MID-IR LASER ABSORPTION DIAGNOSTICS FOR HYDROCARBON VAPOR...

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




(Jay B. Jeffries)




(Chris Edwards)

Approved for the University Committee on Graduate Studies.

iii

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


5.3.2 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


9.1.2 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . 113

9.1.3 Measured Cross Sections at High-Temperatures . . . . . . . . 116

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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

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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


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


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


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.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.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.


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.


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


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


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


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.


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


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


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


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.


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


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.


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.


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.


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


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]


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.


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


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)


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.


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


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


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


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.


A

500x103

400

300

200

100

0

Cro

ss S

ectio

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cm

2m

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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


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.


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

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ectio

n [

cm

2m

ole

-1]

5004003002001000

Temperature [°C]

This Work (HeNe)

This Work (FTIR)


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)


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.


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


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


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.


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


scattering only

Two-Wavelength DFG Laser


and vapor absorption

Near-IR Laser


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


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


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


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


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


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.


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


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.


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


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


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


6.2.2 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


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]


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.


A

140x10-9

120

100

80

60

40

20

0

Concentr

ation [m

ole

/cc]

4003002001000-100

Time [µsec]


B

1400

1200

1000

800

600

400

200

0

Te

mp

era

ture

[K

]

4003002001000-100

Time [µsec]


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.


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.


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.


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


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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


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Main Fuel

Arrival

Main Fuel

Arrival

Residual

Fuel

Residual

Fuel

Detonation

Arrival

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Arrival

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Arrival

Residual

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Residual

Fuel

Detonation

Arrival

Eth

yle

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Mo

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Eth

yle

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Mo

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ract

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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.


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


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


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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


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


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.

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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.


8.1.3 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


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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.


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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.


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.


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B

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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.


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.


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

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.


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


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.


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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100

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Modelle

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6005004003002001000

Measured Cross Section [cm2mole

-1]

3366.4 nm 3392.23 nm 3471 nm

500x103

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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.


1.0x106

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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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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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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.

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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.


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400

300

200

100

0

Cro

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ectio

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cm

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ole

-1]

140012001000800600400200

Temperature [K]


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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100

0

Cro

ss S

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140012001000800600400200

Temperature [K]


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.



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


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


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.


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.


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


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


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.


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.


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.


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)


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


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.


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


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


A

1600

1400

1200

1000

800

600

400

200

0

Te

mp

era

ture

[K

]

-400 -200 0 200 400

Time [µsec]


B

250x10-9

200

150

100

50

0

Co

nce

ntr

atio

n [

mo

le/c

c]

-400 -200 0 200 400

Time [µsec]


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.


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


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


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.

Bibliography

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[2] G.D. Roy, S.M. Frolov, A.A. Borisov, and D.W. Netzer. Pulse detonation propul-

sion: Challenges, current status, and future perspective. Progress in Energy and

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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

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3600340032003000Wavelength [nm]

50° C 250° C 450° C

Figure A.1: Absorption spectra of methane.

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0.0Cro

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36003500340033003200Wavelength [nm]

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Figure A.2: Absorption spectra of ethane.

149

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36003500340033003200Wavelength [nm]

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Figure A.3: Absorption spectra of n-pentane.

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36003500340033003200Wavelength [nm]

50° C 250° C 450° C

Figure A.4: Absorption spectra of n-heptane.


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36003500340033003200Wavelength [nm]

100° C 250° C 450° C

Figure A.5: Absorption spectra of n-dodecane.

151

A.2 Absorption Spectra of Branched Alkanes

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50° C 250° C 450° C

Figure A.6: Absorption spectra of 2-methyl-propane.

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36003500340033003200Wavelength [nm]

50° C 250° C 450° C

Figure A.7: Absorption spectra of 2-methyl-butane.


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36003500340033003200Wavelength [nm]

50° C 250° C 450° C

Figure A.8: Absorption spectra of 2-methyl-pentane.

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50° C 250° C 450° C

Figure A.9: Absorption spectra of 3-methyl-hexane.

153

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50° C 250° C 450° C

Figure A.10: Absorption spectra of 2,2,4-trimethyl-pentane (iso-octane).


A.3 Absorption Spectra of Olefins

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Figure A.11: Absorption spectra of ethylene.

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360035003400330032003100Wavelength [nm]

50° C 250° C 450° C

Figure A.12: Absorption spectra of propene.

155

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36003500340033003200Wavelength [nm]

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Figure A.13: Absorption spectra of 1-butene.

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Figure A.14: Absorption spectra of cis-2-pentene.


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Figure A.15: Absorption spectra of 2-methyl-2-butene.

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Figure A.16: Absorption spectra of 2-methyl-2-pentene.

157

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Figure A.17: Absorption spectra of 1-heptene.

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36003500340033003200Wavelength [nm]

50° C 250° C 450° C

Figure A.18: Absorption spectra of 2,4,4-trimethyl-1-pentene.


A.4 Absorption Spectra of Aromatics

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3400330032003100Wavelength [nm]

50° C 250° C 450° C

Figure A.19: Absorption spectra of benzene.

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360035003400330032003100Wavelength [nm]

50° C 250° C 450° C

Figure A.20: Absorption spectra of toluene.

159

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Figure A.21: Absorption spectra of m-xylene.

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36003500340033003200Wavelength [nm]

50° C 250° C 450° C

Figure A.22: Absorption spectra of o-xylene.


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50° C 250° C 450° C

Figure A.23: Absorption spectra of ethyl-benzene.

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Figure A.24: Absorption spectra of 3-ethyl-toluene.

161

A.5 Absorption Spectra of Formaldehyde

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3800360034003200Wavelength [nm]

100° C 200° C 350° C

Figure A.25: Absorption spectra of formaldehyde.

A.6 Absorption Spectra of Ethanol

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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

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Wavelength [nm]

50° C 450° C

Figure B.1: Absorption spectra of sample R1 at 50◦ and 450◦ C.

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165

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36003500340033003200

Wavelength [nm]

50° C 450° C



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36003500340033003200

Wavelength [nm]

50° C 450° C


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167

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169

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36003500340033003200

Wavelength [nm]

50° C 450° C


B.2 FTIR Absorption Spectra of Premium-Grade

Gasoline

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36003500340033003200

Wavelength [nm]

50° C 460° C

Figure B.12: Absorption spectra of sample P1 at 50◦ and 460◦ C.


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36003500340033003200

Wavelength [nm]

50° C 450° C


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50° C 450° C


171

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Wavelength [nm]

50° C 450° C


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Wavelength [nm]

50° C 450° C



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36003500340033003200

Wavelength [nm]

50° C 450° C


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173

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Wavelength [nm]

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36003500340033003200

Wavelength [nm]

50° C 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


Tomita:2003 760 457000 2%* HeNe

n-decane This Work 760 546000 3.4% 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

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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].

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8000

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Cro

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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].


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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

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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].


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This Work


Tomita:2003 (10 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].

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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

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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]

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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].


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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

100

80

60

40

20

0

Cro

ss S

ectio

n [

cm

2m

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


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


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


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


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]


0.8

0.6

0.4

0.2

0.0A

bso

rba

nce

10008006004002000

Time [µsec]


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


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


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


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


-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].


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


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

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105

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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,


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

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0.0

0.1

0.2

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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.


A

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IsoOctane

3-Methyl-Hexane

2-Methyl-Pentane

2-Methyl-Butane

nPentane

n-Heptane n-Dodecane

B

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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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