MID-IR LASER ABSORPTION DIAGNOSTICS FOR
HYDROCARBON VAPOR SENSING IN HARSH ENVIRONMENTS
A DISSERTATION
SUBMITTED TO THE DEPARTMENT OF MECHANICAL
ENGINEERING
AND THE COMMITTEE ON GRADUATE STUDIES
OF STANFORD UNIVERSITY
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
Adam Edgar Klingbeil
December 2007
c© Copyright by Adam Edgar Klingbeil 2008
All Rights Reserved
ii
I certify that I have read this dissertation and that, in my opinion, it
is fully adequate in scope and quality as a dissertation for the degree
of Doctor of Philosophy.
(Ronald K. Hanson) Principal Adviser
I certify that I have read this dissertation and that, in my opinion, it
is fully adequate in scope and quality as a dissertation for the degree
of Doctor of Philosophy.
(Jay B. Jeffries)
I certify that I have read this dissertation and that, in my opinion, it
is fully adequate in scope and quality as a dissertation for the degree
of Doctor of Philosophy.
(Chris Edwards)
Approved for the University Committee on Graduate Studies.
iii
iv
Preface
Fuel/air stoichiometry is an important parameter in modern combustion devices be-
cause it has a profound influence on efficiency, power, and pollutant formation. As
engine technologies continue to advance, diagnostics and sensors are becoming essen-
tial for studying fundamental combustion processes and characterizing performance of
combustion-based engines. Optical-absorption diagnostics have been used previously
to probe various species in these environments and to infer quantities such as concen-
tration, temperature, pressure, and velocity. However, there have been only a limited
number of demonstrations of optical diagnostics for hydrocarbon fuels. This thesis
describes the development of mid-IR optical-absorption sensors for time-resolved mea-
surements of hydrocarbon species to infer critical parameters such as concentration
and temperature. These sensors provide the necessary sensitivity and time resolution
for measurements in shock tubes, pulse detonation engines, and internal combustion
engines. Different aspects of the research conducted are summarized below.
An FTIR spectrometer is used to measure the temperature-dependent absorption
spectra of a selection of hydrocarbon species and blended fuels in the ∼3.3 µm region
of the fundamental C-H stretching vibration. This spectroscopic library provides
the first high-temperature spectral information for many of the species studied and
facilitates development of sensitive diagnostics for various applications. This unique
database also enables modelling of the absorption spectra of blended fuels such as
gasoline.
An ethylene and propane diagnostic is designed for measuring fuel concentration in
a pulse detonation engine using a fixed-wavelength helium-neon laser. Time-resolved
v
measurements during fired tests of a repetitively pulsed engine reveal non-ideal cycle-
to-cycle interactions that cause a substantial amount of fuel to leave the engine un-
burned. By quantifying the fuel loading and identifying the amount of unburned fuel,
engine performance can be characterized and future engine designs can be improved
to utilize all of the fuel supplied to the engine.
Simultaneous measurement of absorption at two wavelengths is used as a basis for
hydrocarbon detection in severe environments. A novel wavelength-tunable mid-IR
laser is modified to rapidly switch between two wavelengths, improving the versatility
of this laser system. The two-wavelength technique is then exploited to measure va-
por concentration while rejecting interferences such as scattering from liquid droplets
and absorption from other species. This two-wavelength laser is also used to si-
multaneously determine temperature and vapor concentration. These techniques, in
combination with the library of temperature-dependent hydrocarbon spectra, lay the
groundwork necessary to develop fuel diagnostics for laboratory experiments and tests
in pulse detonation engines and internal combustion engines.
The temperature-dependent spectroscopy of gasoline is examined to develop a
sensor for fuel/air ratio in an internal combustion engine. A wavelength was selected
for good sensitivity to gasoline concentration. A spectroscopic model is developed
that uses the relative concentrations of five structural classes to predict the absorption
spectrum of gasoline samples with varying composition. The model is tested on 21
samples of gasoline for temperatures ranging from 300 to 1200 K, showing good
agreement between model and measurements over the entire temperature range.
Finally, a two-wavelength diagnostic was developed to measure the post-evaporation
temperature and n-dodecane concentration in an aerosol-laden shock tube. The ex-
perimental data validate a model which calculates the effects of shock-wave com-
pression on a two-phase mixture. The measured post-shock temperature and vapor
concentration compare favorably for gas-phase and aerosol experiments. The agree-
ment between the two fuel-loading techniques verifies that this aerosol shock tube
can be used to study hydrocarbon chemistry for low-vapor-pressure compounds. The
diagnostics and techniques presented here illustrate the utility and some potential
applications of mid-IR laser absorption diagnostics for combustion systems.
vi
Acknowledgements
I want to express my gratitude to my advisor, Ron Hanson, for taking me on as a
graduate student. His constant attention to minute details taught me to polish my
work and his uncanny ability to ask the question for which I had no answer taught
me to be prepared to answer that question.
I would like to thank Jay Jeffries and Dave Davidson for their advice during my
career at Stanford. Their many years of technical experience have provided valuable
guidance while I was beginning my graduate studies at Stanford, and their experience
with presenting scientific information has been invaluable as I complete my degree.
I am also grateful to my fellow Hanson group members, both past and present,
for the many friendships I have made and for the valuable research advice that I have
received. I especially thank Jon Koch, Tom Hanson, Dan Mattison, Dave Rothamer,
Dan Haylett, and Megan MacDonald for being particularly generous with their time
and and for being patient with my sometimes eeyore attitude.
I thank my girls, Fiona, Kyla, Olivia, and Yeva, for reminding me about what is
truly important and for being able to cheer me up with a simple smile, no matter
what broke, how much it cost, and how long it will take to fix.
Most importantly, I must thank my wife, Gretchen, for always supporting and
caring for me. Without her, I surely would have remained a restless wanderer.
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Contents
Preface v
Acknowledgements vii
1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Experimental Objectives . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Organization of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Literature Survey 5
2.1 Infrared Absorption Spectroscopy of Hydrocarbons . . . . . . . . . . 5
2.2 Fuel Sensing using Optical Absorption . . . . . . . . . . . . . . . . . 6
3 Background 9
3.1 Fundamentals of Optical Absorption and Scattering . . . . . . . . . . 9
3.1.1 The Beer-Lambert Relation for a Single Species . . . . . . . . 10
3.1.2 Determination of Temperature using the Absorbance Ratio . . 10
3.1.3 Optical Absorption Measurements with Interference Phenomena 11
3.1.4 Optical Interference from Liquids . . . . . . . . . . . . . . . . 12
3.2 Mid-IR Optical Equipment . . . . . . . . . . . . . . . . . . . . . . . . 14
3.2.1 Mid-IR Optical Fibers . . . . . . . . . . . . . . . . . . . . . . 14
3.2.2 Mid-IR Detectors . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.2.3 Mid-IR Lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.2.4 The FTIR Spectrometer . . . . . . . . . . . . . . . . . . . . . 21
viii
4 IR Spectroscopy of Hydrocarbons 24
4.1 Experimental Apparatus and Procedure . . . . . . . . . . . . . . . . 24
4.1.1 Mixture Preparation . . . . . . . . . . . . . . . . . . . . . . . 26
4.1.2 Surface Adsorption and Condensation . . . . . . . . . . . . . . 27
4.2 Temperature-Dependent Spectra of Hydrocarbons . . . . . . . . . . . 28
4.2.1 Temperature-Dependence of the Integrated Absorption Band
Intensity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4.2.2 Representative Hydrocarbon Spectra . . . . . . . . . . . . . . 30
4.3 Absorption Cross Sections at 3392.2 nm . . . . . . . . . . . . . . . . 43
4.3.1 Optical Arrangement for Measurements at 3392.2 nm . . . . . 43
4.3.2 Hydrocarbon Cross Sections at 3392.2 nm . . . . . . . . . . . 43
4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
5 Interference Rejection 47
5.1 Modified DFG Laser for Two-Wavelength Operation . . . . . . . . . . 48
5.2 Species-Specific Detection . . . . . . . . . . . . . . . . . . . . . . . . 49
5.2.1 Differential Absorption for Vapor Concentration . . . . . . . . 49
5.2.2 Wavelength Selection . . . . . . . . . . . . . . . . . . . . . . . 50
5.2.3 MCH Concentration with n-Heptane Interference . . . . . . . 51
5.3 Vapor Concentration in an Aerosol . . . . . . . . . . . . . . . . . . . 52
5.3.1 Wavelength Selection . . . . . . . . . . . . . . . . . . . . . . . 53
5.3.2 n-Dodecane Vapor Concentration in an Evaporating n-Dodecane
Aerosol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
5.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
6 Sensor for T and n-Heptane Concentration 62
6.1 Wavelength Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
6.1.1 Selection Rules . . . . . . . . . . . . . . . . . . . . . . . . . . 63
6.1.2 Selection of Candidate Wavelength Pairs using FTIR Spectra . 64
6.2 High-Temperature Cross Sections . . . . . . . . . . . . . . . . . . . . 65
6.2.1 Experimental Setup for High-Temperature Absorption Cross
Section Measurements of n-Heptane . . . . . . . . . . . . . . . 66
ix
6.2.2 High-Temperature n-Heptane Cross Sections . . . . . . . . . . 69
6.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
7 Fuel Diagnostic for a PDE 75
7.1 PDE Design and Operation . . . . . . . . . . . . . . . . . . . . . . . 75
7.1.1 Fuel Diagnostic Design . . . . . . . . . . . . . . . . . . . . . . 77
7.1.2 Fuel Concentration Measurements in a PDE . . . . . . . . . . 79
7.2 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
8 Mid-IR Absorption Spectrum of Gasoline 83
8.1 Model for Gasoline Absorption . . . . . . . . . . . . . . . . . . . . . . 84
8.1.1 Class-Averaged Absorption Spectrum: Normal Akanes . . . . 87
8.1.2 Class-Averaged Absorption Spectrum: Branched Alkanes . . . 88
8.1.3 Class-Averaged Absorption Spectrum: Cyclo-Alkanes . . . . . 91
8.1.4 Class-Averaged Absorption Spectrum: Olefins . . . . . . . . . 92
8.1.5 Class-Averaged Absorption Spectrum: Aromatics . . . . . . . 93
8.1.6 Class-Averaged Absorption Spectra: Summary . . . . . . . . . 94
8.1.7 Class-Averaged Spectra Computed from Regular- and Premium-
Grade Gasoline . . . . . . . . . . . . . . . . . . . . . . . . . . 96
8.2 Conversion from Liquid Fraction to Mole Fraction . . . . . . . . . . . 96
8.2.1 Conversion from Liquid Volume Fraction to Mass Fraction . . 98
8.2.2 Conversion from Mass Fraction to Mole Fraction . . . . . . . . 98
8.3 Model Tests at 50◦ and 450◦ C . . . . . . . . . . . . . . . . . . . . . . 99
8.4 High-T Hydrocarbon Cross Sections at 3366.4 nm . . . . . . . . . . . 103
8.5 High-T Gasoline Cross Sections at 3366.4 nm . . . . . . . . . . . . . 105
8.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
9 Sensor for a Shock-Evaporated Aerosol 111
9.1 High-Temperature Cross Sections . . . . . . . . . . . . . . . . . . . . 112
9.1.1 Wavelength Selection . . . . . . . . . . . . . . . . . . . . . . . 113
9.1.2 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . 113
9.1.3 Measured Cross Sections at High-Temperatures . . . . . . . . 116
x
9.1.4 Measurements of n-Dodecane Concentration . . . . . . . . . . 118
9.2 Measurements in a Shock-Evaporated Aerosol . . . . . . . . . . . . . 118
9.2.1 Description of AEROFROSH Code for Shock-Heated Aerosol . 121
9.2.2 Experimental Arrangement for Aerosol Shock Experiments . . 123
9.2.3 Concentration and Temperature Measurements in a Shock-Evaporated
Aerosol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
9.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
10 Summary and Future Work 129
10.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
10.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
Bibliography 135
A Temperature-Dependent Hydrocarbon Spectra 146
A.1 FTIR Absorption Spectra of Normal Alkanes . . . . . . . . . . . . . . 148
A.2 Absorption Spectra of Branched Alkanes . . . . . . . . . . . . . . . . 151
A.3 Absorption Spectra of Olefins . . . . . . . . . . . . . . . . . . . . . . 154
A.4 Absorption Spectra of Aromatics . . . . . . . . . . . . . . . . . . . . 158
A.5 Absorption Spectra of Formaldehyde . . . . . . . . . . . . . . . . . . 161
A.6 Absorption Spectra of Ethanol . . . . . . . . . . . . . . . . . . . . . . 161
B Temperature-Dependent Gasoline Spectra 162
B.1 FTIR Absorption Spectra of Regular-Grade Gasoline . . . . . . . . . 164
B.2 FTIR Absorption Spectra of Premium-Grade Gasoline . . . . . . . . 169
C Absorption Cross Sections at 3.39 µm 175
C.1 Neat Hydrocarbons with Structured Spectra . . . . . . . . . . . . . . 177
C.2 Neat Hydrocarbons with Unstructured Spectra . . . . . . . . . . . . . 179
C.3 Blended Hydrocarbon Fuels . . . . . . . . . . . . . . . . . . . . . . . 181
D Data Analysis for Two-Wavelength Sensor 183
xi
E Diagnostics for Hydrocarbon Chemistry 188
E.1 Determination of Decomposition Rates . . . . . . . . . . . . . . . . . 189
E.2 Ethylene Pyrolysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
E.2.1 Wavelength Selection . . . . . . . . . . . . . . . . . . . . . . . 190
E.2.2 Ethylene Decomposition Rates . . . . . . . . . . . . . . . . . . 192
E.3 n-Heptane Pyrolysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
E.3.1 Wavelength Selection . . . . . . . . . . . . . . . . . . . . . . . 196
E.3.2 n-Heptane Pyrolysis Measurements . . . . . . . . . . . . . . . 197
E.3.3 Unimolecular Decomposition Rates of n-Heptane . . . . . . . 199
E.4 n-Dodecane Pyrolysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
E.4.1 Kinetic Models for n-Dodecane . . . . . . . . . . . . . . . . . 203
E.4.2 Determination of Decomposition Rates . . . . . . . . . . . . . 203
E.5 Pyrolysis of Multiple Hydrocarbon Species . . . . . . . . . . . . . . . 206
E.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
xii
List of Tables
4.1 Molecular weight, structural class, and room-temperature vapor pres-
sure for the hydrocarbon species measured using FTIR spectroscopy. 31
4.2 Temperature-averaged band intensity for the 26 hydrocarbon species
studied here. The measured data are compared to the data from the
PNNL database measured at 25◦ C. . . . . . . . . . . . . . . . . . . . 35
8.1 Distribution of species within each hydrocarbon structural class for one
sample of regular and premium gasoline. . . . . . . . . . . . . . . . . 86
8.2 Branched-alkane species in weighted-averaged and class-averaged spec-
tra. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
8.3 Mole fractions used to compute the class-averaged cyclo-alkane spec-
trum. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
8.4 Mole fractions used to compute the alkane absorption spectrum with
and without cyclo-alkanes. . . . . . . . . . . . . . . . . . . . . . . . 91
8.5 Species and relative mole fractions used to compute the class-averaged
olefin spectrum. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
8.6 Species and relative mole fractions used to calculate class-averaged
aromatic spectrum. . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
8.7 Liquid densities of four hydrocarbon species at 25◦ C. . . . . . . . . . 98
8.8 Sample calculations for conversion from liquid volume fraction to mole
fraction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
8.9 Polynomial coefficients for temperature-dependent absorption cross sec-
tions at 3366.4 nm (See Equation 8.4) for 13 hydrocarbon species, with
temperatures ranging from 25◦ to 930◦ C. . . . . . . . . . . . . . . . 104
xiii
A.1 Experimental details of measured hydrocarbon spectra. . . . . . . . 147
B.1 Characteristics of gasoline samples studied using FTIR spectroscopy. 163
C.1 Experimental details of HeNe cross section measurements presented in
this appendix and compared to previous measurements. . . . . . . . 176
xiv
List of Figures
3.1 Schematic of an optical absorption experiment. . . . . . . . . . . . . 10
3.2 Room-temperature absorption spectra of liquid and vapor toluene at
1 atm with resolution of ∼1 nm (FWHM). Measurement of the vapor
data is described in Chapter 4. . . . . . . . . . . . . . . . . . . . . . . 13
3.3 Schematic of a collimated beam being coupled into and optical fiber. 15
3.4 Performance characteristics of some common mid-IR detectors. A:
Wavelength operating range. B: Detection bandwidth. The vertical
bar in ‘A’ indicates the strong hydrocarbon absorption band associated
with the C-H stretching vibration. . . . . . . . . . . . . . . . . . . . . 18
3.5 Schematic of our tunable mid-IR DFG laser. . . . . . . . . . . . . . 21
3.6 Experimental setup for optical absorption using an FTIR spectrometer. 22
4.1 Apparatus used for preparation of gaseous mixtures. . . . . . . . . . 25
4.2 Heated cell and oven used to measure temperature-dependent cross
sections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4.3 Temperature-dependent absorption spectrum of 2,2,4-trimethyl-pentane
for temperatures ranging from 25 to 500◦ C at 1 atm of total pressure
with resolution of ∼1 nm (FWHM). . . . . . . . . . . . . . . . . . . 32
4.4 Comparison of high-resolution (∼0.1 nm FWHM) FTIR spectra for
methane measured here, reported by PNNL, and computed using the
HITRAN database for 1 atm of total pressure and room temperature. 33
4.5 Measured absorption spectrum of n-heptane (T = 26◦ C, P = 1 atm,
∼1 nm resolution, FWHM) compared to the data reported by PNNL
(T = 25◦ C, P = 1 atm, ∼0.1 nm resolution, FWHM). . . . . . . . . 34
xv
4.6 Integrated band intensity from 25◦ to 500◦ C for three normal alkanes. 36
4.7 Measured and rescaled n-dodecane absorption spectrum at 50◦ C com-
pared to PNNL measurements. . . . . . . . . . . . . . . . . . . . . . 37
4.8 Integrated band intensity versus number of C-H bonds for four struc-
tural classes of hydrocarbon molecules studied here. . . . . . . . . . 38
4.9 Measured absorption spectra for 3-methyl-hexane (a branched alkane),
n-heptane (a straight alkane) and toluene (an aromatic) at 25◦ C and
1 atm, with ∼1 nm resolution (FWHM). . . . . . . . . . . . . . . . . 39
4.10 Absorption spectra of three normal alkanes at 100◦ C and 1 atm, mea-
sured with ∼1 nm resolution (FWHM). . . . . . . . . . . . . . . . . 40
4.11 Absorption spectra of regular-grade (A) and premium-grade (B) gaso-
line for a temperature of 50◦ C and pressure of 1 atm, measured with
a resolution of ∼1 nm (FWHM). Regular-grade, high-alkane compo-
sition: alkanes: 75.1 liq. vol.%, olefins: 6.0 liq. vol.%, aromatics:
18.9 liq. vol.%. Regular-grade, high-aromatic composition: alkanes:
55.5 liq. vol.%, olefins: 4.6 liq. vol.%, aromatics: 39.9 liq. vol.%.
Premium-Grade, high-alkane composition: alkanes: 74.5 liq. vol.%,
olefins: 11.9 liq. vol.%, aromatics: 13.6 liq. vol.%. Premium-grade,
high-aromatic composition: alkanes: 52.5 liq. vol.%, olefins: 8.5 liq.
vol.%, aromatics: 39.0 liq. vol.%. . . . . . . . . . . . . . . . . . . . . 42
4.12 Optical arrangement for cross section measurements using a 3.39 µm
HeNe laser. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.13 Temperature-dependent cross section of methane at 3392.2 nm mea-
sured at 1 atm with the FTIR and with the HeNe laser compared to
the HeNe measurements reported by Perrin and Hartmann. . . . . . . 45
4.14 Comparison of temperature-dependent cross section of A: n-heptane,
and B: 2,2,4-trimethyl-pentane, measured at 1 atm and 3392.2 nm
using an FTIR spectrometer and a HeNe laser. Also plotted are FTIR
data from PNNL, HeNe measurements of n-heptane from Horning et
al., and HeNe measurements of 2,2,4-trimethyl-pentane from Tsuboi
et al.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
xvi
5.1 Schematic of the modified DFG laser for two-wavelength operation. . 48
5.2 Absorption spectra of n-heptane and methyl-cyclo-hexane at 50◦ C
and 1 atm, measured with resolution of ∼1 nm (FWHM) via FTIR
spectroscopy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
5.3 Ratio of measured to actual MCH mole fraction (left axis) and ratio
of heptane to MCH absorbance (right axis) plotted versus the actual
n-heptane/MCH mole fraction ratio. The boxes indicate the measured
concentration ratio, the dashed line shows a concentration ratio of one,
and the solid line indicates absorbance ratio. . . . . . . . . . . . . . 52
5.4 Absorption spectrum of n-dodecane at 401◦ C and 1 atm with reso-
lution of ∼1 nm (FWHM). The two wavelengths for the differential
absorbance sensor are indicated by the arrows. . . . . . . . . . . . . 53
5.5 Temperature-dependent differential cross section of n-dodecane at 1
atm for wavelengths of 3417.6 and 3429.4 nm measured using an FTIR
spectrometer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
5.6 Schematic of aerosol shock tube for studying multi-phase mixtures. . 55
5.7 Differential absorption measurements for an evaporating aerosol. Post-
shock conditions: P2 = 0.783 atm, T2 = 436 K, n-dodecane mole frac-
tion = 0.55% in argon. . . . . . . . . . . . . . . . . . . . . . . . . . 56
5.8 Measured absorbance by flowing n-dodecane vapor in argon for high
and low bath gas flow rates. (P = 0.16 atm, T = 25◦ C, resolution of
∼1 nm (FWHM). Also shown is the calculated absorbance for 0.123
torr of n-dodecane at 25◦ C. . . . . . . . . . . . . . . . . . . . . . . . 58
5.9 Measured n-dodecane vapor absorption (right axis), measured total
extinction from vapor and droplets (left axis), and inferred droplet
extinction (left axis) for an n-dodecane aerosol. . . . . . . . . . . . . 59
5.10 Measured n-dodecane vapor concentration and near-IR droplet extinc-
tion for an evaporating shock-heated n-dodecane aerosol. Dashed line
indicates the mole fraction for saturated n-dodecane at 24◦ C. Tem-
perature and pressure after the shock wave passes are 436 K and 0.783
atm, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
xvii
6.1 Absorption spectrum of n-heptane at 50◦ and 400◦ C, 1 atm with reso-
lution of ∼1 nm (FWHM). The operating range of the DFG lasers and
the three candidate wavelength pairs are also indicated in the figure. 64
6.2 Experimental setup for measurements of high-temperature absorption
cross sections in a shock tube. . . . . . . . . . . . . . . . . . . . . . 66
6.3 High-temperature absorption cross sections and absorbance ratio of
n-heptane using the three wavelength pairs indicated in Figure 6.1.
Closed symbols indicate cell measurements using the FTIR and open
symbols indicate data measured in a shock tube. A: λ1 = 3471 nm,
λ2 = 3446 nm, B: λ1 = 3371 nm, λ2 = 3384 nm, C: λ1 = 3410 nm,
λ2 = 3433 nm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
6.4 Measured n-heptane concentration (A), and temperature (B) in a shock
tube using a two-wavelength diagnostic at 3410 and 3433 nm. Shock
conditions: P1 = 0.11 atm, T1 = 295 K P2 = 0.613 atm, T2 = 645 K P5
= 2.017 atm, T5 = 1066 K, with initial n-heptane mole fraction=0.67%
in argon. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
6.5 Measured n-heptane concentration (A), and temperature (B) in a shock
tube using a two-wavelength diagnostic at 3410 and 3433 nm. Shock
conditions: P1 = 0.072 atm, T1 = 295 K P2 = 0.488 atm, T2 = 730 K P5
= 1.832 atm, T5 = 1258 K, with initial n-heptane mole fraction=0.64%
in argon. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
6.6 Concentration (A) and temperature (B) measured using the two-wavelength
mid-IR sensor at 3410 and 3433 nm plotted versus modelled values us-
ing the 1-D shock equations. . . . . . . . . . . . . . . . . . . . . . . 74
7.1 Schematic of the pulse detonation engine. The optics section was
mounted near the head-end (top picture) or the tail-end (bottom pic-
ture) of the engine. . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
7.2 Optical arrangement for fuel measurements in a pulse detonation en-
gine. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
xviii
7.3 Propane concentration measurements in a PDE for 5 Hz fired and
unfired operation. The dashed line indicates a stoichiometric mixture
at 1 atm and 25◦ C. . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
7.4 Ethylene measurements in a fired PDE measured near (A) the head-
end and (B) the tail-end of the engine for 10 Hz operation. The dashed
line indicates a stoichiometric mixture at 1 atm and 25◦ C. . . . . . 82
8.1 PNNL absorption spectra of the primary normal alkanes in gasoline, at
50◦ C and 1 atm, with resolution of ∼0.1 nm (FWHM). The weighted-
average spectrum for normal alkanes is plotted as a dashed line. . . . 88
8.2 Absorption spectra of four branched alkanes reported by PNNL for
50◦ C, 1 atm, and resolution of ∼0.1 nm (FWHM). Also shown are the
approximate weighted average and the class average using the mole
fractions listed in Table 8.2. . . . . . . . . . . . . . . . . . . . . . . . 90
8.3 Class-averaged cyclo-alkane spectrum using 78% cyclo-pentane, 6%
cyclo-hexane and 16% methyl-cyclo-hexane. . . . . . . . . . . . . . . 92
8.4 Comparison of modelled alkane absorption spectra at 50◦ C using the
relative compositions listed in Table 8.4. . . . . . . . . . . . . . . . . 93
8.5 Calculated class-averaged absorption spectra for four primary hydro-
carbon structural classes with resolution of ∼1 nm (FWHM). (A): 50◦
C and 1 atm. (B): 450◦ C and 1 atm. . . . . . . . . . . . . . . . . . 95
8.6 Comparison of class-averaged absorption spectra computed using the
regular- and premium-grade gasoline for a temperature of 50◦ C, 1 atm,
and resolution of ∼1 nm (FWHM). . . . . . . . . . . . . . . . . . . . 97
8.7 Composition of 21 samples of gasoline used in the current study. The
arrows indicate the four gasoline samples selected for high-temperature
shock tube studies described in Section 8.5 . . . . . . . . . . . . . . 100
xix
8.8 Comparison of measured and modelled spectra of two gasoline samples
for a temperature of 50◦ C, mole fraction of 0.6%, total pressure of
1 atm, and resolution of ∼1 nm (FWHM). Composition of sample P1
(A): 71.0/14.2/14.9 Alkane/Olefin/Aromatic by mole. Composition of
sample R6 (B): 55.2/18.1/26.6 Alkane/Olefin/Aromatic by mole. . . 101
8.9 Modelled cross section versus measured cross section from the FTIR
data for temperatures of (A) 50◦ and (B) 450◦ C, pressure of 1 atm,
and wavelengths of 3366.4, 3392.23, and 3471 nm. . . . . . . . . . . 107
8.10 Measured temperature-dependent absorption cross section for 3-methyl-
hexane at 3366.4 nm with mole fraction ranging from ∼0.7 to 1.3% in
argon with post-reflected-shock pressures ranging from 1.4 to 1.8 atm. 108
8.11 Measured temperature-dependent absorption cross section for toluene
at 3366.4 nm with mole fraction ranging from ∼1.5 to 6% in argon
with post-reflected-shock pressures ranging from 1.5 to 2.5 atm. . . . 108
8.12 Measured and modelled temperature-dependent cross sections at 3366.4
nm for a sample of regular-grade gasoline (sample R6) with 55.2% alka-
nes, 26.6% aromatics, 18.1% olefins and 0% oxygenates by mole. The
mole fraction of gasoline was 0.2 to 0.8% in argon with post-reflected-
shock pressure was ∼1.5 atm. . . . . . . . . . . . . . . . . . . . . . . 109
8.13 Measured and modelled temperature-dependent cross sections at 3366.4
nm for a sample of regular-grade gasoline (sample R9) with 54.4% alka-
nes, 36% aromatics, 9.7% olefins and 0% oxygenates by mole. The mole
fraction of gasoline was 0.2 to 0.8% in argon with post-reflected-shock
pressure was ∼1.5 atm. . . . . . . . . . . . . . . . . . . . . . . . . . 109
8.14 Measured and modelled temperature-dependent cross sections at 3366.4
nm for a sample of premium-grade gasoline (sample P1) with 71.0%
alkanes, 14.9% aromatics, 14.2% olefins and 0% oxygenates by mole.
The mole fraction of gasoline was 0.2 to 0.8% in argon with post-
reflected-shock pressure was ∼1.5 atm. . . . . . . . . . . . . . . . . . 110
xx
8.15 Measured and modelled temperature-dependent cross sections at 3366.4
nm for a sample of premium-grade gasoline (sample P8) with 48.7%
alkanes, 41.5% aromatics, 9.8% olefins and 0% oxygenates by mole.
The mole fraction of gasoline was 0.2 to 0.8% in argon with post-
reflected-shock pressure was ∼1.5 atm. . . . . . . . . . . . . . . . . . 110
9.1 n-Dodecane absorption spectra at 100◦ and 450◦ C and 1 atm measured
with 1 nm resolution (FWHM) using FTIR spectroscopy. . . . . . . 114
9.2 Experimental setup for measurements of shock-heated n-dodecane va-
por/argon mixtures. . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
9.3 Measured absorbance at 3409.0 and 3432.4 nm for shock-heated n-
dodecane vapor in argon. Initial n-dodecane mole fraction was 0.058%
with post-reflected-shock temperature and pressure of 1226 K and 6.10
atm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
9.4 Temperature-dependent cross sections and absorbance ratio of n-dodecane.
A: σ(3409.0 nm), B: σ(3432.4 nm), and C: absorbance ratio. . . . . . 117
9.5 Measured data for shock-heated mixture of 0.058% n-dodecane vapor in
argon with post-reflected-shock pressure of 6.10 atm and temperature
of 1226 K. A: Temperature. B: Concentration. Dashed lines indicate
calculations using the 1-D shock equations. Solid lines indicate data
measured by two-wavelength sensor. . . . . . . . . . . . . . . . . . . 119
9.6 Comparison of measured and calculated data for shock-heated mixtures
of n-dodecane vapor in argon. A: Temperature; B: Concentration.
Dashed lines indicate perfect agreement. . . . . . . . . . . . . . . . . 120
9.7 Measured extinction at 1550 nm, 3409.0 nm, and 3432.4 nm for a
shock-heated n-dodecane aerosol with the sensor located 5 cm from
the endwall. P5 = 7.56 atm, T5 = 1109 K, n-dodecane mole fraction
= 0.26%. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
xxi
9.8 Time-dependent temperature and concentration measurements for a
shock-evaporated n-dodecane aerosol. Dashed lines values calculated
using AEROFROSH. A: Temperature, B: Concentration. P5 = 7.56
atm, T5 = 1109 K, n-dodecane mole fraction = 0.26%. . . . . . . . . 126
9.9 Measured temperature versus modelled temperature for post-evaporation
n-dodecane-aerosol shocks. . . . . . . . . . . . . . . . . . . . . . . . 128
A.1 Absorption spectra of methane. . . . . . . . . . . . . . . . . . . . . . 148
A.2 Absorption spectra of ethane. . . . . . . . . . . . . . . . . . . . . . . 148
A.3 Absorption spectra of n-pentane. . . . . . . . . . . . . . . . . . . . . 149
A.4 Absorption spectra of n-heptane. . . . . . . . . . . . . . . . . . . . . 149
A.5 Absorption spectra of n-dodecane. . . . . . . . . . . . . . . . . . . . 150
A.6 Absorption spectra of 2-methyl-propane. . . . . . . . . . . . . . . . . 151
A.7 Absorption spectra of 2-methyl-butane. . . . . . . . . . . . . . . . . 151
A.8 Absorption spectra of 2-methyl-pentane. . . . . . . . . . . . . . . . . 152
A.9 Absorption spectra of 3-methyl-hexane. . . . . . . . . . . . . . . . . 152
A.10 Absorption spectra of 2,2,4-trimethyl-pentane (iso-octane). . . . . . 153
A.11 Absorption spectra of ethylene. . . . . . . . . . . . . . . . . . . . . . 154
A.12 Absorption spectra of propene. . . . . . . . . . . . . . . . . . . . . . 154
A.13 Absorption spectra of 1-butene. . . . . . . . . . . . . . . . . . . . . . 155
A.14 Absorption spectra of cis-2-pentene. . . . . . . . . . . . . . . . . . . . 155
A.15 Absorption spectra of 2-methyl-2-butene. . . . . . . . . . . . . . . . . 156
A.16 Absorption spectra of 2-methyl-2-pentene. . . . . . . . . . . . . . . . 156
A.17 Absorption spectra of 1-heptene. . . . . . . . . . . . . . . . . . . . . . 157
A.18 Absorption spectra of 2,4,4-trimethyl-1-pentene. . . . . . . . . . . . . 157
A.19 Absorption spectra of benzene. . . . . . . . . . . . . . . . . . . . . . 158
A.20 Absorption spectra of toluene. . . . . . . . . . . . . . . . . . . . . . . 158
A.21 Absorption spectra of m-xylene. . . . . . . . . . . . . . . . . . . . . . 159
A.22 Absorption spectra of o-xylene. . . . . . . . . . . . . . . . . . . . . . 159
A.23 Absorption spectra of ethyl-benzene. . . . . . . . . . . . . . . . . . . 160
A.24 Absorption spectra of 3-ethyl-toluene. . . . . . . . . . . . . . . . . . . 160
xxii
A.25 Absorption spectra of formaldehyde. . . . . . . . . . . . . . . . . . . 161
A.26 Absorption spectra of ethanol. . . . . . . . . . . . . . . . . . . . . . . 161
B.1 Absorption spectra of sample R1 at 50◦ and 450◦ C. . . . . . . . . . . 164
B.2 Absorption spectra of sample R2 at 50◦ and 450◦ C. . . . . . . . . . . 164
B.3 Absorption spectra of sample R3 at 50◦ and 450◦ C. . . . . . . . . . . 165
B.4 Absorption spectra of sample R4 at 50◦ and 450◦ C. . . . . . . . . . . 165
B.5 Absorption spectra of sample R5 at 50◦ and 450◦ C. . . . . . . . . . . 166
B.6 Absorption spectra of sample R6 at 50◦ and 450◦ C. . . . . . . . . . . 166
B.7 Absorption spectra of sample R7 at 50◦ and 450◦ C. . . . . . . . . . . 167
B.8 Absorption spectra of sample R8 at 50◦ and 450◦ C. . . . . . . . . . . 167
B.9 Absorption spectra of sample R9 at 50◦ and 450◦ C. . . . . . . . . . . 168
B.10 Absorption spectra of sample R10 at 50◦ and 450◦ C. . . . . . . . . . 168
B.11 Absorption spectra of sample R11 at 50◦ and 450◦ C. . . . . . . . . . 169
B.12 Absorption spectra of sample P1 at 50◦ and 460◦ C. . . . . . . . . . . 169
B.13 Absorption spectra of sample P2 at 50◦ and 450◦ C. . . . . . . . . . . 170
B.14 Absorption spectra of sample P3 at 50◦ and 450◦ C. . . . . . . . . . . 170
B.15 Absorption spectra of sample P4 at 50◦ and 450◦ C. . . . . . . . . . . 171
B.16 Absorption spectra of sample P5 at 50◦ and 450◦ C. . . . . . . . . . . 171
B.17 Absorption spectra of sample P6 at 50◦ and 450◦ C. . . . . . . . . . . 172
B.18 Absorption spectra of sample P7 at 50◦ and 450◦ C. . . . . . . . . . . 172
B.19 Absorption spectra of sample P8 at 50◦ and 450◦ C. . . . . . . . . . . 173
B.20 Absorption spectra of sample P9 at 50◦ and 450◦ C. . . . . . . . . . . 173
B.21 Absorption spectra of sample P10 at 50◦ and 450◦ C. . . . . . . . . . 174
C.1 Absorption cross section of methane at 3392.2 nm from 28◦ to 405◦ C
compared to the HITRAN database, Jaynes and Beam, Yoshiyama et
al., Tomita et al., Perrin et al., and Sharpe et al.. . . . . . . . . . . . 177
C.2 Absorption cross section of ethylene at 3392.2 nm from 26◦ to 400◦ C
compared to the HITRAN database, Sharpe et al., and Hinckley et al.. 177
xxiii
C.3 Absorption cross section of propane at 3392.2 nm from 26◦ to 400◦ C
compared to measurements by Sharpe et al., Tsuboi et al., Yoshiyama
et al., and Jaynes and Beam. . . . . . . . . . . . . . . . . . . . . . . . 178
C.4 Absorption cross section of n-heptane at 3392.2 nm from 26◦ to 400◦ C
compared to measurements by Sharpe et al., Tsuboi et al., Drallmeier,
Jaynes and Beam, and Horning et al.. . . . . . . . . . . . . . . . . . . 179
C.5 Absorption cross section of 2,2,4-trimethyl-pentane at 3392.2 nm from
26◦ to 400◦ C compared to measurements by Sharpe et al., Tomita et
al., Tsuboi et al., and Drallmeier. . . . . . . . . . . . . . . . . . . . . 180
C.6 Absorption cross section of n-decane at 3392.2 nm from 26◦ to 400◦ C
compared to Drallmeier, Horning et al., and Jaynes and Beam. . . . . 180
C.7 Absorption cross section of gasoline at 3392.2 nm from 26◦ to 400◦ C
compared to measurements by Jaynes and Beam. . . . . . . . . . . . 181
C.8 Absorption cross section of Jet-A at 3392.2 nm from 26◦ to 400◦ C
compared to measurements of kerosene, JP-4 and JP-5 by Jaynes and
Beam. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
C.9 Absorption cross section of JP-10 at 3392.2 nm from 26◦ to 400◦ C. . 182
D.1 Raw data for one cycle of the two-wavelength DFG laser for the evac-
uated shock tube (solid line) and for the shock tube filled to 0.1 atm
with a mixture of 1.5% 2-methyl-butane in argon. . . . . . . . . . . 184
D.2 Calculated absorbance versus time for the data in Figure D.1. . . . . 185
D.3 Measured background signal and laser signal at two wavelengths for
a shock-tube experiment with a mixture of 1.5% 2-methyl-butane in
argon. Shock conditions: P1 = 0.109 atm, T1 = 297 K, P2 = 0.505
atm, T2 = 568 K, P5 = 1.61 atm, T5 = 884 K. . . . . . . . . . . . . 186
D.4 Measured background signal and laser signal at two wavelengths for
a shock-tube experiment with a mixture of 1.5% 2-methyl-butane in
argon. Shock conditions: P1 = 0.109 atm, T1 = 297 K, P2 = 0.505
atm, T2 = 568 K, P5 = 1.61 atm, T5 = 884 K. . . . . . . . . . . . . 187
xxiv
E.1 Temperature-dependent absorption cross section of ethylene at 3346.5
nm. FTIR data were measured at 1 atm and and resolution of ∼0.1 nm
(FWHM). Shock-tube measurements were performed with pressures
ranging 0.085 to 6 atm. . . . . . . . . . . . . . . . . . . . . . . . . . . 191
E.2 Modelled decomposition of ethylene and formation of products for ini-
tial concentration of 5%, initial temperature of 1780 K and initial pres-
sure of 5.207 atm. The GRI-Mech 3.0 mechanism was used to model
these reactions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
E.3 Measured, modelled, and fit ethylene concentration for initial mole
fraction of 5% in argon, initial temperature of 1780 K and initial pres-
sure of 5.207 atm. The overall decomposition rate inferred from the
measured data was 1805 sec−1. . . . . . . . . . . . . . . . . . . . . . 193
E.4 Sensitivity analysis of ethylene pyrolysis for initial mole fraction of 5%
in argon, initial temperature of 1780 K and initial pressure of 5.207
atm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
E.5 Measured and modelled ethylene removal rates for mixtures of 5% eth-
ylene in argon at ∼6 atm with temperatures ranging from 1680 to
1890 K. The GRI-Mech 3.0 mechanism was used to model the overall
removal rate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
E.6 FTIR spectra of n-heptane (resolution of ∼1 nm (FWHM)) and its
primary pyrolysis products (resolution of ∼0.1 nm (FWHM)). The
spectra were measured at 450◦ C with a total pressure of 1 atm and
mole fraction of ∼ 1% in nitrogen. Arrows indicate the wavelengths
chosen for this sensor (3410 and 3433 nm). . . . . . . . . . . . . . . 196
E.7 Modelled pyrolysis products (left) and absorbance (right) at 3410 nm
for 0.737% n-heptane in argon at 1258 K and 1.832 atm. . . . . . . . 197
E.8 Measured and modelled species time-history of n-heptane for a temper-
ature of 1258 K, a pressure of 1.832 atm and concentration of 0.737%
n-heptane in argon. . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
xxv
E.9 Measured, corrected, and fit n-heptane mole fraction for an initial tem-
perature of 1258 K, pressure of 1.832 atm and concentration of 0.737%
n-heptane in argon. . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
E.10 Measured and modelled temperature-dependent removal rate for∼0.8%
n-heptane in argon at ∼1.8 atm, assuming pseudo-first-order decompo-
sition. The mechanism by Chaos et al. was used to model the reaction. 200
E.11 Sensitivity analysis for the pyrolysis of 0.737% n-heptane in argon at
1258 K and 1.83 atm. Reaction enclosed in the box were adjusted to
fit the measured data shown in Figure E.12. . . . . . . . . . . . . . . 201
E.12 Measured and fit decomposition of 0.737% n-heptane in argon for a
temperature of 1258 K and a pressure of 1.83 atm. Dashed lines rep-
resent calculations using the original and adjusted Chaos models. . . 201
E.13 Comparison of the adjusted decomposition rate of n-heptane with that
predicted by the original Chaos mechanism at 1-2 atm with mole frac-
tions of 0.7 to 0.9% n-heptane in argon and also compared with mea-
surements by Davidson et al. at 1-2 atm with mole fractions of 0.01 to
0.02% in argon. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
E.14 Measured and corrected n-dodecane mole fraction for initial tempera-
ture of 1226 K, pressure of 6.10 atm and n-dodecane concentration of
0.058% in argon. These data were taken using a gaseous mixture (i.e.,
no aerosol was present in the initial mixture). A pseudo-first-order fit
to the corrected data is indicated by the dashed line. . . . . . . . . . 204
E.15 Measured and Modelled temperature-dependent removal rate of n-
dodecane for pressures ranging from 1.5 to 7 atm and mole fractions
of 0.05 to 0.5%. assuming pseudo-first-order behavior. The measured
rates have been corrected for interference absorption by other hydro-
carbon species. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
xxvi
E.16 Sensitivity analysis for n-dodecane pyrolysis using the Zhang mech-
anism with initial temperature of 1226 K, pressure of 6.10 atm and
n-dodecane concentration of 0.058% in argon. These data were mea-
sured using a gaseous mixture (i.e., no aerosol was present in the initial
mixture). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206
E.17 Measured overall removal rate for multiple alkanes (A) as well as olefins
and ethanol (B) for pressures ranging from 1 to 2 atm and mole frac-
tions of 0.5 to 2%. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
xxvii
xxviii
Chapter 1
Introduction
1.1 Motivation
In the past 350 years, combustion science has advanced significantly from early practi-
cal steam engines [1] to the latest propulsion technologies including pulse detonation
engines (PDE’s) [2], low-NOx gas turbine combustors [3] and homogeneous charge
compression ignition (HCCI) engines [4]. The limits of engine performance are con-
tinuously driven by ongoing efforts to minimize acoustic noise, fuel consumption, and
greenhouse gases and toxic pollutants, while maximizing power output and power den-
sity. In the 1970’s, scientists and engineers began to rely increasingly on diagnostics
that enable understanding and control of engines in real time. On-Board Diagnostics
(OBD) are now standard equipment on most new engines produced for the automo-
bile industry, providing feedback to an engine computer which controls, among other
things, spark timing and the amount of fuel injected. Developing technologies like
PDE’s and HCCI engines also rely on diagnostics to obtain reliable performance and
to study the effects of equivalence ratio, valve timing, and other variables. Hence,
combustion diagnostics are necessary for both research and production engines.
Optical absorption diagnostics using infrared (IR) lasers continue to show promise
in many applications [5–7] because they provide accurate and nonintrusive measure-
ments, have a fast time response, and can target specific species of interest. Laser
diagnostics have been used to measure temperature and species concentration in
1
2 CHAPTER 1. INTRODUCTION
PDE’s [8–10] where this information is required to improve models of engine perfor-
mance and to aid in understanding of cycle-to-cycle interactions. Similar diagnostics
have been demonstrated on gas turbine combustors [11, 12], direct-injection spark-
ignition (DISI) engines [13], HCCI engines [14], and scramjet combustors [15]. In all
of these studies, the sensors provide useful knowledge of the time-evolution of the
quantity of interest (e.g., species concentration or temperature).
There are many examples of optical diagnostics using ultraviolet (UV) sources [16–
19], near-IR sources [8, 9, 15, 20–22], and mid-IR sources [23–31]. UV diagnostics
are sensitive to many species and UV absorption cross sections are generally quite
large. However, sometimes the absorption cross sections are too large, resulting in
an optically thick measurement, and oftentimes, multiple species absorb at the same
wavelength. Near-IR sensors utilize compact and inexpensive diode lasers. These
lasers are wavelength-tunable, rugged, and often fiber-coupled. Additionally, many
species have near-IR absorption spectra which result from overtone- and combination-
band rovibrational transitions. Near-IR diagnostics have been used to study a host
of low-molecular-weight species including H2O, CO2, CH4, and O2 [5]. However,
the absorption cross sections of the fundamental vibrational modes in the mid-IR
are ∼100 times stronger than for the overtone and combination bands. Thus, mid-IR
diagnostics exhibit significantly higher sensitivity. There are several examples of mid-
IR diagnostics that have been used to measure hydrocarbons [10, 32, 33] and other
species [34], illustrating the sensitivities that can be achieved with these sensors.
1.2 Experimental Objectives
This research has multiple objectives with the underlying theme of developing optical
absorption diagnostics to measure fuels in harsh environments. First, temperature-
dependent spectroscopic data are reported for selected hydrocarbon species and blended
fuels. These data are critical for the design of optical absorption sensors and are re-
quired for quantitative concentration measurements. By studying the spectroscopy of
a variety of hydrocarbons and fuel blends, absorption diagnostics can be tailored to
1.3. ORGANIZATION OF THESIS 3
the species and the expected conditions (i.e., temperature, pressure, optical interfer-
ences). Second, diagnostic techniques using a modified two-wavelength laser system
are developed for robust measurements in practical environments. Demonstrations of
the measurement techniques in controlled environments illustrate the sensitivity that
can be achieved. Finally, mid-IR absorption diagnostics are applied to harsh environ-
ments. Several fuel sensors are designed to study important systems including PDE’s
and internal combustion (IC) engines.
1.3 Organization of Thesis
In this work, mid-IR diagnostics are designed to measure temperature and hydrocar-
bon concentration. Chapter 2 summarizes the relevant literature for mid-IR spec-
troscopy and mid-IR optical diagnostics. Chapter 3 provides the background theory
for optical absorption and optical scattering. This chapter also gives technical de-
tails about much of the optical equipment necessary to construct mid-IR absorption
sensors.
In Chapter 4, the absorption spectroscopy of hydrocarbons near 3.4 µm is exam-
ined using a Fourier transform infrared (FTIR) spectrometer and a fixed-wavelength
helium neon (HeNe) laser. Temperature-dependent absorption cross sections are mea-
sured for many hydrocarbon species and blended fuels. In Chapters 5-9 the funda-
mental spectroscopic data from Chapter 4 are used to design fuel and temperature
diagnostics for severe environments (e.g., shock tubes and PDE’s).
In Chapters 5 and 6, experimental techniques are developed for simultaneous
measurement of temperature and concentration and for measurement of concentration
in the presence of optical interference.
In Chapter 7, a fiber-coupled HeNe laser is used to make time-resolved measure-
ments in fired PDE’s, enabling investigation of the effects of fuel loading. The sensor
reveals cycle-to-cycle interactions which alter the fuel concentration profile during
fired operation.
4 CHAPTER 1. INTRODUCTION
Chapter 8 investigates the spectroscopy of gasoline with the ultimate goal of mea-
suring equivalence ratio in a gasoline-fueled reciprocating engine. A model is de-
veloped for predicting the absorption spectra of blended gasoline samples, requiring
only the relative proportions of primary hydrocarbon structural classes (i.e., alkanes,
olefins, aromatics, and oxygenates) as input. Modelled values are compared with
FTIR spectra of 21 gasoline samples at 50◦ and 450◦ C and high-temperature cross
section data measured by laser absorption in a shock tube. The good agreement be-
tween model and measurements validates this spectroscopic model for gasoline blends.
In Chapter 9, the two-wavelength technique developed in Chapter 6 is applied to
an aerosol shock tube to explore the potential of this facility to study chemistry in
an aerosol-gas mixture.
The mid-IR optical absorption sensors demonstrated here are practical and robust
and are capable of providing essential information in both fundamental shock tube
studies as well as practical systems such as PDE’s and IC engines.
Chapter 2
Literature Survey
Scientists have been studying the strong mid-IR absorption bands of hydrocarbons
for many years [35], so there is a great deal of spectroscopic data and sensor design
information that pertains to mid-IR absorption diagnostics. Section 2.1 summarizes
the available mid-IR spectroscopic data for hydrocarbons. Section 2.2 reviews various
hydrocarbon sensors that have been demonstrated previously.
2.1 Infrared Absorption Spectroscopy of Hydro-
carbons
To design a robust optical-absorption diagnostic for hydrocarbons, it is necessary to
first explore the spectroscopic data that are available. Absorption spectra of numer-
ous hydrocarbon species can be found in the Aldrich library of FTIR spectra [36]
and also at the National Institute of Standards and Technology (NIST) website [37]
for wavelengths ranging from ∼1-20 µm. The path length and concentration are not
reported for these data so an absorption cross section cannot be calculated. However,
this information is useful for comparing relative absorption at different wavelengths
and identifying regions of strong absorption. Quantitative spectral databases are
available from other institutions such as the Environmental Protection Agency [38]
and Pacific Northwest National Laboratories (PNNL) [39]. These fee-based sources
5
6 CHAPTER 2. LITERATURE SURVEY
provide high-quality data, but over a limited temperature range (typically ∼5-50◦
C). Finally, the HITRAN database, maintained by the Harvard-Smithsonian Center
for Astrophysics, is a quantitative database that offers detailed spectral informa-
tion for a wide array of species [40]. For many gaseous species, HITRAN provides
linestrength and line-broadening data which can be used to calculate the temperature-
and pressure-dependence of the absorption spectra. For many larger molecules, HI-
TRAN also provides temperature- and pressure-dependent cross section data. How-
ever, this database does not contain many of the high-molecular-weight hydrocarbons
that are present in practical combustion systems. Lacking from all of these sources
are quantitative, high-temperature absorption spectra for high-molecular-weight hy-
drocarbons. These data are necessary to design optical absorption diagnostics for
practical combustion systems and will also be useful for modelling radiative heat
transfer in combustion environments.
Whereas temperature-dependent spectral data are lacking for many hydrocarbons,
there is a significant amount of cross section data at 3.392 µm. For more than 30
years, the fixed-wavelength mid-IR HeNe laser has been exploited for sensing of hy-
drocarbon concentration because of the strong absorption that many hydrocarbons
exhibit at this wavelength [30]. Several studies report temperature-dependent absorp-
tion coefficient data for small gaseous hydrocarbons [31,41–46]. There are also some
temperature- and pressure-dependent absorption coefficient data for larger hydrocar-
bon molecules at 3.392 µm, but some of these measurements have large uncertainties
and the data are not consistent among the various sources [26,30,32,47]. Because of
the pervasive use of the HeNe laser in hydrocarbon detection, it is critical that the
temperature- and pressure-dependent absorption coefficients at 3.39 µm be known for
hydrocarbon species that are of interest in practical combustion experiments.
2.2 Fuel Sensing using Optical Absorption
There are many examples of optical absorption diagnostics for fuel concentration be-
cause fuel concentration is an important quantity. Near-IR diagnostics have become
2.2. FUEL SENSING USING OPTICAL ABSORPTION 7
popular because of the advent of high-quality telecommunications diode lasers. Near-
IR fuel diagnostics generally exploit the first overtone of the C-H stretch near 1.6-1.8
µm and often take advantage of the tunability of diode lasers to enhance sensitiv-
ity [20–22]. Fiber-coupled near-IR sensors have been used to study fuel concentration
in PDE’s [9] and IC engines [48, 49]. However, the signal-to-noise ratio (SNR) for
the sensor can be low because the near-IR absorption cross sections are small. For
increased sensitivity to concentration, mid-IR diagnostics should be considered.
Mid-IR diagnostics using the 3.39 µm HeNe laser are popular because this laser
is commonly available and the absorption cross sections of hydrocarbons are large at
this wavelength. Additionally, spectroscopic data are available because this laser has
been in use for three decades. Tomita et al. demonstrated a fiber-coupled HeNe-laser-
absorption sensor to measure methane [44] and Tomita et al. and Kawahara et al.
demonstrated a similar sensor for gasoline [32, 33] in an IC engine. Winklhofer and
Plimon observed liquid- and vapor-phase fuel distribution in an optical research engine
using a visible and a mid-IR HeNe laser [50]. Nguyen et al. used a 3.39µm HeNe
laser sensor to measure fuel concentration in a gas turbine combustor [11]. This laser
also has been used to measure hydrocarbon concentration in a shock tube [29] and
in unfired pulse detonation engines [8, 28]. Both Chraplyvy [24] and Drallmeier [25]
used two HeNe lasers at different wavelengths (0.632 and 3.39 µm) to measure vapor
concentration in a spray. The use of a second wavelength that is not absorbed by
the fuel vapor enables the resonant-wavelength extinction (i.e., the extinction at 3.39
µm) to be corrected for droplet scattering.
Fiber-coupling was not utilized for most of these sensors because it increases the
cost and complexity of the system. However, when optical access is restricted or when
the system experiences significant movement, fiber-coupling is necessary [23,32,33,44].
Because HeNe lasers are fixed-wavelength devices and can show large intensity
fluctuations, other mid-IR sources continue to be explored. Hall and Koenig designed
a mid-IR sensor using a broadband light source and a mid-IR bandpass filter [23].
This technique circumvents the need for a HeNe laser, but offers little advantage over
the HeNe-laser-based sensors. Additionally, because the source is not monochromatic,
absorption follows an integral form of the Beer-Lambert relation. In this case, the
8 CHAPTER 2. LITERATURE SURVEY
absorbance cannot be expected to retain a linear dependence on concentration.
Wavelength-tunable mid-IR lasers are becoming commercially available, providing
more freedom in wavelength selection for increased sensitivity to key hydrocarbon
species [51]. Using a nonlinear frequency-mixing technique, tunable mid-IR light can
be generated from tunable near-IR lasers. These mid-IR lasers have already begun to
show promise in atmospheric sensing of trace gases [52,53] and are expected to make
valuable contributions to the combustion community.
The present work extends the state-of-the-art in mid-IR optical absorption di-
agnostics for hydrocarbons. Temperature-dependent spectroscopy of hydrocarbons
is studied using an FTIR spectrometer, a HeNe laser and a difference-frequency-
generation (DFG) laser. Sensors are designed for hydrocarbon measurements in
PDE’s and shock tubes. Simultaneous absorption measurements at two wavelengths
are used to infer temperature and to reject interference absorption and scattering,
illustrating the potential of mid-IR diagnostics for a host of practical applications.
Chapter 3
Background on Optical Absorption
and Mid-Infrared Spectroscopic
Equipment
This chapter describes many of the fundamental details of infrared absorption spec-
troscopy and the equipment used in the present study, beginning with the equations
that describe optical absorption and scattering. This is followed by a practical dis-
cussion of coupling optical beams into fibers and collimating beams that are emerging
from fibers. Finally, basic operation and performance details are provided for various
pieces of equipment that were used in this research.
3.1 Fundamentals of Optical Absorption and Scat-
tering
Several types of optical phenomena are important when designing optical-absorption-
based sensors. For monochromatic sources, the Beer-Lambert relation describes how
the wavelength-dependent cross section affects optical transmission through a gaseous
mixture. By measuring the transmitted intensity at one wavelength, the concentration
of a species can be determined. Because the cross section is temperature-dependent,
9
10 CHAPTER 3. BACKGROUND
the ratio of absorbance at two wavelengths can be used to determine temperature.
This effect is valuable in systems such as direct-injection spark-ignition (DISI) en-
gines where neither temperature nor concentration is well-known. In addition, some
applications require robust sensors that are able to withstand interferences from other
species, thin films, and scattering particles (e.g., soot or droplets). This warrants a
discussion of interference from these different phenomena.
3.1.1 The Beer-Lambert Relation for a Single Species
A simple optical absorption experiment is shown in Figure 3.1. A monochromatic
source with wavelength λ and intensity I0λ passes through a cell with path length L
which contains a concentration, ni, of species i, uniformly distributed in the cell. The
fractional transmission, Iλ/I0λ, is described by the Beer-Lambert relation:
−ln
(Iλ
I0λ
)= σλ,i(T, P )niL = αi (3.1)
where σλ,i(T, P ) is the absorption cross section of the molecule and can be dependent
on temperature and pressure. The quantity αi is called the absorbance. If the cross
section and path length are known, then the species concentration can be inferred
from the measured fractional transmission.
L
Absorbing Species, ni0
I I
Figure 3.1: Schematic of an optical absorption experiment.
3.1.2 Determination of Temperature using the Absorbance
Ratio
In many cases, neither the temperature nor the species concentration is known and
both must be determined simultaneously. Temperature and species concentration can
3.1. FUNDAMENTALS OF OPTICAL ABSORPTION AND SCATTERING 11
be determined simultaneously by measuring the absorbance at two wavelengths and
by having sufficient knowledge of the temperature-dependent cross sections at these
wavelengths. If the pressure is known, or if the pressure dependence of the cross
sections is negligible, then the ratio of absorbances can be used to infer temperature:
αλ1
αλ2
=σλ1,i(T, P )niL
σλ2,i(T, P )niL=
σλ1,i(T, P )
σλ2,i(T, P )= f(T, P ) (3.2)
Once the temperature is calculated, the concentration can be determined from Equa-
tion 3.1. Note that the absorbance ratio is independent of path length and species
concentration.
3.1.3 Optical Absorption Measurements with Interference
Phenomena
Equation 3.1 describes transmitted intensity for absorption by a single species, but
many experiments suffer from interferences associated with other absorbing species,
liquid films, and droplets. The equation then needs to be modified to account for
these additional interferences:
−ln
(Iλ
I0λ
)= σλ,iniL +
∑j
σλ,jnjL + τfilm + τdroplets = αλ (3.3)
In this equation, ni is the number density of the target species, nj is the number
density of the interfering species j, τfilm represents interference absorption from a
liquid film, τdroplets represents interference due to scattering and absorption by droplets
in the system and αλ is the total extinction from all of these sources. Note that
interference from liquids is discussed in more detail in Section 3.1.4. Generally, each
additional source of interference requires an additional wavelength to quantify the
interference and each wavelength should be carefully selected to maximize sensitivity
and minimize uncertainty. For example, if temperature and species concentration are
to be measured in a system where droplets are present then total extinction must be
measured for at least three different wavelengths.
12 CHAPTER 3. BACKGROUND
3.1.4 Optical Interference from Liquids
Liquid Film Interference
Liquids can interfere with an absorption measurement in the form of liquid films or
droplets. When a liquid film is deposited on a window surface, the amount of light
reflected at the surface changes and the transmitted power changes.
An additional concern with liquid films is bulk absorption by the liquid, which
can be described by Equation 3.1 if L is taken to be the film thickness. For many
hydrocarbons, the cross section of the liquid is similar in magnitude to the cross
section of the vapor. For example, the peak absorption cross section of toluene vapor
between 3125 and 3700 nm, at 27◦ C, is 123,000 cm2/mole and is found at 3287 nm
(See Figure 3.2). The peak absorption cross section for liquid toluene at 25◦ C, is
124,000 cm2/mole at 3305 nm [54]. Because the liquid density is much higher than
the vapor density, a small film thickness can result in a large source of interference
(Note: the density of liquid toluene is > 1000 times that of the saturated vapor at 25◦
C). While multiple wavelengths can be selected to measure the liquid film thickness
and vapor concentration simultaneously, the film must be thin enough so as not to
completely absorb all of the light. A toluene liquid film with thickness of 40 µm
would transmit only 1% of the light at 3305 nm. Thus, for absorption measurements
of vapor concentration, it is desirable to minimize or eliminate liquid films.
Droplet Interference
Attenuation of an optical beam by a homogeneous cloud of monodispersed droplets
(i.e., droplets having exactly the same diameter) is described by the following equa-
tion:
−ln
(Iλ
I0λ
)= QextndropsL
πD2
4(3.4)
where ndrops is the number density of the particles, and D is the droplet diameter.
Qext is called the extinction coefficient and describes how efficiently the droplets
attenuate the light with respect to their cross sectional area. Equation 3.4 is limited
to conditions where multiple scattering events are negligible (i.e., a scattered beam
3.1. FUNDAMENTALS OF OPTICAL ABSORPTION AND SCATTERING 13
140x103
120
100
80
60
40
20
0
Cro
ss S
ectio
n [
cm
2m
ole
-1]
3700360035003400330032003100
Wavelength [nm]
Toluene Vapor @ 27° C Toluene Liquid @ 25° C
Figure 3.2: Room-temperature absorption spectra of liquid [54] and vapor toluene at1 atm with resolution of ∼1 nm (FWHM). Measurement of the vapor data is describedin Chapter 4.
exits the system before being scattered a second time). Equation 3.4 can be easily
extended to a distribution of droplets [55].
−ln
(Iλ
I0λ
)= L
∫Qextndrops(D)
πD2
4dD (3.5)
The wavelength-dependent extinction coefficient can be calculated using Mie the-
ory, but this calculation requires the wavelength-dependent real and imaginary parts
of the refractive index. (Note that the total extinction from particles is described by
Mie theory and is the sum of scattering and absorption by the particles.) The real
part of the refractive index is the component traditionally associated with the bend-
ing of light (refraction) and is often referred to as the refractive index. The imaginary
component of the refractive index describes how a material absorbs light and can be
related to the absorption cross section of the material. Many details and nuances of
droplet scattering are described in reference [56]. For this thesis, it is sufficient to
state that the extinction coefficient is dependent on droplet size, wavelength of light,
and the temperature-dependent complex refractive indices of both the droplet and
surrounding media.
14 CHAPTER 3. BACKGROUND
3.2 Mid-IR Optical Equipment
Design of a robust mid-IR optical absorption sensor requires careful attention to
optical equipment including optical fibers, lasers, and detectors. General performance
characteristics and relevant technical data are explained in this section.
3.2.1 Mid-IR Optical Fibers
Selection of mid-IR optical fiber requires specification of several parameters including
core diameter, numerical aperture, length and fiber material. First, it is important
that the laser can be efficiently coupled into the fiber, because excessive coupling
losses will result in a poor signal-to-noise ratio (SNR). Second, it is important that
the beam exiting the fiber can be collimated and refocused as needed. Finally, the
optical material used in the fiber can affect transmission, durability, and cost.
Focusing of Single- and Multi-Mode Beams
Before launching into a discussion about fiber specifications, it is important to de-
scribe focusing and propagation of single- and multi-mode beams. For a collimated
beam with a first-order Gaussian mode, the diffraction-limited focused spot size (1/e
radius), amin, is described by the following equation:
amin =fλ
πain
(3.6)
where ain is the 1/e radius of the collimated beam, f is the focal length of the lens
and λ is the wavelength of light of the beam. For a beam with multiple transverse
modes, the focused spot size increases with the number of modes [57]. Thus, to obtain
a small focused spot size, it is desirable to minimize the number of transverse modes
and to minimize the focal length of the lens or mirror.
Specifying the Properties of Optical Fibers
Figure 3.3 shows a collimated beam coupled into an optical fiber. The beam is recol-
limated as it exits the other end of the fiber. An optical fiber has a core and cladding.
3.2. MID-IR OPTICAL EQUIPMENT 15
The core material has a higher refractive index than the cladding. Because of this
refractive index difference, total internal reflection can be achieved and the beam
propagates through the core via multiple reflections at the core/cladding interface.
In this figure, dcore is the core diameter and NA is the numerical aperture of the fiber.
The numerical aperture is the acceptance angle of the fiber and is also the maximum
angle of divergence of the beam exiting the fiber. The variables f and 2ain are the
lens focal length and the diameter of the beam that is being focused, respectively.
2aind
core
f
2(NA)2ain
dcore
f
2(NA)
Figure 3.3: Schematic of a collimated beam being coupled into and optical fiber.
Figure 3.3 clearly illustrates that the focused beam diameter must be smaller than
the core diameter of the fiber (dcore) for the entire beam to be coupled into the fiber.
This can be achieved if the fiber diameter is large, if the beam has few transverse
modes, and if the lens focal length is short. However, the numerical aperture limits
the acceptance angle of the fiber. If the focal length of the lens is too short, its nu-
merical aperture will exceed that of the fiber, limiting the coupling efficiency. Hence,
the coupling lens, optical fiber, and optical beam should be matched for optimal
performance.
The discussion thus far indicates that a large-diameter, large-numerical-aperture
fiber is preferred for efficient coupling. But increasing the diameter and numerical
aperture increases the number of transverse modes that can be supported in the fiber,
as described by the following equation [58]:
N = 0.5
(πdcoreNA
λ
)2
(3.7)
In this equation, N is the number of transverse modes that can be supported in a fiber.
When a beam is coupled into a multi-mode fiber, the total power can be randomly
16 CHAPTER 3. BACKGROUND
distributed among all of the transverse modes. This distribution of power among the
modes changes as the fiber moves. In multi-mode fibers, it is imperative that all of
the modes be collected with equal efficiency. Otherwise, as the power is redistributed
among the modes, large intensity fluctuations can be observed. An additional benefit
of reducing the number of modes of the fiber is that the recollimated beam is more
easily focused, as explained in Section 3.2.1. To summarize, the following guidelines
should be followed when specifying a laser, lens, and optical fiber:
• The fiber core diameter and numerical aperture should be large enough to accept
the entire beam.
– The numerical aperture of the focusing lens should be less than the nu-
merical aperture of the optical fiber.
– The lens focal length should be short enough so the focused spot size is
smaller than the fiber core diameter.
• The fiber core diameter and numerical aperture should be small enough to
minimize the number of transverse modes of the beam exiting the fiber.
Materials for Mid-IR Optical Fibers
Mid-IR optical fibers can be made from a variety of materials, including:
• Sapphire
• Silver Halide
• Chalcogenide
• Fluoride Glass
Sapphire fibers are brittle and expensive and they generally cannot be made with
lengths of more than ∼2 m. The transmission range of silver halide fibers is optimized
for wavelengths of ∼6-10 µm, and are not ideal for wavelengths in the ∼3-4 µm range
that is of interest for this work. Both chalcogenide and fluoride glass fibers are
3.2. MID-IR OPTICAL EQUIPMENT 17
useful in this wavelength range and should be considered. The cost and mechanical
strength of the fibers are comparable. Fluoride glass fibers have a lower refractive
index, which reduces reflection losses at the fiber surfaces. Additionally, fluoride glass
fibers transmit visible light, which can be used to align the optics before switching to
a mid-IR source. For these reasons, fluoride glass fibers were used in the fiber-coupled
mid-IR sensors described here.
3.2.2 Mid-IR Detectors
Like mid-IR optical fibers, there is a large variety of materials used in mid-IR de-
tectors and no particular detector is universally better than the others. Instead, the
detector must be selected for the desired performance characteristics. Because we are
interested in designing mid-IR sensors (particularly for wavelengths between 3 and 4
µm or frequencies between 2500 and 3300 cm−1), the present discussion is focused on
detectors that are sensitive in this wavelength region.
Mid-IR detectors can be divided into two groups, based on how the detected pho-
tons are converted to a voltage; these two groups are photoconductive (PC) detectors
and photovoltaic (PV) detectors [59]. A PC detector is a semiconductor-based detec-
tor with an electrical resistance that is sensitive to the light incident on it. A voltage
placed across the detection element is used to measure the resistance. Photoconduc-
tive detectors are available for wavelengths ranging from ∼1 to 50 µm.
The bandgap energy of semiconductor-based detectors, including photoconduc-
tive detectors, is an important parameter that affects the wavelength range of the
detector. The detector is not sensitive to photons with energy that is smaller than
this bandgap energy [60]. For photons with energy that is greater than the bandgap
energy, the current generated is proportional to the number of photons striking the
active area. Thus, for fixed incident power, the detector sensitivity increases linearly
with wavelength until the bandgap energy is reached, then the sensitivity drops off
rapidly.
A PV detector (also known as a photodiode) is a semiconductor that generates a
voltage or current when light is incident on it. Like PC detectors, PV detectors have
18 CHAPTER 3. BACKGROUND
a minimum photon energy associated with the energy bandgap of the semiconduc-
tor. PV detectors offer one notable advantage over PC detectors which is related to
detector noise. Most detectors exhibit something known as ‘1/f ’ noise. This means
that the noise is not white noise, but instead is concentrated at low frequencies and
the amplitude of the noise decreases with increasing frequency. While most detectors
exhibit some ‘1/f ’ noise, it is more pronounced in PC detectors.
There are many criteria that might be used to choose a detector for a particular
application including wavelength, time response, noise characteristics, simplicity, and
cost. Wavelength range and frequency bandwidth are two important characteristics
that vary significantly with the detector material and architecture. Figure 3.4 shows
the wavelength range and frequency bandwidth for some common mid-IR detectors.
PV
Dete
cto
rsP
V D
ete
cto
rs
0 1 2 3 4 5
HgCdTe
PbSe
PbS
HgCdTe
InSb
InAs
Wavelength [ m]
A
PV
Dete
cto
rsP
V D
ete
cto
rs
0 1 2 3 4 5
HgCdTe
PbSe
PbS
HgCdTe
InSb
InAs
Wavelength [ m]
PV
Dete
cto
rsP
V D
ete
cto
rs
0 1 2 3 4 5
HgCdTe
PbSe
PbS
HgCdTe
InSb
InAs
Wavelength [ m]
A
1.E+00 1.E+02 1.E+04 1.E+06 1.E+08
HgCdTe
PbSe
PbS
HgCdTe
InSb
InAs
Max Bandwidth [Hz]
B
1.E+00 1.E+02 1.E+04 1.E+06 1.E+08
HgCdTe
PbSe
PbS
HgCdTe
InSb
InAs
Max Bandwidth [Hz]
B
PC
De
tecto
rsP
V D
ete
cto
rsP
V D
ete
cto
rs
0 1 2 3 4 5
HgCdTe
PbSe
PbS
HgCdTe
InSb
InAs
Wavelength [ m]
A
PV
Dete
cto
rsP
V D
ete
cto
rs
0 1 2 3 4 5
HgCdTe
PbSe
PbS
HgCdTe
InSb
InAs
Wavelength [ m]
PV
Dete
cto
rsP
V D
ete
cto
rs
0 1 2 3 4 5
HgCdTe
PbSe
PbS
HgCdTe
InSb
InAs
Wavelength [ m]
A
1.E+00 1.E+02 1.E+04 1.E+06 1.E+08
HgCdTe
PbSe
PbS
HgCdTe
InSb
InAs
Max Bandwidth [Hz]
B
1.E+00 1.E+02 1.E+04 1.E+06 1.E+08
HgCdTe
PbSe
PbS
HgCdTe
InSb
InAs
Max Bandwidth [Hz]
B
PC
De
tecto
rs
Figure 3.4: Performance characteristics of some common mid-IR detectors [59, 60].A: Wavelength operating range. B: Detection bandwidth. The vertical bar in ‘A’indicates the strong hydrocarbon absorption band associated with the C-H stretchingvibration.
Sensitivity to the desired wavelengths is an obvious requirement for an optical de-
tector and frequency bandwidth is important for time-resolved measurements. Band-
width can be dependent on the detector area and temperature as well as the pre-
amplifier gain and the detector material. By increasing the detector area or the
preamplifier gain, the frequency bandwidth will generally be reduced. Conversely,
the bandwidth can often be increased by decreasing the gain and detector area.
3.2. MID-IR OPTICAL EQUIPMENT 19
Detector noise can also be an important issue, especially when measuring weak
signals. Detector noise is characterized by the detectivity (D∗) [59]:
D∗ =
√ADetector∆f
NEP(3.8)
where ADetector is the detector area, f is the bandwidth and the noise equivalent
power (NEP ), is the amount of optical power required to equal the magnitude of
the detector noise. The SNR for a measurement dominated by detector noise can be
calculated using this equation:
SNR =Pincident
NEP=
PincidentD∗√ADetector∆f
(3.9)
where Pincident is the incident optical power. Thus a high D∗ is required for sensitive
optical measurements.
Additional considerations include the method of detector cooling and spatial vari-
ations in responsivity. Nonuniform responsivity can manifest itself as noise in a poorly
designed experiment. Oftentimes smaller detectors are more uniform than large detec-
tors and cooled detectors are more uniform that uncooled detectors. Some detectors
require liquid nitrogen cooling, others use thermo-electric coolers, and some operate
at room temperature. Generally, detectors that operate at lower temperatures have
better performance characteristics, but are more expensive and bulkier than uncooled
alternatives.
For the work described here, InSb detectors were used for multiple reasons. First,
liquid-nitrogen-cooled InSb detectors are photovoltaic and thus exhibit less ‘1/f ’
noise. Second, they provide the necessary bandwidth and wavelength range needed for
all of the measurements. Finally, the detectivity of InSb detectors is approximately
an order of magnitude better than the PV-style HgCdTe detectors.
3.2.3 Mid-IR Lasers
Many optical sources that generate mid-IR light are available, including broadband
sources, lead-salt lasers, the helium-neon (HeNe) laser, and lasers that use nonlinear
20 CHAPTER 3. BACKGROUND
techniques to generate mid-IR light. Broadband sources are not wavelength-tunable
(although they can be spectrally filtered for some wavelength specificity) and their
transmission does not directly obey the Beer-Lambert relation because they are not
monochromatic. Instead, a wavelength-integrated Beer-Lambert relation is required.
Lead-salt diode lasers have been used in the past [27], but these lasers have a small
tuning range and are expensive. The present work utilizes two other mid-IR sources:
1) the fixed-wavelength helium-neon laser and 2) a wavelength-tunable difference-
frequency-generation (DFG) laser.
The 3.39 µm Helium-Neon Laser
The HeNe laser was among the earliest lasers to be demonstrated [61]. While there are
examples of HeNe lasers operating at many different wavelengths, the most common
visible wavelengths are 543, 594, 612 and 633 nm and infrared wavelengths of 1.15,
1.52, and 3.39 µm. The 3.39 µm HeNe (which has an optical frequency of 2947.909
cm−1) is particularly useful for measuring hydrocarbon concentration because, for
most hydrocarbons, the fundamental frequency of the C-H stretch oscillates between
2800 and 3200 cm−1, which corresponds to a wavelength of light between 3100 and
3500 nm. Many mid-IR optical absorption diagnostics utilize a 3.39 µm HeNe be-
cause they are inexpensive and reliable and have high power outputs. However, HeNe
lasers can suffer from large intensity fluctuations (∼2-5%), resulting in poor SNR.
Additionally, these lasers have a fixed wavelength that cannot be optimized for sen-
sitivity to temperature or a particular species. Hence, the HeNe laser is suitable for
hydrocarbon detection via optical absorption, but it lacks versatility because it is a
fixed-wavelength device.
The Difference-Frequency-Generation Laser
Nonlinear wavelength-mixing techniques can provide broad wavelength tunability in
the mid-IR. DFG lasers create mid-IR light by mixing two near-IR lasers in a special
crystal. For the laser described here, that crystal is made of periodically poled lithium
niobate (PPLN). A schematic of our DFG system is shown in Figure 3.5. A mid-IR
3.2. MID-IR OPTICAL EQUIPMENT 21
laser beam is created with a frequency that is equal to the difference in frequencies
of the two near-IR beams (hence the term ‘difference-frequency generation’).
1
λmid−IR
=1
λpump
− 1
λsignal
(3.10)
For example, if the two near-IR wavelengths are 1.064 and 1.563 µm (9398.5
and 6398 cm−1), then the difference frequency created would be 3000 cm−1 and the
wavelength would be 3.333 µm. High-powered near-IR lasers are needed for efficient
conversion in the crystal. However, recent advances in crystal technology and the
availability of fiber amplifiers have resulted in commercial benchtop DFG units [51].
The DFG lasers used in this work, produced by Novawave Technologies, have an
average power of ∼100 to 200 µW and a total tuning range of ∼100 nm (3320-3432
nm for one laser and 3439-3561 nm for the other laser). The tuning bandwidth is
limited by the amplifier bandwidth for the signal laser.
Mid-IR Light Yb/Er Fiber
Amplifier
Near-IR Pump
Laser
Fiber
Combiner
Near-IR
DFBPPLN
CrystalMid-IR Light
Yb/Er Fiber
Amplifier
Near-IR Pump
Laser
Fiber
Combiner
Near-IR
DFBPPLN
Crystal
Figure 3.5: Schematic of our tunable mid-IR DFG laser.
3.2.4 The FTIR Spectrometer
One piece of equipment that is invaluable for modern spectroscopy is the Fourier
transform infrared (FTIR) spectrometer. The Nicolet 6700 FTIR spectrometer used
in the present work can be used to measure absorption spectra in the mid-IR at
moderate resolution (400-10,000 cm−1 with 0.1 cm−1 FWHM resolution or ∼ 1− 25
µm range with ∼0.1 nm FWHM resolution in the 3.4 µm region of interest here). A
schematic of an FTIR experimental setup is shown in Figure 3.6.
A broadband light source is focused through an aperture and then collimated.
The collimated beam enters a Michelson interferometer where each wavelength be-
comes intensity modulated at a different modulation frequency. The modulated beam
22 CHAPTER 3. BACKGROUND
Michelson
Interferometer
Light
Source
Iris
Cell Empty Cell Fill
HgCdTe
Detector
Oven
Michelson
Interferometer
Light
Source
Iris
Cell Empty Cell Fill
HgCdTe
Detector
Oven
Figure 3.6: Experimental setup for optical absorption using an FTIR spectrometer.
travels through a cell that can be filled with a gaseous mixture and is focused onto a
detector. The Omnic 7.0 software bundle provided with the spectrometer controls the
spectrometer hardware (e.g., mirror displacement, aperture size, and source intensity)
and performs the Fourier transform calculations, separating the different frequency
components and calculating the relative spectral intensity.
The FTIR resolution is affected by several variables including alignment of the
interferometer mirrors, size of the aperture, apodization function, and distance trav-
elled by the moving mirror in the interferometer [62]. A larger aperture results in
poorer resolution, but more light throughput. Various apodization functions can be
selected in the software. Changing the apodization function from a boxcar function
to any other function has the effect of smoothing the data at the cost of reduced res-
olution. For all of the data reported here, the boxcar apodiaztion function was used
to retain the original spectral information. The instrument linewidth scales inversely
with distance travelled. Thus, increasing the total mirror displacement of the mov-
ing mirror improves the resolution at the cost of increased test time and lower SNR.
3.2. MID-IR OPTICAL EQUIPMENT 23
While the resolution of an FTIR is often specified using the mirror displacement, it
is prudent to measure the resolution for verification. This can be done by measuring
absorption of a target species with narrow absorption features (e.g., carbon monoxide
at low-pressure).
Chapter 4
Infrared Spectroscopy of
Hydrocarbons
The temperature-dependent absorption cross sections of hydrocarbons must be stud-
ied to properly tailor optical-absorption diagnostics to the hydrocarbon species or
fuel blend of interest and to yield quantitative concentration measurements. In this
chapter, temperature-dependent absorption spectra in the ∼3.4 µm region of the C-H
stretch are reported for select hydrocarbon species and fuel blends for temperatures
ranging from 25 to 530◦ C. Additionally, cross sections measured with a 3.39 µm
HeNe laser are given for temperatures ranging from 25 to 500◦ C.
4.1 Experimental Apparatus and Procedure for
Measuring Absorption Cross Sections
A high-purity stainless steel mixing tank and heated cell were assembled, enabling
accurate measurement of absorption cross sections for temperatures between 25◦ and
530◦ C. A schematic of the apparatus is shown in Figure 4.1. A heated manifold
connects the mixing tank, pressure gauges, vacuum pump, and cell. The pressure
gauges attached to the manifold permit precise mixture preparation. A thermocou-
ple pressure gauge was used to verify that the system was evacuated to <1 millitorr.
24
4.1. EXPERIMENTAL APPARATUS AND PROCEDURE 25
A low-pressure Baratron gauge with a range of 0-100 torr and a measurement uncer-
tainty of ±10 millitorr was used for all pressure measurements below 100 torr. The
high-pressure gauge with a range of 0 to 3000 torr and a measurement uncertainty of
±2 torr was used to measure pressures above 100 torr. The mixing tank contains a
magnetically actuated stirring tower with three tiers of mixing vanes to continuously
agitate the contents. A valve and septum located at the top of the mixing tank enable
liquid injection, which is necessary for low-vapor-pressure species and for blended fu-
els. The leak rate of the septum was measured (<0.01 torr/min) and found to be
negligible with respect to the ∼10 sec time required for liquid injection. A valve iso-
lates the mixing tank from the septum after the liquid is injected so leakage through
the septum over longer time periods is avoided.
0-1
00 to
rr
Pre
ssure
gauge
0-3
00
0 to
rr
Pre
ssure
gauge
Manifold
septum
Vacuum
Pump
Magnetic
Stirrer
Neat
Liq
uid
To heated cell
To heated cell
0-1
00 to
rr
Pre
ssure
gauge
0-3
00
0 to
rr
Pre
ssure
gauge
Manifold
septum
Vacuum
Pump
Magnetic
Stirrer
Neat
Liq
uid
To heated cell
To heated cell
Figure 4.1: Apparatus used for preparation of gaseous mixtures.
The absorption cell, schematically shown in Figure 4.2, is completely enclosed
inside an oven, providing uniform heating of the cell. Two oven walls are fitted
with calcium fluoride windows, providing optical access to the cell within. Sapphire
windows are brazed to stainless steel fittings on the cell, providing a vacuum-tight
26 CHAPTER 4. IR SPECTROSCOPY OF HYDROCARBONS
system that has been tested at cell temperatures as high as 530◦ C. For temperatures
higher than 530◦ C and pressures higher than 7 atm, there is some concern about the
strength of the brazing which holds the windows in place. A K-type thermocouple
is mounted in the cell near the beam path to measure the gas temperature. A 60
cm length of corrugated stainless steel tubing connects the manifold to the cell. This
tubing is coiled inside the oven to insure that the gaseous mixture reaches a uniform
temperature before entering the cell. Valves separate the cell from the manifold and
vacuum pump so measurements can be made with a stationary gas (valves closed) or
with a flowing gas (valves open). The flowing arrangement also allows the cell to be
purged with an inert gas, when necessary.
K-type
thermocouple
Sapphire
window
Sapphire
window
Calcium
Fluoride
Window
Calcium
Fluoride Window
To
vacuumFrom
manifold
K-type
thermocouple
Sapphire
window
Sapphire
window
Calcium
Fluoride
Window
Calcium
Fluoride Window
To
vacuumFrom
manifold
Figure 4.2: Heated cell and oven used to measure temperature-dependent cross sec-tions.
4.1.1 Mixture Preparation
A carefully designed procedure was followed to prepare the mixtures and introduce
them into the cell. First, the cell, manifold and mixing tank were evacuated to a
pressure of less than 1 millitorr. Next, the hydrocarbon was introduced into the
mixing tank and the pressure was measured using the 0-100 torr pressure gauge.
For single-species liquids with a vapor pressure higher than ∼2 torr (e.g., n-
heptane), the vapor sample was drawn directly from a flask, under vacuum. For
gaseous hydrocarbons (e.g., methane), the sample was drawn from the gas cylinder.
4.1. EXPERIMENTAL APPARATUS AND PROCEDURE 27
For blended fuels and low-vapor-pressure liquids (e.g., gasoline and n-dodecane), the
liquid was injected through a septum into the mixing tank and allowed to evaporate
before the tank was opened to the manifold and the pressure measured.
After measuring the pressure of the hydrocarbon vapor, a valve was closed, iso-
lating the tank, and the manifold was evacuated. The tank was then back-filled
with nitrogen gas, diluting the sample to a total pressure of ∼1400-3000 torr. The
mole fraction of the sample was calculated from the ratio of the two pressures. The
back-filling process typically occurred over a period of about 2 minutes. However, for
low-vapor-pressure samples like n-dodecane, this process was extended to a period of
∼10 minutes to minimize condensation in the tank.
After the sample was diluted, it was allowed to mix for a minimum of 10 minutes
after which time a small amount of the mixture was pumped out of the tank. This
was done to clear out the small ‘dead volume’ near the valve which may not have
undergone complete mixing. The baseline intensity was measured in the evacuated
cell. The mixture was then introduced into the evacuated cell and the fractional
transmission, temperature and total pressure were recorded.
4.1.2 Surface Adsorption and Condensation
Surface adsorption and condensation are of concern when measuring spectra of high-
molecular-weight species and blended fuels because, if significant, they can reduce the
concentration of these species, affecting the measured absorption spectra. For these
experiments, several steps have been taken to minimize condensation and adsorption
and to test for their presence.
To minimize condensation and surface adsorption, the mixing tank and manifold
were heated to 100◦ and 80o C because both of these phenomena are reduced at
elevated temperatures. The protocol for recognizing adsorption and condensation
in this system is twofold. First, the measured cross sections (FTIR spectra and
HeNe absorption measurements) are compared with previously reported data. If
condensation or adsorption were occurring, the data presented here would likely show
consistent discrepancies with previous measurements, but because good agreement
28 CHAPTER 4. IR SPECTROSCOPY OF HYDROCARBONS
is found with the bulk of current literature, condensation and adsorption are not
suspected. Second, mixtures prepared at different concentrations (e.g., 0.25% and
0.5% hydrocarbon in nitrogen) yield the same cross section. Because condensation
and adsorption are both nonlinear with vapor concentration, a different fraction of the
vapor will be lost to these effects for the two mixtures, and therefore measurements
using different concentrations would be expected to show different results if these
problems were present.
With these measures in place, adsorption and condensation effects were only ob-
served for the n-dodecane measurements at 50◦ C. For these measurements, poor
agreement was found with measurements reported by PNNL and with our own high-
temperature data. Additionally, for this temperature, mixtures of different concen-
trations yielded cross sections that varied by ∼10%.
When measuring the absorption spectrum of gasoline, condensation and sur-
face adsorption can reduce the concentration of the high-molecular-weight species
in the sample. Many of the hydrocarbons studied here (e.g., toluene, 2,2,4-trimethyl-
pentane, and n-heptane) are representative of those present in gasoline. Since these
effects were not observed for the constituents of gasoline, it is not likely that the
effects are significant for a blend of the species. However, surface effects are expected
to be more problematic for fuel blends like kerosene and diesel which contain a large
fraction of high-molecular-weight species, similar to n-dodecane.
4.2 Temperature-Dependent Absorption Spectra
of Neat Hydrocarbons and Fuel Blends
The optical arrangement used to measure temperature-dependent absorption spectra
is shown in Figure 3.6. The broadband light exits the spectrometer, passes through
the oven and cell and is focused onto an external detector. The signal from the
detector is coupled to the spectrometer data acquisition computer which records the
detector signal and calculates the relative spectral intensity.
4.2. TEMPERATURE-DEPENDENT SPECTRA OF HYDROCARBONS 29
4.2.1 Temperature-Dependence of the Integrated Absorption
Band Intensity
Infrared absorption by gaseous molecules is the result of rovibrational transitions.
When the molecule absorbs a photon, it undergoes a change in vibrational quantum
number and often (but not always) a change in rotational quantum number. The
width of a rovibrational band is associated with the number of rotational levels that
are populated. At higher temperatures, more rotational levels are populated and the
width of the absorption band increases. Edwards and Menard state that the absorp-
tion strength at a particular wavelength is dependent primarily on the population in
the lower-state energy level, which is determined by the Boltzmann distribution. Fur-
thermore, they assert that other variations of intensity with wavelength or rotational
energy level can be neglected [63]. By making these simplifications, integration of the
absorption cross section over the entire rovibrational band will yield a temperature-
independent value, which, in the present work, is called the ‘band intensity’, Ψ. In
other words:
Ψ =
∫
Band
σν,T dν 6= f(T ) (4.1)
where ν is the optical frequency (in cm−1). If the difference in units are taken into ac-
count, Penner confirms this assertion of temperature-independent band intensity [64].
This assumption of constant band intensity can fail under certain conditions.
First, if some transitions have a higher probability of absorbing a photon than other
transitions, then the band intensity may not be independent of temperature. Second,
when the temperature becomes high enough that the higher vibrational energy levels
become populated, then the assumption may fail. For a vibrational absorption band,
this will occur at temperatures where the first excited vibrational energy level contains
some measurable fraction of the population. In other words, this occurs near the
characteristic vibrational temperature:
Tvib =hcν
k(4.2)
where h is Planck’s Constant, c is the speed of light and k is the Boltzmann constant.
30 CHAPTER 4. IR SPECTROSCOPY OF HYDROCARBONS
For the ∼3-4µm region, the characteristic vibrational temperature is ∼3600-4800
K, which is much higher than the temperatures of interest here. For a vibrational
band centered at 3.5µm (2857 cm−1), it can be shown that only ∼1% of the total
population is in the first vibrational level for a temperature of 900 K. This is a
more conservative estimate than the temperature of 1667 K given by Penner [64] for
the high-temperature limit of the constant-band-intensity assumption. Thus, for the
spectra reported here at temperatures below 775 K, the integrated band intensity is
expected to be independent of temperature. Experimentally, it was found that the
integrated band intensity is independent of temperature for all but one of the species
studied (n-dodecane), within the estimated uncertainty of the measurements.
4.2.2 Representative Hydrocarbon Spectra
The absorption spectra of 26 hydrocarbon species were measured for temperatures
ranging from 25◦ to 500◦ C, at a nominal pressure of 1 atm and are plotted in Ap-
pendix A. Table 4.1 lists molecular weight, structural class, and room-temperature
vapor pressure [65] of the species measured. The vapor pressure of the species is an
important parameter when measuring absorption cross sections because species with
low vapor pressure (e.g., n-dodecane) are difficult to dilute and transfer to the cell.
Hence, liquids with a vapor pressure less than ∼0.15 torr must be diluted very care-
fully. In the present experiments, it was found that back-filling with nitrogen slowly
(over a period of 10 minutes) effectively minimized condensation.
The selected species are some of the most common species in blended hydrocarbon
fuels, surrogate fuels, or exhaust gases of combustion systems and are therefore strong
candidates for hydrocarbon diagnostics. Because many of these hydrocarbons are
present in systems where the temperature varies over a wide range (e.g., during the
compression stroke of an IC engine), it is crucial to obtain spectral information over a
large temperature range. Sample temperature-dependent spectra for 2,2,4-trimethyl-
pentane are shown in Figure 4.3.
4.2. TEMPERATURE-DEPENDENT SPECTRA OF HYDROCARBONS 31
Table 4.1: Molecular weight, structural class, and room-temperature vapor pres-
sure [65] for the hydrocarbon species measured using FTIR spectroscopy.
[%] [torr] [g/mole]
Ethanol alcohol 1.0-2.3 59.55 46.07
Formaldehyde aldehyde 0.4-1.0 gas 30.03
Methane alkane 0.4 gas 16.04
Benzene aromatic 1.6-3.7 95.8 78.11
Toluene aromatic 1.0-1.5 28.3 92.14
m-xylene aromatic 0.4-0.6 8.7 106.17
Ethyl-benzene aromatic 0.3-0.6 9.5 106.17
O-xylene aromatic 0.3-1.4 6.7 106.17
3-ethyl-toluene aromatic 0.2-0.4 3.04 120.19
2-methyl-propane branched alkane 0.3-1.7 gas 58.12
2-methyl-butane branched alkane 0.2-1.1 686.3 72.15
2-methyl-pentane branched alkane 0.4-1.3 211.4 86.18
3-methyl-hexane branched alkane 0.6-1.0 62.2 100.2
2,2,4-trimethyl-pentane branched alkane 0.3-1.6 49.6 114.23
Ethylene olefin 0.7-1.7 gas 28.05
Propene olefin 1.0-6.0 gas 42.08
1-butene olefin 1.2-2.6 gas 56.11
2-methyl-2-butene olefin 0.06-2.3 473.4 70.13
cis-2-pentene olefin 0.7-2.5 501.2 70.13
2-methyl-2-pentene olefin 0.4-1.8 156.5 84.16
1-heptene olefin 0.2-1.2 56.5 98.19
2,4,4-trimethyl-1-pentene olefin 0.3-1.3 46.1 112.21
Ethane straight alkane 0.8-1.7 gas 30.07
n-pentane straight alkane 0.4-1.3 521.6 72.15
n-heptane straight alkane 0.3-1.1 46.2 100.2
n-dodecane straight alkane 0.07-0.1 0.14 170.33
Mole
FractionName Structural Class
Molecular
Weight
Vapor Pressure
at 25o C
It is well-known that rovibrational absorption bands become broadened at high
temperatures [66]. This occurs because the rotational energy of the molecule is dis-
tributed over more energy levels and consequently, more transitions absorb light. It
is not surprising, then, that the absorption spectrum of 2,2,4-trimethyl-pentane be-
comes broadened at high temperatures, causing the peak cross sections to decrease
with temperature and the cross sections in the valleys to increase with temperature.
Temperature-broadening of the vibrational band can be seen in all of the spectra
studied here.
32 CHAPTER 4. IR SPECTROSCOPY OF HYDROCARBONS
1.2x106
1.0
0.8
0.6
0.4
0.2
0.0Cro
ss S
ectio
n [
cm
2m
ole
-1]
36003500340033003200Wavelength [nm]
50° C 250° C 450° C
Figure 4.3: Temperature-dependent absorption spectrum of 2,2,4-trimethyl-pentanefor temperatures ranging from 25 to 500◦ C at 1 atm of total pressure with resolutionof ∼1 nm (FWHM).
Comparison of Measured Absorption Spectrum of Methane with HITRAN
Database
Absorption spectra were measured for several hydrocarbons exhibiting resolved rota-
tional structure in the absorption spectra (e.g., methane and ethane) for temperatures
ranging from 25◦ to 500◦ C and resolution of 0.1 cm−1 (∼0.1 nm) FWHM. When the
species exhibits spectrally narrow absorption features, it is important to understand
that additional measurement error can be incurred from instrument broadening. To
examine the magnitude of this effect, the room-temperature absorption spectrum of
methane is compared to the modelled absorption spectrum from the HITRAN data-
base in Figure 4.4.
This figure shows that for these narrow methane features, some instrument broad-
ening is evident. The discrepancy between the FTIR data and the modelled results
is < 15%. Whereas instrument broadening adds some additional error to the FTIR
data, the measured spectra are still useful for predicting the temperature-dependent
4.2. TEMPERATURE-DEPENDENT SPECTRA OF HYDROCARBONS 33
1.0x10 6
0.8
0.6
0.4
0.2
0.0
Cro
ss S
ection [cm
2 m
ole
-1 ]
3382.0 3381.0 3380.0 3379.0
Wavelength [nm]
FTIR @ 27 o C
HITRAN @ 27 o C
PNNL FTIR @ 25 o C
Figure 4.4: Comparison of high-resolution (∼0.1 nm FWHM) FTIR spectra formethane measured here, reported by PNNL [39] and computed using the HITRANdatabase for 1 atm of total pressure and room temperature.
trends and approximate magnitudes of the cross sections for species like methane that
have narrow absorption features.
Absorption Spectrum of n-Heptane
For species with moderate to high molecular weights, the absorption spectra evolve
into broad, unresolved features that can be quantitatively measured with low instru-
ment resolution. For these species, line-by-line data are not available in the HITRAN
database. Instead, the broadband spectra are measured and reported at specific tem-
peratures. One particular database, maintained by PNNL, reports the vapor-phase
absorption spectra of several hundred species for temperatures of 5◦, 25◦ and 50◦
C [39]. This database has been verified extensively and provides a good reference for
comparison to the spectra measured here.
Figure 4.5 shows the measured absorption spectrum of n-heptane at room temper-
ature and pressure with 1 nm resolution, compared to the data reported by PNNL [39]
34 CHAPTER 4. IR SPECTROSCOPY OF HYDROCARBONS
7x105
6
5
4
3
2
1
0
Cro
ss S
ectio
n [
cm
2m
ole
-1]
36003500340033003200Wavelength [nm]
PNNL This Work
Figure 4.5: Measured absorption spectrum of n-heptane (T = 26◦ C, P = 1 atm, ∼1nm resolution, FWHM) compared to the data reported by PNNL [39] (T = 25◦ C, P= 1 atm, ∼0.1 nm resolution, FWHM).
at 0.1 nm resolution. Excellent agreement is found between the two measurements.
Likewise, comparisons of other spectra have shown good agreement. While it is impor-
tant to compare these measured spectra to previous measurements, a more compact
comparison can be performed using the integrated band intensity. Table 4.2 shows
the temperature-averaged band intensity for the measured spectra compared to the
room-temperature band intensity from PNNL [39]. The two sets of data generally
agree to within the estimated uncertainty of the measurements with the exception
of 3-ethyl-toluene and cis-2-pentene which exhibit a difference that is marginally
higher than the estimated uncertainty. The larger uncertainty in the band inten-
sity of methane, ethane and ethylene is due to increased sensitivity to baseline shifts
for these structured absorbers. The large uncertainty in the measured formaldehyde
band intensity is due to the strong tendency for formaldehyde to polymerize, making
mixture preparation difficult.
4.2. TEMPERATURE-DEPENDENT SPECTRA OF HYDROCARBONS 35
Table 4.2: Temperature-averaged band intensity for the 26 hydrocarbon species stud-ied here. The measured data are compared to the data from the PNNL database [39]measured at 25◦ C.
[cm
2m
ole
-1cm
-1]
[%]
[cm
2m
ole
-1cm
-1]
[%]
Me
tha
ne
alk
an
e4
7.2
2E
+0
61
06
.71
E+
06
-7.0
Eth
an
ea
lka
ne
61
.76
E+
07
10
1.7
8E
+0
71
.3
n-P
en
tan
ea
lka
ne
12
3.9
0E
+0
72
3.9
6E
+0
71
.4
n-H
ep
tan
ea
lka
ne
16
5.1
6E
+0
72
5.1
3E
+0
7-0
.5
n-D
od
eca
ne
alk
an
e2
68
.34
E+
07
68
.57
E+
07
2.8
2-M
eth
yl-P
rop
an
ea
lka
ne
10
2.9
8E
+0
74
3.1
0E
+0
74
.1
2-M
eth
yl-B
uta
ne
alk
an
e1
23
.70
E+
07
33
.71
E+
07
0.1
2-M
eth
yl-P
en
tan
ea
lka
ne
14
4.3
2E
+0
72
4.3
8E
+0
71
.4
3-M
eth
yl-H
exa
ne
alk
an
e1
65
.02
E+
07
34
.93
E+
07
-1.9
2,2
,4-T
rim
eth
yl-P
en
tan
ea
lka
ne
18
5.3
6E
+0
72
5.3
7E
+0
70
.1
Eth
yle
ne
ole
fin
44
.31
E+
06
10
4.1
4E
+0
6-4
.0
Pro
pe
ne
ole
fin
61
.01
E+
07
21
.03
E+
07
2.0
1-B
ute
ne
ole
fin
81
.75
E+
07
31
.75
E+
07
-0.5
2-M
eth
yl-2
-Bu
ten
eo
lefin
10
2.4
7E
+0
72
2.5
1E
+0
71
.3
cis
-2-P
en
ten
eo
lefin
10
2.5
2E
+0
73
2.3
7E
+0
7-5
.8
2-M
eth
yl-2
-Pe
nte
ne
ole
fin
12
3.3
0E
+0
73
3.2
5E
+0
7-1
.5
1-H
ep
ten
eo
lefin
14
3.7
2E
+0
73
3.7
3E
+0
70
.1
2,4
,4-T
rim
eth
yl-1
-Pe
nte
ne
ole
fin
16
3.9
8E
+0
72
4.0
6E
+0
72
.1
Be
nze
ne
aro
ma
tic
67
.81
E+
06
37
.70
E+
06
-1.4
To
lue
ne
aro
ma
tic
81
.32
E+
07
21
.32
E+
07
0.4
M-X
yle
ne
aro
ma
tic
10
1.8
3E
+0
75
1.8
8E
+0
72
.7
Eth
yl-B
en
ze
ne
aro
ma
tic
10
1.9
4E
+0
74
2.0
1E
+0
73
.8
O-X
yle
ne
aro
ma
tic
10
1.8
4E
+0
75
1.8
9E
+0
72
.7
3-E
thyl-T
olu
en
ea
rom
atic
12
2.4
6E
+0
75
2.6
2E
+0
76
.7
Fo
rma
lde
hyd
ea
lde
hyd
e2
1.5
5E
+0
71
51
.71
E+
07
10
.4E
tha
no
la
lco
ho
l5
1.6
4E
+0
73
1.5
9E
+0
7-3
.3
Sp
ecie
sS
tru
ctu
ral
Cla
ss
No
. C
-H
Bo
nd
s
Te
mp
era
ture
-Ave
rag
ed
Ba
nd
In
ten
sity
Estim
ate
d
Un
ce
rta
inty
Ba
nd
In
ten
sity f
rom
Sh
arp
e e
t a
l.D
iffe
ren
ce
36 CHAPTER 4. IR SPECTROSCOPY OF HYDROCARBONS
Observed Temperature Dependence of the Integrated Band Intensity
The integrated band intensity can also be used to compare absorption spectra at
different temperatures and absorption spectra of different molecules. As discussed in
Section 4.2.1, the integrated band intensity is expected to be independent of tem-
perature. As an example, the temperature-dependent integrated band intensity is
plotted in Figure 4.6 for three normal alkanes. The band intensity does not vary with
temperature with the exception of the n-dodecane measurements at 50◦ C. This par-
ticular measurement is subject to greater uncertainty due to the low vapor pressure
of n-dodecane and the resulting tendency for adsorption and condensation.
100x106
80
60
40
20
0
Inte
gra
ted B
and Inte
nsity [cm
2m
ole
-1cm
-1]
6005004003002001000
Temperature [°C]
n-Pentane n-Heptane n-Dodecane
Figure 4.6: Integrated band intensity from 25◦ to 500◦ C for three normal alkanes.
For this low-temperature measurement, the integrated band intensity is ∼15%
lower than that measured at higher temperatures. The data at 50◦ C can be rescaled
using the ratio of band intensities to correct the low temperature data:
σλ,corrected(50oC) =ΨHighT
Ψ50oC
σλ,measured(50oC) (4.3)
4.2. TEMPERATURE-DEPENDENT SPECTRA OF HYDROCARBONS 37
The measured and rescaled data from the present work are compared to the PNNL
data in Figure 4.7. The rescaled data show good agreement with the PNNL measure-
ments, validating this correction procedure when necessary.
2.0x106
1.5
1.0
0.5
0.0
Cro
ss S
ection [cm
2m
ole
-1]
3600355035003450340033503300
Wavelength [nm]
PNNL This Work (Original) This Work (Rescaled)
Figure 4.7: Measured and rescaled n-dodecane absorption spectrum at 50◦ C com-pared to PNNL measurements [39].
With the exception of n-dodecane measurements at 50◦ C, it was found that the
variation in the integrated band intensity with temperature for all of the measure-
ments reported here is within the estimated uncertainty of the measurements. Thus,
the temperature-independence of the band intensity was confirmed for all 26 species
studied. This quantity is useful when comparing the temperature-dependent spectra
measured here to room-temperature spectra measured by Sharpe et al. [39] (see Ta-
ble 4.2). It is particularly important to calculate and compare the measured band
intensity at different temperatures when there is concern about condensation at low
temperatures (e.g., with n-dodecane) or thermal decomposition at high temperatures.
38 CHAPTER 4. IR SPECTROSCOPY OF HYDROCARBONS
Observed Size Dependence of the Integrated Band Intensity
The present work focuses on the mid-IR absorption band of hydrocarbons near 3.4
µm, which is associated with the fundamental C-H stretching vibration. Hence, the
absorption band intensity is expected to be strongly dependent on the number of
C-H bonds in the molecule. Figure 4.8 shows the temperature-averaged integrated
band intensity for the species that were included in this spectral library. As expected,
the integrated band intensity shows an almost linear dependence on the number of
C-H bonds in the molecule. Not surprisingly, some structural dependence can also be
observed.
100x106
80
60
40
20
0Inte
gra
ted B
and Inte
nsity [cm
2m
ole
-1cm
-1]
302520151050
Number of C-H Bonds
Alkanes Alcohol Aromatics Olefins
Figure 4.8: Integrated band intensity versus number of C-H bonds for four structuralclasses of hydrocarbon molecules studied here.
This information can be used to estimate the band intensity for blended fuels
and low-vapor-pressure fuels and to check experimental measurements when there
are no other spectroscopic data available for comparison. The number of C-H bonds
4.2. TEMPERATURE-DEPENDENT SPECTRA OF HYDROCARBONS 39
in the molecule (for a neat hydrocarbon) or the average number of C-H bonds (for a
hydrocarbon blend) can be used to approximate the band intensity. The absorption
spectrum of the hydrocarbon or fuel can then be measured via FTIR and the band
intensity can be compared to the expected value to validate the measurement.
Comparison of Spectra for Species from Different Structural Classes
The measured spectra provide useful quantitative cross sections to aid in the design
of fuel diagnostics. However, comparison of absorption spectra of different species
also provides valuable insight into the general effect of molecular structure on the
absorption spectrum of a molecule. For example, Figure 4.9 shows the measured
absorption spectra at ∼25◦ C for species from three different structural classes: n-
heptane (C7H16, a normal alkane), 3-methyl-hexane (C7H16, a branched alkane) and
toluene (C7H8, an aromatic).
1.4x106
1.2
1.0
0.8
0.6
0.4
0.2
0.0Cro
ss S
ectio
n [
cm
2m
ole
-1]
36003500340033003200
Wavelength [nm]
Toluene n-Heptane 3-Methyl-Hexane
Figure 4.9: Measured absorption spectra for 3-methyl-hexane (a branched alkane),n-heptane (a straight alkane) and toluene (an aromatic) at 25◦ C and 1 atm, with ∼1nm resolution (FWHM).
Both n-heptane and 3-methyl-hexane have 16 C-H bonds and the integrated band
40 CHAPTER 4. IR SPECTROSCOPY OF HYDROCARBONS
intensity for these two species is within 3%. However, the spectra for the two mole-
cules are very different. 3-methyl-hexane has a stronger absorption peak at 3368 nm
(2969 cm−1) and n-heptane has a stronger peak at 3407 nm (2935 cm−1). This sug-
gests that CH3 groups generate a strong absorption peak at ∼3368 nm. Conversely,
CH2 groups generate a strong absorption peak at ∼3407 nm.
Toluene has fewer C-H bonds than either n-heptane or 3-methyl-hexane. Hence
the integrated band intensity of toluene is considerably smaller. Furthermore, the
absorption spectrum of toluene reveals an absorption feature between 3200 and 3350
nm that is not present for either n-heptane or 3-methyl-hexane. Absorption in this
region is characteristic of all aromatics and can be attributed to the C-H bonds on
the aromatic ring.
Comparison of Spectra of Three Normal Alkanes
1.6x106
1.2
0.8
0.4
0.0Cro
ss S
ectio
n [
cm
2m
ole
-1]
3600350034003300
Wavelength [nm]
n-Pentane n-Heptane n-Dodecane
Figure 4.10: Absorption spectra of three normal alkanes at 100◦ C and 1 atm, mea-sured with ∼1 nm resolution (FWHM).
Figure 4.10 shows the absorption spectra of three normal alkanes (n-pentane, n-
heptane and n-dodecane) for a nominal temperature of 100◦ C (Note that the actual
4.2. TEMPERATURE-DEPENDENT SPECTRA OF HYDROCARBONS 41
temperature for each of the measurements was within 3◦ C of 100◦ C). Each of these
species has two CH3 groups (one at each end), but a different number of CH2 groups.
The two large peaks at 3492 nm and 3410 nm increase with increasing chain length and
can be attributed primarily to the CH2 groups in the molecule. The peak at 3368
nm shows much less sensitivity to the chain length because this peak is primarily
sensitive to the number of CH3 groups in the molecule.
Temperature-Dependent Absorption Spectra of Blended Fuels
The spectroscopy of neat hydrocarbons is important, but the absorption spectra of
fuel blends are also critical for some applications. One such application, described in
detail in Chapter 8, requires information about the temperature-dependent absorption
spectrum of gasoline. Absorption spectra were measured for 21 samples of gasoline
at 50◦ and 450◦ C and are displayed in Appendix B.
Gasoline is composed of over 200 species and the composite absorption spectrum
is a result of absorption from all of these species. These gasoline samples contain
normal, cyclic, and branched alkanes, olefins and aromatics. Hence the absorption
spectrum of gasoline shows characteristic features of all of these hydrocarbon classes.
Absorption spectra of two samples of regular-grade gasoline and two samples of
premium-grade gasoline, shown in Figure 4.11, illustrate that the absorption spec-
trum of gasoline is sensitive to composition. The samples containing a larger amount
of alkanes exhibit stronger absorption from 3300 to 3600 nm (where alkanes absorb
strongly). Conversely, the samples with higher aromatic content show stronger ab-
sorption for wavelengths between 3200 and 3350 nm (where aromatics absorb strongly,
but alkanes do not). Spectra were measured for 21 gasoline samples at 50◦ and 450◦
C, and are plotted in Appendix B. These data show that the temperature dependence
of gasoline spectra is similar to that of the neat hydrocarbons; the peaks decrease
with increasing temperature and the valleys increase with increasing temperature.
42 CHAPTER 4. IR SPECTROSCOPY OF HYDROCARBONS
A
500x103
400
300
200
100
0
Cro
ss S
ectio
n [
cm
2m
ole
-1]
36003500340033003200
Wavelength [nm]
Regular-Grade, High Alkane Regular-Grade, High Aromatic
B
600x103
500
400
300
200
100
0
Cro
ss S
ectio
n [
cm
2m
ole
-1]
36003500340033003200
Wavelength [nm]
Premium-Grade, High Alkane Premium-Grade, High Aromatic
Figure 4.11: Absorption spectra of regular-grade (A) and premium-grade (B) gasolinefor a temperature of 50◦ C and pressure of 1 atm, measured with a resolution of ∼1 nm(FWHM). Regular-grade, high-alkane composition: alkanes: 75.1 liq. vol.%, olefins:6.0 liq. vol.%, aromatics: 18.9 liq. vol.%. Regular-grade, high-aromatic composition:alkanes: 55.5 liq. vol.%, olefins: 4.6 liq. vol.%, aromatics: 39.9 liq. vol.%. Premium-Grade, high-alkane composition: alkanes: 74.5 liq. vol.%, olefins: 11.9 liq. vol.%,aromatics: 13.6 liq. vol.%. Premium-grade, high-aromatic composition: alkanes:52.5 liq. vol.%, olefins: 8.5 liq. vol.%, aromatics: 39.0 liq. vol.%.
4.3. ABSORPTION CROSS SECTIONS AT 3392.2 NM 43
4.3 Absorption Cross Sections at 3392.2 nm
The 3.39 µm HeNe laser is a practical tool for measuring hydrocarbon concentration.
The first HeNe laser was demonstrated in the 1960’s and it was quickly noted that the
mid-IR transition at 3392.23 nm in vacuum (2947.91 cm−1) is strongly absorbed by
many hydrocarbons. Because of its long history, the technology behind the HeNe laser
is well-developed and these systems can be purchased at an affordable price. For these
reasons, the HeNe is a logical candidate for fuel diagnostics. But, before diagnostics
based on a HeNe laser are designed, the necessary absorption cross sections should
be measured. The following section reports temperature-dependent absorption cross
sections for many hydrocarbons at the 3.39 µm HeNe laser wavelength.
4.3.1 Optical Arrangement for Measurements at 3392.2 nm
The optical arrangement for cross section measurements at 3.39 µm, shown schemat-
ically in Figure 4.12, utilized a reference detector to correct for laser power drift.
The HeNe laser used here is known to emit simultaneously at 3.39 and 1.15 µm so
a bandpass filter was used to reject the near-IR light. The beam was linearly polar-
ized using a Rochon polarizer which causes the two perpendicular polarizations of a
beam to diverge at an angle of ∼1◦. Polarizing the beam insured that the wedged
beam splitter separated a fixed fraction of the laser light onto the reference detector.
Next the beam passed through an iris which expedited the process of beam alignment
and blocked the unwanted polarization of light exiting the polarizer. The beam then
passed through a zinc selenide wedge, splitting a portion of the light onto a reference
detector and the transmitted beam passed through the cell onto the signal detector.
4.3.2 Hydrocarbon Cross Sections at 3392.2 nm
The temperature-dependent absorption cross sections were measured at 3.39 µm for
several hydrocarbons and blended fuels. Some of the data are discussed here, but
the entire set of measurements are reported in Appendix C. The mid-IR HeNe laser
44 CHAPTER 4. IR SPECTROSCOPY OF HYDROCARBONS
HeNe
Laser
Heated oven with
absorption cell
0.01 < P < 6.8 atm
25º < T < 530º C
60 nm
bandpass
filter
Rochon
polarizing
beamsplitter
IrisZnSe wedged
beamsplitter
Signal
detector
Reference
detector
HeNe
Laser
Heated oven with
absorption cell
0.01 < P < 6.8 atm
25º < T < 530º C
60 nm
bandpass
filter
Rochon
polarizing
beamsplitter
IrisZnSe wedged
beamsplitter
Signal
detector
Reference
detector
Figure 4.12: Optical arrangement for cross section measurements using a 3.39 µmHeNe laser.
emits light at a vacuum wavelength of 3392.202 ±0.01 nm and is spectrally nar-
row compared to the FTIR measurements. To illustrate the limitations of FTIR
spectroscopy for resolving structured spectra, Figure 4.13 compares the temperature-
dependent absorption cross section of methane at 3392.2 nm measured via HeNe
laser absorption spectroscopy and FTIR spectroscopy. The data are compared to
temperature-dependent HeNe measurements reported by Perrin and Hartmann [31].
In Appendix C these HeNe data as well as cross section data for other hydrocarbon
species are compared to previous measurements.
The three sets of data in Figure 4.13 exhibit the same trend of decreasing cross
section with increasing temperature, but the FTIR data are as much as 15% lower
than the laser absorption measurements, because instrument broadening reduces the
accuracy of the FTIR measurements. This underscores the fact that for species
with narrow absorption features (i.e., methane, ethane and ethylene), the FTIR data
can only be relied upon for an estimate of the temperature-dependent cross section.
However, for more accurate cross section information, a spectrally narrow instrument
(i.e., a laser) must be used.
For species with spectrally broad absorption features, the FTIR provides very
accurate measurements of the cross section. Figure 4.14 compares the temperature-
dependent cross section of n-heptane and 2,2,4-trimethyl-pentane measured with the
FTIR and the HeNe laser. For these species, the FTIR measurements agree well with
4.4. SUMMARY 45
2.5x105
2.0
1.5
1.0
0.5
0.0
Cro
ss S
ection [cm
2m
ole
-1]
6005004003002001000Temperature [°C]
HeNe at 3392.2 nm (This Work)
HeNe at 3392.2 nm (Perrin:1989)
FTIR at 3392.2 nm (This Work)
Figure 4.13: Temperature-dependent cross section of methane at 3392.2 nm measuredat 1 atm with the FTIR and with the HeNe laser compared to the HeNe measurementsreported by Perrin and Hartmann [31].
the laser absorption measurements and the FTIR data can be considered quantita-
tively accurate.
4.4 Summary
Temperature-dependent absorption cross section data are required for quantitative
sensing of concentration. The cross-section data reported in this chapter have been
used as a reference to design several single- and multi-wavelength sensors and ul-
timately to infer species concentration and temperature (See Chapters 5-9). Ad-
ditionally, a model introduced in Chapter 8 estimates the temperature-dependent
absorption cross section of gasoline based on the relative composition of the various
hydrocarbon classes (e.g., aromatics or olefins). This model incorporates many of
the absorption spectra reported here. This cross-section data will be useful for other
applications requiring quantitative concentration measurements and the techniques
described can be applied to other hydrocarbon species and blended fuels.
46 CHAPTER 4. IR SPECTROSCOPY OF HYDROCARBONS
500x103
450
400
350
300
Cro
ss S
ection [cm
2m
ole
-1]
5004003002001000
Temperature [°C]
This Work (HeNe)
This Work (FTIR)
Sharpe:2004 (760 Torr)
Horning:2002 (10 Torr)
600x103
550
500
450
400
350
300
Cro
ss S
ectio
n [
cm
2m
ole
-1]
5004003002001000
Temperature [°C]
This Work (HeNe)
This Work (FTIR)
Sharpe:2004 (760 Torr)
Tsuboi:1985 (~760 Torr)
Figure 4.14: Comparison of temperature-dependent cross section of A: n-heptane,and B: 2,2,4-trimethyl-pentane, measured at 1 atm and 3392.2 nm using an FTIRspectrometer and a HeNe laser. Also plotted are FTIR data from PNNL [39], HeNemeasurements of n-heptane from Horning et al. [29], and HeNe measurements of2,2,4-trimethyl-pentane from Tsuboi et al. [47].
Chapter 5
Differential Absorption for Vapor
Concentration with Interference
Rejection
Optical diagnostics that utilize the HeNe laser are sensitive to many hydrocarbons,
as illustrated by the cross section data in Appendix C. However, the wavelength of
the HeNe laser is fixed and cannot be adjusted for a specific hydrocarbon or applica-
tion. For example, low concentrations and short path lengths motivate the need to
tune to an absorption peak for maximum sensitivity. Recently, a new class of tunable
mid-IR lasers has become commercially available, enabling the wavelength to be tai-
lored to a specific experiment. Section 3.2.3 describes the basic operating principles
of our tunable DFG laser. This chapter describes two experiments that use a modi-
fied DFG laser to generate two simultaneous mid-IR wavelengths. The wavelengths
are selected specifically to reject interference and measure vapor concentration of a
specific species. In the first experiment, vapor concentration of methyl-cyclo-hexane
(MCH) is measured in a cell with interference absorption from n-heptane. In the
second experiment, n-dodecane vapor concentration is measured in an evaporating
aerosol where the extinction by the droplets is considerable.
47
48 CHAPTER 5. INTERFERENCE REJECTION
5.1 Modified DFG Laser for Two-Wavelength Op-
eration
The standard single-wavelength configuration of the Novawave DFG laser is shown
in Figure 3.5. The architecture of this DFG system is such that the total operating
range of the mid-IR laser is ∼100 nm (3320-3432 nm for the DFG laser used in this
chapter). This entire range can be accessed by replacing the near-IR DFB laser and
simultaneously adjusting the temperature of the PPLN crystal to maintain a quasi-
phasematching condition.
A single-wavelength tunable mid-IR laser is a valuable tool for measuring hydro-
carbon vapor concentration, but cannot distinguish vapor absorption from interfer-
ences (e.g., extinction from droplets or absorption by another vapor species). When
interferences are present, multiple wavelengths can be used to infer vapor concentra-
tion. Our DFG laser was modified as shown in Figure 5.1 to generate two rapidly
alternating wavelengths. The near-IR DFB laser is replaced with two near-IR DFB
lasers, which are alternately turned on and off at rates as high as 200 kHz. This
alternating-wavelength near-IR beam is then combined with the fixed-wavelength
near-IR pump laser and the beams are coupled into the PPLN crystal. The DFG
process generates an alternating-wavelength mid-IR beam.
Mid-IR Light
at 1 & 2Near-IR
DFB #1
Near-IR
DFB #2
Yb/Er Fiber
Amplifier
Near-IR Pump
Laser #3
Fiber
Combiner
PPLN
DFG
1 2
I
I
Time
Signal
DFB Signal
Lasers
Mid-IR Light
at 1 & 2Near-IR
DFB #1
Near-IR
DFB #2
Yb/Er Fiber
Amplifier
Near-IR Pump
Laser #3
Fiber
Combiner
PPLN
DFG
1 2
I
I
Time
Signal
DFB Signal
Lasers
Figure 5.1: Schematic of the modified DFG laser for two-wavelength operation.
The temperature of the PPLN cannot be adjusted for phasematching at both
wavelengths simultaneously. Instead, the temperature of the PPLN crystal is chosen
5.2. SPECIES-SPECIFIC DETECTION 49
for equal mid-IR power output at the two wavelengths. This temperature is approx-
imately halfway between the two temperatures that result in phasematching at each
of the two wavelengths. Because the phasematching condition is no longer met, the
conversion efficiency of the DFG laser is reduced. A larger wavelength separation
between the two lasers results in lower mid-IR power output. For the experiments
described in this chapter, a wavelength separation of ∼10 nm was used, resulting in
a ∼50% decrease in average laser power.
Because the laser emits an alternating-wavelength beam, a special procedure de-
scribed in Appendix D, was used to analyze the data. To summarize the procedure,
the measured detector signal is averaged over the time that each wavelength is acti-
vated. The averaged signal for each wavelength is then saved in a separate data array
to calculate absorbance at that wavelength.
5.2 Two-Wavelength Measurements for Species-
Specific Detection
Because most hydrocarbons absorb in the 3-4 µm region, it may be necessary in some
experiments to differentiate between hydrocarbon species. To demonstrate the capa-
bilities of a two-wavelength mid-IR laser system for species-specific detection, MCH
concentration was measured in a cell with varying amounts of n-heptane, an inter-
fering hydrocarbon species. MCH and n-heptane are both important species in jet
fuel surrogates [67] and diagnostics for these species can show utility for fundamental
chemistry studies and also investigations of real combustors.
5.2.1 Differential Absorption for Vapor Concentration
Differential absorption was used to make the vapor concentration measurements in
the presence of interferences. The measured absorbance at a single wavelength is
described by the following equation:
−ln
(Iλ
I0λ
)= σλ,iniL + τλ = αλ (5.1)
50 CHAPTER 5. INTERFERENCE REJECTION
where σλ,iniL is the vapor absorbance from the species of interest, τλ is the interference
term (i.e., extinction from droplets or interference absorption), and αλ is the total
extinction from vapor absorption and interference.
In the simplest implementation of this technique, the interference term is equal at
the two wavelengths (i.e., τλ1 = τλ2). With this technique, the measured absorbances
at the two wavelengths are subtracted, removing the interference term and leaving
only the differential absorption:
−ln
(Iλ
I0λ2
)+ ln
(Iλ
I0λ1
)= (σλ2niL)− (σλ1niL) = ∆σλ2,1niL (5.2)
where ∆σλ2,1 is the differential absorption cross section, which should be large for
maximum sensitivity.
5.2.2 Wavelength Selection
1.4x10 6
1.2
1.0
0.8
0.6
0.4
0.2
0.0
Cro
ss S
ection [cm
2 m
ole
-1 ]
3430 3420 3410 3400 3390 Wavelength [nm]
n-Heptane
MCH
3402.8 nm
3413.4 nm
Figure 5.2: Absorption spectra of n-heptane and methyl-cyclo-hexane at 50◦ C and1 atm, measured with resolution of ∼1 nm (FWHM) via FTIR spectroscopy.
5.2. SPECIES-SPECIFIC DETECTION 51
To maximize the sensitivity to MCH concentration, wavelengths were selected
based on FTIR spectra of the two species. The absorption spectra of the two species
at 50◦ C are shown in Figure 5.2. The wavelengths 3402.8 and 3413.4 nm were chosen
for a maximum MCH differential cross section and with an n-heptane differential cross
section of zero. The FTIR data reveal that for the wavelengths chosen, the differential
cross section of MCH is quite large.
5.2.3 MCH Concentration with n-Heptane Interference
Cell measurements of n-heptane/MCH mixtures illustrate the potential of differential
absorption for species-specific detection of hydrocarbons. The mixtures were pre-
pared in a cell with a total pressure of 1 atm and temperature of 50◦ C. The MCH
concentration was fixed at ∼650 ppm and the n-heptane concentration was varied
from ∼0.1% to ∼1.6%. For these tests, the wavelengths were alternated at 20 kHz,
which is sufficient for many practical applications. However, it will be shown in Chap-
ters 6, 8, and 9 that switching rates as high as 200 kHz can be achieved with this
laser system.
The results of this test are plotted in Figure 5.3. The ratio of measured MCH
mole fraction to the actual MCH mole fraction is plotted on the left axis as a func-
tion of the heptane/MCH concentration ratio. For a perfect measurement, the ratio
Xmeasured/XMCH would be unity (indicated by the dashed line). The error increases
significantly as the n-heptane attenuates the beam and reduces the ability to detect
the differential absorption by the MCH. The ratio of n-heptane absorbance to MCH
absorbance is plotted on the right axis to indicate the magnitude of the interference
from n-heptane. For n-heptane/MCH ratios as high as∼15, the differential absorption
technique recovers accurate concentration measurements. However, as the n-heptane
concentration is increased further, the total absorbance increases to greater than 4,
corresponding to a transmission of less than 2%. Thus, for very high concentrations
of n-heptane, the mixture becomes optically thick.
52 CHAPTER 5. INTERFERENCE REJECTION
10
8
6
4
2
0
αh
ep
tan
e /αM
CH
20151050
Xheptane/XMCH
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
Xm
easure
d/X
MC
H
Figure 5.3: Ratio of measured to actual MCH mole fraction (left axis) and ratio ofheptane to MCH absorbance (right axis) plotted versus the actual n-heptane/MCHmole fraction ratio. The boxes indicate the measured concentration ratio, the dashedline shows a concentration ratio of one, and the solid line indicates absorbance ratio.
5.3 Two-Wavelength Measurements for Vapor Con-
centration in an Aerosol
A second important use of the differential absorption technique is for the detection
of a vapor-phase species in a two-phase system. The following section describes the
measurement of vapor-phase n-dodecane concentration in an aerosol shock tube with
significant interference from a liquid-phase n-dodecane aerosol. This has potential
applications relating to both combustion and atmospheric sciences where droplets
and small particles are often present.
5.3. VAPOR CONCENTRATION IN AN AEROSOL 53
5.3.1 Wavelength Selection
Wavelength selection for this experiment is no different than the wavelength selection
process described in section 5.2.2, except that the absorption spectrum of n-dodecane
is slightly different and the interference term (i.e., extinction by the aerosol) is initially
assumed to be wavelength-independent (note that this assumption is revisited below).
With this in mind, the wavelengths 3429 and 3418 nm were selected to maximize the
differential absorption cross section of n-dodecane.
The absorption spectrum of n-dodecane, measured using FTIR spectroscopy, is
plotted in Figure 5.4 for a temperature of 401◦ C. A ∼12 nm wavelength separation
was chosen as the maximum wavelength separation for this experiment, limiting the
decrease in laser power to ∼50%. For this wavelength separation, the wavelengths
indicated in Figure 5.4 provide the largest n-dodecane differential cross section.
1.2x10 6
1.0
0.8
0.6
0.4
0.2
0.0
Cro
ss S
ectio
n [
cm
2 m
ole
-1 ]
3600 3550 3500 3450 3400 3350 3300 Wavelength [nm]
3417.6 nm
3429.4 nm
Figure 5.4: Absorption spectrum of n-dodecane at 401◦ C and 1 atm with resolutionof ∼1 nm (FWHM). The two wavelengths for the differential absorbance sensor areindicated by the arrows.
Figure 5.5 shows the differential cross section of n-dodecane measured using the
54 CHAPTER 5. INTERFERENCE REJECTION
FTIR spectrometer for temperatures ranging from 100◦ to 500◦ C. The cross section
data cover the temperature range of interest for this experiment (∼100◦ − 300o C).
The differential cross section remains large over this temperature range so sensitive
measurements of concentration are possible.
700x103
600
500
400
300
200
100
0
Diffe
rential C
ross S
ection [cm
2m
ole
-1]
6005004003002001000
Temperature [°C]
Figure 5.5: Temperature-dependent differential cross section of n-dodecane at 1 atmfor wavelengths of 3417.6 and 3429.4 nm measured using an FTIR spectrometer.
5.3.2 n-Dodecane Vapor Concentration in an Evaporating n-
Dodecane Aerosol
The evaporation experiments were performed in a modified aerosol shock tube. A
schematic of the shock tube is shown in Figure 5.6 and more details of the design
can be found in [68–70]. For these experiments, n-dodecane aerosol was generated
by an ultrasonic nebulizer and this aerosol was carried into the shock tube by the
bath gas through poppet valves in the endwall. A vacuum pump located near the
diaphragm was used to continuously draw the aerosol-laden bath gas out of the tube.
5.3. VAPOR CONCENTRATION IN AN AEROSOL 55
A steady flow of the two-phase mixture was introduced into the shock tube through
the endwall valves and pumped out of the shock tube far upstream of the endwall.
Just before the diaphragm was broken, the endwall valves and the pump valves were
closed, causing the mixture to stagnate. After the mixture was shock-heated, the
droplets rapidly evaporated.
Two-Wavelength DFG Laser
Extinction via aerosol
and vapor absorption
Near-IR Laser
Extinction via aerosol
scattering only
Two-Wavelength DFG Laser
Extinction via aerosol
and vapor absorption
Near-IR Laser
Extinction via aerosol
scattering only
Figure 5.6: Schematic of aerosol shock tube for studying multi-phase mixtures.
Figure 5.6 also shows the setup of the laser diagnostics. The two-wavelength mid-
IR beam was located 10 cm from the endwall and was used to measure the n-dodecane
concentration as the aerosol evaporated. Additionally, a near-IR laser beam passed
through at the same location. The near-IR wavelength is not absorbed by n-dodecane
vapor and is therefore only sensitive to the droplet extinction. Hence the extinction
of this beam illustrates the magnitude of interference from droplet extinction.
Sample evaporation data are shown in Figure 5.7. For the ambient fill conditions,
extinction of the near-IR beam is approximately 0.6. When the incident shock wave
arrives, the mixture is compressed and heated. Because it is compressed, the droplet
number density increases, causing the near-IR extinction to increase further. However,
because the mixture is at a higher temperature behind the shock wave, the aerosol
evaporates, causing the near-IR extinction to decay to zero after ∼400 µsec.
The differential absorption is also plotted in Figure 5.7. During the ambient pre-
shock conditions, the differential absorption is slightly negative, as discussed below.
Then, when the shock wave passes and the droplet evaporate, the differential absorp-
tion increases and reaches a plateau value. This shows that, while the total extinction
is quite large (extinction of ∼0.6 before the shock wave), the differential absorption
56 CHAPTER 5. INTERFERENCE REJECTION
1.0
0.8
0.6
0.4
0.2
0.0
-0.2
-0.4
Near-IR
Tra
nsm
issio
n
4002000-200
Time [µsec]
2.0
1.5
1.0
0.5
0.0
-0.5
Diffe
ren
tia
l A
bso
rba
nce
Figure 5.7: Differential absorption measurements for an evaporating aerosol. Post-shock conditions: P2 = 0.783 atm, T2 = 436 K, n-dodecane mole fraction = 0.55%in argon.
technique has effectively rejected much of the droplet interference.
The slightly negative value of differential absorption would lead to a negative mea-
surement of concentration prior to arrival of the shock wave. While the vapor pressure
of n-dodecane is low and the differential absorption is expected to be low, it cannot
be negative for these conditions. To explain the negative value, more information is
required about extinction by small droplets. For aerosols where the particle size is
much larger than the wavelength, the scattering cross section can be considered to
be independent of wavelength. However, for aerosols where the particle size is on
the same order as the wavelength, the scattering efficiency varies with wavelength.
The estimated mean diameter for this aerosol is ∼3-5 µm, and thus some wavelength
dependence is expected.
To exacerbate this problem, extinction is also dependent on the real and imaginary
5.3. VAPOR CONCENTRATION IN AN AEROSOL 57
refractive indices. It is well-known that the complex refractive index varies gradu-
ally with wavelength except near a strong absorption feature. Our measurements
are made at wavelengths where n-dodecane vapor shows strong absorption, but liquid
n-dodecane also has a strong absorption feature at these wavelengths. Hence the com-
plex refractive index of the liquid is expected to show strong wavelength dependence.
These arguments suggest that the simplistic assumption of wavelength-independent
scattering is responsible for the observed negative differential absorption.
To further investigate the issue of wavelength-dependent extinction, a series of
FTIR experiments were performed in the aerosol shock tube at ambient temperature
(i.e., no shock was generated). The optical arrangement was similar to that shown in
Figure 5.6, but the two lasers and laser detectors were replaced by the FTIR and its
detector. This arrangement provided spectral measurements of the vapor absorption
and droplet scattering in the shock tube at ambient conditions. (However, the FTIR
does not provide sufficient time resolution to observe post-shock evaporation.) The
total measured extinction is equal to the vapor absorption plus droplet extinction (See
Equation 3.3). In the first experiment, the vapor absorption was measured with no
aerosol. In the second experiment, the total extinction (aerosol plus vapor absorption)
was measured as the bath gas continuously flowed through the tube, carrying a steady
stream of the aerosol past the measurement location. Finally, the vapor absorption
(Experiment #1) was subtracted from the total extinction (Experiment #2), leaving
only the droplet extinction term.
Determination of the vapor absorption in the shock tube required that the vapor
concentration be equal for the vapor-only and vapor-plus-aerosol tests. This condition
is most easily satisfied by saturating the bath gas with n-dodecane vapor. The bath-
gas plumbing was furnished with a fritted gas washing bottle which bubbled the
bath gas through liquid n-dodecane. To verify that the bath gas was saturated, two
measurements were made: one measurement with a high flow rate of bath gas and
the other measurement with a low flow rate of bath gas. The measured data are
displayed in Figure 5.8. If the measured absorption (and thus, concentration) were
higher for the low-flow-rate case, then it could be reasoned that the apparatus was
not 100% saturated. This data clearly shows that the gas flow rate through the gas
58 CHAPTER 5. INTERFERENCE REJECTION
washing bottle has no effect on the vapor absorption. Hence, it can be concluded
that the gas is saturated with n-dodecane vapor.
These data also were used to infer the partial pressure of the n-dodecane in the
shock tube by fitting the room-temperature absorption spectrum of n-dodecane to
the measurements. The room-temperature absorption spectrum was obtained from
reference [39]. This fit reveals that the partial pressure of n-dodecane is ∼0.123 torr,
which is equal to the saturation pressure of n-dodecane at 24◦ C [65]. This result
confirms that the measured partial pressure of n-dodecane is equal to the room-
temperature saturation pressure of n-dodecane.
0.16
0.14
0.12
0.10
0.08
0.06
0.04
0.02
0.00
Ab
so
rba
nce
35503500345034003350
Wavelength [nm]
High Flow Rate Low Flow Rate Pdodecane=0.123 torr (PNNL)
Figure 5.8: Measured absorbance by flowing n-dodecane vapor in argon for high andlow bath gas flow rates. (P = 0.16 atm, T = 25◦ C, resolution of ∼1 nm (FWHM).Also shown is the calculated absorbance for 0.123 torr of n-dodecane at 25◦ C [39].
Once it was confirmed that the bath gas was saturated with n-dodecane vapor,
the aerosol extinction was measured in the aerosol shock tube with the FTIR spec-
trometer. The saturated bath gas flowed over the nebulizer, into the shock tube
and was pumped out of the shock tube, near the diaphragm. The nebulizers were
activated and the bath gas continued to flow through the shock tube, providing a
5.3. VAPOR CONCENTRATION IN AN AEROSOL 59
measurement of the total extinction (vapor absorption and droplet extinction). By
subtracting the absorbance of the saturated bath gas from the total extinction of
the bath gas plus aerosol, the droplet extinction was determined. These results are
plotted in Figure 5.9.
0.9
0.8
0.7
0.6
0.5
0.4
0.3
Extinction
35503500345034003350
Wavelength [nm]
0.30
0.25
0.20
0.15
0.10
0.05
0.00
Vapor A
bsorb
ance
Scattering + Absorption Scattering Absorption
λ1
λ2
Figure 5.9: Measured n-dodecane vapor absorption (right axis), measured total ex-tinction from vapor and droplets (left axis), and inferred droplet extinction (left axis)for an n-dodecane aerosol.
The droplet extinction data show strong wavelength dependence, though the mag-
nitude of the scattering interference is lower near the strong absorption features. The
two wavelengths used for this n-dodecane sensor are indicated in the graph. Because
the scattering interference is larger at λ2 than it is at λ1, the differential scattering
is negative for α(λ1) − α(λ2). Therefore, large amounts of droplet interference will
cause negative differential absorption like that displayed in Figure 5.7. However, with
the relative scattering coefficients known, the data from Figure 5.7 can be reanalyzed
to calculate vapor concentration. In this case, the solution is no longer a simple dif-
ferential absorption calculation, but instead requires simultaneous solution of three
60 CHAPTER 5. INTERFERENCE REJECTION
equations:
α(λ1) = σ(λ1)niL + τDroplets(λ1) (5.3)
α(λ2) = σ(λ2)niL + τDroplets(λ2) (5.4)
τDroplets(λ1) = C0(λ1, λ2)τDroplets(λ2) (5.5)
where C0 is the proportionality constant of the scattering coefficient at the two wave-
lengths (C0 was previously assumed to be unity). These equations were solved for
the shock tube data shown in Figure 5.7 to determine the corrected vapor concentra-
tion which is plotted in Figure 5.10. It should be noted that as long as the relative
scattering cross sections are known, this differential absorption technique can remove
the interference and does not depend on the quantity of droplets present. With the
wavelength-dependent scattering properly accounted for, the measured vapor con-
centration agrees well with the room-temperature concentration for a saturated n-
dodecane vapor. The wavelength-dependent scattering measured in Figure 5.9 could
potentially be used to infer details about the droplet size distribution, as illustrated
by the multi-wavelength measurements by Hanson [68], however, these calculations
are highly dependent on the liquid refractive index and are beyond the scope of the
work presented here.
5.4 Summary
This chapter describes the modification of a DFG laser system to alternately generate
two mid-IR wavelengths. Demonstrated switching rates were as high as 100 kHz for
the data presented here, but Chapters 6, 8, and 9 describe measurements with 200
kHz switching rates. The two-wavelength laser was used to demonstrate differential
absorption for rejection of optical interferences including interference absorption from
another hydrocarbon species and interference from droplets. The fast switching rates
and the demonstrated rejection of interferences illustrate the versatility of the laser
system and the potential benefits of the differential absorption technique.
5.4. SUMMARY 61
1.0
0.8
0.6
0.4
0.2
0.0
-0.2
-0.4
Near-IR
Tra
nsm
issio
n
4002000-200
Time [µsec]
1.0
0.8
0.6
0.4
0.2
0.0
-0.2
Mo
le F
ractio
n [
%]
Figure 5.10: Measured n-dodecane vapor concentration and near-IR droplet extinc-tion for an evaporating shock-heated n-dodecane aerosol. Dashed line indicates themole fraction for saturated n-dodecane at 24◦ C [65]. Temperature and pressure afterthe shock wave passes are 436 K and 0.783 atm, respectively.
Chapter 6
Two-Wavelength Mid-IR Sensor
for Simultaneous Temperature and
n-Heptane Concentration
Equation 3.2 indicates how the ratio of absorbance measured at two wavelengths can
be used to infer temperature. A second use of a two-wavelength mid-IR laser is for
simultaneous measurements of concentration and temperature. Such a sensor will be
invaluable in systems where both of these parameters affect performance (e.g., DISI
and HCCI engines). In this chapter, a two-wavelength sensor is demonstrated for
simultaneous measurement of temperature and n-heptane concentration in a shock
tube. Wavelength-selection criteria are used to carefully select several candidate wave-
length pairs. Shock tube measurements are then used to demonstrate the accuracy
and time response that can be achieved using this technique.
6.1 Wavelength Selection
Wavelength-selection strategies for two-wavelength, optical-absorption-based temper-
ature measurements have been previously developed to identify optimal wavelength
pairs for high-temperature applications [71]. These previous selection rules were de-
veloped for species such as CO2 and H2O which have spectrally resolved features. In
62
6.1. WAVELENGTH SELECTION 63
this section, these selection rules are adapted to species with broad absorption features
(e.g., n-heptane). The new selection criteria for species with broadband absorption
spectra are listed and explained in the following paragraphs.
6.1.1 Selection Rules
Selection Rule #1: Select Wavelengths with Large Absorption Cross Sec-
tion at Both Wavelengths
For measurements that are sensitive to temperature and concentration, the absorbance
SNR at both wavelengths must be large, requiring a large absorption cross section.
However, for high concentrations and/or long path lengths, care should be taken that
the mixture does not become optically thick (which can sometimes be a problem [72]).
For the measurements described here, the transmission was always greater than 15%
at both wavelengths and optical thickness was not a problem.
Selection Rule #2: Select Wavelengths with Minimal Interference from
Other Species
When measuring hydrocarbon concentration using mid-IR diagnostics, the most com-
mon interfering species are other hydrocarbons. In particular, methane, ethane, and
ethylene interference may cause significant uncertainty in pyrolysis experiments be-
cause the absorption features can have large peak cross sections and these species are
major products in pyrolysis experiments. Hence, our wavelengths were selected to
minimize interferences from these species.
Selection Rule #3: Select Wavelengths that are Accessible with One Laser
The cost and complexity of the experimental setup increases with the number of
lasers required. Thus, it was desired to demonstrate this technique using the two-
wavelength DFG system described in Chapter 5. Each of the candidate wavelength
pairs were selected in part because they could be simultaneously accessed by one laser
system.
64 CHAPTER 6. SENSOR FOR T AND N-HEPTANE CONCENTRATION
Selection Rule #4: Select Wavelengths with a Temperature-Sensitive Ab-
sorbance Ratio
The absorbance ratio, which is independent of concentration, is used to infer tem-
perature for a two-wavelength measurement. Consequently, the sensitivity of the
temperature measurement is directly related to the temperature-sensitivity of the
absorbance ratio. The temperature-dependent absorption spectra described in Chap-
ter 4 enable selection of candidate wavelength pairs that simultaneously maximize
sensitivity to concentration and temperature.
6.1.2 Selection of Candidate Wavelength Pairs using FTIR
Spectra
800x103
600
400
200
0
Cro
ss S
ection [cm
2m
ole
-1]
3600355035003450340033503300
Wavelength [nm]
34
71
34
45
33
71
33
84
34
10
34
33
Tuning Range of DFG Lasers
50° C 400° C
Figure 6.1: Absorption spectrum of n-heptane at 50◦ and 400◦ C, 1 atm with res-olution of ∼1 nm (FWHM). The operating range of the DFG lasers and the threecandidate wavelength pairs are also indicated in the figure.
Figure 6.1 shows the absorption spectrum of n-heptane at 50◦ and 400◦ C. The
two bars near the bottom of the figure indicate the operating range of the two DFG
6.2. HIGH-TEMPERATURE CROSS SECTIONS 65
lasers used in this study and the three wavelength pairs are indicated by the three
pairs of markers.
As explained in Section 4.2.2, the absorption cross section at an absorption peak
decreases with increasing temperature. This temperature sensitivity is exploited for
the measurements described here. Each of the wavelength pairs utilizes one wave-
length that is located at the peak of an absorption feature. The second wavelength
is chosen such that the absorption cross section is constant or increases with tem-
perature, resulting in good temperature-sensitivity over the temperature range of the
FTIR measurements (i.e., 25◦ to 500◦ C). In Section 6.2, shock-tube measurements
are used to extend the absorption cross section measurements to higher temperatures.
6.2 Temperature-Dependent Absorption Cross
Sections above 500◦ C
The three wavelength pairs were selected for sensitivity to temperature and n-heptane
concentration using the temperature-dependent FTIR spectra. However, no theory is
available that can accurately predict the high-temperature absorption cross sections
of high-molecular-weight hydrocarbons using the spectral data measured at lower
temperatures. Because practical engines routinely operate over temperature ranges
that extend beyond 800 K, it is critical to understand the high-temperature spectral
behavior of key hydrocarbons. The shock tube provides an ideal environment to
study high-temperature hydrocarbons because a uniform gaseous mixture can be
heated on microsecond timescales and measurements can be made before the species
begins to decompose. In the following section, a shock tube is used to extend the
temperature-dependent absorption cross section data for the three wavelength pairs
to temperatures as high as 1130◦ C (∼1400 K). The laser is modulated between the
two wavelengths at 200 kHz, providing the rapid time response required for shock
tube experiments.
66 CHAPTER 6. SENSOR FOR T AND N-HEPTANE CONCENTRATION
6.2.1 Experimental Setup for High-Temperature Absorption
Cross Section Measurements of n-Heptane
Mid-IR
Laser
DetectorL=15.24 cm
Iris
Filter
Reference
Detector
I
Io
End wall
Wedge
Mid-IR
Laser
DetectorL=15.24 cm
Iris
Filter
Reference
Detector
I
Io
End wall
WedgeFilter
Mid-IR
Laser
DetectorL=15.24 cm
Iris
Filter
Reference
Detector
I
Io
End wall
Wedge
Mid-IR
Laser
DetectorL=15.24 cm
Iris
Filter
Reference
Detector
I
Io
End wall
WedgeFilter
Figure 6.2: Experimental setup for measurements of high-temperature absorptioncross sections in a shock tube.
A schematic of the optical arrangement can be found in Figure 6.2. A reference
detector was used to correct for intensity fluctuations of the laser beam. The re-
maining portion of the beam passed through the shock tube at a location that was
∼2 cm from the endwall. When using a beamsplitter and reference detector, it is
important to maintain the polarization orientation. The reflectivity of a beamsplitter
is polarization dependent (i.e., the reflectivity of a vertically polarized beam may be
20% while the reflectivity for a horizontally polarized beam may be 23%). If the
laser remains linearly polarized with an orientation that is fixed relative to the beam-
splitter reflection axis, the reflectivity will be constant. On the other hand, if the
polarization direction of the beam varies in time (i.e., the direction of polarization is
6.2. HIGH-TEMPERATURE CROSS SECTIONS 67
not constant), then the reflectivity of the beamsplitter will appear to vary in time.
For these DFG laser systems, the mid-IR beam is inherently vertically polarized and
thus, no external polarization control is required.
Pressure-induced birefringence of the windows could potentially rotate the po-
larization of the mid-IR beam that is transmitted through the shock tube windows.
However, this was not a concern in here because the sapphire windows are not sus-
ceptible to this effect, which is more commonly observed with quartz windows. Ad-
ditionally, there are no polarization-sensitive optics (i.e., a grating or beamsplitter)
downstream of the shock tube windows that would alter the detected signal if the
polarization were to rotate.
The transmitted beam passed through a narrow band filter (Spectrogon BP-3450-
100nm, 100 nm FWHM) and an aperture to limit the thermal emission on the detec-
tor. Even with these precautions, emission was large and needed to be subtracted.
Thus, the two-wavelength near-IR laser modulation was modified to allow 2µsec where
both lasers were turned off and no mid-IR light was produced so the background ther-
mal emission could be measured. (Appendix D provides details of how these data
with are analyzed.) This period of time when the mid-IR light was turned off enabled
a real-time measurement of (and correction for) the time-varying thermal emission.
The shock tube was filled with mixtures of n-heptane in an argon bath gas. While
the mixtures were nominally 1% n-heptane in argon, the actual concentration was
measured using the laser absorption signal, prior to arrival of the shock wave. This
concentration was then used in the ideal-shock equations, together with measurements
of the initial pressure (i.e., P1) and measured shock speed to calculate the post-
shock temperature and pressure behind the incident and reflected shock waves. The
conditions predicted by the shock equations were used in conjunction with the post-
shock laser absorption measurements to calculate the absorption cross section of n-
heptane at the six wavelengths studied.
68 CHAPTER 6. SENSOR FOR T AND N-HEPTANE CONCENTRATION
A
350x103
300
250
200
150
100
50
0
Cro
ss S
ection [cm
2m
ole
-1]
12008004000Temperature [°C]
2.0
1.5
1.0
0.5
0.0
Ratio (
α 3471 n
m/α
3446 n
m)
σ3471 nm
σ3446 nm
Ratio (α3471 nm/α3446 nm)
B
600x103
500
400
300
200
100
0
Cro
ss S
ectio
n [
cm
2m
ole
-1]
12008004000Temperature [°C]
2.0
1.5
1.0
0.5
Ratio (
α 33
71
nm
/α3
38
4 n
m)
σ3371 nm
σ3384 nm
Ratio (α3371 nm/α3384 nm)
C
1.0x106
0.8
0.6
0.4
0.2
0.0
Cro
ss S
ectio
n [
cm
2m
ole
-1]
12008004000
Temperature [°C]
2.5
2.0
1.5
1.0
0.5
0.0
Ratio (
α 34
10
nm
/α3
43
3 n
m)
σ3410 nm
σ3433 nm
Ratio (α3410 nm/α3433 nm)
Figure 6.3: High-temperature absorption cross sections and absorbance ratio of n-heptane using the three wavelength pairs indicated in Figure 6.1. Closed symbolsindicate cell measurements using the FTIR and open symbols indicate data measuredin a shock tube. A: λ1 = 3471 nm, λ2 = 3446 nm, B: λ1 = 3371 nm, λ2 = 3384 nm,C: λ1 = 3410 nm, λ2 = 3433 nm
6.2. HIGH-TEMPERATURE CROSS SECTIONS 69
6.2.2 High-Temperature n-Heptane Cross Sections
The measured high-temperature absorption cross sections for the three line pairs are
shown in Figure 6.3. First, it should be noted that there is significant curvature
in the cross section with respect to temperature, and as a result, the cross section
cannot be easily extrapolated from the moderate-temperature cell measurements.
More importantly, the slope of the absorbance ratio decreases at high temperatures for
all three pairs of wavelengths and thus the sensitivity of the temperature measurement
decreases.
Comparing the first two wavelength pairs (6.3A and 6.3B), the absorbance ratio
remains temperature-sensitive to about 630◦ C for both pairs. However, the second
wavelength pair offers higher sensitivity because of the larger cross sections at these
two wavelengths. Conversely, the first wavelength pair would be preferred for long
path lengths or high concentrations if optical thickness is an issue.
For the third wavelength pair, the absorbance ratio is temperature-sensitive up to
∼1000◦ C, offering a clear advantage for studies at high temperatures. It was noted
in Section 4.2.2 that local peaks in the absorption spectrum decrease with increasing
temperature while local valleys increase with increasing temperature. It is now noted
that the wavelength pair exhibiting the best high-temperature sensitivity corresponds
to the wavelengths where the spectrum retains the peak and valley shape in the FTIR
data measured at 400◦ C (See Figure 6.1). This suggests that the 400-500◦ C FTIR
spectra can be used to select candidate wavelength pairs to provide good temperature
sensitivity for temperatures beyond the range of the FTIR data.
Smooth curves were fit to the temperature-dependent cross sections from Fig-
ure 6.3, enabling the two-wavelength measurements in a shock tube to be analyzed to
infer temperature and concentration (i.e., temperature is inferred from the absorbance
ratio, then the temperature-dependent cross section is determined from the measured
temperature). Sample data are shown in Figures 6.4 and 6.5 for a low-temperature
and a high temperature shock. The dashed lines indicate the expected concentration
and temperature based on the ideal-shock equations and the measured shock speed.
The measured data are displayed as solid lines.
The measured temperature and concentration in Figure 6.4 show good agreement
70 CHAPTER 6. SENSOR FOR T AND N-HEPTANE CONCENTRATION
A
200x10-9
150
100
50
0
Concentr
ation [m
ole
/cc]
5004003002001000-100
Time [µsec]
Measured 1-D Shock Equations
B
1400
1200
1000
800
600
400
200
0
Te
mp
era
ture
[K
]
5004003002001000-100
Time [µsec]
Measured 1-D Shock Equations
Figure 6.4: Measured n-heptane concentration (A), and temperature (B) in a shocktube using a two-wavelength diagnostic at 3410 and 3433 nm. Shock conditions: P1
= 0.11 atm, T1 = 295 K P2 = 0.613 atm, T2 = 645 K P5 = 2.017 atm, T5 = 1066 K,with initial n-heptane mole fraction=0.67% in argon.
6.2. HIGH-TEMPERATURE CROSS SECTIONS 71
A
140x10-9
120
100
80
60
40
20
0
Concentr
ation [m
ole
/cc]
4003002001000-100
Time [µsec]
Measured 1-D Shock Equations
B
1400
1200
1000
800
600
400
200
0
Te
mp
era
ture
[K
]
4003002001000-100
Time [µsec]
Measured 1-D Shock Equations
Figure 6.5: Measured n-heptane concentration (A), and temperature (B) in a shocktube using a two-wavelength diagnostic at 3410 and 3433 nm. Shock conditions: P1
= 0.072 atm, T1 = 295 K P2 = 0.488 atm, T2 = 730 K P5 = 1.832 atm, T5 = 1258K, with initial n-heptane mole fraction=0.64% in argon.
72 CHAPTER 6. SENSOR FOR T AND N-HEPTANE CONCENTRATION
with the values calculated from the 1-D shock equations, illustrating the fast time
response and low noise of this sensor. In Figure 6.5, the measured data agree with
the calculated values before and after the incident shock passes the measurement lo-
cation. Immediately after the reflected shock passes, there is good initial agreement
between the measured and modelled data. The measured concentration rapidly de-
creases in time because the n-heptane decomposes at this temperature. The measured
temperature also decreases behind the reflected shock wave because, as the n-heptane
is pyrolyzed, it absorbs thermal energy from the bath gases, reducing the gas tem-
perature. However, if the n-heptane concentration is extrapolated back to the arrival
of the reflected shock wave, the measurement is within 1% of that predicted by the
1-D shock equations. In Appendix E, it is shown how data like this can be used to
infer chemical reaction rates.
Using the shock tube data for all of the shocks performed, the measured temper-
ature and concentration were compared to the modelled values using the 1-D shock
equations. Figure 6.6 compares the measured concentration and temperature to the
modelled values for all of the shocks. The measured concentration shows a 1.7% RMS
deviation from that predicted by the 1-D shock equations and a 4.3% RMS deviation
is found between the measured and modelled temperature. The uncertainty in the
temperature measurement is largest prior to shock arrival where the absorbance is
small (0.06 to 0.13 at 3433 nm), resulting in a 2-7% error in measured temperature.
However, overall, excellent agreement is found between the measurements and model,
illustrating the accuracy of this diagnostic over a large range of temperatures and
concentrations.
6.3 Summary
This chapter describes a two-wavelength measurement technique for simultaneous
temperature and vapor concentration. Three wavelength pairs were selected for si-
multaneous n-heptane vapor concentration and temperature measurements in a shock
tube. Each pair had one wavelength probing a peak and one wavelength probing a
valley of the n-heptane absorption spectrum. A modified DFG laser was used to
6.3. SUMMARY 73
extend the temperature-dependent cross sections for three wavelength pairs, using a
shock tube to attain temperatures up to 1130◦ C. One wavelength pair (3410 and 3433
nm) exhibited good temperature sensitivity over a larger temperature range than the
other two pairs. It was observed that the n-heptane absorption spectrum measured at
400◦ C still retained the peak and valley structure at these two wavelengths, but not
at the other four wavelengths. Smooth curves were fit to the temperature-dependent
cross section data at 3410 and 3433 nm, which were then used to infer temperature
and n-heptane concentration for the shock tube measurements. The sensor exhibited
good sensitivity for temperatures up to 1000◦ C, where decomposition was clearly ob-
servable. In Chapter 9, a similar two-wavelength sensors is designed for n-dodecane.
74 CHAPTER 6. SENSOR FOR T AND N-HEPTANE CONCENTRATION
A
200x10-9
150
100
50
0
Me
asu
red
Co
nce
ntr
atio
n [
mo
le/c
c]
200x10-9
150100500
Modeled Concentration [mole/cc]
Ambient Fill Post-Incident Shock Post-Reflected Shock Agreement with Model
B
1400
1200
1000
800
600
400
200
0
Me
asu
red
Te
mp
era
ture
[K
]
12008004000
Modeled Temperature [K]
Ambient Fill Post-Incident Shock Post-Reflected Shock Agreement wtih Model
Figure 6.6: Concentration (A) and temperature (B) measured using the two-wavelength mid-IR sensor at 3410 and 3433 nm plotted versus modelled values usingthe 1-D shock equations.
Chapter 7
Fiber-Coupled Helium-Neon-Laser
Sensor for Fuel Measurements in a
Pulse Detonation Engine
The pulse detonation engine (PDE) is an experimental engine with the potential for
increased thermodynamic efficiency and decreased mechanical complexity compared
to other standard aeropropulsion engines [73,74]. However, PDE performance is heav-
ily dependent on average stoichiometry and fuel distribution throughout the combus-
tor [2]. Therefore, robust fuel diagnostics are crucial for engine characterization and
development. This chapter describes a fiber-coupled mid-IR diagnostic to measure
fuel concentration in PDE’s. The sensor uses a HeNe laser as the source and is used
to measure ethylene and propane in fired PDE’s. Measurements reveal unburned fuel
leaving the engine, underscoring the importance of nonintrusive diagnostics for PDE
research.
7.1 PDE Design and Operation
The PDE in its most basic form is simply a long tube that is closed at one end (the
head end) and open at the other end (the tail end). This tube is filled with a mixture
of fuel and oxidizer. The mixture is ignited near the head end of the tube, a flame
75
76 CHAPTER 7. FUEL DIAGNOSTIC FOR A PDE
develops and quickly transitions into a detonation wave that propagates towards the
tail end of the engine, consuming the fuel. The hot, high-pressure exhaust gases exit
the tube, creating thrust. Practical PDE’s often utilize more complex geometries,
but the basic operating principles are retained.
Test SectionSection Containing ObstacleAir
117 cm
147 cm
5 cmigniter
Fuel
From Laser
To Detector
Test SectionSection Containing ObstacleAir
117 cm
147 cm
5 cmigniter
Fuel
From Laser
To Detector
5 cm
Test Section Section Containing ObstacleAir
Fuel
From Laser
To Detector147 cm
5 cm
Test Section Section Containing ObstacleAir
Fuel
From Laser
To Detector147 cm
Figure 7.1: Schematic of the pulse detonation engine. The optics section was mountednear the head-end (top picture) or the tail-end (bottom picture) of the engine.
The fuel diagnostic was demonstrated on a PDE at GE Global Research Center
in Niskayuna, NY. A schematic of that PDE is shown in Figure 7.1. The air flows
continuously, while the fuel is injected through a proprietary valve. The fuel and air
are at room temperature and pressure prior to detonation. The engine can be fueled
by ethylene or propane. The optics section is a modular section of the engine and
can be placed near the head or tail end of the engine. Fuel measurements were made
in both locations for similar operating conditions with firing rates ranging from 5 to
20 Hz. An obstacle inside the engine accelerated the transition from deflagration to
detonation.
7.1. PDE DESIGN AND OPERATION 77
7.1.1 Fuel Diagnostic Design
Figure 7.2 shows a schematic of the sensor, mounted to the optics section. The sensor
is fiber-coupled to isolate delicate components (e.g., the laser and detector) from the
detonations and vibrations generated by the engine. As discussed in Chapter 3, it is
crucial that the beam be focused to a smaller size than the core diameter to minimize
fiber mode noise. Hence, the sensor utilizes a carefully selected series of optical
components with an increasing tolerance for the gradually increasing beam spot size.
Test Section
HeNe Laser
Electronics BunkerCoupling lens
in mount
Collimating lens
in mount
Collimating lens
in mount
Coupling lens
in mount
Focusing lens
in mountBandpass
filter
DetectorTest Section
HeNe Laser
Electronics BunkerCoupling lens
in mount
Collimating lens
in mount
Collimating lens
in mount
Coupling lens
in mount
Focusing lens
in mountBandpass
filter
Detector
Figure 7.2: Optical arrangement for fuel measurements in a pulse detonation engine.
The HeNe laser (Spectra-Physics model model SP-124B) emits ∼5 mW of light at
3.39 µm with an RMS intensity noise of ∼0.3%. Mid-IR optical fiber transmits the
light from the electronics bunker to the engine. The light is coupled into the mid-
IR fiber using a fused-silica coupling lens (Avantes model COL-UV/VIS, diameter
= 6 mm, focal length = 8.7 mm) which focuses the beam to a spot size of ∼62
µm (1/e diameter). Fused-silica lenses can absorb mid-IR light, but these lenses are
sufficiently thin that ∼80% of the light is transmitted through the lens. Uncoated
mid-IR lenses are only marginally more transparent because the lower absorption
of mid-IR materials is counteracted by higher reflection losses of mid-IR materials.
78 CHAPTER 7. FUEL DIAGNOSTIC FOR A PDE
Hence, an inexpensive fused-silica lens was selected for this application. The lens
is mounted in a 5 degree-of-freedom rotation/translation mount, enabling precise
alignment of the lens, fiber and laser beam.
The optical fiber is made from fluoride glass and has a core diameter of 200 µm,
a numerical aperture of 0.27, and a length of 7 m. This diameter is large enough to
collect the entire 62 µm beam with some tolerance for misalignment of the optics. It
is also small enough to enable re-collimation and refocusing in the optics section. The
optical fiber transmits the beam to the optics section of the engine. A collimating
lens, identical to the first coupling lens, is mounted directly to the engine. The
beam passes through a tapered sapphire window (1.25 cm clear aperture, 1.25 cm
thickness), through the engine, and back through a second tapered sapphire window.
The taper of the windows is such that the high-pressure impulse of the detonation
process presses the windows into their mounts.
After the beam exits the optics section, it is focused to a diameter of ∼200 µm
and coupled into a catch fiber (480 µm core diameter). This fiber transmits the beam
to the detection apparatus which is located in the electronics bunker. The coupling
lens and rotation/translation stage are identical to the first coupling lens and stage
described above.
In the electronics bunker, the beam is re-collimated using a collimating lens iden-
tical to the other lenses. The collimated beam is then focused to a diameter of
∼640 µm onto a mid-IR detector (Judson Technologies model J10D-M204-R02M-60,
2-mm-diameter detection element) using a sapphire plano-convex lens (2.54 cm di-
ameter, 2.54 cm focal length). A bandpass filter (3392 nm center wavelength, 60 nm
FWHM) rejects thermal emission from the hot combustion gases in the engine. The
liquid-nitrogen-cooled InSb detector was chosen primarily because it exhibits uniform
sensitivity over the face of the detector, which is required in this application to avoid
fiber mode noise in the measurements.
7.1. PDE DESIGN AND OPERATION 79
7.1.2 Fuel Concentration Measurements in a PDE
The fiber-coupled fuel sensor was used to measure ethylene and propane concentra-
tion in a PDE for firing rates ranging from 5 to 20 Hz. The temperature-dependent
absorption cross section of ethylene and propane can be found in Appendix C. Fig-
ure 7.3 shows sample propane measurements, acquired at the tail-end of the engine,
for both fired and unfired tests. The measurements for the unfired tests reveal a
nearly ideal fuel-filling profile. The cycle begins when the fuel valve is opened. Ap-
proximately 70 msec later, the fuel reaches the measurement location and the fuel
concentration increases to a slightly rich condition and the concentration levels off.
The fuel valve closes and the propane is flushed from the engine by the continuously
flowing air.
At the beginning of the fired cycle, the fuel concentration begins to increase, as
with the unfired case. However, the detonation wave arrives at the measurement loca-
tion after∼80 msec, consuming all of the fuel along the sensor line-of-sight. The sensor
reveals that the concentration never reaches the plateau value and that the engine
is under-filled. After ∼160 msec, a second burst of residual fuel is observed passing
the measurement location, which was not observed in the unfired case. Because this
residual fuel exits behind the detonation wave, it neither reacts nor contributes to
thrust. However, the wasted fuel must be accounted for to properly model engine
performance. This information can also be used to improve future engine designs to
eliminate the wasted fuel. This fiber-coupled fuel diagnostic has revealed that, for
fired tests, some unburned fuel is ejected during the exhaust process. The presence
of the unburned fuel can be attributed to interactions of the detonation waves with
the fuel injection system and thus the residual burst of fuel is not observed in the
unfired case. This crucial information could not have been obtained using a flow
meter that measures average fuel flow rate. These results highlight the importance
of fuel diagnostics for PDE research.
Sensors based on the HeNe laser can be used to measure a variety of hydrocarbon
fuels. The engine described in Figure 7.1 also operates on ethylene, which is more
easily detonated than propane. For ethylene, measurements were made near the head
and tail end of the engine. Sample data, shown in Figure 7.4, were measured at the
80 CHAPTER 7. FUEL DIAGNOSTIC FOR A PDE
0.08
0.06
0.04
0.02
0.00
Pro
pa
ne
Mo
le F
ractio
n
0.5 0.4 0.3 0.2 0.1 0.0
Time [sec]
Detonation Arrival
Unfired
Fired
φ=1
Residual Fuel
Figure 7.3: Propane concentration measurements in a PDE for 5 Hz fired and unfiredoperation. The dashed line indicates a stoichiometric mixture at 1 atm and 25◦ C.
two locations for similar operating conditions. Each test lasted for 1 sec, providing
data for 10 cycles. However, the first cycle is not indicative of steady-state operation,
and thus is not considered in this analysis. The remaining 9 cycles were averaged to
increase the signal-to-noise ratio of the measurement. Cycle averaging was needed for
the ethylene measurements because the room-temperature absorption cross section
of ethylene (4695 cm2mole−1) is only 2.5% that of propane (200000 cm2mole−1).
Note that Figure 7.4 shows the detonation wave arriving at the tail-end location
before it arrives at the head-end location. Only one sensor was available for the
measurements and separate experiments were required for the head-end and tail-end
measurements. The variation in arrival time for the two sets of data can be attributed
to differences in operating conditions (e.g., equivalence ratio and spark timing) for
the two sets of data, which led to differences in detonation wave speed and differences
in arrival time at the sensor location. This is illustrated by the fact that, for the
head-end measurements, the plateau concentration is constant, while for the tail-end
measurements, there appears to be two plateaus, the second of which shows a higher
7.2. SUMMARY 81
fuel concentration than measured in the head-end measurements.
Even with cycle averaging, the noise of the sensor is apparent. The dominant
source of noise comes from the optical fiber which imposes ∼ 0.7% intensity noise on
the the laser signal when the fiber moves. Laboratory experiments found that the
intensity noise of a near-IR telecom fiber due to fiber movement is ∼60% less than
that of a mid-IR fluoride glass fiber, when similar diameter fibers were tested with
a near-IR laser. Thus, improvements in fiber quality would be expected to reduce
the impact of intensity noise. However, unlike near-IR telecom fibers, mid-IR optical
fibers are a developing technology and improved fibers are not currently available.
Another potential solution would be to increase the absorption signal, which could be
done multiple ways. Utilizing a tunable laser, wavelengths could be selected where
the absorption cross sections of the fuel are higher. Instead, fuels could be chosen
that strongly absorb the HeNe laser (e.g., propane or JP-10). Finally, a multi-pass
scheme would also result in stronger absorption and increased SNR.
The ethylene measurements at the two locations are useful to infer the bulk ve-
locity of the gas, which is ∼55 m/sec for these conditions. The bulk velocity can then
be used to calculate the time needed to partially or completely fill the engine with a
mixture. Additionally, fuel concentration and fuel time-of-arrival are measured. Note
the residual burst of fuel can be seen at the end of the cycle for measurements made
at the head-end. For measurements made at the tail-end of the engine, the resid-
ual fuel appears to arrive at the beginning of the cycle. However, because there are
consecutive cycles, this fuel is actually the residual unburned fuel from the previous
cycle.
7.2 Summary
A fiber-coupled HeNe laser was used to measure fuel concentration in fired and unfired
PDE’s. This sensor measures important engine parameters including bulk velocity,
fuel concentration, and fuel time-of-arrival. The measurements also provide valu-
able insight regarding cycle-to-cycle interactions for fired tests. The sensor revealed
82 CHAPTER 7. FUEL DIAGNOSTIC FOR A PDE
0.12
0.10
0.08
0.06
0.04
0.02
0.00
-0.02Eth
yle
ne P
art
ial P
ressure
[atm
]
0.080.060.040.020.00
0.12
0.10
0.08
0.06
0.04
0.02
0.00
-0.02Eth
yle
ne P
art
ial P
ressure
[atm
]
0.100.080.060.040.020.00
Time [sec]
20 msec 20 msec
Main Fuel
Arrival
Main Fuel
Arrival
Residual
Fuel
Residual
Fuel
Detonation
Arrival
Eth
yle
ne
Mo
le F
ract
ion
Eth
yle
ne
Mo
le F
ract
ion
Time [sec]
0.12
0.10
0.08
0.06
0.04
0.02
0.00
-0.02Eth
yle
ne P
art
ial P
ressure
[atm
]
0.080.060.040.020.00
0.12
0.10
0.08
0.06
0.04
0.02
0.00
-0.02Eth
yle
ne P
art
ial P
ressure
[atm
]
0.100.080.060.040.020.00
Time [sec]
20 msec 20 msec
Main Fuel
Arrival
Main Fuel
Arrival
Residual
Fuel
Residual
Fuel
Detonation
Arrival
Eth
yle
ne
Mo
le F
ract
ion
Eth
yle
ne
Mo
le F
ract
ion
Time [sec]
Figure 7.4: Ethylene measurements in a fired PDE measured near (A) the head-endand (B) the tail-end of the engine for 10 Hz operation. The dashed line indicates astoichiometric mixture at 1 atm and 25◦ C.
unburned fuel exiting the engine, which could only be observed with an in situ time-
resolved sensor capable of withstanding the harsh conditions generated by a fired
PDE. Data from robust sensors like these will help guide research and development
efforts for practical propulsion systems.
Chapter 8
Model for the Mid-IR Absorption
Spectrum of Gasoline
One practical application of mid-IR optical absorption diagnostics is for the detection
of fuel in practical engines. Chapter 7 describes a sensor for monitoring ethylene and
propane concentration in pulse detonation engines, but many engines operate on fuel
blends such as gasoline or kerosene, which contain several hundred species. Adding
to the complexity, the composition of these fuels changes by location, manufacturer,
season, and sample age. While designing an in-cylinder gasoline sensor is a complex
engineering problem, the payoff from a robust sensor will be considerable and there-
fore, a sensor that can accurately measure stoichiometry will be useful in developing
the next generation of gasoline engines.
This chapter focuses on the spectroscopy of gasoline and gasoline constituents
in support of a fuel/air ratio sensor for gasoline engines. A model is developed to
estimate the absorption cross section as the gasoline composition changes. The model
is then tested on multiple gasoline samples up to ∼773 K using FTIR measurements
in a cell and up to ∼1200 K using laser absorption measurements in a shock tube.
83
84 CHAPTER 8. MID-IR ABSORPTION SPECTRUM OF GASOLINE
8.1 Model for Gasoline Absorption
Because the composition of gasoline is dependent on many factors, the absorption
spectrum is not likely to be constant (see, for example, Figure 4.11), but depends
on the individual species contained in the blend. It would be difficult to model the
absorption spectrum of gasoline using the weighted sum of the spectra of all of the
species contained in the sample because there are more than 200 different hydrocarbon
species in gasoline and many of them are only present in trace amounts. This would
require an extensive library of temperature-dependent absorption spectra and also
expensive and time-consuming detailed analyses of each gasoline sample. Therefore, a
simpler model to account for compositional changes in gasoline is required to estimate
the absorption spectra of gasoline samples.
Tomita et al. proposed a model for the absorption cross section of gasoline at 3.39
µm which utilized the cross sections of the top 25 species present in one gasoline
sample [32]. The model was tested for the gasoline sample and found to agree well
with the measured cross section for that sample. However, the primary constituents
of gasoline are likely to change with the sample, so a large spectral library is still
required to model multiple samples of gasoline. Instead a simpler model is needed
that is independent of the exact composition of the gasoline.
The temperature-dependent FTIR spectra described in Chapter 4 and Appendix A
provide a valuable library of hydrocarbon spectra to design this model. Figures 4.9
and 4.10 illustrate that the absorption spectrum of a hydrocarbon is dependent on
both the structure and the size of the molecule, suggesting that the absorption spec-
trum of gasoline will also be sensitive to the size and structure of the constituent
species. Likewise, a robust model will incorporate these factors to account for vari-
able composition.
The model presented here groups the hydrocarbon constituents into structural
classes. A ‘class-averaged’ absorption spectrum is then developed for each structural
class. The fuel is analyzed to determine the relative concentration of the individual
classes (e.g., aromatics or olefins). The class-averaged absorption spectra are weighted
8.1. MODEL FOR GASOLINE ABSORPTION 85
by the relative concentration of the individual classes to model the absorption spec-
trum of gasoline in the ∼3.4 µm region of the C-H stretching vibration:
σ(T, λ)modelled =classes∑
i=1
(Xiσ(T, λ)i) (8.1)
where Xi is the mole fraction of class i and σ(T, λ)i is the class-averaged cross section.
The advantages of this model are that neither the spectra of all ∼200 species present
in gasoline nor a detailed analysis of the gasoline sample is required.
The ASTM D1319 test quantifies the liquid volume percent of aromatics and
olefins in a sample. Additionally, the concentration of ethanol and other common
oxygenates is often determined for fuels used in research facilities using the ASTM
D4815 test. The remaining gasoline is assumed to be alkanes and the relative propor-
tion of normal alkanes to total alkanes is approximated in the present model using
information from the detailed analysis of two real samples of gasoline. Thus, our
proposed model uses five input variables (concentration of classes) to predict the
absorption spectra of the gasoline samples.
In developing the model, careful attention was given to the size of the constituent
species because, as observed in Section 4.2.2, absorption cross section and integrated
band intensity increase with the number of C-H bonds in the molecule. In the present
discussion, the size of each of the molecules is characterized by the C-number, which
is the number of carbon atoms in the molecule. The model is first developed for
gasoline at 50◦ C where the PNNL database provides a substantial number of hy-
drocarbon spectra [39]. After selecting the hydrocarbon species for the model, the
temperature-dependent spectra of these species allow the model to be extended to
high temperatures.
A gas chromatograph analysis was performed on one sample of regular-grade and
one sample of premium-grade gasoline to determine primary gasoline constituents and
aid in the development of a spectral model for gasoline. Table 8.1 summarizes the
information regarding molecular size and structural class. Note that these two gaso-
line samples did not contain oxygenates (e.g., ethanol), but oxygenates are common
in American gasolines and are included in the model as a separate structural class.
86 CHAPTER 8. MID-IR ABSORPTION SPECTRUM OF GASOLINE
Table 8.1: Distribution of species within each hydrocarbon structural class for onesample of regular and premium gasoline.
C - No. n-alkanes iso-alkanes olefins aromatics
3 0.00 0.00 0.00 0.00
4 0.15 0.02 0.01 0.00
5 0.58 0.44 0.10 0.00
6 0.22 0.36 0.33 0.00
7 0.04 0.11 0.29 0.44
8 0.01 0.04 0.19 0.40
9 0.00 0.02 0.06 0.12
10 0.00 0.01 0.02 0.03
11 0.00 0.00 0.00 0.00
12 0.00 0.00 0.00 0.00
13 0.00 0.00 0.00 0.00
Total 1.00 1.00 1.00 1.00
Average C - No. 5.2 5.8 6.8 7.7
C - No. n-alkanes iso-alkanes olefins aromatics
3 0.00 0.00 0.00 0.00
4 0.46 0.01 0.12 0.00
5 0.19 0.30 0.51 0.00
6 0.12 0.21 0.30 0.00
7 0.17 0.11 0.06 0.43
8 0.04 0.34 0.01 0.35
9 0.01 0.01 0.00 0.19
10 0.00 0.00 0.00 0.02
11 0.00 0.01 0.00 0.00
12 0.00 0.01 0.00 0.00
13 0.00 0.00 0.00 0.00
Total 1.00 1.00 1.00 1.00
Average C - No. 5.2 6.6 5.4 7.8
Mole Fraction in Premium Gasoline
Mole Fraction in Regular Gasoline
8.1. MODEL FOR GASOLINE ABSORPTION 87
Both samples of reference gasoline had a cyclo-alkane mole fraction of less than 5%,
but some samples can contain as much as 12% cyclo-alkanes [75,76]. In Section 8.1.3,
it is demonstrated that the contribution of cyclo-alkane absorption in the C-H stretch
region is effectively modelled by normal- and branched-alkane spectra.
While the two grades of gasoline do not have identical composition, they do have
similar characteristics. Each hydrocarbon class has the majority of constituents
spread over three to five C-numbers. For example, 95% of the normal alkanes in
the sample of regular gasoline are represented by only three species: n-butane (C-
4), n-pentane (C-5) and n-hexane (C-6). The sample of premium gasoline is only
slightly different because 95% of the normal alkanes are represented by four species:
n-butane (C-4), n-pentane (C-5), n-hexane (C-6), and n-heptane (C-7). Additionally,
while the exact composition is different for the two samples, the average C-number of
each class, and therefore the average molecular size for each class, is approximately
equal for the two samples.
To develop the present model, class-averaged absorption spectra were developed
for each structural class. The detailed analysis of the premium gasoline was used to
select the species for each hydrocarbon class. These class-averaged spectra can then
be used in the model with the ASTM D1319 and ASTM D4815 test results as input to
account for changes in the absorption spectrum of gasoline as the composition varies.
8.1.1 Class-Averaged Absorption Spectrum: Normal Akanes
The simplest group of hydrocarbons to model is the normal alkanes because there
is only one isomer for each C-number. First, the detailed compositional analysis of
the premium-grade gasoline sample is used to determine what the class-averaged ab-
sorption spectrum looks like when the primary normal alkanes are combined in their
relative proportions (renormalized so the sum of mole fractions is unity). Then, the
number of species is reduced as much as possible while maintaining a good reproduc-
tion of the true class-averaged absorption spectrum.
Figure 8.1 shows the absorption spectra of the primary normal alkanes identified
from the detailed analysis. These spectra, measured at 50◦ C, were obtained from the
88 CHAPTER 8. MID-IR ABSORPTION SPECTRUM OF GASOLINE
800x103
600
400
200
0
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3600355035003450340033503300
Wavelength [nm]
n-Butane (C4) n-Pentane (C5) n-Hexane (C6) n-Heptane (C7) Weighted Average
Figure 8.1: PNNL absorption spectra of the primary normal alkanes in gasoline, at50◦ C and 1 atm, with resolution of ∼0.1 nm (FWHM) [39]. The weighted-averagespectrum for normal alkanes is plotted as a dashed line.
PNNL database [39]. The weighted-average absorption spectrum is indicated by the
dashed line. Although n-butane accounts for 46% of the normal-alkane composition,
the average C-number for this sample is 5.2 and the weighted average spectrum closely
resembles that of n-pentane (C-number = 5). This highlights the importance of
average molecular size on the class-averaged absorption spectrum. For the model
presented here, the class-averaged spectrum for normal alkanes is represented by the
absorption spectrum of n-pentane.
8.1.2 Class-Averaged Absorption Spectrum: Branched Alkanes
Computing the class-averaged absorption spectrum for normal alkanes was straight-
forward, requiring the spectrum of only one hydrocarbon. The class-averaged spec-
trum for the branched alkanes is more complex because there are many different
branched alkanes in gasoline. We select the spectra of the primary branched alkanes
in our reference sample and weight them by their relative concentrations to obtain
8.1. MODEL FOR GASOLINE ABSORPTION 89
a ‘weighted-average’ spectrum. For the purposes of developing this model, it is as-
sumed that this weighted-average spectrum is a good representation of the actual
branched-alkane spectrum and therefore our class-averaged spectrum should closely
approximate the weighted-average. Note that many of the spectra were not available
in the PNNL database so the weighted-average spectrum was approximated and the
class-averaged spectrum for the model was compared to this approximate weighted-
average.
Table 8.2: Branched-alkane species in weighted-averaged and class-averaged spectra.
C-No. Species
Mole Fraction in
Primary Branched
Alkanes
Substitute Species
Mole Fraction in
Weighted-
Average
Mole Fraction
in Class-
Average
5 2-Methyl-butane 0.37 0.37 0.32
8 2,2,4-Trimethyl-pentane 0.16 0.31 0.35
6 2-Methyl-pentane 0.12 0.12 0.22
8 2,3,3-Trimethyl-pentane 0.09 2,2,4-Trimethyl-pentane 0.00 0.00
8 2,3,4-Trimethyl-pentane 0.07 2,2,4-Trimethyl-pentane 0.00 0.00
6 3-Methyl-pentane 0.07 0.07 0.00
6 2,3-Dimethyl-butane 0.05 0.05 0.00
7 3-Methyl-hexane 0.04 0.07 0.117 2-Methyl-hexane 0.03 3-Methyl-hexane 0.00 0.00
Nine species account for ∼75% of the branched alkanes in our detailed analysis.
Of these nine species, the PNNL database has absorption spectra for six. To approxi-
mate the weighted-average absorption spectra, the spectra of hydrocarbons with simi-
lar structure were substituted for those that were absent from the database. Table 8.2
lists the top nine species by mass. The three species which required a spectra sub-
stitute were 2,3,3-trimethyl-pentane, 2,3,4-trimethyl-pentane and 2-methyl-hexane.
2,2,4-trimethyl-pentane was substituted for the other two iso-octanes because of its
similar molecular structure and 3-methyl-hexane was substituted for 2-methyl-hexane.
Table 8.2 lists the mole fraction used to calculate the weighted-average absorption
spectrum of the branched-alkane class. The number of spectra were reduced further,
as described below, to obtain the final class-averaged cross section that was used in
the model.
To reduce the number of species in each class, it was assumed that the overall
class-averaged cross section was dependent on the average C-number (Figures 4.10
90 CHAPTER 8. MID-IR ABSORPTION SPECTRUM OF GASOLINE
and 8.1 show that the absorption increases with increasing C-number). Therefore, one
hydrocarbon was selected from each C-number to be used in the class-averaged cross
section. The spectra of these representative species were then weighted by the mole
fraction of that C-number in the class. C-numbers contributing less than 3% (i.e.,
C-4 and C-9 for premium gasoline) were not included in the class-averaged analysis so
the relative mole fractions in the class-average listed in Table 8.2 are slightly different
than the relative mole fractions listed in Table 8.1 for the same class.
The absorption spectra of several branched alkanes are plotted in Figure 8.2 along
with the weighted-average absorption spectrum and the class-averaged absorption
spectrum. Comparison between the weighted-average spectrum (6 distinct species)
and the class-averaged spectrum (4 distinct species) shows that very little has been
lost by reducing the number of species and this four-species representation should
provide a good class-averaged absorption spectrum for the model.
1.0x106
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3600355035003450340033503300
Wavelength [nm]
2-Methyl-Butane 2-Methyl-Pentane 3-Methyl-Hexane 2,2,4 Trimethyl-Pentane Weighted Average Class Average
Figure 8.2: Absorption spectra of four branched alkanes reported by PNNL for 50◦
C, 1 atm, and resolution of ∼0.1 nm (FWHM) [39]. Also shown are the approximateweighted average and the class average using the mole fractions listed in Table 8.2.
8.1. MODEL FOR GASOLINE ABSORPTION 91
8.1.3 Class-Averaged Absorption Spectrum: Cyclo-Alkanes
Table 8.3: Mole fractions used to compute the class-averaged cyclo-alkane spectrum.
Relative Mole
Fraction in
Reference
Mole Fraction in
Class Average
Methyl-cyclo-pentane 42.0% 0.0%
Cyclo-Pentane 38.8% 80.8%
Methyl-cyclo-hexane 13.2% 13.2%
Cyclo-hexane 6.0% 6.0%
As mentioned previously, cyclo-alkanes account for less than 5% of the reference
gasoline samples, however, their unique structure results in absorption spectra that
are somewhat different from those of the normal and branched alkanes. A class-
averaged cyclo-alkane absorption spectrum, plotted in Figure 8.3, was developed us-
ing the detailed compositional analyses of the reference gasoline samples to select
the species and determine their relative concentrations. Table 8.3 lists the species
and relative mole fractions used to compute the class-averaged cyclo-alkane spec-
trum. Note that the absorption spectrum of cyclo-pentane was substituted for that
of methyl-cyclo-pentane because of their similar spectra [37].
The total alkane absorption spectrum was modelled with and without cyclo-
alkanes using the proportions listed in Table 8.4. The proportions used for spectrum A
are those used in the model for regular-grade gasoline. For spectrum B, the ratio of
normal to branched alkanes is retained, but 10% cyclo-alkanes have been added to
the total alkane composition.
Table 8.4: Mole fractions used to compute the alkane absorption spectrum with andwithout cyclo-alkanes.
Spectrum A Spectrum B
Normal Alkanes 38.6% 34.7%
Branched Alkanes 61.4% 55.3%
Cyclo-Alkanes 0.0% 10.0%
Figure 8.4 compares the modelled total-alkane absorption spectrum at 50◦ C with
and without cyclo-alkanes. This comparison shows that adding 10% cyclo-alkanes to
92 CHAPTER 8. MID-IR ABSORPTION SPECTRUM OF GASOLINE
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3600355035003450340033503300
Wavelength [nm]
Figure 8.3: Class-averaged cyclo-alkane spectrum using 78% cyclo-pentane, 6% cyclo-hexane and 16% methyl-cyclo-hexane.
the total alkane composition changes the absorption by ∼ 2.5% (RMS deviation) be-
tween 3350 and 3500 nm. Hence, cyclo-alkanes were not treated as a separate class in
this analysis, but instead were grouped together with the normal and branched alka-
nes. For samples where more than ∼10% cyclo-alkanes are expected, this model could
be extended to include the cyclo-alkane contribution to the total alkane absorption
spectrum.
8.1.4 Class-Averaged Absorption Spectrum: Olefins
The class-averaged absorption spectrum of the olefins was determined in a similar
manner to that of the branched alkanes. However, it is difficult to compare the class-
averaged spectrum to a true weighted-averaged spectrum because nearly all of the
olefins are trace species, contributing less than 1% each to the composition of gasoline.
In this case, one species was selected for each C-number with a mole fraction of more
than 3%. The species were chosen based on the relative concentration and availability
of the spectra in the PNNL database. The species selected and mole fractions used
to compute the class-averaged spectra are listed in Table 8.5.
8.1. MODEL FOR GASOLINE ABSORPTION 93
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3600355035003450340033503300Wavelength [nm]
Spectrum A: No Cyclo-Alkanes Spectrum B: 10% Cyclo-Alkanes
Figure 8.4: Comparison of modelled alkane absorption spectra at 50◦ C using therelative compositions listed in Table 8.4.
Table 8.5: Species and relative mole fractions used to compute the class-averagedolefin spectrum.
C-No. Species Mole Fraction
4 1-Butene 12%
5 cis-2-Pentene 51%
6 2-Methyl-2-Pentene 30%
7 1-Heptene 6%
8.1.5 Class-Averaged Absorption Spectrum: Aromatics
The class-averaged spectrum for aromatics was calculated in a similar fashion as that
for the branched alkanes. A weighted-average spectrum was calculated based on the
detailed compositional analysis of our sample of gasoline using the absorption spectra
of 9 hydrocarbon species. A representative species was chosen for each C-number
with a mole fraction greater than 3% in our detailed analysis (C-7, C-8, and C-9).
The class-averaged absorption spectrum was then calculated using the species and
mole fractions given in Table 8.6.
94 CHAPTER 8. MID-IR ABSORPTION SPECTRUM OF GASOLINE
Table 8.6: Species and relative mole fractions used to calculate class-averaged aro-matic spectrum.
C-No. Species Mole Fraction
7 Toluene 44%
8 O-Xylene 36%
9 3-Ethyl-Toluene 20%
8.1.6 Class-Averaged Absorption Spectra: Summary
The detailed compositional analysis of premium-grade gasoline identified 243 hy-
drocarbon species present in the sample. The number of species necessary for the
class-averaged analysis was reduced to only thirteen. FTIR spectra were measured
for these species for temperatures ranging from 25◦ to 500◦ C using the apparatus
described in Chapter 4. Class-averaged spectra were computed for normal alkanes,
branched alkanes, olefins, aromatics, and oxygenates using properly weighted spectra
of individual species. Oxygenates were represented in the model by ethanol, which
is the only oxygenate that was present in any of teh gasoline samples studied here.
Cyclo-alkanes were not included in the model because they were present in trace
quantities in the reference gasoline samples and they were determined to have a neg-
ligible affect on the model for these low concentrations. The resulting class-averaged
absorption spectra at 50◦ and 450◦ C are plotted in Figure 8.5.
Note that ethanol is unique when compared to all of the other species studied
because, at temperatures above 325◦ C, it was found to decompose faster than the
FTIR could accurately measure the spectrum, while all of the other species were
stable to ∼500◦ C. Thus, the ethanol spectra measured between 25◦ and 325◦ C
were extrapolated to 450◦ C to determine the approximate spectrum of ethanol for
this temperature. The effect of ethanol decomposition on the measured gasoline
spectra is considered below. In the following section, the temperature-dependent
class-averaged cross sections are used to model the absorption spectra for multiple
samples of gasoline.
8.1. MODEL FOR GASOLINE ABSORPTION 95
A
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36003500340033003200
Wavelength [nm]
n-Alkane iso-Alkane Olefin Aromatic Oxygenate
B
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Wavelength [nm]
n-Alkane iso-Alkane Olefin Aromatic Oxygenate
Figure 8.5: Calculated class-averaged absorption spectra for four primary hydrocar-bon structural classes with resolution of ∼1 nm (FWHM). (A): 50◦ C and 1 atm.(B): 450◦ C and 1 atm.
96 CHAPTER 8. MID-IR ABSORPTION SPECTRUM OF GASOLINE
8.1.7 Class-Averaged Spectra Computed from Regular- and
Premium-Grade Gasoline
Detailed compositional analyses were obtained for one sample of regular-grade gaso-
line and one sample of premium-grade gasoline. Thus far, the model has been de-
veloped using the information from the detailed analysis of premium gasoline, but a
similar procedure was followed for regular gasoline. Figure 8.6 compares the class-
averaged spectra of the aromatics and branched alkanes using the two detailed analy-
ses. The class-averaged absorption spectra for the aromatics are very similar for the
two samples. The branched alkanes show approximately 10% difference between the
two class-averaged spectra. According to Table 8.1, the average C-number for this
sample of premium gasoline is ∼10% larger than the average C-number for the regu-
lar gasoline. The average molecular weight of the regular-grade gasoline was only 91
g/mole which is ∼17% lower than expected based on a survey of gasoline samples per-
formed in this research. Since the maximum absorption tends to increase with increas-
ing molecular size, the sample of regular is expected to underpredict the absorption
strength. Hence, the class-averaged compositions derived from the premium-grade
gasoline were used for this study for both regular and premium blends.
The ratio of normal alkanes to the total alkanes in a sample of gasoline is expected
to be dependent on the grade of fuel because, in general, branched alkanes have a
higher octane rating than normal alkanes. Therefore, the two detailed analyses were
used to estimate this ratio for the two grades of gasoline. For the model of regular-
grade gasoline spectra, normal alkanes contribute 38.6% to the total alkane spectrum
and for the model of premium-grade gasoline spectra, normal alkanes contribute only
14.1%.
8.2 Conversion from Liquid Fraction to Mole Frac-
tion
The class-averaged cross section model from equation 8.1 was tested on 21 samples of
gasoline at 50◦ and 450◦ C using the class-averaged spectra in Figure 8.5. The model
8.2. CONVERSION FROM LIQUID FRACTION TO MOLE FRACTION 97
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36003500340033003200
Wavelength [nm]
Regular (iso-Alkanes) Premium (iso-Alkanes) Regular (Aromatics) Premium (Aromatics)
Figure 8.6: Comparison of class-averaged absorption spectra computed using theregular- and premium-grade gasoline for a temperature of 50◦ C, 1 atm, and resolutionof ∼1 nm (FWHM).
relies on input from the ASTM D1319 test to identify the relative concentrations of
olefins and aromatics and uses data from the ASTM D4815 test to determine the mass
fraction of various common oxygenates present in gasoline. (Note that ethanol was the
only oxygenate present in the samples studied here.) Additionally, the ratio of normal
alkanes to total alkanes, obtained from the two detailed analyses, was assumed to be
constant for all gasolines of a particular grade (i.e., normal alkanes contribute 38.6%
to the total alkane content for regular-grade gasoline while normal alkanes contribute
only 14.1% for premium-grade gasoline). However, the ASTM tests provide the liquid
volume fraction, but optical absorption is dependent on mole fraction. Therefore, it
is necessary to convert the liquid volume fraction data into mole fraction data. There
are two steps to this conversion. First, the liquid volume fraction is converted to mass
fraction. Then the mass fraction data is converted to mole fraction.
98 CHAPTER 8. MID-IR ABSORPTION SPECTRUM OF GASOLINE
8.2.1 Conversion from Liquid Volume Fraction to Mass Frac-
tion
To convert from liquid volume fraction to mass fraction, the liquid densities of the
individual classes are required. The liquid density is strongly dependent on the struc-
tural class, but does not vary strongly from species to species within a class. Table 8.7
lists the liquid densities of four species as an example. The densities of 2-methyl-
butane and 2,2,4-trimethyl-pentane (two branched alkanes) vary by ∼10% [65]. The
densities of toluene and 3-ethyl-toluene (two aromatics) are different by only ∼0.6%.
However, the density of 2,2,4-trimethyl-pentane is ∼20% less than the density of 3-
ethyl-toluene. By using a class-averaged liquid density, ρi, the liquid volume fraction
of a class, Zi, can be converted to class mass fraction, Yi:
Yi =Ziρi∑classes
j Ziρi
(8.2)
Table 8.7: Liquid densities of four hydrocarbon species at 25◦ C [65].
Species Class Density [g/cc]
2-Methyl-Butane Branched Alkane 0.616
2,2,4-Trimethyl-Pentane Branched Alkane 0.69
Toluene Aromatic 0.865
3-Ethyl-Toluene Aromatic 0.86
8.2.2 Conversion from Mass Fraction to Mole Fraction
The conversion from mass fraction, Yi, to mole fraction, Xi, can be also performed
on a class basis. The molecular weight of a species can be computed knowing just
the C-number and the structural class of the species. Therefore, the class-averaged
molecular weight can be computed using mole fractions of each C-number within a
class (from Table 8.1). The mass fraction, computed from equation 8.2, can then be
converted to mole fraction, Xi:
Xi =Yi
MWi∑classesj
Yi
MWi
(8.3)
8.3. MODEL TESTS AT 50◦ AND 450◦ C 99
Sample calculated data are shown in Table 8.8, converting from liquid volume
fraction to mole fraction. This table shows that the mole fraction of aromatics is
higher than the liquid volume fraction of aromatics, while the mole fractions of olefins
and alkanes are lower than the liquid volume fractions. This is due to the higher liquid
density of aromatics compared to alkanes and olefins.
Table 8.8: Sample calculations for conversion from liquid volume fraction to molefraction.
ClassLiquid Volume
Fraction
Liquid Density
[g/cc]Mass Fraction
Molecular Weight
[g/mole]Mole Fraction
Aromatics 26.6% 0.865 32.6% 103 27.2%
Olefins 4.2% 0.686 4.1% 75 4.7%
Normal Alkanes 8.9% 0.634 8.0% 86.5 8.0%
Branched Alkanes 54.9% 0.634 49.3% 86.5 49.0%
Ethanol 5.4% 789 6.0% 46.07 11.2%
8.3 Model Tests at 50◦ and 450◦ C
The model was tested on 21 samples of gasoline which cover a wide range of compo-
sitions. Of the 21 samples tested, 11 were regular grade and 10 were premium grade.
Additionally, 13 of the samples were obtained before oxygenates and other additives
could be mixed into the fuel and the remaining 8 samples were taken directly from
gas station pumps and contained ethanol and potentially other additives. Of these 8
samples, 4 were stored at room temperature in glass jars and suffered effects of aging.
Figure 8.7 shows the range of compositions of the gasoline samples, calculated using
Equations 8.2 and 8.3. For each of these samples, alkanes and aromatics dominate
the composition with olefins and oxygenates comprising less than 25% by mole of
each sample. The average alkane content was 59.5% by mole, the average aromatic
content was 29.1%, the average olefin content was 9.1%, and the average oxygenate
content was 2.3%.
FTIR spectra were measured for each of these samples at 50◦ and 450◦ C and
are displayed in Appendix B. In Figure 8.8, measured and modelled spectra are
compared for two gasoline samples at 50◦ C. In general, good agreement is found
100 CHAPTER 8. MID-IR ABSORPTION SPECTRUM OF GASOLINE
100
80
60
40
20
0
Cu
mu
lative
Mo
le F
ractio
n [
%]
20151050
Normal Alkanes Olefins
Branched Alkanes Oxygenates
Aromatics
R1 R5 R11 P1 P5 P10
Figure 8.7: Composition of 21 samples of gasoline used in the current study. Thearrows indicate the four gasoline samples selected for high-temperature shock tubestudies described in Section 8.5
between the modelled and measured spectra and the temperature dependence of the
absorption spectrum is accurately reproduced. The model does show some deviation
from the measured spectra of Figure 8.8-B near 3400 nm which can be attributed to
a species or group of species that has a larger cross section in this wavelength region
(for example, n-heptane).
The temperature dependence was investigated further at the 3366.4 nm because
this wavelength is near the absorption peak of gasoline, but avoids potential inter-
ference absorption from methane at 3368 nm. The model was studied further at
3392.23 nm because this wavelength is coincident with the output wavelength of a
mid-IR HeNe laser, and the model predictions at 3471 nm were investigated because
this wavelength represents a second peak in the gasoline absorption spectrum. These
wavelengths are indicated by the arrows in Figure 8.8. Figure 8.9 compares the
modelled cross section to the measured cross section at the three wavelengths, for
8.3. MODEL TESTS AT 50◦ AND 450◦ C 101
A
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3600355035003450340033503300
Wavelength [nm]
Measured Modelled
33
66
.4 n
m
3392.2
3 n
m
3471 n
m
B
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3600355035003450340033503300
Wavelength [nm]
Measured Modelled
33
66
.4 n
m
33
92
.23
nm
3471 n
m
Figure 8.8: Comparison of measured and modelled spectra of two gasoline sam-ples for a temperature of 50◦ C, mole fraction of 0.6%, total pressure of 1 atm,and resolution of ∼1 nm (FWHM). Composition of sample P1 (A): 71.0/14.2/14.9Alkane/Olefin/Aromatic by mole. Composition of sample R6 (B): 55.2/18.1/26.6Alkane/Olefin/Aromatic by mole.
102 CHAPTER 8. MID-IR ABSORPTION SPECTRUM OF GASOLINE
temperatures of 50◦ and 450◦ C.
For the 21 samples studied, a 6.9% RMS deviation of the model from the mea-
surement was calculated for these two temperatures (5.9% at 50◦ C and 7.8% at
450◦ C), indicating reasonable agreement between model and measurement. If the 4
aged samples are neglected from the analysis, the RMS prediction error is reduced
to 5.7% (4.9% at 50◦ C and 6.4% at 450◦ C), suggesting that this model is more
accurate for fresh samples of gasoline. Because the aged samples were stored for two
years at room temperature, it is likely that many of the high-vapor-pressure (and
low-molecular-weight) species evaporated from the blend. A comparison of the ab-
sorption spectra of these 4 samples at 50◦ C, measured when the sample was fresh
and then again after the sample had aged, showed a ∼15% increase in the absorption
near 3.4 µm. This is consistent with the idea that the aged samples contain a larger
fraction of high-molecular-weight (low-vapor-pressure) species that will tend to have
larger absorption cross sections (see section 4.2.2).
Recall that ethanol was found to decompose at temperatures above 325◦ C so
the measurements of the 8 samples that contained ethanol may also incur some ad-
ditional uncertainty (4 of these samples were the aged samples discussed above). If,
in addition to neglecting the 4 aged samples, we neglect the other 4 samples that
contain oxygenates, the model prediction gives a 6.2% RMS deviation (5.4% at 50◦
C and 6.9% at 450◦ C). Thus the effect of oxygenate decomposition on the model
predictions appears to be smaller than the effect of aging. A simple calculation shows
that this is because ethanol contributes only ∼5% to the cross section at 450◦ C.
For FTIR measurements at this temperature, and for the ∼60 sec measurement time
that was used for gasoline, the absorption from the ethanol is reduced by 30% due to
decomposition. For 10% mole fraction, ethanol only contributes ∼5% to the absorp-
tion cross section of gasoline, and therefore, the measured gasoline cross section will
be reduced by only ∼1.5%, which is smaller than the prediction uncertainty of the
model. Hence, the decomposition of ethanol for the gasoline measurements at 450◦
C was not clearly observable.
8.4. HIGH-T HYDROCARBON CROSS SECTIONS AT 3366.4 NM 103
8.4 Shock-Tube Measurements of High-
Temperature Hydrocarbon Cross Sections at
3366.4 nm
FTIR cell measurements provide valuable information for temperatures below ∼450◦
C. At higher temperatures, the hydrocarbons decompose faster than the FTIR spec-
trometer can record the data. However, it was desired that quantitative measurements
of gasoline be possible for temperatures as high as 930◦ C (∼1200 K). Therefore,
laser absorption measurements at 3366.4 nm were performed in a shock-tube facility
to determine the absorption cross sections of the species used in the model at higher
temperatures. The experimental arrangement (shock tube, laser and optics) was the
same as that described in Section 6.2 with the exception that the DFG laser was
operated at 3366.4 nm, which is near the absorption peak of gasoline, but isolated
from a nearby methane feature. The concentration was measured in situ in region 1.
The FTIR-measured cross section at room temperature was used to infer the initial
concentration. The cross sections could then be determined in region 2 and 5. A
polynomial curve of the form:
σ (T ) = A + B
(T
Tref
)+ C
(T
Tref
)2
+ D
(T
Tref
)3
(8.4)
was fit to the shock tube measurements for each of the species studied. The term
Tref is the reference temperature of 298 K. The polynomial coefficients and estimated
uncertainties are listed in Table 8.9. The primary sources of measurement uncertainty
were laser noise and uncertainty in initial concentration.
Temperature-dependent absorption cross section measurements are displayed in
Figure 8.10 for 3-methyl-hexane. The dashed line is a curve that was fit to the
FTIR data at this wavelength. The dotted line is the polynomial curve that was
fit to the combination of FTIR and shock tube data. Note that the two curves
overlap, indicating good agreement between the FTIR measurements and the shock
tube measurements. These results are representative of most of the cross section
104 CHAPTER 8. MID-IR ABSORPTION SPECTRUM OF GASOLINE
Table 8.9: Polynomial coefficients for temperature-dependent absorption cross sec-tions at 3366.4 nm (See Equation 8.4) for 13 hydrocarbon species, with temperaturesranging from 25◦ to 930◦ C.
n-Pentane 6.36E+05 -2.60E+05 5.41E+04 -4.50E+03 4%
2-Methyl-Butane 6.82E+05 -2.10E+05 2.01E+04 3.59E+01 4%
2-Methyl-Pentane 1.00E+06 -4.45E+05 8.53E+04 -6.23E+03 4%
3-Methyl-Hexane 1.22E+06 -5.56E+05 1.02E+05 -6.21E+03 4%
2,2,4-Trimethyl-Pentane 1.07E+06 -2.30E+05 -1.26E+04 5.19E+03 4%
1-Butene 2.13E+05 -6.64E+04 1.32E+04 -1.20E+03 4%
cis-2-Pentene 3.19E+05 -1.37E+05 3.26E+04 -2.95E+03 4%
2-Methyl-2-Pentene 4.87E+05 -1.73E+05 2.54E+04 -1.07E+03 4%
1-Heptene 4.66E+05 -2.12E+05 5.17E+04 -4.83E+03 4%
Toluene 3.21E+04 -1.68E+04 5.93E+03 -4.78E+02 6%
O-Xylene 7.10E+04 3.80E+04 -2.89E+04 4.74E+03 8%
3-Ethyl-Toluene 4.56E+05 -2.51E+05 6.51E+04 -6.15E+03 10%
Ethanol 1.43E+05 -3.01E+04 3.17E+03 -5.36E+01 4%
UncertaintyA B C D
data measured in the shock tube with the exception of the aromatics. This class of
hydrocarbons suffered from a combination of low absorption cross section and low
vapor pressure, reducing the accuracy of the shock-tube measurements. To increase
the accuracy of the in situ concentration measurement of the aromatics, the region-2
absorbance was used to measure the concentration. Sample measurements for toluene
are shown in Figure 8.11. The room-temperature measurements show larger scatter
for toluene because the absorbance for these conditions is only ∼3 to 6%. After the
shock wave arrives, the mixture is compressed and the absorbance increases to above
6%, and the uncertainty in the data is reduced significantly.
8.5. HIGH-T GASOLINE CROSS SECTIONS AT 3366.4 NM 105
8.5 High-Temperature Cross Sections of Gasoline
Samples at 3366.4 nm
The procedure for measuring the high-temperature cross sections of real gasoline
samples was similar to the procedure used to measure the high-temperature cross
sections of the neat hydrocarbons. The experimental apparatus and arrangement
were both identical. The only differences were in the mixture preparation and the in
situ determination of concentration.
To prepare gaseous mixtures of hydrocarbon blends like gasoline, a more complex
process was required. A small amount (∼0.5 mL) of the liquid was transferred into a
flask which was then connected to the mixing tank manifold. The flask was immersed
in liquid nitrogen, causing the gasoline to freeze. While the gasoline was frozen, the
air was evacuated from the flask, leaving frozen gasoline under vacuum. Next, the
flask was isolated from the evacuated manifold and the gasoline was heated to ∼38◦
C. The flask was then reconnected to the evacuated manifold and mixing tank. The
evacuated tank then began to fill with gasoline vapor, causing the remaining liquid
to evaporate. Because preferential distillation was a concern (i.e., the high-vapor-
pressure species evaporate and the low-vapor-pressure species remain condensed in
the flask), the amount of gasoline transferred into the flask was small, encouraging
complete evaporation of all species present in the gasoline sample.
Because the amount of gasoline in the sample was small, the measured absorbance
was low. Like the aromatics, the concentration of the gasoline was measured in situ
in region 2 where the absorbance was higher. The four gasoline samples selected
for the shock tube experiments were chosen to study a wide variation in gasoline
characteristics. Two samples of regular-grade and two samples of premium-grade
gasoline were selected for the study. One sample of each grade contained a relatively
large amount of aromatics, one sample of premium contained a large concentration
of alkanes and one sample of regular contained a relatively large amount of olefins
with moderate amounts of alkanes and aromatics. The four samples are indicated by
arrows in Figure 8.7.
106 CHAPTER 8. MID-IR ABSORPTION SPECTRUM OF GASOLINE
Figures 8.12- 8.15 show the measured cross section data as a function of tempera-
ture for 4 samples of gasoline. Open symbols indicate the FTIR measurements at 50◦
and 450◦ C. The filled symbols indicate the cross section measured in the shock tube.
The dashed lines in the figures indicate the predictions from the model. These four
samples show excellent agreement between the measurements and the model over the
entire temperature range.
8.6 Summary
The temperature-dependent spectroscopy of gasoline was studied and a wavelength
was selected to maximize sensitivity to concentration. A model was then developed
to estimate the temperature-dependent absorption cross section of gasoline while
accounting for variations in composition. The model was tested on multiple samples
of gasoline over a wide range of temperatures and showed good agreement with cross
section measurements. These results suggest that the final sensor design will provide
accurate measurement of gasoline mole fraction in a gasoline-fueled IC engine.
8.6. SUMMARY 107
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ross S
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700x103
6005004003002001000
Measured Cross Section [cm2mole
-1]
3366.4 nm 3392.23 nm 3471 nm
500x103
400
300
200
100
0
Modelle
d C
ross S
ection [cm
2m
ole
-1]
500x103
4003002001000
Measured Cross Section [cm2mole
-1]
3366.4 nm 3392.23 nm 3471 nm
Figure 8.9: Modelled cross section versus measured cross section from the FTIR datafor temperatures of (A) 50◦ and (B) 450◦ C, pressure of 1 atm, and wavelengths of3366.4, 3392.23, and 3471 nm.
108 CHAPTER 8. MID-IR ABSORPTION SPECTRUM OF GASOLINE
1.0x106
0.8
0.6
0.4
0.2
0.0
Cro
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ectio
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cm
2m
ole
-1]
140012001000800600400200
Temperature [K]
Post-Incident-Shock Data Post-Reflected-Shock Data Curve Fit to FTIR Data Curve Fit to All Data
Figure 8.10: Measured temperature-dependent absorption cross section for 3-methyl-hexane at 3366.4 nm with mole fraction ranging from ∼0.7 to 1.3% in argon withpost-reflected-shock pressures ranging from 1.4 to 1.8 atm.
60x103
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20
10
0
Cro
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-1]
140012001000800600400200
Temperature [K]
Pre-Shock Data Post-Incident-Shock Data Post-Reflected-Shock Data Curve Fit to FTIR Data Curve Fit to All Data
Figure 8.11: Measured temperature-dependent absorption cross section for toluene at3366.4 nm with mole fraction ranging from ∼1.5 to 6% in argon with post-reflected-shock pressures ranging from 1.5 to 2.5 atm.
8.6. SUMMARY 109
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0
Cro
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Temperature [K]
FTIR Measurements Shock Tube Measurement Modelled Values
Figure 8.12: Measured and modelled temperature-dependent cross sections at 3366.4nm for a sample of regular-grade gasoline (sample R6) with 55.2% alkanes, 26.6%aromatics, 18.1% olefins and 0% oxygenates by mole. The mole fraction of gasolinewas 0.2 to 0.8% in argon with post-reflected-shock pressure was ∼1.5 atm.
500x103
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100
0
Cro
ss S
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ole
-1]
140012001000800600400200
Temperature [K]
FTIR Measurements Shock Tube Measurements Modelled Values
Figure 8.13: Measured and modelled temperature-dependent cross sections at 3366.4nm for a sample of regular-grade gasoline (sample R9) with 54.4% alkanes, 36%aromatics, 9.7% olefins and 0% oxygenates by mole. The mole fraction of gasolinewas 0.2 to 0.8% in argon with post-reflected-shock pressure was ∼1.5 atm.
110 CHAPTER 8. MID-IR ABSORPTION SPECTRUM OF GASOLINE
600x103
500
400
300
200
100
0
Cro
ss S
ectio
n [
cm
2m
ole
-1]
140012001000800600400200
Temperature [K]
FTIR Measurements Shock Tube Measurements Modelled Values
Figure 8.14: Measured and modelled temperature-dependent cross sections at 3366.4nm for a sample of premium-grade gasoline (sample P1) with 71.0% alkanes, 14.9%aromatics, 14.2% olefins and 0% oxygenates by mole. The mole fraction of gasolinewas 0.2 to 0.8% in argon with post-reflected-shock pressure was ∼1.5 atm.
500x103
400
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200
100
0
Cro
ss S
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2m
ole
-1]
140012001000800600400200
Temperature [K]
FTIR Measurements Shock Tube Measurements Modelled Values
Figure 8.15: Measured and modelled temperature-dependent cross sections at 3366.4nm for a sample of premium-grade gasoline (sample P8) with 48.7% alkanes, 41.5%aromatics, 9.8% olefins and 0% oxygenates by mole. The mole fraction of gasolinewas 0.2 to 0.8% in argon with post-reflected-shock pressure was ∼1.5 atm.
Chapter 9
Two-Wavelength Temperature and
Vapor Concentration Sensor for a
Shock-Evaporated n-Dodecane
Aerosol
The high-temperature chemistry of low-vapor-pressure fuels is currently being stud-
ied at Stanford using a unique shock tube facility that enables the bath gas to be
loaded with a hydrocarbon aerosol [68–70]; initial chemistry experiments have fo-
cused on determining ignition times of various jet fuels and jet fuel surrogates (e.g.,
n-dodecane) [77, 78]. This shock tube provides relatively high concentrations of low-
vapor-pressure species by entraining a liquid aerosol in the bath gas. The incident
shock wave compresses the two-phase mixture, raising the gas temperature and caus-
ing the droplets evaporate. When the reflected shock wave passes, the liquid has
completely evaporated and the high-temperature chemistry of the gaseous mixture
can be examined.
The 1-D shock-tube equations have been adapted to determine the post-shock
conditions of a two-phase homogeneous mixture [77]. However, to validate chemistry
studies using a shock-evaporated aerosol, it is important to compare measurements
from a two-phase shock experiment with measurements from a purely gas-phase shock
111
112 CHAPTER 9. SENSOR FOR A SHOCK-EVAPORATED AEROSOL
experiment. These experiments can be used to validate the two-phase shock-jump
equations that describe the thermodynamic conditions of a shock-heated aerosol and
to confirm that the shock tube is operating as expected.
In this chapter and in Section E.4, shock tube measurements of a gas-phase mix-
ture of n-dodecane in argon are compared to post-evaporation measurements of a
shock-heated two-phase mixture of n-dodecane in argon. In the present chapter, a
two-wavelength temperature sensor is developed to measure post-evaporation temper-
atures in the aerosol shock tube. Wavelengths are selected to maximize sensitivity to
n-dodecane concentration and temperature. Vapor-phase shock tube experiments are
then used to extend the temperature-dependent cross sections to 1320 K. Finally, tem-
perature measurements in a shock-evaporated aerosol are compared to calculations
from a model that determines the temperature of a shock-wave-induced evaporated
liquid aerosol. The measured temperature shows good agreement with the modelled
temperature, confirming the accuracy of the two-phase shock tube calculations.
9.1 High-Temperature Cross Section
Measurements of a Gaseous Mixture in a Shock
Tube
The procedure for developing a two-wavelength temperature and concentration sensor
was outlined in Chapter 6 and is duplicated here for n-dodecane. First, wavelengths
are selected to maximize sensitivity over a wide temperature range. Then, shock-
heated mixtures of n-dodecane vapor in argon are used to extend the temperature-
dependent cross sections to > 1000o C. These measurements provide an accurate
calibration for the sensor because the post-shock conditions for a vapor mixture can
be accurately determined using the measured shock speed and initial conditions. In
Section 9.2, these temperature-dependent cross sections will be used to infer post-
evaporation temperature and concentration in a shock-heated aerosol.
9.1. HIGH-TEMPERATURE CROSS SECTIONS 113
9.1.1 Wavelength Selection
Because n-dodecane has a low vapor pressure (∼0.1 torr at 25◦ C), it is important to
select laser wavelengths that provide good sensitivity to temperature and concentra-
tion for very low concentrations. The absorption spectrum of n-dodecane is shown in
Figure 9.1 for temperatures of 100◦ and 450◦ C (373 and 723 K). The tuning ranges
of the two DFG lasers are indicated by the colored bars at the bottom of the graph.
These spectra show absorption features at several wavelengths that are candidates for
a two-wavelength sensor according to the wavelength selection criteria in Section 6.1.1.
However, rather than evaluating the high-temperature cross sections for the various
absorption features, as done in Chapter 6, the previous experiments with n-heptane
can be used to guide wavelength selection for this sensor. Because n-heptane and
n-dodecane have similar structural and spectral characteristics, it is likely that their
high-temperature cross sections will follow similar trends. Therefore, the wavelengths
3409.0 and 3432.4 nm were selected for this study of n-dodecane, which are nearly
identical to those chosen for n-heptane that yielded good temperature sensitivity over
the largest temperature range (3410 and 3433 nm).
9.1.2 Experimental Setup to Measure High-Temperature n-
Dodecane Cross Sections
Mixtures of n-dodecane vapor in argon were shock-heated to measure high-temperature
absorption cross sections for n-dodecane at the selected wavelengths. Because n-
dodecane has a low vapor pressure, several steps were taken to increase the magni-
tude of the absorption signal. First, the lab temperature was increased to ∼29◦ C
to increase the saturation vapor pressure of the n-dodecane. Second, a double-pass
optical arrangement was used (See Figure 9.2) to increase the amount of absorption
from the vapor and a reference detector provided a correction for laser power fluc-
tuations. Finally, rather than preparing mixtures in a mixing tank, the bath gas
was bubbled through liquid n-dodecane as it was introduced into the shock tube so
the n-dodecane partial pressure in the shock tube was near the saturation pressure
at the lab temperature. This maximized the n-dodecane vapor concentration in the
114 CHAPTER 9. SENSOR FOR A SHOCK-EVAPORATED AEROSOL
2.0x106
1.5
1.0
0.5
0
Cro
ss S
ection [cm
2m
ole
-1]
3600355035003450340033503300
Wavelength [nm]
34
09
.0
34
32
.4
Tuning Range of DFG Lasers
100° C 450° C
Figure 9.1: n-Dodecane absorption spectra at 100◦ and 450◦ C and 1 atm measuredwith 1 nm resolution (FWHM) using FTIR spectroscopy.
shock tube with the additional benefit of providing nearly identical filling procedures
for both single- and two-phase shocks. The bath gas mixture flows in through the
end-wall valves for both experiments and the only difference is whether the nebulizer
is on or off.
These experiments were performed in the aerosol shock tube using a modified
experimental procedure. The evacuated shock tube was filled from the endwall valves
in the normal fashion (see Section 5.3.2 for details about the standard filling procedure
for this shock tube). However, for these measurements, the ultrasonic nebulizers were
not activated and no aerosol was produced. Argon bath gas flowed through a fritted
gas washing bottle (chemglass model CG-1114) filled with liquid n-dodecane. As the
argon bubbled through the frit, n-dodecane vapor was entrained in the bath gas and
carried into the shock tube. The n-dodecane concentration was measured in situ prior
to shock arrival using the FTIR cross sections reported in Chapter 4 extrapolated to
room temperature. Note that the corrected measurements at 50◦ C, discussed in
9.1. HIGH-TEMPERATURE CROSS SECTIONS 115
DFG Laser
@ 2- Bandpass filter
2 cm
Poppet
Valves
Signal DetectorReference
Detector
ZnSe
Beamsplitter
ApertureDFG Laser
@ 2- Bandpass filter
2 cm
Poppet
Valves
Signal DetectorReference
Detector
ZnSe
Beamsplitter
Aperture
Figure 9.2: Experimental setup for measurements of shock-heated n-dodecane va-por/argon mixtures.
Section 4.2.2, were used for the extrapolation. The absorption at 3409.0 nm was
used to infer concentration because n-dodecane exhibits stronger room-temperature
absorption at this wavelength. Even with the low concentrations, the absorbance prior
to shock-wave arrival (∼18%) was sufficient to accurately determine the n-dodecane
concentration. The measured pre-shock n-dodecane partial pressure ranged from 0.12
to 0.15 torr, while the saturation pressure at the laboratory temperature of 29◦ C is
0.18 torr [65]. Thus, this method yielded a concentration that was at ∼80% of the
saturation pressure. A second bubbler placed in series with the first or lower bath gas
flow rates could have been used to increase the n-dodecane mole fraction to attain
100% of the saturation pressure.
Figure 9.3 shows sample absorbance data for a shock tube experiment using a
gas-phase mixture. For this experiment, the measured absorbance increases after
the incident and reflected shock waves pass because the mixture is compressed. Af-
ter the reflected shock wave passes, the measured absorbance at both wavelengths
decreases because the post-reflected-shock temperature (1226 K) is high enough to
cause decomposition of the n-dodecane.
116 CHAPTER 9. SENSOR FOR A SHOCK-EVAPORATED AEROSOL
0.6
0.5
0.4
0.3
0.2
0.1
0.0
Abso
rbance
5004003002001000-100
Time [µsec]
3409 nm
3432 nm
Incident Shock
Reflected Shock
Figure 9.3: Measured absorbance at 3409.0 and 3432.4 nm for shock-heated n-dodecane vapor in argon. Initial n-dodecane mole fraction was 0.058% with post-reflected-shock temperature and pressure of 1226 K and 6.10 atm.
9.1.3 Measured Cross Sections at High-Temperatures
The measured temperature-dependent cross section data and the absorbance ratio
are shown in Figure 9.4. The crosses indicate data that were measured via FTIR
spectroscopy in a heated cell. The filled symbols indicate data that were measured
in the shock tube. Two different diaphragm thicknesses were used, resulting in two
different ranges of pressure. The square symbols represent data where the post-
reflected-shock pressure was ∼1.5 atm. The triangular symbols represent data where
the post-reflected-shock pressure was ∼6 atm. No pressure dependence is observable
for the range of pressures studied here (∼0.1 to 6 atm). Comparison of the shock
tube measurements with our FTIR measurements and the FTIR measurements from
PNNL [39] provides a means to validate the current shock-tube measurements. Good
agreement (< 3%) is found between our the three data sets, confirming the reliabil-
ity of the shock tube data. The absorbance ratio for the selected wavelength pair
shows good temperature sensitivity between 300 and 1320 K. At temperatures above
∼1320 K, the n-dodecane rapidly decomposes (>1%/µsec) and the accuracy of the
absorption measurement decreases. The dashed lines represent polynomial fits to the
data.
9.1. HIGH-TEMPERATURE CROSS SECTIONS 117
A
2.0x106
1.5
1.0
0.5
0.0
Cro
ss S
ection [cm
2m
ole
-1]
140012001000800600400200
Temperature [K]
P5~1.5 atm
P5~6 atm
Stanford FTIR
PNNL FTIR
Incident Shock
Reflected Shock
2.0x106
1.5
1.0
0.5
0.0
Cro
ss S
ection [cm
2m
ole
-1]
140012001000800600400200
Temperature [K]
P5~1.5 atm
P5~6 atm
Stanford FTIR
PNNL FTIR
Incident Shock
Reflected Shock
B
1.0x106
0.8
0.6
0.4
0.2
0.0
Cro
ss S
ection [cm
2m
ole
-1]
140012001000800600400200
Temperature [K]
P5~1.5 atm
P5~6 atm
Stanford FTIR
PNNL FTIR
Incident Shock
Reflected Shock
Pre-Shock
1.0x106
0.8
0.6
0.4
0.2
0.0
Cro
ss S
ection [cm
2m
ole
-1]
140012001000800600400200
Temperature [K]
P5~1.5 atm
P5~6 atm
Stanford FTIR
PNNL FTIR
Incident Shock
Reflected Shock
Pre-Shock
C
1.2
1.0
0.8
0.6
0.4
0.2
0.0
Absorb
ance R
atio (
(3432 n
m)/
(3409 n
m))
140012001000800600400200
Modeled Temperature [K]
P5~1.5 atm, vapor
P5~6 atm, vapor
Stanford FTIR
PNNL FTIR
Incid
ent Shock
Reflected Shock
Pre
-Sh
ock
1.2
1.0
0.8
0.6
0.4
0.2
0.0
Absorb
ance R
atio (
(3432 n
m)/
(3409 n
m))
140012001000800600400200
Modeled Temperature [K]
P5~1.5 atm, vapor
P5~6 atm, vapor
Stanford FTIR
PNNL FTIR
Incid
ent Shock
Reflected Shock
Pre
-Sh
ock
Figure 9.4: Temperature-dependent cross sections and absorbance ratio of n-dodecane. A: σ(3409.0 nm), B: σ(3432.4 nm), and C: absorbance ratio.
118 CHAPTER 9. SENSOR FOR A SHOCK-EVAPORATED AEROSOL
9.1.4 High-Temperature Measurements of Temperature and
n-Dodecane Vapor Concentration
Using the data from the temperature-dependent curve fits shown in Figure 9.4, the
laser absorbtion data for shock-heated vapor n-dodecane were reprocessed to infer
time-dependent temperature and concentration. The sample measurements in Fig-
ure 9.5 show good agreement with the values calculated from the ideal shock equa-
tions. For these data, the post-shock temperature was 1226 K, which is high enough
for observable thermal decomposition of the n-dodecane within the ∼1 msec test time
of this shock tube. Because the n-dodecane absorbs thermal energy as it decomposes,
the temperature also decreases with time. In Appendix E, these high-temperature
data are used to infer n-dodecane overall decomposition rates for both the single- and
two-phase measurements, which are compared to overall decomposition rates of other
hydrocarbons.
The measured temperature and concentration from the shock tube experiments
are compared to the expected values in Figure 9.6 for temperatures ranging from 300
to 1320 K. The temperature measurements have a 2.8% RMS deviation over the entire
temperature range and the concentration measurements have a 3.6% RMS deviation
over this same range. Thus, the measured data show excellent agreement with the
predicted values. This comparison validates the sensitivity of our measurement for
concentration and temperature up to 1320 K. Next, this diagnostic is used to measure
gas temperature and n-dodecane concentration for shock tube experiments where the
ambient mixture contains n-dodecane droplets.
9.2 Concentration and Temperature in a Shock-
Evaporated n-Dodecane Aerosol
As previously stated, the aerosol-laden shock tube is being developed as a tool to study
high-temperature chemistry of low-vapor-pressure species (e.g., n-dodecane) and fuel
blends (e.g., jet-A, RP-1, and diesel). High-concentration gaseous mixtures cannot be
generated when the substance has a low vapor pressure. This shock tube overcomes
9.2. MEASUREMENTS IN A SHOCK-EVAPORATED AEROSOL 119
A
1400
1200
1000
800
600
400
200
0
Tem
pera
ture
[K
]
5004003002001000-100
Time[µsec]
B
40x10-9
30
20
10
0
Co
ncen
trati
on
[m
ole
/cc]
5004003002001000-100
Time[µsec]
Figure 9.5: Measured data for shock-heated mixture of 0.058% n-dodecane vapor inargon with post-reflected-shock pressure of 6.10 atm and temperature of 1226 K. A:Temperature. B: Concentration. Dashed lines indicate calculations using the 1-Dshock equations. Solid lines indicate data measured by two-wavelength sensor.
120 CHAPTER 9. SENSOR FOR A SHOCK-EVAPORATED AEROSOL
A
1400
1200
1000
800
600
400
200
0
Me
asu
red
Te
mp
era
ture
[K
]
1200 800 400 0
Modelled Temperature [K]
P 5 ~1.5 atm
P 5 ~6 atm
B
50x10 -9
40
30
20
10
0 Measure
d C
oncentr
ation [m
ole
/cc]
50x10 -9
40 30 20 10 0
Modelled Concentration [mole/cc]
P 5 ~1.5 atm
P 5 ~6 atm
Figure 9.6: Comparison of measured and calculated data for shock-heated mixtures ofn-dodecane vapor in argon. A: Temperature; B: Concentration. Dashed lines indicateperfect agreement.
9.2. MEASUREMENTS IN A SHOCK-EVAPORATED AEROSOL 121
that challenge by loading the hydrocarbon into the shock tube as a liquid aerosol.
The shock tube has been fitted with ultrasonic nebulizers that generate a fine aerosol
which is carried into the shock tube by the bath gas. Particle size measurements
indicate a volume-mean droplet diameter of ∼5 µm [68]. The incident shock wave
propagates into the two-phase mixture, shock-heating it and causing the liquid to
completely evaporate, leaving a gaseous mixture in its wake. When the reflected shock
wave passes, this purely gas-phase mixture is shock-heated to temperatures where
chemical reactions take place on ∼µsec timescales (>1000 K). Significant effort has
been invested in the design and characterization of this shock tube, but thus far, few
measurements have been made to confirm the calculated thermodynamic conditions
behind the reflected shock wave.
In this section, the two-wavelength sensor developed for n-dodecane is used to
monitor gas temperature and concentration after the aerosol has evaporated. Mea-
surements of temperature are compared to calculations based on the measured shock
speed and initial conditions. It is shown that the temperature measured after com-
plete evaporation is in good agreement with the modelled temperature.
9.2.1 Description of AEROFROSH Code for Shock-Heated
Aerosol
The ideal shock equations for a gas-phase mixture are derived from the ideal gas law
and three thermodynamic conservation conditions that must be met across the shock
interface (shock-fixed coordinates): conservation of mass, conservation of momen-
tum, and conservation of energy (see Equations 9.1, 9.2, 9.3, and 9.4). If the shock
velocity, gas composition, gas temperature, and total pressure are all known for the
conditions in front of a shock wave, then these equations can be solved to determine
the thermodynamic conditions behind the shock wave.
P = ρRT (9.1)
ρ1u1 = ρ2u2 (9.2)
122 CHAPTER 9. SENSOR FOR A SHOCK-EVAPORATED AEROSOL
P1 + ρ1u21 = P2 + ρ2u
22 (9.3)
h1 +u2
1
2= h2 +
u22
2(9.4)
The AEROFROSH program has been previously developed to solve these equa-
tions for a two-phase mixture by assuming a two-step shock-heating process [68, 69,
77, 78]. In the first step, the two-phase mixture is compressed, but no evaporation
occurs. The liquid is assumed to remain at a fixed temperature and density during
this first process and the mole fraction of liquid in the bath gas is also assumed to
be constant (i.e., the droplets are sufficiently small to remain entrained in the gas
during compression). The density used in Equations 9.1- 9.4 is equal to the volumet-
ric average density of the two-phase mixture. In the second step, the droplets fully
evaporate and the mixture reaches thermal equilibrium, assuming constant volume
and constant energy for the mixture.
To solve these shock equations for a two-phase mixture of n-dodecane aerosol in
argon, the composition of the mixture is required (i.e., the species concentrations must
be known). A laser absorption diagnostic provides the post-evaporation absorbance
(behind the incident shock) which is proportional to the vapor concentration. An it-
erative calculation is required to determine the amount of n-dodecane initially present
because the absorption cross section behind the shock wave (and therefore the ab-
sorbance) is also dependent on temperature. Hence, the post-shock temperature and
pressure are first estimated so the n-dodecane concentration can be calculated. Using
this concentration, the post-shock temperature and pressure are then recalculated,
resulting in a corrected value of n-dodecane concentration. This calculation is iter-
ated until it produces a convergent solution (typically <5 iterations). The pre-shock
vapor concentration is assumed to be the room-temperature saturation pressure of
the liquid and the remaining n-dodecane is assumed to come from evaporated aerosol.
The shock velocity is measured in 5 locations over the last 2 m of the end wall.
A linear fit to the velocity measurements versus location is used to determine the
shock velocity at the sensor location, which is subsequently used to calculate the
post-shock conditions. In reality, the test-gas mixture at the measurement location
is shock-heated upstream of the measurement location where the shock velocity is
9.2. MEASUREMENTS IN A SHOCK-EVAPORATED AEROSOL 123
slightly higher. For the current experiments, the test gas sample measured at the 5
cm from the endwall location was originally processed by the incident shock wave at
an upstream location ∼20 cm from the end wall, and the measured incident shock
wave attenuations for 1-2%/m. For incident shock attenuations of order 1.5%/m,
the shock speed at this upstream location is ∼0.2% higher than at the measurement
location. This translates to a ∼0.4% higher temperature than that predicted at the
measurement location. In general, these small corrections can be neglected except in
cases when sensitivity to temperature is large.
Because the model assumes a homogeneous mixture and neglects the effects of local
nonuniformities, it is important that it be compared to measurements. By comparing
temperature measurements in this shock tube with the AEROFROSH calculations, it
will be shown that the model does accurately predict the post-evaporation conditions.
9.2.2 Experimental Arrangement for Aerosol Shock Experi-
ments
Because loading the shock tube with an aerosol provides 2-6 times as much n-dodecane
as the previous gas-phase experiments, a single-pass arrangement was employed to
reduce absorption of the mid-IR beam. A near-IR nonresonant beam at the same
measurement location verified complete evaporation of the aerosol. Measurements
were made at two locations. When the sensor was located 2 cm from the endwall
(which is the location used for the gas-phase experiments in Section 9.1), the aerosol
usually did not evaporate completely before the reflected shock arrived and mean-
ingful data could only be measured after the reflected shock. Therefore, most of the
measurements were made with the lasers located ∼5 cm from the endwall. At this
location, the aerosol completely evaporated before the reflected shock arrived and
data were measured behind both incident and reflected shock waves.
124 CHAPTER 9. SENSOR FOR A SHOCK-EVAPORATED AEROSOL
2.0
1.5
1.0
0.5
0.0
Extinction
-500 -250 0 250 500
Time [µsec]
1550 nm 3432 3410
Incomplete Evaporation
Figure 9.7: Measured extinction at 1550 nm, 3409.0 nm, and 3432.4 nm for a shock-heated n-dodecane aerosol with the sensor located 5 cm from the endwall. P5 = 7.56atm, T5 = 1109 K, n-dodecane mole fraction = 0.26%.
9.2.3 Concentration and Temperature Measurements in a
Shock-Evaporated Aerosol
Sample measurements of total extinction are shown in Figure 9.7 for an aerosol shock
experiment. Prior to arrival of the shock wave, there is significant extinction at
each of the three wavelengths. This can be attributed primarily to droplet scattering
because the near-IR beam is not absorbed by n-dodecane vapor. After the incident
shock wave passes the measurement location (t=-235 µsec), the extinction at all three
wavelengths increases. However, because the gas temperature has increased to 660
K, the droplets quickly evaporate and the near-IR extinction decays to zero. The
extinction at the two mid-IR wavelengths decreases, but remains nonzero because,
as the droplets evaporate, the n-dodecane vapor concentration increases and absorbs
the mid-IR light. After the reflected shock wave passes, the mixture is compressed a
9.2. MEASUREMENTS IN A SHOCK-EVAPORATED AEROSOL 125
second time and the total extinction at the mid-IR wavelengths increases.
The measured extinction data can be used to determine temperature and con-
centration once the aerosol has completely evaporated. Sample temperature and
concentration measurements are shown in Figure 9.8 which were computed from the
extinction data in Figure 9.7. The measured data are plotted as solid lines and the
calculated values are plotted as dashed lines. Before the incident shock wave arrives,
the measured data are erroneous because the extinction is dominated by aerosol ex-
tinction and this sensor was not designed for use in a two-phase environment.
After the incident shock wave arrives and the droplets evaporate, there is good
agreement between the modelled and measured temperature. The measurements are
∼3% lower than the modelled data, which can be attributed to uncertainty in the
measured shock velocity. As the shock wave propagates into the test mixture, it is
attenuated strongly by the aerosol, and this aerosol is not uniformly loaded along the
length of the tube. This result in an estimated uncertainty in shock velocity of ∼1%
which translates into an uncertainty in modelled temperature of ∼2%.
The difference between measured and modelled temeprature might also be at-
tributed to nonuniformities. If the n-dodecane vapor is not well-mixed across the
measurement path, the regions with high concentration will be at a lower tempera-
ture. The measurement will be weighted towards these rich pockets and the measured
temperature will be lower than the actual average gas temperature. However, if large-
scale nonuniformities were substantial, concentration fluctuations would be apparent
behind the incident shock wave as the gases flow past the sensor. If small-scale nonuni-
formities were important, then the measured temperature would tend to increase as
heat is conducted from the high-temperature argon bath gas into the low-temperature
n-dodecane. The measurements do not indicate a significant increases in the temper-
ature during these timescales and therefore the effect of local nonuniformities appears
to be small.
The measured temperature is compared to the modelled temperature in Figure 9.9
for post-incident-shock temperatures ranging from 580 to 840 K and post-reflected-
shock temperatures ranging from 920 to 1380 K. The temperature was measured after
the incident and reflected shocks; however, because of the interference from droplet
126 CHAPTER 9. SENSOR FOR A SHOCK-EVAPORATED AEROSOL
A
1600
1400
1200
1000
800
600
400
200
0
Te
mp
era
ture
[K
]
-400 -200 0 200 400
Time [µsec]
Incomplete Evaporation
B
250x10-9
200
150
100
50
0
Co
nce
ntr
atio
n [
mo
le/c
c]
-400 -200 0 200 400
Time [µsec]
Incomplete Evaporation
Figure 9.8: Time-dependent temperature and concentration measurements fora shock-evaporated n-dodecane aerosol. Dashed lines values calculated usingAEROFROSH. A: Temperature, B: Concentration. P5 = 7.56 atm, T5 = 1109 K,n-dodecane mole fraction = 0.26%.
9.3. SUMMARY 127
scattering, no temperature data is available prior to incident shock arrival. The
AEROFROSH model, which incorporates droplet evaporation physics into the ideal-
shock equations, is shown to provide reliable temperature data. A careful analysis of
the present measurements finds that in general, the AEROFROSH model systemati-
cally overpredicts the shock temperatures by as much as 2%.
We attribute differences in the measured and modelled temperature seen in Fig-
ures 9.8 and 9.9, at least partially, to uncertainty in the shock speeds used in the
AEROFROSH calculations. Variations in the aerosol density over the last 2 m of the
shock tube have the effect of introducing larger uncertainties ( 1%) into the incident
shock speed measurements near the end wall. These uncertainties directly affect the
predicted incident and reflected shock temperatures. Because the aerosol density is
higher near the end wall, the shock wave decelerates faster than predicted by a linear
fit to the velocity measurements. This may cause the shock speed near the end wall to
be overpredicted, resulting in an AEROFROSH predicted temperature that is higher
than the measured temperature.
9.3 Summary
A two-wavelength temperature and vapor concentration diagnostic was designed for
n-dodecane to validate a model of post-evaporation conditions in an aerosol shock
tube. Temperature-dependent cross sections were measured at the two wavelengths
in shock-heated mixtures of vapor-phase n-dodecane and argon. The temperature-
dependent cross sections were then used to infer post-evaporation temperature and
n-dodecane vapor concentration in a series of two-phase shock tube experiments. The
good agreement found between the model and the measurements provides confidence
in the AEROFROSH model.
128 CHAPTER 9. SENSOR FOR A SHOCK-EVAPORATED AEROSOL
1400
1200
1000
800
600
400
200
0
Measu
red
Tem
pera
ture
[K
]
12008004000
Modelled Temperature [K]
Figure 9.9: Measured temperature versus modelled temperature for post-evaporationn-dodecane-aerosol shocks.
Chapter 10
Summary and Future Work
This thesis describes the design and development of mid-IR optical-absorption di-
agnostics for measuring fuel concentration. A library of temperature-dependent ab-
sorption data is generated to facilitate the design of various fuel diagnostics. Mea-
surement techniques using a two-wavelength sensor are developed to measure vapor
concentration with interferences and also to simultaneously infer temperature and va-
por concentration. Sensors are then designed to measure fuel concentration in pulse
detonation engines, IC engines, and shock tubes.
10.1 Summary
Spectroscopic Measurements
Temperature-dependent absorption spectra were measured for 26 hydrocarbon species
for temperatures ranging from 25◦ to 500◦ C in the 3.4 µm region associated with
the C-H stretch. Good agreement was found between the measured data and the
room-temperature data available in the literature [39]. Temperature-dependent cross
sections measured with a 3.39 µm HeNe laser were found to agree with the FTIR mea-
surements and are consistent with other available data. This library of spectroscopic
data was used in the current research to develop hydrocarbon sensors for a variety of
applications and also to develop a spectroscopic model for gasoline absorption using
129
130 CHAPTER 10. SUMMARY AND FUTURE WORK
only 13 of the >200 species that are present in gasoline.
Measurement Techniques
A two-wavelength switching technique was developed using a tunable DFG laser,
increasing the capabilities of an already valuable spectroscopic tool. Two-wavelength
switching was used to measure fuel concentration in the presence of interference effects
such as droplet extinction and interference absorption from another species. This
method of interference rejection can be used in applications where window fouling
and particle extinction prohibit single-wavelength optical diagnostics from providing
accurate concentration measurements.
Two-wavelength switching was also used to simultaneously measure temperature
and vapor concentration in a shock tube. The wavelength-switching technique pro-
vides fast and accurate measurements of both temperature and concentration with a
time response of 5 µsec. A sensor using this technique can be used to accurately infer
temperature and equivalence ratio in a system like an IC engine where control of this
variable is critical for clean and efficient operation.
Fuel Diagnostics
Fuel sensors were designed for a host of practical applications. A fiber-coupled fuel
sensor was designed to measure ethylene and propane concentration in a pulse det-
onation engine. The sensor revealed non-ideal interactions between the detonation
waves and the fuel injection system. By identifying these cycle-to-cycle interactions,
models of engine operation could account for unburned fuel when predicting engine
performance. Additionally, future engines can be designed to correct the issue.
The temperature-dependent spectroscopy of multiple gasoline samples was care-
fully examined and a wavelength was selected for maximum sensitivity to gasoline
concentration. To account for variations in gasoline composition, a model was devel-
oped that uses the relative concentration of individual structural classes (i.e., alkanes
or aromatics) to approximate the temperature-dependent absorption cross section for
the selected wavelength. The model was tested on 21 gasoline samples showing a 6.5%
10.2. FUTURE WORK 131
RMS deviation from measurements. This strategy of approximating the absorption
cross section of fuel blends will be useful for other blended fuels (e.g., Jet-A, RP-1,
or diesel) where compositional effects are likely to be equally important.
A third sensor was designed to measure the temperature and n-dodecane vapor
concentration in a shock tube. Wavelengths were selected to maximize sensitivity
to temperature and n-dodecane at high temperatures. Absorption cross sections
were then extended to high temperatures using a shock-heated gaseous mixture of
n-dodecane in argon. Next these cross sections were used to measure the post-
evaporation temperature and n-dodecane concentration for shock-evaporated aerosol.
Good agreement was found between the measurements and the AEROFROSH pre-
dictions, confirming the accuracy of the AEROFROSH model. These diagnostics
illustrate the power of mid-IR absorption diagnostics to provide useful information
in a variety of harsh environments.
10.2 Future Work
Spectroscopy
Because fuel concentration and stoichiometry are important in combustion systems,
there are many potential applications of mid-IR spectroscopy and absorption diag-
nostics. In terms of hydrocarbon spectroscopy, most of the FTIR measurements
presented here are for temperatures between 25◦ and 500◦ C. Measurements at higher
temperatures were not attempted because many of the samples decompose in the sta-
tic cell at higher temperatures and the cell cannot tolerate temperatures above ∼550◦
to 650◦ C. However, several of the species studied are stable at temperatures above
500◦ C (e.g., methane and ethylene). The spectroscopy of these important species
should be studied at higher temperatures and over a larger wavelength range using
the FTIR spectrometer. These data would provide valuable spectroscopic information
to aid in wavelength selection for optical detection of unburned hydrocarbons.
The spectroscopic model for gasoline can be extended to other fuels such as diesel
and kerosene, but spectroscopic measurements will become increasingly difficult for
132 CHAPTER 10. SUMMARY AND FUTURE WORK
high-molecular-weight species because condensation and surface adsorption will begin
to affect the data. To overcome this problem, a liquid-injection system with a flowing
gas, such as the one described by Johnson et al. [79] can be used to carefully prepare
mixtures and saturate the surfaces. In this way, the spectroscopic capabilities of the
heated cell and FTIR can be extended to species like hexadecane and fuel blends like
diesel and kerosene. Additionally, the linear trend in absorption band intensity with
number of C-H bonds observed in Figure 4.8 can be used to estimate the absorption
band intensity of low-vapor-pressure species and fuel blends, providing a method to
validate the spectroscopic measurements.
Techniques
The two-wavelength techniques described here utilized two fiber-combined signal
lasers that were rapidly switched using the injection current. However, this can
present a challenge in some situations because the laser wavelength is ‘chirped’ when
operated this way. Instead, a more elegant solution would be to use an optical switch
(i.e., an acousto-optic or electro-optic modulator) to alternate between the two lasers,
thereby eliminating wavelength chirp and enabling more precise determination of the
signal laser wavelength. This is of particular importance when measuring species with
narrow absorption features (e.g., methane).
It might also be possible to significantly improve the power output of the two-
wavelength system by simultaneously alternating between two pump lasers and at
the same time, alternate between two signal lasers. If the signal and pump lasers
are carefully chosen, it might be possible to maintain quasi-phasematching for two
mid-IR wavelegnths simultaneously. A recently acquired DFG laser has the capability
of alternating between two pump lasers and would therefore permit further investiga-
tion. Additionally, if the pump lasers are rapidly switched 90◦ out of phase with the
signal lasers, then 4 mid-IR wavelengths can be generated during one switching cycle,
potentially enabling determination of additional quantities with one laser system.
The future of multi-wavelength techniques will be to utilize three- and four-
wavelength systems for measuring fuel concentration and temperature in the pres-
ence of interferences such as droplets and particulates. This will be an interesting
10.2. FUTURE WORK 133
problem for practical two-phase systems like DISI and diesel engines. Furthermore,
trace pollutants continue to become increasingly important in the design of new en-
gines. Multi-wavelength techniques may provide a means to study the formation and
oxidation of these species in situ in practical combustion environments. Knowledge
of the formation and oxidation pathways will then lead to techniques for reduction of
engine-out emissions.
Multi-wavelength techniques should also be considered for shock-tube chemistry
studies. Ethylene is a particularly interesting species because it is very relevant
to combustion systems. However, absorption in the mid-IR suffers from excessive
interference by larger species. In the region near 10.6 µm, ethylene has a strong
absorption band that is isolated from many other hydrocarbon absorption features.
Either a CO2 laser or a tunable quantum cascade laser can be used to access these
ethylene transitions for investigation of ethylene chemistry in reacting hydrocarbon
systems.
Mid-IR Diagnostics
One avenue of importance for mid-IR diagnostics is that of shock-tube chemistry
measurements. Mid-IR diagnostics should be developed to measure hydrocarbon
species (reactants, intermediated and products) and infer chemical reaction rates for
specific reactions. For example, experiments should be performed to isolate the uni-
molecular decomposition and to extend the temperature range of the measurements.
A fixed-wavelength technique should be utilized to provide a faster time response
than was possible with the wavelength-switching technique described here. Initial de-
composition measurements reported in Appendix E show that second-order reactions
interfere with the first-order reactions at high concentrations and that the tempera-
ture decreases as the species react, further complicating analysis of the kinetic data.
To minimize the interference from second-order reactions and to reduce the temper-
ature change during the pyrolysis experiments, the experiments should be performed
with lower concentrations of the hydrocarbon species. High-concentration shock-tube
experiments should be used to measure the temperature-dependent absorption cross
section, then low-concentration shock-tube experiments should use this cross section
134 CHAPTER 10. SUMMARY AND FUTURE WORK
data to measure hydrocarbon concentration and infer decomposition rates.
Mid-IR diagnostics hold significant potential for practical propulsion systems as
well. The gasoline sensor described in Chapter 8 is part of a project to study next-
generation gasoline engines. Mid-IR diagnostics like this could also be applied to
diesel engines and pulse detonation engines. By understanding the time-evolution of
fuel concentration, efficiency and pollutant emissions can be controlled and optimized.
Similar diagnostics can be easily applied to alternative fuels, such as E85 and biodiesel.
Detection of E85 may actually be more straightforward than that of gasoline because
the composition is dominated by ethanol and a similar spectroscopic model can be
used to estimate the absorption from the remaining species.
Mid-IR diagnostics offer the potential to study unburned hydrocarbons and com-
bustion intermediates to help determine the sources of unburned hydrocarbons. Mid-
IR diagnostics for trace pollutants would offer incredible potential for the design and
characterization of low-emissions vehicles. Mid-IR diagnostics for NO, CO, and poly-
aromatic hydrocarbons could be applied to practical systems, such as IC engines, to
improve the understanding of the chemistry of trace species in these systems.
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and Z. Qin. Gri-mech 3.0 (http : //www.me.berkeley.edu/gri mech/).
BIBLIOGRAPHY 145
[82] M. Chaos, A. Kazakov, Z.W. Zhao, and F.L. Dryer. A high-temperature chemical
kinetic model for primary reference fuels. International Journal of Chemical
Kinetics, 39(7):399–414, 2007.
[83] D.F. Davidson, M.A. Oehlschlaeger, and R. K. Hanson. Methyl concentration
time-histories during iso-octane and n-heptane oxidation and pyrolysis. Proceed-
ings of the Combustion Institute, 31(1):321–328, 2007.
[84] E. Ranzi, T. Faravelli, and A. Frassoldati. Online database available at url:
Http://www.chem.polimi.it/creckmodeling/kinetic.html, 2006.
[85] H.R. Zhang. PhD thesis, University of Utah, 2005.
[86] H.R. Zhang, E.G. Eddings, and A.F. Sarofim. Criteria for selection of compo-
nents for surrogate of natural gas and transportation fuels. Proceedings of the
Combustion Institute, 31(1):401–409, 2007.
Appendix A
Temperature-Dependent
Absorption Spectra of
Hydrocarbons Measured by FTIR
Absorption spectra were measured for 26 hydrocarbon species using FTIR spec-
troscopy with the hydrocarbon diluted in nitrogen to 1 atm. The details of the
measurements are provided in Chapter 4. Chapter 4 explains that, because the inte-
grated band intensity is expected to be temperature-independent, the integrated band
intensity provides a convenient comparison between different sources, which may have
been measured at different temperatures. The integrated band intensity for each of
the measurements plotted here is within the estimated uncertainty of the measure-
ment, providing confidence in these temperature-dependent spectra. Sample spectra
for each of the species are provided in this appendix. Computed 3-D structures of
each of the molecules are displayed below each figure caption. Details of how these
structures were calculated can be found at (http://webbook.nist.gov/chemistry/3d-
structs/).
146
147
Table A.1: Experimental details of measured hydrocarbon spectra.
[%]
[torr]
[g/m
ole
]
Eth
an
ol
alc
oh
ol
99
25
-32
50
.11
.0-2
.35
9.5
54
6.0
7
Fo
rma
lde
hyd
ea
lde
hyd
e?
?1
00
-35
00
.10
.4-1
.0g
as
30
.03
Me
tha
ne
alk
an
e9
92
5-5
00
0.1
0.4
ga
s1
6.0
4
Be
nze
ne
aro
ma
tic9
92
5-5
00
0.1
1.6
-3.7
95
.87
8.1
1
To
lue
ne
aro
ma
tic9
92
5-5
00
11
.0-1
.52
8.3
92
.14
m-x
yle
ne
aro
ma
tic9
92
5-5
00
10
.4-0
.68
.71
06
.17
Eth
yl-b
en
ze
ne
aro
ma
tic9
92
5-5
00
10
.3-0
.69
.51
06
.17
O-x
yle
ne
aro
ma
tic9
82
5-5
00
10
.3-1
.46
.71
06
.17
3-e
thyl-to
lue
ne
aro
ma
tic9
92
5-5
00
10
.2-0
.43
.04
12
0.1
9
2-m
eth
yl-p
rop
an
eb
ran
ch
ed
alk
an
e9
92
5-5
00
0.1
0.3
-1.7
ga
s5
8.1
2
2-m
eth
yl-b
uta
ne
bra
nch
ed
alk
an
e9
9.5
25
-50
01
0.2
-1.1
68
6.3
72
.15
2-m
eth
yl-p
en
tan
eb
ran
ch
ed
alk
an
e9
92
5-5
00
10
.4-1
.32
11
.48
6.1
8
3-m
eth
yl-h
exa
ne
bra
nch
ed
alk
an
e9
92
5-5
00
10
.6-1
.06
2.2
10
0.2
2,2
,4-trim
eth
yl-p
en
tan
eb
ran
ch
ed
alk
an
e9
92
5-5
00
10
.3-1
.64
9.6
11
4.2
3
Eth
yle
ne
ole
fin9
9.5
25
-50
00
.10
.7-1
.7g
as
28
.05
Pro
pe
ne
ole
fin9
92
5-5
00
0.1
1.0
-6.0
ga
s4
2.0
8
1-b
ute
ne
ole
fin9
92
5-5
00
0.1
1.2
-2.6
ga
s5
6.1
1
2-m
eth
yl-2
-bu
ten
eo
lefin
99
25
-50
01
0.0
6-2
.34
73
.47
0.1
3
cis
-2-p
en
ten
eo
lefin
98
25
-50
01
0.7
-2.5
50
1.2
70
.13
2-m
eth
yl-2
-pe
nte
ne
ole
fin9
82
5-5
00
10
.4-1
.81
56
.58
4.1
6
1-h
ep
ten
eo
lefin
97
25
-50
01
0.2
-1.2
56
.59
8.1
9
2,4
,4-trim
eth
yl-1
-pe
nte
ne
ole
fin9
92
5-4
50
10
.3-1
.34
6.1
11
2.2
1
Eth
an
estra
igh
t alk
an
e9
92
5-5
00
0.1
0.8
-1.7
ga
s3
0.0
7
n-p
en
tan
estra
igh
t alk
an
e9
92
5-5
00
10
.4-1
.35
21
.67
2.1
5
n-h
ep
tan
estra
igh
t alk
an
e9
92
5-5
00
10
.3-1
.14
6.2
10
0.2
n-d
od
eca
ne
stra
igh
t alk
an
e9
95
0-5
00
10
.07
-0.1
0.1
41
70
.33
Na
me
Stru
ctu
ral C
lass
Mo
lecu
lar
We
igh
t
Va
po
r Pre
ssu
re
at 2
5o C
Te
mp
era
ture
Ra
ng
e [C
]
Re
so
lutio
n
[cm
-1]P
urity
[%]
Mo
le
Fra
ctio
n
148APPENDIX A. TEMPERATURE-DEPENDENT HYDROCARBON SPECTRA
A.1 FTIR Absorption Spectra of Normal Alkanes
1.4x106
1.2
1.0
0.8
0.6
0.4
0.2
0.0Cro
ss S
ectio
n [
cm
2m
ole
-1]
3600340032003000Wavelength [nm]
50° C 250° C 450° C
Figure A.1: Absorption spectra of methane.
1.0x106
0.8
0.6
0.4
0.2
0.0Cro
ss S
ectio
n [
cm
2m
ole
-1]
36003500340033003200Wavelength [nm]
50° C 250° C 450° C
Figure A.2: Absorption spectra of ethane.
149
600x103
500
400
300
200
100
0Cro
ss S
ectio
n [
cm
2m
ole
-1]
36003500340033003200Wavelength [nm]
50° C 250° C 450° C
Figure A.3: Absorption spectra of n-pentane.
700x103
600
500
400
300
200
100
0Cro
ss S
ection [cm
2m
ole
-1]
36003500340033003200Wavelength [nm]
50° C 250° C 450° C
Figure A.4: Absorption spectra of n-heptane.
150APPENDIX A. TEMPERATURE-DEPENDENT HYDROCARBON SPECTRA
1.6x106
1.2
0.8
0.4
0.0Cro
ss S
ectio
n [
cm
2m
ole
-1]
36003500340033003200Wavelength [nm]
100° C 250° C 450° C
Figure A.5: Absorption spectra of n-dodecane.
151
A.2 Absorption Spectra of Branched Alkanes
1.0x106
0.8
0.6
0.4
0.2
0.0Cro
ss S
ectio
n [
cm
2m
ole
-1]
36003500340033003200Wavelength [nm]
50° C 250° C 450° C
Figure A.6: Absorption spectra of 2-methyl-propane.
600x103
500
400
300
200
100
0Cro
ss S
ection [cm
2m
ole
-1]
36003500340033003200Wavelength [nm]
50° C 250° C 450° C
Figure A.7: Absorption spectra of 2-methyl-butane.
152APPENDIX A. TEMPERATURE-DEPENDENT HYDROCARBON SPECTRA
800x103
600
400
200
0Cro
ss S
ectio
n [
cm
2m
ole
-1]
36003500340033003200Wavelength [nm]
50° C 250° C 450° C
Figure A.8: Absorption spectra of 2-methyl-pentane.
800x103
600
400
200
0Cro
ss S
ectio
n [
cm
2m
ole
-1]
36003500340033003200Wavelength [nm]
50° C 250° C 450° C
Figure A.9: Absorption spectra of 3-methyl-hexane.
153
1.2x106
1.0
0.8
0.6
0.4
0.2
0.0Cro
ss S
ectio
n [
cm
2m
ole
-1]
36003500340033003200Wavelength [nm]
50° C 250° C 450° C
Figure A.10: Absorption spectra of 2,2,4-trimethyl-pentane (iso-octane).
154APPENDIX A. TEMPERATURE-DEPENDENT HYDROCARBON SPECTRA
A.3 Absorption Spectra of Olefins
200x103
150
100
50
0Cro
ss S
ectio
n [
cm
2m
ole
-1]
3600340032003000Wavelength [nm]
50° C 250° C 450° C
Figure A.11: Absorption spectra of ethylene.
120x103
100
80
60
40
20
0Cro
ss S
ection [cm
2m
ole
-1]
360035003400330032003100Wavelength [nm]
50° C 250° C 450° C
Figure A.12: Absorption spectra of propene.
155
200x103
150
100
50
0Cro
ss S
ectio
n [
cm
2m
ole
-1]
36003500340033003200Wavelength [nm]
50° C 250° C 450° C
Figure A.13: Absorption spectra of 1-butene.
250x103
200
150
100
50
0Cro
ss S
ectio
n [
cm
2m
ole
-1]
36003500340033003200Wavelength [nm]
50° C 250° C 450° C
Figure A.14: Absorption spectra of cis-2-pentene.
156APPENDIX A. TEMPERATURE-DEPENDENT HYDROCARBON SPECTRA
300x103
250
200
150
100
50
0Cro
ss S
ectio
n [
cm
2m
ole
-1]
36003500340033003200Wavelength [nm]
50° C 250° C 450° C
Figure A.15: Absorption spectra of 2-methyl-2-butene.
400x103
300
200
100
0Cro
ss S
ectio
n [
cm
2m
ole
-1]
36003500340033003200Wavelength [nm]
50° C 250° C 450° C
Figure A.16: Absorption spectra of 2-methyl-2-pentene.
157
500x103
400
300
200
100
0Cro
ss S
ectio
n [
cm
2m
ole
-1]
36003500340033003200Wavelength [nm]
50° C 250° C 450° C
Figure A.17: Absorption spectra of 1-heptene.
600x103
500
400
300
200
100
0Cro
ss S
ection [cm
2m
ole
-1]
36003500340033003200Wavelength [nm]
50° C 250° C 450° C
Figure A.18: Absorption spectra of 2,4,4-trimethyl-1-pentene.
158APPENDIX A. TEMPERATURE-DEPENDENT HYDROCARBON SPECTRA
A.4 Absorption Spectra of Aromatics
200x103
150
100
50
0Cro
ss S
ectio
n [
cm
2m
ole
-1]
3400330032003100Wavelength [nm]
50° C 250° C 450° C
Figure A.19: Absorption spectra of benzene.
140x103
120
100
80
60
40
20
0Cro
ss S
ection [cm
2m
ole
-1]
360035003400330032003100Wavelength [nm]
50° C 250° C 450° C
Figure A.20: Absorption spectra of toluene.
159
160x103
120
80
40
0Cro
ss S
ectio
n [
cm
2m
ole
-1]
36003500340033003200Wavelength [nm]
50° C 250° C 450° C
Figure A.21: Absorption spectra of m-xylene.
140x103
120
100
80
60
40
20
0Cro
ss S
ection [cm
2m
ole
-1]
36003500340033003200Wavelength [nm]
50° C 250° C 450° C
Figure A.22: Absorption spectra of o-xylene.
160APPENDIX A. TEMPERATURE-DEPENDENT HYDROCARBON SPECTRA
250x103
200
150
100
50
0Cro
ss S
ectio
n [
cm
2m
ole
-1]
36003500340033003200Wavelength [nm]
50° C 250° C 450° C
Figure A.23: Absorption spectra of ethyl-benzene.
300x103
250
200
150
100
50
0Cro
ss S
ectio
n [
cm
2m
ole
-1]
36003500340033003200Wavelength [nm]
50° C 250° C 450° C
Figure A.24: Absorption spectra of 3-ethyl-toluene.
161
A.5 Absorption Spectra of Formaldehyde
800x103
600
400
200
0Cro
ss S
ectio
n [
cm
2m
ole
-1]
3800360034003200Wavelength [nm]
100° C 200° C 350° C
Figure A.25: Absorption spectra of formaldehyde.
A.6 Absorption Spectra of Ethanol
200x103
150
100
50
0Cro
ss S
ection [cm
2m
ole
-1]
36003500340033003200Wavelength [nm]
50° C 175° C 325° C
Figure A.26: Absorption spectra of ethanol.
Appendix B
Temperature-Dependent FTIR
Absorption Spectra of Gasoline
Absorption spectra were measured for 21 samples of gasoline using FTIR spectroscopy
(1 cm−1 resolution, FWHM). The details of the measurements are provided in Chap-
ter 4. Table B.1 presents calculated mole fraction of each of the samples presented
in this appendix, based on the chemical analyses that were performed. Details of the
calculations can be found in Chapter 8
162
163
Table B.1: Characteristics of gasoline samples studied using FTIR spectroscopy.
Aromatics Olefins EthanolNormal
Alkanes
Branched
Alkanes
R1 Regular 28.3 19.7 0.0 20.1 31.9
R2 Regular 20.8 7.2 0.0 27.8 44.2
R3 Regular 42.7 5.4 0.0 20.0 31.9
R4 Regular 22.3 10.1 0.0 26.1 41.5
R5 Regular 27.9 18.6 0.0 20.6 32.8
R6 Regular 26.6 18.1 0.0 21.3 33.9
R7 Regular 37.3 1.8 0.2 23.5 37.3
R8 Regular 27.5 5.8 0.5 25.6 40.7
R9 Regular 36.0 9.7 0.0 21.0 33.4
R10 Regular 27.1 2.2 10.9 23.1 36.7
R11 Regular 31.0 2.7 11.3 21.2 33.8
P1 Premium 14.9 14.2 0.0 9.9 61.1
P2 Premium 43.4 23.5 0.0 4.6 28.4
P3 Premium 7.1 5.4 0.0 12.3 75.3
P4 Premium 35.9 2.4 0.0 8.6 53.1
P5 Premium 35.2 14.7 0.0 7.0 43.1
P6 Premium 32.0 6.9 0.8 8.4 51.8
P7 Premium 22.0 2.5 2.6 10.2 62.7
P8 Premium 41.5 9.8 0.0 6.8 41.9
P9 Premium 25.3 5.6 11.0 8.1 50.0P10 Premium 27.2 4.7 11.2 8.0 49.0
Sample
IdentifierGrade
Calculated Mole Fraction [%]
164 APPENDIX B. TEMPERATURE-DEPENDENT GASOLINE SPECTRA
B.1 FTIR Absorption Spectra of Regular-Grade
Gasoline
500x103
400
300
200
100
0
Cro
ss S
ectio
n [
cm
2m
ole
-1]
36003500340033003200
Wavelength [nm]
50° C 450° C
Figure B.1: Absorption spectra of sample R1 at 50◦ and 450◦ C.
500x103
400
300
200
100
0
Cro
ss S
ectio
n [
cm
2m
ole
-1]
36003500340033003200
Wavelength [nm]
50° C 450° C
Figure B.2: Absorption spectra of sample R2 at 50◦ and 450◦ C.
165
400x103
300
200
100
0
Cro
ss S
ection [cm
2m
ole
-1]
36003500340033003200
Wavelength [nm]
50° C 450° C
Figure B.3: Absorption spectra of sample R3 at 50◦ and 450◦ C.
500x103
400
300
200
100
0
Cro
ss S
ection [cm
2m
ole
-1]
36003500340033003200
Wavelength [nm]
50° C 450° C
Figure B.4: Absorption spectra of sample R4 at 50◦ and 450◦ C.
166 APPENDIX B. TEMPERATURE-DEPENDENT GASOLINE SPECTRA
500x103
400
300
200
100
0
Cro
ss S
ection [cm
2m
ole
-1]
36003500340033003200
Wavelength [nm]
50° C 450° C
Figure B.5: Absorption spectra of sample R5 at 50◦ and 450◦ C.
500x103
400
300
200
100
0
Cro
ss S
ection [cm
2m
ole
-1]
36003500340033003200
Wavelength [nm]
50° C 450° C
Figure B.6: Absorption spectra of sample R6 at 50◦ and 450◦ C.
167
500x103
400
300
200
100
0
Cro
ss S
ection [cm
2m
ole
-1]
36003500340033003200
Wavelength [nm]
50° C 450° C
Figure B.7: Absorption spectra of sample R7 at 50◦ and 450◦ C.
500x103
400
300
200
100
0
Cro
ss S
ection [cm
2m
ole
-1]
36003500340033003200
Wavelength [nm]
50° C 450° C
Figure B.8: Absorption spectra of sample R8 at 50◦ and 450◦ C.
168 APPENDIX B. TEMPERATURE-DEPENDENT GASOLINE SPECTRA
400x103
300
200
100
0
Cro
ss S
ection [cm
2m
ole
-1]
36003500340033003200
Wavelength [nm]
50° C 450° C
Figure B.9: Absorption spectra of sample R9 at 50◦ and 450◦ C.
500x103
400
300
200
100
0
Cro
ss S
ection [cm
2m
ole
-1]
36003500340033003200
Wavelength [nm]
50° C 450° C
Figure B.10: Absorption spectra of sample R10 at 50◦ and 450◦ C.
169
500x103
400
300
200
100
0
Cro
ss S
ection [cm
2m
ole
-1]
36003500340033003200
Wavelength [nm]
50° C 450° C
Figure B.11: Absorption spectra of sample R11 at 50◦ and 450◦ C.
B.2 FTIR Absorption Spectra of Premium-Grade
Gasoline
600x103
500
400
300
200
100
0
Cro
ss S
ectio
n [
cm
2m
ole
-1]
36003500340033003200
Wavelength [nm]
50° C 460° C
Figure B.12: Absorption spectra of sample P1 at 50◦ and 460◦ C.
170 APPENDIX B. TEMPERATURE-DEPENDENT GASOLINE SPECTRA
400x103
300
200
100
0
Cro
ss S
ection [cm
2m
ole
-1]
36003500340033003200
Wavelength [nm]
50° C 450° C
Figure B.13: Absorption spectra of sample P2 at 50◦ and 450◦ C.
800x103
600
400
200
0
Cro
ss S
ection [cm
2m
ole
-1]
36003500340033003200
Wavelength [nm]
50° C 450° C
Figure B.14: Absorption spectra of sample P3 at 50◦ and 450◦ C.
171
500x103
400
300
200
100
0
Cro
ss S
ection [cm
2m
ole
-1]
36003500340033003200
Wavelength [nm]
50° C 450° C
Figure B.15: Absorption spectra of sample P4 at 50◦ and 450◦ C.
500x103
400
300
200
100
0
Cro
ss S
ection [cm
2m
ole
-1]
36003500340033003200
Wavelength [nm]
50° C 450° C
Figure B.16: Absorption spectra of sample P5 at 50◦ and 450◦ C.
172 APPENDIX B. TEMPERATURE-DEPENDENT GASOLINE SPECTRA
500x103
400
300
200
100
0
Cro
ss S
ection [cm
2m
ole
-1]
36003500340033003200
Wavelength [nm]
50° C 450° C
Figure B.17: Absorption spectra of sample P6 at 50◦ and 450◦ C.
600x103
500
400
300
200
100
0
Cro
ss S
ection [cm
2m
ole
-1]
36003500340033003200
Wavelength [nm]
50° C 450° C
Figure B.18: Absorption spectra of sample P7 at 50◦ and 450◦ C.
173
400x103
300
200
100
0
Cro
ss S
ection [cm
2m
ole
-1]
36003500340033003200
Wavelength [nm]
50° C 450° C
Figure B.19: Absorption spectra of sample P8 at 50◦ and 450◦ C.
500x103
400
300
200
100
0
Cro
ss S
ection [cm
2m
ole
-1]
36003500340033003200
Wavelength [nm]
50° C 450° C
Figure B.20: Absorption spectra of sample P9 at 50◦ and 450◦ C.
174 APPENDIX B. TEMPERATURE-DEPENDENT GASOLINE SPECTRA
500x103
400
300
200
100
0
Cro
ss S
ection [cm
2m
ole
-1]
36003500340033003200
Wavelength [nm]
50° C 450° C
Figure B.21: Absorption spectra of sample P10 at 50◦ and 450◦ C.
Appendix C
Temperature-Dependent
Absorption Cross Sections at 3.39
µm
Absorption cross sections were measured for 9 hydrocarbon species and fuel blends
using a 3.39 µm HeNe laser. The details of the measurements are provided in Chap-
ter 4. The measured cross sections are compared to previous measurements in the
following figures. The gasoline sample measured here is different than tha samples
measured in Appendix B, but details about its composition (including the relative
concentration of the top 12 species) can be found in reference [80]. For this sample,
gas chromatpgraph tests were used to identify 34 of the species present. Of the species
identified, 69% by mole were alkanes, 30% were aromatics and 1% were olefins. Note
that this particular sample contained ∼20% by mole of cyclo-pentane, which was
added to the sample to artificially adjust the octane number.
175
176 APPENDIX C. ABSORPTION CROSS SECTIONS AT 3.39 µM
Table C.1: Experimental details of HeNe cross section measurements presented inthis appendix and compared to previous measurements.
Hydrocarbon Reference Total Pressure (25o C) Uncertainty Technique
[torr] [cm2mole
-1]
Methane This Work 760 211000 3% HeNe
Yoshiyama:1996 760 253000 x HeNe
Tomita:2003 760 219000 2%* HeNe
Perrin:1989 760 225000 5% HeNe
Rothman:2004 760 214000 x Calculation
Jaynes:1969 30.4 367000 x HeNe
Sharpe:2004 760 195000 3% FTIR
Ethylene This Work 760 4590 3.5% HeNe
Rothman:2004 760 3860 x Calculation
Sharpe:2004 760 4260 3% FTIR
Hinckley:2004 760 3910 2% HeNe
Propane This Work 760 202000 3.4% HeNe
Sharpe:2004 760 212000 3% FTIR
Tsuboi:1985 760 207000 20% HeNe
Yoshiyama:1996 760 239000 x HeNe
Jaynes:1969 760 489000 x HeNe
Jaynes:1969 23 203000 x HeNe
n-heptane This Work 760 452000 3.4% HeNe
Klingbeil:2006 10 450000 4% HeNe
Sharpe:2004 760 443000 3% FTIR
Tsuboi:1985 760 465000 20% HeNe
Drallmeier:2003 650 369000 5% HeNe
Jaynes:1969 7.6 489000 x HeNe
Horning:2002 10 449000 1% HeNe
iso-octane This Work 760 473000 3.4% HeNe
Sharpe:2004 760 470000 3% FTIR
Tsuboi:1985 760 465000 20% HeNe
Drallmeier:2003 650 399000 5% HeNe
Tomita:2003 760 457000 2%* HeNe
n-decane This Work 760 546000 3.4% HeNe
Drallmeier:2003 650 159000 5% HeNe
Horning:2002 1 563000 1% HeNe
Jaynes:1969 3.04 281000 x HeNe
Gasoline This Work 760 281000** 3.2% HeNe
Jaynes:1969 15.2 257000 x HeNe
Jet-A This Work 760 438000 4.2% HeNe
Jaynes:1969 (kerosene) 2.3 281000 4% HeNe
Jaynes:1969 (JP-4) 22.8 416000 x HeNe
Jaynes:1969 (JP-5) 2.3 538000 5% HeNe
JP-10 This Work 760 900000 3.4% HeNe
*Uncertainty estimates using statistical analysis only
**Temperature of 323 K
177
C.1 Neat Hydrocarbons with Structured Spectra
400x103
300
200
100
0
Cro
ss S
ectio
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cm
2m
ole
-1]
6005004003002001000
Temperature [°C]
This Work
Rothman:2004
Jaynes:1969
Yoshiyama:1996
Tomita:2003
Perrin:1989
Sharpe:2004
Figure C.1: Absorption cross section of methane at 3392.2 nm from 28◦ to 405◦ Ccompared to the HITRAN database [40], Jaynes and Beam [30], Yoshiyama et al. [45],Tomita et al. [44], Perrin et al. [31], and Sharpe et al. [39].
10000
8000
6000
4000
2000
0
Cro
ss S
ection [cm
2m
ole
-1]
5004003002001000
Temperature [°C]
This Work Rothman:2004 Sharpe:2004 Hinckley:2004
Figure C.2: Absorption cross section of ethylene at 3392.2 nm from 26◦ to 400◦ Ccompared to the HITRAN database [40], Sharpe et al. [39], and Hinckley et al. [28].
178 APPENDIX C. ABSORPTION CROSS SECTIONS AT 3.39 µM
250x103
200
150
100
50
0
Cro
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ectio
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cm
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-1]
5004003002001000
Temperature [°C]
This Work Sharpe:2004 Tsuboi:1985 Yoshiyama:1996 Jaynes:1969 (760 torr) Jaynes:1969 (23 torr)
Figure C.3: Absorption cross section of propane at 3392.2 nm from 26◦ to 400◦ Ccompared to measurements by Sharpe et al. [39], Tsuboi et al. [47], Yoshiyama etal. [45], and Jaynes and Beam [30].
179
C.2 Neat Hydrocarbons with Unstructured Spec-
tra
500x103
400
300
200
100
0
Cro
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ectio
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cm
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ole
-1]
5004003002001000
Temperature [°C]
This Work
Sharpe:2004 (760 Torr)
Tsuboi:1985 (~760 Torr)
Drallmeier:2003 (650 Torr)
Jaynes:1969 (~7 Torr)
Horning:2002 (10 Torr)
Figure C.4: Absorption cross section of n-heptane at 3392.2 nm from 26◦ to 400◦ Ccompared to measurements by Sharpe et al. [39], Tsuboi et al. [47], Drallmeier [26],Jaynes and Beam [30], and Horning et al. [29].
180 APPENDIX C. ABSORPTION CROSS SECTIONS AT 3.39 µM
600x103
500
400
300
200
100
0
Cro
ss S
ectio
n [
cm
2m
ole
-1]
5004003002001000
Temperature [°C]
This Work
Sharpe:2004 (760 Torr)
Tomita:2003 (10 Torr)
Tsuboi:1985 (~760 Torr)
Drallmeier:2003 (650 Torr)
Figure C.5: Absorption cross section of iso-Octane at 3392.2 nm from 26◦ to 400◦ Ccompared to measurements by Sharpe et al. [39], Tomita et al. [32], Tsuboi et al. [47],and Drallmeier [26].
600x103
500
400
300
200
100
0
Cro
ss S
ection [cm
2m
ole
-1]
5004003002001000
Temperature [°C]
This Work
Drallmeier:2003 (650 torr)
Horning:2002 (<10 torr)
Jaynes:1969 (3 torr)
Figure C.6: Absorption cross section of n-decane at 3392.2 nm from 26◦ to 400◦ Ccompared to Drallmeier [26], Horning et al. [29], and Jaynes and Beam [30].
181
C.3 Blended Hydrocarbon Fuels
300x103
250
200
150
100
50
0
Cro
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ectio
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cm
2m
ole
-1]
5004003002001000
Temperature [°C]
This Work
Jaynes:1969
Figure C.7: Absorption cross section of gasoline at 3392.2 nm from 26◦ to 400◦ Ccompared to measurements by Jaynes and Beam [30]. The composition of the gasolinestudied here is described in reference [80]
600x103
500
400
300
200
100
0
Cro
ss S
ection [cm
2m
ole
-1]
5004003002001000
Temperature [°C]
This Work
Jaynes:1969 (kerosene)
Jaynes:1969 (JP-4)
Jaynes:1969 (JP-5)
Figure C.8: Absorption cross section of Jet-A at 3392.2 nm from 26◦ to 400◦ Ccompared to measurements of kerosene, JP-4 and JP-5 by Jaynes and Beam [30].
182 APPENDIX C. ABSORPTION CROSS SECTIONS AT 3.39 µM
1.0x106
0.8
0.6
0.4
0.2
0.0
Cro
ss S
ectio
n [
cm
2m
ole
-1]
5004003002001000
Temperature [°C]
Figure C.9: Absorption cross section of JP-10 at 3392.2 nm from 26◦ to 400◦ C.
Appendix D
Data Analysis Procedure for
Two-Wavelength Absorption
Measurements
When operating the DFG laser in two-wavelength mode, a simple computer routine
was designed to quickly analyze the data. This appendix provides a summary of the
procedure used to convert the raw data into two-wavelength absorbance data while
removing the time-dependent background emission. As example data, raw data will
be analyzed from shock-tube measurements of 2-methyl-butane where the laser was
switched at 200 kHz. The optical arrangement for the shock-tube experiment is shown
in Figure 6.2.
Sample raw data are shown in Figure D.1 for one complete period (i.e., 1/200 kHz
= 5 µsec). For each shock tube measurement, a baseline measurement (indicated by
the solid line in Figure D.1) is made after the shock tube is evacuated, to determine
I0(λ1) and I0(λ2). Then a second measurement (indicated by the dashed line in
Figure D.1) is made during the shock tube experiment to calculate I(λ1) and I(λ2).
The data indicated by the dashed line in Figure D.1 were measured before the arrival
of the incident shock wave (i.e., region 1), when the mixture was at room temperature.
The ratio of these measurements is used to calculate the fractional transmission and
the absorbance.
183
184 APPENDIX D. DATA ANALYSIS FOR TWO-WAVELENGTH SENSOR
The first step in analysis of the two-wavelength data is to process each 5 µsec
period, splitting the time-dependent detector signal into background signal, I(λ1)
and I(λ2). For the data in Figure D.1, the detector signal is at a minimum when
t = 0.5 µsec, and the background signal can be determined using the measured data
at this instant in time. From t = 1.6 to 2.4 µ sec, λ1 is active and from t = 3.8 to 4.6
µ sec, λ2 is active. While the near-IR signal lasers were driven with a square-wave
current pulse, the measured intensity is smoothed due to transient signal laser effects
and transient optical amplifier effects. These transient laser effects can be reduced in
the future by switching the signal lasers with an electro- or acousto-optic modulator
(to eliminate signal laser transients) and by eliminating the 2 µsec dormant period
(to eliminate the fiber amplifier transient upon re-seeding with the signal beam).
While the measured laser signals are not exactly square-wave in nature, the cal-
culated absorbance is still nearly ideal. When the background is subtracted, and the
absorbance is calculated, a flat plateau region is observed, as shown in Figure D.2
(note that the from 0 to 1.2 µsec and from 2.6 to 3.6 µsec, where the laser intensity
is near zero, have been removed to aid viewing of the useful absorbance data).
4
3
2
1
0
De
tecto
r V
olta
ge
[V
]
543210
Time [µsec]
Evacuated Shock Tube Shock Tube Filled to 0.1 atm
I(λ1) I(λ2)Background Signal
I0(λ1)
I0(λ2)
Figure D.1: Raw data for one cycle of the two-wavelength DFG laser for the evacuatedshock tube (solid line) and for the shock tube filled to 0.1 atm with a mixture of 1.5%2-methyl-butane in argon.
185
For this particular condition, each of the two wavelengths was activated for 1.5
µsec and a 0.5 µsec delay occurred between each pulse during which time the back-
ground detector signal could be subtracted. Once the raw data are acquired, each 5
µsec period is analyzed individually by a software routine. The minimum detector
voltage during the period is recorded in the background-signal data array. The mea-
sured detector signal for each of the two wavelengths is averaged over ∼0.8 µsec and
recorded in separate arrays. Then the absorbance can be calculated by subtracting
the background array from the intensity at each of the two wavelengths.
0.6
0.5
0.4
0.3
0.2
0.1
0.0
Absorb
ance
543210
Time [µsec]
Low Laser SignalAveraging
Period
Averaging Period
Low Laser Signal
Figure D.2: Calculated absorbance versus time for the data in Figure D.1.
The computer routine analyzes each 5 µsec segment in the same fashion to gener-
ate three arrays: background intensity, transmitted intensity at the first wavelength
and transmitted intensity at the second wavelength. The three arrays are displayed
in Figure D.3 (Note that the measured signal at each of the two wavelengths does not
have the background emission subtracted from it in this graph). This background sig-
nal, which is caused by ambient light from the room and also thermal emission of the
shock-heated gases, is quite large after the reflected shock wave passes even though a
narrow-band filter (60 nm FWHM) and an aperture were used to limit the amount of
thermal emission on the detector. For these data, the post-shock emission accounts
for ∼30% of the total signal because the power output of this laser (∼80 µW) is not
186 APPENDIX D. DATA ANALYSIS FOR TWO-WAVELENGTH SENSOR
significantly larger than the infrared light that passes through the aperture and filter.
Hence the correction for background emission is critical for obtaining quantitative,
high-temperature absorption measurements for this experimental arrangement. Be-
cause filters and apertures have already been employed to minimize the background
signal, the best way to further improve the signal is to increase the power of the
laser, which will increase the signal-to-background ratio. (Alternatively, narrower
band filters and better spatial filtering may also further reduce, but not eliminate,
the background emission.)This can be achieved by using the higher-power DFG lasers
that will soon be available, with an average power output for two-wavelength opera-
tion of >750 µW (a factor of ∼10 improvement).
5
4
3
2
1
0
Measure
d S
ignal [V
]
25002000150010005000
Time [µsec]
I(λ1) + BG I0(λ1) + BG
I(λ2) + BG I0(λ2) + BG
Background Signal (BG)
Reflected Shock
Incident Shock
Figure D.3: Measured background signal and laser signal at two wavelengths fora shock-tube experiment with a mixture of 1.5% 2-methyl-butane in argon. Shockconditions: P1 = 0.109 atm, T1 = 297 K, P2 = 0.505 atm, T2 = 568 K, P5 = 1.61atm, T5 = 884 K.
The background emission is subtracted from the two other measurements in a
subsequent step and this background-subtracted signal is then used in Equation 3.1
to calculate absorbance at the two wavelengths. These calculations were performed
on the data in Figure D.3 and the resulting absorbance data are plotted in Figure D.4.
187
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
Absorb
ance
25002000150010005000
Time [µsec]
α (λ1)
α (λ2)
Reflected Shock
Incident Shock
Figure D.4: Measured background signal and laser signal at two wavelengths fora shock-tube experiment with a mixture of 1.5% 2-methyl-butane in argon. Shockconditions: P1 = 0.109 atm, T1 = 297 K, P2 = 0.505 atm, T2 = 568 K, P5 = 1.61atm, T5 = 884 K.
Appendix E
Mid-IR Diagnostics to Study
Hydrocarbon Chemistry in Shock
Tubes
Mid-IR laser absorption sensors have many applications related to the detection of
hydrocarbons. Some practical applications are described in Chapters 6 through 8.
Other applications are related to more fundamental scientific studies. In this appen-
dix, preliminary experiments illustrate the potential of mid-IR absorption diagnostics
to study hydrocarbon chemistry in shock tubes. Multiple hydrocarbons are studied,
and the measured decomposition rates are compared to predictions by available ki-
netic mechanisms. Overall decomposition rates are calculated using a pseudo-first-
order assumption. In Section E.3.3, unimolecular decomposition reactions from an
n-heptane mechanism are adjusted so the modelled n-heptane data match the mea-
surements, illustrating how these data can be used to improve hydrocarbon reaction
mechanisms.
188
E.1. DETERMINATION OF DECOMPOSITION RATES 189
E.1 Determination of Hydrocarbon Decomposition
Rates Using Mid-IR Absorption Diagnostics
Time-dependent hydrocarbon mole fractions were measured in a shock tube with
post-shock temperatures sufficiently high to observe pyrolysis. A pseudo-first-order
assumption was applied to quantify the overall rate of removal for the species being
studied. An exponential-decay curve of the following form was fit to the measured
time-dependent mole fraction:
X(t) = X0e(−kt) (E.1)
where X(t) is the measured mole fraction, X0 is the initial mole fraction, t is the
time in sec and k is the overall removal rate in sec−1. For an optical absorption
measurement, the pseudo-first-order rate can be written in terms of the fractional
transmission, I/I0:
−kt = ln
(−ln
(I
I0
))+ ln
(RT
X0PLσ
)(E.2)
where R is the universal gas constant, P is the pressure, L is the path length and
T is the temperature of the gas that is being measured. Because the double natural
logarithm of the fractional transmission is calculated to determine the decomposition
rate, the measurement will not have good sensitivity if only small amounts of the
species has decomposed. This results in increased uncertainty when determining slow
decomposition rates over short time periods.
By fitting the data in this manner, the removal rate of the species was character-
ized over a range of temperatures. To compare the measurements to modelled data,
the same conditions were modelled and equation E.1 was also fit to the modelled
data. Note that the reaction pathways associated with the overall removal rate gen-
erally include both first- and second-order reactions and that this pseudo-first-order
assumption enables quantitative characterization of the species lifetime without sep-
arating first-order reactions from higher-order reactions. Comparison of the overall
190 APPENDIX E. DIAGNOSTICS FOR HYDROCARBON CHEMISTRY
removal rate of the species with the modelled removal rate is a good indicator of
the accuracy of the model, but cannot be used to infer the quantitative rates of any
specific reactions. However, it is shown in Section E.3.3 that, in some cases, the
first-order unimolecular decomposition rate of n-heptane can be inferred by fitting a
mechanism to the measured data.
E.2 Ethylene Pyrolysis
Ethylene is an important species in reaction mechanisms that model hydrocarbon
chemistry. As hydrocarbons break down into smaller species, many of the fragments
decompose into ethylene before they are eventually oxidized. For this reason, the
high-temperature chemistry of ethylene has been studied extensively and the individ-
ual reactions are well-known. Because the chemistry of ethylene has been thoroughly
characterized, it is an excellent candidate to validate the use of mid-IR optical ab-
sorption diagnostics for studying chemical reaction rates.
E.2.1 Wavelength Selection and Measurement of High-
Temperature Cross Section
Two criteria were used to select a wavelength for the ethylene diagnostic. First, a large
cross section was desired to maximize sensitivity. Second, interference absorption from
other species was studied and confirmed to be negligible. GRI-Mech 3.0 is a chemistry
mechanism that contains 53 species and 325 reactions, including nitrogen species and
reactions [81]. This mechanism was used to predict the rate of ethylene pyrolysis
and to identify the major products that could interfere with the ethylene absorption
diagnostic. Figure E.2 shows the modelled species time-history for decomposition
of 5% ethylene in argon for a temperature of 1780 K and a pressure of 5.207 atm.
The major products for this reaction are hydrogen and acetylene, neither of which
have absorption that interferes with the mid-IR absorption band of ethylene. Hence,
interfering species are not an issue for this measurement.
The absorption spectrum of ethylene is plotted in Figure A.11. The wavelength
E.2. ETHYLENE PYROLYSIS 191
140x103
120
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80
60
40
20
0
Cro
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ectio
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ole
-1]
2000150010005000
Temperature [°C]
FTIR Region 1 Region 2 Region 5 Fit to Shock Tube Data
Figure E.1: Temperature-dependent absorption cross section of ethylene at 3346.5nm. FTIR data were measured at 1 atm and and resolution of ∼0.1 nm (FWHM).Shock-tube measurements were performed with pressures ranging 0.085 to 6 atm.
3346.5 nm was chosen to maximize the absorption signal of the ethylene diagnostic
within the tuning range of our DFG lasers. The high-temperature cross section was
measured in a shock tube for temperatures up to 1617◦ C (1890 K) using a simi-
lar method to that described in Section 8.5. A certified mixture of 5.00% ethylene in
argon was used as the test gas in the shock tube and an in situ measurement of concen-
tration was not required. The ideal-shock equations provided the necessary pressure
and temperature information to convert the measured absorbance into temperature-
dependent cross sections, which are plotted in Figure E.1 over the temperature range
studied.
There is a ∼5% uncertainty in the room-temperature cross section because at the
low pressures of a typical pre-shock mixture (P1 ∼0.085 to 0.3 atm for these tests),
the measured cross section shows sensitivity to wavelength drift of the laser (∼0.1
nm for these tests) and to pressure broadening. However, the measured cross sec-
tions in region 2 and region 5 are less sensitive to these effects because the pressure is
above 1 atm where the effect of pressure broadening diminishes. The shock-tube mea-
surements of the cross section show good agreement with the temperature-dependent
192 APPENDIX E. DIAGNOSTICS FOR HYDROCARBON CHEMISTRY
5
4
3
2
1
0
Mo
le F
ractio
n [
%]
10008006004002000
Time [µsec]
Ethylene Methane*100 Hydrogen Acetylene
Figure E.2: Modelled decomposition of ethylene and formation of products for initialconcentration of 5%, initial temperature of 1780 K and initial pressure of 5.207 atm.The GRI-Mech 3.0 mechanism was used to model these reactions.
FTIR data that were measured in a heated cell.
E.2.2 Ethylene Decomposition Rates
Because the ethylene/argon pyrolysis mechanism is not complex and these reactions
have been studied extensively, these data validate the technique of using mid-IR
absorption to examine hydrocarbon removal rates. Figure E.3 shows a comparison
of the measured and pseudo-first-order fit data for an initial temperature of 1780 K
and pressure of 5.207 atm. The measured data are compared to model predictions
using the GRI-Mech 3.0 mechanism. The measurements show excellent agreement
with the model, illustrating the good sensitivity that can be achieved using mid-IR
absorption sensors. The curvature of the data on the semi-log plot is caused by
two effects. First, the second-order reactions are important for this system, even at
very early times, but as the reaction proceeds, the concentration of radical species
(i.e., H and CH3) decreases, reducing the rate of the second-order reactions. Second,
as the ethylene decomposes, thermal energy is absorbed and the decomposition rate
E.2. ETHYLENE PYROLYSIS 193
5.0
4.5
4.0
3.5
3.0
2.5
2.0
Eth
yle
ne
Mo
le F
ractio
n [
%]
10008006004002000
Time [µsec]
Measured Data GRI Mech
Pseudo-First-Order Rate = 1805 sec-1
Pseudo-First-Order Fit ± 25%
Figure E.3: Measured, modelled, and fit ethylene concentration for initial mole frac-tion of 5% in argon, initial temperature of 1780 K and initial pressure of 5.207 atm.The overall decomposition rate inferred from the measured data was 1805 sec−1.
decreases. To reduce these effects, additional measurements could be made with lower
ethylene concentrations, which would reduce the effect of the second-order reactions
and reduce the amount of temperature change as the ethylene decomposes.
A sensitivity analysis was performed to identify the most important reactions in
the ethylene pyrolysis experiments. The sensitivity is calculated using the following
equation:
S =
(dX
dki
ki
X
)
t
(E.3)
where X is the species mole fraction (of ethylene in this case) and ki is the reaction
rate and the subscript t indicates that these values are recalculated for each instant
in time. A large-magnitude sensitivity (either positive or negative) indicates that the
the modelled species concentration is highly dependent on a particular reaction rate.
Results of a sensitivity analysis are shown in Figure E.4 for an initial concentra-
tion of 5% ethylene in argon, an initial temperature of 1780 K and an initial pressure
194 APPENDIX E. DIAGNOSTICS FOR HYDROCARBON CHEMISTRY
of 5.207 atm. This figure shows that the measurement is sensitive to unimolecular
decomposition as well as several second-order reactions for times longer than ∼ 10
µsec. Therefore, the measured time-dependent ethylene concentration in Figure E.3
provides some confirmation of the overall kinetic model, but cannot be used to infer a
specific reaction rate. Instead, the pseudo-first-order decomposition rate is reported
and this rate is recognized as being dependent on first-order and second-order reac-
tions.
-0.15
-0.10
-0.05
0.00
0.05
0.10
0.15
Se
nsitiv
ity
10008006004002000
Time [µsec]
H+C2H2(+M)<=>C2H3(+M) H+C2H3(+M)<=>C2H4(+M) H+C2H3<=>H2+C2H2 H+C2H4<=>C2H3+H2 C2H4(+M)<=>H2+C2H2(+M)
Figure E.4: Sensitivity analysis of ethylene pyrolysis for initial mole fraction of 5%in argon, initial temperature of 1780 K and initial pressure of 5.207 atm.
These measurements were performed for temperatures as high as 1890 K (1617◦ C)
and the pseudo-first-order analysis described in Section E.1 was used to characterize
the removal rates and compare them to predictions using the GRI-Mech 3.0 mecha-
nism. This comparison, shown in Figure E.5, shows excellent agreement between the
modelled and measured removal rates of ethylene. Next, the more complex pyrolysis
of n-heptane is examined.
E.3. N-HEPTANE PYROLYSIS 195
102
2
4
6
810
3
2
4
6
810
4
Re
mo
va
l R
ate
[se
c-1
]
0.600.580.560.540.52
1000/T [1/K]
Pseudo-1st-Order Fit to Measurements
Pseudo-1st-Order Fit to GRI-Mech 3.0
Figure E.5: Measured and modelled ethylene removal rates for mixtures of 5% eth-ylene in argon at ∼6 atm with temperatures ranging from 1680 to 1890 K. TheGRI-Mech 3.0 mechanism was used to model the overall removal rate.
E.3 n-Heptane Pyrolysis
n-Heptane is an important hydrocarbon species because it is commonly used in fuel
surrogates for gasoline and jet fuels. In Chapter 6, a two-wavelength n-heptane sen-
sor was shown to have a fast time response and good sensitivity to temperature and
concentration. In this section, data from that sensor are used to study the decompo-
sition of n-heptane at high temperatures. First, a kinetic model is used to predict the
interfering decomposition products. Then it is shown that the chosen wavelengths
maximize the signal from n-heptane while avoiding many of the strong absorption fea-
tures from the product species. The measured removal rate of n-heptane is compared
to model predictions using a mechanism developed at Princeton University by Chaos
et al. [82], revealing that the mechanism underpredicts n-heptane removal rates. The
unimolecular decomposition rates in the Chaos mechanism are then adjusted to match
the measured n-heptane time-history, showing good agreement with values reported
196 APPENDIX E. DIAGNOSTICS FOR HYDROCARBON CHEMISTRY
by Davidson et al. [83]
E.3.1 Wavelength Selection
Pyrolysis of ethylene at high temperatures results primarily in the formation of acety-
lene and hydrogen, but pyrolysis of n-heptane is considerably more complex and leads
to the formation of many product species including ethylene, propene, methane, and
ethane. Because each of these product species absorbs mid-IR light, it is important
to understand the magnitude of interference from the product species and to select
wavelengths that maximize the signal-to-interference ratio for n-heptane.
600x103
500
400
300
200
100
0
Cro
ss S
ectio
n [
cm
2m
ole
-1]
3600355035003450340033503300
Wavelength [nm]
n-Heptane Ethylene Propene Ethane Methane
Figure E.6: FTIR spectra of n-heptane (resolution of ∼1 nm (FWHM)) and itsprimary pyrolysis products (resolution of ∼0.1 nm (FWHM)). The spectra were mea-sured at 450◦ C with a total pressure of 1 atm and mole fraction of ∼ 1% in nitrogen.Arrows indicate the wavelengths chosen for this sensor (3410 and 3433 nm).
The measured absorption spectra of n-heptane and its primary pyrolysis products
are compared in Figure E.6. The absorption spectrum of methane exhibits resolved
structure. The spectra of ethylene and ethane exhibit some broadband absorption
with some structured features and the spectra of n-heptane and propene show only
broadband absorption. The wavelengths selected for this sensor (3410 and 3433 nm)
avoid the narrow absorption features of methane, ethane and ethylene. However, the
E.3. N-HEPTANE PYROLYSIS 197
broad absorption features from these species cannot be completely avoided. Instead,
the absorption from n-heptane is maximized while interference from these species is
minimized. Note that the primary interfering hydrocarbon is ethylene, which exhibits
weak absorption at the selected wavelengths.
1.0
0.8
0.6
0.4
0.2
0.0
Mo
le F
ractio
n [
%]
10008006004002000
Time [µsec]
n-Heptane Ethylene Propene Ethane Methane
0.8
0.6
0.4
0.2
0.0A
bso
rba
nce
10008006004002000
Time [µsec]
n-Heptane Ethylene Propene Ethane Methane
Figure E.7: Modelled pyrolysis products (left) and absorbance (right) at 3410 nm for0.737% n-heptane in argon at 1258 K and 1.832 atm.
Figure E.7 shows the time-dependent concentration and absorbance of n-heptane
and its major product species for 0.737% n-heptane in argon at 1258 K and 1.832
atm. This reaction was modelled using a recent mechanism by Chaos et al. [82],
which was developed for modelling high-temperature chemistry of primary fuels (e.g.,
n-heptane and iso-octane) and contains 107 species and 720 reactions. The most
prevalent hydrocarbon formed in this reaction is ethylene. Other important species
include methane, ethane, and propene. By comparing the absorption spectra of n-
heptane and its decomposition products, wavelengths were selected to minimize the
effect of interference from these species. From this figure, it is evident that interference
absorption is small for early times.
E.3.2 n-Heptane Pyrolysis Measurements
Sample time-dependent measurements of n-heptane concentration are shown in Fig-
ure E.8. The measured overall removal rate is ∼30% faster than the Chaos mechanism
198 APPENDIX E. DIAGNOSTICS FOR HYDROCARBON CHEMISTRY
predicts, which is a reasonable degree of accuracy for this complex system. The mag-
nitude of interference from the product species was estimated using the modelled
reaction products in Figure E.7, and the absorption cross section data in Figure E.6.
This interference was subtracted from the raw concentration measurements and the
corrected data are also plotted in Figure E.8. The interference is time-dependent
and after 1 msec represents only ∼15% of the measured concentration. Note that
correcting for the interference increases the discrepancy between the model and mea-
surements.
0.8
0.6
0.4
0.2
0.0
n-H
epta
ne M
ole
Fra
ction [%
]
10008006004002000
Time [µsec]
Current Measurements Current Measurements - Interference Chaos et al. (2007)
Figure E.8: Measured and modelled species time-history of n-heptane for a temper-ature of 1258 K, a pressure of 1.832 atm and concentration of 0.737% n-heptane inargon.
A pseudo-first-order fit was applied to the data in Figure E.8 to determine the over-
all decomposition rate of n-heptane. The results of the fit are displayed in Figure E.9.
The fit shows good agreement with the data for short times, but the measurements
deviate from the fit at longer times, because, as with the ethylene measurements,
second-order reaction rates decrease and the temperature decreases as the n-heptane
decomposes.
Using measurements like those in Figure E.8, which were made over a range of
temperatures, removal rates were extracted and compared to modelled data using
E.3. N-HEPTANE PYROLYSIS 199
0.8
0.7
0.6
0.5
0.4
0.3
0.2
n-H
epta
ne M
ole
Fra
ction [%
]
10008006004002000
Time [µsec]
Current Measurements Current Measurements - Interference
Pseudo-1st-Order Rate = 443 1/sec
Pseudo-1st-Order Rate ± 20%
Figure E.9: Measured, corrected, and fit n-heptane mole fraction for an initial tem-perature of 1258 K, pressure of 1.832 atm and concentration of 0.737% n-heptane inargon.
the pseudo-first-order assumption. The results of this comparison are plotted in Fig-
ure E.10 for temperatures ranging from 1140 to 1287 K. Over this temperature range,
the measured removal rate is 20 to 50% faster than the modelled rate, suggesting that
the measurements can be used to improve the mechanism. Uncertainties in the Chaos
mechanism for the simple unimolecular decomposition of n-heptane and H-abstraction
reactions are not given by the authors, though a previous comparison of the decom-
position rate of n-heptane by Davidson et al. shows that variations from mechanism
to mechanism can easily be larger than a factor of 3 [83].
E.3.3 Unimolecular Decomposition Rates of n-Heptane
A sensitivity analysis was performed using the Chaos mechanism to determine the
reactions that the n-heptane concentration measurement is most sensitive to. The
results of the sensitivity analysis are displayed in Figure E.11. Of the seven most
important reactions, the three most influential belong to the unimolecular decompo-
sition group (i.e., n-heptane⇒products). The specific reactions are those enclosed in
200 APPENDIX E. DIAGNOSTICS FOR HYDROCARBON CHEMISTRY
101
102
103
104
105
Rem
oval R
ate
[sec
-1]
0.900.850.800.750.70
1000/T [1/K]
Pseudo-1st-Order Fit to Corrected Data
Pseudo-1st-Order Fit to Chaos et al. (2007)
Figure E.10: Measured and modelled temperature-dependent removal rate for ∼0.8%n-heptane in argon at ∼1.8 atm, assuming pseudo-first-order decomposition. Themechanism by Chaos et al. [82] was used to model the reaction.
a box in Figure E.11. Some sensitivity to the bimolecular reaction of n-heptane with
H and CH3 is found. As a simple example of the use of the current data, the three
unimolecular decomposition rates in the mechanism can be adjusted to match our
data.
To ascertain improved values for the three dominant unimolecular decomposition
rates in the Chaos mechanism, the rates were simultaneously rescaled (i.e., all rates
were scaled equally from their initial values) so the modelled heptane time-history
matched the measured data. Sample data plotted in Figure E.12 show that the model
is brought into agreement with the measurements by rescaling these unimolecular de-
composition rates in the mechanism. Thus, the measured concentration time-history
can be used to infer the overall unimolecular decomposition rate by adjusting the
model to fit the measured data. Note that the mechanism was fit to the measurements
which have been corrected for interference absorption. The interference absorption
imposes ∼20% uncertainty in the adjusted rate.
By repeating this analysis for the other experiments, the overall temperature-
dependent unimolecular decomposition rate of n-heptane can be compared to other
E.3. N-HEPTANE PYROLYSIS 201
-0.12
-0.10
-0.08
-0.06
-0.04
-0.02
0.00
0.02
0.04
Se
nsitiv
ity
5004003002001000
Time [µsec]
H+C2H
4(+M)<=>C
2H
5(+M)
nC7H16+H<=>C7H15+H2
nC7H16+CH3<=>C7H15+CH4
C7H15=>C4H8=1+nC3H7
nC7H16<=>C6H13+CH3
nC7H16<=>C5H11+C2H5
nC7H16<=>pC4H9+nC3H7
Figure E.11: Sensitivity analysis for the pyrolysis of 0.737% n-heptane in argon at1258 K and 1.83 atm. Reaction enclosed in the box were adjusted to fit the measureddata shown in Figure E.12.
0.8
0.6
0.4
0.2
0.0
n-H
ep
tan
e M
ole
Fra
ctio
n [
%]
10008006004002000
Time [µsec]
Current Measurements Chaos et al. (2007) Original Chaos et al. (2007) Adjusted
Figure E.12: Measured and fit decomposition of 0.737% n-heptane in argon for atemperature of 1258 K and a pressure of 1.83 atm. Dashed lines represent calculationsusing the original and adjusted Chaos models [82].
202 APPENDIX E. DIAGNOSTICS FOR HYDROCARBON CHEMISTRY
measurements. In Figure E.13, the sum of the three rates inferred here by adjusting
the Chaos mechanism are compared to the single rate determined by Davidson et
al. [83] using methyl concentration time-histories (Note that the sum of the three
rates in the Chaos mechanism is equivalent to the single rate reported by Davidson et
al.). Additionally, the predictions from the original Chaos mechanism are indicated
by the solid line.
The overall decomposition rate inferred from the mid-IR diagnostic is consistent
with the Davidson measurements and decomposition rate proposed by Davidson:
k(T )[sec−1] = 9.00× 1014[sec−1]e−67300[cal/mole]
RT (E.4)
The low-temperature data point does not match expectations due to larger uncertain-
ties in the measured rate at low temperature. These mid-IR measurements extend
the range of temperatures for which there are measured rate coefficient data.
101
102
103
104
105
De
co
mp
ositio
n R
ate
[se
c-1
]
0.900.850.800.750.700.65
1000/T [1/K]
Davidson et al. (2007)
Adjusted Rate
Original Mechanism
k[sec-1
] = 9.00x1014
[sec-1
] e-67300 [cal/mole]/RT
Figure E.13: Comparison of the adjusted decomposition rate with that predicted bythe original Chaos mechanism [82] at 1-2 atm with mole fractions of 0.7 to 0.9%n-heptane in argon and also compared with measurements by Davidson et al. [83] at1-2 atm with mole fractions of 0.01 to 0.02% in argon.
E.4. N-DODECANE PYROLYSIS 203
E.4 n-Dodecane Pyrolysis
Chapter 9 describes a two-wavelength diagnostic that was used to measure n-dodecane
vapor concentration in a shock tube. Studies were performed with mixtures of n-
dodecane vapor in argon as well as shock-evaporated n-dodecane aerosol in argon. At
high temperatures (T>1150 K), the n-dodecane was found to pyrolyze. Figure 9.3
shows sample absorbance measurements at 3409.0 and 3432.4 nm for a shock-heated
mixture of n-dodecane vapor in argon for an experiment where the temperature was
sufficiently high to cause measurable decomposition. In this section, high-temperature
time-resolved data such as those shown in Figure 9.3, provide quantitative concen-
tration measurements which are used to infer pseudo-first-order removal rates for the
vapor and aerosol shocks and these rates are then compared to predictions of two
chemistry models.
E.4.1 Kinetic Models for n-Dodecane
The first of the two reaction mechanisms, described by Ranzi et al. [84], contains 280
species and 7800 reactions. The second mechanism, from Zhang et al. [85,86], contains
208 species and 1087 reactions. Both of these mechanisms were developed to model
JP-8 chemistry and contain reactions and species involved in n-dodecane pyrolysis
because n-dodecane is often used as a jet-fuel surrogate. The two mechanisms were
used here to model the chemistry of n-dodecane. An exponential decay was fit to the
modelled time-dependent n-dodecane mole fraction to quantify the overall removal
rate and compare it to the measurements. Additionally, the Zhang mechanism was
used to perform a sensitivity analysis and to model the formation of interfering species.
E.4.2 Determination of Decomposition Rates
The removal rates of n-dodecane were measured for both vapor- and aerosol-loading
of the shock tube using argon as the bath gas (refer to Chapter 9 for representative
data). The Zhang mechanism was used to identify and estimate the concentration
of the interfering species. For the conditions studied here, the mechanism indicated
204 APPENDIX E. DIAGNOSTICS FOR HYDROCARBON CHEMISTRY
that the primary hydrocarbon reaction products for n-dodecane pyrolysis are ethyl-
ene, propene, butene, hexene, methane, pentene and ethane. Using our library of
high-temperature FTIR spectra of hydrocarbons (See Appendix A), the interference
absorption from each of these species was calculated, except for hexene, where the in-
terference was estimated based on the absorption spectrum of heptene. The measured
n-dodecane concentration data were then corrected for the predicted interference ab-
sorption and it was found that after ∼50% of the n-dodecane has decomposed, inter-
ference absorption constitutes ∼20% of the absorption signal. The pseudo-first-order
analysis was applied to the corrected data to quantify the overall removal rate of the
n-dodecane. Sample data are shown in Figure E.14. By subtracting the estimated
interference absorption, the inferred decomposition rate increased by ∼25%. At the
low concentrations used for these experiments, a quasi-linear removal of n-dodecane
is expected at early times, and this is manifested during the first ∼400 µsec for the
data Figure E.14.
60x10-3
50
40
30
20
Mo
le F
racti
on
[%
]
5004003002001000
Time[µsec]
Current Measurements
Current Measurements - Interference
Pseudo-1st-Order Rate = 1801 1/sec
Pseudo-1st-Order Rate ± 25%
Figure E.14: Measured and corrected n-dodecane mole fraction for initial temperatureof 1226 K, pressure of 6.10 atm and n-dodecane concentration of 0.058% in argon.These data were taken using a gaseous mixture (i.e., no aerosol was present in theinitial mixture). A pseudo-first-order fit to the corrected data is indicated by thedashed line.
To compare the measurements to the two mechanisms, an exponential-decay curve
E.4. N-DODECANE PYROLYSIS 205
was also fit to the modelled time-dependent n-dodecane concentration for the same
conditions. The results of the pseudo-first-order analysis are plotted in Figure E.15.
The figure shows that the overall removal rate predicted by the Ranzi mechanism [84]
is approximately three times higher than the measurement while the rate predicted by
the Zhang mechanism [85, 86] shows reasonable agreement at low temperatures, but
deviates by ∼50% at high temperatures. The Zhang mechanism predicts that higher-
order reactions contribute significantly to n-dodecane removal, while unimolecular
decomposition accounts for only ∼35% of the n-dodecane removal. Thus, just as
with the measurements of n-heptane and ethylene, the deviation from the pseudo-
first-order fit seen in Figure E.14 can be attributed to a decrease in the rate of the
second-order reactions and decrease in temperature as the n-dodecane decomposes.
101
102
103
104
105
Rem
oval
Rate
[se
c-1
]
0.950.900.850.800.75
1000/T [1/K]
Zhang et al.
Ranzi et al.
Present Work (Vapor)
Present Work (Aerosol)
Present Work (Fit)
Figure E.15: Measured and Modelled temperature-dependent removal rate of n-dodecane for pressures ranging from 1.5 to 7 atm and mole fractions of 0.05 to 0.5%.assuming pseudo-first-order behavior. The measured rates have been corrected forinterference absorption by other hydrocarbon species.
A sensitivity analysis was performed using the Zhang mechanism to understand
the important reactions in the pyrolysis of n-dodecane. The sensitivity analysis,
206 APPENDIX E. DIAGNOSTICS FOR HYDROCARBON CHEMISTRY
plotted in Figure E.16, shows that the n-dodecane concentration is sensitive to uni-
molecular decomposition reactions, but is also strongly sensitive to two competing
reactions involving C3H7. Thus, the current data could not be used to precisely de-
termine the unimolecular decomposition rate. Future experiments aimed at directly
determining the unimolecular decomposition rate for n-dodecane would require ei-
ther lower reactant concentrations (to reduce the sensitivity of the determination to
secondary reactions) or improved knowledge of C3H7/C3H6 reaction rates.
-0.2
-0.1
0.0
0.1
0.2
Se
nsitiv
ity
5004003002001000
Time [µsec]
NC3H7(+M)=C2H4+CH3(+M) NC3H7=>H+C3H6 NC12H26=C2H5+C10H21-1 NC12H26=NC3H7+C9H19-1 NC12H26=PC4H9+C8H17-1 NC12H26=C5H11-1+C7H15-1 NC12H26=C6H13-1+C6H13-1
Figure E.16: Sensitivity analysis for n-dodecane pyrolysis using the Zhang mecha-nism [85,86] with initial temperature of 1226 K, pressure of 6.10 atm and n-dodecaneconcentration of 0.058% in argon. These data were measured using a gaseous mixture(i.e., no aerosol was present in the initial mixture).
E.5 Pyrolysis of Multiple Hydrocarbon Species
High-temperature shock-tube measurements of 13 hydrocarbon species are described
in Chapter 8. The primary purpose of those measurements was to determine the
temperature-dependent cross sections at specific wavelengths. However, many of the
tests were performed at temperatures high enough to observe pyrolysis. While the
E.5. PYROLYSIS OF MULTIPLE HYDROCARBON SPECIES 207
measurements were performed at limited temperatures, the data are useful because
the removal rates of many of these species have never been measured.
The wavelengths chosen for the measurements were 3366.7 nm. This wavelength
was selected to avoid narrow absorption features from methane and water and be-
cause it provides good sensitivity for gasoline measurements. Once the temperature-
dependent absorption cross sections were determined, a polynomial was fit to the data
and the time-dependent mole fraction was measured for each of the experiments using
the measured absorbance. Temperature and pressure were assumed to be constant
for these tests and a pseudo-first-order assumption was used to quantify the overall
removal rate. The mole fractions of the species were typically 0.7 to 1.8% in argon
with a post-shock pressure of approximately 1.5 atm.
The removal rates are plotted in Figure E.17. Figure E.17-A shows the measured
removal rates for several branched alkanes and normal alkanes. The lines indicate
Arrhenius curve fits to the measurements from the previous sections. Figure E.17-B
shows the removal rates for normal and branched olefins as well as ethanol. Ethylene
was not added to these plots because the pyrolysis rate of ethylene is very low at
these temperatures.
For a particular structural class, the removal rate increases with increasing mole-
cular size with the exception of 2-methyl-pentane which exhibits a slower removal
rate than 2-methyl-butane. For species with multiple measurements (i.e., iso-octane
and 1-heptene), the data appear to follow an Arrhenius form. These data can be
used to improve chemistry models of hydrocarbon pyrolysis by adjusting the relevant
rate parameters in the reaction mechanism. Some analysis was performed to attempt
to determine a decomposition rate. However, it was generally found that the mea-
surements were sensitive to first- and second-order reactions, making it difficult to
extract a rate for a specific set of reactions. If additional measurements were per-
formed at sufficiently low concentrations, the second-order reactions would become
less significant and unimolecular decomposition rates could be determined.
208 APPENDIX E. DIAGNOSTICS FOR HYDROCARBON CHEMISTRY
A
101
2
4
6
102
2
4
6
103
2
4
6
104
Rem
oval R
ate
[sec
-1]
0.950.900.850.800.75
1000/T [1/K]
IsoOctane
3-Methyl-Hexane
2-Methyl-Pentane
2-Methyl-Butane
nPentane
n-Heptane n-Dodecane
B
101
2
4
6
102
2
4
6
103
2
4
6
104
Re
mo
va
l R
ate
[se
c-1
]
0.950.900.850.800.75
1000/T [1/K]
1-heptene
2-methyl-2-pentene
cis-2-pentene
1-butene
Ethanol
Figure E.17: Measured overall removal rate for multiple alkanes (A) as well as olefinsand ethanol (B) for pressures ranging from 1 to 2 atm and mole fractions of 0.5 to2%.
E.6. SUMMARY 209
E.6 Summary
Mid-IR absorption diagnostics were used in shock-tube measurements to determine
decomposition rates of various hydrocarbon species that are important for under-
standing fuel chemistry. Overall removal rates for the species were compared to avail-
able models and, for n-heptane, this data was used to infer the rate of unimolecular
decomposition. A sensitivity analysis revealed that the overall removal rate is primar-
ily sensitive to unimolecular decomposition, but two bimolecular reactions are also
important. Sensitivity analyses for other species indicated that second-order reactions
were important in the pyrolysis experiments. To reduce sensitivity to second-order
reactions, lower initial concentrations are required for the species of interest to mini-
mize the concentration of radicals (i.e., CH3 and H), thereby reducing sensitivity to
second-order reactions. Reducing the hydrocarbon concentration will have the addi-
tional benefit of maintaining the post-shock temperature as the species react in the
system.
Future work using mid-IR measurements to determine decomposition rates of hy-
drocarbons should be performed in two stages. First, high-concentration shock tube
measurements should be used to accurately determine the temperature-dependent ab-
sorption cross section at the wavelength of interest. Then, low-concentration mixtures
should be used to measure the decomposition rate at high temperatures to isolate the
unimolecular decomposition rates. This could be combined with other diagnostics
(e.g., an ethylene diagnostic at ∼10.6 µm or a methyl diagnostic near 216 nm) to
observe reaction intermediates and products, revealing species evolution throughout
the decomposition process.
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