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This dissertation is online at: http://purl.stanford.edu/zz406xz1522

© 2016 by Shengkai Wang. All Rights Reserved.

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

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ii



http://purl.stanford.edu/zz406xz1522

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

Ronald Hanson, Primary Adviser


Craig Bowman


Hai Wang

Approved for the Stanford University Committee on Graduate Studies.

Patricia J. Gumport, Vice Provost for Graduate Education

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

iii

v

Abstract

The world’s ever-increasing needs for energy, currently fulfilled primarily by the

combustion of hydrocarbon fuels, are demanding development of more efficient and

cleaner combustion processes, which ultimately requires improved knowledge of

fundamental combustion kinetics. Present in the combustion of most hydrocarbon fuels,

aldehydes are important intermediate species that hold key information to such

knowledge. Recognizing the critical role of aldehydes in combustion research, the current

study presents (1) an advanced aldehydes diagnostic system for use in combustion

environments, (2) a set of improved rate constant measurements for several key reactions

of aldehydes, and (3) a toolbox that will facilitate future kinetics studies of aldehydes.

A system of continuous-wavelength (CW) laser absorption diagnostic methods was

developed for the quantitative measurement of formaldehyde (CH2O) and acetaldehyde

(CH3CHO) in shock tube kinetic studies. Investigation of the high-temperature CH2O

spectrum showed that the optimal wavelength for CH2O detection using commercially

available lasers was near 2896 cm−1. By exploiting the structural difference between the

absorption spectra of CH2O and that of broadband interfering species, the current study

proposed a two-color (2895.92 and 2895.60 cm−1) interference-free detection scheme for

CH2O sensing in combustion environments. A third color (32601.10 cm−1) was also

added to develop a UV/IR detection scheme for combined CH3CHO/CH2O

measurements. Aldehyde absorption cross-sections at all three colors were measured

behind reflected shock waves over a wide range of temperatures (600–1800 K) and

pressures (0.8–3.6 atm), with an uncertainty of ±5%. The diagnostic system was then

validated in two well-controlled experiments, and demonstrated in shock tube pyrolysis

experiments of 1,3,5-trioxane, CH2O and CH3CHO.

The rate constant of acetaldehyde thermal dissociation, CH3CHO (+M) = CH3 + HCO

(+M), was measured behind reflected shock waves at temperatures of 1273 - 1618 K

using a sensitive CO diagnostic. Example simulations of existing reaction mechanisms

updated with the current rate constant values demonstrated substantial improvements

with regard to the acetaldehyde pyrolysis chemistry.

vi

The rate constant of the H-abstraction reaction of formaldehyde (CH2O) by hydrogen

atoms (H), CH2O + H = H2 + HCO, was also studied behind reflected shock waves using

the same CO absorption diagnostic, over temperatures of 1304–2006 K. These

experiments were carefully designed to maintain relatively constant H radical

concentrations, which significantly boosted the measurement sensitivity of the target

reaction and suppressed the influence of interfering reactions. Compared to previous

studies, the current work has significantly reduced the measurement uncertainty.

The overall rate constants of the H-abstraction reactions of 10 different aldehydes,

namely formaldehyde (CH2O), acetaldehyde (CH3CHO), propionaldehyde (C2H5CHO)

and n-butyraldehyde (n-C3H7CHO), isobutyraldehyde (i-C3H7CHO), n-valeraldehyde (n-

C4H9CHO), isovaleraldehyde (i-C4H9CHO), trans-2-pentenal (C2H5CHCHCHO),

trimethylacetaldehyde ((CH3)3CCHO) and benzaldehyde (C6H5CHO), by hydroxyl

radicals (OH), were studied behind reflected shock waves at temperatures of 958 – 1391

K, using UV laser absorption at 306.69 nm. The current study reported the first direct rate

constant measurement for C2 and higher aldehydes + OH at temperatures above 1000 K.

To aid future kinetics research in shock tubes, a novel toolset of advanced laser

absorption diagnostics, namely shock-tube-integrated cavity-enhanced absorption

spectroscopy (CEAS), was also developed in the current study. This CEAS technique

utilized high reflectivity mirrors directly mounted on the shock tube to enhance the

effective optical pathlength in shock tube/laser absorption measurements by factors of

about 50 - 90, thereby greatly improving the species detection limits in shock tube

kinetics studies. A CW laser CEAS method was explored and applied to ultra-sensitive

CO detection in rate constant measurements for the acetone thermal dissociation reaction,

CH3COCH3 (+ M) = CH3 + CH3CO (+ M), over 1004-1094 K. A pulsed-laser CEAS

was also explored in the current study to develop an improved laser absorption diagnostic

for CH3 at 216.62 nm. Example application of this diagnostic was demonstrated in rate

constant measurements for the thermal dissociation reaction of methane, CH4 + M = CH3

+ H + M over 1487 - 1866 K. This CEAS toolset should prove very useful in future shock

tube kinetics studies, including but not limited to, the studies of aldehydes.

vii

Acknowledgments

I would like to thank my advisor, Professor Ronald Hanson, for his continuous

encouragement, guidance and support during my time at Stanford University. His

dedication to research, critical thinking and attention to details have set an excellent

model for me to look up to as a proper scientist. I would also like to thank my reading

committee, Professor Tom Bowman and Professor Hai Wang, for their valuable

suggestions and feedback regarding the content of this dissertation.

It has been a great fortune for me to work with many outstanding people at Stanford,

especially in the Hanson laboratory. I am deeply grateful to Dr. David Davidson, who has

offered tremendous help during my Ph.D. study and has been my co-author in every

paper. Besides, his great sense of humor has also inspired a lot of laughter and helped me

overcome occasional frustrations in research. I am also grateful to Dr. Jay Jeffries for

sharing with me his wisdom about lasers and optics. It is also my pleasure to work

alongside many talented fellow students and researchers at Stanford, and among them are

my coauthors: Matt Campbell, Xing Chao, Enoch Dames, Chris Goldenstein, Zekai Hong,

Brian Lam, Sijie Li, Marcel Nations, Genny Pang, Tom Parise, Wei Ren, Mitch Spearrin,

Kai Sun, Ritobrata Sur, Andy Tulgestke, Luke Zaczek and Yangye Zhu. They have made

my time at Stanford a very delightful experience.

Everything would not be possible without the support from my family and friends. I am

particularly grateful to my parents for having cultivated in me a curiosity about science,

and for always encouraging me to pursue my passions. Finally, I would like to give my

special thanks to my dearest friend, Alex Pingmei Xu, for her love, support, and above all,

for always making me smile.

ix

Table of Contents

Abstract ................................................................................................................................v

Acknowledgment .............................................................................................................. vii

List of Tables ................................................................................................................... xiii

List of Figures ....................................................................................................................xv

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

1.1 Background and Motivations ........................................................................................... 1

1.2 Overview of Dissertation .................................................................................................. 4

Chapter 2. Experimental Methods .......................................................................................5

2.1 Shock Tubes ....................................................................................................................... 5

2.1.1 Operation principle of shock tubes ........................................................................... 5

2.1.2 Stanford kinetic shock tube (KST) .......................................................................... 6

2.1.3 Stanford NASA shock tube (NASA-ST) ................................................................ 7

2.2 Laser Absorption Diagnostics .......................................................................................... 7

2.2.1 Principle of laser absorption spectroscopy ............................................................. 8

2.2.2 307 nm UV laser diagnostics for aldehydes and OH ............................................ 9

2.2.3 3.45 µm IR laser diagnostics for CH2O ................................................................ 10

2.2.4 4.56 µm IR laser diagnostics for CO ..................................................................... 11

Chapter 3. Development and Initial Applications of Laser Absorption Diagnostics for

Aldehydes Detection at Elevated Temperatures ...............................................................13

3.1 Introduction ...................................................................................................................... 13

3.2 Wavelength Selection ..................................................................................................... 14

3.2.1 IR wavelengths for CH2O detection ...................................................................... 14

3.2.2 UV wavelengths for CH2O and CH3CHO detection .......................................... 18

3.2.3 Multi-color aldehyde detection scheme ................................................................ 19

x

3.3 Cross-Section Measurement ........................................................................................... 20

3.4 Example Applications ..................................................................................................... 23

3.4.1 Validation experiments ............................................................................................ 23

3.4.2 CH2O pyrolysis ........................................................................................................ 24

3.4.3 CH3CHO pyrolysis .................................................................................................. 26

3.5 Summary ........................................................................................................................... 27

Chapter 4. Shock Tube Measurement for the Thermal Dissociation Rate Constant of

CH3CHO using a Sensitive CO Diagnostic .......................................................................29

4.1 Introduction ...................................................................................................................... 29

4.2 Rate Constant Measurement ........................................................................................... 31

4.3 Results and Discussions .................................................................................................. 33

4.4 Summary ........................................................................................................................... 38

Chapter 5. Shock Tube Measurement for the Rate Constant of CH2O + H = HCO + H2 .39

5.1 Introduction ...................................................................................................................... 39

5.2 Experiment Design .......................................................................................................... 40

5.3 Measurement Results ...................................................................................................... 41

5.4 Comparison with Previous Studies ............................................................................... 46

5.5 Summary ........................................................................................................................... 48

Chapter 6. High-Temperature Measurements for the Rate Constants of a Series of

Aldehydes + OH ...............................................................................................................49

6.1 Introduction ...................................................................................................................... 49

6.2 Experiment Design .......................................................................................................... 50

6.3 Rate Constant Determination ......................................................................................... 52

6.4 Measurement Results ...................................................................................................... 58

6.5 Comparison with Previous Studies .............................................................................. 60

6.6 Summary ........................................................................................................................... 62

xi

Chapter 7. CEAS: A Toolbox for Future Shock Tube Kinetic Studies ............................63

7.1 Motivation ........................................................................................................................ 63

7.2 Scientific Concept ........................................................................................................... 65

7.2.1 CW laser CEAS ........................................................................................................ 66

7.2.2 Pulsed laser CEAS ................................................................................................... 68

7.3 Example Applications ..................................................................................................... 70

7.3.1 Sub-ppm sensitivity CO diagnostic ....................................................................... 71

7.3.2 Sub-ppm sensitivity CH3 diagnostic ..................................................................... 77

7.4 Outlook ............................................................................................................................. 85

Chapter 8. Concluding Remarks ......................................................................................87

8.1. Summary of the Current Study ..................................................................................... 87

8.2. Recommendations for Future Work ............................................................................ 89

Appendices .........................................................................................................................91

A: CO time-histories measured in shock tube pyrolysis of 1000ppm CH3CHO/Ar......91

B: Rate Constant Data for CH2O + H ............................................................................95

C: High-Temperature Rate Constants Data for Ten Different Aldehydes + OH ...........97

D: Rate Constants Data for the Thermal Dissociation Reaction of Acetone ...............105

E: Effect of the Pulsed Laser Linewidth on the Effective CH3 Absorbance ...............107

F: Analysis for the Laser-Cavity Coupling Noise in Current Pulsed Laser CEAS ......109

G: Rate Constant Data for the Thermal Dissociation Reaction of Methane ................111

References ........................................................................................................................113

xiii

List of Tables

Table 4.1. Summary of the current measurement of k4.1, with comparison to previous

theoretical calculations ......................................................................................................33

Table 5.1. Reaction mechanism for the CH2O + H rate constant measurement ..............42

Table 6.1. Rate constants updated in the Veloo et al. [25], [26] mechanism for modeling

the TBHP / i-C3H7CHO reaction system .........................................................................53

Table B.1. Summary of the measured rate constant data for R4.2 ...................................95

Table C.1. Rate constant data for formaldehyde (CH2O) + OH ......................................97

Table C.2. Rate constant data for acetaldehyde (CH3CHO) + OH .................................97

Table C.3. Rate constant data for propionaldehyde (C2H5CHO) + OH ..........................98

Table C.4. Rate constant data for n-butyraldehyde (n-C3H7CHO) + OH ........................98

Table C.5. Rate constant data for isobutyraldehyde (i-C3H7CHO) + OH .......................99

Table C.6. Rate constant data for n-valeraldehyde (n-C4H9CHO) + OH ......................100

Table C.7. Rate constant data for iso-valeraldehyde (i-C4H9CHO) + OH ....................101

Table C.8. Rate constant data for trimethylacetaldehyde ((CH3)3CCHO) + OH ...........102

Table C.9. Rate constant data for trans-2-pentenal (C2H5CH=CHCHO) + OH ............103

Table C.10. Rate constant data for benzaldehyde (C6H5CHO) + OH ............................104

Table D.1. Summary of Acetone Decomposition Rate Constant Measurement .............105

Table G.1. Rate constant data for CH4 + Ar = CH3 + H + Ar ........................................111

xv

List of Figures

Figure 2.1. Schematic of the shock tube apparatus. Top panel: the driver and driven

sections. Middle panel: incident shock wave. Bottom panel: reflected shock wave. .........6

Figure 2.2. Schematic of the 307 nm laser diagnostic system. ...........................................9

Figure 2.3. Schematic of the 3.45 µm laser diagnostic system. ........................................10

Figure 2.4. Schematic of the 4.56 µm laser diagnostic system .........................................11

Figure 3.1. IR absorption spectra of CH2O, calculated using data from Perrin et

al. [65] and Jaquemart et al. [66]. Blue: 1200 K, 1 atm; orange: 298 K, 1 atm (scaled by

half to fit in this plot). Also shown are the tuning ranges of commercially available lasers.

............................................................................................................................................15

Figure 3.2. Absorption line-strengths of CH2O, H2O, CO and CO2 at 1200 K, calculated

using the HITRAN 2008 database [73]. ...........................................................................16

Figure 3.3. Simulated absorption spectra of CH2O, CH4 and H2O near 2896 cm−1. Dash

lines denote the line pairs selected by the current study. ..................................................16

Figure 3.4. Measured absorption spectra of CH2O, CH3CHO and CH4 near 2896 cm−1.

............................................................................................................................................17

Figure 3.5. UV absorption spectra of CH3CHO and CH2O at 296 K, 1 atm. Also shown

in the figure is the tuning range of our frequency-doubled ring dye laser. .......................18

Figure 3.6. Wavelength- and temperature-dependence of the aldehyde absorption

coefficients near 306.7 nm. ...............................................................................................19

Figure 3.7. Sample CH2O absorbance traces. ...................................................................20

Figure 3.8. Temperature dependence of CH2O IR cross-sections at three pressures. Dash

lines are best fit for each pressure. ....................................................................................21

Figure 3.9. Fitted IR absorption cross-sections of CH2O. ................................................22

Figure 3.10. UV absorption cross-sections of CH2O and CH3CHO at 32601.10 cm−1. ..22

http://www.sciencedirect.com/science/article/pii/S0010218013001776#b0115



xvi

Figure 3.11. Four-color absorption time-histories measured during the pyrolysis of

0.167% trioxane/0.5% CH3CHO/Ar mixture at reflected shock conditions of 965 K and

2.26 atm. Results at 32601.10 and 32606.52 cm−1 are almost coincident, as expected. ...23

Figure 3.12. Aldehydes time-histories of the example in Fig. 3.11. .................................23

Figure 3.13. Measured aldehydes time-histories of 0.167% trioxane/0.5% CH3CHO/Ar

pyrolysis at reflected shock conditions of 1418 K and 1.82 atm. .....................................24

Figure 3.14. Comparison of measured and simulated CH2O traces in 1% CH2O/Ar

pyrolysis. Simulations done with original and modified USC Mech II [75]. ...................25

Figure 3.15. CH2O sensitivity, ∂ ln χCH2O / ∂ ln ki, of the example in Fig. 3.14. ............26

Figure 3.16. Comparison of measured and simulated CH3CHO traces in 1% CH3CHO/Ar

pyrolysis. Simulations done with original and modified USC Mech II [75]. ...................27

Figure 3.17. CH3CHO sensitivity, ∂ ln χCH3CHO / ∂ ln ki, of the example in Fig. 3.16. ..27

Figure 4.1. Comparison of measured and simulated CH3CHO profiles during 1%

CH3CHO / Ar pyrolysis. Dashed lines: simulations with USC Mech II [75], which are

almost identical to simulations with JetSurF 2.0 [77]; short dashes: simulations with

ARAMCO [78]; dash dots: simulations with the Cong and Dagaut mechanism [79];

dotted lines: simulations with the Chatelain et al. mechanism [80]. Note that both USC

Mech II/ JetSurF 2.0 and ARAMCO underpredict the CH3CHO decay rates, while the

other mechanisms overpredict the decay rates. Figure adapted from Mével et al. [76] ...30

Figure 4.2. Example CO time-history in the pyrolysis of 1000ppm CH3CHO/Ar.

Reflected shock conditions: T = 1447 K, P = 1.60 atm. ..................................................31

Figure 4.3. CO sensitivity, ∂ln𝜒𝜒𝐶𝐶𝐶𝐶 (t)/ ∂lnki , of the time-history shown in Fig. 4.3,

highlighting the reactions with a maximum sensitivity larger than 0.05. Calculated using

USC Mech II as the base mechanism, with updated values of k4.1 from the current study.

Note that the interferences from R4.2-R4.4 have been substantially suppressed. ............32

Figure 4.4. Uncertainty analysis for the measurement of k4.1 at 1447 K. .........................33

Figure 4.5. Comparison of the current measurement results with previous experimental

studies at similar pressures. ...............................................................................................34

xvii

Figure 4.6. Comparison of the current data with previous theoretical calculations. ........35

Figure 4.7. CH3CHO time-histories during 1% CH3CHO/Ar pyrolysis, simulated using

the original and updated mechanisms of (a) USC-Mech II [75], (b) ARAMCO [78], (c)

the Cong and Dagaut mechanism [79], and (d) the Chatelain et al. mechanism [80], in

comparison with the previous measurement results in Chapter 3. For all four mechanisms,

the current values of k4.1 significantly improve their predictions for the CH3CHO time-

histories. ............................................................................................................................37

Figure 5.1. Example CO time-histories in the pyrolysis of 1,3,5-trioxane/C2H5I/Ar. .....41

Figure 5.2. Rate constant inference from the 1659 K, 1.06 atm example in Fig. 5.1. ......43

Figure 5.3. CO sensitivity analysis for the 1659 K, 1.06 atm example in Fig. 5.1. ..........44

Figure 5.4. Uncertainty analysis for the measured rate constant of CH2O + H. ..............44

Figure 5.5. Rate constants of CH2O + H measured at different mixture compositions. ..45

Figure 5.6. Arrhenius plot for the rate constant of CH2O + H over 1000−4000 K. .........47

Figure 6.1. List of the aldehydes investigated in the current study ..................................50

Figure 6.2. Example data trace of the aldehydes + TBHP experiment. ............................52

Figure 6.3. Example OH time-history of i-C3H7CHO + OH. ..........................................54

Figure 6.4. OH sensitivity of the example i-C3H7CHO + TBHP experiment. .................55

Figure 6.5. Uncertainties in the measured rate constant of i-C3H7CHO +OH at 1160 K.

............................................................................................................................................55

Figure 6.6. Apparent rate constant obtained from exponential fit to OH time-history. ....57

Figure 6.7. Apparent rate constant measured at different initial TBHP/aldehyde ratios. ..57

Figure 6.8. Rate constant k6.5 determined from the mechanism-independent approach. . 57

Figure 6.9. Cross-comparison between the rate constants of 10 different aldehydes + OH.

............................................................................................................................................59

Figure 6.10. Comparison between the current measurement and the SAR model. ..........60

Figure 6.11. Veloo et al. [25], [26] model vs. the current measurement. .........................61

Figure 6.12. Mendes et al. [27] TST calculation vs. the current measurement. ..............61

xviii

Figure 7.1. Schematic of the optical arrangement of CW laser CEAS in a shock tube. ...66

Figure 7.2. Example signals from a CW laser CEAS measurement of atmospheric H2O

near 1.5 µm. (a) Under on-axis alignment and at fixed wavelength, the measurement is

overwhelmed by laser-cavity coupling noise that causes the detector signal to fluctuate

from zero to maximum. (b) Rapid wavelength scanning suppresses the coupling noise,

making the absorption transition visible. (c) Off-axis alignment, in combination with

rapid wavelength scanning, completely eliminates the coupling noise. ............................67

Figure 7.3. Schematic of the optical arrangement of pulsed laser CEAS in a shock tube.

............................................................................................................................................68

Figure 7.4. Noise immunity concept of the ps-pulsed CEAS: time-domain picture. .......69

Figure 7.5. Noise immunity concept of the ps-pulsed CEAS: frequency-domain picture.

Note that the cavity FSR is exaggerated in scale to facilitate visualization. The total

transmitted laser intensity through the cavity equals the integral of the product of the laser

lineshape function and the cavity transmission function. As the cavity modes are very

dense within the laser linewidth, this integral is proportional to the total area under the

laser lineshape, which is a constant irrespective of the cavity mode jittering (dash lines).

............................................................................................................................................70

Figure 7.6. Example signal in the shock tube/CEAS measurement of CO. (a) Transmitted

laser intensity (blue) and laser wavelength (red) during a single scan in a vacuum shock

tube. (b) Transmitted laser intensity during a single scan of shock-heated 10ppm CO/

1%H2/ Ar mixture at the reflected shock condition of T = 1499 K and P = 1.51 atm.

Hydrogen was added to the test gas to accelerate the vibrational relaxation of CO. ........72

Figure 7.7. Example CO absorption measurement in a shock tube using CEAS. (a) The

CO absorbance signal in a single scan cycle; absorbance extracted from the data in Fig.

7.6. (b) The measured CO mole fraction within the first 1 ms after the reflected shock. .72

Fig. 7.8. CEAS gain calibration using CO mixtures of known concentrations.

Experimental conditions: T = 1100 – 2100 K, P = 1.2 - 1.6 atm, χCO = 2 - 100ppm. .....73

xix

Figure 7.9. Example CO time-histories measured in the pyrolysis of acetone/Ar mixtures.

(a) 16.3 ppm acetone/Ar at 1398 K, 1.52 atm. (b) 1.00% acetone/Ar at 1024 K, 1.75 atm.

............................................................................................................................................74

Figure 7.10. CO sensitivity analysis for the acetone pyrolysis experiments shown in Fig.

7.9. (a) CO sensitivity in the 1398 K case, simulated with the Saxena et al. mechanism

[131]; (b) CO sensitivity at the 1/e decay time of acetone (τ1/e) in the 1398 K case,

simulated with the Saxena et al. mechanism, the Pichon et al. mechanism [132] and USC

Mech II [75], highlighting reactions with sensitivity higher than 10−4. (c) CO sensitivity

in the 1024 K case, simulated with the Pichon et al. mechanism. (d) CO sensitivity at 1.5

ms in the 1024 K case, simulated with the Pichon et al. mechanism and USC Mech II,

highlighting reactions with sensitivity higher than 10−4. The Saxena et al. mechanism was

not validated at T < 1300 K and therefore were not used in the analyses of (c) and (d). .75

Figure 7.11. Arrhenius plot for the current k7.1 data in comparison with previous studies.

............................................................................................................................................76

Figure 7.12. Comparison of the 1σ detection limits of CH3 in different shock tube

studies. Values calculated from the typical minimum detectable absorbances and the

effective CH3 absorption coefficients in these studies, and normalized to a shock tube

diameter of 15 cm and a pressure of 1 atm. ......................................................................77

Figure 7.13. Schematic of the experimental setup in pulsed UV CEAS. .........................78

Figure 7.14. Comparison of the laser output spectrum and the CH3 absorption spectrum.

The CH3 absorption spectrum near 1565 K was adapted from Oehlschlaeger et al. [143].

Note that linewidth of the pulsed laser used in the current study (FWHM ~ 0.15 nm) was

about 20 times smaller than that of the CH3 absorption feature (FWHM ~ 3 nm). .........79

Figure 7.15. Signal-to-noise ratio of CH3 detection in a typical single-pass measurement

(blue) and the current CEAS measurement (red) as functions of CH3 mole fraction. Note

that the current CEAS scheme substantially improved both the minimum detection limit

and the detection dynamic range of CH3 over the conventional single-pass scheme. .....81

xx

Figure 7.16. Example CH3 time-history measured in the pyrolysis of 500ppm CH4/Ar at

1757 K, 1.69 atm, in comparison with simulation results assuming different sources of

impurities. Note that the CH3 formation rate was insensitive to impurities after 200 µs. 83

Figure 7.17. 2σ uncertainties in the measured rate constant k7.2 at 1757 K. ...................84

Figure 7.18. Arrhenius plot for k7.2. (a) Comparison between the current and previous

experiment results. Note that the results from Roth [145], Tabayashi and Bauer [146] and

Heffington et al. [147] are almost identical. (b) Comparison of current and Davidson et

al. [148] data to theories and review. The current study is close to the low-pressure limit.

............................................................................................................................................84

Figure A.1. CO time-history at T = 1618 K, P = 1.45 atm ...............................................91






Figure E.1. Effective CH3 absorbance vs. laser linewidth, calculated using the CH3

absorption spectrum shown in Fig. 7.14. Note that the current ps-pulsed laser yields

almost identical effective single-pass CH3 absorbance as narrow-linewidth CW-lasers.

..........................................................................................................................................108

Figure F.1. Two major sources of laser-cavity coupling noise. (a) Cavity mode shifting.

(b) Cavity mode stretching. .............................................................................................109

Figure F.2. The current laser linewidth vs. cavity free spectral range. Note that the

FWHM linewidth of the current pulsed laser (top panel) encompasses about a thousand

cavity modes (bottom panel), which grants excellent immunity to laser-cavity coupling

noise. ...............................................................................................................................110

1

Chapter 1 Introduction

1.1 Background and Motivation

Modern advances in human civilization are utterly dependent on an abundant and

uninterrupted supply of energy for living and working. Currently, nearly 90% of the

global energy usage is ultimately supplied by the combustion of chemical fuels [1],

including about 86% from fossil-extracted hydrocarbon fuels such as oil, coal and natural

gas. Consequently, one critical issue and continuous challenge for humans to better

harness energy is to find paths to more efficient and cleaner combustion, usually via

refining the designs of combustion engines, and to improve control over combustion-

related toxic emissions. A better understanding of fuel combustion chemistry will aid

such endeavors.

Of all major species involved in fuel combustion chemistry, aldehydes, which are organic

compounds containing a –CHO functional group, are among the most important

intermediate products present in the pyrolysis and oxidation of hydrocarbon fuels. Lying

on the primary oxidation pathway of alkanes [2], aldehydes are produced in the pre-

ignition phase of hydrocarbon combustion [3] and are key species participating in

hydrocarbon oxidation chemistry, especially in the low-temperature chemistry regime [4].

Aldehydes are also widely found in the combustion of bio-derived oxygenated fuels; they

can be generated via molecular dehydrogenation reactions during the pyrolysis and

partial oxidation of alcohols [5], ethers [6], esters [7] and other oxygenated fuels that are

increasingly used as alternative energy sources.

Despite their abundance in the combustion process of various chemical fuels, aldehydes

are usually undesirable in the final combustion products. In fact, they are known as toxic

emissions in the exhaust gas of spark-ignition or compression-ignition engines [8], [9],

which if not removed properly can lead to environmental pollutions and potential threats

to public health [10]. As well, a high level of aldehydes in engine exhaust can be a

warning of incomplete combustion or abnormal reaction quenching [11]. Moreover,

aldehydes are also associated with the cool flame reactions [12], [13] that are usually

2

responsible for engine knock [14] – an undesired erratic and noisy ignition in internal

combustion engines. Thus an important topic of combustion research is to accurately

monitor aldehydes concentrations in combustion environments and to improve our

understanding of aldehydes chemistry, especially their removal chemistry.

So far, conventional methods of aldehydes measurement in combustion environments

mostly involve gas chromatography (GC) and mass spectrometry (MS). Despite their

success in characterizing aldehydes during low-temperature combustion studies, these

methods typically require the combustion process to be quenched before sampling and

therefore are usually not suitable for time-resolved in situ measurements of aldehydes

concentration time-histories. Another common approach to monitor aldehydes is through

laser-induced fluorescence (LIF), as has been demonstrated for time- and space-resolved

imaging of formaldehyde (CH2O) in engines [15], but this approach typically requires

calibration measurements with formaldehyde seeding and can suffer from broadband

interference emissions of hydrocarbons. As an alternative to these approaches, time-

resolved species time-histories can be measured non-intrusively with laser absorption

spectroscopy. Compared with LIF, laser absorption spectroscopy typically is more

quantitative and can potentially be interference-free. It thus promises to be a better

technique for single line-of-sight aldehydes detection. The first part of this study aims to

develop a sensitive and accurate laser absorption diagnostic method optimized for

aldehydes detection in shock tube experiments.

Combustion-generated aldehydes are usually removed either through direct thermal

dissociation or via dehydrogenation/H-abstraction by radicals (e.g. H, OH, CH3 etc.). In

most combustion systems, the aldehydes removal rates are usually dominated by the

following reactions: (1) aldehydes + H, (2) aldehydes + OH and (3) aldehydes + M.

Recognizing the importance of these reactions, combustion researchers have conducted

various theoretical and experimental studies on their rate constants over the last two

decades [16]–[33]. However, due to limitations of previous experimental facilities and

measurement techniques, there are still considerable uncertainties in the experimentally

determined rate constants of these key reactions, which usually manifest themselves as

large data scatter and variations between different studies; in other situations, such as for

3

the rate constants of the C2-C7 aldehydes + OH reactions, previous experimental data are

limited to room temperatures, whereas data are mostly needed at high temperatures

related to combustion systems. On the other hand, modern theoretical calculations, for

example, transition-state-theory (TST) calculations, can supplement these experimental

studies by extrapolating beyond the currently accessible experimental conditions, but

they usually have broader uncertainty limits compared to state-of-the-art measurements

and often need to be calibrated or validated against experimental results. Thus from both

experimental and theoretical points of view, high-quality rate constant data are greatly

needed to improve our current understanding of aldehydes combustion chemistry. This

has motivated the second part of this study, which strives to provide direct and high-

accuracy rate constant measurements of the aforementioned three key types of aldehydes

removal reactions, through the use of modern shock tube/laser absorption experimental

methods.

As the current measurements for these key rate constants are inferred from species time-

histories obtained in well-designed shock tube/laser absorption experiments, their

accuracies are ultimately limited by the sensitivities of the laser absorption diagnostics

for the species under investigation. For further improvement in the accuracy of rate

constant determination, it is pertinent to revisit the laser diagnostics utilized in the

experiments. Hence, the third part of this study is dedicated to the development of a

powerful toolset of advanced laser absorption diagnostic methods for future combustion

research, based on shock-tube-compatible cavity-enhanced absorption spectroscopy

(CEAS). This CEAS technique has greatly enhanced the effective optical pathlength in

laser absorption measurements by about two orders of magnitude, and thereby

significantly improves the detection limits of several key species in combustion kinetics

studies, such as CO [34], O [35], and CH3 [36] etc. With hopes that this toolset will

strongly benefit future combustion kinetics studies, including, but not limited to the

studies of aldehydes, this study has also pointed out some interesting directions of

potential future work.

4

1.2 Overview of Dissertation

The subsequent chapters of this dissertation are organized as follows:

(1) Chapter 2 will introduce the experimental methods and describe the shock tube

facilities and the laser diagnostic techniques utilized in the current work.

(2) Chapter 3 will present a set of multi-color laser absorption diagnostics for high-

temperature aldehydes detection.

(3) Chapter 4 will discuss the rate constant measurement for the dissociation reaction of

acetaldehyde, i.e. CH3CHO (+ M) = CH3 + HCO (+ M).

(4) Chapter 5 will discuss the rate constant measurement for the H-abstraction reaction of

formaldehyde by H-atom radicals, i.e. CH2O + H = HCO + H2, in conjunction with a

complementary high-level TST calculation.

(5) Chapter 6 will discuss the overall rate constant measurements for the H-abstraction

reactions of OH radicals with a series of aldehydes, i.e. CH2O, CH3CHO, C2H5CHO, n-

C3H7CHO, i-C3H7CHO, n-C4H9CHO, i-C4H9CHO, (CH3)3CCHO, C2H5CHCHCHO

and C6H5CHO.

(6) Chapter 7 will introduce a novel toolset (cavity-enhanced absorption spectroscopy)

applicable to shock tube studies and demonstrate its potential benefits to future

combustion kinetics research with a few example applications.

(7) Chapter 8 will conclude the dissertation with a summary of its major contributions

and propose a few directions of potential future work.

5

Chapter 2. Experimental Methods

2.1 Shock Tubes

Shock tubes have served for decades as one of the most effective experimental systems

for chemical kinetics studies, thanks to their capacity of almost instantaneously creating a

uniform, well-controlled test environment of high-temperature gases at a user-specified

pressure and temperature [37]. A detailed description of shock tube operation principles

is presented in the next section.

2.1.1 Operation principle of shock tubes

As shown in Fig. 2.1, a gas-driven shock tube consists of a long tube with a driver section

and a driven section separated by a diaphragm (in the present work a plastic film, i.e.

LexanTM). The driven section is filled with low-pressure test gas, and the driver section is

then filled with high-pressure inert gas, usually helium or nitrogen, until the pressure

difference across the diaphragm causes it to burst and generates an incident shock wave

traveling down the shock tube. The shock wave almost instantaneously increases the

temperature and pressure of the test gas behind it, and when it reaches the endwall of the

shock tube, it reflects back toward the driver section, stagnating the test gas, further

raising the gas temperature and pressure. This creates a stable and near-ideal test

environment for combustion kinetics studies. The temperature and pressure jumps across

the incident and reflected shock waves are well determined through normal shock wave

equations from the incident shock speed, which is measured with pressure-triggered time

counters located on the sidewall close to the end of the shock tube. Typical test times of

conventional reflected shock wave experiments are on the order of milliseconds

(although recent advances have shown that steady gas conditions can be maintained for

up to 100 ms [38]). The test times are usually terminated by the arrival of rarefaction

wave from the driven section or reflected waves from the shock-contact surface

interaction, and dependent on the geometry of the shock tube. Two different shock tubes

used in this work are described in the following sections.

6

Figure 2.1. Schematic of the shock tube apparatus. Top panel: the driver and driven

sections. Middle panel: incident shock wave. Bottom panel: reflected shock wave.

2.1.2 Stanford kinetic shock tube (KST)

A majority of the kinetics experiments presented in this dissertation [39]–[43] were

conducted in the Stanford kinetics shock tube (KST). This 14.13-cm inner diameter shock

tube had a driver section of 3.35 m driver section and a driven section of 8.54 m,

allowing for steady test time of about 2 ms under typical shock conditions and with

helium as driver gas. The incident shock speeds were measured using four differential

time counters triggered by five PCBTM model 113A26 piezoelectric pressure transducers

spaced axially over the last 1.5 m of the shock tube. From these counter times, the

reflected shock conditions could be calculated using an in-house frozen-chemistry shock

calculator code known as FROSH. A KistlerTM model 603B1 piezoelectric pressure

transducer, located at 2 cm from the endwall, was used to measure the pressure time-

histories during shock experiments. Three pairs of optical windows, also located at 2 cm

from the endwall, allowed for multiple laser access of various species diagnostics.

7

The shock tube was equipped with a Teflon-coated 14-L mixing tank that was connected

to the tube through a mixing manifold. During kinetics experiments, test gas mixtures

were manometrically prepared and mixed in the mixing tank for at least 2 hours. The tank

was equipped with a magnetic stirrer to accelerate the mixing and to ensure the

homogeneity of the mixtures, and covered in a heating jacket typically heated to 50 C to

prevent wall condensation of low-vapor pressure chemicals. To remove possible residual

impurities, the shock tube and the mixing assembly were routinely pumped to about 6

µtorr between shock experiments, and the subsequent leak-plus-outgassing rate was

typically below 5 µtorr/min.

2.1.3 Stanford NASA shock tube (NASA-ST)

Some other experiments discussed in this dissertation [44]–[46] were conducted in

another shock tube, namely the Stanford NASA shock tube (NASA-ST). This shock tube

has an inner diameter of 15.24 cm, a driver section of 3.7 m and a driven section of 10 m.

It also had five PCBTM pressure transducers, located at 184, 127, 97, 36 and 2 cm from

the shock tube endwall, for measurement of the incident shock speed. Attached with the

shock tube was a 40-L mixing tank that was also equipped with a magnetic stirrer and a

heating jacket. Except for these small differences in geometry, the NASA-ST facility had

almost identical configuration as the KST.

2.2 Laser Absorption Diagnostics

As a result of their capability to provide time-resolved, high-accuracy and species-

selective measurements for various combustion products and key combustion parameters,

laser absorption diagnostics have long been recognized as powerful tools for combustion

kinetics studies [47]. The current study has exploited a subset of laser absorption

diagnostics, namely the fixed-wavelength direct laser absorption method (fixed-DA), the

principle of which is presented in the next section.

8

2.2.1 Principle of laser absorption spectroscopy

In a laser absorption measurement, the fractional transmission of the incident laser light is

related to the concentration of the absorbing species through the Beer-Lambert relation:

−𝑙𝑙𝑙𝑙 �𝐼𝐼𝐼𝐼0� = 𝛼𝛼 = 𝜒𝜒𝜒𝜒𝑙𝑙𝜒𝜒 (Eqn. 2.1)

where I and I0 (a.u.) are the transmitted laser intensities with and without the absorbing

species, respectively; α (unitless) is the logarithmic transmission, also known as

absorbance; 𝜒𝜒 (unitless) is the mole fraction of the absorbing species; 𝜒𝜒 (cm2/molecule) is

its absorption cross-section; n (molecule/cm3) is the total number density of the test gas;

and L (cm) is the absorption path length, which usually equals the inner diameter of the

shock tube. This relation can also be expressed in an equivalent form as follows:

𝛼𝛼 = 𝜒𝜒𝜒𝜒𝜒𝜒𝜒𝜒 (Eqn. 2.2)

with k (cm-1atm-1) being the absorption coefficient of the target species, and P (atm)

being the total test gas pressure. The values of 𝜒𝜒 and k are usually pre-determined from

calibration experiments prior to the absorption measurement. Once the absorbance α is

measured, the target mole fraction χ can be calculated from Eqn. 2.1 or 2.2.

There are also situations when multiple absorbing species are present. In such cases, the

absorbance at a given wavelength/color will be the sum of contributions from all

absorbing species:

𝛼𝛼 = �� 𝜒𝜒𝑖𝑖𝑖𝑖

𝜒𝜒𝑖𝑖� 𝑙𝑙𝜒𝜒 = �� 𝜒𝜒𝑖𝑖𝑖𝑖

𝜒𝜒𝑖𝑖� 𝜒𝜒𝜒𝜒 (Eqn. 2.3)

and a multi-color scheme is needed to separate out the mole fractions (χi) of different

absorption species. Particularly, if a target species’ absorption feature is spectrally much

narrower than the other absorbing species, its mole fraction can be extracted using a

differential absorption scheme that probes the absorbance on and off its peak resonance

wavelength within a range where absorbances of other species are essentially constant, as

explained in previous study of MacDonald et al. [48]:

9

𝜒𝜒 =𝛼𝛼𝑜𝑜𝑜𝑜 − 𝛼𝛼𝑜𝑜𝑜𝑜𝑜𝑜

(𝜒𝜒𝑜𝑜𝑜𝑜 − 𝜒𝜒𝑜𝑜𝑜𝑜𝑜𝑜)𝑙𝑙𝜒𝜒 =

𝛼𝛼𝑜𝑜𝑜𝑜 − 𝛼𝛼𝑜𝑜𝑜𝑜𝑜𝑜(𝜒𝜒𝑜𝑜𝑜𝑜 − 𝜒𝜒𝑜𝑜𝑜𝑜𝑜𝑜)𝜒𝜒𝜒𝜒

(Eqn. 2.4)

Example applications of this differential absorption scheme will be explored in Chapter

3. Details about individual laser absorption diagnostics used in the current study are

discussed in the following sections.

2.2.2 307 nm UV laser diagnostics for aldehydes and OH

Figure 2.2. Schematic of the 307 nm laser diagnostic system.

Quantitative measurements of aldehydes and OH can be achieved using UV laser

absorption near 307 nm. To access the UV transitions, the current study employed a

Spectra-PhysicsTM 380A tunable ring dye laser. Inside the dye laser cavity, a rhodamine

6G dye jet was excited by the CW output of a 5 W CoherentTM Verdi pump laser at

532 nm, creating visible laser light at 613.4 nm; the visible light was then intra-cavity

frequency-doubled by a temperature-tuned AD*A crystal to generate about 1 mW of UV

light near 306.7 nm. Due to the intrinsic jittering of the dye jet, the laser output power

had rapid fluctuations (up to about 10% peak-to-peak changes), but the wavelength

remained stable. Thus a common-mode-rejection scheme was used to remove these

fluctuations in the detected laser signal: before entering the shock tube, part of the laser

light was redirected by a beam splitter and sampled as a reference to normalize the

intensity of the diagnostic beam. The reference and the diagnostic beams were captured

with a pair of ThorlabsTM PDA36A detectors (bandwidth = 1 MHz, active

area = 3.6 × 3.6 mm), whose output signals were sampled and recorded with a 14-bit

10

National InstrumentsTM digital data acquisition system at a rate of 2.5 M sample/s. Under

common mode rejection, noise caused by the laser intensity fluctuations could be

suppressed to less than 0.1%. In shock tube measurements, this laser intensity noise was

usually overshadowed by other noise sources, especially the beam steering noise induced

by density fluctuations in the turbulent boundary layer near the shock tube wall. The 1σ

minimum detectable absorption (MDA) of typical common-mode-rejected UV absorption

experiments, calculated from the root-mean-square error of the transmitted laser intensity

during nonreactive shocks, was found to about 0.1%.

For measurement of OH radicals, the laser was tuned to 306.687 nm (32606.52 cm-1),

targeting the R1(5) transition in the OH A-X (0,0) band. This strong and isolated

transition had been well characterized by Rae et al. [49] and Herbon et al. [50], and

successfully demonstrated in previous OH time-history measurements [21], [51], [52]. A

1σ minimum detection limit of as low as 0.3 ppm OH can be achieved at typical shock

conditions of 1200 K and near atmospheric pressures. Measurements were also conducted

to verify that there was no significant interference absorption or emission by repeating

the experiments with the laser tuned off the OH transition and with the laser beam

blocked. Aside from OH radicals, this UV laser system could also be used for

measurement of CH2O and CH3CHO at 306.738 nm (32601.10 cm-1). Details about the

aldehydes diagnostics will be discussed in Chapter 3.

2.2.3 3.45 µm IR laser diagnostics for CH2O

Figure 2.3. Schematic of the 3.45 µm laser diagnostic system.

11

An interference-immune IR diagnostic for CH2O detection was developed in the current

study, utilizing a two-color differential absorption scheme near 3.45 µm. The IR

wavelengths were probed using a NovawaveTM prototype differential-frequency

generation (DFG) laser. Inside this DFG laser were a fixed-wavelength (1064 nm) pump

laser and a tunable fiber-coupled DFB laser (centered around 1538 nm), whose outputs

were mixed in a temperature-controlled periodically-poled lithium niobate (PPLN)

crystal for difference-frequency-generation. The PPLN crystal was phase-matched for

maximum output in the mid-IR, enabling a typical output power of 170 μW. The IR

signals were measured using an InfraRed AssociatesTM liquid-nitrogen-cooled InSb

detector that was connected to a 1-MHz bandwidth transimpedance amplifier. The

wavelength of the laser was monitored using a BristolTM 721 wavemeter, which had a

spectral resolution of 0.002 cm−1. The output of the DFG laser was very stable; over

30 min, its wavelength and power drifts were measured to be less than 0.02 cm−1 and 1%,

respectively. Two irises and a narrow bandpass spectral filter (supplied by SpectrogonTM,

center wavelength = 3465 nm, FWHM = 43 nm) were used to minimize the thermal

emission from the shock-heated gas mixture. A typical 1σ MDA of 0.3% could be

achieved in reflected shock wave experiments.

2.2.4 4.56 µm IR laser diagnostics for CO

Figure 2.4. Schematic of the 4.56 µm laser diagnostic system

12

In the current study, absorption of CO was monitored by mid-IR absorption at the v” = 0,

R(13) rovibrational transition near 4.56 μm. This strong and isolated transition has been

well characterized by Ren et al. [53]. This transition was accessed with a narrow-

linewidth distributed-feedback (DFB) quantum-cascade laser (QCL) manufactured by

AlpesTM. The average line width of the laser, governed by the current noise of the laser

driver (root-mean-squared noise < 40 μA), was estimated to be less than 0.001 cm−1,

more than 2 orders of magnitude smaller than that of the CO transition; the instantaneous

line width of the laser was even narrower. The wavelength of the laser was monitored

with a BristolTM 721 wavemeter, which had a spectral resolution of 0.002 cm−1. The laser

wavelength was found to be very stable, with peak-to-peak drifting of less than 0.006

cm−1 within 5 min. Transmitted laser light was collected with a thermoelectrically cooled

VigoTM detector (type PVI-2TE-5, bandwidth = 10 MHz, active area = 3 × 3 mm). The

laser intensity was seen to be stable, with peak-to-peak drifting of less than 0.4% within 5

min. A typical 1σ MDA of less than about 0.2% was achieved behind reflected shock

waves, which was equivalent to a 1σ minimum detection limit of about 10 ppm of CO at

typical shock conditions of 1600 K and 1 atm. In the kinetics experiments reported in the

current study, interference absorption at the CO wavelength was negligible, as suggested

by simulations using the HITRAN 2012 spectroscopic database [54] and confirmed by

measurements with the laser tuned away from the CO transition.

13

Chapter 3. Development and Initial Applications

of Laser Absorption Diagnostics for Aldehydes

Detection at Elevated Temperatures

The contents of this chapter have been published in Combustion and Flame under the

title "High-temperature laser absorption diagnostics for CH2O and CH3CHO and their

application to shock tube kinetic studies" [55] and presented in the 29th International

Symposium on Shock Waves [56].

3.1 Introduction

As discussed in the Chapter 1, aldehydes are important intermediate species that are

produced in relatively large quantities during the combustion of various fuels.

Recognizing the need for advanced aldehyde detection techniques in combustion

environments, the current work aims to develop a sensitive and accurate laser absorption

diagnostic method optimized for the measurement of two major aldehydes formed in

most combustion processes, namely formaldehyde (CH2O) and acetaldehyde (CH3CHO),

at elevated temperatures.

Previous shock tube studies have demonstrated the promise of quantitative absorption-

based detection of CH2O using UV lamps at 174 nm [19], [57] and IR helium-neon (He-

Ne) lasers at 3.39 μm and 3.51 µm [58], [59]. Recently, advances in mid-IR lasers [60]–

[62] have enabled access to much stronger transitions of CH2O near 3.6 μm and spurred

the development of novel room-temperature CH2O sensors [63], [64], but their

application to high-temperature CH2O measurement is yet to be explored. Using the

latest spectroscopic database from Perrin et al. [65] and Jacquemart et al. [66], this study

has identified, within the capability of current commercially available lasers, the optimal

wavelength for CH2O detection at combustion conditions. A two-color IR CH2O

detection scheme capable of eliminating broadband interference absorptions is

subsequently developed.

14

Very few studies have been reported for high temperature absorption measurement of

CH3CHO. Most relevant to the current study is the work by Cook et al. [67], who have

measured the overall absorption of CH2O and CH3CHO during n-butanol pyrolysis near

306.8 nm, a few wavenumbers away from the A–X(0, 0) R1(5) OH transition. The

current study has revisited the Cook et al. method and extended the aldehydes cross-

section measurement to a wider temperature range. In conjunction with the two-color

interference-free CH2O diagnostic mentioned above, the current study has also proposed

a three-color combined UV/IR scheme for simultaneous CH2O and CH3CHO detection.

This method can easily be extended to a four-color aldehydes/OH diagnostic for

combustion systems where OH may also be present.

3.2 Wavelength Selection

3.2.1 IR wavelengths for CH2O detection

The ultimate goal of wavelength selection is to find a wavelength where (1) the

sensitivity of the target species is maximized, and (2) the interfering absorption from

other species is minimized. To achieve this goal, quantitative CH2O absorption spectra in

the UV and IR are needed. However, although various studies have been reported on

room-temperature CH2O absorption spectra [68]–[72], quantitative measurements at high

temperatures are quite limited. An estimate of the high-temperature spectra can be

obtained through spectroscopic simulations using a line-by-line transition database. The

HITRAN 2008 database [73], which has incorporated the recent updates on CH2O line

intensities from Perrin et al. [65], is used in the current study, in combination with the

updated line-broadening coefficients from Jacquemart et al. [66]. With this update, the

line parameters of CH2O are identical to that in HITRAN 2012 [54]. Absorption spectra

of major potential interfering species (H2O, CO, CO2 and CH4) are also calculated using

HITRAN 2008. Calculations using HITRAN 2012 have yielded identical results.

Fig 3.1 shows the simulated IR absorption spectra of CH2O at 296 K and at 1200 K. The

entire IR spectrum of CH2O is composed of two regions. The 3.6 μm region is the

location of the ν1 (centered around 2782 cm−1) and ν5 (centered around 2844 cm−1) bands

of CH2O, together with several weaker overtones or combination dark bands, and is

15

accessible with difference-frequency-generation (DFG) lasers. The 5.7 μm region is the

location of the ν2 band (centered around 1746 cm−1) and is accessible with quantum

cascade lasers (QCL).

Figure 3.1. IR absorption spectra of CH2O, calculated using data from Perrin et

al. [65] and Jaquemart et al. [66]. Blue: 1200 K, 1 atm; orange: 298 K, 1 atm (scaled by

half to fit in this plot). Also shown are the tuning ranges of commercially available lasers.

Although the 5.7 μm region may seem attractive for CH2O detection due to its stronger

peak absorption feature, comparison with potential interferers (Fig. 3.2) has suggested

that this band may suffer from strong interference from H2O, and therefore is not suitable

for CH2O sensing in combustion environments. On the other hand, the 3.6 μm region is

completely free from CO and CO2 interference, and H2O interference is, on average, two

orders of magnitude weaker. In this region, the strongest transition within the laser tuning

range of the current study occurs near 2896 cm−1. Compared to the strongest transition in

the entire IR spectrum of CH2O, this transition is more than half of its strength, leaving

little room for significant improvement in CH2O detection sensitivity even when new

lasers become available. A closer examination of the CH2O spectrum (Fig. 3.3) within

2890–2900 cm−1also indicates that the 2896 cm−1 transition is free from H2O

interference.

16

Figure 3.2. Absorption line-strengths of CH2O, H2O, CO and CO2 at 1200 K, calculated

using the HITRAN 2008 database [73].

Figure 3.3. Simulated absorption spectra of CH2O, CH4 and H2O near 2896 cm−1.

Dashed lines denote the line pair selected by the current study.

To eliminate other possible interference absorptions, particularly the broadband

interference from large hydrocarbon molecules, a two-color differential absorption

scheme is proposed, utilizing the structural difference between the very narrow

absorption feature of CH2O (FWHM ~ 0.3 cm−1) and the effectively flat absorption

spectra of most hydrocarbons near 2896 cm−1. By tuning on and off the peak of the CH2O

feature, one can easily subtract the interference absorbance from the total absorbance and

17

recover the CH2O concentration from Eqn. 2.4. However, special caution is needed in the

selection of the off-line wavelength, as CH4, being an exception to the broadband

character of most hydrocarbons, also has narrow absorption features near 2896 cm−1 (Fig.

3.3). By trying to (1) maximize the differential absorption cross-section of CH2O and (2)

minimize the differential absorption cross-section of CH4 between the two wavelengths,

the current study has carefully selected a line pair for CH2O detection: 2895.92 cm−1 (on-

line) and 2895.60 cm−1 (off-line), which is expected to work over a wide range of

temperatures (900–1800 K) and pressure (0.5–5 atm).

Figure 3.4. Measured absorption spectra of CH2O, CH3CHO and CH4 near 2896 cm−1.

Fig. 3.4 shows the CH2O and CH4 absorption spectra near 2896 cm−1 measured at shock

conditions around 1200 K and 2 atm, with the dashed lines representing the line pair

selected in the current study. Though it cannot completely remove CH4 interference, the

current line selection has suppressed the differential absorption cross-section of CH4 to

less than 1/20 that of CH2O. As well, because CH2O is usually formed on a shorter

characteristic timescale than CH4 during the oxidation of hydrocarbon fuels, the current

line selection is often sufficient for accurate early-time detection of CH2O in typical

combustion processes, where its concentration can be an order of magnitude higher than

that of CH4. Also shown in the figure is the absorption spectrum of CH3CHO, which

represents typical broadband absorbing species whose interference can be completely

eliminated by the current two-color scheme.

18

Figure 3.5. UV absorption spectra of CH3CHO and CH2O at 296 K, 1 atm. Also shown

in the figure is the tuning range of our frequency-doubled ring dye laser.

3.2.2 UV wavelengths for CH2O and CH3CHO detection

Due to the lack of sharp features in the high-temperature absorption spectrum of

CH3CHO (see Fig. 3.4), there is no simple two-color scheme to isolate CH3CHO from

broadband interference absorptions (e.g. of large hydrocarbons) in the IR region. To

avoid the prevalent hydrocarbon interferences in the IR, the current study has turned to

the UV region for quantitative detection of CH3CHO. Shown in Fig. 3.5 are the room

temperature UV absorption spectra of CH3CHO and CH2O. Due to the overlap between

the spectra of the two aldehydes, the concentration of CH3CHO needs to be measured in

conjunction with CH2O. For the choice of the UV wavelength, the absorption features

around 307 nm appears to be attractive, because (1) they lie in the middle of the tuning

range of the current frequency-doubled ring dye laser, and (2) the CH3CHO absorption

cross-section is larger than that of CH2O. However, as suggested in the previous study of

Cook et al. [67], the wavelength dependence of the aldehydes’ absorption cross-sections

near 307 nm diminishes at high temperatures due to spectral broadening. This essentially

means that the exact UV color can be chosen freely as long as one avoids the OH

transitions (Fig. 3.6). The current work has selected 306.738 nm (32601.10 cm−1) as the

UV wavelength for aldehydes detection. Together with the two IR wavelengths for CH2O

detection, it provides a combined UV/IR diagnostic for simultaneous CH2O/CH3CHO

19

measurement. This diagnostic scheme can be easily extended to include OH detection by

the addition of another color at 32606.52 cm−1.

Figure 3.6. Wavelength- and temperature-dependence of the aldehyde absorption

coefficients near 306.7 nm.

3.2.3 Multi-color aldehyde detection scheme

In summary, simultaneous measurement of CH2O and CH3CHO concentrations can be

obtained using laser absorption at νIR1 = 2895.92 cm-1, νIR2 = 2895.60 cm-1 and νUV =

32601.10 cm-1:

𝜒𝜒𝐶𝐶𝐶𝐶2𝐶𝐶 = 𝛼𝛼𝐼𝐼𝐼𝐼1 − 𝛼𝛼𝐼𝐼𝐼𝐼2

�𝜒𝜒𝐶𝐶𝐶𝐶2𝐶𝐶,𝐼𝐼𝐼𝐼1 − 𝜒𝜒𝐶𝐶𝐶𝐶2𝐶𝐶,𝐼𝐼𝐼𝐼2�𝑙𝑙𝜒𝜒 (Eqn. 3.1)

𝜒𝜒𝐶𝐶𝐶𝐶3𝐶𝐶𝐶𝐶𝐶𝐶 = 𝛼𝛼𝑈𝑈𝑈𝑈 − 𝜒𝜒𝐶𝐶𝐶𝐶2𝐶𝐶𝜒𝜒𝐶𝐶𝐶𝐶2𝐶𝐶,𝑈𝑈𝑈𝑈𝑙𝑙𝜒𝜒

𝜒𝜒𝐶𝐶𝐶𝐶3𝐶𝐶𝐶𝐶𝐶𝐶,𝑈𝑈𝑈𝑈𝑙𝑙𝜒𝜒 (Eqn. 3.2)

The corresponding absorption cross-sections σCH2O,IR1, σCH2O,IR2, σCH2O,UV and

σCH3CHO,UV will be presented in the next section.

20

3.3 Cross-Section Measurements

Figure 3.7. Sample CH2O absorbance traces.

Absorption cross-sections of CH2O were measured behind reflected shock waves using

1,3,5-trioxane as a clean pyrolytic precursor. When shock heated, 1,3,5-trioxane

dissociates neatly into three parts of CH2O without generating any by-product [74].

High-purity trioxane (>99%, supplied by Sigma–AldrichTM) was purified using a freeze-

pump-thaw method to remove dissolved air. Research grade high-purity gases (argon and

helium; >99.999%, supplied by PraxairTM) were used without further purification. Gas

mixtures of 0.333%, 0.167% and 0.083% trioxane/Ar (equivalent to 1%, 0.5% and 0.25%

CH2O/Ar, respectively) were filled into the driven section of the shock tube to the

desired initial pressures. Depending on the temperatures behind the reflected shock

waves, three distinct types of absorption signal have been observed (see Fig. 3.7). At low

temperatures (870–1050 K), the thermal dissociation of trioxane was resolved and the

plateau absorbance was used to determine CH2O cross-sections. In the temperature range

of 1050–1400 K, trioxane decomposed near-instantaneously into CH2O and generated

highly uniform absorption profiles throughout the test time. At even higher temperatures,

CH2O began to decompose within the test time, and its absorption cross-sections were

determined immediately after the arrival of the reflected shock wave (defined as time

zero). To correct for distortions by the schlieren spike (an artifact caused by deflection of

the laser beam during shock wave passage) within the first few microseconds of the test

21

time, extrapolation of the absorption signal to time zero was performed for measurements

at very high temperatures (>1700 K).

Similar experiments have been conducted with mixtures of 1%, 0.5% and 0.25%

CH3CHO (>99.5% purity, supplied by Sigma–AldrichTM) in argon, and the CH3CHO

absorption cross-sections were measured behind both incident and reflected shock waves

over a wide range of temperatures (592 K < T2 < 955 K, 918 K < T5 < 1672 K).

Figure 3.8. Temperature dependence of CH2O IR cross-sections at three pressures.

Dashed lines are best-fit for each pressure.

Fig. 3.8 shows measured IR absorption cross-sections of CH2O. The uncertainty in the

absorption coefficient obtained through these experiments, estimated to be ±5% from the

root-mean-squared (RMS) scatter, resulted from uncertainties in experimental

temperature and pressure and uncertainties in the concentration of CH2O precursors. The

CH2O absorption cross-sections at the two IR wavelengths were fitted as functions of

temperature and pressure (see Fig. 3.9). The least-squares fits yield:

𝜒𝜒𝐶𝐶𝐶𝐶2𝐶𝐶,2895.92𝑐𝑐𝑐𝑐−1[𝑐𝑐𝑐𝑐2/𝑐𝑐𝑚𝑚𝑙𝑙𝑚𝑚𝑐𝑐𝑚𝑚𝑙𝑙𝑚𝑚]

= 1.35 × 10−7 𝑇𝑇[𝐾𝐾]−3.56exp (−2277/𝑇𝑇[𝐾𝐾])𝜒𝜒[𝑎𝑎𝑎𝑎𝑐𝑐]−0.283 (Eqn. 3.3)

𝜒𝜒𝐶𝐶𝐶𝐶2𝐶𝐶,2895.60𝑐𝑐𝑐𝑐−1[𝑐𝑐𝑐𝑐2/𝑐𝑐𝑚𝑚𝑙𝑙𝑚𝑚𝑐𝑐𝑚𝑚𝑙𝑙𝑚𝑚]

= 4.90 × 10−17 𝑇𝑇[𝐾𝐾]−0.96exp (−166/𝑇𝑇[𝐾𝐾])𝜒𝜒[𝑎𝑎𝑎𝑎𝑐𝑐]0.256 (Eqn. 3.4)

which are valid over 900–1800 K and 0.8–3.3 atm.

22

Figure 3.9. Fitted IR absorption cross-sections of CH2O.

Fig. 3.10 shows the measured UV absorption cross-sections of CH3CHO and CH2O. No

pressure dependence was observed for either species. The least-square fits

𝜒𝜒𝐶𝐶𝐶𝐶2𝐶𝐶,32601.10𝑐𝑐𝑐𝑐−1[𝑐𝑐𝑐𝑐2/𝑐𝑐𝑚𝑚𝑙𝑙𝑚𝑚𝑐𝑐𝑚𝑚𝑙𝑙𝑚𝑚] = 4.58 × 10−20 (Eqn. 3.5)

𝜒𝜒𝐶𝐶𝐶𝐶3𝐶𝐶𝐶𝐶𝐶𝐶,32601.10𝑐𝑐𝑐𝑐−1[𝑐𝑐𝑐𝑐2/𝑐𝑐𝑚𝑚𝑙𝑙𝑚𝑚𝑐𝑐𝑚𝑚𝑙𝑙𝑚𝑚]

= −1.88 × 10−20 + 8.43 × 10−23𝑇𝑇[𝐾𝐾] − 2.14 × 10−26𝑇𝑇[𝐾𝐾]2 (Eqn. 3.6)

are valid over the ranges 900–1600 K and 500–1700 K, respectively, and are seen to

agree with the measurement within an RMS error of 3%.

Figure 3.10. UV absorption cross-sections of CH2O and CH3CHO at 32601.10 cm−1.

23

3.4 Example Applications

3.4.1 Validation experiments

Figure 3.11. Four-color absorption time-histories measured during the pyrolysis of

0.167% trioxane/0.5% CH3CHO/Ar mixture at reflected shock conditions of 965 K and

2.26 atm. Results at 32601.10 and 32606.52 cm−1 are almost coincident, as expected.

Figure 3.12. Aldehydes time-histories of the example in Fig. 3.11.

The performance of the 3-color CH2O/CH3CHO/OH diagnostic scheme has been

validated through two controlled experiments, where mixtures of 0.167% trioxane/0.5%

CH3CHO/Ar were pyrolyzed behind reflected shock waves. The first experiment was

performed at a low temperature where the formation of CH2O during trioxane pyrolysis

24

was observed. Shown in Fig. 3.11 are the measured absorbances time-histories at the

three colors. Also included in the figure is the absorbance time-history measured at the

OH color (32606.52 cm-1), which is almost identical to the absorbance at 32601.10 cm-1.

From these absorption measurements, the concentration time-histories of CH2O and

CH3CHO were exacted using Eqn. 3.1-3.6, and plotted in Fig. 3.12. As the figure clearly

shows, the current study has successfully recovered the expected steady-state

concentrations of both aldehydes. The second experiment was conducted at a higher

temperature where the aldehydes began to dissociate. The results are shown in Fig. 3.13,

which indicates that the current study has recovered the initial concentrations of the two

aldehydes and captured their asymptotic decay behaviors at long time. The concentrations

of both aldehydes approach zero at similar rates, probably due to kinetic coupling through

reactions with intermediate radical species (for example, H radicals). Results from

chemical kinetics simulations also support the current observation.

Figure 3.13. Measured aldehydes time-histories of 0.167% trioxane/0.5% CH3CHO/Ar

pyrolysis at reflected shock conditions of 1418 K and 1.82 atm.

3.4.2 CH2O pyrolysis

As another example application of the current diagnostics, CH2O pyrolysis time-histories

were measured behind reflected shock waves over 1560 - 1782 K via IR absorption at

2895.92 cm-1. Shown in Fig. 3.14 are three representative traces from the current study,

in comparison with numerical simulations using a detailed C0-C4 reaction mechanism,

25

USC Mech II [75]. In the 1560 K case, excellent agreement is seen between the

simulation and the measurement. However, at higher temperatures, the simulations

underpredict the decay rates of CH2O by 20–40%. Analysis of the local CH2O sensitivity

(Fig. 3.15), which is defined as the ratio of the percentage change in the CH2O mole

fraction to the percentage change in the rate constant of the reaction under investigation

(∂ ln χCH2O / ∂ ln ki), reveals that the CH2O time-histories at the current experimental

conditions were most sensitive to the following reactions:

HCO +H (+M) = CH2O (+M) (R3.1)

CH2O + H = HCO + H2 (R3.2)

HCO + M = H + CO + M (R3.3)

HCO + H = CO + H2 (R3.4)

Recently, the study by Friedrichs et al. [29] has provided a more accurate expression for

the rate constant of reaction R3.1 over 1400–3000 K. When updated with this new rate

expression, USC-Mech II shows substantially improved agreement with the current high-

temperature measurements (see Fig. 3.14).

Figure 3.14. Comparison of measured and simulated CH2O traces in 1% CH2O/Ar

pyrolysis. Simulations done with original and modified USC Mech II [75].

26

Figure 3.15. CH2O sensitivity, ∂ ln χCH2O / ∂ ln ki, of the example in Fig. 3.14.

3.4.3 CH3CHO pyrolysis

Similar measurements were conducted on CH3CHO pyrolysis over 1278 - 1606 K using

UV absorption at 32601.10 cm−1. Three representative CH3CHO time-histories are

displayed in Fig. 3.16, in comparison with kinetic simulations using USC Mech II. The

simulations are seen to underpredict the decay rates of CH3CHO, which, according to the

CH3CHO sensitivity analysis (Fig. 3.17), are governed by the following reactions:

CH3 + HCO (+M) = CH3CHO (+M) (R3.5)

CH3CHO + CH3 = CH3CO + CH4 (R3.6)

CH3 + CH3 (+M) = C2H6 (+M) (R3.7)

CH3CHO + H = CH3CO + H2 (R3.8)

The recent study by Bentz et al. [31] has reported revised rate constants of reactions R3.5

and R3.8. When updated with these revised rate constants, USC Mech II provides better

predictions for the CH3CHO decay rates, but still has room for further improvement.

Future shock tube/laser absorption measurements of other CH3CHO decomposition

products (for example, CO, CH3 and CH4) should provide kinetics targets that will better

constrain the mechanism and allow refinements in key reaction rates.

27

Figure 3.16. Comparison of measured and simulated CH3CHO traces in 1% CH3CHO/Ar

pyrolysis. Simulations done with original and modified USC Mech II [75].

Figure 3.17. CH3CHO sensitivity, ∂ ln χCH3CHO / ∂ ln ki, of the example in Fig. 3.16.

3.5 Summary

A system of multi-color laser absorption diagnostics for interference-immune CH2O

sensing and combined CH3CHO/CH2O detection was developed and validated. This

system utilized mid-IR absorptions at 2895.92 and 2895.60 cm−1 and UV absorption at

32601.10 cm−1, which were accessed with a DFG laser and a frequency-doubled ring dye

laser, respectively. Absorption cross-sections of CH2O at the two IR wavelengths were

measured behind reflected shock waves over 900–1800 K, 0.8–3.3 atm, within an

uncertainty of ±5%. Absorption cross-sections of CH3CHO and CH2O at the UV

28

wavelength were measured to the same accuracy, over 900–1600 K and 500–1700 K,

respectively. The current diagnostics were then applied to shock tube pyrolysis

experiments of CH2O and CH3CHO, where the aldehydes time-histories were measured

and compared to kinetic simulations with the USC-Mech II mechanism. These

simulations were seen to underpredict the decay rates of both aldehydes, which,

according to the current analysis, could be remedied by updating key reaction rate

constants in the mechanism. Aside from their initial applications demonstrated above, the

current diagnostics also promise to be useful in studies of other reaction systems, for

example, the oxidation of hydrocarbons and the pyrolysis of oxygenated fuels. Future

shock tube experiments will apply these diagnostics to investigate the pyrolysis and

oxidation chemistry of alcohols, ethers and biodiesel fuel surrogates, with hopes to

provide unique kinetics targets that may guide the development, validation and

calibration of modern reaction mechanisms.

29

Chapter 4. Shock Tube Measurement of the

Thermal Dissociation Rate Constant of CH3CHO

using a Sensitive CO Diagnostic

The contents of this chapter have been published in the Journal of Physical Chemistry A

under the title "Shock Tube Measurement for the Dissociation Rate Constant of

Acetaldehyde using Sensitive CO Diagnostics" [40].

4.1 Introduction

The previous chapter has reported CH3CHO time-histories measured during the pyrolysis

of 1% CH3CHO/Ar mixture behind reflected shock waves. These results have been

adopted by a group of combustion kinetics modelers to validate and optimize their

reaction mechanism [76]. Their comparison of simulations using various reactions

mechanisms [75], [77]–[80] and the measurement results from this study (see Fig. 4.1)

has revealed large discrepancies between these simulations as well as deviations of these

simulations from the experiment. These differences have suggested the need for further

investigations of the acetaldehyde pyrolysis system.

As the sensitivity analysis in Fig. 3.17 suggested, the CH3CHO removal rate was mainly

governed by the following four reactions, among which the unimolecular decomposition

of aldehydes (R4.1) was recognized to be one of the dominant reactions:

CH3CHO (+M) = CH3 + HCO (+M) (R4.1)

CH3 + CH3CHO = CH4 + CH3CO

(R4.2)

CH3 + CH3 (+M) = C2H6 (+M) (R4.3)

H + CH3CHO = H2 + CH3CO (R4.4)

However, due to the heavy cross-interferences of the above reactions (R4.1-R4.4) with

each other in a high-concentration CH3CHO pyrolysis system, directly extraction of rate

30

constants was not possible in the previous experiment. Therefore new experiments

exploiting more dilute mixtures were designed and conducted to isolate these reactions

and accurately determine their rate constants, with the current study focusing on the

reaction rate constant of R4.1 (k4.1).

Figure 4.1. Comparison of measured and simulated CH3CHO profiles during 1%

CH3CHO/Ar pyrolysis. Dashed lines: simulations with USC Mech II [75], which are

almost identical to simulations with JetSurF 2.0 [77]; short dashes: simulations with

ARAMCO [78]; dash dots: simulations with the Cong and Dagaut mechanism [79];

dotted lines: simulations with the Chatelain et al. mechanism [80]. Note that both USC

Mech II/ JetSurF 2.0 and ARAMCO underpredict the CH3CHO decay rates, while the

other mechanisms overpredict the decay rates. Figure adapted from Mével et al. [76]

Instead of monitoring the decay of CH3CHO, the current study utilized a more sensitive

diagnostic to monitor the stable product formed during its pyrolysis, CO, which was

produced via the following reactions:

HCO (+M) = H + CO (+M) (R4.5)

CH3CO (+M) = CH3 + CO (+M) (R4.6)

Because the concentrations of other oxygenated products, such as CH3CO and HCO,

were negligibly low due to their very short life-times, the CO formation rate correlated

with the removal rate of CH3CHO in a 1:1 ratio. Details about the CO diagnostic and its

example applications can be found in the studies by Ren et al. [53] and Lam et al. [81].

31

With a 1σ detection limit of about 10ppm, this highly sensitive CO diagnostic allowed

the use of lower CH3CHO concentration (1000ppm) without sacrificing the signal-to-

noise ratio, and hence significantly suppressed the influences of secondary reactions and

temperature changes (to less than 8K), leading to accurate determination of k4.1.

4.2 Rate Constant Measurement

Figure 4.2. Example CO time-history in the pyrolysis of 1000ppm CH3CHO/Ar.

Reflected shock conditions: T = 1447 K, P = 1.60 atm.

As shown in Fig. 4.2, the rate constant k4.1 is inferred by best-fitting the simulated CO

time-history from a comprehensive reaction mechanism, USC Mech II [75], to the

experiment result. Also shown in the figure are CO time-histories with k4.1 perturbed by

+/-30%, which highlight the sensitivity of the current rate constant measurement. This is

further illustrated by a formal CO sensitivity analysis displayed in Fig. 4.3. As the figure

clearly shows, the CO sensitivity is dominated by the title reaction, i.e. the thermal

dissociation of acetaldehyde, whereas sensitivities of other reactions, especially the

radical abstraction reactions, are relatively low.

32

Figure 4.3. CO sensitivity, ∂ln𝜒𝜒𝐶𝐶𝐶𝐶 (t)/ ∂lnki, of the time-history shown in Fig. 4.3,

highlighting the reactions with a maximum sensitivity larger than 0.05. Calculated using

USC Mech II as the base mechanism, with updated values of k4.1 from the current study.

Note that the interferences from R4.2-R4.4 have been substantially suppressed.

A detailed uncertainty analysis, which includes secondary reactions and other uncertainty

sources, is shown in Fig. 4.4. Rate constants of the secondary reactions, k4.2, k4.3 and k4.4

are assigned an uncertainty factor of 2, in accordance with recommendations by Baulch et

al. [82] The resulting uncertainties in k4.1 are determined from a brute-force approach, i.e.

by adjusting the individual values of k4.2, k4.3 and k4.4 to their uncertainty limits and

calculating the subsequent changes in the best-fit inference of k4.1. Uncertainty in the

reflected shock temperature (T5), translates to about +/-18% uncertainty in k4.1. Fitting

uncertainty, determined by varying k4.1 to fit the upper and lower envelopes of the

measured CH3 profile, is about +/-10%. Uncertainty in the CO absorption cross-section

(+/-5%) is quoted from Ren et al. [53], and the uncertainty in the CH3CHO concentration

of the manometric mixture is estimated to be +/-5%.. The overall (root-mean-squared) 2σ

uncertainty in k4.1 is calculated to be +28% / -32% at 1447 K.

33

Figure 4.4. Uncertainty analysis for the measurement of k4.1 at 1447 K.

4.3 Results and Discussions

A total of 6 reflected shock experiments were conducted at temperatures between 1273 K

and 1618 K and pressures near 1.6 atm (see Table 1), which resulted in an Arrhenius

expression for the rate constant of R1 as k4.1(1.6 atm) = 1.1 x 1014 exp(-36900 K/ T) s-1,

with a 2σ uncertainty of about +/- 30%. CO time-histories of these 6 shock experiments

are also available in the Appendix A.

Table 4.1. Summary of the current measurement of k4.1, with comparison to previous

theoretical calculations

Current Measurement Previous Theoretical Calculations

T (K) P (atm) k4.1 (s-1) 2σ Uncertainty Harding et al.

[33]

Gupte et al.

[30]

USC- Mech II

[75]

1618 1.45 1.4 x 104 +25% / -28% 9.5 x 103 1.1 x 104 1.7 x 103

1522 1.54 3.5 x 103 +27% / -30% 2.6 x 103 3.1 x 103 5.5 x 102

1447 1.60 1.0 x 103 +28% / -32% 8.2 x 102 9.8 x 102 2.0 x 102

1382 1.66 3.0 x 102 +30% / -34% 2.7 x 102 3.2 x 102 7.0 x 101

1331 1.72 9.7 x 101 +32% /- 37% 1.0 x 102 1.2 x 102 2.8 x 101

1273 1.75 3.1 x 101 +36% / -40% 3.0 x 101 3.5 x 101 8.7 x 100

34

Previous experimental studies of k4.1 using other approaches have been reported in the

literature, whose results are now compared to the current data in Fig. 4.5. Gupte et al.

[30] examined the pyrolytic decomposition of acetaldehyde and measured k4.1 through

shock tube laser-schlieren experiments at temperatures of 1550 - 2400 K and pressures of

0.05 – 0.66 atm. The highest-pressure data from Gupte et al. are selected for the

comparison, and they appear to have similar activation energy as the current study, with a

small offset in the magnitude of k4.1 probably resulting from the pressure dependence

(both measurements are in the pressure fall-off region). Bentz et al. [31] investigated k4.1

at temperatures ranging from 1250 to 1650 K and pressures of about 1.3, 2.9 and 4.5 atm

using H-atom resonance absorption spectrometry in a shock tube. Fig. 4.5 shows that the

1.3 atm data from Bentz et al. agree very well with the current data at a slightly larger

pressure (1.6 atm). Recently, Sivaramakrishnan et al. [32] used a similar method as Bentz

et al. to measure k4.1 over temperatures of 1200 – 1800 K and pressures of 0.26 – 1.3 atm.

Yet their 1.3 atm data, as displayed in Fig. 4.5, show more scatter and agree less well

with the current study.

Figure 4.5. Comparison of the current measurement results with previous experimental

studies at similar pressures.

The results of the current measurement are also compared with recent theoretical

calculations. Fig. 4.6 shows the RRKM predictions of k4.1 from Harding et al. [33] and

Gupte et al. [30] evaluated at the mean pressure of the current study (1.6 atm). Both of

35

them lie within the error limits of the current data. A more detailed comparison at the

individual shock conditions, as shown in Table 4.1, suggest that Gupte et al. agree better

with the present study on the high-temperature end, whereas Harding et al. agree better

on the low-temperature end. Also included in Fig. 4.6 is the evaluation of the original k4.1

expression in USC-Mech II, which is seen to underpredict k4.1 by about half an order of

magnitude at 1.6 atm.

Figure 4.6. Comparison of the current data with previous theoretical calculations.

It is worth noting that the following roaming channel of acetaldehyde dissociation was

also recognized by Harding et al. [33]:

CH3CHO (+M) = CH4 + CO (+M) (R4.1a)

with a theoretically predicted branching ratio (BRroam) of about 10%. This was supported

by the experimental results of Sivaramakrishnan et al. [32] with a measured BRroam of

23+/-9%. However, this roaming channel is not included in the base mechanism of the

current study (USC-Mech II). As the current measurement of k4.1 is inferred from the

formation rate of CO, which can be estimated via quasi-equilibrium approximation as

𝑑𝑑[𝐶𝐶𝐶𝐶]/𝑑𝑑𝑎𝑎 = 2𝜒𝜒4.1[𝐶𝐶𝐶𝐶3𝐶𝐶𝐶𝐶𝐶𝐶] + 𝜒𝜒4.1𝑎𝑎[𝐶𝐶𝐶𝐶3𝐶𝐶𝐶𝐶𝐶𝐶], inclusion of this roaming channel will

effectively scale the current rate expression by a factor of 1-BRroam/2. Because this

roaming correction (7-16%) is well below the measurement uncertainty, it is not included

in the current rate expression. Contributions from other reaction channels (listed below)

36

are negligible (<5%), according to theoretical estimates of Gupte et al. [30] and Harding

et al. [33]:

CH3CHO (+M) = CH2CO + H2 (+M) (R4.1b)

CH3CHO (+M) = CH3CO + H (+M) (R4.1c)

CH3CHO (+M) = CH2CHO + H (+M) (R4.1d)

With the new rate constant expression for k4.1, it is time to revisit the previous study of

1% CH3CHO/Ar pyrolysis. Fig. 4.7a compares the predictions of the original USC Mech

II mechanism and the mechanism with k4.1 updated from the current study, to the

previous measurement results reported in Chapter 3. Substantial improvement of USC

Mech II in the CH3CHO chemistry is achieved by using the current values of k4.1, as the

updated mechanism is now in much better agreement with the measurement.

Improvements at various degrees are also observed in other mechanisms, including the

ARAMCO [78] mechanism (Fig. 4.7b), the Cong and Dagaut [79] mechanism (Fig. 4.7c)

and the Chatelain et al. [80] mechanism (Fig. 4.7d), when the current k4.1 is adopted.

Among the four mechanisms, the ARAMCO mechanism is the least affected by the

current update, since it has adopted a rate expression for k4.1 (from Harding et al. []) that

is in close agreement with the current study near 1.6 atm. The modest difference between

the ARAMCO simulation and the previous measurement is probably due to uncertainties

in the rate constants of other reactions, for example, R4.2 and R4.4, which can be

subjects of future research.

37

Figure 4.7. CH3CHO time-histories during 1% CH3CHO/Ar pyrolysis, simulated using

the original and updated mechanisms of (a) USC-Mech II [75], (b) ARAMCO [78], (c)

the Cong and Dagaut mechanism [79], and (d) the Chatelain et al. mechanism [80], in

comparison with the previous measurement results in Chapter 3. For all four mechanisms,

the current values of k4.1 significantly improve their predictions for the CH3CHO time-

histories.

38

4.4 Summary

A comparative examination of recent combustion mechanisms related to acetaldehyde

chemistry revealed large variations between simulations utilizing these mechanisms as

well as their deviations from the experiment results reported in Chapter 3, which

motivated the current study to revisit the classic pyrolytic system of acetaldehyde.

Experiments were conducted to measure the direct thermal dissociation rate constant of

acetaldehyde, k4.1. By employing a sensitive CO diagnostic, the current measurement

achieved accurate and direct determination of k4.1 from high-quality CO time-histories

obtained in the pyrolysis of 1000ppm CH3CHO / Ar mixtures. A total of six reflected

shock experiments were conducted at temperatures of 1273 - 1618 K and pressures

around 1.6 atm, resulting in an Arrhenius expression for the target rate constant as

k4.1(1.6 atm) = 1.1 x 1014 exp(-36900 K/T) s-1, with 2σ uncertainty of about +/- 30%. In

general, the current results were seen to be in good agreement with previous experimental

and theoretical studies. When incorporated into several existing reaction mechanisms, the

current values of k4.1 substantially improved their performances in modeling the previous

1% acetaldehyde pyrolysis data. Future studies of acetaldehyde pyrolysis using CH4 and

CH3 diagnostics are also planned, which aim to provide additional kinetics targets for

further improving acetaldehyde reaction models, especially regarding the rate constant of

reaction R4.2.

39

Chapter 5. Shock Tube Measurement of the Rate

Constant of CH2O + H = HCO + H2

The contents of this chapter have been published in the Journal of Physical Chemistry A

under the title "Reaction Rate Constant of CH2O + H = HCO + H2 Revisited: A

Combined Study of Direct Shock Tube Measurement and Transition State Theory

Calculation" [83].

5.1 Introduction

As discussed in Chapter 1, the CH2O removal chemistry has great importance in both

theoretical studies and practical applications. Under the typical fuel-lean conditions of

hydrocarbon combustion, CH2O is mainly removed through the H-abstraction reactions

of H, OH, O, and CH3 [2], [29], [84], among which CH2O + H is a dominant reaction

pathway. However, there is still large uncertainty in the reaction rate constant of CH2O +

H, and literature values are seen to vary over an order of magnitude at high temperatures

[2], [16]–[20], [82], [85], [86]. According to the comprehensive review and evaluation by

Baulch et al. [82], the experimental study from Friedrichs et al. [19], though yielding

results that are significant higher than most of other studies, has been considered the most

accurate over 1510−1960 K. Friedrichs et al. [19] inferred the CH2O + H rate constant

from VUV absorption of CH2O behind reflected shock waves, utilizing 1,3,5-trioxane

and C2H5I as the precursors of CH2O and H, respectively. But the non-monochromatic

nature of the VUV lamp has led to relatively weak absorption of CH2O and interference

absorption from other species, which posed significant challenges to the measurement

and limited the minimum CH2O loading to 1000 ppm. Consequently, the uncertainties

(2σ uncertainty factor = 1.66) in the rate constant measurement of Friedrichs et al. were

not optimized and still had room for improvement. Recently, a sensitive and interference-

free mid-IR laser absorption diagnostic for CO has been developed at Stanford, which

shows paths to circumvent these past challenges and open up new alternatives for kinetics

measurements [40], [81]. This diagnostic has been successfully applied to shock tube

40

measurements of several important rate constants, including the one discussed in the

previous chapter. With the application of this advanced CO diagnostic becoming mature,

it is time to revisit the rate constant measurement for CH2O + H.

5.2 Experiment Design

Previous shock tube studies have identified the following chain reactions to be the

governing mechanism for the pyrolysis chemistry of CH2O [16]–[18], [28], [29], [58],

[87]–[89]:

CH2O + M = HCO + H + M (R5.1a)

CH2O + M = H2 + CO + M (R5.1b)

CH2O + H = HCO + H2 (R5.2)

HCO + M = H + CO + M (R5.3)

H + HCO = H2 + CO (R5.4)

HCO + HCO = CH2O + CO (R5.5)

The current study utilized ethyl iodide (C2H5I) as a pyrolytic precursor for H atoms.

When heated by the reflected shock waves, C2H5I underwent thermal decomposition via

the following two reaction channels:

C2H5I = C2H5 + I (R5.6a)

C2H5I = HI + C2H4 (R5.6b)

with C2H5 rapidly decomposing to give H radicals by:

C2H5 = H + C2H4 (R5.7)

The total rate constant and the branching ratio were studied by Herzler and Frank [90]

and by Kumaran et al. [91], and recently reevaluated by Friedrichs et al. [19]. The values

from Friedrichs et al. [19] were used for the kinetics simulations in this work. The current

study also used 1,3,5-trioxane, which decomposed into three parts of CH2O upon shock

heating, as a clean precursor for CH2O. The solid-phase 1,3,5-trioxane (>99% purity),

supplied by Sigma-Aldrich, was vaporized by gentle heating with warm water of 40−50

°C. This gas was then mixed with the C2H5I vapor, generated from its liquid form (>99%

41

purity, also supplied by Sigma-Aldrich), and diluted in argon for use as test gas in the

shock tube experiments. Prior to the mixture preparation, both 1,3,5-trioxane and C2H5I

were purified by using a freeze−pump−thaw procedure to remove dissolved air. The bath

gas argon (>99.999% purity) was supplied by Praxair and used without further

purification.

5.3 Measurement Results

Fig. 5.1 shows several representative CO time-history traces from pyrolysis experiments

of 333 ppm of 1,3,5-trioxane and 20 ppm of C2H5I in argon. The initial distortion in the

CO signals near time zero is an artifact due to deflection of the laser beam at shock wave

passage, and should not be confused as a physical CO signal. Note, however, the

measurement results are not influenced by this artifact despite a loss of about 5 μs test

time. The time zero is determined by extrapolating the measured CO profile back to the

zero level. The initial composition of the gas mixture (1000 ppm of CH2O/20 ppm of

C2H5I/Ar) is determined from the partial pressure of each component during the

manomeric preparation, and is confirmed with the CO measurement at the end of the test

time. The final plateau value of CO is measured to be about 980 ppm, which agrees

closely with the manometric value within measurement uncertainty. In the incident shock

region before time zero, no CO formation has been observed, which is expected due to

the relatively low gas temperature and pressure.

Figure 5.1. Example CO time-histories in the pyrolysis of 1,3,5-trioxane/C2H5I/Ar.

42

The CH2O + H rate constant is inferred from best fitting the model prediction to match

the measured CO time-history by varying the target rate constant. The mechanism used in

this study is listed in Table 5.1. For the particular case shown in Fig. 5.2, the residual

error in the best fit is less than ±1%. Also shown are the simulated CO time-histories

corresponding to the best-fit rate modified by ±30%, which indicate the very high

sensitivity of CO time-history to the rate of CH2O + H. It is also worth noting that the

current study focuses on the first 200 μs of the test time, where the sensitivity of the

target reaction CH2O + H is dominant over the other reactions. This is further explained

in the sensitivity analysis discussed below.

Table 5.1. Reaction mechanism* for the CH2O + H rate constant measurement No. Reaction B m EB Reference

Updated CH2O Chemistry

5.1a CH2O + M = HCO + H + M** 3.30 x 1039 -6.3 99.9 [29]

5.1b CH2O + M = CO + H2 + M** 3.10 x 1045 -8.0 97.5 [29]

5.2 CH2O + H = H2 + HCO 1.97 x 1011 1.06 7.59 This study

5.3 HCO + M = H + CO + M 9.35 x 1016 -1.00 17.0 [92]

5.4 H + HCO = H2 + CO 1.20 x 1014 0 0 [92]

5.5 HCO + HCO = CH2O + CO 2.70 x 1013 0 0 [93]

Iodine Sub-mechanism

5.6a C2H5I = C2H5 + I 3.66 x 109 0 26.6 [19]

5.6b C2H5I = C2H4 + HI 2.21 x 107 0 19.0 [19]

5.8 I + CH2O = HI + HCO 8.32 x 1013 0 17.4 [94]

5.9 I + HCO = HI + CO 5.00 x 1013 0 0 [19]

5.10 I + H2 = HI + H 2.72 x 1014 0 33.9 [95]

5.11 I + HI = I2 + H 8.02 x 1014 0 37.1 [96]

5.12 I + C2H4 = HI + C2H3 1.00 x 1012 0 6.93 [19]

5.13 I + C2H2 = HI + C2H 1.60 x 1012 0 17.0 [19]

5.14 I + CH4 = HI + CH3 1.48 x 1014 0 33.0 [97]

5.15 HI + M = H + I + M 1.00 x 1014 0 62.6 [19]

5.16 I2 + M = I + I + M 9.79 x 1013 0 30.4 [98] *: Rate constants are expressed in the modified Arrhenius form: ki = B Tm exp(-EB/RT) (units kcal, cm3 ,

mol, s, and K). The USC Mech II [75] mechanism is used as base mechanism; only the reactions not

included in USC Mech II or the reactions reported with a different set of rate parameters are listed here. **: RRKM fit for T = 1400 – 3000 K and P = 1 bar. Collision efficiencies: M 1.0, Ar 0.7, H2 2.0, CO 1.5,

CH2O 3.0.

43

Figure 5.2. Rate constant inference from the 1659 K, 1.06 atm example shown in Fig. 5.1.

Shown in Fig. 5.3 is a CO sensitivity analysis for the above example. The sensitivity

analysis clearly indicates that the CO formation is dominated by the target reaction:

CH2O + H = HCO + H2 (reaction R5.2), especially during the first 200 μs of the test

time. The reactions of HCO converting into CO, especially R5.3 and R5.4, are typically

very fast and hence are not the rate-limiting factors for CO formation. However, these

two reactions, along with the target reaction, establish quasi-equilibrium for the H-atom

concentration, and therefore influence the rate of conversion from CH2O to CO. For

example, changing the reaction rate of HCO + M = CO + H + M by a factor of 2 would

perturb the CO formation rate by roughly 20%. For this particular reaction, it is worthy to

note that there are some discrepancies between its rate constant values in the literature

[57], [92], [99]–[106]. The rate expression from a direct measurement by Friedrichs et al.

[92], although appears to be lower than the values from a few indirect studies [57], [58]

and the review by Li et al. [106], is seen to agree reasonably well with most direct

measurements [99]–[101], and therefore it is adopted in the current study. Recently, the

laminar burning velocity measurement and Monte Carlo rate optimization by Santner et

al. [107] has suggested a reduction of the Li et al. [106] rate by about a factor of 2, which

is now consistent with the value of Friedrichs et al. [92]. Other reactions, such as CH2O +

M = HCO + H + M (R5.1a) and C2H5I = HI + C2H4 (R5.6b), have only minor influence

44

on the CO formation rate (changing each reaction rate by a factor of 2 would perturb the

CO formation rate by less than 7%).

Figure 5.3. CO sensitivity analysis for the 1659 K, 1.06 atm example.

Figure 5.4. Uncertainty analysis for the measured rate constant of CH2O + H.

The individual uncertainty contributions from all interference reactions mentioned above

are listed in a detailed uncertainty analysis as shown in Fig. 5.4. Also included in the

analysis are various experimental uncertainties, which are small as compared to the

uncertainties from reaction kinetics. The primary uncertainty source in the current rate

measurement is the uncertainty in the rate of R5.3 (uncertainty factor = 1.7, which

translates to +12%/−20% uncertainty in the referred rate constant). However, this

45

uncertainty can be reduced by repeating the measurement at different C2H5I/CH2O

ratios, where the quasi-steady-state H concentrations are different.

Fig. 5.5 summarizes the target reaction rate measured at four C2H5I/CH2O ratios in an

Arrhenius diagram. Guided by the uncertainty analysis mentioned above, different

C2H5I/CH2O ratios are optimized for different temperature regions. For example, the

20ppm C2H5I/1000ppm CH2O mixture is good for 1500 K ≤ T ≤ 1800 K, but the

corresponding uncertainty escalates at lower and higher temperatures; for T > 1800 K the

50ppm C2H5I/1000ppm CH2O mixture yields smaller measurement uncertainty; and for

T < 1500 K, 5ppm C2H5I/500ppm CH2O is a better choice. Measurements have also

been conducted at even lower CH2O concentration (250 ppm) to minimize the

temperature change during the pyrolysis of 1,3,5-trioxane and CH2O (less than 5 K).

Despite the variations in their uncertainty limits, all data follow the same trend and are

seen to consistent, which provides a good cross-validation for the current measurement

results. The used of lower CH2O loading, combined with the sensitive CO diagnostic,

also allows the current study to extend the rate constant measurement for R5.2 to lower

temperatures previously inaccessible. A total number of 42 shocks were conducted, and

the results (listed in Appendix B) have yielded a modified Arrhenius rate expression of

k5.2 = 1.97 × 1011(T/K)1.06 exp(−3818 K/T) cm3 mol−1 s−1 over 1304−2006 K.

Figure 5.5. Rate constants of CH2O + H measured at different mixture compositions.

46

5.4 Comparison with Previous Studies

Fig. 5.6 compares the target reaction rate constant from different studies at temperatures

from 1000 to 2500 K. The recent shock tube study with Vis-UV CH2O absorption by

Friedrichs et al. [19] is seen to agree relatively well with the current study, within their

respective error bars. The small differences between the two studies are overshadowed by

the single-shot uncertainties in both data sets (estimated to be ±20% for the study of

Friedrichs et al. [19] and +10/−15% for the current study), which result primarily from

the uncertainties in the mixture concentrations and in the fitting. The minor discrepancy

between the mean values of the two studies is possibly due to (1) different choice of the

R5.1a rate constant (the current rate has adopted an expression for k5.1a from a more

recent study [29]), and (2) influences from interfering absorptions. Notably, by

employing a narrow line width and species-selective mid-IR laser absorption diagnostic

for CO, the current study is free from interference absorption. As a result, the current

study has reduced the uncertainty in the target rate constant measurement by roughly a

factor of 2 as compared to Friedrichs et al. [19]. The earlier shock tube laser-schlieren

measurement by Irdam et al. [20] lies above the temperature range of the current

measurement and is seen to agree in trend with the current study but with larger scatter.

Irdam et al. also performed a conventional TST calculation, assuming an energy barrier

of 6.6 kcal/mol for the transition state. Their result, shown in Fig. 6, is in reasonable

agreement with the current measurement and TST calculation over 1000 – 2000 K. The

low-pressure flame study from Vandooren et al. [17] and the shock tube study from Dean

et al. [16] have also yielded rate constant expressions for the target reaction, but with

much higher uncertainties. The rate constant expression from Vandooren et al. agrees

reasonably well with the current study at lower temperatures, but begins to diverge from

the current results near the high temperature end (1500 K) of their study. The rate

expression from Dean et al. agrees less well with the current study. Choudhury and Lin

[18] have attempted to infer the target reaction rate from shock tube measurements of

methyl nitrite and 1,3,5-trioxane pyrolysis. However, due to the strong coupling between

the target reaction (R5.2) and reaction R5.1a, their measurement has suffered from much

uncertainty and significantly underpredicted the target rate constant.

47

Figure 5.6. Arrhenius plot for the rate constant of CH2O + H over 1000−4000 K.

Aside from these experimental data, there are also a few literature reviews for the rate

constant of R5.2. Tsang and Hampson [85] have conducted a comprehensive review on

the combustion of methane and related compounds, and their recommended rate constant

expression for k5.2 is seen to be in excellent agreement with the current study. Baulch et

al. [82], [86] have also conducted a series of critical reviews for the fundamental rate

constants used in kinetics modeling. The rate expression for k5.2 from an earlier version

of Baulch et al. review [86] is seen to be lower than the current study, but the difference

is still within its uncertainty limit (uncertainty factor = 3.16). A more recent version of

the Baulch et al. [82] review has incorporated the findings of Friedrichs et al. [19], and is

seen to yield better agreement with the current study. Warnatz [2] has also provided a

recommendation for k5.2 based on review of indirect measurements prior to 1980, but the

result is subject to higher uncertainty and is seen to be much lower than the current study.

48

5.5 Summary

The current study inferred the rate constant of CH2O + H = H2 + HCO from accurate CO

time-histories measured in shock tube pyrolysis experiments of 1,3,5- trioxane and C2H5I

mixtures. A modified Arrhenius equation for this rate constant, valid over 1304 - 2006 K,

was obtained from the current measurement: k5.2 = 1.97×1011(T/K)1.06exp(−3818 K/T)

+18/−26% cm3mol−1s−1. Compared to previous studies, the current work has significantly

reduced the measurement uncertainty. For a rate constant expression over a wider range

of temperatures the reader is referred to a complementary TST calculation conducted by

Dr. Enoch Dames in recent collaboration with the author [83], which supported the shock

tube measurements and extended the temperature range to 200−3000 K: k5.2 =

5.86×103(T/K)3.13exp(−762 K/T) cm3mol−1s−1. These results should enable improved

future combustion kinetics modeling.

49

Chapter 6. High-Temperature Measurements of

the Rate Constants of a Series of Aldehydes + OH

The contents of this chapter have been published in Proceedings of the Combustion

Institute under the titles "High Temperature Measurements for the Rate Constants of C1-

C4 Aldehydes with OH in a Shock Tube" [42] and "Rate Constants of Long, Branched

and Unsaturated Aldehydes with OH at Elevated Temperatures" [43].

6.1 Introduction

Aside from the unimolecular decomposition reaction discussed in Chapter 4, and the H-

abstraction reaction by H atoms discussed in Chapter 5, another important pathway for

aldehydes removal during hydrocarbon combustion is the H-abstraction reaction by the

hydroxyl radical (OH), which is the focus of this chapter. For formaldehyde (CH2O), this

removal pathway has been studied by various researchers at combustion temperatures.

For example, Vasudevan et al. [21] has measured the rate constant of CH2O + OH over

934–1670 K in shock tube experiments. Despite the abundance of rate constant data for

CH2O + OH, however, there has been no previous direct measurement for higher

aldehydes reacting with OH at T > 1000 K. This has strongly motivated the current study

to measure the overall rate constants of a series of C2-C7 aldehydes + OH, including both

small straight-chain aldehydes and long, branched and unsaturated aldehydes (for a

complete list of aldehydes please see Fig. 6.1), in hopes that the new data obtained would

not only enrich fundamental combustion kinetic databases, but also provide insights into

site-specific reactivity of these H-abstraction reactions, or create unique targets for

testing/calibrating state-of-the-art transition-state-theory calculations.

50

Figure 6.1. List of the aldehydes investigated in the current study

6.2 Experiment Design

The current study inferred the aldehydes + OH rate constants from OH time-histories

measured in carefully designed pseudo-first order systems. In such systems, the initial

concentration of aldehyde was much higher than that of OH and was roughly constant

throughout the measurement (Eqn. 6.1), therefore the measured OH concentration time-

history decayed exponentially in time, with the logarithmic decay rate approximately

equal to the product of the target rate constant and the initial aldehyde concentration

(Eqn. 6.2).

𝑑𝑑[𝐶𝐶𝐶𝐶]/𝑑𝑑𝑎𝑎 = −𝜒𝜒[𝐴𝐴𝑙𝑙𝑑𝑑𝑚𝑚ℎ𝑦𝑦𝑑𝑑𝑚𝑚][𝐶𝐶𝐶𝐶] ≈ 𝑐𝑐𝑚𝑚𝑙𝑙𝑐𝑐𝑎𝑎 × [𝐶𝐶𝐶𝐶] (Eqn. 6.1)

𝑙𝑙𝑙𝑙 ([𝐶𝐶𝐶𝐶])𝑡𝑡 ≈ 𝑙𝑙𝑙𝑙 ([𝐶𝐶𝐶𝐶])0 − 𝜒𝜒[𝐴𝐴𝑙𝑙𝑑𝑑𝑚𝑚ℎ𝑦𝑦𝑑𝑑𝑚𝑚]0 × 𝑎𝑎 (Eqn. 6.2)

In the current study, tert-butyl hydroperoxide (TBHP, (CH3)3COOH) was used as the

pyrolytic precursor for OH. When heated by reflected shock waves at temperatures above

1000 K, TBHP decomposed almost instantaneously into OH, CH3 and acetone

(CH3COCH3). Note that the CH3 radical and acetone, together with aldehyde fragments

after H-abstraction, would also react with OH and create some secondary effects.

However, as will be discussed in later sections of this chapter, the influence of these

secondary reactions could be minimized by keeping the TBHP concentration very low

compared to aldehyde. Decomposition of TBHP behind the incident shock waves was

generally negligible, due to the relatively low gas temperatures and pressures and the

relatively short time interval between the incident and the reflected shock waves.

formaldehyde HCHO

n-butyraldehyde propionaldehyde acetaldehyde

n-C4H9CHO i-C4H9CHO

isobutyraldehyde

trimethylacetaldehyde trans-2-pentenal isovaleraldehyde n-valeraldehyde 2-C4H7CHO

n-C3H7CHO i-C3H7CHO

(CH3)3CCHO benzaldehyde

C2H5CHO CH3CHO

C6H5CHO

51

Gas-phase TBHP, vaporized from a TBHP/water solution of 70% TBHP by weight

(supplied by Sigma–Aldrich), was mixed with aldehyde that was vaporized from high-

purity liquid (isobutyraldehyde, >99.5% purity; n-valeraldehyde, >97% purity;

isovaleraldehyde, >97% purity; trimethylacetaldehyde, >96% purity; trans-2-pentenal,

>95% purity; benzaldehyde, >99.5% purity; all supplied by Sigma–Aldrich), and diluted

in argon (>99.999% purity, supplied by Praxair). The small amount of impurities (<5%)

in the aldehydes were expected to be either low-volatile hydrocarbons that were not

vaporized into the test gas mixtures, or dissolved air that had been removed through a

freeze-pump-thaw procedure before the mixture preparation. Even in the extreme case

that a maximum impurity level in the mixtures was assumed, a conservative estimate

would suggest an uncertainty of at most ±5% in the current rate constant measurement

from contributions of impurities.

To confirm the composition of the test mixtures, small portions of the mixtures were

sampled from the endwall location of the shock tube, and analyzed external to the shock

tube in a 29.9 m Herriott type multi-pass cell using DFG laser absorption. Fuel

concentrations were calculated using the aldehydes cross-sections obtained from the

PNNL database [108]. Measured mixture compositions were consistent for various fuel

concentrations, and agreed within ±5% from expected values of the manometrical

preparation.

Previous studies [25], [26], [109] also suggested that long and branched aldehydes could

undergo unimolecular decomposition at high temperatures and produce CO as a by-

product. This aldehyde unimolecular decomposition ultimately limited the temperature

range of our measurements. To quantify its effect on our current measurement, a sensitive

CO absorption diagnostic, implemented with the same setup as in Chapter 4 and 5, was

employed to monitor the decomposition of aldehydes (see Fig. 6.2 for an example). The

upper temperature limit of the current measurements was chosen to ensure that less than

5% aldehydes decomposed within the 1/e decay time of OH.

52

Figure 6.2. Example data trace of the aldehydes + TBHP experiment.

6.3 Rate Constant Determination

Rate constants of the following reactions were determined from the current study:

CH2O + OH = H2O + HCO (R6.1)

CH3CHO + OH = H2O + other products (R6.2)

C2H5CHO + OH = H2O + other products (R6.3)

n-C3H7CHO + OH = H2O + other products (R6.4)

i-C3H7CHO + OH = H2O + other products (R6.5)

n-C4H9CHO + OH = H2O + other products (R6.6)

i-C4H9CHO + OH = H2O + other products (R6.7)

(CH3)3CCHO + OH = H2O + other products (R6.8)

C2H5CHCHCHO + OH = H2O + other products (R6.9)

C6H5CHO + OH = H2O + other products (R6.10)

To account for effects of secondary reactions as mentioned in section 6.2, detailed

reaction mechanisms were employed for high-accuracy rate constant determinations. The

USC-Mech II [75] mechanism was chosen as the base mechanism for studies of CH2O

and CH3CHO, and a comprehensive model for aldehydes combustion, recently developed

by Veloo et al. [25], [26], was used for C2H5CHO, n-C3H7CHO and i-C3H7CHO. The

53

measured aldehydes + OH rate constants were found insensitive to the different base

mechanisms used in the study. To accurately describe the TBHP chemistry, a TBHP sub-

mechanism comprising the following reactions was also included in the kinetics

modeling:

(CH3)3COOH = (CH3)3CO + OH (R6.11)

(CH3)3CO = CH3COCH3 + CH3 (R6.12)

OH + (CH3)3COOH = H2O + O2 + t-C4H9 (R6.13)

OH + (CH3)3COOH = H2O + HO2 + i-C4H8 (R6.14)

where the rate constants of reactions R6.11, R6.13 and R6.14 were obtained from Pang et

al. [110], and R6.12 from Choo and Benson [111]. The thermodynamic parameters for

TBHP and tert-butoxy radical were taken from the thermodynamic database from Goos et

al. [112], and the thermodynamic parameters for OH were updated with the values from

Herbon et al. [50].

The rate constants of the following reactions were updated with more recent values:

H + O2 = O + OH (R6.15)

OH + OH = O + H2O (R6.16)

CH3COCH3 + OH = H2O + CH2CO + CH3 (R6.17)

CH3 + OH = CH2(s) + H2O (R6.18)

where the rate constants for R6.15 – R6.18 were obtained from Hong et al. [113],

Wooldrige et al. [114], Lam et al. [52], and Vasudevan et al. [115], respectively. The

effects of other reactions, such as TBHP + OH, were found negligible and therefore not

discussed here.

Table 6.1. Rate constants* updated in the Veloo et al. [25], [26] mechanism for modeling

the TBHP / i-C3H7CHO reaction system

Rxn. # B m EB Ref. Rxn. # B m EB Ref.

R6.11 2.15 x 1037 0.00 149.4 [110] R6.15 1.04 x 1014 0.00 126.8 [113]

R6.12 7.59 x 1037 0.00 60.0 [111] R6.16 3.57 x 104 2.40 -8.8 [114]

R6.13 2.30 x 1013 0.00 21.8 [110] R6.17 2.95 x 1013 0.00 19.2 [52]

R6.14 2.49 x 1013 0.00 22.0 [110] R6.18 1.65 x 1013 0.00 0.00 [115]

*: expressed in the form of k = B Tm exp(-EB/RT) and in units of kJ, cm3, mol, s and K.

54

A representative OH concentration time-history trace from a TBHP/i-C3H7CHO

experiment is shown in Fig. 6.3. The initial TBHP concentration in the mixture (6.6ppm)

was inferred from the measured OH concentration extrapolated to time zero, and the

balance water concentration (43ppm) was inferred from the total partial pressure of

TBHP and water in the manometrically-prepared mixture. These values agreed well with

the ideal gas-phase TBHP/H2O ratio calculated from Raoult's law (roughly 1:7 at the

mixing tank temperature of about 50 °C). The small distortion in the OH signal near t = 0

was an artifact (known as the schlieren spike) due to deflection of the laser beam at shock

passage. Note, however, under the condition of near pseudo-first-order reaction

(aldehyde:OH > 10:1), the measured reaction rates were insensitive to the initial TBHP

concentration. The aldehyde + OH rate constant was inferred from fitting the model

simulation to the measured OH time-history by varying the target reaction rate constant,

and the best fit was determined by minimizing the root-mean-squared (RMS) residual

error. Also shown in Figure 6.3 are the simulated OH time-histories at the target rate

modified by ±30%, which have demonstrated the high sensitivity of the current rate

constant measurement.

Figure 6.3. Example OH time-history of i-C3H7CHO + OH.

Figure 6.4 shows a formal OH sensitivity analysis for the above TBHP/i-C3H7CHO

system. The OH sensitivity was defined as the ratio of the percentage change in the local

55

OH mole fraction (XOH) and the percentage change in the reaction rate under

investigation (ki ): S O H =(∂X O H /∂k i ) / (X O H /k i ) . Throughout the test time of the

experiment, the target reaction i-C3H7CHO + OH clearly dominated all secondary

reactions.

Figure 6.4. OH sensitivity of the example i-C3H7CHO + TBHP experiment.

From the above example, a nominal value of k = 1.83 × 1013 cm3/mol-s was obtained for

the rate constant of isobutyraldehyde + OH at T = 1160 K. According to a detailed

uncertainty analysis, as shown in Fig. 6.5, its 2σ-uncertainty limits were as low as ±7%,

with a majority of the uncertainty derived from experimental sources such as the mixture

composition, but very little contributed from secondary chemistry such as the CH3 + OH

= CH2(s) + H2O reaction.

Figure 6.5. Uncertainties in the measured rate constant of i-C3H7CHO + OH at 1160 K.

56

Unfortunately, not every aldehyde in this study had a corresponding reaction mechanism

available, which has also motivated the current study to try a mechanism-independent

approach for inferring the target rate constants. Under the current pseudo-first-order

setup, the measured OH concentration decayed exponentially in time. An “apparent” OH

+ aldehyde rate constant, k’, could be calculated from a least-square fit of ln [OH] versus

time, as illustrated in Fig. 6.6. The resulting value, k’ = 1.91 × 1013 cm3/mol-s at T = 1160

K, was slightly (about 4%) larger than the value of k determined from the mechanism-

assisted approach, due to contributions from secondary reactions, such as (1) OH + CH3,

(2) OH + CH3COCH3, and (3) OH + aldehyde fragments generated from H-abstraction.

Note that the contributions of these secondary reactions to the OH depletion rate were all

proportional to the initial TBHP concentration, while the target reaction was proportional

to the initial aldehyde concentration. This lead to a simple relation between k’ and k, i.e.

k’ = k + [TBHP]0/[Aldehyde]0×k*, with k* being a correction constant accounting for the

overall effects of the secondary reactions. The correction term, [TBHP]0/[Aldehyde]0×k*,

was usually small under our typically experimental conditions (<5% of k at

[TBHP]0/[Aldehyde]0 around 1/50), and one could obtain the value of k* (that may be

different for each aldehyde) and hence recover the target rate constant k by varying the

initial TBHP/aldehyde ratio in the measurement, as illustrated in Figure 6.7. The rate

constant k obtained from this method, as displayed in Figure 6.8, was consistent with the

mechanism-assisted approach; its 2σ uncertainty, estimated from the RMS scatter of

individual data points in combination with possible contributions from the impurities in

the aldehydes, was calculated to be ±7%, also consistent with the mechanism-assisted

approach. After the success on isobutyraldehyde + OH, this mechanism-independent

approach was readily applied to the rate constant measurements for other aldehydes +

OH.

57

Figure 6.6. Apparent rate constant obtained from exponential fit to OH time-history

Figure 6.7. Apparent rate constant measured at different initial TBHP/aldehyde ratios

Figure 6.8. Rate constant k6.5 determined from the mechanism-independent approach

58

6.4 Measurement Results

A total number of 219 reflected shock waves experiments, including 32 for i-C3H7CHO,

31 for n-C4H9CHO, 28 for i-C4H9CHO, 25 for (CH3)3CCHO, 20 for C2H5CHCHCHO,

and 22 for C6H5CHO, were performed to determine the rate constants of these aldehydes

reacting with OH. These experiments were carried out over the temperature range of

958–1391 K, at pressures between 0.6 and 2 atm, and at different initial TBHP/aldehyde

ratios. Measurement was also conducted at higher pressures. No pressure dependence

was observed, which suggested that the overall OH + aldehydes rates measured under the

current conditions were dominated by H-abstraction. A complete list of all rate constant

data can be found in Appendix C.

The resulting reaction rate constants can be expressed in Arrhenius equations, in units of

cm3mol–1 s−1, as below:

k6.1 = 3.0 × 1013 exp(–1580 K/T) ± 13% (Eqn. 6.3)

k6.2 = 5.1 × 1013 exp(–1640 K/T) ± 22% (Eqn. 6.4)

k6.3 = 6.7 × 1013 exp(–1380 K/T) ± 27% (Eqn. 6.5)

k6.4 = 8.2 × 1013 exp(–1700 K/T) ± 25% (Eqn. 6.6)

k6.5 = 7.70 × 1013 exp(–1700 K/T) ± 7% (Eqn. 6.7)

k6.6 = 1.03 × 1014 exp(–1730 K/T) ± 7% (Eqn. 6.8)

k6.7 = 1.02 × 1014 exp(–1750 K/T) ± 10% (Eqn. 6.9)

k6.8 = 7.20 × 1013 exp(–1670 K/T) ± 8% (Eqn. 6.10)

k6.9 = 6.93 × 1013 exp(–1340 K/T) ± 8% (Eqn. 6.11)

k6.10 = 3.10 × 1013 exp(–1380 K/T) ± 8% (Eqn. 6.12)

And the temperature ranges of these expressions are 1096-1391 K, 999-1388 K, 958-

1288 K, 1004-1315 K, 976–1346 K, 986–1313 K, 976–1322 K, 979–1243 K, 993–1285

K, and 983–1333 K, respectively.

59

Figure 6.9. Cross-comparison between the rate constants of 10 different aldehydes + OH.

Fig. 6.9 summarizes the high-temperature H-abstraction rate constants of 10 different

aldehydes by OH. As the figure clearly shows, the overall rate constant of a saturated

aldehyde reacting with OH is seen to increase with its carbon chain length (in this

comparison, the rate constant of formaldehyde + OH has been divided by 2), primarily a

result of the increased number of H-abstraction sites in the aldehyde. In a saturated

aldehyde, there are two types of H-abstraction sites, namely the aldehydic H atoms (also

known as the alpha sites) as in R–(C=O)–H, and the alkylic H atoms (beta, gamma, delta

sites and so on, which are one, two, three and more carbons away from the formyl group

–CHO) as in R–CH3 or R–CH2–R’. The aldehydic H-abstraction sites are generally more

reactive than their alkylic counterparts, but there is only one such site in each aldehyde

molecule; the only exception being formaldehyde, which has two aldehydic sites, making

it more reactive with OH even than propionaldehyde. The alkylic sites, on the other hand,

accumulate as the aldehyde carbon chain length progresses. Their contribution to the

overall rate constant appears to be roughly proportional to the number of sites, but can

also be affected by the aldehyde molecular structure. This is evident in the case of

trimethylacetaldehyde ((CH3)3CCHO), whose rate constant of reaction with OH is

substantially lower that of its isomers n-valeraldehyde and isovaleraldehyde, though less

difference is seen between the latter two. This observation is also supported by the typical

dissociation energies of different C–H bonds in these aldehydes, which have been

reported in the works of Pelucchi et al. [109] and da Silva and Bozzelli [116]. Both

studies have suggested that the C–H bonds at the alpha and beta sites are the weakest and

60

second weakest, respectively, which explains why the alpha and beta sites have the most

contribution per site to the overall H-abstraction rate constants. As for the unsaturated

aldehydes reacting with OH, trans-2-pentenal has a rate constant slightly lower than that

of its saturated counterpart, valeraldehyde, but the difference diminishes at temperatures

close to 1000 K; benzaldehyde, the least reactive aldehyde in the current study, has a rate

constant only slightly higher than half of the formaldehyde + OH value.

6.5 Comparison with Previous Studies

Figure 6.10. Comparison between the current measurement and the SAR model.

Fig. 6.10 compares the current measurement rate constants of C1–C5 straight-chain

aldehydes with the estimated values using the structure−activity relationship (SAR)

developed by Atkinson and co-workers [117]–[119]. This SAR model estimates the rate

constants for the reactions of OH with organic compounds by summing the contributions

of primary (−CH3), secondary (−CH2−), and tertiary (−CH<) groups, whose rate

constants can be affected by the identity of the substituents (X) attached to them

according to their corresponding substituent factors (F(X)). This SAR model has

successfully predicted the high-temperature rate constant of alkanes + OH in the studies

of Pang et al. [110] and Badra et al. [120], and recovers the ketones + OH rate constants

in the study of Lam et al. [52] under a scaling factor of 0.75. In this study we extend the

comparison to aldehydes + OH. As shown in Fig. 6.10, the SAR model accurately

61

recovers the rate constants of formaldehyde and acetaldehyde + OH, but significantly

overpredicts the values of C3–C5 aldehydes. This could possibly be attributed to errors in

the high-temperature values of the substituent factors: in the SAR model, the substituent

factors were obtained at 298 K and extrapolated to elevated temperatures assuming a

simple temperature-dependence of F(X) = exp(Ex/T). Another possible reason is the

unaccounted effects from the next-nearest neighbors, which were discussed in the studies

of Cohen [121] and Sivaramakrishnan and Michael [122]. Further improvements to

structural estimation models are needed to fully resolve this discrepancy.

Figure 6.11. Veloo et al. [25], [26] model vs. the current measurement.

Figure 6.12. Mendes et al. [27] TST calculation vs. the current measurement.

62

Also compared with the current measurement are two theoretical and modeling studies.

Fig. 6.11 shows the rate constants of propionaldehyde, normal- and iso-butyraldehyde +

OH from the Veloo et al. model [25], [26]. Compared to the current study, the Veloo et

al. model is seen to underpredict all these rate constants by about 30%. The transition-

state-theory (TST) calculation from Mendes et al. [27] (see Fig. 6.12), on the other hand,

overpredicts the rate constants of formaldehyde, acetaldehyde, propionaldehyde and

isobutyraldehyde + OH by factors of about 2.3, 4.6, 5.5 and 4.9, respectively. The

discrepancies between the model estimates, the TST calculations and the experiment

results are possibly due to large uncertainties in the vibrational partition functions,

particularly of the torsion and other low-frequency modes, or due to uncertainties in the

barrier height, as evident in the study of Mendes et al. [27] (uncertainty of 1 kcal/mol or

higher, which translates to a factor of about 1.6 difference in the rate constant at 1000 K).

This may suggest a need for future refinement to the H-abstraction reaction rate constants

of aldehydes in combustion models, where the current data can be useful.

6.6 Summary

The current study reported the first direct measurements for the H-abstraction rate

constants of six long, branched and unsaturated aldehydes by OH at temperatures above

1000 K. The use of pseudo-first order reaction systems with dilute reactant mixtures, in

combination with our sensitive OH absorption diagnostic, yielded high-precision data

with tight uncertainty bounds. A cross-comparison of these data, performed between 10

different aldehydes, revealed effects of both the carbon chain length and the molecular

structure of the aldehyde on its rate constant for reaction with OH. The results from this

study should prove very useful for validating/calibrating future structural estimation

models and transition-state-theory calculations.

63

Chapter 7. CEAS: A Toolbox for Future Shock

Tube Kinetic Studies

The contents of this chapter have been published in Optical Express under the titles

"Sensitive and Rapid Laser Diagnostic for Shock Tube Kinetics Studies using Cavity-

Enhanced Absorption Spectroscopy" [123], "Time-Resolved in situ Detection of CO in a

Shock Tube using Cavity-Enhanced Absorption Spectroscopy with a Quantum-Cascade

Laser near 4.6 µm" [34] and "Cavity-Enhanced Absorption Spectroscopy with a ps-

Pulsed UV Laser for Sensitive, High-Speed Measurements in a Shock Tube" [45], in

Proceedings of the Combustion Institute under the title " Time-resolved sub-ppm CH3

detection in a shock tube using cavity-enhanced absorption spectroscopy with a ps-

pulsed UV laser" [36] and in the Journal of Physical Chemistry A under the titles

"Shock-Tube Measurement of Acetone Dissociation using Cavity-Enhanced Absorption

Spectroscopy of CO" [44] and "Improved Shock Tube Measurement of the CH4 + Ar =

CH3 + H + Ar Rate Constant using UV Cavity-Enhanced Absorption Spectroscopy of

CH3" [46].

7.1 Motivation

Examples in the previous chapters have shown that the accuracy of a well-designed shock

tube/laser absorption measurement for fundamental rate constants is, in general,

ultimately limited by the sensitivity of the laser absorption diagnostic. A more sensitive

diagnostic will not only allow study of highly dilute mixtures that enable more direct

study of specific reaction channels (see examples in Chapter 4 and 5), but also enable

probing of minor reaction channels or earliest stage of reactions where populations are

low and strong nonequilibrium may occur, the results of which can provide truly unique

targets for testing theoretical models of chemical kinetics of combustion. This has

strongly motivated the current study to search for in-situ diagnostic methods with

dramatically improved detection limits for radicals and stable species, with high temporal

resolution, and aimed particularly at use in shock tubes.

64

Generally, in an ideal experimental situation where noise has been minimized, the

detection sensitivity of an absorption diagnostic can be improved either spectroscopically

by selection of a stronger transition or geometrically by increasing the absorption path-

length. On the spectroscopy side, access to strong absorption transitions has

conventionally been limited by the availability of advanced lasers. But with the recent

developments in laser manufacturing technology, modern diagnostics are now increasing

available at the optimal wavelengths where the spectroscopic sensitive are at the

theoretical limit, leaving not much space for further improvement. On the geometry side,

the optical path-length in a shock tube experiment is usually limited by the physical

diameter of the tube. However, studies from Su et al. [124], Krasnoperov and Michael

[125], and Grebenkin and Krasnoperov [126] have suggested possibilities of increasing

the optical path-length using multi-pass configurations, generally arranged with mirrors

external to the shock tube. As recently reported in the study of Fjodorow et al. [127], this

concept has been further extended to the idea of intracavity absorption spectroscopy

(ICAS) that incorporates the shock tube as part of the laser cavity. A related approach is

cavity-ringdown spectroscopy (CRDS), as demonstrated in, for example, the low-

pressure laminar flame study by Scherer et al. [128]. However, because its alignment is

typically sensitive to mechanical vibration and gas disturbance, CRDS usually requires

averages and is generally not suitable for very-high-speed measurements in transient

environments such as shock tubes. An alternative approach, recently explored in the

current study, is to increase the effective path-length via cavity-enhanced absorption

spectroscopy (CEAS). The current CEAS setup utilizes a pair of high-reflectivity

concave mirrors that is directly integrated into the shock tube, i.e. by replacing the usual

shock tube windows, to form an optical cavity along the transverse direction of the shock

tube. Compared to the external multi-pass configuration, the integrated CEAS setup

excludes the additional round-trip loss from anti-reflection-coated shock tube windows

and enables a higher potential path-length gain. An additional benefit of this CEAS setup

is the refocusing of the laser beam after each reflection, which greatly improves its

robustness against beam-steering noise. Recognizing that this new toolbox can strongly

benefit future shock tube kinetics studies, including, but not limited to the studies of

65

aldehydes, this chapter aims to provide a brief overview on the scientific concept and

initial applications of CEAS for future references.

7.2 Scientific Concept

The basic concept of CEAS is to propagate a laser beam into the optical cavity through a

partially transmitting entrance mirror, allowing some small fraction of the laser light to be

transmitted on each pass through the weakly transmitting exit mirror. Because the

mirrors are curved, the light is retained in the cavity (in spite of beam-steering) and

undergoes multiple passes before the intensity is reduced due to absorption in the cavity

and transmission loss through the mirrors. This latter quantity, i.e. the transmitted light,

is the signal beam that is focused onto a single detector. The beauty of this concept is

that beam steering has little effect since all the light that is transmitted toward the

detector can be captured by a simple lens.

In a CEAS measurement, the ratio of the total cavity output intensities in the absence (I0)

and presence (I) of an absorbing species can be related to the single-pass absorbance

(αSP) and the mirror reflectivity (R), assuming standard Beer-Lambert behavior, via the

following equation adapted from Fiedler et al. [129]:

𝐼𝐼0𝐼𝐼

= 1 − 𝑅𝑅2exp (−2𝛼𝛼𝑆𝑆𝑆𝑆)(1 − 𝑅𝑅2)exp (−𝛼𝛼𝑆𝑆𝑆𝑆)

(Eqn. 7.1)

that can be simplified to the following equation in the limit of αSP approaching zero and

R approaching unity:

𝐼𝐼0𝐼𝐼

= 1 +𝛼𝛼𝑆𝑆𝑆𝑆

1 − 𝑅𝑅= 1 + 𝐺𝐺𝛼𝛼𝑆𝑆𝑆𝑆 (Eqn. 7.2)

The factor 1/(1-R), denoted as G, is the absorption gain factor. In the optically thin limit

where αSP is sufficiently small (GαSP<<1), the total CEAS absorbance, defined as αCEAS

= ln(I0/I), can be simply approximated by GαSP. The current study has utilized mirrors of

98-99% reflectivity, which can achieve absorption gain of about 50-100!

66

However, there is one challenge for conventional CEAS method, which is the laser-cavity

coupling noise. Basically, the cavity produces constructive and destructive interference

patterns, or modes, and in shock tubes, the mechanical vibration and gas disturbances will

cause the cavity modes to jitter, which translate to noise in the transmitted intensity. To

overcome this challenge, the current study has explored a series of coupling-noise-

suppression strategies in two distinct categories of the CEAS methods, namely CW and

pulsed laser CEAS, and achieved success. Details of these strategies in each CEAS

category will be discussed below.

7.2.1 CW laser CEAS

Figure 7.1. Schematic of the optical arrangement of CW laser CEAS in a shock tube.

A schematic of the CW laser CEAS setup in shown in Fig. 7.1. To suppress the laser-

cavity coupling noise, the current study employs an off-axis alignment that allows spatial

separation of the CW laser beam from multiple reflections and hence minimizes the

constructive/destructive interferences. For optimal spatial and temporal resolution in

shock tube experiments, the beam pattern of the off-axis CEAS is arranged in an elliptical

form, with the short axis aligned to the axial direction of the shock tube. The ellipse waist

is typically less than 5 mm, which translates to a time resolution of less than 10 µs under

a reflected shock velocity of 500 m/s. A focusing lens (f < 5 cm) then collects all the

output beams from the CEAS cavity and images the elliptical pattern onto the center

portion of a large-area photodetector; it thereby avoids stray light and defeats beam-

steering noise. Note that the beams are not focused to a single point; instead, they are in a

miniaturized elliptical pattern on the detector. This property ensures spatial separation of

beams from different round-trips and is essential for coupling noise suppression.

5 mm

67

Another important coupling-noise-suppression strategy employed by the current study is

rapid scanning/modulation of the laser wavelength/frequency. The CW laser frequency is

typically scanned over 1 cm-1 (or equivalently, 30 GHz) with a linear sawtooth or a

sinusoid waveform at 50 kHz, and the CEAS signal is collected with a photodetector of

1-10 MHz bandwidth, and sampled with a fast data acquisition system (at least 10MS/s in

the current study) to avoid aliasing. Within the 1/e response time of the detector, the laser

wavelength is scanned over a few cavity modes (which now have a reduced FSR due to

the off-axis configuration), and thus the detector is effectively looking at a time-averaged

signal where the influence of individual mode jittering is minimized. The combination of

wavelength scanning and off-axis alignment successfully suppresses the laser-cavity

coupling noise as apparent in the results of single-scan absorption data shown in Fig. 7.2.

0 0.01 0.02 0.03 0.040

0.2

0.4

0.6

0.8

1

Time [ms]

Det

ecto

r Sig

nal [

a.u.

]

Time [ms]

Det

ecto

r Sig

nal [

a.u.

]

On-axis alignment w.o./ wavelength scanning

Measurement overwhelmed by laser-cavity coupling noise

On-axis alignment w./ wavelength scanning

(a)

(b)

68

Figure 7.2. Example signals from a CW laser CEAS measurement of atmospheric H2O

near 1.5 µm. (a) Under on-axis alignment and at fixed wavelength, the measurement is

overwhelmed by laser-cavity coupling noise that causes the detector signal to fluctuate

from zero to maximum. (b) Rapid wavelength scanning suppresses the coupling noise,

making the absorption transition visible. (c) Off-axis alignment, in combination with

rapid wavelength scanning, completely eliminates the coupling noise.

7.2.2 Pulsed laser CEAS

Figure 7.3. Schematic of the optical arrangement of pulsed laser CEAS in a shock tube.

Another category of the CEAS method explored in the current study is pulsed-laser

CEAS, implemented using a mode-locked Ti-sapphire laser. The pulsed laser enables

on-axis and fixed-wavelength measurement while maintaining immunity to laser-cavity

mode coupling noise. This on-axis configuration (see Fig. 7.3.) allows single line-of-sight

0 0.01 0.02 0.03 0.040

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Time [ms]

Det

ecto

r Sig

nal [

a.u.

] Off-axis alignment w./ wavelength scanning

(c)

69

measurement perpendicular to the shock wave propagation with a spatial resolution of

less than 1 mm, which corresponds to a temporal resolution of about 2 µs under typical

reflected shock velocity of about 500 m/s.

The noise immunity principle of the ps-pulsed direct-absorption CEAS method can be

visualized through either time-domain or frequency-domain analysis. In the time domain,

as illustrated by the conceptual plot in Fig. 7.4., the pulsed laser emits short packets of

light (ps-level duration at a spacing of about 12.8 ns) that have little chance to interact

with each other even after hundreds of reflections in the cavity. On the output side of the

cavity, the photodetector looking at these non-overlapping pulses has a bandwidth (f-3dB

= 150 kHz) much less than the laser repetition rate (78 MHz); it thus time-averages more

than 500 pulses and generates a smooth signal.

Figure 7.4. Noise immunity concept of the ps-pulsed CEAS: time-domain picture.

In the frequency domain, both the pulsed-laser output spectrum and the cavity

transmission spectrum are represented by dense teeth structures with sharp peaks at

frequencies of fn = nfr + fceo and fm = mFSR, respectively, where FSR is the free spectral

range of the cavity, fr is the repetition rate of the laser, m and n are the mode numbers of

the cavity and of the laser, and fceo is the carrier envelop offset frequency, which takes on

values between –fr/2 and + fr/2. In reality, these teeth structures are usually not static,

since fr, fceo and FSR are susceptible to independent jittering from the acoustic or

vibration-induced noise of the laser and the measurement cavities [130]. As a result, the

CEAS Cavity

Detector

Mirror

Pulsed UV Laser

ps-level pulses at 78 MHz repetition rate

Detector bandwidth = 150 kHz

70

cavity is effectively looking at a continuous spectrum, i.e. the envelope of the laser mode

structure. The width of this envelope, as described by its Fourier transform, is

proportional to the reciprocal of the pulse duration. For a ps-pulsed laser, its FWHM

linewidth is in the THz range, three orders of magnitude larger than the nominal FSR of a

15-cm cavity (1 GHz). Thus the laser output is simultaneously coupled into over a

thousand cavity modes, and as illustrated in Fig. 7.5, any small deviation induced by the

jittering of individual cavity modes is effectively averaged, resulting in a constant

coupling efficiency.

Figure 7.5. Noise immunity concept of the ps-pulsed CEAS: frequency-domain picture.

Note that the cavity FSR is exaggerated in scale to facilitate visualization. The total

transmitted laser intensity through the cavity equals the integral of the product of the laser

lineshape function and the cavity transmission function. As the cavity modes are very

dense within the laser linewidth, this integral is proportional to the total area under the

laser lineshape, which is a constant irrespective of the cavity mode jittering (dash lines).

7.3 Example Applications

This section presents two example applications of the CEAS method to advanced shock

tube/laser absorption studies. The first example illustrates a sub-ppm sensitivity CO

diagnostic developed from mid-IR CW laser CEAS, and the second example discusses a

sub-ppm sensitivity CH3 diagnostic developed from UV pulsed laser CEAS. Both

diagnostics are then demonstrated in shock tube kinetics measurements.

Cavity FSR

~ 1 GHz

Laser Linewidth FWHM ~ 1

THz

71

7.3.1 Sub-ppm sensitivity CO diagnostic

An ultra-sensitive CO diagnostic for high-temperature measurements in shock tubes was

developed in the current study using CEAS. The absorption of CO was probed at the

R(13) transition in its fundamental rovibrational band with an AlpesTM distributed-

feedback (DFB) quantum cascade laser (QCL) near 4.56µm. Similar to the setup shown

in Fig. 7.1., the laser was launched into a CEAS cavity formed by a pair of concave

dielectric-coated CaF2 mirrors (radius of curvature = −1 m, diameter = 25 mm, nominal

reflectivity = 98.9% at 4.559μm, polished and antireflection-coated on the back side,

manufactured by Rocky Mountain Inc. USA) on a 15.24-cm diameter shock tube. The

transmitted laser light through the cavity was then collected by a lens and focused onto a

thermoelectrically cooled photovoltaic HgCdTe detector (VigoTM model PVI-2TE-5, f-3dB

= 10 MHz, active area diameter = 2 mm x 2 mm). The laser wavelength was rapidly

modulated/scanned by a 50 kHz sinusoid imposed on the laser injection current.

Fig. 7.6. shows two example scans with and without CO in the shock tube, respectively.

During each scan cycle there was a period of time where the injection current was below

the lasing threshold and the laser output was disabled; the detector signal during this time

was then used to characterize the thermal emission from the shock-heated gas. The

thermal emission signal was only a few percent of the peak laser signal even at the

highest measurement temperature of the current study. Moreover, the emission signal was

also found to be relatively steady behind the reflected shock waves, and therefore could

be easily subtracted during each scan without corrupting the absorption signal. Note that

the artifact apparent at the peak of the sinusoidal scan was caused by laser-cavity

coupling noise as the local scan rate of the laser wavelength was close to zero. This noise,

however, was suppressed elsewhere in every scan cycle and did not affect the current CO

measurement. With a fiber-coupled long etalon, the range of the laser wavelength scan

was measured to be ± 0.32 cm−1, which corresponded to an average scan rate of 0.064

cm−1/μs during each cycle; in the local region where CO transition was probed, the scan

rate was even higher and close to 0.1 cm−1/μs. This rapid wavelength scanning

successfully defeated the coupling noise and yielded a clean CO absorption signal.

72

Figure 7.6. Example signal in the shock tube/CEAS measurement of CO. (a) Transmitted

laser intensity (blue) and laser wavelength (red) during a single scan in a vacuum shock

tube. (b) Transmitted laser intensity during a single scan of shock-heated 10ppm CO/

1%H2/ Ar mixture at the reflected shock condition of T = 1499 K and P = 1.51 atm.

Hydrogen was added to the test gas to accelerate the vibrational relaxation of CO.

Figure 7.7. Example CO absorption measurement in a shock tube using CEAS. (a) The

CO absorbance signal in a single scan cycle; absorbance extracted from the data in Fig.

7.6. (b) The measured CO mole fraction within the first 1 ms after the reflected shock.

The CEAS method was then validated by shock-heating gas mixtures of known amount

of CO in argon. To accelerate the vibrational relaxation of CO, 1% H2 was also added to

the test gas. An example measurement of 10ppm CO is shown in Fig. 7.7. As shown in

the left panel of the figure, the CO absorbance signal had two peaks because the R(13)

(a) (b)

(a) (b)

73

transition was visited twice during each scan cycle, and a typical 1σ minimum detectable

absorbance (MDA) αCEAS of about 0.002 was achieved at a measurement time resolution

of 10μs. The CO mole fraction time-history, calculated from the peak absorbances of

both the up-scans and the down-scans using the CO spectroscopic parameters from Ren

et al. [53], is shown in the right panel of the figure. Note that the current measurement

recovered the expected value of CO mole fraction and had a standard deviation of only

0.11ppm!

The CEAS gain factor G was then calibrated over several CO mixtures of different

manometric concentrations (χCO = 2 - 100ppm). Based on the prior knowledge of CO

mole fraction, the current CEAS measurement obtained a gain factor of G = 91, which

agreed very well with the expected value calculated from the manufacture-specified

mirror reflectivity (R = 98.9%). No variation in G was observed over the entire

measurement campaign (two weeks and more than 30 shock experiments). The

repeatability of the current measurement was also verified over a wide range of shock

conditions (T = 1100 – 2100 K, P = 1.2 - 1.6 atm), as illustrated in Fig. 7.8.

Fig. 7.8. CEAS gain calibration using CO mixtures of known concentrations.

Experimental conditions: T = 1100 – 2100 K, P = 1.2 - 1.6 atm, χCO = 2 - 100ppm.

To demonstrate the application of this diagnostic in kinetics studies, an example

measurement was carried out for the rate constant of acetone unimolecular decomposition:

CH3COCH3 (+M) = CH3 + CH3CO (+M) (R7.1)

Manometric CO Concentration [ppm]

CO

Con

cent

ratio

n fr

om C

EAS

Mea

sure

men

t [p

pm]

74

Shown in Fig. 7.9 are two sample CO time-histories measured in the pyrolysis of acetone

at 1398 K and 1024 K, respectively. In the high temperature case there was less than

20ppm acetone in the test gas mixture. Due to the extremely low concentration of acetone,

the influences of secondary reactions and temperature change was significantly

suppressed, leading to a direct measurement for the decomposition rate constant of

acetone. The rate constant value could simply be extracted from a direct exponential fit to

the CO time-history, a process independent of any reaction mechanism. In the low

temperature case, a 1% acetone/Ar mixture was used. But since the current study only

looked at the very early stage of the pyrolysis where only a few ppm of acetone had

decomposed, the reaction system was still strongly dominated by the thermal

decomposition of acetone, with its rate constant easily obtainable from a simple linear fit.

Figure 7.9. Example CO time-histories measured in the pyrolysis of acetone/Ar mixtures.

(a) 16.3 ppm acetone/Ar at 1398 K, 1.52 atm. (b) 1.00% acetone/Ar at 1024 K, 1.75 atm.

The benefit of using a more sensitive diagnostic and a dilute reactant mixture to rate

constant measurement can be better illustrated by the CO sensitivity analysis shown in

Fig. 7.10. The analysis was performed using the acetone reaction mechanisms of Saxena

et al. [131] and of Pichon et al. [132], and a general C1-C4 mechanism named USC Mech

II [75]. In both the high temperature and the low temperature cases, the total sensitivity of

the secondary reactions was less than 1% of the target reaction.

(a) (b)

75

Figure 7.10. CO sensitivity analysis for the acetone pyrolysis experiments shown in Fig.

7.9. (a) CO sensitivity in the 1398 K case, simulated with the Saxena et al. mechanism

[131]; (b) CO sensitivity at the 1/e decay time of acetone (τ1/e) in the 1398 K case,

simulated with the Saxena et al. mechanism, the Pichon et al. mechanism [132] and USC

Mech II [75], highlighting reactions with sensitivity higher than 10−4. (c) CO sensitivity

in the 1024 K case, simulated with the Pichon et al. mechanism. (d) CO sensitivity at 1.5

ms in the 1024 K case, simulated with the Pichon et al. mechanism and USC Mech II,

highlighting reactions with sensitivity higher than 10−4. The Saxena et al. mechanism was

not validated at T < 1300 K and therefore was not used in the analyses of (c) and (d).

A total number of 32 reflected shock wave experiments were conducted over the

temperature range of 1004 – 1494 K and at pressures around 1.6 atm, yielding a modified

Arrhenius expression for the acetone unimolecular decomposition rate constant as k7.1

(a)

(c)

(b)

(d)

76

(1004 – 1494 K, 1.6 atm) = 4.39x1055 T-11.394 exp(-52140K/T) s-1. For a complete list of

the current rate constant data, please refer to Appendix D.

Figure 7.11. Arrhenius plot for the current k7.1 data in comparison with previous studies.

The current data are also displayed in Fig. 7.11, in comparison with results from several

previous studies. These data are seen to have very low scatter, which is a sign of high

experimental reproducibility and measurement accuracy. The overall 2σ uncertainty in

the current measurement of k7.1 is estimated to be +/-24%. The current results agree

closely with the recent shock tube/laser absorption study of Lam et al. [81] in the

overlapped measurement range, and agree in trend with the earlier studies by Saxena et

al. [131] and Szwarc and Taylor [133] at lower pressures. Also shown in Fig. 7.11 are the

RRKM calculations by Saxena et al. [131] and Pichon et al. [132]. The theoretical

calculation by Saxena et al. is in reasonable agreement (within a factor of 2) with the

current study, and recovers the activation energy very well. The calculation by Pichon et

al. agrees less well with the current study, especially at high temperatures, which is

possibly due to uncertainties in their pressure dependence model.

Not only has the current CEAS method lead to more direct and more accurate rate

constant measurement, it has also greatly extended the measurement range. Note that the

current study is the first-ever direct measurement of k7.1 over 5.5 orders of magnitude!

Extension to 6 orders of magnitude could also be achieved with additional measurement

near 950 K using 5% acetone mixture.

77

7.3.2 Sub-ppm sensitivity CH3 diagnostic

Figure 7.12. Comparison of the 1σ detection limits of CH3 in different shock tube

studies. Values calculated from the typical minimum detectable absorbances and the

effective CH3 absorption coefficients in these studies, and normalized to a shock tube

diameter of 15 cm and a pressure of 1 atm.

Another promising application of the CEAS method involves the development of an

ultra-sensitive CH3 diagnostic. Over the last few decades, there has been an increasing

need for optical diagnostics of ever-higher sensitivity and ever-faster time-response in

shock tube measurements of CH3. Since the pioneering experiment of Harvey and Jessen

[134] on a low-pressure flame showed the feasibility of quantitative CH3 absorption

measurement using a Xe-lamp, similar Xe-lamp absorption schemes near 216 nm have

been implemented in various shock tube studies by Glanzer et al. [135], Tsuboi [136],

Moller et al. [137] and Hwang et al. [138]. CH3 absorption measurements at 214 nm have

also been explored by Gardiner et al. [139] and Hwang et al. [140] with Zn lamps. More

recently, Davidson et al. [141], [142] demonstrated improved CH3 detection sensitivity in

a shock tube using a narrow-linewidth (FWHM ~ 40 MHz) dye laser. This work was later

revisited by Oehlschlaeger et al. [143], who then improved the accuracy of the CH3

absorption coefficient. Very recently, Lam et al. [81] used the high power (~ 7 mW)

frequency-quadrupled output of a pulsed Ti:sapphire laser at 216.6 nm to improve the

CH3 detection limit of Davidson et al. and Oehlschlaeger et al. by another factor of 2 (to

78

ppm-level). Now with the pulsed CEAS method, the study has further improved state-of-

the-art detection limit of CH3 in a shock tube by another order of magnitude.

Figure 7.13. Schematic of the experimental setup in pulsed UV CEAS.

A schematic of the typical experimental setup is shown in Fig. 7.13. The current study

used a 18W CW laser at 532 nm (CoherentTM Verdi V-18) to pump a wavelength-tunable

Ti:sapphire laser (CoherentTM Mira-HP ps-model). The Ti:sapphire laser was passively

mode-locked via the Kerr-lensing effect to generate ~2 ps pulse trains at a repetition rate

of 78 MHz. Due to its pulsed nature, the Ti:sapphire laser output had a finite spectral

linewidth (FWHM ~ 0.60 nm, or equivalently, ~ 220 GHz; measured by a BristolTM 721

spectral analyzer) that was proportional to the reciprocal of the pulse width (for a

transform-limited Gaussian pulse, the pulse-bandwidth product is approximately 0.44).

The laser was tuned to 866.48 nm and frequency-quadrupled through two angle-tuned

LBO crystals to generate 216.62 nm output for the measurement of CH3. The average

power of this UV output was measured to be about 7 mW. The spectral linewidth of this

UV output (FWHM ~ 0.15 nm) was one-fourth of the fundamental linewidth in

wavelength units, or four times the fundamental linewidth in frequency units (FWHM ~

79

880 GHz). Although much broader compared to narrow-linewidth CW lasers, the current

pulsed UV laser was still narrow enough compared to the absorption feature of CH3,

especially at elevated temperatures and pressures. As shown in Fig. 7.14, the current laser

FWHM linewidth was only about 1/20 of the FWHM of the CH3 absorption feature; it

thus behaved almost the same as a narrow-linewidth CW laser in terms of single-pass

CH3 absorption. For a more detailed analysis of the effect of laser linewidth on the

effective CH3 absorbance, please refer to Appendix E.

Figure 7.14. Comparison of the laser output spectrum and the CH3 absorption spectrum.

The CH3 absorption spectrum near 1565 K was adapted from Oehlschlaeger et al. [143].

Note that linewidth of the pulsed laser used in the current study (FWHM ~ 0.15 nm) was

about 20 times smaller than that of the CH3 absorption feature (FWHM ~ 3 nm).

The pulsed UV light was then injected into a 15.24-cm diameter high-purity shock tube,

through the back of a weakly focusing mirror (radius of curvature = -100 cm) directly

mounted on the shock tube sidewall (i.e. by replacing the usual shock tube windows).

The mirror was coated in the wavelength region of 210 - 230 nm to achieve a reflectivity

of R = 0.98. This mirror, together with an identical mirror on the opposite side of the

shock tube, transformed the tube into a stable cavity of G ~ 50 (G was also calibrated

using a room temperature UV absorber, methyl formate, to be 49 +/- 2).

On the other side of the shock tube, all the transmitted light was collected with a CaF2

focusing lens (f = 15 cm) onto a HamamatsuTM R1104 high-gain photo-multiplier tube,

which had a transimpedance amplifier of DC gain = 100 V/mA and f-3dB = 150 kHz. A

80

common-mode rejection scheme was implemented to remove the influence of laser

intensity fluctuations: part of the UV light was split onto a reference detector (New

FocusTM 2032 UV-enhanced detector with f-3dB = 150 kHz) before entering the shock

tube, whose intensity was then used to normalize the diagnostic detector signal. All

detector data were sampled by a 14-bit National InstrumentTM PXI-5122 digitizer at a rate

of 100 MS/s, and stored digitally for off-line post-processing.

Due to reasons explained in section 7.2.2, the laser-cavity coupling noise was negligible

in the current ps-pulsed CEAS measurement. A more detailed analysis for the coupling

noise can be found in Appendix F, which has suggested a conservative upper bound of

0.1% for the coupling noise. In the current experiment this noise was overshadowed by

other noise sources, such as the detector noise. The current study used two different types

of detectors to accommodate different magnitudes of light intensity before and after the

CEAS cavity, but this non-balanced detection has led to slightly higher noise compared to

balanced common-mode rejection using matched detectors [144]. As a result, the current

minimum detectable CEAS absorbance was about 0.005. Based on the CH3 absorption

coefficient from Oehlschlaeger et al. [143]: kCH3 = 1.475 x 104 T-1.004 exp(2109 K/T) +/-

5% atm-1 cm-1, the corresponding minimum detection limit of CH3 in the current study

was approximately 0.2ppm at 1500 K, and 0.4ppm at 2000 K.

Assuming a noise level of 0.5% in the transmitted laser intensity, the signal-to-noise ratio

(SNR) of the current CH3 diagnostic was then calculated as a function of CH3 mole

fraction. The result is displayed in Fig. 7.15, in comparison with sthe SNR of the

conventional single-pass diagnostic (assuming a typical noise level of 0.2% in the

transmitted laser intensity). As the figure clearly shows, the current CH3 diagnostic

substantially enhanced the SNR in the region of 0.2 – 100ppm CH3. Note that the SNR

would roll off at high CH3 concentration where the transmitted intensity became very

low, which would eventually limit the dynamic range of the diagnostic. According to Fig.

7.15, the 1σ dynamic range of the current CH3 diagnostic (0.2-3000ppm) was more than

4 orders of magnitude, about half an order of magnitude higher than that of the

conventional diagnostic. Future improvement of the minimum detectable αCEAS to 0.002

81

is expected with use of balanced detectors, which will further enhance the detection

sensitivity by another factor of 2.5.

Figure 7.15. Signal-to-noise ratio of CH3 detection in a typical single-pass measurement

(blue) and the current CEAS measurement (red) as functions of CH3 mole fraction. Note

that the current CEAS scheme substantially improved both the minimum detection limit

and the detection dynamic range of CH3 over the conventional single-pass scheme.

As a kinetic demonstration of this sub-ppm-sensitivity CH3 diagnostic, rate constant

measurement of CH4 decomposition was then carried out in a 15.24-cm diameter shock

tube. When heated by the reflected shock waves, CH4 decomposed into CH3 and H

radicals via the following reaction:

CH4 + M = H + CH3 + M (R7.2)

The H-atom radicals then quickly reacted with CH4, forming more CH3 radicals in a

chain-reaction fashion:

H + CH4 = CH3 + H2 (R7.3)

Because reaction R7.3 is almost barrier-less, its rate constant (k7.3) was significantly

higher than that of reaction R7.2 (k7.2) at the typical conditions of the current

measurement, which made R7.2 the rate-limiting reaction. The competition between R7.2

and R7.3 also established a quasi-steady-state for the H-atom radical concentration,

[H]QSS = k1/k2×[M], during the early stage of CH4 pyrolysis. As a result, the overall CH3

82

formation rate was approximately a constant, d[CH3]/dt = 2k1[CH4][M], which led to a

linear CH3 profile. Thus by pyrolyzing CH4/Ar mixtures behind reflected shock waves

and monitoring the resulting CH3 time-histories, the current study was able to directly

determine the rate constant of reaction R7.2 (k7.2) from the CH3 formation rates.

Previous measurements of k7.2 were often complicated by the CH3 recombination

reaction:

CH3 + CH3 (+ M) = C2H6 (+ M) (R7.4)

The current study, on the other hand, has minimized the effect of reaction R7.4 by

employing dilute mixtures and carefully designing the experiments so that less than 25

ppm CH4 was consumed during the test time of the measurement. For more accurate rate

constant determination, the current study also used a detail reaction mechanism, USC

Mech II [75], to account for the effects of secondary reactions (for example, reactions

R7.3 and R7.4). The rate constant k7.1 was inferred by fitting the simulated CH3 time-

histories to the measurement, as illustrated in Fig. 7.16 with a representative example.

Note that there was a small initial CH3 signal (~ 2ppm) immediately after the reflected

shock wave, which was probably caused by impurities in the mixture (2.0-grade CH4 and

5.0-grade Ar). Nonetheless, the current measurement of k7.2 was mostly unaffected by the

initial 2ppm of CH3, since k7.2 was mainly determined from later part (t > 200 µs) of the

CH3 time-history, whose shape and slope, according to simulations with USC-Mech II,

were insensitive to the initial concentration of CH3 at the conditions of the current

experiment. Further analysis also showed that the specific form of impurities had little

influence on the current rate constant determination. As shown in Fig. 7.16, doping

impurities of 1ppm C2H6, or 1ppm C3H8, or 2ppm H radicals in the simulation would

yield nearly identical CH3 profiles after 200 µs.

83

Figure 7.16. Example CH3 time-history measured in the pyrolysis of 500ppm CH4/Ar at

1757 K, 1.69 atm, in comparison with simulation results assuming different sources of

impurities. Note that the CH3 formation rate was insensitive to impurities after 200 µs.

A detailed uncertainty analysis for the above example is shown in Fig. 7.17. One primary

uncertainty contributor was the uncertainty in the reflected shock temperature (T5 = 1757

+/- 9 K), which translated to about +/-10% uncertainty in k7.2 at the nominal shock

condition. Fitting uncertainty, determined from a brute-force method of varying k7.2 to fit

the upper and lower envelopes of the measured CH3 profile, was about 5%. Rate

constants of secondary reactions, k7.3 and k7.4, were assigned with an uncertainty factor

of 2, in accordance with recommendations from Baulch et al [82]. Since the current rate

constant determination was dependent on the diagnostic calibration (i.e., CEAS gain

factor and CH3 cross-section) and the initial CH4 concentration, uncertainties in the

CEAS gain factor (G+/-σ = 49+/-2), the CH3 absorption cross-section (+/-5%), and the

manometric CH4 mole fraction (+/-5%) were also include in the analysis. For reasons

explained earlier, impurities in the test gas mixture had negligible effect (less than +/-1%)

on the current rate constant measurement. Based on the above analysis, the overall 2σ

uncertainty in the value of k7.2 at 1757 K was calculated to be +/-18%.

84

Figure 7.17. 2σ uncertainties in the measured rate constant k7.2 at 1757 K.

A total of 9 reflected shock experiments were conducted at temperatures between 1487 K

and 1866 K and pressures about 1.7 atm, conditions near the low-pressure limit of k7.2.

Details of the shock conditions, the measured rate constant data and their overall

uncertainties are summarized in Appendix G. A numerical fit to these data yielded an

Arrhenius expression as k7.2(1.7 atm) = 3.7 x 1016 exp(-42200 K/T) cm3/mol-s, with an

overall 2σ uncertainty factor of 1.25.

Figure 7.18. Arrhenius plot for k7.2. (a) Comparison between the current and previous

experiment results. Note that the results from Roth [145], Tabayashi and Bauer [146] and

Heffington et al. [147] are almost identical. (b) Comparison of current and Davidson et

al. [148] data to theories and review. The current study is close to the low-pressure limit.

85

Fig. 7.18 compares the current data with previous studies reported in the literature. Note

that the current study has provided the first shock tube/laser absorption measurement for

k7.2 at T < 1700 K. The high temperature end of the current measurement is seen to agree

closely with the study of Davidson et al. [148], which was also performed using UV laser

absorption of CH3 and hence is considered most relevant to the present study. Also

evident from this comparison is that the improved CH3 detectivity of the current study

has led to significantly reduced scatter in the data. The earlier ARAS study by Roth

[145], laser schlieren study by Tabayashi and Bauer [146] and IR emission/absorption

study by Heffington et al. [147] also agree in trend with the current measurement. The

most recent experimental measurement from Koike et al. [149], on the other hand, is seen

to be higher than the current work by about a factor of 2 in the overlapping temperature

region and appears to have lower activation energy, but this difference is probably due to

the relatively large scatter of the Koike et al. data. At much higher temperatures, the laser

schlieren data from Kiefer and Kumaran [150] also show lower activation energy than the

current study, probably suggesting non-Arrhenius behaviors at extreme temperatures. In

general, the current study was in good consensus with most of the previous experiments.

Also shown in Fig. 7.18 are the recent theoretical calculations from Golden [151], the ab

initio calculation by Troe and Ushakov [152] and the comprehensive review by Baulch et

al. [82]. These theoretical and review studies have yielded almost identical expressions

for k7.2, and are in generally good agreement with the current measurement.

7.4 Outlook

Absorption gains of about 50-90 have been successfully achieved in the initial

applications of CEAS demonstrated in the current study. It is clear that by using even

higher values of R, further gains in detection sensitivity can be achieved. However, care

is advised when using very high values of R, as they may significantly reduce the

transmitted laser intensity, and increase the photon lifetime in the cavity that may

eventually limit the temporal resolution. Extension of the CEAS idea to the measurement

of other species (e.g. CH4) and properties (e.g. T and P), and future applications to other

fundamental rate constant measurements, are also anticipated.

87

Chapter 8. Concluding Remarks

8.1. Summary of the Current Study

In the first part of the current study, a system of multi-color laser absorption diagnostics

for interference-immune CH2O sensing and combined CH3CHO/CH2O detection was

developed. This diagnostic system utilized IR absorptions at 2895.92 and 2895.60 cm−1

and UV absorption at 32601.10 cm−1, which were accessed with a tunable DFG laser and

a frequency-doubled dye laser, respectively. Absorption cross-sections of CH2O at the

two IR wavelengths were measured behind reflected shock waves over 900–1800 K, 0.8–

3.3 atm, within an uncertainty of ±5%. Absorption cross-sections of CH3CHO and CH2O

at the UV wavelength were measured over 900–1600 K and 500–1700 K, respectively,

also within an uncertainty of ±5%. The diagnostics were then validated in a set of

controlled experiments, and demonstrated in shock tube kinetic measurements of CH2O

and CH3CHO pyrolysis.

In the second part of the current study, the rate constants of three important types of

reactions in aldehydes removal chemistry, i.e. thermal dissociation, H-abstraction by H

and H-abstraction by OH, were measured. The thermal dissociation rate constant of

CH3CHO, k4.1, was measured in shock tube pyrolysis of 1000ppm CH3CHO / Ar

mixtures with a sensitive CO diagnostic. A total of six reflected shock experiments were

conducted at temperatures of 1273 - 1618 K and pressures around 1.6 atm, resulting in an

Arrhenius expression for the target rate constant as k4.1(1.6 atm) = 1.1 x 1014 exp(-36900

K/T) s-1, with a 2σ uncertainty of about +/- 30%. The current data were in generally good

agreements with previous studies and showed less scatter. The current rate expression for

k4.1 was also seen to improve the performances of several existing aldehyde reaction

mechanisms to a substantial extent.

The current study also inferred the rate constant of CH2O + H = H2 + HCO from accurate

CO time-history measurement in shock tube pyrolysis of 1,3,5- trioxane and C2H5I

mixtures. A modified Arrhenius equation for this rate constant, valid over 1304 - 2006 K,

was obtained from the current measurement: k5.2 = 1.97×1011(T/K)1.06exp(−3818 K/T)

88

+18/−26% cm3mol−1s−1. Compared to previous studies, the current work has significantly

reduced the measurement uncertainty.

The current study also reported the first direct measurements for the H-abstraction rate

constants of a series of long, branched and unsaturated aldehydes by OH at temperatures

above 1000 K. The use of pseudo-first order reaction systems with dilute reactant

mixtures, in combination with our sensitive OH absorption diagnostic, yielded high-

precision data with tight uncertainty bounds. A cross-comparison of these data,

performed between 10 different aldehydes, revealed effects of both the carbon chain

length and the molecular structure of the aldehyde on its rate constant for reaction with

OH. The results from this study should prove very useful for validating/calibrating future

structural estimation models and transition-state-theory calculations.

In the third and last part of the current study, a novel toolset of advanced laser absorption

diagnostics, namely the shock-tube-integrated cavity-enhanced absorption spectroscopy

(CEAS), was introduced. By replacing the standard shock tube windows with high

reflectivity mirrors, this CEAS technique significantly enhanced the effective optical

pathlength in shock tube/laser absorption measurements by about two orders of

magnitude, and thereby greatly improved the detection limits of several key species in

combustion kinetics studies. Two different types of CEAS method, i.e. CW laser CEAS

and pulsed laser CEAS, were explored in the current study. The CW laser CEAS method

employed off-axis alignment and rapid wavelength scanning to suppress the laser-cavity

coupling noise. An example application of this method was the development of a sub-

ppm sensitivity CO diagnostic, which was then used by the current study to obtain a

direct and accurate measurement of the acetone thermal dissociation rate constant over

5.5 orders of magnitude. The pulsed laser CEAS, on the other hand, was essentially free

of coupling noise even under an on-axis and fix-wavelength configuration. This nice

feature of the pulsed CEAS method was then exploited by the current study to develop a

microsecond-resolved, sub-ppm sensitivity CH3 diagnostic, which allowed for the first

shock tube/laser absorption measurement of the CH4 decomposition rate constant at T <

1700 K. This CEAS toolset will strongly benefit future combustion kinetics studies,

including, but not limited to the studies of aldehydes.

89

8.2. Recommendations for Future Work

One possible extension of the current work is to apply the aldehyde diagnostics to

investigate the pyrolysis and oxidation chemistry of alcohols, ethers and biodiesel fuel

surrogates, which will provide unique kinetics targets that may guide the development,

validation and calibration of future reaction mechanisms.

Another potential extension is to measure the rate constants of CH3 + CH3CHO, H +

CH3CHO, and the thermal decomposition reactions of longer aldehydes. These data will

further improve future kinetic modeling.

Another promising direction is to continue exploring the potential of CEAS, either by

extending the CEAS measurement to other species (e.g. CH4), gas properties (e.g. T and

P), and reaction systems, or by investigating different noise-suppression schemes (e.g. via

artificial laser linewidth broadening), optimizing the absorption gains, and improving the

temporal resolution.

91

Appendix A: CO Time-Histories Measured in Shock

Tube Pyrolysis of 1000ppm CH3CHO/Ar

Figure A.1. CO time-history at T = 1618 K, P = 1.45 atm


92



93



95

Appendix B: Rate Constant Data for CH2O + H

Table B.1. Summary of the measured rate constant data for R4.2

T (K) k4.2 (cm3mol-1s-1) T (K) k4.2 (cm3mol-1s-1)

1000 ppm CH2O + 20 ppm C2H5I 500 ppm CH2O + 5 ppm C2H5I

1452 3.4 x 1013 1761 6.1 x 1013

1493 3.6 x 1013 1966 8.7 x 1013

1758 6.1 x 1013 1550 3.8 x 1013

1807 6.8 x 1013 1468 3.2 x 1013

1747 5.9 x 1013 1393 2.6 x 1013

1880 7.7 x 1013 1436 2.8 x 1013

1583 4.4 x 1013 1378 2.5 x 1013

1546 3.9 x 1013 1341 2.3 x 1013

1659 5.0 x 1013 1668 5.1 x 1013

1304 2.2 x 1013 1609 4.6 x 1013

1410 2.7 x 1013 1534 3.7 x 1013

1000 ppm CH2O + 50 ppm C2H5I 1490 3.5 x 1013

1589 4.4 x 1013 1490 3.5 x 1013

1581 4.3 x 1013 1888 7.7 x 1013

1590 4.3 x 1013 1793 6.8 x 1013

1762 6.1 x 1013 250 ppm CH2O + 5 ppm C2H5I

1669 5.3 x 1013 1876 7.4 x 1013

1510 3.7 x 1013 1599 4.6 x 1013

1878 7.6 x 1013 1928 8.0 x 1013

2006 8.9 x 1013 1463 3.3 x 1013

1931 8.1 x 1013 1351 2.5 x 1013

1821 6.8 x 1013

1673 5.1 x 1013

1737 5.8 x 1013

97

Appendix C: High-Temperature Rate Constants Data

for Ten Different Aldehydes + OH

Table C.1. Rate constant data for formaldehyde (CH2O) + OH T (K) P (atm) [Aldehyde]0

[TBHP]0 (ppm) k (1013 cm3/mol-s) 1391 1.33 300 16.0 2.0 1201 1.31 300 16.0 1.6 1096 1.35 300 16.0 1.5 1249 1.27 300 16.0 1.7 1333 1.11 300 16.0 1.9 1127 0.94 150 6.9 1.5 1161 0.88 150 6.9 1.6 1242 0.84 150 6.9 1.7

Table C.2. Rate constant data for acetaldehyde (CH3CHO) + OH T (K) P (atm) [Aldehyde]0

[TBHP]0 (ppm) k (1013 cm3/mol-s) 1367 1.94 500 23.0 1.6 1216 2.14 500 23.0 1.3 1085 2.20 500 23.0 1.1 1327 1.89 500 23.0 1.5 1252 1.96 300 23.5 1.4 1101 2.16 300 23.5 1.2 1029 2.21 300 23.5 1.0 1342 1.92 300 23.5 1.5

1176 2.03 300 23.5 1.3 1354 2.07 300 23.5 1.5 1152 2.20 200 19.0 1.2 1366 1.94 200 19.0 1.5 999 2.29 100 25.6 1.0

1388 1.99 100 25.6 1.6 1248 3.91 100 25.6 1.4

98

Table C.3. Rate constant data for propionaldehyde (C2H5CHO) + OH T (K) P (atm) [Aldehyde]0

[TBHP]0 (ppm) k (1013 cm3/mol-s) 1208 2.13 300 24.5 1.5 1093 2.25 300 24.5 1.3 985 2.24 300 24.5 1.2

1195 2.09 300 12.0 1.5 1288 2.06 300 12.0 1.6 1244 0.99 300 12.0 1.6 1189 1.04 300 12.0 1.5 958 1.25 300 12.0 1.1

1279 0.95 300 12.0 1.6 1104 1.14 300 12.0 1.4 958 1.24 500 35 1.1

1143 1.09 500 35 1.4 1241 1.01 500 35 1.6

Table C.4. Rate constant data for n-butyraldehyde (n-C3H7CHO) + OH T (K) P (atm) [Aldehyde]0

[TBHP]0 (ppm) k (1013 cm3/mol-s) 1202 2.13 300 17.8 2.0 1199 2.10 150 9.0 2.0 1267 2.01 150 9.0 2.2 1125 2.09 150 9.0 1.8 1209 2.06 500 50 2.0 1140 0.99 500 50 1.9 1004 1.04 500 50 1.6 1196 1.25 200 20.4 2.0 1124 0.95 200 20.4 1.8 1069 1.14 250 21.3 1.7 1114 1.24 250 21.3 1.8 1135 1.09 250 21.3 1.8 1167 1.01 250 21.3 1.9 1235 1.14 250 21.3 2.1 1315 1.24 250 21.3 2.3 1307 1.01 250 12.3 2.3 1295 1.14 250 12.3 2.3 1274 1.24 250 12.3 2.2 1240 1.09 250 12.3 2.1 1203 1.01 250 12.3 2.0 1013 1.14 250 12.3 1.6 1015 1.24 500 15.7 1.6 1086 1.09 500 15.7 1.7 1177 1.01 500 15.7 2.0 1237 1.01 500 15.7 2.1

99

Table C.5. Rate constant data for isobutyraldehyde (i-C3H7CHO) + OH T (K) P (atm) [Aldehyde]0

[TBHP]0 (ppm) k’ (1013 cm3/mol-s) k (1013cm3/mol-s) 1239 0.55 250 6.9 2.15 2.04 1182 0.58 250 6.9 1.97 1.86 1212 0.57 350 6.7 1.96 1.88 1195 0.59 350 6.7 1.88 1.81 1160 0.63 350 6.7 1.91 1.84 1247 0.56 350 6.7 1.99 1.92 1255 0.55 350 6.7 1.99 1.91 1101 0.67 350 6.7 1.75 1.67 996 0.76 350 6.7 1.52 1.45

1294 0.55 350 6.7 2.13 2.06 1252 0.56 500 10.2 2.02 1.95 1245 0.59 500 10.2 2.00 1.92 1298 0.55 500 10.2 2.14 2.06 1183 0.64 500 10.2 1.92 1.84 1156 0.68 500 10.2 1.86 1.78 1305 0.54 500 10.2 2.26 2.18 1105 0.69 500 10.2 1.72 1.64 1043 0.72 500 10.2 1.58 1.51 1309 0.53 500 10.2 2.22 2.15 1004 0.78 500 10.2 1.47 1.40 1346 0.52 500 10.2 2.29 2.21 1270 0.57 253 25.0 2.40 2.03 1233 0.6 253 25.0 2.27 1.90 1099 0.67 253 25.0 2.03 1.66 1041 0.72 253 25.0 1.88 1.51 1303 0.54 253 25.0 2.52 2.15 984 0.78 253 25.0 1.76 1.39 976 0.83 253 25.0 1.71 1.34

1266 0.57 126 12.4 2.38 2.01 1153 0.67 126 12.4 2.14 1.77 1048 0.74 126 12.4 1.91 1.54 1138 2.16 126 12.4 2.08 1.71

100

Table C.6. Rate constant data for n-valeraldehyde (n-C4H9CHO) + OH T (K) P (atm) [Aldehyde]0

[TBHP]0 (ppm) k’ (1013 cm3/mol-s) k (1013cm3/mol-s) 1262 0.58 500 8.0 2.72 2.63 1176 0.63 500 8.0 2.48 2.38 1081 0.66 500 8.0 2.24 2.14 1311 0.55 500 8.0 2.93 2.83 1043 0.73 500 8.0 2.05 1.95 1008 0.80 500 8.0 1.96 1.86 1135 0.67 500 8.0 2.32 2.22 1195 0.61 500 8.0 2.53 2.44 1115 0.70 500 8.0 2.23 2.13 1201 0.60 250 14.3 2.81 2.47 1286 0.56 250 14.3 2.99 2.64 1149 0.66 250 14.3 2.70 2.35 1266 0.58 250 14.3 3.02 2.68 1063 0.76 250 14.3 2.38 2.03 1009 0.78 250 14.3 2.25 1.90 1192 0.62 250 14.3 2.75 2.40 1105 0.69 250 14.3 2.54 2.20 1238 0.61 350 10.8 2.66 2.48 1302 0.60 350 10.8 2.94 2.75 1109 0.70 350 10.8 2.27 2.08 1047 0.74 350 10.8 2.15 1.97 1136 0.65 350 10.8 2.42 2.23 986 0.83 350 10.8 1.95 1.76

1175 2.15 350 10.8 2.50 2.32 1193 0.57 250 24.7 3.05 2.46 1152 0.66 250 24.7 2.89 2.29 1098 0.71 250 24.7 2.80 2.21 1313 0.55 250 24.7 3.31 2.72 1263 0.58 250 24.7 3.13 2.53 1070 0.75 250 24.7 2.65 2.05 1016 0.81 250 24.7 2.46 1.87

101

Table C.7. Rate constant data for iso-valeraldehyde (i-C4H9CHO) + OH T (K) P (atm) [Aldehyde]0

[TBHP]0 (ppm) k’ (1013 cm3/mol-s) k (1013cm3/mol-s) 1209 0.60 500 10.2 2.42 2.37 1205 0.59 500 10.2 2.40 2.35 1262 0.58 500 10.2 2.54 2.49 1081 0.66 500 10.2 2.03 1.98 1039 0.72 500 10.2 1.95 1.90 1158 0.62 500 10.2 2.19 2.13 995 0.76 500 10.2 1.79 1.73

1239 0.55 250 10.2 2.66 2.56 1195 0.60 250 10.2 2.54 2.43 1283 0.53 250 10.2 2.92 2.81 1174 0.65 250 10.2 2.49 2.38 1146 0.67 250 10.2 2.46 2.36 1121 0.71 250 10.2 2.32 2.22 1004 0.78 250 10.2 1.94 1.83 1254 0.57 350 10.2 2.64 2.56 1297 0.54 350 10.2 2.80 2.72 1173 0.63 350 10.2 2.25 2.17 1100 0.68 350 10.2 2.02 1.94 1279 2.04 350 10.2 2.67 2.59 1139 2.16 350 10.2 2.18 2.10 1011 0.78 350 10.2 1.90 1.82 976 0.83 350 10.2 1.82 1.75

1322 0.56 1000 21.5 2.74 2.69 1274 0.58 250 21.5 2.68 2.45 1202 0.62 250 21.5 2.52 2.29 1132 0.68 250 21.5 2.35 2.13 1075 0.69 250 21.5 2.19 1.96 1029 0.75 250 21.5 2.10 1.87

102

Table C.8. Rate constant data for trimethylacetaldehyde ((CH3)3CCHO) + OH

T (K) P (atm) [Aldehyde]0

[TBHP]0 (ppm) k’ (1013 cm3/mol-s) k (1013cm3/mol-s) 1243 0.58 500 13.0 2.05 1.95 1189 0.60 500 13.0 1.87 1.77 1192 0.63 500 13.0 1.89 1.79 1132 0.66 500 13.0 1.66 1.56 1109 0.70 500 13.0 1.67 1.57 1063 0.75 500 13.0 1.56 1.46 1015 0.79 500 13.0 1.50 1.40 992 0.80 500 13.0 1.44 1.34

1083 0.72 500 13.0 1.59 1.49 1027 0.75 500 13.0 1.56 1.46 1155 0.64 500 13.0 1.82 1.72 1223 0.59 350 15.6 2.01 1.84 1155 0.64 350 15.6 1.82 1.65 1116 0.69 350 15.6 1.72 1.55 1056 0.70 350 15.6 1.68 1.51 1035 0.76 350 15.6 1.64 1.47 979 0.79 350 15.6 1.48 1.31

1153 0.62 250 13.9 1.90 1.69 1097 2.07 250 13.9 1.76 1.55 1181 2.07 250 13.9 1.91 1.70 1155 2.09 258 28.7 2.07 1.65 1223 0.59 258 28.7 2.26 1.84 1132 0.66 258 28.7 2.18 1.76 1047 0.71 258 28.7 1.86 1.44 1006 0.79 258 28.7 1.74 1.32

103

Table C.9. Rate constant data for trans-2-pentenal (C2H5CH=CHCHO) + OH T (K) P (atm) [Aldehyde]0

[TBHP]0 (ppm) k’ (1013 cm3/mol-s) k (1013cm3/mol-s) 1261 0.58 400 9.7 2.40 2.33 1274 0.53 400 9.7 2.55 2.48 1061 0.69 400 9.7 2.03 1.97 1125 0.64 400 9.7 2.11 2.04 1207 0.60 400 9.7 2.37 2.30 1033 0.75 400 9.7 1.98 1.91 993 0.80 400 9.7 1.89 1.82

1244 0.56 200 12.8 2.47 2.29 1179 0.64 200 12.8 2.37 2.20 1285 0.53 200 12.8 2.59 2.42 1013 0.79 200 12.8 1.96 1.79 1098 0.68 200 12.8 2.26 2.09 1047 0.73 200 12.8 2.11 1.93 1271 2.02 200 12.8 2.62 2.44 1130 2.16 200 12.8 2.22 2.04 1138 0.67 200 27.7 2.49 2.11 1091 0.74 200 27.7 2.43 2.05 1276 0.58 200 27.7 2.86 2.48 1222 0.62 200 27.7 2.64 2.26 1043 0.77 200 27.7 2.26 1.88

104

Table C.10. Rate constant data for benzaldehyde (C6H5CHO) + OH T (K) P (atm) [Aldehyde]0

[TBHP]0 (ppm) k’ (1013 cm3/mol-s) k (1013cm3/mol-s) 1257 0.57 300 28.7 1.29 0.99 1220 0.61 300 28.7 1.34 1.03 1167 0.63 300 28.7 1.26 0.96 1302 0.54 300 28.7 1.37 1.07 1110 0.69 300 28.7 1.15 0.85 1046 0.73 300 28.7 1.12 0.81 1251 0.59 500 10.5 1.09 1.02 1169 0.63 500 10.5 0.99 0.92 1135 0.65 500 10.5 0.96 0.89 1072 0.70 500 10.5 0.91 0.84 1290 0.56 500 10.5 1.11 1.04 1238 0.58 500 10.5 1.11 1.04 1008 0.78 500 10.5 0.86 0.79 1211 0.56 300 17.2 1.22 1.03 1180 0.61 300 17.2 1.10 0.92 1115 0.67 300 17.2 1.07 0.89 1295 0.55 300 17.2 1.29 1.11 1039 0.76 300 17.2 1.02 0.84 983 0.78 300 17.2 0.97 0.79

1333 1.89 300 17.2 1.33 1.14 1182 2.05 300 17.2 1.15 0.96 1068 2.15 300 17.2 1.08 0.89

105

Appendix D: Rate Constants Data for the Thermal

Dissociation Reaction of Acetone

Table D.1. Summary of Acetone Decomposition Rate Constant Measurement

T [K] P [atm] k7.1 [s-1] 5 – 20 ppm acetone / Ar

1494 1.46 2.09 x 104

1481 1.47 1.49 x 104

1461 1.44 1.20 x 104

1440 1.42 8.29 x 103

1421 1.45 6.48 x 103

1420 1.46 6.21 x 103 1398 1.52 3.97 x 103 1382 1.56 2.98 x 103

1348 1.49 1.58 x 103

1332 1.55 1.10 x 103

1271 1.59 3.46 x 102

100 ppm acetone / Ar 1433 1.49 9.26 x 103

1419 1.46 5.08 x 103 1402 1.52 4.39 x 103 1387 1.50 2.68 x 103 1287 1.62 4.68 x 102

1252 1.55 1.80 x102

1215 1.61 7.78 x 101

1172 1.52 2.65 x 101 1142 1.57 9.06 x 100

1000 ppm acetone /Ar 1201 1.67 4.94 x 101

1187 1.74 3.04 x 101 1156 1.74 1.26 x 101

1119 1.75 4.91 x 100

1.00% acetone /Ar 1098 1.75 1.79 x 100

1049 1.68 4.48 x 10-1

1048 1.84 3.28 x 10-1

1033 1.68 2.33 x 10-1 1024 1.75 1.65 x 10-1

1019 1.76 1.70 x 10-1

1016 1.67 1.35 x 10-1

1004 1.80 8.06 x 10-2

107

Appendix E: Effect of the Pulsed Laser Linewidth on

the Effective CH3 Absorbance

When using a spectrally broad light source, it is pertinent to analyze the effect of

linewidth on the measured absorbance. As shown in Fig. 7.14., the FWHM linewidth of

the laser (~ 0.15 nm) is about 20 times narrower than that of CH3 absorption feature (~ 3

nm), therefore the current pulsed laser is expected to behave similar to a narrow-

linewidth CW laser in terms of single-pass CH3 absorption. This can be further examined

through a detailed calculation for the effective single-pass absorbance as defined below:

𝛼𝛼 = − ln �∫ 𝑚𝑚𝑒𝑒𝑒𝑒[−𝛼𝛼0𝜙𝜙(𝜆𝜆)]+∞−∞ 𝐼𝐼(𝜆𝜆)𝑑𝑑𝜆𝜆

∫ 𝐼𝐼(𝜆𝜆)𝑑𝑑𝜆𝜆+∞−∞

� (𝐸𝐸𝐸𝐸𝑙𝑙. 𝐸𝐸1)

In the above equation, α0 is the single-pass absorbance at the CW limit (laser linewidth

approaching zero), φ(λ) is the CH3 absorption lineshape function, i.e. the absorption

spectrum of CH3 normalized to unity at λ0 = 216.62 nm, and I(λ) is the lineshape

function, or spectral density function, of the laser output. As measurement shows that I(λ)

of the current pulsed laser is close to a Gaussian function, we assume a Gaussian I(λ)

throughout this analysis:

𝐼𝐼(𝜆𝜆) ∝ exp �−4𝑙𝑙𝑙𝑙2 ⋅ (𝜆𝜆 − 𝜆𝜆0)2

(∆𝜆𝜆)2 � (𝐸𝐸𝐸𝐸𝑙𝑙. 𝐸𝐸2)

where ∆λ is the FWHM linewidth of the laser. In the CW-limit, Ι(λ) approaches a delta-

function around λ0 and we recover α = α0. Fig. E.1 shows the ratio of α to α0 calculated

as functions of ∆λ at α0 = 0.01, 0.1 and 1. Also displayed in the figure is the transform-

limited pulsed width associated with each value of ∆λ. As the figure clearly indicates, ps-

level pulsed lasers, including the current laser, yield almost identical single-pass

absorbance compared to the narrow-linewidth CW-lasers (α/α0 > 0.99). Some early UV

lamp measurements (for example [135]–[137]), however, have values of ∆λ on the order

of 1-2 nm and hence reduced sensitivities as α/α0 decreases. Measurements with light

108

sources of higher ∆λ are further complicated by nonlinear α0-dependence resulting from

partial saturation. Similarly, care is advised for measurement of molecules with narrow

absorption features. For example, in the previous pulsed UV CEAS study that

demonstrated measurements of the vibrational relaxation of O2 [45] (which has an

absorption linewidth comparable to the laser linewidth), the maximum single-pass

absorbance was limited to less than 0.03 to avoid partial saturation. Nonetheless, for

detection of CH3 at elevated temperatures and pressures, the current use of the ps-pulsed

laser is almost ideal.

Figure E.1. Effective CH3 absorbance vs. laser linewidth, calculated using the CH3

absorption spectrum shown in Fig. 7.14. Note that the current ps-pulsed laser yields

almost identical effective single-pass CH3 absorbance as narrow-linewidth CW-lasers.

109

Appendix F: Analysis for the Laser-Cavity Coupling

Noise in Current Pulsed Laser CEAS

Figure F.1. Two major sources of laser-cavity coupling noise.

(a) Cavity mode shifting. (b) Cavity mode stretching.

As mentioned earlier, pulsed CEAS can defeat laser-cavity coupling noise by avoiding

interaction between the short light packets. This noise-suppression principle can also be

explained through an equivalent frequency domain analysis. In the frequency domain, the

total transmitted laser intensity through a vacuum cavity equals the integral of the product

of the laser output spectrum (effectively a continuum relative to the cavity modes) and

the cavity transmission spectrum, and laser-cavity coupling noise results from either

shifting or stretching of the cavity modes, as illustrated in Fig. F.1. Under the current

CEAS setup, however, the pulsed laser is simultaneously coupled into about a thousand

cavity modes (see Fig. F.2); any effect of cavity mode drifting is thus readily smoothed

out, and the consequent noise is negligible. On the other hand, cavity mode stretching

affects the transmitted laser intensity as it changes the density of the cavity modes; the

resulting noise is proportional to the change in cavity free spectral range, FSR = c/2nL,

where c is the speed of light, and n is the refractive index of the gas in the shock tube.

For mode-stretching-related noise, our most conservative estimation suggests that the

maximum change in the tube inner diameter due to mechanical vibration is less than 0.1

110

mm throughout the reflected shock experiment, which translates to a maximum relative

change in L of less than 7 x 10-4; and the maximum change in the refractive index n of

typical test gas is less than 3 x 10-4. In summary, the overall fluctuation in the transmitted

laser intensity caused by laser-cavity coupling noise is less than 0.1%.

Figure F.2. The current laser linewidth vs. cavity free spectral range. Note that the FWHM

linewidth of the current pulsed laser (top panel) encompasses about a thousand cavity

modes (bottom panel), which grants excellent immunity to laser-cavity coupling noise.

111

Appendix G: Rate Constant Data for the Thermal

Dissociation Reaction of Methane

Table G.1. Rate constant data for CH4 + Ar = CH3 + H + Ar

T5 (K) P5 (atm) [CH4]0 (ppm) kCH4+M (cm3/mol-s) Uncertainty*

1866 1.57 200 5.3 x 106 +21% / -25%

1860** 1.67 200 5.0 x 106 +22% / -26%

1757 1.69 500 1.6 x 106 +18% / -18%

1721 1.72 1050 8.2 x 105 +19% / -19%

1698 1.69 500 5.8 x 105 +20% / -20%

1636 1.72 1050 2.6 x 105 +19% / -19%

1610 1.70 1050 1.3 x 105 +27% / -27%

1561 1.76 1050 6.9 x 104 +26% / -26%

1487** 1.82 10000 1.7 x 104 +26% / -35%

*: uncertainty limits corresponding to the 0.95-confidence interval (2σ-equivalent)

**: mixtures using >99.97% purity CH4 and 6.0-grade Ar; others using >99% purity CH4

and 5.0-grade Ar

113

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SHOCK TUBE / LASER ABSORPTION STUDY OF ALDEHYDES KINETICS

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