practical applications of laser absorption spectroscopy for aeroengine testing...

PRACTICAL APPLICATIONS OF LASER ABSORPTION

SPECTROSCOPY FOR AEROENGINE TESTING

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

Ian Schultz

June 2014

http://creativecommons.org/licenses/by-nc/3.0/us/

This dissertation is online at: http://purl.stanford.edu/rb827vr6771

© 2014 by Ian Alexander Schultz. All Rights Reserved.

Re-distributed by Stanford University under license with the author.

This work is licensed under a Creative Commons Attribution-Noncommercial 3.0 United States License.

ii



http://purl.stanford.edu/rb827vr6771

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

Ronald Hanson, Primary Adviser


David Davidson


Reginald Mitchell

Approved for the Stanford University Committee on Graduate Studies.

Patricia J. Gumport, Vice Provost for Graduate Education

This signature page was generated electronically upon submission of this dissertation in electronic format. An original signed hard copy of the signature page is on file inUniversity Archives.

iii

Abstract

Reliable air-breathing hypersonic propulsion systems offer the potential to revolu-

tionize aircraft performance in a variety of high-speed aerospace applications through

substantial efficiency gains and hardware cost savings. Supersonic combustion ram-

jet (scramjet) engines are one such device that promise propulsion capabilities up to

about Mach 10. At these speeds, a flight from San Francisco to Paris would take

around an hour. However, before these devices are ever practically realized, consid-

erable technical challenges must be overcome in combustor-inlet interaction, fuel-air

mixing, and coupled turbulent flow/combustion modeling. The growing power of com-

putational tools have accelerated the pace of solving these problems, but the accuracy

of computational approaches can only be validated by rigorous experimental testing.

Thus, there is a need for both facilities capable of creating conditions experienced

during hypersonic flight, as well as diagnostics that can characterize the operation

of those facilities and provide experimental data for the validation of computational

models.

Optical diagnostics such as laser absorption spectroscopy are capable of providing

non-intrusive, in situ measurements of important flow-field parameters such as tem-

perature, velocity, species concentrations, which makes them an invaluable resource

to hypersonic aeroengine researchers. Absorption spectroscopy, in particular, has

benefited from recent advances in laser and optics technology, allowing access to a va-

riety of wavelengths corresponding to absorption transitions of important combustion

species such as O2, H2O, and CO2. Moreover, these sensors only require compact,

low-power laser sources and light can be delivered via fiber-optics, which enables the

v

sensor to more easily integrate with test facility hardware. As a result, laser absorp-

tion spectroscopy has become a workhorse in experimental scramjet research, and has

been applied in test facilities around the world.

Building upon this prior work, here the design and results of several different spec-

troscopic sensors for facility characterization and distinct scramjet operation modes

are presented. Both hydrogen-fueled and hydrocarbon-fueled scramjets are investi-

gated in a variety of geometric configurations. These results comprise the largest

data set of laser absorption spectroscopy measurements within scramjet combustors

published to date, and are a valuable resource for computational researchers who wish

to compare their models with experimental data. A primary drawback of laser ab-

sorption spectroscopy is that some techniques are sensitive to nonuniformity along the

measurement line-of-sight. In highly three-dimensional flows such as within a scramjet

combustor, this can prove to be a considerable hindrance. However, in the work here

particular care has been taken to account for nonuniformity along the measurement

path, and new techniques, including a new approach to wavelength-modulation spec-

troscopy data reduction, have been developed and applied to provide quantitatively

accurate path-integrated measurements in the presence of nonuniformities. Addition-

ally, novel applications of laser absorption spectroscopy are presented, including the

use of absorption data to place an upper bound on the cavity residence time within

a scramjet combustor, and a new sensor design for measuring air temperature in

high-enthalpy facilities by tracking the formation of nitric oxide.

Results include two-dimension spatially-resolved measurements of temperature,

H2O concentration, and velocity downstream of fuel injection in a hydrogen-fueled

Mach 5 scramjet combustor, which reveal combustion progress through the develop-

ment of a high-temperature, water-rich product plume. Measurements are compared

to computational fluid dynamics (CFD) simulations, which reveal some inaccuracies

in the CFD, including a general over-prediction of combustion progress. Additional

tests in a Mach 10 scramjet combustor for measurements of temperature and H2O

concentration downstream of fuel injection identify the presence of driver-gas con-

tamination during the test time in a non-combusting case, and ignition onset during

hydrogen-air combustion experiments. CFD comparisons yield similar results to Mach

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5 testing: there is reasonable agreement between measurements and simulations, but

there is a general over-prediction of extent of combustion by the CFD. The application

of mid-infrared laser absorption sensors for detection of temperature, H2O, CO, and

CO2 concentration in an ethylene-fueled Mach 5 scramjet is also discussed. Results

from field measurements reveal combustion progress with axial progression, however

a large concentrations of the combustion intermediate species CO indicates incom-

plete combustion. Temporal variation in measurements are analyzed and attributed

to unsteady shear-layer interactions in the cavity-flameholder combustor geometry.

Finally, the design, development, and laboratory validation of a mid-infrared nitric

oxide sensor for measuring air temperature at high-temperatures and -pressures is

presented.

This work leverages recent advances in laser hardware and spectroscopic data

processing technology to present a suite of laser absorption diagnostic tools for char-

acterizing performance in aeroengine test environments. The results demonstrate the

usefulness of these sensors for investigating the many competing physical processes

in these complex devices. Moreover, these measurements provide a feedback mecha-

nism for CFD modelers who wish to validate simulation performance, and the sensors

described here can be integrated into other scramjet combustion facilities where the

simplicity and diagnostic power of laser absorption spectroscopy is desirable.

vii

Acknowledgments

Throughout my academic career, I have been exceptionally fortunate to enjoy sup-

port from a wide array of family, friends, mentors, and colleagues who have made my

graduate studies possible. Going all the way back to grade school, I remember all the

encouragement from my teachers to pursue math and science as career possibilities.

Without that early support, I am not sure I would be writing this today. In my un-

dergraduate days at UCLA, Professor Ann Karagozian was always available to discuss

research or life in general, and encouraged me to pursue a Ph.D. at Stanford. My first

taste of research was at UCLA as an undergraduate research assistant with Sophonias

Teshome, then a graduate student. His patience and effort was an important part of

motivating me to advance my career as a scientist. Finally, my roommate through

three years of undergraduate work was James Umali, whose mastery of engineering

coursework pushed me to excel, even if I had to settle for second-best.

Stanford is a particularly special place and I have been lucky to spend five years

of my life studying here. The combination of motivated colleagues, excellent mentors,

and stimulating classes cannot be beat. I owe a debt of gratitude to Professor Hanson,

who took a chance on me straight out of my undergraduate studies and hired me as

a research assistant. He didn’t just teach me how to make spectroscopic sensors, but

more importantly, he showed me how far exacting standards and attention to detail

can take you in research and in life. Professor Hanson’s high expectations certainly

made life challenging at times, but ultimately the skills I have developed as a result

will allow me to succeed in any future endeavor. He truly is a world-class researcher

and I have been lucky to study under his tutelage.

Professor Hanson’s research group has been a pleasure to work in throughout my

viii

time at Stanford, largely due to the wonderful people that it consists of. Not only is

the atmosphere friendly and collegial, but there were nearly constant opportunities to

learn when surrounded by so many intelligent people. In particular, Dr. Jay Jeffries

worked tirelessly to make sure measurement campaigns at remote facilities could

be completed successfully. He has always been available for research advice and a

friendly conversation, and his knowledge of lasers and optics is unparalleled. Dr. Dave

Davidson truly is a shock-tube guru and has been an invaluable resource whenever

issues arose with shock-tube experiments. Chris Goldenstein was an excellent research

partner and travel companion for nearly every field campaign contained in this thesis

(and a few trips that aren’t even here!). His passion for developing new sensors

and techniques is admirable, and his depth of knowledge in wavelength modulation

spectroscopy was crucial to many of our successes. Thanks also to Mitchell Spearrin,

Christopher Strand, Ritobrata Sur, Matthew Campbell, Tom Parise, Yangye Zhu,

Leyen Chang, Brian Lam, Ivo Stranic, Vic Miller, and the rest of the Hanson Group

– I have had the good fortune to work with many great colleagues over the years, and

I will miss afternoon coffee and discussions of our research.

Most of all, though, I would like to thank my family. My parents, Brad and

Debbie, have always been there to help me with studies and provided me with a great

childhood environment where I had the luxury of spending my time doing homework

and playing instead of worrying about the real world. My sister Alene and brother

in-law Tony have constantly inspired me with their creative spirit and easy-going

attitude. My uncles, aunts, cousins and all of the Schultz family has always been

supportive. On my mother’s side, the life my grandparents Suzie and Rene (or Meme

and Papa as I have always called them) have made here in America after emigrating

from Switzerland always been inspirational, and their support has been unconditional.

One last person deserves special mention. Had I never come to Stanford, I would

have never met my girlfriend, Jennifer. She has patiently supported me through late

nights sitting behind the glow of the computer, interrupted movies to respond to

emails, Saturdays at home processing data, and all of the other less-desirable aspects

of being a graduate student. She has never questioned my resolve to finish what I

had started, and her love and support has made my graduate studies infinitely more

ix

enjoyable. I am deeply grateful for her presence in my life, and would like to thank

her for all that she has done.

x

Contents

Abstract v

Acknowledgments viii

1 Introduction and Motivation 1

1.1 Scramjet Engine Development . . . . . . . . . . . . . . . . . . . . . . 1

1.2 The Role of Absorption Spectroscopy . . . . . . . . . . . . . . . . . . 4

1.3 Overview of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2 Spectroscopic Theory 8

2.1 Introduction to Spectroscopic Theory . . . . . . . . . . . . . . . . . . 8

2.2 Direct-Absorption Spectroscopy . . . . . . . . . . . . . . . . . . . . . 9

2.3 Wavelength-Modulation Spectroscopy . . . . . . . . . . . . . . . . . . 14

2.3.1 WMS Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.3.2 Scanned-Wavelength-WMS-2f /1f . . . . . . . . . . . . . . . . 21

2.4 Velocimetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.5 Spectroscopic Sensing in Nonuniform Flows . . . . . . . . . . . . . . 24

2.5.1 In Situ Measurement of Collision Linewidth . . . . . . . . . . 27

2.5.2 Column Density as a Concentration Measurement . . . . . . . 28

2.5.3 Line Selection Principles for Nonuniform Flows . . . . . . . . 29

3 Measurements in a Continuous Flow, H2-Fueled Model Scramjet

Combustor 33

3.1 Sensor Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

xi

3.1.1 Scramjet Facility Description . . . . . . . . . . . . . . . . . . 35

3.1.2 Wavelength Selection and Spectroscopic Model . . . . . . . . . 37

3.1.3 TDLAS Sensor Description . . . . . . . . . . . . . . . . . . . . 39

3.2 Uncertainty Analysis of WMS Measurements . . . . . . . . . . . . . . 42

3.3 TDLAS Measurements: “Configuration A” . . . . . . . . . . . . . . . 44

3.3.1 Φ = 0.17 Equivalence Ratio Combustion Results . . . . . . . . 44

3.3.2 Comparisons of TDLAS Data with CFD Simulations . . . . . 46

3.4 TDLAS Measurements: “Configuration C” . . . . . . . . . . . . . . . 49

3.4.1 Steam Addition Measurements . . . . . . . . . . . . . . . . . . 49

3.4.2 Combustion Measurements . . . . . . . . . . . . . . . . . . . . 51

4 Multispecies Measurements in a Hydrocarbon-Fueled Scramjet Com-

bustor 58

4.1 Mid-IR Absorption Transition Selection . . . . . . . . . . . . . . . . . 60

4.2 Facility Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

4.3 Absorption Spectroscopy Sensor Hardware . . . . . . . . . . . . . . . 64

4.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

4.4.1 Multispecies Combustion Product Measurements . . . . . . . 66

4.4.2 Combustion Unsteadiness . . . . . . . . . . . . . . . . . . . . 70

4.4.3 Transient Measurements Within the Cavity During Flame Ex-

tinction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

5 Hypersonic Scramjet Combustor Measurements Within a Reflected

Shock Tunnel 77

5.1 Hardware Description . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

5.1.1 ATK HyPulse Test Facility . . . . . . . . . . . . . . . . . . . . 79

5.1.2 TDLAS Sensor Layout . . . . . . . . . . . . . . . . . . . . . . 80

5.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

5.2.1 Normalized WMS-2f Signals . . . . . . . . . . . . . . . . . . . 85

5.2.2 Non-combusting Test . . . . . . . . . . . . . . . . . . . . . . . 89

5.2.3 Hydrogen-Air Combustion (θ = 1◦, Φ = 1.31) . . . . . . . . . 91

5.2.4 Hydrogen-Air Combustion (θ = 7.5◦, Φ = 1.03) . . . . . . . . 92

xii

6 Shock Tube Demonstration of a Temperature Sensor for High-T and

-P Air Using NO Absorption 94

6.1 Measurement Methods . . . . . . . . . . . . . . . . . . . . . . . . . . 95

6.1.1 Chemical Equilibrium . . . . . . . . . . . . . . . . . . . . . . 95

6.1.2 Nitric Oxide Absorption Spectrum . . . . . . . . . . . . . . . 97

6.2 Measurement Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

6.2.1 Facility and Sensor Hardware . . . . . . . . . . . . . . . . . . 100

6.2.2 Spectral Characterization . . . . . . . . . . . . . . . . . . . . 102

6.2.3 Thermometer Demonstration . . . . . . . . . . . . . . . . . . 106

7 Summary and Future Work 109

7.1 TDLAS in an H2-Fueled Scramjet . . . . . . . . . . . . . . . . . . . . 109

7.2 Multispecies Measurements in a Scramjet . . . . . . . . . . . . . . . . 111

7.3 Hypersonic Scramjet Combustor Measurements . . . . . . . . . . . . 112

7.4 High-Enthalpy Air Temperature Sensing . . . . . . . . . . . . . . . . 113

7.5 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

7.5.1 High-Bandwidth Measurements in a Hypersonic Test Facility . 114

7.5.2 Facility Characterization via Nitric Oxide Absorption Sensor . 116

7.5.3 TDLAS for Flight Testing . . . . . . . . . . . . . . . . . . . . 116

A A Numerical Solution for Peak-WMS Measurements 118

A.1 The Newton-Raphson Method . . . . . . . . . . . . . . . . . . . . . . 119

A.2 Newton’s Method Applied to WMS . . . . . . . . . . . . . . . . . . . 120

xiii

List of Tables

3.1 Spectroscopic parameters of dominant H2O transitions used in H2-air

combustion UVaSCF experiments . . . . . . . . . . . . . . . . . . . . 37

4.1 Spectroscopic parameters of H2O, CO, and CO2 transitions used in

ethylene-air combustion UVaSCF experiments. . . . . . . . . . . . . . 61

5.1 Experimental flow conditions within the model scramjet combustor for

each of three tests conducted at ATK HyPulse. . . . . . . . . . . . . 85

xiv

List of Figures

1.1 Cartoon diagram of a typical scramjet geometry. . . . . . . . . . . . . 2

2.1 Simulated laser scans to measure direct-absorption lineshapes based

on H2O absorption near 1392 nm over a 10 cm path length at 1000

K, 1 atm, with 10% H2O in air balance. a) Baseline and transmitted

intensity signals. b) Absorbance determined from Beer’s Law using the

ratio of transmitted to baseline intensity. . . . . . . . . . . . . . . . . 10

2.2 Integrated absorbance from two neighboring H2O transitions near 1392

nm, and the total absorbance from the superposition of both. Two

Voigt profiles were simultaneously least-squares fit to the measured

absorbance to obtain the individual integrated absorbances. . . . . . 12

2.3 A simulation of typical incident and transmitted detector signals as

measured by a photodetector in a WMS experiment. The laser output

is slowly scanned in wavelength at 250 Hz over the entire absorption

feature, and simultaneously modulated at 50 kHz with a smaller am-

plitude. The inset image shows a detailed view of the modulation

superposition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.4 WMS lineshape measured using scanned-WMS on an H2O absorption

feature near 2551 nm. Data captured within the University of Vir-

ginia scramjet combustor 4.62 cm downstream of fuel injection in an

ethylene-fueled cavity flameholder configuration. . . . . . . . . . . . . 20

xv

2.5 Experimental measurements and least-squares-fit simulation of the scanned-

WMS-2f /1f lineshape for the H2O absorption transition near 2551 nm.

Data captured within UVaSCF combustor at a point 4.62 cm down-

stream of fuel injection and 9.75 mm from the flame holder cavity wall. 22

2.6 Schematic diagram of a TDLAS sensor for velocity which measured a

Doppler-shifted spectra on an angled beam path, and the un-shifted

spectra on a beam path horizontal to the flow. . . . . . . . . . . . . . 23

2.7 Simulated spectra of absorbance near 1391.7 nm at 1000 K, over a 10

cm path length. The flow speed is 1000 m/s. The solid line corre-

sponds to a path length perpendicular to the flow and the dashed line

corresponds to a Doppler-shifted spectra due to a path length tilted

40◦ from the perpendicular path. . . . . . . . . . . . . . . . . . . . . 24

2.8 Line-of-sight distributions of H2O mole fraction and temperature from

CFD calculations 11.25 mm from the injector side-wall and 7.62 cm

downstream of H2 fuel injection in a scramjet combustor. . . . . . . . 25

2.9 Comparison between the path-integrated absorbance and absorbance

from a uniform distribution of the arithmetic average conditions. Val-

ues are based on CFD calculations 11.25 mm from the injector side-wall

and 7.62 cm downstream of H2 fuel injection in a scramjet combustor.

The arithmetic average pressure over the path length is 0.74 atm. . . 26

2.10 Maximum error in assuming a linear linestrength as a function of tran-

sition lower-state energy for H2O transitions and a temperature range

of 1200 to 1700 K over the LOS. Two distinct cusps are observed where

error in the assumption is minimized. These points represent the opti-

mal low- and high-E” to use in a two-transition sensor over the specified

temperature range. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

2.11 Linestrength plotted against temperature for linear-linestrength lower-

state energies highlighted by red dots in Fig. 2.10. Also shown is the

best-fit linear function to the linestrength over the range of 1200-1700K

considered. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

xvi

3.1 Cartoon diagram of UVaSCF Configurations “A” and “C” with dimen-

sions. Not to scale. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.2 Rendered diagram of the UVaSCF Configuration C with select TDLAS

measurement planes noted. Note fuel injection occurred at x = 0 and

distances are shown normalized to the injector ramp height, H = 6.4

mm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.3 Error in a linear linestrength approximation as a function of mean

temperature across the LOS for the spectroscopic transitions with E ′′ =

1045.1 cm−1 and E ′′ = 3291.2 cm−1 used in the UVaSCF Configuration

A and C experiments. . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.4 Diagram of TDLAS system in relation to UVaSCF facility. . . . . . . 40

3.5 Rendered images of TDLAS optical setup for Configuration A and C

experiments, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . 41

3.6 Single-scan absorbance profile for absorption feature near 1391.7 nm,

measured within the University of Virginia scramjet combustor (Con-

figuration C) using scanned-direct-absorption at a location approxi-

mately 7.62 cm downstream of fuel injection and 4.5 mm from the

injector-side wall. Data was collected during H2-air combustion exper-

iments at equivalence ratio Φ = 0.17. A best-fit Voigt function, used

to measure the empirical collision linewidth, is shown overlaid on top

of measured absorbance. . . . . . . . . . . . . . . . . . . . . . . . . . 42

3.7 WMS 2f, 1f, and 2f /1f signals for the H2O transition near 1391.7 nm

measured in the University of Virginia supersonic combustor (Config-

uration C) at a location approximately 7.62 cm downstream of fuel

injection and 4.5 mm from the injector-side wall. Data was collected

during H2-air combustion experiments at equivalence ratio Φ =0.17. . 43

3.8 TDLAS Measurement results for φ = 0.17 combustion in UVa Com-

bustor Configuration A. a) Water column density, b) Path-averaged

temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

xvii

3.9 Comparisons of TDLAS measurements with CFD simulations using

Jachimowski kinetics model in UVa Combustor Configuration A. a)

Water column density, b) Path-averaged temperature . . . . . . . . . 47

3.10 Comparisons of TDLAS measurements with CFD simulations using

Burke kinetics model in UVa Combustor Configuration A. a) Water

column density, b) Path-averaged temperature . . . . . . . . . . . . . 48

3.11 TDLAS measurement results for the UVa Combustor Configuration C

inlet at x = -10H. a) Water column density b) Path-average temperature 50

3.12 TDLAS measurement results of axial velocity in UVa Combustor Con-

figuration C for a non-combusting case with free-stream steam addition. 51

3.13 TDLAS measurement results compared to CFD simulation for H2-air

combustion at equivalence ratio of Φ = 0.17, facility Configuration C.

a) Water column density b) Path-average temperature . . . . . . . . 53

3.14 TDLAS measurement of axial velocity compared to CFD simulation

for equivalence ratio of Φ = 0.17, facility Configuration C. . . . . . . 54

3.15 TDLAS measurements of H2O column density compared to CARS-

inferred column density for H2-air combustion at equivalence ratio of

Φ = 0.17, facility Configuration C. H2O column density is inferred

from CARS by assuming complete combustion of consumed H2 fuel.

a) Axial position x = 6H b) Axial position x = 18H . . . . . . . . . . 56

3.16 TDLAS measurement results compared to CFD simulation for H2-air

combustion at equivalence ratio of Φ = 0.46, facility Configuration C.

a) Water column density b) Path-average temperature . . . . . . . . 57

4.1 CO, H2O, and CO2 spectra over a large range of infrared wavelengths

at 1500 K. The sensor presented targeted absorption transitions at

wavelengths noted on the figure. . . . . . . . . . . . . . . . . . . . . . 61

4.2 Error in a linear linestrength approximation for selected H2O, CO, and

CO2 transitions as a function of mean temperature across the LOS. . 62

xviii

4.3 Photo of the UVaSCF direct-connect scramjet combustor (left) and car-

toon diagram of the combustor and flame holder cavity configuration

(right, not to scale) with three absorption spectroscopy measurement

planes noted. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

4.4 CO and CO2 sensor hardware layout for hydrocarbon-fueled scramjet

testing. The CO and CO2 lasers were both coupled through a single

fiber and were de-multiplexed with a beam splitter after transmission

through the combustor. . . . . . . . . . . . . . . . . . . . . . . . . . . 65

4.5 H2O sensor hardware layout for hydrocarbon-fueled scramjet testing.

Two distributed feed-back tunable diode lasers were multiplexed onto a

single fiber-optic line for simultaneous temperature and column density

measurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

4.6 Axial pressure traces measured without fuel injection and with ethylene

fuel injection at equivalence ratio of Φ = 0.15 for CO/CO2 testing and

H2O testing. Also shown is a scale drawing of the axial geometry of

the combustor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

4.7 Measurements of CO and H2O temperature at two planes downstream

of fuel injection: a) Plane 2 and b) Plane 1. . . . . . . . . . . . . . . 68

4.8 Measurements of CO, CO2 and H2O column density at two planes

downstream of fuel injection: a) Plane 2 and b) Plane 1. . . . . . . . 70

4.9 Measurements of H2O temperature and column density at three planes

downstream of fuel injection: a) H2O number-density-weighted average

temperature and b) H2O column density. . . . . . . . . . . . . . . . . 71

4.10 Time-history of H2O temperature and column density measurements

from plane 1 at a location 9 mm from the injector-side wall: a) Tem-

perature and b) Temperature-normalized column density, NH2O×T nH2O. 72

4.11 Histogram of column density data from Fig. 4.10, best-fit normal dis-

tribution, and expected normal distribution based on error in best-fit

area. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

xix

4.12 Time history of fixed-WMS measurements during flame extinction: a)

Temperature and b) H2O column density. Both plots show a logis-

tic curve fit to the experimental data and list the best-fit parameters

obtained. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

5.1 Rendered view of inlet and combustor model used for Mach 10 scram-

jet testing at ATK HyPulse. Note the fuel injector ramp seen through

large diagnostic windows and TDLAS hardware 27.6 cm aft of the in-

jector ramp. Forebody not shown. Wedged cover plate shown removed

for visibility of TDLAS system. . . . . . . . . . . . . . . . . . . . . . 79

5.2 Drawing of model scramjet flow path, with three TDLAS measurement

locations noted. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

5.3 Diagram of TDLAS hardware layout for ATK HyPulse measurements. 82

5.4 Detailed view of TDLAS hardware attached to HyPulse model com-

bustor. a) Rendered view b) Photograph . . . . . . . . . . . . . . . . 83

5.5 Cross section view of TDLAS hardware with LOS labeling. . . . . . . 84

5.6 Detailed view of dovetail bracket and 90◦ turning mirror holder (holder

translucent for visualization). A single set screw in the center acts

as a fulcrum against the three bolts threaded into the mirror holder,

allowing for two rotational degrees of freedom. . . . . . . . . . . . . . 84

5.7 Measured 1f -normalized WMS-2f signals before, during and after test

time on absorption feature at 1391.7 nm over LOS 3: a) Non-combusting

mixing case, b) Combustion with angle of attack θ = 1◦, equivalence

ratio Φ = 1.31, c) Combustion with angle of attack θ = 7.5◦, equiv-

alence ratio Φ = 1.03. In each case, fuel flow was initiated at the

beginning of TDLAS data acquisition, 1.5 ms before the arrival of the

test gas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

xx

5.8 Axial pressure distribution snapshots throughout the measurement test

time. Fuel injection occurs at approximately 107 cm, and the TDLAS

measurements were located at 134.6 cm. Also shown is the pressure

time-history for each test at the TDLAS measurement location. a)

Non-combusting mixing case, b) Combustion with angle of attack θ =

1◦, equivalence ratio Φ = 1.31, c) Combustion with angle of attack

θ = 7.5◦, equivalence ratio Φ = 1.03, d) Pressure time-histories at the

TDLAS measurement location. . . . . . . . . . . . . . . . . . . . . . 88

5.9 TDLAS column density measurements from Mach 10 non-combusting

tare test case. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

5.10 TDLAS results for Mach 10 combustion case θ = 1◦, Φ = 1.31 com-

pared with steady-state CFD solutions. a) H2O column density b)

H2O-averaged temperature . . . . . . . . . . . . . . . . . . . . . . . . 92

5.11 TDLAS results for Mach 10 combustion case θ = 7.5◦, Φ = 1.03 com-

pared with steady-state CFD solutions. a) H2O column density b)

H2O-averaged temperature . . . . . . . . . . . . . . . . . . . . . . . . 93

6.1 Air in chemical equilibrium at 50 atm, T = 900 - 3000 K. . . . . . . . 96

6.2 Nitric oxide mole fraction in equilibrium air from 1200 to 3000 K at 15

atm (black) and 150 atm (red). . . . . . . . . . . . . . . . . . . . . . 97

6.3 Characteristic time required for NO to reach equilibrium when forming

from neat air (79% N2, 21% O2). . . . . . . . . . . . . . . . . . . . . 98

6.4 Infrared absorption linestrengths of nitric oxide at 2000 K from 1.5 -

7.5 µm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

6.5 Simulated absorbance spectra of equilibrium nitric oxide near 5.2 µm

at 2000 K and 3000 K; water vapor also simulated at 2000 K, 1000

ppm; L = 10 cm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

6.6 Simulated absorbance and temperature sensitivity at 1927.3 cm−1 from

1400 - 3000 K; P = 50 atm (black) and P = 100 atm (red). . . . . . . 101

6.7 Diagram of sensor hardware for NO measurements through a high-

pressure cell and the Stanford High-Pressure Shock Tube. . . . . . . . 102

xxi

6.8 Room temperature measurements of 1% NO in N2 balance, measured

at various pressures to assess accuracy of Hitemp line parameters and

Voigt lineshape model at elevated gas density. . . . . . . . . . . . . . 104

6.9 Measured and best-fit collision linewidth for NO R(15.5) transition

near 1927.3 cm−1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

6.10 Measured absorption and pressure traces in non-reacting, 2% NO in

N2 balance mixture. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

6.11 Measured temperature versus known temperature across a broad range

of temperatures and pressures. Data points with x-axis error bars were

measured by observing equilibrium formation of NO from mixtures of

N2O, N2, and O2. Remaining data points were measured in fixed-

chemistry mixtures of 2% NO in N2 balance. . . . . . . . . . . . . . . 108

A.1 Graphical representation of Newton’s method for a one-dimensional

function. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

xxii

Chapter 1

Introduction and Motivation

1.1 Hypersonic Propulsion and Scramjet Engine

Development

Supersonic combustion ramjet (scramjet) engines offer a promising avenue to hyper-

sonic aircraft propulsion. A practical scramjet engine may be employed in a variety

of civilian and defense applications, including single-stage-to-orbit space access or ad-

vanced missile and missile intercept technology [1]. Moreover, these devices have no

moving parts and are conceptually simple. From a thermodynamic standpoint, they

are considerably more efficient and have higher specific impulse than rockets, which

are the prevailing hypersonic propulsion system [2].

A cartoon of a typical scramjet geometry is shown in Fig. 1.1. The engine opera-

tion begins by capturing and compressing air through the forebody and inlet. Oblique

shocks through the inlet and isolator sections slow the flow, though it remains super-

sonic, and raise the temperature and pressure. Because supersonic flow is required

after the isolator shock train has slowed the flow, there is a minimum operational

speed for scramjets, generally around Mach 3 or 4. Fuel is injected into the flow at

the combustor, and combustion will occur as the fuel mixes with the shock-heated

supersonic air. The highly energetic flow is then expanded through an exit nozzle to

the atmosphere, providing thrust to the vehicle.

1

2 CHAPTER 1. INTRODUCTION AND MOTIVATION

Forebody Inlet Isolator Combustor Nozzle

Bow Shock

Shock TrainFuel Injection

Mixing and

Combustion

Figure 1.1: Cartoon diagram of a typical scramjet geometry.

Supersonic air-breathing combustion as a means of aeroengine propulsion dates

back to the mid-1940s, when Roy suggested that fuel could be burned in a super-

sonic flow to produce thrust [3]. Since that time, there has been substantial interest

in variants of scramjet engines as propulsion devices for high Mach number flight.

Besides the obvious advantage of such an engine drawing its supply of oxygen from

air, the main benefit of scramjet engines is efficient high-speed combustion [4]. Initial

scramjet research focused on using a standing detonation wave to combust fuel and

oxidizer premixed upstream (e.g. see [3, 5, 6]), however, this approach poses some

significant practical challenges in detonation stability and fuel-air mixing, and there-

fore has somewhat fallen out of favor [7]. In the late 1950s, experiments by Ferri

et al. showed that a steady diffusion flame without standing shocks could be main-

tained in a supersonic flow [8]. Since then, a great deal of research has been focused

on these “mixing-controlled” supersonic combustors, which have become synonymous

with scramjets [9].

Despite over 50 years of scramjet research, practical devices remain elusive, and

flight tests have been limited to a handful of experiments [10]. In particular, combustor-

inlet interactions and challenges in fuel-air mixing have frustrated progress. The

1.1. SCRAMJET ENGINE DEVELOPMENT 3

pressure rise due to combustion can push the shock train upstream and out of the

combustor inlet, causing a potentially catastrophic failure known as unstart [11, 12].

Additionally, because combustion chemistry occurs over the same time scales as mass

transport and mixing in a supersonic flow, sufficient mixing is difficult to achieve

in these combustors [13]. Both of these problems can be mitigated by adding extra

length to the combustor, in the form of an isolator section placed between the nozzle

and combustor inlet, and by making the combustor section itself longer [14, 15]. How-

ever, the drag on the system is a function of the internal surface area, and therefore

in order for the engine to generate the maximum amount of thrust, the needs for

combustor isolation and sufficient mixing must be balanced with demand for overall

engine performance [16]. Optimizing the system for these competing effects is an

ongoing process, and the substantial advantages associated with scramjet propulsion

continue to compel researchers to search for solutions to these problems.

As computational power has grown and and new algorithms for numerical solutions

to the Navier-Stokes equations have been developed, computational fluid dynamics

(CFD) approaches to scramjet analysis have become popular. From its early days

when only inlet models were considered accurate, this field has matured to enable

complete simulation of an entire engine flowpath [17–19]. With these capabilities,

CFD has emerged as a robust design and analysis tool for scramjet engine develop-

ment, and can be used for low-cost parameter optimization and engine performance

estimates. However, several technical challenges make CFD modeling difficult. Thor-

ough and computationally-efficient modeling of the interaction between turbulence

and combustion chemistry, in particular, remains an active area of research [19, 20].

This can lead to considerable divergences between predictions from the computational

model and experimental measurements [20, 21]. Although there is substantial power

in CFD modeling, the accuracy of these models must be tested and quantified through

comparison with experiments [22]. Thus, primary challenges in scramjet technology

include development of more accurate computational tools and sophisticated non-

intrusive diagnostics to better understand complex flow physics [10].


1.2 The Role of Absorption Spectroscopy

There are many different diagnostic choices for investigating hypersonic flow and

combustion physics, each with its own advantages and drawbacks. Invasive probes

such as thermocouples are simple to operate, but they may perturb the flow through

either flow disturbance, catalysis, or altering thermal behavior [23]. Probes are also

difficult to engineer for survival in the harsh conditions encountered within a scram-

jet. For these reasons, optical diagnostics have become a popular alternative, since

they are generally non-invasive and thus there almost no risk of the sensor altering

the thermochemical behavior of the probed system. Optical sensors are capable of

providing measurements of a variety of relevant thermodynamic properties and of-

fer good spatial and temporal resolution that allow investigation of phenomena such

as boundary-layer development [24], recirculation zones [25], and combustor unstart

[26]. A detailed review of many optical diagnostics is given in Ref. [27], but popular

choices for scramjet research have included planar laser-induced fluorescence (PLIF)

[28–30], coherent anti-Stokes Raman spectroscopy (CARS) [31–33], particle image

velocimetry (PIV) [34, 35], and laser absorption spectroscopy (LAS) [36], which is

the focus of this dissertation.

As with PLIF, CARS, and PIV, absorption spectroscopy provides non-intrusive,

in situ measurements of important flowfield properties such as temperature, density,

composition, and velocity. However, these other diagnostics require extensive optical

hardware, large, high-power lasers, and complicated data processing schemes. Con-

versely, an entire LAS sensor can be placed on a small table top area and the basic

theory of LAS measurements is relatively intuitive. Room-temperature diode lasers

in particular have been used extensively for measurements of combustion product

species [37–43]. Combustion sensing has profited greatly from technological develop-

ment in the telecommunications industry of tunable diode lasers and optics in the

region of 1.3 µm to 2.5 µm. These lasers have enabled low-cost access to absorp-

tion transitions of a variety of species important to combustion problems, and given

rise to the field of tunable diode laser absorption spectroscopy (TDLAS) [39, 44, 45].

TDLAS sensors utilizing this technology are portable, rugged, and highly versatile,

1.3. OVERVIEW OF THESIS 5

which makes them ideal for transporting to remote facilities for field testing. As such,

TDLAS sensors have been used extensively in aeroengine and scramjet research.

Diode laser sensors were first proposed and developed for aeroengine applications

in the early 1990s [46–49] and applied in practical test facilities later that decade

[50, 51]. Since then, laser absorption sensors have been used extensively as a char-

acterization tool for both scramjet combustion and facility operation. Sensors have

been developed for O2, H2O, CH4, CO, and CO2 concentration [25, 52–56], as well as

pressure [57, 58], velocity [37, 59], temperature [60–62], and mass flux [37, 63]. These

measurements have provided a variety of important insights into scramjet operation,

and are a valuable resource for CFD researchers who need this data to validate their

computational models.

1.3 Overview of Thesis

The work presented in this thesis aims to build upon the existing body of work in

laser absorption sensing for scramjet testing by presenting development and results

of several new sensors, each utilizing state-of-the-art technologies to improve mea-

surement capabilities in practical conditions. The result is an extensive database of

measurements that provides a new resource for hypersonic combustion researchers.

The dissertation is organized as follows:

1. Chapter 1 motivates the use of laser absorption spectroscopy for hy-

personic scramjet research by presenting a review of the engine de-

velopment process. A description of scramjet operation and a brief review

of historical scramjet development is provided. The role of laser absorption

spectroscopy and other optical diagnostics as a feedback mechanism for com-

putational modeling is discussed. Finally, the advantages of absorption sensing

for practical combustion systems are presented, and the prior work is reviewed.


2. Chapter 2 presents fundamental theory used in laser absorption spec-

troscopy sensors. Equations for modeling direct-absorption and wavelength-

modulation-spectroscopy are presented, and the process of converting absorp-

tion to measurements of temperature, concentration, and velocity is discussed.

Considerations for measurements though nonuniform flows are reviewed.

3. Chapter 3 contains measurements using a spatially-resolved TDLAS

sensor for temperature, velocity, and water vapor in a hydrogen-

fueled scramjet combustor. Two unique combustor geometries are studied.

In each, the TDLAS line-of-sight is sequentially scanned across and along the

combustor to provide two-dimensional spatial resolution, which illuminates the

development of the combustion product plume with downstream progression.

Measurements are compared to CFD calculations as part of a collaborative effort

between numerical modelers and experimental diagnosticians.

4. Chapter 4 describes absorption measurements of temperature, H2O,

CO, and CO2 in an hydrocarbon-fueled scramjet combustor. The sen-

sor utilizes recently-available diode and quantum-cascade laser sources to af-

ford access to fundamental band transitions of the targeted species in the mid-

infrared. This new technology, coupled with the application of newly-proposed

scanned-wavelength-modulation spectroscopy data processing techniques, yields

exceptional measurement fidelity.

5. Chapter 5 reports the implementation of a TDLAS sensor for tem-

perature and H2O concentration in a hypervelocity model scramjet

combustor. Spatially resolved measurements across three lines-of-sight down-

stream of hydrogen fuel injection are presented. This sensor provides the first

TDLAS measurements in a hypervelocity scramjet combustor that thoroughly

accounts for nonuniformity in temperature and composition along the measure-

ment line-of-sight.

6. Chapter 6 summarizes the development of a new temperature sen-

sor for high-temperature and -pressure air facility characterization

1.3. OVERVIEW OF THESIS 7

using nitric oxide absorption. The proposed sensor relies upon equilibrium

formation of NO at high temperatures to provide temperature-sensitive absorp-

tion measurements. Measurements of NO spectral parameters provide a needed

characterization for accurate quantitative temperature measurements. A shock-

tube demonstration of the temperature sensing capabilities is presented.

7. Chapter 7 summarizes the results of this thesis and presents possible

avenues for future work.

Chapter 2

Spectroscopic Theory

2.1 Introduction to Spectroscopic Theory

Diagnostic methods used in this thesis rely on absorption spectroscopy, which is the

process of inferring physical properties from the attenuation of light due to atomic

or molecular absorption. At the heart of this process lies the model used to connect

measured signals to gas properties. Thus, this chapter will outline models of spec-

troscopic absorption, lineshapes, and signal processing techniques with the aim of

providing a foundation for practical measurements in harsh combustion conditions.

First, a discussion is presented of the fundamentals of absorption as well direct-

absorption spectroscopy, which is a simple and intuitive measurement technique.

Next, the direct-absorption technique is extended to show how wavelength-modulation

spectroscopy can be used to increase signal-to-noise ratio of measurements. A descrip-

tion of how spectroscopic techniques can be used to make measurements of axial flow

velocity is given. Finally, because effects of nonuniformity can drastically alter the

proper interpretation of absorption signals, the transition selection and data process-

ing approaches adopted for sensing through nonuniform conditions are discussed.

8

2.2. DIRECT-ABSORPTION SPECTROSCOPY 9

2.2 Direct-Absorption Spectroscopy

Direct-absorption spectroscopy is a simple and intuitive technique that offers fewer op-

portunities for mistakes than more complicated strategies. Therefore, direct-absorption

is very attractive when absorption signals are large and the signal-to-noise ratio is

high. In direct-absorption, the laser wavelength is tuned over a large wavelength range

in order to capture the entire absorption feature. The transmitted light is then atten-

uated as the wavelength is scanned across an absorption feature of the test gas. The

relationship between the ratio of transmitted to incident light and the thermophysical

properties of the absorbing gas is given by Beer’s Law, shown in Eq. (2.1).(ItI0

)ν

= exp (−αν) (2.1)

The left-hand side of Eq. (2.1) is the ratio of transmitted (It) to incident (I0) light

intensity at optical frequency ν, and inside the exponential on the right-hand side

is the absorbance at frequency ν, αν . Simulations of incident and transmitted laser

intensities are shown in Fig. 2.1a. In practice, the transmitted intensity is usu-

ally measured, and the incident intensity is then inferred by fitting a baseline curve

through the non-absorbing region of the laser scan (e.g., the incident intensity in Fig.

2.1a is accurately recovered by fitting a sinusoid to the non-absorbing regions of the

transmitted intensity curve).

The absorbance term in the right-hand side of Eq. (2.1) is described by a path-

integral of the product of several terms over the optical line-of-sight (LOS), L, shown

in Eq. (2.2)

αν =

∫ L

0

S (T )niφ (ν, T, P, χ) dl (2.2)

The terms under the integral are the linestrength S at temperature T of the probed

absorption transition, the number density n of absorbing species i, and a lineshape

function which depends on the temperature, pressure P , gas composition χ, and

optical frequency ν.

In modeling the lineshape function, there are two types of line-broadening that

are often primary contributors in combustion applications: Doppler and collisional

10 CHAPTER 2. SPECTROSCOPIC THEORY

0 2 4 6 8 100

1

2

3

4

Time, ms

De

tecto

r S

ign

al, V

olts

Incident Laser Intensity, I0

Transmitted Laser Intensity, It

0 2 4 6 8 100

0.1

0.2

0.3

0.4

Time, ms

Ab

so

rba

nce

a)

b)

Figure 2.1: Simulated laser scans to measure direct-absorption lineshapes based onH2O absorption near 1392 nm over a 10 cm path length at 1000 K, 1 atm, with 10%H2O in air balance. a) Baseline and transmitted intensity signals. b) Absorbancedetermined from Beer’s Law using the ratio of transmitted to baseline intensity.

broadening. Doppler broadening occurs when the absorbing molecule has a velocity

component in the direction of the propagating light, which alters the frequency of

the absorption feature. This effect is inhomogeneous in frequency, and the Doppler

lineshape function is modeled as a Gaussian profile. Collisional broadening occurs

when molecules in the absorbing gas transfer energy during collisions. Heuristically,

the collisional broadening of the lineshape is due to greater uncertainty in the energy

of the transition. Because collisions occur uniformly to all molecules, this type of

broadening is termed homogeneous and is modeled by a Lorentzian lineshape. Often,

both the Doppler lineshape φD and the collision lineshape φC broaden an absorption

feature substantially. In this case, the combined lineshape function, termed the Voigt

profile, is given by the convolution of the Doppler and collisional lineshape, as shown


in Eq. (2.3). Additionally, accurate numerical approximations of the Voigt profile

speed up computations when Voigt profiles are used in practice [64].

φV (ν) =

∫ ∞−∞

φD (u)φC (ν − u) du (2.3)

However, at times modeling the broadening accurately can prove particularly chal-

lenging. For this reason it is desirable to eliminate the lineshape function from calcu-

lations when possible. This is possible by integrating the absorption over all optical

frequencies, since the lineshape function is defined to have an area of unity. The

resulting value is termed the integrated absorbance, A, shown in Eq. (2.4).

A =

∫ +∞

−∞ανdν =

∫ L

0

S (T )nidl (2.4)

Figure 2.2 shows the absorbance in a case where the spectra of two features are

blended together. The individual integrated absorbances for each feature, also shown

in Fig. 2.2 as the shaded regions, were obtained by simultaneously fitting two Voigt

profiles to the measured absorption. In this way direct-absorption spectroscopy can

be applied to substantially blended absorption features.

The integrated absorbance cannot be simplified any further than as shown in

Eq. (2.4) without assumptions regarding conditions along the measurement LOS. If

temperature and species number density are constant along the LOS, the integrated

absorbance is simply the product of the linestrength, the absorbing species num-

ber density, and the path length. More realistically – particularly in the scramjet

combustor studies in this work – if absorption transitions are selected such that the

linestrength scales linearly with temperature over the range of temperatures across

the LOS, then the linestrength can be removed from the integral in Eq. (2.4) which

is then evaluated at the number-density-weighted average temperature, T ni, defined

in Eq. (2.5) [65]. This assumption is examined in greater detail in Section 2.5.

T ni=

∫ L0niTdl∫ L

0nidl

(2.5)


7185 7185.2 7185.4 7185.6 7185.8 71860

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Frequency, cm−1

Ab

so

rba

nce

Integrated Absorbance, Feature 1

Integrated Absorbance, Feature 2

Total Measured Absorbance

Figure 2.2: Integrated absorbance from two neighboring H2O transitions near 1392nm, and the total absorbance from the superposition of both. Two Voigt profiles weresimultaneously least-squares fit to the measured absorbance to obtain the individualintegrated absorbances.

Column density, Ni, is then defined as the path-integral of number-density along the

LOS in Eq. (2.6), and corresponds to the remaining portion of Eq. (2.4) under the

path-integral.

Ni =

∫ L

0

nidl (2.6)

Similarly, column density can be defined on a mass basis according to Eq. (2.7),

where ρi is the mass-density of species i.

σi =

∫ L

0

ρidl (2.7)

Thus, the integrated absorbance reduces to the product of the linestrength and the


column density, as shown in Eq. (2.8).

A = S(T ni

)Ni (2.8)

Integrated absorbance can be used for thermometry if two different absorption

features are measured. As shown in Eq. (2.9), the column density terms cancel out

of the ratio of integrated absorbance of the two absorption features.

A1

A2

=S1

(T ni

)S2

(T ni

) (2.9)

Equation (2.10) shows that the linestrength function only depends on the gas tem-

perature, T ; the partition function, Q; transition properties including the linecenter

frequency, ν0, and lower-state energy, E ′′; and Boltzmann (k), Planck (h), and speed

of light (c) constant terms.

S (T ) = S (T0)Q (T0)T0Q (T )T

·[1 − exp

(hcν0kT

)]·[

1 − exp

(hcν0kT0

)]−1· exp

[−hcE ′′

k

(1

T− 1

T0

)](2.10)

Based on Eqs. (2.9) and (2.10) there is an explicit solution for the gas temperature,

given by Eq. (2.11).

T =hck

(E ′′2 − E ′′1 )

ln(A1

A2

)+ ln

(S2(T0)S1(T0)

)+ hc

k

(E′′2−E′′

1 )T0

(2.11)

Once the temperature is known, either absorption feature can be used to solve for

the column density from Eq. (2.8). In practice, it is best to solve for the column den-

sity from the integrated area of the absorption absorption feature whose linestrength

varies the least with temperature over the expected operating conditions for a par-

ticular application. For a sensor employing H2O absorption transitions near 1.4 µm

to measure temperature and column density in a scramjet combustor, of the selected

line pair, the absorption feature with the lower E ′′ should be used to solve for column


density once temperature is known.

2.3 Wavelength-Modulation Spectroscopy

In practical combustion applications such as ground-based aeroengine test facilities,

interfering emission and non-absorption losses from mechanical vibration, beam steer-

ing, window fouling, and drifting detector gain can seriously hinder the performance of

direct-absorption spectroscopy sensors. To overcome these challenges, several differ-

ent techniques have been developed to increase the signal-to-noise ratio of of TDLAS

sensors [36, 66, 67]. Wavelength modulation spectroscopy (WMS) is one such tech-

nique that offers a variety of noise-rejection benefits. As presented here, in WMS, a

laser with synchronous intensity and wavelength tuning is modulated over a portion

of an absorption transition, typically at rates of over 100 kHz. Modulation allows for

two advantages of WMS over direct-absorption: it shifts absorption information to

harmonics of the modulation frequency which are well separated from low-frequency

noise sources, drifts and emissions [68], and since all harmonic signals are proportional

to laser intensity, it allows for normalization of one harmonic signal by another, which

accounts for non-absorption losses in transmitted intensity without requiring mea-

surement over the non-absorbing wings of the transition [69]. These advantages make

WMS particularly useful in noisy conditions such as those encountered in a scramjet

combustor, and thus, the work presented here leans heavily on this technique.

However, in practice WMS measurements can be challenging to implement because

WMS signals depend on the transition lineshape, just as absorption at a specific

wavelength will depend on the transition lineshape. In situ signal calibration can be

performed with a known gas mixture at known conditions, however this is cumbersome

and often impractical in many applications. In response to these issues, researchers

have developed “calibration-free” WMS methods to enable absolute measurements of

temperature, concentration, and/or velocity without the need of an on-site reference

at known mixture conditions [70]. Li, et al. [71] originally proposed the model for the

WMS signals based on the laser dynamics during modulation and presented a method

for comparing measured signals to a simulated spectral model. Note, however, even

2.3. WAVELENGTH-MODULATION SPECTROSCOPY 15

these methods require laboratory work to characterize the laser dynamics and spectral

parameters such as linestrength and collision broadening of the probed absorption

transition [72]. Nevertheless, these calibration-free methods have proven quite useful,

and have been implemented successfully in facilities as wide-ranging as ground-based

power plants [73] and gasifiers [74] to advanced aeroengine devices ranging from gas

turbine combustors [75] to pulse-detonation engines [76] and scramjets [26].

The equations used to model the WMS signals are fundamentally similar to those

of the the direct-absorption model discussed previously, however the additional com-

plexity in signal processing tends to obscure some of the fundamentals concepts.

Therefore, for practitioners attempting to harness the improved signal-to-noise char-

acteristics that WMS offers, it is worthwhile to take a slow, methodical approach and

to understand the complete WMS model before attempting to implement a WMS

sensor. While WMS is thoroughly covered elsewhere in the literature [57, 66, 68–

70, 77–79], it is also presented here to preserve the completeness of the measurement

theory in this thesis. First, the model for the laser output intensity and wavelength

is discussed. Next, the Fourier series form of the transmitted laser intensity is pre-

sented. Together, these models allow application of Beer’s Law in a method that is

analogous to direct-absorption spectroscopy.

2.3.1 WMS Model

In WMS measurements, the laser injection current is slowly (compared to the mod-

ulation frequency) scanned over a large amplitude, while an additional sinusoidal

modulation at a higher frequency and smaller amplitude is superimposed on the laser

injection current scan. For a distributed-feedback laser such as those used in the work

here, injection current tuning causes a simultaneous change in both the output laser

frequency and light intensity. Therefore, a detector signal such as the simulated WMS

detector signal in Fig. 2.3, will show both the low- and high-frequency modulation.

Common with all continuous-width laser absorption spectroscopy techniques, WMS


0 1 2 3 4 5 6 7 8 9 100

0.5

1

1.5

2

2.5

3

3.5

4

Time, ms

Dete

cto

r S

ignal, V

olts

Incident Laser Intensity, I0

Transmitted Laser Intensity, It4.5 5 5.5 6

2

2.5

3

3.5

Figure 2.3: A simulation of typical incident and transmitted detector signals as mea-sured by a photodetector in a WMS experiment. The laser output is slowly scannedin wavelength at 250 Hz over the entire absorption feature, and simultaneously mod-ulated at 50 kHz with a smaller amplitude. The inset image shows a detailed view ofthe modulation superposition.

relies upon Beer’s Law, Eq. (2.1). Therefore, to make quantitative WMS measure-

ments, the baseline laser intensity, I0 (t), must either be measured or accurately mod-

eled. Ideally a measurement is used since it will accurately account for any residual

background absorbance or distortions such as etalon reflections in optical compo-

nents. However, here we briefly present an analytical model for the laser frequency

and baseline intensity output, both because it helps illuminate the WMS data reduc-

tion process and because it is useful in cases where the background intensity is not

measured. For distributed-feedback lasers, Eq. (2.12) shows the model of the tun-

ing of the laser frequency via the superposition of scanning and modulation terms,

denoted by the subscripts s and m, respectively, over the laser center-frequency, ν

[80].

ν (t) = ν + νs (t) + νm(t) (2.12)


The scanning and modulation terms are decomposed into superposition of first- and

second-order cosinusoids at frequencies fs and fm, respectively, shown in Eqs. (2.13)

and (2.14).

νs(t) = a1,s cos (2πfst+ Ψ1,s) + a2,s cos (2 · 2πfst+ Ψ2,s) (2.13)

νm (t) = a1,m cos (2πfmt+ Ψ1,m) + a2,m cos (2 · 2πfmt+ Ψ2,m) (2.14)

The a1 and a2 terms are first- and second-order amplitudes (modulation depths) of

frequency cosinusoids, and Ψ1 and Ψ2 are their respective absolute phase-shifts. Note

that higher-order terms are neglected from Eqs. (2.13) and (2.14). Laser baseline

intensity is modeled in a form analogous to the laser frequency; the total intensity is

composed of the superposition of scan and modulation components, as shown in Eq.

(2.15).

I0 (t) = I0,s (t) + I0,m (t) (2.15)

As before, the scan and modulation components are each broken into first- and second-

order cosinusoid terms, with higher-order terms neglected. Their constituent pieces

are written in Eqs. (2.16) and (2.17).

I0,s (t) = I0

(1

2+ i1,s cos (2πfst+ ψ1,s) + i2,s cos (2 · 2πfst+ ψ2,s)

)(2.16)

I0,m (t) = I0

(1

2+ i1,m cos (2πfmt+ ψ1,m) + i2,m cos (2 · 2πfmt+ ψ2,m)

)(2.17)

Here I0 is the average laser intensity over the scan and i1 and i2 are the amplitudes

of the first- and second-order laser intensity terms normalized by I0. Terms ψ1 and

ψ2 are the absolute phase-shifts of the first- and second-order-intensity cosine waves.

Thus the WMS optical frequency and baseline intensity are adequately defined, and

Beer’s law (Eq. (2.1)) can be applied to obtain the expected transmitted intensity,

It(t).

The harmonic terms used in WMS measurements (signals around the 2fm and 1fm


harmonics of the modulation frequency) are modeled using a Fourier series represen-

tation of Eq. (2.1), given in Eq. (2.18). However, it should be noted this model is

a simplified expression that only considers modulation and has no scan component.

Because of this, the model is only valid at one particular point in the scan where

I0, i1,m, ψ1,m, i2,m, and ψ2,m are measured. Usually this point is chosen at the 2fm

peak in order to maximize the absorption signal. Furthermore, the laser wavelength

is assumed to follow a sinusoidal modulation of the form ν (t) = ν + a1,m cos (2πfmt).

It (ν(t))

I0 (ν(t))=∞∑k=0

Hk (ν(t)) cos (k · 2πfmt) (2.18)

Here, the H terms represent the Fourier coefficients used in the expansion. Note, too,

that because only modulation is considered in this expression, the baseline intensity is

written as I0 (t) = I0 (1 + i1,m cos (2πfmt+ ψ1,m) + i2,m cos (2 · 2πfmt+ ψ2,m)). The

Fourier coefficients are determined from Beer’s Law and given in Eqs. (2.19) and

(2.20).

H0(T, P, χ, ν) =1

2π

∫ π

−πexp (−α(T, P, χ, ν + a1,m cos θ)) dθ (2.19)

Hk(T, P, χ, ν) =1

π

∫ π

−πexp (−α(T, P, χ, ν + a1,m cos θ)) cos (kθ) dθ (2.20)

The summation term in Eq. (2.18) can then be written out over the first five

harmonic terms (k = 0 − 4) and combined using trigonometric identities. Each term

in the resulting expression is in the form of a coefficient multiplied by a cosine or sine


wave at harmonics of the modulation frequencies, as shown in Eq. (2.21).

It (ν(t))

I0 (ν(t))= H0 +

H1

2cosψ1 +H2i2 cosψ2

+ cos(2πft)

[H1 +H0i1 cosψ1 +

H1i22

cosψ2 +H2i1

2cosψ1 +

H3i22

cosψ2

]+ sin(2πft)

[H0i1 sinψ1 +

H1i22

sinψ2 −H2i1

2sinψ1 −

H3i22

sinψ2

]+ cos(2 · 2πft)

[H2 +H0i2 cosψ2 +

H1i12

cosψ1 +H3i1

2cosψ1 +

H4i22

cosψ2

]+ sin(2 · 2πft)

[H0i2 sinψ2 +

H1i12

sinψ1 −H3i1

2sinψ1 −

H4i22

sinψ2

]+ Higher-order harmonic terms (2.21)

All terms above neglect the subscript m indicating a modulation parameter, because

there are no scan terms considered. By lock-in filtering the ratio of transmitted to

baseline signal at the first and second harmonics of the modulation frequency, the

individual frequency components of Eq. (2.21) can be isolated. The phase of this

signal is given by the sine and cosine terms in Eq. (2.21), which are defined as the X

and Y components of the WMS signal, given in Eqs. (2.22) to (2.25).

X1f =1

2

[H1 + i1

(H0 +

H2

2

)cosψ1 +

i22

(H1 +H3) cosψ2

](2.22)

Y1f = −1

2

[i1

(H0 −

H2

2

)sinψ1 +

i22

(H1 −H3) sinψ2

](2.23)

X2f =1

2

[H2 +

i12

(H1 +H3) cosψ1 + i2

(H0 +

H4

2

)cosψ2

](2.24)

Y2f = −1

2

[i12

(H1 −H3) sinψ1 + i2

(H0 −

H4

2

)sinψ2

](2.25)

The magnitude of the WMS harmonic signal is then given by the Euclidean norm of

the X and Y phase components, as shown in Eq. (2.26).

Snf =√X2nf + Y 2

nf (2.26)


It was first shown in [81] that for modulation frequency fm, the ratio of the 2fm

to the 1fm WMS signals provides absorption information normalized to account for

non-absorption losses such as beam steering, scattering, and drifting detector gain.

Therefore the final step in the calibration-free WMS model is to divide the 2f har-

monic signal by the 1f , as shown in Eq. (2.27).

S2f/1f =S2f

S1f

(2.27)

The resulting WMS lineshape has a characteristic three-lobe pattern, as shown in Fig.

2.4. The exact shape WMS-2f/1f signal depends on the lineshape of the interrogated

absorption transition, the laser dynamic characteristics, and user choices including

the modulation amplitude, termed the modulation depth, a. Particular care is given

in Refs. [70] and [82] to the selection of the modulation depth that maximizes signal

strength for a particular set of conditions, and readers are referenced to those works

for a thorough discussion of these issues. In practical measurements, some background

3919.9 3919.95 3920 3920.05 3920.1 3920.15 3920.2 3920.250

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

Frequency, cm−1

WM

S−

2f/

1f

Sig

na

l

Figure 2.4: WMS lineshape measured using scanned-WMS on an H2O absorptionfeature near 2551 nm. Data captured within the University of Virginia scramjet com-bustor 4.62 cm downstream of fuel injection in an ethylene-fueled cavity flameholderconfiguration.


signal is commonly observed due to the presence of an absorbing species along the

ambient portions of the optical path length or non-linearity in the laser intensity

modulation not accounted for in Eq. (2.17). The background signal can be subtracted

from the measured signals and the resulting WMS-2f/1f lineshape is given by Eq.

(2.28).

S2f/1f =

√√√√[(X2f

S1f

)meas

−(X2f

S1f

)bg

]2+

[(Y2fS1f

)meas

−(Y2fS1f

)bg

]2(2.28)

2.3.2 Scanned-Wavelength-WMS-2f /1f

While the WMS model described by Eqs. 2.12 to 2.20 is accurate over the entire

absorption lineshape, in the past WMS practitioners have often performed measure-

ments using only the peak-WMS value (the 2f /1f signal at the 2f peak) [74, 83].

This is because the calibration-free models originally proposed in Refs. [70] and [71]

use laser characterization parameters that only apply at a single point along the ab-

sorption feature (usually chosen to be the absorption peak for maximum SNR). More

recently, an extension of this original calibration-free WMS work has been proposed

by Sun, et al. [84] and Goldenstein, et al. [82]. The work in Chapters 4 and 5 here

represent the first applications of this new technique, termed scanned-wavelength-

WMS-2f /1f, within a model scramjet combustor.

The scanned-wavelength-WMS-2f /1f strategy seeks to least-squares fit a sim-

ulated scanned-WMS-2f /1f spectra to the measured scanned-WMS-2f /1f spectra

with the line-center, integrated absorbance, and collision linewidth as free parame-

ters. Signals are transformed into quantitative measurements by first isolating the

WMS-2f and 1f harmonic signals via digital lock-in filtering. The 1f -normalized

2f signal gives the scanned-WMS-2f /1f lineshape, shown in Fig. 2.5. Similarly,

simulated lineshapes are obtained by applying Eq. (2.1) to a measured baseline in-

tensity, and then by applying the lock-in filter to the simulated signal to produce a

simulated scanned-WMS-2f /1f lineshape. (Note a modeled laser intensity such as

that presented in Section. 2.3.1 may be used in this step instead of the measured


baseline intensity.) The simulated 2f /1f lineshape is then least-squares fit to the ex-

perimental 2f /1f lineshape. Figure 2.5 shows the best-fit lineshape for example H2O

absorption data measured within a scramjet combustor, and exemplifies the precision

with which this method replicates measured signals, particularly over the central lobe

of the WMS-2f /1f lineshape containing most of the absorption information. Because

this strategy returns the integrated absorbance from the best-fit lineshape, the species

temperature, concentration, and velocity can be extracted from the measured signals

using the same techniques as presented in Section 2.2 for direct-absorption spec-

troscopy. This technique is important step forward because the collision linewidth

is left as a fitting parameter, and therefore one does not need to impose a collision

broadening model on the simulated spectra, which may be sensitive to nonuniformity

in thermodynamic properties along the LOS. Therefore this technique is an excellent

choice when there may be temperature, pressure, and/or composition nonuniformity

along the LOS and the noise-rejection capabilities of WMS are desirable.

3919.9 3919.95 3920 3920.05 3920.1 3920.15 3920.2 3920.25−0.05

0

0.05

Frequency, cm−1

Resid

ual

0

0.5

1

1.5

2

WM

S−

2f/1f S

ignal

Measured Lineshape

Best−Fit Lineshape

Figure 2.5: Experimental measurements and least-squares-fit simulation of thescanned-WMS-2f /1f lineshape for the H2O absorption transition near 2551 nm. Datacaptured within UVaSCF combustor at a point 4.62 cm downstream of fuel injectionand 9.75 mm from the flame holder cavity wall.

2.4. VELOCIMETRY 23

2.4 Velocimetry

Absorption measurements can also yield velocity through measurement of Doppler

shifted frequency in the line center of the absorption transition. This measurement

is achieved through horizontal reference beam, and a second beam path angled with

a component along the flow direction, as shown in Fig. 2.6. As the angled beam

propagates through the test gas, the bulk flow causes molecular velocities to be dis-

tributed in a non-Maxwellian manner. In high-speed aeroengine applications, the

relatively large magnitude of the flow velocity causes a significant Doppler shift in

the line center frequency of the absorption transition transition lineshape according

to Eq. (2.29).∆ν

ν0=U sin θ

c(2.29)

Here ∆ν is the measured shift in the line center, ν0 is the original line-center position

as measured by the horizontal beam path, U is the flow velocity perpendicular to the

horizontal beam path, θ is the crossing angle of the reference and angled beam, and

c is the speed of light.

Fiber Optics/

Splitter/

Collimating Lens

Laser

Horizontal Beam

Detector Measures 0

Angled Beam Detector

Measures 0-

Test Gas

Flow Direction

Figure 2.6: Schematic diagram of a TDLAS sensor for velocity which measured aDoppler-shifted spectra on an angled beam path, and the un-shifted spectra on abeam path horizontal to the flow.

∆ν may be calculated by either direct-absorption or WMS measurements, from a

comparison of the shift in line-center values corresponding to the peak signals (either


absorption or WMS-2f /1f ) from the reference and angled beams. If the reference

beam is horizontal, there is no Doppler shift to its line-center position because there

is no net velocity component along the beam propagation direction. This is shown

in the simulated horizontal and angled beam absorbances in Fig. 2.7. In WMS

velocimetry, the SNR of measurements is maximized by using a WMS modulation

index of m = 0.9 (defined as the ratio of modulation depth to half-width at half-

maximum of the transition lineshape), which maximizes the magnitude of the WMS-

2f /1f signal [63, 85].

7185.4 7185.5 7185.6 7185.7 7185.80

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Frequency, cm−1

Absorb

ance

Horizontal LOS

LOS Angle θ=40°

Figure 2.7: Simulated spectra of absorbance near 1391.7 nm at 1000 K, over a 10cm path length. The flow speed is 1000 m/s. The solid line corresponds to a pathlength perpendicular to the flow and the dashed line corresponds to a Doppler-shiftedspectra due to a path length tilted 40◦ from the perpendicular path.

2.5 Spectroscopic Sensing in Nonuniform Flows

Undoubtedly, one of the greatest challenges to making accurate laser absorption mea-

surements in many combustion environments is nonuniformity in temperature, pres-

sure, and composition along the laser LOS. This problem is particularly acute in

high-velocity aeroengine applications such as scramjets, where bulk mass transport

2.5. SPECTROSCOPIC SENSING IN NONUNIFORM FLOWS 25

occurs on the same time scales as mixing and chemical reaction. The result is a flow

field with stratified temperature, pressure, and composition. Because absorption is

a nonlinear function of these quantities, care must be taken when interpreting mea-

surements through nonuniform conditions. This section begins by highlighting the

problems this can cause for spectroscopic measurements by using an example. Then

there is a discussion of techniques that have been developed to account for nonuniform

conditions along the flow path.

Figure 2.8, shows CFD simulations of temperature and H2O mole fraction over a

3.6 cm path length, 7.62 cm downstream of fuel injection in an H2-fueled scramjet

combustor [86]. The bimodal plateau over the central 3 cm of the path length corre-

sponds to a “plume” of localized combustion products in the wake of the fuel injector.

Also shown in Fig. 2.8 are the arithmetic averages values over the path length for

temperature and mole fraction. As evident in the figure, significant portions of the

flow vary by more than ±20% of the average value, indicating extreme nonuniformity.

0 0.5 1 1.5 2 2.5 3 3.50

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

H2O

Mole

Fra

ction

Path Distribution

Arithmetic Average

0 0.5 1 1.5 2 2.5 3 3.5600

700

800

900

1000

1100

1200

1300

1400

1500

1600

LOS−direction, cm

Tem

pera

ture

, K

Figure 2.8: Line-of-sight distributions of H2O mole fraction and temperature fromCFD calculations 11.25 mm from the injector side-wall and 7.62 cm downstream ofH2 fuel injection in a scramjet combustor.

To highlight how nonuniform temperature and mole fraction can alter the absorp-

tion spectra from what one would expect based on average conditions across the path,

the distributions from Fig. 2.8 were used to simulate H2O absorbance near 1392 nm


and are shown in Fig. 2.9. Also shown in Fig. 2.9 is the absorbance computed from

the arithmetic averages of temperature, H2O mole fraction, and pressure along the

path length (the average pressure is 0.74 atm). There is a large disparity between

the path-integrated and path-averaged absorbance; at the line center location this

difference is more than 30%. This figure shows that in the presence of nonuniformity,

significant errors will be introduced if the path-integrated data are measured and

subsequently reduced using techniques that assume uniform temperature and mole-

fraction across the path length. To remedy this issue, three important techniques to

account for these nonuniformities in path-integrated spectroscopic measurements are

presented: 1) In situ measurement of the collision linewidth, 2) The adoption of col-

umn density to measure the total amount of absorbing species along the LOS, and 3)

Line selection principles so that a measured temperature is the species number-density

weighted average temperature.

7185 7185.2 7185.4 7185.6 7185.8 71860

0.01

0.02

0.03

0.04

0.05

0.06

0.07

Frequency, cm−1

Ab

so

rba

nce

Path−Integrated

Arithmetic−Averaged

Figure 2.9: Comparison between the path-integrated absorbance and absorbance froma uniform distribution of the arithmetic average conditions. Values are based on CFDcalculations 11.25 mm from the injector side-wall and 7.62 cm downstream of H2 fuelinjection in a scramjet combustor. The arithmetic average pressure over the pathlength is 0.74 atm.


2.5.1 In Situ Measurement of Collision Linewidth

Nonuniformity in composition alters absorption spectra primarily through differing

collisional broadening of transition lineshapes along each differential element of the

laser path length. To properly explain this effect, the Voigt lineshape model must

be developed further. Recall from Eq. (2.3) that the Voigt lineshape function is

modeled as the convolution of Doppler and collision lineshapes. In the Voigt model,

the collision lineshape, φC , is determined by the collision full-width, half-maximum

(FWHM) of the absorption feature, denoted ∆νC . Equation 2.30 shows that the

collision FWHM of an absorption feature of species B can be modeled as a sum of

collision-broadening contributions for each species (the set of species A) in the test

gas.

∆νC = P∑A

χA · 2γB−A (2.30)

Here, γB−A is the collisional broadening coefficient for species B-A collisions where

species B is the absorber. In practice, even a simple hydrogen-air flame contains

enough species that Eq. (2.30) can rapidly become unwieldy. However, one can often

simplify this expression by making a two key assumptions: 1) All minor species can

be neglected if their mole fractions are small, and 2) Sometimes, the collision broad-

ening coefficient γB−A is similar for different collision partners, and when this occurs

collisions with all species that have similar broadening coefficients can be lumped

together. For example, in the combustion products of a H2-air flame, H2O, H2, O2,

N2, and many minor species may all be present. Neglecting minor species, we observe

that, for the near-infrared H2O transitions around 1.4 µm that are studied in this

work, the broadening coefficients between H2O-O2, H2O-H2, and H2O-N2 collisions

are all similar. Therefore, for this example, it is sufficient to model the collision

FWHM as ∆νC = P (χH2O · 2γH2O−H2O + (1 − χH2O) · 2γH2O−N2).

Effects of nonuniformity are introduced to the collision broadening in cases where

γB−A1 is very different than γB−A2 and species A1 and A2 are distributed unevenly

along the LOS. When this occurs, the collision FWHM may vary significantly com-

pared to when the species are assumed to be distributed evenly along the LOS. The

magnitude of this error depends on how different the collision broadening coefficients


are for each nonuniformly distributed species. In many cases, such as within a scram-

jet combustor, there is no way to know the distributions of species along the path

length a priori, and use such distributions to model the expected collision width,

∆νC , contributing to a transition lineshape. Therefore, here we adopt a strategy of

taking direct, in situ in situ measurements of ∆νC . It is shown in Ref. [65] that

this method accurately accounts for the effective lineshape due to nonuniform species

distributions along the LOS.

In the measurements through nonuniform conditions presented in this thesis, the

collisional width was measured in two analogous ways: by scanned direct-absorption

measurements of the transition lineshape and by the lineshape inferred from wavelength-

scanned WMS measurements. The measurements described in Chapter 3 used the

former technique, while the measurements in Chapters 4 and 5 used the latter. In both

cases, the integrated absorbance, A, defined by Eq. (2.4), and the collision FWHM,

∆νC , were free parameters to a Voigt lineshape function that were least-squares fit to

the experimentally-obtained absorption lineshape (either the direct-absorption line-

shape or the wavelength-scanned-WMS-2f /1f lineshape). In this way the collision

linewidth was empirically determined in situ and could be fixed at this measured

value in any subsequent lineshape-sensitive data reduction, such as in converting

peak-WMS-2f /1f signals to temperature and concentration (see Appendix A).

2.5.2 Column Density as a Concentration Measurement

Column density was previously introduced in Section 2.2, Eq. (2.6) as the path-

integrated total number or mass density along a LOS. Although column density is

a well-known form of molecular concentration that is often used in astrophysics [87]

and atmospheric sciences [88], it has not been widely used for aeroengine testing.

However, column density is a natural choice for line-of-sight measurements through

a nonuniform path length, particularly because, like absorption measurement tech-

niques, it effectively “counts” the total number of absorbers along the path length.

When a measurement interrogates an unknown, nonuniform distribution along the

path length, column density is the best representation of molecular concentration as


it makes no assumptions of uniformity or the distribution shape. Additionally, column

density measurements provide an intuitive path to comparison with CFD simulations

that is not sensitive to small variations in boundary conditions.

2.5.3 Line Selection Principles for Nonuniform Flows

Selection of appropriate spectral transitions is critical to the success of any laser ab-

sorption sensor design. As noted previously, temperature is often determined from the

ratio of absorption signals from two separate transitions. The temperature sensitivity

for a ratio of integrated absorbances (see Eq. (2.9)) is given by Eq. (2.31).

d (S1/S2)

dT=

(hc

k

)· (E ′′1 − E ′′2 ) (S1/S2)

T 2(2.31)

Based on Eq. (2.31), it is clear that the maximum temperature sensitivity is obtained

when two transitions are selected with a large difference in lower-state energy, E”.

However, several other practical considerations must be accounted for when selecting

spectral transitions for use in a sensor. Laser, fiber-optic, and detection hardware may

only be available at select wavelengths and may limit access some spectral transitions.

Additionally, according to the line selection rules set forth by Zhou, et al. [89], one

must ensure that both lines provide sufficient absorption over the temperature range

that the sensor is expected to operate, and they should be relatively free of interference

from both neighboring transitions of the same species and also overlapping transitions

of other species in the measurement path length (including both the gas sample and

absorption over any ambient path length the beam traverses).

When there is a nonuniform temperature across the absorption path length, addi-

tional constraints must be added because the linestrength is desired to scale linearly

with temperature over the temperature range across the LOS [65]. However, the

linestrength is never truly a linear function of temperature over any practical temper-

ature range, and therefore care must be taken to select transitions such that the errors

introduced by this assumption are minimized. Figure 2.10 shows simulated maximum

error in the linear-linestrength assumption compared to the actual linestrength of an

H2O transition as a function of the transition lower-state energy over a temperature


range of 1200 K to 1700 K across the path length. There are two cusp points in

the figure where the error in the linear-linestrength assumption is minimized to less

than 1% of the linestrength at the mean temperature over the path length (1450

K in this case). These minimizing points occur at E ′′ =1095 and 5260 cm−1. Be-

cause there is a very large separation in lower-state energy between these two points,

they represent an ideal compromise between maximizing temperature sensitivity and

minimizing error due to the linear-linestrength approximation. However, note that

this pair is only ideal for the specific temperature range and species simulated, in

this case H2O from 1200 K to 1700 K. To further clarify the linear-linestrength as-

1000 2000 3000 4000 50000

2

4

6

8

Lower−State Energy (E"), cm−1

Ma

x %

Err

or

in L

ine

ar−

Lin

estr

en

gth

Ap

po

xim

atio

n

Temperature Range= 1200−1700 K

Low and High E" for BestLinear−Linestrength ApproximationOver Simulated Temperature Range

Figure 2.10: Maximum error in assuming a linear linestrength as a function of transi-tion lower-state energy for H2O transitions and a temperature range of 1200 to 1700 Kover the LOS. Two distinct cusps are observed where error in the assumption is mini-mized. These points represent the optimal low- and high-E” to use in a two-transitionsensor over the specified temperature range.

sumption, the simulated linestrength at these two minimizing points is plotted as

a function of temperature from 800 K to 2100 K in Fig. 2.11. From this figure it

is clear that the cusp in points in Fig. 2.10 correspond to inflection points in the

lineshape as a function of temperature, S(T ). Different lower-state energies shift the

linestrength curve left and right along Fig. 2.11, and therefore the optimal E ′′ for

the linear-linestrength assumption will occur for a transition whenever an inflection

point in S(T ) corresponds to the mean temperature across the nonuniformity path


considered. The magnitude of the maximum error will depend on the extent of the

temperature range across the LOS. Recall from Eq. (2.4) that the linear linestrength

1000 1500 20000

0.2

0.4

0.6

0.8

1

Temperature, K

No

rma

lize

d L

ine

str

en

gth

E"=1095 cm−1

E"=5160 cm−1

Linear Best−Fit

TRange

= 1200−1700K

Figure 2.11: Linestrength plotted against temperature for linear-linestrength lower-state energies highlighted by red dots in Fig. 2.10. Also shown is the best-fit linearfunction to the linestrength over the range of 1200-1700K considered.

assumption allows integrated absorbance to be written as A = S(T ni)Ni, given by

Eq. (2.8). When the linear-linestrength assumption is applied, the linestrength is

modeled by Eq. (2.32).

S(T ) = a · T + b (2.32)

Here, a and b are constants that are fit to the linestrength function given by Eq.

(2.10) over the range of temperatures along the LOS. This expression can be used to

replace S(T ) in Eq. (2.4), as given by Eq. (2.33):

A =

∫ L

0

(a · T + b)nidl = a

∫ L

0

Tnidl + b

∫ L

0

nidl (2.33)

The right-hand integral in Eq. (2.33) is simply the column density as defined by Eq.

(2.6). Diving both sides by Ni, the expression becomes:

A

Ni

= a

∫ L0Tnidl

Ni

+ b = a

∫ L0Tnidl∫ L

0nidl

+ b (2.34)


The path-integral of the product of temperature and number density, divided by the

column density, is exactly the number-density weighted path-average temperature,

T ni, defined in Eq. (2.5). Therefore, the right hand side Eq. (2.34) becomes the

linestrength evaluated at T ni, S(T ni

), and Eq. (2.8) for the integrated absorbance

is recovered.

Chapter 3

Measurements in a Continuous

Flow, H2-Fueled Model Scramjet

Combustor

In the last fifty years of scramjet engine development, focus has narrowed to liquid-

hydrogen fueled scramjet engines for high-performance applications such as airbreath-

ing propulsion for reusable spacecraft [90]. Hydrogen is an attractive fuel for these

applications because of its short ignition delay relative to hydrocarbon fuels, which

makes hydrogen-fueled scramjets capable of flight speeds above Mach 10 [16]. Hydrogen-

fueled scramjets also enjoy significantly reduced chemical mechanisms compared to

hydrocarbon counterparts, which substantially reduces the complexity of simulating

coupled fluid dynamics and thermodynamics within a scramjet combustor.

To that end, researchers in the field of computational fluid dynamics (CFD) have

directed a great deal of effort towards towards simulation of hydrogen-air combustion

within scramjet engines, and there is a need for high-fidelity diagnostics to validate

the results of those models against experimental data [21, 86, 91]. TDLAS is an

excellent option for providing these needed scramjet diagnostics: the method is non-

intrusive, in situ, and, when using WMS, extremely resilient to common noise sources

such as window-fouling and mechanical vibration. Because water is the major com-

bustion product of an H2-air flame, a TDLAS diagnostic for temperature and H2O

33

34 CHAPTER 3. MEASUREMENTS IN AN H2-FUELED SCRAMJET

concentration is a natural choice that can provide a measure of both thermal and

combustion efficiency. Mature telecommunications-industry diode laser technology

makes many near-infrared H2O transitions near 1.4 µm readily accessible. Moreover,

the laser sources are compact, fiber-coupled, and are easy to transport and setup at

a remote scramjet facility. Thus, TDLAS sensors for H2O are a popular choice of

optical diagnostic for scramjet combustors [26, 92–94].

Here, we extend the body of work on TDLAS H2O diagnostics in scramjets by

providing measurements of temperature, H2O column density, and velocity with axial

and transverse spatial resolution within a continuous-flow H2-fueled model scramjet

combustor [95, 96]. Measurement results are presented for two different combustor

geometries. For both data sets, wavelength-modulation spectroscopy with second-

harmonic detection (WMS-2f /1f ) was used. Measurements were conducted as part

of a collaborative program including CFD at North Carolina State University [86],

coherent anti-Stokes Raman scattering (CARS) by The George Washington Univer-

sity [33], and planar laser induced fluorescence (PLIF) imaging by NASA Langley

Research Center [97]. These diagnostics reveal significant nonuniformities along the

TDL LOS throughout the combustor. Therefore, direct-absorption spectroscopy was

used to obtain empirical measurements of the transition collision linewidth in order

to make quantitatively accurate measurements in the presence of these nonuniformi-

ties. Comparisons with CFD simulations are included and illustrate the use of LOS

TDLAS measurements to validate computational efforts. A significant contribution

of this work is that it provides the most complete database of scramjet TDLAS mea-

surements obtained to date. Additionally, this work is the first of its kind to use

a simple two-color path-integrated measurement to produce quantitatively accurate

WMS measurements over a highly nonuniform LOS path.

This chapter begins with a description of the sensor architecture, including the

model scramjet facility used in these tests, the TDLAS sensor design, and the TDLAS

hardware layout. This is followed by an assessment of error in TDLAS measurements,

and an explanation of how TDLAS measurements are compared to CFD in this

work. Finally, measurement results from each of the two combustor geometries are

presented.

3.1. SENSOR ARCHITECTURE 35

3.1 Sensor Architecture

3.1.1 Scramjet Facility Description

Measurements were conducted in a direct-connect model scramjet combustor at the

University of Virginia Supersonic Combustion Facility (UVaSCF). This is a continuous-

flow facility that produces conditions equivalent to Mach 5 flight speed. Electrical

heating, rather than vitiation, was used to heat the air prior to expansion to increase

the enthalpy, and the Mach 2 flow had a total temperature of 1200 K and a total

pressure of 330 kPa [98]. Steam could be added to the heated air prior to expansion

to use H2O absorption to monitor the core flow without combustion. Combustion

tests were conducted with H2 fuel at global fuel-air equivalence ratios of Φ = 0.17

and Φ = 0.46. Hydrogen was injected through a Mach 1.7 conical nozzle at the base

of a 10 degree ramp with ramp height of H = 6.4 mm [99].

Configuration A:

Configuration C:

y-axis

x-axis z-axis

(Out of page)

Combustor Extender

Isolator Combustor Extender Constant

Area Section

Ramp Fuel Injector

Ramp Fuel Injector

Flow

Flow 2.54 cm

28.92 cm 18.01 cm

2.54 cm

28.92 cm 18.01 cm 14.90 cm 26.60 cm

Figure 3.1: Cartoon diagram of UVaSCF Configurations “A” and “C” with dimen-sions. Not to scale.

Results are presented here for two different combustor configurations: 1) with


the combustor directly connected to the facility nozzle exit, and 2) with the isola-

tor upstream of the combustor and an additional constant area section immediately

downstream of the combustor. These configurations will be referred to as “Configu-

ration A” and “Configuration C” in the remainder of the text, as this nomenclature is

consistent with other literature covering these combustor geometries [97, 100]. Car-

toons of the cross-sectional geometries are shown in Fig. 3.1. In both geometries,

beginning at the leading edge of the ramp, the flow path diverged along the injector

wall at an angle of of 2.9 degrees. In Configuration A, this divergence continued all

the way to the combustor exit. However, in Configuration C an additional constant

area section was installed between the combustor and the extender to facilitate other

diagnostic methods [101]. The combustor side walls consisted of 20 cm by 6 cm fused-

silica windows for access of optical diagnostics. For these tests the window outer faces

were wedged at 2 degrees to avoid internal reflections in the window (etalons) when

the laser wavelength was scanned. TDLAS combustion measurements presented here

focused on a total of five separate axial planes within the combustor, at distances of

x/H = 6, x/H =12, x/H =15, and x/H =18 downstream of fuel injection (where H

= 6.4 mm ramp fuel injector height), as shown in Fig. 3.2.

Figure 3.2: Rendered diagram of the UVaSCF Configuration C with select TDLASmeasurement planes noted. Note fuel injection occurred at x = 0 and distances areshown normalized to the injector ramp height, H = 6.4 mm.


Table 3.1: Spectroscopic parameters of dominant H2O transitions used in H2-aircombustion UVaSCF experiments

Wavelength, nm(HITEMP ’10)

Frequency, cm−1

(HITEMP ’10)

Linestrength(296K), cm−2/atm

(Measured)

Lower-StateEnergy, cm−1

(HITEMP ’10)1391.7 7185.59 1.95 × 10−2 1045.11469.3 6806.02 6.39 × 10−7 3291.2

3.1.2 Wavelength Selection and Spectroscopic Model

As discussed in Section 2.5.3, proper line selection requires weighing many competing

factors to maximize both the sensor practicality and measurement fidelity. Due to the

need for reliable fiber-coupled laser hardware and optics, only the ν1 + ν3 combina-

tion band of H2O transitions were examined for use in this sensor, as this wavelength

region overlaps with mature telecommunications-industry laser and fiber-optic tech-

nology. Lines with small linestrengths at combustion temperatures were immediately

filtered out, and spectral absorption simulations were performed using the HITEMP

2010 database [102]. Examining the simulated spectra revealed those transitions that

were still too weak or that suffer from too much interfering absorption from other

nearby transitions to be considered for use. The implementation of thermometry

used here requires the selection of two absorption transitions, and according to Eq.

(2.31) the selected transitions should have a large separation of lower-state energy

in order to maximize temperature sensitivity, which places an additional constraint

on line selection. Ultimately, lines at 1391.7 nm and 1469.3 nm were selected for

use in the sensor, as these were deemed the strongest pair transitions at combus-

tion temperatures that are both relatively isolated and offer excellent temperature

sensitivity. Both transitions were used for thermometry, and column density was

determined from the transition at 1391.7 nm. Spectral properties of these transi-

tions, summarized in Table 3.1, were then refined through experimental testing in a

high-uniformity three-zone furnace at Stanford University [103].

There is one additional consideration on line selection that merits discussion: how

well does the assumption that linestrength scales linearly with temperature apply

to the selected transitions? Recall that this assumption allows the interpretation


that measured signals from both direct-absorption and WMS measurements through

nonuniform flows will yield the species number-density-weighted path-average tem-

perature. However, in reality the linestrength is never perfectly linear across any

meaningful temperature range, and therefore it is helpful to quantify how linear the

behavior of S(T ) is over the expected nonuniformity across the path length. This

is plotted in Fig. 3.3, which shows the maximum percent error between the actual

linestrength function S(T ) and its linear approximation, aT + b, for a 500 K temper-

ature variation along the LOS and as a function of the mean temperature along the

LOS. Both of the selected transitions have errors of less than 4% for average temper-

atures above 1400 K, which is within the range of the vast majority of measurements

presented here. This implies that only small errors are introduced to the data analysis

when assuming that linestrengths scale linearly with temperature.

1400 1600 1800 2000 22000

1

2

3

4

5

Mean Temperature, K

Err

or

in L

inear

S(T

) A

ppro

x., (

% o

f S

(Tm

ean))

ν0 = 7185.59 cm

−1, E’’ = 1045.1 cm

−1

ν0 = 6806.02 cm

−1, E’’ = 3291.2 cm

−1

Results shown forT = T

mean ± 250 K

Figure 3.3: Error in a linear linestrength approximation as a function of mean tem-perature across the LOS for the spectroscopic transitions with E ′′ = 1045.1 cm−1 andE ′′ = 3291.2 cm−1 used in the UVaSCF Configuration A and C experiments.


3.1.3 TDLAS Sensor Description

Figure 3.4 shows the layout of the TDLAS hardware used in the measurements.

Both lasers and data acquisition hardware were placed in a control room adjacent to

the tunnel room. Two separate lasers provided fiber-coupled light near 1391.7 nm

and 1469.3 nm, which were combined onto a single-mode polarization-maintaining

fiber optic and routed to the tunnel room. A ThorLabs F240APC-C lens was used

to collimate the output light into a free-space beam with an approximate diameter

of 1.5 mm, which was then directed across the combustor duct. The transmitted

light was collected through a 1 cm (maximum) aperture, followed by a 25 mm focal-

length mirror turning light 90 degrees (Configuration A measurements) or a 12 mm

f2 lens (Configuration C measurements). In both measurements, the focused light

was directed onto a 3 mm ScienceTech InGaAs photodetector (3 MHz bandwidth

subsequently anti-aliasing filtered to 1 MHz). For direct absorption measurements the

signal at the two wavelengths was demultiplexed in time. For WMS measurements

the two colors were demultiplexed by modulation frequency. The laser at 1391.7 nm

was modulated at 160 kHz and the laser at 1469.3 nm was modulated at 200 kHz,

with modulation depths selected to achieve approximately m = 2.2 over the range

of conditions in the combustor. In both measurement techniques the laser slow-scan

was at 250 Hz over a large enough amplitude to capture the entire lineshape.

As shown in Fig. 3.5, the entire optical assembly was attached to a set of computer-

controlled translation stages (Zaber, Inc.) that were controlled remotely, and allowed

the TDLAS LOS to span 15 cm of travel in the axial direction along the duct and 5

cm in the transverse direction across the duct. In Configuration A measurements, the

transverse translation stages sat on platforms and used a focusing mirror to turn light

90 degree into the detector, whereas for Configuration C measurements a linear setup

using a focusing lens was adopted. The primary advantage of the Configuration C

optical setup was to allow room for an additional beam path to enable Doppler-shift

velocity measurements (discussed in Section 2.4). Measurements focused on axial

locations of x/H = -10 (combustor inlet) and x = 0 for steam-added tests and x/H

= 6, x/H =12, x/H =15, and x/H =18 for various combustion tests, where H = 6.4

mm is the injector ramp height. In each axial measurement plane, measurement LOS


Figure 3.4: Diagram of TDLAS system in relation to UVaSCF facility.

were spaced evenly by 1.5 mm, corresponding to the laser beam diameter, totaling

up to 24 separate LOS per plane (recall the duct expands at 2.9◦ downstream of fuel

injection). The optics were located several cm off of the outer face of the window, and

the ambient path was purged with N2 to limit absorption from H2O present in the

lab air. A small amount of remaining background absorbance was subtracted from

the measured signals.

Measurements reported here were obtained using an iterative combination of

direct-absorption and peak-WMS-2f /1f. This approach was taken because the peak-

WMS signal is sensitive to the lineshape just as the peak-direct-absorption signal is

(see Eq. (2.2)) and significant nonuniformity in temperature and composition were

expected along the LOS. Nonuniformity manifests itself as a nonuniform linewidth in

the measured spectra. Therefore, a separate in situ measurement of the empirical col-

lision linewidth was obtained from a Voigt lineshape fit to scanned-direct-absorption


15 cm Translation Stages

5 cm Translation Stage

Transmission Optics

(fiber optics +

collimating lens)

Detector

Large Quartz

Viewing Windows

Nozzle

Flow Direction

Configuration A

=40°

Configuration C

Figure 3.5: Rendered images of TDLAS optical setup for Configuration A and Cexperiments, respectively.

measurements (see Fig. 3.6), as described in Section 2.5.3. The measured effective

linewidth was then fixed within WMS data processing of the WMS-2f /1f signal at

the location of the WMS-2f peak (see Fig. 3.7). See Appendix A for a detailed

exposition on how peak-WMS measurements with a fixed linewidth are converted

to quantitative temperature and column density measurements. Although methods


have been proposed to recover the direct-absorption lineshape from WMS signals

directly (for example, see Ref. [104]), this iterative approach was chosen because

direct-absorption spectroscopy offers a simple interpretation that helps ensure that

the more complicated WMS signals are understood correctly.

7185.4 7185.5 7185.6 7185.7 7185.8−0.01

0

0.01

0.02

0.03

0.04

0.05

Absorb

ance

Relative Frequency (cm−1

)

Measured AbsorbanceAbsorbance Voigt Fit

Figure 3.6: Single-scan absorbance profile for absorption feature near 1391.7 nm,measured within the University of Virginia scramjet combustor (Configuration C)using scanned-direct-absorption at a location approximately 7.62 cm downstream offuel injection and 4.5 mm from the injector-side wall. Data was collected during H2-aircombustion experiments at equivalence ratio Φ = 0.17. A best-fit Voigt function, usedto measure the empirical collision linewidth, is shown overlaid on top of measuredabsorbance.

3.2 Uncertainty Analysis of WMS Measurements

Through Nonuniform Scramjet Flow

Two primary effects complicate the absorption of light propagating in a nonuniform

environment: 1) variation in gas temperature and absorbing species number den-

sity cause the integrated absorbance to vary in each volumetric element along the

LOS, and 2) variation in temperature, pressure and composition all cause the tran-

sition lineshape to change along the LOS. As a result, precise interpretation of the

measured path-integrated absorbance spectra requires knowledge of the distribution

3.2. UNCERTAINTY ANALYSIS OF WMS MEASUREMENTS 43

39.5 40 40.5 410.02

0.03

0.04

Time, msW

MS

−1f S

ignal

39.5 40 40.5 410

2

4x 10

−3

Time, ms

WM

S−

2f S

ignal

39.5 40 40.5 410

0.05

0.1

0.15

0.2

0.25

Time, ms

WM

S−

2f/1f S

ignal

a)

b)c)

Figure 3.7: WMS 2f, 1f, and 2f /1f signals for the H2O transition near 1391.7 nmmeasured in the University of Virginia supersonic combustor (Configuration C) ata location approximately 7.62 cm downstream of fuel injection and 4.5 mm fromthe injector-side wall. Data was collected during H2-air combustion experiments atequivalence ratio Φ =0.17.

functions describing the variations in gas state across the LOS. While this can be done

using CFD results, which provide spatially-resolved temperature, pressure, and gas

composition, the extraction of flow field parameters (temperature, column density,

etc.) from measured TDLAS data relies on strategies that either model the nonuni-

formities along the LOS with path-averaged thermodynamic quantities, assume the

nonuniform conditions are distributed according to user-selected functions with input

parameters that are inferred using absorption signals over multiple transitions [105],

or use a more complicated hardware and data reduction system for tomographic

imaging of nonuniform conditions [106]. The former strategy was used in the analysis

of the TDLAS data measured here, and CFD simulations are used to estimate the

error introduced by using path-averaged thermodynamic quantities coupled with an

empirical lineshape function.

Because of the difference in the collisional-broadening efficiency of H2O and N2,

the transition linewidth varies by a factor of 5 between a gas composed of pure N2

and pure H2O. For the H2-air combustion presented here at a global equivalence

ratio of Φ = 0.17, the average water vapor mole fraction is 6.9% in equilibrium


combustion products. However, the combustion products are not uniformly mixed,

and the maximum water vapor mole fraction predicted in any CFD volume element is

31.2%. To examine the effects of the nonuniform flow field on the quantities inferred

from the TDLAS data, the CFD solution was used to simulate the H2O absorption in

each volume element along each measurement LOS. Then, the total absorption was

calculated by integrating along the LOS (evaluating Eq. (2.2)) and a best-fit Voigt

profile was fit to the absorption lineshape to find the effective lineshape. Peak-WMS

signals from the CFD-simulated-absorption were then least-squares fit to simulations

fixing the linewidth to the effective value and using uniform conditions to determine

temperature and column density. This process directly replicates the data reduction

method used for the scramjet combustor measurements. These simulated-TDLAS

signals from the CFD solution implied that temperatures inferred from the ratio of

path-integrated peak-WMS signals were within 5.5% of the water-weighted average

CFD temperature at all locations and that the column density determined from a

peak-WMS signal agreed with its absolute CFD value within 3% at x/H = 6 and x/H

= 12, and within 6% at x/H = 18. Thus, even though the flow field has nonuniform

temperature and water distributions, the flow parameters determined from TDLAS

measurements in this nonuniform flow have only modest errors and are sufficiently

accurate to allow useful comparisons with CFD simulations of this complex flow field.

It is worth noting that this level of accuracy is only possible because of the effective

lineshape measurements used here, as discussed in Section 2.5.1.

3.3 TDLAS Measurements: “Configuration A”

3.3.1 Φ = 0.17 Equivalence Ratio Combustion Results

Combustion runs with dry air were conducted during steady facility operation us-

ing the scanned-wavelength WMS-2f sensor at Φ = 0.17 equivalence ratio on the

Configuration A combustor geometry. Both temperature and column density were

determined across the width of the combustor with a resolution of approximately 1.5

mm at each of two measurement planes downstream of fuel injection (at distances

3.3. TDLAS MEASUREMENTS: “CONFIGURATION A” 45

x/H = 12 and x/H = 18, normalized by fuel-injector ramp height H = 6.4 mm).

Because the flow path diverged linearly along the fuel-injector wall, the measurement

plane at x/H = 18 was approximately 2 mm wider than x/H = 12. The width of

the duct (y-direction) was 2.58 cm at the injector and 3.34 cm at x/H = 18. At each

measurement point, 0.5 seconds of WMS-2f data was collected at a bandwidth of 250

Hz (WMS scan frequency) and with modulation frequencies of 160 kHz and 200 kHz

for lines at 1391.7 nm and 1469.3 nm respectively. Reported values are the average

over this sample time, with example uncertainty bars reported based on statistical

precision of one standard deviation in WMS signal measurements (Note these error

assessments are repeated in Fig. 3.8-3.10). Results are shown with the abscissa de-

noted as distance from the wall opposite the fuel-injector. This was done because the

fuel injector was along the angled wall and therefore the fuel injector wall is along the

right edge of each graph. For ease of comparison with other diagnostic measurements

(e.g. Refs. [97, 100]), the top of each graph shows the abscissa with non-dimensional

units of distance normalized by ramp-height, y/H.

Results for TDLAS column density and temperature measurements are shown in

Fig. 3.8 for measurement planes x/H = 12 and x/H = 18. Column density results

in Fig. 3.8a reveal a plume of products downstream of the fuel injector penetrating

successively greater distances into the flow to a maximum of about 2.5 cm at x/H

= 18. Throughout much of the product plume there is a significant increase in peak

column density between x/H = 12 and x/H = 18 corresponding to increased com-

bustion progress with axial distance. For both planes, peak column densities occur

near the center of the product plume before descending rapidly towards zero at the

plume edge farthest from the fuel injector ramp. Along the wall downstream of the

fuel injector ramp, only a small rise in H2O products is observed between x/H = 12

and x/H = 18. Note the measurement value for x/H = 12 closest to the injector

wall appears unusually large. Possibly this point was perturbed by interference of

transmission from reflections by the wall in the vibrating combustor. These qualita-

tive assessments of the TDLAS measurements are in good agreement with PLIF and

CARS data [33, 97].


−2 −1 0 1 2 3

0

0.2

0.4

0.6

0 1 2 30

0.2

0.4

0.6

y/H

Distance from Wall Opposite Injector, cm

H2O

Co

lum

n D

en

sity,

g m

−2

x/H = 18 TDLASx/H = 12 TDLAS

a)

−2 −1 0 1 2 3

800

1200

1600

2000

2400

0 1 2 3800

1200

1600

2000

2400

y/H


H2O

−A

ve

rage

d T

em

pera

ture

, K

x/H = 18 TDLASx/H = 12 TDLAS

b)

Figure 3.8: TDLAS Measurement results for φ = 0.17 combustion in UVa CombustorConfiguration A. a) Water column density, b) Path-averaged temperature

Figure 3.8b shows the corresponding path-averaged H2O temperature measure-

ments for Φ = 0.17 combustion. Over most of the product plume successive planes

(i.e., at increasing axial distance from the injector) show significant increases in tem-

perature, up to a peak of nearly 1900 K at x/H = 18. Recall the TDLAS temperature

was determined from H2O absorption. Thus in regions where H2O column density

is small no temperature is reported. The free stream static temperature was 770 K,

thus the H2O absorption reveals elevated temperatures from combustion heat release

near the injector wall. At the edge of the combustion product plume farthest from

the fuel injector wall the temperature rolls off gradually, as expected.

3.3.2 Comparisons of TDLAS Data with CFD Simulations

Hybrid large eddy simulation/Reynolds-averaged Navier-Stokes CFD computations

were performed at North Carolina State University on the same scramjet combustor

geometry and reported in Ref. [86]. To compare these simulations with the TDLAS

measurements, column density was computed from the spatially-resolved simulation

by directly integrating H2O partial density results along the LOS corresponding to

the TDLAS measurement locations. The TDLAS determines temperature from water

vapor absorption; thus, a water-weighted temperature was computed from the CFD

using Eq. 2.5 to compare with the measured TDLAS temperature.

3.3. TDLAS MEASUREMENTS: “CONFIGURATION A” 47

−2 −1 0 1 2 3

0

0.2

0.4

0.6

0.8

0 1 2 30

0.2

0.4

0.6

0.8

y/H


H2O

Co

lum

n D

en

sity,

g m

−2

x/H = 18 TDLASx/H = 18 CFDx/H = 12 TDLASx/H = 12 CFD

a)

−2 −1 0 1 2 3

800

1200

1600

2000

2400

0 1 2 3800

1200

1600

2000

2400

y/H


H2O

−A

ve

rage

d T

em

pera

ture

, K

x/H = 18 TDLASx/H = 18 Water−weighted CFD T, T

CFD


CFD

b)

Figure 3.9: Comparisons of TDLAS measurements with CFD simulations using Jachi-mowski kinetics model in UVa Combustor Configuration A. a) Water column density,b) Path-averaged temperature

Figure 3.9 shows comparisons between TDLAS measurements and CFD simulation

using a H2-air kinetics mechanism by Jachimowski [107] for axial planes at x/H =

12 and x/H = 18. Column density results in Fig. 3.9a show reasonable agreement

in shape and peak values over most of the plume. However, two primary differences

are observed. TDLAS-measured column density rolls off at nearly the same distance

from the injector wall at both measurement planes, indicating larger penetration of

the product plume into the flow at x/H =12 than in the CFD simulations, and less

plume growth between the planes. Also, at x/H = 18, the CFD simulations fail to

capture the decline in column density adjacent to the injector wall, perhaps signaling

limited fuel/oxidizer mixing in the wake of the ramp injector. The area under each

column density curve is related to the total amount of water in the flow, allowing

computation of combustion progress as determined by either TDLAS or simulation.

This computation gives a metric for comparing all column density results at a given

plane, and shows agreement within 7% at x/H =18. However, TDLAS measures

about 20% less total water at x/H = 12 than the CFD prediction, perhaps in part

due to increased uncertainty in the collisional width assigned to each LOS from smaller

absorbance at this axial plane. Temperature results in Fig. 3.9b show good agreement

in peak temperatures and overall good agreement close to the injector wall for x/H


= 18, but for x/H = 12, the TDLAS value of water-weighted average temperature

is about 200 K higher at some points in the plume core. Coupled with the reduced

amount of H2O seen in the column density results at x/H = 12, this suggests there

was less heat transfer from the combustion products to unreacted gas than CFD

predicts.This idea is supported by the fact that TDLAS measurements show the

water remained much hotter than the CFD water-weighted mixture temperature far

from the injector wall as temperature rolls off at the plume edge.

−2 −1 0 1 2 3

0

0.2

0.4

0.6

0.8

0 1 2 30

0.2

0.4

0.6

0.8

y/H


H2O

Colu

mn D

ensity,

g m

−2

x/H = 18 TDLASx/H = 18 CFDx/H = 12 TDLASx/H = 12 CFD

a)

−2 −1 0 1 2 3

800

1200

1600

2000

2400

0 1 2 3800

1200

1600

2000

2400

y/H


H2O

−A

vera

ged

Tem

pera

ture

, K


CFD


CFD

b)

Figure 3.10: Comparisons of TDLAS measurements with CFD simulations usingBurke kinetics model in UVa Combustor Configuration A. a) Water column density,b) Path-averaged temperature

CFD simulations were also performed using a H2-air chemical mechanism by

Burke, et al. [108]. The same comparison methods used for the Jachimowski-kinetics

CFD were used for this simulation, and the resulting column density and tempera-

ture comparisons are shown in Fig. 3.10. The profile shapes for both column density

and temperature are largely unchanged and therefore many of the same conclusions

can be drawn in comparing TDLAS data to CFD prediction of plume shape. One

important distinction is that column density results in Fig. 3.10a show that the CFD

with Burke, et al. kinetics predicts higher peak values of the H2O column density

compared to measurements, particularly near the injector wall. The Burke-kinetics

CFD also predicts that the product plume penetrates slightly farther into the flow

at both planes. This produces better plume penetration agreement at x/H = 12,

3.4. TDLAS MEASUREMENTS: “CONFIGURATION C” 49

but at x/H = 18, the Burke-based CFD does not agree with measurement as well as

the Jachimowski mechanism. Taken together with the increased peak column densi-

ties, the conclusion is that the Burke chemical mechanism predicts more combustion

progress than the Jachimowski mechanism. Such increased combustion progress im-

plies greater heat release, which can be seen in a comparison of temperature results

in Fig. 3.10b. In this case, the CFD predicts slightly higher peak temperatures com-

pared to the Jachimowski results. Although this difference is small, it does in fact

reduce the disparity between TDLAS and CFD at x/H = 12.

3.4 TDLAS Measurements: “Configuration C”

As in results reported for the Configuration A combustor geometry, the following

figures show measurements with the abscissa representing distance across the trans-

verse direction (y-direction) along successive axial x-planes. Distances between the

TDLAS LOS on the abscissa have an origin at the wall opposite the injector because

the injector-side wall diverges at 2.9 degrees beginning at the base of the fuel injector

ramp. At each measurement point 0.5 seconds of data were collected resulting in 250

scans for the WMS technique and 125 scans for direct absorption. The facility oper-

ation was found to be quite steady, and hence only the average values are reported

here. Quoted uncertainty levels were calculated from the propagation of random er-

rors based on one standard deviation in measured signals. Error bars are shown for

only a single point but are representative of the entire plane.

3.4.1 Steam Addition Measurements

Steam was added to the flow for non-combustion tests to validate the facility hardware

and sensor performance for a uniform flow with known pressure, temperature, and

H2O concentration. Here, temperature and column density was measured upstream

of the fuel injector at x/H = -10. These data provide validated boundary conditions

for CFD models; in particular any irregularities found in experimental measurements


could be included in the model to properly match conditions. The WMS-2f /1f strat-

egy was used for these measurements. Because of the uniform H2O seeding and

expected uniform flow conditions, the empirical collision linewidth was not needed

for these measurements and a peak-WMS approach as in [70] was used. Figure 3.11

shows the resulting column density and path-average temperature measurements. The

results show very uniform column density conditions. There is slightly more scatter

in the temperature results, but the only significant deviations correspond to the four

measurement points nearest the injector which also show more scatter in column

density. Together these results may suggest a perturbation to the flow just upstream

of the injector. However, both column density and temperature measurements have

values very close to those expected based on the facility operation targets.

−2 −1 0 1 2 3

0

0.1

0.2

0.3

0 0.5 1 1.5 2 2.50

0.1

0.2

0.3

y/H


H2O

Co

lum

n D

en

sity,

g m

−2

Expected Column Density for 4% steam addedx/H = −10 (Combustor Inlet) TDLAS

a)

−2 −1 0 1 2 3

0

200

400

600

800

0 0.5 1 1.5 2 2.50

200

400

600

800

y/H


H2O

−A

ve

rag

ed

Te

mp

era

ture

, K

Expected Static Temperaturex/H = −10 (Combustor Inlet) TDLAS

b)

Figure 3.11: TDLAS measurement results for the UVa Combustor Configuration Cinlet at x = -10H. a) Water column density b) Path-average temperature

Tests of the velocity sensor were also performed with steam addition and are

shown in Fig. 3.12. The velocity was measured across the width of the duct at x =

0, x/H = 6, x/H = 12, and x/H = 15. Note the velocity measurements at x = 0

are not possible for LOSs close to the injector ramp. The peak velocity at the x =

0 plane is significantly lower than subsequent planes because the supersonic flow is

slowed by the reduction in the cross-section area of the duct due to the ramp. At

x/H = 6 the velocity had nearly recovered, and by x/H = 12 and x/H = 15 the

peaks of the velocity profiles were nearly identical. The asymmetric velocity profiles


along the edges are likely due to the increased turbulence in the wake of the injector.

The isentropic velocity for a Mach 2 flow with gamma calculated for 4% H2O in

air balance at 770 K is approximately 1070 m/s. This value compares favorably with

peak velocities measured at x/H = 12 and x/H = 15. Finally, error bars representing

one standard deviation ranged from 11 to 33 m/s and are shown on the plot.

−2 −1 0 1 2 3

500

700

900

1100

0 0.5 1 1.5 2 2.5 3 3.5500

700

900

1100y/H


H2O

LO

S V

elo

city, m

/s

x/H = 15x/H = 12x/H = 6x/H = 0

Figure 3.12: TDLAS measurement results of axial velocity in UVa Combustor Con-figuration C for a non-combusting case with free-stream steam addition.

3.4.2 Combustion Measurements

Combustion measurements of temperature and column density were conducted across

the width of the combustor spaced 1.5 mm apart and at distances of x/H = 6, x/H

= 12, and x/H = 18 downstream of fuel injection, with H2-air equivalence ratios of Φ

= 0.17 and Φ = 0.46. These equivalence ratios were chosen to validate specific CFD

test cases. Velocity measurements at x/H = 6, x/H = 12, and x/H = 15 were made

for the equivalence ratio Φ = 0.17 only. All reported values were determined using

the WMS-2f /1f strategy, which was analyzed incorporating the empirical lineshape

function measured from direct absorption. Additionally, it should be noted that

because TDLAS measurements require the presence of water and the inflow air was

dry, results are only shown over the portion of the duct width that contained enough

combustion product H2O for sufficient SNR. Hence these measurements reveal the


development of the combustion product plume with increasing axial distance from

the fuel injector.

Φ = 0.17 Equivalence Ratio Combustion Results

TDLAS measurements of column density shown in Fig. 3.13a reveal the combustion

product plume grows significantly with each successive axial plane. Many simple

metrics show this behavior: the peak value of column density increases at each plane,

the transverse penetration of H2O increases, and finally the total area under the

column density curve - which is directly related to overall combustion progress -

increases significantly between each plane. The most significant rise in column density

is seen between x/H = 12 and x/H = 18, where the core of the product plume rises

from about 0.4 g/m2 to 0.7 g/m2. Close to the injector wall, there is very little rise

in column density at any location. This may indicate limited combustion progress

near the injector wall between the TDLAS measurement planes. Fig. 3.13b shows

corresponding TDLAS temperatures (H2O-weighted) for this combustion case. The

temperature results reinforce conclusions drawn from the column density results. Near

the injector wall, the temperature is more than 1400 K by x/H =6, but rises about

200 K between x/H = 6 and x/H = 18. Because heat transfer to the wall would

likely be a dominant effect only near boundary layers and not well into the combustion

product plume as observed in the results, this effect likely indicates little heat release

from combustion between x/H = 6 and x/H = 18. Farther from the injector wall

the temperature rise between each plane is significant, indicating more combustion

progress.

CFD calculations using a hybrid large-eddy simulation/Reynolds-averaged Navier-

Stokes approach on the Configuration C combustor geometry and conditions were

performed at North Caroline State University using a chemistry mechanism from

Burke, et al. [108]. CFD-calculated column density computed via Eq. (2.6) are

also shown in Fig. 3.13a as dashed and solid lines. Across all three planes, there

is modest agreement in the magnitude of column density. Agreement is best just

downstream of the injector at x/H = 6, but by x/H = 18 TDLAS measurements

show both a higher peak column density magnitude and a different peak location.


TDLAS measurements also show that H2O products penetrate farther into the flow

than the CFD predicts. In the immediate wake of the injector ramp, CFD captures

some of the limited combustion progress observed by TDLAS, however it still tends

to over-predict H2O in this region. CFD-computed temperatures were determined

from the H2O-weighted average temperature over the LOS and are shown in Fig.

3.13b. There is good agreement between CFD and TDLAS measurements across

all three measurement planes close to the injector wall, however farther from the

injector wall TDLAS measurements show higher temperatures than CFD predicts.

This makes some sense because the TDLAS measurements show the product plume

extends farther into the flow, and we expect higher temperatures wherever there are

hot combustion products. Another possible explanation is that the CFD over-predicts

heat transfer from the combustion products to the free stream gas gas since the sensor

measured the static temperature of H2O. This plume-edge behavior is consistent with

the Configuration A measurements presented in section 3.3.1.

−2 −1 0 1 2 3

0

0.2

0.4

0.6

0.8

0 0.5 1 1.5 2 2.5 3 3.50

0.2

0.4

0.6

0.8

y/H


H2O

Co

lum

n D

en

sity,

g m

−2

x/H = 18 TDLASx/H = 18 CFDx/H = 12 TDLASx/H = 12 CFDx/H = 6 TDLASx/H = 6 CFD

a)

−2 −1 0 1 2 3

500

700

900

1100

1300

1500

1700

1900

2100

0 0.5 1 1.5 2 2.5 3 3.5500

700

900

1100

1300

1500

1700

1900

2100

y/H


H2O

−A

ve

rag

ed

Te

mp

era

ture

, K

x/H = 18 TDLASx/H = 18 H

2O−avg. CFD T


2O−avg. CFD T


2O−avg. CFD T

b)

Figure 3.13: TDLAS measurement results compared to CFD simulation for H2-aircombustion at equivalence ratio of Φ = 0.17, facility Configuration C. a) Water columndensity b) Path-average temperature

Measurements of axial velocity at x/H = 6, x/H = 12, and x/H = 15 for Φ = 0.17

global equivalence ratio combustion are shown in Fig. 3.14. Note that as with the

other combustion measurements, velocities are only shown over the product plume

where significant H2O concentrations provided sufficient signal for measurements.


Near the injector wall the core flow velocity is significantly reduced compared to

the unmixed case (core velocity approximately 1070 m/s) shown in Fig. 3.12 due

to the addition and mixing of the fuel. Limited velocity recovery with downstream

progression was observed. Likewise, the edge of the plume far from the injector wall

showed significant velocity recovery towards the free stream values observed in the

unmixed case. CFD axial velocities are shown as the dashed and solid connected lines

in Fig. 3.14. The shape and magnitude of the velocity distribution shows excellent

agreement with CFD across the width of the duct, particularly at x/H = 6 and x/H

= 15. The plane at x/H = 12, however, shows some moderate discrepancy with

the TDLAS results suggesting CFD over-predicts velocity, however this difference is

contained by the experiment error bars. Far from the injector wall, near the edge of

the combustion product plume, the TDLAS measurement is much lower than CFD.

Measurements in this region of the flow suffer from increased uncertainty due to

small H2O concentrations at the combustion plume edge, which may explain this

discrepancy.

−2 −1 0 1 2 3

0

200

400

600

0 0.5 1 1.5 2 2.5 3 3.50

200

400

600

y/H


H2O

LO

S V

elo

city,

m/s

x/H = 15x/H = 15 H

2O−avg. CFD V

x/H = 12x/H = 12 H

2O−avg. CFD V

x/H = 6x/H = 6 H

2O−avg. CFD V

Figure 3.14: TDLAS measurement of axial velocity compared to CFD simulation forequivalence ratio of Φ = 0.17, facility Configuration C.

CARS measurements of H2, N2, and O2 mole fraction were made by Cutler, et al.

in the UVaSCF in the Configuration C geometry for the same H2-air equivalence ratio

Φ = 0.17 case at axial distances of x/H = 6 and x/H = 18 [33]. However, because


CARS does not measure H2O directly, CARS-inferred H2O column density was calcu-

lated from χCARSH2O

= 1−χCARSH2

−χCARSN2

−χCARSO2

using the CARS measurements. This

equation is analogous to assuming complete combustion of consumed H2 and ignores

free atoms and radicals which are combustion intermediates. Therefore, the value

of χCARSH2O

is an upper bound on the amount of water. To compare with the TDLAS

data, χCARSH2O

was converted to column density by integration along the LOS. Note the

CFD predicts a mole fraction of combustion intermediates ranging from 0-8% along

the TDLAS measurement LOS. Because CARS measurements capture H2, N2, O2

concentrations and TDLAS measures H2O, the difference between the CARS-inferred

and TDLAS H2O column densities gives a measure of the local concentration of in-

termediate species in the product plume. Comparisons between the CARS-inferred

and TDLAS H2O column density are shown in Fig. 3.15a (x/H = 6) and 3.15b

(x/H = 18). These comparisons allow identification of two distinct regions of the

combustion product plume. For both planes, near the injector wall TDLAS column

density is significantly smaller than CARS-inferred column density, indicating that

this region of the flow contained large intermediate species concentrations and ongo-

ing chemistry in good agreement with CFD predictions. Near the edge of the product

plume, however, TDLAS measurements approach the CARS-inferred column density

values. This result suggests the complete combustion assumption of consumed H2

used for the CARS-inferred values is accurate at the plume edge and may perhaps

be interpreted that the combustion product H2O at these locations is the result of

transport as opposed to local reaction. Note that although CARS measurements also

report temperature, we do not include any comparisons with TDLAS measurements

because the H2O-weighted temperature using χCARSH2O

would contain significant errors

over large regions of the product plume where combustion is not complete and the

CARS-inferred H2O is inaccurate. Thus, meaningful comparisons between the two

temperature measurements are difficult to identify.

Φ = 0.46 Equivalence Ratio Combustion Results

Combustion tests at a fuel-air equivalence ratio of Φ = 0.46 were also performed and

TDLAS measurements of temperature and column density were obtained. Column


−2 −1 0 1 2 3

0

0.2

0.4

0.6

0.8

0 0.5 1 1.5 2 2.5 3 3.50

0.2

0.4

0.6

0.8

y/H


H2O

Colu

mn D

ensity, g m

−2

CARS−inferredTDLASCFD

a)

−2 −1 0 1 2 3

0

0.2

0.4

0.6

0.8

0 0.5 1 1.5 2 2.5 3 3.50

0.2

0.4

0.6

0.8

y/H


H2O

Co

lum

n D

en

sity,

g m

−2

CARS−inferredTDLASCFD

b)

Figure 3.15: TDLAS measurements of H2O column density compared to CARS-inferred column density for H2-air combustion at equivalence ratio of Φ = 0.17, facilityConfiguration C. H2O column density is inferred from CARS by assuming completecombustion of consumed H2 fuel. a) Axial position x = 6H b) Axial position x = 18H

density results are shown in Fig. 3.16a and, as noted with Φ = 0.17 equivalence

ratio results, each successive measurement plane shows increasing column density

corresponding to combustion progress. Peak column densities are observed in the

center of the plume, although the rise in peak column density between successive

planes is limited. CFD predictions for this equivalence ratio are also shown in Fig.

3.16. There is reasonable agreement between TDLAS measurements and CFD at

the edges of the plume, indicating the CFD captures the plume penetration physics

well. However, peak values at the center of the combustion plume for the CFD

predictions are significantly larger than the TDLAS measurements. Temperatures

measured by TDLAS and corresponding H2O-averaged CFD temperatures are shown

in Fig. 3.16b. TH2O measurements show a large dip in temperature in the central

region of the product plume, possibility indicating limited combustion extent due to

the increased concentration of fuel in this richer stoichiometry, cooling of the flow

by the fuel injection, and the large momentum of the fuel jet. As with the lower

equivalence ratio case, the CFD temperature predictions show fairly good agreement

with TDLAS results. It does appear that the CFD solution tends to over-predict

the temperature slightly, which reinforces the conclusion from column density that


CFD over-predicts extent of combustion for this case. The over-prediction of CFD

temperature compared to TDLAS measurements is unlikely to fully account for the

over-prediction of CFD column density, however the correlation between the two

suggests at least some of the discrepancies in TDLAS-CFD comparisons may be

accounted for by CFD over-prediction of the completeness of combustion.

−2 −1 0 1 2 3

00 0.5 1 1.5 2 2.5 3 3.5

0

0.2

0.4

0.6

0.8

1y/H


H2O

Colu

mn D

ensity, g m

−2

x/H = 18 TDLASx/H = 18 CFDx/H = 12 TDLASx/H = 12 CFDx/H = 6 TDLASx/H = 6 CFD

a)

−2 −1 0 1 2 3

300

500

700

900

1100

1300

1500

1700

1900

0 0.5 1 1.5 2 2.5 3 3.5300

500

700

900

1100

1300

1500

1700

1900

y/H


H2O

−A

vera

ged T

em

pera

ture

, K


2O−avg. CFD T


2O−avg. CFD T


2O−avg. CFD T

b)

Figure 3.16: TDLAS measurement results compared to CFD simulation for H2-aircombustion at equivalence ratio of Φ = 0.46, facility Configuration C. a) Water columndensity b) Path-average temperature

Chapter 4

Multispecies Measurements in a

Hydrocarbon-Fueled Scramjet

Combustor

While hydrogen fueled scramjets are primarily viewed as a potential source of low-

cost orbital vehicle propulsion, there is also substantial interest in hydrocarbon-fueled

scramjets, mostly for low-cost expendable vehicles to be used in defense applications

[10]. For these vehicles, hypersonic flight speeds greater than Mach 5 are of particular

interest [16, 109]. However, with hydrocarbon fuels, effects of the finite-rate chemistry

amplify already complicated considerations in scramjet combustor operation: hydro-

carbon fuels typically have ignition delay times that compete with fuel residence

times in the combustor and the greatly increased number of species make both mea-

surement strategies and computational models more complex. To that end, robust

diagnostic methods are needed to track combustion progress and aid understanding of

the gas dynamic behavior within hydrocarbon-fueled scramjet combustors. One use-

ful method is absorption spectroscopy, which has a long history of providing reliable

diagnostics that can withstand harsh scramjet conditions [26, 36, 61, 63, 93, 94, 110].

This chapter presents the results of multispecies spectroscopic diagnostic measure-

ments to detect the H2O and CO temperatures and H2O, CO, and CO2 column den-

sities in an ethylene-fueled direct-connect model scramjet combustor [25, 111, 112].

58

59

Tracking carbon species is vitally important within the scramjet combustor, and

strong CO and CO2 transitions with minimal interference from H2O are only avail-

able in the fundamental vibrational bands at wavelengths longer than 4 µm. For H2O

measurements near 2.5 µm, mid-infrared laser sources enable access to strong funda-

mental band absorption transitions that offer considerably larger signal-to-noise ratio

over sensors using telecommunications diode lasers probing overtone or combination

band (2ν1 and ν1 + ν3) transitions near 1.4 µm. Many earlier diode laser absorption

applications in scramjets have been restricted to measuring H2O using these robust

telecommunications devices [58, 59, 61]. Here we exploit new commercially-available

technology to access stronger fundamental band transitions to monitor CO and CO2

in addition to H2O. Fiber-coupling of the laser source to the aeroengine test article

provides needed robust hardware mounting and only recently have fiber solutions

become available for these mid-IR wavelengths for CO and CO2 [111, 113]. Measure-

ments presented in Chapter 3 from a similar hydrogen-fueled scramjet combustor ge-

ometry revealed the presence of nonuniformities in temperature and composition and

have shown they can introduce significant error in absorption measurements [95, 96].

However, use of mid-infrared absorption transitions allowed optimal line-selection to

account for nonuniform conditions [65]. Here, measurements of CO and H2O employed

the recently-described scanned-wavelength-modulation (scanned-WMS) spectroscopy

technique, which helps to account for nonuniform conditions along the LOS with in

situ measurements of the absorption lineshape obtained directly from the WMS line-

shape [84, 82]. Measurements of CO2 used an external cavity quantum cascade laser

source that was not capable of the rapid wavelength tuning needed for WMS mea-

surements, and thus CO2 column density was measured using scanned-wavelength

direct-absorption, which also provides an integrated in situ lineshape. Species were

measured sequentially; first simultaneous CO and CO2 data were acquired and then

runs were repeated three days later to acquire H2O data at the same facility condi-

tions. As in the H2-air scramjet combustor measurements presented in Chapter 3, the

measurement line-of-sight (LOS) was translated throughout the combustor to map

combustion progress across several planes downstream of fuel injection.

Results reveal peak temperatures of about 2200 K occur within the combustor

60 CHAPTER 4. MULTISPECIES MEASUREMENTS IN A SCRAMJET

flame-holding cavity. Downstream of the cavity no temperature rise occurs in ei-

ther CO or H2O, indicating competition between thermal dilution and combustion

progress. Column density measurements show increasing concentration of combustion

products downstream of the fuel injection, revealing the spatial evolution of combus-

tion progress. However, large concentrations of the intermediate CO species were

also observed, indicating incomplete combustion heat release. Error analysis indi-

cates only a small measurement uncertainty compared to the observed time-variation

of the data, and therefore these temporal fluctuations in combustion products likely

represent unsteady combustion. In addition, measurements of H2O were made in the

cavity during flame extinction that provide an upper bound on the cavity residence

time of about 3.4 ms. These measurements are the first demonstration of this tech-

nique, and the results offer a promising avenue to future direct measurements of the

cavity residence time in a supersonic flame holder, which is an important parameter

to aid understanding of competition between ignition delay and mass transport in

supersonic flows.

4.1 Mid-IR Absorption Transition Selection

Measurements in the UVaSCF presented several important challenges that were ad-

dressed in selecting the laser absorption transitions. Hydrocarbon fuel reduced the

expected H2O concentration compared to the previously-studied hydrogen-fueled case,

resulting in less absorption. Because there are multiple major product species in an

ethylene-air flame, multispecies measurements are a necessity if one hopes to generate

a complete view of combustion progress and efficiency. In addition, compared to the

chemistry that converts OH to H2O, the chemistry that converts CO to CO2 is no-

toriously slow, and measurements of both CO and CO2 are important to understand

incomplete combustion. Moreover, nonuniform conditions within the scramjet com-

bustor present a distinct challenge to any sensor design. Thus, here the species CO,

CO2, and H2O were selected for measurement, and Fig. 4.1 shows the linestrengths of

these species from 1-6 µm at 1500 K. Two transitions near 4.85 µm were selected for

CO measurements of temperature and column density, two transitions near 2.5 µm

4.1. MID-IR ABSORPTION TRANSITION SELECTION 61

Table 4.1: Spectroscopic parameters of H2O, CO, and CO2 transitions used inethylene-air combustion UVaSCF experiments.

SpeciesFrequency, cm−1

(HITEMP ’10)

Linestrength(296K), cm−2/atm

(Measured)

Lower-StateEnergy, cm−1

(HITEMP ’10)H2O 3920.09 63.5 × 10−2 704.214H2O 4030.73 26.8 × 10−10 4889.488CO 2059.91 87.6 × 10−2 806.4CO 2060.33 26.4 × 10−5 2543.1CO2 2394.42 73.9 × 10−6 3329.0

for H2O measurements of temperature and column density, and a single transition

near 4.18 µm for CO2 measurements of column density (using the temperature pro-

vided by CO measurements and assuming the two species are in thermal equilibrium).

These transitions were selected based upon the sensor design studies by Goldenstein,

et al. [111] and Spearrin, et al. [113], and spectroscopic characteristics of the selected

transitions are summarized in Table 4.1.

4.85 m

4.18 m

2.48 m

Figure 4.1: CO, H2O, and CO2 spectra over a large range of infrared wavelengths at1500 K. The sensor presented targeted absorption transitions at wavelengths notedon the figure.

These mid-infrared transitions were selected not only to provide strong absorption


signals and good temperature sensitivity, but also to minimize errors introduced by

assuming linestrength scales linearly with temperature, as discussed in Section 2.5.

Figure 4.2 shows the maximum percent deviation of the actual linestrength from a

linear approximation as a function of the mean temperature along the line of sight

for a temperature distribution spanning 500 K. These results are shown for all five

of the absorption transitions used in the results presented here, and confirm that

the errors introduced by this linear linestrength assumption are small, particularly

at high average temperatures such as those encountered in scramjet combustion.

Additionally, access to mid-infrared H2O absorption transitions allows for a more

than 50% reduced error in H2O linear linestrength approximation at temperatures

between 1300K and 1800 K compared to results presented in Section 3.1.2. This

translates directly to improved measurement fidelity in the results presented here.

1400 1600 1800 2000 22000

1

2

3

4

5

6

7

8

Mean Temperature, K

Err

or

in L

inear

S(T

) A

ppro

x., (

% o

f S

(Tm

ean))

H2O Transition, E’’ = 704.2 cm

−1

H2O Transition, E’’ = 4889.5 cm

−1

CO Transition, E’’ = 806.4 cm−1

CO Transition, E’’ = 2543.1 cm−1

CO2 Transition, E’’ = 3329.0 cm

−1

Results shown forT = T

mean ± 250 K

Figure 4.2: Error in a linear linestrength approximation for selected H2O, CO, andCO2 transitions as a function of mean temperature across the LOS.

4.2. FACILITY DESCRIPTION 63

4.2 Facility Description

Measurements were performed on the University of Virginia Supersonic Combustion

Facility (UVaSCF), in a slightly different combustor geometry configuration than the

measurements presented in Chapter 3. The UVaSCF is a direct-connect, continuous-

flow wind tunnel, as shown in Fig. 4.3. The facility was oriented vertically, with

the heater below ground, the test section above floor level, and with an atmospheric

exhaust through an open pipe to the roof of the building. Air was provided to the

facility by a compressor and desiccant dryer system [114]. Flow originated at the

top of a pressurized heater tank at 300 kPa and proceeded downward through an

outer annulus section before entering a 14-stage electrical-resistance heater core at

the bottom of the tank [115]. Air out of the heater had a total temperature of 1200 K,

making conditions equivalent to Mach 5 flight speeds. After leaving the heater, the

flow proceeded through a ceramic flow straightener and then a Mach 2 nozzle. The

nozzle was directly attached to a constant area isolator followed by the combustor.

Dimensions of the isolator section were 26.6 cm in length (x-axis), 2.54 cm in the

transverse direction (y-axis), and 3.81 cm along the LOS direction (z-axis). Within

the combustor and approximately 3.2 cm upstream of fuel injection, the flow path

diverged along the injector-side wall at an angle of 2.9 degrees. Heated ethylene was

injected through 5 ports spanning along the z-axis of the combustor 2.45 cm upstream

of the leading edge of a cavity flame holder [116]. The cavity had depth (y-direction)

of h = 0.9 cm and length 4.73 cm along the axial direction (x-axis) (L/D = 5.25), with

the rear edge of the cavity closed out with a ramp. There was optical access to the

combustor through large 20 cm by 6 cm fused-silica windows for H2O measurements

near 2.5 µm. Sidewalls with smaller slot-shaped sapphire windows at measurement

planes 1 and 2, noted in Fig. 4.3, allowed transmission of longer wavelengths (over 4

µm) for CO and CO2 measurements. All windows were wedged on the outer face to

avoid interference from internal etalon-type reflections as the laser wavelengths were

scanned. After the combustor, the flow continued through a 14.9 cm long constant

area section and an 18 cm long extender before exiting to the exhaust pipe.


Y

X

Fuel Injection

Reaction Zone

Cavity

Plane 1

Plane 2

Plane 3

Free-Stream Recirculation

Zone

Flow Direction

Z

Combustor

Isolator Residence Time

Measurement

Figure 4.3: Photo of the UVaSCF direct-connect scramjet combustor (left) and car-toon diagram of the combustor and flame holder cavity configuration (right, not toscale) with three absorption spectroscopy measurement planes noted.

4.3 Absorption Spectroscopy Sensor Hardware

To simplify the hardware footprint and the combination of multiple wavelengths onto

one line-of-sight, simultaneous CO and CO2 measurements were first performed, then

H2O data was collected at the same facility conditions several days later. Figure

4.4 shows a diagram of the CO and CO2 measurement hardware. Two lasers were

used: a distributed-feedback quantum cascade laser (Alpes) near 4.87 µm for CO

measurements and an external cavity quantum cascade laser (Daylight Solutions)

near 4.2 µm for CO2 measurements. A mechanical beam chopper periodically blocked

the beam from the CO2 laser to measure the emission background signal needed

to correct the direct-absorption baseline. Light from each laser was independently

focused onto two hollow-core fibers (OKSI) via adjustable alignment stages, and the

two fibers combined into a common shield with the center of the two independent

fiber cores separated by 0.3 mm. Light out of the fiber pair was collimated by a 40

mm focal length silicon lens with the beam-centers separated by 1.5 mm and directed

through sapphire windows across UVaSCF combustor flow path. The beam was then

split onto two separate filtered mercury-cadmium-telluride (MCT) thermoelectrically

cooled detectors (Vigo) whose signals were digitized and saved.

4.3. ABSORPTION SPECTROSCOPY SENSOR HARDWARE 65

4.87 m

DFB QC Laser

(CO)

4.2 m

ECQC Laser

(CO2)

Multi-axis

Alignment

Stage

2-to-1 Fiber System

(Hollow-Core)

Beam Chopper (12.5 Hz)

CO/CO2 Sensor Hardware Layout

N2 purge of breadboard, hollow-core

fiber, and catch optics

100 Hz

Air

Flow

Combustor

Beam Splitter

Iris

Filter

MCT Detector

Lens40 mm f.l. Si Lens

200 Hz

50 kHz

+

Figure 4.4: CO and CO2 sensor hardware layout for hydrocarbon-fueled scramjettesting. The CO and CO2 lasers were both coupled through a single fiber and werede-multiplexed with a beam splitter after transmission through the combustor.

A sensor hardware diagram for H2O measurements is shown in Fig. 4.5. Light

originated in two distributed-feedback tunable diode lasers (nanoplus) emitting near

2551 nm and 2482 nm. Output light from each laser was collimated and passed onto

a beam splitter that combined both laser beams onto a single path. The multiplexed

light was focused onto a 400 µm-core multimode fiber (Fiberguide). At the combustor,

light was pitched across the test section by a 20 mm focal length zinc selenide lens.

Transmitted light was then filtered and focused onto a single MCT detector. The two

laser beams were demultiplexed in post-processing by isolating signals at modulation-

frequency harmonics harmonics (fm = 75 kHz for 2551 nm and 100 kHz for 2482 nm).

Lasers were scanned over absorption transitions with a 250 Hz sinusoid, resulting in

a repetition-rate of 500 Hz as each scan passed over the transition twice.

The position of the laser LOS in the combustor flow field for CO, CO2, and

H2O was mechanically translated using a set of computer-controlled high-precision

translation stages (Zaber). This stage system allowed the measurement LOS to span

up to 15 cm in the axial direction (x-axis) and 5 cm in the transverse direction (y-

axis). Measurements presented here focus on three axial planes 2.18 cm (Plane 1),

6.01 cm (Plane 2), and 9.83 cm (Plane 3) downstream of the cavity flame holder


leading edge, as shown in Fig. 4.3.

2551 nm

DFB TDL laser

2482 nm

DFB TDL laser

H2O Sensor Hardware Layout

N2 purge of breadboard, fiber,

and catch optics

Air

Flow

Combustor

Filter

MCT Detector

Lens

20 mm f.l.

ZnSe Lens250 Hz

75 kHz

+

Beam Splitter

250 Hz

100 kHz

+

Collimating Lens

5-axis

Fiber-Mount

400 m

MM Fiber

Figure 4.5: H2O sensor hardware layout for hydrocarbon-fueled scramjet testing. Twodistributed feed-back tunable diode lasers were multiplexed onto a single fiber-opticline for simultaneous temperature and column density measurements.

4.4 Results

4.4.1 Multispecies Combustion Product Measurements

Combustion measurements were conducted at the UVaSCF for ethylene-air combus-

tion at a global equivalence ratio of Φ = 0.15. First, the CO and CO2 sensor was

used in a single run, then the H2O sensor was installed and measurements were made

in the following week at the same run conditions. As shown in Fig. 4.6, the axial

pressure trace from CO and CO2 testing overlaps strongly with the pressure trace

from H2O testing, indicating tunnel conditions are highly repeatable across different

runs and making comparisons between these sensor results from different times pos-

sible. Figure 4.6 also notes the three measurement planes, and shows all three planes

are downstream of the largest pressure rise due to the primary shocks. Measurement

results are shown for CO temperature and CO and CO2 column density in measure-

ment planes 1 and 2. Results for H2O temperature and column density are shown

4.4. RESULTS 67

for all three planes. In each plot, the abscissa is shown in units of distance from the

wall opposite the fuel injector. This convention was chosen because the wall opposite

the injector was straight; it did not diverge like the injector-side wall. The location

of the injector wall is noted on the plots for each plane. Each measurement point

represents the average over 1 s of integrated absorption data. H2O measurements

were acquired at a rate of 500 Hz, while CO and CO2 measurements were conducted

at 200 Hz and 100 Hz, respectively. Tunnel conditions are steady for time scales of

minutes or hours, with a 95% confidence interval of 1.5% in pressure [22], therefore

averaging absorption spectroscopy data tends to reduce random sensor noise. Error

bars shown are the standard deviation in measurements, but, as discussed below, they

are interpreted to represent the temporal fluctuations in combustion extent observed

over a particular LOS, rather than the measurement uncertainty.

−40 −30 −20 −10 0 10 20 30 40 50 600

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Axial Distance (zero at cavity leading edge), cm

Pre

ssure

, atm

Fuel Off

φ=0.15, CO/CO2 Testing

φ=0.15, H2O Testing

Measurement Planes

Nozzle Exit

CombustorExit

Fuel Injection

Line Drawing of Axial Geometry

Figure 4.6: Axial pressure traces measured without fuel injection and with ethylenefuel injection at equivalence ratio of Φ = 0.15 for CO/CO2 testing and H2O testing.Also shown is a scale drawing of the axial geometry of the combustor.

CO and H2O temperature measurements are shown in Fig. 4.7, with subplot


(a) showing data from Plane 2 and subplot (b) showing data from Plane 1. Note

that measurements from Plane 1 extend into the cavity flame holder. CO and H2O

temperature measurements agree within 17% at all locations, and with an average

difference of about 7%, suggesting that both species are distributed in regions of the

flame where temperatures are approximately equal. Peak temperatures from both

CO and H2O occur within the cavity where residence times are longest and there

is more time to oxidize complex molecules, resulting in temperatures in excess of

2150 K. Outside of the cavity in Fig. 4.7b, the temperature gradually descends to-

wards the free-stream static temperature of 770 K. However, note that measurements

only penetrate into the flow as far as there are substantial concentrations of com-

bustion products. Therefore, the measurements tend to track the development of a

combustion product plume with axial progression through the combustor. Results

for the downstream plane (Fig. 4.7a) reveal similar results compared with locations

outside of the cavity in Plane 1. This indicates that combustion progress and heat

release compete roughly equally with thermal dilution of combustion products by the

relatively cool free stream air.

0 0.5 1 1.5 2 2.5 3 3.5

1000

1500

2000

Te

mpe

ratu

re, K

H2O Temperature

CO Temperature

Injector Wall

0 0.5 1 1.5 2 2.5 3 3.5

1000

1500

2000


Tem

pera

ture

, K

H2O Temperature

CO Temperature

Cavity Floor

Injector Wall

a)

b)

Figure 4.7: Measurements of CO and H2O temperature at two planes downstream offuel injection: a) Plane 2 and b) Plane 1.

Column density results for CO, CO2, and H2O at Planes 1 and 2 are shown in Figs.

4.4. RESULTS 69

4.8b and 4.8a, respectively. All three species trend very similarly. Within the cavity

they peak near the injector wall, gradually plateau at a lower value, and then roll off

towards zero outside the cavity. At Plane 2, peak values are again observed at the

injector wall, but in at this plane there is virtually no plateau in the product plume.

An important observation is that in both planes there is a significant concentration of

CO (thermal equilibrium CO would be only 1.7% by mole at stoichiometric conditions,

or about 0.004 mole/m2 in terms of column density at 1500 K, 0.75 atm), indicating

that there is incomplete combustion throughout the product plume. The measured

CO concentration is not significantly affected by ambient CO in the tunnel air (about 2

ppm), which is (surprisingly) larger than than the equilibrium CO in the combustion

products. Nevertheless, ambient CO is expected to correspond to only 4 × 10−7

mole/m2 in terms of column density. Compared with the H2O measurements, this

implies that conversion of CO to CO2 is a relatively slow process within the combustor.

Figure 4.8 also shows the summation of CO and CO2 column densities, effectively

counting the total molar column density of carbon atoms in combustion products

at each location in the flow. This is an important parameter because the column

density of carbon-containing atoms (CO and CO2) should match the H2O column

density for ethylene-air combustion. As ethylene fuel (C2H4) is consumed in the flow,

it is expected that most hydrogen atoms will proceed to water (two H2O per ethylene

molecule) and carbon atoms will proceed to CO, CO2, and possibly other molecules.

The results from both planes show that there is good agreement between H2O and

CO+CO2 column densities, suggesting that measurement of CO and CO2 accounts

for nearly all the carbon atoms that have been consumed based on the production of

H2O. However, unburnt ethylene is not accounted in the measurement and may be

present in significant quantities throughout the flow.

Figures 4.9a and 4.9b show temperature and column density results, respectively,

from the H2O sensor for all three planes. Standard deviation error bars indicating

the fluctuation of the fraction of combustion product sampled are shown as error bars

for all three planes. H2O measurements show the seemingly conflicting observations

that temperature does not increase with downstream progression, while the column

density does increase. This result suggests that outside the cavity, thermal dilution


0 0.5 1 1.5 2 2.5 3 3.50

0.01

0.02C

olu

mn D

ensity,

mole

/m2

H2O Column Density

CO Column DensityCO

2 Column Density

CO+CO2 Column Density

Injector Wall

0 0.5 1 1.5 2 2.5 3 3.50

0.01

0.02


Colu

mn D

ensity,

mole

/m2

H2O Column Density

CO Column DensityCO

2 Column Density

CO+CO2 Column Density

Cavity Floor

Injector Wall

a)

b)

Figure 4.8: Measurements of CO, CO2 and H2O column density at two planes down-stream of fuel injection: a) Plane 2 and b) Plane 1.

occurs as unburned pockets of fuel mix with the cold free-stream air, which dampens

the temperature rise expected from the heat release from combustion. However,

as unburned fuel oxidizes, the number of absorbers along the LOS increases, which

corresponds to increased column density. Thus there is strong competition between

this thermal dilution and combustion progress. Note that pressure is not expected

to significantly vary across each measurement plane as strong shocks and expansions

occur well upstream of the measurement planes, although some of these gas dynamic

effects could have a small influence on column density. Furthermore, the available

wall pressure data do not enable meaningful corrections for these effects.

4.4.2 Combustion Unsteadiness

The time-resolved temperatures TCO and TH2O and their respective column densities

have much larger temporal fluctuations than expected from the statistics of the fits

of the scanned-WMS measurements. The 95% confidence interval for the integrated

absorbance returned in the best-fit lineshape was about ±2%. Standard error propa-

gation techniques were used to determine the influence of integrated absorbance error

4.4. RESULTS 71

0 0.5 1 1.5 2 2.5 3 3.5800

1000

1200

1400

1600

1800

2000

2200

2400


H2O

−A

vera

ged T

em

pera

ture

, K

Plane 1

Plane 2

Plane 3

Injector Wall

a)0 0.5 1 1.5 2 2.5 3 3.5

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04


H2O

Colu

mn D

en

sity, m

ole

/m2

Plane 1Plane 2Plane 3

b)

Figure 4.9: Measurements of H2O temperature and column density at three planesdownstream of fuel injection: a) H2O number-density-weighted average temperatureand b) H2O column density.

on the measured temperature and column density. These calculations yielded single

standard deviation uncertainties no larger than 12 K and 3.5×10−3 mole/m2 through-

out all measurement locations. Moreover, at no point in the flow does the statistical

error represent more than 1.5% of the measurement value in either column density or

temperature. However, time-resolved temperature and temperature-corrected H2O

column density shown in Fig. 4.10 reveal pronounced time-variations. Note that

because column density scales inversely with temperature, in the limit of uniform

temperature across the LOS, multiplying column density by temperature in Fig. 4.10

isolates the variations in species. That these time-variations exceed the measurement

uncertainty is illustrated by Fig. 4.11, which shows a histogram of the column den-

sity data from Fig. 4.10b, a normal distribution best-fit to the experimental data,

and the normal distribution that would be expected based on the WMS-fitting error

propagation. In this case the full-width at half-maximum of the expected error distri-

bution is less than 19% of the experimental best-fit distribution, which implies that

most of the observed variation in the experimental data can be attributed to sources

other than measurement error, including time-varying interaction of shear layers with

the recirculation zones in the cavity flame holder. Therefore we conclude that the


majority of the observed standard deviation in measurements over a 1 s measure-

ment period is due to temporal variation of combustion products due to transport,

and thus, in the previous section the error bars shown on the data represent statistics

about the mean reflecting the unsteadiness of combustion and not the fitting errors of

the scanned-WMS measurements. This interpretation is supported by correlation of

the temperature and temperature-normalized column density measurements. Within

each plane, higher temperatures occur when more combustion products are measured.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1500

2000

2500

H2O

−A

ve

rag

ed

Tem

pera

ture

, K

Time, s

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.920

30

40

50

H2O

Colu

mn D

ensity*

Tem

pera

ture

, m

ole

−K

/m2

Time, s

a)

b)

Figure 4.10: Time-history of H2O temperature and column density measurementsfrom plane 1 at a location 9 mm from the injector-side wall: a) Temperature and b)Temperature-normalized column density, NH2O × T nH2O

.

4.4.3 Transient Measurements Within the Cavity During Flame

Extinction

Cavity flame holders promote combustion by reducing the effects of finite-rate chem-

istry in several ways, including creating recirculation zones to allow fuel/air mixing

at low velocities, providing a continuous source of free radicals for combustion, and

generation of coherent structures of fuel and air through shear layer interactions [117].

4.4. RESULTS 73

0.01 0.012 0.014 0.016 0.018 0.02 0.0220

50

100

150

200

H2O Column Density, mole/m

2

Num

ber

of

Occu

rren

ces in

Bin

Best−fit Distribution to Experimental Data

Expected Distribution Based on Systematic Error in Fitting

Figure 4.11: Histogram of column density data from Fig. 4.10, best-fit normal distri-bution, and expected normal distribution based on error in best-fit area.

The cavity residence time, τ , is directly proportional to mass transfer into and out of

the cavity, and therefore is an important characteristic of the effectiveness of flame

holder mixing. Here, H2O measurements were made for a LOS inside the cavity

during flame extinction to determine an upper bound on cavity residence time. The

measurement point was 2.5 mm upstream of Plane 1 and 4.5 mm from the injector

sidewall. Note that H2O is a better candidate than CO for these transport time mea-

surements due to its faster chemistry. To achieve the 31.25 µs time resolution, the

WMS-2f /1f H2O sensor was used without scanning (fixed-WMS), sacrificing mea-

surement error for increased bandwidth (16 kHz). The data set consists of 3 seconds

of fixed-WMS data just prior to flame extinction (observed by visible emission); these

data are then examined to identify the extinction event from change in temperature

and disappearance of combustion product H2O. The flame was extinguished by turn-

ing the fuel down slowly over the course of many seconds until the fuel equivalence

ratio reached a critical value of about Φ = 0.09, below which the flame suddenly ex-

tinguished. Measured absorption signals were converted to temperature and column

density measurements by assuming a constant pressure from data at an equivalence

ratio of Φ = 0.10. While this technique is not yet fully developed, these measurements

represent an exciting new application of laser absorption spectroscopy to obtain flow

field parameters needed by computational researchers.


Measurements of H2O temperature and a temperature-normalized column den-

sity are shown in Fig. 4.12 for a 25 ms period capturing the flame extinction event.

The temperature-normalized column density is obtained by multiplying column den-

sity by the measured temperature, since density scales inversely to temperature. As

noted in the previous section, this normalization process is only approximate, but

is exact in the limit of uniform temperature across the line-of-sight. Because of the

slow fuel turn-down during the flame extinction, fuel was still flowing to the cavity

throughout the duration of these tests, but the temperature and column density both

declined suddenly over a period of milliseconds indicating sudden flame extinction.

This implies that flame extinction measurements are decoupled from the fuel delivery

hardware and therefore it is not necessary to fully model the fuel plumbing in order

to draw conclusions from this data. Moreover, these transient measurement of com-

bustion products are only a convolution of the time for combustion extinction and

the residence time.

0 5 10 15 20 25500

1000

1500

2000

Tem

pera

ture

, K

Experimental Data

Logistic Curve Fit

0 5 10 15 20 250

5

10

15

20

time, ms

H2O

Colu

mn D

ensity*

Tem

pera

ture

, m

ole

−K

/m2

Experimental Data

Logistic Curve Fit

T (t) =T0

1 + exp(a · (t − t1/2))T0 = 1517 K, a = 2.08 ms−1,

t1/2 = 11.45 ms

NT (t) =NT,0

1 + exp(a · (t − t1/2))

NT,0 = 15.5 mole-K/m2, a = 1.74 ms−1,t1/2 = 11.66 ms

a)

b)

Figure 4.12: Time history of fixed-WMS measurements during flame extinction: a)Temperature and b) H2O column density. Both plots show a logistic curve fit to theexperimental data and list the best-fit parameters obtained.

Comparing Figs. 4.12a and 4.12b, the column density declines more slowly than

4.4. RESULTS 75

the temperature, identifying differences between thermal and mass transport in the

cavity. This result has never been observed before to our knowledge. A steady tem-

perature near 1500 K was observed near the 10 ms time in the plot, which then rapidly

declined to a steady value of about 650 K, indicating complete flame extinction as

this value is slightly lower than the static temperature of the inlet gas flow (perhaps

due to expansion effects in the cavity, however temperature measurements after flame

extinction suffer from a low signal-to-noise ratio due to the small amount of H2O in

the flow). A logistic function of the form 1/ (1 + e−x) was fit to the temperature

data (shown in Fig. 4.12a), and yields a time of 2.8 ms for the temperature to drop

from 5% to 95% of the total temperature range over the test. However, temperature

measurements may not be the best indicator of residence time because heat transfer

from products to the combustor walls and the bath gas will complicate the inter-

pretation of the temperature time-history. Measurements of temperature-normalized

column density offer fewer complications because once the flame is extinguished, the

production of new combustion product H2O rapidly ceases and the normalization

eliminates most of the influence of temperature on detecting transport of products

from the cavity. However, note that these measurements do not correct for variations

in pressure, which occur during flame extinction and will affect column density. H2O

column density measurements corrected for the changing temperature observed are

shown in Fig. 4.12b, and maintain a steady value of about 15.5 mole-K/m2 for a short

period after the temperature begins declining. However, after the 11 ms mark, the

column density begins to rapidly decline, ultimately to a steady value of about 0.98

mole-K/m2. Also shown in Fig. 4.12b is a logistic curve fit to the measurement data

with fitting parameters shown in the figure. The column density logistic fit yields a

time of 3.4 ms to drop from 5% to 95% of the total column density range over the test.

This value is 20% larger than the measured temperature time to decline, which rein-

forces the conclusion that there may be some significant differences between thermal

and mass transport in the cavity.

Because these measurements occurred during a flame extinction event, the mea-

sured times for combustion products in the cavity are limited by either the extinction

event time, the residence time in the cavity, or a convolution of both effects. If the


flame extinction contributes to the measured time for combustion products to disap-

pear, then the cavity residence time must be shorter than the measurements presented

here. Thus, these measurements place an upper bound on the cavity residence time.

Future work may refine this technique to decouple flame extinction and residence time

effects and provide direct measurements of cavity residence time. However, note the

results presented here are consistent with CFD calculations of residence time based

on similar combustor geometries (around 2.3 ms for 5% to 95% of the total dynamic

range), and therefore this technique represents a valuable starting point in this new

application of laser absorption spectroscopy [118].

Chapter 5

Hypersonic Scramjet Combustor

Measurements Within a Reflected

Shock Tunnel

There is substantial interest in air-breathing hypersonic propulsion systems capable of

operating at flight speeds in the range of Mach 8-15 [16]. Vehicles operating at these

conditions would be fueled by liquid hydrogen and may be used for either manned

hypersonic cruising or for single-stage to orbit space vehicles [119]. At these flight

speeds, the flow within the combustor is hypersonic rather than just supersonic as it

was for the results presented in Chapters 3 and 4. This presents many challenges to

combustor design, chief among which is that fuel-air mixing is not well understood

at high Mach numbers where the bulk flow velocity is approximately equal to the

injector flow speed [120]. In order to better understand hypersonic combustion pro-

cesses, reflected shock tunnels have been commonly used to generate hypervelocity

conditions and test scramjet combustors at conditions equivalent to flight speeds of

Mach 10 or higher [121]. While model scramjet combustors used in these types of fa-

cilities commonly include instrumentation such as pressure transducers and heat flux

gauges, additional diagnostics are needed, particularly to determine temperature and

composition of species in the combustor [51, 122]. Optical sensors utilizing tunable

diode laser absorption spectroscopy (TDLAS) are an attractive source of temperature

77

78 CHAPTER 5. TDLAS IN A HYPERSONIC SCRAMJET COMBUSTOR

and H2O measurements in these facilities, as they offer both mechanical reliability as

well as fast time-resolution needed for measurements in a reflected shock tunnel.

Historically, tunable diode laser absorption spectroscopy (TDLAS) sensors have

played a pivotal role in characterizing hypersonic scramjet ground test facilities by

supplying in situ measurements of important thermophysical properties such as tem-

perature, species concentration, and velocity of the free-stream flow to better under-

stand test times and test gas contamination [51, 123–125]. More recently, researchers

have begun to apply TDLAS diagnostics to measure temperature and water vapor for

tracking combustion progress within model scramjet combustors during hypersonic

testing [80, 92]. However, these past studies have assumed that the conditions were

uniform along the line-of-sight (LOS) in their data reduction methods, and the flow

within hypersonic combustors is known to be highly three-dimensional [120]. Here we

acknowledge nonuniformity along the the LOS, but use a new scanned wavelength-

modulation spectroscopy (WMS) strategy to measure changes to the transition line-

shape due to nonuniformity and provide quantitative WMS absorption results [82, 84].

This work represents one of the first practical implementations of this new tech-

nique in a scramjet engine [126]. Scanned-WMS measurements are an important new

tool for characterizing scramjet combustion or any other flow where nonuniformi-

ties are present and the noise-rejection capabilities of WMS are desired. The sensor

probed two H2O absorption transitions near 1.4 µm to measure H2O column density

and water-weighted temperature downstream of fuel injection across three LOSs in

a model scramjet at the HyPulse reflected shock tunnel facility at ATK General Ap-

plied Science Laboratory (GASL) in Ronkonkoma, New York. Implementation of this

sensor presented several design challenges in delivery of light across multiple LOSs on

a model scramjet inside a pressure vessel. A detailed description of the facility and

TDLAS sensor hardware is included. Measurement results are presented from three

separate tests: one non-combusting mixing case and H2-air combustion at two unique

angles of attack and fuel-air equivalence ratio combinations.

5.1. HARDWARE DESCRIPTION 79

5.1 Hardware Description

5.1.1 ATK HyPulse Test Facility

Tests were performed on the NASA HyPulse facility, operated by ATK-GASL in

Ronkonkoma, New York at conditions equivalent to Mach 10 flight. HyPulse was

operated in reflected-shock-tunnel mode; a detonable H2/O2/Ar driver mixture ini-

tialized propagation of a shock through the test gas (N2 or air) over the length of

the 15.2 cm diameter tube, shock heating the test gas. The shock reflected off the

end-wall and propagated back upstream, stagnating and further shock-heating of the

test gas. This shock-heated air at the end-wall was the plenum for a hypersonic noz-

zle that accelerated flow into a large test cabin (diameter = 2.1 m). Here, the flow

was captured by a model scramjet forebody, inlet, and combustor, shown in Fig. 5.1.

The model inlet and combustor was machined from a solid block of aluminum and

the forebody from stainless steel. Because this is an impulse facility no cooling of the

model was necessary.

Fuel injector ramp

TDLAS hardware

with protective

cover plates

TDLAS @

x = 27.6 cm x = 0

Figure 5.1: Rendered view of inlet and combustor model used for Mach 10 scramjettesting at ATK HyPulse. Note the fuel injector ramp seen through large diagnosticwindows and TDLAS hardware 27.6 cm aft of the injector ramp. Forebody not shown.Wedged cover plate shown removed for visibility of TDLAS system.

Hydrogen fuel was injected into the captured flow at the base of a 10◦ unswept


compression ramp (height H = 6.4 mm). As shown in the flow path diagram in Fig.

5.2, beginning 6.3 cm behind the injector ramp, the flow path diverged at an angle of

2.9◦ until exiting at the end of the rig (30.2 cm downstream of fuel injection). Three

separate sets of windows offered optical access to the flow path inside the scramjet.

Large viewing windows centered around the injector ramp were used for Schlieren

imaging. TDLAS measurements were made through windows 27.6 cm downstream

of fuel injection with clear aperture of 2.8 cm (height) by 0.64 cm (along flow path).

Here the duct height was 3.6 cm and the span between TDLAS LOS 1 (lower) and

LOS 3 (upper) was 2.3 cm. The LOS path length spanned 3.81 cm across the flow

path. Other instrumentation on the model included piezoelectric pressure transducers

and thin-film resistance and coaxial thermocouple heat flux gauges [127].

27.6 cm Flow

3 TDLAS LOS

2.3 cm

Figure 5.2: Drawing of model scramjet flow path, with three TDLAS measurementlocations noted.

5.1.2 TDLAS Sensor Layout

Figure 5.3 shows a diagram view of the the TDLAS hardware used in the sensor.

Signal generation, data acquisition, and laser hardware were all located outside of the

test cabin. Two lasers were used to probe H2O absorption transitions near 1391.7 nm

and 1469.3 nm. Note these were the same transitions as used in the Mach 5 H2-air

combustion tests presented in Chapter 3, and therefore for a discussion of line selection

the reader is referenced to Section 3.1.2. Sinusoid waveforms to scan and modulate

the laser injection current were generated digitally with a desktop computer; the scan

rate was 1 kHz and modulation was at 160 kHz and 200 kHz for the lasers near 1391.7

nm and 1469.3 nm, respectively. The fiber-coupled output light from the two lasers

was multiplexed onto one 9 µm core single-mode fiber and the combined signal was

5.1. HARDWARE DESCRIPTION 81

then split onto two separate single-mode fibers. A wall feed-through allowed both

fibers to be routed inside the test cabin where the fiber-coupled light was split again

to give a total of three fibers, each bringing light to a separate LOS. All three fibers

were routed to the scramjet model where they were attached to collimating optics

to transmit light on three measurement LOSs. On the opposite side of the model,

light was turned 90◦ by mirrors and collected by focusing lenses and routed onto 600

micron multi-mode fibers to an adjacent metal box containing detection hardware.

The output light from each fiber was focused onto a detector (Thorlabs PDA10CS)

by doublet lenses. Detectors had a bandwidth of 17 MHz, which was anti-aliasing

filtered to 1 MHz. The detector signal was routed out of the tunnel on BNC cables,

through BNC wall-feedthroughs, and back to a computer for data acquisition at a

rate of 10 MHz, with 12-bit resolution over a 2 V dynamic range. All cabling within

the test cabin was enclosed in 1.25 cm or 2.5 cm diameter steel-reinforced hosing

to protect it from the hypersonic flow from the expansion nozzle. The metal box

enclosing the detectors protected that hardware.

The optical system mounted on the model scramjet, shown in Fig. 5.4, had three

parallel LOSs spaced evenly by 1.15 cm, spanning 2.3 cm. Fig. 5.5 shows dashed

lines and labels depicting all three TDLAS measurement LOSs, numbered “LOS 1,”

“LOS 2,” and “LOS 3.” LOS 1 was 0.15 cm from the injector wall, LOS 2 was 1.30

cm from the injector wall, and LOS 3 was 2.45 cm from the injector wall (or 3.45

cm, 2.3 cm, and 1.15 cm from the top of the flow channel, respectively). All three

LOSs were 27.6 cm downstream of fuel injection. Adjacent optical LOSs alternated

between transmission and receiving on each side of the combustor in order to allow

this compact spacing arrangement. The optical mounting system consisted of a large

plate with a rectangular hole in the center used as an interface between the optics and

the model combustor. Optics were attached to a second, smaller, plate that sat away

from the large plate on 2.5 cm spacers. Each LOS was individually adjustable over one

translational and two rotational degrees of freedom. Vertical translation was allowed

by mounting each optical element on dovetail brackets that were clamped into their

final position by a bolt and washer. As shown in Fig. 5.6, the optics themselves were

attached to a second piece floating below the bracket on several bolts with a set screw


+ +

+ +

Slow scan

1 kHz

+++

++++++ Fast scan

200 kHz

160 kHz

1392 nm 1469 nm

Fiber

Combiner/

Splitter

Single-Mode Fiber

Computer

Detectors

Air

Flow

Detector Signals

Test Cabin

Fiber-Wall

Feedthrough

sss

Protective Box

Multi-Mode

Fiber

Figure 5.3: Diagram of TDLAS hardware layout for ATK HyPulse measurements.

acting as a fulcrum. By tightening the bolts to varying degrees, adjustments could

be made in two axes of rotation about the fulcrum. Because each optical element

could be individually adjusted and locked in position, optimizing alignment of light

across the flow path in the model proved fairly simple, and this alignment was robust

through multiple facility operation cycles.

Light was transmitted across the combustor on each LOS using a 3.8 mm diameter

fiber-coupled GRIN (gradient-index) lens (OZ Optics). On the receiver side the light

was first turned parallel to the flow path with a 5 mm right-angle mirror, and then

was collected on a 10 mm diameter ThorLabs F240SMA-C aspheric lens to couple

the transmitted light onto the collection fiber. The large collection optic diameter

ensured complete light collection in the presence of beam steering due to density

gradients that can skew the LOS. The entire optical assembly was protected from the

5.2. RESULTS 83

Fore and aft TDLAS windows

(Only aft used in experiments)

LOS

“Pitch” Lens

“Catch” turning mirror

and collection lens

Set screws for

alignment

adjustment a) b)

Interface Bracket

Window Optics

Bracket

Rear Cover

Plate with

Fiber Routing

Figure 5.4: Detailed view of TDLAS hardware attached to HyPulse model combustor.a) Rendered view b) Photograph

hypersonic flow with a two-piece steel wedged cover plate. A rear cover plate was

threaded to accept the protective cabling (shown in Fig. 5.4b), allowing all fibers

to be routed to the optics and complete access to adjustment screws while mounted

to the model. A three-sided wedge-shaped cover plate was then bolted over the rest

of the optics to completely protect them from the oncoming flow. The edges of the

entire assembly were sealed with aluminum tape to minimize leaking of the test gas

into ambient optical path during the test.

5.2 Results

TDLAS results from three Mach 10 tests will be presented here. First, raw WMS-

2f /1f signals are presented and qualitative results are discussed. Next, quantitative

results are shown, beginning with column density measurements from a tare run with-

out combustion in the model. Then column densities and temperatures of two com-

bustion cases are presented, the first at an angle of attack of θ = 1◦ and hydrogen-air

equivalence ratio of Φ = 1.31 and the second at angle of attack of θ = 7.5◦ and equiv-

alence ratio Φ = 1.03. The flow conditions for all three runs are summarized in Table

5.1. Results are shown as time-histories with the abscissa in milliseconds and TDLAS


Pressure transducer

LOS 1

LOS 2

LOS 3

Figure 5.5: Cross section view of TDLAS hardware with LOS labeling.

Dovetail

Bracket

5 mm 90° Turning Mirror

Fulcrum Bolts Adjust

Angle and Lock

in Place

Figure 5.6: Detailed view of dovetail bracket and 90◦ turning mirror holder (holdertranslucent for visualization). A single set screw in the center acts as a fulcrumagainst the three bolts threaded into the mirror holder, allowing for two rotationaldegrees of freedom.

measurements reported every 0.5 ms (2 measurements per 1 kHz scan). The time ori-

gin is defined by the arrival of the test gas at the measurement location and the 3 ms

test window was defined based upon the steady duration of pressure traces from the

5.2. RESULTS 85

Table 5.1: Experimental flow conditions within the model scramjet combustor foreach of three tests conducted at ATK HyPulse.

Angle ofattack,

deg.Test gas

EquivalenceRatio, Φ

Free-streamtemperature,

K

CombustorPressure, atm

MachNumber

1 N2 N/A 1180 0.302 4.141 air 1.31 1180 0.302 4.14

7.5 air 1.03 1477 0.475 3.5

model collected upstream of the TDLAS measurement. The beginning and end of the

test window is marked on each plot. Results were calculated using the scanned-WMS

methodology discussed in Section 2.3.2. Due to the unsteady conditions in these

measurements, the differences between measurement error and flow field fluctuation

are difficult to quantify. Estimated measurement uncertainty includes errors of about

1.5% in temperature and column density measurements, based on heated static-cell

experiments at known conditions conducted at Stanford University [82] and similar

measurements in a continuous-flow Mach 5 model scramjet combustor (See Chapter

3). The sensors used to estimate the uncertainty employed the same absorption tran-

sitions and similar measurement techniques. These other measurements had errors of

less than 1% when compared to facility conditions. However, this estimate does not

account for additional facility flow field noise and rapid transients, and hence to be

conservative the uncertainty estimated here is larger.

5.2.1 Normalized WMS-2f Signals

Because of the robust and high signal-to-noise ratio of the data acquired, a qualitative

understanding of the flow-physics is obtained by examining the raw WMS data. Fig-

ure 5.7 shows measured WMS-2f /1f signals for the absorption transition at 1391.7

nm over each of the three tests before, during, and after the steady test time. Note

that for each test, the laser wavelength scan is not synchronous with the facility test

trigger and hence the timing of absorption signals relative to the test time varies in

each experiment. Data was acquired for all tests for 1.5 ms before the arrival of the

test gas, however only about 0.75 ms of data is shown before the test gas arrival to


account for data buffering in the digital low-pass filter. Figure 5.7a shows measured

signals for the non-combusting measurements. The first millisecond shows no strong

absorption signals despite test gas arrival at 0 ms. Although there is a spike in the

signal near 1.4 ms, the shape of this feature is not consistent with the characteristic

three-lobe WMS-2f /1f lineshape from absorption, and it is believed to be caused

by interference from debris in the flow blocking a portion of the beam. The first

WMS-2f /1f lineshape from absorption is observed at approximately 1.8 ms after test

gas arrival, when only driven N2 should be present in the measurement region. This

well-defined lineshape is interpreted as evidence of H2O present in the combustor.

Subsequently, the measured absorption signal increased in magnitude throughout the

remainder of the test. This behavior is consistent with increasing H2O concentration

in time at constant temperature. Because no absorption was observed in measure-

ments between -0.75 ms and 1.8 ms, the rise in H2O concentration versus time must

be from mixing of driver (H2 and O2 combustion products and Ar) and driven gas

(N2 for the non-combusting case and air for combustion cases) in the facility. The

penetration of driver gas into the test gas in shock-driven hypersonic test facilities

is well known [128–132], although the measurements reported here are perhaps the

most sensitive yet made (H2O mole fraction at 2 ms of about 1.5%).

The combustion cases shown in Figs. 5.7b and 5.7c tell two different stories:

the first indicates almost no combustion until the test time was nearly over and the

second shows strong evidence of combustion even before the steady test time began.

A low angle of attack, high equivalence ratio case shown in Fig. 5.7b shows no strong

absorption signals until 1.8 ms after the arrival of the test gas. Only weak absorption

is observed until about 4 ms, indicating very limited combustion up to this point.

After 4 ms, the absorption signal doubled, indicating sudden combustion initiation

near the end of the steady test time. The signal in Fig. 5.7c, however, shows fairly

strong H2O absorption signals beginning immediately after the test gas arrival. The

larger angle of attack produces higher enthalpy flow conditions in the combustor,

thereby promoting ignition. By the beginning of the test time, absorption signals

were significantly stronger than the corresponding absorption observed during the

mixing case, indicating a significant presence of H2O due to combustion.

5.2. RESULTS 87

0 1 2 3 4 5 60

0.05

0.1

0.15

0.22

f/1

f S

ign

al

0 1 2 3 4 5 60

0.1

0.2

Time, ms

2f/

1f

Sig

na

l

Test Gas

Arrival

2

Begin Test

Time End Test

Time

a)

b)

c)

Signal interference

due to beam blockage

0 5

0 1 2 3 4 5 60

0.05

0.1

0.15

0.2

2f/

1f

Sig

na

l Background Signal

Background-subtracted Measured Signal

Figure 5.7: Measured 1f -normalized WMS-2f signals before, during and after testtime on absorption feature at 1391.7 nm over LOS 3: a) Non-combusting mixingcase, b) Combustion with angle of attack θ = 1◦, equivalence ratio Φ = 1.31, c)Combustion with angle of attack θ = 7.5◦, equivalence ratio Φ = 1.03. In each case,fuel flow was initiated at the beginning of TDLAS data acquisition, 1.5 ms before thearrival of the test gas.

These conclusions based on raw WMS-2f signals are in good agreement with

axial pressure measurements to detect combustion onset, shown in Fig. 5.8. In the

mixing case, there is a moderate pressure rise over the test time consistent with

fuel injection, but not combustion. The low angle of attack, high equivalence ratio

case initially shows only a gradual pressure rise similar to the mixing case, followed

by a significant pressure rise around t = 4 ms due to combustion. At the higher

angle of attack there is an immediate pressure rise, indicating prompt combustion.

Also shown in Fig. 5.8d are the pressure time-histories at the TDLAS measurement

location (134.6 cm downstream of the forebody leading edge) over each of the three


tests. Of particular interest in this plot is very small pressure rise compared to the

non-combusting test in the low-angle of attack combustion case. This observation is

consistent with the limited combustion observed in the WMS signals and the axial

pressure data. With these qualitative assessments of the measurements in mind, the

results of quantitative WMS data analysis are presented next.

20 40 60 80 100 120 1400.0

0.2

0.4

0.6

0.8

1.0

Pres

sure

, atm

Axial distance from forebody leading edge, cm

t = 0.5 ms t = 1.5 ms t = 2.5 ms t = 3.5 ms t = 4.5 ms t = 5.5 ms t = 6.5 ms

a)

TDLASLocation

0 20 40 60 80 100 120 1400.0

0.2

0.4

0.6

0.8

1.0

Pres

sure

, atm

Axial distance from forebody leading edge, cm.


b)

TDLASLocation

20 40 60 80 100 120 1400.0

0.2

0.4

0.6

0.8

1.0

Pres

sure

, atm

Axial distance from forebody leading edge, cm


c)

TDLASLocation

0 1 2 3 4 5 6 7 8 90.0

0.1

0.2

0.3

0.4

0.5

0.6

Pres

sure

, atm

Time, ms

Non-Combusting Test Combustion Case 1 ( ) Combustion Case 2 ( )

d)

Test Window

Figure 5.8: Axial pressure distribution snapshots throughout the measurement testtime. Fuel injection occurs at approximately 107 cm, and the TDLAS measurementswere located at 134.6 cm. Also shown is the pressure time-history for each test atthe TDLAS measurement location. a) Non-combusting mixing case, b) Combustionwith angle of attack θ = 1◦, equivalence ratio Φ = 1.31, c) Combustion with angle ofattack θ = 7.5◦, equivalence ratio Φ = 1.03, d) Pressure time-histories at the TDLASmeasurement location.

5.2. RESULTS 89

5.2.2 Non-combusting Test

In the non-combusting test, nitrogen replaced air as the test gas of the shock tube so

that fuel could be injected into the scramjet without combustion and mixing of the

driver gas and test gas could be evaluated. The shock tube driver was a stoichiometric

mixture of H2 and O2 diluted in 30% Ar, and H2O combustion products were formed

by the driver detonation. If the test gas and driver had been un-mixed in the shock

tube, the TDLAS sensor would begin to detect H2O at the end of the test gas flow

and the beginning of the driver gas. However, early arrival of H2O could signal mixing

of the test and driver gases before the expansion nozzle. Therefore, TDLAS measure-

ments of H2O in this test case aimed to track the arrival of the driver gas. This test

also served as a validation of the TDLAS hardware to maintain optical alignment and

mechanically survive the harsh conditions experienced in this facility. The gas was

too cool and H2O concentration was too low to maintain strong absorption for the

feature at 1469.3 nm. However, the feature at 1391.7 nm maintained strong absorp-

tion in these conditions, as evidenced by the measured time-series of the WMS-2f /1f

signal shown in Fig. 5.7a, discussed previously. Because absorption on the 1469.3 nm

feature was so weak, the conventional two-line thermometry approach was discarded

to reduce the propagation of temperature uncertainty into column density measure-

ments. Instead, 1-D shock-jump and isentropic relations were used in conjunction

with the known total and static conditions out of the facility nozzle to calculate the

temperature downstream of the combustor to be 1158 K. This temperature was used

in conjunction with the absorption signal from the feature at 1391.7 nm to determine

column density. Additionally, it should be noted that this measured column density

solution is not strongly dependent on the temperature solution – the column density

sensitivity to temperature is 6% per 100 K at these conditions.

The resulting plot of column density, shown in Fig. 5.9, reveals early arrival of

H2O. This result is consistent on all three LOSs and H2O is seen throughout the test

window, increasing up to a maximum of 0.075 g/m2 at 5 ms. This value corresponds

to about 5.3% H2O by mole, which is 20 times larger than the sensor detection

limit based on minimum signal levels required at these conditions. The mixing of

driver gas into the test gas in reflected shock tunnels is a well-known phenomenon,


-2 0 2 4 6 8 10 12 14 16 18 20

0.0

0.1

0.2

0.3

0.4

0.5

Col

umn

Den

sity

, g/m

2

Time, ms

LOS 1 LOS 2 LOS 3

Test Window

Figure 5.9: TDLAS column density measurements from Mach 10 non-combustingtare test case.

occurring due to boundary-layer “jetting” as the reflected shock propagates through

the shock tube [124, 133]. While the presence of driver gas has a minimal effect on

the gas-dynamic flow properties in this facility due to the similarity of the driver

γ with that of the test gas [132], it will alter combustion chemistry and thus this

TDLAS measurement of the driver gas concentration provides an important input for

modelers attempting to compare their results with facility measurements. Previous

measurements at these conditions have estimated that driver gas did not appear in

the test gas until approximately 3.5 ms after the arrival of the test gas [132]. Our

measurements confirm that finding at levels of approximately 2% H2O by mole at

t = 3.5 ms. In addition, because of better SNR of the scanned-WMS TDLAS sensor,

we also report smaller concentrations of driver gas in the test gas at even earlier times

in the test window.

5.2. RESULTS 91

5.2.3 Hydrogen-Air Combustion (θ = 1◦, Φ = 1.31)

The first of two combustion tests was conducted at an angle of attack of θ = 1◦

with H2-air equivalence ratio Φ = 1.31. Results for this test are shown in Fig. 5.10.

Steady-state CFD computation results along the three TDLAS LOSs are shown as

matching line-style arrows on the ordinate axis of each plot. The CFD is based upon

the work in [134], but with pure hydrogen fuel to match the test condition. CFD

column density was computed by direct evaluation of Eq. (2.7), and temperature

is the H2O-weighted average along the LOS, as given by (2.5). Column density

results are given in Fig. 5.10a. At the beginning of the test window there are many

similarities to results from the non-combusting case, with relatively small column

density observed. However, after t = 3 ms the column density jumps up drastically,

and by the end of the steady test time, measurements are equivalent to 15.0% H2O by

mole, providing clear evidence of ignition. However, complete, uniform combustion

would correspond to a column density of about 0.28 g/m2 and peak column densities

over the test window are only about two-thirds of this value, indicating combustion

is incomplete. CFD calculations agree almost exactly with peak measurement results

on LOS 2, however measurements on LOSs 1 and 3 are about 30% smaller than the

CFD values. This indicates that the measurements show less-complete combustion

than CFD predicts.

Temperature results in Fig. 5.10b do not show values before t = 3 ms, as the

absorption signal was too weak to confidently determine temperature. All tempera-

ture measurements over the test window show a significant temperature rise over the

static temperature based on 1-D calculations, confirming heat release from combus-

tion. The results are also in reasonable agreement with CFD, with peak temperature

values during the test time within 6%, 5%, and 16% for LOS 1, 2, and 3 respectively.

LOS 1 and LOS 2 are mostly lower than CFD predictions and LOS 3 is mostly higher

throughout the test time. These results indicate some combustion, but that CFD once

again tends to over-estimate the extent of combustion at the TDLAS measurement

location. At very late times after the test window (t = 8 − 18 ms) the temperature

drops uniformly on all three LOSs as the driver gas cools and expands through the

test cabin.


-2 0 2 4 6 8 10 12 14 16 18 200.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

CFD

Test Window

Col

umn

Den

sity

, g/m

2

Time, ms

LOS 1 LOS 2 LOS 3

Approx. H2O forcomplete combustion

a)

Driver combustion products

-2 0 2 4 6 8 10 12 14 16 18 200

500

1000

1500

2000

Tem

pera

ture

, K

Time, ms

LOS 1 LOS 2 LOS 3

Test Window

b)

Static T

CFD

Figure 5.10: TDLAS results for Mach 10 combustion case θ = 1◦, Φ = 1.31 com-pared with steady-state CFD solutions. a) H2O column density b) H2O-averagedtemperature

5.2.4 Hydrogen-Air Combustion (θ = 7.5◦, Φ = 1.03)

Results for the second combustion test at angle of attack θ = 7.5◦ and equivalence

ratio Φ = 1.03 are shown in Fig. 5.11. This higher angle of attack was chosen for the

higher static temperature it would achieve in the combustor (1477 K) in an effort to

promote ignition. Once again, values from steady CFD calculations for each LOS are

shown as matching line-style arrows along the ordinate axis. Column density results

in Fig. 5.11a show significant concentration of combustion products even before the

test time begins, suggesting prompt ignition at this higher static temperature. Near

the end of the steady test time, these results are in fairly good agreement with the

steady-state CFD. Peak measurements at LOSs 1 and 2 are within 10% of the CFD

values, but LOS 3 measurements are more than 25% higher than the CFD prediction.

There are also significant point-to-point fluctuations in the data values. Some of this

variation, particularly at LOS 3 which is farthest from fuel injection in the flow, may

be because H2O does not penetrate as far into the flow as given by CFD simulation.

Peak column density measurements over the test time are also lower than the expected

uniform-flow column density of about 0.6 g/m2 for complete combustion, indicating

combustion has not proceeded to completion. Measurements of temperature in Fig.

5.2. RESULTS 93

5.11b show only a small rise over the static temperature, which gives credit to the

notion of limited combustion progress. Moreover, these results are in reasonable

agreement with the CFD values, although once again CFD appears to over-predict

the temperature slightly. However, peak temperature measurements are generally

about 15% higher than CFD predictions and occur sporadically, which may indicate

the presence of temporary “pockets” of hot combustion products passing along the

LOS. Temperature measurements do not have the monotonic decrease after the test

time, as observed in the first combustion test, however a general trend of declining

temperature can be seen. In both combustion tests, the temperature and column

density appear to be related inversely; the column density rises over the test time

while the temperature decreases. At first this result may seem counter intuitive,

but in addition to column density increasing due to combustion progress, column

density scales like all density measurements – proportional to pressure and inverse

to temperature. Therefore, one interpretation of these measurements (though not

the only one, given the complex flow physics) is that the density of the gas increases

during the test time since the pressure rises (see Fig. 5.8c) and temperature falls,

which in turn leads to larger values of column density.

-2 0 2 4 6 8 10 12 14 16 18 200.0

0.1

0.2

0.3

0.4

0.5

H2O ~0.6 g/m2 forcomplete combustion

Col

umn

Den

sity

, g/m

2

Time, ms

LOS 1 LOS 2 LOS 3

Test Window

a)

CFD

-2 0 2 4 6 8 10 12 14 16 18 200

200400600800

10001200140016001800200022002400

Tem

pera

ture

, K

Time, ms

LOS 1 LOS 2 LOS 3

Test Window

b)

CFD

Static T

Figure 5.11: TDLAS results for Mach 10 combustion case θ = 7.5◦, Φ = 1.03 com-pared with steady-state CFD solutions. a) H2O column density b) H2O-averagedtemperature

Chapter 6

Shock Tube Demonstration of a

Temperature Sensor for High-T

and -P Air Using NO Absorption

As evidenced by the preceding chapters, hypersonic aeropropulsion facilities rely on

high-enthalpy air as a critical input for operation. These facilities simulate supersonic

flight conditions by heating and pressurizing air for enthalpy matching prior to nozzle

expansion to high gas velocities. Enthalpy limitations in such facilities have been in

part attributed to difficulties in controlling or modeling the heating process such that

the enthalpy condition in the preheater is not well known at high temperatures (T >

2000 K) [135]. This challenge is exacerbated by a lack of options for directly measuring

gas temperature above the limits of conventional thermocouple materials, which melt

or oxidize at such extreme conditions. Alternative thermometry techniques are needed

for system evaluation and quantitative control feedback. Here we propose and validate

a spectroscopic strategy to measure temperature in high enthalpy air (T = 1200 - 3000

K) by probing the infrared absorption spectra of nitric oxide (NO).

Nitric oxide is selected amongst the species in high-temperature air due to the

sensitivity of its relative concentration to temperature at chemical equilibrium and

the strength of the vibrational absorption bands of NO in the infrared domain wherein

tunable, coherent light sources are readily available. For this work, the fundamental

94

6.1. MEASUREMENT METHODS 95

band near 5.2 µm is probed using a quantum cascade laser system. Key spectroscopic

parameters were measured in controlled thermodynamic environments to build a Voigt

lineshape spectral model, and the model was assessed at high gas densities (∼20

Amagat) in an optical cell. Fixed-wavelength direct absorption measurements were

conducted in non-reactive shock tube experiments to measure gas temperature over

a range of high enthalpy conditions (T = 1100 - 2950 K, P = 12 - 145 atm) with

known concentrations of NO in nitrogen. Lastly, the technique was demonstrated to

measure temperature in air at equilibrium behind reflected shock waves.

6.1 Measurement Methods

6.1.1 Chemical Equilibrium

Due to the temperature dependence of the composition of air in chemical equilibrium,

a measurement of nascent species concentration can be used to infer temperature. The

equilibrium composition of neat air (79% N2, 21% O2) is shown in Fig. 6.1 from 800 -

3000 K at 50 atm. Over this temperature range, diatomic nitrogen (N2) and diatomic

oxygen (O2) remain nearly constant, and the two most abundant minor species are

nitric oxide (NO) and atomic oxygen (O), which rise monotonically. The latter two

minor species present the greatest potential for equilibrium-based thermometry, and

serve as the primary candidates for spectroscopic sensing in the target temperature

domain. Other minor species such as nitrogen dioxide (NO2) and atomic nitrogen (N)

also have strong temperature sensitivity, but are present at much lower concentrations.

In higher temperature applications, such as arc heaters (T > 4000 K) laser absorption

sensing of nitrogen and oxygen atoms has been utilized to measure gas temperature

[136, 137]. Here nitric oxide is the target species for thermometry due to its relative

abundance from 1500 - 3000 K and convenient spectroscopic activity in the infrared.

The sensitivity of nitric oxide concentration to temperature and pressure in equi-

librium air is further illustrated in Fig. 6.2. As observed on this linear scale, the

mole fraction of NO changes by more than two orders of magnitude between 1200

K and 3000 K. Moreover, there is negligible pressure dependence between 15 atm

96 CHAPTER 6. HPST NITRIC OXIDE MEASUREMENTS

1000 1500 2000 2500 3000

0.001

0.01

0.1

1

Temperature [K]

Mole

Fra

ction

NO

O2

N2

O

P = 50 atm

Figure 6.1: Air in chemical equilibrium at 50 atm, T = 900 - 3000 K.

and 150 atm, which implies that over this domain mole fraction and temperature are

uniquely coupled. In the range of 2000 - 3000 K, a higher priority due to thermocou-

ple inadequacy, the equilibrium mole fraction ranges from 0.8% to 4.4%, which is an

appreciable quantity for sensing purposes. The strong dependence on temperature

leads to a sensitive thermometry technique, such that around 2300 K, a measurement

of mole fraction with 5% uncertainty would yield a measurement of temperature to

within 1% uncertainty.

An underlying assumption of the current approach to thermometry is that the gas

being probed is in chemical equilibrium, which requires time. Figure 6.3 provides a

kinetic analysis of the characteristic time required for NO to reach equilibrium when

forming from air at a given temperature. Similar characteristic times are observed

when air is being cooled after heating. These characteristic times can be compared

with residence times in the heater system to establish a lower bound to the tem-

perature at with the equilibrium-based strategy would be effective. For reference,

in stagnation conditions wherein the gas particle residence times are on the order of

seconds, the lower temperature bound would be 1700 - 2000 K, depending weakly


1500 2000 2500 30000.00

0.01

0.02

0.03

0.04

0.05

1%NO

Mol

e Fr

actio

n

Temperature [K]

P = 15 bar P = 150 bar

5%

XNO(1200 K) = 200 ppm

Figure 6.2: Nitric oxide mole fraction in equilibrium air from 1200 to 3000 K at 15atm (black) and 150 atm (red).

on pressure and other processes like mixing. A more rigorous chemical kinetic anal-

ysis, unique to each gas system or heating process, is recommended to establish a

precise lower bound for a given application. Overall, the equilibrium-based assump-

tion is more reliable at higher temperatures, which is where the thermometry need is

greater.

6.1.2 Nitric Oxide Absorption Spectrum

Absorption spectroscopy is a well-established technique for non-intrusive gas sens-

ing. Numerous laser-based absorption diagnostics have been successfully utilized to

measure gas properties in harsh environments wherein conventional, more intrusive

sensors are less suitable [92, 111, 138, 139]. Moreover, absorption spectroscopy in the

infrared wavelength domain allows for the utilization of compact, room-temperature

semiconductor lasers, advantageous for applications outside of the laboratory. Figure

6.4 shows the infrared absorption spectra of nitric oxide at 2000 K over the wavelength

range of 1.5 - 7.5 µm. Previous work using tunable diode lasers for NO detection has


1500 2000 2500 3000

10-3

10-1

101

103 P = 50 atm P = 150 atm

[s]

Temperature [K]

Figure 6.3: Characteristic time required for NO to reach equilibrium when formingfrom neat air (79% N2, 21% O2).

been well-established in the overtone vibrational bands near 1.8 µm and 2.7 µm

[140, 141]. Falcone, et al. characterized many transitions in the fundamental band

spectrum of NO, however at the time these wavelengths were accessed by low-power

cryogenic tunable diode lasers, making field measurements impracticable [142]. The

more recent availability of quantum cascade lasers has further enabled practical field

sensing by probing the fundamental band of NO near 5.2 µm [143, 144]. Here the

fundamental absorption band was selected for its superior strength and potential for

sensitive detection of nitric oxide in high-enthalpy air.

Wavelength selection within the fundamental band relies on the relative strength

of the rotational transitions that comprise the band, as well as spectral isolation

from water vapor. Expected absorbance values are simulated using the Hitemp 2010

database [102], coupled with a Voigt lineshape model, to guide in wavelength selection.

The validity of this lineshape model is evaluated experimentally and discussed in a

later section. Figure 6.5 depicts the expected absorbance spectrum of the fundamental

band at 2000 K and 3000 K (P = 50 atm), highlighting the strength and temperature


Figure 6.4: Infrared absorption linestrengths of nitric oxide at 2000 K from 1.5 - 7.5µm

sensitivity of NO absorbance in chemical equilibrium. It can be observed that the R-

branch (1890 - 2010 cm−1) is stronger and more isolated from water than the P-branch

(1700 - 1890 cm−1). A target wavelength was chosen near the peak of the R-branch

at 1927.3 cm−1, where water interference is minimal (<0.5%). To model water vapor

interference, it was assumed that the air is compressed near room temperature prior

to heating, and thus the majority of ambient moisture condenses out prior to the

temperature measurement. At a pressure of 25 atm, which is toward the lower end

of the target pressure range, moisture in humid ambient air would be reduced to

1000 ppm by such a process, which is the level simulated in Fig. 6.5. Further fixed-

wavelength simulations of absorbance as a function of temperature at 1927.3 cm−1

are shown in Fig. 6.6. The selected wavelength is near the peak of the R(15.5) line

of the Π3/2 electronic ground state, but at such pressures the absorbance at a fixed

wavelength includes contributions from several neighboring NO transitions.


1800 1900 20000.0

0.5

1.0

2000 K

P = 50 atmL = 10 cmXNO = XNO,eq

Absorba

nce

Wavenumber [cm-1]

3000 K

H2O

TargetWavelength

Figure 6.5: Simulated absorbance spectra of equilibrium nitric oxide near 5.2 µm at2000 K and 3000 K; water vapor also simulated at 2000 K, 1000 ppm; L = 10 cm

6.2 Measurement Results

6.2.1 Facility and Sensor Hardware

Measurements to characterize the NO spectrum in the region of the R(15.5) transition

near 1927.3 cm−1 and to demonstrate the sensor concept were performed in two

primary facilities: a high-pressure optical cell (see Ref. [145]) and the Stanford High

Pressure Shock Tube (HPST). The HPST facility consists of a 7.62 cm inner diameter,

3 m long driver section and a 5 cm inner diameter, 5 m driven section. Driver and

driven sections are separated by a diaphragm made either of aluminum or steel,

which is scribed to control the rupture [146]. Shocks are generated by filling the

driven section with a test gas (here, N2 and NO, or N2, O2, and N2O), then filling the

driver section with helium until the diaphragm bursts. There are five fast-response

piezo-electric pressure transducers (PCB Pl 13A) along the last 1.5 m of the driven

section of the shock tube, which trigger time-interval counters (Phillips PM6666)

as the incident shock passes over them. Using the known distances between the

6.2. MEASUREMENT RESULTS 101

1500 2000 2500 30000.0

0.5

1.0

1.5

2.0

(d / )/(dT/T)N

O A

bsor

banc

e

Temperature [K]

P = 50 atm P = 100 atm

1

L = 10 cmXNO = XNO,equilibrium

2

4

6

8

Temperature S

ensitivity

Figure 6.6: Simulated absorbance and temperature sensitivity at 1927.3 cm−1 from1400 - 3000 K; P = 50 atm (black) and P = 100 atm (red).

counters, the incident shock velocity was calculated and used to obtain the test gas

temperature behind the reflected shock using standard normal shock relations. This

method is generally accurate to within 0.7% [147].

A diagram of the NO sensor hardware is provided in Fig. 6.7. An external-

cavity quantum-cascade laser (ECQCL) from Daylight Solutions, emitting near 5.2

µm, provided light for the present experiments. The 50 mW beam was split using a 2-

degree wedged CaF2 window, directing a reference beam consisting of about 3% of the

total output light to a thermoelectrically-cooled Mercury-Cadmium-Telluride (MCT)

detector (Vigo). Recording this reference signal allowed normalization for common-

mode components of the laser signal, which significantly improved the sensor detection

limits [148]. After passing through the high-pressure cell or shock tube, the primary

beam was focused using a 10 cm focal-length CaF2 lens into a 2.54 cm diameter, gold

coated integrating sphere with 6.4 mm ports (Sphere Optics). The integrating sphere

provided decreased sensitivity to beam steering, which is particularly important due

to severe density gradients in the HPST [146]. Light diffusely reflects over the entire


Data Acquisition

Computer

EC QCL

5.2 µm

High-P Cell/Shock Tube

BeamsplitterCaF2 Lens

4.9 µm LP

Filter

Integrating

Sphere

Reference

Detector

Detector

Figure 6.7: Diagram of sensor hardware for NO measurements through a high-pressurecell and the Stanford High-Pressure Shock Tube.

surface of the integrating sphere, which provides a margin for error as the beam

can wander from its initial alignment without any significant change in the detector

signal [149]. However, when using an integrating sphere, the detector only samples a

fraction of the total light no larger than the ratio of the active area of the detector

to the total area of the sphere surface, which results in at least a 98% laser power

loss through the optical system. The output light from the integrating sphere was

filtered with a 4.9 µm long-pass spectral filter to mitigate any emission signal on the

detector. Additional spatial filtering was provided by irises at the shock tube exit

port and directly in front of the CaF2 focusing lens, but these components are not

shown in Fig. 6.7. Transmitted light was captured on a liquid-nitrogen cooled Indium

Antimonide detector with a 4 mm2 active area (InfraRed Associates). For shock tube

tests at fixed wavelength, the output wavelength was monitored using a standalone

high-accuracy wavelength meter (Bristol, not shown in Fig. 6.7).

6.2.2 Spectral Characterization

While databases of spectral parameters such as Hitemp [102, 150] provide a valuable

starting point for understanding spectral absorption of nitric oxide, these databases

are sometimes found to be inaccurate, particularly at very high temperatures where


they were not originally designed to be used. The quoted uncertainty in Hitemp for

the linestrength of the R(15.5) transition is 10% and the collision-width uncertainty at

1500 K is 15%. Therefore, in order for the proposed sensor to achieve quantitatively

accurate measurements at high-temperature and -pressure conditions, the NO absorp-

tion spectrum was characterized under controlled conditions. Two separate spectral

characterization and validation studies were conducted, both using controlled mix-

tures of NO in N2 balance. First, NO absorption was measured across a range of

pressures to assess whether the Hitran database using a Voigt lineshape model would

accurately represent the NO spectrum at high densities. Next shock tube measure-

ments characterize the temperature dependence of the collision-broadening coefficient

for the NO spectrum near 1927.3 cm−1 from 1300 to 3000 K and 10 to 70 atm.

Room temperature measurements at pressures ranging from 2-20 atm were con-

ducted to measure the NO spectrum across a range from 1920 cm−1 to 1937 cm−1 using

the grating-scan tuning of the ECQCL. These conditions correspond to gas densities

from 2 to 20 Amagat (12 Amagat is approximately equal to 100 atm, 2500 K), and

are therefore representative of the density conditions expected in high-temperature

and -pressure test applications. Burch, et al. showed that absorption spectra may

exhibit non-ideal behavior at only a few atmospheres [151]. More recent studies

have shown that finite-duration collisions at high gas densities can introduce a non-

Lorentzian lineshape component that causes measured spectra to deviate from the

Voigt lineshape model [152, 153]. Therefore, the goal of these tests was to assess

the accuracy of the measured spectrum versus simulation using a Voigt lineshape

model with spectral parameters from the Hitran 2012 database. Figure 6.8 shows the

results from these experiments, obtained in a 1% NO in N2 balance mixture in the

high-pressure cell. The target wavelength near 1927.3 cm−1 is noted near the center

of the scan. There is good agreement between the measured spectrum and the Hitran

2012 model for all five of the different pressures shown, with residuals of less than 4%

in the vicinity of the target wavelength. This residual is due to simulation systemat-

ically over-predicting absorption, which is consistent with non-Lorentzian lineshape

behavior due finite-duration collision effects [76]. Because these errors are small, only


a modest correction to the Hitran/Hitemp Voigt lineshape model parameters is re-

quired to account for this behavior. We next describe measurements to characterize

the collision-broadened lineshape of the NO spectrum near 1927.3 cm−1. By utilizing

the characterized collision-lineshape in simulations, the systematic discrepancy be-

tween the simulated and measured absorbance is reduced, which allows the sensor to

produce more accurate results.

Figure 6.8: Room temperature measurements of 1% NO in N2 balance, measured atvarious pressures to assess accuracy of Hitemp line parameters and Voigt lineshapemodel at elevated gas density.

The Stanford HPST was used to generate controlled, high-temperature and -

pressure conditions to measure NO absorption. Measurements used a mixture of

2% NO in N2 balance as the test gas, and He was the driver gas. NO absorption

was monitored at a single wavelength near 1927.3 cm−1 with a 5 MHz measure-

ment bandwidth (10 MHz sample rate). The temperature and pressure behind the

reflected shock were determined from measured shock speed and normal shock wave

relationships. With the conditions known and held constant, the collision linewidth of

NO transitions was scaled in simulations until the simulated absorbance matched the


measured absorbance, giving a measured collision linewidth of NO with N2 as the col-

lision partner. This process was repeated in several experiments to yield the collision

linewidth, γNO−N2 , as a function of temperature. Figure 6.9 shows the results of these

measurements on a log-log scale. Also shown is the Hitemp 2012 collision linewidth

as a function of temperature and the measured parameters γ(T0) and n best-fit to the

collision linewidth coefficient function γ(T ) = γ(T0) · (T0/T )n. The best-fit linewidth

matches the Hitemp linewidth quite well, particularly at temperatures below about

1700 K where Hitemp is designed to be accurate. At higher temperatures, measure-

ments diverge from Hitemp slightly. This is entirely due to the smaller measured

temperature exponent, n, (0.655 measured versus 0.67 in Hitemp). Both measure-

ment and Hitemp agree within 0.5% that γ(T0 = 1000K) = 0.0238 cm−1. As shown

in Fig. 6.9, measurements were repeated across a broad pressure range, up to 70

atm, in order to validate that the measured lineshape had no pressure dependence, as

assumed in the model. The measured collision linewidth was then used in subsequent

experiments in order to determine the gas temperature, as discussed next.

1500 2000 2500 30000.005

0.01

0.02

Temperature [K]

me

asu

red

γN

O−

N2

(T)

[cm

−1]

P = 10−15 atmP = 20−25 atmP = 30−40 atm

P = 60−70 atmBest−FitHITEMP

n=0.655γ (T

0 = 1000 K) = 0.0238

Figure 6.9: Measured and best-fit collision linewidth for NO R(15.5) transition near1927.3 cm−1.


6.2.3 Thermometer Demonstration

To validate the sensor concept and demonstrate its performance, several shock tube

experiments were conducted wherein absorbance was measured near 1927.3 cm−1

across a wide range of temperatures and pressures relevant to practical facility opera-

tion. Figure 6.10 shows representative absorbance and pressure data collected in these

shock tube experiments. Here, the test gas was a non-reacting mixture of 2% NO in an

N2 balance. The first step in pressure and absorbance in Fig. 6.10, occurring near the

400 µs mark, indicates the incident shock passing over the measurement path length.

This corresponds to a nearly instantaneous rise in temperature and pressure, which

causes the absorbance to rise as well. Shortly thereafter, the reflected shock passes

back over the measurement path length, causing a further rise in temperature and

pressure and stagnating the test gas. For this particular case, the final temperature

and pressure were 1700 K and 112 atm, respectively. Note, however, that the pressure

rise between the incident shock and the reflected shock is not a step, but rather it

occurs over a finite period of time and the pressure rolls off to its steady value. This is

due to shock-bifurcation, a well-documented phenomenon in shock tubes with N2 or

air test gas (although it is not limited to only these test gases) [133, 154, 155]. Shock

bifurcation makes it difficult to resolve measurements during the first 10-50 µs after

the reflected shock passes the measurement plane. However, here we are interested

in the steady absorption signal later in the test time, and therefore these effects can

be neglected. The steady test time begins at about 550 µs on Fig. 6.10 and lasts a

total of about 350 µs.

Temperatures measured from NO absorption are shown in Fig. 6.11 against the

known temperature based on measured shock speed and normal shock relations. Mea-

sured temperature was obtained by fitting simulated absorbance with the specified

pressure and measured lineshape as fixed parameters to the measured average ab-

sorbance over the test time. The temperature corresponding to the best-fit simula-

tion is reported as the measured temperature. Two types of experiments are shown

in Fig. 6.11: 1) non-reacting mixtures of 2% NO in an N2 balance, and 2) reacting

mixtures of N2O, N2, and O2, where NO was formed in the hot, shock-heated gas.

For the reacting mixtures, temperature measurements were determined by assuming


300 400 500 600 700 800 900

0

25

50

75

100

125

Pre

ssur

e [a

tm]

Time [ s]

0.0

0.5

1.0

1.5

2.0

2.5

Steady Test Time

T = 1700 K2% NO/N2

Abs

orba

nce

Figure 6.10: Measured absorption and pressure traces in non-reacting, 2% NO in N2

balance mixture.

chemical equilibrium of the mixture, as evidenced by steady measured absorption

and pressure traces later in the test time. These two cases are distinguished in Fig.

6.11 by x-axis error bars, which are not shown for the non-reacting 2% NO mixtures

where the known temperature is based entirely on the shock counters and normal

shock relations, and is therefore accurate to within 1%. However, in the reacting

mixture, there are significant uncertainties associated with the kinetic modeling of

NO formation, and hence here the x-axis error bars shown are approximately ±3.5%.

Measured temperatures in Fig. 6.11 show good agreement with the known tem-

peratures over the range from 1150 to 2950 K and at pressures from 12 to 145 atm.

This demonstrates the accuracy of this sensor concept across a wide variety of high-

enthalpy conditions. For the non-reacting test gas mixtures, high-pressure tests below

about 2000 K display significantly smaller error bars than those at lower-pressures

and above 2000 K. This is because the uncertainty in these measurements is absorp-

tion limited, and at higher temperatures the decreased absorbance is not offset by


1000 1500 2000 2500 30001000

1500

2000

2500

3000

Known T [K]

Measu

red T

[K

]

P = 10−25 atmP = 30−60 atmP = 60−85 atm

P = 90−110 atmP = 120−150 atmSlope = 1

Tmeasured

=1.03 ⋅ Tknown

± 3%

Figure 6.11: Measured temperature versus known temperature across a broad rangeof temperatures and pressures. Data points with x-axis error bars were measured byobserving equilibrium formation of NO from mixtures of N2O, N2, and O2. Remainingdata points were measured in fixed-chemistry mixtures of 2% NO in N2 balance.

production of more NO, as it would be in the reacting, equilibrium NO formation

case. As temperature goes up in the fixed mixture, the NO absorption goes down,

and therefore uncertainty must grow larger. Note that for the reacting mixtures in the

region of T > 2000 K, the uncertainty in measured temperature is much smaller than

the non-reacting tests because the NO absorption grows larger rather than smaller

with increasing temperature. Also shown on Fig. 6.11 is a regression equation for

the measured versus known temperature, which gives a slope of 1.03 with an uncer-

tainty of 3%. Despite these experimental uncertainties in the non-reacting mixture,

this regression shows that the sensor concept is quite accurate over a large range of

temperatures and pressures.

Chapter 7

Summary and Future Work

In the last two decades, laser absorption spectroscopy has matured dramatically. This

includes both the development of reliable telecommunications fiber-coupled diode

lasers, the introduction of quantum cascade lasers enabling access to mid-infrared

fundamental band transitions of combustion product species, and the recent proposal

of new measurement strategies such as scanned-wavelength-modulation-spectroscopy.

Together, these developments have made laser absorption spectroscopy an increas-

ingly relevant diagnostic tool for understanding flows in advanced aeropropulsion

devices. This dissertation presented the design and results of sensor implementation

in several aeroengine test facilities, and, as summarized in the following sections, this

work has expanded the scope of our understanding of the many competing physical

processes in these complex devices.

7.1 Spatially-Resolved Measurements in an H2-Fueled,

Continuous Flow Scramjet Combustor

The design and implementation of a two-color TDLAS sensor for monitoring temper-

ature, H2O column density, and velocity was presented. The sensor was used in a

model scramjet combustor for two different geometric configurations and employed a

hybrid direct absorption-WMS strategy to account for non-uniform conditions along

109

110 CHAPTER 7. SUMMARY AND FUTURE WORK

the LOS. The measurement LOS was traversed with a system of computer-controlled

stages to sequentially shift the TDLAS LOS throughout the combustor. The sensor

targeted H2O absorption transitions at 1391.7 nm and 1469.3 nm. Measurements

were first presented for equivalence ratio Φ = 0.17 combustion in a geometry con-

sisting of a combustor and extender only. Comparisons of TDLAS measurements to

CFD simulations showed reasonable agreement in the shape over most of the product

plume. However, TDLAS detected less combustion progress overall, and in particular,

limited combustion progress between x/H = 12 and x/H = 18 near the fuel-injector

wall.

Next, measurement results were shown for a configuration with two constant area

sections added to the geometry, one upstream of the combustor and another directly

downstream of the combustor. In this configuration, the first results presented were

a H2O-seeded flow at the combustor inlet, which validated the sensor and facility

performance and showed uniform temperature and composition. Axial velocity mea-

surements for the non-combusting, H2O-seeded tests showed peak velocities through

the combustor that compare well with isentropic calculations. Temperature, col-

umn density, velocity measurements were then shown for H2-air combustion at an

equivalence ratio Φ = 0.17 and were compared to CFD simulation. Good agreement

was found between the TDLAS and CFD temperature measurements. While column

density showed reasonable agreement at x/H = 6 and x/H = 12 downstream of fuel

injection, by x/H = 18 there were significant discrepancies in both the size and shape

of the H2O product plume. However, axial velocity measurements showed excellent

agreement with CFD in the shape and magnitude of the velocity profile, particularly

at planes x/H = 6 and x/H = 15. Comparisons with CARS measurements indicate

large concentrations of combustion intermediate species in central portions of the

product plume, and that composition is consistent with near-complete combustion at

the plume edge. Finally, temperature and column density results were presented for

H2-air combustion at an equivalence ratio Φ = 0.46 along with CFD comparisons.

Agreement between TDLAS and CFD remained strong in the temperature results,

with bias towards higher temperatures predicted by CFD. TDLAS column density

results were significantly smaller than CFD predictions, suggesting less combustion

7.2. MULTISPECIES MEASUREMENTS IN A SCRAMJET 111

progress at the higher equivalence ratio. These results show that relatively simple

TDLAS measurements are a useful tool for characterizing thermophysical parameters

in harsh combustion conditions. In particular, this work has made important ad-

vances that are needed to address effects on TDLAS measurements of non-uniformity

in practical combustion facilities. The results presented comprise a useful data set for

those interested in development and evaluation of the complex flow-physics associ-

ated with scramjet propulsion. Finally, efforts made to compare these measurements

with CFD calculations provide a needed feedback for numerical modelers, who require

measurements to validate and calibrate their models.

7.2 Measurements of CO, CO2, and H2O in an

Ethylene-Fueled Scramjet

Laser absorption measurements CO, CO2 and H2O column density and CO and

H2O density-weighted temperatures were performed in the direct-connect scramjet

combustor fueled by ethylene. The model scramjet combustor had a cavity flame

holder flow path configuration fueled with ethylene-air at an overall equivalence ra-

tio of 0.15 at Mach 5 flight conditions. The sensors employed the recently-described

scanned-wavelength-modulation (scanned-WMS) spectroscopy technique using dis-

tributed feedback (DFB) quantum-cascade and DFB diode lasers for CO and H2O

measurements near 4.87 µm and 2.5 µm, respectively. These measurements provided

reliable, high-SNR signals with quantitative interpretation despite significant nonuni-

formities in temperature and composition along the sensor line-of-sight. An external-

cavity quantum-cascade laser was used for wavelength-scanned direct-absorption mea-

surements on a CO2 transition near 4.2 µm to complete the suite of multispecies mea-

surements of primary products in the ethylene-air flame. Analysis of fitting errors in

scanned-WMS integrated absorbance measurements strongly suggests that the mea-

sured fluctuations of temperature and column density are temporal variations in the

mixing and combustion efficiency (progress) at the measurement LOS and not sensor

measurement error. This interpretation is consistent with laboratory validation of the


sensors in Refs. [111, 112]. It is speculated that temporal variations in the combustor

flow field due to shear layer interaction with the cavity flame holder are the cause of

much of the observed temporal fluctuation of temperature and combustion product

column density. Measurements of temperature and column density reveal combustion

progress at each successive axial plane. However, the large observed concentration of

CO reveals incomplete combustion within the combustor. Additionally, there is virtu-

ally no temperature rise between planes, suggesting that thermal dilution of products

with the free stream air competes strongly with combustion progress, shocks, and ex-

pansions. Direct laser absorption measurements of cavity residence time during flame

extinction showed a duration of approximately 3.4 ms for column density to drop by

90% of the total dynamic range observed. This work describes the first implementa-

tion of new scanned-WMS strategies and fiber-coupled mid-IR absorption sensors to

scramjet research. Additionally, it is hoped that these measurements will provide a

useful database to compare with future computational fluid dynamics modeling of the

complex gas dynamics occurring within a hydrocarbon-fueled scramjet combustor.

7.3 Hypersonic Scramjet Combustor Measurements

The design, deployment, and use of a TDLAS sensor monitoring H2O absorption

to determine H2O column density and weighted average temperature in a model

scramjet at the HyPulse reflected shock tunnel facility was presented. This facility

provided short-duration tests of approximately 3 ms at Mach 10 flight conditions.

Scanned-WMS was used for high-SNR measurements; this work represents one of the

first implementations of this technique for absorption sensing in a practical facility.

Telecommunications lasers targeting transitions at 1391.7 nm and 1469.3 nm were

used in the sensor to deliver fiber-coupled light directly to the scramjet model within

the test cabin. Results were first shown for a non-combusting test which quantified

the presence of detonable driver gas products throughout the duration of the test

window. Two H2-air combustion cases were also presented. Both cases showed a

significant rise in column density above levels in the non-combusting case and a

temperature rise above the expected static conditions, strongly indicating the presence

7.4. HIGH-ENTHALPY AIR TEMPERATURE SENSING 113

of combustion in the model. However, the results were significantly below those

expected for complete combustion at the measurement location 27.6 cm downstream

of fuel injection. Results also showed reasonable agreement with CFD simulations

of the combustor at the same conditions, with the CFD marginally over-predicting

both extent of combustion and temperature rise compared to TDLAS results. This

work represents an important step forward in the practical implementation of TDLAS

diagnostics for detection of combustion products in hypersonic scramjet conditions.

Few other techniques offer the desirable traits of simplicity in implementation coupled

with robust diagnostic capabilities as described here, and therefore there will most

definitely be a place for these diagnostics in future hypersonic testing.

7.4 Shock Tube Measurements of Temperature in

High-T and -P Air via NO Absorption

A new sensor strategy for thermometry in high-temperature and -pressure air via

temperature-sensitive nitric oxide absorption was presented, with the purpose of char-

acterizing test facility conditions. The sensor utilizes the monotonic increase in equi-

librium NO mole fraction with temperature, and the independence of mole fraction

with pressure. As a result, strong mid-infrared absorption of NO near 5.2 µm is highly

temperature sensitive and can be utilized to characterize the temperature of air across

a wide range of pressures and temperatures. The NO R(15.5) transition near 1927.3

cm−1 was selected for its avoidance of nearby H2O interference and accessibility with

a high-power external-cavity quantum-cascade laser source. A demonstration of the

sensor concept was performed. First, room temperature measurements of the NO

spectrum from 1920 cm−1 to 1936 cm−1 verified that only small corrections to the

Hitemp database spectral parameters are needed to account for non-Lorentzian col-

lision effects at gas densities above 10 Amagat. These corrections were incorporated

into the Voigt lineshape model by characterizing the collision linewidth as a function

of temperature in shock-tube experiments at pressures ranging from 10 to 70 atm.

Finally, the sensor performance was demonstrated via measurements of temperature


over the range of 1100 to 2950 K and 12 to 145 atm, in both non-reacting NO seeded

experiments, and reacting experiments where NO was formed in the hot, shock-heated

gas. The sensor provided accurate measurements of temperature over this entire do-

main, and is a promising method for improving high-enthalpy facility operation and

characterization.

7.5 Future Work

Practical, air-breathing hypersonic propulsion devices remain elusive despite decades

of research. While researchers have made important strides in understanding of these

systems, barriers still exist in our understanding. Turbulent mixing, combustion and

heat transfer in scramjet combustors is exceedingly complicated and their theory is

not yet on firm ground. Other problems such as shock-boundary layer interaction

continue to plague both practical facilities as well as well as numerical modelers. So,

there is a continued role to be played for robust diagnostic measurements, capable

of illuminating the physical processes that drive these phenomena. Researchers have

many diagnostic methods to choose from, but over the decades, laser absorption spec-

troscopy has earned its place as a tool of choice because of ease of implementation and

powerful measurement capabilities. Those capabilities have grown dramatically in the

last ten years, with each generation of sensor substantially improving measurement

fidelity over previous iterations. The work presented here represents one small part

of those improvements, but there are many more opportunities to improve further.

Here, we outline some potential directions for future work.

7.5.1 High-Bandwidth Measurements in a Hypersonic Test

Facility

The Mach 10 scramjet combustor measurements presented in Chapter 5 were the first

WMS measurements of their kind, and as such they are an important step in imple-

menting advanced optical diagnostics within an impulse facility capable of creating

these hypersonic conditions. Those measurements utilized scanned-WMS to provide

7.5. FUTURE WORK 115

measurements with a bandwidth of 1 kHz, or six measurement points over a 3 ms

test time. While these measurements were sufficient to identify ignition onset as well

as other basic trends such as increasing combustion progress over the course of a sin-

gle test, the relatively low bandwidth relative to the test time significantly hindered

the depth of interpretation allowed by the data. Future measurements with higher

bandwidth would offer greater insight into combustion progress at high Mach num-

bers, and a better understanding of unsteady combustion dynamics within hypersonic

scramjet combustors.

Measurements from Chapter 5 took place during winter at the HyPulse facility

in Ronkonkoma, NY. At the time it was found that changes in the ambient facility

temperature were large enough that the laser temperature controller could not hold

the lasers at a constant wavelength. Fixed-wavelength experiments were therefore

impractical, and only wavelength-scanned-WMS offered both insensitivity to laser

set-point drift as well as excellent signal-to-noise ratio needed in a noisy experimental

facility. This technique was only in its infancy at the time, therefore the scan-rate

was restricted to 1 kHz based on experience with calibration-free WMS experiments.

However, there is no reason that scanned-WMS measurements can not be applied to

measurements with a scan rate far in excess of 1 kHz (although, the scan frequency

should still be smaller than the modulation frequency). The only caveat on this

statement is that the model presented in Chapter 2 for the laser wavelength and

output intensity (Eqs. (2.12) to (2.17)) assumes that terms higher than the second

harmonic, and cross-product terms can be neglected. This assumption may not be

satisfied at very high scan-rates, and therefore care should be taken to either use

an appropriate model for laser dynamics, or simply measure the baseline intensity

directly. However, if these conditions are satisfied, high-bandwidth scanned-WMS

measurements in a hypersonic scramjet combustor should be possible, and would

provide a new and valuable piece of information to the community of researchers

interested in scramjet engines.


7.5.2 Facility Characterization via Nitric Oxide Absorption

Sensor

The motivation, design, and initial demonstration of a temperature sensor for high-

enthalpy air by monitoring nitric oxide absorption was presented in Chapter 6. An

important next step would be to implement this sensor strategy to characterize the

inlet flow in a practical test facility. In addition to this test providing a true vali-

dation of the sensor concept, it would also produce valuable information needed by

both facility operators who want to know if their hardware is operating on target,

as well as computational modelers who are trying to compare simulations to exper-

imental data collected in that particular facility. To accomplish this, considerable

effort must be placed in engineering the optical system to deliver 5.2 µm light to

the test article and detect transmitted signals, while maintaining robust alignment

in the face of inevitable facility noise due to mechanical vibration and beam steer-

ing, etc. Hollow-core fiber like that which was used to deliver mid-infrared infrared

light to the University of Virginia scramjet combustor in Chapter 4 could be used for

this application as well [113, 156]. Adding multiple wavelengths to the sensor would

complicate the optical engineering slightly, but has many potential benefits. A non-

absorbing reference beam would reduce measurement sensitivity to non-absorption

losses due to vibration, scatting, beam steering, or window birefringence [146]. A sec-

ond wavelength targeting an NO transition with a different temperature sensitivity

would allow the sensor to provide two independent temperature measurements, one

from two-color direct absorption and the other from assuming NO is in equilibrium

and solving for temperature using a single transition (as in the work presented in

this dissertation). This approach would also test the equilibrium assumption, since

a two-line sensor can also solve for the NO concentration directly and compare that

value to the NO expected to be present in the equilibrium mixture.

7.5.3 TDLAS for Flight Testing

While the work in this dissertation has focused on absorption diagnostics for ground

test facilities, it also bears mentioning that TDLAS sensors hold great promise flight

7.5. FUTURE WORK 117

testing. Already, TDLAS sensors have been used in two flight-test experiments by

NASA, the Air Force Research Laboratory (AFRL), and Australia’s Defense Science

and Technology Organization (DSTO) under the banner of HIFiRE [157–159]. These

tests showed that laser absorption sensors can be designed with a small enough hard-

ware footprint for flight testing, all while maintaining good optical alignment and

sufficient insensitivity to harsh flight test conditions. However, these tests only rep-

resent a small piece of what TDLAS sensors may be used for the future. For exper-

imental flight testing sensors, WMS methods including both calibration-free WMS

and scanned-WMS offer the potential to improve the quality of measurements. Even-

tually, new laser technology may also enable the monitoring of species beyond O2

and H2O as demonstrated in the HIFiRE experiments, which would allow a better

understanding of hydrocarbon combustion in scramjets within the most practical con-

ditions imaginable. Additionally, there is also an opportunity to develop absorption

diagnostics for in-flight, real-time monitoring combustion. Previously Rieker, et al.

used a TDLAS sensor to detect unstart in a scramjet engine [26]. It may be possible

to install a similar sensor into a flight system to detect unstart, to provide feedback

for active control, or to monitor engine emissions.

Appendix A

A Numerical Solution for

Peak-WMS Measurements

Measurements of the peak WMS-2f /1f signal are related to the temperature and

species column density through a nonlinear set of equations that in general have no

explicit solution. Therefore, one must devise a numerical approach for converting

these WMS signals into quantitative thermodynamic measurements. One approach

that has been used successfully in the past is to simulate the WMS signal over a range

of gas temperatures, pressures, and column densities using the theoretical framework

described in Section 2.3 at the characterized laser settings (modulation depth and laser

dynamics). The measured signals can then be compared to the array of simulated

values to make quantitative measurements. While this technique is effective, it does

not scale favorably when additional parameters are accounted for. For instance, when

nonuniform conditions along the laser line-of-sight (LOS) are considered, the empirical

collision linewidth of the absorption feature must be included in calculations to make

quantitatively accurate measurements. In these situations, it is worthwhile to make

use of numerical solution techniques that do not require brute-force simulations over

a large domain of potential temperature, pressure, composition, and collisional width

conditions. A multidimensional Newton-Raphson algorithm offers a simple method

of iteratively simulating WMS signals at guess values of temperature and column

density with fixed collisional width (to account for LOS nonuniformity) and fixed

118

A.1. THE NEWTON-RAPHSON METHOD 119

modulation depth and laser characteristics.

Simulating WMS signals by brute-force over a range of temperature, pressure, and

mole fraction conditions takes several hours of computation. Moreover, adding an ad-

ditional degree of freedom such as collisional width extends the computation time to

days. In contrast, a properly implemented Newton-Raphson technique gives numer-

ically identical results in as few as 7 seconds based on the Matlab implementation

used in this study.

A.1 The Newton-Raphson Method

The Newton-Raphson method is a numerical root-finding technique that is described

here in a single dimension to offer a basic explanation of the solution method. We

seek the solution to the function y = f (x), by finding the root of the equation

y − f (x) = 0. We begin by supplying the algorithm with an initial guess value for

the solution, x0, and then evaluate the function and its derivative at x0. The guess

value x0 is updated by tracing the derivative f ′(x0) from the point f(x0) back to the

line y = 0. This process is given by the Eq. (A.1) below:

x1 = x0 −f(x0)

f ′(x0)(A.1)

In most cases, the updated guess value will be closer to the true root of the function.

The accuracy of the solution can be improved by using the new guess value to make

an additional updates to the solution iteratively. Generally, the updated guess value

will always take the form:

xj+1 = xj −f(xj)

f ′(xj)(A.2)

The algorithm is stopped by the user when the function value at the guess is within

a specified tolerance of zero. This iterative process is shown graphically in Fig. A.1

for the first five updates of the root guess value of a polynomial function. For this

particular function, after five iterations the guess value is very close to the actual

root.

120APPENDIX A. A NUMERICAL SOLUTION FOR PEAK-WMSMEASUREMENTS

0

X

f(X

)

0

X

f(X

)

f(x0)

x0

x1

f(x1)

x2

f(x2)

x3

f(x3)

f(x4)

x4

x5

Figure A.1: Graphical representation of Newton’s method for a one-dimensional func-tion.

A.2 Newton’s Method Applied to WMS

With WMS, as with any two-line sensor for temperature and composition, one line

is used to solve for column density and the ratio of both lines is used to solve for

temperature. The solution of these two equations are coupled, however, which ne-

cessitates a simultaneous solution and therefore multivariate approach. We begin by

assuming that the user has supplied measured WMS-2f /1f peak signals from each of

a pair of lines, to be denoted S12f/1f and S2

2f/1f . From Section 2.3, the WMS signals

can be written as functions of temperature T , pressure P , composition N (determined

by the column density of constituent species), and laser characteristics such as the

center-wavelength of the laser ν, modulation depth a1,m, and the amplitudes of the

laser harmonics i1,m and i2,m. Additionally, the WMS signal may depend on other

parameters such as the collisional width of the absorption lineshape (∆νc) in cases

where it is fixed in order to account for nonuniform conditions along the measurement

line-of-sight. Here we consider only the general function of WMS signals of the form

A.2. NEWTON’S METHOD APPLIED TO WMS 121

shown in Eq. (A.3) for a laser targeting transition k.

Sk2f/1f = f(T,N, P,∆νkc , ν

k, ak, ik1,m, ik2,m

)(A.3)

Although the laser characteristics are considered constants in Eq. (A.3), it is impor-

tant to recognize that these parameters will change whenever any of the laser settings

are changed, and therefore they are shown as variables above. The exact functional

form of Eq. (A.3) is not explicitly stated because it is overly lengthy and complicated.

Generally, the best practice when simulating WMS signals is to break the calculation

into its constituent pieces as described in Sections 2.2 and 2.3; first compute the ab-

sorbance over the entire wavelength range, and then use this absorbance as an input

to simulate the WMS lineshape.

For this application, Newton’s method seeks the solution to the following equation: R =S22f/1f

S12f/1f

S12f/1f

=

[g (T,N, P,∆ν1c ,∆ν

2c )

f (T,N, P,∆ν1c , )

](A.4)

This equation can be approximated using a Taylor series expansion about T +δT and

N + δN , including only the first-order terms, as shown in Eq. (A.5):[g (T + δT,N + δN)

f (T + δT,N + δN)

]≈

[g (T,N)

f (T,N)

]+

[∂g∂T

∂g∂N

∂f∂T

∂f∂N

][δT

δN

](A.5)

The goal of the multivariate Newton’s method in the case of WMS is to use Eq. (A.5)

to solve for the δT and δN needed in order to achieve equality. In other words, each

iteration seeks to update the guess values of temperature and column density for the

solution to Eq. (A.4) by solving Eq. (A.5) for the magnitude of the change in the

guess values.

In practice, the algorithm begins by computing the simulated peak WMS-2f /1f

values at the specified temperature and column density values supplied by the user’s

122APPENDIX A. A NUMERICAL SOLUTION FOR PEAK-WMSMEASUREMENTS

initial solution guess, T(0) and Ni,(0), as shown in Eqs. (A.6) and (A.7).

S1(0) = f

(T(0), P,

Ni,(0)RiT(0)PL

,∆ν1c , ν1, a1, ij1,m, i

12,m

)(A.6)

S2(0) = f

(T(0), P,

Ni,(0)RiT(0)PL

,∆ν2c , ν2, a2, i21,m, i

22,m

)(A.7)

Note that the subscript “2f /1f ” has been neglected above for compactness. These

values are then plugged in to Eq. (A.4) to obtain the vector[R(0), S

1(0)

]T. Next,

we must compute the derivatives of the WMS signal with respect to changes in the

guess value of temperature and column density. There are several different ways

to numerically approximate derivatives; here a finite central difference method will

be used. As shown in Eq. (A.8), the derivative with respect to variable x at the

coordinate(x(j), y(j)

)is obtained by computing the function value at x(j) + ∆x and

x(j) − ∆x, and then computing the slope between the two function evaluations.

∂f(x(j), y(j))

∂x=f(x(j) + ∆x, y(j)) − f(x(j) − ∆x, y(j))

2∆x(A.8)

The size of ∆x is left to the user. For the studies in this work, the step size was

set as ∆x = ε1/3x(j), where epsilon is defined as 10−6. The finite central difference

derivatives of R and S1 with respect to temperature and column density are combined

together into a Jacobian matrix J , shown in Eq. (A.9), which defines the sensitivity

of the function to the guess solution values.

J =

[∂R∂T

∂R∂Ni

∂S1

∂T∂S1

∂Ni

](A.9)

Once the Jacobian matrix is defined, the next step is to update the guess values for

temperature and column density. Based on the first-order approximation of Eq. (A.4)

given in Eq. (A.5), we can use the Jacobian along with the measured WMS signals

and WMS signals simulated at the guess temperature and column density values to

A.2. NEWTON’S METHOD APPLIED TO WMS 123

estimate how much our guess values should change.[δT

δNi

]= J−1

([R(j)

S1(j)

]−

[RmeasuredS1

measured

])(A.10)

Here δT and δNi are the estimated changes in the guess value needed, as shown in

Eq. (A.11). [T(j+1)

Ni,(j+1)

]=

[T(j)

Ni,(j)

]+

[δT

δNi

](A.11)

At this point, the algorithm has updated the guess values for temperature and column

density, and the user may either stop the algorithm and consider T(j+1) and Ni,(j+1)

the solution, or the user may use these updated guess values for continued iteration.

Whether to continue iterating or not depends on convergence of the change in guess

values to within machine accuracy, and the convergence of the functions f and g to

within machine accuracy. Once either set has converged, the other will no longer

change.

Usually, implementing the preceding algorithm will give sufficiently accurate so-

lutions after only a few iterations. However, if the initial guesses of temperature

and column density is not close enough to the solution value, Newton’s method may

sometimes erroneously propose large steps that may cause the method to converge on

an erroneous solution or diverge altogether. Therefore, to help ensure convergence,

it is sometimes advantageous to not take the full step in δT and δN . If a case is

discovered where Newton’s method will not converge, an algorithm is presented in

Ref. [160] to optimally backtrack along the full Newton’s method step.

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practical applications of laser absorption spectroscopy for aeroengine testing...

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