E-6 2321.81 12 1764.45 5667.489 2.731E-7 3211.06 889.25 1.5 0.370 D

Notes: A: some interfering absorption by room air from nearby transitions, need purge

B: isolated from nearby interference C: good for high pressure experiments D: close to other promising line pair, measurement accuracy could be improved by averaging

results with nearby line pair E: verified experimentally

Table 5.2 Line selection result using the selection criteria in the near-infrared region based on HITRAN2004.

Transitions between 1.0µm and 2.0 µm 15907

Transitions, satisfying 1 963 Transitions, satisfying 1,2 558

Line pairs, satisfying 1, 2, 3 188 Line pairs, satisfying 1,2, 3, 4 33

Line pairs, satisfying 1,2, 3, 4, 5 12 Line pairs, satisfying 1,2, 3, 4, 5, 6 4

Chapter 5

92

0.010

0.008

0.006

0.004

0.002

0.000

Spe

ctra

l abs

orpt

ion

coef

ficie

nt [c

m-1

]

748074797478747774767475Frequency [cm

-1]

0.010

0.008

0.006

0.004

0.002

0.0006933693269316930 7156715571547153

T = 296 K T = 1000 K T = 2000 K

1 2

3, 4

P = 1 atmX = 10%

Figure 5.3 Expanded view of absorption spectra for the four selected H2O line pairs

in the 1.4 µm region based on the HITRAN2004 database; evaluated for P=1 atm,

10% H2O, 90% air.

Figure 5.3 shows segments of the calculated H2O (10%) absorption spectra for the four line pairs

based on HITRAN2004 [Rothman 2003] parameters; spectroscopic constants are listed in Table 2.

The pair of features at 7154.35cm-1 & 7153.75 cm-1 , labeled pair 2, is selected for several reasons,

as follows. Both features are well resolved at one atmosphere pressure, avoiding interference by

neighboring transitions. Both have similar absorption coefficients and thus will have similar

measurement uncertainty. Additionally, they have sufficiently different lower state energy E” to

yield a high temperature sensitivity while the large E” values of 1789 cm-1 and 2553 cm-1 insure

that the transitions will be strongest at temperatures much larger than room temperature, thereby

minimizing any interference from room temperature water in the measurement path. Finally, the

wavelengths of these two transitions are close enough to be covered in a single laser scan but

separated enough to be isolated from each other. These two transitions thus offer an attractive

opportunity to examine the potential for a practical single laser-based combustion temperature

sensor with potential for control applications.


93

0.010

0.008

0.006

0.004

0.002

0.000

Spe

ctra

l abs

orpt

ion

coef

ficie

nt [c

m-1

]

50445043Frequency [cm

-1]

50465045 50635062

P = 1 atmX = 10% T = 296 K

T = 1000 K T = 2000 K

5 6 7

0.010

0.008

0.006

0.004

0.002

0.000

Spe

ctra

l abs

orpt

ion

coef

ficie

nt [c

m-1

]

50835082Frequency [cm

-1]

53995398 56685667

P = 1 atmX = 10%

T = 296 K T = 1000 K T = 2000 K

8 9 10,11,12

Figure 5.4. Expanded view of absorption spectra for the selected H2O line pairs in

the 1.8µm region based on the HITRAN2004 database; evaluated for P=1 atm, 10%

H2O, 90% air.

It is noteworthy that 70% of the promising transitions (see Table 5.1) were rejected because of the

wavelength limitation in criteria 6. Our spectral simulations show that the water spectrum in the

1.8µm spectral region is stronger and has more isolated features than the 1.4µm spectral region,

and hence holds promise for gas sensing. In the future, the wavelength limitation in criteria 6 can

Chapter 5

94

be avoided when fiber-coupled laser and fiber-optic component technology becomes available in

the 1.8 µm region. Figure 5.4 shows the simulated spectra (P=1 atm, 10% H2O and 90% air) for

the 8 best candidate H2O pairs (pairs 5-12 in Table 5.1) in the 1.8 µm region based on the

HITRAN2004 database.

Table 5.1 includes an estimate of the maximum suitable pressure for a combustion temperature

1500K and a limit of 10% interference from overlap or nearby transitions. Among the 8

promising candidate H2O pairs (pairs 5-12 in Table 5.1) in the 1.8 µm region, line pair 9 has the

best temperature sensitivity, but it suffers some room air water interference from nearby

transitions. Line pair 5 and line pair 8 are suitable for relatively low pressure (< 3 atm)

application due to their relatively small line spacing. Line pair 6 and line pair 7 are well isolated

and good for high pressure application. Line pairs 10, 11 and 12 are so closely spaced that they

can be covered by a single laser scan, and although they are only useful for applications at

atmospheric pressure and below, they provide a unique sensor which can improve measurement

accuracy by averaging results from three line pairs in one laser scan.

5.2.2 Spectroscopic verification

Measurement strategies based on absorption spectroscopy techniques require accurate values of

important spectroscopic parameters of the probed species. Experimental verification of pure water

vapor spectra at low pressure in a heated cell is used to generate (or validate) spectroscopic

databases for line assignment (E”) and line strength S(T). Additional controlled experiments are

performed to provide accurate pressure broadening data.

Figure 5.5 illustrates the experimental arrangement of a diode laser, a heated quartz cell,

appropriate mirrors and lenses, and two InGaAsP detectors that measure the transmitted intensity

and a solid etalon (FSR = 2.01 GHz) to calibrate laser wavelength. One fiber-coupled DFB laser

emitting near 1.4 µm is used in this study. The output from the laser is split into two beams by a

50/50 beam splitter. One beam passes through the cell and a double-pass configuration is used to

improve SNR. An ILX Lightwave LDC-3900 is used to control laser temperature and current. A

function generator is used to vary the laser injection current and thus tune the wavelength of the

laser over the desired absorption features. The 35.6 cm long static cell is made of quartz with

0.5°-wedged windows mounted at a 3° angle to minimize interference effects in the transmission

signal. The cell temperature is measured with three type-K thermocouples that are equally spaced


95

along the cell axis. The temperature deviations along the cell are determined to be <0.5%. Two

pressure gauges (MKS Baratron with a full scale deflection of 100 Torr and 1000 Torr, accuracy

of ±1%) are used to measure the cell pressure, and a mechanical pump evacuates the cell.

Distilled liquid water contained in a flask is used as a source of water vapor to measure

spectroscopic parameters. The flask is pumped down for an hour prior to measurements to

remove all gaseous impurities. The laser, detectors, and optics are enclosed in a nitrogen-purged

area to prevent interfering absorption by room air. The experimental profiles are best-fit using

Voigt profiles to get fundamental spectroscopic parameters of the probed water transitions.

Fiber Coupled DFB 1400nm 14” Sample Path

3-Zone Tube Furnace

Transmission Detector

DAQ Computer

EtalonDetector

Purged with N2

Quartz CellPurged with N2

Mixing Tank

Air Cylinder

Low P Baratron High P Baratron

Mullite Tube

Etalon

Mirror

LaserController

FunctionGenerator

Fiber Coupled DFB 1400nm 14” Sample Path

3-Zone Tube Furnace


DAQ Computer

EtalonDetector

Purged with N2


Mixing Tank

Air Cylinder


Mullite Tube

Etalon

Mirror

LaserController

FunctionGenerator


spectroscopic parameters.

Sample raw data (50-scan average) are shown in Figure 5.6. The laser is scanned at 200Hz with a

sampling rate of 1MHz, and the transmission (I) is normalized by the unattenuated signal (I0).

Since the total scan includes the far wings on both sides of the probed features, the unattenuated

signal could be determined accurately by mathematically fitting the part of the trace with no

absorption to a simple polynomial.

Chapter 5

96

1.4

1.2

1.0

0.8

0.6

Nor

mal

ized

Raw

Sig

nal I

/I 0

4321Time [ms]

Baseline Normalized Raw Signal

T = 951 KP = 15.47 TorrL = 71.12 cm

Laser Scan Rate = 200 HzSampling Rate = 1MHz50-scan average

Figure 5.6 Sample data (50-scan average) obtained from cell experiment at T = 951

K, PH2O = 15.47 Torr.

0.30

0.25

0.20

0.15

0.10

0.05

0.00

Abso

rban

ce

3.02.52.01.5Relative Frequency [cm-1]

-1.0

0.0

1.0

Res

idua

l (%

)

Raw Data Voigt fit

T = 951 KP = 15.47 TorrL = 71.12 cm

High T Line

Low T Line

Figure 5.7 Reduced H2O lineshape recorded in the cell at T = 951 K, PH2O = 15.47

Torr. The low T line is the line with the smaller value of lower-state E”.


97

10x10-3

8

6

4

2

0

Line

stre

ngth

[cm

-2/a

tm]

7155.07154.57154.07153.57153.0Frequency [cm

-1]

T =951 KLow T Line

High T Line 2High T Line 1

Figure 5.8 Line strength of the selected transitions at 1000 K based on HITRAN2004

parameters revealing that the high T line is composed of two lines.

Figure 5.7 shows the experimental data at 951 K. Based on the HITRAN2004 database (figure

5.8), the high T line is composed of two transitions which are labeled as “High T Line 1” and

“High T Line 2” in the figure; these lines have the same lower state energy and very similar

broadening coefficients. The experimental profiles are best-fit using Voigt profiles. The fitting

procedure minimizes the integrated squared difference between the experimental profile and the

Voigt profile.

As mentioned before, the integrated absorbance area of an individual transition is proportional to

partial pressure,

0

ln( )

I dI AS T

P L X P L X

ν

− = =⋅ ⋅ ⋅ ⋅

∫

(5.7)

where P[atm] is the total pressure, L[cm] is the path length, S(T) [cm-2/atm] is the line strength，

X is the mole fraction of absorbing species, and A[cm-1] is the integrated area. Thus, line strength

can be obtained by performing a linear fit on multiple area measurements at various pressures, as

shown in figure 5.9, and using the slope to measure the line strength. This procedure exploits the

improved pressure gage accuracy for P∆ measurements and avoids a “zero” pressure calibration

influence on the line strength uncertainty.

Chapter 5

98

14x10-3

12

10

8

6

4

2

0

Inte

grat

ed A

rea

[cm

-1]

181614121086Pressure [Torr]

Low T Line High T Line 1 High T Line 2

Linestrength inferred from the slope

T = 951 KL = 71.12 cm

Figure 5.9 Measured integrated absorbance area vs. H2O pressure at T=951K for the

“Low T Line”, “High T Line 1” and “High T Line 2”. The line strength can be

calculated from the slope.

10x10-3

8

6

4

2

0

Col

lisio

nal w

idth

∆ν c [

cm-1

]

161412108Pressure [Torr]

T = 951 KL = 71.12 cm

Low T Line High T Line

Self-broadening coefficient inferred from the slope

Figure 5.10 Measured collision width vs. H2O pressure at T=951K for the “Low T

Line”, “High T Line 1” and “High T Line 2”. The self-broadening coefficient can be

calculated from the slope.


99

The self-broadening coefficient, γself, is measured in a manner analogous to the line strength,

since the collision width is linear with pressure.

2 ) (2 )(C selfjjj

P PXν γγ∆ = = ⋅∑ (5.8)

where cν∆ [cm-1] is the collision width (FWHM)

By holding the Doppler width fixed at the appropriate value for the measurement temperature

during Voigt fits, the collision width is extracted from the overall width of the absorption profile

using the inferred (best-fit) Voigt a parameter. The broadening coefficient is determined by

performing a linear fit of the measured collision widths at various pressures, as shown in figure

5.10, and using the slope to calculate the broadening coefficient.

For measurements of air-broadening coefficient, an air-water vapor mixture is made of pure water

vapor and dry air. The air-broadening coefficients can be determined using

(2 )2

(1 )C self

air

X PX P

ν γγ

∆ − ⋅ ⋅=

− ⋅ (5.9)

where cν∆ [cm-1] is the collision width (FWHM), X is the mole fraction of absorbing

species and P[atm] is the total pressure. The uncertainty for the individual line strength,

self-broadening and air-broadening coefficient measurements is estimated to be <3% due to

measurement uncertainties of 1% in the total pressure, and primarily 2% in the area under

each Voigt profile.

Chapter 5

100

8x10-3

6

4

2

0

Line

stre

ngth

[cm

-2/a

tm]

30002500200015001000500Temperature [K]

Low T Line (HITRAN 2004 ) Low T Line (Exp Fit) Low T Line (Experiment)

E"=1789cm-1

Figure 5.11 Calculated and measured line strengths for the “Low T Line” as a

function of temperature.

3.0x10-3

2.5

2.0

1.5

1.0

0.5

0.0

Line

stre

ngth

[cm

-2/a

tm]

30002500200015001000500Temperature [K]

High T Line 1 (HITRAN 2004) High T Line 2 (HITRAN 2004) High T Line 2 (Experiment) Experiment

E"=2553cm-1

Figure 5.12 Calculated and measured line strengths for the “High T Line 1” and

“High T Line 2” as a function of temperature.


101

0.1

2

3

4

5

6

7

89

1

2γse

lf [c

m-1

/atm

]

3 4 5 6 7 8 91000

Temperature [K]

E"=1789cm-1 Low T Line (HITRAN 2004)

Low T Line (Experiment) Experiment

Experiment

2γself=0.302(296/T)0.65

HITRAN 2004

2γself=0.354(296/T)0.50

Figure 5.13 Calculated and measured self-broadening coefficients for the “Low T

Line” as a function of temperature.

0.1

2

3

4

5

6

7

89

1

2γse

lf [c

m-1

/atm

]

3 4 5 6 7 8 91000

Temperature [K]

E"=2553cm-1 High T Line (HITRAN 2004)

High T Line (Experiment) Experiment

Experiment

2γself=0.616(296/T)0.82

HITRAN 2004

2γself=0.598(296/T)0.50

Figure 5.14 Calculated and measured self-broadening coefficients for the “High T


Chapter 5

102

3x10-2

4

5

6

2γai

r [c

m-1

/atm

]

3 4 5 6 7 8 91000

Temperature [K]

Experiment

2γair=0.06212(296/T)0.51803

Exp Data Exp fit HITRAN 2004

HITRAN 2004

2γair=0.0642(296/T)0.53

E"=1789cm-1

Figure 5.15 Calculated and measured air-broadening coefficients for the “Low T


5

6

7

8

9

0.1

2γai

r [c

m-1

/atm

]

3 4 5 6 7 8 91000

Temperature [K]

2γair=0.08424(296/T)0.3439

Exp Data Exp fit HITRAN 2004

HITRAN 2004

2γair=0.1106(296/T)0.64

HighT Line E"=2553cm-1

Figure 5.16 Calculated and measured air-broadening coefficients for the “High T


The line strengths, self-broadening coefficients, and air-broadening coefficients for these three

transitions are measured over a range of temperature. They are plotted versus temperature in


103

figure 5.11 – 5.16, as calculated using HITRAN2004 parameters and measured in our cell. The

temperature dependence of the measured line strength is first fit to Eqn (5.4) with both E” and

S(296K) as free parameters. The agreement between the inferred E” and the HITRAN value

confirms the spectroscopic assignment. Once this assignment is confirmed the HITRAN value of

E” is used to determine S(296K). The experimentally determined spectroscopic parameters of the

selected H2O line pair are listed in table 5.3. Discrepancies are found between measured and

HITRAN data and we suggest using our measured results in future work.

5.2.3 2f temperature sensor validation

5

4

3

2

1

0

Det

ecto

r si

gnal

(V

olts

)

1.00.80.60.40.20.0Sampling time (ms)

Laser Scan with Modulation

Laser intensity I1

Laser intensity I2

0.06

0.04

0.02

0.00

-0.02

-0.04

2f S

igna

l (ar

b. u

nits

)

1.00.80.60.40.20.0Sampling time (ms)

2f Line Shape

2f Peak Height 1

2f peak height 2

Figure 5.17 Schematic of single-laser scanned-wavelength method.

As pointed out in chapter 2, there are two key issues for the WMS technique: intensity

modulation effects and calibration procedures. The problems associated with these two concerns

Table 5.3 Spectroscopic data for the selected H2O line pair

γair γself Line ν0

[cm-1]

S [cm-2/atm]

@296K

E” [cm-1] [cm-1/atm] @ 296K

nair nself

High T 1 7153.72 1.90E-6

High T 2 7153.75 6.15E-6 2552.9 0.0421 0.308 0.34 0.82

This

wor

k

Low T 7154.35 3.67E-4 1789.0 0.0311 0.151 0.52 0.65

High T 1 7153.72 1.90E-6 2552.9 0.0553 0.299 0.64 0.50

High T 2 7153.75 5.50E-6 2552.9 0.0536 0.299 0.64 0.50

HIT

RA

N

Low T 7154.35 3.85E-4 1789.0 0.0321 0.177 0.53 0.50

Chapter 5

104

are greatly simplified here. The laser wavelength is modulated by driving the laser with a

sinusoidally modulated injection current, which also modulates the laser intensity. Since we

detect the 2f signal at line center (there is little effect on the 2f signal at line center from this

intensity modulation [Liu 2004; Philippe 1993]), the intensity modulation is neglected here.

Because the 2f signal is proportional to laser intensity, many hardware-related parameters

including detector sensitivity, signal amplification, lock-in gain and bandwidth, etc. are required

exclusive of measuring the 2f signal itself. The usual approach is to calibrate the WMS sensor at a

reference condition (with the exact same settings) to eliminate the dependence of hardware-

related parameters. Performing such calibration is usually difficult and adds additional

uncertainty to the measurement results. The dependence of these instrumental parameters are

removed in this work by using a single-laser scanned-wavelength method (as shown in figure

5.17), since two transitions lie in the same laser scan and they share the same lock-in amplifier

and detector, and thus utilize identical hardware settings. Thus the 2f peak ratio simplifies:

1 1 2 12

2 2 2 2

( )( )

peakf

peak

Height I HRatioHeight I H

νν

= = ⋅ (5.10)

Where I1 and I2 are the laser intensity at line center of peak 1 and peak 2, respectively, and

2 1( )H ν and 2 2( )H ν are the second harmonic Fourier coefficients which are given by Eqn.

(2.40). The first term in Eqn. (5.10) I1/I2 is constant for a given laser temperature and laser scan

range. The second term is calculated using Eqn. (2.44). The calibration procedure becomes a

measurement of I1/I2. This is done here in two ways: (1) calibrate from measurements at a single

point in the low-pressure heated-cell experiment or (2) fit baseline to the low-pass filtered raw

data and determine I1/I2 directly. Once I1/I2 is determined using either of the methods above, this

sensor does not require further calibration even when the hardware-related parameters change

later. This is a unique advantage of using single-laser scanned-wavelength 2f WMS method.

Heated-cell experiments were performed to validate the sensor accuracy and reliability for the

temperature inferred from the ratio of the two transitions.

The experimental setup is illustrated in figure 5.18. The DFB diode laser operating near 1.4 µm is

driven by a 2 kHz sawtooth ramp to tune the wavelength combined with a faster 500 kHz sine

wave to provide the wavelength modulation. The output from the laser passes through the cell to

monitor the transmitted intensity. A flat mirror, which provides a double-pass configuration to

improve SNR, is used to reflect the laser beam to pass through the cell again. The laser, detectors,

and optics are enclosed in a nitrogen-purged area to prevent interfering absorption by room air. A


105

lock-in amplifier (Perkin-Elmer Model 7280) is used to measure the second-harmonic component

of the transmitted laser signal.

14” Sample Path

3-Zone Tube Furnace


DAQ Computer


Mixing Tank

Air Cylinder


Mullite Tube

Mirror

2kHz ramp

Modulate at f=500 kHz

+

LaserController

FunctionGenerator

FunctionGenerator

Lock-in amplifier

Reference signal Harmonic Signal

14” Sample Path

3-Zone Tube Furnace


DAQ Computer


Mixing Tank

Air Cylinder


Mullite Tube

Mirror

2kHz ramp


+

LaserController

FunctionGenerator

FunctionGenerator

Lock-in amplifier

Reference signal Harmonic Signal

Figure 5.18 Arrangement for the 2f sensor validation experiments.

Two sets of static heated cell experiments were carried out to validate the 2f sensor thermometry.

The first experiment was performed with 3 Torr pure water vapor. Two different modulation

depths (0.037 cm-1 and 0.056 cm-1) are used in this experiment. The top graph in figure 5.19

shows the comparison between the measured 2f peak ratios and the theoretical simulations. A

single point at 803K (a=0.056 cm-1) is used to calibrate the 2f sensor for both values of a. Good

agreement between measurements and simulations confirm the accuracy of the measured

fundamental spectroscopic parameters over the full range of conditions studied. The

corresponding temperatures are shown in the bottom graph in figure 5.19. The temperatures

inferred from the 2f sensor are seen to agree extremely well with the thermocouple measurements

(+/- 10K).

Chapter 5

106

1400

1200

1000

800

600

Tem

pera

ture

[K]

14001300120011001000900800700600Temperature [K]

0.4

0.3

0.2

0.1

0.0

2f p

eak

ratio

P=3 TorrXH2O=100%L=71.12 cm

Simulation

a = 0.037 cm-1

a = 0.056 cm-1

Experiment

a = 0.037 cm-1

a = 0.056 cm-1Single Point Calibration

Figure 5.19 Comparison of measured 2f peak ratio with simulated 2f peak ratio (top);

Comparison of measured temperature with thermocouple temperature. (bottom)

To demonstrate the applicability of the 2f sensor at atmospheric conditions, the heated cell

experiment was repeated with ambient air at atmospheric pressure. The water concentration in the

ambient air was determined to be 1.1% using a direct absorption method. Two different

modulation depths (0.037 cm-1 and 0.056 cm-1) are also used in this experiment. The experimental

results are plotted in figure 5.20. The top graph in figure 5.20 shows the comparison between the

measured 2f peak ratios and the theoretical simulations. The signal data point at 877K (a=0.037

cm-1) is used to calibrate the 2f sensor. The inferred temperatures from the 2f sensor are plotted in

the bottom graph in figure 5.20. Comparison of the measured temperatures and thermocouple

data shows good agreement (+/- 20 K).


107

1200

1000

800

600

Tem

pera

ture

[K]

1300120011001000900800700600Temperature [K]

0.30

0.25

0.20

0.15

0.10

0.05

0.00

2f P

eak

Rat

io

Simulation

a = 0.037 cm-1

a = 0.056 cm-1

Experiment

a = 0.037 cm-1

a = 0.056 cm-1

P =1 atmXH2O=1.1%L=71.12 cm

Single Point Calibration

Figure 5.20 Comparison of measured 2f peak ratio with simulated 2f peak ratio (top);

Comparison of measured temperature with thermocouple temperature. (bottom)

Good agreement is found for both sets of experiments with different modulation depths. The

upper curves in figure 5.19 and 5.20 confirm the accuracy of the measured fundamental

spectroscopic parameters over the full range of conditions studied. The lower curves in figures

5.19 and 5.20 demonstrate the efficiency and accuracy of the 2f sensor thermometry, which

shows good potential for combustion sensing and control.

5.2.4 Real-time capabilities

Many measurement and control applications require high performance in real-time. Real-time

data acquisition and signal processing are the core of real-time performance. The hardware-

software architecture of the 1.4 µm temperature sensor is described in this section.

Chapter 5

108

Detector

DAQ Computer

2kHz ramp

Laser

FunctionGenerator

FunctionGenerator

Harmonic Signal

Transmission

Collimator

DAQ Computer


+

LaserController

FunctionGenerator

FunctionGenerator

Perkin Elmer 7280 Lock-in amplifier

Reference signal

Harmonic Signal

DFB Laser

Bias TEE

DG535 DelayGenerator

Trigger 1

Measurement Path length

Trigger 2

Real Time T

2kHz

Detector

DAQ Computer

2kHz ramp

Laser

FunctionGenerator

FunctionGenerator

Harmonic Signal

Transmission

Collimator

DAQ Computer


+

LaserController

FunctionGenerator

FunctionGenerator


Reference signal

Harmonic Signal

DFB Laser

Bias TEE

DG535 DelayGenerator

Trigger 1

Measurement Path length

Trigger 2

Real Time T

2kHz

Figure 5.21 Complete hardware-software framework

+

+

+ _

_

_

5.6 kΩ 5.6 kΩ 5.6 kΩ 5.6 kΩ

11 kΩ 11 kΩ

470 kΩ 470 kΩ

470kΩ 470 kΩ

11 kΩ 11 kΩ

2N3904 2N3904

2N3904 2N3904

22 μF 22 μF

0.1 μF 0.1 μF

~ 500 kHz sine wave

~ 2 kHz sawtooth wave

Output

+9V

+9V +9V

+9V +9V

+9V +9V

Figure 5.22 Diagram of the bias-tee

Figure 5.21 presents the complete schematic of hardware-software implementation for the 1.4 µm

single-laser sensor. A 2 kHz sawtooth ramp is combined with a faster 500 kHz sinusoidal signal

through a bias-TEE. The high quality bias-TEE is designed using a differential circuit which is


109

shown in figure 5.22. The values of resistors and capacitors are chosen based on the transistor’s

(2N3904) parameters and the frequencies of ramp and modulation.

3.0

2.0

1.0

0.0

Sig

nal [

V]

10008006004002000Time [us]

5

4

3

2

1

0

Sig

nal [

V]

Transmission

Trigger1Laser Scan Rate = 2000 HzModulation Frequency = 500 kHz

Figure 5.23 The trigger signal (top) and the laser transmission signal (bottom).

The detected signal, which is shown in the bottom graph of figure 5.23, is fed into a Perkin-Elmer

lock-in amplifier (Model 7280). The reference signal is provided to the lock-in by the function

generator that generates the 500 kHz sinusoidal signal. The trigger signal (Trigger 1, top graph of

figure 5.23) of the other function generator (which provides 2 kHz ramp) is connected to a digital

delay generator (Stanford Research System DG535) to generate a timing trigger signal (Trigger

2). Trigger 2 and the resulting second-harmonic components of the transmitted laser signal from

lock-in are transferred to PC for data analysis. There are two DAQ cards installed in the DAQ

computer: one is Gage CompuScope 1250 which is used for data acquisition, and the other one is

National Instruments PCI 6120 which is used to output the 2f ratio (voltage).

Chapter 5

110

Sign

al [V

]

10008006004002000Time [us]

Sig

nal [

V]

Acqu

ired

Sign

al [V

]

Data Acquisition Data Acquisition

Trigger 2

2f signal

Acquired 2f signal

Transfer & Calculation

Output Output

Rising Edge

Falling Edge

Figure 5.24 Timing diagram: timing trigger signal (Top), the second-harmonic signal

(Middle) and the acquired signal (Bottom)

Figure 5.24 presents the detailed timing diagram of the 1.4 µm single-laser sensor. The timing

trigger signal, detected second-harmonic signal and acquired signal are shown in the top, middle

and bottom graphs of figure 5.24, respectively. A laboratory code is written in C/C++ for data

acquisition and analysis. At the instant when the falling edge of trigger 2 is detected, a selected

data record (usually 1000 points) is captured into the on-board memory of CompuScope 1250 and

the acquisition is stopped. The falling edge of trigger 2 and the number of data points are adjusted

so that all the useful information (2f peaks in the current study) is captured. Once the acquisition

is complete, the signal processing program transfers the captured data from on-board memory to

PC memory. This program takes advantage of the high speed PCI bus-mastering data transfer

technique, whose transfer rate is up to 100 MB/s. Data analysis, including peak finding and ratio

calculation, is then performed on the accumulated data. When the rising edge of trigger 2 is

detected, the program outputs the calculated 2f ratio through National Instruments PCI 6120. The

system is then ready for the next acquisition. 2 kHz real-time performance is achieved for the 1.4

µm single-laser sensor, which is sufficient for many combustion sensing and control applications.


111

5.3 Combustion Demonstration 5.3.1 Identification of Acoustic Instabilities

Detector

DAQ Computer

2kHz ramp

Laser

FunctionGenerator

FunctionGenerator

Lock-in amplifier

Harmonic Signal

Transmission Collimator

DAQ Computer


+

LaserController

FunctionGenerator

FunctionGenerator

Lock-in amplifier

Reference signal

Harmonic Signal

Forced Fuel (100Hz)

DFB Laser

Detector

DAQ Computer

2kHz ramp

Laser

FunctionGenerator

FunctionGenerator

Lock-in amplifier

Harmonic Signal

Transmission Collimator

DAQ Computer


+

LaserController

FunctionGenerator

FunctionGenerator

Lock-in amplifier

Reference signal

Harmonic Signal

Forced Fuel (100Hz)

DFB Laser

Figure 5.25 Schematic diagram of the measurement system applied to a Hencken

burner.

To illustrate the potential of the sensor for monitoring fluctuations of acoustic instabilities in

combustion gases from a time history of temperature data, measurements were made on a flat-

flame Hencken burner, as shown in figure 5.25. The Hencken burner can produce a uniform,

constant-pressure flow field, as described in chapter 4 and ref. [Furlong 1998]. The burner

consists of a 5-cm square array of inner tubes (0.5-mm internal diameter), which supply the fuel

(C2H4). Coannual air streams mix with fuel stream at the top of the burner to produce an array of

shot diffusion flames. The 1.4 µm single-laser sensor is driven by an external modulation, which

consists of a 2 kHz sawtooth ramp combined with a faster 500 kHz sinusoidal signal. The second-

harmonic components of the transmitted laser signal are obtained by a Perkin-Elmer lock-in

amplifier (Model 7280) with a time constant of 1 µs. The temperature is inferred from the ratio of

2f peak heights. 2 kHz real-time data processing and reduction is achieved by a fast PC

combined with a laboratory code written in C++ as described above.

Chapter 5

112

3000

2500

2000

1500

1000

Tem

pera

ture

[K]

1.00.80.60.40.20.0Time [s]

Hencken BurnerC2H4/AirSpeaker On (100Hz)

Time [s]

Tem

pera

ture

[K]

5x104

4

3

2

1

0

Trm

s2 [K2 ]

10008006004002000Frequency [Hz]

Real-time 2000Hz100 Hz

Figure 5.26 Measured temperature and its power spectrum in the burned region

above the C2H4-air flame.

The H2O sensor was aligned to probe the burned gases 2 cm above the burner surface. A

disturbance was introduced in the flame by modulating the fuel flow with a speaker attached to

the bottom of the Hencken burner (see figure 5.25). The speaker was driven with a 100 Hz sine

wave, thus producing an oscillating gas temperature (top panel in figure 5.26) and associated

Fourier transform (lower panel in figure 5.26). The dominant and harmonic modes of the

temperature fluctuations are clearly shown in the 2 kHz real-time power spectrum. These results

are similar to those shown in chapter 4 for the 1.8 µm direct absorption temperature sensor.

However, the 1.8 µm sensor requires post data processing while this 1.4 µm sensor is a real-time

sensor. These results demonstrate the utility of this fast temperature sensor for accurate


113

characterization of acoustic disturbances, and suggest good potential for applications to real-time

combustion sensing and control.

5.3.2 Real-time measurements in a Swirl Spray Combustor The real-time 1.4 µm WMS sensor is used for measurements in a liquid-fuel swirl-stabilized

spray combustor at University of Cincinnati. A detailed description of the swirl-stabilized spray

combustor can be found in ref. [Li 2004]

Computer

Lock-in amplifier

Real-time T@ 2000Hz

Round duct (47cm) generate natural flame instability

Collimator

2kHz ramp


Functiongenerator


Functiongenerator

+

Reference signal

Filter

N2 purge

N2 purge

Microphone

Computer

Lock-in amplifier

Real-time T@ 2000Hz

Round duct (47cm) generate natural flame instability

Collimator

2kHz ramp


Functiongenerator


Functiongenerator

+

Reference signal

Filter

N2 purge

N2 purge

Microphone

Figure 5.27 Schematic diagram of the measurement system applied to the swirl-

stabilized spray combustor.

The experimental setup for the 1.4 µm, 2f temperature sensor is illustrated in figure 5.27. The

DFB diode laser operating near 1.4 µm is driven by an external modulation, which consists of a 2

kHz saw tooth ramp combined with a faster 500 kHz sinusoidal modulation signal. The laser

beam exits the fiber and is collimated with a lens across the flame, and filtered and detected. The

fiber optics provides set-up flexibility and ease of alignment, which is advantageous for practical

applications under industrial conditions.

A round quartz duct is utilized to generate natural flame instability. The natural flame instability

is driven by the strong coupling between oscillations in heat release and pressure oscillations of

the combustion chamber. The driving mechanisms for thermo-acoustic combustion dynamics are

reviewed in ref. [McManus, 1992]. Acoustic signals are detected by a Brüel & Kjær microphone

(Model 4939-A-011) which is located 0.5 m away from the combustor chamber. The laser beam

Chapter 5

114

is intentionally kept away from the centerline of the round quartz duct to minimize etalon

interference. The second-harmonic components of the transmitted laser signal are obtained by a

Perkin-Elmer lock-in amplifier (Model 7280) with a time constant of 1 µs. The temperature is

inferred from the simple ratio of 2f peak height. 2 kHz real-time data processing and reduction is

achieved by a fast industrial PC combined with a laboratory code written in C++.

3

2

1

0

-1

-2

2f S

igna

l [ar

b. u

nits

]

500400300200100

Time [us]

500400300200100

Propane Ethanol

Peak 1Peak 2

Peak 1Peak 2

Figure 5.28 Reduced H2O 2f line shapes (single scan) recorded in gas fuel (propane)

and liquid fuel (ethanol), a = 0.065 cm-1.

Measurements with the 1.4 µm sensor were carried out at a radial position 15 mm from the spray

centerline and an axial position 50.8 mm downstream of the nozzle exit. The total path length is

97 mm. Figure 5.28 shows the representative 2f lineshape (single scan) corresponding to the

absorption features using gas and liquid fuel. Figure 5.28 (left) is for an air flow rate of 29.0

SCFM and propane flow rate of 40.9 SLM. Figure 5.28 (right) is for an air flow rate of 57.5

SCFM and ethanol flow rate of 0.15 kg/min. As seen from figure 5.28, SNR is about same for

liquid fuel and gas fuel. Due to the superior noise properties of the high-frequency detection

(1MHz in the present study), the 1.4 µm sensor provides precise temperature measurements even

in the liquid-fueled swirl flame.


115

0.12

0.08

0.04

0.00

A. U

. rms

10008006004002000Frequency [Hz]

-1.0

-0.5

0.0

0.5

1.0

A. U

.

0.50.40.30.20.10.0Time [s]

FFT

MicrophonePropane


above the propane-air flame.

200

150

100

50

0

Trm

s [K

]

10008006004002000Frequency [Hz]

4000

3000

2000

1000 Tem

pera

ture

[K]

0.50.40.30.20.10.0Time [s]

FFT

Propane 1.4 µm sensor


above the propane-air flame.

Chapter 5

116

1.2

0.8

0.4

0.0

A. U

. rms

10008006004002000Frequency [Hz]

-10

-5

0

5

10A

. U.

0.50.40.30.20.10.0Time [s]

FFT

MicrophoneEthanol


above the ethanol-air flame.

100

80

60

40

20

0

Trm

s [K

]

10008006004002000Frequency [Hz]

4000

3000

2000

1000 Tem

pera

ture

[K]

0.50.40.30.20.10.0Time [s]

FFT

Ethanol 1.4 µm sensor


above the ethanol-air flame.

Figure 5.29 shows the measured acoustic signal and its power spectrum in the burned region

above the propane-air flame with an air flow rate of 29.0 SCFM and propane flow rate of 40.9

SLM. In figure 5.30, real-time temperature and its power spectrum are depicted under the same


117

condition. With a laser scan rate of 2 kHz, a time resolution of 0.5 ms is achieved. It can be seen

that the dominant mode (232 Hz) and harmonic (464 Hz) modes of fluctuations (sound pressure

and temperature), determined by calculating the magnitude of the discrete Fourier transform of

the measured time-varying pressures and temperatures from 0 to 0.5 sec, are clearly revealed. The

measured temperature fluctuation is in good agreement with the measured pressure fluctuation

from the microphone.

Figure 5.31 shows the measured acoustic signal and its power spectrum in the burned region

above the ethanol-air flame with an air flow rate of 57.5 SCFM and ethanol flow rate of 0.15

kg/min. Figure 5.32 shows the measured temperature and its power spectrum under the same

condition. With laser scan rate of 2 kHz a time resolution of 0.5 ms is achieved. It can be seen

that the dominant mode (350 Hz) and harmonic (700 Hz) modes of fluctuations (sound pressure

and temperature), determined by calculating the magnitude of the discrete Fourier transform of

the measured time-varying temperatures from 0 to 0.5 sec, are again clearly revealed. These

results demonstrate the sensor’s ability to track and quantify the temperature fluctuations, as

needed to control combustion instability.

5.3.3 Comparison with 1.8 µm sensor

A comparison of the critical differences between the 1.4 µm scanned-WMS sensor and the

scanned-wavelength direct-absorption 1.8 µm sensor is now discussed.

0.010

0.008

0.006

0.004

0.002

0.000

Abs

orpt

ion

coef

ficie

nt [c

m-1

]

7155.07154.57154.07153.57153.0Frequency [cm

-1]

0.010

0.008

0.006

0.004

0.002

0.000

5555.05554.55554.05553.55553.0

T = 296 K T = 1000 K T = 2000 K

P = 1 atmX = 10%

1.8 µm sensor

1.4 µm sensor

Figure 5.33 Calculated spectroscopic features for water line pairs in the 1.4 µm and

1.8 µm sensors based on HITRAN; XH2O = 10%.

Chapter 5

118

The 1.4 µm scanned-WMS sensor exploits the lessons learned with the earlier 1.8 µm direct-

absorption sensor described in chapter 4. The calculated spectroscopic features for the water line

pairs of the 1.4 µm sensor and the 1.8 µm sensor are shown in figure 5.33. Both sensors are built

on the wavelength-scanned, single-laser, two-line-ratio thermometry concept, which measures the

ratio of absorption on two nearby temperature water transitions with a single laser scan. This

sensor architecture simplifies the sensor hardware and reduces its cost.

The 1.4 µm sensor includes several important improvements over the 1.8 µm sensor. First, the 1.4

µm sensor minimizes ambient air interference by using transitions with weak absorption at room

temperature, as shown in figure 5.33. The existence of ambient air interference can reduce the

measurement accuracy and lead to increased measurement uncertainty. It is usually necessary to

purge the optical path outside the target measurement zone with nitrogen or dry air to eliminate

the ambient water interference. The amount of purge gas necessary to attain a desired low

humidity set-point depends not only on the ambient humidity level, but also on the absorption

strength of the transition. Due to overlap with a cold water transition, the 1.8 µm sensor has a

very strong water absorption at room temperature, and therefore the purging requirements of the

1.8 µm sensor are quite significant. This difficulty is mitigated by the 1.4 µm sensor which

requires modest purging for long ambient pathlengths and no purging for short pathlengths.

Second, the 1.4 µm sensor uses sensitive WMS to achieve better SNR and lower detection limits.

WMS is a widely used technique for sensitive trace-species detection, and can significantly

reduce the dominating 1/f noise by shifting detection to higher frequencies [Reid 1981], which

provides a substantial sensitivity enhancement compared to the direct absorption methods used in

the 1.8 µm sensor. Therefore, the 1.4 µm sensor can be used in noisy environments like the

liquid-fueled spray flame where the 1.8 µm sensor showed significant uncertainty.


119

3x10-3

2

1

0

-1

2f s

igna

l [a.

b. u

nits

]

7155.07154.57154.07153.57153.0Frequency [cm

-1]

0.010

0.008

0.006

0.004

0.002

0.000Abs

orpt

ion

coef

ficie

nt [c

m-1

]

5555.05554.55554.05553.55553.0

T = 1000 K T = 2000 K

P = 1 atmX = 10%

1.8 µm sensor

1.4 µm sensor

Figure 5.34 Comparison of the measurement strategy of the 1.4 µm sensor and 1.8

µm sensor.

Third, the 1.4 µm WMS sensor has a simpler data reduction computation than the direct

absorption method and thus can achieve better real-time performance. The data reduction

strategies used in the 1.4 µm sensor and 1.8 µm sensor are illustrated in figure 5.34. The 1.8 µm

sensor first must subtract the baseline to infer I0, and then must fit Voigt lineshapes to extract the

integrated absorbance needed to determine temperature. The non-linear and time-consuming

Voigt fitting of the lineshape often requires post-processing data analysis, and is impractical to

rapidly determine temperature in real-time. The 1.4 µm sensor uses the ratio of the 2f peak

heights to avoid time-consuming fits to the line shape, and can reach a 2 kHz real-time

measurement rate (2 kHz scan repetition rate). Hence, the 1.4 µm sensor could be utilized in

many applications where the instability and control response is > 1 ms.

Fourth, the 1.4 µm WMS sensor takes advantage of the mature telecommunication laser

techniques at 1.4 µm where fiber-coupled lasers and fiber components are readily available. The

fiber-coupled lasers and fiber optics at 1.4 µm have many attractive features that are superior to

the free-space lasers and optics at 1.8 µm. These include advanced laser performance, simple

installation, easy laser beam alignment, improved ruggedness and flexibility, and reduced overall

system cost.

Chapter 5

120

5.4 Summary

A single-diode-laser temperature sensor based on wavelength modulation absorption

spectroscopy in H2O vapor is designed for rapid and accurate temperature measurements in a

combustion environment. The strategies and criteria to select optimum water features in the 1-2

micron wavelength range have been detailed. The 12 best NIR water transition line pairs for

temperature measurements with a single DFB laser in flames were determined by systematic

analysis of the HITRAN simulation of the water spectra in the 1-2 µm spectral region. A specific

line pair near 1.4 µm was identified and investigated experimentally, and the pertinent

spectroscopic parameters were determined from cell experiments. These measurements provide

useful improvements to the current spectroscopic database for H2O for the target transitions and

their neighbors. The sensor enables a real-time temperature readout rate of 2 kHz and immunity

from ambient water vapor interference (using a common PC). Demonstration experiments were

conducted in a heated cell and a forced Hencken burner. Cell experiments confirmed sensitivity

and accuracy of the sensor. The burner experiments illustrate its ability to monitor temperature

fluctuations with potential applications to combustion control. Temperature is an important

parameter for combustion control because it is a sensitive measure of heat release. Compared

with traditional pressure-based sensor like microphone, temperature-based TDL sensor has many

advantages such as good spatial resolution, immunity to vibration and suitability in noisy

environments. Chapter 6 will present the application of the 1.4 µm sensor to combustion control.

121

Chapter 6: Application of fast temperature sensor to

combustion control

In this chapter, the 1.4 µm real-time WMS temperature sensor is used for combustion sensing in a

swirl-stabilized combustor and the potential for combustion control is demonstrated. Two

problems are investigated in the swirl-stabilized flame: lean blowout (LBO) and acoustic

instabilities. The use of the 1.4 µm WMS TDL is compared with a traditional microphone sensor.

It is shown that the 1.4 µm WMS temperature sensor has advantages for lean blowout prediction,

and is especially promising for lean blowout control. A phase-delay control strategy is used to

suppress temperature fluctuation in this experiment, and the results illustrate the potential of this

sensor for real-time combustion instability control. Conclusions are summarized in the final

section.

6.1 Motivation

The reduction of NOx emissions from practical combustion is an important problem [Martin 1990;

John 1997], and many schemes to reduce NOx emissions have been investigated. Lean premixed

combustion is one of the most effective approaches to reduce NOx emissions because of its lower

flame temperatures [Martin 1990]. Unfortunately, this scheme has two major drawbacks: First, it

is susceptible to lean blowout (LBO) of the combustion, which can lead to significant potential

safety hazards, energy loss, and substantial costs from power shut-down [Thiruchengode 2003;

Muruganandam 2003; Nair 2003]. Second, this scheme is susceptible to thermoacoustic

combustion instabilities from the coupling of heat release to acoustic oscillations [Mcmanus 1993;

Docquier 2002; Lieuwen 2003], which can lead to decreased combustion efficiency, increased

noise pollution, and serious system performance degradation. Thus, practical use of lean

premixed combustion likely will require real-time control to avoid LBO and suppress acoustic

instabilities. An important part of any control strategy is a robust sensor to monitor a good control

variable. Gas temperature is a sensitive measure of heat release and is investigated here as a

control variable.

There is a large literature for flame behavior during the lean blowout process [Thiruchengode

2004; Nair 2004; Muruganandam 2005; Prakash 2005]. This previous work shows that significant

low frequency fluctuations increase near lean blowout. Acoustic noise measurement with a

Chapter 6

122

microphone and optical chemiluminescence measured with a photo detector are the most

frequently used methods for LBO experiments. Although the microphone has the desired

sensitivity and response time, it is sensitive to the signal from the entire flame, and thus is

unsuitable to detect a blowout event in a local region of the flame. While chemiluminescence can

provide a rough measure of heat release rate, it is much less quantitative. To be a useful sensor for

this application, any potential spectroscopic strategy must have fast time response, high

sensitivity, high spectral resolution, robustness, reasonable spatial resolution and be non-intrusive

in character.

The control of combustion acoustic instabilities has also been the subject of numerous theoretical

and experimental studies [for example, Kemal 1996; Candel 2002; Lieuwen 2001; Park 2002;

Fleifil 1996; Furlong 1998]. A variety of models and mechanisms [Lieuwen 2003] have been

proposed to explain the occurrence of thermoacoustic instabilities and different experimental

methods were used to suppress these combustion instabilities. A review of these studies can be

found in refs. [Mcmanus 1993; Docquier 2002]. Previous work in this laboratory [Furlong 1996;

Furlong 1998] demonstrated that temperature is a good control variable for combustion instability

control. The aim of the current work is to illustrate the potential of our 1.4 µm WMS temperature

sensor to suppress the natural combustion instabilities in a practical swirl-stabilized flame using

active control.

In the following sections, the 1.4 µm WMS temperature sensor is first applied to a swirl-

stabilized combustor to illustrate the potential of this sensor to observe a clear indication of the

approach to the lean blowout limit. The sensor is then used to provide active feedback control to

suppress natural thermoacoustic instabilities for the same combustor. The LBO experiments show

that the 1.4 µm WMS temperature sensor has good potential to predict the lean blowout limits.

The instability control experiments show that the 1.4 µm WMS temperature sensor has the

desired flexibility, speed, sensitivity and accuracy to be a useful tool for fundamental and applied

combustion monitoring and control.

6.2 Swirl-stabilized combustor

To investigate the potential to predict the approach to the lean blow out limit, the WMS

temperature sensor is applied to a swirl-stabilized combustor at Stanford. This combustor is a

Application of fast temperature sensor to combustion control

123

copy of the swirl-stabilized combustor utilized in chapters 4 and 5. Illustration of the combustor

design is presented in figure 6.1 and a full description can be found in ref. [Li 2003].

Air

Speaker Port

Air Conditioning Chamber

Triple Annular Research Swirler

Seeding Fuel

80 cm

10.2 cm

Figure 6.1 Schematic of swirl-stabilized combustor.

The combustor is assembled vertically and the flow is from bottom to top. A combination of

honeycomb and different size mesh screens is used to create a uniform flow in the air

conditioning chamber. For the purpose of investigation and thermoacoustic instability control of

the swirl-stabilized combustion, four identical acoustic ports are placed at the air conditioning

chamber. A triple-annular research swirler (TARS) [Li 2004] is used here to investigate the

effects of various swirler configurations on combustion performance. The details of the TARS are

Chapter 6

124

given in ref. [Li 2004]. The outer, intermediate, and inner swirlers can be changed independently,

and the available swirler configurations are summarized in table 6.1, where 30o means that “the

swirler angle is 30o in the clockwise direction”, and -30o means that “the swirler angle is 30o in

the counterclockwise direction”. An inner swirler (-45 o), intermediate swirler (0o) and outer

swirler (-55o) configuration is used for current work.

Table 6.1 Different inter, intermediate and outer swirler configurations

Swirler #1 #2 #3 #4 #5 #6

Inner 30o 45o -30o -45o

Intermediate 45o 30o 0o

outer 30o 45o 55o -30o -45o -55o

The fuel is delivered through a separate main and pilot system. The main fuel is injected through

8 injection holes into outer swirler, and the pilot fuel is injected through 4 injection holes into

intermediate swirler. There are also two air-assist lines (not shown in figure 6.1) to provide a

small amount of air to premix the fuel. The fuel flow and air flow rate are independently

controlled by valves and measured using calibrated flow meters.

6.3 Lean blowout (LBO) prediction

6.3.1 Experimental setup

Detector

DAQ Computer

2kHz ramp

Laser

FunctionGenerator

FunctionGenerator

-Harmonic Signal

Transmission

Collimator

DAQ Computer


+

LaserController

FunctionGenerator

FunctionGenerator


Reference signal

Harmonic Signal

DFB Laser

Bias TEE

GeneratorDG535 DelayTrigger 1 Trigger 2

Real Time T

2kHz

Flat mirror

N2 purge N2 purgeFocusingmirror

Band passfilter

MicrophoneFilter

Detector

DAQ Computer

2kHz ramp

Laser

FunctionGenerator

FunctionGenerator

-Harmonic Signal

Transmission

Collimator

DAQ Computer


+

LaserController

FunctionGenerator

FunctionGenerator


Reference signal

Harmonic Signal

DFB Laser

Bias TEE

GeneratorDG535 DelayTrigger 1 Trigger 2

Real Time T

2kHz

Flat mirror


Band passfilter

MicrophoneFilter

Figure 6.2 Scheme of the experimental setup.


125

The experimental setup is illustrated in figure 6.2. The hardware-software architecture of the 1.4

µm temperature sensor was detailed in chapter 5, and will not be repeated here. The DFB diode

laser operating near 1.4 µm is driven by an external modulation, which consists of a 2 kHz saw

tooth ramp combined with a faster 500 kHz sinusoidal modulation signal. The laser beam is

collimated and directed across the flame. Simultaneously with the TDL sensor signal, acoustic

signals are detected by a Brüel & Kjær microphone (Model 4939-A-011) located 0.3 m away

from the combustor chamber. The combustion chamber is a 200mm long round quartz duct

whose diameter is 90mm. The laser beam is intentionally aligned off the centerline of the duct to

minimize etalon interference. A flat mirror provides a double-pass configuration to improve SNR.

The reflected laser beam is focused, then passes through a narrow band pass filter (NB-1400-030-

B) and is detected by a large area InGaAs detector (3 mm diameter active area, ELECTRO-

OPTICAL SYSTEMS). The large area detector is used here to reduce beam steering noise. The

detected signal is filtered with a 320 kHz (818H8B-5 High Pass 8-Bit Programmable 8-Pole Filter)

and 1.28 MHz (818L8B-5 Low Pass 8-Bit Programmable 8-Pole Filter) to remove unwanted

frequency components.

7

6

5

4

3

2

1

0

Sig

nal [

V]

543210Time [ms]

7

6

5

4

3

2

1

0

Sig

nal [

V]

With beam steering

Without beam steering

Figure 6.3 Raw data with/without beam steering noise.

Chapter 6

126

Figure 6.3 illustrates the typical raw data with beam steering noise (bottom) and without beam

steering (top, this experiment). The existence of beam steering noise will reduce measurement

accuracy. Proper optical design should be adopted to minimize the beam steering effects in laser

absorption experiments. Some effective anti-beamsteering approaches are summarized in the ref.

[Sanders 2001].

-2

-1

0

1

2

2f s

igna

l [ar

b. u

nits

]

0.50.40.30.20.10.0Time [ms]

2f line shape

Low T Line Peak High T Line Peak

Figure 6.4 Reduced H2O 2f line shape (single scan) recorded in gas fuel (propane).

The second-harmonic components of the transmitted laser signal are obtained by a Perkin-Elmer

lock-in amplifier (Model 7280) with a time constant of 1 µs. Figure 6.4 shows the representative

2f lineshape (single scan) corresponding to the absorption features using gas fuel (propane). A

modulation amplitude a = 0.047 cm-1 is adopted in current work. 2 kHz real-time data processing

and reduction is achieved by a fast PC combined with a laboratory code written in C++.

6.3.2 Results and discussions Four sets of experiments were conducted to evaluate the performance of the 1.4 µm WMS

temperature sensor for lean blow out prediction. All experiments have roughly the same initial


127

propane flow rate (1.2 SCFM) but different air flow rates (a. 27.3 SCFM b. 38.7 SCFM c. 52.0

SCFM 4. 63.9 SCFM). During the lean blowout process, the propane flow rate was decreased by

slowly adjusting a needle valve while keeping the air flow constant. All experiments were carried

out with the sensor at a radial position 22 mm from the centerline to avoid etalon noise. To

examine the effects of sensing position, each set of experiment was performed at two axial

positions (20mm and 50 mm downstream of the nozzle exit). The total path length is 156 mm for

both flame heights.

(a) (b) (c) (d) (e)

Figure 6.5 The blowout process for the first set of experiments (air flow rate = 27.3 SCFM)

Figure 6.5 shows the images of flame during the blowout process for the first set of experiment

(air flow rate = 27.3 SCFM). The initial flame is slightly fuel rich, and a luminous swirling flame

is clearly observed (image a). The full flame height is about 50 cm, and composed of three

regions: 1.) A blue flame on the top (25 cm), 2.) A pinkish flame in the middle (20 cm) 3.) A very

bright flame in the bottom (5 cm). As fuel flow decreases, the top blue flame gradually vanishes

and the middle pinkish flame and bottom bright flame decreases in length. The full flame height

decreases to 25 cm (image b). The pinkish flame slowly disappears and the bright flame zone

appears indistinguishable with further decrease of fuel flow. The total flame length reduces to 8

cm (image c). The bright flame zone disappears and the whole flame becomes dark blue. The

flame near the wall increases in length (flame height increases to 15 cm) and a flame instability is

observed (image d). As the flame approaches lean blowout limit, the flame becomes unstable,

moves to center and fills the whole chamber (image e). Finally the flame is lifted and blowout

occurs.

Chapter 6

128

Figure 6.6 (a) Microphone and 2f sensor result during the lean blowout process for the first set of

experiments. (Air flow rate = 27.3 SCFM). Laser beam: 20mm height from the injector

0.30

0.25

0.20

0.15

0.10

0.05

0.00

T rms[

0,50

]/T rm

s[0,

1000

]

50403020100Time [s]

Blowout2f T sensor

Low Frequency TAll frequency T

2.0

1.5

1.0

0.5

0.0

2f p

eak

ratio

50403020100Time [s]

0.7

0.6

0.5

0.4

0.310.410.210.0

0.5

0.4

0.3

0.2

0.139.439.239.0

Blowout

2f T Sensor4

3

2

1

0

-1

Pres

sure

[V]

50403020100Time [s]

-1.0

-0.5

0.0

0.5

1.0

10.410.210.0-0.10

-0.05

0.00

0.05

0.10

39.439.239.0

Blowout

Microphone

0.30

0.25

0.20

0.15

0.10

0.05

0.00

P rm

s[0,

50]/

Prm

s[0,

1000

]

50403020100Time [s]

BlowoutMicrophone

Low Frequency P

All frequency P

0.030

0.025

0.020

0.015

0.010

0.005

0.000

Nor

mal

ized

Powe

r Spe

ctru

m

10008006004002000Frequency [Hz]

Near Blowout (39~39.5 s) Steady combustion (10~10.5 s)

2f T sensor

0.020

0.015

0.010

0.005

0.000

Nor

mal

ized

Powe

r Spe

ctru

m

10008006004002000Frequency [Hz]


Microphone


129

Figure 6.6 (b) Microphone and 2f sensor result during the lean blowout process for

the first set of experiments. (Air flow rate = 27.3 SCFM). Laser beam: 50mm height

from the injector

Figure 6.6 shows the measurement results from microphone and the 1.4 µm WMS temperature

sensor during the lean blowout process for the first set of experiments. Panel (a) and (b) of figure

2.0

1.5

1.0

0.5

0.0

2f p

eak

ratio

50403020100Time [s]

0.7

0.6

0.5

0.4

0.310.410.210.0

0.5

0.4

0.3

0.2

0.139.439.239.0

Blowout

2f T Sensor

0.30

0.25

0.20

0.15

0.10

0.05

0.00

T rms[

0,50

]/T rm

s[0,

1000

]

50403020100Time [s]

Blowout2f T sensor


4

3

2

1

0

-1

Pres

sure

[V]

50403020100Time [s]

-1.0

-0.5

0.0

0.5

1.0

10.410.210.0-0.10

-0.05

0.00

0.05

0.10

39.439.239.0

Blowout

Microphone

0.30

0.25

0.20

0.15

0.10

0.05

0.00

Prm

s[0,

50]/

Prm

s[0,

1000

]

50403020100Time [s]

BlowoutMicrophone

Low Frequency P

All frequency P

0.030

0.025

0.020

0.015

0.010

0.005

0.000

Nor

mal

ized

Powe

r Spe

ctru

m

10008006004002000Frequency [Hz]


2f T sensor

0.020

0.015

0.010

0.005

0.000

Norm

alize

d Po

wer S

pect

rum

10008006004002000Frequency [Hz]


Microphone

Chapter 6

130

6.6 illustrate the results measured at an axial position 20mm and 50 mm downstream of the

nozzle exit, respectively.

The microphone signal and 2f peak ratio as a function of time during the lean blowout process are

shown in the first row of figure 6.6. The insets of each figure show the microphone signal and 2f

peak ratio from the TDL sensor for steady combustion condition (10~10.5 s) and near blowout

(39~39.5 s). There are two things to note: First, the amplitude of the microphone signal gradually

decreased during the lean blowout process because it is proportional to the total combustion

energy. Near blowout, the amplitude of the microphone signal is close to the amplitude of

background acoustic signal. At the same time, a significant decrease in the 2f peak ratio is

observed as it is directly related to temperature. Second, there is no significant difference between

steady combustion and near-blowout limit for 2f signal in position 1 (20mm downstream of the

nozzle exit, figure 6.6 (a)). In contrast, the presence of low frequency disturbance (significant

drop) in 2f peak ratio is clearly shown in position 2 (50 mm downstream of the nozzle exit, figure

6.6 (b)) as the combustor approaches the lean blowout limit. It is clearly shown that position 2 is

more sensitive to temperature fluctuation than position 1. To achieve the best performance,

therefore, it is critical to find the most sensitive position for the 2f sensor. Since the microphone

is not a location-selective component, its signal is not sensitive to its positioning.

The second row of figure 6.6 illustrates the power spectrum from the microphone signal and 2f

peak ratio from the TDL sensor for steady combustion (10~10.5 s) and near-blowout (39~39.5 s)

conditions. As mentioned above, the absolute amplitude of microphone signal changes during the

blowout process. To make a meaningful comparison, the power spectra are normalized by the

sum of all frequency components. The laser scan rate of the 2f WMS temperature sensor and

microphone’s sampling rates are set to 2000 Hz, so the upper detection limit of 1000Hz is

achieved for both sensors. The width of each bar is 2 Hz, which corresponds to the frequency

resolution in the determination of the discrete Fourier transform over a 0.5 s sampling interval. It

is clearly shown that the low-frequency components increase as the flame approaches blowout.

Such low-frequency components correspond to the local flame extinction events and become

more frequent (thus flame becomes unstable) as the flame approaches the blowout limit. Once the

rate of heat release is not sufficient to heat the fuel and air to the required ignition temperature,

the flame approaches blowout. Therefore, these low-frequency disturbances can be used as a

symptom for lean blowout prediction.


131

The third row of figure 6.6 shows a strategy for quantitative prediction of approach to the lean

blowout limit. Since the flame extinction events are not periodic, there is no characteristic

frequency in the power spectrum. Here the ratio of the sum of low-frequency (0~50 Hz in current

work) components to the sum of all-frequency (0~1000 Hz) components is plotted. This quantity

illustrates the variety of low-frequency flame extinction events during the lean blowout process.

As shown in figure 6.6, there is a significant increase in low frequency events near blowout for

both the microphone and the 1.4 µm WMS temperature sensor. From steady combustion to near

blowout conditions, the low-frequency components increase from 2% to 12% of the total noise

power for microphone and from 5% to 28% of the total noise power for the 1.4 µm WMS

temperature sensor. However, it should be noted that the low-frequency components for the

microphone are only 5% of the total noise power after the flame blowout from the background

acoustic signals (air flow etc.). Near blowout the amplitude of microphone signal is close to the

background acoustic signal, thus the microphone’s performance for LBO prediction is limited by

the influence of background acoustic signal. In addition, the microphone can only detect the

overall sound so it is unable to detect local flame extinction events.

Similar results were obtained with other air flow rates: 38.7 SCFM, 52.0 SCFM and 63.9 SCFM.

Figures 6.7~6.9 show the corresponding flame behavior during the blowout process. The

measurement results for microphone and the 1.4 µm WMS temperature sensors are presented in

figures 6.10~6.12. For all cases the approach to LBO is captured by the WMS temperature sensor.

Chapter 6

132

Figure 6.7 The blowout process for the second set of experiments (air flow rate=38.7

SCFM)

Figure 6.8 The blowout process for the third set of experiments (air flow rate= 52.0 SCFM)

Figure 6.9 The blowout process for the fourth set of experiments (air flow rate= 63.9

SCFM)


133

Figure 6.10 (a) Microphone and 2f sensor result during the lean blowout process for the second

set of experiments. (Air flow rate = 38.7 SCFM). Laser beam: 20mm height from the injector

4

3

2

1

0

-1

Pres

sure

[V]

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-1.0

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0.0

0.5

1.0

10.410.210.0-0.10

-0.05

0.00

0.05

0.10

39.439.239.0

Blowout

Microphone

0.020

0.015

0.010

0.005

0.000

Norm

alize

d Po

wer S

pect

rum

10008006004002000Frequency [Hz]


Microphone

0.030

0.025

0.020

0.015

0.010

0.005

0.000

Norm

alize

d Po

wer S

pect

rum

8006004002000Frequency [Hz]


2f T sensor

0.30

0.25

0.20

0.15

0.10

0.05

0.00

T rms[

0,50

]/T rm

s[0,

1000

]

50403020100Time [s]

Blowout2f T sensor


2.0

1.5

1.0

0.5

0.0

2f p

eak

ratio

50403020100Time [s]

0.7

0.6

0.5

0.4

0.310.410.210.0

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0.4

0.3

0.2

0.139.439.239.0

Blowout

2f T Sensor

0.30

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0.20

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0.05

0.00

P rm

s[0,

50]/

Prm

s[0,

1000

]

50403020100Time [s]

BlowoutMicrophone

Low Frequency P

All frequency P

Chapter 6

134


the second set of experiments. (Air flow rate = 38.7 SCFM). Laser beam: 50mm

height from the injector

0.30

0.25

0.20

0.15

0.10

0.05

0.00

T rms[

0,50

]/T rm

s[0,

1000

]

50403020100Time [s]

Blowout2f T sensor


0.030

0.025

0.020

0.015

0.010

0.005

0.000

Norm

alize

d Po

wer S

pect

rum



2f T sensor

2.0

1.5

1.0

0.5

0.0

2f p

eak

ratio

50403020100Time [s]

0.7

0.6

0.5

0.4

0.310.410.210.0

0.5

0.4

0.3

0.2

0.139.439.239.0

Blowout

2f T Sensor

0.020

0.015

0.010

0.005

0.000

Norm

alize

d Po

wer S

pect

rum

10008006004002000Frequency [Hz]


Microphone

4

3

2

1

0

-1

Pres

sure

[V]

50403020100Time [s]

-1.0

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0.0

0.5

1.0

10.410.210.0-0.10

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0.00

0.05

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39.439.239.0

Blowout

Microphone

0.30

0.25

0.20

0.15

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0.05

0.00

Prm

s[0,

50]/

Prm

s[0,

1000

]

50403020100Time [s]

BlowoutMicrophone

Low Frequency P

All frequency P


135

Figure 6.11 (a) Microphone and 2f sensor result during the lean blowout process for the third set

of experiments. (Air flow rate = 52.0 SCFM). Laser beam: 20mm height from the injector

2.0

1.5

1.0

0.5

0.0

2f p

eak

ratio

50403020100Time [s]

0.7

0.6

0.5

0.4

0.310.410.210.0

0.5

0.4

0.3

0.2

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2f T Sensor

0.020

0.015

0.010

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0.000

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alize

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wer S

pect

rum

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Microphone

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mal

ized

Powe

r Spe

ctru

m



2f T sensor

0.30

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0.00

T rms[

0,50

]/T rm

s[0,

1000

]

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Blowout2f T sensor


0.30

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0.15

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0.05

0.00

Prm

s[0,

50]/

Prm

s[0,

1000

]

50403020100Time [s]

BlowoutMicrophone

Low Frequency P

All frequency P

4

3

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1

0

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sure

[V]

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39.439.239.0

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Microphone

Chapter 6

136


the third set of experiments. (Air flow rate = 52.0 SCFM). Laser beam: 50mm height

from the injector

0.020

0.015

0.010

0.005

0.000

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mal

ized

Powe

r Spe

ctru

m

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eak

ratio

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2f T Sensor

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0,50

]/T rm

s[0,

1000

]

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mal

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2f T sensor

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s[0,

50]/

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s[0,

1000

]

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All frequency P

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sure

[V]

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Microphone


137

Figure 6.12 (a) Microphone and 2f sensor result during the lean blowout process for the fourth set

of experiments. (Air flow rate = 63.9 SCFM). Laser beam: 20mm height from the injector

0.020

0.015

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mal

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]/T rm

s[0,

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]

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eak

ratio

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0,50

]/P rm

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]

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BlowoutMicrophone

Low Frequency P

All frequency P

Chapter 6

138


the fourth set of experiments. (Air flow rate = 63.9 SCFM). (b) Laser beam: 50mm

height from the injector

2.0

1.5

1.0

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eak

ratio

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0,50

]/T rm

s[0,

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]

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s[0,

1000

]

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All frequency P

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sure

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139

In this section, the 1.4 µm WMS temperature sensor has been used to detect approach to the lean

blowout limit in a swirl-stabilized combustor. Experiments were performed under different air

flow conditions and sensing positions. These results demonstrate the potential of this sensor for

accurate identification of low-frequency temperature fluctuations near the lean blowout limit, and

suggest strategies for lean blowout control. The ability of the 1.4 µm WMS temperature sensor to

measure the low-frequency increase near the lean blowout limit shows good potential for LBO

control.

6.4 Combustion instability control

6.4.1 Experimental setup

Detector

DAQ Computer

Harmonic Signal

Transmission

Collimator

DAQ Computer

Perkin Elmer 7280 Lock-in amplifier Harmonic Signal

DFB Laser

Real Time 2f ratio

2kHz

Flat mirror


Band passfilter 1

Microphone

Filter

Band passfilter 2

Time-Delay GeneratorΔt

AmplifierGain: α

Gas Fuel (Propane)

Detector

DAQ Computer

Harmonic Signal

Transmission

Collimator

DAQ Computer

Perkin Elmer 7280 Lock-in amplifier Harmonic Signal

DFB Laser

Real Time 2f ratio

2kHz

Flat mirror


Band passfilter 1

Microphone

Filter

Band passfilter 2

Time-Delay GeneratorΔt

AmplifierGain: α

Gas Fuel (Propane)

Figure 6.13 Scheme of the experimental setup.

Detailed descriptions of the 1.4 µm WMS temperature sensor can be found in chapter 5 and

section 6.2; figure 6.13 illustrates the fundamentals of its use for the phase-delay control strategy.

The DFB diode laser operating near 1.4 µm is driven by an external modulation, which consists

of a 2 kHz saw tooth ramp combined with a faster 500 kHz sinusoidal modulation signal (a =

0.047 cm-1). The laser beam is collimated and directed across the flame 15 mm above the nozzle

exit. Acoustic signals are detected by a Brüel & Kjær microphone (Model 4939-A-011) which is

Chapter 6

140

located 0.3 m away from the combustor chamber. The 200 mm long round quartz duct is replaced

with a 450 mm long quartz duct to generate natural flame instability. The second-harmonic

components of the transmitted laser signal are obtained by a Perkin-Elmer lock-in amplifier

(Model 7280) with a time constant of 1 µs. 2 kHz real-time data reduction is achieved by a fast

PC combined with a laboratory code written in C++. The C++ program conditioned the 2f ratio

and output only the ac component of the signal (in voltage), is directed into a time-delay

generator. The time-delay scheme is implemented using a dSPACE 1104 real-time control board.

The analog signal (2f ratio) is first converted to digital signal through an analog-to-digital

converter (ADC), then output as an analog signal with a digital-to-analog converter (DAC) after a

specified time delay. The delayed signal is then filtered (SR640 Low Pass Filter and SR645 High

Pass Filter) and amplified by a Phast Landmark PLB-AMP8 8-channel power amplifier. The

amplified signal is used to drive four speakers (75 Watts each) mounted 51 cm upstream of the

nozzle at the air conditioning chamber.

6.4.2 Results and discussions

1.0

0.8

0.6

0.4

0.2

0.0

2f p

eak

ratio

20151050Time [s]

2f Ratio

Control off Control On

(a) Time history of 2f peak ratio (Gas fuel propane).


141

-10

-5

0

5

10

Am

plifi

ed 2

f pea

k ra

tio

20151050Time [s]

2f Ratio (AC)

Control off Control On

(b) Amplified ac components of 2f peak ratio.

0.5

0.4

0.3

0.2

0.1

0.0

Pow

er S

pect

rum

[a.u

. rms2 ]

10008006004002000Frequency [Hz]

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0.1

0.0

Pow

er S

pect

rum

[a.u

. rms2 ]

10008006004002000Frequency [Hz]

Control On (10∼10.5 s)2f Sensor

(c) Power spectrum with and without control

Figure 6.14 2f peak ratio and its power spectra before and after control were applied

on the swirl-stabilized combustor (Propane/Air).

Chapter 6

142

-10

-5

0

5

10M

icro

phon

e [a

rb.u

nits

]

20151050Time [s]

Control Off Control On

Microphone

(a) Time history of microphone signal

5

4

3

2

1

0

Pow

er S

pect

rum

[a.u

. rms2 ]

10008006004002000Frequency [Hz]

Control Off (9.5∼10 s) Microphone

5

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Pow

er S

pect

rum

[a.u

. rms2 ]

10008006004002000Frequency [Hz]

Control On (10∼10.5 s) Microphone

(b) Power spectrum with and without control

Figure 6.15 Microphone signal and its power spectra before and after control were

applied on the swirl-stabilized combustor (Propane/Air).


143

Experiments were carried out with a fuel (propane) flow rate of 1.1 SCFM and air flow rate of

46.5 SCFM. Figure 6.14 and 6.15 illustrates the raw data of the 1.4 µm WMS temperature sensor

and microphone and their representative power spectrum with and without control. Figure 6.14 (a)

shows the time history of 2f peak ratio. For this application, the ac components of the temperature

(2f peak ratio) provide the control signal. Thus, the dc component is first calculated and

subtracted from 2f peak ratio, then this ac signal is amplified at constant gain (50 in this case).

The amplified ac components of 2f peak ratio as shown in figure 6.14 (b) are then output to the

dSPACE 1104 real-time control board and delayed by ∆t (0.002 s in this case). The delayed

signal is then filtered by a band pass filter (375Hz and 425 Hz) and amplified to drive four audio

speakers to provide pressure feedback to the air supply and suppress the instabilities. The power

spectrum of 2f ratio and microphone signal are shown in figure 6.14 (c) and 6.15 (c) with and

without control. In the uncontrolled case (9.5~10 s), a 388 Hz fluctuation is clearly seen in both

2f signal and microphone signal, which confirms the ability of the 1.4 µm WMS temperature

sensor for quantitative, accurate identification of flame disturbances. With the controller on, the

temperature oscillations are reduced by a factor of 10 (figure 6.14 (c)) and the pressure

oscillations are reduced by a factor of 2. It should be pointed out, however, that the signal

detected by microphone may contain components from control speakers. Therefore, extra efforts

should be taken to remove such influence when adopting the microphone approach for

acoustically driven flames. In addition, the microphone may also suffer other interference from

background acoustic signal especially in noisy environments. Such limitations are avoided by

detecting temperature fluctuations using the 1.4 µm WMS temperature sensor, and the results

clearly indicate that the temperature sensor is able to determine the correct frequency, phase and

amplitude of the flame fluctuations, and provide the appropriate feedback. The 1.4 µm WMS

temperature sensor could be a very useful tool for active control of combustion.

Chapter 6

144

1.4

1.2

1.0

0.8

0.6

0.4

0.2

0.0

AC

ontr

ol O

n/A

Con

trol

Off

2.5x10-3

2.01.51.00.5Delay time [s]

Baseline

Figure 6.16 Control performances versus controller time-delay

To illustrate the effect of delay-time on the control results, experiments were performed for

different time delays. The measurement time is 20 s (10 s for control off and 10 s for control on)

for each experiment. The FFT analysis was performed every 0.5s. The maximum fluctuation

amplitude between 375 Hz and 425 Hz are calculated for control-on and control-off, and the ratio

AControl On/AControl Off is used as a measure of control performance. Figure 6.16 shows the control

performance vs. delay time (phase). The best control performance is obtained between 2.0~2.25

ms.


145

1.4

1.2

1.0

0.8

0.6

0.4

0.2

0.0

AC

ontr

ol O

n/A

Con

trol

Off

10080604020Gain

Baseline

Figure 6.17 Control performances versus amplifier gain

.

Similar experiments were performed to find the optimum gain to suppress the natural combustion

instabilities. Figure 6.17 shows the attenuation of the peak frequency as functions of the amplifier

gain. The maximum reduction was found at the gain of 50. These results demonstrate the

feasibility and utility of this sensor for feedback control on combustion instabilities.

6.5 Summary

The 1.4 µm WMS temperature sensor has been successfully applied to LBO prediction and

thermoacoustic instability control. Four flow conditions and two sensing positions were chosen to

study the flame characteristics near lean blowout limit. For comparison purposes, a microphone is

used to detect acoustic signal during the blowout process. Experiments show that low frequency

components in both acoustic and temperature increase significantly near lean blowout limit, and it

can be used as a precursor for lean blowout. The microphone approach, however, has two

intrinsic limitations: First, it is susceptible to background acoustic signals and thus unsuitable for

lean blowout control under noisy environments. Second, it can only detect global acoustic signals,

so it is unable to detect local flame extinction events. Unlike the microphone, the 1.4 µm WMS

temperature sensor can be applied to a wide range of environments because it does not suffer

Chapter 6

146

background interference. Furthermore, the line-of-sight measurements enable sensitive detection

of any local flame extinction events. It was demonstrated that this sensor has the desired speed

and sensitivity to precisely detect the low frequency fluctuations near lean blow out, for LBO

prediction, which has significant potential for LBO control.

Phase-delay control was implemented using the 1.4 µm WMS temperature sensor to suppress the

combustion natural instabilities in a swirl-stabilized combustor. It is shown that the amplitudes of

natural instabilities are greatly reduced by the phase-delay control at the optimum phase and

amplifier gain. These results offer the strong evidence that the 1.4 µm WMS temperature sensor

has the desired accuracy to monitor dynamics of combustion oscillations and provide effective

feedback signal for active combustion control.

147

Chapter 7: Conclusions and future work The overall objective of this thesis is to design and develop time-resolved and real-time tunable

diode laser sensors with the potential for combustion control. A crucial element in the design of a

tunable-diode-laser optical-absorption-based sensor is the selection of optimum transitions. The


combinations are developed for two-line thermometry. The development of this design-rule

approach establishes a new paradigm to optimize tunable diode laser sensors for the target

application. Two single-laser TDL sensors are developed in this thesis. Both sensors are

demonstrated in a heated cell, a forced Hencken burner and a swirl-stabilized spray combustor.

The following sections summarize the major findings of this thesis.

7.1 Summary of the use of design rules to identify the optimum transitions for IC

engine applications

The optimum selection of H2O lines in the 1.25-1.65 µm region for TDL WMS-based

temperature measurements in an internal combustion engine is investigated in chapter 3. The

strategy and spectroscopic criteria are discussed for selection of optimum wavelength regions and

absorption line combinations for the time-varying pressures and temperatures expected during the

compression portion of an engine cycle. We have identified 14 of the water transitions in this

spectral region as promising for this application. Based on these findings, 16 potential line pairs

of H2O were considered for a wavelength-modulated absorption sensor for in-cylinder gas

temperature during the compression stroke. As part of the sensor development effort, expected

performance is modeled for a variety of engine cycles. Simulations show that these line pairs

have good potential for TDL thermometry.

7.2 Design of a single laser absorption sensor for temperature measurements using

direct absorption

Design rules for the selection of optimum transitions for a robust sensor system using two-line

thermometry and a single laser are proposed and elucidated in chapter 4 of this dissertation. The


combinations are discussed for direct absorption spectroscopy.

Chapter 7

148

Following the design rules developed for combustion conditions, a short optical path, and direct

absorption, the water vapor spectrum in the 1-2 µm near-infrared (NIR) region is systematically

analyzed to find the best absorption transitions for sensitive measurement of H2O concentration

and temperature. The use of a single laser, even with relatively narrow (~1cm-1) tuning range, can

offer advantages over wavelength-multiplexing techniques. Our investigation reveals that the 1.8

µm spectral region is especially promising, and we have identified 10 of the best line pairs for

water vapor in this spectral region for temperature measurements in flames. Based on these

findings, a pair of H2O transitions near 1.8 µm was selected as an example for the design and

development of a single-laser sensor for simultaneously measuring H2O concentration and

temperature in atmospheric-pressure flames. The greatest advantage of these water line pairs is

the potential to measure with a single scan for one diode laser.

As part of the sensor development effort, fundamental spectroscopic parameters including the line

strength, line-center frequency, and lower state energies of the probed transitions were measured

experimentally to improve the HITRAN database values. Discrepancies between the

experimentally determined spectroscopic parameters and HITRAN/HITEMP database are found

in this region. Thus, it is recommended that the fundamental spectroscopic parameters be

experimentally verified or measured during the development of a practical sensor.

The line pair selected is applicable for temperature measurements in the range from 960 to 3300

K. Demonstration experiments were conducted in a steady and a forced Hencken burner. The

presence of cold boundary layers was shown to impact the temperature inferred assuming

uniform conditions, but a simple assumption of a trapezoidal temperature distribution was shown

to recover an accurate value for the core temperature of the flow. Experiments with forced flames

confirmed the utility of the sensor to monitor temperature fluctuations. In addition, the sensor was

used for closed loop set-point temperature adjustment. Qualitative sensing of temperature

fluctuations and frequencies were demonstrated in liquid fuel swirl spray combustor. The results

offer clear evidence that this sensor system has the flexibility, speed and accuracy to be a useful

tool for fundamental and applied combustion monitoring and control.

Although this sensor has the capability to measure temperature of both the gas and liquid swirling

flames, several limitations are encountered. First, special effort is required for the laser alignment

and nitrogen purge due to the low power of the laser and strong absorption of ambient water

vapor near room temperature. Second, the 1.8 µm direct absorption sensor may require averaging

Conclusions and future work

149

to obtain sufficient SNR under noisy conditions, which limits the measurement bandwidth. Third,

complex data reduction needed for wavelength-scanned direct absorption renders it impractical

for real-time measurements.

7.3 Design of a single laser absorption sensor for temperature measurements using

WMS

The experiences using the 1.8 µm direct absorption scanned-wavelength temperature sensor led to

changes in the design rules to improve the performance. Scanned-wavelength WMS offers

several advantages that improve performance. First, the increased sensitivity of WMS over direct

absorption allows selection of weaker transitions which provide three solutions to problems

encountered with the 1.8 µm sensor. (1) This enables selection of transitions with larger internal

energy E” reducing the sensitivity to cold ambient water vapor. (2) This also provides availability

of fiber-coupled telecommunications lasers, which overlap with the 2ν1, 2ν3 and ν1+ν3 bands of

water vapor. (3) WMS has a simpler data reduction computation than the direct absorption

method and makes real-time measurements possible with a laboratory PC. The design rules to

select optimum water absorption features in the 1-2 micron wavelength range for a WMS sensor

are detailed. The 12 best NIR water transition line pairs for temperature measurements with a

single DFB laser in flames are determined by systematic analysis of the HITRAN simulation of

the water spectra in this spectral region. A specific line pair near 1.4 µm was identified and

investigated experimentally, and the pertinent spectroscopic parameters were determined from

cell experiments. These measurements provide useful improvements to the current spectroscopic

database for H2O for the target transitions and their neighbors. Gas temperature is inferred from

the ratio of the second harmonic signals of two selected H2O transitions. Demonstration

experiments were conducted in a heated cell and a forced Hencken burner. These cell and

laboratory flame experiments confirmed sensitivity and accuracy of the temperature sensor.

Both 1.4 µm and 1.8 µm sensors are based on a single-laser two-line concept, and have the

advantage of a simple optical system. Their use is demonstrated in a liquid-fuel swirl spray

combustor, providing the first demonstration of TDL sensors in such flames. The 1.4 µm WMS

temperature sensor incorporates several improvements over the 1.8 µm sensor design. The 1.4 µm

sensor uses a line pair with relatively weak absorption at room temperature to minimize

interference from ambient air in the measurement path. Second, a very compact and robust setup

Chapter 7

150

was realized by fiber optics, which has advantages for practical application under industrial

conditions. Third, a wavelength modulation spectroscopy technique is employed to shift

measurements to high frequency, and significantly reduces the dominating 1/f noise. Fourth, the

ratio of integrated area is replaced by the ratio of peak-to-peak 2f signals. We have achieved a

real-time repetition rate of 2 kHz with the 1.4 µm sensor. These changes greatly improve the

sensor performance and allow us to further demonstrate the utility of in situ temperature sensing

for combustion control.

7.4 Investigation of the 1.4 µm WMS T sensor for combustion control

To investigate the ability to predict the lean blowout limit, the 1.4 µm WMS temperature sensor

was used for experiments with a swirl-stabilized combustor. Four flow conditions and two

sensing positions were chosen to study the combustion characteristics near lean blowout limit.

For comparison purposes, a microphone is used to simultaneously detect the acoustic signal

during blowout. Experiments show that low frequency components of both acoustic and

temperature measurements increase significantly near lean blowout limit, and can be used as a

precursor for lean blowout. The microphone approach, however, has two intrinsic limitations:

First, it is susceptible to background acoustic signal and thus unsuitable for lean blowout control

under noisy environments. Second, it can only detect global acoustic signal, so it is unable to

detect local flame extinction events. Unlike a microphone, the 1.4 µm WMS sensor can be

applied to a wide range of environments because it does not suffer background interference.

Furthermore, the line-of-sight measurements enable sensitive detection of any local flame

extinction events. It was demonstrated that this sensor has the desired speed and sensitivity to

precisely detect the low frequency fluctuations near lean blowout and has significant potential for

LBO control.

Phase-delay control was implemented using the 1.4 µm WMS temperature sensor to suppress the

natural combustion instabilities in a swirl-stabilized combustor. It is shown that the amplitude of

natural instabilities is greatly reduced by phase-delay control at the optimum phase and amplifier

gain. These results offer strong evidence that the 1.4 µm WMS sensor has the desired accuracy to

monitor dynamics of combustion oscillations and provide effective feedback signal for active

combustion control.

Conclusions and future work

151

7.5 Potential Plan for future work

This thesis has presented the development of systematic sensor design rules, used such rules to

select transitions for a piston engine, and developed two-generations of single-laser temperature

sensors for combustion sensing and control. There are several directions for future work.

1. With the continued improvements in tunable diode lasers and increased availability in laser

wavelengths, a larger region of the spectrum is becoming available. The design rules

developed in this dissertation can be extended to find transitions to achieve better

performance with these new laser choices. (a.) It is possible to select two transitions which

have nearly the same air-broadened halfwidth, self-broadened halfwidth and temperature-

dependence coefficients, thus the effects of the lineshape function (the dependence of species

concentration) could be removed for a 2-line WMS temperature sensor. (b.) By extending 2-

line thermometry to multi-line thermometry, expanded temperature information could be

collected and temperature distribution measurements in non-uniform conditions could be

investigated.

2. The 1.4 µm WMS sensor can precisely detect the approach to the LBO limit in a gas-fueled

swirl-stabilized combustor with significant potential for LBO control. This could be extended

to a LBO control demonstration for both gas- and liquid-fueled combustors.

3. Phase-delay combustion instability control has been implemented in a gas-fueled swirl-

stabilized combustor using the 1.4 µm WMS temperature sensor. The extension to liquid-

fueled flames and further investigations of advanced control strategies such as model-based

adaptive control and fuel modulation are recommended. In addition, further investigations of

sensing at multiple-locations are suggested since it could allow detection of thermal waves.

4. A useful continuation of this work would be the extension to other combustion gas

components (such as NOx and CO). The investigation of the correlation between combustion

instabilities and pollutant emission levels would be very useful. This could enable

combustion control strategies based on CO and/or NOx emission levels, and enable optimized

combustion emissions.

Chapter 7

152

153

Appendix: Architecture of the real-time WMS sensor

The data acquisition and analysis for the real-time 1.4 µm WMS sensor is written using the

C/C++ programming language. The DAC computer utilizes two separate DAQ cards: (1) a Gage

CompuScope 1250, which is used for data acquisition and (2) a National Instruments PCI 6115,

which is used to output 2f ratio (voltage). These are connected as shown in the simplified block

diagram in figure A.1. The input 2f signal is first captured to the on-board memory of the Gage

CompuScope 1250 card. This data is then transferred over the PCI bus into PC RAM for further

analysis. In the bus-mastering mode, the Gage CompuScope 1250 is capable of a PCI bus data

transfer rate up to 100Megabytes/sec. [Gage 2003] After the PC calculates the ratio of the 2f

signals on the target transitions, this ratio is passed to the NI PCI 6115 card where an analog

voltage proportional to the 2f ratio is produced for use by the control computer.

PCI BUS

Input 2f A/D Gage CompusScope 1250

On-board memory Gage CompusScope 1250

PC RAM Data analysis by CPU

D/A NI PCI 6115 Output signal

Output 2f ratio

2f signal 2f ratio

Figure A.1 A simplified block diagram.

Applications Programming Interface (API) routines are supported by Gage CompuScope 1250

and National Instruments PCI 6115. The hardware functionality of the Gage CompuScope 1250

and NI PCI 6115 cards are controlled by these API routines. The detailed descriptions of these

API routines are provided in ref. [Gage 2003; NI 2003], and the manual for their use is found in

ref. [Petzold 1998]. A flow-chart of the sensor logic is illustrated in figure A.2.

Appendix

154

START

Initialize Program Structures and Variables

Initialize the driver and the CompuScope and NI PCI 6115 hardware

Initialize the CompuScope and NI PCI 6115 cards with the desired settings

Triggered? (Falling edge)

Start Capture

Transfer data using DMA method

Data analysis

NI PCI 6115 card output 2f ratio

Triggered? (Rising edge)

More data acquisition?

End

Set the CompuScope and NI PCI 6115 back to initial states

N

Y

N

Y

N

Y

Figure A.2 Flow chart for the data acquisition and analysis program.

Architecture of the real-time WMS sensor

155

The complete source codes is available from the Hanson laboratory library, and only the essential

components specific to the measurements in Chapters 5 and 6 are given here, including: DAQ

card setting, data transfer, peak finding algorithms and output signal.

1. DAQ card setting

Gage CompuScope 1250 and NI PCI 6115 settings are listed below, and comments are provided

between /* and */ using Italic fonts.

Gage CompuScope 1250

/*This parameter is the current trigger source for the data acquisition, and set to external mode

*/

board.source = GAGE_EXTERNAL;

/*This parameter is the GAGE card operating mode, and set to dual channel mode */

board.opmode = GAGE_DUAL_CHAN;

/*This parameter is the sampling rate, and set to 5 MHz */

board.srindex = SRTI_5_MHZ;

/*This parameter is the total data acquisition points, and set to 1000 */

board.depth = 1000;

/*This parameter is the current trigger slope , and set to falling edge as shown in figure 5.24 */

board.slope = GAGE_NEGATIVE;

/*This parameter is the input range for channel A , and set to 500mV */

board.range_a = GAGE_PM_500_MV;

/*This parameter is the input coupling for channel A , and set to DC */

board.couple_a = GAGE_DC;

NI PCI 6115

/* Set output at 0 volts. */

iStatus = AO_VWrite(iDevice, iChan, 0.0);

/* Configure for bipolar mode, internal reference, and external updates. */

iStatus = AO_Configure(iDevice, iChan, iOutputPolarity, iIntOrExtRef, dRefVolts,

iUpdateModeEXT);

/* Setup PFI line for external updates. (PFI0 is setup with AO_Configure.), the trigger slope is

set to rising edge as shown in figure 5.24 */

iRetVal = NIDAQErrorHandler(iStatus, "AO_Configure/ExternalUpdate", iIgnoreWarning);

iStatus = Select_Signal(iDevice, ND_OUT_UPDATE, ND_PFI_0, ND_LOW_TO_HIGH);

Appendix

156

2. Data transfer

/* Adjust this number for data acquisition start position */

location = trigger[0];

/* Adjust this number for data acquisition length for two peaks, as shown in figure 5.24*/

points = 100;

/* gage_transfer_buffer_3 is used to copy “points” data from the channel A to the supplied buffer

beginning from address” location”, this is for the peak 1 data acquisition*/

offset_a1 = gage_transfer_buffer_3 (location, GAGE_CHAN_A, chan_a_12, points);

/*This converts offset_a from a byte pointer to a sample pointer for 12, 14 and 16 bit

CompuScopes, whose samples are 16 bits.*/

offset_a1 = offset_a1 /2;

/* gage_transfer_buffer_3 is used to copy “points” data from the channel A to the supplied buffer

beginning from address” location+690”, adjust the “location+690” so that the program transfer

the data for peak 2*/

offset_a2 = gage_transfer_buffer_3 (location+690, GAGE_CHAN_A, chan_a2_12, points);

/*This converts offset_a from a byte pointer to a sample pointer for 12, 14 and 16 bit

CompuScopes, whose samples are 16 bits.*/

offset_a2 = offset_a2 /2;

3. Peak finding algorithm

The obtained data for 2f peak 1 and 2f peak 2 are best fit using a second order polynomial. 2

i i iy a bx cx= + + (A.1)

Where a, b and c are the polynomial coefficients.

These coefficients can be calculated using the following equations [Bevington 1992]: 2

2 3

2 3 4

1 i i i

i i i i

i i i i

y x xa x y x x

x y x x=

∆

∑ ∑ ∑∑ ∑ ∑∑ ∑ ∑

(A.2)

2

3

2 2 4

1 i i

i i i i

i i i i

N y xb x x y x

x x y x=

∆

∑ ∑∑ ∑ ∑∑ ∑ ∑

(A.3)


157

2

2 3 2

1 i i

i i i i

i i i i

N x yc x x x y

x x x y=

∆

∑ ∑∑ ∑ ∑∑ ∑ ∑

(A.4)

2

2 3

2 3 4

i i

i i i

i i i

N x xx x xx x x

∆ =∑ ∑

∑ ∑ ∑∑ ∑ ∑

(A.5)

Thus the peak can be found by derive equation (A.1)

2

max02 4

dy b bx y adx c c

= ⇒ = − ⇒ = − (A.6)

The source codes for peak finding are listed below:

for (k = 0; k < LG; k++)

/*for 2f peak 1*/

Tf1_SX1Y1 += k*(double)(board_info->sample_offset_32 - chan_a_12[offset_a1+k]) * sign_res;

Tf1_SX2Y1 += k*k*(double)(board_info->sample_offset_32 - chan_a_12[offset_a1+k]) *

sign_res;

Tf1_SY1 += (double)(board_info->sample_offset_32 - chan_a_12[offset_a1+k]) * sign_res;

/*for 2f peak 2*/

Tf2_SX1Y1 += k*(double)((board_info->sample_offset_32 - chan_a2_12[offset_a2+k]) *

sign_res);

Tf2_SX2Y1 += k*k*(double)((board_info->sample_offset_32 - chan_a2_12[offset_a2+k]) *

sign_res);

Tf2_SY1 += (double)((board_info->sample_offset_32 - chan_a2_12[offset_a2+k]) * sign_res);

/*Calculate polynomial coefficients for 2f peak 1*/

Tf1_a_coeff=((Tf1_SY1)*(SX2)*(SX4)+(SX1)*(SX3)*(Tf1_SX2Y1)+(Tf1_SX1Y1)*(SX3)*(S

X2)-(SX2)*(SX2)*(Tf1_SX2Y1)-(SX1)*(Tf1_SX1Y1)*(SX4)-(Tf1_SY1)*(SX3)*(SX3))/Delta;

Tf1_b_coeff=(LG*(Tf1_SX1Y1)*(SX4)+(Tf1_SY1)*(SX3)*(SX2)+(SX1)*(Tf1_SX2Y1)*(SX2)

-(SX2)*(SX2)*(Tf1_SX1Y1)-(SX1)*(Tf1_SY1)*(SX4)-LG*(SX3)*(Tf1_SX2Y1))/Delta;

Appendix

158

Tf1_c_coeff=(LG*(SX2)*(Tf1_SX2Y1)+(SX1)*(Tf1_SX1Y1)*(SX2)+(SX1)*(SX3)*(Tf1_SY1)

-(SX2)*(SX2)*(Tf1_SY1)-(SX1)*(SX1)*(Tf1_SX2Y1)-LG*(SX3)*(Tf1_SX1Y1))/Delta;

/* Calculate polynomial coefficients for 2f peak 2*/

Tf2_a_coeff=((Tf2_SY1)*(SX2)*(SX4)+(SX1)*(SX3)*(Tf2_SX2Y1)+(Tf2_SX1Y1)*(SX3)*(S

X2)-(SX2)*(SX2)*(Tf2_SX2Y1)-(SX1)*(Tf2_SX1Y1)*(SX4)-(Tf2_SY1)*(SX3)*(SX3))/Delta;

Tf2_b_coeff=(LG*(Tf2_SX1Y1)*(SX4)+(Tf2_SY1)*(SX3)*(SX2)+(SX1)*(Tf2_SX2Y1)*(SX2)

-(SX2)*(SX2)*(Tf2_SX1Y1)-(SX1)*(Tf2_SY1)*(SX4)-LG*(SX3)*(Tf2_SX2Y1))/Delta;

Tf2_c_coeff=(LG*(SX2)*(Tf2_SX2Y1)+(SX1)*(Tf2_SX1Y1)*(SX2)+(SX1)*(SX3)*(Tf2_SY1)

-(SX2)*(SX2)*(Tf2_SY1)-(SX1)*(SX1)*(Tf2_SX2Y1)-LG*(SX3)*(Tf2_SX1Y1))/Delta;

/*Calculate peak position for 2f peak 1*/

index1=-(Tf1_b_coeff)/(2*Tf1_c_coeff);

/*Calculate peak position for 2f peak 2*/

index2=-(Tf2_b_coeff)/(2*Tf2_c_coeff);

/*Calculate 2f peak 1*/

maxpeak1=(Tf1_a_coeff)-(Tf1_b_coeff)*(Tf1_b_coeff)/(4*Tf1_c_coeff);

/*Calculate 2f peak 2*/

maxpeak2=(Tf2_a_coeff)-(Tf2_b_coeff)*(Tf2_b_coeff)/(4*Tf2_c_coeff);

4. Output signal

The 2f peak ratio is output through NI PCI 6115, and the source code is as follow:

/*Specify the 2f background signal */

basevalue=0;

/*Calculate the 2f peak ratio */

peakratio=(basevalue-maxpeak2)/(basevalue-maxpeak1);

/*Output the 2f peak ratio (voltage) through channel “iChan” through NI PCI 6115, as shown in

figure 5.24*/

iStatus = AO_VWrite(iDevice, iChan, peakratio);

/* Set update mode back to initial state. */


159

iStatus = AO_Configure(iDevice, iChan, iOutputPolarity, iIntOrExtRef, dRefVolts,

iUpdateModeINT);

/* Set PFI line back to initial state. */

iStatus = Select_Signal(iDevice, ND_OUT_UPDATE, ND_INTERNAL_TIMER,

ND_LOW_TO_HIGH);

Appendix

160

161

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