shock tube measurements of oxygenated fuel combustion
TRANSCRIPT
SHOCK TUBE MEASUREMENTS OF OXYGENATED FUEL
COMBUSTION USING LASER ABSORPTION SPECTROSCOPY
A DISSERTATION
SUBMITTED TO THE DEPARTMENT OF MECHANICAL ENGINEERING
AND THE COMMITTEE ON GRADUATE STUDIES
OF STANFORD UNIVERSITY
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
King Yiu Lam June 2013
http://creativecommons.org/licenses/by-nc/3.0/us/
This dissertation is online at: http://purl.stanford.edu/ty513tt0976
© 2013 by King Yiu Lam. All Rights Reserved.
Re-distributed by Stanford University under license with the author.
This work is licensed under a Creative Commons Attribution-Noncommercial 3.0 United States License.
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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
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.
Craig Bowman
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.
David Davidson
Approved for the Stanford University Committee on Graduate Studies.
Patricia J. Gumport, Vice Provost 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.
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Abstract In the current engine development, fuel reformulation is considered as one of the
potential strategies to improve fuel efficiency, reduce petroleum consumption, and
minimize pollutant formation. Oxygenated fuels can be used as neat fuels or additives in
spark-ignition and diesel engines to allow for more complete combustion. To understand
the influence of oxygenated fuels on engine performance, accurate comprehensive kinetic
mechanisms, which can consist of hundreds to thousands of elementary reactions, are
needed to describe the chemistry of the combustion events, such as autoignition and
pollutant formation.
The primary objective of the research presented in this dissertation is to provide
reliable experimental kinetic targets, such as ignition delay times, species time histories,
and direct reaction rate constant measurements, using shock tube and laser absorption
techniques in order to evaluate and refine the existing kinetic mechanisms for two
different types of oxygenated fuels (i.e., ketones and methyl esters) and to reexamine the
kinetics of the H2 + OH reaction. The topics of this work are mainly divided into three
sections: (1) H2 + OH kinetics, (2) ketone combustion chemistry, and (3) methyl ester +
OH kinetics.
The reaction of OH with molecular hydrogen (H2)
H2 + OH → H2O + H (1)
is an important chain-propagating reaction in all combustion systems, particularly in
hydrogen combustion, and its direct rate constant measurements are discussed in the first
part of this dissertation. The rate constant for reaction (1) was measured behind reflected
shock waves over the temperature range of 902-1518 K at pressures of 1.15-1.52 atm.
OH radicals were produced by rapid thermal decomposition of tert-butyl hydroperoxide
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(TBHP) at high temperatures, and were monitored using the narrow-linewidth ring dye
laser absorption of the well-characterized R1(5) line in the OH A–X (0, 0) band near
306.69 nm. Consequently, this work aims to report the rate constant for reaction (1) with
a much lower experimental scatter and overall uncertainty (as compared to the data
available in the literature).
Ketones are important to a variety of modern combustion processes. They are
widely used as fuel tracers in planar laser-induced fluorescence (PLIF) imaging of
combustion processes due to their physical similarity to gasoline surrogate components.
Additionally, they are often formed as intermediate products during oxidation of large
oxygenated fuels, such as alcohols and methyl esters. In the second part of this
dissertation, the combustion characteristics of acetone (CH3COCH3), 2-butanone
(C2H5COCH3), and 3-pentanone (C2H5COC2H5) are discussed in the context of the
reflected shock wave experiments. These experiments were performed using different
laser absorption methods to monitor species concentration time histories (i.e., ketones,
CH3, CO, C2H4, CH4, OH, and H2O) over the temperature range of 1100-1650 K at
pressures near 1.6 atm. These speciation data were then compared with the simulations
from the detailed mechanisms of Pichon et al. (2009) and Serinyel et al. (2010).
Consequently, the overall rate constants for the thermal decomposition reactions of
acetone, 2-butanone, and 3-pentanone
CH3COCH3 (+ M) → CH3 + CH3CO (+ M) (2)
C2H5COCH3 (+ M) → Products (+ M) (3)
C2H5COC2H5 (+ M) → Products (+ M) (4)
were inferred by matching the species profiles with the simulations from the detailed
mechanisms at pressures near 1.6 atm. In addition, an O-atom balance analysis from the
speciation data revealed the absence of a methyl ketene removal pathway in the original
models. Furthermore, the overall rate constants for the reactions of OH with a series of
ketones
CH3COCH3 + OH → CH3COCH2 + H2O (5)
C2H5COCH3 + OH → Products (6)
C2H5COC2H5 + OH → Products (7)
C3H7COCH3 + OH → Products (8)
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were determined using UV laser absorption of OH over the temperature range of 870-
1360 K at pressures of 1-2 atm. These measurements included the first direct high-
temperature measurements of the overall rate constants for reactions (6)-(8), and were
compared with the theoretical calculations from Zhou et al. (2011) and the estimates
using the structure-activity relationship (SAR) (1995).
Biodiesel, which consists of fatty acid methyl esters (FAMES), is a promising
alternative to fossil fuels. The four simplest methyl esters include methyl formate
(CH3OCHO), methyl acetate (CH3OC(O)CH3), methyl propanoate (CH3OC(O)C2H5),
and methyl butanoate (CH3OC(O)C3H7), and their combustion chemistry is a building
block for the chemistry of large methyl esters. In the third part of this dissertation, the
rate constant measurements for the reactions of OH with four small methyl esters are
discussed:
CH3OCHO + OH → Products (9)
CH3OC(O)CH3 + OH → Products (10)
CH3OC(O)C2H5 + OH → Products (11)
CH3OC(O)C3H7 + OH → Products (12)
These reactions were studied behind reflected shock waves using UV laser absorption of
OH over 876-1371 K at pressures near 1.5 atm. This study presented the first direct high-
temperature rate constant measurements of reactions (9)-(12). These measurements were
also compared with the estimated values from different detailed mechanisms and from
the structure-activity relationship (SAR).
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Acknowledgements First, I would like to thank my advisor, Prof. Ronald Hanson, for the opportunities
and support he has offered throughout my graduate studies at Stanford. His critical
thinking, carefulness, and wisdom have shaped me into a better and more careful
researcher. I would like to thank Dr. David Davidson for offering numerous advice and
guidance throughout my Ph.D. career. His willingness to help students at the lab has
made my time at Stanford much smoother. I am also thankful to Prof. Bowman for
serving on my qualification exam committee and my reading committee.
I have been very fortunate to work with many outstanding students in the Hanson
group. In particular, I am immensely grateful to Zekai Hong, Genny Pang, and Robert
Cook for teaching me how to operate shock tubes and different laser equipment, allowing
me to accomplish the work presented in this dissertation. I am very grateful to Wei Ren
for his friendship and the collaborative efforts we have made together in research and
course works. I am also grateful to many students in the Hanson group who have made
my life at Stanford more meaningful and joyful. Finally, I am sincerely grateful to my
parents for their support and encouragement in times of trouble and frustration.
This work was supported by the U.S. Department of Energy, Basic Energy
Sciences (DE-FG02-88ER13857) with Dr. Wade Sisk as program manager.
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Table of Contents Abstract .................................................................................................................... v
Acknowledgements .......................................................................................................... ix
Table of Contents ............................................................................................................. xi
List of Tables .................................................................................................................. xv
List of Figures ................................................................................................................ xvii
Chapter 1 Background and Motivation ......................................................................... 1
1.1 Introduction ............................................................................................................1
1.2 Background and Motivation ..................................................................................2
1.2.1 H2 + OH Kinetics ........................................................................................ 2
1.2.2 Ketone Combustion Chemistry ................................................................... 5
1.2.3 Methyl Ester + OH Kinetics ....................................................................... 6
1.3 Scope and Organization of Thesis .........................................................................8
Chapter 2 Experimental Methods ................................................................................ 11
2.1 Shock Tube Facility .............................................................................................11
2.2 Laser Absorption Methods ..................................................................................12
2.2.1 UV Laser Absorption of OH ..................................................................... 12
2.2.2 UV Laser Absorption of Ketones ............................................................. 13
2.2.3 UV Laser Absorption of CH3 .................................................................... 14
2.2.4 IR Laser Absorption of CO ....................................................................... 16
2.2.5 CO2 Laser Absorption of C2H4 ................................................................. 17
2.2.6 IR Laser Absorption of H2O ..................................................................... 18
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2.2.7 IR Laser Absorption of CH4 ..................................................................... 19
2.3 Summary ..............................................................................................................20
Chapter 3 A Shock Tube Study of H2 + OH → H2O + H using OH Laser
Absorption .................................................................................................... 21
3.1 Introduction ..........................................................................................................21
3.2 Experimental Details ...........................................................................................21
3.3 Kinetic Measurements .........................................................................................22
3.3.1 Kinetic Mechanism Description ............................................................... 22
3.3.2 H2 + OH Kinetics ...................................................................................... 24
3.4 Comparison with Earlier Work ............................................................................29
3.5 Summary ..............................................................................................................32
Chapter 4 Multi-Species Time History Measurements during High-Temperature
Acetone and 2-Butanone Pyrolysis ............................................................. 33
4.1 Introduction ..........................................................................................................33
4.2 Experimental Details ...........................................................................................34
4.2.1 Mixture Preparation .................................................................................. 34
4.2.2 Species Absorption Coefficient Evaluations ............................................ 35
4.3 Results and Discussion ........................................................................................35
4.3.1 Acetone Pyrolysis ..................................................................................... 35
4.3.2 2-Butanone Pyrolysis ................................................................................ 45
4.4 Summary ..............................................................................................................53
Chapter 5 Shock Tube Measurements of 3-Pentanone Pyrolysis and Oxidation .... 55
5.1 Introduction ..........................................................................................................55
5.2 Experimental Details ...........................................................................................56
5.2.1 Mixture Preparation .................................................................................. 56
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5.2.2 Species Absorption Coefficient Evaluations ............................................ 57
5.3 Results and Discussion ........................................................................................60
5.3.1 3-Pentanone Pyrolysis ............................................................................... 60
5.3.2 3-Pentanone Oxidation.............................................................................. 72
5.3.3 Comparisons of Ketone Oxidation Characteristics ................................... 84
5.4 Summary ..............................................................................................................87
5.5 Possible Future Work ..........................................................................................87
Chapter 6 High-Temperature Measurements of the Reactions of OH with a Series
of Ketones: Acetone, 2-Butanone, 3-Pentanone, and 2-Pentanone ......... 89
6.1 Introduction ..........................................................................................................89
6.2 Experimental Details ...........................................................................................91
6.3 Kinetic Measurements .........................................................................................91
6.3.1 Choice of Kinetic Mechanisms ................................................................. 91
6.3.2 Acetone + OH Kinetics ............................................................................. 93
6.3.3 2-Butanone + OH Kinetics........................................................................ 98
6.3.4 3-Pentanone + OH Kinetics .................................................................... 101
6.3.5 2-Pentanone + OH Kinetics .................................................................... 105
6.3.6 Comparison of Ketone + OH Kinetics .................................................... 109
6.4 Comparison with Low Temperature Data .........................................................110
6.5 Comparison with Structure-Activity Relationship ............................................114
6.6 Summary ............................................................................................................116
Chapter 7 High-Temperature Measurements of the Reactions of OH with Small
Methyl Esters: Methyl Formate, Methyl Acetate, Methyl Propanoate,
and Methyl Butanoate ............................................................................... 117
7.1 Introduction ........................................................................................................117
7.2 Experimental Details .........................................................................................118
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7.3 Kinetic Measurements .......................................................................................118
7.3.1 Choice of Kinetic Mechanisms ............................................................... 119
7.3.2 Methyl Formate (MF) + OH Kinetics ..................................................... 120
7.3.3 Methyl Acetate (MA) + OH Kinetics ..................................................... 125
7.3.4 Methyl Propanoate (MP) + OH Kinetics ................................................ 130
7.3.5 Methyl Butanoate (MB) + OH Kinetics ................................................. 135
7.4 Comparison with Low Temperature Data .........................................................141
7.5 Comparison with Structure-Activity Relationship ............................................143
7.6 Summary ............................................................................................................145
Chapter 8 Conclusions and Future Work ................................................................. 147
8.1 Summary of Results ...........................................................................................147
8.1.1 H2 + OH Kinetics .................................................................................... 147
8.1.2 Ketone Combustion Chemistry ............................................................... 148
8.1.3 Methyl Ester + OH Kinetics ................................................................... 150
8.2 Publications ........................................................................................................151
8.3 Recommendations for Future Work ..................................................................152
8.3.1 Ethyl Radical Diagnostics and Decomposition Pathway ........................ 152
8.3.2 Methyl Ester Kinetics ............................................................................. 153
Appendix A Shock Tube Ignition Delay Time Measurements in Propane/O2/Argon
Mixtures at Near-Constant-Volume Conditions ..................................... 155
Appendix B Ignition Delay Time Measurements of Normal Alkanes and
Cycloalkanes ............................................................................................... 173
Appendix C Multi-Species Time History Measurements during the Oxidation of n-
Decane, iso-Octane, and Toluene ............................................................. 179
Bibliography ................................................................................................................ 191
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List of Tables Table 3.1: Reactions Describing H2 + OH Experiments at P = 1.3 atm. ........................................ 23
Table 3.2: Rate Constant Data for H2 + OH → H2O + H. ............................................................. 27
Table 4.1: Summary of acetone unimolecular dissociation rate constant data. ............................. 41
Table 4.2: Summary of overall 2-butanone decomposition rate constant data. ............................. 48
Table 5.1: Summary of test gas mixture compositions and measured species. ............................. 56
Table 5.2: Kinetic parameters employed in the Serinyel et al. mechanism. .................................. 64
Table 5.3: Summary of overall 3-pentanone decomposition rate constant data. ........................... 65
Table 6.1: CH3COCH3 + OH → Products: Rate Constant Data. ................................................... 95
Table 6.2: C2H5COCH3 + OH → Products: Rate Constant Data. ................................................ 100
Table 6.3: C2H5COC2H5 + OH → Products: Rate Constant Data. ............................................... 104
Table 6.4: C3H7COCH3 + OH → Products: Rate Constant Data. ................................................ 108
Table 7.1: CH3OCHO + OH → Products: Rate Constant Data. .................................................. 122
Table 7.2: CH3OC(O)CH3 + OH → Products: Rate Constant Data. ............................................ 128
Table 7.3: CH3OC(O)C2H5 + OH → Products: Rate Constant Data. .......................................... 133
Table 7.4: CH3OC(O)C3H7 + OH → Products: Rate Constant Data. .......................................... 138
Table 7.5: Comparison of the rate constants for channels (12a)-(12d) from Fisher et al.
[48], Dooley et al. [54], and Hakka et al. [55] at 1133 K and 1300 K. ................... 140
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List of Figures Figure 1.1: (a) Arrhenius plot for the reaction of OH with H2 at all temperatures. (b)
Arrhenius plot for the reaction of OH with H2 at high temperatures (1000-
2500 K). ...................................................................................................................... 4
Figure 1.2: Impact of the rate constant for the reaction of H2 + OH → H2O + H and its
uncertainty (within a factor of 2) on the laminar flame speed predictions of
H2-air mixtures at 298 K and 1 atm. Laminar flame speed simulations were
performed using the preliminary CEFRC foundational fuel model [33] with
the H2 + OH reaction rate constant from Michael and Sutherland [18]. ..................... 5
Figure 2.1: Schematic of OH detection using a narrow-linewidth ring dye laser near
306.69 nm. Figure adapted from refs. [23-24]. ........................................................ 13
Figure 2.2: High-temperature ketone absorption cross-sections at 306.65 nm. ............................. 14
Figure 2.3: Schematic of CH3 detection near 216.6 nm using the frequency-quadrupled
output of near-infrared radiation from a pulsed Ti:Sapphire laser. Figure
adapted from ref. [63]. .............................................................................................. 15
Figure 2.4: Schematic of CO detection using cw quantum cascade laser near 4.56 µm.
Figure adapted from ref. [66]. ................................................................................... 16
Figure 2.5: Schematic of C2H4 detection using cw CO2 laser near 10.5 µm. Figure
adapted from ref. [67]. .............................................................................................. 18
Figure 2.6: Schematic of H2O detection using cw DFB laser near 2.55 µm. Figure
adapted from ref. [69]. .............................................................................................. 18
Figure 2.7: Schematic of CH4 detection using a scanned-wavelength mid-IR laser near
3.4 µm. Figure adapted from ref. [70]. ..................................................................... 19
Figure 3.1: OH sensitivity plot for the rate constant measurement of H2 + OH at 1228 K
and 1.29 atm. ............................................................................................................. 25
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Figure 3.2: Sample H2 + OH rate constant measurement using the mixture of 1001 ppm
H2 with ~26 ppm TBHP (and 99 ppm water) in Ar at 1228 K and 1.29 atm.
Simulation from USC-Mech v2.0 [72] for the best-fit rate constant, along
with variations of ±20%, is also shown. ................................................................... 26
Figure 3.3: H2 + OH rate constant measurements at various temperatures, along with the
simulations from USC-Mech v2.0 for the best-fit rate constants. ............................. 26
Figure 3.4: Uncertainty analysis for the rate constant of H2 + OH → H2O + H at 1228 K
and 1.29 atm. ............................................................................................................. 28
Figure 3.5: Arrhenius plot for H2 + OH (k1) at temperatures above 833 K. ................................... 29
Figure 3.6: Comparison with previous studies at temperatures above 833 K. ............................... 32
Figure 4.1: CO sensitivity for 0.25% acetone in Ar using the Pichon et al. mechanism
[89]. ........................................................................................................................... 36
Figure 4.2: CO rate of production (ROP) plot for 0.25% acetone in Ar using the Pichon et
al. mechanism [89]. ................................................................................................... 37
Figure 4.3: Sample CO time histories: measured and calculated values. ...................................... 37
Figure 4.4: Summary of acetone dissociation rate constant (k2). ................................................... 38
Figure 4.5: Acetone sensitivity for 1% acetone in Ar using the Pichon et al. mechanism
[89]. ........................................................................................................................... 39
Figure 4.6: Acetone time histories for 1% acetone in Ar: measured and simulated values. .......... 40
Figure 4.7: CH3 time histories for 0.25% acetone in Ar: measured and calculated values. ........... 42
Figure 4.8: C2H4 time histories for 1% acetone in Ar: measured and calculated values. .............. 43
Figure 4.9: CH4 time histories for 1.5% acetone in Ar: measured and calculated values. ............. 44
Figure 4.10: Arrhenius plot of the rate constants for the reaction of CH3COCH3 + CH3 →
CH3COCH2 + CH4 from Saxena et al. [88], Sato and Hidaka [87], and
Pichon et al. [89]. ...................................................................................................... 45
Figure 4.11: 2-Butanone time histories for 1% 2-butanone in Ar: measured and simulated
values. ....................................................................................................................... 46
Figure 4.12: 2-Butanone sensitivity for 1% 2-butanone in Ar. ...................................................... 46
Figure 4.13: Arrhenius plot for overall 2-butanone decomposition rate constant (k3). .................. 47
Figure 4.14: CH3 time histories for 0.25% 2-butanone in Ar: measured and calculated
values. ....................................................................................................................... 48
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Figure 4.15: CO rate of production (ROP) plot for 1% 2-butanone in Ar using the original
Serinyel et al. mechanism (with the revised k3). ....................................................... 49
Figure 4.16: CO time histories for 1% 2-butanone in Ar: measured and calculated values. ......... 50
Figure 4.17: C2H4 time histories for 1% 2-butanone in Ar: measured and calculated
values. ....................................................................................................................... 51
Figure 4.18: CH4 time histories for 1.5% 2-butanone in Ar: measured and calculated
values. ....................................................................................................................... 52
Figure 5.1: Comparison of CO mole fraction time histories at 1325 K and 1.60 atm with
different absorption coefficients in Beer’s law. ........................................................ 58
Figure 5.2: Comparison of OH mole fraction time histories at 1486 K and 1.52 atm with
different absorption coefficients in Beer’s law. The OH mole fractions by
constant U, V and constant H, P are virtually indistinguishable for OH. ................. 59
Figure 5.3: Measured and simulated 3-pentanone time histories for 1% 3-pentanone in
Ar. Simulations used the Serinyel et al. mechanism. ................................................ 61
Figure 5.4: 3-pentanone sensitivity analysis for 1% 3-pentanone in Ar at 1323 K and 1.6
atm. ............................................................................................................................ 61
Figure 5.5: CH3 time histories for 0.1% 3-pentanone in Ar. Simulations were done using
the Serinyel et al. mechanism. .................................................................................. 62
Figure 5.6: CH3 sensitivity analysis for 0.1% 3-pentanone in Ar at 1433 K and 1.6 atm. ............. 63
Figure 5.7: (a) Best-fit 3-pentanone time histories and (b) best-fit CH3 time histories
using the Serinyel et al. mechanism with revised overall 3-pentanone
decomposition rate constant (k4). .............................................................................. 66
Figure 5.8: Arrhenius plot for the overall 3-pentanone decomposition rate constant (k4) at
1.6 atm. ...................................................................................................................... 67
Figure 5.9: Measured 3-pentanone and CO time histories during 3-pentanone pyrolysis at
1248 K and 1.6 atm. .................................................................................................. 68
Figure 5.10: CO sensitivity analysis for 1% 3-pentanone in Ar at 1248 K and 1.6 atm. ............... 68
Figure 5.11: CO time histories for 0.25% 3-pentanone in Ar: measured and calculated
values from the (a) original and (b) modified Serinyel et al. mechanisms. .............. 70
Figure 5.12: C2H4 time histories for 0.25% 3-pentanone in Ar: measured and calculated
values. ....................................................................................................................... 71
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Figure 5.13: Sample sidewall pressure and endwall OH* emission time histories recorded
during an experiment of 3-pentanone ignition at 1113 K and 1.1 atm (3-
pentanone/ 4.0% O2/ Ar, Φ = 0.5). A tailored gas mixture of 60% helium/
40% nitrogen was used as driver gas to achieve a long test time. For high
fuel concentration mixtures, the definition of the endwall ignition delay time
is shown in the figure. ............................................................................................... 72
Figure 5.14: Measured and simulated 3-pentanone ignition delay times at (a) Φ = 1.0 and
(b) Φ = 0.5 and P5 = 1.0 atm. .................................................................................... 74
Figure 5.15: Comparison of model predictions between (a) the Serinyel et al. mechanism
of NUI Galway [98] and (b) the modified mechanism on ignition delay time
measurements from Serinyel et al. ............................................................................ 75
Figure 5.16: OH sensitivity analysis for 400 ppm 3-pentanone with 0.28% O2 in Ar (Φ =
1.0) at 1486 K and 1.52 atm. ..................................................................................... 76
Figure 5.17: H2O sensitivity analysis for 400 ppm 3-pentanone with 0.28% O2 in Ar (Φ =
1.0) at 1486 K and 1.52 atm. ..................................................................................... 77
Figure 5.18: Comparisons of measured and simulated H2O time histories from the (a)
original and (b) modified Serinyel et al. mechanisms for 400 ppm 3-
pentanone with 0.28% O2 in Ar (Φ = 1.0). ............................................................... 79
Figure 5.19: Comparisons of measured and simulated H2O time histories from the (a)
original and (b) modified Serinyel et al. mechanisms for 400 ppm 3-
pentanone with 0.56% O2 in Ar (Φ = 0.5). ............................................................... 80
Figure 5.20: Comparisons of measured and simulated OH time histories from the (a)
original and (b) modified Serinyel et al. mechanisms for 400 ppm 3-
pentanone with 0.28% O2 in Ar (Φ = 1.0). Inset figures are provided to
show the early-time features over 0-400 µs. ............................................................. 83
Figure 5.21: Comparisons of measured and simulated OH time histories from the (a)
original and (b) modified Serinyel et al. mechanisms for 400 ppm 3-
pentanone with 0.56% O2 in Ar (Φ = 0.5). Inset figures are provided to
show the early-time features over 0-400 µs. ............................................................. 84
Figure 5.22: Comparison of ignition delay times for different ketones (acetone, 2-
pentanone and 3-pentanone). .................................................................................... 85
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Figure 5.23: Comparison of OH time histories for the mixtures of ketone (i.e., acetone, 2-
pentanone and 3-pentanone) with 0.525% O2 in Ar at a pressure of 2.6 atm
and an equivalence ratio of 1.0. An inset figure is provided to show the
early-time features over 0-400 µs. ............................................................................ 86
Figure 6.1: OH sensitivity plot for the rate constant measurement of acetone + OH at
1148 K and 1.95 atm. ................................................................................................ 94
Figure 6.2: Sample acetone + OH rate constant measurement using the mixture of 304
ppm acetone with ~28 ppm TBHP (and 73 ppm water) in Ar at 1148 K and
1.95 atm. Simulation from the modified Pichon et al. mechanism for the
best-fit rate constant, along with perturbations of ±50%, is also shown. .................. 95
Figure 6.3: Uncertainty analysis for the rate constant of CH3COCH3 + OH → products at
1148 K and 1.95 atm. ................................................................................................ 96
Figure 6.4: Arrhenius plot for acetone + OH (k5) at temperatures above 833 K. .......................... 97
Figure 6.5: OH sensitivity plot for the rate constant measurement of 2-butanone + OH at
1039 K and 1.41 atm. ................................................................................................ 98
Figure 6.6: Sample 2-butanone + OH rate constant measurement using the mixture of 152
ppm 2-butanone with ~14 ppm TBHP (and 41 ppm water) in Ar at 1039 K
and 1.41 atm. Simulation from the modified Serinyel et al. mechanism for
the best-fit rate constant, along with perturbations of ±50%, is also shown. ............ 99
Figure 6.7: Arrhenius plot for 2-butanone + OH (k6) at temperatures above 833 K. ................... 101
Figure 6.8: OH sensitivity plot for the rate constant measurement of 3-pentanone + OH at
1188 K and 1.94 atm. .............................................................................................. 102
Figure 6.9: Sample 3-pentanone + OH rate constant measurement using the mixture of
213 ppm 3-pentanone with ~17 ppm TBHP (and 59 ppm water) in Ar at
1188 K and 1.94 atm. Simulation from the modified Serinyel et al.
mechanism for the best-fit rate constant, along with perturbations of ±50%,
is also shown. .......................................................................................................... 103
Figure 6.10: Arrhenius plot for 3-pentanone + OH (k7) at temperatures above 833 K. ............... 105
Figure 6.11: Sample 2-pentanone + OH rate constant measurement using the mixture of
161 ppm 2-pentanone with ~15 ppm TBHP (and 45 ppm water) in Ar at
1186 K and 1.30 atm. Simulation from the modified Serinyel et al.
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mechanism for the best-fit rate constant, along with perturbations of ±50%,
is also shown. .......................................................................................................... 107
Figure 6.12: Arrhenius plot for 2-pentanone + OH (k8) at temperatures above 900 K. ............... 108
Figure 6.13: Arrhenius plot of the measured rate constants for reactions (5)-(8) at
temperatures above 870 K. ...................................................................................... 109
Figure 6.14: Arrhenius plot for acetone + OH → products (k5) at all temperatures. ................... 111
Figure 6.15: Arrhenius plot for 2-butanone + OH → products (k6) at all temperatures. ............. 112
Figure 6.16: Arrhenius plot for 3-pentanone + OH → products (k7) at all temperatures. ............ 113
Figure 6.17: Arrhenius plot for 2-pentanone + OH → products (k8) at all temperatures. ............ 114
Figure 7.1: OH sensitivity plot for the rate constant measurement of methyl formate +
OH at 1168 K and 1.40 atm. ................................................................................... 121
Figure 7.2: Sample methyl formate + OH rate constant measurement using the mixture of
322 ppm methyl formate with ~26 ppm TBHP (and 70 ppm water) in Ar at
1168 K and 1.40 atm. Simulation from the Dooley et al. mechanism [49] for
the best-fit rate constant, along with perturbations of ±50%, is also shown. .......... 122
Figure 7.3: Uncertainty analysis for the rate constant of methyl formate + OH → products
at 1168 K and 1.40 atm. .......................................................................................... 123
Figure 7.4: Arrhenius plot for methyl formate + OH (k9) at temperatures above 833 K. ............ 125
Figure 7.5: OH sensitivity plot for the rate constant measurement of methyl acetate + OH
at 1091 K and 1.37 atm. .......................................................................................... 126
Figure 7.6: Sample methyl acetate + OH rate constant measurement using the mixture of
384 ppm methyl acetate with ~28.5 ppm TBHP (and 73.5 ppm water) in Ar
at 1091 K and 1.37 atm. Simulation from the Dooley et al. mechanism [49]
for the best-fit rate constant, along with perturbations of ±50%, is also
shown. ..................................................................................................................... 127
Figure 7.7: Arrhenius plot for methyl acetate + OH (k10) at temperatures above 833 K. ............ 129
Figure 7.8: OH sensitivity plot for the rate constant measurement of methyl propanoate +
OH at 1208 K and 1.33 atm. ................................................................................... 132
Figure 7.9: Sample methyl propanoate + OH rate constant measurement using the
mixture of 281 ppm methyl propanoate with ~22 ppm TBHP (and 68 ppm
water) in Ar at 1208 K and 1.33 atm. Simulation from the Dooley et al.
xxiii
mechanism [54] for the best-fit rate constant, along with variations of ±50%,
is also shown. .......................................................................................................... 133
Figure 7.10: Arrhenius plot for methyl propanoate + OH (k11) at temperatures above 870
K. ........................................................................................................................... 135
Figure 7.11: Chemical notations for fuel radicals from MCH + OH reactions used by
Orme et al. [133]. .................................................................................................... 136
Figure 7.12: OH sensitivity plot for the rate constant measurement of methyl butanoate +
OH at 1133 K and 1.37 atm. ................................................................................... 137
Figure 7.13: Sample methyl butanoate + OH rate constant measurement using the mixture
of 241 ppm methyl butanoate with ~20 ppm TBHP (and 60 ppm water) in
Ar at 1133 K and 1.37 atm. Simulation from the Dooley et al. mechanism
[54] for the best-fit rate constant, along with variations of ±50%, is also
shown. ..................................................................................................................... 138
Figure 7.14: Arrhenius plot for methyl butanoate + OH (k12) at temperatures above 870
K. ........................................................................................................................... 140
Figure 7.15: Arrhenius plots for methyl ester + OH reactions at temperatures above 250
K. ........................................................................................................................... 143
Figure 7.16: Comparison of the present rate constant measurements with the modified
SAR estimations. ..................................................................................................... 145
Figure A.1: Previous ignition delay time measurements for propane oxidation in air at Φ
= 0.5. The constant U, V model calculations utilize the Curran et al.
mechanism [100]. .................................................................................................... 157
Figure A.2: Comparison of pressure profiles for a mixture of 0.8% C3H8/ 8% N2/ Ar
obtained with and without driver insert in the Stanford 14.13 cm diameter
shock tube. The fractional pressure rise without driver insert (over 20 ms) is
approximately 20%, compared to ±3.0% local pressure variations with
driver insert. The decay beginning at 25 ms is due to arrival of the
rarefaction wave from the driver section. ............................................................... 162
Figure A.3: Comparison of pressure profiles for reactive mixture with and without LPST
driver insert. Pressure rise without driver insert (over 10 ms) is 20%,
compared to ±3.0% pressure variations with driver insert. Initial reflected
xxiv
shock conditions: T5 = 1034 K and P5 = 7.1 atm (with dP5/dt ~ 2%/ms), T5 =
1044 K and P5 = 6.7 atm (with dP5/dt ~ 0%/ms). .................................................... 163
Figure A.4: Comparison of pressure profiles for reactive mixture with and without HPST
driver insert. Pressure rise without driver insert (over 2.5 ms) is 17.5%,
compared to ±1.0% pressure variations with driver insert. Initial reflected
shock conditions: T5 = 996 K and P5 = 54.7 atm (with dP5/dt ~ 7%/ms), T5 =
1008 K and P5 = 53.7 atm (with dP5/dt ~ 0%/ms). .................................................. 164
Figure A.5: Ignition delay times for 0.8% C3H8/ 8% O2/ Ar mixture at P5 = 6 atm, plotted
at the initial post-shock T5. Experimental data and calculated values from
JetSurF v1.0 mechanism [155] and Curran et al. mechanism [100]. ...................... 166
Figure A.6: Low-pressure experimental data and CHEMSHOCK modeling using JetSurF
v1.0 mechanism. ..................................................................................................... 168
Figure A.7: High-pressure experimental data (at P5 = 24 and 60 atm), along with
CHEMKIN and CHEMSHOCK modeling using JetSurF v1.0 and Curran et
al. mechanisms. ....................................................................................................... 170
Figure B.1: n-Pentane ignition delay time measurements at pressures of 1.8 and 3.6 atm
and equivalence ratios of 1.0 and 0.5. ..................................................................... 175
Figure B.2: n-Hexane ignition delay time measurements at pressures of 1.8 and 3.6 atm
and equivalence ratios of 1.0 and 0.5. ..................................................................... 175
Figure B.3: n-Octane ignition delay time measurements at pressures of 1.8 and 3.6 atm
and equivalence ratios of 1.0 and 0.5. ..................................................................... 176
Figure B.4: n-Nonane ignition delay time measurements at pressures of 1.8 and 3.6 atm
and equivalence ratios of 1.0 and 0.5. ..................................................................... 176
Figure B.5: Cyclohexane (CH) ignition delay time measurements at pressures of 1.5 and
3.0 atm and equivalence ratios of 1.0 and 0.5. ........................................................ 177
Figure B.6: Methylcyclohexane (MCH) ignition delay time measurements at pressures of
1.5 and 3.0 atm and equivalence ratios of 1.0 and 0.5. ........................................... 177
Figure B.7: n-Butylcyclohexane (BCH) ignition delay time measurements at pressures of
1.5 and 3.0 atm and equivalence ratios of 0.88 and 0.45. ....................................... 178
Figure C.1: OH and C2H4 time history measurements for the mixture of 424 ppm JP-8
with 0.813% O2 in Ar. Two JP-8 proposed surrogate models were
employed. Simulations were done using the Dooley et al. mechanism [172]. ....... 181
xxv
Figure C.2: OH time histories for the mixture of ~360 ppm n-decane with 0.813% O2 in
Ar. Simulations were done using JetSurF v1.1 mechanism. An inset figure
is also shown to provide the early-time features. .................................................... 183
Figure C.3: C2H4 time histories for the mixture of ~360 ppm n-decane with 0.813% O2 in
Ar. Simulations were done using JetSurF v1.1 mechanism. .................................. 184
Figure C.4: CO time histories for the mixture of ~360 ppm n-decane with 0.813% O2 in
Ar. Simulations were done using JetSurF v1.1 mechanism. .................................. 185
Figure C.5: OH time histories for the mixture of 511 ppm iso-octane with 0.813% O2 in
Ar. Simulations were done using LLNL mechanism (iso-octane mech. v3).
An inset figure is also shown to provide the early-time features. ........................... 186
Figure C.6: CO time histories for the mixture of 511 ppm iso-octane with 0.813% O2 in
Ar. Simulations were done using LLNL mechanism (iso-octane mech. v3). ........ 187
Figure C.7: OH time histories for the mixture of 640 ppm toluene with 0.813% O2 in Ar.
Simulations were done using JetSurF v1.1 mechanism. An inset figure is
also shown to provide the early-time features. ........................................................ 188
Figure C.8: CO time histories for the mixture of 640 ppm toluene with 0.813% O2 in Ar.
Simulations were done using JetSurF v1.1 mechanism. ......................................... 189
Figure C.9: Comparison of ignition delay time measurements for JP-8, n-decane, iso-
octane, and toluene at 1.6 atm. ................................................................................ 190
xxvi
1
Chapter 1 Background and Motivation
1.1 Introduction
The path towards cleaner and more efficient fuel burning is highly desirable
worldwide. To mitigate CO and particulate matter (PM) emissions in the United States,
strict federal regulations have been implemented into the engine industries. For instance,
PM and NOx emissions from heavy-duty diesel engines produced after 2010 must be
reduced by 90% of the emission levels that were recorded in 2004. Owing to these strict
regulations, further improvements in combustion chamber and fuel injection systems are
required. In conjunction with these improvements, the use of oxygenated fuels to
supplement petroleum-based fuels is also considered as one of the potential strategies in
achieving higher fuel efficiency and reducing pollutant emissions. In particular,
oxygenated fuels are known to assist in more complete combustion by adding oxygen as
part of the fuel, thereby lowering CO and hydrocarbon emissions. Hence, optimizing the
use of oxygenated fuels as neat fuels or additives is pertinent to the current engine
development.
To further understand the influence of oxygenated fuels on engine performance, a
comprehensive model, that can predict important observables such as efficiency and
pollutant emissions, is needed. This type of predictive model generally requires intensive
knowledge in the areas of heat transport, fluid dynamics, and chemistry. Additionally, in
some advanced combustion systems (e.g., homogeneous charge compression ignition
(HCCI) engines), chemistry plays a critical role in governing the overall system
performance, such as autoignition of the fuel-oxidizer mixtures, exhaust gas compositions
2
(i.e., CO, CO2, and NOx), and heat release rates. A detailed kinetic mechanism is
typically used to describe the chemistry of these particular combustion events, and is
comprised of hundreds to thousands of elementary reactions specified by rate constants,
which are strong functions of temperature and pressure. Unfortunately, most of the
existing mechanisms are likely to be error-prone, and require some sort of experimental
validation via several kinetic targets. Typical kinetic targets for these mechanisms are
ignition delay times, species concentration time histories, and direct reaction rate constant
measurements [1]. In this dissertation, the kinetics of the H2 + OH reaction is
reexamined, and the combustion characteristics of two types of oxygenated fuels (i.e.,
ketones and methyl esters) are investigated. Several important kinetic targets are
provided in order to evaluate and refine the existing kinetic mechanisms, and some
definite conclusions regarding these mechanisms can be drawn from these experimental
observations.
1.2 Background and Motivation
1.2.1 H2 + OH Kinetics
The reaction of hydroxyl radicals with molecular hydrogen
H2 + OH → H2O + H (1)
is an important chain-propagating reaction in all combustion systems, particularly in
hydrogen combustion. Its reverse reaction plays a critical role in the establishment of
partial equilibrium in the post-combustion regime.
Because of its important role in combustion, numerous direct rate constant
measurements for reaction (1) have been conducted across a broad range of temperatures
[2-21]. Figure 1.1 demonstrates some of the previous experimental determinations for
reaction (1). Ravishankara and co-workers [8-9] measured the rate constant for the title
reaction (under pseudo-first-order kinetic conditions) using the flash photolysis–
resonance fluorescence technique to monitor the temporal profiles of OH decays in a
heated quartz cell over 250-1050 K. Their measurements confirmed the nonlinearity of
the Arrhenius plot for reaction (1) over this wide temperature range. Recently, Orkin et
3
al. [15] reexamined the rate constant for reaction (1) using the flash photolysis–resonance
fluorescence technique in a Pyrex reactor over a narrower temperature range of 200-479
K, and their results are in excellent agreement with the measured values from
Ravishankara and co-workers [8-9]. At combustion-relevant conditions (T > 1000 K),
the measurements for reaction (1) were generally carried out using shock tubes, and these
high-temperature data have a much larger scatter (within a factor of 2) than the low-
temperature data, as illustrated in Figure 1.1. Frank and Just [17] measured the rate
constants for the reactions of H + O2 → OH + O and H2 + OH → H2O + H by employing
atomic resonance absorption spectrometry (ARAS) to monitor H- and O-atom
concentration profiles behind reflected shock waves over 1700-2500 K. Michael and
Sutherland [18] studied the rate constant for the reaction of H + H2O → H 2 + OH
(reaction (-1)) using flash photolysis of H2O to generate H-atoms and using ARAS to
monitor the temporal profiles of H-atom decays behind reflected shock waves over 1246-
2297 K. The rate constant for reaction (1) was calculated from the measured reverse rate
constant and the equilibrium constant, and the resulting data were then compiled with the
earlier experimental work from Ravishankara and co-workers [8-9] and Frank and Just
[17] to form a three-parameter least-squares fit: k1(T) = 2.16 × 108 T1.51 exp(-3430
[cal/mol]/RT) cm3 mol-1 s-1 over 250-2500 K. This expression is currently adopted in
GRI-Mech 3.0 [22]. It is pertinent to note that the recent revised standard enthalpy of
formation for OH at 298 K [23-24] seems to suggest a lower rate constant expression for
reaction (1) (~15% lower) if the rate constant is evaluated from the reverse reaction and
the revised equilibrium constant. Figure 1.1 also shows the revised evaluations from
Michael and Sutherland [18] using the revised equilibrium constants. Similarly,
Davidson et al. [19] studied the rate constant for the reverse reaction by using laser
photolysis of H2O and UV laser absorption of OH near 307 nm behind reflected shock
waves over 1600-2500 K, and the rate constant for reaction (1) can be evaluated from
their measured values and the revised equilibrium constants, as shown in Figure 1.1.
Oldenborg et al. [20] conducted direct rate constant measurements for reaction (1) (under
pseudo-first-order kinetic conditions) using the laser photolysis / laser-induced
fluorescence technique to monitor OH radical concentration profiles in a heated cell over
4
800-1550 K. Moreover, Krasnoperov and Michael [21] reexamined the rate constant for
reaction (1) using a novel multi-pass absorption spectrometric detection technique to
monitor OH species profiles at 308 nm in reflected shock wave experiments over 832-
1359 K.
Figure 1.1: (a) Arrhenius plot for the reaction of OH with H2 at all temperatures. (b) Arrhenius plot for the reaction of OH with H2 at high temperatures (1000-2500 K).
An accurate knowledge of the rate constant for reaction (1) is important in
interpreting laminar flame speed measurements of H2-O2 mixtures. Figure 1.2 presents
the unstretched laminar flame speed measurements of H2-air mixtures as a function of
equivalence ratio at standard initial temperature (298 K) and ambient pressure (1 atm)
5
[25-32], along with the simulations from the preliminary CEFRC foundational fuel model
[33] with the rate constant for reaction (1) from Michael and Sutherland [18]. Note that
the previous rate constant measurements of reaction (1) have a relatively large scatter
(within a factor of 2) at elevated temperatures, and such large uncertainty in reaction (1)
can affect the laminar flame speed predictions of H2-air mixtures from the model by
approximately ±11%, as demonstrated in Figure 1.2.
Figure 1.2: Impact of the rate constant for the reaction of H2 + OH → H2O + H and its uncertainty (within a factor of 2) on the laminar flame speed predictions of H2-air mixtures at 298 K and 1 atm. Laminar flame speed simulations were performed using the preliminary CEFRC foundational fuel model [33] with the H2 + OH reaction rate constant from Michael and Sutherland [18].
1.2.2 Ketone Combustion Chemistry
There has been an increased interest in studying bio-derived oxygenated fuels
because of their potential to help minimize fossil fuel consumption. Among these
oxygenated fuels, methyl esters and alcohols have attracted a great deal of attention in the
form of both theoretical and experimental studies. Other oxygenates, such as ketones,
though not used as fuels, play a large role in the oxidation of the hydrocarbon and
6
oxygenated fuels. Fewer experimental studies at combustion conditions, however, have
been carried out for ketones (e.g., acetone, 2-butanone, and 3-pentanone).
Ketones are also used as fuel tracers for quantitative planar laser-induced
fluorescence measurements (PLIF) of temperature and species concentration distributions
in internal combustion engine research [34-37]. They are chosen for this purpose because
they exhibit broad absorption spectra in the ultraviolet region (π* ← n transition) and
sufficient quantum yields and strong fluorescence spectra in the visible region to be
easily monitored. 3-pentanone, in particular, is a popular ketone fuel tracer due to its
similar physical characteristics (e.g., boiling point) to that of the gasoline primary
reference fuels (n-heptane and iso-octane). The impact of 3-pentanone in internal
combustion engine studies requires more detailed information about its oxidation and
pyrolysis chemistry in order to predict its influence as an additive on the ignition
processes of the main fuel.
Moreover, ketones are listed as a class of volatile organic compounds (VOCs),
and are massively produced and used as solvents or polymer precursors in industries. As
one of the common pollutants, some amounts of ketones are emitted into the atmosphere
from a variety of natural and anthropogenic sources. The reactions with OH radicals are
the primary removal pathways for ketones in the atmosphere, which may result in the
formation of ozone and other components of the photochemical smog in urban areas [38].
In addition, these reactions of OH with ketones are one of the primary fuel consumption
pathways during oxidation, and are poorly understood at high temperatures. Hence, an
accurate knowledge of these H-atom abstraction reactions is needed in the development
of successful detailed mechanisms suitable for high-temperature applications.
1.2.3 Methyl Ester + OH Kinetics
Biodiesel is a promising alternative fuel because it has physical properties similar
to conventional crude-oil-derived fossil fuels, and it provides the opportunity to reduce
overall emissions of atmospheric pollutants [39]. Biodiesel is generally comprised of a
mixture of extended alkyl chain methyl esters 16-18 carbon atoms long [40], that are
7
typically derived from soybean oil in U.S. or rapeseed oil in Europe. Despite the
complexity of these molecules, there has been a growing effort to develop comprehensive
reaction mechanisms that can be used to describe the combustion of these large methyl
esters [41-44]. In these detailed mechanisms, the reaction rate constants for large methyl
esters are primarily based on the kinetic parameters of smaller methyl esters (e.g., methyl
formate and methyl butanoate) [41, 42, 45-47]. Thus, accurate knowledge of the kinetic
parameters for smaller methyl esters is crucial to the development of the detailed
mechanism for practical biodiesel fuels.
The combustion chemistry of small methyl esters has been a subject of interest for
the past decade. Fisher et al. [48] developed the first comprehensive chemical kinetic
mechanisms for the oxidation of methyl formate and methyl butanoate. However, the
mechanisms were validated against only a limited set of low-temperature experimental
data. Recently, Dooley et al. [49] have compiled a detailed mechanism for methyl
formate oxidation, and the mechanism has been validated against a wide variety of
experimental data, including shock tube ignition delay times, speciation data from a
variable-pressure flow reactor, and laminar burning velocities of outwardly propagating
spherical flames. Similarly, Ren et al. [50] conducted direct rate constant measurements
of the initial dissociation pathways of methyl formate over 1202-1607 K at pressures near
1.6 atm using shock tube/laser absorption techniques, and their measurements are in close
accord with the estimated values adopted in the Dooley et al. mechanism [49].
Concurrently, Peukert et al. [51-52] investigated the high-temperature thermal
decomposition and the H-atom abstraction reactions by H-atoms for methyl formate and
methyl acetate over 1194-1371 K at pressures around 0.5 atm using shock tube/atomic
resonance absorption spectrometry technique. In addition, Westbrook et al. [53]
developed a detailed mechanism for a group of four small alkyl esters, including methyl
formate, methyl acetate, ethyl formate, and ethyl acetate. The mechanism was validated
against the speciation data from fuel-rich, low-pressure, premixed laminar flames.
Similarly, Dooley et al. [54] and Hakka et al. [55] developed two separate detailed
mechanisms for methyl butanoate oxidation, and the mechanisms were tested against
different sets of experimental data, including shock tube and rapid compression machine
8
ignition delay times and speciation data from a flow reactor, a jet-stirred reactor, and an
opposed-flow diffusion flame. Moreover, numerous experimental studies [56-59] for
methyl butanoate pyrolysis and oxidation were performed in order to improve the global
performance of the existing detailed mechanisms. However, among most of these
studies, little attention has been given to a better understanding of the elementary kinetics
of these methyl esters. In particular, the H-atom abstraction reactions by OH radicals for
methyl esters, which are one of the major fuel consumption pathways during oxidation,
are not well known at combustion-relevant conditions.
1.3 Scope and Organization of Thesis
The dissertation is organized as follows:
1) Chapter 2 describes the shock tube facility and different laser absorption techniques,
which were utilized in this work to monitor key combustion radicals and intermediate
species (i.e., OH, ketones, CH3, CO, C2H4, H2O, and CH4).
2) Chapter 3 presents the high-temperature experimental determination of the important
chain-propagating reaction in all combustion systems.
H2 + OH → H2O + H (1)
The present high-temperature measurements were also compared with the previous
experimental determinations, the values employed in several detailed kinetic
mechanisms, and the theoretical calculation using semi-classical transition state
theory (SCTST).
3) Chapter 4 discusses the multi-species time history measurements during high-
temperature acetone and 2-butanone pyrolysis. In this chapter, five different species,
namely ketone, CH3, CO, C2H4, and CH4, were presented and compared with the
simulations from the detailed kinetic mechanisms. During acetone pyrolysis, the CO
and acetone concentration time histories were used to infer the rate constant for
acetone unimolecular decomposition reaction at pressures of 1.23-1.66 atm:
CH3COCH3 (+ M) → CH3 + CH3CO (+ M) (2)
9
Similarly, during 2-butanone pyrolysis, the measured 2-butanone time histories were
used to determine the overall rate constant (k3 = k3a + k3b + k3c) for 2-butanone
decomposition at pressures of 1.39-1.62 atm:
C2H5COCH3 (+ M) → C2H5 + CH3CO (+ M) (3a)
C2H5COCH3 (+ M) → CH3 + C2H5CO (+ M) (3b)
C2H5COCH3 (+ M) → CH3 + CH3COCH2 (+ M) (3c)
In addition, using the measured 2-butanone and CO time histories and an O-atom
balance analysis, a missing removal pathway for methyl ketene (one of the major
products predicted by the model) was identified.
4) Chapter 5 discusses the shock tube measurements of 3-pentanone pyrolysis and
oxidation. In this chapter, we provided six species time history measurements (i.e., 3-
pentanone, CH3, CO, C2H4, OH, and H2O), along with 3-pentanone ignition delay
time measurements. These measurements were also compared with the simulations
from the detailed kinetic mechanism. More importantly, during 3-pentanone
pyrolysis, the measured 3-pentanone and CH3 time histories were used to determine
the overall rate constant (k4 = k4a + k4b) for 3-pentanone decomposition at pressures of
1.32-1.75 atm:
C2H5COC2H5 (+ M) → C2H5 + C2H5CO (+ M) (4a)
C2H5COC2H5 (+ M) → CH3 + C2H5COCH2 (+ M) (4b)
Similar to 2-butanone pyrolysis, an O-atom balance analysis from the measured 3-
pentanone and CO time histories identified the absence of the methyl ketene
decomposition pathway in the detailed mechanism.
5) Chapter 6 provides the direct high-temperature overall rate constant measurements of
acetone + OH, 2-butanone + OH, 3-pentanone + OH, and 2-pentanone + OH
reactions.
CH3COCH3 + OH → CH3COCH2 + H2O (5)
C2H5COCH3 + OH → Products (6)
C2H5COC2H5 + OH → Products (7)
C3H7COCH3 + OH → Products (8)
10
6) Chapter 7 presents the first direct high-temperature overall rate constant
measurements of methyl formate + OH, methyl acetate + OH, methyl propanoate +
OH, and methyl butanoate + OH reactions.
CH3OCHO + OH → Products (9)
CH3OC(O)CH3 + OH → Products (10)
CH3OC(O)C2H5 + OH → Products (11)
CH3OC(O)C3H7 + OH → Products (12)
7) Chapter 8 summarizes the present rate constant determinations of reactions (1)-(12),
and proposes some future plans, which include multi-species time history
experiments and direct rate constant measurements of H-atom abstraction reactions
for large methyl esters (i.e., methyl decanoate).
8) At long shock tube test times, as are needed at low reaction temperatures, small
gradual increases in pressure that result from incident shock wave attenuation and
boundary layer growth can significantly shorten measured ignition delay times. In
Appendix A, we investigated such pressure effects on propane ignition delay times at
pressures of 6, 24, and 60 atm.
9) Appendix B presents the ignition delay time measurements of four n-alkanes (e.g., n-
pentane, n-hexane, n-octane, and n-nonane) and three cycloalkanes (e.g.,
cyclohexane, methylcyclohexane, and n-butylcyclohexane) at various reflected shock
temperatures and pressures (between 1240 and 1500 K and 1.5 and 3.8 atm) and at
two equivalence ratios, namely Φ = 1.0 and Φ = 0.5.
10) Appendix C presents the species time history measurements of OH, C2H4, and CO
during the high-temperature oxidation of n-decane, iso-octane, and toluene, which are
the proposed surrogate fuel components for JP-8. Concurrently, the measured
ignition delay times of these surrogate fuel components were compared with the
measured JP-8 ignition delay times.
11
Chapter 2 Experimental Methods This chapter discusses the shock tube facility and different laser diagnostic
systems employed in this work.
2.1 Shock Tube Facility
Experiments were performed in a stainless-steel, high-purity, low-pressure shock
tube at Stanford. The shock tube is comprised of a 3.7-m driver section and a 10-m
driven section, with an inner diameter of 15.24 cm. The shock tube driver and driven
sections are separated by a polycarbonate diaphragm of 0.005-0.08” in thickness.
Incident shock velocity measurements were made using a series of five piezoelectric
pressure transducers (PCB 113A26 transducer, PCB 483B08 amplifier) over the last 1.5
m of the shock tube and linearly extrapolated to the endwall. Average shock velocity
attenuation rates were between 0.5-1.5% per meter. Reflected shock temperatures and
pressures were determined from the incident shock velocity at the endwall using standard
normal shock relations, with uncertainties of approximately ±0.7% and ±1%,
respectively, mainly due to the uncertainty in the measured shock velocity (±0.2%) [23].
For all experiments presented in this dissertation, vibrational equilibrium can be assumed
immediately behind the incident and reflected shock waves. In addition to the five
piezoelectric pressure transducers, a Kistler™ pressure transducer was utilized to
measure the pressure time histories upon shock-heating. All laser absorption diagnostics,
along with the Kistler™ pressure transducer, were located at a test section 2 cm from the
driven section endwall. Concurrently, prior to every experiment, the shock tube and
12
mixing assembly were routinely turbomolecular pumped down to ~5 µtorr to ensure
purity of the test mixtures, with a typical subsequent leak-plus-outgassing rate of less
than 50 µtorr/min. Further details of the shock tube facility can be found elsewhere [60-
62].
2.2 Laser Absorption Methods
2.2.1 UV Laser Absorption of OH
OH radical concentration was measured using the frequency-doubled output of a
narrow-linewidth ring dye laser near 306.69 nm, as illustrated in Figure 2.1. The laser
wavelength was tuned to the peak of the well-characterized R1(5) absorption line in the
OH A–X (0, 0) band. Visible light near 613.4 nm was generated by pumping Rhodamine
6G dye in a Spectra Physics 380A laser cavity with the 5 W, cw output of a Coherent
Verdi laser at 532 nm. The visible light was then intracavity frequency-doubled using a
temperature-tuned AD*A nonlinear crystal to generate ~1 mW of light near 306.69 nm.
Using a common-mode-rejection detection scheme, a minimum absorbance of 0.1% can
be detected, which resulted in the current experiments in a minimum detection sensitivity
of ~0.2 ppm at 1400 K and 1.5 atm (with kλ = 199.3 cm-1 atm-1). Further details of the
OH laser diagnostic setup are discussed elsewhere [23-24]. The overall estimated
uncertainty in the measured OH mole fraction (XOH) is approximately ±3%, mainly due
to the uncertainty in temperature (±0.7%). To check for the interference absorption, the
laser was also tuned away from the narrow OH absorption line by approximately 4 cm-1.
If the interference absorption was found, an OH off-line measurement was required for
each OH on-line measurement. Under the assumption that the interfering species has
wavelength-independent absorption near 306.69 nm, the interference absorbance of the
off-line measurement can be directly subtracted from the total absorbance of the OH
online measurement. OH species concentration can then be calculated from Beer’s law:
-ln(I/Io)corrected = -ln(I/Io)online + ln(I/Io)offline
-ln(I/Io)corrected = kOHXOHPL
13
where I and Io are the transmitted and incident laser intensities, kOH is the OH absorption
coefficient, XOH is the OH mole fraction, P is the total pressure, and L is the path length
(15.24 cm).
Figure 2.1: Schematic of OH detection using a narrow-linewidth ring dye laser near 306.69 nm. Figure adapted from refs. [23-24].
2.2.2 UV Laser Absorption of Ketones
Ketones (i.e., acetone, 2-butanone, 2-pentanone, and 3-pentanone) are known to
have a near-UV absorption spectrum that corresponds to the symmetry forbidden
electronic π* ← n transition where an electron from a non-binding orbital localized near
the oxygen atom is excited to an anti-bonding orbital around the CO group [34-35]. At
current experimental conditions, the spectrum is broad, lacks any fine structure, and
varies gradually from 220 to 340 nm with peak absorption at around 295 nm. This is
completely consistent with the interfering absorption seen in the OH measurements
during ketone combustion studies. Taking advantage of this fact, we have measured
ketones (off-line of OH) at 306.65 nm using the same laser system as was used for OH
measurements. Figure 2.2 shows the absorption cross-sections (at 306.65 nm) of acetone,
2-butanone, and 3-pentanone over 1050-1650 K at pressures near 1.5 atm, which were
determined by measuring the absorption (from the mixtures of 1% ketone in Ar)
immediately behind reflected shock waves when only ketone existed. The uncertainties
14
in ketone cross-sections were estimated to be ±5%. Using a common-mode-rejection
detection scheme, a minimum ketone detection sensitivity of ~300 ppm at 1300 K and 1.5
atm can be achieved (with kλ ≈ 0.52 cm-1 atm-1).
Figure 2.2: High-temperature ketone absorption cross-sections at 306.65 nm.
2.2.3 UV Laser Absorption of CH3
Methyl radical has a wide predissociatively broadened absorption feature (B2A′1–
X2A″2) near 216 nm, with peak absorption at 216.6 nm. In this work, CH3 was measured
using the frequency-quadrupled output of near-infrared radiation from a pulsed
Ti:Sapphire laser, as illustrated in Figure 2.3. Stable mode-locking of the Ti:Sapphire
laser (MIRA HP, Coherent Inc.) was obtained at a wavelength of 866.4 nm with a peak
output of 1 W, a repetition rate of approximately 76 MHz, and a pulse duration of
approximately 2 picoseconds. Deep UV light was generated by frequency conversion,
using fourth harmonic generation (FHG, Coherent Inc.), to obtain output at 216.6 nm.
Further details of this laser setup can be found elsewhere [63]. Similar to the other laser
absorption methods described here, using a common-mode-rejection detection scheme, a
minimum absorbance of ~0.1% can be detected, resulting in a minimum detection
sensitivity of ~1 ppm at 1300 K and 1.5 atm (with kλ = 55.8 cm-1 atm-1).
15
It is also known that there is some interference absorption near 216 nm from the
intermediate products of pyrolysis, such as ethylene, higher olefins and conjugated
olefins. To account for the interference absorption, another wavelength at 218.7 nm was
also employed in this study. Here we assume that the interference absorbances at 216.6
nm and 218.7 nm are identical, based on the fact that these two wavelengths are very
close to each other, and at high temperatures, these hydrocarbons show wide broad
absorption features near 216 nm. CH3 absorption coefficients at 216.6 nm and 218.7 nm
were previously determined in our laboratory [64-65]. Thus, methyl radical
concentration can then be calculated as follows:
-ln(I/Io)217 = kCH3,217XCH3PL + kintXintPL
-ln(I/Io)219 = kCH3,219XCH3PL + kintXintPL
-ln(I/Io)217 + ln(I/Io)219 = (kCH3,217 – kCH3,219)XCH3PL
where kCH3 is the CH3 absorption coefficient, XCH3 is the CH3 mole fraction, P is the total
pressure, and L is the path length. Based on the two-wavelength subtraction scheme, the
interference absorption contributes about 25% to the total absorption signal at 216.6 nm.
Figure 2.3: Schematic of CH3 detection near 216.6 nm using the frequency-quadrupled output of near-infrared radiation from a pulsed Ti:Sapphire laser. Figure adapted from ref. [63].
16
2.2.4 IR Laser Absorption of CO
A quantum cascade laser (QCL) operating in cw mode has recently become an
important diagnostic tool for many combustion products, such as CO, CO2 and H2O.
This mid-IR CO laser allows access to the R(13) transition line in the CO fundamental
rovibrational band at 4.56 µm, where H2O and CO2 absorption interference is minimal.
As compared to previous CO diagnostics near 1.2, 1.5 and 2.3 µm, this new diagnostic
scheme offers orders-of-magnitude greater sensitivity, resulting in ppm-level CO
detectivity in shock tube measurements.
A fixed-wavelength direct-absorption strategy was employed to monitor the peak
intensity of the R(13) absorption line at 2193.359 cm-1 (with kλ = 12.1 cm-1 atm-1 at 1300
K and 1.5 atm), as illustrated in Figure 2.4. The spectroscopic parameters for the R(13)
transition, including the line-strength and self-broadening coefficient, were taken directly
from the HITRAN database. The collisional broadening coefficient for CO with argon
(not available in HITRAN) was measured in the shock tube over the temperature range of
1000-1800 K. Further details regarding the CO diagnostic setup are described elsewhere
[66].
Figure 2.4: Schematic of CO detection using cw quantum cascade laser near 4.56 µm. Figure adapted from ref. [66].
17
2.2.5 CO2 Laser Absorption of C2H4
C2H4 was measured using CO2 laser absorption at 10.532 µm, as illustrated in
Figure 2.5. This diagnostic takes advantage of the strong overlap of the P(14) line of the
CO2 laser transition with the strong Q-branch of the ν7 ethylene band. It is capable of
detecting 100 ppm levels of C2H4 over a path length of 15 cm at 1200 K and 3 atm (with
σλ = 9.69 m2/mol or kλ = 0.98 cm-1 atm-1). Details regarding this diagnostic and the C2H4
absorption cross-sections are described elsewhere [67]. There is some weak interference
absorption directly from acetone, 2-butanone, and 3-pentanone at this wavelength. In
addition, higher alkenes, such as propene and butene, have weak absorption features at
10.532 µm. However, the pyrolysis of acetone, 2-butanone, and 3-pentanone generate
negligible amounts of these higher alkenes, and thus, the primary interfering species are
ketones. In the present study, C2H4 was also measured at 10.675 µm to account for
ketone interference absorbance; C2H4 absorption cross-sections at 10.675 µm were found
to be 4.0 ± 0.1 m2/mol over 1100-1500 K at 1-6 atm [68]. Moreover, ketone absorption
cross-sections at 10.532 µm and 10.675 µm were determined by measuring the
absorption immediately behind reflected shock waves when only ketone existed. Thus,
using these two wavelengths, C2H4 species concentration can be found by solving the
following two equations:
-ln(I/Io)10.532 = nC2H4σC2H4,10.532L + nketσket,10.532L
-ln(I/Io)10.675 = nC2H4σC2H4,10.675L + nketσket,10.675L
where σC2H4 and σket are the absorption cross-sections of C2H4 and ketone, nC2H4 and nket
are the number densities of C2H4 and ketone, and L is the path length.
18
Figure 2.5: Schematic of C2H4 detection using cw CO2 laser near 10.5 µm. Figure adapted from ref. [67].
2.2.6 IR Laser Absorption of H2O
H2O concentration was measured using a DFB (distributed feedback) diode laser
at 2550.96 nm (3920.09 cm−1) within the ν3 fundamental vibrational band, as illustrated
in Figure 2.6. This absorption feature has been well-characterized previously in our
laboratory [69]. During experiments, the beam path (outside the shock tube) was
continuously purged with pure N2 to minimize the laser attenuation due to ambient water.
A minimum H2O detection sensitivity of ~40 ppm can be achieved at 1400 K and 1.5 atm
(with kλ = 2.05 cm-1 atm-1).
Figure 2.6: Schematic of H2O detection using cw DFB laser near 2.55 µm. Figure adapted from ref. [69].
19
2.2.7 IR Laser Absorption of CH4
CH4 was measured near 3.4 µm using a scanned-wavelength mid-IR laser
absorption diagnostic developed by Pyun et al. [70], as illustrated in Figure 2.7. Mid-IR
light near 3.4 µm was generated using difference-frequency-generation (DFG) of a near-
IR signal laser and a near-IR pump laser combined in a PPLN crystal. Due to the
structural differences of the absorption spectrum of methane and other hydrocarbons near
3.4 µm, a differential absorption (peak minus valley) scheme was employed to obtain
interference-free CH4 concentration. To attain this scheme, the signal laser was current
modulated at a 50 kHz scanning frequency and a 0.5 Vp-p scanning amplitude by a
function generator. Then the modulated signal laser was combined with the pump laser
through the PPLN crystal to create a modulated mid-IR laser light near 3.4 µm that
included the peak and valley wavelengths in each scan. To maximize the signal-to-noise
ratio of CH4 and minimize that of the interfering species, 2917.64 cm-1 and 2917.45 cm-1
were selected as the optimal peak and valley wavelength pair in this work. Using this
method, CH4 concentration time histories with a time resolution of 20 µs and a minimum
detection sensitivity of ~250 ppm at 1300 K and 1.5 atm were obtained (with a
differential absorption coefficient of kpeak-valley = 0.73 cm-1 atm-1).
Figure 2.7: Schematic of CH4 detection using a scanned-wavelength mid-IR laser near 3.4 µm. Figure adapted from ref. [70].
20
2.3 Summary
In this dissertation, a low-pressure shock tube facility and several laser absorption
diagnostics were utilized to monitor key combustion radicals and intermediate species,
including OH radicals near 306.69 nm, ketones at 306.65 nm, CH3 radicals near 216 nm,
CO near 4.56 µm, C2H4 near 10.5 µm, H2O near 2.55 µm, and CH4 near 3.4 µm.
21
Chapter 3 A Shock Tube Study of H2 + OH → H2O + H using OH Laser Absorption
3.1 Introduction
As introduced in Chapter 1, the reaction of OH with molecular hydrogen
H2 + OH → H2O + H (1)
is an important chain-propagating reaction in all combustion systems, particularly in
hydrogen combustion. Its reverse reaction plays a critical role in the establishment of
partial equilibrium in the post-combustion regime. At elevated temperatures, the
previous rate constant evaluations have an uncertainty factor of 2, and this relatively large
uncertainty has a significant impact on the laminar flame speed predictions of H2-air
mixtures from the detailed kinetic mechanism. Thus, there is motivation to reduce the
existing experimental uncertainty in k1 at combustion-relevant conditions. In this
chapter, we aim to report the rate constant for reaction (1) with a much lower
experimental scatter and overall uncertainty over the temperature range of 902-1518 K.
3.2 Experimental Details
Test mixtures were prepared manometrically in a 40 liter stainless-steel tank
heated uniformly to 50 oC and mixed with a magnetically-driven stirring vane. A double-
dilution process was employed to allow for more accurate pressure measurements in the
22
manometrical preparation of a highly dilute mixture. A highly concentrated mixture was
first prepared and mixed for at least 2 hours to ensure homogeneity and consistency, and
the mixture was then further diluted with argon and mixed for additional 2 hours prior to
the experiments. The gases utilized in this work were hydrogen (Research Grade)
99.999% and argon (Research Grade) 99.999%, which were supplied by Praxair and used
without further purification. The liquid chemical was commercially available 70% tert-
butyl hydroperoxide (TBHP) in water from Sigma-Aldrich, and was purified using a
freeze-pump-thaw procedure to remove dissolved volatiles and air prior to mixture
preparation.
3.3 Kinetic Measurements
3.3.1 Kinetic Mechanism Description
A series of 21 reflected shock wave experiments were conducted to determine the
rate constant for the reaction of H2 + OH → H2O + H over the temperature range of 902-
1518 K at pressures of 1.15-1.52 atm. Dilute test mixtures with 94-125 ppm TBHP (and
water) and 1001-1516 ppm H2 in argon were used to minimize the temperature drop
caused by the chemistry effects, and the temperature profile behind the reflected shock
wave was nearly constant (<1 K change) over the time frame of the experiment. In the
present study, the CHEMKIN PRO package [71] was used to simulate the consumption
of OH radicals by molecular hydrogen under the standard constant energy and volume
assumption, and a comprehensive reaction mechanism of Wang et al. (USC-Mech v2.0)
[72] was selected as the base mechanism. This mechanism consists of 111 species and
784 elementary reactions, and has been validated against a series of shock tube ignition
delay times, laminar flame speeds, and speciation data from a shock tube and a flow
reactor during high-temperature oxidation of H2, CO, and C1-C4 hydrocarbons. It is
pertinent to note that the conclusions of the present study are effectively independent of
the mechanism used, and near-identical results could be obtained using the GRI-Mech 3.0
[22].
23
Tert-butyl hydroperoxide (TBHP or (CH3)3−CO−OH) was chosen as an OH
radical precursor in the present study, because it decomposes very rapidly to form an OH
radical and a tert-butoxy radical, (CH3)3CO, at temperatures greater than 1000 K [73].
(Note that the weakest bond in TBHP is the O−O bond with the bond dissociation energy
of ~47 kcal/mol at 298 K.) The tert-butoxy radical further decomposes to form acetone
and a methyl radical. Additionally, TBHP reacts with OH to form other products, and
hence a TBHP sub-mechanism was also incorporated into the base mechanism, i.e.
(CH3)3−CO−OH → (CH3)3CO + OH (13)
(CH3)3CO → CH3COCH3 + CH3 (14)
(CH3)3−CO−OH + OH → H2O + O2 + tert-C4H9 (15)
(CH3)3−CO−OH + OH → H2O + HO2 + iso-C4H8 (16)
The rate constants for reactions (13), (15) and (16) were adopted from Pang et al.
[74], and the rate constant for reaction (14) was obtained from Choo and Benson [75].
The rate constants for reactions (13)-(16) are listed in Table 3.1. In addition, the
thermodynamic parameters for TBHP and tert-butoxy radical were taken from the
thermodynamic database from Goos et al. [76], and the standard enthalpy of formation
for OH radical was updated with the measured value from Herbon et al. [23-24].
Table 3.1: Reactions Describing H2 + OH Experiments at P = 1.3 atm.
Rate Constant Reaction A [†] b E [cal/mol] No. Reference
H2 + OH → H2O + H see text 1 this work TBHP → (CH3)3CO + OH 3.57E+13 0 3.575E+04 13 [74]
(CH3)3CO → CH3COCH3 + CH3 1.26E+14 0 1.530E+04 14 [75] TBHP + OH → H2O + O2 + tert-C4H9 2.30E+13 0 5.223E+03 15 [74]
TBHP + OH → H2O + HO2 + iso-C4H8 2.49E+13 0 2.655E+03 16 [74] CH3 + OH → CH2(s) + H2O 1.65E+13 0 0 17 [74]
C2H6 (+ M) → CH3 + CH3 (+ M) 1.88E+50 -9.72 1.073E+05 18 [80] Low-Pressure Limit: 3.72E+65 -13.14 1.015E+05 Troe centering: 0.39 100 1900 6000
CH3COCH3 + OH → CH3COCH2 + H2O 3.30E+13 0 4.840E+03 5 [82] CH3OH + M → CH3 + OH + M 5.62E+15 0 6.128E+04 19 [77]
† Units of A are in s-1 for unimolecular reactions and cm3 mol-1 s-1 for bimolecular reactions.
24
3.3.2 H2 + OH Kinetics
A local OH sensitivity analysis for the mixture of 1001 ppm H2 with ~26 ppm
TBHP (and 99 ppm H2O) in Ar at 1228 K and 1.29 atm is shown in Figure 3.1. The OH
sensitivity is calculated as SOH = (∂XOH/∂ki)×(ki/XOH), where XOH is the local OH mole
fraction and ki is the rate constant for reaction i. The analysis reveals that the OH time
history is predominantly sensitive to reaction (1) over the time frame of the experiment,
with some minor interference from the following secondary reactions:
CH3 + OH → CH2(s) + H2O (17)
C2H6 (+ M) → CH3 + CH3 (+ M) (18)
CH3COCH3 + OH → CH3COCH2 + H2O (5)
The rate constant for reaction (17) was updated with the value of 1.65×1013 cm3
mol-1 s-1 recently inferred by Pang et al. [74], which is in good agreement with the
measurements from Srinivasan et al. [77] and Vasudevan et al. [78] and the theoretical
calculation from Jasper et al. [79] (within ±35%). The rate constant for reaction (18) was
updated with the measured values from Oehlschlaeger et al. [80], and the measurements
from Oehlschlaeger et al. are in close accord with another experimental study from Kiefer
et al. [81]. Recently, Lam et al. [82] have measured the rate constant for reaction (5)
using UV laser absorption of OH near 306.69 nm behind reflected shock waves over 872-
1355 K at pressures near 2 atm, and their measured rate constant was adopted for reaction
(5) in the present study. (For more details, please read Chapter 6.) In addition, the rate
constant for the reaction of CH3OH + M → CH 3 + OH + M (reaction (19)) was updated
with the measured values from Srinivasan et al. [77] at ~0.3-1.1 atm, and their values
agree well with the theoretical calculation from Jasper et al. [79] and the measurements
from Vasudevan et al. [78] at 1.3 atm. The rate constants for reactions (5) and (17)-(19)
are also provided in Table 3.1.
25
Figure 3.1: OH sensitivity plot for the rate constant measurement of H2 + OH at 1228 K and 1.29 atm.
Figure 3.2 shows an OH time history measurement for the mixture of 1001 ppm
H2 in argon at 1228 K and 1.29 atm, and the measured peak OH mole fraction is
approximately 26 ppm. Due to wall adsorption and condensation of TBHP, the initial
TBHP mole fraction was assumed to be the same as the measured peak OH mole fraction.
This assumption is valid because the OH radical is formed very rapidly after the thermal
decomposition of TBHP at T > 1000 K. More importantly, the presence of H2O in the
mixture has a negligible influence on the simulated OH time history; hence, its presence
would not affect our rate constant evaluation. As illustrated in Figure 3.2, a best-fit rate
constant for reaction (1) of 2.45×1012 cm3 mol-1 s-1 was obtained between the
experimental data and the simulation at 1228 K and 1.29 atm. Simulations for the
variations of ±20% in the inferred rate constant are also shown in Figure 3.2. Similarly,
Figure 3.3 shows the measured OH time histories for different test mixtures at different
temperatures, along with the simulations from USC-Mech v2.0 [72] for the best-fit rate
constants. Interestingly, our measured values are identical to or very close to the values
originally proposed by Michael and Sutherland [18], within ±4% at most temperatures,
and their expression is currently adopted in GRI-Mech 3.0 [22]. Additionally, Table 3.2
summarizes the rate constant measurements of reaction (1) at T = 902-1518 K and P =
1.15-1.52 atm.
26
Figure 3.2: Sample H2 + OH rate constant measurement using the mixture of 1001 ppm H2 with ~26 ppm TBHP (and 99 ppm water) in Ar at 1228 K and 1.29 atm. Simulation from USC-Mech v2.0 [72] for the best-fit rate constant, along with variations of ±20%, is also shown.
Figure 3.3: H2 + OH rate constant measurements at various temperatures, along with the simulations from USC-Mech v2.0 for the best-fit rate constants.
27
Table 3.2: Rate Constant Data for H2 + OH → H2O + H.
T5 [K] P5 [atm] k1 [cm3 mol-1 s-1]
94 ppm TBHP (and water), 1516 ppm H2, Ar 1343 1.16 3.12E+12 1053 1.36 1.48E+12 984 1.34 1.31E+12 972 1.46 1.19E+12 933 1.52 1.03E+12
95 ppm TBHP (and water), 1500 ppm H2, Ar
1466 1.15 4.10E+12 1405 1.18 3.68E+12 1279 1.23 2.83E+12 1225 1.25 2.38E+12 1217 1.19 2.33E+12 1157 1.30 2.05E+12 1152 1.24 2.03E+12 1140 1.33 1.96E+12 1098 1.35 1.75E+12 981 1.47 1.25E+12 902 1.49 9.23E+11
125 ppm TBHP (and water), 1001 ppm H2, Ar
1518 1.15 4.71E+12 1228 1.29 2.45E+12 1189 1.32 2.20E+12 1058 1.43 1.56E+12 1032 1.42 1.40E+12
A detailed error analysis was performed to estimate the overall uncertainty in the
measured rate constant for reaction (1) at 1228 K. The following contributions were
considered: (a) temperature (±1%), (b) OH absorption coefficient (±3%), (c) wavemeter
reading in the UV (±0.01 cm-1), (d) fitting the data to computed profiles (±5%), (e)
locating time-zero (±0.5 µs), (f) the rate constant for CH3 + OH → CH2(s) + H2O
28
(uncert. factor = 2), (g) the rate constant for C2H6 (+ M) → CH3 + CH3 (+ M) (±20%),
and (h) the rate constant for CH3COCH3 + OH → CH3COCH2 + H2O (±28%). As
demonstrated in Figure 3.4, the individual error sources were introduced independently
(within the estimated positive and negative bounds of their 2σ uncertainties) and their
effects on the rate constant for the title reaction were studied. These uncertainties were
combined in a root-sum-squared method to give an overall (2σ) uncertainty of ±17% at
1228 K. Similar error analysis was conducted for k1 at 972 K, and the overall (2σ)
uncertainty was also estimated to be ±17%.
Figure 3.4: Uncertainty analysis for the rate constant of H2 + OH → H2O + H at 1228 K and 1.29 atm.
Figure 3.5 shows the Arrhenius plot for the present rate constant measurements of
reaction (1) at T = 902-1518 K and P = 1.15-1.52 atm, along with the non-Arrhenius
expression originally proposed by Michael and Sutherland [18]. The measured values
from the present study can be expressed in Arrhenius form as k1(T) = 4.38×1013 exp(-
3518/T) cm3 mol-1 s-1 over 902-1518 K. As illustrated in Figure 3.5, the current data
have a relatively low scatter (<7%). In the present study, three different mixture
compositions were utilized to demonstrate that the inferred rate constants are not strongly
29
dependent on any secondary chemistry contributions, and the measured values from these
mixtures are consistent with each other. It is interesting to note that the present
measurements are in excellent agreement with the non-Arrhenius expression proposed by
Michael and Sutherland (within ±6%).
Figure 3.5: Arrhenius plot for H2 + OH (k1) at temperatures above 833 K.
3.4 Comparison with Earlier Work
Figure 3.6 presents the current data along with some earlier measurements of
reaction (1) at temperatures above 833 K. Note that the present measurements have a
much lower scatter (<7%) than the previous work. Frank and Just [17] investigated the
rate constant for reaction (1) using the test mixtures with a few ppm N2O and 100-500
ppm H2 and O2 in Ar behind reflected shock waves over 1700-2500 K. In their
experiments, the thermal dissociation of N2O upon shock-heating was used to generate
O-atoms, followed by the reaction of O + H2 → OH + H to produce H-atoms and OH
radicals. These OH radicals would then react with H2 through reaction (1), and atomic
resonance absorption spectrometry (ARAS) was used to monitor H- and O-atom
concentration profiles simultaneously. These measured species time histories were also
30
quite sensitive to another major reaction (H + O2 → OH + O), which was one of the
targeted reactions in their study. Their estimated uncertainty limit for k1 was found to be
less than ±40%. Michael and Sutherland [18] examined the reverse rate constant using
the test mixtures of 0.1-1% H2O in Ar behind reflected shock waves over 1246-2297 K.
H-atoms were generated in the post-shock regions using the flash photolysis of H2O and
were monitored using ARAS. In the present study, their measured values were also
converted to the forward rate constants using the revised equilibrium constants (with the
revised standard enthalpy of formation for OH from Herbon et al. [23-24]), as shown in
Figure 3.6. The new calculated values for reaction (1) are approximately 15% lower than
the old values evaluated by Michael and Sutherland. Such differences are solely due to
the equilibrium constant evaluations. Nevertheless, their values for reaction (1) have a
relatively large experimental scatter (within a factor of 2). Similarly, Davidson et al. [19]
measured the reverse rate using the test mixtures of 0.915-1.83% H2O in Ar behind
reflected shock waves over 1600-2500 K. An ArF excimer laser at 193.3 nm was
employed to photo-dissociate a small amount of H2O in order to generate H-atoms and
OH radicals, and a cw, narrow-linewidth ring dye laser at 306.6 nm was then used to
monitor the temporal evolution of OH radicals. The errors of their measurements varied
from ±40% at 1600 K to ±12% at 2500 K. Their measured values were also converted to
the forward rates using the revised equilibrium constants.
As illustrated in Figure 3.6, the data from Frank and Just [17], Michael and
Sutherland [18], and Davidson et al. [19] are in good agreement with each other (within
their experimental scatter). Oldenborg et al. [20] also conducted direct rate constant
measurements of reaction (1) using the laser photolysis / heated flow cell technique and
using laser-induced fluorescence method to monitor the temporal profiles of OH decays
at 800-1550 K. Their experiments were performed under pseudo-first-order kinetic
conditions with an excess of H2. In addition, Ravishankara et al. [9] studied reaction (1)
using the flash photolysis–resonance fluorescence technique (under pseudo-first-order
kinetic conditions) in a heated quartz cell over 250-1050 K, and their high-temperature
measurements (at 960 and 1050 K) are ~20% higher than the measurements from
Oldenborg et al. [20]. Moreover, Krasnoperov and Michael [21] reexamined reaction (1)
31
using a test mixture of ~5 ppm TBHP with 404 ppm H2 in krypton behind reflected shock
waves at lower temperatures (832-1359 K). TBHP was utilized as the OH precursor in
their study, and a novel multi-pass absorption spectrometric detection method (with a
MW discharge driven resonance OH lamp) was employed to measure OH species
profiles. Although their experimental scatter is slightly high (±25%), their measured
values are generally in good agreement with Oldenborg et al. [20] and Ravishankara et al.
[9]. Concurrently, the present measurements are in excellent agreement with all previous
studies.
Figure 3.6 also shows the values of k1 employed in three different comprehensive
reaction mechanisms: GRI-Mech 3.0 [22], USC-Mech v2.0 [72], and Hong et al. [83].
The present measurements agree well with the values from GRI-Mech 3.0 and Hong et al.
(within ±6%). However, the values of k1 from USC-Mech v2.0 are ~20% lower than the
present measurements. Concurrently, Nguyen et al. [84] computed the rate constant for
the title reaction with semi-classical transition state theory (SCTST), which implemented
non-separable coupling among all degrees of freedom (including the reaction coordinate)
in the transition state region and multi-dimensional quantum mechanical tunneling along
the curved reaction path. Their theoretical calculation (the black dashed line in Figure
3.6) is also in excellent agreement with the present and previous experimental studies,
and their calculation is nearly indistinguishable from the rate constant adopted in GRI-
Mech 3.0.
32
Figure 3.6: Comparison with previous studies at temperatures above 833 K.
3.5 Summary
The rate constant for the reaction of H2 + OH → H 2O + H was studied behind
reflected shock waves over the temperature range of 902-1518 K at pressures of 1.15-
1.52 atm using OH laser absorption. The current high-temperature data can be expressed
in Arrhenius equation as k1(T) = 4.38×1013 exp(-3518/T) cm3 mol-1 s-1 over the
temperature range studied. A detailed error analysis was carried out with the
consideration of both experimental and secondary chemistry contributions, and the
overall (2σ) uncertainties in k1 were found to be ±17% at 972 and 1228 K. Note that the
experimental scatter from the present study is less than 7%, which is much lower than in
previous work [17-21]. The present data are consistent with the previous measurements
from Frank and Just [17], Michael and Sutherland [18], Davidson et al. [19], Oldenborg
et al. [20], and Krasnoperov and Michael [21]. Additionally, the present measurements
are in excellent agreement with the non-Arrhenius expression from GRI-Mech 3.0 [22]
and the recent theoretical calculation using semi-classical transition state theory (SCTST)
from Nguyen et al. [84].
33
Chapter 4 Multi-Species Time History Measurements during High-Temperature Acetone and 2-Butanone Pyrolysis
4.1 Introduction
The pyrolysis of acetone (IUPAC name: propanone) has been studied by many
researchers, particularly at temperatures below 1000 K. At temperatures above 1000 K,
five recent studies have been performed. Capelin et al. [85] examined acetone pyrolysis
utilizing flash vaporization into a heated reaction chamber, and suggested a pyrolysis
mechanism with CH3COCH3 (+ M) → CH3COCH2 + H (+ M) as the initiation reaction,
based on the product distributions from gas chromatography. Ernst et al. [86] studied
acetone pyrolysis using a shock tube and UV laser absorption technique. They
recommended a similar mechanism with a different initiation reaction:
CH3COCH3 (+ M) → CH3 + CH3CO (+ M) (2)
Similarly, Sato and Hidaka [87] investigated acetone pyrolysis and oxidation in a shock
tube; they evaluated the rate constant (k2) for reaction (2) by monitoring acetone
concentrations using laser absorption at 200 nm and 3.39 µm. Saxena et al. [88]
performed direct rate constant measurements of reaction (2) using laser-schlieren
technique. And finally, Pichon et al. [89] developed a detailed kinetic mechanism for
acetone, which was validated against their flame speed and ignition delay time
measurements.
34
In contrast to acetone, fewer 2-butanone studies have been performed. Early low-
temperature 2-butanone oxidation static reactor studies were conducted by Bardwell and
Hinshelwood [90-93]. Decottignies et al. [94] investigated 2-butanone oxidation using
laminar premixed methane/air flames doped with different amounts of 2-butanone.
Based on the product distributions from gas chromatography, they postulated a kinetic
mechanism and suggested three initial decomposition pathways:
2-Butanone (+ M) → C2H5 + CH3CO (+ M) (3a)
2-Butanone (+ M) → CH3 + C2H5CO (+ M) (3b)
2-Butanone (+ M) → CH3 + CH3COCH2 (+ M) (3c)
with channel (3b) as the dominant pathway. Similarly, Serinyel et al. [95] developed a
comprehensive kinetic mechanism, which was validated against their shock tube ignition
delay times. However, they suggested that channel (3a) is the primary initial 2-butanone
decomposition channel.
This chapter presents high-temperature pyrolysis studies of acetone and 2-
butanone behind reflected shock waves using laser absorption methods to measure time
histories of five species: ketone, CO, CH3, CH4, and C2H4. These measurements were
used to determine the decomposition rate constants for both acetone and 2-butanone.
4.2 Experimental Details
4.2.1 Mixture Preparation
Test mixtures were prepared manometrically in a 40 liter stainless steel tank
heated uniformly to 50 oC and mixed with a magnetically-driven stirring vane for at least
2 hours prior to the experiments. The mixture compositions were 0.25%, 1%, and 1.5%
ketone in argon. Research grade argon (99.999%) from Praxair was used with the ACS
spectrophotometric grade acetone (≥ 99.5%) and the CHROMASOLV® grade 2-butanone
(≥ 99.7%) from Sigma Aldrich. All liquid chemicals were purified using a freeze-pump-
thaw procedure to remove dissolved volatiles and air.
35
4.2.2 Species Absorption Coefficient Evaluations
Individual species time histories for dilute fuel mixtures (0.25% acetone or 2-
butanone in Ar) were determined from Beer’s law using a constant absorption coefficient
value for each species, evaluated at the initial reflected shock temperatures and pressures.
On the other hand, for the higher fuel concentration mixtures (1% and 1.5% ketone in
Ar), the changes in temperature and pressure that occur during pyrolysis slightly
perturbed the absorption coefficients of CO, C2H4 and CH4 up to 10%, 7% and 15%,
respectively, for experiments with initial temperatures higher than 1400 K, and the use of
constant absorption coefficients in determining the species mole fractions was not valid.
To determine the experimental species time histories more quantitatively, the temperature
and pressure profiles were first calculated by solving the energy equation under the
standard constant energy (U) and volume (V) assumption (using CHEMKIN PRO [71]).
The species mole fraction time histories were then inferred from the measured absorption
data using values of the absorption coefficients evaluated at the simulated T and P.
4.3 Results and Discussion
4.3.1 Acetone Pyrolysis
High-temperature acetone pyrolysis was investigated using five species time
history measurements over the temperature range of 1200-1650 K at pressures around 1.6
atm. In the present study, the CHEMKIN PRO package [71] was used to simulate all
species time histories under the standard constant energy and volume assumption. Fig.
4.1 shows the CO sensitivity analysis for the mixture of 0.25% acetone in argon at 1393
K and 1.55 atm simulated using the Pichon et al. mechanism of NUI Galway [89]. The
CO time history is predominantly sensitive to reaction (2), with some minor interference
from the reactions of C2H6 (+ M) → CH3 + CH3 (+ M), C2H6 + H → C2H5 + H2, and CH3
+ CH3 → C2H5 + H. Similar result for the CO sensitivity analysis was obtained for the
mixture of 1% acetone in Ar.
36
Figure 4.1: CO sensitivity for 0.25% acetone in Ar using the Pichon et al. mechanism [89].
Fig. 4.2 shows the CO rate of production (ROP) analysis for the mixture of 0.25%
acetone in Ar at 1393 K and 1.55 atm simulated using the Pichon et al. mechanism [89].
The ROP analysis reveals that the primary CO formation pathway is via the reaction of
CH3CO (+ M) → CH3 + CO (+ M) over the time frame of the experiment, and the acetyl
(CH3CO) radical is directly formed from reaction (2). In particular, the CH3CO radical is
rather short-lived at T > 1100 K; once it is formed, it will decompose near-
instantaneously to form a CH3 radical and a CO molecule. According to the CO
sensitivity and ROP analysis, the measured CO time histories can then be used to infer
the acetone dissociation rate constant (k2) over the temperature range of 1150-1600 K at
pressures of 0.54-5.28 atm. The measured CO mole fractions were best-fit with the
simulated profiles by varying the value of k2 in the detailed kinetic mechanism of Pichon
et al.
37
Figure 4.2: CO rate of production (ROP) plot for 0.25% acetone in Ar using the Pichon et al. mechanism [89]. Fig. 4.3 shows a sample measured CO concentration time history during acetone
pyrolysis for the mixture of 0.25% acetone in argon at 1393 K and 1.55 atm, and the best-
fit rate constant (k2) of 3516 s-1, along with perturbations of ±30%, using the Pichon et al.
mechanism. The best-fit simulation curve is virtually indistinguishable from the data.
Figure 4.3: Sample CO time histories: measured and calculated values.
38
The present rate constant measurements (k2) of reaction (2) (inferred from the CO
profiles) at pressures near 1.6 atm are summarized in an Arrhenius diagram, Fig. 4.4,
along with three recent evaluations [87-89]. It should be noted that the acetone
concentration was varied from 0.25% to 1% in order to confirm that the current rate
constant measurements were weakly dependent on any secondary reaction effects, and
the measured values from these two mixtures were consistent with each other. Using a
least-squares fit, the acetone dissociation rate constant can be expressed in Arrhenius
form as k2 = 2.46×1014 exp(-69.3 [kcal/mol]/RT) s-1 over the temperature range of 1200-
1600 K at pressures around 1.6 atm (see the dashed line in Fig. 4.4). The primary
contributions to uncertainties in the rate constant were: temperature (±10%), CO
absorption cross-section (±5%), fitting the data to computed profiles (±5%), and
uncertainties resulting from secondary reactions (±5%), giving an overall uncertainty in
k2 of ±25%. Similar experiments performed at different pressures (0.5-0.7 atm and 5
atm) show only a very weak pressure-dependence for k2, confirming the assumption that
these measurements were performed close to the high-pressure limit. In addition, Table
4.1 summarizes the rate constant measurements of acetone dissociation reaction that are
inferred from the measured CO profiles over 1150-1600 K at pressures of 0.54-5.28 atm.
Figure 4.4: Summary of acetone dissociation rate constant (k2).
39
Similarly, as is evident in Fig. 4.5, the acetone sensitivity analysis shows that the
acetone concentration time history is strongly sensitive to reaction (2), with some minor
interference from the reactions of C2H6 (+ M) → CH3 + CH3 (+ M), CH3 + CH3 → C2H5
+ H, and CH3COCH3 + H → CH 3COCH2 + H2. Hence, the measured acetone time
histories can also be used to determine the acetone dissociation rate constant (k2).
Figure 4.5: Acetone sensitivity for 1% acetone in Ar using the Pichon et al. mechanism [89].
Fig. 4.6 shows the measured acetone time histories, along with the simulations
from the original Pichon et al. mechanism. Similar to the previous analysis based on the
CO profiles, the experiments suggest much faster acetone removal rates than the original
Pichon et al. mechanism. To infer the acetone dissociation rate constant, the measured
acetone concentration time histories were also best-fit with the simulated profiles by
varying the value of k2 in the detailed kinetic mechanism of Pichon et al. [89], as depicted
in Fig. 4.6. Table 4.1 also includes the rate constant measurements of reaction (2) that
are inferred from the acetone profiles over 1340-1650 K at pressures of 1.23-1.41 atm.
The inferred values based on the acetone profiles are consistent with those from the CO
profiles. Note that the measurements seem to experience some slight non-Arrhenius
curvature at higher temperatures, as illustrated in Fig. 4.4. By compiling the rate constant
40
measurements based on the CO and acetone time histories, the acetone dissociation rate
constant can be represented by the following three-parameter equation:
k2(1.23-1.66 atm) = 9.38 × 1041 T-7.85 exp(-44,236/T) s-1
over the temperature range of 1200-1650 K.
Figure 4.6: Acetone time histories for 1% acetone in Ar: measured and simulated values. As illustrated in Fig. 4.4, the measurements of Saxena et al. [88] and the high-
temperature measurements of Sato and Hidaka [87] are in good agreement with the
current results (within 30% at T > 1450 K) at pressures near 1.6 atm. However, at lower
temperatures, the determination from Sato and Hidaka departs significantly from the
current study. For instance, their determination is at least three times slower than the
measured rate constant from the current study at T < 1250 K. In addition, the theoretical
estimate by Pichon et al. [89] using a chemical activation formulation based on Quantum
Rice-Ramsperger-Kassel theory
k2, theoretical(1.6 atm) = 2.88 × 1041 T-8 exp(-43,400/T) s-1
recovers an activation energy similar to the current measurements, but its A-factor is
approximately three times lower than the measured A-factor from the current study, as
shown in Fig. 4.4.
41
Table 4.1: Summary of acetone unimolecular dissociation rate constant data.
T5 [K] P5 [atm] k2 [s-1] Initial Mixture: 0.25% Acetone / Ar (from CO)
1273 1.65 3.61E+02 1351 1.62 1.61E+03 1393 1.55 3.52E+03 1469 1.48 1.29E+04 1545 1.42 3.76E+04 1166 0.73 1.70E+01 1226 0.71 8.90E+01 1324 0.63 8.22E+02 1404 0.62 3.31E+03 1458 0.59 7.82E+03 1567 0.54 4.14E+04 1260 5.28 2.72E+02 1350 4.98 2.30E+03
Initial Mixture: 1% Acetone / Ar (from CO)
1213 1.66 8.53E+01 1332 1.59 1.01E+03 1423 1.53 5.42E+03 1507 1.47 2.06E+04
Initial Mixture: 1% Acetone / Ar (from CH3COCH3)
1340 1.41 1.19E+03 1352 1.24 1.27E+03 1474 1.23 9.76E+03 1561 1.26 3.51E+04 1650 1.28 1.17E+05
Other species (CH3, C2H4, and CH4) were also measured during pyrolysis, and
comparisons with the simulations demonstrate how the current evaluated k2 significantly
improves the overall performance of the detailed mechanism. Fig. 4.7 displays the
measured CH3 time histories during acetone pyrolysis, along with the computed values
from the original Pichon et al. mechanism and the modified mechanism (with our revised
value for k2). The computed CH3 peak values from the original Pichon et al. mechanism
are approximately half of the measured values. Additionally, the CH3 sensitivity analysis
reveals that CH3 time histories are strongly sensitive to two reactions: CH3COCH3 (+ M)
42
→ CH3 + CH3CO (+ M) (reaction (2)) and the relatively well-established CH3 + CH3 (+
M) → C2H6 (+ M) [80-81]. Consequently, using the revised (higher) values for k2 brings
the simulations from the Pichon et al. mechanism into closer agreement with the
measured CH3 time histories. Note that the uncertainty in the CH3 concentration during
the first 100 µs was approximately ±20%, which was mainly attributed to the
uncertainties in the absorption coefficient and the interference subtraction scheme. The
CH3 plateau levels (after 500 µs) had a much larger uncertainty of ±30%, owing to larger
interference absorption (from other intermediate products, such as C2H4).
Figure 4.7: CH3 time histories for 0.25% acetone in Ar: measured and calculated values.
Ethylene is an important major product formed during acetone pyrolysis. Fig. 4.8
shows the measured C2H4 time histories, along with the simulations from the original and
modified Pichon et al. mechanisms. The original Pichon et al. mechanism clearly fails to
predict the formation rates and the ultimate yields of ethylene. During acetone pyrolysis,
C2H4 is mainly formed from the direct competition between two reactions: CH3 + CH3 (+
M) → C2H6 (+ M) and CH3 + CH3 → C2H5 + H, immediately followed by C2H5 (+ M) →
C2H4 + H (+ M). The higher formation rates of CH3 in the modified mechanism (via the
higher values for k2) significantly improve the simulations at early times.
43
Figure 4.8: C2H4 time histories for 1% acetone in Ar: measured and calculated values.
Methane is another major product formed during acetone pyrolysis. Fig. 4.9
shows the measured CH4 time histories, along with the simulations from the modified
Pichon et al. mechanisms (i.e., with the revised values for k2) with two different
CH3COCH3 + CH3 reaction rate constants adopted by Pichon et al. [89] and Saxena et al.
[88]. The original Pichon et al. mechanism significantly underpredicted the CH4 time
histories by at least a factor of 4, and the modified Pichon et al. mechanism v1 (with
revised k2 and original acetone + CH3 rate constant used by Pichon et al.) was still not
able to capture the CH4 formation rates at T < 1400 K. However, at T = 1556 K, the
modified mechanism v1 predicted the CH4 concentration reasonably well. Additionally,
the CH4 sensitivity analysis (not presented here) shows the importance of reaction (2),
and the reactions of CH3 plus CH3, C2H6, and CH3COCH3. There are only limited
uncertainties in the CH3 + CH3 and the CH3 + C2H6 reaction rate constants as given by
Baulch et al. [96] (±20%). Thus, the rate constant for the reaction of CH3COCH3 + CH3
→ CH3COCH2 + CH4 in the original Pichon et al. mechanism
kPichon et al. = 7.96 × 1011 exp(-9741 [cal/mol]/RT) cm3 mol-1 s-1
is likely to be too slow at T < 1400 K. In particular, the Saxena et al. mechanism uses a
significantly different value for the rate constant of CH3COCH3 + CH3 (see Fig. 4.10),
which is:
44
kSaxena et al. = 0.550 T4 exp(-8290 [cal/mol]/RT) cm3 mol-1 s-1
The rate constant used by Saxena et al. [88] is at least three times faster than the value of
the rate constant adopted by Pichon et al. [89] at 1250 K, and is approximately six times
faster at 1538 K. When the rate constant from Saxena et al. is used in the modified
Pichon et al. mechanism (labeled as modified mechanism v2), the simulated time
histories show excellent agreement with the measured time histories at T < 1400 K.
However, the modified mechanism v2 seems to overpredict the ultimate methane yield at
T = 1556 K. This reveals that the activation energy of the acetone + CH3 reaction likely
still requires some fine adjustment.
Figure 4.9: CH4 time histories for 1.5% acetone in Ar: measured and calculated values.
45
Figure 4.10: Arrhenius plot of the rate constants for the reaction of CH3COCH3 + CH3 → CH3COCH2 + CH4 from Saxena et al. [88], Sato and Hidaka [87], and Pichon et al. [89].
4.3.2 2-Butanone Pyrolysis
High-temperature 2-butanone pyrolysis was studied using multi-species time
history measurements over the temperature range of 1100-1500 K at pressures around 1.5
atm. Fig. 4.11 shows the measured 2-butanone time histories during 2-butanone
pyrolysis, along with the simulations from the original Serinyel et al. mechanism [95].
Serinyel et al. postulated three initial 2-butanone decomposition pathways:
2-Butanone (+ M) → C2H5 + CH3CO (+ M) (3a)
2-Butanone (+ M) → CH3 + C2H5CO (+ M) (3b)
2-Butanone (+ M) → CH3 + CH3COCH2 (+ M) (3c)
As illustrated in Fig. 4.12, the 2-butanone sensitivity analysis reveals that the 2-
butanone time history is predominantly sensitive to its three initial decomposition
pathways, with channel (3a) as the primary decomposition channel. In addition, there is
some minor interference from the reactions of 2-butanone + H → CH3CHCOCH3 + H2
and CH3CHCOCH3 → CH3CHCO + CH3. To determine the overall initial 2-butanone
decomposition rates, the measured 2-butanone time histories were best-fit with the
simulated profiles by adjusting the rate constants for channels (3a)-(3c), without
46
modifying their branching ratios. The best-fit simulated 2-butanone time histories are
also shown on Fig. 4.11. At all temperatures, the modified Serinyel et al. mechanism
captures the initial 2-butanone decomposition rates very accurately, at least for the first
500 µs. (Note that some simulations are nearly indistinguishable from the data traces.)
Figure 4.11: 2-Butanone time histories for 1% 2-butanone in Ar: measured and simulated values.
Figure 4.12: 2-Butanone sensitivity for 1% 2-butanone in Ar.
The overall 2-butanone decomposition rate constant measurements (k3 = k3a + k3b
+ k3c) are plotted on Fig. 4.13, along with the estimated values from the Serinyel et al.
mechanism. Using a least-squares fit, the overall 2-butanone decomposition rate constant
47
was found to be k3 = 6.08×1013 exp(-63.1 [kcal/mol]/RT) s-1 over the temperature range
of 1119-1412 K at pressures around 1.5 atm (see the dashed line in Fig. 4.13). (Note that
the current data are the first direct high-temperature rate constant measurements for the
initial 2-butanone decomposition.) The major contributions to uncertainties in the rate
constants were: temperature (±10%), 2-butanone absorption cross-section (±5%), fitting
the data to computed profiles (±5%), and uncertainties resulting from secondary reactions
(±15%), giving an overall uncertainty in k3 of ±35%. In addition, Table 4.2 summarizes
the overall 2-butanone decomposition rate constant measurements over 1119-1412 K at
pressures near 1.5 atm. The effect of the branching ratios of the initial 2-butanone
decomposition pathways on the measured rate constant was investigated by perturbing
the branching ratio of channel (3a) from 0.70 to 0.50 at 1361 K, and no significant
difference on the simulated 2-butanone time histories was found. In the following
discussion, the original branching ratios of the 2-butanone decomposition pathways used
by Serinyel et al. were retained. Our measured value for k3 is approximately 30% faster
than Serinyel et al. at 1119 K, and is approximately 100% faster at 1412 K. Our inferred
rate constants for channels (3a)-(3c) at 1.5 atm can be expressed as follows:
k3a = 1.31×1013 exp(-59.9 [kcal/mol]/RT) s-1
k3b = 8.47×1014 exp(-75.3 [kcal/mol]/RT) s-1
k3c = 3.49×1014 exp(-72.9 [kcal/mol]/RT) s-1
Figure 4.13: Arrhenius plot for overall 2-butanone decomposition rate constant (k3).
48
Table 4.2: Summary of overall 2-butanone decomposition rate constant data.
T5 [K] P5 [atm] k3 [s-1] Initial Mixture: 1% 2-Butanone / Ar
1119 1.62 3.00E+01 1170 1.61 1.00E+02 1214 1.53 2.60E+02 1252 1.48 5.45E+02 1299 1.47 1.42E+03 1361 1.48 4.11E+03 1412 1.39 1.17E+04
Fig. 4.14 shows the measured CH3 time histories during 2-butanone pyrolysis,
along with the simulations from the original and modified Serinyel et al. mechanisms.
The modified Serinyel et al. mechanism captures the initial CH3 formation rates more
closely, but the simulated CH3 peak values are still underpredicted. According to the
CH3 sensitivity analysis, the CH3 time histories are mainly sensitive to channels (3a)-(3c)
and the relatively well-established reaction of CH3 + CH3 (+ M) → C 2H6 (+ M) [80-81].
Thus, discrepancies between the measured and simulated CH3 peak values may be
attributed, at least partially, to uncertainties in the relative branching ratios of the initial
2-butanone decomposition pathways. (Note that the agreement here is not sacrificed by
the subsequent addition of a methyl ketene decomposition channel, which will be
discussed in the following section.)
Figure 4.14: CH3 time histories for 0.25% 2-butanone in Ar: measured and calculated values.
49
Similar to acetone pyrolysis, CO is another important stable species formed
during 2-butanone pyrolysis. Fig. 4.15 shows the CO rate of production (ROP) analysis
for the mixture of 1% 2-butanone in Ar at 1292 K and 1.58 atm simulated using the
Serinyel et al. mechanism with the revised k3, and the ROP analysis reveals that CO is
mainly generated via two reaction pathways over the time frame of the experiment, which
are CH3CO (+ M) → CH3 + CO (+ M) and C2H5CO → C2H5 + CO. The acetyl (CH3CO)
radical can be formed via 2-butanone (+ M) → C 2H5 + CH3CO (+ M) (channel (3a)) and
2-butanone + H → CH 2CH2COCH3 + H2, followed by the fuel radical decomposition
(CH2CH2COCH3 → C2H4 + CH3CO). Additionally, the propionyl (C2H5CO) radical can
be formed via 2-butanone (+ M) → CH3 + C2H5CO (+ M) (channel (3b)).
Figure 4.15: CO rate of production (ROP) plot for 1% 2-butanone in Ar using the original Serinyel et al. mechanism (with the revised k3). Fig. 4.16 shows the measured and simulated CO time histories during 2-butanone
pyrolysis. Based on the measured 2-butanone and CO time histories at T ≈ 1292 K, the
measurements suggest ~87% conversion to CO from 2-butanone, while the original
Serinyel et al. mechanism [95] predicts only about 57% conversion to CO. The model
with the revised overall 2-butanone decomposition rate constant (k3) generates slightly
higher CO concentration (~67%), but still well below that measured. According to the
simulations, the major species containing O atoms are 2-butanone, CO, and CH3CHCO
50
(methyl ketene), and the model seems to predict significant amounts of methyl ketene
formed during 2-butanone pyrolysis. This implies that some of the CO formation
pathways might be incomplete in the model, particularly the methyl ketene sub-
mechanism. Methyl ketene is produced through the reaction of 2-butanone + H →
CH3CHCOCH3 + H2, followed by CH3CHCOCH3 → CH3CHCO + CH3. According to
the model, the removal pathway of methyl ketene is only through the H-abstraction
reaction from methyl ketene (CH3CHCO + H → C2H5 + CO). Since methyl ketene is not
a stable species, it should undergo a unimolecular decomposition process, which is not
included in the original Serinyel et al. mechanism [95]. In the present analysis, a methyl
ketene decomposition pathway (CH3CHCO (+ M) → C2H4 + CO (+ M)) was
incorporated, and the corresponding rate constant was assumed to be the same as the
value for ketene decomposition (CH2CO (+ M) → CH2 + CO (+ M)). The modified
mechanism (with revised k3 and added methyl ketene decomposition reaction) simulates
the CO concentrations rather accurately, as illustrated in Fig. 4.16.
Figure 4.16: CO time histories for 1% 2-butanone in Ar: measured and calculated values.
Fig. 4.17 displays the measured C2H4 time histories, along with the simulations
from the original and modified Serinyel et al. mechanisms. The measurement suggests
the ethylene yield (defined as the ratio of the long-time C2H4 concentration to the initial
51
2-butanone concentration) to be ~0.88 at 1412 K, while the original Serinyel et al.
mechanism predicts the yield to be ~0.73 and the modified mechanism predicts the yield
of ~0.87. In general, the modified mechanism is able to accurately simulate the ultimate
yields of C2H4. (Note that the simulated C2H4 time history from the modified mechanism
lies exactly on top of the measured time history at 1252 K.) The C2H4 sensitivity analysis
shows the significance of the initial 2-butanone decomposition pathways (channels (3a)-
(3c)) and the H-abstraction reactions from 2-butanone. C2H4 is initially formed through
the following processes:
(i) 2-Butanone (+ M) → C2H5 + CH3CO (+ M), followed by C2H5 (+ M) → C2H4 +
H (+ M);
(ii) 2-Butanone + H → CH2CH2COCH3 + H2, followed by CH2CH2COCH3 → C2H4
+ CH3CO.
Hence, fine refinement on the branching ratios of the initial 2-butanone decomposition
pathways and the H-abstraction reaction rate constants appears needed to perfectly match
the initial formation rates of C2H4.
Figure 4.17: C2H4 time histories for 1% 2-butanone in Ar: measured and calculated values.
In addition to CO and C2H4, methane is another major product formed during 2-
butanone pyrolysis. A plot of the measured methane time histories, along with the
52
computed values from the modified Serinyel et al. mechanism, is illustrated in Fig. 4.18.
As compared to the measurements, the modified mechanism underpredicts the methane
concentrations by at least a factor of 2 at temperatures less than 1400 K. However, at
temperatures higher than 1400 K, the modified mechanism is able to capture the methane
formations reasonably well. Methane is mainly formed through the H-abstraction
reactions from 2-butanone by CH3 radicals, which are:
2-Butanone + CH3 → CH2CH2COCH3 + CH4
2-Butanone + CH3 → CH3CHCOCH3 + CH4
2-Butanone + CH3 → C2H5COCH2 + CH4
Such huge differences between the measurements and simulations may be caused by the
inaccurate model predictions for CH3 concentrations and the uncertainties in the rate
constants for 2-butanone + CH3 reactions, particularly their activation energies. Further
increases in the rate constants for 2-butanone + CH3 reactions at temperatures less than
1400 K appear needed in order to improve the model predictions on methane.
Figure 4.18: CH4 time histories for 1.5% 2-butanone in Ar: measured and calculated values.
53
4.4 Summary
High-temperature acetone and 2-butanone pyrolysis was investigated behind
reflected shock waves using multi-species time history measurements (acetone/2-
butanone, CO, CH3, C2H4, and CH4). Direct determinations of the acetone dissociation
rate constant (k2) and the overall 2-butanone dissociation rate constant (k3 = k3a + k3b +
k3c) were made by taking advantage of the measured species time histories for CO (and
acetone) and 2-butanone, respectively.
In the 2-butanone pyrolysis system, an analysis of the O-atom balance based on
the simulated and measured 2-butanone and CO time history measurements revealed
pooling of methyl ketene in the simulations. The addition of the methyl ketene
decomposition pathway to remove this pooling significantly improved the mechanism’s
performance. Further improvement in the 2-butanone mechanism will require a better
understanding and refinement of the branching ratios of the initial 2-butanone
decomposition pathways and the rate constants for the H-abstraction reactions from 2-
butanone.
54
55
Chapter 5 Shock Tube Measurements of 3-Pentanone Pyrolysis and Oxidation
5.1 Introduction
In contrast to acetone and 2-butanone, very little experimental data are available
for high-temperature 3-pentanone combustion studies. Three studies of this fuel are of
note. Davidson et al. [97] measured shock tube ignition delay times for a series of
oxygenated fuels, including 3-pentanone, over temperatures of 1150-1550 K and a
pressure of ~1.8 atm. From their experiments, they concluded that 3-pentanone has much
faster ignition delay times than found for acetone, n-pentane, methyl butanoate, and
butanal. Similarly, Serinyel et al. [98] performed shock tube ignition delay time
measurements in the temperature range 1250-1850 K, pressures near 1 atm, and
equivalence ratios of 0.5-2.0 for mixtures of 0.875-1.31% 3-pentanone in O2/argon. They
also conducted laminar flame speed measurements in a spherical bomb for mixtures of 3-
pentanone in air with various equivalence ratios at an initial temperature of ~305 K and
an initial pressure of 1 atm. Through their flame speed measurements, they concluded
that 3-pentanone has higher reactivity than acetone and 2-butanone. Finally, Hong et al.
[99] examined the influence of oxygenates (such as 3-pentanone) on soot formation
during fuel rich n-heptane oxidation at temperatures of 1600-1900 K and pressures of 20-
30 atm. A significant reduction in the overall soot yield was discovered with the addition
of small quantities of oxygenates.
56
In this chapter, we present high-temperature pyrolysis and oxidation studies of 3-
pentanone behind reflected shock waves using laser absorption methods to measure time
histories of six species: 3-pentanone, CH3, CO, C2H4, H2O, and OH. In addition, 3-
pentanone oxidation behavior was compared with the oxidation behavior of two other
ketones, acetone and 2-pentanone, by examining their ignition delay times and OH time
histories.
5.2 Experimental Details
5.2.1 Mixture Preparation
Test mixtures were prepared manometrically in a 40 liter stainless steel tank
heated uniformly to 50 oC and mixed with a magnetically driven stirring vane for at least
2 hours prior to the experiments. Research grade (99.999%) gases (from Praxair) and
ReagentPlus® grade (≥99%) 3-pentanone (from Sigma-Aldrich), which was further
treated using a freeze-pump-thaw procedure, were used in mixture preparation. The
mixture compositions from this study are summarized in Table 5.1, along with the
measured species for the corresponding mixtures. For the lower fuel concentration
mixtures (<0.25% 3-pentanone), a double-dilution method was used in mixture
preparation to allow for more accurate mixture compositions.
Table 5.1: Summary of test gas mixture compositions and measured species.
Mix #
Gas Compositions Species Time histories τign
3-Pent. O2 Ar 3-Pent. CH3 CO C2H4 OH H2O A 1.00% -- 99.00% x x x B 0.25% -- 99.75% x x C 0.10% -- 99.90% x D 0.040% 0.280% 99.68% x x x E 0.040% 0.560% 99.40% x x x F 0.075% 0.525% 99.40% x x x G 0.571% 4.00% 95.43% x H 0.286% 4.00% 95.71% x I 0.875% 12.25% 86.88% x
57
5.2.2 Species Absorption Coefficient Evaluations
Because of the endothermic nature of the pyrolysis reaction, there is a temperature
drop in the reacting test gas mixture during the experiment, which increases with the
initial 3-pentanone mole fraction. This change in temperature can perturb (generally
increase) the absorption coefficients of individual species, and hence perturb the
conversion of measured absorbance to mole fraction. More accurate species mole
fraction time histories are obtained by accounting for this effect rather than assuming a
constant coefficient evaluated at the initial temperature. To determine these approximate
time-varying absorption coefficients, the temperature and pressure profiles were
calculated using the Serinyel et al. mechanism of NUI Galway [98] under either constant
energy (U) and volume (V) constraints or constant enthalpy (H) and pressure (P)
constraints (using CHEMKIN PRO [71]). The species mole fraction time histories were
then inferred from the measured absorption data using known values of the absorption
coefficients evaluated at the simulated T and P.
The 3-pentanone mole fraction time history for a 1% 3-pentanone/Ar mixture and
an initial temperature of 1248 K and an initial pressure of 1.58 atm was calculated from
the measured absorption data using three different approaches: (1) constant absorption
coefficient for Beer’s law (as has been common in the past), (2) T- and P-dependent
absorption coefficients based on constant U, V calculation, and (3) T- and P-dependent
absorption coefficients based on constant H, P calculation. The 3-pentanone mole
fraction time histories from these three approaches are nearly indistinguishable. Hence,
the measured 3-pentanone mole fraction time histories are effectively insensitive to any
small variation in temperature and pressure change that is a result of the gasdynamic
model used. In this chapter, constant absorption coefficients for Beer’s law are thus
employed for 3-pentanone time history measurements.
On the other hand, the absorption coefficients of CO and C2H4 can increase by up
to 10% and 7%, respectively, during the pyrolysis of 1% 3-pentanone in Ar. Clearly, to
minimize the effects of temperature drop during pyrolysis, lower fuel concentration
mixtures (0.1% or 0.25% 3-pentanone in Ar) are preferred. The drop in temperature for
58
the mixture of 0.25% 3-pentanone in Ar is ~30 K (approximately 4 times less than 1% 3-
pentanone mixture) at an initial temperature of 1325 K and an initial pressure of 1.60
atm. As shown in Fig. 5.1, the CO mole fraction time history for the mixture of 0.25% 3-
pentanone in Ar at 1325 K and 1.60 atm was calculated using absorption coefficients
based on three different gas dynamic models. The initial CO formation rates (for the first
400 µs) from these three approaches are very nearly identical, but the ultimate yield from
the constant absorption coefficient approach (labeled as method 1 and generally
employed in most past studies) is ~2% higher than the yields from the T- and P-
dependent absorption coefficient approaches that are based on constant U, V (method 2)
and constant H, P (method 3) calculations. To correct for this slight difference at later
times, all the CO mole fraction time histories in the present work were calculated using
the T- and P-dependent absorption coefficients based on constant U, V calculations; the
estimated uncertainty in the measured yields using this approach is ±2-3%. Similarly, all
the C2H4 time histories were also calculated from the measured absorption data using the
T- and P-dependent absorption coefficients based on constant U, V calculations.
Figure 5.1: Comparison of CO mole fraction time histories at 1325 K and 1.60 atm with different absorption coefficients in Beer’s law.
During 3-pentanone oxidation, very dilute mixtures (e.g., 400 ppm 3-pentanone)
are used for OH and H2O species time history measurements in order to minimize the
59
rapid energy release at the time of ignition, which increases the temperature (and reduces
the absorption coefficient). As illustrated in Fig. 5.2, for the mixture of 400 ppm 3-
pentanone with 0.28% O2 in Ar, the early-time features of OH obtained from the
measured absorption data using three different absorption coefficient approaches are
effectively identical. Similar results can be observed from the H2O time history profiles.
This is particularly important because these early-time features are unique to individual
fuels, as will be discussed in the later section. However, the final plateau levels of OH
and H2O from method 1 are lower than the levels from methods 2 and 3 by 4% and 2%,
respectively. This is mainly due to the fact that there is a temperature rise of ~50 K at the
time of ignition, and the use of a constant absorption coefficient for Beer’s law is not
strictly valid at these later times. Interestingly, the final plateau levels of OH and H2O
obtained from methods 2 and 3 are indistinguishable. Hence, the temperature corrections
on the measured species are independent of the specific gasdynamic model (const. U, V
or const. H, P). Similar to CO and C2H4 measurements (as described above), all the
measured OH and H2O time histories are corrected using the T- and P-dependent
absorption coefficients based on constant U, V calculations.
Figure 5.2: Comparison of OH mole fraction time histories at 1486 K and 1.52 atm with different absorption coefficients in Beer’s law. The OH mole fractions by constant U, V and constant H, P are virtually indistinguishable for OH.
60
5.3 Results and Discussion
5.3.1 3-Pentanone Pyrolysis
A high-temperature 3-pentanone pyrolysis study was performed behind reflected
shock waves using four species time history measurements (fuel, CH3, CO, and C2H4)
over 1070-1530 K at a pressure of ~1.6 atm. The test mixtures were 0.1% to 1% 3-
pentanone in balance argon. In the present study, the CHEMKIN PRO package [71] was
used to simulate all species time histories under the standard constant energy and volume
assumption (constant U, V), and the Serinyel et al. mechanism of NUI Galway [98] was
chosen as the base mechanism. To the best of our knowledge, the Serinyel et al.
mechanism is the only available detailed mechanism in the literature that is suitable for
high temperature 3-pentanone combustion. The sub-mechanism of 3-pentanone was
developed by Serinyel et al. and implemented into the well-established C4 mechanism of
NUI Galway [100]. In particular, the rate constants for 3-pentanone unimolecular
decomposition reactions were estimated in the reverse direction, and their high-pressure
limit values were further assumed and treated using Quantum Rice-Ramsperger Kassel
(QRRK) theory with a master equation analysis to include the pressure fall-off effects. In
addition, the detailed mechanism of Serinyel et al. was then validated against their
ignition delay time and laminar flame speed measurements.
Fig. 5.3 shows the measured 3-pentanone time histories during pyrolysis of 1% 3-
pentanone in argon, along with the simulations from the Serinyel et al. mechanism of
NUI Galway [98]. The measured fuel time histories are inconsistent with the simulated
profiles from the model, and the model significantly underpredicts the fuel removal rates
at current experimental conditions. As illustrated in Fig. 5.4, the 3-pentanone sensitivity
analysis was performed to determine which reactions are pertinent to 3-pentanone time
histories. As expected, 3-pentanone time histories are primarily sensitive to the initial
fuel decomposition pathways:
C2H5COC2H5 (+ M) → C2H5 + C2H5CO (+ M) (4a)
C2H5COC2H5 (+ M) → CH3 + C2H5COCH2 (+ M) (4b)
61
In addition, there is some minor interference from the reactions of C2H4 + H (+ M) →
C2H5 (+ M), CH3 + CH3 → C2H5 + H, and the H-atom abstraction reactions from 3-
pentanone by H radicals. The branching fraction of the initial fuel decomposition
through reaction (4a) ranges from 0.59 to 0.53 over 1070-1530 K at 1.6 atm [98]. This
indicates that 3-pentanone undergoes unimolecular decomposition through these two
reaction pathways at similar rates.
Figure 5.3: Measured and simulated 3-pentanone time histories for 1% 3-pentanone in Ar. Simulations used the Serinyel et al. mechanism.
Figure 5.4: 3-pentanone sensitivity analysis for 1% 3-pentanone in Ar at 1323 K and 1.6 atm.
62
Methyl radical (CH3) is an important transient species during 3-pentanone
pyrolysis. CH3 radicals are first formed through reaction (4b) of the initial fuel
decomposition pathways, and hence the initial CH3 formation rates are a good measure of
the initial fuel decomposition rates. Fig. 5.5 shows the measured CH3 time histories
during pyrolysis of 0.1% 3-pentanone in argon, along with the computed profiles from
the Serinyel et al. mechanism. It should be noted that the uncertainty of the CH3
concentration during the first 100 µs was approximately ±10%, which was mainly
contributed from the uncertainties in the absorption coefficient and the interference
subtraction scheme. At later times, the CH3 plateau levels had a slightly larger
uncertainty of ±20% due to larger interference absorption (primarily from C2H4). Similar
to the fuel time histories, the model fails to capture the initial CH3 formation rates, and
the predicted CH3 peak values are approximately 30% lower than the measured values.
However, the model does simulate the CH3 removal rates reasonably well from which we
can infer that the reaction rate constants for these CH3 removal channels are reasonable.
Figure 5.5: CH3 time histories for 0.1% 3-pentanone in Ar. Simulations were done using the Serinyel et al. mechanism.
As shown in Fig. 5.6, the CH3 sensitivity analysis reveals that the CH3 time
histories are mainly sensitive to the initial fuel decomposition pathways (reactions (4a)
63
and (4b)) at early times. At later times, there is some interference from the secondary
reactions, which are described as follows:
C2H4 + H (+ M) → C2H5 (+ M) (20)
CH3 + CH3 → C2H5 + H (21)
C2H6 (+ M) → CH3 + CH3 (+ M) (18)
Of note is that the rate constants for reactions (18), (20), and (21) are relatively
well-established. In particular, the reverse of reaction (18) is a primary CH3 removal
channel at high temperatures. In the present analysis, we updated the rate constant for
reaction (18) with the values measured by Oehlschlaeger et al. [80], whose measured
values are consistent with another recent study from Kiefer et al. [81]. The rate constants
for reactions (18), (20), and (21) (and the H-atom abstraction reactions from 3-pentanone
by H radicals) are also provided in Table 5.2. Additionally, the most uncertain rate
constants among reactions (4a), (4b), (18), (20), and (21) are the initial fuel
decomposition pathways, reactions (4a) and (4b). Hence, the measured 3-pentanone and
CH3 time histories can be used to infer the overall fuel decomposition rate constant (k4 =
k4a + k4b) at the measured pressure.
Figure 5.6: CH3 sensitivity analysis for 0.1% 3-pentanone in Ar at 1433 K and 1.6 atm.
64
Table 5.2: Kinetic parameters employed in the Serinyel et al. mechanism.
Rate Constant
Reaction A [†] b E [cal/mol] No. Reference
C2H4 + H (+ M) → C2H5 (+ M) 1.081E+12 0.45 1.822E+03 20 [98] Low-Pressure Limit: 1.200E+42 -7.62 6.970E+03 Troe centering: 0.975 210 984 4374
CH3 + CH3 → C2H5 + H 4.990E+12 0.10 1.060E+04 21 [98] C2H6 (+ M) → CH3 + CH3 (+ M) 1.880E+50 -9.72 1.073E+05 18 [80]
Low-Pressure Limit: 3.720E+65 -13.14 1.015E+05 Troe centering: 0.39 100 1900 6000
C2H5COC2H5 + H → C2H5COC2H4p + H2
1.332E+06 2.54 6.756E+03 22a [98]
C2H5COC2H5 + H → C2H5COC2H4s + H2
1.913E+06 2.29 2.875E+03 22b [98]
C2H5COC2H4p → C2H5CO + C2H4 7.170E+13 -1.93 2.626E+04 23 [98]
C2H5COC2H4s → CH3CHCO + C2H5 1.210E+19 0.42 4.272E+04 24 [98] CH3CHCO + H → C2H5 + CO 4.400E+12 0 1.459E+03 25 [98]
C2H4 + CO (+ M) → CH3CHCO (+ M) 8.100E+11 0 0 26 this study
Low-Pressure Limit: 2.690E+33 -5.11 7.095E+03 Troe centering: 5.907E-01 275 1226 5185
H + O2 → OH + O 3.547E+15 -0.41 1.660E+04 27 [98] C2H4 + OH → C2H3 + H2O 1.800E+06 2.00 2.500E+03 28 [98]
† Units of A are in s-1 for unimolecular reactions, cm3 mol-1 s-1 for bimolecular reactions, and cm6 mol-2 s-1 for termolecular reactions.
Fig. 5.7 shows the measured 3-pentanone and CH3 time histories, along with their
best-fit profiles simulated from the Serinyel et al. mechanism by revising the overall 3-
pentanone decomposition rates. As a result, the measured 3-pentanone time histories
provided the values for k4 over 1070-1330 K at 1.6 atm, and the measured CH3 time
histories provided the values for k4 over 1230-1530 K at 1.6 atm, as are shown in Fig. 5.8.
A best-fit expression for the overall 3-pentanone decomposition rate constant
measurements can be given as k4 = 4.383×1049 T-10 exp(-44,780/T) s-1 over 1070-1530 K
(see the dashed line in Fig. 5.8). (In addition, the measured values can be expressed in
Arrhenius form as k4 = 1.501×1015 exp(-34,640/T) s-1 over 1070-1330 K.) The major
contributions to the uncertainties in the overall rate constant were: temperature (±10%),
65
3-pentanone absorption coefficient (±5%) (or CH3 absorption coefficient and interference
subtraction scheme (±10%)), fitting the data to computed profiles (±5%), and
uncertainties resulting from secondary reactions (±15%), giving an overall uncertainty in
k4 of ±35% over 1070-1330 K from the measured 3-pentanone time histories (or ±40%
over 1230-1530 K from the measured CH3 time histories). The values for k4 are also
summarized in Table 5.3. The influence of the branching ratio (k4a/k4) of reaction (4a) on
the overall fuel decomposition rate constant was examined by perturbing the branching
ratio from 0.4 to 0.7 and keeping k4 constant, and the changes in the computed profiles
were negligible. Hence, the measured 3-pentanone and CH3 time histories are insensitive
to the branching ratios of the initial fuel decomposition pathways. In the present analysis,
the original branching ratios postulated from Serinyel et al. are utilized.
As illustrated in Fig. 5.8, the measured overall 3-pentanone decomposition rate
constant is approximately 3.5 times those of Serinyel et al. over 1070-1330 K at 1.6 atm,
and as such, the high-pressure limit rate constants for reactions (4a) and (4b) as given by
Serinyel et al. are in need of revision. Note that the measured and predicted overall 3-
pentanone decomposition rate constants both experience severe non-Arrhenius curvature,
which explains the large values inferred for the A-factor and pre-exponential temperature
dependence.
Table 5.3: Summary of overall 3-pentanone decomposition rate constant data.
T5 [K] P5 [atm] k4 [s-1] Initial Mixture: 0.1% 3-Pentanone / Ar 1237 1.75 1.29E+03 1346 1.67 8.97E+03 1433 1.60 2.86E+04 1524 1.52 9.08E+04
Initial Mixture: 1% 3-Pentanone / Ar 1071 1.70 1.39E+01 1113 1.64 4.24E+01 1164 1.64 1.81E+02 1248 1.58 1.41E+03 1323 1.32 6.10E+03
66
Figure 5.7: (a) Best-fit 3-pentanone time histories and (b) best-fit CH3 time histories using the Serinyel et al. mechanism with revised overall 3-pentanone decomposition rate constant (k4).
67
Figure 5.8: Arrhenius plot for the overall 3-pentanone decomposition rate constant (k4) at 1.6 atm.
Fig. 5.9 shows the measured 3-pentanone and CO time histories during pyrolysis
of 1% 3-pentanone in argon at 1248 K and 1.6 atm, along with the simulations from the
Serinyel et al. mechanism with the revised k4. Note that initially, all O atoms (100
percent) are present in 3-pentanone. At 750 µs, approximately 35% of the total O atoms
remains in 3-pentanone, with about 55% of the O atoms in CO; together the O atoms
from these species add up to ~90% of the total available O atoms. Similarly, at 1500 µs,
there are approximately 23% of the O atoms in 3-pentanone and 67% of the O atoms in
CO, and these O atoms also sum up to ~90%. Therefore, the measurements suggest
approximately 90% conversion of 3-pentanone to CO. However, the model with the
revised k4 only predicts ~57% conversion of 3-pentanone to CO.
68
Figure 5.9: Measured 3-pentanone and CO time histories during 3-pentanone pyrolysis at 1248 K and 1.6 atm.
Based on the CO sensitivity analysis (see Fig. 5.10), the CO time histories, and
particularly the initial formation rates, are mainly sensitive to the initial 3-pentanone
decomposition pathways (reactions (4a) and (4b)), the ethyl radical decomposition
(reaction (20)), and the H-atom abstraction reactions from 3-pentanone, which are:
C2H5COC2H5 + H → C2H5COC2H4p + H2 (22a)
C2H5COC2H5 + H → C2H5COC2H4s + H2 (22b)
Figure 5.10: CO sensitivity analysis for 1% 3-pentanone in Ar at 1248 K and 1.6 atm.
69
Abstraction of hydrogen atom from the fuel molecule yields the formation of fuel
radicals C2H5COC2H4p and C2H5COC2H4s, where p and s denote the primary and
secondary sites, respectively. However, these reactions do not seem to significantly
affect the final CO plateau values, and only minor changes in the computed CO plateaus
are found if the rate constants for these reactions are increased by a factor of 3. One
possible explanation for the discrepancy between the measurements and simulations is
the incomplete CO formation pathways in the model. Based on the Serinyel et al.
mechanism with the revised k4, the major species that contain O-atoms are 3-pentanone,
CO, and methyl ketene (CH3CHCO). Hence, we infer that the model overpredicts the
concentration of methyl ketene. Methyl ketene is formed through the H-atom abstraction
reaction (C2H5COC2H5 + H → C 2H5COC2H4s + H2), immediately followed by the
decomposition of the fuel radical.
C2H5COC2H4s → CH3CHCO + C2H5 (24)
Methyl ketene is then removed via one pathway only in the original Serinyel et al.
mechanism [98], as described in the following:
CH3CHCO + H → C2H5 + CO (25)
As discussed in Chapter 4, methyl ketene should also undergo thermal
decomposition to form other stable species, as suggested in one previous study [101].
Here we also incorporate the methyl ketene unimolecular decomposition pathway into the
Serinyel et al. mechanism:
CH3CHCO (+ M) → C2H4 + CO (+ M) (-26)
The rate constant for methyl ketene unimolecular decomposition was assumed to have the
same value as the rate constant for ketene unimolecular decomposition (CH2CO (+ M) →
CH2 + CO (+ M)). With this modification, the model can now predict higher CO
concentrations and lower methyl ketene concentrations. In addition, based on the model,
the remaining O-atom containing species is primarily ketene and an accurate knowledge
of the ketene sub-mechanism becomes particularly important in predicting the CO
plateau levels during 3-pentanone pyrolysis.
Fig. 5.11 shows the measured CO time histories during 0.25% 3-pentanone in Ar,
along with the simulations from the (a) original and (b) modified Serinyel et al.
70
mechanisms. As expected, the original Serinyel et al. mechanism underpredicts the CO
time histories by at least 30% at current experimental conditions. With the revised
overall 3-pentanone decomposition rate constant and the addition of the methyl ketene
decomposition reaction, the computed profiles from the modified mechanism show much
better agreement with the measurements at all temperatures. Similar agreement between
the measurements and the simulations from the modified mechanism can also be found
for the mixture of 1% 3-pentanone in Ar. As mentioned previously, the initial CO
formation rates are sensitive to the H-atom abstraction reactions (reactions (22a) and
(22b)). Hence, the current study supports the use of the Serinyel et al. values for these
reaction rate constants.
Figure 5.11: CO time histories for 0.25% 3-pentanone in Ar: measured and calculated values from the (a) original and (b) modified Serinyel et al. mechanisms.
71
During 3-pentanone pyrolysis, ethylene is mainly formed through either
unimolecular decomposition pathways or H-atom abstraction reactions, and these H-atom
abstraction reactions are particularly important at later times when H atoms are abundant
in the system. The primary H-atom abstraction reactions are C2H5COC2H5 + H →
C2H5COC2H4p + H2 and C2H5COC2H5 + H → C 2H5COC2H4s + H2. These fuel radicals
(C2H5COC2H4p and C2H5COC2H4s) can then form ethylene through the following
processes:
(i) C2H5COC2H4p → C2H5CO + C2H4 (23)
(ii) C2H5COC2H4s → CH 3CHCO + C2H5, followed by methyl ketene and ethyl
radical decompositions.
Thus, in addition to CO, ethylene is another major product during 3-pentanone
pyrolysis, and each 3-pentanone molecule eventually turns into at least one C2H4
molecule. As illustrated in Fig. 5.12, the measured ethylene yields (defined as the ratio
of the long-time C2H4 concentration to the initial 3-pentanone concentration) for the
mixture of 0.25% 3-pentanone in Ar at 1248-1491 K are approximately 1.4. When
compared to the measurements, the Serinyel et al. mechanism fails to capture the initial
C2H4 formation rates, and the simulated ethylene yield at 1248 K is ~30% lower than the
measured value. On the other hand, the modified mechanism simulates the initial C2H4
formation rates and ultimate yields quite accurately at the measured temperatures.
Figure 5.12: C2H4 time histories for 0.25% 3-pentanone in Ar: measured and calculated values.
72
5.3.2 3-Pentanone Oxidation
Ignition delay times were measured with mixtures varying in concentration from
0.040% to 0.875% 3-pentanone in O2/balance argon over 1150-1550 K at a pressure of
~1 atm and equivalence ratios of 1.0 and 0.5. For high fuel concentration mixtures (X3-
pentanone > 0.1%), the endwall ignition delay time is defined as the time interval between
the arrival of the incident shock and the initial rise in the OH* emission
chemiluminescence trace at the endwall. The initial rise is located by linear extrapolation
of the signal at the time of maximum rate of rise to the baseline. A representative
ignition delay time plot is also provided in Fig. 5.13. On the other hand, for lower fuel
concentration mixtures, the emission signal is rather weak, and a different definition of
ignition delay time is employed. It is defined as the time to reach 50% of the peak OH
concentration (measured using OH absorption method), with time zero being defined as
the arrival of the reflected shock at the sidewall measurement location.
Figure 5.13: Sample sidewall pressure and endwall OH* emission time histories recorded during an experiment of 3-pentanone ignition at 1113 K and 1.1 atm (3-pentanone/ 4.0% O2/ Ar, Φ = 0.5). A tailored gas mixture of 60% helium/ 40% nitrogen was used as driver gas to achieve a long test time. For high fuel concentration mixtures, the definition of the endwall ignition delay time is shown in the figure.
73
Fig. 5.14 shows the measured ignition delay times from the current study (see the
solid points) at Φ = 1.0 and 0.5, along with the simulations from the original and
modified Serinyel et al. mechanisms under the assumption of constant internal energy
and constant volume. In addition, Davidson et al. [97] performed ignition delay time
measurements for the mixture of 0.571% 3-pentanone with 4% O2 in Ar (Φ = 1.0) over
1173-1306 K at pressures of 1.68-1.85 atm. Their ignition delay time data were
normalized to 1 atm using an overall correlation pressure dependence of P-0.52 (see the
hollow points), and their data are in good agreement with the current measurements
within 7%. As is evident in Fig. 5.14, fuel-lean mixtures ignite much faster than
stoichiometric mixtures, and this general trend is consistent with other hydrocarbon
studies at similar temperatures and pressures [62, 97, 102-103]. At high temperatures (T
> 1100 K), the overall reactivity is mainly controlled by the chain branching reaction (H
+ O2 → OH + O), so that reactivity is very sensitive to molecular oxygen concentration.
Therefore, at Φ = 0.5, the mixture of 0.875% 3-pentanone (with the highest O2 content)
ignites much faster than other lower fuel concentration mixtures. Interestingly, for the
mixture of 0.875% 3-pentanone with 12.25% O2 in Ar, the current measurements are
approximately 30% faster than the measurements from Serinyel et al. [98].
74
Figure 5.14: Measured and simulated 3-pentanone ignition delay times at (a) Φ = 1.0 and (b) Φ = 0.5 and P5 = 1.0 atm.
A linear regression analysis was performed on the current ignition delay time
measurements, and these measurements can be expressed in a correlation with an R2
value of 0.974:
τ [µs] = 1.232×10-5 P-0.52 Φ0.89 XO2-0.61 exp(20,450/T)
where P is the total pressure [atm], Φ is the equivalence ratio, and XO2 is the oxygen mole
fraction. As shown in Fig. 5.14, the simulated ignition times from the Serinyel et al.
mechanism are in agreement with the measured values for low fuel concentration
mixtures (400 ppm 3-pentanone) within ~35%. However, for higher fuel concentration
mixtures, the computed ignition times are approximately twice those of the
measurements. On the other hand, the modified Serinyel et al. mechanism shows much
better agreement with the measurements at all concentrations (within 30%), and the
revision of the overall 3-pentanone decomposition rate constant and the addition of the
methyl ketene decomposition pathway significantly improve the general performance of
the 3-pentanone oxidation chemistry model. When compared to the measurements from
Serinyel et al. [98], the modified mechanism also shows improved agreement with their
data (within 15%) over 1200-1550 K at 1 atm. The simulations from the original and
75
modified mechanisms at the test conditions of Serinyel et al. are also provided in Fig.
5.15.
Figure 5.15: Comparison of model predictions between (a) the Serinyel et al. mechanism of NUI Galway [98] and (b) the modified mechanism on ignition delay time measurements from Serinyel et al.
In addition to ignition delay time measurements, OH and H2O time histories were
acquired behind reflected shock waves using the mixtures of 400 ppm 3-pentanone with
O2 in balance argon over 1200-1550 K at pressures around 1.6 atm and equivalence ratios
of 1.0 and 0.5 (see Figs. 5.18-5.21). Low fuel concentration mixtures are preferred in
species time history measurements during hydrocarbon oxidation in order to minimize
76
the rapid energy release at the time of ignition, which increases the reflected shock
temperature. This would affect the analysis of species mole fractions, particularly if
constant absorption coefficients for Beer’s law are used, as has been common in the past.
For the mixture of 400 ppm 3-pentanone with 0.28% O2 in argon, there is approximately
a 50 K increase in temperature after ignition for the case at 1377 K and 1.54 atm (under
constant energy and volume constraints), which slightly perturbs (reduces) the OH and
H2O absorption coefficients by up to 4% and 2%, respectively, an effect which has been
accounted for in our data processing.
Sensitivity analysis reveals that both OH and H2O time histories (for the mixture
of 400 ppm 3-pentanone / 0.28% O2 / Ar) are mainly sensitive to the following set of
reactions (see Figs. 5.16 and 5.17):
H + O2 → OH + O (27)
C2H5COC2H5 (+ M) → C2H5 + C2H5CO (+ M) (4a)
C2H5COC2H5 (+ M) → CH3 + C2H5COCH2 (+ M) (4b)
C2H4 + H (+ M) → C2H5 (+ M) (20)
C2H4 + OH → C2H3 + H2O (28)
CH3 + CH3 → C2H5 + H (21)
Figure 5.16: OH sensitivity analysis for 400 ppm 3-pentanone with 0.28% O2 in Ar (Φ = 1.0) at 1486 K and 1.52 atm.
77
Figure 5.17: H2O sensitivity analysis for 400 ppm 3-pentanone with 0.28% O2 in Ar (Φ = 1.0) at 1486 K and 1.52 atm.
During hydrocarbon oxidation, H2O is regarded as an important combustion
progress marker, which gives nearly identical information to that of another combustion
progress marker, CO. The H2O profiles for typical hydrocarbons [60-61, 102, 104]
exhibit sequential features: an initial gradual formation of H2O is followed by a rapid
increase indicating ignition, which is in turn succeeded by a very slow rise in H2O
concentration. During 3-pentanone oxidation, the H2O profiles are slightly different from
those of common hydrocarbons (n-alkanes and cycloalkanes). There is no obvious
distinction between the initial gradual H2O formation and the rapid increase in H2O
concentration during ignition. The formation of H2O is fast and steady starting from time
zero, followed by a nearly constant H2O concentration. After this post-ignition H2O
plateau level has been reached, all volatile hydrocarbons have been depleted and only
small intermediates (i.e., H, O, OH, CO, CO2, and H2) would remain, gradually
approaching chemical equilibrium. The kinetics that controls these small intermediates
(after ignition) is well-established and subject to small uncertainties [22, 33, 72].
Additionally, this nearly constant H2O plateau level (after ignition) is primarily sensitive
to the relatively well-established thermodynamic parameters, as suggested by Hong et al.
[102]. This observation was also validated through the perturbation of the rate constants
78
for the above important reactions, following which the post-ignition H2O concentration
level effectively remained the same. Thus, the post-ignition H2O plateau level can be
used to confirm pre-shock fuel concentration.
Fig. 5.18 shows the measured H2O time histories for the mixture of 400 ppm 3-
pentanone with 0.28% O2 in argon (Φ = 1.0), along with the computed profiles from the
(a) original (top) and (b) modified (bottom) Serinyel et al. mechanisms. At a first glance,
the measured and computed H2O plateau levels are consistent with each other, and this
agreement justifies the accuracy of the initial fuel loading in our experiments. The
original Serinyel et al. mechanism captures the general shape of the measured H2O
profiles, but it does not predict the initial H2O formation rates accurately. In addition, the
modified mechanism performs slightly better at higher temperatures (1486 K and 1542
K), and the computed profiles from the modified mechanism show much better
agreement with the measurements at lower temperatures (1343 K and 1377 K).
Similarly, Fig. 5.19 illustrates the measured H2O time histories for the mixture of
400 ppm 3-pentanone with 0.56% O2 in argon (Φ = 0.5), along with the simulations from
the (a) original (top) and (b) modified (bottom) Serinyel et al. mechanisms. Here also,
the measured and computed H2O plateau levels (after ignition) are consistent with each
other. For this fuel-lean mixture, the computed profiles from the original Serinyel et al.
mechanism are quite different from the measured profiles in terms of the initial formation
rates and the ignition delay times, especially when compared to the stoichiometric
mixture. At 1217 K and 1.74 atm, the model significantly underpredicts the formation
rate of H2O, and the computed ignition delay time based on the H2O time history is at
least twice that of the measured value. On the other hand, the modified mechanism is
able to capture the H2O formation rates reasonably well at all temperatures, particularly at
1217 K. Hence, the revision of the overall 3-pentanone decomposition rate constant and
the addition of the methyl ketene decomposition pathway greatly improve the model
predictions of H2O concentrations under oxidizing conditions.
79
Figure 5.18: Comparisons of measured and simulated H2O time histories from the (a) original and (b) modified Serinyel et al. mechanisms for 400 ppm 3-pentanone with 0.28% O2 in Ar (Φ = 1.0).
80
Figure 5.19: Comparisons of measured and simulated H2O time histories from the (a) original and (b) modified Serinyel et al. mechanisms for 400 ppm 3-pentanone with 0.56% O2 in Ar (Φ = 0.5).
81
OH species time histories provide another important kinetic target for the
validation of detailed kinetic mechanisms during hydrocarbon oxidation. At early times,
there is the rapid formation of OH simultaneous with the initial fuel decomposition.
Based on the temperature, the OH species develops a well-defined plateau level during
the induction period, especially at lower temperatures. At the time of ignition, the OH
mole fraction rapidly increases to its post-ignition plateau level. More importantly, the
early-time feature of OH appears to provide important information about the breakdown
of the fuel, because this feature is governed by the fuel unimolecular decomposition and
the H-atom abstraction reactions from the fuel (mainly by H radicals). At later times, the
rapid OH rise at ignition is not unique to this fuel. At the time of ignition, fuel molecules
have mostly decomposed into small intermediate radicals or molecules, such as H, H2,
C2H4, C3H6, etc., and these small fragments tend to control the rate of ignition (the rapid
OH rise at ignition) during hydrocarbon oxidation, as suggested by Warnatz et al. [105].
Fig. 5.20 illustrates the measured OH time histories for the mixture of 400 ppm 3-
pentanone with 0.28% O2 in argon (Φ = 1.0), along with the simulated profiles from the
(a) original (top) and (b) modified (bottom) Serinyel et al. mechanisms. At higher
temperatures (1486 K and 1542 K), the original Serinyel et al. mechanism captures the
rapid OH rise at the time of ignition reasonably well, but it underpredicts the initial OH
formation rates and the initial OH plateau levels (see inset on Fig. 5.20). At lower
temperatures (1343 K and 1377 K), the model underpredicts both the initial and final OH
formation rates, but it is able to simulate the initial plateau levels quite well. When
compared to the original Serinyel et al. mechanism, the modified model generally
provides a much better agreement with the measurements, in terms of the initial plateau
levels and both the initial and final formation rates. However, the modified model still
cannot capture the slight overshoot prior to the formation of the initial plateau. The
overshoot seems to be more obvious at higher temperatures, and such overshoot is quite
sensitive to the H-atom abstraction reactions from 3-pentanone by H radicals and these
rate constants may require some fine adjustment at higher temperatures.
Fig. 5.21 shows the measured OH time histories for the mixture of 400 ppm 3-
pentanone with 0.56% O2 in argon (Φ = 0.5), along with the simulations from the (a)
82
original (top) and (b) modified (bottom) Serinyel et al. mechanisms. It should be noted
that there is now no noticeable overshoot in OH concentration prior to the formation of
the initial plateau for the fuel-lean mixture. Instead, there is a smooth transition from the
initial OH rise to the first plateau level. In addition, with more O2 molecules in the
system, the initial and post-ignition plateau levels are much higher than those of the
stoichoimetric mixture, and this observation is well-simulated by the model. This is
mainly due to the fact that more oxygen molecules are available to undergo the chain
branching reaction (H + O2 → OH + O). The Serinyel et al. mechanism underpredicts
both the initial and final OH formation rates by at least 30% at all temperatures.
Similarly, it does not simulate the initial plateau levels properly at temperatures greater
than 1300 K. On the other hand, the modified model is able to simulate the OH time
histories very accurately, in terms of the initial plateau levels and the initial and final
formation rates, particularly at 1217 K. Hence, the revision of the overall 3-pentanone
decomposition rate constant greatly improves the model predictions on the first OH
plateau levels and its initial formation rates, and the branching ratio of reaction (4a) for
the initial fuel decomposition pathways predicted by Serinyel et al. seems to be quite
reasonable. More importantly, the methyl ketene decomposition pathway seems to
promote the ignition behavior. One possible explanation is that more CO molecules are
now introduced to the system, and each CO molecule reacts with an OH radical through
the reaction of CO + OH → CO2 + H, which is an important exothermic reaction in
combustion chemistry. As a result, more heat is generated during 3-pentanone oxidation,
thereby promoting the ignition behavior.
83
Figure 5.20: Comparisons of measured and simulated OH time histories from the (a) original and (b) modified Serinyel et al. mechanisms for 400 ppm 3-pentanone with 0.28% O2 in Ar (Φ = 1.0). Inset figures are provided to show the early-time features over 0-400 µs.
84
Figure 5.21: Comparisons of measured and simulated OH time histories from the (a) original and (b) modified Serinyel et al. mechanisms for 400 ppm 3-pentanone with 0.56% O2 in Ar (Φ = 0.5). Inset figures are provided to show the early-time features over 0-400 µs.
5.3.3 Comparisons of Ketone Oxidation Characteristics
In addition to 3-pentanone oxidation, the oxidation characteristics of acetone and
2-pentanone were examined and compared with that of 3-pentanone using ignition delay
85
time and OH time history measurements for the mixtures of ketone with 0.525% O2 in
balance argon at Φ = 1.0. Shown in Fig. 5.22 is a plot of the measured ignition delay
times for these three ketone mixtures. Strikingly, the ignition delay times of 3-pentanone
mixtures are only about half those of acetone and 2-pentanone mixtures. However, the
apparent activation energies of these ketone mixtures are quite similar.
Figure 5.22: Comparison of ignition delay times for different ketones (acetone, 2-pentanone and 3-pentanone).
Shown in Fig. 5.23 is a plot of the measured OH time histories for the above
ketone mixtures at T ≈ 1370 K and P = 2.6 atm. Note that the OH time history for the 3-
pentanone mixture is at a slightly lower temperature (1354 K). Interestingly, the 3-
pentanone mixture has a much higher initial OH plateau level than the acetone and 2-
pentanone mixtures, while the initial OH plateau levels for the acetone and 2-pentanone
mixtures are approximately the same. As discussed above, this early-time OH feature is
unique to the individual fuel, and is primarily controlled by the initial fuel decomposition
pathways and the H-atom abstraction reactions from the fuel by H radicals. In addition,
as suggested by Davidson et al. [62], the initial OH plateau level is quite sensitive to the
branching ratios of the fuel decomposition pathways. For instance, there is often a direct
86
competition between the C2H5 and CH3 formation channels during 3-pentanone
decomposition. A slight increase in the rate constant for the C2H5 channel can further
increase the first OH plateau level, and a slight increase in the rate constant for the CH3
channel can reduce the plateau level. Once the C2H5 radical is formed, it is quickly
followed by its decomposition to form an H radical. The H radical can then undergo the
chain branching reaction (with O2) to form an OH radical. On the other hand, if the CH3
radical is formed, it tends to form ethane through the methyl-methyl recombination
reaction and fewer H radicals are formed. In the case of acetone and 2-pentanone
decomposition, CH3 radicals are generally formed, and insufficient amounts of C2H5
radicals are developed to give H radicals. Thus, the initial OH plateau levels of acetone
and 2-pentanone are much less than that of 3-pentanone. More importantly, there seems
to be a strong positive correlation between the initial OH plateau level and the ignition
delay time. This correlation further explains why 3-pentanone has the fastest ignition
delay times among these ketone mixtures at current experimental conditions.
Figure 5.23: Comparison of OH time histories for the mixtures of ketone (i.e., acetone, 2-pentanone and 3-pentanone) with 0.525% O2 in Ar at a pressure of 2.6 atm and an equivalence ratio of 1.0. An inset figure is provided to show the early-time features over 0-400 µs.
87
5.4 Summary
High-temperature 3-pentanone pyrolysis and oxidation studies were investigated
using laser-based species time history measurements for 3-pentanone, CH3, CO, C2H4,
H2O and OH. To our knowledge, these measurements are the first laser-based species
time history measurements for high-temperature 3-pentanone pyrolysis and oxidation.
Using these time histories and the Serinyel et al. 3-pentanone mechanism [98],
improved determinations of the initial 3-pentanone unimolecular decomposition reactions
were possible. As well, a comparison of the measured and modeled CO time history
pathways identified the need to include the methyl ketene decomposition pathway to
improve the simulations. These two modifications to the Serinyel et al. mechanism also
significantly improved the agreement with ignition delay times and OH and H2O time
histories during 3-pentanone oxidation. Finally, a comparison of OH time histories
during the oxidation of 3-pentanone, acetone, and 2-pentanone showed that the initial OH
plateau level of 3-pentanone was higher than that of acetone and 2-pentanone and this
was consistent with the shorter ignition delay times seen with this fuel.
5.5 Possible Future Work
More work is definitely needed to further improve the model predictions under 3-
pentanone pyrolytic and oxidizing conditions. As discussed in Section 5.3.1, the original
Serinyel et al. mechanism [98] appears to overpredict the methyl ketene concentration
during 3-pentanone pyrolysis, and such effect cannot currently be observed
experimentally (based on the O-atom balance). In the present analysis, the possible
solution to such discrepancy is to introduce a unimolecular decomposition reaction for
methyl ketene (reaction (26)) in order to remove the pooling of methyl ketene in the
original model, and reasonable agreement can be obtained between the current
measurements and the simulations from the modified model. Despite its improved
predictive capability, the modified model is very likely to suffer from other deficiencies
that have not been addressed in this dissertation. For instance, the rate constant for
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reaction (24) (C2H5COC2H4s → C2H5 + CH3CHCO) is possibly too fast, resulting in the
pooling of methyl ketene and prohibiting the CO formation. Therefore, a slower rate
constant for reaction (24) is recommended. Additionally, as demonstrated in Chapters 4
and 5, the kinetics of methyl ketene is poorly understood, and more experimental and
theoretical studies for methyl ketene are definitely required. In particular, the rate
constant for reaction (26) (CH3CHCO (+ M) → C2H4 + CO (+ M)) was only estimated by
analogy with the rate constant for ketene unimolecular decomposition in the present
analysis, and there is a need for a more accurate rate constant expression.
One of the major weaknesses in the modified mechanism is the fact that it is not
able to accurately predict the ignition delay times for high fuel concentration mixtures
(X3-pentanone > 0.2%), as shown in Fig. 5.14. Ignition delay time is an important global
kinetic target that is commonly used for the validation of the detailed models, but this
global target is quite sensitive to many secondary chemistry reactions. In particular, the
C2 chemistry, such as the ethyl radical decomposition reaction, is very crucial to the
development of the successful 3-pentanone kinetic model suitable for high-temperature
application. In the future, different base mechanisms, which might consist of different
C2 chemistry sets, should also be considered.
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Chapter 6 High-Temperature Measurements of the Reactions of OH with a Series of Ketones: Acetone, 2-Butanone, 3-Pentanone, and 2-Pentanone
6.1 Introduction
Due to their significant roles in atmospheric chemistry, the rate constants for the
reactions of OH radicals with a series of ketones, including acetone, 2-butanone, 3-
pentanone and 2-pentanone, have been extensively studied by many researchers [38, 106-
116] over the temperature range of 240-400 K. However, the kinetic data on ketones +
OH at combustion-relevant conditions are generally scarce. There were a few
experimental studies for the acetone + OH reaction rate constant over 500-1300 K.
Yamada et al. [117] utilized two different OH precursors (HONO and N2O/H2O) and
measured the rate constants for OH + CH3COCH3 and CD3COCD3 in a reactor over 298-
832 K using the pulsed laser photolysis/pulsed laser-induced fluorescence technique.
Bott and Cohen [118] pioneered the use of tert-butyl hydroperoxide as an OH precursor
and monitored the OH decay in a shock tube using the UV lamp absorption method at
309 nm in order to study the rate constant for acetone + OH reaction near 1200 K and 1
atm. Similarly, Vasudevan et al. [119] and Srinivasan et al. [77] both measured the
acetone + OH rate constant using shock tubes and UV absorption methods over the
combustion-relevant temperature range of 980-1300 K. These measurements are in good
90
agreement with each other. In contrast to acetone, there was only one experimental study
available for larger ketone + OH kinetic data. Tranter and Walker [120] added small
amounts of ketones (acetone, 2-butanone and 3-pentanone) individually to slowly
reacting mixtures of H2 + O2 at 753 K, and measured the consumption of ketones and H2
with the use of gas chromatography. This method allowed them to study the relative rate
constants for the reactions of H and OH with ketones at 753 K. Furthermore, Zhou et al.
[121] recently performed a theoretical study on the mechanism and kinetics of the
reactions of OH with three methyl ketones: acetone, 2-butanone and isopropyl methyl
ketone. They employed the computationally less expensive G3 and G3MP2BH&H
methods to calculate the energy barriers, and utilized the Variflex code including Eckart
tunneling corrections to compute the total rate constants over 500-2000 K. In addition,
all possible abstraction channels have been accounted for in their calculation. However,
except for acetone, their theoretical calculations have not been validated against any
high-temperature experimental data.
The overall rate constants for the reactions of OH with four ketones, namely
acetone (CH3COCH3), 2-butanone (C2H5COCH3), 3-pentanone (C2H5COC2H5) and 2-
pentanone (C3H7COCH3), were determined behind reflected shock waves over the
temperature range of 870-1360 K at pressures of 1-2 atm:
CH3COCH3 + OH → Products (5)
C2H5COCH3 + OH → Products (6)
C2H5COC2H5 + OH → Products (7)
C3H7COCH3 + OH → Products (8)
These measurements include the first direct high-temperature measurements of the
overall rate constants for reactions (6)-(8). These high-temperature kinetic data, along
with the earlier work [38, 77, 106-120], are compared with the theoretical calculations
(from Zhou et al. [121]) and the estimates using the group-additivity model.
91
6.2 Experimental Details
Test mixtures were prepared manometrically in a 40 liter stainless steel tank
heated uniformly to 50 oC and mixed with a magnetically-driven stirring vane. A double-
dilution process was employed to allow for more accurate pressure measurements in the
manometrical preparation of a highly dilute mixture. A highly concentrated mixture was
first prepared and mixed for at least 2 hours to ensure homogeneity and consistency, and
the mixture was then further diluted with argon and mixed for additional 2 hours prior to
the experiments. The gas utilized in this study was argon (Research Grade) 99.999%,
which was supplied by Praxair and used without further purification. The liquid
chemicals were 70% tert-butyl hydroperoxide (TBHP) in water, CHROMASOLV® grade
acetone (≥99.9%), CHROMASOLV® grade 2-butanone (≥99.7%), ReagentPlus® grade 3-
pentanone (≥99%), and ReagentPlus® grade 2-pentanone (≥99%) from Sigma-Aldrich,
and were purified using a freeze-pump-thaw procedure to remove dissolved volatiles and
air prior to mixture preparation.
The mixture composition was confirmed by sampling a portion of the mixture
(from near the endwall) into an external multi-pass absorption cell with a path length of
29.9 m and monitoring the fuel concentration in the cell with a Jodon™ Helium-Neon
laser at 3.39 µm. The details of the laser diagnostic set-up are discussed elsewhere [122].
Beer’s law was used to convert the measured absorption data into the fuel mole fraction.
The absorption cross-sections of ketones for Beer’s law were directly obtained from the
PNNL database [123], and the measured fuel concentrations were consistent with the
values expected from the manometrical preparation within ±5%.
6.3 Kinetic Measurements
6.3.1 Choice of Kinetic Mechanisms
A total of 58 reflected shock wave experiments were performed to determine the
overall rate constants for the reactions of OH with four ketones (acetone, 2-butanone, 3-
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pentanone and 2-pentanone) at near-pseudo-first-order conditions. Experiments were
carried out over the temperature range of 870-1360 K at pressures of 1-2 atm using
different initial fuel concentrations: acetone (304 ppm), 2-butanone (152 ppm, 161 ppm
and 206 ppm), 3-pentanone (151 ppm and 211 ppm), and 2-pentanone (161 ppm). These
ketones were prepared with 53-101 ppm TBHP/water and diluted in argon. To properly
simulate the consumption of OH radicals by ketones, the Pichon et al. mechanism of NUI
Galway [89] with the revised k2 was chosen as the base mechanism for acetone, and the
Serinyel et al. mechanism of NUI Galway [95, 98] with the revised k3 and k4 and the
addition of the methyl ketene decomposition pathway was utilized as the base mechanism
for 2-butanone, 3-pentanone, and 2-pentanone. In addition, the tert-butyl hydroperoxide
(TBHP) sub-mechanism was incorporated in these base mechanisms. (Please read
Chapter 3 for more details on the TBHP chemistry.) Similarly, the thermodynamic
parameters for TBHP and tert-butoxy radical were taken from the thermodynamic
database from Goos et al. [76], and the thermodynamic parameters for OH were updated
with the values from Herbon et al. [23-24].
As discussed in Chapters 4 and 5, the initial decomposition pathways for acetone,
2-butanone, and 3-pentanone can be described as follows:
CH3COCH3 (+ M) → CH3CO + CH3 (+ M) (2)
C2H5COCH3 (+ M) → C2H5 + CH3CO (+ M) (3a)
C2H5COCH3 (+ M) → CH3 + C2H5CO (+ M) (3b)
C2H5COCH3 (+ M) → CH3 + CH3COCH2 (+ M) (3c)
C2H5COC2H5 (+ M) → C2H5 + C2H5CO (+ M) (4a)
C2H5COC2H5 (+ M) → CH3 + C2H5COCH2 (+ M) (4b)
For 2-butanone and 3-pentanone (and 2-pentanone), their initial decomposition pathways
consist of multiple channels. High-temperature decomposition pathways for 2-butanone
and 3-pentanone were first investigated by Serinyel et al. [95, 98]. Recently, Lam et al.
[124-125] have performed experimental studies during high-temperature acetone, 2-
butanone, and 3-pentanone pyrolysis, as were discussed in Chapters 4 and 5. In their
studies, they measured the rate constant for reaction (2) and the overall values for
reactions (3) and (4) at pressures near 1.6 atm. At T > 1300 K, the consumption of
93
ketones in the present study is mainly controlled by the H-atom abstraction reactions by
OH radicals and the ketone decomposition pathways. Hence, reactions (2)-(4) are
pertinent to the determinations of the overall rate constants for reactions (5)-(7) at higher
temperatures, and the rate constants for reactions (2)-(4) were updated with the values
from Lam et al. [124-125] (the rate constants from Chapters 4 and 5). In addition, a
review of the literature shows that there is currently no experimental or theoretical study
for high-temperature 2-pentanone pyrolysis. Thus, 2-pentanone decomposition
pathways, along with the corresponding rate constants, are not known in this study, and
the overall rate constant for 2-pentanone + OH reaction (reaction (8)) cannot be inferred
accurately at T > 1300 K. A thorough theoretical or experimental study for 2-pentanone
decomposition pathways is required. Nevertheless, at T < 1300 K, the consumption of 2-
pentanone in the present study is predominantly controlled by the H-atom abstraction
reactions by OH radicals, and the overall rate constant for reaction (8) was determined
over a narrower temperature range 900-1300 K. In addition, all simulations were
performed using the CHEMKIN PRO package [71] under the standard constant internal
energy and volume assumption.
6.3.2 Acetone + OH Kinetics
An OH radical sensitivity analysis for the mixture of 304 ppm acetone with 28
ppm TBHP (and 73 ppm H2O) in Ar at 1148 K and 1.95 atm is provided in Figure 6.1.
The analysis reveals that the reaction of OH with acetone (reaction (5)) is the dominant
reaction over the time frame of the experiment, with some minor interference from the
secondary reactions:
CH3 + OH → CH2(s) + H2O (17)
C2H6 (+ M) → CH3 + CH3 (+ M) (18)
CH3OH (+ M) → CH3 + OH (+ M) (19)
The rate constants for reactions (17)-(19) were updated with the values from Table 3.1 (in
Chapter 3).
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Figure 6.1: OH sensitivity plot for the rate constant measurement of acetone + OH at 1148 K and 1.95 atm.
Figure 6.2 shows a sample measured OH concentration time history for the
mixture of 304 ppm acetone in Ar at 1148 K and 1.95 atm, and the measured peak OH
mole fraction is ~28 ppm. Due to wall adsorption and condensation of TBHP, the initial
TBHP mole fraction was assumed to be the same as the measured peak OH mole fraction,
which was formed immediately after the decomposition of TBHP behind the reflected
shock wave at T > 1000 K. Note that a 70%, by weight, solution of TBHP in water in the
liquid phase corresponds, initially, to 69% water and 31% TBHP in the vapor phase,
based on Raoult’s law [126]. Therefore, a 101 ppm TBHP/water mixture should have at
most 31.3 ppm TBHP. In the present study, the mixtures of 101 ppm TBHP/water
consist of ~28-30 ppm TBHP, based on the measured peak OH yields, hence suggesting
very little loss to the walls. In addition, the test mixtures were chosen such that the ratio
of the initial acetone concentration to the initial TBHP concentration is ~10, thereby
achieving near-pseudo-first-order conditions. For the conditions described in Figure 6.2,
a best-fit overall rate constant for reaction (5) of 3.83×1012 cm3 mol-1 s-1 was obtained
between the experimental data and the simulation. Simulations for the perturbations of
±50% in the inferred rate constant are also illustrated in Figure 6.2. In addition, Table 6.1
95
summarizes the rate constant measurements of reaction (5) at 872-1355 K and 1.69-2.12
atm.
Figure 6.2: Sample acetone + OH rate constant measurement using the mixture of 304 ppm acetone with ~28 ppm TBHP (and 73 ppm water) in Ar at 1148 K and 1.95 atm. Simulation from the modified Pichon et al. mechanism for the best-fit rate constant, along with perturbations of ±50%, is also shown.
Table 6.1: CH3COCH3 + OH → Products: Rate Constant Data.
T5 [K] P5 [atm] k5 [cm3 mol-1 s-1]
101 ppm TBHP (and water), 304 ppm CH3COCH3, Ar 934 2.01 2.52E+12 1008 2.09 2.72E+12 1011 1.85 2.83E+12 1111 1.98 3.47E+12 1148 1.95 3.83E+12 1221 1.86 4.50E+12 1247 1.82 4.96E+12 1280 1.78 4.90E+12 1307 1.69 5.29E+12 1355 1.75 5.63E+12
92 ppm TBHP (and water), 304 ppm CH3COCH3, Ar 872 1.96 2.14E+12 996 2.12 2.79E+12
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A detailed error analysis was performed to estimate the uncertainty limits of the
measured rate constant for reaction (5) at 1148 K. The primary contributions to the
uncertainties in the rate constant are: (a) temperature (±1%), (b) mixture composition
(±5%), (c) OH absorption coefficient (±3%), (d) wavemeter reading in the UV (±0.01 cm-
1), (e) fitting the data to computed profiles (±5%), (f) locating time-zero (±0.5 µs), (g) the
rate constant for CH3 + OH → CH2(s) + H2O (uncert. factor = 2), (h) the rate constant
for CH3OH (+ M) → CH3 + OH (+ M) (uncert. factor = 2), and (i) the rate constant for
C2H6 (+ M) → CH3 + CH3 (+ M) (±20%). As shown in Figure 6.3, the individual error
sources were introduced separately and their effects on the rate constant for reaction (5)
were determined. These uncertainties were combined in a root-sum-squared method to
give an overall uncertainty estimate of ±28% at 1148 K.
Figure 6.3: Uncertainty analysis for the rate constant of CH3COCH3 + OH → products at 1148 K and 1.95 atm.
Figure 6.4 shows the Arrhenius plot for the present rate constant measurements of
reaction (5) at T = 872-1355 K, along with the previous measurements of Vasudevan et
al. [119] from the same laboratory. The current measurements agree well with the
previous values (within ±5%). These measured values can then be expressed in
Arrhenius form as k5 = 3.30×1013 exp(-2437/T) cm3 mol-1 s-1 over 872-1355 K. Bott and
Cohen [118] also utilized TBHP as the OH precursor and employed both the shock tube
97
and UV lamp absorption method at 309 nm to monitor the OH decay and study reaction
(5) near 1200 K and 1 atm. The current measurements are consistent with Bott and
Cohen’s measured value within 20%. In addition, Srinivasan et al. [77] used a similar
method to investigate the rate constant for reaction (5) and determined a rate constant of
4.40×1012 cm3 mol-1 s-1 over 1178-1299 K. Their value is in close accord with our
previous and current measurements. Figure 6.4 also shows the rate constants for reaction
(5) adopted by two different detailed mechanisms: Pichon et al. [89] and Herbinet et al.
[45]. The values of k5 from the original Pichon et al. mechanism are approximately 24%
and 43% faster than the current measurements at 1000 K and 1250 K, respectively; the
values employed from the Herbinet et al. mechanism are in excellent agreement with the
current measured values (within ±11%).
Additionally, a theoretical calculation from Zhou et al. [121], which modeled all
possible abstraction channels, was performed using the computationally less expensive
G3 and G3MP2BH&H methods to calculate the energy barriers and using the Variflex
code including Eckart tunneling corrections to compute the total rate constants for the
reactions of OH with ketones (acetone, 2-butanone, and isopropyl methyl ketone) over
500-2000 K. As shown in Figure 6.4, the computed values from Zhou et al. are
consistently lower than all high-temperature experimental data by ~55%.
Figure 6.4: Arrhenius plot for acetone + OH (k5) at temperatures above 833 K.
98
6.3.3 2-Butanone + OH Kinetics
The OH sensitivity analysis was also carried out for the rate constant
determination of 2-butanone + OH → products (reaction (6)) using the mixture of 152
ppm 2-butanone with 14 ppm TBHP (and 41 ppm water) in Ar at 1039 K and 1.41 atm,
as shown in Figure 6.5. Note that reaction (6) consists of 3 different abstraction channels,
as described in the original Serinyel et al. mechanism [95, 98]:
C2H5COCH3 + OH → CH2CH2COCH3 + H2O (6a)
C2H5COCH3 + OH → CH3CHCOCH3 + H2O (6b)
C2H5COCH3 + OH → C2H5COCH2 + H2O (6c)
At 1100 K, channel (6b) is the dominant pathway with a branching ratio of 0.53 due to
the weaker C-H bond energy at the secondary site, and channel (6a) is the next most
important pathway with a branching ratio of 0.41. However, channel (6c) is nearly
insignificant with a branching ratio of 0.06. More importantly, reaction (6) is the most
sensitive reaction at the conditions depicted in Figure 6.5, with some minor interference
from the secondary reactions (reactions (13), (17) and (18)). As shown here, as
temperature decreases, the reaction for TBHP decomposition becomes more important at
the early times.
Figure 6.5: OH sensitivity plot for the rate constant measurement of 2-butanone + OH at 1039 K and 1.41 atm.
99
Figure 6.6 shows an example of the overall rate constant measurement (k6 = k6a +
k6b + k6c) for reaction (6) at 1039 K and 1.41 atm. The mixture is 152 ppm 2-butanone in
Ar, with the measured peak OH yield to be ~14 ppm. Thus, we infer that the initial
TBHP mole fraction is 14 ppm. The model predictions from the modified Serinyel et al.
mechanism with the best-fit overall rate constant of k6 = 6.82×1012 cm3 mol-1 s-1 and the
variations of ±50% in the inferred rate constant are also shown in Figure 6.6. Due to the
near-pseudo-first-order conditions, the measured overall rate constant should be
insensitive to the branching ratios of the individual channels. The effect of the branching
ratios on the rate constant determination was also investigated at 1039 K by
interchanging the branching ratios of channels (6a) and (6b) while maintaining the total
value, and a negligible change in the inferred rate constant was found. In addition, a
detailed error analysis (similar to the analysis for reaction (5)) was performed for the rate
constant measurement of reaction (6) at 1039 K and 1.41 atm, and the overall uncertainty
was estimated to be ±22%. Table 6.2 summarizes the rate constant measurements of
reaction (6) at 879-1364 K and 1.21-1.63 atm. Three different mixture compositions
were employed to confirm that the inferred rate constants are independent of any
secondary chemistry effects.
Figure 6.6: Sample 2-butanone + OH rate constant measurement using the mixture of 152 ppm 2-butanone with ~14 ppm TBHP (and 41 ppm water) in Ar at 1039 K and 1.41 atm. Simulation from the modified Serinyel et al. mechanism for the best-fit rate constant, along with perturbations of ±50%, is also shown.
100
Table 6.2: C2H5COCH3 + OH → Products: Rate Constant Data.
T5 [K] P5 [atm] k6 [cm3 mol-1 s-1]
55 ppm TBHP (and water), 152 ppm C2H5COCH3, Ar 962 1.51 6.10E+12 999 1.45 6.42E+12
1039 1.41 6.82E+12 1119 1.27 8.25E+12 1174 1.24 9.01E+12 1247 1.26 1.05E+13
53 ppm TBHP (and water), 161 ppm C2H5COCH3, Ar
879 1.57 5.06E+12 955 1.63 5.93E+12 1110 1.39 8.00E+12 1282 1.26 1.09E+13 1297 1.23 1.14E+13
65 ppm TBHP (and water), 206 ppm C2H5COCH3, Ar
905 1.55 5.30E+12 1088 1.42 7.51E+12 1104 1.34 7.80E+12 1320 1.21 1.17E+13 1364 1.25 1.24E+13
Figure 6.7 shows the Arrhenius plot for the overall rate constant measurements of
reaction (6) at T > 833 K, along with the estimated values adopted in the original Serinyel
et al. mechanism [95, 98] and the theoretical values from Zhou et al. [121]. The
measured values can be expressed in Arrhenius form as k6 = 6.35×1013 exp(-2270/T) cm3
mol-1 s-1 over 879-1364 K. The values used in the original Serinyel et al. mechanism are
~40% lower than the measurements. Interestingly, the theoretical values from Zhou et al.
are in excellent agreement with the measurements within 10%. Note that the
measurements and the theoretical calculations both exhibit some slight non-Arrhenius
curvature at the present test conditions.
101
Figure 6.7: Arrhenius plot for 2-butanone + OH (k6) at temperatures above 833 K.
6.3.4 3-Pentanone + OH Kinetics
As illustrated in Figure 6.8, the OH sensitivity reveals that the reactions of OH
with 3-pentanone are the dominant pathways for the consumption of OH at 1188 K and
1.94 atm. In particular, reaction (7) consists of two channels, in which the OH radical
can abstract the H-atom from 3-pentanone at the primary or secondary site.
C2H5COC2H5 + OH → CH2CH2COC2H5 + H2O (7a)
C2H5COC2H5 + OH → CH3CHCOC2H5 + H2O (7b)
Based on the original Serinyel et al. mechanism [95, 98], the branching ratios of channels
(7a) and (7b) are 0.42 and 0.58, respectively, at 1188 K. In addition, there is some minor
interference from the following reactions at later times:
CH3 + OH → CH2(s) + H2O (17)
C2H4 + H (+ M) → C2H5 (+ M) (20)
CH3COCH3 + OH → CH3COCH2 + H2O (5)
In the current analysis, the rate constant for reaction (5) was updated with the Arrhenius
expression from Section 6.3.2, with an uncertainty of approximately ±28%. In addition,
102
the rate constant for reaction (20) adopted by the original Serinyel et al. mechanism was
used, and we assumed that its uncertainty is approximately a factor of 2.
Figure 6.8: OH sensitivity plot for the rate constant measurement of 3-pentanone + OH at 1188 K and 1.94 atm. Figure 6.9 shows a representative OH time history trace at 1188 K and 1.94 atm
using the mixture of 213 ppm 3-pentanone with 17 ppm TBHP (and 59 ppm H2O) in Ar.
The model predictions from the modified Serinyel et al. mechanism with the best-fit rate
constant of k7 = 1.23×1013 cm3 mol-1 s-1 and the variations of ±50% in k7 are also shown
in Figure 6.9. Note that the overall rate constant for reaction (7) is insensitive to the
branching ratios of its individual channels due to the near-pseudo-first-order conditions.
A detailed error analysis was then conducted for k7 at 1188 K and 1.94 atm, and the
overall uncertainty was estimated to be ±20%.
103
Figure 6.9: Sample 3-pentanone + OH rate constant measurement using the mixture of 213 ppm 3-pentanone with ~17 ppm TBHP (and 59 ppm water) in Ar at 1188 K and 1.94 atm. Simulation from the modified Serinyel et al. mechanism for the best-fit rate constant, along with perturbations of ±50%, is also shown.
Table 6.3 summarizes the overall rate constant determinations of reaction (7) at T
= 878-1353 K and P = 1.21-2.20 atm. Note that two different mixture compositions were
used to confirm that the inferred rate constants are free of any secondary chemistry
effects, and the values determined from these two mixtures are consistent with each
other. Figure 6.10 shows the Arrhenius plot for our measured values, along with the
estimated values in the original Serinyel et al. mechanism [95, 98], at temperatures above
833 K. The measured values can be expressed in Arrhenius form as k7 = 9.29×1013 exp(-
2361/T) cm3 mol-1 s-1 over 878-1353 K. Interestingly, the values for reaction (7) from the
original Serinyel et al. mechanism were estimated by analogy with the H-atom
abstraction rate constants from alkanes [98], and their values are in close accord with the
present measurements within ±5%. As is evident in Figure 6.10, the measurements and
the estimated values from Serinyel et al. both experience slight non-Arrhenius curvature
at the current experimental conditions.
Additionally, based on the theoretical study of the reactions of OH with ketones
from Zhou et al. [121], the expressions of the group rate constants (on a per H-atom
104
basis) for different carbon atom sites (primary, secondary, and tertiary carbon atoms)
were provided. In the present analysis, we can estimate the overall rate constant for
reaction (7) using these group rate constants, and the estimated rate constant is k7 = 6 ×
k(CH3CH2C(O)) + 4 × k(–CH2C(O)), where k(CH3CH2C(O)) and k(–CH2C(O)) are the
group rate constants (per H-atom) for the primary carbon atom adjacent to the –
CH2C(O)– group and for the secondary carbon atom adjacent to the –C(O)– group,
respectively. As shown in Figure 6.10, the estimated values are in good agreement with
the measurements within 15%.
Table 6.3: C2H5COC2H5 + OH → Products: Rate Constant Data.
T5 [K] P5 [atm] k7 [cm3 mol-1 s-1]
76 ppm TBHP (and water), 213 ppm C2H5COC2H5, Ar 1140 1.61 1.12E+13 1188 1.94 1.23E+13 1248 1.76 1.33E+13 1296 1.79 1.57E+13 1310 1.74 1.61E+13
76 ppm TBHP (and water), 211 ppm C2H5COC2H5, Ar 936 2.02 7.38E+12 1025 2.13 8.90E+12 1068 1.94 9.54E+12
75 ppm TBHP (and water), 211 ppm C2H5COC2H5, Ar 878 1.98 6.61E+12 955 2.20 7.86E+12 981 2.13 8.09E+12 1093 1.91 1.06E+13 1339 1.71 1.67E+13
53 ppm TBHP (and water), 151 ppm C2H5COC2H5, Ar 1091 1.46 1.03E+13 1157 1.34 1.16E+13 1192 1.29 1.26E+13 1258 1.27 1.43E+13 1301 1.21 1.57E+13 1353 1.23 1.69E+13
105
Figure 6.10: Arrhenius plot for 3-pentanone + OH (k7) at temperatures above 833 K.
6.3.5 2-Pentanone + OH Kinetics
As mentioned previously, a comprehensive mechanism for high-temperature 2-
pentanone kinetics is not available in the literature. In the present work, we have
assumed the pathways for the reactions of OH with 2-pentanone to be similar to those of
methyl butanoate [54].
C3H7COCH3 + OH → C2H4 + CH3COCH2 + H2O (8a)
C3H7COCH3 + OH → C3H6 + CH3CO + H2O (8b)
C3H7COCH3 + OH → C2H5CHCO + CH3 + H2O (8c)
C3H7COCH3 + OH → n-C3H7 + CH2CO + H2O (8d)
Channel (8a) describes the H-atom abstraction from 2-pentanone at the γ site to form a
CH2CH2CH2COCH3 radical and a H2O molecule. Through β-scission, the fuel radical
decomposes very rapidly to form a C2H4 molecule and a CH3COCH2 radical. Due to the
rapid decomposition of the fuel radical, we assumed that the products from the fuel
radical are formed immediately after the H-atom abstraction. Similarly, channels (8b)
and (8c) describe the H-atom abstraction from 2-pentanone at the β and α sites,
respectively. Due to its similar structure to methyl butanoate, the rate constants for
106
channels (8a)-(8c) were approximated to be the same as the rate constants for methyl
butanoate (MB) + OH reactions at the α, β and γ sites, and these values for MB + OH
reactions were obtained from the Dooley et al. mechanism [54]. Among these three
channels, channel (8b) (the H-atom abstraction at the β position) should be the fastest
route for the removal of OH, which was also suggested in previous experimental studies
[38, 107]. In addition, the rate constant for channel (8d) was assumed to be the same as
that of channel (6c) (C2H5COCH3 + OH → C2H5COCH2 + H2O). The resulting
branching ratios of channels (8a)-(8d) at 1186 K are 0.23, 0.38, 0.37 and 0.02. These
four channels were then incorporated in the modified Serinyel et al. mechanism. As
expected, the estimated branching ratios of channels (8a)-(8d) have no discernible effect
on the determinations of the overall rate constant at near-pseudo-first-order conditions.
In the present analysis, we also included the pathways for the reactions of H with
2-pentanone in the modified Serinyel et al. mechanism, which can be described as
follows:
C3H7COCH3 + H → C2H4 + CH3COCH2 + H2 (29a)
C3H7COCH3 + H → C3H6 + CH3CO + H2 (29b)
C3H7COCH3 + H → C2H5CHCO + CH3 + H2 (29c)
C3H7COCH3 + H → n-C3H7 + CH2CO + H2 (29d)
In a similar way, the rate constants for channels (29a)-(29c) were assumed to be the same
as the rate constants for the reactions of H with methyl butanoate at the α, β and γ sites,
and these values were also adopted from the Dooley et al. mechanism [54]. Additionally,
the rate constant for channel (29d) was assumed to be the same as that of 2-butanone
(C2H5COCH3 + H → C2H5COCH2 + H2). Interestingly, the addition of reactions (29a)-
(29d) has negligible influence on the overall rate constant determinations of reaction (8).
Figure 6.11 shows a representative OH time history trace at 1186 K and 1.30 atm
using the mixture of 161 ppm 2-pentanone with 15 ppm TBHP (and 45 ppm H2O) in Ar.
The simulations from the modified Serinyel et al. mechanism with the best-fit rate
constant of k8 = 1.24×1013 cm3 mol-1 s-1 and the variations of ±50% in k8 were also
illustrated. A detailed error analysis was then conducted to estimate the overall
uncertainty in k8 at 1186 K, and the uncertainty was found to be ±24%.
107
Figure 6.11: Sample 2-pentanone + OH rate constant measurement using the mixture of 161 ppm 2-pentanone with ~15 ppm TBHP (and 45 ppm water) in Ar at 1186 K and 1.30 atm. Simulation from the modified Serinyel et al. mechanism for the best-fit rate constant, along with perturbations of ±50%, is also shown.
Table 6.4 summarizes the overall rate constant measurements of reaction (8) at
902-1302 K and 1.23-1.59 atm, and Figure 6.12 also presents the Arrhenius plot for these
measured values. These measured values are expressed in Arrhenius form as k8 =
7.06×1013 exp(-2020/T) cm3 mol-1 s-1 over 902-1302 K. It should be noted that the
overall rate constant measurements for 2-pentanone + OH reaction are quite similar to the
values obtained for 3-pentanone + OH reaction at our experimental conditions.
Additionally, Figure 6.12 presents the estimated overall rate constant for reaction (8)
using the group rate constants for the reactions of OH with ketones developed by Zhou et
al. [121], and the estimated values are in excellent agreement with the measurements
within 7%.
108
Table 6.4: C3H7COCH3 + OH → Products: Rate Constant Data.
T5 [K] P5 [atm] k8 [cm3 mol-1 s-1]
60 ppm TBHP (and water), 161 ppm C3H7COCH3, Ar 902 1.59 7.58E+12 1104 1.37 1.14E+13 1186 1.30 1.24E+13 1216 1.23 1.31E+13 1302 1.26 1.51E+13
63 ppm TBHP (and water), 161 ppm C3H7COCH3, Ar 955 1.50 8.45E+12 1009 1.46 9.38E+12 1042 1.43 1.04E+13 1093 1.37 1.12E+13 1125 1.30 1.17E+13 1264 1.25 1.48E+13
Figure 6.12: Arrhenius plot for 2-pentanone + OH (k8) at temperatures above 900 K.
109
6.3.6 Comparison of Ketone + OH Kinetics
Figure 6.13 presents the Arrhenius plot of the measured rate constants for
reactions (5)-(8) at temperatures above 870 K. Among all four ketone + OH reactions,
the reaction of OH with acetone has the lowest reactivity due to the fact that there are less
C–H bonds available for H-atom abstraction in acetone. As the number of C–H bonds in
the fuel molecule increases, the fuel + OH reaction becomes more reactive. As
demonstrated in Figure 6.13, the rate constant for 3-pentanone + OH is much faster than
that for 2-butanone + OH, because 3-pentanone has one more secondary carbon atom site
than 2-butanone. In addition, the rate constant for 2-pentanone + OH is about the same as
that for 3-pentanone + OH due to the fact that both molecules have the same number of
primary and secondary carbon atom sites. Note that the rate constant measurements of
the 2-pentanone + OH reaction are slightly higher than the values of the 3-pentanone +
OH reaction at T < 1100 K. This can be explained by the fact that the secondary carbon
atom site at the β position from 2-pentanone is supposed to be more reactive than that at
the α position from 3-pentanone, as suggested in previous experimental studies [38, 107].
Figure 6.13: Arrhenius plot of the measured rate constants for reactions (5)-(8) at temperatures above 870 K.
110
6.4 Comparison with Low Temperature Data
Figure 6.14 presents the current data along with some earlier measurements of
reaction (5) at temperatures greater than 250 K. In the study from Wollenhaupt et al.
[106], the rate constant for reaction (5) was measured over 202-395 K at 20-100 torr of
Ar or N2 bath gas using the pulsed laser photolysis technique to generate OH radicals
from the sequential two-photon dissociation of NO2 in the presence of H2 at 439 nm, or
from the photolysis of HONO at 351 nm. They monitored the OH radicals using either
resonance fluorescence or laser-induced fluorescence detection scheme, and they also
concluded that their measurements are independent of pressure. Similarly, Le Calvé et al.
[38] and Gierczak et al. [109] studied k5 over 199-383 K by generating OH via pulsed
laser photolysis and detecting it via laser-induced fluorescence, while Wallington and
Kurylo [107] investigated k5 over 240-440 K using the flash photolysis/resonance
fluorescence measurement technique. Moreover, Yamada et al. [117] examined k5 over a
wide temperature range 298-832 K using the pulsed laser photolysis/pulsed laser-induced
fluorescence technique. They then performed a detailed analysis using Variational
Transition State theory and suggested that the dominant products of reaction (5) are
CH3COCH2 and H2O through direct abstraction at all temperatures (particularly above
450 K). Additionally, Tranter and Walker [120] added small amounts of acetone to
slowly reacting mixtures of H2 + O2 at 753 K, and monitored the consumption of acetone
and H2 with the use of gas chromatography. This method allowed them to infer the
relative rate constant for reaction (5) at 753 K. It is pertinent to note that these low-
temperature measurements are in excellent agreement with each other. As is evident in
Figure 6.14, the rate constants employed in the comprehensive mechanisms of Pichon et
al. [89] and Herbinet et al. [45] are able to predict the low-temperature data reasonably
well over 298-832 K, but not for T < 298 K. In particular, the rate constant from
Herbinet et al. provides much better agreement with the existing high-temperature data.
In addition to the values from the detailed mechanisms, the theoretical calculation from
Zhou et al. [121] agrees well with earlier low-temperature measurements (at T < 500 K),
but the calculated values are at least 40% lower than the measurements at T > 500 K.
111
Figure 6.14: Arrhenius plot for acetone + OH → products (k5) at all temperatures.
Figure 6.15 shows the Arrhenius plot for the overall rate constant measurements
of reaction (6) at temperatures greater than 250 K. Kinetic measurements of reaction (6)
were performed at room temperature by different researchers using both relative [112-
115] and absolute [38, 107, 110-111] methods. In general, these room temperature
measurements are in close accord with each other, except for the value obtained from
Atkinson et al. [112]. Concurrently, the rate constant for reaction (6) was examined as a
function of temperature (213-598 K) by Wallington and Kurylo [107] using the flash
photolysis/resonance fluorescence technique and by Le Calvé et al. [38], Carr et al. [110]
and Jimenez et al. [111] using the pulsed laser photolysis/laser-induced fluorescence
technique. Their measurements are in excellent agreement with each other, and no
pressure dependence can be found at their experimental conditions. Based on these low-
temperature data, k6 exhibits only slight positive temperature dependence over 250-400
K. In addition to the rate constant determination for acetone + OH reaction, Tranter and
Walker [120] measured the relative rate constant for reaction (6) at 753 K. Figure 6.15
also presents the estimated values of k6 from Serinyel et al. [95] and the theoretical values
from Zhou et al. [121]. As described previously, the calculated values from Zhou et al.
are consistent with the present high-temperature data (at T > 879 K) within 10%.
However, the calculated values are faster than the earlier low-temperature data by a factor
112
of 2 at 500 K and by a factor of 6 at 250 K. Consequently, the theoretical study predicts a
pronounced negative temperature dependence of k6 over 250-500 K, and this effect does
not appear in the existing data. On the other hand, the estimated values from Serinyel et
al. are ~40% lower than the current high-temperature data, and are in good agreement
with the low-temperature data over 345-600 K. In addition, the overall rate constant from
Serinyel et al. does not exhibit any negative temperature dependence over 250-500 K.
Figure 6.15: Arrhenius plot for 2-butanone + OH → products (k6) at all temperatures.
Figure 6.16 also shows the current high-temperature data (at T > 878 K) and three
previous low-temperature measurements (at T < 800 K) for the reaction of OH with 3-
pentanone, along with the rate constant from the original Serinyel et al. mechanism [98].
As compared to acetone and 2-butanone, fewer experimental and theoretical studies are
available in the literature. Tranter and Walker [120] measured the relative rate constant
for reaction (7) at 753 K (using the same approach as the one they employed for reactions
(5) and (6)). Atkinson et al. [116] also measured the relative rate constant for reaction (7)
at 299 K using methyl nitrite (CH3ONO) photolysis in air as a source of OH radicals.
They monitored the organic reactants using gas chromatography with flame ionization
detection. In their work, they took advantage of their previous knowledge on the rate
constant for cyclohexane + OH reaction and inferred the rate constant for reaction (7)
113
from the ratio of k7/kcyclohexane+OH at 299 K. Moreover, Wallington and Kurylo [107]
determined the absolute rate constant for reaction (7) over 240-440 K using the flash
photolysis/resonance fluorescence measurement technique, and they suggested that k7 did
not exhibit any temperature dependence at their test conditions. Furthermore, the rate
constant from the original Serinyel et al. mechanism is able to predict the existing data
rather accurately over 440-1353 K.
Figure 6.16: Arrhenius plot for 3-pentanone + OH → products (k7) at all temperatures.
Similarly, Figure 6.17 illustrates the current high-temperature data and previous
low-temperature measurements [107, 111, 116] of reaction (8) over 250-1302 K. More
importantly, the rate constant provided by Jimenez et al. [111] exhibits a pronounced
negative temperature dependence over 248-388 K, and this trend does not appear in the
kinetic measurements of reactions (5)-(7). This pronounced negative temperature
dependence of k8 is mainly attributed to the H-atom abstraction from the CH2 group in
the β position, which is the predominant reaction pathway at low temperatures. For
instance, Jimenez et al. [111] determined that the branching ratios of channels (8a)-(8d)
are 0.04, 0.76, 0.18, and 0.02, respectively, at 298 K. Some researchers [107, 111] also
postulated that the H-abstraction reaction could proceed via an OH-addition complex,
114
resulting in a six- or seven-membered ring complex which enhances the abstraction of an
H atom from the CH2 group in the β position.
Figure 6.17: Arrhenius plot for 2-pentanone + OH → products (k8) at all temperatures.
6.5 Comparison with Structure-Activity Relationship
The measured overall rate constants for reactions (5)-(8) over 250-1360 K can be
compared with the estimated values using the structure-activity relationship (SAR)
developed by Atkinson and his co-workers [127-129]. Their method of calculating the
rate constants for the reactions of OH with organic compounds is based on the estimation
of primary (–CH3), secondary (–CH2–), and tertiary (–CH<) group rate constants, and
these group rate constants depend on the nature of the neighboring atoms (substituents
bound to the groups). The group rate constants can be expressed as k(CH3–X) = kprim
F(X), k(Y–CH2–X) = ksec F(X) F(Y), and k((Z)CH(X)(Y)) = ktert F(X) F(Y) F(Z), where
kprim, ksec and ktert are the rate constants for the H-atom abstraction from –CH3, –CH2– and
–CH< groups, and F(X), F(Y) and F(Z) are the substituent factors. Recently, Pang et al.
[74] have demonstrated that the SAR estimation accurately predicts the measured rate
constants for n-alkane + OH reactions (i.e., n-pentane + OH, n-heptane + OH, and n-
115
nonane + OH) over 250-1364 K. In particular, the SAR estimation captures the
temperature dependence of their measurements reasonably well. In addition, Kwok and
Atkinson [129] provided a revised list of the substituent factors F(X) at 298 K, and they
assumed that the temperature dependence of the substituent factors can be expressed in
the form of F(X) = exp(Ex/T). In the present analysis, the Ex term in the preceding
expression was calculated from the substituent factor at 298 K, thereby allowing us to
determine the substituent factors at different temperatures.
The estimated rate constants for reactions (5)-(8) based on the SAR approach are
provided in Figures 6.14-6.17. For instance, the estimated rate constant for 2-pentanone
+ OH reaction can be evaluated as k8 = kprim F(–CH2–) + ksec F(CH3–) F(–CH2C(O)R) +
ksec F(–CH2–) F(–C(O)–) + kprim F(–CO–). It is pertinent to note that the substituent
factor F(–CH2C(O)R) is 3.9 at 298 K and is much higher than F(–CH2–), which is 1.23 at
298 K. This confirms the increased reactivity of the H-atom abstraction at the β position,
as observed by Atkinson et al. [116]. As expected, the SAR estimation shows good
agreement with the kinetic measurements of reactions (5)-(8) at 298 K, but the estimated
values are higher than the measured values over 333-1360 K. In particular, the estimated
values are ~25% faster than the present high-temperature data over 870-1360 K.
Nevertheless, the SAR estimation can capture the temperature dependence of reactions
(5)-(8) reasonably well, implying that the pre-exponential factors for the group rate
constants kprim and ksec should be reduced by ~25%, particularly for ketone + OH
reactions. With this modification, the estimated rate constants for reactions (5)-(7) show
excellent agreement with the measurements over a wide temperature range 298-1360 K
(see Figures 6.14-6.16). In addition, the modified SAR estimation for reaction (8)
precisely predicts the present high-temperature data (at 902-1302 K), and is in close
accord with the previous data from Wallington and Kurylo [107] and Jimenez et al. [111]
at temperatures near 298 K, as seen in Figure 6.17.
116
6.6 Summary
The overall rate constants for the reactions of OH with acetone (k5), 2-butanone
(k6), 3-pentanone (k7) and 2-pentanone (k8) were studied behind reflected shock waves
over 870-1360 K at pressures of 1-2 atm using OH laser absorption. The present high-
temperature measurements can be expressed in Arrhenius form as:
k5 = 3.30×1013 exp(-2437/T) cm3 mol-1 s-1
k6 = 6.35×1013 exp(-2270/T) cm3 mol-1 s-1
k7 = 9.29×1013 exp(-2361/T) cm3 mol-1 s-1
k8 = 7.06×1013 exp(-2020/T) cm3 mol-1 s-1
Detailed error analyses, which account for both experimental and secondary chemistry
contributions, yielded the uncertainty estimates of ±28% at 1148 K for k5, ±22% at 1039
K for k6, ±20% at 1188 K for k7, and ±24% at 1186 K for k8. In addition, the structure-
activity relationship (SAR) from Atkinson and his co-workers [127-129] was used to
estimate the rate constants for reactions (5)-(8), and the estimated values are in good
agreement with the present high-temperature data (within ~25%).
117
Chapter 7 High-Temperature Measurements of the Reactions of OH with Small Methyl Esters: Methyl Formate, Methyl Acetate, Methyl Propanoate, and Methyl Butanoate
7.1 Introduction
In this chapter, the overall rate constants for the reactions of OH with four small
methyl esters, namely methyl formate (CH3OCHO), methyl acetate (CH3OC(O)CH3),
methyl propanoate (CH3OC(O)C2H5), and methyl butanoate (CH3OC(O)C3H7), were
determined behind reflected shock waves over the temperature range of 876-1371 K at
pressures near 1.5 atm:
CH3OCHO + OH → Products (9)
CH3OC(O)CH3 + OH → Products (10)
CH3OC(O)C2H5 + OH → Products (11)
CH3OC(O)C3H7 + OH → Products (12)
We believe these are the first direct high-temperature measurements of the overall rate
constants for reactions (9)-(12). These kinetic data were compared with the values
adopted in several detailed kinetic mechanisms and the estimates using the structure-
activity relationship (SAR) developed by Atkinson and co-workers [127-129].
118
7.2 Experimental Details
Test mixtures were prepared manometrically in a 40 liter stainless-steel tank
heated uniformly to 50 oC and mixed with a magnetically-driven stirring vane. A double-
dilution process was employed to allow for more accurate pressure measurements in the
manometrical preparation of a highly dilute mixture. A more concentrated mixture was
first prepared and mixed for at least 2 hours to ensure homogeneity and consistency, and
the mixture was then further diluted with argon and mixed for additional 2 hours prior to
the experiments. The gas utilized in this study was argon (Research Grade) 99.999%,
which was supplied by Praxair and used without further purification. The liquid
chemicals were commercially available 70% tert-butyl hydroperoxide (TBHP) in water,
methyl formate (≥99%), methyl acetate (≥99%), methyl propanoate (≥99%), and methyl
butanoate (≥99%) from Sigma-Aldrich, and were purified using a freeze-pump-thaw
procedure to remove dissolved volatiles and air prior to mixture preparation.
The mixture composition was confirmed by sampling a portion of the mixture
(from near the endwall) into an external multi-pass absorption cell with a path length of
29.9 m and monitoring the fuel concentration in the cell with a Jodon™ Helium-Neon
laser at 3.39 µm [82, 122]. Beer’s law was then used to convert the measured absorption
data into the fuel mole fraction. The absorption cross-sections of methyl esters for Beer’s
law were directly obtained from the PNNL database [123], and the measured fuel
concentrations were consistent with the values expected from the manometrical
preparation within ±5%.
7.3 Kinetic Measurements
A total of 52 reflected shock wave experiments were performed to determine the
overall rate constants for the reactions of OH with four methyl esters (methyl formate,
methyl acetate, methyl propanoate, and methyl butanoate) over 876-1371 K at pressures
near 1.5 atm. Experiments were carried out using different initial fuel concentrations:
methyl formate (322 ppm, 404 ppm), methyl acetate (323 ppm, 384 ppm), methyl
119
propanoate (~281 ppm), and methyl butanoate (241 ppm, 270 ppm). Test mixtures with
individual methyl esters and 80-102 ppm TBHP (and water) diluted in argon were
utilized in the present study. Note that dilute mixtures were preferred in order to
minimize the temperature change resulted from the chemistry effects, and the temperature
profile behind the reflected shock wave (from the present study) was nearly constant (less
than 1 K change based on the calculation from CHEMKIN PRO [71]) over the time
frame of the experiment (the first 100 µs).
7.3.1 Choice of Kinetic Mechanisms
The CHEMKIN PRO package [71] was used to simulate the OH time histories
under the standard constant energy and volume assumption. A comprehensive chemical
kinetic mechanism of Dooley et al. [49] was chosen as the base mechanism for methyl
formate and methyl acetate. This mechanism can successfully simulate shock tube
ignition delay times, laminar burning velocities of outwardly propagating spherical
flames, and speciation data from a shock tube and a variable-pressure flow reactor [49-
50] during methyl formate pyrolysis and oxidation. Additionally, this kinetic mechanism
incorporates the sub-mechanism for methyl acetate, which was previously developed by
Westbrook et al. [53]. The sub-mechanism for methyl acetate consists of the
unimolecular decomposition pathways and the H-atom abstraction reactions by H, OH,
and CH3 radicals, and was validated against speciation data from fuel-rich, low-pressure,
premixed laminar flames. A detailed kinetic mechanism of Dooley et al. [54] was also
selected as the base mechanism for methyl propanoate and methyl butanoate. This
mechanism was originally developed to predict the autoignition of methyl butanoate in a
shock tube and a rapid compression machine over a wide range of experimental
conditions, and was further validated against speciation data available in the literature
from a flow reactor, a jet-stirred reactor, and an opposed-flow diffusion flame. As were
done in Chapters 3 and 6, tert-butyl hydroperoxide (TBHP or (CH3)3−CO−OH) was used
as an OH radical precursor at the present experimental conditions, and the TBHP sub-
120
mechanism was also implemented into the base mechanisms for these methyl ester + OH
studies. (Please read Chapter 3 for more details on the TBHP chemistry.)
7.3.2 Methyl Formate (MF) + OH Kinetics
The reaction of OH with methyl formate consists of 2 different channels:
CH3OCHO + OH → CH3OCO + H2O (9a)
CH3OCHO + OH → CH2OCHO + H2O (9b)
The branching ratios of channels (9a) and (9b) are 0.32 and 0.68, respectively, at 1168 K,
based on the Dooley et al. mechanism [49]. In their analysis, the estimated rate constant
for channel (9a) was assumed to be an intermediate value between typical primary and
secondary C–H bonds (as in propane) due to the weaker bond strength of the CH3OCO–H
position (100.1 kcal/mol at 298 K). Similarly, the estimated rate constant for channel
(9b) (per H-atom) was assumed to be 5% faster than the value for a typical primary C–H
bond, and the corresponding bond strength was estimated to be 100.9 kcal/mol at 298 K.
An OH radical sensitivity analysis for the mixture of 322 ppm methyl formate
with 26 ppm TBHP (and 70 ppm H2O) in Ar at 1168 K and 1.40 atm is shown in Figure
7.1. The analysis reveals that the reaction of OH with methyl formate (reaction (9)) is the
dominant reaction over the time frame of the experiment, with some minor interference
from the secondary reactions:
CH3 + OH → CH2(s) + H2O (17)
C2H6 (+ M) → CH3 + CH3 (+ M) (18)
CH2O + OH → HCO + H2O (30)
In this modeling, the rate constants for reactions (5) and (17)-(19) in the Dooley et al.
mechanism [49] were updated with the values in Table 3.1. The rate constant for reaction
(30) was previously measured using UV laser absorption of OH near 307 nm behind
reflected shock waves over 934-1670 K at pressures near 1.6 atm by Vasudevan et al.
[126], and their measured rate constant was also adopted in the present study.
121
Figure 7.1: OH sensitivity plot for the rate constant measurement of methyl formate + OH at 1168 K and 1.40 atm.
Figure 7.2 illustrates a sample measured OH concentration time history for the
mixture of 322 ppm methyl formate in Ar at 1168 K and 1.40 atm, and the measured peak
OH concentration is approximately 26 ppm. According to the measured peak OH yields,
the mixtures with 96 ppm TBHP/water are comprised of ~25-28 ppm TBHP in the
present study. It should also be noted that the presence of H2O in the test mixtures does
not have any significant influence on the computed OH profiles. As shown in Figure 7.2,
a best-fit overall rate constant for reaction (9) of 4.26×1012 cm3 mol-1 s-1 was obtained
between the experimental data and the simulation at 1168 K and 1.40 atm. The
simulations for the perturbations of ±50% in the inferred rate constant are also shown in
Figure 7.2. Additionally, the effect of the branching ratios for reaction (9) on the overall
rate constant determination was tested at 1168 K by interchanging the branching ratios of
channels (9a) and (9b) while maintaining the overall value, and no discernible effect
could be observed from the simulated OH profiles. Hence, the original branching ratios
proposed by Dooley et al. [49] were kept in our simulations. In addition, Table 7.1
summarizes the overall rate constant measurements (k9 = k9a + k9b) of reaction (9) at T =
880-1344 K and P = 1.24-1.63 atm.
122
Figure 7.2: Sample methyl formate + OH rate constant measurement using the mixture of 322 ppm methyl formate with ~26 ppm TBHP (and 70 ppm water) in Ar at 1168 K and 1.40 atm. Simulation from the Dooley et al. mechanism [49] for the best-fit rate constant, along with perturbations of ±50%, is also shown.
Table 7.1: CH3OCHO + OH → Products: Rate Constant Data.
T5 [K] P5 [atm] k9 [cm3 mol-1 s-1]
96 ppm TBHP (and water), 322 ppm CH3OCHO, Ar 1337 1.36 5.87E+12 1315 1.25 5.60E+12 1264 1.28 4.98E+12 1229 1.37 4.81E+12 1168 1.40 4.26E+12 1114 1.39 3.99E+12 1024 1.51 3.50E+12 965 1.55 3.10E+12 913 1.63 2.81E+12 904 1.55 2.91E+12
101 ppm TBHP (and water), 404 ppm CH3OCHO, Ar 1344 1.27 5.85E+12 1289 1.24 5.62E+12 1124 1.37 4.04E+12 1060 1.44 3.66E+12 880 1.62 2.57E+12
123
A detailed error analysis was conducted to estimate the overall uncertainty of the
measured rate constant for reaction (9) at 1168 K. The primary contributions to the
overall uncertainty in k9 were considered: (a) temperature (±1%), (b) mixture
composition (±5%), (c) OH absorption coefficient (±3%), (d) wavemeter reading in the
UV (±0.01 cm-1), (e) fitting the data to the simulated profiles (±5%), (f) locating time-
zero (±0.5 µs), (g) the rate constant for CH3 + OH → CH2(s) + H2O (uncert. factor = 2),
(h) the rate constant for CH2O + OH → HCO + H2O (uncert. factor = 2), and (i) the rate
constant for C2H6 (+ M) → CH3 + CH3 (+ M) (±20%). As demonstrated in Figure 7.3,
the individual error sources were introduced separately (within the positive and negative
bounds of their 2σ uncertainties) and their effects on the overall rate constant for reaction
(9) were studied. These uncertainties were combined in a root-sum-squared method to
give an overall (2σ) uncertainty of ±24% at 1168 K. Similar error analyses were
performed for k9 at 913 K and 1289 K, and the overall uncertainties were estimated to be
±29% and ±18%, respectively.
Figure 7.3: Uncertainty analysis for the rate constant of methyl formate + OH → products at 1168 K and 1.40 atm.
Figure 7.4 presents the Arrhenius plot for the overall rate constant measurements
of reaction (9) at T = 880-1344 K, along with the estimated values proposed by Fisher et
124
al. [48] and Dooley et al. [49]. Note that two different mixture compositions (322 ppm
and 404 ppm methyl formate) were used to confirm that the current measurements are
weakly dependent on the secondary chemistry effects from the model, and the measured
values from these two mixtures are consistent with each other. The measured values can
be expressed in Arrhenius form as k9 = 2.56×1013 exp(-2026/T) cm3 mol-1 s-1 over 880-
1344 K. As is evident in Figure 7.4, the present measurements are in good agreement
with the estimated values from Fisher et al. and Dooley et al. within 10%, and the
activation energy from the present measurements seems to be slightly higher.
Interestingly, the estimated values from Fisher et al. and Dooley et al. are nearly identical
over 833-1150 K and start to deviate at higher temperatures (T > 1150 K). It also appears
that the estimated overall rate constant from Fisher et al. is in better agreement with the
present measurements at T > 1150 K.
Recently, Tan et al. [130] performed a systematic ab initio quantum mechanical
investigation of the H-atom abstraction reactions for methyl formate by five radicals: H,
CH3, O, HO2, and OH. They employed a multi-reference correlated wave function
method (the CBS-MRSDCI composite scheme) including size-extensivity corrections to
calculate the barrier heights and reaction enthalpies of these H-atom abstraction reactions.
The rate constants for these H-atom abstraction reactions were computed using transition
state theory within the separable-hindered-rotor approximation for torsions and the
harmonic oscillator approximation for other vibrational modes [130]. As illustrated in
Figure 7.4, the calculated overall rate constant for reaction (9) from Tan et al. [130] is
substantially lower than the present measurements and the estimated values from Fisher
et al. [48] and Dooley et al. [49] (by a factor of 2.2 at 1250 K and a factor of 4.8 at 850
K). To investigate this large discrepancy between the present measurements and the
theoretical calculation, the rate constants for the reactions of H, CH3, O, and HO2 with
methyl formate in the Dooley et al. mechanism [49] were first updated with the
expressions provided by Tan et al. [130]. The overall rate constant for reaction (9) was
then reexamined by matching the measured OH time histories with the simulated profiles
from the detailed mechanism, and the same measured rate constant expression (as the one
provided previously) was obtained. This indicates that our rate constant measurements
125
are insensitive to the H-atom abstraction reactions for methyl formate by other species
(i.e., H, CH3, O, and HO2), and also that the theoretical calculations for these H-atom
abstraction reactions may require further review.
Figure 7.4: Arrhenius plot for methyl formate + OH (k9) at temperatures above 833 K.
7.3.3 Methyl Acetate (MA) + OH Kinetics
The reaction of OH with methyl acetate consists of 2 different channels:
CH3OC(O)CH3 + OH → CH3OC(O)CH2 + H2O (10a)
CH3OC(O)CH3 + OH → CH2OC(O)CH3 + H2O (10b)
The branching ratios of channels (10a) and (10b) are 0.14 and 0.86, respectively, at 1091
K, based on the estimated values from the Dooley et al. mechanism [49]. Note that the
sub-mechanism for methyl acetate adopted in the Dooley et al. mechanism was
previously developed by Westbrook et al. [53]. In the development of the methyl acetate
sub-mechanism from Westbrook et al., the rate constant for channel (10b) (the H-atom
abstraction from the methyl group bound to the O-atom in the ester group) was taken
directly from that of the structurally similar methyl group in methyl butanoate (developed
by Fisher et al. [48]). In addition, the bond strength of the C–H bond adjacent to the
carbonyl group is 97.7 kcal/mol (at 298 K), which is similar to that of a tertiary C–H
126
bond in methylcyclohexane. Thus, the rate constant for channel (10a) (per H-atom) was
first assumed to be the same as the rate constant for the tertiary C–H bond in
methylcyclohexane. Channel (10a) produces the CH3OC(O)CH2 radical, followed by the
formation of ketene (CH2CO) and methoxy radical (CH3O) via β-scission. Concurrently,
the methoxy radical can react with CH3 to form dimethyl ether. When compared with
their flame measurements [53], the model predicted excessively high levels of ketene and
dimethyl ether, which suggested the need to reduce the rate constant for channel (10a).
Consequently, the rate constant for channel (10a) was reduced by a factor of 10 to match
their experimental data.
The OH sensitivity analysis was performed for the overall rate constant
determination (k10 = k10a + k10b) of reaction (10) using the mixture of 384 ppm methyl
acetate with 28.5 ppm TBHP (and 73.5 ppm water) diluted in argon at 1091 K and 1.37
atm. As illustrated in Figure 7.5, the analysis shows that reaction (10) is the dominant
reaction over the time frame of the experiment, with some minor interference from
reactions (13), (17), (18), and (30). Note that the TBHP decomposition reaction (reaction
(13)) becomes more important at the early times as temperature decreases.
Figure 7.5: OH sensitivity plot for the rate constant measurement of methyl acetate + OH at 1091 K and 1.37 atm.
127
Figure 7.6 shows a sample OH time history measurement for the mixture of 384
ppm methyl acetate in argon at 1091 K and 1.37 atm, and the measured peak OH mole
fraction is ~28.5 ppm. Thus, we inferred that the initial TBHP mole fraction was around
28.5 ppm, and there was approximately 73.5 ppm H2O. As illustrated in Figure 7.6, a
best-fit overall rate constant for reaction (10) of 3.93×1012 cm3 mol-1 s-1 was obtained
between the experiment and the simulation using the Dooley et al. mechanism [49]. In
addition, the simulations with the variations of ±50% in the inferred rate constant are
shown in Figure 7.6. The same test (as the test for methyl formate) was performed at
1091 K to confirm that the branching ratios have negligible influence on the overall rate
constant determination of reaction (10). Thus, the original branching ratios from
Westbrook et al. [53] were maintained in our simulations. Table 7.2 summarizes the
present overall rate constant measurements of reaction (10) at T = 876-1371 K and P =
1.25-1.60 atm.
Figure 7.6: Sample methyl acetate + OH rate constant measurement using the mixture of 384 ppm methyl acetate with ~28.5 ppm TBHP (and 73.5 ppm water) in Ar at 1091 K and 1.37 atm. Simulation from the Dooley et al. mechanism [49] for the best-fit rate constant, along with perturbations of ±50%, is also shown.
128
Table 7.2: CH3OC(O)CH3 + OH → Products: Rate Constant Data.
T5 [K] P5 [atm] k10 [cm3 mol-1 s-1]
100 ppm TBHP (and water), 323 ppm CH3OC(O)CH3, Ar 1371 1.25 5.88E+12 1258 1.29 5.09E+12 1160 1.36 4.33E+12 1078 1.44 3.74E+12 1028 1.50 3.41E+12
102 ppm TBHP (and water), 384 ppm CH3OC(O)CH3, Ar
1299 1.27 5.39E+12 1215 1.34 4.91E+12 1126 1.36 4.40E+12 1091 1.37 3.93E+12 1017 1.43 3.29E+12 961 1.54 2.82E+12 930 1.58 2.63E+12 907 1.59 2.38E+12 876 1.60 2.18E+12
Figure 7.7 presents the Arrhenius plot for the current overall rate constant
measurements of reaction (10) over the temperature range of 876-1371 K, along with the
estimated values proposed by Westbrook et al. [53]. Note that the measured values from
two different mixture compositions (323 ppm and 384 ppm methyl acetate) were
compared and were found to be consistent with each other. These measured values can
be expressed in Arrhenius form as k10 = 3.59×1013 exp(-2438/T) cm3 mol-1 s-1 over 876-
1371 K. Detailed error analyses were carried out with the consideration of experimental
and mechanism-induced contributions, and the overall (2σ) uncertainties in k10 were
estimated to be ±29% at 930 K, ±23% at 1091 K, and ±17% at 1299 K. As illustrated in
Figure 7.7, the activation energy of reaction (10) inferred from the present measurements
is higher than that of Westbrook et al. [53]. The estimated value from Westbrook et al. is
approximately 30% lower than the current data at 1371 K, while the estimated values are
in good agreement with the current data (within 8%) over a limited temperature range of
876-960 K.
129
Moreover, theoretical studies of the reactions of OH with ethers (dimethyl, ethyl
methyl, and isopropyl methyl ethers) and ketones (dimethyl, ethyl methyl, and isopropyl
methyl ketones) were performed by Zhou et al. [121, 131] using the computationally less-
expensive methods of G3 and G3MP2BH&H to calculate the energy barriers and using
the Variflex code including Eckart tunneling corrections to compute the total rate
constants over 500-2000 K. They also provided the expressions of the group rate
constants (per H-atom) for three different carbon sites (primary, secondary, and tertiary
carbon atoms) adjacent to the ether group (–O–) and the carbonyl group (–C(O)–). In the
present analysis, we can estimate the overall rate constant for reaction (10) using the
group rate constants provided by Zhou et al. [121, 131], and the estimated overall rate
constant is k10 = 3 × k(CH3O) + 3 × k(CH3C(O)), where k(CH3O) and k(CH3C(O)) are
the group rate constants (per H-atom) for primary carbon sites adjacent to the ether group
and the carbonyl group, respectively. As illustrated in Figure 7.7, the estimated values
are at least 60% higher than the present measurements, but the estimation seems to
capture the temperature dependence of reaction (10) reasonably well.
Figure 7.7: Arrhenius plot for methyl acetate + OH (k10) at temperatures above 833 K.
130
7.3.4 Methyl Propanoate (MP) + OH Kinetics
The reaction of OH with methyl propanoate is comprised of 3 different channels:
CH3OC(O)C2H5 + OH → C2H4 + CH3OCO + H2O (11a)
CH3OC(O)C2H5 + OH → CH3CHCO + CH3O + H2O (11b)
CH3OC(O)C2H5 + OH → C2H5CO + CH2O + H2O (11c)
Channel (11a) is the H-atom abstraction reaction from methyl propanoate at the β
position (on the same side of the carbonyl group), and channel (11b) is the H-atom
abstraction reaction from methyl propanoate at the α position. In addition, channel (11c)
is the H-atom abstraction reaction from methyl propanoate at the methyl group bound to
the O-atom in the ester group. Note that the Dooley et al. mechanism of NUI Galway
[54], which was originally developed for methyl butanoate oxidation, was used to model
the OH consumption from methyl propanoate. Unfortunately, the mechanism does not
contain a sub-mechanism for methyl propanoate. In the present analysis, we assumed
that the fuel radicals formed right after the H-atom abstraction reactions would
decompose immediately into the (relatively) stable products through β-scission. For
instance, channel (11a) forms a CH3OC(O)CH2CH2 radical and a H2O molecule, and the
CH3OC(O)CH2CH2 radical is rather short-lived and will further decompose to form C2H4
and CH3OCO through β-scission. Similar treatments were applied to channels (11b) and
(11c). Due to the structure similarity between methyl propanoate and ethyl propanoate,
the rate constants for channels (11a) and (11b) were first assumed to be the same as the
rate constants for the reactions of OH with ethyl propanoate at the β and α sites,
respectively, which were taken from the Metcalfe et al. mechanism of NUI Galway [132].
In addition, the rate constant for channel (11c) was first assumed to be the same as the
rate constant for the reaction of OH with methyl butanoate at the methyl group bound to
the O-atom in the ester group, which was taken directly from the Dooley et al.
mechanism [54]. The resulting branching ratios of channels (11a)-(11c) at 1208 K are
0.20, 0.31, and 0.49, respectively. These 3 channels, along with their corresponding rate
constants, were then incorporated into the Dooley et al. mechanism [54].
131
The reaction of H-atom with methyl propanoate was also considered in the
present study. Similar to the reaction of OH with methyl propanoate, it consists of 3
different channels:
CH3OC(O)C2H5 + H → C2H4 + CH3OCO + H2 (31a)
CH3OC(O)C2H5 + H → CH3CHCO + CH3O + H2 (31b)
CH3OC(O)C2H5 + H → C2H5CO + CH2O + H2 (31c)
Channel (31a) describes the H-atom abstraction at the β position, and channel (31b)
describes the H-atom abstraction at the α position. In addition, channel (31c) describes
the H-atom abstraction at the methyl group bound to the O-atom in the ester group.
Similarly, the rate constants for channels (31a) and (31b) were assumed to be the same as
the rate constants for the reactions of H with ethyl propanoate at the β and α sites,
respectively, which were also taken from Metcalfe et al. [132]. Additionally, the rate
constant for channel (31c) was assumed to be the same as the rate constant for the
reaction of H with methyl butanoate at the methyl group bound to the O-atom in the ester
group, which was also taken from Dooley et al. [54]. It is important to note that the
simulated OH profiles of the present study are effectively insensitive to channels (31a)-
(31c); hence, the computed OH profiles are nearly identical with and without the addition
of these 3 channels. This conclusion is expected as there are very few H-atoms available
in the initial test mixtures. Nevertheless, channels (31a)-(31c) were included in the
Dooley et al. mechanism [54] for completeness.
The OH sensitivity analysis was performed for the overall rate constant
determination (k11 = k11a + k11b + k11c) of reaction (11) using the mixture of 281 ppm
methyl propanoate with 22 ppm TBHP (and 68 ppm H2O) in Ar at 1208 K and 1.33 atm.
As demonstrated in Figure 7.8, the analysis reveals that the OH time history is
predominantly sensitive to reaction (11) over the time frame of the experiment. There is
also some minor interference from the secondary reactions (reactions (17), (19), and
(30)).
132
Figure 7.8: OH sensitivity plot for the rate constant measurement of methyl propanoate + OH at 1208 K and 1.33 atm.
Figure 7.9 shows a representative OH time history measurement for the mixture
of 281 ppm methyl propanoate in Ar at 1208 K and 1.33 atm, and the measured peak OH
mole fraction is ~22 ppm. Thus the initial TBHP mole fraction was approximately 22
ppm and the initial water mole fraction was around 68 ppm. As is evident in Figure 7.9,
a best-fit overall rate constant for reaction (11) of 8.01×1012 cm3 mol-1 s-1 was used to
match the experimental data with the computed profile, and the simulations for the
variations of ±50% in the inferred rate constant are also shown. Concurrently, the effect
of the branching ratios on k11 was found to be negligible at 1208 K (by interchanging the
branching ratios of channels (11b) and (11c) while maintaining the total value). Thus, the
original branching ratios based on the structure similarity were kept in our simulations.
Moreover, Diévart et al. [46] have recently developed a methyl propanoate sub-
mechanism, which includes the unimolecular decomposition reactions and the H-atom
abstraction reactions for methyl propanoate. This sub-mechanism was also implemented
into the Dooley et al. mechanism [54], and the thermodynamic parameters for the fuel
radicals from methyl propanoate (provided by Diévart et al.) were also added to the
thermo database of Dooley et al. Interestingly, near-identical results were found with and
without the use of the detailed sub-mechanism for methyl propanoate. Hence, the present
measurements are insensitive to the secondary chemistry effects strictly from methyl
133
propanoate. In addition, Table 7.3 summarizes the overall rate constant measurements of
reaction (11) over the temperature range of 909-1341 K at pressures of 1.23-1.58 atm.
Figure 7.9: Sample methyl propanoate + OH rate constant measurement using the mixture of 281 ppm methyl propanoate with ~22 ppm TBHP (and 68 ppm water) in Ar at 1208 K and 1.33 atm. Simulation from the Dooley et al. mechanism [54] for the best-fit rate constant, along with variations of ±50%, is also shown.
Table 7.3: CH3OC(O)C2H5 + OH → Products: Rate Constant Data.
T5 [K] P5 [atm] k11 [cm3 mol-1 s-1] 90 ppm TBHP (and water), 281 ppm CH3OC(O)C2H5, Ar
1341 1.26 1.01E+13 1208 1.33 8.01E+12 1124 1.39 6.70E+12 1049 1.36 5.81E+12 954 1.58 4.76E+12
91 ppm TBHP (and water), 283 ppm CH3OC(O)C2H5, Ar 1289 1.26 9.58E+12 1252 1.27 8.67E+12 1200 1.23 8.08E+12 1181 1.30 7.79E+12 1016 1.44 5.37E+12 909 1.52 4.11E+12
134
Figure 7.10 presents the Arrhenius plot for the present overall rate constant
measurements of reaction (11) over the temperature range of 909-1341 K, along with the
estimated values used by Diévart et al. [46]. The measured values can be expressed in
Arrhenius form as k11 = 6.65×1013 exp(-2539/T) cm3 mol-1 s-1 over 909-1341 K. Detailed
error analyses were conducted with the consideration of experimental and mechanism-
induced contributions, and the overall (2σ) uncertainties in k11 were estimated to be
±25% at 909 K, ±21% at 1208 K, and ±17% at 1341 K. It is also interesting to note that
the estimated rate constants for channels (11a)-(11c) provided by Diévart et al. are
exactly identical to our initial approximations for these three rate constants. Thus,
Diévart et al. employed the same type of approximation to estimate the rate constants for
the H-atom abstraction reactions based on the structure similarity between methyl
propanoate and ethyl propanoate. However, the estimated value is ~53% higher than the
measured value at 1341 K, and is higher than the data by at least a factor of 2 at 909 K.
Additionally, the activation energy of reaction (11) inferred from the present
measurements is higher than that of the estimation from Diévart et al. This demonstrates
the importance of direct rate constant measurements in validating the current estimation
methods in the literature. Moreover, Figure 7.10 presents the estimated overall rate
constant for reaction (11) using the group rate constants for the reactions of OH with
ethers and ketones provided by Zhou et al. [121, 131]. Interestingly, the estimated values
are at least 65% higher than the current data, but the estimation appears to capture the
temperature dependence of reaction (11) reasonably well.
135
Figure 7.10: Arrhenius plot for methyl propanoate + OH (k11) at temperatures above 870 K.
7.3.5 Methyl Butanoate (MB) + OH Kinetics
The reaction of OH with methyl butanoate consists of 4 different channels, which
are:
CH3OC(O)C3H7 + OH → CH3OC(O)CH2CH2CH2 + H2O (12a)
CH3OC(O)C3H7 + OH → CH3OC(O)CH2CHCH3 + H2O (12b)
CH3OC(O)C3H7 + OH → CH3OC(O)CHCH2CH3 + H2O (12c)
CH3OC(O)C3H7 + OH → CH2OC(O)C3H7 + H2O (12d)
Channels (12a)-(12c) describe the H-atom abstraction from methyl butanoate at the γ, β,
and α positions, respectively. In addition, channel (12d) describes the H-atom
abstraction from methyl butanoate at the methyl group bound to the O-atom in the ester
group. On the basis of the Dooley et al. mechanism [54], the resulting branching ratios of
channels (12a)-(12d) are 0.15, 0.24, 0.25, and 0.36, respectively, at 1133 K. In their
analysis, the rate constants for channels (12a)-(12d) were estimated based on the nature
of the C–H bonds (primary, secondary, or tertiary carbon atoms), and were strictly based
on a study of methylcyclohexane (MCH) oxidation from Orme et al. [133]. The rate
constant for channel (12a) was assumed to be the same as the rate constant for the
136
reaction of MCH + OH → CYCHEXCH2 + H 2O, and the rate constant for channel (12b)
was assumed to be the same as the rate constant for the reaction of MCH + OH → MCH -
R4 + H2O. The chemical notations for the fuel radicals formed from the reactions of OH
with MCH are taken directly from Orme et al. [133], as illustrated in Figure 7.11. In
addition, due to the weaker C–H bond enthalpy, the carbon atom attached to the carbonyl
group (at the α position) was treated as a tertiary carbon atom, and the corresponding rate
constant for channel (12c) (per H-atom) was taken from the rate constant for the reaction
of MCH + OH → MCH -R1 + H2O. Similarly, the carbon atom at the methyl group
bound to the O-atom in the ester group was treated as a secondary carbon atom, and the
corresponding rate constant for channel (12d) (per H-atom) was taken from the rate
constant for the reaction of MCH + OH → MCH-R4 + H2O (per H-atom).
Figure 7.11: Chemical notations for fuel radicals from MCH + OH reactions used by Orme et al. [133].
Figure 7.12 shows the OH sensitivity analysis for the mixture of 241 ppm methyl
butanoate with 20 ppm TBHP (and 60 ppm H2O) in argon at 1133 K and 1.37 atm.
Similarly, the analysis reveals that reaction (12) is the dominant reaction pathway over
the time frame of the experiment, with some minor interference from the secondary
reactions (reactions (17)-(19)).
137
Figure 7.12: OH sensitivity plot for the rate constant measurement of methyl butanoate + OH at 1133 K and 1.37 atm.
Figure 7.13 shows a sample OH time history measurement for the mixture of 241
ppm methyl butanoate in Ar at 1133 K and 1.37 atm, and the measured peak OH mole
fraction is ~20 ppm. Based on the measured peak OH yield, the initial TBHP mole
fraction was ~20 ppm and the initial H2O mole fraction was around 60 ppm. As
illustrated in Figure 7.13, a best-fit overall rate constant (k12 = k12a + k12b + k12c + k12d) of
1.17×1013 cm3 mol-1 s-1 was used to match the experimental data with the simulated
profile from the Dooley et al. mechanism [54]. Additionally, the simulations for the
variations of ±50% in the inferred rate constant are also shown. Similar to the previous
methyl esters, the branching ratios of reaction (12) have negligible influence on the
overall rate constant determination at the present experimental conditions. This was also
confirmed by interchanging the branching ratios of channels (12a) and (12d) while
maintaining the total value at 1133 K. Moreover, Table 7.4 summarizes the present
overall rate constant measurements of reaction (12) over the temperature range of 897-
1355 K at pressures of 1.23-1.59 atm.
138
Figure 7.13: Sample methyl butanoate + OH rate constant measurement using the mixture of 241 ppm methyl butanoate with ~20 ppm TBHP (and 60 ppm water) in Ar at 1133 K and 1.37 atm. Simulation from the Dooley et al. mechanism [54] for the best-fit rate constant, along with variations of ±50%, is also shown.
Table 7.4: CH3OC(O)C3H7 + OH → Products: Rate Constant Data.
T5 [K] P5 [atm] k12 [cm3 mol-1 s-1] 80 ppm TBHP (and water), 241 ppm CH3OC(O)C3H7, Ar
1303 1.27 1.65E+13 1225 1.30 1.40E+13 1181 1.32 1.30E+13 1133 1.37 1.17E+13 1016 1.48 9.38E+12 897 1.59 6.85E+12
85 ppm TBHP (and water), 270 ppm CH3OC(O)C3H7, Ar
1355 1.23 1.87E+13 1320 1.23 1.71E+13 1262 1.27 1.56E+13 1062 1.44 1.02E+13 961 1.53 8.50E+12 925 1.57 7.74E+12
139
Figure 7.14 shows the Arrhenius plot for the present overall rate constant
measurements of reaction (12) over the temperature range of 897-1355 K, along with the
estimated values from Fisher et al. [48], Dooley et al. [54], and Hakka et al. [55]. Note
that two different mixture compositions were employed to verify that the current rate
constant evaluations are weakly dependent on the secondary chemistry effects, and the
measured values from these two mixtures agree well with each other. These measured
values can be expressed in Arrhenius form as k12 = 1.13×1014 exp(-2515/T) cm3 mol-1 s-1
over 897-1355 K. Similar detailed error analyses were also carried out with the
consideration of experimental and mechanism-induced contributions, and the overall (2σ)
uncertainties in k12 were estimated to be ±24% at 925 K, ±20% at 1133 K, and ±16% at
1320 K. As is evident in Figure 7.14, the estimated rate constants adopted in three
different detailed mechanisms are quite different from each other. In particular, the
estimated value from Fisher et al. [48] is lower than the values from Dooley et al. [54]
and Hakka et al. [55] by approximately 40% and 83%, respectively, at 1133 K.
Interestingly, the temperature dependence of these rate constants seems to be consistent
with each other.
Table 7.5 shows a comparison of the rate constants for channels (12a)-(12d)
employed in these three mechanisms at 1133 K and 1300 K. The rate constants for
channels (12a)-(12c) proposed by Fisher et al. and Dooley et al. are nearly identical, but
the rate constant for channel (12d) from Fisher et al. is lower than that of Dooley et al. by
a factor of 2.48 at 1133 K. Fisher et al. treated the rate constant for channel (12d) the
same as the rate constant for channel (12a). On the other hand, Dooley et al. proposed
that channel (12d) should be more reactive than channel (12a) due to the weaker C–H
bond enthalpy at the methyl group bound to the O-atom. Interestingly, the rate constants
for channels (12a)-(12d) proposed by Hakka et al. are consistently higher than those of
Fisher et al. As illustrated in Figure 7.14, the present measurements display somewhat
higher activation energy than the previous estimations. Of all three estimations, the
values from Fisher et al. seem to be in closer agreement with the present measurements.
The measured rate constant is ~17% higher than the value from Fisher et al. at 1355 K,
and is ~35% lower at 897 K. Furthermore, Figure 7.14 presents the estimated overall rate
140
constant for reaction (12) using the group rate constants for the reactions of OH with
ethers and ketones developed by Zhou et al. [121, 131], as was done for reactions (10)
and (11). The estimated values are at least 27% higher than the current data, but it
appears that the estimation captures the temperature dependence of reaction (12) very
well.
Figure 7.14: Arrhenius plot for methyl butanoate + OH (k12) at temperatures above 870 K.
Table 7.5: Comparison of the rate constants for channels (12a)-(12d) from Fisher et al. [48], Dooley et al. [54], and Hakka et al. [55] at 1133 K and 1300 K.
Authors A [cm3 mol-1 s-1] b EA
[cal/mol] 1133 K rate
1300 K rate
Ratio (1133 K) to
Fisher et al. CH3OC(O)C3H7 + OH → CH3OC(O)CH2CH2CH2 + H2O Fisher et al. 5.250E+09 0.97 1590 2.376E+12 2.973E+12 1.00 Dooley et al. 5.280E+09 0.97 1586 2.394E+12 2.995E+12 1.01 Hakka et al. 2.700E+06 2.00 450 2.838E+12 3.833E+12 1.19
CH3OC(O)C3H7 + OH → CH3OC(O)CH2CHCH3 + H2O Fisher et al. 4.680E+07 1.61 -35 3.929E+12 4.893E+12 1.00 Dooley et al. 4.680E+07 1.61 -35 3.929E+12 4.893E+12 1.00 Hakka et al. 2.600E+06 2.00 -765 4.689E+12 5.909E+12 1.19
CH3OC(O)C3H7 + OH → CH3OC(O)CHCH2CH3 + H2O Fisher et al. 1.146E+11 0.51 63 4.024E+12 4.332E+12 1.00
141
Dooley et al. 1.146E+11 0.51 63 4.024E+12 4.332E+12 1.00 Hakka et al. 2.400E+06 2.00 -2450 9.153E+12 1.048E+13 2.27
CH3OC(O)C3H7 + OH → CH2OC(O)C3H7 + H2O Fisher et al. 5.250E+09 0.97 1590 2.376E+12 2.973E+12 1.00 Dooley et al. 7.020E+07 1.61 -35 5.894E+12 7.340E+12 2.48 Hakka et al. 3.600E+06 2.00 -100 4.831E+12 6.324E+12 2.03
7.4 Comparison with Low Temperature Data
Figure 7.15 presents the current high-temperature data for the reactions of OH
with four small methyl esters, along with some earlier experimental work [134-138] at
low temperatures (250-440 K). At a first glance, these kinetic data cannot be described
accurately by simple Arrhenius expressions over a wide range of temperatures. Le Calvé
et al. [134] measured the rate constants for the reactions of OH with a series of formates
(including methyl formate) under pseudo-first-order kinetic conditions using the pulsed
laser photolysis–laser induced fluorescence technique in a reaction cell over 233-372 K,
as illustrated in Figure 7.15a. Surprisingly, they suggested that the H-atom abstraction
from the –OC(O)H group (channel (9a)) is negligible over their temperature range
studied, and their suggestion is very different from the observation based on the high-
temperature measurements. Similarly, Wallington et al. [135] measured the rate constant
for reaction (9) at room temperature (296 K) under pseudo-first-order kinetic conditions
using the flash photolysis–resonance fluorescence technique in a reaction cell, and their
room temperature rate constant is ~24% higher than that of Le Calvé et al. [134]. As
mentioned previously, the estimated rate constants for reaction (9) from Fisher et al. [48]
and Dooley et al. [54] are in good agreement with the present high-temperature data.
However, neither of them can predict the low-temperature data from Le Calvé et al. and
Wallington et al. For instance, the value from Fisher et al. is higher than the measured
room temperature data by a factor of 2.8, and the value from Dooley et al. is lower than
the data by a factor of 2.2. Additionally, the estimated rate constant from Fisher et al.
seems to exhibit more non-Arrhenius curvature than that of Dooley et al., as illustrated in
Figure 7.15a.
142
As shown in Figure 7.15b, Wallington et al. [135] studied reaction (10) under
pseudo-first-order kinetic conditions over the temperature range of 240-440 K. El
Boudali et al. [136] measured the absolute rate constants for the reactions of OH with a
series of acetates (including methyl acetate) using the pulsed laser photolysis–laser
induced fluorescence technique in the cell over 243-372 K, and their measurements are
consistent with the data from Wallington et al. [135]. Similarly, the estimated rate
constant for reaction (10) from Westbrook et al. [53] cannot accurately predict the present
high-temperature data and the previous low-temperature data. The value from Westbrook
et al. is ~30% lower than the present data at 1371 K, and is ~77% higher than the
previous data at 333 K.
Figures 7.15c and 7.15d present the experimental results for the rate constant
measurements of reactions (11) and (12), respectively, at temperatures above 250 K. Le
Calvé et al. [138] measured the absolute rate constants for the reactions of OH with
methyl propanoate, methyl butanoate, methyl valerate, and methyl caproate using the
pulsed laser photolysis–laser induced fluorescence technique in the cell over 253-372 K.
They concluded that the reaction of OH with methyl caproate was the most reactive one
among those 4 methyl esters due to more –CH2– groups available in the molecule. In
addition, their rate constant measurements exhibited slight negative temperature
dependence, except for methyl propanoate. Wallington et al. [135] also measured the
room temperature rate constants for reactions (11) and (12), and their results agree well
with the data from Le Calvé et al. [138] at 296 K. Furthermore, the estimated rate
constants for reactions (11) and (12) from several detailed kinetic mechanisms [46, 48,
54-55] are rather different from the measurements over the temperature range of 250-
1355 K.
143
Figure 7.15: Arrhenius plots for methyl ester + OH reactions at temperatures above 250 K.
7.5 Comparison with Structure-Activity Relationship
Similar to the reactions of OH with ketones, the present high-temperature overall
rate constant measurements for reactions (9)-(12) can also be compared with the
estimations using the structure-activity relationship (SAR) developed by Atkinson and
co-workers [127-129]. For instance, the estimated rate constant for the reaction of OH
with methyl propanoate using SAR can be expressed as k11 = kprimF(–OC(O)R) + ksecF(–
C(O)OR)F(–CH3) + kprimF(–CH2–), where R is defined as the alkyl group. As
demonstrated in Figure 7.15, the SAR estimations for reactions (9)-(12) cannot accurately
predict the present high-temperature measurements. More importantly, the SAR
estimation for the reaction of OH with methyl formate requires some additional attention.
Le Calvé et al. [134] suggested that the H-atom abstraction from the –OC(O)H group
144
(channel (9a)) is negligible for the methyl formate + OH reaction over 233-372 K. The
SAR estimation without the consideration of channel (9a) seems to agree well with the
room temperature measurements from Le Calvé et al. [134] and Wallington et al. [135],
but the estimated values are ~40% lower than the present high-temperature data. Hence,
there is a need to consider the effect of channel (9a) in the SAR estimation at high
temperatures. In the present analysis, we could treat the C–H bond in the –OC(O)H
group as a tertiary site, and the estimated rate constant for reaction (9) can be expressed
as k9 = ktertF(=O)F(–OR) + kprimF(–OC(O)H), where R is the alkyl group. The present
SAR estimation with the consideration of channel (9a) is ~25% higher than the current
high-temperature data, but the estimated values are quite different from the previous low-
temperature measurements [134-135]. Similarly, the SAR estimations show good
agreement with the kinetic measurements of reactions (10)-(12) at 298 K, but the
estimated values are higher than the measured values over 333-1371 K. In particular, the
estimated values are ~25% faster than the current rate constant measurements of reactions
(10)-(12) over 876-1371 K. Interestingly, the SAR estimations seem to capture the
temperature dependence of reactions (9)-(12) reasonably well, implying that the pre-
exponential factors for the group rate constants kprim, ksec, and ktert should be reduced by
25%, particularly for these methyl ester + OH reactions. The modified SAR estimations
are in excellent agreement with the present high-temperature measurements, as shown in
Figure 7.16. Note that the measured rate constants for reactions (9) and (10) are nearly
identical at T > 1000 K, but they start to deviate at lower temperatures. The data for
reaction (9) is ~16% higher than the data for reaction (10) at T = 880 K. This trend is
also well-captured by the modified SAR estimations, as demonstrated in Figure 7.16.
145
Figure 7.16: Comparison of the present rate constant measurements with the modified SAR estimations.
7.6 Summary
The overall rate constants for the reactions of OH with methyl formate (k9),
methyl acetate (k10), methyl propanoate (k11), and methyl butanoate (k12) were measured
using OH laser absorption near 306.69 nm behind reflected shock waves over 876-1371
K at pressures near 1.5 atm. These measured rate constants can be expressed in
Arrhenius form as:
k9 = 2.56×1013 exp(-2026/T) cm3 mol-1 s-1
k10 = 3.59×1013 exp(-2438/T) cm3 mol-1 s-1
k11 = 6.65×1013 exp(-2539/T) cm3 mol-1 s-1
k12 = 1.13×1014 exp(-2515/T) cm3 mol-1 s-1
over the temperature ranges studied. Detailed error analyses were conducted with the
consideration of both experimental and secondary chemistry contributions, and the
overall (2σ) uncertainties were estimated to be ±29% at 913 K and ±18% at 1289 K for
k9, ±29% at 930 K and ±17% at 1299 K for k10, ±25% at 909 K and ±17% at 1341 K for
k11, and ±24% at 925 K and ±16% at 1320 K for k12. Additionally, the structure-activity
relationship (SAR) developed by Atkinson and co-workers [127-129] was utilized to
146
estimate the overall rate constants for reactions (9)-(12), and the estimated values are
consistent with the current data (within ~25%).
147
Chapter 8 Conclusions and Future Work
8.1 Summary of Results
The objective of the research presented in this dissertation is to provide reliable
experimental kinetic targets, including ignition delay times, species time histories, and
direct reaction rate constant measurements, using shock tube and laser absorption
methods in order to validate and refine the comprehensive reaction mechanisms for two
different types of oxygenated fuels (i.e., ketones and methyl esters) and to reexamine the
kinetics of the H2 + OH reaction. The topics of this work are mainly divided into three
sections: (1) H2 + OH kinetics, (2) ketone combustion chemistry, and (3) methyl ester +
OH kinetics. Consequently, this work provides accurate rate constant measurements of
reactions (1)-(12), including H2 + OH, ketone decomposition, ketone + OH, and methyl
ester + OH reactions, that are practically important to oxygenated fuel combustion.
These measured rate constants are summarized here.
8.1.1 H2 + OH Kinetics
The rate constant for the reaction of H2 + OH → H 2O + H was measured behind
reflected shock waves using UV laser absorption of OH radicals near 306.69 nm over the
temperature range of 902-1518 K at pressures of 1.15-1.52 atm. The rate constant for
reaction (1) is given by:
k1(T) = 4.38 × 1013 exp(-3518/T) cm3 mol-1 s-1
148
over the temperature range studied. The overall uncertainties of reaction (1) were
estimated to be ±17% at 972 and 1228 K. The present measurements are in excellent
agreement with the previous experimental studies [17-21]. In addition, the measured rate
constant is in close accord with the non-Arrhenius expression from GRI-Mech 3.0 [22]
and the theoretical calculation using semi-classical transition state theory (SCTST) from
Nguyen et al. [84].
8.1.2 Ketone Combustion Chemistry
High-temperature acetone and 2-butanone pyrolysis studies were performed
individually behind reflected shock waves using five species time history measurements
(ketone, CO, CH3, CH4 and C2H4). Experimental conditions covered temperatures of
1100-1650 K at pressures around 1.6 atm, for mixtures of 0.25-1.5% acetone or 2-
butanone in argon. During acetone pyrolysis, the CO and acetone time histories were
found to be strongly sensitive to the rate constant for acetone unimolecular
decomposition reaction, and this could be directly determined from the measured CO and
acetone time histories, yielding:
k2(1.23-1.66 atm) = 9.38 × 1041 T-7.85 exp(-44,236/T) s-1
with an uncertainty of ±25%. The inferred rate constant is in good agreement with the
previous shock tube studies from Sato and Hidaka [87] and Saxena et al. [88] (within
30%) at temperatures above 1450 K, but is at least three times faster than the evaluation
from Sato and Hidaka at temperatures below 1250 K. Using the revised values for k2
with the detailed mechanism of Pichon et al. [89], the simulated profiles during acetone
pyrolysis showed excellent agreement with all five species time history measurements.
Similarly, the overall 2-butanone decomposition rate constant was inferred from
the measured 2-butanone time histories, yielding:
k3(1.39-1.62 atm) = 6.08×1013 exp(-31,762/T) s-1
with an uncertainty of ±35%. This rate constant is ~30% faster than that proposed by
Serinyel et al. [95] at 1119 K, and ~100% faster at 1412 K. Using the measured 2-
butanone and CO time histories and an O-atom balance analysis, a missing removal
149
pathway for methyl ketene was identified. The rate constant for the decomposition of
methyl ketene was assumed to be the same as the value for the ketene decomposition
reaction. Using the revised values for k3 and adding the methyl ketene decomposition
reaction to the Serinyel et al. mechanism [95], the simulated profiles during 2-butanone
pyrolysis were in better agreement with the measurements for all five species.
Moreover, high-temperature 3-pentanone pyrolysis and oxidation studies were
conducted behind reflected shock waves using laser-based species time history
measurements (3-pentanone, CH3, CO, C2H4, OH and H2O) and ignition delay time
measurements. The measured species time histories and ignition delay times were
compared to the simulations from the detailed kinetic mechanism of Serinyel et al. [98].
In particular, the overall 3-pentanone decomposition rate constant was determined from
the measured 3-pentanone and CH3 time histories during pyrolysis at temperatures of
1070-1530 K and pressures around 1.6 atm, yielding:
k4(1.32-1.75 atm) = 4.383×1049 T-10 exp(-44,780/T) s-1
with an uncertainty of ±35% over 1070-1330 K. The measured k4 was approximately 3.5
times faster than the value used by Serinyel et al. [98]. Using this revised overall 3-
pentanone decomposition rate constant and the additional methyl ketene decomposition
pathway, the modified mechanism was able to successfully simulate all six species time
histories, and showed a significant improvement in the predictions of ignition delay
times.
In addition to the thermal decomposition reactions, another important class of
reactions, which is pertinent to ketone combustion, is the H-atom abstraction reactions by
OH radicals. In this dissertation, the overall rate constants for the reactions of OH with a
series of ketones, namely acetone (k5), 2-butanone (k6), 3-pentanone (k7), and 2-
pentanone (k8), were measured using UV laser absorption of OH over the temperature
range of 870-1360 K at pressures of 1-2 atm. The measured rate constants for reactions
(5)-(8) are given by:
k5 = 3.30×1013 exp(-2437/T) cm3 mol-1 s-1
k6 = 6.35×1013 exp(-2270/T) cm3 mol-1 s-1
k7 = 9.29×1013 exp(-2361/T) cm3 mol-1 s-1
150
k8 = 7.06×1013 exp(-2020/T) cm3 mol-1 s-1
The overall uncertainties were estimated to be ±28% at 1148 K for k5, ±22% at 1039 K
for k6, ±20% at 1188 K for k7, and ±24% at 1186 K for k8. The measured rate constant
for acetone + OH reaction from the current study is consistent with three previous
experimental studies [77, 118-119] within ±20%. In this dissertation, we also presented
the first direct high-temperature rate constant measurements of 2-butanone + OH, 3-
pentanone + OH, and 2-pentanone + OH reactions. The measured values for 2-butanone
+ OH reaction are in close accord with the theoretical calculation from Zhou et al. [121],
and the measured values for 3-pentanone + OH reaction are in excellent agreement with
the estimates (by analogy with the H-atom abstraction rate constants from alkanes) from
Serinyel et al. [98].
8.1.3 Methyl Ester + OH Kinetics
The overall rate constants for the reactions of OH with methyl esters, namely
methyl formate (k9), methyl acetate (k10), methyl propanoate (k11), and methyl butanoate
(k12), were studied by monitoring the OH decays over the temperature range of 876-1371
K at pressures around 1.5 atm. These measured rate constants for reactions (9)-(12) are
given by:
k9 = 2.56×1013 exp(-2026/T) cm3 mol-1 s-1
k10 = 3.59×1013 exp(-2438/T) cm3 mol-1 s-1
k11 = 6.65×1013 exp(-2539/T) cm3 mol-1 s-1
k12 = 1.13×1014 exp(-2515/T) cm3 mol-1 s-1
over the temperature ranges studied. The overall uncertainties were found to be ±29% at
913 K and ±18% at 1289 K for k9, ±29% at 930 K and ±17% at 1299 K for k10, ±25% at
909 K and ±17% at 1341 K for k11, and ±24% at 925 K and ±16% at 1320 K for k12. We
believe these are the first direct high-temperature rate constant measurements for the
reactions of OH with these small methyl esters.
151
8.2 Publications
The work detailed in this dissertation has been published in the following papers:
1) K.-Y. Lam, D.F. Davidson, R.K. Hanson, “A shock tube study of H2 + OH → H2O +
H using OH laser absorption,” Int. J. Chem. Kinet. (2013), doi: 10.1002/kin.20771.
2) K.-Y. Lam, W. Ren, S.H. Pyun, A. Farooq, D.F. Davidson, R.K. Hanson, “Multi-
species time history measurements during high-temperature acetone and 2-butanone
pyrolysis,” Proc. Combust. Inst. 34 (2013) 607-615.
3) K.-Y. Lam, W. Ren, Z. Hong, D.F. Davidson, R.K. Hanson, “Shock tube
measurements of 3-pentanone pyrolysis and oxidation,” Combust. Flame 159 (2012)
3251-3263.
4) K.-Y. Lam, D.F. Davidson, R.K. Hanson, “High-temperature measurements of the
reactions of OH with a series of ketones: acetone, 2-butanone, 3-pentanone, and 2-
pentanone,” J. Phys. Chem. A 116 (2012) 5549-5559.
5) K.-Y. Lam, D.F. Davidson, R.K. Hanson, “High-temperature measurements of the
reactions of OH with small methyl esters: methyl formate, methyl acetate, methyl
propanoate, and methyl butanoate,” J. Phys. Chem. A 116 (2012) 12229-12241.
6) K.-Y. Lam, Z. Hong, D.F. Davidson, R.K. Hanson, “Shock tube ignition delay time
measurements in propane/O2/argon mixtures at near-constant-volume conditions,”
Proc. Combust. Inst. 33 (2011) 251-258.
The additional work that is not discussed in this dissertation has been published
elsewhere:
7) Z. Hong, D.F. Davidson, K.-Y. Lam, R.K. Hanson, “A shock tube study of the rate
constants of HO2 and CH3 reactions,” Combust. Flame 159 (2012) 3007-3013.
8) Z. Hong, K.-Y. Lam, R. Sur, S. Wang, D.F. Davidson, R.K. Hanson, “On the rate
constants of OH + HO2 and HO2 + HO2: A comprehensive study of H2O2 thermal
decomposition using multi-species laser absorption,” Proc. Combust. Inst. 34 (2013)
565-571.
152
9) Z. Hong, K.-Y. Lam, D.F. Davidson, R.K. Hanson, “Broad-linewidth laser
absorption measurements of oxygen between 211 and 235 nm at high temperatures,”
JQSRT 112 (2011) 2698-2703.
10) Z. Hong, K.-Y. Lam, D.F. Davidson, R.K. Hanson, “A comparative study of the
oxidation characteristics of cyclohexane, methylcyclohexane, and n-butylcyclohexane
at high temperatures,” Combust. Flame 158 (2011) 1456-1468.
11) W. Ren, K.-Y. Lam, S.H. Pyun, A. Farooq, D.F. Davidson, R.K. Hanson, “Shock
tube/laser absorption studies of the decomposition of methyl formate,” Proc.
Combust. Inst. 34 (2013) 453-461.
12) A. Farooq, W. Ren, K.-Y. Lam, D.F. Davidson, R.K. Hanson, C.K. Westbrook,
“Shock tube studies of methyl butanoate pyrolysis with relevance to biodiesel,”
Combust. Flame 159 (2012) 3235-3241.
13) S.H. Pyun, W. Ren, K.-Y. Lam, D.F. Davidson, R.K. Hanson, “Shock tube
measurements of methane, ethylene and carbon monoxide time-histories in DME
pyrolysis,” Combust. Flame (2013), doi: 10.1016/j.combustflame.2012.12.004.
14) D.F. Davidson, S.C. Ranganath, K.-Y. Lam, M. Liaw, Z. Hong, R.K. Hanson,
“Ignition delay time measurements of normal alkanes and simple oxygenates,” J.
Propul. Power 26 (2010) 280-287.
8.3 Recommendations for Future Work
8.3.1 Ethyl Radical Diagnostics and Decomposition Pathway
Ethyl radical (C2H5) is an important intermediate species formed during
oxygenated fuel combustion (e.g., 3-pentanone, n-butanol, and ethyl esters). It is rather
short-lived, and decomposes near-instantaneously to form an ethylene molecule (C2H4)
and an H atom. In particular, this decomposition reaction, C2H5 (+ M) → C2H4 + H (+
M), is of practical significance in all hydrocarbon combustion systems, and the
corresponding rate constant has an uncertainty factor of 2-3 (especially in the fall-off
range). This reaction has been primarily studied by researchers at relatively low
153
temperatures (<1100 K) [139-145], and the high-temperature values for this reaction were
poorly known and were extrapolated from the low-temperature data [146]. Hence,
reliable rate constant measurements at combustion-relevant conditions are definitely
needed in order to enhance our understanding of oxygenated fuel combustion.
To study the rate constant for the ethyl radical decomposition reaction, we need a
C2H5 radical precursor and a C2H5 diagnostic system to monitor its decay rates. C2H5
radical can be produced instantaneously upon shock-heating of ethyl iodide (C2H5I) or
azoethane (C2H5N2C2H5). Additionally, C2H5 radical is known to have a broad spectrum
over 200-260 nm, with peak absorption at around 216 and 245 nm [147-148]. During the
thermal decomposition of C2H5 radical, CH3 radical can be formed through a bimolecular
reaction of C2H5 + H → CH3 + CH3. More importantly, CH3 radical has a strong
absorption feature near 200-225 nm [65], and this feature is approximately four times
stronger than the absorption feature of C2H5 radical. To avoid the interference absorption
from CH3 radicals, the wavelength of 245 nm is preferred to monitor C2H5 species time
histories. C2H5 can be measured at 245 nm using the frequency-tripled output of near-
infrared radiation from the pulsed Ti:Sapphire laser (using third harmonic generation).
Unfortunately, the C2H4 molecule (a primary product formed from C2H5 decomposition)
also has a weak absorption feature over 200-250 nm. To account for this interference
absorption, C2H4 should be monitored simultaneously using cw fixed-wavelength laser
absorption at 10.532 µm with a CO2 laser source, and the interference absorption signal
from C2H4 can then be subtracted from the total absorption signal at 245 nm.
8.3.2 Methyl Ester Kinetics
Owing to the practical importance of biodiesel fuels, more experimental studies
are still needed for methyl ester combustion. Many of the reaction rate constants adopted
in the existing kinetic models are poorly known. In particular, the rate constants for the
H-atom abstraction reactions by H, CH3, and HO2 species, which are crucial to the
oxidation chemistry of methyl esters, have not been well studied experimentally and
theoretically. These estimated rate constants were strictly based on the rate constants
154
from other hydrocarbons. Therefore, accurate rate constant measurements of these
reactions are of great interest in the combustion community. Similar to the work
presented in Chapters 6 and 7, fast sources of H, CH3, and HO2 species at elevated
temperatures are required in order to perform these measurements. For instance, ethyl
iodide (C2H5I) and azomethane (CH3N2CH3) can be chosen as H and CH3 species
precursors, respectively. H atoms can be measured using atomic resonance absorption
spectrometry (ARAS) at the Lyman-α wavelength [51-52], while CH3 species can be
easily monitored at 216.6 nm using the frequency-quadrupled output of near-infrared
radiation from the pulsed Ti:Sapphire laser [63-65]. In this dissertation, we have
measured the overall rate constants for the reactions of OH with four small methyl esters.
This work can be further extended to larger methyl esters (i.e., methyl decanoate, a
proposed surrogate fuel for biodiesel).
Moreover, biodiesel fuels are comprised of 5 major components, which are
methyl palmitate (C17H34O2), methyl stearate (C19H38O2), methyl oleate (C19H36O2),
methyl linoleate (C19H34O2), and methyl linolenate (C19H32O2). Owing to the
complexities of these fuel molecules, there are very few experimental studies available in
the literature [43-44, 149-153], and only a few comprehensive kinetic mechanisms [41-
42] have been developed and validated against the existing data. The resulting
performance of these mechanisms is rather poor, and more accurate experimental data are
needed over a wide range of temperatures and pressures in order to evaluate and refine
these models. In particular, speciation (e.g., OH, CH3, CO, CO2, H2O, and CH2O) and
ignition delay time data can be acquired using different laser absorption methods at
Stanford, and can be used as the kinetic targets to provide very strong constraints on the
internal workings of the detailed mechanisms. Additionally, practical methyl esters have
very low vapor pressures, necessitating the use of the aerosol shock tube at Stanford. The
AST works by creating tiny aerosols from the fuels, drawing them into the shock tube,
evaporating them, and shock-heating them into ignition [43, 104].
155
Appendix A Shock Tube Ignition Delay Time Measurements in Propane/O2/Argon Mixtures at Near-Constant-Volume Conditions
Shock tube measurements of ignition delay times with high activation energies
are strongly sensitive to variations in reflected shock temperatures. At longer shock tube
test times, as are needed at low reaction temperatures, small gradual increases in pressure
(and simultaneous increases in temperature) that result from incident shock wave
attenuation and boundary layer growth can significantly shorten measured ignition delay
times. To obviate this pressure increase, we made use of a recently developed driver-
insert method of Hong et al. [154] that allows generation of near-constant-volume test
conditions for reflected-shock measurements. Using this method, we have measured
propane ignition delay times in a lean mixture (0.8% C3H8/ 8% O2/ Ar) over temperatures
between 980 and 1400 K and nominal pressures of 6, 24, and 60 atm, under both
conventional shock tube operation (with post-shock fractional pressure variation dP5/dt ~
1-7 %/ms) and near-constant-volume operation (with dP5/dt ~ 0%/ms). The near-
constant-volume ignition delay times provide a database for low-temperature propane
model development that is independent of non-ideal fluid flow and heat transfer effects.
Comparisons of these near-constant-volume measurements with predictions using the
JetSurF v1.0 mechanism of Sirjean et al. [155] and the Curran et al. mechanism of NUI
Galway [100] were performed. Ignition delay times measured with dP5/dt ~ 1-7 %/ms
156
were found to be significantly shorter (about 1/3 of the near-constant-volume values) at
the lowest temperatures and highest pressures studied. However, these ignition times are
successfully simulated using the JetSurF v1.0 mechanism when an appropriate
gasdynamic model that accounts for changes in pressure and temperature is used.
A.1 Introduction
Recently, there has been an increased interest in propane ignition data at high
pressures and low temperatures due to their significance in the validation of detailed
chemical kinetic mechanisms at these conditions. Both shock tubes and rapid
compression machines (RCM) have been used for these studies. Cadman et al. [156]
examined auto-ignition delay times in shock-heated lean propane-air mixtures (Φ = 0.5)
in the low temperature region of 835-1400 K at pressures of 5-40 bars. Similar shock
tube studies, performed by Herzler et al. [157] and Petersen et al. [158] at temperatures of
750-1300 K and pressures of 10 and 30 bars, are in agreement with the measurements by
Cadman et al. These shock tube ignition delay times start to deviate (roll off) from
detailed model simulations at temperatures around 1000 K. More recently, Gallagher et
al. [159] studied propane oxidation in air using an RCM over temperatures between 680
and 970 K at different compressed gas pressures and equivalence ratios. The measured
RCM ignition delay times are approximately two orders of magnitude longer than the
shock tube data, and a characteristic negative coefficient behavior was observed. Of
critical importance is the fact that modeling of the ignition delay times using a detailed
propane oxidation mechanism (Curran et al. [100]) under commonly employed constant
internal energy (U) and volume (V) constraints cannot reproduce the measurements at
lower temperatures for either shock tube or RCM data (see Figure A.1).
157
Figure A.1: Previous ignition delay time measurements for propane oxidation in air at Φ = 0.5. The constant U, V model calculations utilize the Curran et al. mechanism [100].
A similar discrepancy has been observed in recent reflected-shock studies of
hydrogen-oxygen-argon mixtures. Pang et al. [160] found that hydrogen ignition delay
times are at least an order of magnitude shorter than the constant U, V predictions of
detailed kinetic mechanisms at temperatures less than 930 K. For these low temperature
experiments, a gradual pressure increase (dP5/dt) was observed. That study concluded
that the post-shock pressure variation contributed significantly to shorter ignition delay
times in long-duration (low temperature) experiments. In an ideal shock tube experiment,
the incident shock travels at a constant speed and is reflected from the driven-section
endwall. The reflected shock further compresses the incident-shocked test gas, yielding a
stagnant and uniform high-temperature region. Computationally, this reflected shock
region is often approximated as a constant volume reactor. Additionally, gases in the
reflected shock region are often assumed to have constant internal energy (U), as would
be appropriate for adiabatic systems without work addition or chemical energy change.
However, due to viscous effects, sidewall boundary layers are developed behind incident
shock waves, causing incident shock attenuation and leaving a non-uniform flow field in
the incident shock region. As the reflected shock propagates into this flow field and
interacts with the growing boundary layers, changes in the post-reflected-shock pressure
0.6 0.8 1.0 1.2 1.4 1.60.01
0.1
1
10
100
1000
Petersen (2007) Herzler (2004) (Ar) Herzler (2004) Gallagher & Curran
(2008) (RCM)
2.1% C3H8 / O2 / N2Φ = 0.5, P = 30 atm
Igni
tion
Tim
e [m
s]
1000/T [1/K]
1250K 1000K 833K 714K
Const.U,VModel
158
may occur that can penetrate into the reflected shock region [161]. Consequently, an
increase in pressure (and a concomitant increase in temperature) is typically observed in
the reflected shock region, introducing uncertainties in the ignition delay time
measurements. In such experiments, the constant-volume assumption is not strictly valid.
Furthermore, the undiluted mixtures at elevated pressures exhibit an accelerated
ignition caused by some localized pre-ignition energy release, resulting in a dramatic and
sudden pressure rise prior to the primary ignition event (as discussed by Petersen et al.
[158]). Such dramatic pressure effect is different from the normal, gradual pressure
increase (dP5/dt) observed in dilute mixtures. Both pressure effects cannot be simply
reproduced by a detailed kinetic mechanism under constant U, V constraints. In the
current study, we investigate only the effects of the gradual pressure increase on ignition
delay time measurements using a dilute mixture. Hence, we measured propane ignition
delay times in a lean mixture (0.8% C3H8/ 8% O2/ Ar) at nominal pressures of 6, 24 and
60 atm, first using a conventional shock tube, to confirm the discrepancies between
experimental data and simulations based on two current chemical mechanisms using
constant U and V constraints. We then employed a driver-insert method (developed in
our laboratory [154]) to minimize the post-shock pressure variations and generate near-
constant-volume test conditions for the propane oxidation study. These near-constant-
volume measurements were compared to constant U, V predictions using the JetSurF
v1.0 mechanism of Sirjean et al. [155] and the Curran et al. mechanism of NUI Galway
[100]. Finally, a thermodynamic-gasdynamic model, CHEMSHOCK [162], was used to
simulate the conventional shock tube ignition delay data (i.e., with dP5/dt > 0) by
incorporating the effects of the measured non-ideal growth of pressure (caused by
incident shock wave attenuation and boundary layer growth).
A.2 Experimental Setup
A.2.1 Low-Pressure Shock Tube Experiments
Ignition delay times at pressures near 6 atm were measured in the Stanford
stainless-steel, high-purity low-pressure shock tube (LPST) previously described by
159
Oehlschlaeger et al. [163]. The shock tube inner diameter is 14.13 cm, and the driven
section is 8.54 m in length, separated from the driver section by polycarbonate
diaphragms (0.5 and 1.0 mm in thickness). Under normal shock tube conditions, the
driver section is 3.35-m long, and helium is used as the driver gas to obtain a 2-ms high-
quality test time. To extend the test time for low temperature ignition measurements, the
driver section was lengthened to 7.12 m to allow more time before the arrival of the
rarefaction fan at the test location. The stainless-steel driver-section extension has an
inner diameter of 14.13 cm and a U-shaped structure with a 23-cm radius of curvature on
the centerline. In addition, tailored driver gas mixtures of 30-40% nitrogen in helium
were used to minimize reflected shock-contact surface interactions [164]. These
modifications provide an available test time of approximately 25 ms at a temperature of
about 1000 K.
The gases used, propane (Instrument Grade) 99.5%, oxygen (Research Grade)
99.999%, and argon (Research Grade) 99.999%, were supplied by Praxair and used
without further purification. A test gas mixture (0.8% C3H8, 8% O2, with balance argon)
was prepared manometrically in a 12-liter stainless-steel mixing cylinder and
mechanically mixed with a magnetically-driven stirrer for at least 2 hours prior to the
experiments.
All measurements were performed behind reflected shock waves at a test location
2 cm from the driven-section endwall. Incident shock velocities were measured with five
piezo-electric pressure transducers (PCB 113A) spaced axially over the last 1.5 m of the
tube and extrapolated to the endwall. The signals of the transducers triggered by the
incident shock were delivered to four Philips PM6666 counter timers (with resolution of
0.1 μs), which determined the shock-passage time intervals. The incident shock velocity
at the endwall can then be estimated by a linear extrapolation of the incident shock
velocities determined from the shock-passage time intervals. Typical shock attenuation
rates ranged from 0.8 to 1.5% per meter. Reflected shock conditions were calculated
using one-dimensional shock relations and assuming vibrational equilibrium and frozen
chemistry. Uncertainty in the initial temperature and pressure was approximately ±0.7%
and ±1%, respectively, mainly due to the uncertainty in the measured shock velocity
160
(±0.2%). A Kistler piezo-electric pressure transducer (603B1) coated with RTV silicone
rubber was utilized to measure pressure-time history in the test section at 2 cm from the
endwall. In addition, OH* emission chemiluminescence was monitored at the test section
using a vertical slit, lens, Schott Glass UG5 filter (with >95% transmission at 306 nm),
and modified UV-enhanced Thorlabs PDA36A photodiode detector. The temporal
resolution of this emission set-up is typically 10 μs or better.
A.2.2 High-Pressure Shock Tube Measurements
All experiments at pressures higher than 20 atm were performed in the Stanford
stainless-steel, high-purity, high-pressure shock tube (HPST). A complete description of
this shock tube is provided by Petersen et al. [165]. The driver section is 3-m long with a
7.5-cm inner diameter, and the driven section is 5-m long with a 5-cm inner diameter,
separated by an aluminum diaphragm (1.27-3.18 mm in thickness) with cross-scribing.
Helium was used for the driver gas to provide approximately 2-3 ms of high-quality test
time. At lower temperatures, longer test time was achieved by using tailored driver gas
mixtures of 40-50% nitrogen in helium [164], and the available test time was
approximately 10 ms at a temperature of about 1000 K. All measurements were made
behind reflected shock waves, at a test location 1 cm from the driven-section endwall.
The incident shock velocities were measured using six piezo-electric pressure transducers
(PCB 113A), with five corresponding Philips PM6666 counter timers (with resolution of
0.1 μs), spaced over the last 2 m of the shock tube and extrapolated to the endwall.
Shock attenuation rates varied from 1.0 to 3.5% per meter. Endwall shock velocity,
incident and reflected shock conditions were determined using the same method as
described above. Uncertainty in the initial temperature and pressure is less than ±1%,
with the primary contribution being uncertainty in the measured shock velocity.
Pressure-time history in the test section was monitored by a Kistler pressure transducer
(603B1) coated with RTV. Additionally, emission from OH* chemiluminescence was
measured at the test location using the similar set-up as described above.
161
A.2.3 Driver-Insert-Method
Non-ideal gasdynamic effects of shock waves (primarily incident shock wave
attenuation and sidewall boundary layer growth) can cause a gradual increase in pressure
(and a simultaneous increase in temperature) in the reflected shock region [165-167].
Hong et al. [154] have developed a semi-analytical model for designing shock tube driver
inserts to obviate non-ideal pressure variations in the reflected shock region. Optimal
configuration for the driver insert uses a parabolic shape, which is dependent on the
reflected shock temperature, pressure, and the composition of the driver and driven gases.
The driver insert is used to reflect part of the rarefaction fan back to the test section,
superimposing a pressure decrease on the non-ideal pressure growth due to the boundary
layers. If both effects have the same order of magnitude, the non-ideal pressure rise can
be effectively eliminated, yielding near-constant-volume test conditions (with a fractional
rate of pressure change dP5/dt ~ 0%/ms) in the reflected shock region (see Figure A.2).
With a proper combination of driver insert and tailored driver gas mixtures, long uniform
test times of 25 ms and 10 ms can be acquired at temperatures around 1000 K for the
low-pressure and high-pressure shock tubes, respectively. Additionally, constant
pressure implies a constant temperature profile by assuming isentropic behavior of the
gas at the test section. This has been confirmed with an in situ two-line thermometry
diagnostic using two distributed feedback (DFB) diode lasers near 2.7 μm [168].
162
Figure A.2: Comparison of pressure profiles for a mixture of 0.8% C3H8/ 8% N2/ Ar obtained with and without driver insert in the Stanford 14.13 cm diameter shock tube. The fractional pressure rise without driver insert (over 20 ms) is approximately 20%, compared to ±3.0% local pressure variations with driver insert. The decay beginning at 25 ms is due to arrival of the rarefaction wave from the driver section.
A.3 Results and Discussion
Lean propane ignition delay times were measured at temperatures between 980
and 1400 K and nominal pressures of 6, 24, and 60 atm. The ignition delay time is
defined as the time interval between the arrival of the reflected shock and the initial rise
in the pressure and excited OH (OH*) emission traces. Ignition data obtained from the
pressure and emission traces are consistent within ±1%. The overall uncertainty in
ignition delay time measurements is approximately ±10%, with the primary contribution
from the uncertainty in reflected shock temperatures. The typical facility-related rates of
pressure change in the LPST and the HPST without the use of driver inserts were 1-
3%/ms and 6-7%/ms, respectively. The non-ideal pressure growth is larger in the HPST,
primarily due to the fact that its driven section has a smaller inner diameter. Clearly, the
inner diameter of the shock tube can have a significant impact on post-shock pressure
variations.
0 10 20 300
4
8
12
T5 = 1038 KdP5/dt ~ 1.0%/ms
Pres
sure
[atm
]
Time [ms]
0.8% C3H8/ 8% N2/ ArP5 = 6.7 atm
T5 = 1020 KdP5/dt ~ 0%/ms
163
Representative LPST propane ignition data are illustrated in Figure A.3. In the
reflected shock wave experiment without the driver insert, a gradual pressure rise with a
rate of 2%/ms is observed after the passing of the reflected shock. This non-ideal
behavior causes approximately a 20% increase (over 10 ms) in pressure prior to ignition,
and concomitantly (assuming isentropic compression) approximately an 8% increase in
temperature. Such pressure rise is caused by the incident shock attenuation and boundary
layer growth. In the reflected shock wave experiment with a properly designed driver
insert (also shown in Fig. A.3), the pressure rise behind the reflected shock was
eliminated. The pressure profile obtained using the driver insert is nearly flat with local
pressure variations of ±3% prior to ignition, relatively insignificant when compared to the
20% pressure rise in the uncompensated conventional experiments. The ignition delay
time measured under conventional operating conditions (without the driver insert) at the
initial temperature T5 = 1034 K is approximately 7 ms shorter than that obtained under
near-constant-volume conditions (with the driver insert) at T5 = 1044 K, owing to the
increase in reaction temperature occurring in the former.
Figure A.3: Comparison of pressure profiles for reactive mixture with and without LPST driver insert. Pressure rise without driver insert (over 10 ms) is 20%, compared to ±3.0% pressure variations with driver insert. Initial reflected shock conditions: T5 = 1034 K and P5 = 7.1 atm (with dP5/dt ~ 2%/ms), T5 = 1044 K and P5 = 6.7 atm (with dP5/dt ~ 0%/ms).
0 5 10 150
10
20
τign
T5 = 1044 K
Pres
sure
[atm
]
Time [ms]
T5 = 1034 KdP5/dt ~ 2%/ms
0.8% C3H8/ O2/ Ar Φ = 0.5
τign
OH* Emission (1044 K)
164
Examples of HPST ignition time data with and without driver inserts are shown in
Figure A.4. The initial reflected shock pressure of both experiments is approximately the
same (~54 atm), and the ignition delay time of the measurement taken without the use of
a driver insert (dP5/dt ~ 7%/ms) at a slightly colder initial temperature of 996 K is at least
one-third shorter than the near-constant-volume measurement taken with the driver insert
(dP5/dt ~ 0%/ms) at T5 = 1008 K.
Figure A.4: Comparison of pressure profiles for reactive mixture with and without HPST driver insert. Pressure rise without driver insert (over 2.5 ms) is 17.5%, compared to ±1.0% pressure variations with driver insert. Initial reflected shock conditions: T5 = 996 K and P5 = 54.7 atm (with dP5/dt ~ 7%/ms), T5 = 1008 K and P5 = 53.7 atm (with dP5/dt ~ 0%/ms).
At temperatures less than 1100 K (or test times longer than 5 ms), a small
pressure bump is observed in the LPST experiments (extending from about 5-8 ms in Fig.
A.3), even though a near-perfect tailoring condition has been achieved. (Note that a
small pressure bump is also present in the HPST experiments extending from about 4-6
ms.) This is primarily due to the fact that the contact surface is not actually a thin
interface. Instead, it is a mixing zone, which has a finite width and is caused by non-ideal
diaphragm bursting and boundary layer growth. Several strategies were attempted to
eliminate such a pressure bump (see Davidson et al. [167]) with varying degrees of
success, and eventually relatively small “bumps” were achieved typified by Fig. A.3. To
0 1 2 3 40
50
100
150
τign
T5 = 1008 K
Pres
sure
[atm
]
Time [ms]
T5 = 996 KdP5/dt ~ 7%/ms
0.8% C3H8/ O2/ Ar Φ = 0.5
τign
165
examine the effect of such pressure bump on ignition delay time, CHEMSHOCK (will be
discussed later) with the JetSurF v1.0 mechanism [155] and the actual experimental
pressure profile (with the pressure bump and dP5/dt ~ 0%/ms in Fig. A.3) was first used
to compute the ignition delay time, and the calculated ignition delay time was 17.9 ms at
T5 = 1044 K. After that, the pressure bump present in the experimental pressure profile
was artificially removed, and CHEMSHOCK with the artificial pressure profile gave the
ignition delay time of 18.5 ms at T5 = 1044 K, which is ~3% longer than the former
computed value (with the pressure bump). Hence, such small pressure bumps do not
affect the ignition delay time measurements significantly in the current study.
The low-pressure ignition delay times under both near-constant-volume
conditions and conventional operation conditions are plotted at the initial reflected shock
temperatures in Figure A.5, along with the calculated values from the JetSurF v1.0
mechanism of Sirjean et al. [155] and the Curran et al. mechanism of NUI Galway [100]
under constant U, V constraints. The calculated values from both mechanisms are in
excellent agreement at a pressure of 6 atm. At reflected shock temperatures less than
1250 K and pressures of 5.3-68 atm, an ignition time correlation for the current mixture
can also be determined from a total of 50 near-constant-volume measurements with a R2
value of 0.990: τ = 2.49×10 -5P-0.89exp(15674/T), where the ignition time is in
milliseconds, the pressure is in atmospheres, and the temperature is in kelvins. All data
were then scaled by P-0.89 to their nominal pressures. Note that both sets of measurements
in the current study agree with each other at temperatures above 1110 K (i.e. at short test
times). The discrepancy between the two measurement sets increases with decreasing
temperature, but the constant U, V predictions remain in good agreement with the near-
constant-volume ignition delay time measurements (dP5/dt = 0%/ms) at all temperatures.
In contrast, the current data under conventional operation conditions (dP5/dt = 1-
3%/ms) are shorter than the results from both models, starting at T5 = 1110 K. For
instance, the uncompensated conventional data is approximately 15 milliseconds faster
than the constant U, V models at T5 = 990 K. Figure A.5 also includes the previous
ignition data from Cadman et al. [156] using the same test mixture. In the study
performed by Cadman et al., the data were obtained at a reflected shock pressure of 5
166
atm. To perform a quantitative comparison, those ignition data were also scaled by P-0.89
from P5 = 5 to 6 atm. Notice that those previous measurements are substantially shorter
than the current measurements and the constant U, V model predictions by at least a
factor of 3. As mentioned previously, the inner diameter of the shock tube can have a
significant impact on post-shock pressure variations. The Cadman et al. shock tube
facility has an inner diameter of about 6 cm, which is much smaller than that of the
Stanford low-pressure shock tube (14.13 cm). Based on their published pressure profiles
(Fig. 5 from their publication), a relatively large post-shock pressure variation of
approximately 15%/ms or higher was identified. Such large dP5/dt can contribute to the
substantial differences between the previous and current measurements. For kinetic
modeling of reflected-shock experiments, it is now clear that it is critically important to
account for the post-shock pressure variations in different shock tube facilities and that
pressure growth rates be documented to allow proper modeling of experiments. Incorrect
reaction pathways and rate coefficients may be inferred if uncompensated ignition data
are fit by detailed mechanisms.
Figure A.5: Ignition delay times for 0.8% C3H8/ 8% O2/ Ar mixture at P5 = 6 atm, plotted at the initial post-shock T5. Experimental data and calculated values from JetSurF v1.0 mechanism [155] and Curran et al. mechanism [100].
0.6 0.7 0.8 0.9 1.0 1.1
0.1
1
10
Current Study (dP5/dt~0%/ms) Current Study (dP5/dt~1-3%/ms) Cadman (2000) (dP5/dt~15%/ms) JetSurF v1.0 (Const. U,V) Curran et al. (Const. U,V)
1250K 1000K1111K
Igni
tion
Tim
e [m
s]
1000/T5 [1/K]
1429K
0.8% C3H8/ O2/ ArΦ = 0.5, P5 = 6 atm
167
As discussed by Pang et al. [160], constant U, V modeling of low-temperature
shock tube ignition delay times with finite dP5/dt gives an unsatisfactory and incorrect
representation of the actual chemical kinetics. A gasdynamic solver developed in our
laboratory, named CHEMSHOCK, can be used to reasonably account for the non-ideal
growth of pressure and temperature in the reflected shock region, up to the time of
ignition, at least for simple reaction systems without significant pre-ignition heat release.
CHEMSHOCK performs a two-step simulation process over each small time step: (1)
constant U, V calculations, followed by (2) an assumed isentropic adjustment in
conditions to recover the measured value of pressure at this time. This code has been
validated against simulations from a one-dimensional reacting computational fluid
dynamics code for a heptane/ O2/ Ar mixture using a reduced mechanism, and against
experimental data (such as gas temperature and water vapor concentration) in a hydrogen/
O2/ Ar mixture by Li et al. [162]. The calculated ignition delay times from
CHEMSHOCK using the JetSurF v1.0 mechanism [155] and different pressure
constraints (dP5/dt = 1.5%/ms and 15%/ms) are displayed in Figure A.6. Here, the
computed values are much closer to the uncompensated ignition delay times. By setting
the post-shock pressure variation to 1.5%/ms, the model agrees with the conventional
data in the current study within ±10% at lower temperatures. Additionally, the
CHEMSHOCK modeling is able to capture the early roll-off behavior displayed by the
previous ignition data from Cadman et al. (within 20%) at low temperatures after
incorporating the published post-shock pressure increase of 15%/ms.
168
Figure A.6: Low-pressure experimental data and CHEMSHOCK modeling using JetSurF v1.0 mechanism.
Figure A.7 shows the Arrhenius plots of lean propane ignition delay time
measurements at elevated pressures of 24 and 60 atm, respectively. All experimental
data were scaled to either 24 or 60 atm using P-0.89. The measured facility-related rate-of-
pressure change in the high-pressure shock tube was typically 6-7% per millisecond,
which is much larger than observed in the low-pressure shock tube. Good agreement is
found between the ignition delay data with dP5/dt of ~0%/ms and ~6-7%/ms, at
temperatures higher than 1110 K or when the ignition delay times are shorter than 1
millisecond. Notice, however, that the discrepancy in ignition delay data between
conventional operation and near-constant-volume conditions is larger in the 24 atm
experiments in the high-pressure shock tube than in the 60 atm experiments. For
instance, at the initial reflected shock condition of T5 = 990 K and P5 = 24 atm, the
uncompensated data are 50% shorter than the near-constant-volume data. This is because
the longer ignition delay times for the 24 atm data are more sensitive to changes in the
temperature gradient than the shorter-ignition-time 60 atm data.
The compensated high-pressure experimental data in Fig. A.7 are compared to
predictions using both JetSurF [155] and Curran et al. [100] mechanisms under constant
U, V constraints. At a nominal pressure of 24 atm, the computed ignition delay times
0.8 0.9 1.0
1
10
JetSurF v1.0: CHEMKIN (Const. U,V) CHEMSHOCK (1.5%/ms) CHEMSHOCK (15%/ms)
Curran et al.: CHEMKIN (Const. U,V)
1250K 1000K1111K
Igni
tion
Tim
e [m
s]
1000/T5 [1/K]
0.8% C3H8/ O2/ ArΦ = 0.5, P5 = 6 atm
169
from the JetSurF mechanism show very good agreement with the near-constant-volume
measurements. At a nominal pressure of 60 atm, the constant U, V model predictions
from the JetSurF mechanism agree reasonably well with the compensated data, but are
consistently 15% longer than the measurements. However, the predicted values from the
Curran et al. mechanism are at least 30% shorter than the near-constant-volume
measurements at both pressures. Referring now to the uncompensated (conventional
operation) results, all the experimental data are much shorter than the constant U, V
model predictions at lower temperatures. The uncompensated data are at least three times
shorter than the constant U, V model calculations (JetSurF) at T5 = 950 K and P5 = 24
atm, while they are 66% shorter at T5 = 996 K and P5 = 60 atm. Hence, the
CHEMSHOCK model with the JetSurF mechanism [155] was utilized to account for the
non-ideal pressure rise in the reflected shock region. After incorporating a proper
pressure constraint (dP5/dt = 7%/ms), the uncompensated data are successfully simulated
at both pressures, as illustrated in Figure A.7. However, there does appear to be a small
residual systematic difference between the measured and simulated ignition delay times
in both the compensated and uncompensated 60 atm data. This may indicate a deficiency
in the pressure-dependent chemistry in the JetSurF mechanism. A preliminary sensitivity
analysis indicates that a 50% increase in the pressure-dependent hydrogen peroxide
decomposition rate at 60 atm would eliminate this systematic difference.
170
Figure A.7: High-pressure experimental data (at P5 = 24 and 60 atm), along with CHEMKIN and CHEMSHOCK modeling using JetSurF v1.0 and Curran et al. mechanisms.
A.4 Concluding Remarks
Propane ignition delay times in a lean mixture (0.8% C3H8/ 8% O2/ Ar) were
measured over the temperature range of 980-1400 K at nominal pressures of 6, 24, and 60
atm, under conventional shock tube operating conditions and under near-constant-volume
conditions, using both the low-pressure and high-pressure shock tubes. Under
0.8 0.9 1.0 1.10.1
1
10
Current Study (dP5/dt~0%/ms) Current Study (dP5/dt~6-7%/ms) JetSurF v1.0 (Const. U,V) JetSurF v1.0 (dP5/dt=7%/ms) Curran et al. (Const. U,V)
909K1250K 1000K1111K
Igni
tion
Tim
e [m
s]
1000/T5 [1/K]
0.8% C3H8/ O2/ ArΦ = 0.5, P5 = 24 atm
0.8 0.9 1.0 1.10.1
1
10 Current Study (dP5/dt~0%/ms) Current Study (dP5/dt~6-7%/ms) JetSurF v1.0 (Const. U,V) JetSurF v1.0 (dP5/dt=7%/ms) Curran et al. (Const. U,V)
0.8% C3H8/ O2/ ArΦ = 0.5, P5 = 60 atm
909K1250K 1000K1111K
Igni
tion
Tim
e [m
s]
1000/T5 [1/K]
171
conventional operating conditions, a facility-related rate-of-pressure rise (dP5/dt ~ 1-
7%/ms) is observed in the reflected shock region, introducing strong variations in the
shock tube ignition delay time measurements. Under near-constant-volume test
conditions, a flat pressure profile with small local variations was obtained using a driver-
insert method and tailored driver gas mixtures. Good agreement in both types of
measurements is found only at temperatures higher than 1110 K. As temperature is
decreased, the discrepancy between the two types of measurements becomes larger at all
pressures.
The near-constant-volume measurements of ignition delay times were found to be
in good agreement with the predictions of the JetSurF v1.0 mechanism [155], using
commonly employed constant U, V constraints. The ignition delay time measurements
using conventional shock tube operation (with dP5/dt ~ 1-7%/ms) were also found to be
in good agreement with detailed modeling, when CHEMSHOCK [162] is used to include
the effects of pressure and temperature variations. The new near-constant-volume data
provide a valuable database for low-temperature propane mechanism development that is
independent of fluid flow and heat transfer effects.
172
173
Appendix B Ignition Delay Time Measurements of Normal Alkanes and Cycloalkanes
B.1 Objectives
Ignition delay time experiments were performed on a series of straight-chain
alkanes and cycloalkanes using the Stanford Low Pressure Shock Tube (LPST). These
experiments were performed on n-pentane (n-C5H12), n-hexane (n-C6H14), n-octane (n-
C8H18), n-nonane (n-C9H20), cyclohexane (CH or cC6H12), methylcyclohexane (MCH or
CH3cC6H11), and n-butylcyclohexane (BCH or n-C4H9cC6H11) at various reflected shock
temperatures and pressures (between 1240 and 1500 K and 1.5 and 3.8 atm) and at two
equivalence ratios, namely Φ = 1.0 and Φ = 0.5. These ignition delay time measurements
were then compared with the modeling results obtained using the comprehensive kinetic
mechanism of Sirjean et al. (JetSurF v1.1) [169].
B.2 Experimental Details
Research grade O2 and argon were used in all mixtures, along with ≥ 99.5% pure
fuels from Sigma-Aldrich that were degassed by vacuum pumping prior to mixture
preparation. The fuels are n-pentane (n-C5H12), n-hexane (n-C6H14), n-octane (n-C8H18),
n-nonane (n-C9H20), cyclohexane (C6H12), methylcyclohexane (MCH), and
butylcyclohexane (BCH). Test mixtures (fuel, 4% O2, with balance Ar) were prepared in
174
a 14-liter stainless steel tank. The desired mixture ratio of the reactants was obtained on
the basis of partial pressures as measured with a 10,000 Torr Baratron pressure gauge.
The reactants were mixed by an electrically-driven stirring rod for 2 hours. For all test
mixtures, the mixing tank (with a heating jacket) and the manifold (wrapped with a
flexible constant-wattage silicone rubber heating tape) were heated such that their surface
temperature remained at around 60 °C.
The mixture compositions were validated by monitoring the fuel concentrations in
the shock tube (from near the endwall) with a Jodon™ Helium-Neon laser at 3.39 µm.
The absorption cross-sections of n-alkanes for Beer’s law were directly obtained from the
PNNL database [123], and the values from the PNNL database are in good agreement
with the previous measurements from Klingbeil et al. [122]. The measured fuel
concentrations for these n-alkane mixtures were consistent with the values expected from
the manometrical preparation within ±5%. On the other hand, the absorption cross-
sections of those three cycloalkanes were measured in the shock tube using HeNe laser
absorption at 3.39 µm, and the measured absorption cross-sections for CH, MCH, and
BCH are 75.1, 50.2, and 56.6 m2/mol, respectively, at 25 oC, with uncertainties of ±5%.
By employing these measured absorption cross-sections, the measured fuel
concentrations for the cyclohexane and methylcyclohexane mixtures were in good
agreement with the values expected from the manometrical preparation within ±5%. On
the contrary, the measured fuel concentrations for the n-butylcyclohexane mixtures were
found to be 30% less than the expected values, and these fuel losses were properly
accounted for in the test mixtures when compared to the simulations using the JetSurF
v1.1 mechanism (under constant energy and volume constraints).
175
B.3 Ignition Delay Time Plots
B.3.1 Normal Alkane Ignition
Figure B.1: n-Pentane ignition delay time measurements at pressures of 1.8 and 3.6 atm and equivalence ratios of 1.0 and 0.5.
Figure B.2: n-Hexane ignition delay time measurements at pressures of 1.8 and 3.6 atm and equivalence ratios of 1.0 and 0.5.
176
Figure B.3: n-Octane ignition delay time measurements at pressures of 1.8 and 3.6 atm and equivalence ratios of 1.0 and 0.5.
Figure B.4: n-Nonane ignition delay time measurements at pressures of 1.8 and 3.6 atm and equivalence ratios of 1.0 and 0.5.
177
B.3.2 Cycloalkane Ignition
Figure B.5: Cyclohexane (CH) ignition delay time measurements at pressures of 1.5 and 3.0 atm and equivalence ratios of 1.0 and 0.5.
Figure B.6: Methylcyclohexane (MCH) ignition delay time measurements at pressures of 1.5 and 3.0 atm and equivalence ratios of 1.0 and 0.5.
178
Figure B.7: n-Butylcyclohexane (BCH) ignition delay time measurements at pressures of 1.5 and 3.0 atm and equivalence ratios of 0.88 and 0.45.
B.4 Summary
Ignition delay time measurements were performed on a series of straight-chain
alkanes and cycloalkanes over 1240-1500 K at pressures of 1.5 and 3.8 atm and at two
equivalence ratios of Φ = 1.0 and 0.5. Further details regarding this work can be found
from the following papers:
• D.F. Davidson, S.C. Ranganath, K.-Y. Lam, M. Liaw, Z. Hong, R.K. Hanson,
“Ignition delay time measurements of normal alkanes and simple oxygenates,” J.
Propul. Power 26 (2010) 280-287.
• Z. Hong, K.-Y. Lam, D.F. Davidson, R.K. Hanson, “A comparative study of the
oxidation characteristics of cyclohexane, methylcyclohexane, and n-
butylcyclohexane at high temperatures,” Combust. Flame 158 (2011) 1456-1468.
179
Appendix C Multi-Species Time History Measurements during the Oxidation of n-Decane, iso-Octane, and Toluene
The high-temperature oxidation of n-decane, iso-octane, and toluene was studied
behind reflected shock waves using laser absorption methods to measure time histories of
three species: OH, C2H4, and CO. These species time histories were then compared to
the simulations from the comprehensive reaction mechanisms (JetSurF v1.1 [169] and
LLNL [170] mechanisms). Additionally, ignition delay times for the mixtures of n-
decane, iso-octane, and toluene were compared with the measurements of the JP-8
mixtures, and the ignition times for the iso-octane and JP-8 mixtures were found to be in
good agreement.
C.1 Introduction
Jet aviation fuels such as Jet-A and JP-8 are complicated mixtures of hundreds,
even thousands of different chemical components [171]. To model the chemistry of these
fuels, surrogate fuel models consisting of a small number of representative chemical
components and a limited accompanying detailed reaction mechanism can be used.
These surrogate fuel models are generally able to successfully imitate the gas phase
combustion characteristics of the real fuel being investigated [172]. The major advantage
180
of these surrogate fuel models, of course, is that the size of the detailed kinetic
mechanism is more manageable and requires less computational power.
These surrogate models can be used to predict auto-ignition, heat release rate,
adiabatic flame temperature, extinction, sooting behavior, and other important
combustion property targets. However, it is often difficult to find a surrogate that can
successfully match both the physical properties and the chemical kinetics properties of
the fuel. Several surrogate fuel components are currently being considered, including: n-
decane, n-dodecane, iso-octane, iso-cetane, methyl cyclohexane, n-butyl cyclohexane,
toluene, n-propyl benzene, 1,3,5 tri-methylbenzene, and 1-methyl naphthalene [172].
Some idea of the current state of performance for surrogate models can be gained by
examining two surrogate fuel models for JP-8: the Lindstedt model (89% n-decane/ 11%
toluene) [173] and the CSE model (52.93% n-decane/ 12.96% iso-octane/ 34.11%
toluene) [174]. Fig. C.1 shows the measured OH and C2H4 time histories during high-
temperature JP-8 oxidation, along with the simulations based on the Lindstedt model and
the CSE model using a detailed kinetic mechanism of Dooley et al. [172]. As can be
seen, both surrogate fuel models can capture the general shapes of the OH and C2H4 time
histories. However, neither of these models can accurately predict the ignition delay
times for this JP-8 mixture, nor can they capture the initial formation rates and initial
plateau levels of the important chain-branching radical OH. Interestingly, the Lindstedt
model [173] is able to capture the initial C2H4 plateau levels reasonably well, but the CSE
model [174] underpredicts the plateau levels at the experimental conditions. Clearly,
further experimental and theoretical studies are needed to improve the current surrogate
fuel models.
The validation of multi-component surrogate kinetics is predicated on the
successful validation of each individual surrogate component. Here we present
experimental kinetic targets for the high-temperature oxidation of three individual
surrogate components: n-decane, iso-octane, and toluene. These kinetic targets are
species time histories of OH, C2H4, and CO derived from laser absorption measurements
behind reflected shock waves. These measured species time histories are also compared
with the simulations from the existing detailed mechanisms.
181
Figure C.1: OH and C2H4 time history measurements for the mixture of 424 ppm JP-8 with 0.813% O2 in Ar. Two JP-8 proposed surrogate models were employed. Simulations were done using the Dooley et al. mechanism [172].
C.2 Experimental Details
C.2.1 Mixture Preparation
Test mixtures were prepared manometrically in a 40 liter stainless steel tank
heated uniformly to 60 oC and mixed with a magnetically-driven stirring vane for at least
182
2 hours prior to the experiments. Research grade (99.999%) gases from Praxair were
used in mixture preparation without further purification. In addition, liquid chemicals
were all obtained from Sigma-Aldrich. Anhydrous grade (≥99%) n-decane, anhydrous
grade (≥99.8%) iso-octane, and ACS spectrophotometric grade (≥99.5%) toluene were
further treated using a freeze-pump-thaw procedure to remove dissolved volatiles and air
prior to mixture preparation. The mixture compositions in this study were ~360 ppm n-
decane with 0.813% O2 in Ar (Φ ~ 0.7), 511 ppm iso-octane with 0.813% O2 in Ar (Φ ~
0.8), and 640 ppm toluene with 0.813% O2 in Ar (Φ ~ 0.71).
C.2.2 Helium-Neon Laser Measurement of Fuel
The mixture compositions were confirmed by sampling a portion of the mixture
(from near the endwall) into an external multi-pass absorption cell with a path length of
29.9 m and monitoring the fuel concentration in the cell with a Jodon™ Helium-Neon
laser at 3.39 µm [82, 122]. Beer’s law was used to convert the measured absorption data
into the fuel mole fraction. The absorption cross-sections of n-decane, iso-octane, and
toluene for Beer’s law were directly obtained from the PNNL database [123], and the
measured fuel concentrations were found to be lower than the values expected from the
manometrical preparation by ~30% for n-decane mixtures and ~12% for toluene
mixtures. On the other hand, the measured iso-octane concentrations were found to be
consistent with the values from the manometrical preparation within 3%.
C.3 Results and Discussion
C.3.1 n-Decane Oxidation
OH time histories offer an important kinetic target for the validation of detailed
reaction mechanisms during hydrocarbon oxidation. In particular, the early-time feature
of OH appears to provide important information about the breakdown of the fuel, because
this feature is controlled by the unimolecular decomposition and the H-atom abstraction
183
reactions. Fig. C.2 shows the measured OH time histories for the mixture of ~360 ppm
n-decane with 0.813% O2 in Ar (Φ ~ 0.8), along with the simulations from the detailed
mechanism of Sirjean et al. (JetSurF v1.1) [169]. On the basis of these OH time histories,
the ignition delay times simulated from the JetSurF v1.1 mechanism are slightly shorter
than the measured values at the present experimental conditions. Nevertheless, the model
can accurately predict the initial and final OH plateau levels. More importantly, the
model is able to capture the initial OH formation rates reasonably well. This indicates
that the rate constants for the n-decane unimolecular decomposition pathways and the H-
atom abstraction reactions from n-decane are quite reasonable.
Figure C.2: OH time histories for the mixture of ~360 ppm n-decane with 0.813% O2 in Ar. Simulations were done using JetSurF v1.1 mechanism. An inset figure is also shown to provide the early-time features.
C2H4 species is an important intermediate species during hydrocarbon oxidation.
Fig. C.3 shows the measured C2H4 time histories for the mixture of ~360 ppm n-decane
with 0.813% O2 in Ar, along with the simulations from the JetSurF v1.1 mechanism. The
measured C2H4 plateau levels are around 1050 ppm, which indicates that each n-decane
molecule forms approximately three C2H4 molecules prior to ignition. Similar to the OH
time histories, the model is able to capture the initial formation rates and plateau levels of
C2H4 reasonably well.
184
Figure C.3: C2H4 time histories for the mixture of ~360 ppm n-decane with 0.813% O2 in Ar. Simulations were done using JetSurF v1.1 mechanism.
During hydrocarbon oxidation, CO is considered as an important combustion
progress marker, which gives similar information to that of another combustion progress
marker, H2O. Fig. C.4 shows the measured CO time histories for the mixture of ~360
ppm n-decane with 0.813% O2 in Ar, along with the simulations from the JetSurF v1.1
mechanism. As illustrated in Fig. C.4, the peak CO mole fraction decreases with
temperature. When compared to the model predictions, the measured peak CO mole
fractions are consistently lower than the predicted values. This discrepancy between the
measurement and the model prediction is much more significant at T =1327 K. In
general, the model overpredicts the CO mole fractions prior to ignition at the present
experimental conditions. This might explain why the present model underpredicts the
ignition delay times at the current test conditions.
185
Figure C.4: CO time histories for the mixture of ~360 ppm n-decane with 0.813% O2 in Ar. Simulations were done using JetSurF v1.1 mechanism.
C.3.2 iso-Octane Oxidation
Fig. C.5 illustrates the measured OH time histories for the mixture of 511 ppm
iso-octane with 0.813% O2 in Ar, along with the simulations from the LLNL mechanism
(iso-octane mechanism v3) [170]. The measured OH time histories during iso-octane
oxidation are quite different from the measured time histories during n-decane oxidation,
particularly at early times. During iso-octane oxidation, the OH concentration first
develops a local maximum during the first 50 µs. However, shortly thereafter, the OH
concentration declines to an intermediate minimum prior to ignition, where the OH
concentration rises rapidly. It should be noted that this early-time feature of OH during
iso-octane oxidation resembles the OH feature during JP-8 oxidation. As illustrated in
Fig. C.5, the model can capture the general shape of OH, including the local maxima and
minima prior to ignition. However, at the present experimental conditions, the predicted
local maxima are higher than the measured values by at least a factor of 2. In addition,
the model seems to overpredict the intermediate minimum by a factor of ~2 at 1610 K,
but it is able to simulate the intermediate minimum at 1474 K. Similarly, the model
186
slightly underpredicts the ignition delay time at 1610 K, but the model prediction is in
good agreement with the measurement at 1474 K.
Figure C.5: OH time histories for the mixture of 511 ppm iso-octane with 0.813% O2 in Ar. Simulations were done using LLNL mechanism (iso-octane mech. v3). An inset figure is also shown to provide the early-time features.
As discussed by Davidson et al. [64], during high-temperature pyrolysis, iso-
octane primarily decomposes to form H, CH3, C3H6, and i-C4H8 species. These
intermediate species are relatively stable. In contrast to n-decane pyrolysis, less C2H4 is
formed during iso-octane pyrolysis. Hence, we would not expect to observe any
significant amounts of C2H4 during iso-octane oxidation. As expected, we are not able to
detect any noticeable levels of C2H4 for the mixture of 511 ppm iso-octane with 0.813%
O2 in Ar at the present experimental conditions.
Fig. C.6 also illustrates the measured CO time histories for the mixture of 511
ppm iso-octane with 0.813% O2 in Ar, along with the simulations from the LLNL
mechanism. Note that the measured peak CO mole fractions decrease with decreasing
temperatures, and are slightly higher than the model predictions. When compared to the
measured CO mole fractions, the model shows decent agreement with the measured
187
values at 1474 K; however, the discrepancy between the measurement and the model
becomes larger at higher temperatures, as can be seen from the OH time histories.
Figure C.6: CO time histories for the mixture of 511 ppm iso-octane with 0.813% O2 in Ar. Simulations were done using LLNL mechanism (iso-octane mech. v3).
C.3.3 Toluene Oxidation
Fig. C.7 shows the measured OH time histories for the mixture of 640 ppm
toluene with 0.813% O2 in Ar, along with the simulations from the JetSurF v1.1
mechanism. As mentioned previously, the early-time feature of OH is unique to the
individual fuel. As can be seen, the early-time features of OH during toluene oxidation
are quite distinct from those of n-decane and iso-octane. In particular, during toluene
oxidation, neither initial plateau level nor local maximum can be observed at early times,
but there is a rather gradual OH rise prior to ignition. In addition, the JetSurF v1.1
mechanism [169] seems to underpredict the ignition delay times by ~30% at 1524 and
1602 K. Nevertheless, the model is able to simulate the general shape of OH species, but
it fails to predict the post-ignition OH plateau levels.
188
Figure C.7: OH time histories for the mixture of 640 ppm toluene with 0.813% O2 in Ar. Simulations were done using JetSurF v1.1 mechanism. An inset figure is also shown to provide the early-time features.
Similar to iso-octane oxidation, we cannot detect any noticeable levels of C2H4
during toluene oxidation. This is primarily due to the fact that toluene undergoes
unimolecular decomposition to form H, CH3, C6H5CH2, and C6H5 radicals. There are no
direct reaction pathways from these radicals to produce C2H4 molecules. Instead, these
radicals will eventually form C2H2, C3H3, and C4H4 species. In addition, Fig. C.8 shows
the measured CO time histories during toluene oxidation, along with the simulations from
the JetSurF v1.1 mechanism. The model seems to underpredict the CO mole fractions at
early times; shortly thereafter, the model overpredicts the CO mole fractions prior to
ignition.
189
Figure C.8: CO time histories for the mixture of 640 ppm toluene with 0.813% O2 in Ar. Simulations were done using JetSurF v1.1 mechanism.
C.3.4 Comparison of Ignition Delay Times
Fig. C.9 shows the ignition delay time measurements for the mixtures of 424 ppm
JP-8/ 0.813% O2/ Ar (Φ ~ 0.85), ~360 ppm n-decane/ 0.813% O2/ Ar (Φ ~ 0.7), 511 ppm
iso-octane/ 0.813% O2/ Ar (Φ ~ 0.8), and 640 ppm toluene/ 0.813% O2/ Ar (Φ ~ 0.71).
In the present study, the ignition delay time is defined as the time to reach 50% of the
peak OH concentration, with time zero being defined as the arrival of the reflected shock
at the sidewall measurement location. As is evident in Fig. C.9, the n-decane mixture has
the fastest ignition delay times among all four mixtures. Interestingly, the ignition delay
time measurements for the JP-8 and iso-octane mixtures are in good agreement with each
other. When compared to the other three mixtures, the toluene mixture is the least
reactive one and has the slowest ignition delay times.
190
Figure C.9: Comparison of ignition delay time measurements for JP-8, n-decane, iso-octane, and toluene at 1.6 atm.
C.4 Conclusions
The high-temperature oxidation of n-decane, iso-octane and toluene was
investigated behind reflected shock waves using laser absorption methods to measure
time histories of three species: OH, C2H4, and CO. These species time histories reveal
that refinements in current surrogate/reaction mechanism models are still needed to
improve the predictions of the detailed mechanisms, particularly in the case for toluene
oxidation. Ignition delay time measurements for mixtures of n-decane, iso-octane, and
toluene were compared to measurements for mixtures of JP-8. Ignition delay times for
the iso-octane and JP-8 mixtures were found to be in good agreement with each other.
191
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