wavelength-modulation spectroscopy...

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WAVELENGTH-MODULATION SPECTROSCOPY FOR MEASUREMENTS OF GAS TEMPERATURE AND CONCENTRATION IN HARSH ENVIRONMENTS A DISSERTATION SUBMITTED TO THE DEPARTMENT OF MECHANICAL ENGINEERING AND THE COMMITTEE ON GRADUATE STUDIES OF STANFORD UNIVERSITY IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY TSD-178 Gregory Brian Rieker May 2009

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WAVELENGTH-MODULATION SPECTROSCOPY FOR MEASUREMENTS OF GAS TEMPERATURE AND CONCENTRATION IN HARSH ENVIRONMENTS

A DISSERTATION

SUBMITTED TO THE DEPARTMENT OF MECHANICAL ENGINEERING

AND THE COMMITTEE ON GRADUATE STUDIES

OF STANFORD UNIVERSITY

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS

FOR THE DEGREE OF

DOCTOR OF PHILOSOPHY

TSD-178

Gregory Brian Rieker

May 2009

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© Copyright by Gregory Brian Rieker 2009 All Rights Reserved

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I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy.

______________________________ (Ronald Hanson) Principal Advisor

I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy.

______________________________ (Jay Jeffries)

I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy.

______________________________ (Christopher Edwards)

Approved for the Stanford University Committee on Graduate Studies.

______________________________

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Abstract Key advancements in the method and application of wavelength-modulation

absorption spectroscopy (WMS) enable portable diode-laser sensor systems capable of

measurements of temperature and gas concentration in harsh, high-pressure

environments and supersonic flows, often with absorption levels too low and noise

levels too high for traditional direct-absorption techniques.

Over the last 35 years, tunable-diode-laser (TDL) absorption sensing has become

an established method for non-intrusive measurements of gas properties in combustion

devices due to the robust, compact, low-cost nature of TDL sources, and the

convenient overlap of TDL wavelengths with absorption bands of H2O, CO2, O2 and

other important gases.

Wavelength-modulation spectroscopy (WMS) is a derivative form of absorption

spectroscopy that has been increasingly applied for measurements in harsh

environments due to its improved sensitivity and noise-rejection capabilities over

direct absorption. However, the need for on-site calibration against a known mixture

or measurement has presented a key drawback, inhibiting the widespread use of the

technique.

In this work, a practical implementation of calibration-free wavelength-modulation

spectroscopy with second-harmonic detection (WMS-2f) for measurements of gas

temperature and concentration in harsh environments is presented. The method is

applicable to measurements using lasers with synchronous wavelength and intensity

modulation (such as injection-current-tuned diode lasers). The key factors that enable

measurements without the on-site calibration normally associated with WMS are: 1)

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normalization of the 2f signal by the first-harmonic (1f) signal to account for laser

intensity, and 2) the inclusion of laser-specific tuning characteristics in the spectral

absorption model that is used to compare with measured 1f-normalized, WMS-2f

signals to infer gas properties. The uncertainties associated with the calibration-free

WMS method are discussed, with particular emphasis on the influence of pressure and

optical depth on the WMS signals. Many of these uncertainties are also applicable to

calibrated WMS measurements.

The calibration-free WMS technique is applied to two harsh environments –

internal combustion (IC) engines via a modified spark plug for measurements of

temperature and H2O concentration, and a ground-test scramjet combustor during

operation at Mach 5-equivalent flight speed for measurements of temperature, H2O,

and CO2.

To develop the sensor for IC engine operation, careful laboratory measurements of

direct-absorption and 2f spectra of H2O and CO2 at high pressure were performed to

validate the spectral absorption models used to infer gas properties. The direct-

absorption spectra confirm that the Lorentzian line shape model traditionally used for

pressure-broadened absorption transitions is not sufficiently accurate to model spectra

at high density (greater than a few amagat1) due to the breakdown of the instantaneous

collision assumption inherent to the Lorentzian model. Empirical corrections to the

line shape model suggested by past researchers were found to reduce error in the

spectral models; however, a well-validated model for non-Lorentzian effects on high-

pressure CO2 and H2O absorption still does not exist that delivers the low uncertainty

levels necessary for accurate gas property sensing. Alternatively, the 2f spectra are

shown to be at least a factor of four less-influenced by these non-Lorentzian effects,

eliminating the need in most cases for corrections to the 2f spectral absorption

simulations.

The resulting WMS sensor for IC engines is capable of accurate, crank angle-

resolved measurements of temperature and H2O concentration during the compression

stroke of IC engines at a rate of 15 kHz. The temperature is determined from the ratio

1 The number density in amagat is defined as η=n/no, where no=1 amagat=2.69(10)19 molecules/cm3

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of absorption for two transitions of water vapor in the intake-gas mixture, and the H2O

concentration is determined from this inferred temperature and the absorption for one

of the transitions. The measurements sample a short-path region (6 mm) of the in-

cylinder gases near the spark plug. The accuracy of the sensor was validated in a

static cell, giving RMS errors of less than 3% in temperature and less than 3.6% in

H2O concentration over a wide range of conditions. Measurements performed in

unfired and fired engine cylinders illustrate the potential of this sensor for

investigating a range of difficult-to-model trends in current and proposed IC engine

combustion schemes.

The WMS sensor is extended for measurements of temperature, H2O, and CO2 in

the harsh, supersonic flow of a scramjet combustor. A comparison of direct-

absorption and WMS measurements shows a factor of 4 increase in signal-to-noise

ratio with WMS for measurements of weakly-absorbing CO2 in the supersonic flow.

Two-dimensional computational fluid-dynamics (CFD) calculations are compared

with measurements of temperature and H2O using a simple method that accounts for

the influence of line-of-sight (LOS) non-uniformity on the absorption measurements.

The comparisons show the ability of the LOS technique to gain useful information

about multi-dimensional CFD models. In addition, fluctuations in temperature non-

uniformity along the laser LOS are found to precede backpressure-induced unstart, a

harmful condition which produces catastrophic failure to scramjets in flight. Though

the precise cause of the fluctuations remains unknown, the detection method shows

promise for use in control schemes to avoid back pressure-induced unstart in scramjets.

Overall, these demonstrations show that accurate, non-intrusive, high-bandwidth

measurements can be made in harsh environments using the calibration-free WMS

technique, and open the door to practical implementation of WMS in a variety of new

environments that were previously too difficult for TDL absorption sensing.

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Acknowledgements Interestingly enough, obtaining the information contained at the end of my thesis

(Appendix B) almost ended my thesis before it began. After a year of difficult classes

and a year of failed attempts to seal sapphire windows to a metal optical cell body that

was to be repeatedly cycled to 900 K, kept at that temperature for hours, and filled

with 50 atm gases, I was ready to give up. I went home in July, made the

announcement to my family, and that was it. But, just like a tree that loses its leaves in

the winter, my roots (namely, my mother Marilyn, father Don, and grandparents) were

strong and there to support me while I grew them back…like so many times before.

Of course, I never would have attempted the PhD in the first place had it not been

for my lifelong role model and older brother, Jeff. We have a brotherly way of

keeping life competitive, yet seeing each other through the twists in the road. There is

no chance that I would have finished without his help.

My friends and colleagues made my time at Stanford some of the most interesting

days of my life. It’s hard to envision more unique and widely-varying conversations

than those shared over lunch and during (sometimes) brief visits to each other’s desks

and labs. I will not attempt to list names for fear of leaving someone out, and because

every list must begin and end with someone – those decisions are too difficult for me.

You all know how important you are to me.

To Professor Hanson I owe a large debt of gratitude. He took a gamble on an

unproven student from a small state school in Missouri. Without his support, Stanford

would have never been a possibility for me. It is also hard to quantify the intellectual

and physical resources that Professor Hanson made available to me, through him and

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through his group, that made my PhD such an enriching experience. A great example

is Dr. Jay Jeffries. I simply cannot think of another scientist of Jay’s prominence that

is willing to fly to Oklahoma, grab a roll of optical fiber, and join a graduate student

on a scaffolding in 40 degree rain to make a project happen. I would also like to thank

Professor Chris Edwards for everything from ME370B, to participating on my reading

committee, to my somewhat-premature PhD hooding at graduation last June. The

photo from that ceremony made a lifetime for my now late grandfather.

Finally, I would like to thanks Profs. Richard Zare and Reggie Mitchell for

participating in my oral exam committee, and recognize my sponsors for the work

contained in this thesis: the Air Force Office of Scientific Research (AFOSR) with Dr.

J. Tishkoff as technical monitor, the Electric Power Research Institute with Dr. R.

Steele as technical monitor, and Nissan Motor Co., Ltd. I would also like to thank the

people that contributed so much to the technical content of the thesis: Mark Gruber,

Tarun Mathur, and Cam Carter from the Air Force Research Laboratory, Mark Allen

from Physical Sciences, Inc., Kevin Sholes, Kakuho Akihiko, and Shohei Takatani

from Nissan Motor Company, and Jon Liu, Andrew Fahrland, and Hejie Li from

Stanford University.

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Table of Contents ABSTRACT ............................................................................................................................................ V

ACKNOWLEDGEMENTS ................................................................................................................. IX

TABLE OF CONTENTS ..................................................................................................................... XI

LIST OF TABLES ............................................................................................................................... XV

LIST OF ILLUSTRATIONS ........................................................................................................... XVII

CHAPTER 1 . INTRODUCTION ......................................................................................................... 1 

1.1  BACKGROUND AND MOTIVATION ....................................................................................... 1 

1.2  OVERVIEW OF DISSERTATION ............................................................................................. 4 

CHAPTER 2 . CALIBRATION-FREE WAVELENGTH-MODULATION SPECTROSCOPY ... 7 

2.1  SCANNED-WAVELENGTH DIRECT-ABSORPTION SPECTROSCOPY ........................................ 7 

2.2  WAVELENGTH-MODULATION SPECTROSCOPY .................................................................... 9 

2.2.1  Background ................................................................................................................... 9 

2.2.2  WMS Measurement ..................................................................................................... 13 

2.2.3  WMS Model................................................................................................................. 16 

2.2.4  Comparison of WMS Model and Measurement to Infer Gas Temperature and

Concentration ............................................................................................................. 19 

2.3  ANALYSIS OF UNCERTAINTY IN 2F MEASUREMENTS ........................................................ 21 

2.3.1  Pressure Uncertainty .................................................................................................. 22 

2.3.2  Optical Depth .............................................................................................................. 26 

CHAPTER 3 . DIRECT ABSORPTION AND WMS MEASUREMENTS OF NEAR-IR

ABSORPTION AT HIGH PRESSURE AND IMPLICATIONS ON DIODE-LASER SENSOR

DESIGN .................................................................................................................................................. 29 

3.1  H2O ABSORPTION ............................................................................................................. 34 

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3.1.1  Background ................................................................................................................ 34 

3.1.2  Line Shape Model and Spectral Database ................................................................. 36 

3.1.3  Experimental Setup and Procedure ............................................................................ 39 

3.1.4  Direct Absorption Results .......................................................................................... 41 

3.1.5  WMS Results .............................................................................................................. 46 

3.2  CO2 ABSORPTION ............................................................................................................. 49 

3.2.1  Background ................................................................................................................ 49 

3.2.2  Line Shape Model and Spectral Database ................................................................. 51 

3.2.3  Experimental Setup and Procedure ............................................................................ 54 

3.2.4  Direct Absorption Results .......................................................................................... 56 

3.2.5  WMS Results .............................................................................................................. 58 

3.3  IMPLICATIONS ON SENSOR DESIGN .................................................................................. 61 

CHAPTER 4 . RAPID MEASUREMENTS OF TEMPERATURE AND H2O IN IC ENGINES

WITH A SPARK PLUG-MOUNTED DIODE LASER SENSOR ................................................... 65 

4.1  SENSOR DESIGN ............................................................................................................... 67 

4.1.1  Spectral Feature Selection for Thermometry ............................................................. 67 

4.1.2  Sensor Hardware ....................................................................................................... 69 

4.2  SENSOR VALIDATION ....................................................................................................... 71 

4.3  ENGINE RESULTS .............................................................................................................. 72 

4.3.1  Unfired Case .............................................................................................................. 73 

4.3.2  Fired Case .................................................................................................................. 75 

CHAPTER 5 . A DIODE LASER SENSOR FOR MEASUREMENTS OF TEMPERATURE,

H2O, AND CO2 IN A SCRAMJET COMBUSTOR ........................................................................... 79 

5.1  SENSOR DESIGN ............................................................................................................... 80 

5.1.1  Hybrid Demultiplexing ............................................................................................... 80 

5.1.2  Modulation Frequency Optimization ......................................................................... 82 

5.1.3  Line Selection ............................................................................................................. 84 

5.1.4  Validation ................................................................................................................... 86 

5.2  SCRAMJET FACILITY ......................................................................................................... 87 

5.3  SCRAMJET RESULTS ......................................................................................................... 89 

5.3.1  CO2/H2O Concentration in Vitiated Supersonic Flow ............................................... 89 

5.3.2  Comparison between LOS Measurements and 3D-CFD in Combusting Supersonic

Flow ........................................................................................................................... 91

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CHAPTER 6 . DIODE LASER SENSING OF SCRAMJET COMBUSTOR INSTABILITIES .. 97 

6.1  TEMPERATURE FLUCTUATION DETECTION WITH ABSORPTION SPECTROSCOPY .............. 100 

6.1.1  Detection of Specific Temperature Non-uniformities ................................................ 100 

6.1.2  Detection of Fluctuations in a Flow Field with Non-uniform Temperature ............. 102 

6.2  SCRAMJET TEMPERATURE FLUCTUATION RESULTS ........................................................ 105 

CHAPTER 7 . SUMMARY AND FUTURE DIRECTIONS .......................................................... 111 

7.1  CALIBRATION-FREE WMS FOR MEASUREMENTS OF GAS CONCENTRATION AND

TEMPERATURE ................................................................................................................ 111 

7.2  HIGH-PRESSURE, NEAR-IR ABSORPTION BY H2O AND CO2 ............................................ 112 

7.3  A SPARK PLUG-MOUNTED DIODE LASER SENSOR FOR MEASUREMENTS OF TEMPERATURE

AND H2O IN IC ENGINES ................................................................................................. 113 

7.4  A DIODE LASER SENSOR FOR TEMPERATURE, H2O, AND CO2 IN A SCRAMJET COMBUSTOR .

....................................................................................................................................... 114 

7.5  DIODE LASER SENSING OF SCRAMJET COMBUSTOR INSTABILITIES ................................. 115 

7.6  FUTURE DIRECTIONS ....................................................................................................... 116 

7.6.1  Investigation of Higher Harmonics for Short-Pathlength, Low-Absorbance

Measurements in Harsh Environments ..................................................................... 116 

7.6.2  Pressure-independent Calibration-free Wavelength Modulation Spectroscopy ....... 118 

7.6.3  Single Optical Port WMS Measurements Based on Backscatter Techniques ........... 118 

APPENDIX A . SIGNAL CONDITIONING ................................................................................... 121

APPENDIX B . MEASUREMENT CAMPAIGNS ......................................................................... 123

APPENDIX C . AN OPTICAL CELL FOR ABSORPTION MEASUREMENTS AT HIGH

TEMPERATURE AND PRESSURE ................................................................................................. 127

REFERENCES .................................................................................................................................... 131

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List of Tables Table 2.1: Summary of potential sources of uncertainty in calibration-free WMS. .... 21 

Table 3.1: Expressions for χ-functions [64]. |v-vo| is the frequency de-tuning from line

center. σi are de-tuning cutoff frequencies in cm-1. ............................................. 52 

Table 3.2: Parameters for temperature-dependent terms in χ-function calculations [64].

.............................................................................................................................. 52 

Table 3.3: The average effect of non-Lorentzian behavior on WMS and direct-

absorption signals in the 5005.5 – 5009.5 cm-1 region. ........................................ 59 

Table 5.1: Summary of selected H2O and CO2 transitions. .......................................... 85 

Table 5.2: Estimated uncertainty for calibration-free WMS measurements in the

scramjet combustor at AFRL/WPAFB. ................................................................ 95 

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List of Illustrations Figure 2.1:  Schematic of scanned-wavelength direct-absorption spectroscopy with

a tunable diode laser. Example data is water-vapor absorption measured in a

scramjet combustor at the Air Force Research Laboratory (see Chapter 5). .......... 8 

Figure 2.2:  Demonstration of 1f-normalization to account for laser intensity

perturbations to the 2f signal as (a) the laser beam is increasingly blocked, and (b)

the laser optics are periodically vibrated. ............................................................. 11 

Figure 2.3:  Schematic of wavelength-modulation spectroscopy (1f-normalized,

WMS-2f). Example data is water-vapor absorption measured in a scramjet

combustor at WPAFB (see Chapter 5). The 2f signal is always positive due to the

phase-insensitive lock-in approach taken in these experiments (described below).

The slight distortion on the left side of the primary absorption feature is caused

by a second, smaller absorption feature. .............................................................. 13 

Figure 2.4:  The 2f Voigt line shape integral from Eq. (2.14) for various Lorentzian-

Width/Doppler-Width (L/D) ratios. Though the peak signal is achieved near m =

2.2 for all line shape profiles, the magnitudes of the signals vary significantly. . 23 

Figure 2.5:  Percent difference in 2f line shape integral for a -5% change in pressure.

L/D = Lorentzian-width/Doppler-width. For isolated, optically-thin absorption

transitions this translates directly into percent difference in the 2f signal. .......... 24 

Figure 2.6:  Percent difference in the ratio of 2f line shape integrals for two

absorption features for a -5% change in pressure. L/D Ratio is defined as

(L/D)feature 1 / [(L/D)feature 2=1]. .............................................................................. 25 

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Figure 2.7:  WMS-2f signal for the absorption feature at 7185.6 cm-1 (~1392 nm)

for two different total pressures. The influence of nearby absorption transitions

(2.6 cm-1 away) at larger modulation indices becomes apparent as total pressure

increases. Simulation conditions: T = 300 K, xH2O = 0.01. ................................ 26 

Figure 2.8:  Error induced in partial pressure measurement using Eq. (2.16) due to

deviation between the true partial pressure and the simulated partial pressure as a

function of absorbance (optical depth). Error increases as the true condition

deviates from the simulated condition used to calculate the measured partial

pressure, and as optical depth increases. Simulation conditions: H2O absorption

feature at 7185.6 cm-1 when the simulated H2O mole fraction is x = 0.010 and the

true mole fraction is varied between x = 0.010 and x = 0.012 (holding the total

pressure constant). ................................................................................................ 27 

Figure 3.1:  Simulated Lorentzian line shapes for the H2O spectral feature near

7203.89 cm-1 at 700 K, PH2O = 0.02 atm. Neighboring features have been

neglected. .............................................................................................................. 32 

Figure 3.2:  Foreign-broadened H2O χ-function versus frequency de-tuning from

line center [46]. ..................................................................................................... 37 

Figure 3.3:  Effect of χ-function on the H2O absorption transition near 7203.89 cm-1

at 30 atm and 700 K. Neighboring features are neglected. Inset shows the effect

on a log-log scale. ................................................................................................. 38 

Figure 3.4:  Experimental setup for high-temperature, high-pressure H2O

absorption measurements. .................................................................................... 40 

Figure 3.5:  Direct-absorption spectrum, 7204 cm-1 region, P = 10 atm, T = 700 K,

xH2O = 0.0022. Hybrid database is HITRAN augmented with parameters from

Liu el al [37]. The spectrum at 1 atm is plotted in gray to show the contributing

spectral features. ................................................................................................... 42 

Figure 3.6:  Direct-absorption spectrum, 7435 cm-1 region, P = 10 atm, T = 700 K,

xH2O = 0.0022. The spectrum at 1 atm is plotted in gray to show the contributing

spectral features. ................................................................................................... 43 

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Figure 3.7:  Direct-absorption spectrum, 7204 cm-1 region, P = 30 atm, T = 700 K,

xH2O = 0.0022. Simulations using the χ-function with different C coeffients are

shown. The inset shows the χ-function versus frequency de-tuning from line

center. .............................................................................................................. 44 

Figure 3.8:  Direct-absorption spectra, 7204 cm-1 region, P = 10, 20, 30 atm, T =

700 K, xH2O = 0.0022. .......................................................................................... 45 

Figure 3.9:  Direct-absorption and 1f-normalized, WMS-2f with an absorbance

offset added during simulation. Note the insensitivity of the 2f signal to the

absorbance offset. Spectral feature near 7203.89 cm-1. P = 10 atm, T = 700K,

xH2O = 0.0022. Neighboring features have been neglected. WMS modulation

parameters: a = 0.65 cm-1, f = 50 kHz. ................................................................ 46 

Figure 3.10:  1f-normalized, WMS-2f spectrum, 7204 cm-1 region, T = 700 K, xH2O

= 0.0022 for P = 10 atm, 20 atm, and 30 atm. Hybrid database is HITRAN

augmented with parameters from Liu el al [37]. Hybrid database with and

without χ-function correction result in nearly identical spectra. WMS modulation

parameters: a = 0.65 cm-1, f = 50 kHz. ............................................................... 47 

Figure 3.11:  1f-normalized, WMS-2f spectrum, 7435 cm-1 region, T = 700 K, xH2O

= 0.0022 for P = 10 atm, 20 atm, and 30 atm. Hybrid database is HITRAN

augmented with parameters from Liu el al [37]. Hybrid database with and

without χ-function correction result in nearly identical spectra. WMS modulation

parameters: a = 0.65 cm-1, f = 50 kHz. ................................................................ 48 

Figure 3.12:  Linestrengths of H2O and CO2 transitions in the near-infrared at 296 K

[22]. .............................................................................................................. 50 

Figure 3.13:  CO2-CO2 and CO2-N2 χ-functions versus frequency de-tuning from line

center [64]. ............................................................................................................ 53 

Figure 3.14:  Effect of χ-function on the R50 transition of the 20012 00001 band of

CO2 at 10 atm and 300 K (10.8% CO2 in air). Neighboring features are neglected.

Inset shows the effect on a log-log scale. ............................................................. 53 

Figure 3.15:  Experimental setup with high-pressure static cell. ............................... 55 

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Figure 3.16:  Direct-absorption spectrum, 10.8% CO2 in air, L = 100 cm, T = 296 K.

Absolute deviation is shown for the Voigt profile + χ-function data. .................. 57 

Figure 3.17:  Simulated direct-absorption spectrum of the 20012 00001 band of

CO2 near 2.0 μm. The box denotes the measurement region for this work. 10.8%

CO2 in air, P = 10 atm, L = 100 cm, T = 296 K. ................................................. 58 

Figure 3.18:  1f-normalized, WMS-2f spectrum. 10.8% CO2 in air, L = 100 cm, T =

296 K, a = 0.11 cm-1 for P = 1, 5 and 10 atm. For the P = 1 and 5 atm cases, the

χ-function correction results in very little change from the uncorrected Voigt case.

WMS modulation parameters: a = 0.11 cm-1, f = 50 kHz. .................................. 59 

Figure 3.19:  Comparison of simulations using HITRAN [22] and Toth et al. [74]

spectral parameters. 1f-normalized, WMS-2f at T = 296 K, 10.8% CO2 in air, L

= 100 cm. Both simulated spectra use the χ-function modified Voigt profile.

WMS modulation parameters: a = 0.11 cm-1, f = 50 kHz. .................................. 60 

Figure 4.1:  Three-dimensional rendering of the ratio of 2f/1f signals used to infer

temperature. The ratio is taken between the 7435 cm-1 and 7204 cm-1 features

simulated with 1% H2O vapor in air. The effect of absorption on the 1f

magnitude is neglected. ........................................................................................ 69 

Figure 4.2:  Photo of the sensor system (foreground). ............................................. 69 

Figure 4.3:  Sensor layout. Pressure transducer not shown. ................................... 70 

Figure 4.4:  Schematic of the optical probe. ............................................................ 70 

Figure 4.5:  Validation measurements of the sensor system in a controlled high

temperature and pressure optical cell. .................................................................. 72 

Figure 4.6:  Measured temperature in an unfired, single-cylinder engine. A constant

gamma isentropic simulation is shown for comparison. ...................................... 74 

Figure 4.7:  Measured water concentration and mole fraction in an unfired, single-

cylinder engine. .................................................................................................... 74 

Figure 4.8:  Measured temperature and pressure in a fired, single-cylinder engine.76 

Figure 4.9:  Water concentration and mole fraction measured in a fired, single-

cylinder engine. .................................................................................................... 76 

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Figure 5.1:  Schematic of a hybrid demultiplexing system configured for the

scramjet experiments at AFRL/WPAFB. ............................................................. 82 

Figure 5.2:  Fourier transform of detector signals with (a) one laser scanning fully

across 1 absorption feature using a linear ramp waveform, (b) one laser scanning

fully across 1 absorption feature using a sine waveform, and (c) two lasers

scanning across only the peak of 2 absorption features using a sine waveform.

Note in panel (c) that each laser is modulated at a different frequency so that the

harmonic signals for each can be distinguished. .................................................. 83 

Figure 5.3:  Selected H2O and CO2 transitions. ....................................................... 85 

Figure 5.4:  Temperature and H2O concentration validation measurements in a

uniform furnace and flat flame burner. ................................................................. 87 

Figure 5.5:  Photo of the continuous-flow, direct-connect scramjet test rig at

AFRL/WPAFB. .................................................................................................... 88 

Figure 5.6:  Schematic of AFRL scramjet flowpath. Large optical access windows

allow measurements at multiple vertical locations in the combustor duct. .......... 88 

Figure 5.7:  Comparison of direct-absorption and 2f signals and CO2 partial

pressure measurements in a vitiated supersonic flow using the 1997 nm

absorption feature of CO2. The left panels show single-scan data with (a) the

WMS-2f and (c) direct-absorption techniques, along with the peak or voigt fit

values that are used to calculate the CO2 concentration. The right panels show

the measured CO2 partial pressure at 4 kHz using (b) 2f peak magnitudes and (d)

integrated absorbances. ......................................................................................... 90 

Figure 5.8:  Method for comparison of multi-dimensional CFD with LOS laser

measurement. ........................................................................................................ 93 

Figure 5.9:  Static Temperature and H2O Partial Pressure for different vertical

locations in the scramjet combustor during full operation on ethylene and air.

Each point is the LOS laser-measured value for the experiment (solid squares)

and the expected LOS laser-measured value from the CFD calculated flow field

(open circles). The gray line (no symbols) represents the path-average

temperature from the CFD calculated flow field. ................................................. 94 

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Figure 6.1:  Simulated 2f/1f signal for the three probed H2O spectral features. P =

0.85atm, xH2O = 0.11, L = 23cm. Laser specific characteristics (see Chapter 2):

a~0.07cm-1, io~0.10. ........................................................................................... 101 

Figure 6.2:  Simulated path-averaged inferred temperature using two spectral

feature pairs for a non-uniform absorption path comprised of a section at 600K

and a section at 1500K. The portion of the path that is at 600K is varied with the

remainder of the path at 1500K. ......................................................................... 102 

Figure 6.3:  Full run temperature profiles for stable and unstable cases (100-Hz

filtered). Inset shows blowout at full sensor sampling rate (4 kHz). ................. 105 

Figure 6.4:  Pressure recorded for data acquisition sweeps just before and after inlet

unstart. Pressure sampling rate is ~0.9 Hz. The top panel shows the flowpath

schematic as it corresponds to the pressure tap readings. .................................. 106 

Figure 6.5:  Measured temperature with individual absorption feature pairs. Unstart

(observed in wall pressure data) occurred during the gray time window. .......... 107 

Figure 6.6:  Fraction of frequency content in 1<f<50Hz range for an STFT of the

temperature measured with each absorption feature pair. .................................. 108 

Figure 6.7:  Ratio between fractional STFT of each absorption feature pair. Note

the unstart time window does not apply to the stable case. ................................ 109 

Figure 6.8:  Full run gas temperature, wall temperature, and pressure near laser

sensor location for the unstable case. Also shown is the wall temperature near the

flameholder, which exhibits time lag, but has inflection points which agree with

events measured in the gas temperature. ............................................................ 109 

Figure 7.1:  Example WMS measurement in a harsh process heater used in oil

refineries. The 2f/1f SNR remains unchanged if the 1f signal is >3-4% of max. ...

............................................................................................................ 119 

1

Chapter 1. Introduction

1.1 Background and Motivation Increasing fuel costs and government regulations on combustion systems continue

to drive the development of more efficient combustion devices. As combustion

technologies mature, gains in combustion efficiency become more difficult to achieve

and accurate diagnostics, ideally located near the reaction zone of a device, are

necessary to evaluate small differences between various device designs. In addition,

active control with sensor feedback becomes important to maintain optimum

efficiency through transients in system operating points and changing fuel streams.

Since carbon dioxide (CO2) and water vapor (H2O) are major products of combustion,

measurements of CO2 and H2O in a reacting system provide a good direct measure of

the quality of the combustion process occurring in that system. Measurements of

temperature are also crucial as temperature plays an important role in the ignition

properties, reaction rates, and formation of pollutants in reacting gas mixtures.

Over the last 35 years, tunable diode laser (TDL) absorption spectroscopy has

matured into a robust and convenient means of measuring a wide variety of gas

parameters in difficult, real-world environments [1−7]. Light emitted from robust,

tunable diode sources is passed through a gaseous test sample to a detector, and the

absorption of light can be related to gas temperature, pressure, species concentration,

and velocity using spectral absorption models for the target absorbing species.

For target species with discrete spectral-absorption features (e.g. small molecules

and atoms) where the absorption is wavelength-dependent over a short spectral

2

window (a few cm-1), the laser wavelength can be modulated sinusoidally and the non-

uniform absorption gives rise to components in the detector signal at the harmonics of

the original sinusoid frequency. The harmonic signals can be isolated with lock-in

amplifiers (essentially band-pass filters), which greatly reduce the influence of laser

and electronic noise by filtering out components of the detector signal outside of the

harmonics. The harmonic signals can then be related back to the spectral absorption

models for the target species and used to infer gas properties, but with much higher

sensitivity than direct-absorption measurements.

Modulation spectroscopy is divided into two categories: frequency modulation

spectroscopy (FMS) in which the modulation frequency1 is greater than the half-width

of the probed absorption feature (100 MHz to several GHz range), and wavelength-

modulation spectroscopy (WMS) in which the modulation frequency is less than the

optical frequency half-width of the probed absorption feature (kHz to several MHz

range). A good overview and comparison of the two categories can be found in

companion papers by Silver [8] and Bomse et al. [9], who found that high-frequency

WMS (>100 kHz) offers excellent sensitivity without the burden of extremely fast

detection electronics, as required by FMS. This is an important consideration for

practical, field-deployable systems, which is the concern of this dissertation.

Recognizing the power of WMS for highly-sensitive measurements, many

researchers have applied the technique to enable measurements in difficult

environments that otherwise might not be possible with direct-absorption spectroscopy.

Measurements in a high-pressure coal combustor [10], ground-test scramjet engines

[11], and a variety of trace gas situations [12 and references there-in] are just a few

examples using WMS. A handheld methane leak detector [13] and combustion

measurements in a micro-gravity droptower [14] are excellent examples of portable

WMS systems where the sensor hardware itself is also compact, robust, and capable of

operating in difficult environments.

1 We refer here to the frequency of the modulation sinusoid, not the modulation amplitude (which is also sometimes reported in frequency units)

3

One of the key drawbacks to applying traditional WMS in practical environments

for temperature and concentration measurements is the need to calibrate the WMS

signals to a known mixture and condition (or a direct measurement of absorption) in

order to recover the absolute concentration or temperature. For most real-world

environments and field-deployable sensors this is difficult and impractical, and may

involve the need for additional equipment and complexity in the sensor system.

Several researchers have proposed methods to enable “calibration-free”

measurements using WMS. In this dissertation, we define “calibration-free” as a

method that enables absolute measurements of temperature or concentration without

on-site calibration or comparison with a known mixture or condition. It should be

pointed out immediately that like most absorption-based measurements,

characterization of the probe lasers and certain spectral parameters (such as

linestrength and pressure-broadening of the target absorption feature) are still

necessary for “calibration-free” WMS. Many of the proposed calibration-free WMS

methods [15−17] are useful for certain cases; such as when many of the environmental

conditions are known and stable, the target absorption feature is completely isolated

from other absorption features, and the laser can be tuned across the entire feature so

that the non-absorbing region on either side can be used to normalize the signal for the

incident laser intensity. These methods are difficult in many practical environments,

where most of the environmental conditions are unknown, the incident laser intensity

is rapidly varying due to vibration, window-fouling, beam-steering, etc., and which

often comprise gas mixtures that may contain interfering species and elevated

pressures where pressure-broadening causes neighboring features to blend and overlap

beyond the scan range of the laser.

The calibration-free WMS method in this dissertation uses the 2f signal to gain

absorption information, and is applicable to any WMS light source that exhibits

synchronous wavelength and intensity modulation (such as an injection-current-tuned

diode laser). Cassidy and Reid [18] first recognized that for these types of light

sources, the 1f signal can be used to normalize the 2f signal for variations in laser

intensity. This property has since been successfully exploited by several authors

4

[10,13,19,20]. It was recently suggested by Li et al. [21] that combining this intensity

normalization with a model for the WMS signals based on the specific laser tuning

characteristics for the probe laser and spectral data measured in the laboratory or

obtained from HITRAN [22] eliminates all calibration factors between experiment and

model. The experiment and model can thus be directly compared to infer temperature

and species concentration, as first demonstrated in this dissertation. This method

works at any pressure where a 2f signal can be obtained, works with congested spectra

so long as spectral information for the neighboring features is included in the model,

and is applicable for nearly any laser modulation frequency and amplitude. In

addition, the method does not require that the laser scan across the entire feature –

only the 2f peak must be captured – which is helpful at high pressures and, as will be

shown later, is desirable when using frequency demultiplexing of WMS signals from

different lasers impinging on one detector. The method does have intricacies, such as

different optimal implementations depending on the environment and conditions, and

drawbacks, such as the need for knowledge of the gas pressure in the probe region.

This dissertation studies these topics for calibration-free WMS and presents a

framework for implementing calibration-free WMS measurements and sensors in

harsh environments.

1.2 Overview of Dissertation The dissertation seeks to achieve the following goals:

(1) Clearly describe how calibration-free WMS is performed (Chapter 2). The

focus will be a discussion of the practical implementation of WMS measurements

and models so that they can be compared directly to infer gas properties.

(2) Study the uncertainties involved with WMS, particularly as applied to harsh

environments (Chapter 2). The focus will be placed on understanding the effect

of pressure uncertainties and non-uniformities along the laser line-of-sight (LOS),

and the effects of modulation amplitude and optical thickness on uncertainty.

(3) Compare measured direct-absorption and WMS spectra for H2O and CO2 at

high pressures with corresponding simulations (Chapter 3). These

5

comparisons validate the WMS models, test the spectral databases used for future

practical measurements, and reveal the effects of non-ideal absorption line shapes

caused by high-density gas. These measurements, which represent the first

measured WMS spectra for H2O and CO2 at high pressures, reveal that WMS

measurements are much less sensitive to non-ideal line-shape effects.

(4) Demonstrate the use of calibration-free WMS for measurements with a

spark-plug-mounted optical probe in an internal combustion engine (Chapter

4). A sensor is developed based on the findings of Chapter 3 that enables

measurements of temperature and H2O concentration at pressures up to 30

atmospheres during the compression stroke of a production-type engine. The

sensitive measurements occur in a 6 mm opening near the spark plug and represent

the first practical application of calibration-free WMS.

(5) Apply calibration-free WMS to measure temperature, H2O, and CO2 in the

harsh, non-uniform environment of a ground-test scramjet engine (Chapter

5). The sensor is extended to deal with larger absorbance and a non-uniform

pathlength. A hybrid-demultiplexing technique is developed that uses both

wavelength- and modulation frequency-multiplexing to combine six lasers with

wavelengths ranging from 1.3 μm to 2.0 μm in a single probe beam and later

distinguish their signals. Sensitive WMS measurements of CO2 are compared with

direct absorption. A simple method to compare multi-dimensional CFD with line-

of-sight absorption measurements is applied to study CFD models of temperature

and H2O in the scramjet combustor.

(6) Demonstrate the use of multiple wavelengths to detect combustor instabilities

in scramjet engines (Chapter 6). By probing multiple H2O absorption feature

simultaneously, the sensor is able to detect temporal fluctuations in line-of-sight

non-uniformity in the scramjet combustor. A rise in these fluctuations is shown to

precede backpressure-induced unstart in the scramjet, revealing the possibility of a

new method to detect and mitigate this harmful condition.

6

Chapter 7 summarizes the major findings and conclusions of the dissertation and

discusses future directions. Appendix A discusses analog detector signal conditioning

prior to digital sampling, and Appendix B describes the optical cell that was developed

for the laboratory measurements and validations performed at simultaneously high

temperature and pressure.

7

Chapter 2. Calibration-Free

Wavelength-Modulation Spectroscopy This section presents a method and implementation of calibration-free WMS that

has been developed over the last several years for application in harsh environments

[21,23]. The section begins with a brief overview of traditional scanned-wavelength

direct-absorption spectroscopy. The subsequent calibration-free WMS discussion is

divided into four parts – relevant background, the WMS measurement, the WMS

model, and the comparison between the two to infer gas properties. The final part of

the section is an analysis of the uncertainties relevant to WMS measurements in harsh

environments.

2.1 Scanned-Wavelength Direct-Absorption

Spectroscopy For many years, tunable-diode-laser (TDL) direct-absorption spectroscopy has been

the technique of choice for absorption-based measurements of gas parameters in harsh

environments because of its simplicity, accuracy, and ability to make absolute

measurements. For absorption by small molecules at low to moderate pressures, the

scanned-wavelength variant of direct-absorption spectroscopy is often used.

Figure 2.1 shows a typical scanned-wavelength direct-absorption measurement

using a TDL. The diode-laser injection current is tuned with a repetitive ramp

8

waveform (or similar). This has the effect of repetitively ramping the laser intensity

and the laser wavelength. If the nominal laser wavelength corresponds to a spectral

Figure 2.1: Schematic of scanned-wavelength direct-absorption spectroscopy with a tunable diode laser. Example data is water-vapor absorption measured in a scramjet combustor at the Air Force Research Laboratory (see Chapter 5).

absorption feature for a species present in the probed gas sample, the laser is tuned

across the feature and results in a detector signal similar to the one shown (intensity vs.

time). The non-absorbing areas of the ramping intensity signal are fit with a baseline

which is used to normalize for any changes in the incident laser intensity (e.g. by

window fouling or beam-steering) and allow for the calculation of the absolute

absorbance using the Beer-Lambert relation:

⎟⎟⎠

⎞⎜⎜⎝

⎛−=

o

t

IIlnα (2.1)

Here α denotes the absorbance, It is the transmitted laser intensity (i.e. the detector

signal), and Io is the incident laser intensity (i.e. the baseline). The absorbance can be

related back to the gas properties of a uniform absorbing medium through the

following equation:

∑ ⋅⋅⋅=

jjij vLPTS )()( φα (2.2)

where Sj(T) is the linestrength at temperature T of absorption transition j, Pi is the

partial pressure of the target species i, L is the pathlength of laser beam travel through

the uniform absorbing medium, and φj(ν) is the line shape function at frequency ν

(referring to the optical frequency, which is inverse wavelength). If possible, the

measured absorbance from the target absorption transition is fit with the appropriate

300

400

500

600

700

800

900

1000

Time (also Optical Frequency)

Inte

nsity

, a.

u.

I0 It

Abso

rban

ce

Wavelength

Laser Detector

Inte

nsity

Time

GasSample

RampBaseline fit

+Beer’s Law

Integratedabsorbance

9

line shape profile for the environmental conditions (Lorentzian1, Gaussian2, or Voigt3)

and the integrated absorbance is calculated from the fit. The integrated line shape

function is unity by definition, so the integrated absorbance becomes:

LPTSdvvLPTS ii ××=⋅×××= ∫∞

∞−

)()()(Absorbance Integrated φ (2.3)

The integrated absorbance is directly proportional to species partial pressure (and

therefore concentration) and is related to the temperature of the absorbing gas by S(T),

which is either measured under laboratory conditions or obtained from HITRAN [22].

For thermometry, the ratio of the integrated area of two absorption features is used.

When the ratio is taken, the species partial pressure and pathlength cancel. The

remaining ratio of linestrengths is purely a function of temperature and is used to infer

the temperature from the measured integrated absorbance ratio.

)()(

Absorbance IntegratedAbsorbance Integrated

2

1

2

1

TSTS

= (2.4)

The species concentration is calculated using Eq. (2.3) with one spectral feature.

(The integrated area and pathlength are known, and the linestrength is calculated using

the temperature previously inferred from Eq. (2.4).)

2.2 Wavelength-Modulation Spectroscopy

2.2.1 Background Wavelength-modulation spectroscopy (WMS) is similar to direct-absorption

spectroscopy, except the laser wavelength is additionally modulated with a rapid

1 The Lorentzian profile is used to describe collision-broadened absorption transitions. Collision-broadening results from energy-level perturbations by collisions between molecules, and therefore scales with density and molecular velocity/cross section (∝ P/TN, where N is typically 0.5-1). 2 The Gaussian profile is used to describe Doppler-broadened absorption transitions. Doppler-broadening is due to the random motion of the absorbing molecules and therefore increases with temperature (∝ T0.5). 3 The Voigt profile is a convolution of Doppler and collision broadening. It is used for the common case when both broadening mechanisms are important.

10

sinusoid (at frequency f). The interaction between the rapidly modulating wavelength

and a nonlinear absorption feature gives rise to harmonic components in the detector

signal, which can be isolated with lock-in amplifiers. Generally the second harmonic

(2f) is used because like direct absorption, the 2f signal is strongly dependent on

spectral parameters and gas properties and can therefore be compared with spectral

simulations to infer gas properties. In addition to its sensitivity to gas properties,

however, WMS-2f has several benefits which make it desirable over direct absorption

for certain sensing applications.

The 2f signal is sensitive to spectral shape or curvature rather than absolute

absorption levels, which is useful for certain high-density spectra [24,25], particularly

those that are affected by broadband absorption or emission [26,27]. Also, the use of a

lock-in amplifier serves to reject noise that falls outside of the lock-in pass band, such

as laser intensity and electronic noise.

For laser sources that have synchronous tuning of the laser wavelength and

intensity (such as diode lasers), the intensity modulation is typically the strongest

component of the first harmonic (1f) signal, and can be used to normalize the 2f signal

against perturbations to the laser intensity by laser drift, window fouling, beam

steering, or scattering [10,13,18−20]. This attribute of WMS is particularly useful in

harsh environments, and is demonstrated in Figure 2.2. A simple experiment was

performed in which a laser was tuned to an absorption feature and the 2f and 1f signals

were recorded as the laser beam was partially blocked (left panel), and the laser optics

were periodically vibrated (right panel). Despite the large and rapid changes in the

laser intensity (which affect both the 2f and 1f signals), the 1f-normalized, WMS-2f

signal remains unchanged.

Altogether, the benefits listed above yield a 2-100x improvement in SNR for

WMS-2f over direct absorption, depending on the measurement conditions.

Given these benefits over direct absorption, the technique has been applied to many

harsh or difficult absorption measurements [e.g. 10−14,28−31]. Common to all of

these past measurements however, was the need to calibrate the measurement on-site

with a known gas mixture (or direct-absorption measurement) in order to gain absolute

11

concentration or temperature information. For many real-world situations or practical

implementations of gas sensors, this is an important drawback and adds undesirable

complexity to the sensor or measurement.

Figure 2.2: Demonstration of 1f-normalization to account for laser intensity perturbations to the

2f signal as (a) the laser beam is increasingly blocked, and (b) the laser optics are periodically vibrated.

As discussed in Chapter 1, several researchers have proposed calibration-free WMS

techniques to enable absolute measurements without on-site calibration. Henningsen

and Simonsen [15] proposed a method that relates various parameters of the second-

harmonic (2f) signal such as the peak-to-trough ratio and the line width to develop

algorithms that infer absolute species concentration provided the pressure, pathlength

and temperature in the environment are known. This method is useful for certain

cases where many of the environmental conditions are known, however the method

also requires that the absorption feature is completely isolated (so there is no distortion

to any part of the line shape or wings), and that the laser can be tuned completely

across the absorption feature such that the non-absorbing region on either side of the

feature can be used to extract the laser intensity to normalize the signal. This is

difficult in practical environments, which often comprise gas mixtures that may

contain interfering species such as H2O and elevated pressures where pressure-

broadening expands the feature beyond the scan range of the laser. If H2O itself is the

target molecule, finding an isolated transition is difficult among the many overlapping

transitions even at room temperature.

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.70.00

0.05

0.10

0.15

2f/1

f Sig

nal

Time (s)

0.0

0.3

0.6

1f S

igna

l

(b) Vibrating Optics

0.00

0.03

0.06

2f/1f

1f

2f S

igna

l

2f

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.350.00

0.05

0.10

0.15

2f/1

f Sig

nal

Time (s)

0.0

0.3

0.6

1f S

igna

l

(a) Partially blocking beam

0.00

0.03

0.06

2f/1f

1f

2f S

igna

l

2f

12

Other researchers have developed a form of calibration-free WMS which recovers

the direct-absorption line shape from the 1f signal for measurements of concentration

and pressure [16,17]. This method is useful in that traditional direct-absorption data

reduction methods can be applied once the direct-absorption line shape is obtained;

however, for application in harsh environments the method has several potential

drawbacks. The technique works well for small modulation amplitudes when the

harmonic line shapes closely approximate the derivatives of the direct-absorption line

shape, but when the modulation amplitude is increased to maximize the harmonic

signals (which is necessary in harsh environments to obtain sufficient SNR), the

analysis becomes more complicated. In addition, the technique also requires that the

laser scan across the entire absorption feature to recover a non-absorbing baseline to

normalize for laser intensity, which is difficult when interfering species are present in

gas mixtures or for highly pressure-broadened features.

In the remainder of this chapter, the focus will be on the calibration-free method

first suggested in [21] and demonstrated in this dissertation. This method is

compatible with WMS measurements using laser sources with synchronous

modulation of the laser wavelength and intensity. The method is particularly well-

suited to harsh environments because it does not suffer from many of the drawbacks of

the other techniques. Absorption information is gained from the 2f signal, which is

normalized for laser intensity by the 1f signal. This normalization accounts for the

many perturbations in laser intensity present in harsh environments and also creates a

signal (2f/1f) that can be directly compared to a calculated model without intensity

scaling parameters. A model is developed for the 2f/1f signal that includes the specific

tuning parameters of the laser used in the experiment and the spectral data for the

probed absorption features. This incorporation of experimental parameters into the

model means the two can be directly compared to infer gas properties. The method

can be used for any set of environmental conditions (pressure, temperature,

concentration and pathlength), lasers and laser tuning parameters so long as care is

taken to maintain compatibility between the model and measurement.

13

2.2.2 WMS Measurement Figure 2.3 shows a schematic of a scanned-wavelength WMS measurement using a

diode laser. Much like traditional scanned-wavelength direct-absorption

measurements, the diode-laser injection current is tuned with a repetitive ramp

waveform. This has the effect of repetitively ramping the laser intensity and the laser

wavelength across the absorption feature. Unlike traditional direct absorption

however, an additional high-frequency sinusoid is superimposed on the repetitive

injection-current ramp to generate an additional high-frequency modulation in both the

laser intensity and wavelength. When the laser wavelength is tuned across an

absorption feature (e.g. by the repetitive ramp), the high-frequency wavelength

modulation causes the laser to scan back-and-forth over part of the absorption feature

twice per modulation cycle. Absorption thus affects the shape of the transmitted laser

intensity and introduces harmonic components to the detected signal. An example

detector signal (intensity vs. time) is shown in Figure 2.3.

Figure 2.3: Schematic of wavelength-modulation spectroscopy (1f-normalized, WMS-2f). Example data is water-vapor absorption measured in a scramjet combustor at WPAFB (see Chapter 5). The 2f signal is always positive due to the phase-insensitive lock-in approach taken in these experiments (described below). The slight distortion on the left side of the primary absorption feature is caused by a second, smaller absorption feature.

The detector signal is passed to several digital lock-in amplifiers to isolate the 1f

and 2f signals.1 The lock-in amplifiers act by multiplying the detector signal by a

reference sinusoid at the frequency of interest (1f or 2f) to take advantage of the

1 A discussion of detector signal conditioning prior to digital sampling can be found in Appendix A.

I0 It

Laser Detector

GasSample

400

500

600

700

800

900

1000

Inte

nsity

, a. u

.

Time

Inte

nsity

Time

2f peak height

2fS

igna

lTime

Σ

Sinusoid(Frequency = f)

++

RampLock-in Amplifier

@ 2f

1f@ 2f peak loc.

1fS

igna

l

Time

Lock-in Amplifier@ 1f

x

x

14

trigonometric identity, )cos()cos()cos()cos( 21

21 βαβαβα ++−= , to shift the

harmonic components at the frequency of interest to DC.1 A low-pass filter is then

applied to isolate the DC value and eliminate all components outside of the filter

bandwidth [32].

In order to compare the WMS measurements to the model presented in the next

section, it is important to either tune the phase of the lock-in reference sinusoid to

precisely match the phase of the detected harmonic signal, or use a phase-insensitive

lock-in approach. In our lab, we use the phase-insensitive approach by passing the

detector signal in parallel through two lock-ins for each harmonic. One lock-in

multiplies the detector signal by a reference sine wave (recovering what we refer to as

the Y component of the signal) and the other multiplies the detector signal by a

reference cosine wave (recovering what we refer to as the X component of the signal).

The root-sum-square of the X and Y component is the total magnitude of the harmonic

component, regardless of the phase shift between the detector signal and lock-ins. The

root-sum-square is always positive, and causes the 2f peak and wing lobes to have the

same sign (they have opposite signs if the traditional lock-in approach is taken).

There are several sources of 2f background signals that must be avoided or

subtracted from the experimental measurements before the measurements can be

directly compared with the model presented in the next section. The sources fall in

three categories – background signals induced by etalon effects along the light path,

background signals induced by nonlinear intensity modulation effects in the laser, and

background absorption by gases outside the measurement volume.

Etalon effects are caused by constructive/destructive interference arising from

internal reflections off parallel faces in the optical path. Their wavelength-dependent

nature can induce spurious 2f signals [33]. These effects must be avoided in the

optical design of the sensor system because they may be unstable and therefore cannot

be successfully subtracted from the measured 2f signal or included in the WMS model.

1 cos(α) represents a frequency component of the detector signal and cos(β) represents the reference sinusoid. If β is chosen to be 2πfot, where fo = 2f, then the frequency components of the detector signal with α ≈ β (i.e. components near 2f) will be shifted to α-β ≈ 0, and become the DC output of the lock-in.

15

We have found that for many harsh environments, the use of a 1° to 3° wedge on the

face of all windows or fibers along the light path is sufficient to reduce the

contributions of etalons below that of other noise sources.

Nonlinear intensity modulation effects induce extra components in the absorption-

dependent 2f signal as well as an additional component in the 2f signal in the absence

of absorption. Both effects are included in the model presented in the next section, but

the latter must be subtracted from the measured (and simulated) 2f signal in order to

maintain a linear relationship between the 2f signal and species concentration (see

Section 2.2.4).

Finally, it is best to minimize background absorption by gases outside of the

desired measurement volume (for example between the detector and the outside

window to a high-temperature measurement environment). If background absorption

cannot be avoided, it must be held stable, measured, and subtracted prior to

comparison between measurement and model. For the scramjet measurements

described in Chapter 5 and Chapter 6, regions of the laser path outside the scramjet

combustor were purged with a continuous, regulated flow of nitrogen which greatly

reduced background absorption. The remaining absorption was confirmed to be

steady over the period of the experiments, measured, and then subtracted as outlined in

the next paragraph.

If background subtraction is necessary (because background absorption or

nonlinear intensity modulation effects are present), the measured 2f signal and

background must be normalized for laser intensity (using the 1f signal) and then vector

subtracted. The process is described by the equation:

2

1

2

1

2

2

1

2

1

212⎥⎥⎦

⎢⎢⎣

⎟⎟⎠

⎞⎜⎜⎝

⎛−⎟

⎟⎠

⎞⎜⎜⎝

⎛+

⎥⎥⎦

⎢⎢⎣

⎟⎟⎠

⎞⎜⎜⎝

⎛−⎟

⎟⎠

⎞⎜⎜⎝

⎛=

bgf

f

rawf

f

bgf

f

rawf

f

RY

RY

RX

RX

ff (2.5)

Following the notation of [21], X2f and Y2f refer to the X and Y components of the

lock-in outputs at 2f, and R1f refers to the root-sum-square magnitude of the X and Y

components of the lock-in outputs at 1f. The subscripts raw and bg refer to the raw

WMS signal (i.e. that which contains contributions from the measurement of interest

16

and the background signals), and the background signal (i.e. that which is measured

with the intended measurement region purged or otherwise eliminated from the optical

path). Note that if background absorption is not present, the background signal due to

nonlinear intensity modulation effects can be simulated using the model in the next

section, and then used in place of a measured background in Eq. (2.5).

2.2.3 WMS Model The WMS model used here is based on Li et al. [21], and has been verified

experimentally on H2O and CO2 absorption with different diode lasers, modulation

amplitudes and frequencies, and at a variety of pressures up to 30 atmospheres and

temperatures up to 900 K (see Chapter 3). This model extends the work of many

researchers [8,10,28,33−36] to be compatible with phase-insensitive lock-in detection

and to include laser-specific tuning characteristics. Here, the model is further

extended to be compatible with any optical depth (the model in [21] assumes an

optically-thin medium).

The model is created by simulating the process that occurs in the experiment. First,

the incident laser intensity and wavelength-dependent absorption must be modeled.

The incident laser intensity is represented by:

( ) ( )[ ]221000 2coscos1)( ψωψω ++++= titiItI (2.6)

where 0I is the average laser intensity, i0 and i2 are the amplitudes of the linear and

first term of the nonlinear laser intensity modulation (normalized by 0I ), and ψ1 and

ψ2 are the phase shifts between the laser intensity modulation and frequency

(wavelength) modulation for linear and nonlinear intensity modulation, respectively.

Each of the parameters i0, i2, ψ1, and ψ2 must be measured in the laboratory according

to the procedures in [21] for the laser and laser operation settings (injection current,

modulation frequency, etc.) that are to be used for the measurements. If a repetitive

ramp injection current is used in addition to the high-frequency sinusoidal modulation

to scan the laser across the absorption feature (as described in the section above), the

17

value of 0I , and therefore the values of i0 and i2, change throughout the scan. In this

case, the named laser parameters should be measured at the point in the repetitive

ramp that corresponds to the 2f peak, as this is the only part of the scan that is

compared with the model.

Absorption is simulated by defining a transmission coefficient for the laser light

through the absorbing medium (which depends on the laser frequency (wavelength))

in terms of a Fourier series:

( ) ( ) ( )∑+∞=

=

=k

kk tkaHt

0cos,)( ωνντ (2.7)

where ( )tat ωνν cos)( += is the instantaneous laser frequency (wavelength), ν is the

average laser frequency (wavelength), and a is the amplitude of the frequency

(wavelength) modulation. The parameters ν and a must be measured for the specific

laser and laser operation procedures used for the measurements (see [21] for details).

Combining this with the Beer-Lambert relation (Eq. (2.1) and (2.2)), the H terms can

be defined as:

θθφπ

π

π

dLxPavxPTTSavPTH ijj

ji ∫ ∑− ⎭

⎬⎫

⎩⎨⎧

⋅⋅⋅+⋅−= )cos,,,()(exp21),,,(0

(2.8)

θθθφπ

π

π

dkLxPavxPTTSavPTH ijj

jik ∫ ∑− ⎭

⎬⎫

⎩⎨⎧

⋅⋅⋅+⋅−= cos)cos,,,()(exp1),,,((2.9)

Depending on the experimental conditions, the line shape function (φj) can be modeled

with a Gaussian, Voigt, or Lorentzian profile using broadening parameters that are

known either through careful laboratory measurements of the type shown in [37] or

from HITRAN [22]. The linestrength also must be known in order to calculate the H

terms, and can be obtained through these same sources.

The detector signal is then modeled by multiplying the incident laser intensity (Eq.

(2.6)) with the first few terms of the transmission function (Eq. (2.7)). To simulate the

X and Y components of the phase-insensitive lock-ins tuned to measure the 2f signal,

18

the detector signal is multiplied by ( )tω2cos and ( )tω2sin , respectively. Only DC

terms are carried after the multiplication to simulate the effect of the low-pass filtering

step of the lock-in, resulting in:

( ) ⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ ++++= 2

4213122 cos

2cos

22ψψ HHiHHiHIGX o

oof (2.10)

( ) ⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ −+−−= 2

421312 sin

2sin

22ψψ HHiHHiIGY o

oof (2.11)

G is the electro-optical gain of the detection system. It does not need to be known or

measured since normalization with the 1f signal in the next step cancels this term.

Using the same method but changing the lock-in reference signals to ( )tωcos and

( )tωsin , the components of the 1f signal can be calculated:

( ) ⎥⎦

⎤⎢⎣

⎡++⎟

⎠⎞

⎜⎝⎛ ++= 231

21

2011 cos

2cos

22ψψ HHiHHiHIGX o

of (2.12)

( ) ⎥⎦

⎤⎢⎣

⎡−+⎟

⎠⎞

⎜⎝⎛ −−= 231

21

2001 sin

2sin

22ψψ HHiHHiIGY o

f (2.13)

The 1f magnitude is the root-sum-square: 21

211 fff YXR += .

We are now able to completely simulate the 1f and 2f signals. With knowledge of

the specific laser tuning characteristics and the specific spectral parameters for the

target absorption transition, the H terms can be directly calculated from Eqs. (2.8) and

(2.9). We can then calculate the X and Y components of the 1f and 2f signals using Eq.

(2.10) – (2.13) (omitting the 20IG term since it cancels when the two signals are

divided). The final step is to compute the background-subtracted 2f/1f signal. Here,

we also use Eq. (2.5) so that our simulations mirror our experiment. The raw and bg

terms from Eq. (2.5) are simply replaced with the simulation with and without

absorption.

19

One should note that this model is valid for any optical thickness, for any

modulation amplitude or laser operating conditions, for any environmental condition

(T, P, x), and for spectra with overlapping interference from neighboring features.

2.2.4 Comparison of WMS Model and Measurement

to Infer Gas Temperature and Concentration The method presented here assumes that both the gas temperature and absorbing

species concentration are unknown along the laser line-of-sight (LOS), which is

typical of many practical applications. In this method, the WMS signals from two

absorption features will be used to infer the LOS-average temperature and species

concentration along the beam path. The effects of non-uniform gas property

distributions along the line-of-sight will be discussed in Chapter 5 and Chapter 6.

To understand the dependence of the 2f/1f signal on gas properties, it is easiest to

simplify the full model presented in the previous section for an optically-thin

(absorbance<0.05) line-center measurement of an isolated absorption transition.

Assuming linear intensity modulation with a phase shift of π, the 1f-normalized WMS-

2f signal simplifies to:

( ) θθθφπ

π

π

davi

LxPTSiHff peak

i 2coscos)(1200

2 ∫−

+⋅

⋅⋅⋅=≈ (2.14)

Taking the ratio of the 2f/1f signals from two different absorption features cancels

the direct dependence on species concentration:

( )( ) θθθφ

θθθφπ

π

π

π

dav

dav

TSTS

ii

Ratiopeak

peak

2coscos

2coscos

)()(

2

1

2

1

1,0

2,0

∫∫−

+

+= (2.15)

The ratio of i0,i terms is a constant, the ratio of linestrengths depends solely on T,

and the ratio of line shape integrals depends weakly on T and on xi and P for cases

where the Voigt or Lorentzian profiles are used. The dependence on pressure of the

line shape integral is the subject of the following section as it can be minimized

20

through the judicious selection of absorption features and laser modulation parameters.

However, to maximize the accuracy of the measurement, it is important to

simultaneously measure pressure in the probed region in order to correctly calculate

the expected ratio. The ratio of 2f/1f signals is thus calculated for a range of

temperatures at the measured pressure and at a nominal expected value of xi. The

simulated ratio is compared directly with the measured ratio to infer the temperature.

Next the species partial pressure or mole fraction is inferred using the 2f/1f signal

for one absorption feature. With the temperature now known, Eq. (2.14) can be used

to determine the concentration through the following relationship:

( )( ) .,

.

.., 12

12simi

sim

measmeasi P

ffffP ⋅= (2.16)

If the pressure is well-known, then Pi can be replaced with xi to calculate the mole

fraction directly. For cases where the Voigt or Lorentzian line shapes are used, the

line-shape integral has some dependence on species concentration through the

dependence of pressure broadening on the collision partner. For these cases, if the

absorbing species is a significant portion of the gas mixture and the measured species

concentration using Eq. (2.16) is significantly different than the nominal species

concentration used for the simulations, it is necessary to iterate using the measured

species concentration to re-simulate the 2f/1f signals and subsequently re-calculate the

measured temperature and species concentration.

For cases where any of the simplifying assumptions applied above are not valid, the

same procedure is followed using the full-model equations presented in the previous

section. Using the full equations refines the simulated signals and ratios, but does not

significantly change the dependences described above. Two important points to note

for cases where the absorbance levels fall outside the optically-thin limit: the 1f signal

is somewhat affected by absorption, and Eq. (2.16) is not valid for large deviations

between the simulated and measured conditions (see Section 2.3.2). For these cases, it

therefore becomes important for the simulated concentration to more closely match the

measured concentration (which may require iteration). More on the effects of optical

thickness is included in Section 2.3.2.

21

2.3 Analysis of Uncertainty in 2f Measurements The potential sources of uncertainty in calibration-free WMS are summarized and

explained in Table 2.1. In the following sections we focus specifically on source 7,

measurement uncertainty induced by pressure deviation between the simulated and

experimental conditions, and source 8, uncertainty in concentration measurements

induced by optical depth. Source 7 is particularly relevant to WMS sensors developed

for harsh, practical applications where the pressure may be uncertain, difficult to

measure accurately with a transducer, and/or varying along the laser line-of-sight.

Source 8 is important for sensors developed for harsh environments because it is often

desirable in these environments to use strong absorption features (that exceed the

linear optically-thin limit) to increase signal levels and improve signal-to-noise ratio

(SNR). These two sources have not received much attention in the literature.

Table 2.1: Summary of potential sources of uncertainty in calibration-free WMS. Source of Uncertainty Description Mitigation

1. Spectral parameters

Absorption feature linestrength, line broadening, and broadening temperature dependence errors may induce error in the WMS model

Measure the parameters under controlled laboratory conditions [37]

2. Laser tuning characteristics Error in the laboratory-measured laser tuning characteristics (modulation amplitude, etc.) may induce error in the WMS model

Do not adjust laser operation settings after measuring tuning characteristics

3. Simulation/experiment wavelength matching

The wavelength between the simulation and experiment must be matched (e.g. at the absorption feature peak) to accurately compare the model and simulation

Use laser line-locking technique (adaptations of [38,39]), or scan over peak of absorption feature (see Section 5.1.2)

4. Background absorption Background absorption not included in the WMS model will affect the inferred gas properties

Eliminate background absorption or stabilize, measure, and subtract from measured WMS signals

5. Etalon effects Constructive/destructive interference arising from internal reflections off parallel faces in the optical path can induce errors in the measured WMS signals

Avoid by eliminating parallel surfaces

6. WMS model If the assumptions in the WMS model do not match the experimental conditions, error may be induced in the model

Ensure experimental conditions match model assumptions

7. Pressure deviation between simulation and experiment

For certain measurement conditions, the pressure will affect the line shape and WMS model. Therefore deviation between the simulated/experimental conditions may induce error in the inferred gas properties

See Section 2.3.1

8. Optical depth and concentration deviation between simulation and experiment

Large optical depths (>0.05 absorbance) reduce linearity of the concentration measurement. Therefore deviation between the simulated/experimental conditions may induce error in the inferred concentation

See section 2.3.2

22

2.3.1 Pressure Uncertainty In this section, we focus on the influence of pressure on the 2f signal to understand

the effect that uncertainties in pressure will have on measurements of temperature and

concentration. Since we focus primarily on the 2f signal, the figures and conclusions

drawn in this section are also applicable to calibrated WMS measurements where the

pressure changes from the value at which the signals were calibrated.

The effect of pressure on the 2f signal is most easily seen in the simplified case of

the 2f signal in Eq. (2.14). The signal is directly proportional to the absorbing species

partial pressure (which is the ideal linear pressure dependence that enables the

measurement of concentration), but there is also a ‘non-ideal’ pressure effect

introduced through the line shape (which is pressure dependent) in the integrand of the

equation. The effects of the laser modulation amplitude are also contained in this

integrand. Therefore, the influence of line shape and modulation amplitude on the 2f

signal can be understood by studying the line shape integral.

Figure 2.4 shows the simulated line-shape-integral term as a function of modulation

index for a Voigt profile with different Lorentzian-width/Doppler-width (L/D) ratios.

The Voigt function was used so that the calculated integral is normalized and only

needs to be multiplied by the line center Doppler magnitude to get the actual value of

the line shape integral for any feature. The modulation index is defined as νΔ= am

(where a is the modulation amplitude and νΔ is the half-width at half-maximum of

the absorption feature), and is also used here so that Figure 2.4 is generalized for any

feature. One can immediately see from the figure that the maximum 2f signal occurs

near a modulation index of 2.2 for a wide range of L/D (i.e. from Doppler-dominated

line shapes all the way to Lorentzian-dominated line shapes). This same conclusion

was shown by Reid and Labrie [28]. However, unlike Reid and Labrie, we have used

a generalized Voigt line shape integral for the full range of L/D ratios (instead of pure

Lorentzian or Doppler line shapes with different normalizations) to show the large

effect that L/D has on the overall 2f magnitude, even at m = 2.2.

23

Figure 2.4: The 2f Voigt line shape integral from Eq. (2.14) for various Lorentzian-Width/Doppler-Width (L/D) ratios. Though the peak signal is achieved near m = 2.2 for all line shape profiles, the magnitudes of the signals vary significantly.

To understand the uncertainty that arises in our 2f signal if there is an uncertainty in

pressure in the measurement environment, we calculate the effect of a small change in

pressure on the 2f line shape integral. A variation in the pressure affects the

Lorentzian line width, which changes both the modulation index and L/D. Figure 2.5

shows the percent difference in the 2f line shape integral for a -5% change in pressure

plotted versus the starting modulation index and L/D (i.e. before the 5% change in

pressure is applied). The black line represents the percent difference at m = 2.2, which

is also projected on the modulation index origin plane. For an isolated, optically-thin

absorption feature and linear laser modulation, this difference translates directly into

the percent difference in the 2f signal (Eq. (2.14)). Thus if there is a 5% uncertainty

between the pressure used to generate the WMS model and the actual pressure in the

environment (due to uncertainty in the pressure measurement, pressure variation along

the laser LOS, etc.), the percent difference translates into the uncertainty in the 2f

signal and potentially the uncertainty in a concentration measurement if the 2f signal is

used for this purpose.

For more complex cases, the translation is not direct but Figure 2.5 still offers an

approximation of what one can expect and allows several important conclusions to be

drawn. For small L/D, where the Doppler component of the broadening dominates,

0 2 4 60.0

0.4

0.8

1.2

L/D=10, Lorentzian-dominated

L/D=1

Gen

. Voi

gt L

ine

Sha

pe In

tegr

al

Modulation Index, m

L/D=0.1, Doppler-dominated

24

there is very little difference in the 2f signal with pressure change. The difference

increases with L/D, and appears to asymptote above L/D = 10 for m = 2.2. Most

importantly, we can see that over-modulation (m > 2.2) reduces the difference in the

line shape integral due to pressure change. This suggests that for cases where ample

signal is available, one may choose to over-modulate to reduce uncertainty in

concentration measurements at the expense of reduced signal.

Figure 2.5: Percent difference in 2f line shape integral for a -5% change in pressure. L/D =

Lorentzian-width/Doppler-width. For isolated, optically-thin absorption transitions this translates directly into percent difference in the 2f signal.

It is also important to understand how changes in pressure affect the ratio of 2f

signals, because this ratio is used to infer temperature. Figure 2.6 shows the percent

difference in the ratio of 2f line shape integrals due to a -5% change in pressure,

plotted against the starting modulation index and L/D ratio (i.e. before the 5% change

in pressure is applied). The L/D ratio is defined as the ratio of L/D for two features,

where L/D for feature 2 is unity:

( )

( ) 1/

2

1

==

feature

feature

DLDL

ratioDL (2.17)

The black lines represent the percent difference at the critical values of m = 2.2 and

L/D Ratio = 1, and their respective projections. The percent difference in the ratio of

2f line shape integrals does not translate directly to temperature uncertainty due to the

nonlinear relationship between the ratio of 2f signals and gas temperature. However

% d

iffer

ence

m=2.2

25

Figure 2.6 qualitatively illustrates how pressure uncertainty between the simulated

WMS model conditions and the actual experimental conditions relates to uncertainty

in the ratio of 2f signals and in turn, the inferred temperature.

Two important conclusions are drawn from Figure 2.6. First, over-modulation

reduces the dependence of the ratio of 2f signals on pressure, thus reducing the need

for accurate knowledge of pressure. Second, choosing absorption features with similar

broadening parameters (so that they have an L/D ratio ~ 1) greatly reduces the

influence of pressure. This is because changes in pressure affect both absorption

features similarly, and thus changes in the line shape integral will cancel when the

ratio is taken.

Figure 2.6: Percent difference in the ratio of 2f line shape integrals for two absorption features

for a -5% change in pressure. L/D Ratio is defined as (L/D)feature 1 / [(L/D)feature 2=1].

Figure 2.5 and Figure 2.6 suggest that if sufficient signal is available, choosing to

over-modulate reduces the ‘non-ideal’ dependence of the 2f signal on pressure.

However, over-modulation in moderate pressure environments presents the potential

for interference from neighboring transitions. Simulations of the 2f signal are shown

in Figure 2.7 for the H2O absorption feature at 7185.6 cm-1 (~1392 nm) including and

excluding neighboring features. At the conditions of the simulation (300 K), the

nearest strong neighbor is 2.6 cm-1 away. At 0.1 atm, modulation indices greater than

6 can be used without interference. At 3.5 atm, the neighboring transitions influence

% d

iffer

ence

m=2.2

L/D Ratio=1

26

the WMS signal for indices greater than 3. Note that the precise conditions where

interference becomes an issue are specific to each absorption transition.

Figure 2.7: WMS-2f signal for the absorption feature at 7185.6 cm-1 (~1392 nm) for two different

total pressures. The influence of nearby absorption transitions (2.6 cm-1 away) at larger modulation indices becomes apparent as total pressure increases. Simulation conditions: T = 300 K, xH2O = 0.01.

2.3.2 Optical Depth Under many circumstances, absorption features can be selected that are within the

linear, optically-thin region of absorbance (absorbance < 0.05). However, increasing

the optical thickness is a good way to increase the 2f signal for harsh environments

where more signal is needed (except at very large absorbances where the 2f signal

decreases [40]). Calibration-free WMS using the method and models of Section 2.2 is

still applicable to these non-optically-thin cases provided that one is aware of the

underlying assumptions.

To calculate species concentration using Eq. (2.16), it is implicitly assumed that the

2f signal is directly proportional to the concentration. However, at larger optical

depths this assumption becomes less valid because the exponential in Eqs. (2.8) and

(2.9) cannot be linearized in the same way that it can for the optically-thin condition.

This breakdown in linearity leads to errors in the calculated species concentration if

the simulated species concentration deviates greatly from the true species

concentration in the environment. Figure 2.8 shows the error in the measured species

0 1 2 3 4 5 60.0000

0.0001

0.0002

0.0003

0.0004

0.0005

2f S

igna

l (ar

b. u

nits

)

Modulation Index, m

P = 3.5 atm P = 0.1 atm

Solid: Neglecting nearby transitionsDashed: Including nearby transitions

27

partial pressure using Eq. (2.16) that is caused by deviation between the true partial

pressure and the simulated partial pressure for different optical depths (denoted by

absorbance). This figure is specific to the H2O absorption feature at 7185.6 cm-1 when

the simulated H2O mole fraction is x = 0.010 and the true mole fraction is varied

between x = 0.010 and x = 0.012 (holding the total pressure constant). However the

important message from Figure 2.8 is that the error induced by a deviation in partial

pressure is small in the optically-thin limit and steadily increases with absorbance.

Thus for optically-thick conditions, the simulations must be performed as close to the

expected condition as possible, which may require iteration to draw the simulations

acceptably close to an unknown measurement condition.

Figure 2.8: Error induced in partial pressure measurement using Eq. (2.16) due to deviation

between the true partial pressure and the simulated partial pressure as a function of absorbance (optical depth). Error increases as the true condition deviates from the simulated condition used to calculate the measured partial pressure, and as optical depth increases. Simulation conditions: H2O absorption feature at 7185.6 cm-1 when the simulated H2O mole fraction is x = 0.010 and the true mole fraction is varied between x = 0.010 and x = 0.012 (holding the total pressure constant).

% E

rror

in P

i,Meas

28

29

Chapter 3. Direct Absorption and WMS

Measurements of Near-IR Absorption at

High Pressure and Implications on

Diode-Laser Sensor Design As researchers push the limits of efficiency and emissions from practical

combustion devices, they have discovered many advantages to high-pressure

combustion. To validate, evaluate, and improve high-pressure combustor design

concepts, there is a need for sensors that can diagnose the combustion processes at the

core of these devices. Of particular importance are measurements of temperature

(which plays a crucial role in ignition, reaction rates, and pollutant formation), and

H2O and CO2 (major products of combustion that signal the health of a combustion

system).

The convenient coincidence of the wavelength range of telecommunications diode-

laser sources with several absorption bands of H2O and CO2 make TDL absorption

sensors a good choice for measuring these parameters. In lower-pressure

environments (less than a few atmospheres), the diode-laser wavelength can be swept

over an entire discrete absorption feature and the pressure-independent integrated-

absorbance area used to infer gas properties (temperature or concentration) knowing

only the linestrength and lower-state energy of the feature. However, for high-

pressure environments, even the individual absorption transitions of small molecules

30

such as H2O and CO2 broaden to the point of overlapping. The blending of adjacent

absorption features means that absorption sensors operating in these regimes must rely

on comparison between measurements and pressure-dependent spectral simulations to

infer gas properties. To achieve accurate results, these simulations must be based on

accurate spectral parameters (including pressure broadening and shift), and accurate

line shape models for the individual transitions. Thus, before practical TDL

diagnostics can be designed for high pressure environments, several important aspects

of high-pressure absorption must be studied:

(1) Spectral database – Fortunately, several spectral databases exist that include the

necessary transition parameters for simulations of CO2 and H2O (linestrength,

lower-state energy, pressure-broadening and shift coefficients, and temperature

scaling exponents for the pressure shift coefficients). However, in many cases the

data in these databases are either calculated from theory, or measured at low

pressures in the laboratory. It is therefore important to test the spectral parameters

under controlled, high-pressure conditions in the laboratory before applying them

to measurements obtained in the field. The sections below present several

comparisons of spectral parameters with measurements of CO2 and H2O in the

laboratory under carefully-controlled high-pressure conditions.

(2) Non-Lorentzian effects – Accurate spectral simulations also rely on accurate line

shape models for the individual absorption features. For pressure-broadened

water-vapor transitions at infrared frequencies, the Lorentzian line shape model is

most often applied. It is given by,

( )

22

221)(

⎟⎠⎞

⎜⎝⎛ Δ

+−

Δ=

co

c

vvv

vv

πφ (3.1)

where (v-vo) is the frequency de-tuning from line center and Δvc is the full-width at

half-maximum (FWHM) of the absorption feature, given by,

∑ −=ΔA

ABAc xPv γ2 (3.2)

31

Here, B denotes the absorbing species and A denotes the collision partner. xA is the

mole fraction of the collision partner and 2γB-A is the collision-partner-dependent

broadening coefficient. The sum accounts for multiple collision-partner species.

The Lorentzian line shape model makes use of the impact approximation,

which assumes that collisions between molecules are instantaneous and neglects

energy-level perturbation due to intermolecular forces during the finite duration of

the collision event. Thus the line shape model assumes that molecules exist in a

certain oscillating state (in the classical oscillator model of the molecule), without

regard for, and unperturbed by, other molecules, until the instant a collision occurs,

at which time a phase shift in the oscillation occurs. The Lorentzian line shape is

defined by the average of the Fourier transforms of the finite-time oscillating

waveforms of all possible durations (i.e. lengths of time between collisions). The

width of the Fourier transform feature that represents an oscillating waveform of

finite duration is inversely proportional to its duration, or in this case, the length of

time between collisions. Therefore, the contributions to the line shape far from

line center are primarily due to molecules experiencing short times between

collisions. As the unperturbed time approaches the duration of the collision event,

the impact approximation becomes less valid. That is to say, the time during

which the molecule is perturbed by intermolecular forces during the collision is no

longer negligible compared to the unperturbed time between collisions. The

Lorentzian profile therefore increasingly fails to appropriately model the line

shape as one departs from line center.

There is no definite rule for the spectral region around line center where the

impact approximation is valid. Hartmann et al. [ 41 ] suggest that the

approximation is valid for regions of the line shape that satisfy:

collo tvvc −π2 << 1 (3.3)

where c is the speed of light, v-vo is the frequency detuning from line center, and

tcoll is the collision duration. Equation (3.3) represents a rearrangement of the

impact approximation assumption that tcoll << tunperturbed (the duration of the

32

collision is much less than the unperturbed time between collisions), where the

unperturbed time has been related to the frequency detuning from line center by

tunperturbed ∝ 1/(ν-νo).

Assuming the interaction length of the colliding molecules, L, is equal to the

radius of the collision-broadening cross section [42], the duration of the collision

can be represented by

2

1

1⎟⎟⎠

⎞⎜⎜⎝

⎛ Δ==

gc

Nv

ggLt c

coll (3.4)

where g is the average relative speed of the collision partners, and N is the number

density. Solving Eqs. (3.3) and (3.4) for an example molecule and condition (700

K, air-broadened H2O), leads to a spectral region where the impact approximation

is valid of ovv − << 14.5 cm-1. Note in Eq. (3.4) that both Δvc and N are directly

proportional to the total pressure. Therefore tcoll is independent of pressure and the

valid region remains unchanged for air-broadened H2O at 700 K for all pressures.

However, as pressure increases the line broadens and a decreasing amount of the

integrated area of the line shape is contained in the region near line center where

the impact approximation is valid. Thus an increasing portion of the absorption

falls in the region where non-Lorentzian effects become important. This is

demonstrated in Figure 3.1 for the H2O absorption feature near 7203.89 cm-1.

Figure 3.1: Simulated Lorentzian line shapes for the H2O spectral feature near 7203.89 cm-1 at 700 K, PH2O = 0.02 atm. Neighboring features have been neglected.

7200 7202 7204 72060.00

0.01

0.02

0.03

0.04

Abso

rban

ce

Frequency (cm-1)

4 Amagat (10 atm) 8 Amagat (20 atm) 12 Amagat (30 atm)Impact Approximation

Valid

33

Since the breakdown of the impact approximation is a gradual process and

precise bounds for its application cannot be determined, the impact approximation

bounds of Figure 3.1 are chosen to be ovv − = 1.45 cm-1 for this particular

temperature and mixture. This satisfies the criterion from Eqs. (3.3) and (3.4) that

ovv − << 14.5 cm-1. The choice is further supported by data in Hartmann et al.

[41] that suggest the impact approximation models high temperature H2O

absorption well for densities lower than about 5 amagat. The chosen boundaries

contain 89% of the integrated area of the line shape at 4 amagat.

Accounting for the effects of the breakdown of the impact approximation on

the line shape is a complex problem involving the intermolecular potentials of the

absorbing and collision-partner species. Many researchers have taken different

approaches to modeling H2O and CO2 line shapes (discussed in later sections). In

general, it has been shown for both H2O [41,46,48] and CO2 [64] that the effect of

the breakdown of the impact approximation causes the Lorentzian profile to over-

predict absorption in the far-wing region (>5−100 cm-1 from line center, depending

on the molecule and conditions) and under-predict absorption in the intermediate-

wing region (that which is between the far-wing and the impact approximation

boundaries stated above). These two behaviors are normally termed sub-

Lorentzian and super-Lorentzian effects, respectively.

It should be noted that for high gas densities, another process called line

mixing (or line coupling) becomes important. Line mixing occurs when the

energy states of two transitions are collisionally coupled, that is, when inelastic

collisions shift molecules between the two upper states and between the two lower

states of the transitions. The effect is to couple the two optical transitions, causing

the sum of the Lorentzian profiles from each transition to no longer properly

model their absorption. At high densities, this results in the transfer of absorption

from the outer wings of the coupled transitions to the region between the

transitions. This effect is only important when the energy separation of the lower

or upper states involved are comparable to the translational kinetic energy of the

molecules, and the frequency separation of the two transitions are smaller than the

34

collisional line width. For H2O transitions in the region under study here, Nagali

[42] predicts that line mixing only becomes significant for pressures greater than

100 atm, and therefore this process is not the focus of the work in this chapter.

(3) Absorption measurement strategy – As discussed earlier, several methods for

performing absorption measurements are available. Several attributes of

wavelength-modulation spectroscopy with second-harmonic detection (WMS-2f)

make it desirable over direct absorption for certain harsh, high-pressure

environments. In particular, dividing the 2f signal by the 1f signal normalizes the

2f signal for perturbations in laser intensity [10,13,19,20,28]. This replaces the

need to measure a non-absorbing baseline (as with direct absorption), which is

extremely important for harsh, high pressure environments where laser intensity

changes rapidly due to beam perturbations, and a non-absorbing baseline is not

present between spectral features due to blending of neighboring transitions. Also,

it will be shown that WMS-2f is less influenced by non-Lorentzian effects in high-

density gases. In the work presented here [26,27], both WMS and direct-

absorption spectra and simulations are compared to show the potential benefits

(and drawbacks) of the technique for measuring high-pressure absorption.

3.1 H2O Absorption

3.1.1 Background Despite the importance of quantitative high-pressure and high-temperature TDL

absorption measurements of H2O, little work can be found in the literature to compare

carefully controlled and quantitative TDL laboratory measurements with simulated

spectra at elevated pressure and temperature. In fact, few measurements of high-

pressure and high-temperature infrared water-vapor absorption spectra exist using any

experimental techniques. Varanasi et al. [43,44] used a spectrometer to measure low

resolution pure H2O vapor spectra in the 600−1000 cm-1 region at pressures up to 25

atm. Later, Styrikovich et al. [45, and references therein] used an infrared Fourier

transform spectrometer to study pure H2O vapor at low resolution in the 0-2000 cm-1

35

region at pressures up to 150 atm. The aim of these early papers was to quantify the

H2O absorption coefficient and determine what mechanisms contribute to absorption

at high pressures (water-vapor monomers, dimers, polymers, etc.) in the so-called

water-vapor window region below 1200 cm-1, where a water-vapor absorption band

does not exist.

The most recent measurements at high pressures were by Hartmann et al. [41], who

performed extensive measurements using a medium resolution (~3 cm-1) grating

spectrometer to study pure H2O vapor spectra at the edge of two absorption bands, at

temperatures up to 900 K and pressures up to 70 atm, and compared these with

simulations based on various theoretical line shape models. That study complements a

large body of work by researchers [examples in 46−53] to investigate the potential of

absorption line shapes to resolve the observed discrepancies between measurement

and simulation of long-path absorption measurements in the atmosphere. The

researchers concluded that the impact approximation inherent to the Lorentzian line

shape for pressure broadening is valid only near the center of absorption features. As

density increases, the region about line center over which the approximation is valid

decreases.

In the current work [26], tunable-diode lasers are used to measure high resolution

(0.1 cm-1), NIR H2O absorption spectra at 700 K and pressures up to 30 atm within a

high-pressure and -temperature optical cell in a high-uniformity tube furnace. Both

direct absorption and 2f spectra are obtained for 6 cm-1 regions near 7204 cm-1 and

7435 cm-1, two regions of interest for high-pressure H2O sensor applications. To the

author’s knowledge, these are the first TDL measurements of 2f spectra at high

pressure. The measurements are compared with simulations using spectral parameters

from HITRAN and a hybrid database combining HITRAN with measured spectral

constants for transitions in the two target spectral regions. In addition, the line shape

model of Clough et al. [46] is tested on the data to reveal the effects of breakdown of

the impact approximation at high densities.

36

3.1.2 Line Shape Model and Spectral Database

3.1.2.1 H2O Line Shape Model Several approaches have been taken to model the non-Lorentzian line shape effects

for H2O. Clough et al. [46,50,51] chose a semi-empirical method, in which an

additional function is applied to the impact result to correct for the finite duration of

collisions. The coefficients of this function were determined by fitting with

atmospheric water-vapor absorption data. Thomas and Nordstrom [52,53] used a

statistical-broadening approach to describe far-wing absorption and then used a filter

function to smoothly interpolate between the results of this far-wing theory and the

Lorentzian line shape near the line center. Parameters for the far-wing statistical-

broadening model were determined also by fits with atmospheric absorption data.

Tipping and Ma [48,49] developed a representation that accounts for non-Lorenztian

effects without any adjustable parameters. They use a band-averaged line shape to

make the calculations tractable, but still require significant computing power. Their

results are in general agreement with those of Clough, though direct comparison is

difficult because of the use of different expressions for the absorption coefficient.

Hartmann et al. [41] performed empirical fits to their high-pressure data to obtain a

line shape correction factor similar to Clough et al. for self-broadened water vapor.

They also compared these with the results of Tipping and Ma to find good qualitative

agreement.

The approach of Clough et al. [46], commonly referred to as the CKD model, was

chosen to describe non-Lorentzian line shape effects in the remainder of this work. It

is by far the most widely used of the line shape models, and since the method uses a

correction factor to the Lorentzian line shape, it easily lends itself to integration with

our current line-by-line simulation codes.

The CKD model [46] consists of modification of the Beer-Lambert relation (Eq.

(2.1)) in which a semi-empirical term, referred to as the χ-function, is multiplied by

the line shape function:

37

⎭⎬⎫

⎩⎨⎧

⋅⋅⋅⋅⋅−=⎟⎟⎠

⎞⎜⎜⎝

⎛∑

jijj

vo

t LxPvvxPTTSII )(),,,()(exp χφ (3.5)

Here, φj is the Lorentzian line shape function and the χ-function is given by:

⎪⎩

⎪⎨

≥−

≤−−

−−=

1

12

2

25;'

25;25

)()'1(1

cmvv

cmvvvv

o

oo

χ

χχ (3.6)

where vo is the line center frequency of the transition. For foreign-broadening,

( )2exp' zC −=χ (3.7)

with C = 6.65, and ( ) 75/ovvz −= . One should note that the χ-function does not

account for any temperature dependence of the far-wing absorption. This shortcoming

of the CKD model will be addressed in Section 3.1.4.

The χ-function is plotted in Figure 3.2. One can see that the χ-function is unity

near line center, thereby not modifying the Lorentzian line shape (which accurately

predicts absorption near line center). The intermediate wing shows super-Lorentzian

behavior (enhanced absorption over that predicted by the Lorentzian profile) and the

far wing shows sub-Lorentzian behavior.

Figure 3.2: Foreign-broadened H2O χ-function versus frequency de-tuning from line center [46].

Figure 3.3 demonstrates the effect of the χ-function on an individual H2O

absorption transition at 30 atm.

1 10 100 10000.01

0.1

1

10

χ

ν − νo (cm-1)

38

Figure 3.3: Effect of χ-function on the H2O absorption transition near 7203.89 cm-1 at 30 atm

and 700 K. Neighboring features are neglected. Inset shows the effect on a log-log scale.

Even though the super- and sub-Lorentzian behaviors counteract one another to

preserve the integrated area of the line shape, a limitation of the empirical χ-function

corrections shown here is that they are not able to completely preserve this condition.

This major drawback will undoubtedly lead to inaccuracies in the predicted absorption

for certain conditions and spectral regions, and motivates the use of spectroscopic

techniques (such as WMS) that are less sensitive to non-Lorentzian effects for

practical sensors for measurements of gas parameters.

3.1.2.2 H2O Spectral Database In terms of spectral parameters for H2O absorption transitions, the need for

simulations of atmospheric absorption led to the establishment of the HITRAN and

HITEMP databases [22, and references therein], which catalogue spectral parameters

for individual transitions of many molecules over a broad wavelength range. They are

based on a combination of theoretical calculations and experiments. For the remainder

of this dissertation, “HITRAN” will be used to describe the combined database

including the standard HITRAN and the high-temperature variant HITEMP. This

database is useful to the sensor designer as it provides a search tool to select the

0.1 1 10 1000.000

0.002

0.004

0.006

0.008

0.010

0.012

0.014

0.016

0.018

0.1 1 10 100

1E-5

1E-4

1E-3

0.01

Lorentzian χ-function, C=6.65

Abs

orba

nce

ν − νo (cm-1)

39

particular feature that gives desirable absorption characteristics for the target

measurement from the thousands of available water-vapor transitions. However, to

make accurate quantitative measurements of temperature and species concentration,

especially at high temperatures and pressures where uncertainty in the spectral

parameters is large, it may be important to verify the accuracy of the HITRAN

parameters in a laboratory setting for the selected spectral features.

Liu et al. [37] performed laboratory measurements at sub-atmospheric pressures in

a high-uniformity furnace to obtain parameters for the two spectral regions near 7204

cm-1 and 7435 cm-1 probed in this dissertation. Their work revealed, for example, an

average error of 5% in the HITRAN values for the linestrength coefficient in these

regions. Here, we compare our measured absorption with simulations using spectral

parameters from both HITRAN and HITRAN augmented with the measurements of

Liu et al.

3.1.3 Experimental Setup and Procedure The experimental setup for the H2O measurements is shown in Figure 3.4. The

high-pressure cell detailed in Appendix B is inserted into a high-uniformity tube

furnace and the Inconel supply tubes are connected to a heated-vapor-delivery

manifold. The vapor-delivery manifold interconnects a Setra pressure gage, vacuum

and nitrogen purge lines, and a heated, stainless-steel gas-mixing tank. The supply

lines and mixing tank are heated to increase the maximum allowable concentration of

water vapor in the high-pressure mixture without condensation.

All experiments presented in this work were performed on a single gas mixture.

This mixture was prepared by evacuating the mixing tank, injecting the desired

amount of liquid water, adding synthetic air to the desired total pressure, and heating

well above the saturation temperature for the mixing tank conditions. The mixture

was allowed to equilibrate for three weeks, and teflon balls in the tank were

occasionally agitated to aid the process.

Three fiber-coupled NEL America diode lasers are combined into a singlemode

fiber. Two lasers produce light near 7204 cm-1 and 7435 cm-1, and are wavelength

40

scanned to obtain the absorption spectra. The third laser produces light at a non-

resonant frequency (approximately 7633 cm-1) where no water-vapor transitions exist.

This laser is used to normalize the resonant lasers for cell transmission effects during

direct-absorption measurements (the 1f signal accounts for this during wavelength-

modulation measurements).

The singlemode fiber is split into three fibers. The first goes to a Burleigh

wavemeter (WA-1000) used to monitor the laser frequency. The second terminates to

a Thorlabs PDA-400 detector which monitors the laser intensity during direct-

absorption measurements (again, the 1f signal accounts for this during wavelength

modulation measurements). The third goes to a collimating lens where the beam is

pitched through the tube furnace and optical cell to a spherical mirror that focuses the

light onto another PDA-400 detector. The open path of the tube furnace is purged

with a constant flow of nitrogen to avoid interference from ambient water vapor.

Figure 3.4: Experimental setup for high-temperature, high-pressure H2O absorption measurements.

The direct-absorption and 2f spectra are obtained by temperature-tuning the diode

lasers. The average injection current of the diode laser is held constant (with rapid

current modulation superimposed for WMS) and the laser thermoelectric cooler (TEC)

is used to vary the laser temperature, thereby tuning the average laser wavelength

across the spectral region of interest. The laser control and data acquisition process is

automated using Labview and a GPIB controller in communication with the laser

controller. The optical cell is first filled with pure, dry air to the desired experimental

  Non-resonantLaser

I

Furnace with Static CellCollimating Lens

Fiber combiner/splitters

Iref

7204 cm-1

and 7435 cm-1

LasersN2 purge region

P

Heated High Pressure Gas

Mixture

Pressure gage

To Vacuum/ Purge Lines

Heated Vapor Delivery Lines

Wavemeter

41

pressure. The incident laser intensity for the direct-absorption spectra and the zero-

absorption background for the WMS spectra are acquired by running the automated

program once with the cell filled with this non-absorbing medium. As mentioned in

Section 2.2.2, the WMS background due to laser nonlinearity is subtracted from both

the measurement and simulation before direct comparison. The program tunes the

laser to a temperature setpoint, waits 2 minutes to be sure the laser has completely

stabilized and then acquires 5 seconds of the detector signal. The rapid modulation is

turned on for WMS, the laser is again allowed to stabilize for 2 minutes, and the

detector signal is acquired for 5 seconds. The modulation is turned off, the laser is

moved to the next temperature setpoint, and the process is repeated for each data point.

The cell is then evacuated and filled with the H2O/air mixture to the desired

experimental pressure, and the process repeated to obtain the transmitted laser

intensity for the direct-absorption spectra and the absorbing WMS signal.

Prior to and after the completion of data collection, the automated process was

repeated with the WMS modulation off and the laser output directed to a wavemeter to

obtain the calibration between laser-temperature setpoint and wavelength. The center

wavelength of the laser during WMS cannot be directly measured by the wavemeter.

Instead, spectra at one atmosphere and room temperature are measured using the

automated temperature-tuning program and the same laser-temperature setpoints and

intervals that are used during the high-pressure measurements. The spectra are

compared with simulations at one atmosphere and room temperature, where they are

known to be very accurate, to create a map between the laser set points and the center

wavelength of the modulated laser. All WMS measurements of H2O presented in this

chapter were obtained with a modulation amplitude of 0.65 cm-1 and modulation

frequency of 50 kHz.

3.1.4 Direct Absorption Results Due to uncertainties in line shape models that account for non-Lorentzian effects, a

quantitative comparison of simulations using different spectral parameter databases is

best performed at conditions where the impact approximation is valid over nearly the

42

entire line shape. Figure 3.5 and Figure 3.6 show measured direct-absorption spectra

for the region near 7204 cm-1 and 7435 cm-1 at 700 K and 10 atm. At these conditions,

the density is 3.91 amagat, which is less than the limit of 5 amagat proposed by

Hartmann et al. [41] above which the impact approximation (Lorentzian) line shape no

longer models measured spectra well for H2O. As noted in Figure 3.1, 89% of the

integrated absorbance for an individual transition is within 1.45 cm-1 of line center for

these conditions, which also satisfies the impact approximation criteria, ovv − <<

14.5 cm-1.

Figure 3.5 compares the measured absorbance in the 7204 cm-1 region at 10 atm

and 700 K with simulations performed with parameters from the HITRAN database,

and the hybrid database constructed by Liu et al. [37]. The spectrum at 1 atm is also

plotted to show the individual transitions (5 lines from the ν1+ν3 band) that are

contributing to the blended high-pressure spectrum. The hybrid database contains the

linestrength, pressure-broadening coefficients, and pressure-induced shift coefficients

measured by Liu et al. for all of the major transitions near 7204 cm-1 (except the

feature near 7202.25 cm-1). HITRAN values are used for all other spectral data. The

deviation (in terms of absorbance) between simulations using the hybrid and HITRAN

database and the measurements are shown in the bottom panel of Figure 3.5. The data

clearly demonstrates the improved agreement of the hybrid database over HITRAN.

The RMS error in the region from 7201 to 7207 cm-1 for the hybrid database is

7.6x10-4 compared to 1.4x10-3 for HITRAN – an improvement of 45%.

Figure 3.5: Direct-absorption spectrum, 7204 cm-1 region, P = 10 atm, T = 700 K, xH2O = 0.0022.

Hybrid database is HITRAN augmented with parameters from Liu el al [37]. The spectrum at 1 atm is plotted in gray to show the contributing spectral features.

 

7201 7202 7203 7204 7205 7206 7207

0.0000.0020.004

Dev

iatio

n

Frequency (cm-1)

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

Abs

orba

nce

Measurement Hybrid Database HITRAN Database

Abs. / 2, P=1 atm

43

Figure 3.6 compares the measured absorbance in the 7435 cm-1 region at 700 K and

10 atm with simulations using the hybrid and HITRAN databases. In this region, 8

transitions from the ν1+ν3 band contribute to the absorption. The hybrid database

contains spectral parameters from Liu et al. [37] for all major features except those

near 7439.0 and 7439.2 cm-1. Though the difference between the two databases in this

region is smaller, Figure 3.6 still shows the improvement of the hybrid database over

HITRAN. The RMS error in the region from 7433 to 7439 cm-1 for the hybrid

database is 1.0x10-3 compared to 1.4x10-3 for HITRAN, a reduction of 28%.

Figure 3.6: Direct-absorption spectrum, 7435 cm-1 region, P = 10 atm, T = 700 K, xH2O = 0.0022.

The spectrum at 1 atm is plotted in gray to show the contributing spectral features.

Above 10 atm, the impact approximation applies to a decreasing portion of the

integrated area of the spectral features. At 20 atm and 700 K, the density is 7.8

amagat and the portion of the absorbance area that lies within 1.45 cm-1 of line center

for an individual transition reduces to 76%. At 30 atm and 700 K, the density is 11.7

amagat and 65% of the absorbance area lies within 1.45 cm-1 of line center. At these

conditions, it becomes increasingly important to account for the breakdown of the

impact approximation.

In Section 3.1.2, we presented the CKD model. This model does not account for

temperature dependence in the far-wing absorption, and the coefficients came from

fits to data obtained at atmospheric pressures and approximately 296 K. Many

researchers, however, have observed a reduction in water-vapor absorption in the

window and near-band regions at elevated temperature [41,42,47−53]. Therefore, to

 

7433 7434 7435 7436 7437 7438 7439-0.0020.0000.0020.0040.006

Dev

iatio

n

Frequency (cm-1)

0.00

0.01

0.02

0.03

0.04

Abs. / 2, P=1 atm

Abs

orba

nce

Measurement Hybrid Database HITRAN Database

44

apply the model at high temperatures it is expected that the coefficients of the CKD

model will need to be modified.

Figure 3.7 shows measured data in the 7204 cm-1 region at 30 atm and 700 K and

simulations using the parameters of the hybrid database and the CKD model with

different values of the coefficient C, from Eq. (3.7). One can see that at this density,

the simulation assuming a pure Lorentzian line shape underpredicts the absorption in

the wings of the heavily broadened group of features. The simulation using the CKD

model with its original coefficient, C = 6.65, greatly overpredicts the absorption, while

a modified coefficient, C = 2.5 gives good agreement. The inset to Figure 3.7 shows

the χ-function as a function of frequency detuning from line center for both values of

the coefficient. This reduction in the overall χ-function for the intermediate and far

wings is in agreement with trends noted other researchers. Particularly good

agreement is found with the trends of Hartmann et al. [41], who show similar results

for pure water vapor at high temperatures. The results cannot be directly compared

because the measurements of Hartmann are self-broadened, while the measurements

of Figure 3.7 are primarily foreign-collision broadened.

Figure 3.7: Direct-absorption spectrum, 7204 cm-1 region, P = 30 atm, T = 700 K, xH2O = 0.0022.

Simulations using the χ-function with different C coeffients are shown. The inset shows the χ-function versus frequency de-tuning from line center.

For a given temperature and collision partner, the coefficients of the CKD model

should be fixed. At 700 K for example, one expects the modified χ-function with the

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.10

1 10 1000.01

0.1

1

10

χ

ν − νo

Abs

orba

nce

Measurement χ-function, C=6.65 χ-function, C=2.5 Lorentzian

7201 7202 7203 7204 7205 7206 7207-0.0050.000

0.005

0.010

Frequency (cm-1)

Dev

iatio

n

45

coefficient C = 2.5 to apply at different pressures. Figure 3.8 shows measurements of

the direct-absorption spectrum in the 7204 cm-1 region at 10, 20, and 30 atm at 700 K.

The data are compared with simulations using the hybrid database and assuming a

pure Lorentzian line shape and a Lorentzian line shape modified by the χ-function

with C = 2.5. The results confirm that at 10 atm (4 amagat) the impact line shape is

valid, but as density increases, the approximation begins to break down. The

coefficient C = 2.5 gives good agreement at all three pressures.

Figure 3.8: Direct-absorption spectra, 7204 cm-1 region, P = 10, 20, 30 atm, T = 700 K, xH2O =

0.0022.

Similar comparisons were made with high-pressure data from the 7435 cm-1 region,

however slight discrepancies in the pressure shift of several features in the region

(discussed in Section 3.1.5) make subtle comparisons with the CKD line shape model

difficult.

The value of the modified χ-function coefficient is dependent on the spectral data

used in the model. Here, for example, the value of C = 2.5 was obtained with the

hybrid database. A different value of C would be obtained if the HITRAN database

were used, because the differences in linestrength, line-broadening, and the inclusion

of pressure shift of the line positions leads to a different convolution of the pressure-

broadened Lorentzian line shapes upon which the CKD correction is applied.

Therefore, until the modified CKD model is validated by another means, it is not

possible to make quantitative comparisons of the hybrid and HITRAN spectral

 

7201 7202 7203 7204 7205 7206 7207

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

10 atm20 atm

Abs

orba

nce

Frequency (cm-1)

Measurements χ-function, C=2.5 Lorentzian

30 atm

46

databases in regimes where the breakdown of the impact approximation affects the

measured absorption. However, it is possible to explore other methods of absorption

spectroscopy, such as WMS-2f, which offer sensitivity to line shape curvature and

decreased sensitivity to offsets in the absolute absorption (such as by non-Lorentzian

effects).

3.1.5 WMS Results Sparing the complexities introduced by the intensity modulation of the laser, the 2f

signal is proportional to the curvature of the absorption line shape. As the properties

of the gas change, the curvature of the line shape changes, which in turn causes a

change in the 2f signal. Certain effects, such as emission or broadband absorption (for

example by a fuel) can cause a uniform interference to the absorption signal that is

manifest as a DC offset to the absorbance. This DC offset does not change the

curvature of the line shape, and therefore does not affect the 2f signal. Figure 3.9

illustrates this concept.

Figure 3.9: Direct-absorption and 1f-normalized, WMS-2f with an absorbance offset added

during simulation. Note the insensitivity of the 2f signal to the absorbance offset. Spectral feature near 7203.89 cm-1. P = 10 atm, T = 700K, xH2O = 0.0022. Neighboring features have been neglected. WMS modulation parameters: a = 0.65 cm-1, f = 50 kHz.

In the left panel, the direct-absorption signal for the feature near 7203.89 cm-1 at 700

K and 10 atm is shown (neglecting neighboring features) with two different DC offsets

introduced. In the right panel, the 2f signal is shown for the same conditions and the

7202 7204 7206

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.000

0.005

0.010

0.015

0.020

0.025

0.030WMS

Offset = 0 Offset = 0.005 Offset = 0.01

Abs

orba

nce

Frequency (cm-1)

Direct Absorption

7202 7204 7206

2f/1

f Mag

nitu

de

47

value is unchanged when the two offsets are included. From this figure, one can

readily see that the 2f signal is not affected by DC offsets to the absorption signal.

As shown in Figure 3.7 and Figure 3.8, the breakdown of the impact approximation

results in a nearly uniform increase in absorption in the region studied. It follows that

this nearly uniform DC offset in the absorption will minimally affect the 2f signal.

Figure 3.10 shows the measured 2f spectra in the 7204 cm-1 region at 700 K and 10, 20,

and 30 atm. Simulations of the spectra using the hybrid database with and without the

CKD model correction are also plotted, and confirm that the 2f signal is only

minimally influenced by the non-Lorentzian effects at these conditions.

Figure 3.10: 1f-normalized, WMS-2f spectrum,

7204 cm-1 region, T = 700 K, xH2O = 0.0022 for P = 10 atm, 20 atm, and 30 atm. Hybrid database is HITRAN augmented with parameters from Liu el al [37]. Hybrid database with and without χ-function correction result in nearly identical spectra. WMS modulation parameters: a = 0.65 cm-1, f = 50 kHz.

Since the 2f measurements are only marginally affected by the impact

approximation, they provide a metric to quantitatively compare the hybrid and

HITRAN databases at higher pressures without the added complication of line-shape-

correction factors. One caveat is that the simulations rely on the 2f model, which is

not as simple and well-validated as the Beer-Lambert relation for direct absorption.

However, the excellent agreement between simulation and measurement at 10 atm

7201 7202 7203 7204 7205 7206 7207

0.000

0.005

Dev

iatio

n

Frequency (cm-1)

0.00

0.01

0.02

0.03P=10 atm

2f/1

f Mag

nitu

de

Measurement Hybrid Database Hybrid w/ χ-function HITRAN Database

7201 7202 7203 7204 7205 7206 7207

0.000

0.003

Dev

iatio

n

Frequency (cm-1)

0.000

0.005

0.010

0.015

0.020

0.025

2f/1

f Mag

nitu

de

Measurement Hybrid Database Hybrid w/ χ-function HITRAN Database

P=20 atm

7201 7202 7203 7204 7205 7206 7207-0.002

0.000

0.002

Dev

iatio

n

Frequency (cm-1)

0.000

0.005

0.010

0.015

0.020P=30 atm

2f/1

f Mag

nitu

de

Measurement Hybrid Database Hybrid w/ χ-function HITRAN Database

48

suggests that the model is accurately representing the 2f spectrum. Figure 3.10 shows

that the hybrid database improves on HITRAN, with a reduction in RMS error of 36%

at 10 atm, 26% at 20 atm, and 27% at 30 atm. The discrepancy between the database

simulations and measurement in the region near 7206 cm-1 is likely due to the

influence of nearby lines outside the region studied by Liu et al. [37]. The increase in

this discrepancy with pressure is consistent with this hypothesis. Overall, very good

agreement is found between simulations with the hybrid database and measurement.

Figure 3.11 shows measured 2f spectra for the 7435 cm-1 region at 700 K and 10,

20, and 30 atm. The data are compared with simulations using the hybrid and

HITRAN databases. At 10 atm, simulations using both databases show good

agreement with the measurements. At 20 atm, agreement between the simulation

using the hybrid database is clearly better than that of the HITRAN database, with a

reduction in RMS error in the region from 7433 to 7439 cm-1 of 30%. At 30 atm, the

hybrid database again gives better agreement than HITRAN, with a reduction in RMS

error of 35%.

Figure 3.11: 1f-normalized, WMS-2f spectrum,

7435 cm-1 region, T = 700 K, xH2O = 0.0022 for P = 10 atm, 20 atm, and 30 atm. Hybrid database is HITRAN augmented with parameters from Liu el al [37]. Hybrid database with and without χ-function correction result in nearly identical spectra. WMS modulation parameters: a = 0.65 cm-1, f = 50 kHz.

7433 7434 7435 7436 7437 7438 7439

-0.0050.0000.005

Dev

iatio

n

Frequency (cm-1)

0.00

0.01

0.02

0.03

2f/1

f Mag

nitu

de

Measurements Hybrid Database HITRAN Database

P=10 atm

7433 7434 7435 7436 7437 7438 7439-0.01

0.00

0.01

Dev

iatio

n

Frequency (cm-1)

0.00

0.01

0.02

0.03P=20 atm

2f/1

f Mag

nitu

de

Measurements Hybrid Database HITRAN Database

7433 7434 7435 7436 7437 7438 7439-0.01

0.00

0.01

Dev

iatio

n

Frequency (cm-1)

0.00

0.01

0.02

0.03P=30 atm

2f/1

f Mag

nitu

de

Measurements Hybrid Database HITRAN Database

49

In Figure 3.11 we note a frequency shift between the data and simulations that

increases linearly with pressure. There are two potential explanations of this slight

discrepancy. First, it is possible that the pressure-induced frequency coefficients

(and/or their temperature exponents) could be incorrect, as variation of these values

within their reported uncertainties (5−25%) can account for the observed differences.

Second, if nearby transitions to the blue of the range validated by Liu et al. were

stronger than in the simulation, this could appear as a frequency red-shift of the target

transitions that increases with pressure (as observed). Note that the direct absorption

and 2f simulations fail to capture the measured signal strength of the feature near 7438

cm-1, which is beyond the region studied by Liu et al., providing some support for the

second explanation. Additional experiments would be required to unequivocally

determine the cause of this small discrepancy; however the hybrid database is already

sufficiently accurate to enable the successful measurements with the two-line

temperature sensor using these transitions (see Chapter 4).

3.2 CO2 Absorption

3.2.1 Background Figure 3.12 shows the infrared spectra of H2O and CO2 from 1 to 3 μm at 296 K.

The bands of CO2 near 2 μm were chosen for this study because they offer a 10x−30x

improvement in absorption strength over the bands near 1.4 and 1.6 μm while still

being accessible with telecommunications-grade, fiber-coupled diode lasers. Recently

for example, a 2.0 μm fiber-coupled diode laser was multiplexed together with several

1.4 μm lasers onto one fiber to make simultaneous measurements of CO2 and H2O in a

harsh scramjet environment (see Chapter 5). This example, along with others at 2.0

μm in near-atmospheric environments [e.g. 54−56], show the utility of the 2.0 μm

region for near-term practical sensor development, particularly until diode lasers at

longer wavelengths that access even stronger bands become more mature [57].

50

Figure 3.12: Linestrengths of H2O and CO2 transitions in the near-infrared at 296 K [22].

In terms of quantitative comparisons between measurement and simulation to study

the line shape effects that are important for measurements of CO2 at high pressures,

Winters et al. [58] were among the first to report that the far wings of a strong

absorption band of CO2 near 4.3 μm were not properly modeled by the Lorentzian line

shape. Later, Burch et al. [59] performed measurements on the 1.4, 2.7, and 4.3 μm

regions of CO2 and revealed that even at pressures of a few atmospheres, CO2

absorption spectra exhibit non-ideal behavior. They were followed by a number of

other researchers who studied CO2 absorption [60−66], some at high pressures and

temperatures, and came to the same conclusion: the impact approximation inherent to

the Lorentzian line shape profile used to model absorption line shapes in spectral

simulations is inaccurate for modeling the far wings of absorption features, and that

this effect becomes more important at high gas density. Surprisingly absent from the

literature, however, are comparisons of measurement and simulation on the 2.0 μm

band of CO2 at high density.

In this work [27], we report TDL measurements of direct-absorption and WMS

spectra from the high-frequency edge of the 20012 00001 band of CO2 between

5005 and 5010 cm-1 (~2.0 μm) at room temperature and pressures up to 10 atm

(densities up to 9.2 amagat) in a mixture of 10.8% CO2 in air. This specific spectral

region was chosen because it contains transitions which are useful for combustion

measurements (relatively isolated from H2O vapor and with lower-state energy ~1000

1.0 1.5 2.0 2.5 3.01E-23

1E-22

1E-21

1E-20

1E-19

1E-18 H2O CO2

Line

stre

ngth

(cm

-1/m

ol*c

m-2)

Wavelength (μm)

51

cm-1) [67]. This region is also more generally useful because it is located near the

edge of the band, where non-Lorentzian effects are strongest and large lower-state

energy lines reside. Performing the measurements at 10 atm and room temperature

generates a high-density gas (equivalent to 40 atm at 1200 K) to particularly highlight

non-Lorentzian effects and to decouple the pressure-broadening coefficients and

pressure-shift parameters from their temperature exponents. This simplifies

interpretation of errors in these coefficients, but further high-temperature studies will

be needed to confirm the temperature exponents.

To the authors’ knowledge, we report the first high-density spectra of CO2

absorption at 2.0 μm, and as such provide a means to test the most recent spectral

database and χ-functions, as well as determine the implications on practical sensor

design for high-pressure environments.

3.2.2 Line Shape Model and Spectral Database

3.2.2.1 CO2 Line Shape Model Several researchers developed empirical corrections to the Lorentzian profile for

CO2 based on low-temperature (193−296 K), near-atmospheric data in the 4.3 μm

region [60−63]. Like the corrections for H2O, these corrections are also applied

through a frequency-dependent χ-function that is multiplied with the line shape

function of individual absorption features. Perrin and Hartmann [64] coupled the data

of [60−63] with their own data at 4.3 μm in gases up to 60 atm and 800 K to develop a

temperature- and frequency-dependent χ-function for CO2-CO2 and CO2-N2 collisions.

This model was used by Scutaru et al. [65] at elevated temperatures (<800 K) and low

pressures (<1 atm) for the 4.3 and 2.7 μm region. Good agreement was found at 4.3

μm, however the χ-functions had very little effect for the particular spectra and

conditions used for the 2.7 μm data and thus provided little useful information on

accuracy there. The model was tested in the 2.3 μm window region by Tonkov et al.

[66] for pure CO2 at high pressure (to 50 atm) and room temperature. They found that

52

the χ-functions under-predicted the absorption and proposed new factors. These

researchers believe that the largest influence in the 2.3 μm region is the bands in the

2.7 μm region and that the new factors likely also account for several local effects

which influence the window region (weak allowed bands, collision-induced absorption,

etc.). Theoretical approaches based on first-principles calculations have been

proposed first for CO2 broadened by simple perturbers (e.g. Argon) [68,69] and later

for self-broadened CO2 [70], however these approaches require large computing

resources and to our knowledge are not yet applicable to CO2-N2 mixtures.

The model of Perrin and Hartmann [64] was chosen for this work because it

contains the most recent formulation for CO2-N2 mixtures. The analytical expressions

for the χ-functions used in this work are shown in Table 3.1 below. The temperature-

dependence of the χ-functions is introduced through the analytical law for calculating

B1, B2, and B3:

)exp()( TTB iiii εβα −+=

where the coefficients α, β, and ε are found in Table 3.2.

Table 3.1: Expressions for χ-functions [64]. |v-vo| is the frequency de-tuning from line center. σi are de-tuning cutoff frequencies in cm-1. |v-vo| (cm-1) χ(|ν-vo|,T) CO2-CO2 CO2-N2 0<|v-vo|<σ1 = 3 0<| v -vo|<σ1 = 3 1 σ1<| v -vo|<σ2 = 30 σ1<| v -vo|<σ2 = 10 exp[-B1*(| v -vo|-σ1)] σ2<| v -vo|<σ3 = 120 σ2<| v -vo|<σ3 = 70 exp[-B1*(σ2-σ1)-B2*(| v -vo|-σ2)] | v -vo|>σ3 | v -vo|>σ3 exp[-B1*(σ2-σ1)-B2*(σ3-σ2)-B3*(| v -vo|-σ3)] Table 3.2: Parameters for temperature-dependent terms in χ-function calculations [64]. CO2-CO2 CO2-N2 α β ε α β ε

B1 0.0888 -0.160 0.00410 B1 0.416 -0.354 0.00386 B2 0 0.0526 0.00152 B2 0.00167 0.0421 0.00248 B3 0.0232 0 0 B3 0.0200 0 0

Figure 3.13 is a plot of the χ-functions versus frequency de-tuning from line center

for CO2-CO2 collisions and CO2-N2 collisions at 296 K. Near line center where the

impact approximation is valid, one can see that the χ-functions are unity. As

frequency de-tuning increases, the χ-functions exhibit sub-Lorentzian behavior.

Noticeably missing from these χ-functions is the expected super-Lorentzian behavior

53

in the intermediate wing. This is a major drawback of these χ-functions, and results

from the fact that the χ-functions were derived from measurements at the edges of,

and between absorption bands. Since the χ-functions clearly violate the conservation

of the integrated absorption of the individual transitions, it is expected that the

absorption under certain conditions and in certain spectral regions (especially near the

center of absorption bands where super-Lorentzian behavior is important) will be

incorrectly modeled by the χ-functions.

Figure 3.13: CO2-CO2 and CO2-N2 χ-functions versus frequency de-tuning from line center [64].

The effect of the χ-functions on an individual CO2 absorption transition at 10 atm is

shown in Figure 3.14.

Figure 3.14: Effect of χ-function on the R50 transition of the 20012 00001 band of CO2 at 10 atm

and 300 K (10.8% CO2 in air). Neighboring features are neglected. Inset shows the effect on a log-log scale.

1 10 1000.00

0.25

0.50

0.75

1.00

1.25χ

ν-νo (cm-1)

CO2-CO2

CO2-N2

Black 296 KGray 1000 K

0.1 1 10 1000.00

0.01

0.02

0.03

0.04

0.05

0.06

0.1 1 10 1001E-7

1E-6

1E-5

1E-4

1E-3

0.01

0.1

Abso

rban

ce

Lorentzian χ-function

ν-νo (cm-1)

54

3.2.2.2 CO2 Spectral Database In terms of CO2, HITRAN [22] includes line positions, strengths, lower-state

energies, and broadening parameters; however it does not include pressure-induced

shift coefficients. Recently, Toth et al. peformed an extensive experimental survey of

CO2 absorption from 4500−7000 cm-1 [71−73]. The measurements and modeling

include line position and strength [71], self-broadening and self-induced pressure shift

coefficients [72], and air-broadening and air-induced pressure shift coefficients [73].

The Toth studies have been compiled into a database [ 74 ]. The linestrength

coefficients of Toth et al. are within 3% and the self-broadening coefficients are

within 6.8% of low pressure measurements in the 5005−5010 cm-1 region by Webber

et al. [67]. The Toth et al. coefficients are also in general agreement with linestrength,

broadening, and pressure-shift measurements at low pressure by Corsi et al. [75] in the

4990−5005 cm-1 region. Of significant importance, however, is that the new pressure-

shift parameters of Toth et al. and the broadening coefficients of both HITRAN 2004

and Toth et al. have not been tested in the 2.0 μm region against measurements at

more than 1 atm.

3.2.3 Experimental Setup and Procedure A schematic of the experimental setup is shown in Figure 3.15. Light from a fiber-

coupled diode laser emitting near 1.997 μm (5008 cm-1, NEL America Inc.) is passed

to a fiber-collimator (Thorlabs F220FC-1550nm) and sent through the test cell.

Despite being well outside the optimal wavelength range specified for the collimator,

an acceptably small divergence angle is achieved to maintain a relatively small beam

diameter across the 100 cm length of the test cell. A spherical mirror collects the

beam onto a room temperature extended-InGaAs detector (New Focus, 700 kHz

bandwidth). The detector signal is sent through a low-pass analog filter before digital

sampling by a multifunction data acquisition card (National Instruments 6115, 12-bit

A/D conversion) in a desktop PC. The signal is stored and later post-processed using

55

a software lock-in amplifier to recover the 2f and 1f signals. The laser modulation is

provided by the same PC and multifunction card.

The static optical cell is stainless steel with interchangeable body sections to

form different pathlengths (100 cm was used here). Sapphire windows with 1 cm

open aperture are epoxied in the cell end caps. The surfaces of the window through

which the beam passes have a 1° wedge to avoid creating an etalon within or between

the windows. A vacuum system and mixture tank are connected via stainless manifold.

Temperature is measured with three type K thermocouples and pressure is determined

with 1000 or 10000 Torr Baratron capacitance manometers.

Figure 3.15: Experimental setup with high-pressure static cell.

The spectra shown in the following sections were obtained using the same

procedure outlined in Section 3.1.3. Unlike the results reported for H2O using NIR

diode lasers near 1.4 μm, this particular diode laser exhibited negligible wavelength

shift due to modulation (i.e. less than the 0.005 cm-1 wavelength uncertainty of the

measurement). This may be due in part to the internal temperature stabilization

properties of this particular laser and the lower modulation depth used for these

measurements. All WMS spectra for CO2 reported in this chapter use a modulation

depth of a = 0.11 cm-1 and a modulation frequency of f = 50 kHz (characterized with a

Ge etalon with a 0.016 cm-1 free spectral range).

Diode laser

DetectorL= 100 cm

To Vacuum/Mixture Plumbing

Computer

Laser Temperature & Current Tuning

DetectorSignal

56

3.2.4 Direct Absorption Results In this section, the direct-absorption spectra are presented and compared with

simulations using the database of Toth et al. [74] with 1) an unmodified Voigt line

shape profile and 2) a Voigt line shape profile modified by the χ-functions of Perrin

and Hartmann [64]. The Voigt profile was chosen over the Lorentzian profile for

accuracy at lower pressures, however even at 1 atm the Voigt profile is dominated by

the Lorentzian component.

Figure 3.16 shows the experimental results plotted with the simulations. The

measured spectra, represented by the black squares, covers the R46 through R54 lines

of the 20012 00001 band of 12C16O2 centered at 4978.6 cm-1. The step size of the

measured spectra was chosen to be 0.1 cm-1, which represents a good trade-off

between resolution and acquisition time for each spectrum. The signal to noise ratio is

such that measurement uncertainty bars would fall within the data markers, and

measurement uncertainty is further reduced through the acquisition of 5 s of data at

each point. The largest experimental uncertainty is the mixture CO2 mole fraction,

which is estimated to be +/- 3%. The dashed lines represent the simulations using

only the Voigt profile and the solid lines denote the simulations which include the χ-

functions. At 1 atm the difference between the simulations is negligible, however as

pressure increases, the rising difference illustrates the influence of the far-wings of the

stronger features to the red of the measured spectra. The average error in this region is

reduced by application of the χ-function from 24% to 8.5% for the 5 atm spectrum and

from 40% to 10% for the 10 atm spectrum.

The remaining error is the result of several factors. The Perrin and Hartmann χ-

functions were developed with data from the 4.3 μm region of CO2 [60−64]. The

measurements of Burch et al. [59] on the 4.3, 2.7, and 1.4 μm regions of CO2 show

that the influence of finite-duration collisions on the Lorentzian line shape decreases

with wavelength for the various bands. This would suggest that the χ-function

developed at 4.3 μm should under-predict the absorption measured at 2.0 μm. Also,

the Perrin and Hartmann χ-functions were developed using the GEISA database [76],

57

and though they were tested and gave good agreement with the HITRAN 86 database,

many updates have been made to this database in the years since (line positions in

2004, linestrengths in 1994, and broadening coefficients and temperature exponents in

1992) and it is different than the even more recent measurements and modeling by

Toth et al. used here [74]. Finally, the χ-functions of Perrin and Hartmann do not

include super-Lorentzian corrections in the intermediate-wing of the absorption

feature, which result in enhanced absorption over that predicted by the Lorentzian

profile.

Figure 3.16: Direct-absorption spectrum, 10.8% CO2 in air, L = 100 cm, T = 296 K. Absolute

deviation is shown for the Voigt profile + χ-function data.

The simulated absorbance with and without the χ-function for the entire

20012 00001 band is shown in Figure 3.17 with the measurement region for Figure

3.16 demarcated. One can see the measurement region is near the edge of the band. It

is therefore hypothesized that the slight overprediction of absorbance in this region by

the χ-function with respect to the measured data in Figure 3.16 is the compound result

of the lack of super-Lorentzian effects in the intermediate-wings of nearby features

and over-prediction of sub-Lorentzian effects by the χ-functions that were originally

developed with data from regions of higher wavelength.

 

0.0

0.1

0.2

0.3

0.4

0.5

R54R52R50R48R46

10 atm

5 atm

1 atm

5 atm

Abs

orba

nce

Frequency (cm-1)

Measurement Voigt profile Voigt profile + χ-function

10 atm

5006 5007 5008 5009-0.020.00

0.02

1 atm

Abso

lute

Dev

.of

χ-fu

nctio

n

58

Figure 3.17: Simulated direct-absorption spectrum of the 20012 00001 band of CO2 near 2.0 μm.

The box denotes the measurement region for this work. 10.8% CO2 in air, P = 10 atm, L = 100 cm, T = 296 K.

3.2.5 WMS Results The WMS results are shown in Figure 3.18 for 1, 5, and 10 atm, respectively. At 1

atm, good agreement is obtained between simulation and experiment and the non-

Lorentzian effects result in an average difference of only 0.3% compared to an

unmodified Voigt profile. For the 5 atm case (4.6 amagat), good agreement is

obtained and again the χ-function shows little effect on the simulated spectra (0.8%).

At 10 atm (9.2 amagat), the effect of χ-function corrections to the line shape becomes

apparent in the simulated spectrum (6.3%).

Table 3.3 summarizes the effect of non-Lorentzian behavior on the WMS and

direct-absorption signals at all pressures. The percentage differences in Table 3.3

were calculated by taking the difference between the simulations with and without the

χ-function and comparing with the χ-function corrected case. The reported result is

the average for the region between 5005.5 and 5009.5 cm-1. One can immediately see

that the WMS signals are much less affected by non-Lorentzian behavior than direct

absorption. The 2f signal is sensitive to curvature in the absorption spectrum, and

therefore the difference in the 2f signal between the simulations arises from slight

variation in the curvature of the spectrum due to the non-Lorentzian effects. The

difference in the influence of the non-Lorentzian effects on the direct absorption and

4940 4960 4980 5000 50200

20406080

% D

evia

tion

Frequency (cm-1)

0

1

2

3

Abs

orba

nce

Voigt profile Voigt profile + χ-function Measurement

Location

59

1f signals is due to the different dependences on absolute absorption between the two.

The direct-absorption signal is the absorbance, so if for example, the absorbance at

5007.5 cm-1 is modeled as 28.2% for the unmodified Voigt and 22.4% for the χ-

function modified Voigt, the direct-absorption signal experiences a 26% effect due to

non-Lorentzian effects. The 1f signal is approximately proportional to (1-absorbance).

Therefore for the same example above, we expect the 1f signal to change by ~7.5%

due to non-Lorentzian effects. Indeed the actual simulations show that it changes by

5.7%.

Figure 3.18: 1f-normalized, WMS-2f spectrum.

10.8% CO2 in air, L = 100 cm, T = 296 K, a = 0.11 cm-1 for P = 1, 5 and 10 atm. For the P = 1 and 5 atm cases, the χ-function correction results in very little change from the uncorrected Voigt case. WMS modulation parameters: a = 0.11 cm-1, f = 50 kHz.

Table 3.3: The average effect of non-Lorentzian behavior on WMS and direct-absorption signals in the 5005.5 – 5009.5 cm-1 region. Average % effect of non-Lorentzian behavior on signal* 1 atm 5 atm 10 atm 2f 0.3 1.5 4.6 1f 0.1 1.5 5.7 2f / 1f 0.3 0.8 6.3 Direct absorption 6.7 13.8 27.1 * With respect to χ-function corrected signal

5006 5007 5008 5009-0.05

0.00

0.05

Dev

iatio

n

Frequency (cm-1)

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16 P=1 atm

2f/1

f Mag

nitu

de

Measurements Voigt profile Voigt profile + χ-function

5006 5007 5008 5009-0.005

0.000

0.005

Dev

iatio

n

Frequency (cm-1)

0.000

0.005

0.010

0.015

0.020

0.025 P=5 atm

2f/1

f Mag

nitu

de

Measurements Voigt profile Voigt profile + χ-function

5006 5007 5008 5009-0.001

0.000

0.001

Dev

iatio

n

Frequency (cm-1)

0.000

0.002

0.004

0.006

0.008

0.010

0.012

2f/1

f Mag

nitu

de

Measurements Voigt profile Voigt profile + χ-function

P=10 atm

60

A quantitative comparison between spectral databases cannot be carried out with

direct-absorption spectra at high pressures because the effect of non-Lorentzian

behavior is large and the χ-function corrections carry large uncertainty. We have

shown that the use of WMS reduces the effects of non-Lorentzian behavior, so even

though there are larger uncertainties in the WMS models than in the Beer-Lambert

relation for direct absorption, WMS provides a method to make accurate comparisons

between spectral databases at high pressures. Figure 3.19 shows the WMS data at 5

and 10 atm with simulations using the Toth database and the HITRAN database with a

χ-function-modified Voigt profile.

Figure 3.19: Comparison of simulations using HITRAN [22] and Toth et al. [74] spectral

parameters. 1f-normalized, WMS-2f at T = 296 K, 10.8% CO2 in air, L = 100 cm. Both simulated spectra use the χ-function modified Voigt profile. WMS modulation parameters: a = 0.11 cm-1, f = 50 kHz.

The comparison shows that both databases give accurate values for the

linestrengths and broadening coefficients at room temperature, however the lack of

pressure-induced shift coefficients in the HITRAN 2004 database induces significant

error in the simulations. A slight frequency shift between the experiment and the

simulations using the pressure shift parameters of Toth et al. is apparent (and perhaps

easier to see in the 5 and 10 atm panels of Figure 3.18). Analysis reveals that

augmenting the average pressure-induced shift coefficients of Toth et al. by -0.004 cm-

1/atm provides improved agreement at all pressures. This falls outside the reported

uncertainty of the pressure shift coefficients in Toth et al. [72,73], however one should

5006 5007 5008 50090.000

0.003

0.006

0.009

0.012P=10 atm2f

/1f M

agni

tude

Frequency (cm-1)

0.000

0.005

0.010

0.015

0.020

0.025P=5 atm Measurements

Hitran 2004 Toth et al

61

note that shift coefficients are very difficult to accurately measure at the low pressures

employed for spectral validations, and often uncertainties for spectral parameters are

calculated from fitting uncertainties, which do not take systematic error into account.

3.3 Implications on Sensor Design Direct-absorption and 1f-normalized WMS-2f spectra were reported for the R46

through R54 lines of the 20012 00001 band of CO2 near 2.0 μm at room temperature

and up to 10 atm, and the 7204 cm-1 and 7435 cm-1 regions (near 1.4 μm) of H2O at

700 K and up to 30 atm. The measurements have several important implications to

guide future absorption-based sensor design for high pressure CO2 and H2O

measurements:

(1) Spectral parameters – For H2O, measured 2f spectra provide a means to

quantitatively compare the HITRAN [22] and hybrid spectral database of Liu et al.

[37] at higher pressures. Comparisons of simulations with the 2f measurements in

the 7204 cm-1 region show a reduction in RMS error of 36% at 10 atm, 26% at 20

atm, and 27% at 30 atm with the hybrid database. Comparisons of simulations and

2f measurements in the 7435 cm-1 region show that the hybrid database improves

on HITRAN, but also indicate a remaining discrepancy. This slight discrepancy

could be explained by uncertainties in the difficult-to-measure pressure-induced

shift coefficients (and their temperature dependence) or by the influence of water-

vapor transitions blue of the measurement region that was studied by Liu et al.

For CO2, the WMS spectra show that the recently-measured spectral

parameters of Toth et al. [74] improve upon those found in HITRAN, primarily

due to the inclusion of pressure-induced shift coefficients. These parameters

should be chosen over HITRAN for the simulations needed to infer gas parameters

from measurements at high pressure. The slight discrepancy that remains between

measurements and simulations likely results from remaining errors in the line-shift

parameters. Augmenting line-shift parameters by -0.004 cm-1/atm provides

improved agreement in the 5005-5010 cm-1 region.

62

Non-Lorentzian effects – For H2O, direct-absorption measurements at 20 and

30 atm (700 K) begin to show evidence of the breakdown of the impact

approximation inherent to the Lorentzian line shape. This phenomenon, which is

manifest as a nearly constant offset in the absorption, has been observed by many

researchers and several models have been developed to describe it at atmospheric

temperatures. The CKD model of Clough et al. [46] with a modified coefficient is

applied to the data and gives good agreement at 10, 20, and 30 atm. The

modification to the coefficient is in agreement with trends observed at high

temperatures by Hartmann et al. [41] and others. However, the use of the CKD at

other temperatures will require measurement of the modified coefficient at those

temperatures.

For CO2, the direct-absorption spectra show that non-Lorentzian effects at high

gas densities pose an important challenge to CO2 sensor design, particularly

toward the edge of absorption bands where one finds the large lower-state energy

transitions that are useful for measurements in high temperature environments.

The temperature- and frequency-dependent χ-functions of Perrin and Hartmann

[64] were used to model the non-Lorentzian behavior and reduced the average

error from 24% to 8.5% at 5 atm (4.6 amagat) and 40% to 10% at 10 atm (9.2

amagat). The remaining error is likely due to the lack of inclusion of intermediate-

wing super-Lorentzian effects in the χ-function model and the fact that the model

was developed for the 4.3 μm region of CO2. The applicability of the χ-functions

closer to the band center is still an open question. Thus, an easy-to-implement,

well-validated model for non-Lorentzian effects on high pressure CO2 absorption

in the 2.0 μm region still does not exist that delivers the low uncertainty levels

necessary for accurate inference of gas properties using direct-absorption

spectroscopy. An alternate approach is for the sensor designer to look to

techniques which reduce the influence of non-Lorentzian effects on the final

uncertainty of the measurement.

(2) Absorption measurement strategy – The 1f-normalized WMS-2f spectra are

shown to be significantly less influenced by non-Lorentzian effects than the direct-

63

absorption spectra. For CO2, the average effect of the non-Lorentzian behavior in

this region at 10 atm is 6% for the WMS spectra compared with 27% for the

direct-absorption spectra. This is a very important benefit of WMS for high-

density gases because it reduces reliance on line shape correction for non-

Lorentzian effects. The reduced influence of non-Lorentzian effects also implies

that the WMS signals experience reduced influence by the far-wings of distant

spectral features, thus reducing the size of the spectral region around the

wavelengths used for the sensor for which an accurate spectral database is

necessary.

An additional advantage of WMS at high pressures with laser sources that

exhibit synchronous wavelength and intensity modulation is the ability to use the

1f signal as a ‘baseline’ to track perturbations to the laser intensity (window

fouling, beam-steering, etc.). Direct-absorption-based sensors do not have a direct

means to account for this once the non-absorbing baseline between spectral

features is obscured by the wings of pressure-broadened features.

The disadvantages of WMS need also be considered when choosing a

technique for high-pressure sensing. First, there are more assumptions in the

current WMS models than in the simple Beer-Lambert relation for direct

absorption (truncated higher-order laser nonlinearities, linear wavelength

modulation, etc.) and the model relies on measurements of the laser-specific tuning

characteristics. These assumptions introduce the possibility for error depending on

the experimental conditions. Second, from Figure 3.18, one can see that the peak

WMS signal is reduced by nearly a factor of 20 from 1 to 10 atm, while the direct-

absorption signal grows with pressure. This decrease in signal is caused by the

reduction in curvature of the absorption spectrum, which will continue to diminish

at higher densities. The high-pressure-signal loss can be counteracted by

increasing the wavelength-modulation amplitude [24], however the modulation

amplitude is eventually limited by the injection-current limits of a given diode

laser. Third, since WMS is dependent on the curvature of the absorption spectrum,

it also is more sensitive to near-wing line shape (i.e. broadening parameters).

64

Finally, using WMS to infer gas properties in environments with greater than a

few percent absorption requires an estimate of concentration to nominally account

for absorption in the 1f signal (see Section 2.3.2).

Overall, 1f-normalized WMS-2f is a good candidate for sensing in high-

pressure environments when sufficient spectral curvature is present to support an

acceptable signal-to-noise ratio. When density is increased such that sufficient

signal is not achievable with the highest modulation depth possible for the diode

laser, another technique which is resistant to the influence of non-Lorentzian line

shape behavior should be explored, such as differential absorption [77].

This work represents an important step toward practical, field-deployable sensor

systems for measuring H2O and CO2 in high-pressure environments. The application

of the ideas presented here to rapid measurements of H2O and temperature in internal

combustion engines will be the topic of the next chapter.

65

Chapter 4. Rapid Measurements of

Temperature and H2O in IC Engines

with a Spark Plug-mounted Diode Laser

Sensor The demand for heightened efficiency and decreased emissions has driven internal

combustion (IC) engine designers to consider increasingly-complex combustion

schemes such as exhaust gas recirculation (EGR), supercharging, turbocharging,

variable valve timing, and homogeneous-charge compression ignition (HCCI). All of

these schemes have different effects on the in-cylinder gas temperature and species

composition, which play a pivotal role in the combustion event and the formation of

harmful emissions in engines. Engines using internal EGR, for example, use unique

valve timing to retain or re-induct exhaust gases from one cycle to the next in order to

obtain more desirable combustion characteristics (e.g. reduced NOx emissions). To

properly design, optimize, and control these combustion schemes, it is of utmost

importance to know the temperature and species concentration histories throughout the

mixing and compression processes that occur prior to ignition.

Many TDL combustion sensors developed thus far have focused on high

temperature, near-atmospheric pressure, continuous processes [1−6]. Far fewer TDL

sensors have been developed for high pressure, cyclic applications. Specifically,

sensors that utilize fixed-wavelength direct absorption at multiple wavelengths have

66

been demonstrated on a pulse detonation engine [78], across the diameter of an optical

IC engine [79], and on a steady, high-pressure coal combustor [80]. Sensors using

rapid direct-absorption scans over a large spectral range have also been applied to

pulse detonation engines [81] and for cross-cylinder measurements in IC engines [82].

Finally, calibrated WMS using TDLs was applied to a steady, high-pressure coal

combustor [10].

Internal combustion engines provide a particularly challenging environment for the

application of laser-absorption sensors. During the compression stroke, a wide range

of conditions is encountered, with temperatures ranging from ambient to >1000 K and

pressures up to 50 atm (for turbocharged and supercharged intake configurations).

High pressures lead to broadened, congested, and overlapped spectra, making direct-

absorption spectroscopy difficult. For water vapor-based sensing, only the low

concentration of water vapor available in ambient intake air (as little as 1%) is present

during the compression stroke, leading to small absorption signals. The gas conditions

vary rapidly throughout compression, so high bandwidth is required to capture crank

angle-resolved gas properties. Finally, optical access within typical IC engines is

difficult due to harsh conditions, moving parts, and limited space.

The sensor developed in this work [83,84] is designed to measure gas temperature

and H2O concentration for this range of conditions during the compression stroke of

an IC engine. A 6 mm folded-pathlength (12 mm total), fiber-optic-coupled probe is

mounted to the spark plug and enables optical access to almost any IC engine. The

probe gives localized measurements near the ignition source for spark-ignition engines

and in the compressed gases for HCCI engines that can accommodate the probe. The

short pathlength, combined with the low concentrations of water vapor and high gas

pressures present during the compression stroke require the use of a sensitive

absorption technique — wavelength-modulation spectroscopy with second-harmonic

detection (WMS-2f). This technique has been used for calibrated measurements in the

past when a sensitive, noise-resistant technique was required. This work represents

the first practical application of the calibration-free technique described in Chapter 2.

The sensor gathers absolute temperature information from the ratio of absorption on

67

two spectral features and concentration information from the absorption on one of the

features. The sensor output rate is 15 kHz (7.5 kHz bandwidth), giving it the ability to

measure changes in gas temperature and water concentration that occur over the space

of two crank angle degrees at 2500 rpm.

In this chapter the spectral feature selection, sensor design, and sensor validation in

a laboratory environment will be summarized, and results using the sensor in unfired

and fired IC engine cylinders will be presented. To the author’s knowledge, these

represent the first crank-angle resolved, in-cylinder measurements of temperature and

concentration in production-type IC engines (where no modifications to the cylinder

head, walls, or piston have been performed).

4.1 Sensor Design

4.1.1 Spectral Feature Selection for Thermometry For an optically-thin gas (absorbance < 0.05), the 2f magnitude is directly

proportional to partial pressure, pathlength, and the product of the average laser

intensity and detection system gain. Normalization of the 2f signal by the first

harmonic (1f) signal cancels the signal dependence on the average laser intensity and

detection gain (Eq. (2.14)). Then, if the ratio of the normalized 2f magnitudes for two

different spectral features is taken, the partial pressure and pathlength will cancel,

leaving only a function of the linestrengths and line shapes of the absorbing transitions

(Eq. (2.15)). The linestrength is a pure function of temperature and, for a fixed

modulation depth, the line shape depends strongly on total pressure and weakly on

temperature. Thus at a given pressure, the ratio of two transitions is primarily a

function of temperature, and the functionality comes mainly through the linestrengths

of the two lines.

Two spectral features were chosen for the sensor through a systematic search of the

thousands of water-vapor features tabulated in the HITRAN database [22] for the

near-infrared region from 1.25−1.65 μm. The goal was to find an optimal feature pair

for thermometry and water concentration measurements over a region of pressure and

68

temperature space from approximately 5 to 50 atmospheres and 450 to 1050 K. This

covers most of the possible compression stroke conditions for a variety of different

engine cycles (HCCI, supercharged-intake, large EGR, etc.). Several selection criteria

were applied to choose the optimal lines: strong 2f signal over the entire

temperature/pressure range, high sensitivity and monotonic behaviour of the ratio of 2f

signals, minimal interference from nearby transitions, and low expected temperature

uncertainty arising from noise. Details on the selection process can be found in Zhou

et al. [85]. The search yielded 16 candidate line pairs, from which a single pair was

selected. The ν1+ν3 band transition (J = 5, Ka = 5, Kc = 0) (5, 5,1) with lower-state

energy E” = 742 cm-1 located near 7203.9 cm-1, and the ν1+ν3 band transition

(12,1,12) (13,1,13) with E” = 1558 cm-1 located near 7435.6 cm-1.

An intensive study of the spectral parameters of the two target transitions and

neighboring transitions within ±2 cm-1 was performed by Liu et al. [37]. For the

primary features and their neighbors the following spectral data were measured in a

uniform, low-pressure static cell: linestrength, collision-broadening coefficients

(including temperature dependence for self-, air-, and CO2-colliders), and collision-

induced frequency-shift coefficients (including temperature dependence for air- and

CO2-colliders).

A quantitative comparison of measurements and simulations based on these

parameters at high pressures was performed (detailed in Chapter 3 and [26]). Good

agreement between theory and measurement was obtained, with slight discrepancies

occurring at higher pressures for the 7435 cm-1 region.

The simulation of the ratio of 2f/1f signals between the 7435 cm-1 and 7204 cm-1

spectral features is shown in Figure 4.1 as a function of temperature and pressure. The

simulations are based on the equations of Section 2.2.3 with the laboratory measured

spectral parameters of [37]. They take into account contributions from neighboring

transitions. Absorption in the 1f magnitude is very minor and is therefore neglected in

the simulations.

69

Figure 4.1: Three-dimensional rendering of the ratio of 2f/1f signals used to infer temperature.

The ratio is taken between the 7435 cm-1 and 7204 cm-1 features simulated with 1% H2O vapor in air. The effect of absorption on the 1f magnitude is neglected.

4.1.2 Sensor Hardware The in-cylinder water concentration and temperature sensor is designed to be

portable so measurements can be made on a wide variety of engine test stands. It is

composed of two parts: the sensor system, which contains the lasers, detector, and data

processing equipment, and the sensor probe, which fits into the spark plug hole of the

test engine. The sensor system, which was designed and constructed by Physical

Sciences Inc., is pictured in the foreground of Figure 4.2.

Figure 4.2: Photo of the sensor system (foreground).

Ratio

of 2

f/1f S

igna

ls

70

A basic schematic of the experimental arrangement is shown in Figure 4.3.

Figure 4.3: Sensor layout. Pressure transducer not shown.

The sensor probe (which was designed and constructed by Nissan Motor Co.) was

designed specifically to adapt to the spark plug port of most engines. A schematic of

the optical probe is shown in Figure 4.4.

Figure 4.4: Schematic of the optical probe.

The optics of the probe are integrated with a working spark plug to allow firing

tests. Two fiber-coupled, near-infrared, distributed feedback (DFB) diode lasers are

modulated near the maximum obtainable modulation depth for each laser (~0.7 cm-1)

near the two target spectral features. The laser light is multiplexed into a singlemode

optical fiber that carries the light to the spark plug probe. The multiplexed laser light

travels through the body of the probe in the singlemode fiber, is pitched through a

Tem

pera

ture

Crank AngleData Processor

DetectorTDL (1)

TDL (2)

ν1

ν2

Optical Probe

Sensor System

Optical Fibers

In-cylinder Measurement Location

Mirror 6 mm open pathlength

Spark electrodeSapphire windowFrom lasers;

Singlemode fiber

To detector;Multimode fiber

71

sapphire window, and traverses a 6 mm open path to a mirror. This mirror reflects the

light back across the open path (for a total pathlength of 12 mm) and focuses it onto a

multimode fiber bundled next to the singlemode pitch fiber. The mirror is supported

by posts which are attached to the probe (spark plug) body and designed to allow free

flow of the cylinder gases through the measurement path.

The multimode fiber exits the sensor probe and travels to a large diameter (3 mm)

InGaAs photodetector (bandwidth = 500 kHz). The resulting detector voltage signal

is the superposition of both laser signals, and is bandpass filtered and sampled

continuously at 625 kHz. The individual laser signals are frequency-demultiplexed

using four digital lock-in amplifiers tuned to the first (1f) and second (2f) harmonics of

the two modulation frequencies (70 kHz and 87.5 kHz for this work). More

discussion of frequency-demultiplexing can be found in Section 5.1.1. The lock-in

amplifiers provide approximately 45 dB of rejection to signals outside of a 12 kHz

band centered on their respective target frequencies, greatly reducing crosstalk

between the laser signals and rejecting outside noise sources.

An independent pressure measurement by a transducer mounted on the engine is

sampled by the sensor system. This signal and the lock-in amplifier signals are

processed by the sensor into temperature and water concentration as described in

Chapter 2.

4.2 Sensor Validation The sensor was validated under controlled, static conditions in the same high-

temperature and -pressure optical cell used for the measurements of Chapter 3. A

more detailed description of the experimental setup, full results, and complete

discussion can be found in [84].

Measurements performed in the static cell at known temperatures of 500, 700, and

900 K and pressures ranging from 1 to 25 atm are shown in Figure 4.5. The water-

vapor mole fraction was determined at each condition using an independent

measurement. The top panel of Figure 4.5 shows a comparison of the temperature

measured by the sensor at each condition with the thermocouple-measured static cell

72

temperature. At 500 K, the RMS error between the measured and actual temperatures

over the full range of pressure is 10 K (2%). At 700 K the RMS error is 16 K (2.3%)

and at 900 K it is 26 K (2.9%). The bottom panel of Figure 4.5 shows the ratio of the

mole fraction measured by the sensor using the high E” line (xmeasured), and the

independently measured mole fraction (xactual). Ideally, the value of this ratio would be

unity. At 700 K, the RMS error between the measured mole fraction and the actual

mole fraction is 3%, and at 900 K the RMS error is 3.6%. Thus excellent agreement is

found between expected and measured values for both temperature and mole fraction.

The errors in the measurements are primarily attributed to error in the 2f simulations

that are used by the sensor to calculate the temperature and mole fraction (see Section

3.1.5).

Figure 4.5: Validation measurements of the sensor system in a controlled high temperature and

pressure optical cell.

4.3 Engine Results The sensor was applied to two different internal combustion engines. The first, a

single-cylinder, variable-compression-ratio research engine, was used to test the

sensor in a motoring only (unfired) configuration during sensor and probe

development. The second, a single-cylinder engine with specifications matching a

production automotive engine, was used to test the sensor in a fired arrangement. The

 

400

500

600

700

800

900

1000 Cell Temperature Sensor Measurements

Tem

pera

ture

(K)

Pressure (atm)0 5 10 15 20 25

0.9

1.0

1.1

x Mea

sure

d/xA

ctua

l

73

results from this engine confirm the utility of the sensor for evaluating new engine

concepts of mixture preparation and combustion.

4.3.1 Unfired Case For the unfired case, a single-cylinder, variable-compression-ratio research engine

(8.26 cm bore x 11.43 cm stroke Cooperative Fuel Research engine at the University

of California-Berkeley) operating near 1800 rpm with an estimated 9.5:1 compression

ratio was used. The engine was chosen for its flexibility. Cylinder head access was

possible through multiple spark plug holes, which was beneficial during probe design

and testing. The intake air was humidified to nearly 100% relative humidity by

drawing the air through a water bath.

Figure 4.6 shows the 10-cycle average temperature versus crank angle for a steady

motoring condition. Also shown is a simulation for the temperature based on

polytropic compression (PVn = constant) and the measured pressure. The polytropic

exponent, n, was chosen to be 1.39 (the average value of the ratio of specific heats for

air for the temperature range from -60 to 60 crank angle degrees). This simulation is

an approximation for the temperature in the core region of the compressed gas in the

cylinder since this choice of polytropic exponent is very near that for an isentropic

process. Since the probe is located within a few mm of the cylinder head wall and is

itself a heat sink, one might expect some deviation between the measured and

simulated temperature due to thermal boundary layer effects. Indeed, the measured

temperature at less than approximately -40 crank angle degrees (CAD) is higher than

the simulated temperature, which is consistent with an increased boundary layer

temperature due to warm cylinder surfaces. After -40 CAD, the measured temperature

becomes less than the simulated core temperature, which is consistent with energy

transfer to the cylinder surfaces.

74

Figure 4.6: Measured temperature in an unfired, single-cylinder engine. A constant gamma

isentropic simulation is shown for comparison.

The 10-cycle average water concentration and mole fraction are shown as a

function of crank angle in Figure 4.7. Water mole fraction, xH2O, remains constant

over the cycle and agrees with the estimated humidifier output (xH2O = 2.3%).

Figure 4.7: Measured water concentration and mole fraction in an unfired, single-cylinder

engine.

To quantify the scatter of the data, a moving average is taken through the 10-cycle

average data. This smoothes the data and provides a mean value at each crank angle

against which the scatter can be measured. The standard deviation between the data

-60 -40 -20 0 20 40 600

5

10

15

Pre

ssur

e (a

tm)

Crank Angle (degrees)

350

400

450

500

550

600

650

700

Polytropic Simulation (n = 1.39) Measured Temperature

Tem

pera

ture

(K)

Unfired Case, 10 cycle average(1800 rpm, CR=9.5:1 est.)

-40 -20 0 20 400.0

5.0x10-5

1.0x10-4

1.5x10-4

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

H2O Concentration

H2O

Con

cent

ratio

n (g

/cc)

Crank Angle (degrees)

H2O Mole Fraction

Unfired Case, 10 cycle average(1800 rpm, CR=9.5:1 est.)

H2O

Mol

e Fr

actio

n

75

and this moving mean was calculated for a single cycle, 10-cycle average, and 100-

cycle average. For temperature, the standard deviation was found to be 24 K for the

single-cycle data, 8.4 K for the 10-cycle average, and 4.4 K for the 100-cycle average.

For water concentration, the standard deviation was found to be 1.0(10)-5 g/cm3 for the

single-cycle data, 3.3(10)-6 g/cm3 for the 10-cycle average, and 2.1(10)-6 g/cm3 for the

100-cycle average.

4.3.2 Fired Case For the fired case, a single-cylinder (9.3 cm bore x 7.33 cm stroke at Nissan Motor

Company) engine operating at 1200 rpm with a 12:1 compression ratio was used. The

air-to-fuel ratio was 14 and the ignition timing was set at 15 degrees BTDC. The

water mole fraction of the intake air was set at 1.4% (40% relative humidity at 300 K).

Figure 4.8 shows the 10-cycle average temperature versus crank angle. Data is

shown through the compression stroke and spark ignition until the early flame

development phase when the gas conditions rapidly exceed the range of the sensor,

which was designed for measurements during the compression stroke. The delay

between the spark and the rapid rise in temperature associated with early flame

development is consistent with ignition delay expectations (~1 ms, 7 CAD at this rpm)

and turbulent flame propagation speeds.

There are strong periodic variations in the inferred temperature which show cycle-

to-cycle repeatability, especially at early crank angles. Further investigation remains

to determine whether these variations are due to gas dynamic effects, repeatable

mechanical vibration of the probe tip, or optical interference effects (such as etalons).

With the extremely low absorption levels present during these short path, low water-

vapor measurements in the engine (as low as 0.2% absorption near -60 CAD for the

data in Figure 4.8 and 0.1% absorption near -60 CAD for the data in Figure 4.6), very

small noise sources can cause the +/- 30 K temperature fluctuations measured at these

conditions. We believe the oscillations can be reduced through future design

modifications to optimize the probe tip and possibly to improve the WMS detection

scheme (see Section 7.6.1).

76

Figure 4.8: Measured temperature and pressure in a fired, single-cylinder engine.

The 10-cycle average water concentration and mole fraction are shown in Figure

4.9. The spike in the data at -9 degrees is repeatable from cycle-to-cycle and is likely

due to electric interference related to the spark electronics or the influence of flame

kernel initiation (the spike occurs ~1 ms after the spark, which is consistent with

expected ignition delay times). The water mole fraction is nearly constant, indicating

mixture homogeneity. Compared with the unfired case at around -40 degrees crank

angle, the water density is lower, which is consistent with the higher temperatures of

the fired case (at similar water mole fraction and total pressure).

Figure 4.9: Water concentration and mole fraction measured in a fired, single-cylinder engine.

600

700

800

Tem

pera

ture

(K)

Crank Angle (degrees)

Fired Case, 10 cycle average(1200 rpm, CR=12:1)

Spark

-60 -50 -40 -30 -20 -1005

10152025

Pre

ssur

e (a

tm)

-60 -50 -40 -30 -20 -100.0

5.0x10-5

1.0x10-4

1.5x10-4

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

Spark

Fired Case, 10 cycle average(1200 rpm, CR=12:1)

H2O

Con

cent

ratio

n (g

/cc)

Crank Angle (degrees)

H2O

Mol

e Fr

actio

n

77

The utility of the sensor is confirmed in Figure 4.8 and Figure 4.9. One can see

that the temperature throughout the compression stroke is higher for the fired case than

the unfired case. For the fired case, the incoming gases are heated by the hot intake

and cylinder walls. In addition, hot exhaust-gas residuals left over from the previous

cycle mix with incoming gases, raising their temperature and water mole fraction

(compare the measured value of xH2O = 2.1% with the intake value of xH2O = 1.4%).

In order to predict the temperature and water concentration during the compression

stroke of even this simple fired case, a complex fluid dynamics model including heat

transfer is necessary. For more complicated EGR and variable valve timing schemes,

modeling becomes extremely difficult, making this type of measurement valuable for

engine design and model validation.

78

79

Chapter 5. A Diode Laser Sensor for

Measurements of Temperature, H2O,

and CO2 in a Scramjet Combustor Recent successful tests of scramjet-powered test vehicles at velocities in excess of

Mach 7 have improved the outlook for scramjets as a viable technology for high-speed

air-breathing flight. At the heart of these high-speed vehicles is the combustor, the

region in which a supersonic air/fuel mixture ignites and burns to produce thrust. The

performance of the combustor plays a major role in the stability and efficiency of the

engine, and can be determined by looking at important gasdynamic parameters in the

combustion gases. In the work reported here, a diode laser sensor is developed to

make non-intrusive measurements during ground-test of a model scramjet combustor

at the Air Force Research Laboratory (AFRL) at Wright-Patterson Air Force Base

(WPAFB).

Past TDL sensors developed for H2O, temperature, and velocity measurements in

scramjet or scramjet-like supersonic reacting flows were based on direct-absorption

measurements of H2O [11,86 ,87] and/or O2 [88 ,89]. Preliminary calibrated 2f

measurements of temperature were shown in [11]. In this work [23], we develop a

sensor for calibration-free WMS of H2O concentration and temperature and

measurements of weakly-absorbing CO2 near 2.0 μm.

Comparisons of direct-absorption and WMS measurements in the scramjet

environment show a 4x increase in SNR is obtained with WMS even though the

80

measurement is not limited by laser noise (a situation where WMS shows an even

greater improvement over direct absorption).

The sensor incorporates hybrid demultiplexing – using both wavelength- and

frequency-multiplexing to combine six lasers with wavelengths ranging from 1.3 μm

to 2.0 μm in a single probe beam and later distinguish their signals. Probing several

H2O absorption features with different temperature dependences is important for

achieving good sensitivity over a broad temperature range and enables sensing of line-

of-sight (LOS) temperature non-uniformity.

An important consideration for absorption sensing is the path-integrated nature of

the measurement, and the effect that gas non-uniformities along the laser LOS have on

the quantities inferred from the laser signals. In order to benchmark multi-

dimensional computational fluid dynamics (CFD) simulations against absorption

measurements in harsh, non-uniform environments, a method to compare the two is

necessary. In this chapter, a simple method that takes into account gas non-

uniformities along the laser line-of-sight (LOS) is used to compare sensor

measurements of temperature and H2O with 3D CFD calculations during full scramjet

combustor operation. An expected WMS signal is calculated from the multi-

dimensional CFD and used to infer an expected laser-measured LOS temperature and

H2O concentration. This value, which is slightly different than the simple path-

average temperature and H2O concentration, can be directly compared to the laser

measurement to yield useful information about both the scramjet combustor and CFD

model performance.

5.1 Sensor Design

5.1.1 Hybrid Demultiplexing It is important in many applications to probe absorption at multiple wavelengths

either to gain information about multiple species in the system, achieve good

temperature sensitivity over a large range of conditions, or gain information about

temperature and species non-uniformity along the laser LOS [90−92].

81

In traditional multi-wavelength direct-absorption sensors using DFB diode lasers,

the various wavelengths of light are either wavelength or time demultiplexed. In time-

demultiplexed systems, each laser is turned on in series so that the resulting detector

signal is comprised of each laser signal in sequence. This method offers hardware

simplicity at the expense of time response and temporal accuracy. Wavelength-

multiplexed systems combine all of the laser wavelengths into a single beam and use a

grating located after the light passes through the measurement region to spatially

separate the lasers onto separate detectors. This method solves the temporal issues of

time-demultiplexing at the expense of hardware complexity and the need to choose

wavelengths of sufficient spectral separation that they can be successfully separated by

the grating.

WMS offers another possibility – frequency demultiplexing [93]. In this method,

each laser is modulated with a different frequency, and the lock-in amplifiers separate

the 2f and 1f signals of each laser from the same detector signal based on the

modulation frequency. The method thereby achieves hardware simplicity without

giving up fast temporal resolution. However the number of lasers that can be

demultiplexed in this method is somewhat limited (see the next Section, 5.1.2).

As an alternative, we have taken a hybrid-demultiplexing approach, in which

wavelength and frequency demultiplexing are combined to separate a large number of

signals with reduced complexity. In this scheme, the target absorption features are

chosen so that the wavelengths of the TDLs fall into groups that can be separated onto

different detectors after striking a grating. Each laser from a particular group is

modulated at a different frequency so that it can be frequency-demultiplexed from the

others in that group.

An example setup using this technique is shown in Figure 5.1, and was used to

obtain the results from the ground-test scramjet engine at AFRL/WPAFB shown in

subsequent sections. Here, six lasers (NEL America) tuned to H2O and CO2

absorption features ranging from 1338 nm to 1997 nm are multiplexed using a

singlemode fiber combiner. A 10-meter singlemode fiber (SMF-28) delivers the beam

to the scramjet test section, where it is pitched across the combustor exit with an

82

aspheric collimating lens (Thorlabs F240APC-C). After traversing the test region, the

beam is collected with a large diameter lens (Oz Optics HPUCO-25-1300-M-10BQ),

and focused into a 600 micron multimode fiber. The beam travels through the

multimode fiber to the hybrid demultiplexing setup a few meters from the test section.

The light exits the multimode fiber and is collimated by a large diameter aspheric lens

(Optosigma 023-2392) onto a 600 grooves/mm diffraction grating (Edmund Optics

NT54-851). The dispersed wavelength groups are focused onto separate 3mm

diameter InGaAs photodetectors (Electro-Optical Systems Inc., IGA-030-E5/4MHz)

using a focusing mirror. Each laser in a particular group is either modulated at 160

kHz or 200 kHz for the frequency-demultiplexing step.

Figure 5.1: Schematic of a hybrid demultiplexing system configured for the scramjet

experiments at AFRL/WPAFB.

All laser drive-signal generation and detector-output acquisition are performed by

one computer using two National Instruments multi-function DAQ cards (PCI-6115).

Phase-insensitive software lock-ins are used to frequency demultiplex the remaining

laser groups and recover the 2f and 1f signals for each laser.

5.1.2 Modulation Frequency Optimization One of the most important aspects of frequency-demultiplexing is choosing the

laser modulation parameters to minimize noise and avoid cross-talk between the

Detector Signals

Fuel Injectors

Inlet vitiated air flow Combustor Combustor

Exhaust

Single mode fiber

Diode lasers

Grating

Multi modefiber

Detectors

Wavelength Demultiplexer

Multiplexer

Computer Σ

Laser Drive Signals

Fast sine160 kHz

or200 kHz

Slow sine2 kHz

+

+

1392 nm

1388 nm

1343 nm

1338 nm

1469 nm1997 nm

1997 nm

1469 nm

1388 & 1392 nm

1338 & 1343nm

83

harmonic signals of the different lasers. It is often helpful to calculate Fourier

transforms of the detector signal, such as those shown in Figure 5.2 for three different

WMS laser modulation strategies, to study the level of crosstalk and background noise

present in a system. Since the lock-in amplifier isolates the signal at the target

harmonic plus the region around it that falls within the low-pass filter cut-off of the

lock-in, one can use these Fourier transforms to see what signals are being passed

through the lock-in.

In traditional WMS, the laser is modulated with a high-frequency sinusoid that

produces the desired 2f and 1f signals, and a lower-frequency linear ramp signal that

scans the laser across the absorption feature (this type of modulation strategy is shown

in Figure 2.3 and the resulting FFT is shown in panel (a) of Figure 5.2). An infinite

number of harmonic terms, spaced at the ramp frequency, make up the Fourier

transform of the linear ramp waveform. These harmonics, which can be seen as the

multitude of features that slowly decrease with increasing frequency in panel (a) of

Figure 5.2, generate noise in the WMS harmonic signals and limit the sensitivity of

some WMS signals. To improve the situation, the linear ramp can be replaced with a

sine wave, whose Fourier transform is theoretically only made up of a single harmonic

at the sinusoid frequency. This improved situation is shown in panel (b) of Figure 5.2.

Figure 5.2: Fourier transform of detector signals with (a) one laser scanning fully across 1

absorption feature using a linear ramp waveform, (b) one laser scanning fully across 1 absorption feature using a sine waveform, and (c) two lasers scanning across only the peak of 2 absorption features using a sine waveform. Note in panel (c) that each laser is modulated at a different frequency so that the harmonic signals for each can be distinguished.

0 100 200 300 400 50010-2

100

102

10-2

100

102

10-2

100

102

Frequency (kHz)

Pow

er (a

.u.)

(c) Partial scan, 2 absorption features, sine waveform

(b) Full scan, 1 absorption feature, sine waveform

(a) Full scan, 1 absorption feature, sawtooth waveform2f1

1f1

2f11f1

3f12f2

2f11f2

1f1

84

In the presence of absorption, scanning the laser across the absorption feature

produces sidebands around the modulation frequency and its harmonics. These

sidebands, when converted back to the time domain, make up the WMS signals. Thus

it is important that these sidebands are captured by the lock-in amplifier and the

spacing of these bands determines the minimum low-pass filter frequency that can be

used in the lock-in.

For calibration-free WMS measurements, only the 2f peak value and the

corresponding 1f value are important, and therefore it is only important to scan the

laser across the peak of the feature. Reducing the scan range of the laser to only

capture the peak also reduces the sideband width and allows a more aggressive low-

pass filter step in the lock-in. This in turn allows one to add additional lasers and

modulation frequencies without interference. This is shown in panel (c) of Figure 5.2,

in which two lasers, one modulated at 160 kHz and the other at 200 kHz, are used to

probe only the peak of two absorption features.

5.1.3 Line Selection Three criteria were employed to select the specific H2O transitions for use in the

sensor:

(1) Large spread in lower-state energy (E”) – To achieve good sensitivity over a

broad range of possible operating conditions and enable sensing of LOS non-

uniformity in the scramjet, it was important to select features with a large spread in

E”. The lower-state energy determines the equilibrium molecular population in

the un-excited state for a transition as a function of temperature, and thus describes

how the absorption strength of a particular transition varies with temperature. For

the expected range of temperatures in the scramjet (~600 K to 1700 K), absorption

features with E” near 0 cm-1, 1000 cm-1, 2000 cm-1, 3000 cm-1 were targeted.

(2) 10% to 40% absorption – As mentioned in Section 2.3.2, the 2f signal increases

with optical depth. Though this introduces the need for iteration when comparing

the measurement with the model to infer gas properties, the gains in SNR can be

important for very harsh environments.

85

(3) Wavelength separation must be greater than 15nm or less than ~5nm – This

requirement is imposed by the hybrid-demultiplexing system. Features greater

than 15 nm apart can be separated by the grating onto separate detectors, and

features closer than 5 nm can be focused onto the same detector and frequency-

demultiplexed.

Figure 5.3 shows the location of the final selected absorption transitions in terms of

wavelength, and Table 5.1 summarizes the feature locations, lower-state energies, and

linestrengths. The CO2 feature near 2.0 μm was selected based on past work by

Webber et al. [67]. Their search revealed that the R(50) line of the 20012 00001

band delivered the best combination of linestrength, E”, and avoidance of H2O

absorption interference for measurements in combustion environments.

Figure 5.3: Selected H2O and CO2 transitions.

Table 5.1: Summary of selected H2O and CO2 transitions. Wavelength

nm Frequency

cm-1 Molecule Lower-state Energy

cm-1 Linestrength (296 K)

cm-2atm-1 1468.9 6807.8 H2O 3319 6.48(10)-7 1391.7 7185.6 H2O 1045 1.91(10)-2 1387.9 7205.2 H2O 79 2.29(10)-1 1343.3 7444.4 H2O 1790 1.10(10)-3 1338.3 7472.2 H2O 2952 2.78(10)-6 1996.9 5007.8 CO2 994 1.36(10)-3

The spectral parameters for the target H2O transitions (linestrength, H2O-, CO2-,

air-broadening coefficients and temperature exponents), were measured in the

laboratory according to the procedures in [37]. The lower-state energy was taken from

1300 1350 1400 1450 1500 1950 2000

65431

H2O transitions CO2 transitions

Wavelength (nm)

2

86

HITRAN 2004 [22]. Spectral parameters for the CO2 transition were taken from

measurements by Toth et al. [74] and Webber et al. [67].

5.1.4 Validation The sensor was then validated against known temperatures from 600 K to 1515 K

in a high-uniformity tube furnace and a uniform flat flame burner. The furnace

validations were performed using a quartz cell with a 76 cm pathlength in the same

furnace used for the measurements of Chapter 3. A mixture of 1.7% water vapor in air

was prepared so that the overall absorbance levels would be similar to those expected

for the pathlength and water concentration during full combustion at the measurement

location in the scramjet. The cell pressure was maintained at 0.7 atm, which is also

similar to the scramjet measurement conditions.

The burner validations were performed in a stable, uniform flat flame burner

operating on ethylene and air at 1 atm. Premixed gases are passed through a water-

cooled metal honeycomb matrix, and the flame stabilizes just above the matrix. The

flame measures 25.65 cm by ~2.5 cm. The laser beam is passed just above the flame

along the long dimension of the burner. The temperature at the beam location is

measured using a radiation-corrected thermocouple and water concentration is

determined using an independent, previously-validated laser measurement.

The results of the temperature validation are shown in the upper panel of Figure 5.4.

The inferred temperatures using three different ratios are reported. The 1392/1469 nm

ratio is used in this chapter for measurements that are compared with CFD. The

1388/1338 nm and 1343/1338 nm ratios are used in Chapter 6 to sense LOS non-

uniformity. The RMS error for the temperature measurements is 1.5% for the

1388/1338 nm ratio, 2.8% for the 1343/1338 nm ratio, and 4.2% for the 1392/1469 nm

ratio. Note the anomalous behavior of the data at 900 K for the 1392/1469 nm ratio

and 1392 nm mole fraction measurement. Excluding this point, the RMS error for the

1392/1469 nm ratio is 3.5%.

The lower panel of Figure 5.4 shows the H2O concentration validation for the 1392

nm feature (used for the lower temperature concentration measurements in Section

87

5.3.1) and the 1469 nm feature (used for the high temperature concentration

measurements in Section 5.3.2). The RMS error is 2.7% for the 1469 nm feature and

9.2% for the 1392 nm feature. If the anomalous point at 900 K is excluded, the RMS

error for the 1392 nm feature becomes 7%.

Figure 5.4: Temperature and H2O concentration validation measurements in a uniform furnace

and flat flame burner.

5.2 Scramjet Facility The scramjet test rig used for this study is located in a high-enthalpy, continuous-

flow, direct-connect supersonic combustion facility at AFRL/WPAFB in Dayton, Ohio

[94]. The facility supplies 13.6 kg/s of air at up to 920 K and 5.2 MPa. A methane-

fueled vitiator further increases the temperature and pressure to the desired

experimental conditions, and oxygen is added to re-establish ambient levels.

Interchangeable facility nozzles accelerate the flow to supersonic speeds. Here, a

Mach-2.84 nozzle simulates flight Mach numbers of 5−5.5, and a distortion-generator

simulates the effects of flight conditions on the combustor inlet [ 95 ]. Further

information on the facility can be found in [94]. A photo of the test rig is shown in

Figure 5.5.

The scramjet flowpath is shown in Figure 5.6. It consists of isolator, combustor,

and expansion sections. The combustor has fuel injector banks in multiple locations

so that many fuel-injection configurations can be tested. For the results shown here,

fuel was injected upstream of a cavity flameholder on the body side of the flowpath.

300

600

900

1200

1500

1800

Furnace

Infe

rred

Tem

pera

ture

(K)

1388/1338 nm ratio 1343/1338 nm ratio 1392/1469 nm ratio

Flat FlameBurner

300 600 900 1200 15000.0

0.5

1.0

1469 nm feature 1392 nm feature

Thermocouple Temperature (K)

x Mea

sure

d / x

Act

ual

88

Additional fuel was added between the cavity and rear-facing step flameholders on

both the body and cowl sides of the flowpath. Overall fuel/air equivalence ratios of

φ = 0.6−0.9 were tested.

Figure 5.5: Photo of the continuous-flow, direct-connect scramjet test rig at AFRL/WPAFB.

Figure 5.6: Schematic of AFRL scramjet flowpath. Large optical access windows allow

measurements at multiple vertical locations in the combustor duct.

The combusting gases continue past the flameholders to the optical measurement

location, which is in the expanding section 16.5 cm upstream of the combustor end

plane. The measurement location is fitted with 2.5 cm x 12 cm quartz optical access

ports. The outward face of each window is wedged to avoid optical interference

effects (etalons) that arise when scanning the laser wavelength in the presence of

parallel optical faces in the beam path. The width of the combustor at the

measurement location, and thus the pathlength of the measurement, is 22.9 cm. The

sensor optics are positioned on optical tables approximately 20 cm from the access

ports to avoid thermal damage and the open beam path between the optics and the

  Wall Thermocouple(Combustor exit)Flow Direction

Optical AccessLaser BeamLocation

Wall Thermocouple(Flameholder)

Static Pressure Taps(Open circles)FlameholdersFuel Injectors

(+ 1 bank on cowl side)

IsolatorDistortion Generator

Body Side

Cowl Side

Combustor

89

windows is enclosed by open-ended tubes with a continuous nitrogen flow to reduce

interference from ambient water vapor. The optical tables are capable of being

vertically scanned simultaneously, allowing measurements at multiple vertical

locations in the 10.2 cm tall combustor duct.

The scramjet flowpath is heavily instrumented with pressure and thermocouple taps,

which are sampled at ~0.9Hz throughout each run.

5.3 Scramjet Results

5.3.1 CO2/H2O Concentration in Vitiated Supersonic

Flow The sensor system was applied to the ground-test scramjet combustor to measure

temperature, and H2O and CO2 concentrations under a variety of operating conditions.

One such condition that was used to test the sensor system was with only the

supersonic flow from the vitiator passing through the combustor duct. The vitiator

consists of a lean methane and air combustion chamber upstream of the expansion

nozzle at the entrance to the scramjet test section. The vitiator increases the incoming

air temperature to ensure that the proper scramjet inlet conditions are met when the

supersonic flow is generated in the expansion nozzle. The lean methane/air mixture

produces a well-known H2O/CO2 ratio.

The laser beam was located at the center of the combustor duct at the measurement

location shown in Figure 5.6. The approximate static pressure at the measurement

location for the vitiator-only condition was 0.26 atm with a static temperature around

600 K. The sensor was tested using both direct absorption and calibration-free WMS

to probe absorption on the R50 transition of CO2, which exhibits less than 2%

absorbance at these conditions. Water-vapor measurements were also made on the

feature near 1392 nm, which was most suitable for concentration measurements in this

temperature range.

Figure 5.7 shows representative results of the H2O and CO2 measurements. The

left panels show a single-scan of CO2 absorption using (a) WMS-2f and (c) direct

90

absorption on consecutive runs of the scramjet test rig. The WMS signal appears

smooth compared to the direct absorption because the lock-in amplifier rejects 1/f

laser noise and electronic noise. Only the peak of the feature is scanned, and the line

shape appears distorted near the beginning and end of the scan due to the sinousoidal

waveform used (instead of a linear ramp). Also shown are the 2f peak value and the

Voigt fit. The 2f peak value and the integrated absorbance extracted from the Voigt fit

are used to infer the CO2 concentration with the WMS and direct-absorption methods

described in Chapter 2, respectively. The right panels show the measured

concentrations in terms of partial pressures for a 0.2 s time period using both of these

methods. The measurement rate is 4 kHz.

Figure 5.7: Comparison of direct-absorption and 2f signals and CO2 partial pressure

measurements in a vitiated supersonic flow using the 1997 nm absorption feature of CO2. The left panels show single-scan data with (a) the WMS-2f and (c) direct-absorption techniques, along with the peak or voigt fit values that are used to calculate the CO2 concentration. The right panels show the measured CO2 partial pressure at 4 kHz using (b) 2f peak magnitudes and (d) integrated absorbances.

The SNR was calculated from the partial pressure data and is defined as the ratio of

the mean partial pressure divided by the standard deviation (after a 200 Hz high-pass

filter is used to remove the actual fluctuations in the system). The SNR of the

calibration-free WMS measurement (13.2) is 4x better than the direct-absorption

measurement (3.2). From the single scan data shown in the left panel one might

expect the difference in SNR to be even larger, however the SNR of the direct-

absorption measurement benefits from the use of a Voigt fit while the WMS relies on

0

2

4

6

0.00

0.02

0.04

0.00

0.01

0.02

Voigt fit

2f S

igna

l

x

2f peak

Par

tial P

ress

ure

(atm

)(c) Direct Absorption Signal

(a) WMS Signal (CO2)

CO2

CO2

(d) Direct Absorption Measurement

Par

tial P

ress

ure

(atm

) (b) WMS Measurement

H2O

SNR=13.2 (CO2)

Wavelength

Abs

orba

nce

0.00 0.05 0.10 0.15 0.200.00

0.02

0.04

Time (s)

SNR=3.2

91

a single (peak) point. The SNR obtained with the WMS measurements is excellent

considering the low CO2 absorbance levels (<2%) and the supersonic nature of the

flow.

In terms of concentration levels, the measured H2O/CO2 ratio using calibration-free

WMS is 1.99, which is within 0.5% of the expected value of 2.00 for the methane-air

vitiated heater.

Taken together, these results confirm the SNR benefits of WMS and show that

accurate results can be obtained with WMS without on-site calibration.

5.3.2 Comparison between LOS Measurements and

3D-CFD in Combusting Supersonic Flow An important consideration for laser-absorption measurements in harsh

environments is the path-integrated nature of the measured quantities, which can be

difficult to interpret when the quantities are non-uniform along the beam path. The

absorption signal for every absorption feature has a different, nonlinear response to

temperature that is determined by the feature’s lower-state energy. For a laser path

with non-uniform temperature, this nonlinear absorption behavior of each feature will

cause the temperature inferred from various pairs of absorption features to differ.

Thus the inferred temperature from a laser measurement in a non-uniform

environment is not simply equal to the path-averaged temperature [90, and more

information in Chapter 6], making direct comparison of LOS laser measurements with

multi-dimensional CFD more difficult.

5.3.2.1 Method for Comparison of CFD and LOS

Measurements Two general methods have been proposed to enable the comparison of CFD and

LOS measurements. The temperature profile method first suggested by Sanders et al.

[91] and explored further in [92] uses the CFD to prescribe a general temperature

profile with several key characteristics (e.g. Twall, Tpeak, etc.) that can be solved from

92

the measured absorption of several absorption features with unique temperature

dependence. This method is difficult to apply in harsh, practical environments

because a large number of features must be probed to accurately determine the non-

uniform profile (particularly for complex profiles), and because measurement noise

can affect convergence of the results. In addition, the influence of pressure and mole

fraction on the calibration-free WMS signals further complicates data processing and

the accuracy of the results.

A simpler method [96], is to use the CFD in combination with the WMS models

from Chapter 2 to calculate the expected WMS signals that would result from a

hypothetical laser measurement through the CFD. The expected signals are then

treated like the measured signals and compared with the WMS model to infer the

expected laser-measured temperature for the CFD. In this way, the effect of non-

uniformity on the nonlinear absorption response of the probed spectral features will be

included in both the measurement and the CFD-calculated expected temperature, and

the results can be directly compared.

The details of the technique are illustrated in Figure 5.8. The CFD data reduction is

shown in the left panel of the figure. The temperature, pressure, H2O and CO2 mole

fractions are first extracted from the CFD calculations for each volume element along

a simulated laser LOS that is matched with the LOS used in the actual experiment.

The absorbance by the laser-probed spectral features is calculated for each volume

element and summed to determine the path-integrated CFD-predicted absorbance.

The WMS models from Section 2.2.3 are then used to simulate the CFD-predicted 2f

and 1f signals for each spectral feature and the ratio of the predicted 2f/1f signals is

taken. Finally, both the predicted ratio and the actual measured ratio from the

corresponding scramjet experiment are reduced to the predicted and laser-measured

temperature using the method is Section 2.2.4.

This technique is much simpler to implement than the temperature-profiling

method because it requires only two absorption features, which significantly reduces

hardware and software complexity. The drawback to this technique is that it reduces

the non-uniform temperature along the laser LOS to a single value, which helps to

93

understand how accurately the CFD model is predicting the actual temperature profile,

but does not recover specific regions of the non-uniform profile.

Figure 5.8: Method for comparison of multi-dimensional CFD with LOS laser measurement.

(a) CFD

Sim. laser path

Extract T, P, xH2O, xCO2 for laser path

Simulate absorbance for non-uniform path

Absorbance

Simulate modulation and lock-in using actual

laser characteristics

2f

Flow

CFD Result

1f

(b) Experiment

Laser Pitch

Detector Catch(opposite side)

Apply lock-in to modulated laser signal

(laser scanned only over peak)

Flow

2f

1f

-5.0 -2.5 0.0 2.5 5.0

0.1

0.20.825

0.850

0.875

P (a

tm)

xT

(K)

Horizontal Location (in.)

800

1600

2400

xCO2

xH2O

P

T

1391.60 1391.65 1391.70 1391.750.00

0.15

0.30

1f M

ag.

Wavelength (nm)

0.00

0.06

0.12

2f M

ag.

1391.60 1391.65 1391.70 1391.750.0

0.1

0.2

0.3

0.4

Abs

orba

nce

Wavelength (nm)

1391.60 1391.65 1391.70 1391.750.00

0.15

0.30

1f M

ag.

Wavelength (nm)

0.00

0.06

0.12

2f M

ag.

Laser light passes through actual T, P, xH2O, xCO2 gradients

Absorption occurs along non-uniform path

Perform identical data reduction on both signals to infer LOS temperature

94

5.3.2.2 Results Example results using this method are shown in Figure 5.9 for the scramjet

combustor at AFRL/WPAFB under full operation on ethylene and air at φ = 0.7. The

laser-measured temperature and H2O partial pressure were inferred using calibration-

free WMS on the 6807.8 cm-1 (E” = 3319 cm-1) and 7185.6 cm-1 (E” = 1045 cm-1)

features at several vertical locations in the combustor duct (represented by the solid

squares). The expected laser-measured values based on 3D CFD calculations of the

flow field are represented by the open circles. Figure 5.9 also shows the regular path-

average temperature based on the 3D CFD (gray line, no symbols). Though the

expected laser-measured temperature is different than the path-average temperature,

the trends are retained very well and show that information about the path-average

temperature can be gained from the laser-measured temperature.

Figure 5.9: Static Temperature and H2O Partial Pressure for different vertical locations in the

scramjet combustor during full operation on ethylene and air. Each point is the LOS laser-measured value for the experiment (solid squares) and the expected LOS laser-measured value from the CFD calculated flow field (open circles). The gray line (no symbols) represents the path-average temperature from the CFD calculated flow field.

The uncertainty bars shown on the experimentally-measured values are the

compound result of the uncertainty estimate in Table 5.2 below, which follows from

the discussion of potential sources of uncertainty in Section 2.3.

-2 -1 0 1 20

500

1000

1500

2000

Infe

rred

Tem

pera

ture

(K)

Vertical Location (in.)

Measurement CFD CFD (path-average)

0.00

0.05

0.10

0.15

H2O

Par

tial P

ress

ure

(atm

)

95

Table 5.2: Estimated uncertainty for calibration-free WMS measurements in the scramjet combustor at AFRL/WPAFB.

Source of Uncertainty Estimated Uncertainty Comment

in TMeas in PH2O,Meas 1. Spectral parameters +/- 4.2% +/- 2.7% Estimated from laboratory validation in

Section 5.1.4 2. Laser tuning characteristics 3. Simulation/experiment wavelength matching Negligible Negligible These effects were carefully-controlled 4. Background absorption 5. Etalon effects 6. WMS model Negligible Negligible Model was properly matched to the

experiment 7. Pressure deviation between simulation and experiment +/-0.35% +/-1.75%

Estimated from simulations based on actual measured pressure variation and CFD-predicted pressure non-uniformity

8. Optical depth and concentration deviation between simulation and experiment

+/-0.06% +/-0.9% Estimated from simulations based on CFD-predicted concentration non-uniformity

Total +/- 4.6% +/- 5.4%

By obtaining data from several vertical locations, some information about the non-

uniform gas properties in the combustor can be retained. For example, the

temperature from the sensor measurement and the CFD agree well in the core flow

region (within 4%). The measurements also indicate a lower temperature than

expected near the top and bottom wall of the combustor. These results might suggest

that the heat loss or turbulence models used in the CFD may be underpredicting mass

and energy transport. The H2O partial pressure measurements in the actual combustor

are ~5-12% lower than predicted by the CFD, which may also indicate that OH to H2O

conversion rate is overpredicted by CFD. For more extensive results and comparison

with other numerical codes and laser techniques, see [96].

Figure 5.9 represents the first quantitative comparison between non-intrusive laser

measurements in the AFRL scramjet and multi-dimensional CFD. Though spatially-

resolved measurements of total temperature have been obtained in the scramjet using a

water-cooled probe that traverses the flowpath [94], these measurements have been

limited to the flow upstream of the combustor. This is due to the difficulty and

expense of producing probes with durable thermocouple elements that work in the

high-temperature reacting environment downstream of the combustor, combined with

the expectation of large, uncertain corrections to the total temperature due to the large

amount of water cooling necessary for sensor survival.

96

97

Chapter 6. Diode Laser Sensing of

Scramjet Combustor Instabilities Thrust is maximized in scramjet engines when fuel is increased to a level just

before the isolator shock train is forced out of the inlet by backpressure due to

combustion [97]. For flight tests and engines operating in a freejet, disgorging the

isolator shock train results in inlet unstart, which causes a significant decrease in

captured air mass by the engine and potentially catastrophic failure. Unstart is a

highly unsteady process, owing to unstable phenomena present in the scramjet near

unstart [ 98 , and references therein]. In terms of the inlet and isolator, several

researchers [98−101] have shown that increasing combustor backpressure eventually

leads to severe boundary-layer separation throughout the inlet, which obstructs the

core flow and causes unstart. Strong pressure oscillations associated with this process

have been measured in the inlet and isolator both before and after unstart [100,101].

The combustor also has strong unsteady characteristics associated with its operation.

Numerical analyses for several configurations of a transverse fuel jet upstream of a

cavity flameholder found several sources of instability – flow disturbances stimulated

by shear-layer instability, injected-jet destabilization by disturbances from the

downstream flameholder, and an unstable Mach reflection formed above the jet due to

flow unsteadiness for cases of strong combustion [102,103]. Unfortunately, no studies

have been performed on the interaction of the combustion process with inlet transients

during unstart. However, all of the instabilities above result in large-scale flow

98

fluctuations which are certain to affect the time-dependent behavior of the combustion

process.

Thus far, research on the detection and control of combustion instability has

focused primarily on subsonic turbulent combustors [104]. NOx emission regulations

on gas turbines have driven the use of fuel-lean stoichiometries. Unfortunately,

operation of turbulent combustors in lean regimes increases susceptibility to

thermoacoustic instabilities [105] and lean blowout [106], both of which result in

large-scale fluctuations in pressure and temperature in the combustor.

The primary methods employed by researchers for detecting and controlling

unstable fluctuations have been acoustic techniques [107,108], light emission from

combustion radicals [109], and line-of-sight (LOS) absorption techniques [110−112].

Each technique offers benefits and drawbacks. Acoustic techniques generally use

low-cost and easy-to-use pressure transducers or microphones but can suffer from a

lack of specificity due to background noise and low spatial resolution. Emission

techniques employ photodetectors, but often lack useful spatial resolution and can

suffer from background-light emission and interference from other species. Line-of-

sight absorption sensors rely on more expensive tunable diode lasers (TDLs) and

turnkey sensor packages are not yet available. However, TDL-LOS techniques have

the potential for selected spatial resolution and, as will be discussed below, can be

designed to detect specific aspects of interest in the flow (such as fluctuations in

localized temperature).

Previous fluctuation sensors based on LOS absorption demonstrated the use of a

near-IR TDL to measure time-resolved temperature from the ratio of water-vapor

absorption at two wavelengths and to actively suppress lean blowout and

thermoacoustic instabilities in a swirl-stabilized combustor [110,111]. The sensor

revealed an increase in low-frequency temperature fluctuations near lean blowout due

to localized flame extinction and re-ignition, and used this warning to actuate a fuel

valve to avoid blowout. Another sensor by Palaghita and Seitzman [112] used an

external-cavity diode laser for pattern factor sensing in a stratified methane-air

combustor. Their sensor measured water-vapor absorption at three wavelengths.

99

Based on the interaction of temperature non-uniformity along the absorption path with

the different nonlinear temperature dependence of each absorption feature, they

defined a non-uniformity parameter that increases with stratification and may provide

a suitable control variable for creating more uniform combustor properties.

In this work [113], the application of a three-wavelength, near-IR diode laser sensor

to a scramjet test rig for measurements during unstart presents two key advances in

fluctuation sensing for combustion instabilities. First, the detection strategy extends

the ideas in [110−112] to create a more robust method. The use of fast temperature

measurements and short-time Fourier transforms (STFTs) to track frequency

components in the flow is made more robust by taking the ratio of STFTs for the

measured temperature of two absorption feature pairs with different temperature

dependences. This ratio reduces sensitivity to degradations in signal-to-noise ratio

(SNR) and to certain combustor transients (e.g. during startup). Furthermore, through

the temperature dependence of the selected absorption features, this ratio can isolate

specific aspects of interest in the flow; e.g. low-frequency fluctuations of low-

temperature non-uniformities along the absorption path1.

The second key advance of this work is the application of an optically-based

fluctuation detection strategy to measurements in a supersonic flow. The travel of

acoustic waves in supersonic flows is complicated by the speed of the moving gases.

Wall pressure measurements are subject to acoustic phenomena in subsonic boundary

layers, while pressure waves emanating from events in the center of the combustor

may not be detected at the wall until they traverse the supersonic gas and strike the

wall downstream of the event. Laser absorption strategies that employ light, however,

are capable of capturing fluctuations along the beam path.

This chapter is presented in two parts. First, the sensor and fluctuation detection

method are introduced. Second, data is shown from a representative stable scramjet

combustor run, and from one in which the isolator shock train was forced upstream of

1 The terms “fluctuation” and “non-uniformity” will be used often throughout the remainder of the chapter. Please note that the term “fluctuation” will be used to describe temporal variations in gas properties (usually temperature), and the term “non-uniformity” will be used to describe spatial variations in gas properties.

100

the engine throat in the direct-connect scramjet rig (termed unstart throughout the

paper). The data show that low-frequency fluctuations of low-temperature non-

uniformities downstream of the combustor flameholders increase several seconds

before unstart. Although the precise cause of these fluctuations is not yet understood,

these fluctuations appear to be a precursor to unstart in scramjets and have potential

for use in control strategies.

6.1 Temperature Fluctuation Detection with

Absorption Spectroscopy This section discusses the use of diode laser-based absorption spectroscopy to

detect frequency-resolved temperature fluctuations in non-uniform gases. The method

can isolate fluctuations in a specific temperature range, for example the lower

temperature gases of a non-uniform region. The method can be further tuned to focus

on high- or low-frequency fluctuations in the temperature range of interest, and made

robust against noise and certain transients by using multiple absorption features.

6.1.1 Detection of Specific Temperature Non-

uniformities This section will describe the method of inferring LOS-average temperature in non-

uniform environments using multiple absorption feature ratios to detect changes in

temperature non-uniformity.

Temperature is inferred from the ratio of 2f/1f signals for two absorption features.

To make sensitive temperature measurements, one must choose absorption features

with different temperature-dependent absorption characteristics. The temperature

response of a particular absorption feature is determined by its lower-state energy (E”).

Absorption features with a low E” absorb strongly at low temperature, when a larger

proportion of molecules populate low-energy states. The same is true for high E”

features at high temperatures. Thus temperature-sensitive ratios are formed with

101

features having widely different E”. The temperature dependence of the three features

used in this work, with E” ranging from 79 to 2952cm-1, are shown in Figure 6.1.

Figure 6.1: Simulated 2f/1f signal for the three probed H2O spectral features. P = 0.85atm, xH2O

= 0.11, L = 23cm. Laser specific characteristics (see Chapter 2): a~0.07cm-1, io~0.10.

When the absorption pathlength is non-uniform, the path-averaged nature of

absorption spectroscopy makes signal interpretation more complex [90−92]. The

nonlinear temperature response of each feature in a particular ratio produces a

different sensitivity of that ratio to low- or high-temperature non-uniformities along

the absorption path. By taking advantage of this characteristic, one can select feature

ratios which are highly sensitive to, for example, low temperature gases in the non-

uniform environment, and feature ratios which are insensitive to low temperature

gases. The difference in the path-averaged inferred temperatures from these ratios will

yield information about the relative magnitude of low-temperature non-uniformities

along the measurement path.

This is illustrated in Figure 6.2, which plots the inferred temperature using two

different ratios for a simulated non-uniform path made up of two regions – one at

600K and one at 1500K. Along the abscissa, the ratio of pathlength at 600K/1500K is

varied. At the left and right ends of the abscissa, the path is uniform at 1500K and

600K, respectively, and the measured temperature using both ratios is identical.

However, for non-uniform cases the inferred temperature using the two absorption

ratios differs – the temperature using a ratio of low E” and a high E” features (labeled

500 1000 1500 20000.0

0.5

1.0

1.5

2.0

2f/1

f Mag

nitu

de

Temperature (K)

1388 nm (E"=79 cm-1) 1343 nm (E"=1790 cm-1) 1338 nm (E"=2952 cm-1)

102

mixed E”) is artificially low, while the temperature using a ratio of two relatively high

E” features (labeled high E”) is less affected. In this case, pockets of low-temperature

gas along the absorption path will affect the inferred temperature using the mixed E”

ratio by as much as 18% more than the inferred temperature using the high E” ratio for

this particular example of non-uniformity. Through careful selection of absorption

feature pairs, the experimentalist can tune the sensor to be responsive to different

types of non-uniformities along the absorption path.

Figure 6.2: Simulated path-averaged inferred temperature using two spectral feature pairs for a

non-uniform absorption path comprised of a section at 600K and a section at 1500K. The portion of the path that is at 600K is varied with the remainder of the path at 1500K.

6.1.2 Detection of Fluctuations in a Flow Field with

Non-uniform Temperature The goal of any sensor is to create a robust, high-contrast signal for the target

measurement property. The sensor signal should be robust in that it responds only to

changes in the target property, and high-contrast in the sense that it undergoes a large

change per unit change in the target property. The goal of the current sensor is to

measure low-frequency fluctuations in the low-temperature non-uniformities of the

scramjet flow. We want to look not just at the boundary layer that is always present,

but rather the instability in that boundary layer, and in the unburned or partially burned

gases in the core flow due to combustor instabilities.

0 25 50 75 100600

900

1200

1500

0

6

12

18

Infe

rred

Tem

pera

ture

(K)

% of Pathlength at 600 K

High E" Feature Pair (Insensitive to Low T)

Mixed E" Feature Pair (Sensitive to Low T)

% D

iffer

ence

Bet

wee

n In

ferr

ed T

empe

ratu

res

103

To achieve this goal, two absorption feature ratios are selected such that one ratio is

sensitive to low-temperature non-uniformities in the flow and the other ratio is not (see

previous section). Next, we design a data-reduction scheme to deliver a robust, high-

contrast signal for low-temperature fluctuations measured with these two absorption

ratios. Since the evolution of temperature in the scramjet engine is nonstationary

(statistics change with time), a frequency-analysis technique that is capable of

capturing the temporal development of the frequency content is necessary. The

simplest of these techniques, and the one used here, is the short-time Fourier transform

(STFT), which is a regular Fourier transform applied to a finite, moving time window

of the signal of interest. If x(t) is the signal of interest, the STFT can be represented

by,

( ) ( )∫−

−⋅=t

t

ifx dexftS

TT ττ τπ2,, (6.1)

where f is frequency. The squared magnitude of the STFT is called a spectrogram and

represents the frequency content of the signal as a function of time. The choice of

integration limits is a trade-off between temporal resolution and frequency resolution –

shorter windows give better temporal resolution, but coarser frequency resolution. For

the data presented in this paper, T (and hence the length of the window) was chosen to

be 0.5 s. Also note that the choice of t as the upper integration limit assumes no

knowledge of future events and thus simulates the behavior of a real-time

implementation of the STFT calculation. Other time-frequency methods could also be

applied to achieve similar results, such as the wavelet transform and Wigner-Ville

distribution [114].

The spectrogram has two key drawbacks from the standpoint of a detection system

for application in control – it is two dimensional, and tracking the time evolution of

individual frequency components in the spectrogram may not deliver strong contrast

for instabilities that do not exhibit a strong pattern at one frequency. It is therefore

useful to create a one-dimensional representation that extracts information from a

range of frequencies. To accomplish this, a range of frequencies of interest is chosen,

fl → fh, and the magnitude of the STFT in that range is summed for each time step.

104

This is normalized by the sum of the magnitude of the STFT at all frequencies to

obtain the fraction of frequency content in the range of interest, F:

( )( )

( )∑∑=

=

= maxsensor

0,,

,,,,, f

f x

f

f xhl

ftS

ftStffF

h

l

T

TT (6.2)

For this work, the interest is in low-frequency temperature fluctuations. Thus the

fraction of frequency content in the range fl = 1Hz → fh = 50Hz is chosen.

Harsh combustion environments contain sporadic noise sources such as window

fouling, periods of heavy beam steering, or beam attenuation from particulates in the

flow. Although these sources are accounted for by 1f-normalization, they can still

degrade signal-to-noise ratios. In addition, startup transients in the scramjet lead to

large-scale uniform temperature fluctuations. These factors can lead to increased

frequency content in the fluctuation measurement that is not caused by fluctuations of

low-temperature non-uniformities. The final step then in creating a robust signal is to

minimize these unwanted influences. This can be achieved by taking the ratio of the

fraction of frequency content, F, created from the measured temperature using the

low-temperature sensitive ratio and the F created from the measured temperature using

the insensitive ratio:

( ) ( )( ) einsensitiv

sensitive T Low

,,,,,,

,,,T

TT

tffFtffF

tffRhl

hlhl = (6.3)

Large-scale uniform temperature fluctuations and degradations to signal-to-noise

ratio will affect both temperature measurements similarly; however fluctuations in

low-temperature non-uniformities will only affect F for the low-temperature sensitive

feature pair. As will be shown in the following section, taking the ratio of F from

1<f<50Hz for the two different measured temperatures eliminates common-mode

transients while retaining the specific low-frequency fluctuations in low-temperature

gases that precede unstart.

Using the method presented above, one is able to directly tune the sensor to detect

only fluctuations of temperature non-uniformity. The experimentalist can choose to

105

look at fluctuations in high or low temperature gases through the choice of absorption

features. The frequency range in the summation of the fractional STFT can be

changed to develop contrast in different frequency windows. Finally, taking the ratio

between two fractional STFTs focuses on fluctuations in temperature non-uniformity

along the absorption path.

6.2 Scramjet Temperature Fluctuation Results The diode laser sensor was used to monitor 99 runs of the ground-test scramjet

combustor at AFRL/WPAFB (both the sensor and scramjet are described in Chapter 5).

Here, an unstable case in which unstart occurs is compared with a representative stable

case to demonstrate the utility of the fluctuation detection method. All operating

parameters for the scramjet are identical for the two cases shown, except the overall

fuel/air equivalence ratio is φ ≈ 0.7 for the stable case and φ ≈ 0.85 for the unstable

case.

The average gas temperatures measured with multiple absorption feature ratios for

the stable and unstable cases are shown in Figure 6.3. Because a long time history is

shown, the measured temperatures have been filtered with a 100-Hz lowpass filter to

suppress outliers that increase the appearance of noise in dense plots.

Figure 6.3: Full run temperature profiles for stable and unstable cases (100-Hz filtered). Inset

shows blowout at full sensor sampling rate (4 kHz).

20 30 40 50400

800

1200

1600

36.75 37.00 37.25400

800

1200

1600

Gas

Tem

pera

ture

(K)

Time (s)

Stable Case, φ=0.7 Unstable Case, φ=0.85

106

Both combustor runs begin with only vitiated air at ~575 K passing the measurement

location. Combustor fuel injection begins at approximately 24 s. No ignition source

was used for these measurements, so the autoignition and flame stabilization process

occurs for 6 − 7 s as the flame develops across the combustor and approaches steady-

state. Gas temperatures appear to plateau for several seconds when a sudden

blowout/re-ignition event occurs for the unstable φ ≈ 0.85 case. The inset of Figure

6.3 shows the blowout/re-ignition event at the full sensor sampling rate of 4 kHz.

After this event the average gas temperature at the measurement location is reduced

for the φ ≈ 0.85 case.

The isolator pressure history for the unstable combustor run is used to compare the

timing of the blowout/re-ignition event with unstart. The scramjet flowpath contains

248 pressure taps that record the unstart by tracking the location of the isolator shock

train. The pressure history is plotted over the entire length of the combustor from the

data acquisition system records just prior to and after inlet unstart in Figure 6.4. At

39.1 s, the pressure rise in the isolator section is evidence that the pre-combustion

shock train is properly located there. The next record at 40.2 s reveals that the steep

pressure rise has moved forward to the distortion generator, indicating the inlet has

unstarted.

Figure 6.4: Pressure recorded for data acquisition sweeps just before and after inlet unstart.

Pressure sampling rate is ~0.9 Hz. The top panel shows the flowpath schematic as it corresponds to the pressure tap readings.

-0.50 -0.25 0.00 0.25 0.50 0.75 1.000

1

2

3

4

5

Sta

tic P

ress

ure

(atm

)

Normalized Distance from Inlet

t = 39.1 s t = 40.2 s

Flowpath

IsolatorDistortionGenerator

107

Due to the ~0.9-Hz pressure-sampling rate, there is an uncertainty in the timing of this

rapid event. In addition, the diode-laser-data system was not digitally synchronized

with the pressure-acquisition system introducing an additional ±0.5 s uncertainty.

Finally, a -0.2 s uncertainty is added to account for acquisition time lag and damping

in the pressure lines between the wall of the combustor and the pressure transducers.

This conservative uncertainty is represented by a 2.3 s window during which the

unstart event occurred, which is plotted over the laser sensor data in Figure 6.5

through Figure 6.7.

Figure 6.5 shows the gas temperature measured with the high E” and the mixed E”

absorption feature pairs during the late-startup transient and unstable combustion

periods. Two key features are evident. First, even accounting for the uncertainty in

the exact timing of the inlet unstart, the blowout occurs before the inlet unstart.

Second, looking at the mixed E” measurement 4.8 s before unstart, one can see a

marked decrease in temperature and an increase in measured temperature fluctuations

that are not as apparent in the high E” measurement. Recall from Figure 6.2 that the

high E” ratio is much less sensitive to low-temperature gases in a non-uniform path

than the mixed E” ratio. This suggests that a marked increase in low-temperature

gases as well as fluctuations in these gases occurs before unstart.

Figure 6.5: Measured temperature with individual absorption feature pairs. Unstart (observed

in wall pressure data) occurred during the gray time window.

Unstart

4.8 s

30 35 40 45 50 550

500

1000

1500

2000

Gas

Tem

pera

ture

(K)

Time (s)

High E" Feature Pair (insensitive to low T)

Mixed E" Feature Pair (sensitive to low T)

108

To quantify this increase, the fractional STFT described in Eq. (6.2) is plotted for

both ratios in Figure 6.6. The increase in frequency content in the 1<f<50Hz range for

the mixed E” ratio is apparent prior to unstart. However, by only examining the mixed

E” line pair, one cannot distinguish between the increased transients during startup and

the onset of the particular instability that proceeds unstart. An arbitrary threshold is

plotted in Figure 6.6 to illustrate this point. At early times, the low-frequency content

is similar in magnitude to when the instability begins. Even for the stable combustor

case (bottom panel of Figure 6.6), the fractional STFT is large during startup transients.

Figure 6.6: Fraction of frequency content in 1<f<50Hz range for an STFT of the temperature

measured with each absorption feature pair.

To distinguish between the increased transients during unstart and the fluctuations

preceding unstart, the ratio between the fractional STFTs using different line pairs is

taken according to Eq. (6.3). This rejects common-mode transients in the two signals

and, as shown in Figure 6.7, increases the contrast of the fluctuations of LOS

temperature non-uniformity. From this figure, the increase in low-frequency

fluctuations in low-temperature gases in the non-uniform combustor exit clearly

begins ~4.8 s before unstart. This phenomenon was recorded for all cases that

experienced unstart, with varying initiation times up to 10 s before unstart. The

blowout/re-ignition event was not always present.

Unstart

30 35 40 45 50 550.00

0.02

0.04

0.06

0.08

F (1

to 5

0 H

z)

Time (s)

Mixed E" Feature Pair (Sensitive to low T)

High E" Feature Pair (Insensitive to low T)

00.00

0.02

0.04

0.06

0.08

Stable Case

Unstable Case

109

Figure 6.7: Ratio between fractional STFT of each absorption feature pair. Note the unstart

time window does not apply to the stable case.

Figure 6.8 shows the average gas temperature plotted with 0.9-Hz static pressure

and wall temperature data near the optical measurement location. No distinct change

is seen in the wall pressure before or after unstart. However, the wall temperature data,

which appears to experience a 6.5 s lag with respect to the laser measurement due to

thermocouple response and wall heat capacity, show inflection points that match with

events in the laser data.

Figure 6.8: Full run gas temperature, wall temperature, and pressure near laser sensor location

for the unstable case. Also shown is the wall temperature near the flameholder, which exhibits time lag, but has inflection points which agree with events measured in the gas temperature.

It is presently unclear what physical processes are causing the increase in low-

frequency fluctuations prior to unstart. As discussed in the introduction, isolator

30 35 40 45 50 550

1

2

3

4

Rat

io o

f Low

Fre

quen

cy C

onte

nt,

R (1

to 5

0 H

z)

Time (s)

Unstable Case Stable Case

Unstart4.8 s

400

800

1200

1600

360

400

440

Gas

Tem

pera

ture

(K)

Time (s)

Flameholder Laser Sensor Location

Wal

l Tem

pera

ture

(K)

20 40 600

1

Pre

ssur

e(a

tm)

6.5 s

6.5 s

FluctuationOnset

CombustionOnset

Blowout

110

boundary-layer growth and separation are associated with unstart as well as several

potential instabilities for transverse fuel jets at increased heat-addition rates.

Interaction between the combustor and isolator is also likely to occur, but has not been

studied. Overall, the likelihood is high for large-scale flow-instabilities to exist during

the unstart process. Because the increase in low-frequency fluctuations begins in

advance of unstart, one can see the potential utility of the ratio of fractional STFT

information from two absorption line pairs as a control variable. The variable could

be used to limit fuel flow to the combustor or modify the distribution of fuel among a

series of injection sites at the onset of fluctuations, and thereby avoid a backpressure-

induced unstart.

111

Chapter 7. Summary and Future

Directions Key advancements in the method and application of wavelength-modulation

spectroscopy (WMS) enabled portable diode laser sensor systems capable of

measurements of temperature and gas concentration in harsh, high-pressure

environments and supersonic flows, often with absorption levels too low and noise

levels too high for traditional direct-absorption techniques. The key advancements fall

into several categories, which are summarized in the following sections.

7.1 Calibration-free WMS for Measurements of Gas

Concentration and Temperature A method was presented for direct comparison of WMS measurements with WMS

models to infer gas temperature and concentration. The method uses laser sources

with synchronous wavelength and intensity modulation, which give rise to a 1f signal

that can be used to normalize the 2f signal for laser intensity. Including laser-specific

tuning characteristics and precise spectral data in the WMS model then allows the

model and measurement to be directly compared, eliminating the need for on-site

calibration using a known mixture or operating condition.

The uncertainties associated with calibration-free WMS in harsh environments

were summarized, and it was shown that pressure can have an important effect on the

112

magnitude of the 2f signal by influencing line shape. The influence of pressure was

studied, yielding the following design rules to aid in optimization of the sensor:

(1) If the pressure and the nominal species concentration are accurately known and

incorporated in the simulations, wavelength modulation at modulation index m =

2.2 can be used to maximize the 2f signal.

(2) If pressure is not well-known in the measurement environment, a modulation

index m > 2.2 should be used to reduce error induced by pressure uncertainty. For

temperature measurements, choosing features with similar L/D (Lorentzian-width

to Doppler-width ratio) and broadening parameters further reduces errors

associated with pressure uncertainty.

The effect of absorption-feature optical depth on the calibration-free WMS method

and uncertainty was also studied. By choosing absorption features with greater optical

depth, it is possible to increase the 2f signal strength and improve SNR, however this

can lead to increased error if the nominal pressure and mole fraction are not well-

known (iteration may be necessary when comparing the measurements and model to

infer gas properties).

7.2 High-pressure, Near-IR Absorption by H2O and

CO2

Direct-absorption and 1f-normalized WMS-2f spectra were reported for the R46

through R54 lines of the 20012 00001 band of CO2 near 2.0 μm at room temperature

and up to 10 atm, and the 7204 cm-1 and 7435 cm-1 regions (near 1.4 μm) of H2O at

700 K and up to 30 atm. The spectra were compared with simulations based on

spectral parameters (such as linestrength, line broadening coefficients, pressure shift,

etc.) from the HITRAN database [22] and more recent measurements in the probed

regions by Toth et al. [74] for CO2 and Liu et al. [37] for H2O. In both cases, the more

recent measurements improve upon the HITRAN database.

The direct-absorption spectra for both H2O and CO2 exhibited non-Lorentzian

behavior at higher densities caused by the breakdown of the impact approximation

113

inherent to the Lorentzian line shape. The effect, which is manifest as a nearly

constant absorption offset across the relatively small spectral regions probed here, was

particularly strong for the CO2 spectra due to their location at the edge of the

absorption band. Modifications to the far wing of the Lorentzian line shape proposed

by Perrin and Hartmann [64] for CO2 and Clough et al. [46] with a modified

coefficient for H2O improved the fit between the measured and simulated spectra.

However, an easy-to-implement, well-validated model for non-Lorentzian effects on

high-pressure CO2 and H2O absorption still does not exist that delivers the low

uncertainty levels necessary for accurate sensing of gas properties with direct

absorption.

The 1f-normalized, WMS-2f spectra for both molecules were shown to be

significantly less influenced by the non-Lorentzian effects, eliminating the need for

corrections to the Lorentzian line shape to obtain good agreement between

measurement and simulation. This is because constant offsets in absorption do not

affect the 2f signal, which is also helpful for environments with strong emission or

interference from broadband absorbing molecules.

A more complete summary of the implications of these high pressure

measurements on diode laser sensor design can be found in Section 3.3.

7.3 A Spark Plug-mounted Diode Laser Sensor for

Measurements of Temperature and H2O in IC

Engines A diode laser sensor for crank angle-resolved measurements of temperature and

water concentration in internal combustion engines was developed. A spark plug-

mounted, short-path (12 mm) optical probe makes the sensor compatible with almost

any IC engine. The use of 1f-normalized, WMS-2f permits the sensor to make

successful measurements not only with short pathlengths, but with ambient levels of

water vapor (1 − 2%) during the compression stroke. The use of large modulation

114

amplitude WMS-2f gives the sensor an effective operating range from 1 to 50 atm and

500 K to 1050 K, with a bandwidth of 7.5 kHz.

The accuracy of the sensor was validated in a static cell, giving RMS errors of less

than 3% in temperature and less than 3.6% in H2O concentration over a wide range of

conditions. Subsequently, the sensor was applied to internal combustion engines

operating in the unfired and fired modes, showing the sensor’s ability to make

meaningful measurements for both IC engine operating conditions. Although

improved SNR is anticipated through probe and sensor technique refinements, the

results obtained with this initial design have confirmed the potential for the sensor to

make measurements of temperature and concentration in situations where other

options to obtain these parameters, such as modeling, would be difficult.

The sensor described in this work also shows potential for application in a wide

variety of other rapidly-varying, harsh environments where high pressures may be

encountered: pulse detonation engines, gas turbines, etc. The sensor’s ability to

sensitively detect low absorbances lends itself to measurements over short pathlengths,

allowing measurements in environments where traditional long-path optical access is

not feasible.

7.4 A Diode Laser Sensor for Temperature, H2O, and

CO2 in a Scramjet Combustor A diode laser sensor was developed and applied to the direct-connect, ground-test

scramjet combustor at AFRL/WPAFB to measure H2O, CO2, and temperature. A

hybrid system that combines wavelength and frequency demultiplexing to distinguish

six lasers probing H2O and CO2 transitions from 1.3 to 2.0 μm was described. The

laser modulation parameters were investigated to determine the optimal combination

for frequency demultiplexing with low noise. It was found that a sine wave which

only scans the laser over the absorption feature peak (instead of a linear ramp that

scans across the entire feature) is the optimal waveform for the low-frequency laser

scan modulation (not to be confused with the modulation at 1f, which is always

sinusoidal).

115

Measurements of CO2 using both direct absorption and 1f-normalized, WMS-2f at

the same operating condition showed a 4x increase in SNR for the WMS

measurements. The measured H2O/CO2 ratio for this condition was within 0.5% of

the expected ratio. A cut of 3D CFD at the laser beam location was compared with the

line-of-sight (LOS) temperature and H2O measurements during full scramjet operation

using a method that takes into account the effect of LOS non-uniformity on the

absorption measurements. The comparisons demonstrate the usefulness of the

calibration-free measurements to elucidate information about multi-dimensional CFD.

7.5 Diode Laser Sensing of Scramjet Combustor

Instabilities A method to detect frequency-resolved temperature fluctuations using a diode laser

sensor was developed and applied to the scramjet test rig at AFRL/WPAFB. Ratios of

measured quantities were taken to isolate the sensor response to low-frequency

fluctuations in temperature non-uniformity along the absorption LOS: The 2f signal

was normalized by the 1f signal to suppress perturbations to laser transmission (i.e.

beam steering, window fouling, scattering, etc.). The LOS-averaged temperature was

inferred using the ratio of absorption on two spectral transitions, which suppresses

variation/fluctuation in water-vapor concentration. Inferring different temperatures

based on pairs of water-vapor features with different sensitivities to low-temperature

non-uniformities along the absorption path enabled differentiation of these non-

uniformities from uniform changes in temperature. A Fourier analysis (STFT) of the

time-resolved temperature provided a measure of the temperature fluctuations.

Summing the magnitude of the STFT of measured temperature in the 1<f<50Hz range

and normalizing by the total sum of the STFT produced a measure of the fraction of

frequency content at low frequency, which provided a monitor of stability. Taking the

ratio of the fraction of low-frequency content for the two measured temperatures with

different sensitivity to non-uniformity focused the sensor specifically on low-

frequency fluctuations in temperature non-uniformity, eliminating sensitivity to

overall temperature fluctuations and to changes in SNR.

116

The ability to make high-bandwidth measurements to capture temperature

fluctuations and the use of spectroscopic line selection to identify non-uniformities of

the temperature in the combustor all serve to confirm the potential of diode-laser

absorption sensors for a wide variety of new control strategies.

The first demonstration of this new diagnostic strategy in the high-speed ducted

flow of the model scramjet at AFRL yielded several interesting

conclusions/observations:

(1) There was a distinct increase in low-frequency fluctuations of low-temperature

non-uniformities in the combustor several seconds before the occurrence of

backpressure-induced unstart.

(2) The onset of fluctuations preceding unstart corresponded to changes in wall

thermocouple measurements in the combustor, which lag the optical sensor by 6.5s.

(3) The specificity and fast time response of this diagnostic strategy confirm its

potential utility as a control variable to adjust combustor flow and fueling

properties to achieve high performance while avoiding backpressure-induced

unstart.

7.6 Future Directions

7.6.1 Investigation of Higher Harmonics for Short-

Pathlength, Low-Absorbance Measurements in

Harsh Environments Though this work has focused entirely on WMS with detection at the first and

second harmonics, wavelength modulation in the presence of an absorption feature

produces detectable signals at higher harmonics as well. For sensing, the even

harmonics are of most interest because, like the 2f signal, they have non-zero values at

line center of an absorption feature (odd harmonics do not exhibit much change at line

center, much like the 1f signal).

117

The higher harmonics have not received extensive attention in the past because

each successive harmonic has less power (signal) than the previous harmonic. Cassidy

and Reid [18] and Kluczynski et al. [35] show that for a Lorentzian line shape, the

maximum attainable signal at line center decreases as 1:0.53:0.35:0.26 for the

2nd:4th:6th:8th harmonics. For most situations, it follows that there is no reason to

pursue detection at higher harmonics.

However, these same researchers have suggested that in the limit that noise on the

WMS signals is dominated by “background” signals (i.e. not due to absorption)

generated by short length etalons in the optical system [35,115] or optical feedback

into the laser [18], there is an advantage to working at higher harmonics. Specifically,

Kluczynski et al. [35,115] developed a model for the effect of etalons on the WMS

background signals and showed that the 4th harmonic background decreases by an

order of magnitude or more from the 2nd harmonic background due to short length

etalons. Since the 4th harmonic signal due to absorption decreases only by a factor of

two, the resulting increase in SNR can be quite large. The findings of Kluczynski et al.

are supported by Gustafson et al. [12,116], who achieved a limit of detection in a

window-equipped graphite furnace (which was subject to short length etalon effects)

using 6th harmonic detection that was 10x better than with 4th harmonic and 100x

better than with 2nd harmonic detection. Cassidy and Reid [18] also noted that the

background due to optical feedback decreased by approximately one order of

magnitude per harmonic.

For the measurements shown in Figure 4.8, it is possible that these etalon effects

are responsible for the repeatable oscillations in the measured temperature. Certainly

if the absorbance is further reduced in future applications of the sensor to this or other

environments, higher harmonic detection should be considered to increase SNR. The

models of Chapter 2 can easily be extended to make calibration-free measurements at

higher harmonics possible.

118

7.6.2 Pressure-independent Calibration-free

Wavelength Modulation Spectroscopy One of the biggest drawbacks to calibration-free WMS is the dependence of the 2f

magnitude on the line shape. This dependence requires the experimentalist to either

measure the pressure, or have another accurate means (such as CFD in certain cases)

to calculate the pressure to be included in the WMS models. A potential source of

uncertainty is introduced if neither is available.

As shown in Figure 2.5 and Figure 2.6, a significant reduction in the line shape

dependence of the 2f signal is achieved if one chooses to over-modulate, that is,

modulate at a larger amplitude than an index of m = 2.2 (which gives the maximum

signal). For all of the work contained in this dissertation, an index near m = 2.2 was

used. Thus, this technique for reducing the ‘non-ideal’ pressure-dependence of the 2f

signal has not yet been demonstrated experimentally.

In addition, Figure 2.6 suggests that choosing absorption features with similar

Lorentzian/Doppler ratios at the measurement condition (or even better, similar

pressure-broadening coefficients and temperature exponents) greatly reduces the

pressure dependence of the ratio of 2f signals for those features and their resulting

temperature measurement. This additional line selection rule has not yet been applied

to the search criteria for new water-vapor absorption features, and may yield a new set

of ‘optimal’ absorption features.

7.6.3 Single Optical Port WMS Measurements

Based on Backscatter Techniques Another important drawback to absorption sensing in harsh environments is the

need for line-of-sight optical access. Developing methods to make measurements

using a single optical port to introduce and recover the light may enable access to new

environments, and would certainly increase the commercial attractiveness of

absorption sensors.

119

With the 1f-normalization technique, very little light must be detected to maintain

sufficient SNR for calibration-free WMS. Figure 7.1 shows an experiment by the

author in a harsh process heater flame used in oil refineries. The 1f signal tracks the

laser intensity incident on the detector after the light passes through the flame (8 ft.

pathlength). Also shown is the corresponding 2f/1f signal for a high-temperature

water-vapor absorption feature. One can see that the SNR on the 2f/1f signal remains

largely unchanged as long as >3 − 4% of the light is collected. Coupled with stronger

lasers and efficient collection optics, calibration-free WMS measurements based on

backscattered light from surfaces within a measurement environment should be

possible.

Figure 7.1: Example WMS measurement in a harsh process heater used in oil refineries. The

2f/1f SNR remains unchanged if the 1f signal is >3-4% of max.

Sensors based on this technique have been demonstrated for standoff detection of

methane leaks at distances up to 30 m [13,20], but are thus far only qualitative in

nature.

19.050 19.075 19.100 19.125 19.1500.0

0.1

0.2

0.3

0.4

0.5

0.0

0.2

0.4

0.6

0.8

1.0 2f/1f Signal

1f M

ag. (

norm

aliz

ed to

max

mag

.)

2f/1

f Mag

nitu

de

Time (s)

1f Signal

120

121

Appendix A. Signal Conditioning One should note that before digital sampling by the data-acquisition boards, proper

conditioning should be performed on the analog detector signal to prevent the hard-to-

detect effects of aliasing (interference) from higher harmonics (3f, 4f, etc.) onto the 2f

and 1f signals. Specifically, the detector output should be sampled at greater than

twice the detector bandwidth (Nyquist sampling theorem). This ensures that the

digitally sampled signal accurately reconstructs the original analog detector signal. If

the Nyquist sampling theorem is not adhered to, frequency components of the detector

signal above the Nyquist frequency (fsampling/2) will appear as lower-frequency

components, potentially interfering with the 2f and 1f signal.

Alternatively, a high-bandwidth detector signal can be analog filtered before digital

sampling in order to eliminate the higher-harmonic signals and allow for a slower

sampling frequency. In this case, an analog filter is selected with a stable passband

between 1f and 2f. The digital sampling rate is then chosen to be greater than twice

the analog filter bandwidth. The group delay properties of the filter must be taken into

account when choosing the analog filter type and bandwidth to avoid causing time

delay between the 1f and 2f signals (which can cause errors in 1f normalization of the

2f signals). For all of the measurements in this dissertation, either the Nyquist

sampling theorem was followed during digital sampling of the detector, or a low-pass

Butterworth-type analog filter with a bandwidth of twice the frequency of the highest

desired harmonic was used in conjunction with a digital sampling rate of 2.5 times the

filter bandwidth. The Butterworth bandwidth was chosen to be twice the frequency of

the highest desired harmonic to avoid time delay issues that occur for Butterworth

122

filters near the frequency cutoff, and to ensure a consistent filter response between the

2f and 1f signals.

123

Appendix B. Measurement Campaigns Throughout my PhD, I took 12 measurement trips, 8 of which were week-long

campaigns to various ‘extra-laboratory’ environments, including several that are not

covered in this dissertation. The following paragraphs are a summary of the lessons-

learned from these trips. The summary assumes that you have developed a sensor and

validated it, and are now preparing for a measurement campaign.

Experiments in the laboratory often involve several iterations of the experimental

setup, data collection methods, and data reduction methods. Measurement campaigns

outside your normal laboratory are difficult and stressful because you must try to

foresee and plan for all the possible issues that might arise. The failure of a single

piece of critical hardware or an overlooked need for a window purge might ruin an

entire measurement campaign, while the equivalent issue during a laboratory

measurement would only require that you run next door to pick up a replacement or

forge a makeshift solution from other objects around the lab. While you cannot

possibly attempt to eliminate and plan for all possible failure modes of a measurement

campaign, there are logical steps that can be followed to reduce the risk of failure.

Begin by planning the goals for the trip. Answer the following two questions:

(1) What would the sponsor like to achieve from the campaign?

(2) What would you like to achieve from the campaign?

In general, the sponsor would like to develop a new measurement capability for their

lab or obtain measurements of some specific conditions of interest, and you would like

to obtain a publication. Though these goals often overlap, they may not always

require the same data.

124

Determine what data needs to be taken during the campaign to achieve these goals.

For example, you might want to compare two different measurement techniques or

sensor configurations at the same condition, and the sponsor will be more interested in

data taken across different conditions with the same sensor. Build a test matrix that

satisfies all goals and iterate with the sponsor. Having a good test matrix beforehand

ensures that you will not miss critical data during the sometimes frantic sessions when

the device you are interrogating is in operation.

Next, build the entire sensor, from laser to acquisition, in the lab. Set the sensor up

on the most similar environment available. For example, the scramjet engine at AFRL

is similar in terms of temperature, pressure, and pathlength to a long flat flame burner.

The conditions in an IC engine can be simulated in a shock tube or a high pressure and

temperature static optical cell.

Take data in the laboratory precisely as you would during the measurement

campaign. How long will each data acquisition run need to be? How much time is

between runs? If the measurements are piggy-backed on another test in the facility,

the timing of the runs may be out of your control and could happen in very rapid

succession. How will the data be triggered? Do you need to sync with other data

acquisition systems at the facility?

In general, it is best to acquire raw detector signals instead of partially-reduced (e.g.

lock-in) signals. You may come up with better reduction methods in the future, or

determine that some aspect of the partially-reduced data is incorrect (e.g. a lock-in

time constant). Store a short piece of raw detector signal from your perfectly working

experiment in the laboratory on your oscilloscope or oscilloscope program. When the

sensor is up and running in the field, you can compare this piece of data with the data

you are obtaining from the sensor to quickly tell if something is amiss.

Next, reduce the laboratory experimental data exactly as you will during or after the

measurement campaign, all the way to the final measured quantity. This exercise will

ensure that you have obtained all of the data that you will need to reduce the signals,

such as pressure or a zero-absorption background.

125

Finally, label every piece of the setup, including BNC cables and optical fibers, so

that the sensor can be set up in exactly the same configuration upon arrival at the test

facility. A little anecdote: on one scramjet campaign I did not label fibers and after

setting up, found that the intensity from one laser was greatly attenuated. Over the

course of several hours, I checked for broken fibers, damaged lasers, bad fiber

connections, etc. and finally found that the arms of a 4x1 fused-fiber multiplexer are

wavelength dependent. Several hours is a long time considering that you often only

have one day to set up the sensor at a test facility.

De-construct and pack the sensor carefully. It goes without saying that you should

have 2 or more of every piece of the sensor setup that is economically-feasible, and

certainly 3 or more of breakable pieces (i.e. optical windows). When shipping, pack

fragile equipment together and vice versa. Create a packing list that describes the

equipment in each case (include this inside each case). This will enable faster packing

for the return trip when the campaign is over, and gives a total cost for insuring each

case. Ship via ‘air’ whenever possible to minimize travel time and handling. Stanford

currently has an agreement with UPS, so UPS air is the preferred method. Bring extra

Stanford shipping labels for each case to use for return shipping since some sponsors

do not have a low-cost agreement with UPS air and will revert to ground. A sample

portion of a packing list that shows what information should be included is below:

Item Case # Quantity Total CostSinglemode fiber (5m) 2 2 1204x1 multiplexer 2 1 7002x2 splitter 2 4 600Multimode fiber (5m) - 600 micron 2 5 5001395 nm laser 2 2 20001376 nm laser 2 1 10001349 nm laser 2 1 1000Fiber attenuator 2 1 200BK7 Windows 2 2 400PDA 400 detector 2 2 600Focusing mirror 2 2 200Flat mirror 2 1 100Sciencetech detector 2 5 3000Sapphire windows - 2 inch 2 4 3200Sapphire windows - 1 inch 2 4 1600

Case Total 15220

126

Include a sheet inside each case that lists who the case is from and who it is

intended for. This covers the possibility that the outside shipping label somehow

comes off (this actually happened). Always hand carry the back-up external hard

drive containing the data home after the campaign.

Last, but certainly not least, Good Luck!

127

Appendix C. An Optical Cell for

Absorption Measurements at High

Temperature and Pressure For the purpose of the H2O measurements shown in Chapter 3, a high-pressure

optical cell capable of gas pressures up to 50 atm and temperatures up to 900 K was

developed to be used in a high-uniformity tube furnace. Since a uniform gas

temperature throughout the entire path is desired, the windows must also be able to

withstand heating to 900 K while remaining sealed. To overcome this challenge, a

sapphire-copper compression seal was developed based on previous designs by Rice et

al. [117] and Hahn [118]. Figure B.1 shows a drawing of the entire cell with a

detailed section view of one of the window bodies. Figure B.2 shows an exploded

view of the window casing.

The Inconel window casing is machined with an internal conical taper. A sapphire

window with the optical axis aligned with the beam path is ground with a matching

taper. Note that both faces of the window that the beam path passes through are also

ground with a 1° wedge to avoid etalons (see Section 2.2.2). A thin conical copper

seal is inserted into the window casing followed by the sapphire window. Another

copper seal is placed on the window and then an Inconel retaining nut with external

threads is tightened onto internal threads in the window casing. The nut compresses

the window against the conical copper seal and window casing and establishes an

128

initial seal. When the cell is filled with a high-pressure gas, the window is forced

more tightly against the copper seal and window casing.

Figure B.1: Drawing of the high-pressure cell with a section view of one of the window bodies.

Figure B.2: Exploded view of the window casing assembly.

In practice, the best seal was achieved by heating the cell above the desired

temperature, filling with a high-pressure gas, and then cooling back to the desired

temperature. The Inconel window casing expands more than the sapphire window, so

as the cell is heated, the high pressure gas forces the window further into the conical

seat. Upon cooling, the window casing contracts around the window generating a

leak-free seal.

The window casing is sealed to the main cell body using a metal-to-metal taper seal

(Figure B.1). Slightly mismatched tapers are machined on the window casing and

within the cell body. When the compression nut is tightened, the mismatched tapers

create a knife-edge seal with extremely high contact pressures.

 

Gas mixture delivery port

High pressure gas mixture

Metal-to-metal taper seal

Sapphire-copper compression seal

Cell body

Window casing 1 cm openaperture

L = 37.6 cm

L = 8.2 cm

 Window Casing

Copper Seals

Sapphire Window

Retaining Nut

Compression Nut

129

The gas mixture is delivered to the cell via commercial 1/4” Inconel tubes (High

Pressure Equipment Company) connected to the each window body. The two window

bodies are connected by a commercial 9/16” Inconel tube (High Pressure Equipment

Company) that makes up most of the 37.6 cm pathlength of the cell. A photo taken

from the end of the tube furnace, looking through the sapphire windows of the cell

during operation at 900 K is shown in Figure B.3.

Figure B.3: Endview of the optical cell during operation at 900 K. The light at the center of the

photo is passing through the sapphire windows of the cell.

This particular window design achieved a good seal through many thermal cycles;

however it did not appear that the design would work for an unlimited number of

cycles (the maximum temperature at which a good seal could be achieved was reduced

by ~10 K per cycle). If a new cell is designed in the future, it should incorporate a

spring washer or other compressible device between the retaining nut and the window

to accommodate thermal expansion and contraction differences between the sapphire

window and the Inconel window casing during thermal cycling. The metal-to-metal

taper seal between the window casing and the main cell body did not exhibit any

degradation during thermal cycling of the cell.

130

131

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