SHOCK TUBE STUDIES OF BIOFUEL KINETICS

Transcription

1 SHOCK TUBE STUDIES OF BIOFUEL KINETICS 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 PHOLOSOPHY Ivo Stranic March 2014 i

2 2014 by Ivo Stranic. 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. This dissertation is online at: ii

3 I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. Ronald Hanson, Primary Adviser I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. Craig Bowman I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. David Davidson Approved for the Stanford University Committee on Graduate Studies. Patricia J. Gumport, Vice Provost for Graduate Education This signature page was generated electronically upon submission of this dissertation in electronic format. An original signed hard copy of the signature page is on file in University Archives. iii

4 Abstract The harmful emissions associated with the combustion of fossil fuels combined with the rapidly increasing global demand for energy present serious challenges to the long term sustainability of life on this planet. Fossil fuels currently account for approximately 81% of worldwide energy usage, and approximately 22% of global energy consumption occurs in the transportation sector. One approach for addressing the world s energy challenges is to reduce the consumption of fossil fuels by improving the numerical simulation capabilities of combustion systems, thus enabling engineers to design more efficient combustion devices. A prerequisite for this design capability is the understanding of chemical kinetics of the fuels that are being utilized. An alternative approach for reducing the consumption of fossil fuels is developing renewable energy alternatives that eliminate the need for fossil fuels altogether. Biofuels are of particular interest as an alternative fuel in the transportation sector because their net CO 2 footprints can be significantly lower compared to those of traditional fossil fuels. The goal of this dissertation is to study the chemical kinetics of biofuels, which would ultimately allow them to be used more efficiently in the combustion devices of the future. This work is primarily experimental, and it can be divided into three parts: First, the chemical kinetics of butanol, a promising second generation biofuel, were investigated extensively. A variety of kinetic targets such as ignition delay times and species time-histories were measured accurately over a wide range of conditions. These high-accuracy data have been used by research groups around the world in order to validate and improve chemical kinetic models. Second, rate constants for reactions of ethanol and tert-butanol with OH radicals were investigated. These reactions are one of the primary removal pathways of fuels during combustion, and they significantly affect the combustion properties of these fuels. Measurements v

5 were performed using isotopic labeling of 18 O in the alcohol group in order to eliminate the recycling of OH radicals following H-atom abstraction at β-sites, which commonly perturbs measurements of rate constants for reactions of alcohols with OH radicals. Third, various experimental techniques were developed and improved while performing these measurements. This work presents the first application of isotopic labeling and laser absorption in shock tubes, which shows significant promise for future chemical kinetic studies. Furthermore, the rate constant for cyclohexene decomposition was determined with the highest accuracy to date. These measurements are likely to improve a myriad of comparative rate and chemical thermometry studies that use cyclohexene decomposition as a reference reaction. Finally, a high-temperature laser absorption diagnostic for measuring acetylene concentration was developed. Time-resolved shock tube measurements of this critical combustion intermediate should significantly improve the experimental capabilities for performing chemical kinetic studies. vi

6 Acknowledgements I would like to thank my advisor, Prof. Ronald Hanson, for guiding me throughout my research. He was an invaluable source of wisdom and inspiration throughout my work, and his relentless pursuit of excellence in research will continue to guide me in my future work. I would also like to thank Prof. David Golden and Prof. Thomas Bowman, who in addition to being coauthors on several of my publications, provided valuable insights through many of my research projects. I must also thank Dr. David Davidson, who essentially ensures that our research group maintains its ability to run top-quality experiments. His advice on numerous practical problems helped me quickly overcome experimental obstacles. My primary source of wisdom about spectroscopy came from Dr. Jay Jeffries. I thank him for the numerous helpful discussions we ve had about lasers, optics, and absorption spectra. I would also like to thank my family, especially my parents, for their support during my studies. Their encouragement for pursuing a PhD at Stanford University was critical for the completion of this work. I must also thank all of my colleagues at the Hanson Research Group who were always willing to provide me with valuable research advice. Notably, I would like to thank Prof. Subith Vasu, who helped me understand and operate shock tubes, and Dr. Genny Pang, who was an invaluable co-author and advisor on several publications. I would also like to thank Deanna Chase, Joseph Harmon, and Sheng Yang, whom I had the pleasure of advising during their summers at our lab. Finally, I would like to thank all of my friends for being an excellent source of support, relaxation, and fun over the years. Work presented here was supported by the Combustion Energy Frontier Research Center (funded by the Department of Energy) and the Air Force Office of Scientific Research. vii

7 Table of Contents Abstract......v Acknowledgements...vii List of Tables. xii List of Figures...xiv 1 CHAPTER 1: Introduction Motivation Chemical Kinetic Mechanisms Butanol CHAPTER 2: Experimental Methods Introduction Shock Tube Facility Overview Temperature and Pressure Measurements Experimental Modeling Emission Diagnostics Laser Diagnostics Overview Diagnostic Details Cross-section Measurements Fuel + OH Reaction Rate Constant Measurements Overview viii

8 2.5.2 Secondary Reactions CHAPTER 3: Kinetic Studies of the Butanol Isomers Introduction Ignition Delay Time Measurements Overview Results Multi-Species Time-History Measurements Overview Modeling Shock Tube Experiments of Endothermic Reacting Systems Results Conclusions CHAPTER 4: Isotopic Labeling Introduction OH vs 18 OH Spectra Ethanol + OH Overview Ethanol + OH Kinetics Results tert-butanol + OH Introduction tert-butanol + OH Kinetics ix

9 4.4.3 Results Conclusions CHAPTER 5: Cyclohexene Decomposition Rate Constant Measurements Introduction Experimental Setup Kinetic Modeling Results Conclusions CHAPTER 6: High-Temperature Acetylene Diagnostic Introduction Experimental Methods Interference Absorption Results Diagnostic Application Conclusions CHAPTER 7: Summary and Future Work Summary Future Work Publications APPENDICES APPENDIX A: TABLES OF RAW DATA x

10 A.1 Ignition delay times for the butanol isomers A.2 Ethanol + OH Rate Constant Measurements A.3 tert-butanol + OH Rate Constant Measurements A.4 Cyclohexene Decomposition Rate Constant Measurements APPENDIX B: ADDITIONAL DATA ON THE PYROLYSIS AND OXIDATION OF THE BUTANOL ISOMERS B.1 Ignition Delay Times of 2-Butanol and tert-butanol B.2 Ignition Delay Times of 1-Butanol in Air B.2 Multi-Species Time-histories for 2-Butanol Pyrolysis APPENDIX C: UNCERTAINTY ANALYSIS OF ALCOHOL + OH REACTION RATE CONSTANT MEASUREMENTS Bibliography xi

11 List of Tables Table 2.1: Dimensions of the shock tubes utilized in this work. Diameter refers to the driven section. Table 2.2: Comparison of the measured room-temperature cross-sections in the current work with data from the PNNL database 56. Units are m 2 mol -1. Uncertainty in the current study is ± 3%. Table 5.1: Rate constants for reactions modified and added to the Silke at al. 121 mechanism. Units: s -1 (unimolecular), cm 3 mol -1 s -1 (bimolecular) Table A-1: Summary of measured ignition delay times for 1-butanol diluted in argon. T and P values correspond to the initial post-shock conditions. Table A-2: Summary of measured ignition delay times for 2-butanol diluted in argon. T and P values correspond to the initial post-shock conditions. Table A-3: Summary of measured ignition delay times for iso-butanol diluted in argon. T and P values correspond to the initial post-shock conditions. Table A-4: Summary of measured ignition delay times for tert-butanol diluted in argon. T and P values correspond to the initial post-shock conditions. Table A-5: Summary of measured ignition delay times for 1-butanol in stoichiometric air. Mixtures made with N 2 and O 2 only. T and P values correspond to the initial post-shock conditions. Table A-6: Summary of the measurements of the overall rate constant for the ethanol + OH reaction. Mixtures are balanced in argon. Table A-7: Summary of the measurements of the non-β rate constant for the ethanol + OH reaction. Mixtures are balanced in argon. Table A-8: Summary of the measured 16 k. Mixtures are balanced in argon. Table A-9: Summary of the measured 18 k. Mixtures are balanced in argon. xii

12 Table A-10: Summary of the rate constant measurements for cyclohexene decomposition. All mixtures are balanced in argon. xiii

13 List of Figures Figure 1.1: Molecular structure of the four butanol isomers. Greek letters represent the notation for the various molecular sites. Figure 2.1: Schematic of the shock tube. a-d show the different stages of a shock tube experiment. a.) at vacuum. b.) filled with driver and driven gas. c.) post diaphragm burst. d.) post incidentshock reflection Figure 2.2: Representative pressure for an argon shock using helium driver gas. Post-reflectedshock conditions: T = 1512 K, P = 1.35 atm. Figure 2.3: Representative pressure trace for an argon shock using a driver insert and a tailored 60/40 He/N 2 driver gas. Post-reflected-shock conditions: T = 965 K, P = 2.25 atm. Figure 2.4: Experimental apparatus for emission measurements. Further details on the optical arrangement for emission measurements can be found in previous work 49. BP = Bandpass. Figure 2.5: Experimental apparatus for direct laser absorption measurements using common mode rejection. BP = Bandpass. I and I ref represent the transmitted and reference light intensities, respectively. Figure 2.6: Measured Absorption cross-sections of cyclohexene, 1,3-butadiene, and 1,3- cyclohexadiene from atm. Data exhibited no pressure dependence. Figure 2.7: OH time-histories during the pyrolysis of 15.5 ppm TBHP/H 2 O/Argon. Solid lines represent measurements, dashed lines represent simulations using the Leplat et al. 58 mechanism (see Section 4.3) to which the TBHP sub-mechanism from Pang et al. 57 was appended. Figure 3.1: Ignition delay time measurement of 2-Butanol in 4% O 2 diluted in Ar, = 1. Initial post-reflected-shock conditions: T = 1176 K, P = 40.5 atm. Figure 3.2: Measured ignition delay times for 1-butanol. P = 1.2 atm, ϕ = 1, x O2 = 0.03, diluted in argon. Data by Moss et al. 41 are not scaled to a common pressure (P atm). xiv

14 Figure 3.3: Measured ignition delay times for 1-butanol. P = 1.2 atm, ϕ = 1, x O2 = 0.045, diluted in argon. Figure 3.4: Measured ignition delay times for 1-butanol. P = 3.0 atm, ϕ = 1, x O2 = 0.04, diluted in argon. Figure 3.5: Measured ignition delay times for 2-butanol. P = 1.2 atm, ϕ = 1, x O2 = 0.06, diluted in argon. Data by Moss et al. 41 are not scaled to a common pressure (P atm). Figure 3.6: Measured ignition delay times for 2-butanol. P = 1.2 atm, ϕ = 1, x O2 = 0.03, diluted in argon. Data by Moss et al. 41 are not scaled to a common pressure (P atm). Figure 3.7: Measured ignition delay times for iso-butanol. P = 1.2 atm, ϕ = 1, x O2 = 0.03, diluted in argon. Data by Moss et al. 41 are not scaled to a common pressure (P atm). Figure 3.8: Measured ignition delay times for tert-butanol, P = 1.2 atm, ϕ = 1, x O2 = 0.03, diluted in argon. Data by Moss et al. 41 are not scaled to a common pressure (P atm). Figure 3.9: Measured ignition delay times for 1-butanol, x O2 = 0.04, diluted in argon. Pressure in atmospheres. The Sarathy et al. mechanism 8,9 was modified to include rate constants for the unimolecular decomposition of 1-butanol from work by Rosado-Reyes and Tsang 61. Uncertainties are approximately equal to twice the height of the data points. Figure 3.10: Measured ignition delay times for iso-butanol, x O2 = 0.04, diluted in argon. Pressure in atmospheres. Uncertainties are approximately equal to twice the height of the data points. Figure 3.11: Measured ignition delay times for the butanol isomers at 43 atm, x O2 = 0.04, diluted in argon. Uncertainties are approximately equal to twice the height of the data points. Figure 3.12: Measured and simulated pressure for 1% 1-butanol pyrolysis. Initial post-reflectedshock conditions: T = 1391 K, P = 1.54 atm. Figure 3.13: Simulated temperature for 1% 1-butanol pyrolysis. Initial conditions: T = 1477 K, P = 1.52 atm. xv

15 Figure 3.14: Simulated CO mole fraction for 1% 1-butanol pyrolysis. Initial conditions: T = 1477 K, P = 1.52 atm. CV simulations performed using the Sarathy et al. 8,9 mechanism. Figure 3.15: Measured OH mole fraction for 1% 1-butanol pyrolysis. Figure 3.16: Measured H 2 O mole fraction for 1% 1-butanol pyrolysis. Figure 3.17: Simulated OH mole fraction for 1% 1-butanol pyrolysis. CV simulations performed using the Cook et al. 64 mechanism. Temperature and pressure indicate initial post-reflected-shock conditions. Figure 3.18: Measured H 2 O mole fraction for 1% 1-butanol pyrolysis. Solid lines represent measurements, dotted lines represent CV simulations performed using the simulations performed using the Sarathy et al. 8,9 mechanism. Figure 3.19: Measured OH mole fraction for 1% 1-butanol pyrolysis. Solid lines represent measurements, dotted lines represent CV simulations performed using the Sarathy et al. 8,9 mechanism. Figure 3.20: H 2 O sensitivity analysis for 1% 1-butanol pyrolysis. Initial conditions: T = 1348 K, P = 1.83 atm. CV simulations performed using the Sarathy et al. 8,9 mechanism. Figure 3.21: Measured CO mole fraction for 1% 1-butanol pyrolysis. Solid lines represent measurements, dotted lines represent CV simulations performed using the Sarathy et al. 8,9 mechanism. Figure 3.22: CO sensitivity for 1% 1-butanol pyrolysis. Post-reflected-shock conditions: Initial Conditions: T = 1603 K, P = 1.36 atm. CV simulations performed using the Sarathy et al. 8,9 mechanism. Figure 3.23: Measured CO mole fraction for 1% 1-butanol pyrolysis. Initial post-reflected-shock conditions: T = 1477 K, P = 1.52 atm. Figure 3.24: C 2 H 4 mole fraction for 1% 1-butanol pyrolysis. Solid lines represent measurements, dotted lines represent CV simulations using the Sarathy et al. 8,9 mechanism. xvi

16 Figure 3.25: C 2 H 4 sensitivity analysis for 1% 1-butanol pyrolysis. Initial conditions: T = 1348 K, P = 1.83 atm. CV simulations performed using the Sarathy et al. 8,9 mechanism. Figure 3.26: Measured OH mole fraction for 1% iso-butanol pyrolysis. Solid lines represent measurements, dotted lines represent CV simulations performed using the Sarathy et al. 8,9 mechanism. Figure 3.27: Measured H 2 O mole fraction for 1% iso-butanol pyrolysis. Solid lines represent measurements, dotted lines represent CV simulations performed using the Sarathy et al. 8,9 mechanism. Figure 3.28: OH sensitivity for 1% iso-butanol pyrolysis. Initial Conditions: T = 1440 K, P = 1.73 atm. CV simulations performed using the Sarathy et al. 8,9 mechanism. Figure 3.29: Measured CO mole fraction for 1% iso-butanol pyrolysis. Solid lines represent measurements, dotted lines represent CV simulations performed using the Sarathy et al. 8,9 mechanism. Figure 3.30: CO sensitivity for 1% iso-butanol pyrolysis. Post-reflected-shock conditions: Initial Conditions: T = 1622 K, P = atm. CV simulations performed using the Sarathy et al. 8,9 mechanism. Figure 4.1: 16 OH and 18 OH spectra of the R 22 (5.5) transition in the A-X(0,0) band at 1000 K, 1 atm. 18 OH lineshape assumed to be the same as that of 16 OH as determined by Herbon et al OH linecenter taken from Cheung et al. 68. Figure 4.2: Peak absorbance near the R 22 (5.5) transition of 16 OH at the time of peak OH mole fraction during 0.1% tert-butanol/argon pyrolysis. 16 OH R 22 (5.5) transition linecenter at cm -1. Sub-plot shows absorbance time-history and indicates the time of peak absorbance. Post-reflected shock conditions: T 1515 K, P 1 atm. Figure 4.3: Measured 16 OH time-histories during neat TBHP pyrolysis, acquired at the linecenter of the R 11 (5.5) and R 22 (5.5) transitions in the A-X(0,0) band. 50 ppm TBHP, diluted in argon. Post-reflected shock conditions: T = 1108 K, P = 1.2 atm. xvii

17 Figure 4.4: Dominant reaction pathways related to ethanol + OH reactions. Figure 4.5: Sensitivity analysis of 16 OH in a labeled experiment. T = 1032 K, P = 1.08 atm, 349 ppm ethan 18 ol, 28 ppm TBHP, 80 ppm H 2 O, diluted in argon. Figure 4.6: Sensitivity analysis of 16 OH in an unlabeled experiment. T = 1029 K, P = 1.03 atm, 354 ppm ethan 16 ol, 14 ppm TBHP, 40 ppm H 2 O, diluted in argon. Figure 4.7: Representative 16 OH time-histories for ethan 16 ol/tbhp/argon mixtures (k non-β in units of cm 3 mol -1 s -1 ). Post-reflected shock conditions: T = 1023 K, P = 1.03 atm. Discrepancy in the rise of 16 OH is caused by the limited time resolution of the diagnostic (~5µs). Figure 4.8: Comparison of the measured overall and non-β rate constants for the title reaction with previous theoretical and experimental work at high temperatures. Curves by Zheng and Truhlar 79 represent calculations using the M08-SO/6-31+G(d,p) method. Curve labeled Fit was generated based on all experimental data shown in Figure Figure 4.9: Comparison of the measured branching ratio BR β with previous theoretical work. Figure 4.10: Comparison of the measured overall rate constant for the title reaction with previous theoretical and experimental work. Data from past studies are excluded if they were performed at conditions that are not sensitive to reactivity at the β-site. Data are best fit by the expression: k overall = 5.07 x 10 5 T 2.31 exp(608/t) cm 3 mol -1 s -1 Figure 4.11: Dominant reaction pathways related to tert-butanol + OH reactions. Figure 4.12: Sensitivity analysis of 16 OH in a labeled experiment. T = 1020 K, P = 1.2 atm, 500 ppm tert-butan 18 ol, 29 ppm TBHP, 75 ppm H 2 O, diluted in argon. Figure 4.13: Sensitivity analysis of 16 OH in an unlabeled experiment. T = 1020 K, P = 1.2 atm, 500 ppm tert-butan 16 ol, 17 ppm TBHP, 44 ppm H 2 O, diluted in argon. Figure 4.14: Representative 16 OH time-histories for tert-butanol/tbhp/argon mixtures (k in units of cm 3 molecule -1 s -1 ). Initial post-reflected shock conditions: T = 1020 K, P = 1.2 atm. Figure 4.15: Arrhenius plot of measured 16 k and 18 k. Solid lines show Arrhenius fits. xviii

18 Figure 4.16: Comparison of the measured overall tert-butanol + OH reaction rate constant (k 4.3 = 18 k ) with values used in mechanisms from the literature. Figure 4.17: Comparison of the measured branching ratio product BR 1 BR 2 near 1.1 atm with values used in mechanisms from the literature. Figure 4.18: Comparison of the estimated branching ratio BR 1 with values used in mechanisms from the literature. Figure 4.19: Comparison of the inferred branching ratio BR 2 near 1.1 atm with values used in mechanisms from the literature. Figure 5.1: Representative measurement and simulation of ethylene mole fraction time-histories. Reaction rate constant for simulations specified at the post-reflected-shock temperature. Note that the rate constant changes slightly throughout the measurement time due to a small decrease in temperature. 1% cyclohexene diluted in argon. Post-reflected-shock conditions: T = 1192 K, P = 3.52 atm. Figure 5.2: Measurements of the rate constant for cyclohexene decomposition in the current study, as well as a comparison with measurements from the literature. Pressure range in the current study is atm. Pressure in past studies is indicated if measurements were performed at multiple pressures. Uncertainties in the current study are approximately equal to the height of the data points. Figure 5.3: Subset of measurements of the rate constant for cyclohexene decomposition in the current study, as well as comparisons with measurements from the literature, in the temperature range where cyclohexene is commonly used as a reference. Pressure range in the current study is atm. Figure 5.4: Difference in the inferred temperature using chemical thermometry. ΔT = T previous work - T current work, where T current work is the inferred temperature using the rate constant expression for Reaction 1 from the current study, and T previous work is the inferred temperature using the rate constant for Reaction 5.1 from previous work. xix

19 Figure 6.1: Absorption spectrum of acetylene at 1400 K, 1 atm calculated using HITRAN Primary plot shows the entire spectrum from cm -1, subplot shows spectrum in the 3300 cm -1 band. Figure 6.2: Schematic of the proposed acetylene diagnostic for kinetic studies in shock tubes (BP = Bandpass) Figure 6.3: Comparison of the measured absorption spectrum of acetylene with previous work near cm -1 at 297 K, 1 atm. Brackets indicate the diluent. Measurements were performed using a % mixture in a 79.9 cm static cell. Figure 6.4: Comparison of the measured high-temperature absorption spectrum of acetylene near cm -1 with HITRAN simulations. Measurements were performed with acetylene diluted in argon, simulations assume dilution in air. Figure 6.5: Measured high-temperature absorption coefficient of acetylene at three different wavelengths near cm -1, scaled to 1 atm using Equations Data were acquired from atm. Lines represent the fits using Equations % Errors indicate deviations of the fits from the measurements. Standard deviations of errors at linecenter, cm -1, and cm -1 are 1.7%, 4.6%, and 3.7%, respectively. Figure 6.6: Measured shift of the absorption peak relative to that at room temperature and pressure (ν Shift = ν Hi-temp ν RTP ). Errors indicate the deviation of the fit using Equation 6.2 relative to the experimental data (ν Error = ν Fit ν Measured ).Uncertainty in the measurement is approximately ± cm -1. Figure 6.7: Measured high-temperature absorption coefficient of propyne and 1-butyne at three different wavelengths near cm -1. Propyne data at the wavelength of the acetylene absorption peak are fit using the expression: k ν, [cm -1 atm -1 ]= x10-4 T[K]. Pressures are indicated in selected propyne measurements in order to demonstrate that its absorption coefficient becomes increasingly wavelength independent at higher pressures. xx

20 Figure 6.8: Acetylene time histories during the pyrolysis of 0.75% propene/argon. Solid lines represent measurements, dashed lines represent CV simulations using the USC Mech. V2.0 kinetic mechanism. Legend indicates initial post-reflected shock conditions. Measurements and error bars do not account for the increase in the acetylene absorption coefficient caused by the reduction in temperature associated with the endothermic pyrolysis of propene. A representative temperature time-history is shown in Figure Figure 6.9: Acetylene time histories during the pyrolysis of 0.75% 1-butene/argon. Solid lines represent measurements, dashed lines represent CV simulations using the USC Mech. V2.0 kinetic mechanism. Legend indicates initial post-reflected shock conditions. Measurements and error bars do not account for the increase in the acetylene absorption coefficient caused by the reduction in temperature associated with the endothermic pyrolysis of 1-butene. Figure 6.10: Representative acetylene time-history during the pyrolysis of 0.75% propene/argon. T and P indicate initial post-reflected-shock conditions. Variable T data was calculated based on the simulated temperature time-history using the USC Mech V2.0 kinetic mechanism. Uncertainties in the Variable T data were estimated based on a 30 K uncertainty in the temperature profile from the kinetic simulation. Figure 6.11: Estimated detection limit (SNR = 1) of the proposed acetylene diagnostic as a function of temperature and pressure assuming an absorbance noise of and pathlength of cm. Figure B-1: Measured ignition delay times for 2-butanol, x O2 = 0.04, diluted in argon. Pressure in atmospheres. Uncertainties are approximately equal to twice the height of the data points. Figure B-2: Measured ignition delay times for tert-butanol, x O2 = 0.04, diluted in argon. Pressure in atmospheres. Uncertainties are approximately equal to twice the height of the data points. Figure B-3:Measured ignition delay times for 1-butanol, P = 20 bar, ϕ = 1, in air. Heufer et al. 34 data is subject to non-reactive, facility-dependent, pre-ignition pressure increases. xxi

21 Figure B-4: Ignition delay time measurement of 1-butanol in stoichiometric air. Initial reflected shock conditions: T = 906 K, P = 22.8 atm. Figure B-5: Ignition delay time measurement of 1-butanol in stoichiometric air. Initial reflected shock conditions: T = 833 K, P = 25.0 atm. Figure B-6: Pressure traces from CV autoignition simulations of 1-butanol in stoichiometric air using the Vranckx et al. 33 mechanism. P initial = 20 atm. Temperature refers to T initial. Figure B-7: Measured OH mole fraction for 1% 2-butanol pyrolysis. Solid lines represent measurements, dotted lines represent CV simulations performed using the Sarathy et al. 8,9 mechanism. Figure B-8: Measured H 2 O mole fraction for 1% 2-butanol pyrolysis. Solid lines represent measurements, dotted lines represent CV simulations performed using the Sarathy et al. 8,9 mechanism. Figure B-9: OH sensitivity for 1% 2-butanol pyrolysis. Initial Conditions: T = 1449 K, P = 1.8 atm. CV simulations performed using the Sarathy et al. 8,9 mechanism. Figure B-10: Measured OH mole fraction for 1% 2-butanol pyrolysis. Initial post-reflected-shock conditions: T = 1449 K, P = 1.8 atm Solid lines represent measurements, dotted lines represent CV simulations performed using the Sarathy et al. 8,9 mechanism. Figure B-11: Measured H 2 O mole fraction for 1% 2-butanol pyrolysis. Initial post-reflectedshock conditions: T = 1449 K, P = 1.8 atm Solid lines represent measurements, dotted lines represent CV simulations performed using the Sarathy et al. 8,9 mechanism Figure B-12: Measured C 2 H 4 mole fraction for 1% 2-butanol pyrolysis. Solid lines represent measurements, dotted lines represent CV simulations performed using the Sarathy et al. 8,9 mechanism. Figure B-13: C 2 H 4 sensitivity for 1% 2-butanol pyrolysis. Initial Conditions: T = 1449 K, P = 1.8 atm. CV simulations performed using the Sarathy et al. 8,9 mechanism. xxii

22 Figure B-14: Measured CO mole fraction for 1% 2-butanol pyrolysis. Solid lines represent measurements, dotted lines represent CV simulations performed using the Sarathy et al. 8,9 mechanism. Figure B-15: CO sensitivity for 1% 2-butanol pyrolysis. Initial Conditions: T = 1603 K, P = 1.36 atm. CV simulations performed using the Sarathy et al. 8,9 mechanism. Figure C-1: Magnitude of the uncertainty in the measured overall rate constant for the reaction ethanol + OH associated with each factor considered in the analysis. Random uncertainty factors are indicated by *, the rest are systematic. Uncertainties are ±, unless specified otherwise. 205 ppm ethan 18 ol, 12 ppm TBHP, 35 ppm H 2 O, diluted in argon. T = 914 K, P = 1.09 atm. Figure C-2: Magnitude of the uncertainty in the measured overall rate constant for the reaction tert-butanol + OH associated with each factor considered in the uncertainty analysis. Random uncertainty factors are indicated by *, the rest are systematic. Uncertainties are ±, unless specified otherwise. 500 ppm tert-butan 18 ol, 28 ppm TBHP, 81 ppm H 2 O, diluted in argon. T = 1167 K, P = 1.20 atm. xxiii

23 xxiv

24 1 CHAPTER 1: Introduction 1.1 Motivation One of the primary challenges facing society today is the need for environmentally friendly sources of energy. Fossil fuels, which currently account for 81% of worldwide energy usage 1, are responsible for 66% of the global greenhouse gas emissions 2. Global climate change such as rising temperatures and sea levels caused by increased greenhouse gas emission could potentially have a devastating effect on the sustainability of life on this planet 3. Furthermore, the combustion of fossil fuels in the transportation sector is a primary cause of urban pollution 4. One approach to solving these energy challenges is to convert fossil fuels to energy more efficiently. This approach has two specific goals: improving the energy efficiency of combustion devices in order to maximize the energy output per unit of consumed fossil fuels, and reducing pollutant emissions by designing combustion systems that combust fossil fuels more effectively. Though significant progress has been made in achieving these goals, improvements in efficiency cannot sufficiently reduce the consumption of fossil fuels in order to solve the energy challenges outlined above. Nonetheless, improvements in the design of combustion devices will continue to significantly mitigate the overall consumption of fossil fuels. A more long-term approach to solving the world s energy challenges is to develop affordable and clean energy sources that can replace fossil fuels altogether. Biofuels, which are any organic fuel derived from plants or animals on a renewable basis, are a promising alternative energy source that can be used as a substitute for fossil fuels without major modifications to the energy infrastructure. Due to their similar physical properties, biofuels are a likely candidate for replacing traditional fuels in the transportation sector, which accounts for approximately 21% of energy used worldwide 1. Though the combustion of biofuels has similar pollutant characteristics as the combustion of fossil fuels, biofuels have significantly lower life-cycle-greenhouse-gas- 1

25 emissions due to the removal of greenhouse gasses during the production process. Biofuel production has increased fivefold from 2000 to , and the share of biofuels in the transportation sector is expected to increase from 3% today 6 to 27% in Therefore, advancing the knowledge of both the production and combustion of biofuels is of significant scientific interest. 1.2 Chemical Kinetic Mechanisms The combustion of virtually all fuels proceeds via a series of chemical reactions between the fuel, oxidizer, and their fragments. In order to accurately simulate a chemically reacting system, a series of differential rate equations for each species identified in the reacting system must be solved using the known temperature- and pressure-dependent rate constants for each specified reaction. In addition, the temperature-dependent enthalpy and entropy for each of the species must be known in order to predict the thermodynamic properties of the reacting system. The chemical kinetic mechanism for a particular fuel simply refers to the collection of these kinetic and thermodynamic parameters, that when combined with appropriate gas-dynamic models, are a powerful tool for predicting the performance of combustion devices. The utility of chemical kinetic mechanism has increased significantly with the advent of powerful computing tools. Though past numerical studies of combustion devices required the use of highly simplified kinetic mechanisms in order to reduce computing times to a manageable duration, the continuing increase in computing power will enable engineers to use more complete chemical kinetic mechanisms to simulate their combustion designs. The complexity of chemical kinetic mechanism varies greatly depending on the molecular size of the fuels they describe. For example, the combustion of small molecules such as hydrogen can be accurately modeled using 10 species and 20 reactions 7. However, combustion simulations of the C4 alcohol butanol may require 284 species and 1892 reactions 8,9. The 2

26 significance of chemical reactions to the performance of chemical kinetic mechanisms is often hierarchical in nature, because certain chemical reactions affect the performance of a kinetic mechanism much more than others. For instance, the reaction H + O 2 OH + O is commonly regarded as the most important reaction in combustion because it affects the rate of combustion more than any other reaction for virtually any hydrocarbon. Therefore, the performance of chemical kinetic mechanisms can be improved significantly by studying the subset of chemical reactions that significantly affect its predictive capabilities. The development of chemical kinetic mechanisms is a highly iterative process. Researchers typically postulate the set of chemical reactions and corresponding temperaturedependent reaction rate constants that may occur during the combustion of a particular fuel. Rate constants for particular reactions can be measured, calculated, or estimated using a variety of theoretical and experimental methods. The kinetic mechanism is then tested against a variety of experimental targets such as ignition delay times, species time-histories, spatial concentration profiles, flame speeds, etc. If possible, discrepancies between the experimental measurements and mechanism predictions are then attributed to a subset of chemical reactions in the kinetic mechanism, and rate constants for these reactions are studied in greater detail. The mechanisms are then updated using more accurate reaction rate constants, typically resulting in better agreement with the experimental data. Due to the limited accuracy of theoretical methods for calculating reaction rate constants, experimental measurements of global kinetic targets are invaluable for validating and improving chemical kinetic mechanisms. The purpose of this thesis is to present novel experimental data and techniques that will advance the study of chemical kinetics and ultimately enable significant improvements to chemical kinetic mechanisms. Measurements of butanol ignition delay times and species timehistories presented in this work provide a wide array of kinetic targets for testing and refining chemical kinetic mechanisms. Several of these data have already been used for this purpose since publication. Furthermore, measurements of the rate constants for reactions of ethanol and tert- 3

27 butanol with OH radicals represent a highly accurate determination of critical reaction rate constants for these fuels. In order to perform these rate constant measurements, a novel technique that combines isotopic labeling and laser absorption in shock tubes was developed, and it will serve as a powerful tool of future kinetic studies. Measurements of the rate constant for cyclohexene decomposition will also significantly improve the accuracy of kinetic studies that utilize chemical thermometry or comparative rate techniques. Finally, the development of a laser absorption diagnostic for acetylene provides yet another target species that experiments can use to validate the performance of kinetic mechanism. 1.3 Butanol A primary focus of this thesis is the study of butanol kinetics. As shown in Figure 1.1, butanol is a C4 alcohol with four isomers, and it is a strong biofuel candidate because of its significant advantages compared to the current most abundantly used biofuel, ethanol. It has a larger energy density, it is less hygroscopic, which means it can be transported in gasoline pipelines, it can be blended with gasoline in higher concentrations, and it is less volatile 10,11. The synthesis of butanol has been of significant scientific interest, and a number of private companies have sought to commercialize the production process. The private sector has primarily focused on the commercialization of 1-butanol and iso-butanol due to their relatively low production costs 12,13. Butanol kinetics has been the subject of several recent scientific studies. Though past work has primarily focused on the kinetics of 1-butanol, several of the most recent studies have focused on the other isomers. Past experimental work has been performed in rapid compression machines 14,15, flames 16 22, flow reactors 17,22,23, static reactors 24, and internal combustion engines Shock tubes, in particular, have provided a wide array of kinetic targets including ignition delay times, species time-histories, and elementary reaction rate constant Several kinetic 4

28 mechanisms for the high-temperature oxidation of butanol have also been proposed, with limited success in matching the experimental targets generated in the above studies 8,9,31, In this study, a wide variety of chemical kinetic targets and reaction rate constants for butanol have been measured. These data have been used by scientists around the world to develop and improve their kinetic mechanisms. The details and implications of the various data types that were acquired are presented in their respective chapters. Figure 1.1: Molecular structure of the four butanol isomers. Greek letters represent the notation for the various molecular sites. 5

29 2 CHAPTER 2: Experimental Methods 2.1 Introduction Chemical kinetics can be studied using a variety of tools, though experiments typically contain two key elements. The first is a chemical reactor, which in this work is a shock tube. The second is a variety of diagnostics that are used to measured parameters of interest that are relevant to combustion inside the chemical reactor. In this work, laser absorption is used to measure the concentrations of various species in the shock tube, and light emission is utilized to accurately characterize the time of ignition. The main advantage of these diagnostics is that they operate with high-temporal resolutions necessary for monitoring kinetic processes in real time, and they are also in-situ, which means that they do not interfere with the chemical processes that occur in the shock tube. 2.2 Shock Tube Facility Overview A shock tube is an ideal reactor for studying chemical kinetics due to its gas-dynamic simplicity. Shock tubes create a high-temperature and high-pressure environment that ideally exhibits homogeneous, adiabatic, constant-volume (CV), stagnant gas conditions for the reacting mixture. Therefore, since virtually all non-kinetic processes such as fluid flow, transport, turbulence, and heat transfer are negligible, a shock tube can be modeled as a simple homogeneous, CV, adiabatic reactor. Using this model, the primary computational task of numerical solvers is to solve the differential rate equations for the reactions specified in the kinetic mechanism, which is a relatively simple computational task. It is noted that shock tubes do not exhibit ideal behavior under all conditions, and experiments must be carefully designed if the ideal model is expected to accurately simulate the experimental environment. 6

30 As shown in Figure 2.1a, a shock tube is simply a tube, typically stainless steel and round, divided into two sections separated by a diaphragm. To operate the shock tube, the test mixture is placed into the driven section, and the driver section is filled to a higher pressure, often with an inert gas (Figure 2.1b). When the pressure difference across the diaphragm exceeds the breaking pressure, the diaphragm bursts and an incident shock wave travels toward the endwall of the shock tube, thus increasing the temperature and pressure of the mixture behind it (Figure 2.1c). Once the incident shock wave reaches the endwall, it reflects, and the reflected shock wave further increases the temperature and pressure of the test gas (Figure 2.1d). The gas behind the reflected shock wave exhibits the ideal conditions for studying chemical kinetics that are described above. Measurements are typically performed at an axial location close to the endwall of the shock tube, for example 1-2 cm from the endwall in the Stanford shock tubes, because that is where the performance of the shock tube is most ideal. The dimensions and characteristics of the three Stanford shock tubes used in this study are shown in Table 2.1. Figure 2.1: Schematic of the shock tube. a-d show the different stages of a shock tube experiment. a.) at vacuum. b.) filled with driver and driven gas. c.) post diaphragm burst. d.) post incidentshock reflection 7

31 Shock Tube Diameter [cm] Driver Length [m] Driven Length [m] NASA KST HPST Table 2.1: Dimensions of the shock tubes utilized in this work. Diameter refers to the driven section. A representative pressure time-history for a shock tube experiment in an inert gas on the KST facility is shown in Figure 2.2. The step changes in pressure at points A and B represent the arrival of the incident and reflected shock wave at the measurement location, respectively. The arrival time of the reflected shock wave at the measurement location is defined as time zero, i.e. the time at which chemical reactions begin to occur at this location. In most experiments, this definition of time zero is adequate because the heating of the test mixture in the time interval between the incident and reflected shocks is typically negligible, since the temperature behind the incident shock is much lower than that behind the reflected shock. At times after point C, the pressure and temperature begin to increase slightly due to non-idealities in the shock tube, thus limiting the ideal test time for experiments at the conditions in Figure 2.2 to approximately 1000 µs. Point D represents the termination of the overall test time shock tube due to the arrival of the expansion fans at the measurement location, thus causing a rapid drop in the temperature and pressure. 8

32 P [atm] C D B A time [ s] Figure 2.2: Representative pressure for an argon shock using helium driver gas. Post-reflectedshock conditions: T = 1512 K, P = 1.35 atm. Although the ideal test time at the representative conditions shown in Figure 2.2 is 1000 µs, various methods are utilized in this work in order to extend the ideal test time. Driver inserts are used in order to eliminate the facility dependent increase in pressure and temperature after point C in Figure Furthermore, driver gas tailoring is used to eliminate the increase in pressure associated with the reflection of the reflected shock wave from the contact surface between the driver and driven gasses, as well as to extend the overall test time by reducing the speed of sound in the driver section in order to delay the arrival of the expansion fans at the endwall of the shock tube 45. A representative pressure trace of experiments conducted using driver inserts and driver gas tailoring in order to extend the test time to 8000 µs is shown in Figure

33 P [atm] time [ s] Figure 2.3: Representative pressure trace for an argon shock using a driver insert and a tailored 60/40 He/N 2 driver gas. Post-reflected-shock conditions: T = 965 K, P = 2.25 atm. Mixtures used to perform shock tube experiments are typically generated in a magnetically-stirred stainless steel mixing tank and are typically stirred for at least 30 minutes. Relative molar fractions of the mixture components are calculated manometrically. In order to ensure that the vapors inside the mixing tank do not condense, the partial pressure of each component in the mixture is typically lower than its vapor pressure by at least a factor of three Temperature and Pressure Measurements Due to the sensitivity of chemical kinetic processes to temperature and pressure, accurate knowledge of these parameters in the reflected shock region of the shock tube is critical. Temperature and pressure behind the reflected shock wave were calculated using the normal shock relations with known initial temperature, pressure, mixture composition, and incident shock speed at the endwall. Calculations are performed using an in-house code that is able to account for the temperature-dependent thermodynamic properties of the gas mixtures employed. 10

34 Incident shock speeds are determined from shock arrival times at a series of five (NASA and KST shock tubes) or six (HPST shock tube) pressure sensors distributed over the last 1.5 m of the shock tube. The time interval between the arrival of the incident shock wave at two consecutive transducers is used to calculate the average velocity of the incident shock wave across the known distance between the transducers. It is observed that the incident shock speed attenuates linearly as the shock wave approaches the endwall. Therefore, a linear extrapolation of the incident shock speed is used to calculate the incident shock speed at the endwall. The primary source of the uncertainty in the temperature and pressure behind the reflected shock wave is the determination of incident shock speed at the endwall of the shock tube. In the shock tubes used in this study, the incident shock speed at the endwall is known to within ± 0.13%, and the final uncertainty in the calculated temperature and pressure is known to within ± 0.35% and ± 0.7%, respectively, for dilute mixtures. Mixtures containing high fuel concentrations exhibit greater uncertainties, because the uncertainty in the fuel concentration itself affects the calculation of the post-reflected-shock temperature. A more detailed discussion of the uncertainties in the temperature and pressure behind the reflected shock wave is provided in Section Experimental Modeling Virtually all experiments performed in this work require numerical modelling in order to advance the knowledge of chemical kinetics. Modeling shock tube experiments requires a chemical kinetic mechanism as well as an appropriate gas-dynamic model of the chemical reactor. Generally, parameters of the chemical kinetic mechanism are treated as variables that may be adjusted to achieve better agreement between the experiments and the simulations. However, the choice of an appropriate gas-dynamic model is critical for ensuring that any discrepancies between the experimental data and the simulations are attributed to flaws in the kinetic mechanism. 11

35 In this work, all shock tube experiments are modelled using a homogeneous, constantvolume (CV), constant internal energy (adiabatic) model. This model is a close representation of the performance of the shock tube, as both the temperature and pressure behind the reflected shock wave remain constant in experiments containing unreactive mixtures 46. Furthermore, numerical simulations in previous work indicate that heat transfer from the reacting mixture behind the reflected shock wave to the walls of the shock tube is negligible at the time scales of the current experiments 47. It is noted that significant heat release of the reacting mixture inside the shock tube, such as that caused by ignition, causes the ideal model of the shock tube to break down. Therefore, ignition experiments in this work are not modelled beyond the time of ignition. The shock tube model described above is executed using the CHEMKIN-PRO 48 software suite. A key function of this software program that is used continuously in this work is the ability to perform sensitivity analysis of species concentrations to rate constants in the chemical kinetic mechanism. The normalized sensitivity for the concentration of species i ([C] i ) at a given time to the rate constant for reaction j (k j ) is defined in Equation 2.1: Equation 2.1 Though a given species concentration is typically sensitive to a variety of reaction rate constants, sensitivity analysis is a valuable tool for designing experiments where the measured species timehistories are sensitive to a small subset of chemical reactions. In some experiments where a particular species exhibits sensitivity to a single chemical reaction, the rate constant for that reaction may be inferred directly by adjusting the rate constants in the kinetic mechanism until good agreement is achieved between the experimental data and the simulations. However, the accuracy of the rate constants of secondary reactions in the chemical kinetic mechanism must be 12

36 given careful consideration before any rate constants can be modified in order to achieve agreement with the experimental data. 2.3 Emission Diagnostics Ignition delay time in a shock tube is defined as the time interval between shock heating due to the reflected shock wave and the primary ignition event. A comparison of measured and simulated ignition delay times in shock tubes and rapid compression machines is one of the most common methods for evaluating the accuracy of chemical kinetic mechanisms. During the ignition process, a significant increase in the concentration of radical species occurs. Therefore, one of the methods for identifying the time of ignition in a chemical reactor is to identify the sudden growth in radical species concentrations. This can be achieved by measuring the emission of light from excited OH radicals (OH*) at 307 nm from the A 2 Σ + X 2 Π band. Emission signals from other sources are rejected using a narrow bandpass UG-5 filter. As shown in Figure 2.4, emission of light can be measured at both the sidewall and endwall locations in the shock tube. The simplest measurements are performed at the endwall of the shock tube, where the detector simply collects light emitted at any location in the shock tube. In both endwall and sidewall diagnostics, it is critical that the emission signal can be attributed to a particular axial location in the shock tube, because time zero varies along the axis of the shock tube depending on the arrival time of the reflected shock wave. By assuming that ignition occurs near the endwall of the shock tube before at any other location, the initial rise in the emission signal can be attributed to ignition near the endwall. Therefore, since the arrival time of the reflected shock at the endwall is known, the time interval between shock heating and ignition can be inferred. Emission measurements can also be performed in the direction perpendicular to the axis of the shock tube. In these measurements, the optical setup shown in Figure 2.4 is used to 13

37 constrain the axial length (i.e. spatial resolution Δ) of the shock tube from which light can reach the measurement detector. By minimizing the spatial resolution, the variations in time zero for the gasses whose emission is recorded by the detector are also minimized. The time resolution of the emission diagnostic (assuming it is not limited by the detector bandwidth) is equal to the interaction time of the reflected shock wave with the gasses within the slab of the shock tube of thickness equal to the spatial resolution. This interaction time is calculated by simply dividing the spatial resolution by the speed of the reflected shock wave, and it approximately 10 µs in this work. Further details on the optical arrangement and determination of spatial resolution are described in the discussion of the Type II optical setup in previous work 49. Figure 2.4: Experimental apparatus for emission measurements. Further details on the optical arrangement for emission measurements can be found in previous work 49. BP = Bandpass. 14

38 2.4 Laser Diagnostics Overview Laser diagnostics are a powerful tool for studying chemical kinetics in shock tubes. The primary laser diagnostic technique utilized in this work is fixed-wavelength direct absorption (scanned-wavelength direct absorption is discussed separately in Chapter 6). A significant advantage of this measurement technique compared to traditional gas sampling methods is that it enables rapid measurements at MHz rates that can be used to determine the time evolution of various kinetic targets in chemical reactors. A further advantage of laser diagnostic techniques is that the measurements are performed in-situ, and they do not perturb kinetic processes in the chemical reactor in any way. These rapid in-situ measurements can be used to measure concentrations of radical species with short lifetimes, which serves as an invaluable kinetic target for assessing the performance of chemical kinetic mechanisms. In this work, fixed-wavelength direct absorption was used to measure the time evolution of species mole fractions (species timehistories) for a variety of reacting mixtures in shock tubes. Species mole fractions are inferred from laser intensity measurement via the Beer- Lambert relation shown in Equations 2.2 and 2.3: T = Equation 2.2 Equation 2.3 where T is the transmission, I is the transmitted laser intensity through the shock tube in the presence of absorbing species, I 0 is the transmitted laser intensity through the shock tube without the presence of the absorbing species, α is the absorbance, P is the pressure, k i is the absorption coefficient of species i, and x i is the mole fraction of species i. The absorbance α in the Beer- Lambert relation is also occasionally described using a slightly different parameter convention: 15

39 where n is the overall number density and σ i is the absorption cross-section of species i. Typically, the absorption coefficient is commonly used to describe the absorption spectrum of molecule with narrow absorption features, whereas the absorption cross-section is often used to describe spectra of molecules with broad absorption features. The two conventions are completely equivalent. A schematic for a typical laser absorption experimental setup is shown in Figure 2.5. In most experiments, the transmitted light intensity is normalized by the light intensity (I ref ) measured by a reference detector that collects light that does not pass through the shock tube. This common-mode-rejection scheme is utilized in order to eliminate laser power fluctuations in the measurements of the transmitted laser intensities. Figure 2.5: Experimental apparatus for direct laser absorption measurements using common mode rejection. BP = Bandpass. I and I ref represent the transmitted and reference light intensities, respectively. If measurements are performed in the presence of only one absorbing species i, the Beer- Lambert relation can be rearranged to calculate its mole fraction using the following relation: 16

40 However, several of the measurements in this work are performed in the presence of multiple absorbing species at the target wavelength, though the target species is typically the strongest absorber. Nonetheless, absorption due to the other interfering species must be taken into account in order to correctly infer the mole fraction of the target species from laser absorption measurements. In the presence of interfering species, the mole fraction of a target species can be inferred by performing measurements at multiple wavelengths. Typically, the primary wavelength (online) is selected to overlap with a strong absorption feature of the target species, while the secondary wavelength (off-line) is selected to be near the target wavelength but at spectral location where the target species has a low absorption coefficient. With knowledge of the absorption coefficients of the target species i and interfering species int at both the on-line and off-line wavelengths, the mole fraction of the target species can be inferred directly using Equation 2.4: ( ) Equation 2.4 When the absorption feature of the target species is very narrow and the absorption spectrum of the interfering species is broadband, the on-line and off-line wavelengths can be chosen such that the absorption coefficient of the interfering species is constant at both wavelengths (R = 1), and the absorption coefficient of the target species is negligible at the off-line wavelength. In this case, the mole fraction of the target species can be inferred using a simplified version of Equation 2.4, as shown in Equation 2.5: 17

41 ( ) Equation Diagnostic Details In this work, six different species were measured at a variety of wavelength using several different lasers. Below are the details of each laser diagnostic that was used to perform measurements. 16 OH species time-histories were measured using direct absorption of light in the A- X(0,0) band near 307 nm. Measurements of 16 OH in experiments without the presence of 18 O isotopes were performed at the R 11 (5.5) transition because it has a strong absorption coefficient that has been studied in greatest detail 50,51. Measurements in the presence of 18 O were performed at the R 22 (5.5) in order to avoid spectral overlap between 16 OH and 18 OH at the target wavelength, thus resulting in a 16 OH concentration measurement that is independent of the presence of 18 OH (See Section 4.2). 16 OH species time-history measurements during butanol pyrolysis required characterization of interference absorption due to formaldehyde and acetaldehyde. In these experiments, 16 OH mole fractions were calculated using the two line technique described by Equation 2.5, assuming that the interfering species exhibit broadband absorption near the target wavelengths and that 16 OH does not absorb at the off-line wavelength (32611 cm -1 ). The target wavelengths were accessed by frequency-doubling the visible output of a narrow-linewidth ring dye laser. Visible light near 614 nm was produced by pumping Rhodamine 6G dye in a Spectra Physics 380A laser cavity using a Coherent Verdi 5W continuous wave laser at 532 nm. A temperature-tuned AD*A non-linear crystal was used for intracavity frequency-doubling. Further details on the 16 OH detection system as well as the 16 OH spectrum can be found elsewhere 50,51. C 2 H 4 species time-histories were measured using laser absorption at µm near the peak of a strong absorption feature of C 2 H 4. In some experiments, interference absorption was 18

42 taken into account by performing off-line measurements at µm away from the peak of the absorption feature. Since the separation of the two wavelengths is relatively large and the absorption of C 2 H 4 is non-negligible at the off-line wavelength, it was necessary to explicitly account for absorption of both C 2 H 4 and the interfering species at each wavelength, as described by Equation 2.4. A tunable CO 2 gas laser was used to access both wavelengths for measuring C 2 H 4 concentrations, and a common-mode-rejection scheme was used to significantly reduce laser noise. The major source of error associated with two-line C 2 H 4 measurements stems from data processing during manipulation of on-line and off-line measurements. Since on-line and off-line experiments are not performed simultaneously, shock-to-shock variations may become significant due to the relatively low differences between off-line and on-line absorbance in some experiments. These effects are minimized by ensuring that the post-reflected-shock temperature difference between on-line and off-line experiments did not exceed 15K. Further details about the C 2 H 4 detection scheme and detailed characterization of C 2 H 4 absorption coefficient are available elsewhere 52,53. H 2 O species time-histories were determined by measuring absorption of 2551 nm light at the peak of an absorption feature in the ν 3 fundamental vibrational band of H 2 O. A continuouswave, distributed feedback (DFB) diode laser near 2.5 µm was used to generate the required wavelength. A nitrogen purge system was implemented on the laser path in order to eliminate signal loss due to absorption by atmospheric water. Due to the stability of the DFB laser, common-mode-rejection was not required, and a measured H 2 O uncertainty of ± 6 % was achieved at long times. This uncertainty was largely caused by a temperature uncertainty throughout the test time which propagates into an uncertainty in the absorption coefficient (See Section 3.3.2). Further details on the H 2 O detection system as well as H 2 O line characterization can be found in previous work

43 CO time-histories were determined by measuring direct absorption of 4.56 µm light at the peak of the R(13) transition in the fundamental ro-vibrational band of CO. A quantum cascade (QC) laser operating in continuous mode was used to generate the required wavelength. A common-mode-rejection scheme was used which resulted in an uncertainty of approximately ± 6 % in the measurement, largely caused by a temperature uncertainty throughout the test time (See Section 3.3.2). Further details regarding the CO diagnostic setup are described elsewhere 55. The pre-shock fuel mole fraction inside the shock tube was verified by measuring the absorption of 3.39 µm HeNe laser light across the diameter of the shock tube. This technique takes advantage of broadband absorption exhibited by most hydrocarbons at 3.39 µm due to the presence of C-H bonds. In some experiments, the sensitivity of this detection scheme was increased by sampling gasses from the shock tube into a 29.9 m multi-pass optical cell. A detailed description of the fuel detection diagnostic is described in previous work Cross-section Measurements Though the temperature and pressure dependence of the absorption coefficient for many of the species measured in this study has already been characterized in previous work, a variety of absorption coefficients for new species have been measured here. Absorption coefficient measurements were performed in this work for two distinct reasons. The first was to infer the initial concentration of the fuels being studied in the shock tube before performing experiments, thus requiring knowledge of their absorption coefficient at room temperature. The second was to measure the formation or removal of particular species behind the reflected shock wave, thus requiring knowledge of the absorption coefficient at high temperatures and pressures. In several of experiments performed in this work, the vapor pressure of the fuels was of a similar order of magnitude as the partial pressure of fuel in the mixing tank. A further reduction of the partial pressure of the fuel in the mixing tank was not possible because it would result in an insufficient total mixing tank pressure for the mixture to be used in multiple shock tube 20

44 experiments. Furthermore, some fuels may be sticky, which means that they may absorb onto various surfaces. In experiments where absorption and/or adsorption were considered a possibility, the concentration of the fuel in the shock tube was measured using direct laser absorption at 3.39 µm in order to confirm that its concentration in the shock tube was equal to the manometric calculation. Absorption cross-sections of these fuels were measured using pure fuel mixtures in order to guarantee accurate knowledge of the partial pressure of the fuel in the shock tube. The shock tube was typically filled to a pressure of torr, which was typically limited by the vapor pressure of the fuel. It was observed that the measured cross-sections exhibited no pressure dependence, which is expected for broadband absorbers that were used as fuels in this study. A comparison of the measured absorption cross-sections in this study with data from the PNNL database 56 is shown in Table 2.2. Molecule Current PNNL Study Database 1-Butanol Butanol iso-butanol tert-butanol Ethanol Cyclohexene Table 2.2: Comparison of the measured room-temperature cross-sections in the current work with data from the PNNL database 56. Units are m 2 mol -1. Uncertainty in the current study is ± 3%. Cross-section measurements at high-temperatures were primarily performed for species relevant to inferring the rate constant for cyclohexene decomposition, which is discussed in Chapter 5. This work required measurements of the µm absorption cross-section of 1,3- butadiene, cyclohexene, and 1,3-cyclohexadiene. Experimental measurements as well as fits to 21

45 Absorption Crossection [m 2 mol -1 ] the data are shown in Figure 2.6, and the measurements exhibited no pressure dependence from atm Cyclohexene 1,3-Butadiene 1,3-Cyclohexadiene [m 2 mol -1 ] = T[K] [m 2 mol -1 ] = T[K] [m 2 mol -1 ] = T [K] Figure 2.6: Measured Absorption cross-sections of cyclohexene, 1,3-butadiene, and 1,3- cyclohexadiene from atm. Data exhibited no pressure dependence. 2.5 Fuel + OH Reaction Rate Constant Measurements Overview Rate constant measurements for the reactions fuel + OH products were performed by creating a pseudo-first order reaction environment for the removal of OH radicals. Experiments exhibiting pseudo-first order kinetics are designed by creating mixtures between two reactants where the concentration of one of the reactants is approximately constant. In experiments where OH radicals react with fuel, this can be achieved if the fuel is in excess in the chemical reactor, thus preventing the reaction of OH radicals with the fuel from significantly reducing its absolute concentration. This is quantified mathematically using the rate equation of OH radicals for the reaction fuel + OH products: 22

46 ( ) If the concentration of fuel is approximately constant, the above equation can be integrated explicitly and the concentration time-history of OH can be inferred analytically: Since the concentration of OH exhibits an exponential decay, k reaction can be determined from measurements of the time constant of OH decay, assuming that that fuel concentration is known. Though the above analysis illustrates the utility of pseudo-first order experiments, it does not account for secondary reactions or slight changes in the fuel concentration that may affect the decay rate of OH. In order to account for these phenomena, the rate constant for a target reaction is inferred by fitting the simulated OH time-histories from the kinetic model to the experimental data using the fuel + OH reaction rate constant as a free parameter that affects the pseudo-firstorder decay rate of OH. In this work, the rate constants for relevant secondary reactions are wellcharacterized, thus yielding highly-accurate measurements of the rate constants for fuel + OH reactions (see Section 2.5.2). As shown in Figure 4.7, the representative OH time-history during measurements of the rate constant for the reaction of ethanol + OH products exhibits pseudofirst order decay. In addition, simulations of the measured pseudo-first order decay rate exhibit high sensitivity to the target reaction rate constants Secondary Reactions The accuracy of rate constant measurements for reactions of fuel with OH radicals using kinetic simulations of pseudo-first-order experiments are somewhat dependent on accurate knowledge of the rate constants for secondary reactions. In the current work, since tert- 23

47 butylhydroperoxide (TBHP) is used as a fast source of OH, the rate of TBHP decomposition (OH generation) can affect the simulations of the measured OH time-histories. Measurements of the rate constants for the target fuel + OH reaction are particularly sensitive to the TBHP decomposition rates at temperatures between K, because the timescale of TBHP decomposition is on the same order-of-magnitude as that of OH removal by the fuel. At temperatures above 1000 K, TBHP decomposition becomes so fast that TBHP is fully decomposed by the time that kinetic simulations are fit to the exponential decay of OH, thus resulting in a measurement that is insensitive to the TBHP decomposition rate. At temperatures below 900K, the decomposition of TBHP is too slow for the OH generation and removal process to occur independently, thus constraining the minimum temperature at which experiments can be conducted. Further decomposition of the fragments of TBHP produces CH 3 radicals in similar concentrations as OH radicals. Since the reaction of OH radicals with CH 3 radicals is very fast, it can significantly contribute to the removal of OH in pseudo-first-order experiments. Therefore, it is critical that kinetic simulations in these experiments contain accurate rate constants for these reactions. In the current work, the sub-mechanism for critical reactions in involving TBHP and CH 3 radicals was taken from previous work by Pang et al. 57. As discussed by Pang et al. 57 the accuracy of the TBHP sub mechanism can be validated by measuring concentration time-histories during neat TBHP decomposition. If simulations accurately model the rise in OH radicals during TBHP decomposition as well as the decay in OH due to reactions with CH 3 radicals, it can be concluded that he kinetic mechanism accurately describes the abovementioned reactions. As shown in Figure 2.7, experiments of neat TBHP decomposition in this work indicate that the rise in OH near 900 K, and the decay of OH at near both 900 K and 1200 K is accurate (rise of OH cannot at be resolved at high temperatures). Therefore, it is concluded that the TBHP submechanism developed by Pang et al. 57 is accurate. 24

48 OH Mole Fraction K, 1.13 atm 1162 K, 1.00 atm time [ s] Figure 2.7: OH time-histories during the pyrolysis of 15.5 ppm TBHP/H 2 O/Argon. Solid lines represent measurements, dashed lines represent simulations using the Leplat et al. 58 mechanism (see Section 4.3) to which the TBHP sub-mechanism from Pang et al. 57 was appended. 25

49 3 CHAPTER 3: Kinetic Studies of the Butanol Isomers 3.1 Introduction As discussed in Section 1.3, butanol is a promising biofuel candidate with potential applications in the transportation sector. Therefore, kinetic studies of the isomers of butanol are of significant interest to the scientific community. In this work, ignition delay times for the four butanol isomers were measured behind reflected shock waves across a variety of conditions. In addition, multi-species time-histories during the pyrolysis of 1-,2-, and iso-butanol were measured using direct laser absorption. These data have been used extensively by several research groups in order to validate and improve the performance of chemical kinetic mechanisms. Though a variety of chemical kinetic mechanisms have been developed for the butanol isomers 8,9,31,40 43, the mechanism by Sarathy et al. 8,9 is typically regarded as the most accurate for describing the overall kinetics of the butanol isomers. The accuracy of the mechanism is attributed to the extensive set of experimental and theoretical data against which it was validated, partially because it is the most recent of the comprehensive kinetic mechanisms for butanol. Due to the extensive set of experimental data presented here, not all of the data can be modeled with every available kinetic mechanism. Indeed, an assessment and comparison of the various chemical kinetic mechanisms with the aim of selecting a series of optimal rate constants expressions for reactions relevant to butanol kinetics could span an entire PhD thesis. The purpose of the analysis presented here is to demonstrate how the data acquired in this study can be used to optimize chemical kinetic mechanisms, but the optimization itself is not performed here. As a result, the kinetic mechanism by Sarathy et al. 8,9 is primarily used for comparing experimental data with kinetic simulations, though other mechanisms may also be discussed in 26

50 cases where they offer superior performance to the Sarathy et al. 8,9 mechanism. In addition, due to the overall complexity of the combustion of butanol, a detailed analysis of the oxidation pathways for butanol is not presented here. Finally, the primary focus of the discussion in this work will be on 1-butanol and iso-butanol, because as discussed in Section 1.3, these isomers are the primary biofuel candidates. The majority of data acquired during the pyrolysis and oxidation of 2-butanol and tert-butanol are presented in APPENDIX B, and all ignition delay time measurements are tabulated in APPENDIX A. 3.2 Ignition Delay Time Measurements Overview One of the simplest methods for evaluating the global accuracy of chemical kinetic mechanisms is by comparing the predicted and measured ignition delay time of a fuel behind reflected shock waves in a shock tube. Although shock tube studies of various butanol isomers have been performed in previous studies 31 35,39,41, no single study has measured ignition delay times for all four isomers over a wide range of pressures. In addition, there exists a significant discrepancy between certain previous measurements, especially for isomers other than 1-butanol. Measurements in this work are performed in order to expand the range of conditions available for comparisons of numerical simulations, and to achieve closure on the discrepancies in the experimental data available in the literature. In this study, ignition delay times were measured for all four isomers of butanol. Conditions studied include temperatures from K, pressures from atm, and equivalence ratios of 1.0 and 0.5 in mixtures containing 4% O 2 dilute in argon. Several additional data sets were collected at atm in order to replicate conditions used by previous researchers. Additional data were also collected at 20 atm for stoichiometric 1-butanol mixtures in air at temperatures as low as 800 K. Low-temperature/high-pressure measurements were 27

51 Relative Signal [V] performed using driver inserts and driver gas tailoring to insure near-constant-volume test conditions at long test times. Measurements at pressures below 4 atm were performed on the KST shock tube and endwall emission data was used to infer the ignition delay time. Measurements at pressures above 10 atm were performed on the HPST shock tube, and sidewall emission data was used to infer the ignition delay time (endwall data is not available on this shock tube). In both sets of experiments, ignition delay time was defined as the time between the arrival of the reflected shock wave at the observation port and the extrapolation of the maximum slope of the emission signal to the baseline. Representative data are shown in Figure 3.1. The primary uncertainty in the ignition delay time measurements presented here is caused by the uncertainty in the temperature behind the reflected shock wave (See Sections and 5.3). Ignition delay times of the butanol isomers are not highly sensitive to equivalence ratio, pressure, and impurities (at the levels present in the shock tubes utilized in this work) Photodetector - Sidewall Pressure - Reactive Shock Pressure - Non-Reactive Shock ign time [ s] Figure 3.1: Ignition delay time measurement of 2-Butanol in 4% O 2 diluted in Ar, = 1. Initial post-reflected-shock conditions: T = 1176 K, P = 40.5 atm. It is important to note the role of pre-ignition heat release when modeling shock tube experiments containing butanol mixtures. It was observed in experiments that there exists a slight 28

52 pre-ignition pressure increase even in dilute combustion experiments for all four isomers of butanol. Experiments in unreactive mixtures indicate that these effects are not caused by typical pressure increases that result from shock wave-boundary layer interactions. Figure 3.1 clearly shows that the measured pressure traces exhibit slight pre-ignition pressure increases compared to the pressure trace for an experiment containing pure argon. Such pressure increases are caused by pre-ignition heat release which increases the temperature and pressure in the constant-volume (CV) model calculation. These effects are also present in shock tube experiments, although in this case, the reflected shock adjusts its speed in a way that partially offsets the CV constraint. Preignition pressure increases cause gases inside the measurement volume of a shock tube to expand slightly through perturbations in the reflected shock speed, whereas this effect would be absent in a CV reactor. It is expected that shock tube experiments containing significant pre-ignition pressure rises caused by heat release would thus have longer ignition times than would be found in a true CV experiment, because the temperature increase associated with pre-ignition energy release would be lower in the shock tube than in the CV apparatus. Although pre-ignition pressure increases were observed in this study, their effect was minimized by using dilute mixtures. In the discussion of experiments in stoichiometric air (See APPENDIX B), it is evident that using non-dilute mixtures has significant implications on experimental modeling. Finally, it is noteworthy that pre-ignition pressure increases in 1-butanol experiments have also been observed in rapid compression machine ignition delay time measurements by Weber et al. 14 and in shock tube ignition delay time measurements by Heufer et al

53 3.2.2 Results Mixtures diluted in argon Figures 3.2 and 3.3 show an attempt to repeat 1-butanol ignition delay time experiments at conditions in studies by Moss. et al. 41 and Black et al. 31, respectively. Fairly good agreement is found with these past experiments for 1-butanol, although ignition delay time measurements in this work are shorter by up to 20% compared to those of the other experimenters. In addition, Figures 3.2 and 3.3 show comparisons with an ignition delay time correlation for 1-butanol developed by Noorani et al. 32 based on their shock tube ignition delay time measurements. Although no attempts were made to replicate experiments at the exact conditions used by Noorani et al. 32, their correlation agrees well with our experimental data for 1-butanol at conditions used by Moss et al. 41 and Black et al. 31. It should be noted that the conditions used by Moss et al. 41 and Black et al. 31 are slightly outside of the range of conditions for which the Noorani et al. 32 correlation was developed. Finally, as shown in Figure 3.4, Zhang et al 39 were successfully able to replicate measurement of ignition delay times for 1-butanol from the current work. Overall, there exists reasonable agreement among the experimental data sets for shock-tube ignition delay time measurements for 1-butanol. 30

54 t ign [ s] t ign [ s] 1667 K 1538 K 1429 K 1333 K 1000 Current Study Moss et al. Noorani et al. - Correlation 100 = 1, X O2 = /T [K -1 ] Figure 3.2: Measured ignition delay times for 1-butanol. P = 1.2 atm, ϕ = 1, x O2 = 0.03, diluted in argon. Data by Moss et al. 41 are not scaled to a common pressure (P atm) K 1429 K Current Study Black et al. Noorani et al. - Correlation 1250 K 1000 = 1, X O2 = /T [K -1 ] Figure 3.3: Measured ignition delay times for 1-butanol. P = 1.2 atm, ϕ = 1, x O2 = 0.045, diluted in argon. 31

55 t ign [ s] 1429 K 1333 K 1250 K 1000 Current Study Zhang et al. = 1, X O2 = /T [K -1 ] Figure 3.4: Measured ignition delay times for 1-butanol. P = 3.0 atm, ϕ = 1, x O2 = 0.04, diluted in argon. Despite the agreement between measurements of ignition delay times for 1-butanol, significant disagreement was observed with measurements by Moss et al. 41 for 2-butanol, shown in Figures 3.5 and 3.6, iso-butanol, shown in Figure 3.7, and tert-butanol, shown in Figure 3.8. Although the measured ignition delay times are similar at lower temperatures, divergence is evident at higher temperatures. Several possible causes for this disagreement were proposed and investigated, and it was concluded that the only plausible explanation for the significant disagreement between the experimental data is a significant impurity in the mixing tank and/or shock tube, or accidental confusion of fuel sources and/or oxidizing gases. 32

56 t ign [ s] t ign [ s] K 1538 K 1429 K 1333 K Current Study Moss et al. = 1, X O2 = /T [K -1 ] Figure 3.5: Measured ignition delay times for 2-butanol. P = 1.2 atm, ϕ = 1, x O2 = 0.06, diluted in argon. Data by Moss et al. 41 are not scaled to a common pressure (P atm) K 1538 K 1429 K 1333 K Current Study Moss et al = 1, X O2 = /T [K -1 ] Figure 3.6: Measured ignition delay times for 2-butanol. P = 1.2 atm, ϕ = 1, x O2 = 0.03, diluted in argon. Data by Moss et al. 41 are not scaled to a common pressure (P atm). 33

57 t ign [ s] t ign [ s] K 1515 K 1429 K Current Study Moss et al = 1, X O2 = /T [K -1 ] Figure 3.7: Measured ignition delay times for iso-butanol. P = 1.2 atm, ϕ = 1, x O2 = 0.03, diluted in argon. Data by Moss et al. 41 are not scaled to a common pressure (P atm) K 1667 K 1538 K 1429 K 1000 Current Study Moss et al. = 1, X O2 = /T [K -1 ] Figure 3.8: Measured ignition delay times for tert-butanol, P = 1.2 atm, ϕ = 1, x O2 = 0.03, diluted in argon. Data by Moss et al. 41 are not scaled to a common pressure (P atm). 34

58 From Figures , it is evident that faulty post-reflected shock temperature measurements of about 5-8% below the actual post-reflected shock temperature in this study would explain the disagreement with Moss et al. 41 for isomers other than 1-butanol. Such a large temperature error would require a significant measurement error of the incident shock speed, or a significant error in the thermodynamic properties of the driven gas mixture. The shock velocity measurement system used in this study was carefully evaluated and it was found to be working correctly. Furthermore, the thermodynamic properties of the driven gases were verified. Errors in temperature measurements in this study are unlikely because they would manifest themselves systematically, in which case our measurements would differ significantly with the 1-butanol data by Black et al. 31, Moss et al. 41, and Noorani et al. 32, and Zhang et al. 39, as well as n-heptane data by Horning et al. 59 and Smith et al. 60 (n-heptane data were acquired in order to verify the proper functioning of the experimental apparatus). Uncertainties in temperature due to facility dependent pressure rises are not observed in either study, and they would not explain the large discrepancy observed here. The role of impurities in the mixing tank and/or shock tube was assessed by repeating experiments after cleaning the mixing tank, mixing manifold, and shock tube with acetone, as well as by replacing the 1-butanol, 2-butanol, O 2, and argon sources. Glassware used to supply the mixing tank with the fuel vapor was also replaced. None of the above changes modified the ignition delay time measurements. Simulations performed using 200 ppm of H and OH radicals initially present in the fuel mixture showed only minor variations in the ignition delay time compared to pure mixtures. The author does not wish to speculate on potential errors in the study by Moss et al. 41, and the cause of the discrepancy between the two studies remains unknown. Figure 3.9 shows the variation of ignition delay time as a function of pressure for 1- butanol. As expected, ignition time decreases as a function of pressure, τ ign P -β, with β , though the exact dependence on pressure varies depending on the conditions. Global correlations of ignition delay times for individual isomers were not developed because the wide 35

59 range of conditions does not merit such simplified analysis. Figure 3.9 clearly indicates that there exists relatively good agreement between the experimental data and simulations using the Sarathy et al. 8,9 mechanism for ignition delay times of 1-butanol. However, simulations overpredict the measured ignition delay times by up to 50% at low pressures and high temperatures. This discrepancy is likely explained by inaccuracies in the rate constants for the unimolecular decomposition of butanol in the falloff region in the Sarathy et al. 8,9 mechanism (Similar conclusions are drawn from species time-histories discussed in Section ). The rate constants for the high-pressure-limit of the various 1-butanol unimolecular decomposition channels in the Sarathy et al. 8,9 mechanism are in excellent agreement with recent measurements by Rosado-Reyes and Tsang 61. However, the values of k/k in the Sarathy et al. 8,9 mechanism near 1400 K and 1.5 atm are approximately equal to 0.15, whereas measurements by Rosado- Reyes and Tsang 61 indicate that the rate constants for the unimolecular decomposition of 1- butanol are pressure-independent above 1 atm. Therefore, the rate constants for the unimolecular decomposition of 1-butanol in the Sarathy et al. 8,9 mechanism near 1400 K and 1.5 atm may be too low by an approximate factor of 6. As indicated in Figure 3.9, simulations using a modified version of the Sarathy et al. 8,9 that contains rate constant expressions for the unimolecular decomposition channels of 1-butanol from work by Rosado-Reyes and Tsang 61 show outstanding agreement with the experimental data at all conditions. This improvement occurs because the proposed modifications significantly increase the rate constant for the unimolecular decomposition of 1-butanol at low pressures only, thus maintaining the good agreement with the experimental data at high pressures. As indicated in Figure 3.9, some ignition delay time measurements at high pressures were performed without precise knowledge of the equivalence ratio in individual experiments. This was caused by the tendency of some butanol isomers to adsorb onto the shock tube walls, even at partial pressures lower than the vapor pressure at the wall temperature. These losses can be significant in some experiments, and several of the initial data were acquired without the 36

60 t ign [ s] verification of fuel concentration using direct absorption, which subsequently revealed that these experiments had leaner than assumed fuel mixtures by up to 40%. To overcome this problem, a passivation technique was developed where the shock tube was overfilled beyond the desired initial driven pressure. The excess gas was then evacuated from the shock tube until the desired driven pressure was achieved. This method allowed the initial overfilling of the shock tube to saturate the adsorption sites of the shock tube so that once the excess gas was evacuated, the test gas had the desired mole fraction of fuel. By overfilling the shock tube, the adsorbed butanol had a negligible effect on reducing the fuel mole fraction inside the shock tube simply because the amount of fuel placed in the shock tube was large. This method was validated by direct laser absorption measurements of the test gases in the shock tube K = 1 = = Lines - Sarathy et al. = 1 Solid - Original Dashed - Modified 1250 K P = 1.5 P = K P = 19 P = /T [K -1 ] Figure 3.9: Measured ignition delay times for 1-butanol, x O2 = 0.04, diluted in argon. Pressure in atmospheres. The Sarathy et al. mechanism 8,9 was modified to include rate constants for the unimolecular decomposition of 1-butanol from work by Rosado-Reyes and Tsang 61. Uncertainties are approximately equal to twice the height of the data points. 37

61 Figure 3.10 shows a comparison of the measured ignition delay times of iso-butanol with simulations using the Sarathy et al. 8,9 and Merchant et al. 42 mechanisms. The Merchant et al. 42 mechanism was developed recently for modeling the combustion kinetics of iso-butanol, due to the importance of this particular isomer as biofuel candidate. Since the authors of both mechanisms used the data presented here for guidance and mechanism validation, it is unsurprising that the mechanisms show agreement with the experimental data to within 50%. Reasonable agreement between the mechanisms is encouraging given that they were generated using completely different approaches. The Sarathy et al. 8,9 mechanism was primarily developed by examining previously inferred rate constant measurements for analogous reactions, whereas the Merchant et al. 42 mechanism was generated by calculating rate constants for most reactions using the open-source software RMG 62. Though a detailed comparison between the mechanisms is not discussed here, it is noted that the rate constants for the unimolecular decomposition channels of iso-butanol in the Merchant et al. 42 mechanism are likely more accurate than those in the Sarathy et al. 8,9 mechanism because they were taken from high-level quantum calculations by Zhou et al

62 t ign [ s] K 1333 K 1176 K 1053 K = 1 = = Lines - = 1 Solid - Sarathy et al. Dashed - Merchant et al. P = 3.0 P = 19 P = 1.5 P = X O2 = /T [K -1 ] Figure 3.10: Measured ignition delay times for iso-butanol, x O2 = 0.04, diluted in argon. Pressure in atmospheres. Uncertainties are approximately equal to twice the height of the data points. Figure 3.11 shows a comparison of ignition delay time measurements for the four isomers of butanol at 43 atm, as well as a comparison with kinetic simulations using the Sarathy et al. 8,9 mechanism. The ignition times are shortest for 1-butanol and longest for tert-butanol. iso- Butanol exhibits ignition delay times that are comparable to those of 1-buatnol, whereas and 2- butanol exhibits ignition delay times that are slightly longer than those of iso- and 1-butanol. tert- Butanol appears to have a slightly higher global activation energy compared to the other isomers, as indicated by a steeper slope in the data on an Arrhenius plot. Kinetic simulations using the Sarathy et al. 8,9 mechanism show excellent agreement with the measured ignition delay times for 1-, 2-, and tert-butanol. The mechanism overpredicts the ignition delay times for iso-butanol by up to 50%. 39

63 t ign [ s] K 1250 K 1-butanol, = butanol, = iso-butanol, = tert-butanol, = Lines - = 1 Sarathy et al. t-but 1111 K 2-but i-but X O2 = but /T [K -1 ] Figure 3.11: Measured ignition delay times for the butanol isomers at 43 atm, x O2 = 0.04, diluted in argon. Uncertainties are approximately equal to twice the height of the data points. 3.3 Multi-Species Time-History Measurements Overview Multi-species time-history measurements during the pyrolysis of hydrocarbon fuels can provide valuable insights into the kinetics of fuel decomposition. However, due to the complexity of high-temperature butanol pyrolysis kinetics, it is difficult to design butanol experiments where species-time-histories are sensitive to only a few reaction rates. Similar observations were made by Cook et al. 64. Therefore, the general approach in this work is not to modify specific reaction rates in order to achieve best fits to multi-species measurements, but instead to provide an extensive database of kinetic targets for use by modelers. Analysis is performed in order to determine which reaction classes must be better understood in order to improve agreement between simulations and experiments, and in some cases, reaction rates are modified at specific conditions in order to demonstrate the effect of faster or slower rate coefficients. Several of the 40

64 reaction paths critical to the pyrolysis of butanol are discussed, and the convention used for describing the various molecular sites of the butanol isomers is shown in Figure 1.1. In this work, species time-histories of OH, H 2 O, CO were measured during the pyrolysis of 1-butanol, 2-butanol (data in APPENDIX B), and iso-butanol. C 2 H 4 species time-histories were also measured during the pyrolysis of 1-butanol, and 2-butanol, though measurements were not performed during the pyrolysis of iso-butanol due to the presence of interference from both isobutanol and propene Modeling Shock Tube Experiments of Endothermic Reacting Systems Although dilute fuel mixtures were used throughout this study, the pyrolysis of large fuel molecules is endothermic, thus causing a temperature and pressure drop after shock heating. Accounting for temperature change in species time-history experiments can be critical due to the sensitivity of some spectroscopic parameters to temperature. In addition, the choice of gasdynamic model becomes relevant because endothermicity causes shock tubes to deviate from the ideal constant-volume (CV) behavior often assumed in kinetic simulations. CV and constant-pressure (CP) assumptions are effectively limiting cases for modeling the shock tube during pyrolysis experiments. The CV model represents the most constrained shock tube, while the CP model represents an unconstrained shock tube where pressure variations are fully negated by the expansion or contraction of the test gas. Figure 3.12 shows representative pressure trace data from experiments in this work, which indicate that the measured pressure drop is approximately half of that predicted using CV simulations. This is consistent with the conclusion that the shock tube exhibits gas-dynamic behavior where the pressure trace lies between the CP assumption and CV prediction. Note also that CV simulations using three different mechanisms yield negligible differences in pressure. For non-reacting mixtures, our shock tubes produce near-constant-pressure traces with pressure variations less than 2%. Although shock tubes do not exhibit pure CV or CP behavior in the current experiments, 41

65 P [atm] predictions of temperature and species time-history are relatively insensitive to the choice between these two gas-dynamic models for dilute experiments, as discussed below Constant Pressure Measurement CV Simulations Sarathy et al. Black et al. Hansen et al time [ s] Figure 3.12: Measured and simulated pressure for 1% 1-butanol pyrolysis. Initial post-reflectedshock conditions: T = 1391 K, P = 1.54 atm. Since temperature time-histories were not measured in this study, they are estimated using kinetic simulations. Although it is preferred that shock tube measurements be conducted with mixtures and at conditions that are expected to show little change in test conditions with time, it was confirmed that simulated temperature time-histories in the current pyrolysis experiments are fairly insensitive to kinetic mechanism or gas-dynamic model. As shown in Figure 3.13, temperature time-history simulations using CP and CV gas-dynamic models using three different chemical kinetic mechanism predict temperature reductions of 95 ± 17 K at long times. Similar uncertainties in temperature are observed in all experiments in this study. As expected, the magnitude of temperature reduction is largest using CV simulations and smallest using CP simulations. Though neglecting such drops in temperature could cause a significant error in some species time-history measurements (i.e. when the absorption coefficient is strongly temperature dependent), a ± 17 K uncertainty observed by the locus of points encompassed by all 42

66 T [K] simulations shown in Figure 3.13 contributes to an error of no more than ± 8% for any of the current species monitored Sarathy et al. Black et al. Hansen et al Constant Pressure Constant Volume time [ s] Figure 3.13: Simulated temperature for 1% 1-butanol pyrolysis. Initial conditions: T = 1477 K, P = 1.52 atm. Although temperature time-history simulations enable accurate data processing in this study, it is equally important that future modelers have clear instructions on which gas-dynamic models to use when simulating species time-histories in shock tube experiments. As demonstrated in temperature time-history simulations, both CV and CP simulations provide reasonable estimates for species mole fraction histories at conditions in this study. As shown in Figure 3.14, CV and CP simulations predict CO mole fractions within 10% of each other. For other species measured in this study, lower uncertainties are observed. The discrepancy between CV and CP simulations is caused by temperature time-history variations for different gas-dynamic models, shown in Figure CV simulations will typically predict slightly slower formation of stable species compared to CP simulations due to lower predicted temperatures throughout the simulation. It is the opinion of the author that CV simulations provide a realistic representation of 43

67 CO Mole Fraction the current shock tube study, and hence the CV model is used to simulate temperature and species time-histories, as well as to perform sensitivity analysis. Nonetheless, it is worth noting that further improvements in shock tube experiments could be achieved by employing even higher dilution of reaction mixtures and also by incorporating temperature time-history measurements CV CP time [ s] Figure 3.14: Simulated CO mole fraction for 1% 1-butanol pyrolysis. Initial conditions: T = 1477 K, P = 1.52 atm. CV simulations performed using the Sarathy et al. 8,9 mechanism Results Butanol OH and H 2 O Measurements Figures 3.15 and 3.16 show a comparison of the measured OH and H 2 O species timehistories during the pyrolysis of 1-butanol between this work and the study by Cook et al. 64. Good agreement is observed between the two data sets, though the data in the current work is regarded as more accurate due to the included treatment of temperature variations throughout the test time. It is noted that the slight pressure difference in this study and the study by Cook et al. 64 has a negligible effect on the OH and H 2 O time-histories. When analyzing measured OH species time- 44

68 H 2 O Mole Fraction OH Mole Fraction [ppm] histories, it is important to understand how the uncertainty in post-reflected-shock temperature affects the peak of the OH mole fraction. Figure 3.17 shows the locus of time-history data that are expected within a 0.5% uncertainty in temperature. It is evident that the resulting uncertainty in the peak OH mole fraction is approximately 13%. Therefore, the uncertainty in temperature ultimately limits the resolution with which experimental OH time-history data can be compared with other experimental or numeric data Current study K, 1.83 atm Cook et al. (2011) K, 1.51 atm 6 1% 1-Butanol/Ar time [ s] Figure 3.15: Measured OH mole fraction for 1% 1-butanol pyrolysis Current Study K, 1.83 atm Cook et al K, 1.51 atm time [ s] Figure 3.16: Measured H 2 O mole fraction for 1% 1-butanol pyrolysis. 45

69 OH Mole Fraction [ppm] P = 1.8 atm 1348 K 1352 K 1344 K time [ s] Figure 3.17: Simulated OH mole fraction for 1% 1-butanol pyrolysis. CV simulations performed using the Cook et al. 64 mechanism. Temperature and pressure indicate initial post-reflected-shock conditions. Figures 3.18 and 3.19 show measurements of H 2 O and OH time-histories, respectively, at a variety of temperatures, as well as a comparison with simulations using the Sarathy et al. 8,9 mechanism. The model significantly underpredicts H 2 O and OH mole fractions at all times and temperatures. Kinetic analysis indicates that simultaneous OH and H 2 O species time-history data are very useful for the refinement of chemical kinetic mechanisms of 1-butanol because the majority of water production at lower temperatures occurs due to H atom abstraction from 1- butanol by OH. Therefore, as shown in Figure 3.20, H 2 O mole fraction time-histories are sensitive to the above-mentioned abstraction rates, as well as to reactions that affect the OH radical pool. For instance, the H 2 O mole fraction shows positive sensitivity to 1-butanol + H/OH channels that produce C 4 H 8 OH-δ radicals due to their eventual β-scission into OH. This is not the case for channels producing C 4 H 8 OH-γ, resulting in negative sensitivity of H 2 O to these channels. Cook et al. 64 demonstrated that the 1-butanol + H and 1-butanol + OH reaction sets are critical to 46

70 H 2 O Mole Fraction modeling 1-butanol pyrolysis, and that additional studies are necessary to determine branching ratios of the above reaction sets. This is confirmed by simulations using the Sarathy et al. 8,9 mechanism, which fails to accurately predict OH and H 2 O time-histories although the total 1- butanol + OH reaction rate is in good agreement with experimental measurements 35,37. In addition, at high temperatures, certain 1-butanol unimolecular decomposition reactions also significantly affect the OH radical pool. Therefore, understanding all of the abovementioned reaction classes is critical for improving agreement between simulations and measured OH and H 2 O species time-histories K, 1.83 atm 1385 K, 1.89 atm 1467 K, 1.73 atm time [ s] Figure 3.18: Measured H 2 O mole fraction for 1% 1-butanol pyrolysis. Solid lines represent measurements, dotted lines represent CV simulations performed using the simulations performed using the Sarathy et al. 8,9 mechanism. 47

71 H 2 O Sensitivity OH Mole Fraction K, 1.83 atm 1385 K, 1.89 atm 1467 K, 1.73 atm time [ s] Figure 3.19: Measured OH mole fraction for 1% 1-butanol pyrolysis. Solid lines represent measurements, dotted lines represent CV simulations performed using the Sarathy et al. 8,9 mechanism pc 2 H 4 OH = C 2 H 4 +OH 1-C 4 H 9 OH = CH 3 +C 3 H 6 OH 1-C 4 H 9 OH = C 4 H 8 - +H 2 O 1-C 4 H 9 OH+H = C 4 H 8 OH- +H C 4 H 8 OH- = C 3 H 5 OH+CH time [ s] Figure 3.20: H 2 O sensitivity analysis for 1% 1-butanol pyrolysis. Initial conditions: T = 1348 K, P = 1.83 atm. CV simulations performed using the Sarathy et al. 8,9 mechanism. 48

72 CO Mole Fraction CO Measurements Figure 3.21 shows measured CO time-histories for 1% 1-butanol pyrolysis at a variety of temperatures as well as comparisons with modeling using the Sarathy et al. 8,9 mechanism. Simulations slightly overpredict the measured CO mole fractions at long times, but greatly underpredict the measured CO mole fractions at early times. Rate of production (ROP) analysis indicates that CO is largely produced by the unimolecular decomposition of HCO, which is in turn is generated from the decomposition of CH 2 OH. Therefore, as shown in Figure 3.22, the CO mole fraction during the pyrolysis of 1-butanol is most sensitive to the 1-butanol unimolecular decomposition channel that produces CH 2 OH: 1-C 4 H 9 OH 1-C 3 H 7 + CH 2 OH Reaction T = 1327 K, P = 1.50 atm T = 1477 K, P = 1.52 atm T = 1603 K, P = 1.36 atm time [ s] Figure 3.21: Measured CO mole fraction for 1% 1-butanol pyrolysis. Solid lines represent measurements, dotted lines represent CV simulations performed using the Sarathy et al. 8,9 mechanism. 49

73 CO Sensitivity C 4 H 9 OH = 1-C 3 H 7 +CH 2 OH 1-C 4 H 9 OH = CH 3 +C 3 H 6 OH 1-C 4 H 9 OH = C 2 H 5 +pc 2 H 4 OH 1-C 4 H 9 OH+H = C 4 H 8 OH- +H 2 C 2 H 3 OH = CH 3 CHO time [ s] Figure 3.22: CO sensitivity for 1% 1-butanol pyrolysis. Post-reflected-shock conditions: Initial Conditions: T = 1603 K, P = 1.36 atm. CV simulations performed using the Sarathy et al. 8,9 mechanism. At high temperatures, CO exhibits the largest sensitivity to Reaction 3.1 due to the increased reaction rate of unimolecular decomposition reactions compared to abstraction reactions by radicals. In addition, CO sensitivity to Reaction 3.1 is largest at early times where the CO mole fraction is underpredicted most significantly. These observations are consistent with measurements by Cook et al. 64, who concluded that several existing kinetic mechanisms underpredict the early formation rate of CH 2 O, which is a precursor to CO. As discussed in Section 3.2, rate constants for the unimolecular decomposition channels of 1-butanol in the Sarathy et al. 8,9 mechanism display significant falloff near 1 atm, which is in direct conflict with experimental data by Rosado-Reyes and Tsang 61 that indicate that these rate constants are pressure independent near 1 atm. Therefore, as shown in Figure 3.23, kinetic simulations using the Sarathy et al. 8,9 mechanism using updated rate constants by Rosado-Reyes and Tsang 61 significantly increase the early formation rate of CO near 1 atm, thus significantly improving the agreement between measurements and simulations at early times. It is noted that sensitivity 50

74 CO Mole Fraction analysis performed using the Sarathy et al. 8,9 mechanism with the modification described above demonstrates an even higher sensitivity of CO species time-histories to the rate constant of Reaction 3.1 at early times Measurement CV Simulations Sarathy et al. Sarathy et al. Modified time [us] Figure 3.23: Measured CO mole fraction for 1% 1-butanol pyrolysis. Initial post-reflected-shock conditions: T = 1477 K, P = 1.52 atm. C 2 H 4 Measurements Figure 3.24 shows measured C 2 H 4 time-histories at a variety of temperatures as well as comparisons with simulations using the Sarathy et al. 8,9 mechanism. At all temperatures, C 2 H 4 is slightly underpredicted, even considering the ± 10% uncertainty in the measurement. ROP analysis shows that C 2 H 4 is produced through a variety of pathways. These include C 2 H 5 decomposition, C 3 H 7 decomposition, β-scission of the C 2 H 4 OH-β radical, and β-scission of the C 4 H 8 OH-δ radical. Therefore, as shown in Figure 3.25, C 2 H 4 is sensitive to Reaction 3.1 discussed previously, as well as Reactions 3.2 and 3.3 shown below: 51

75 C 2 H 4 Mole Fraction 1-C 4 H 9 OH C 2 H 5 + C 2 H 4 OH-β Reaction C 4 H 9 OH + H C 4 H 8 OH-δ + H 2 Reaction 3.3 At high temperatures, sensitivity to the unimolecular decomposition reaction dominates, thus providing further evidence that the rate constants for the unimolecular decomposition channels of 1-butanol in the Sarathy et al. 8,9 mechanism are too slow T = 1348 K, P = 1.83 atm T = 1385 K, P = 1.89 atm T = 1467 K, P = 1.73 atm time [ s] Figure 3.24: C 2 H 4 mole fraction for 1% 1-butanol pyrolysis. Solid lines represent measurements, dotted lines represent CV simulations using the Sarathy et al. 8,9 mechanism. 52

76 C 2 H 4 Sensitivity C 2 H 5 = C 2 H 4 +H 1-C 4 H 9 OH = C 2 H 5 +pc 2 H 4 OH 1-C 4 H 9 OH = nc 3 H 7 +CH 2 OH 1-C 4 H 9 OH + H= C 4 H 8 OH- +H time [ s] Figure 3.25: C 2 H 4 sensitivity analysis for 1% 1-butanol pyrolysis. Initial conditions: T = 1348 K, P = 1.83 atm. CV simulations performed using the Sarathy et al. 8,9 mechanism iso-butanol OH and H 2 O Measurements: As shown in Figures 3.26 and 3.27, kinetic simulations using the Sarathy et al. 8,9 mechanism underpredict the measured OH and H 2 O mole fractions during iso-butanol pyrolysis, respectively. It is noted that as during 1-butanol pyrolysis, the mole fractions of these two species are highly interdependent because H-abstraction from iso-butanol by OH is a major production pathway of H 2 O. OH radical branching is relatively simple in iso-butanol because only one isobutanol radical, ic 4 H 8 OH-β, produces OH radicals through a single β-scission pathway. Therefore, as shown in Figure 3.28, OH (and H 2 O) mole fractions are highly sensitive to branching of iso-butanol + H/OH reaction that favor the ic 4 H 8 OH-β radical. Most species also exhibit sensitivity to Reaction 3.4, because it is the primary radical initiation reaction where CH 2 OH and ic 3 H 7 undergo unimolecular decomposition to produce H radicals. 53

77 ic 4 H 9 OH + M ic 3 H 7 +CH 2 OH + M Reaction 3.4 ic 4 H 9 OH + M ic 4 H 8 +H 2 O + M Reaction 3.5 Reaction 3.4 is also an important CO producing pathway because CH 2 OH falls apart to form CH 2 O and then CO. As discussed in the subsequent CO measurements section, CO is overpredicted at long times, and its early formation rate is in good agreement with measurements. Therefore, the rate of Reaction 3.4 cannot be increased in order to improve agreement of OH time-histories. In principle, increasing the rate of Reaction 3.5 could improve agreement between experimental data and simulations using the Sarathy et al. 8,9 mechanism for CO and H 2 O timehistories at long times. However, this modification would not improve agreement for OH timehistories, which are greatly underpredicted. Since OH and H 2 O time-histories are closely related, the proposed modifications improve agreement between simulations and measurements for both species. As a result, the remaining candidates for improving agreement between measurements and simulations are H-abstraction reactions. Though reactions of H and OH radicals with iso-butanol are both significant H- abstraction pathways, it is likely that abstraction reactions by H radicals are largely responsible for the discrepancies described above. The possibility of modifying H-abstraction rates by OH radicals is eliminated because in the Sarathy et al. 8,9 mechanism, these reactions are approximately 20% slower, which is considered good agreement, with experimental measurements provided by Pang et al. 38. Furthermore, increasing OH concentrations by modifying individual iso-butanol + OH-abstraction rates without further decreasing the overall iso-butanol + OH rate constant would require unrealistic modifications to the iso-butanol + OH branching ratios. Therefore, it is postulated that inaccurate rate constants for iso-butanol + H reactions are responsible for the underprediction of OH and H 2 O mole fractions. One clear path to improving agreement between mechanisms and simulations is to adjust the rate constant of H- abstraction reactions by H radicals to favor the ic 4 H 8 OH-β pathway, though the data presented 54

78 OH Mole Fraction [ppm] here do not exhibit sufficient specificity to justify quantitative modification of these reaction rate constants K, 1.75 atm 1440 K, 1.73 atm 1477 K, 1.77 atm 1518 K, 1.72 atm time [ s] Figure 3.26: Measured OH mole fraction for 1% iso-butanol pyrolysis. Solid lines represent measurements, dotted lines represent CV simulations performed using the Sarathy et al. 8,9 mechanism. 55

79 OH Sensitivity H 2 O Mole Fraction K, 1.75 atm 1440 K, 1.73 atm 1477 K, 1.77 atm 1518 K, 1.72 atm time [ s] Figure 3.27: Measured H 2 O mole fraction for 1% iso-butanol pyrolysis. Solid lines represent measurements, dotted lines represent CV simulations performed using the Sarathy et al. 8,9 mechanism ic 4 H 9 OH = ic 3 H 7 +CH 2 OH ic 4 H 9 OH+H = ic 4 H 8 OH- +H 2 ic 4 H 9 OH+H = ic 4 H 8 OH- +H 2 ic 4 H 9 OH+OH = ic 4 H 8 OH- +H 2 O ic 4 H 9 OH+OH = ic 4 H 8 OH- +H 2 O time [ s] Figure 3.28: OH sensitivity for 1% iso-butanol pyrolysis. Initial Conditions: T = 1440 K, P = 1.73 atm. CV simulations performed using the Sarathy et al. 8,9 mechanism. 56

80 CO Measurements Figure 3.29 shows the measured CO mole fractions for iso-butanol pyrolysis, as well as comparisons with simulations using the Sarathy et al. 8,9 mechanism. There exists fair agreement overall, though CO time-histories are overpredicted at high temperatures and long times, once oxygenated intermediate species such as formaldehyde and acetaldehyde have largely decomposed into CO. This is expected due to the underprediction of H 2 O described previously, since H 2 O and CO measurements at high temperatures and long times account for over 90% of the O atoms in the system. As shown in sensitivity analysis in Figure 3.30, CO is sensitive to Reaction 3.4, especially at early times, to Reaction 3.5, as well as to the CH 2 O + H reaction which has been studied in detail. CO also shows positive long-time sensitivity to H-abstraction reactions which result in less OH, because their faster rates reduce H 2 O production, thus increasing the CO yield. Therefore, the proposed modification to the H-atom abstraction rates by H radicals from iso-butanol discussed in the previous section would improve the agreement between measurements and simulation of CO time-histories, because they would partially replace CO production for the production of H 2 O. 57

81 CO Sensitivity CO Mole Fraction K, 1.50 atm 1485 K, 1.46 atm 1622 K, 1.36 atm time [ s] Figure 3.29: Measured CO mole fraction for 1% iso-butanol pyrolysis. Solid lines represent measurements, dotted lines represent CV simulations performed using the Sarathy et al. 8,9 mechanism ic 4 H 9 OH = ic 3 H 7 +CH 2 OH CH 2 O+H = HCO+H 2 ic 4 H 9 OH = H 2 O+iC 4 H 8 ic 4 H 9 OH+H = ic 4 H 8 OH- +H 2 ic 4 H 9 OH+H = ic 4 H 8 OH- +H time [ s] Figure 3.30: CO sensitivity for 1% iso-butanol pyrolysis. Post-reflected-shock conditions: Initial Conditions: T = 1622 K, P = atm. CV simulations performed using the Sarathy et al. 8,9 mechanism. 58

82 3.4 Conclusions In this work, a substantial amount of chemical kinetic data during the pyrolysis and oxidation of the four isomers of butanol was generated for the purposes of validating and improving chemical kinetic mechanisms. Ignition delay times for the four butanol isomers were measured behind reflected shock waves across a variety of conditions from K, 1-50 atm. In addition, multi species time-histories during the pyrolysis of 1-,2-, and iso-butanol were measured using direct laser absorption from K near 1.5 atm. The utility of this data for improving chemical kinetic mechanisms was demonstrated, though a complete optimization of the mechanisms against the experimental data is reserved for future work. Several of the latest chemical kinetic mechanism that have utilized the data presented here for mechanism development show good agreement with a numerous chemical kinetic targets generated in a variety of reactive environments. 59

83 4 CHAPTER 4: Isotopic Labeling 4.1 Introduction H-atom abstraction of alcohols by OH radicals from β-sites produces hydroxyalkyl intermediates that may rapidly dissociate to OH + alkenes at elevated temperatures (above approximately 500 K). Therefore, psudo-first-order reaction rate constant measurements at high temperatures performed by monitoring the rate of OH decay (See Section 2.5) typically exclude reactivity at the β-site. In this work, isotopic labeling of 18 O in alcohols was used to distinguish the 16 OH radicals that are generated by the OH-precursor and react with alcohols from the 18 OH radicals that are recycled via the reaction pathways discussed above, thus enabling measurements of the overall rate constant for the reactions tert-butanol + OH and ethanol + OH. Hess and Tully 65 and Dunlop and Tully 66 have demonstrated this method in measuring the overall reaction rate constant for ethanol + OH and propanol + OH using laser photolysis of H 18 2 O as an OH precursor. In order to spectrally distinguish 16 OH and 18 OH radicals in laser absorption measurements, the 16 OH measurements were performed at the R 22 (5.5) transition, which does not exhibit significant spectral overlap with 18 OH. Isotopic substitution of 18 O is preferred to isotopic substitution of deuterium in this work due to the lower expected kinetic isotope effect. Furthermore, Carr et al. 67 have demonstrated that in alcohols with a deuterium-labeled alcohol group, proton exchange may occur with trace amounts of water present in the experiments, thus reducing the deuterium enrichment of the alcohol mixture. 60

84 Absorption Coefficient [cm -1 atm -1 ] OH vs 18 OH Spectra In order to correctly infer the 16 OH mole fractions in the presence of 18 OH, it is necessary to perform measurements at a 16 OH transition that that does not exhibit overlap with the 18 OH spectrum. Transition selection was performed by comparing the well-characterized 51 UV spectrum of 16 OH with measured transition linecenters 68 of 18 OH. Though spectral parameters of 18 OH transitions such as line broadening and line strength have not been measured, it was assumed that for a given transition, the line strength and linewidth of the 18 OH transitions were equal to those of 16 OH. Thus, as demonstrated in Figure 4.1, there is negligible spectral overlap for the R 22 (5.5) transition between the peak of the 16 OH transition and the 18 OH spectrum OH 18 OH R 22 (5.5) Wavenumber [cm -1 ] Figure 4.1: 16 OH and 18 OH spectra of the R 22 (5.5) transition in the A-X(0,0) band at 1000 K, 1 atm. 18 OH lineshape assumed to be the same as that of 16 OH as determined by Herbon et al OH linecenter taken from Cheung et al. 68. The absence of spectral overlap between 16 OH and 18 OH at the selected 16 OH transition was confirmed experimentally by monitoring absorbance at the peak of the R 22 (5.5) transition of 16 OH during the shock heating of separate 0.1% mixtures of tert-butan 16 ol and tert-butan 18 ol 61

85 diluted in argon. By assuming that the OH formation kinetics during tert-butanol pyrolysis are the same for the two isotopes, the pyrolysis of the above-mentioned mixtures at similar post-reflected shock conditions should produce nearly-identical 16 OH and 18 OH concentration time-histories. As a result, differences in measured absorbance during the pyrolysis of mixtures of the different isotopically-labeled tert-butanol species can be directly attributed to variations in the absorption coefficient of 16 OH and 18 OH at the measurement wavelength, which is that at the peak of the R 22 (5.5) transition of 16 OH ( cm -1 ). During the pyrolysis of 0.1% mixtures of the tert-butanol, low concentrations of formaldehyde and acetaldehyde are produced in addition to OH, which exhibit broadband absorption near the wavelength used to probe 16 OH. Since the absorption of these species is broadband, their absorption coefficient is expected to remain constant around a narrow wavelength range near the R 22 (5.5) transition of 16 OH. Therefore, interference absorption of acetaldehyde and formaldehyde can be characterized by measuring absorbance at a wavelength a short distance away from the R 22 (5.5) transition of 16 OH. The subplot in Figure 4.2 shows measured absorbance time-histories at the linecenter of the R 22 (5.5) transition of 16 OH during the pyrolysis of tert-butan 16 ol and tert-butan 18 ol, as well as off-line absorbance time-histories due to formaldehyde and acetaldehyde absorption measured away from this transition using tert-butan 16 ol. By comparing the absorbances at the time of peak absorbance (t peak ), it is immediately evident that 16 OH, which is produced during tert-butan 16 ol pyrolysis, results in a significantly larger absorbance than 18 OH, which is produced during tertbutan 18 ol pyrolysis. The ratio of the absorption coefficients can be quantified as: [ ] 22 62

86 Peak Absorbance Absorbance Therefore, it is concluded that since the absorption coefficient of 16 OH at the linecenter of the R 22 (5.5) transition of 16 OH is over 20 times greater than that of 18 OH, the presence 18 OH will not interfere with measurements of 16 OH time-histories. This is consistent with what is expected from the 16 OH lineshape from Herbon et al. 51 and the 18 OH linecenter from Cheung et al. 68, as shown in Figure tert-butan 16 ol - linecenter tert-butan 18 ol - linecenter tert-butan 16 ol - offline cm t peak time [ s] 0.00 tert-butan 16 ol (linecenter) tert-butan 18 ol (linecenter) tert-butan 16 ol (offline cm -1 ) Figure 4.2: Peak absorbance near the R 22 (5.5) transition of 16 OH at the time of peak OH mole fraction during 0.1% tert-butanol/argon pyrolysis. 16 OH R 22 (5.5) transition linecenter at cm -1. Sub-plot shows absorbance time-history and indicates the time of peak absorbance. Post-reflected shock conditions: T 1515 K, P 1 atm. In addition to confirming the absence of spectral interference between 16 OH and 18 OH, the accuracy of the absorption coefficient at the linecenter of the R 22 (5.5) transition of 16 OH was verified. This was done by comparing measurements of 16 OH time-histories during neat TBHP pyrolysis at nearly identical conditions, acquired separately at the linecenters of the R 11 (5.5) and R 22 (5.5) transitions. Since the spectral properties of the R 11 (5.5) transition, which is commonly used to probe 16 OH in this laboratory, have been characterized in great detail 50,51, measurements 63

87 OH Mole Fraction [ppm] of 16 OH using this transition are assumed to be accurate. As shown in Figure 4.3, 16 OH timehistories measured using the two transitions are nearly identical in experiments with identical initial conditions. Therefore, it is concluded that the absorption coefficient at the linecenter of the R 22 (5.5) transition of 16 OH is known accurately. 100 R 22 (5.5) R 11 (5.5) time [ s] Figure 4.3: Measured 16 OH time-histories during neat TBHP pyrolysis, acquired at the linecenter of the R 11 (5.5) and R 22 (5.5) transitions in the A-X(0,0) band. 50 ppm TBHP, diluted in argon. Post-reflected shock conditions: T = 1108 K, P = 1.2 atm. 4.3 Ethanol + OH Overview Biofuels, primarily ethanol, currently account for approximately 3% of overall roadtransport fuel use globally 6. The share of biofuels in road-transport fuel is expected to increase to 27% worldwide by 2050, with ethanol accounting for approximately 40% of the total biofuel quantity 5. Due to the increasing demand for ethanol, there is significant interest in developing accurate combustion models for this fuel. 64

88 Rate constants for reactions of ethanol with OH radicals are critical for accurately modeling ethanol combustion. In this study, the overall high-temperature rate constant for the reaction ethanol + OH products was measured using isotopic labeling of 18 O in the alcohol group of ethanol. Isotopic labeling was utilized in order to eliminate the interference of OHproducing reaction pathways that typically perturb rate constant measurements for reactions of alcohols with OH radicals at high temperatures. Experiments using unlabeled ethanol were also performed in order to determine the rate constant for the title reaction that excludes reactivity at the β-site (non-β). By combining measurements of the overall and non-β reaction rate constants, the branching ratio of the ethanol + OH reaction at the β-site (BR β ) was inferred Ethanol + OH Kinetics The reaction ethanol + OH proceeds via three possible reaction sites, α, β, and o, defined by reaction rate constants k 4.1a, k 4.1b, and k 4.1c, respectively. The reaction pathways for these reactions as well as structural formulas of relevant species are illustrated in Figure 4.4. C 2 H 5 OH + OH CH 3 CHOH + H 2 O Reaction 4.1a CH 2 CH 2 OH + H 2 O Reaction 4.1b CH 3 CH 2 O + H 2 O Reaction 4.1c Reaction of ethanol with OH radicals at the β-site (Reaction 4.1b) produces CH 2 CH 2 OH radicals that rapidly decompose at temperatures above 500 K via Reaction 4.2 to form ethylene and OH, thus resulting in zero net OH consumption 65,69. CH 2 CH 2 OH C 2 H 4 + OH Reaction

89 Therefore, high-temperature rate constant measurements for the reaction ethanol + OH performed by monitoring the rate of removal of OH radicals typically exclude the contribution from the β- site. A branching ratio for the reaction at the β-site is defined as: Figure 4.4: Dominant reaction pathways related to ethanol + OH reactions. The rate constant for the reaction of ethanol with OH radicals has been studied extensively in previous work. Measurements were performed near atmospheric temperatures by Wallington and Kurylo 70, Jiménez et al. 71, Greenhill and O Grady 72, Dillon et al. 73, and Orkin et al. 74, at intermediate temperatures by Carr et al. 67, Hess and Tully 65, and Meier et al. 75, and at combustion temperatures by Sivaramakrishnan et al. 76 and Bott and Cohen 77. Theoretical studies have also been performed Xu and Lin 78, Zheng and Truhlar 79, and Galano et al. 80, and chemical kinetic mechanisms for ethanol combustion have been developed by Marinov 81, Leplat et al. 58, Natarajan and Baskharan 82, Norton and Dryer 23, and Dunphy and Simmie 83. Notably, experiments by Hess and Tully 65 at 295 K and 599 K utilized isotopically labeled H 18 2 O as the 18 OH precursor, 66

90 thus overcoming the recycling of OH described previously. A comparison of their measurements using unlabeled and labeled OH radicals clearly indicate that the rate of removal of OH in unlabeled experiments begins to lose sensitivity to H-abstraction at the β-site near 500 K, with a complete loss of sensitivity above 650 K. Therefore, high-temperature measurements performed using unlabeled ethanol by Carr et al. 67, Sivaramakrishnan et al. 76 and Bott and Cohen 77 do not account for reactivity at the β-site. The rate constants for the title reaction were determined by fitting the simulated 16 OH time-histories from the kinetic model to the experimental data using the ethanol + OH reaction rate constants as free parameters that affect the pseudo-first-order decay rate of 16 OH. As discussed in the introduction and demonstrated in Figure 4.5, the concentration of 16 OH in the presence of excess ethan 18 ol exhibits sensitivity to all three ethanol + OH reaction sites. However, as shown in Figure 4.6, the concentration of 16 OH in the presence of excess ethan 16 ol is not sensitive to reaction at the β-site due the fast decomposition of the CH 2 CH 2 OH radical via Reaction 4.1b. Therefore, experimental data in the labeled and unlabeled experiments may be used to infer the overall and non-β rate constants for the ethanol + OH reaction, respectively. It is noted that the relative branching of the reaction ethanol + OH at the α- and o- sites, with rate constants k 4.1a and k 4.1c, respectively, remains an undetermined free parameter in the kinetic simulations. However, brute force sensitivity analysis indicates that variations in the ratio k 4.1c /k 4.1a from 0 to 1, which is a reasonable range based on theoretical calculations 78,79, do not perturb the measurements of the overall or non-β rate constants for the title reaction by more than 4%. 67

91 Normalized 16 OH Sensitivity time [ s] Primary Reactions C 2 H 5 OH + OH -> CH 3 CHOH + H 2 O C 2 H 5 OH + OH -> CH 3 CH 2 O + H 2 O C 2 H 5 OH + OH -> CH 2 CH 2 OH + H 2 O Secondary Reactions tert-c 4 H 9 OOH -> tert-c 4 H 8 O + OH CH 3 + OH -> 1 CH 2 +H 2 O CH 3 + OH -> CH 3 OH C 2 H 5 OH + H -> CH 3 CHOH + H 2 Figure 4.5: Sensitivity analysis of 16 OH in a labeled experiment. T = 1032 K, P = 1.08 atm, 349 ppm ethan 18 ol, 28 ppm TBHP, 80 ppm H 2 O, diluted in argon. 68

92 Normalized 16 OH Sensitivity time [ s] Primary Reactions C 2 H 5 OH + OH -> CH 3 CHOH + H 2 O C 2 H 5 OH + OH -> CH 3 CH 2 O + H 2 O Secondary Reactions tert-c 4 H 9 OOH -> tert-c 4 H 8 O + OH CH 3 + OH -> 1 CH 2 + H 2 O CH 3 + OH -> CH 3 OH C 2 H 5 OH + H -> C 2 H 4 OH + H 2 Figure 4.6: Sensitivity analysis of 16 OH in an unlabeled experiment. T = 1029 K, P = 1.03 atm, 354 ppm ethan 16 ol, 14 ppm TBHP, 40 ppm H 2 O, diluted in argon. Simulations were performed using a modified version of the ethanol mechanism proposed by Leplat et al. 58. The primary modifications to the mechanism were the addition of reactions necessary for modeling TBHP decomposition, as well updates to the rate constants for reactions of OH radicals with CH 3 radicals, which are the principal source for secondary OH removal. Rate constants for both of these reaction sets were taken from work by Pang et al 57. The kinetic mechanism was also updated to include duplicate reactions for ethan 18 ol and its labeled fragments that are assumed to have equivalent reaction rate constants as their unlabeled counterparts. An examination of the literature revealed that the decomposition timescale of the CH 3 CHOH radical at experimental temperatures near 900 K is similar to the ~100µs timescale of 69

93 16 OH decay. This slow decomposition rate is a consequence of the geometry of CH 3 CHOH radical, which only contains β-scission pathways that require the rupture of C-H bonds. Similar radicals with different structures such as CH 2 CH 2 OH or CH 3 CH 2 O decompose much more rapidly at similar conditions because β-scission pathways are available that rupture the weaker C- C or C-O bonds, respectively 69,84. Since the decomposition rate of the CH 3 CHOH is relatively slow, its concentration may reach levels similar to those of CH 3 radicals, and thus its potential to consume a non-negligible amount of 16 OH radicals must be considered. Critically, an accurate kinetic model must contain reasonable rate constant estimates for both the decomposition of CH 3 CHOH, which primarily affects its absolute concentration, as well as for the reaction CH 3 CHOH + OH, which affects the rate of removal 16 OH radicals. It is concluded that the Leplat et al. 58 mechanism does not contain accurate rate constants for either reaction. The decomposition reaction for the CH 3 CHOH radical was described by a bimolecular rate constant expression that was estimated in previous work 82 on ethanol ignition in shock tubes. A comparison with more recent work described in the following paragraph indicates that this rate constant estimate is too low at the conditions in this study. The reaction CH 3 CHOH + OH was described in the Leplat et al. 58 mechanism using a temperature-independent rate constant of 5 x cm 3 mol -1 s -1, which is also significantly too low because it is 30% slower than the measured rate constant in this work for the reaction ethanol + OH. It is expected that the rate constant for this reaction would be comparable to that of other hydrocarbon radical + OH reactions, whose rate constants are typically on the order of 2 x cm 3 mol -1 s -1. In the current mechanism, the rate constant for the decomposition of the CH 3 CHOH radical was taken from recent theoretical calculations by Dames 69. That work utilizes the RRKM/Master Equation approach with electronic energies, molecular geometries, and force constant from computations by Senosian et al. 84. The rate constant calculations by Dames 69 are preferred to similar calculations by Xu et al. 85, though the latter are slower by approximately a factor of four at the conditions of the current experiments. The rate constants for the reaction 70

94 channels CH 3 CHOH + OH CH 2 CHOH + H 2 O and CH 3 CHOH + OH CH 3 CHO + H 2 O were assumed to be equal to the rate constant for the reaction C 2 H 5 + OH C 2 H 4 + H 2 O estimated by Tsang and Hampson 86. The effect of the uncertainties in the above rate constants on the inferred rate constant for the reaction ethanol + OH is discussed in the uncertainty analysis. Notably, data reduction preformed using the Leplat et al. 58 and Marinov 81 mechanisms with updated rate constants for the reactions discussed above resulted in nearly identical inferred values of the title reaction rate constant Results Measurements were acquired between 910 and 1274 K near 1.1 atm for a variety of mixture compositions. The non-β rate constant was measured in 31 unlabeled experiments, and the concentrations of ethan 16 ol and TBHP were varied from ppm and ppm, respectively. Rate constant measurements show excellent repeatability for a variety of mixture compositions, which suggests that secondary reactions are accurately described in the kinetic mechanism. Due to the high cost of ethan 18 ol, the overall rate constant was measured in only 15 labeled experiments, and the concentrations of ethano 18 ol and TBHP were varied from ppm and ppm, respectively. All overall and non-β rate constant measurements are tabulated in APPENDIX A. Measured 16 OH time-histories exhibit a high signal-to-noise ratio, and simulations indicate excellent sensitivity to the title reaction rate constants, as shown in Figure

95 10 Measurement k non- = 6.03 x OH Mole Fraction [ppm] 354 ppm ethan 16 ol 14 ppm TBHP Diluted in argon 1.2k non- 0.8k non time [ s] Figure 4.7: Representative 16 OH time-histories for ethan 16 ol/tbhp/argon mixtures (k non-β in units of cm 3 mol -1 s -1 ). Post-reflected shock conditions: T = 1023 K, P = 1.03 atm. Discrepancy in the rise of 16 OH is caused by the limited time resolution of the diagnostic (~5µs). As shown in Figure 4.8, measurements of the non-β rate constant for the title reaction agree within the uncertainty limits with previous studies by Sivaramakrishnan et al. 76 (absorption, TBHP precursor) and Carr et al. 67 (flash photolysis/laser-induced fluorescence). The single measurement from the study by Bott and Cohen 87 (absorption, TBHP precursor) is 35% lower and lies outside of the uncertainty bounds of the current data. A comparison of the overall and non-β rate constant measurements, which differ by approximately 20%, can be used to infer the temperature-dependent branching ratio of reaction at the β-site (BR β ), which is shown in Figure 4.9. Since labeled and unlabeled experiments were not carried out at identical temperatures, it is not possible to calculate point values for BR β. Instead, for the purposes of determining BR β, separate best fits to the current data valid from K were generated, yielding 8.14 x 10-6 T[K] 5.39 exp(4162/t[k]) for the overall rate constant and 1.57 x 10-8 T[K] 6.11 exp(5194/t[k]) for the non-β rate constant (units of cm 3 mol -1 s -1 ). These expressions are then used to compute a curve for BR β using the following expression: 72

96 Rate Constant [cm 3 mol -1 s -1 ] BR β = (Fit overall Fit non-β ) / Fit overall The result is plotted in Figure E13 1E13 8E K 1000 K 833 K 6E12 4E12 Overall Current Study Fit Xu and Lin Zheng and Truhlar Non- This work Carr et al. Sivaramakrishnan et al. Bott and Cohen Xu and Lin Zheng and Truhlar /T [K -1 ] Figure 4.8: Comparison of the measured overall and non-β rate constants for the title reaction with previous theoretical and experimental work at high temperatures. Curves by Zheng and Truhlar 79 represent calculations using the M08-SO/6-31+G(d,p) method. Curve labeled Fit was generated based on all experimental data shown in Figure

97 Current Study Xu and Lin Zheng and Truhlar M08-SO/6-31+G(d,p) Sivaramakrishnan et al. BR T [K] Figure 4.9: Comparison of the measured branching ratio BR β with previous theoretical work. A comparison of the measurement for the overall rate constant with previous measurements at lower temperatures is shown in Figure Generally, there is good agreement among the 9 experimental data sets that are presented, and the data are well fit using the following expression valid from K: k overall = 5.07 x 10 5 T[K] 2.31 exp(608/t[k]) cm 3 mol -1 s -1 It is observed that measurements of both the overall and non-β rate constants for the title reaction exhibit a slight reduction in temperature dependence from K. This is evident in Figures 4.8 and 4.10, where the slopes of the experimental data from the current study between K (Figure 4.8) are lower than those of the fit to the aggregated experimental data across the full temperature range (Figure 4.10). The author believes that the apparent reduction in the temperature dependence in the current study may be caused by inaccuracies of the CH 3 CHOH radical chemistry in the kinetic mechanism, which are discussed in detail in the uncertainty analysis section (See APPENDIX C). Adjustments of the rate constant for relevant CH 3 CHOH 74

98 k overall [cm 3 mol -1 s -1 ] radical chemistry reactions within their uncertainties can reduce the measured title reaction rate constant by up to 7% at 900 K. Nonetheless, the author does not believe that rate constants for these reactions should be adjusted based only on the measurements of the overall and non-β rate constant for the ethanol + OH reaction in this study. 1E K 500 K 333 K 250 K Current Study Hess and Tully Jimenez et al. Dillon et al. Wallington and Kurylo Carr et al. Greenhill and O'Grady Meier et al. Orkin et al. Fit Xu and Lin Galano et al. Zheng and Truhlar (M08-SO/6-31+G(d,p)) Sivaramakhrishnan et al. 1E /T [K -1 ] Figure 4.10: Comparison of the measured overall rate constant for the title reaction with previous theoretical and experimental work. Data from past studies are excluded if they were performed at conditions that are not sensitive to reactivity at the β-site. Data are best fit by the expression: k overall = 5.07 x 10 5 T 2.31 exp(608/t) cm 3 mol -1 s -1 Theoretical calculations show good agreement with the experimental data across a variety of temperatures, as shown in Figures Quantum chemistry calculations by Xu and Lin 78, Zheng and Truhlar 79, and Sivaramakhrishnan et al. 76, which were performed using variational transition state theory (VTST), muti-structural VTST, and variable reaction coordinate TST, respectively, are in excellent agreement with the experimental data for the overall reaction rate constant. However, Xu and Lin 78 predict a branching ratio for the β-site that is below the current measurement at temperatures above 1100K and is essentially at the limit of our experimental 75

99 uncertainty. The discrepancy between the theoretical calculations by Sivaramakhrishnan et al. 76 and the experimental data for the branching ratio of the β-site could be explained by the fact that their calculations for abstraction at the OH- and β-sites were performed at a lower level of theory compared to calculations for abstraction at the α-site, which is the primary abstraction channel. Nonetheless, fair agreement between the three studies is encouraging given that critical parameters such as molecular geometries and potential energies were calculated using different theoretical methods, the details of which can be found in the respective publications. It should be noted that Zheng and Truhlar 79 compute rate constants for the various pathways of the title reaction using several density functionals that produce results that differ by up to a factor of four at room temperatures. However, all of their calculations predict a branching ratio for the β-site that is between 0.15 and 0.3 from K. In this study, the results using the M08-SO/6-31+G(d,p) method are presented because they show superior agreement with the experimental data. It may also be noted that calculations by Galano et al. 80, which were performed using conventional TST, significantly underpredict the measured data at intermediate temperatures where the calculations were performed. 4.4 tert-butanol + OH Introduction tert-butanol is a common fuel additive used as an octane booster to prevent knock in spark-ignition engines. Several experimental studies 22,41,88 94, many of which were performed in the last decade, have explored the combustion kinetics of tert-butanol. In addition, several detailed kinetic mechanisms have been developed 8,9,40,41,95 with varying success in matching the kinetic targets produced in these experimental studies. Discrepancies in mechanism performance are ultimately explained by order-of-magnitude differences in rate constants for several reactions 76

100 important to combustion, including for those of the H-atom abstraction of tert-butanol by OH and the β-scission decomposition of the tert-c 4 H 8 OH radical tert-butanol + OH Kinetics The reaction tert-butanol + OH proceeds via H-atom abstraction from the methyl (CH 3 ) and alcohol (OH) groups in tert-butanol, as specified by Reactions 4.3a and 4.3b, respectively. Figure 4.11 illustrates the network of chemical reactions relevant to the production and consumption of OH as a result of these reactions, as well as the structural formulas of relevant chemical species. tert-c 4 H 9 OH + OH tert-c 4 H 8 OH + H 2 O Reaction 4.3a tert-c 4 H 9 O + H 2 O Reaction 4.3b Figure 4.11: Dominant reaction pathways related to tert-butanol + OH reactions. 77

101 The overall rate constant for the reaction tert-butanol + OH, defined as k 4.3 = k 4.3a +k 4.3b was previously measured using relative rate methods by Cox and Goldstone 96, and Wu et al. 97, and absolute measurement methods by Wallington et al 98, Teton et al. 99, Saunders et al. 100, and McGillen at al. 101, all near room temperature. However, these measured values cannot be accurately extrapolated to combustion temperatures. Measurements of the overall rate constant for the reaction tert-butanol + OH at high temperatures are complicated by the existence of an OH-producing pathway that effectively reduces the apparent OH consumption rate. This OH regeneration occurs at the β-sites occurs via the tert-c 4 H 8 OH radical produced by Reaction 4.3a, which as described by Reaction 4.4a and depicted in Figure 4.11, can undergo β-scission to produce OH radicals. It can also undergo β-scission via an alternative major pathway that does not produce OH, described by Reaction 4.4b. tert-c 4 H 8 OH OH + iso-c 4 H 8 Reaction 4.4a CH 3 + iso-c 3 H 5 OH Reaction 4.4b It follows that consecutive reaction of OH with tert-butanol via Reactions 4.3a and 4.4a leads to the production of OH, and the relative production of the different products via Reactions (4.3a/b) and (4.4a/b), which can be defined through the branching ratios: BR 1 = k 4.3a /(k 4.3a +k 4.3b ) BR 2 = k 4.4a /(k 4.4a +k 4.4b ) 78

102 are critical kinetic parameters which significantly affect simulations of tert-butanol oxidation. It is noted that Reaction 4.5, which represents the decomposition of the tert-c 4 H 9 O radical (produced by Reaction 4.3b), is not expected to form OH. Therefore, this reaction channel does not significantly affect the OH concentration in this study. tert-c 4 H 9 O C 3 H 6 O + CH 3 Reaction 4.5 The overall rate constant for the reaction tert-butanol + OH (k 4.3 ) can be determined from experiments with tert-butan 18 ol by fitting the simulated 16 OH time-history from the kinetic mechanism to the experimental data using the overall rate constant as the free parameter. Since there are no secondary 16 OH generation pathways in these experiments, the decay rate of 16 OH is not affected by the existence of OH regenerating pathways. The kinetic mechanism used in this work was developed Sarathy et al. 8,9, and it was modified with well-characterized rate constants for TBHP decomposition chemistry and secondary OH-consuming chemistry from Pang et al. 57. Rate of production analyses using this kinetic mechanism indicate that 75-90% of the 16 OHconsumption results from reactions with tert-butanol at the conditions in the current experiments, though secondary reactions that consume OH exist and the Sarathy et al. 8,9 mechanism was modified with well-characterized rate constants for these reactions. The overall rate constant for the reaction tert-butanol + OH needed to best fit the measured data is independent of BR 1 for experiments with tert-butan 18 ol. The high sensitivity of this measurement of k 4.3 is demonstrated by the OH sensitivity analysis shown in Figure 4.12, which reveals that the OH concentration is overwhelmingly sensitive to the tert-butanol + OH reaction rate constant. Secondary reactions that consume OH exist and appear in the OH sensitivity analysis shown in Figure 4.12, though the rate constants for these reactions are wellcharacterized, and the kinetic model was modified to account for secondary OH-consuming 79

103 Normalized 16 OH Sensitivity reactions (See Section 2.5). The experiments are pseudo-first-order, so the first-order decay constant due to reactions of 16 OH with tert-butan 18 ol can be defined by 18 k = k 4.3 = (k 4.3a + k 4.3b ) This value can be combined with the experimental data with tert-butan 16 ol to provide information about the branching ratio BR time [ s] Primary Reactions tert-c 4 H 9 OH + OH tert-c 4 H 8 OH + H 2 O tert-c 4 H 9 OH + OH tert-c 4 H 9 O + H 2 O Secondary Reactions CH 3 + OH CH 3 OH CH 3 + OH 1 CH 2 + H 2 O iso-c 4 H 8 + OH iso-c 4 H 7 + H 2 O tert-c 4 H 9 OOH tert-c 4 H 9 O + OH Figure 4.12: Sensitivity analysis of 16 OH in a labeled experiment. T = 1020 K, P = 1.2 atm, 500 ppm tert-butan 18 ol, 29 ppm TBHP, 75 ppm H 2 O, diluted in argon. The measured 16 OH removal rate in experiments with tert-butan 16 ol also demonstrates a pseudo-first-order decay. However, as shown in Figure 4.13, sensitivity analysis for a 80

104 representative experiment in tert-butan 16 ol shows that after initial TBHP decomposition, 16 OH time-histories are most sensitive to multiple rate constants including k 4.3a, k 4.3b, k 4.4a, and k 4.4b. This is expected considering that in experiments containing tert-butan 16 ol, 16 OH is expected to be consumed by Reactions 4.3a and 4.3b, and is produced by Reaction 4.4a. This complex OH sensitivity behavior makes it difficult to measure any single rate constant from these experiments. However, since the tert-c 4 H 8 OH radical decomposes rapidly, a quasi-steady state assumption can be invoked (d[tert-c 4 H 8 OH]/dt = 0), and the rate law describing the disappearance of 16 OH due to the reaction with tert-butan 16 ol simplifies to: ( [ ] ) [ ] The component of the first-order decay rate due to reactions with tert-butan 16 ol is thus: 16 k = (k 4.3a + k 4.3b ) (1 - BR 1 BR 2 ) = 18 k (1 - BR 1 BR 2 ) While the first-order rate constant is a function of more than one kinetic parameter, the overall value of 16 k needed to simulate the experimental data is unique. Therefore, 16 k was inferred by best-fitting kinetic simulations of OH time-histories to the experimental measurements of 16 OH decay in the experiments with excess tert-butan 16 ol. Given the measured 18 k, it was verified the value of 16 k required to best fit the experimental data is independent of the value of the free parameters BR 1 and BR 2. It is observed that measurements cannot be fit using kinetic simulations if either BR 1 or BR 2 are below A brute force analysis indicates that within the span of BR 1 :BR 2 combinations examined, using possible values of BR 1 and BR 2 ranging from 0.72 to 1.0, the value of 16 k that fits the experimental data can be determined to 81

105 Normalized 16 OH Sensitivity within 3%. It is noted that the inferred values of 16 k are independent of the chosen value for k 4.3, though the measured value of k 4.3 = 18 k is preferred. After determining 18 k and 16 k from the experimental data, the ratio of these two values leads to the value of the product BR 1 BR 2. As discussed in the Section 4.4.3, estimates of BR 1 can then be used to infer BR time [ s] Primary Reactions tert-c 4 H 9 OH + OH tert-c 4 H 8 OH + H 2 O tert-c 4 H 9 OH + OH tert-c 4 H 9 O + H 2 O tert-c 4 H 8 OH OH + iso-c 4 H 8 ] tert-c 4 H 8 OH CH 3 + iso-c 3 H 5 OH Secondary Reactions CH 3 + OH 1 CH 2 + H 2 O CH 3 + OH CH 3 OH iso-c 4 H 8 + OH iso-c 4 H 7 + H 2 O tert-c 4 H 9 OOH tert-c 4 H 9 O + OH Figure 4.13: Sensitivity analysis of 16 OH in an unlabeled experiment. T = 1020 K, P = 1.2 atm, 500 ppm tert-butan 16 ol, 17 ppm TBHP, 44 ppm H 2 O, diluted in argon. 82

106 4.4.3 Results Measurements of 18 k were acquired from 896 to 1208 K for a variety of mixtures, with tert-butan 18 ol concentrations near 500 ppm, and TBHP concentrations varying from 14 ppm to 29 ppm. Measurements of 16 k were performed from 896 to 1204 K for a variety of mixtures, with tert-butan 16 ol concentrations varying from 307 to 2080 ppm, and TBHP concentrations varying from 9 ppm to 26 ppm. Measurements of 18 k were generally performed at lower tert-butanol concentrations compared to measurements of 16 k, because, as the data will demonstrate, the decay rate of 16 OH in tert-butan 18 ol is much faster compared to that in equal amounts of tertbutan 16 ol. All experiments were performed near 1.1 atm. Figure 4.14 shows representative measurements and kinetic simulations of 16 OH timehistories in the presence of excess tert-butan 18 ol and tert-butan 16 ol. Measured 16 OH time-histories exhibit low noise, and kinetic simulations of the pseudo-first-order decay rate of 16 OH demonstrate excellent sensitivity to 18 k and 16 k, as shown in Figure 4.14 by simulations with 18 k and 16 k adjusted by ± 20%. It is estimated that the fitting uncertainty of 18 k and 16 k is ± 3%. 83

107 16 OH Mole Fraction [ppm] ppm tert-butan 18 ol 29 ppm tbhp Measurement 18 k' = 1.06x k' 0.818k' 500 ppm tert-butan 16 ol 17 ppm tbhp Measurement 16 k' = 2.12x k' k' time [ s] Figure 4.14: Representative 16 OH time-histories for tert-butanol/tbhp/argon mixtures (k in units of cm 3 molecule -1 s -1 ). Initial post-reflected shock conditions: T = 1020 K, P = 1.2 atm. Measurements of 18 k and 16 k exhibit Arrhenius behavior with low scatter and uncertainty over the temperature range studied, as shown in Figure 4.15 (tabulated data are presented in APPENDIX A). Arrhenius fits for these parameters are: 18 k = (k 4.3a + k 4.3b ) = 1.24 x exp(-2501/t [K]) cm 3 molecule -1 s k = (k 4.3a + k 4.3b ) (1-BR 1 BR 2 ) = 3.87 x exp(-2935/t [K]) cm 3 molecule -1 s -1 84

108 Net OH decay rate due to reaction with tert-butanol [cm 3 molecule -1 s -1 ] 1250 K 1111 K 1000 K 909 K k ' = k 4.3a +k 4.3b 16 k ' = (k 4.3a +k 4.3b ) (1-BR 1 BR 2 ) /T [K -1 ] Figure 4.15: Arrhenius plot of measured 16 k and 18 k. Solid lines show Arrhenius fits. As demonstrated in Figure 4.16, kinetic mechanisms offer a wide variety of values for the overall rate constant for the reaction tert-butanol + OH. Notably, good agreement is shown with the Moss et al. 41 mechanism, which agrees with the current measurements within the estimated uncertainties. The Moss et al. 41 mechanism estimates the rate of Reaction 4.3a using an Evans-Polanyi type correlations based on H-atom abstraction rates from ethane 102. The mechanism also assumes that the rate of Reaction 4.3a is greater than that of Reaction 4.3b by exactly a factor of nine, which is a reasonable estimate that is discussed in detail later in this section. The rate constant estimate for the overall reaction tert-butanol + OH in the Sarathy et al. 8,9 mechanism, obtained from a combination of theory and experimental data, is 50% lower than the current measurement. The Grana et al. 40 mechanism suggests a rate constant for the overall reaction tert-butanol + OH which is also 50% lower than the current measurement; their rate constants were derived from previous work on predicting kinetic parameters for H-atom abstraction reactions, validated against a wide array of experimental data 103. The Grana et al. 40 mechanism also assumes that the rate of Reaction 4.3a is greater than that of Reaction 4.3b by exactly a factor of nine. The Van Geem et al. 95 mechanism estimates the rates for Reactions 4.3a 85

109 k 4.3 [cm 3 molecule -1 s -1 ] and 4.3b using the open source software package Reaction Mechanism Generator (RMG) 62, and these rate constants yield a value for the rate constant for the reaction tert-butanol + OH which is 80% slower than the current measurement K 1111 K 1000 K 909 K Measurement Sarathy et al. Grana et al. Van Geem et al. Moss et al /T [K -1 ] Figure 4.16: Comparison of the measured overall tert-butanol + OH reaction rate constant (k 4.3 = 18 k ) with values used in mechanisms from the literature. The ratio of 18 k and 16 k enables an experimentally-determined value for BR 1 BR 2 approximately equal to 0.8 over the entire temperature range studied, as shown in Figure This indicates that for every OH molecule that reacts with tert-butanol, there is an 80% probability that another OH molecule will be produced through the β-scission of the resulting tert-c 4 H 8 OH radical. This provides further evidence that a rate constant measurement for the reaction tert-butanol + OH is difficult without the use of isotopic substitution, because the net OH decay rate in a mixture of tert-butan 16 ol is strongly reduced by the regeneration of OH radicals. Since neither BR 1 nor BR 2 can be greater than unity, the measurement of BR 1 BR 2 places an upper limit on both BR 1 and BR 2. The comparison of the measured BR 1 BR 2 product with the values of BR 1 BR 2 obtained using the rate constants in the different mechanisms studied is shown in Figure

110 K 1000 K 909 K 0.8 BR 1 BR Measurement Sarathy et al. Grana et al. Van Geem et al. Moss et al /T [K -1 ] Figure 4.17: Comparison of the measured branching ratio product BR 1 BR 2 near 1.1 atm with values used in mechanisms from the literature. An estimation of BR 1 can be used to infer BR 2. To first order, BR 1 can be estimated to be between 0.9 and 1.0 based on the number of H atoms that are available for abstraction at the methyl and alcohol sites (i.e. Reaction 4.3a can proceed via nine different H atoms in the methyl groups of tert-butanol, whereas Reaction 4.3b can only proceed via a single H atom in the alcohol group), and with the assumption that C-H bonds are generally weaker than O-H bonds. As shown in Figure 4.18, the Sarathy et al. 8,9, Grana et al. 40, and Moss et al. 41 mechanisms indicate that BR 1 lies within this range, though the Van Geem et al. 95 mechanism does not. The Sarathy et al. 8,9 mechanism value of BR 1 is a consequence of separate reaction rate estimates of Reactions 4.3a and 4.3b described previously, whereas the Grana et al. 40 and Moss et al. 41 mechanism values of BR 1 are equal to 0.9 based solely on the degeneracy of reaction sites. The Van Geem et al. 95 mechanism, which uses RMG to estimate the rate constants for Reactions 4.3a and 4.3b, does not provide a reasonable estimate for BR 1, 87

111 K 1000 K 909 K 0.9 BR Measurement Sarathy et al. Grana et al. Van Geem et al. Moss et al /T [K -1 ] Figure 4.18: Comparison of the estimated branching ratio BR 1 with values used in mechanisms from the literature. In the current analysis, BR 1 will be estimated more accurately than in the mechanisms discussed previously through the use of quantum calculations for H-atom abstraction reactions by OH radicals from the alcohol group and the measurements of the overall tert-butanol + OH reaction rate from this study. Similar O-H bond dissociation energies in the alcohol group 104 for methanol, ethanol, and 1-butanol lead to calculated rate constants for the H-atom abstraction in the alcohol group by OH in these alcohols that agree within 40% of one another 78,105. Because the O-H bond dissociation energy in tert-butanol is also expected to be similar, quantum calculations for the rate of H-atom abstraction by OH from the alcohol group of 1-butanol provide a reasonable estimate for the rate constant of Reaction 4.3b. Using this estimate for Reaction 4.3b, the rate constant for Reaction 4.3a was calculated under the constraint that the sum of the two reaction rates, the overall tert-butanol + OH reaction rate, must lie within the uncertainty of the measurement in this study. Using this method, an estimate of BR 1 equal to 0.96 is calculated with an overall uncertainty (peak-to-peak) of 6%, as shown in Figure Despite an uncertainty estimate of a factor of four on in the rate of Reaction 4.3b, BR 1 is calculated accurately because 88

112 the relatively large measured value of the overall tert-butanol + OH reaction rate requires that the vast majority of H-atom abstraction by OH in tert-butanol proceeds via Reaction 4.3a. Using the above estimate of BR 1, BR 2 is calculated from the measurement of BR 1 BR 2 with overall uncertainties (peak-to-peak) of approximately 17% and 12% near 900 K and 1200 K, respectively. As shown in Figure 4.19, the probability of the tert-c 4 H 8 OH radical undergoing β- scission through Reaction 4.4a is greater than 80% at the conditions studied. These results are significant because high-accuracy measurements of the branching of radicals produced during decomposition of organic compounds are rare, though accurate knowledge of these kinetic parameters can be important in developing kinetic mechanisms. Because of the previous lack of knowledge surrounding these kinetic parameters, kinetic mechanisms provide a wide range of estimates for BR 2 ranging from 0.09 to 0.98, as shown in Figure K 1000 K 909 K 0.8 BR Measurement Sarathy et al. Grana et al. Van Geem et al. Moss et al /T [K -1 ] Figure 4.19: Comparison of the inferred branching ratio BR 2 near 1.1 atm with values used in mechanisms from the literature. The Moss et al. 41 and Sarathy et al. 8,9 mechanisms provide reasonable estimates of BR 2, compared to the inferred value. It should be noted that these mechanisms present rate constant 89

113 expressions for Reactions 4.4a and 4.4b that were estimated at the high-pressure-limit, and depending on the relative falloff behavior of these reactions, BR 2 may exhibit some pressure dependence. Rate constants for Reactions 4.4a and 4.4b in the Moss et al. 41 mechanism were derived from estimates of β-scission reaction rate constants in alkanes and ethers. Evans-Polanyi type correlations using enthalpies obtained from THERGAS 106 software are used to adjust the rate constant for Reaction 4.4b, due to the effect of the alcohol group on the strength of the C-C bond. The rates of Reactions 4.4a and 4.4b in the Sarathy et al. 8,9 mechanism were determined from rate constants for similar reverse reactions. Because the estimated rate constants from the Sarathy et al. 8,9 mechanism for the β-scission directions of these reactions are sensitive to thermodynamic properties used in the estimation process, the uncertainty limits of the BR 2 suggested by the Satathy et al. 8,9 mechanism are likely to overlap with the inferred value of BR 2 from the current experimental data. As shown in Figure 4.19, calculations of BR 2 using the Van Geem et al. 62 mechanism, which are based on RMG estimates, predict a value of BR 2 which is significantly below the lower bound imposed by measurements of BR 1 BR 2. Calculations of BR 2 using the Grana et al. 40 mechanism exhibit the same problem. 4.5 Conclusions The overall rate constants for the reactions tert-butanol + OH and ethanol + OH were measured behind reflected shock waves in a shock tube. In addition, the branching ratio for the β- scission pathways of the tert-c 4 H 8 OH radical as well as the branching ratio for the ethanol + OH reaction at the β-site were determined. Isotopic labeling of 18 O in tert-butan 18 ol and ethan 18 ol was used as a critical tool for overcoming the recycling of OH radicals that typically occurs when measuring the overall rate constants for reactions of alcohols with OH radicals at high temperatures. By spectrally distinguishing the recycled 18 OH radicals from the consumed 16 OH 90

114 radicals, the decay rates of 16 OH in the labeled experiments were sensitive to reactivity of OH at all reaction sites of the alcohols. To the author s knowledge, this is the first instance that isotopic substitution and narrow-linewidth laser absorption have been used for high-temperature reaction rate constant measurements behind reflected shock waves. 91

115 5 CHAPTER 5: Cyclohexene Decomposition Rate Constant Measurements 5.1 Introduction A common experimental technique deployed to measure rates of reaction in shock tubes, especially in single pulse facilities, is the comparative rate method 107, where the rate constant of a test reaction is measured relative to that of a reference reaction. If the rate constant for the reference reaction is well-known, the absolute rate constant for the test reaction can be inferred. The reference reaction can also be used as a chemical thermometer to explicitly determine the experimental temperature, which is critical in experiments where the rate constants of the reference and test reactions have different temperature dependences. Both comparative rate and chemical thermometry methods require accurate knowledge of the rate constant for the reference reaction as a function of temperature and pressure. A common reaction used as reference near 1000 K is the decomposition of cyclohexene via the pathway shown in Reaction 5.1. cyclohexene ethylene + 1,3-butadiene Reaction 5.1 The rate constant for Reaction 5.1 has been studied extensively using a variety of experimental methods Based on the detected species during the decomposition of cyclohexene, all-butone of these past studies concluded that Reaction 5.1 is the major decomposition pathway at temperatures between K. However, a single study 119 measured the rate constant for 92

116 alternative decomposition pathways and found that decomposition to 1,3-cyclohexadiene and H 2 accounts for approximately 40% of cyclohexene decomposition at temperatures near 500 K. Nonetheless, the scientific community generally agrees that Reaction 5.1 is the major cyclohexene decomposition pathway in the temperature range where cyclohexene decomposition is typically used as a reference reaction, between K. In this work, the rate constant for Reaction 5.1 was determined by observing the rate of formation of ethylene using direct laser absorption during the decomposition of cyclohexene behind reflected shock waves. These appear to be the most accurate measurements of the rate constant for Reaction 5.1 thus far at elevated temperatures, and the results are in fair agreement with past studies. 5.2 Experimental Setup Experiments were performed behind reflected shock waves in the KST shock tube, and direct laser absorption at 3.39 µm was used to confirm that the initial cyclohexene mole fraction inside the shock tube was equal to the manometrically calculated value inside the mixing tank. The ethylene mole fraction was measured using direct laser absorption at µm. In this study, it was necessary to consider absorption of cyclohexene and 1,3-butadiene at µm when calculating the mole fraction of ethylene. Since ethylene and butadiene are stable species at the conditions in this study, their concentrations are equal in these experiments because they are produced in a one-to-one ratio via Reaction 5.1. Furthermore, assuming that Reaction 5.1 is the dominant cyclohexene decomposition pathway, the mole fraction of cyclohexene is related to that of ethylene by the simple relation: x ethylene = x cyclohexene,initial x cyclohexene Equation

117 Therefore, since the mole fractions of cyclohexene, butadiene, and ethylene are directly related, the ethylene mole fraction can be explicitly calculated from the measured absorbance using the following equation: The absorption cross-section of ethylene at µm was taken from previous work 52, and the absorption cross-section of cyclohexene, 1,3-butadiene, and 1,3-cyclohexadiene at µm were measured behind reflected shock waves in this study (See Section 2.4.3). Since the absorption cross-section of cyclohexene is over an order of magnitude lower than that of ethylene and 1,3-butadiene, the above analysis which accounts for the variations in absorbance caused by the reduction in the cyclohexene mole fraction results in only a minor perturbation on the measurement of the ethylene mole fraction. In addition, since the absorption cross-section of 1,3- cyclohexadiene is low compared to that of ethylene and 1,3-butadiene, and since the alternative cyclohexene decomposition pathway to 1,3-cyclohexadiene and H 2 (which does not absorb µm light) is at least an order of magnitude lower than the primary decomposition pathway shown in Reaction 5.1 (see Section 5.3), decomposition of cyclohexene via this alternative pathway would not perturb the measured ethylene mole fraction by more than 2.5%. 5.3 Kinetic Modeling Simulations were performed using ideal shock tube model discussed in Section A comprehensive cyclohexane mechanism by Silke et al. 121 was used as a basis for secondary reactions that may occur in the shock tube. However, since this mechanism was not validated for cyclohexene decomposition, the rate constants of several potential secondary reactions were 94

118 added and modified based on the latest values suggested in the literature, as summarized in Table 5.1. Though the rate constants for H-atom abstraction reactions from cyclohexene by H-radicals were not modified, it was verified that these reactions had reasonable rate estimates in the Silke et al. 121 mechanism. The mechanism also indicates that H-radical generation is negligible at the conditions in this study, because kinetic pathways that lead to H-radicals are at least two orders of magnitude slower compared to decomposition of cyclohexene via Reaction 5.1. Therefore, since H-radical generating pathways are very slow at the conditions in this study, simulations are not affected by these reaction pathways and high-accuracy rate constant estimates for cyclohexene + H reactions are not necessary. Reaction k Ref. Cyclohexene 2-Cyclohexenyl + H 5.01x10 15 exp(-41140/t[k]) 122 1,3-butadiene C 2 H 2 +C 2 H x10 12 exp(-33790/t[k]) 123 1,3-butadiene C 4 H 4 +H x10 15 exp(-47680/t[k]) 124 1,3-butadiene i-c 4 H 5 +H 5.70x10 36 T[K] exp(-56570/t[k]) 125 1,3-butadiene n-c 4 H 5 +H 5.30x10 44 T[K] exp(-62240/t[k]) 125 C 2 H 4 +Ar C 2 H 2 +H 2 +Ar 2.61x10 16 exp(-34130/t[k]) 52 C 2 H 4 +Ar C 2 H 3 +H+Ar 2.59x10 17 exp(-48590/t[k]) 126 Table 5.1: Rate constants for reactions modified and added to the Silke at al. 121 mechanism. Units: s -1 (unimolecular), cm 3 mol -1 s -1 (bimolecular) As expected, rate-of-production analysis indicates that virtually all chemical processes occur via Reaction 5.1 at the conditions studied. The mechanism also confirms that 1,3-butadiene and ethylene are equimolar at low conversion rates of cyclohexene because their overall unimolecular decomposition rate constants are slower than that of Reaction 5.1 by a factor of 300 at the conditions in this study. This is explicitly confirmed in past studies by Tsang 109 and Heyne et al. 127, the latter of which indicates that ethylene and 1,3-butadiene are equimolar even at 60% conversion rates of cyclohexene. 95

119 Simulations were performed with a rate constant estimate for the reaction cyclohexene 1,3-cyclohexadiene + H 2 nominally equal to zero. Though the rate constant for this reaction was measured previously to be approximately one third of that for Reaction 5.1 near 500 K 119, several subsequent studies have concluded that this pathway must be negligible at temperatures below 1200 K, based on the observed pyrolysis products of cyclohexene decomposition 109, Therefore, past work suggests that this pathway is approximately one to two orders of magnitude slower compared to that of Reaction 5.1 below 1200 K, though an agreed upon reaction rate constant in the literature does not exist. Brute force analysis using an assumed rate constant for the reaction cyclohexene 1,3-cyclohexadiene + H 2 that is up to 10% of the value for Reaction 1 does not perturb the experimentally inferred rate constant for Reaction 5.1 by more than 2%. This is expected because the decomposition of cyclohexene via alternative pathways does not significantly perturb the absolute cyclohexene mole fraction at low conversion rates where simulations were fit to experimental data. Therefore, since the rate of ethylene formation via Reaction 1 is proportional to the concentration of cyclohexene, it remains unperturbed by alternative cyclohexene decomposition pathways at low conversion. At a given post-reflected-shock condition, the rate constant for Reaction 5.1 was inferred by adjusting its Arrhenius A-factor to achieve a best-fit between simulations and measurements of ethylene formation. Simulations were performed using a temperature-dependent rate constant for the Reaction 5.1 in order to account for small temperature changes which may occur throughout the measurement time at high post-reflected-shock temperatures, due to the endothermic decomposition of cyclohexene (details are provided in following paragraphs). Data presented in this study are the values of the rate constant for Reaction 5.1 at the initial postreflected-shock temperature, calculated using the fitted Arrhenius A-factor and the Arrhenius activation energy from the simulation. As a starting point, data were analyzed using a value of the activation energy for Reaction 5.1 suggested by Tsang (1973) 110. Measurements of the rate constant as a function of temperature were then used to calculate a new activation energy, and the 96

120 above data analysis procedure was repeated. Values of the measured reaction rate constant converged after a single iteration, indicating that a point measurement behind a given reflected shock wave is insensitive to the activation energy of the rate constant for Reaction 5.1 used to fit the measured ethylene mole fraction time-history. Since the rate of ethylene decomposition spans four orders of magnitude across the temperature range in this study, various strategies were deployed to optimize measurements at different temperatures. At low temperatures, due to the slow decomposition of ethylene, driver inserts and driver gas tailoring were used in order to extend the measurement test time to 4 ms and to eliminate non-ideal effects typically present in shock tubes at long test times. In addition, the laser beam was passed twice through the diameter of the shock tube at the measurement location in order to double the sensitivity of the ethylene diagnostic. Finally, an initial concentration of cyclohexene of 3% was used in order to generate measurable concentrations of ethylene throughout the test time. At low post-reflected-shock temperatures, temperature remains constant throughout the test time due to the low conversion of cyclohexene. Based on the accuracy of the shock speed measurement system, which is discussed at the end of this section, and the uniformity in pressure observed throughout the test time, it is estimated that temperature uncertainty throughout the test time in low post-reflected-shock temperature experiments is ± 0.8%. At high temperatures, endothermic decomposition of cyclohexene causes a slight temperature drop as a function of time behind the reflected shock wave. This affects measurements of ethylene mole fraction due to the temperature dependence of the absorption cross-sections. Furthermore, temperature variations as low as 5 K behind the reflected shock wave must be taken into account while modeling the ethylene time-histories in order to account for the time-evolution of the rate constant for Reaction 5.1, which is highly temperature dependent. In order to minimize the uncertainty in the measured rate constant associated with temperature changes behind the reflected shock wave, dilute 0.333% mixtures of cyclohexene 97

121 were used in high post-shock-temperature experiments. Furthermore, rate constants were inferred by examining ethylene formation at early times when cyclohexene conversation was below 30% and significant temperature change did not occur. On timescales where data were fitted to simulations, temperature dropped by no more than 15 K, and absorption cross-sections were corrected using simulated temperature time-histories, as described in previous work 128. At the conditions studied, the magnitude of the temperature correction on ethylene mole fraction measurements was less than 5%. Furthermore, by fitting the rate of ethylene formation using simulations with a temperature-dependent rate constant for Reaction 5.1, simulations provide good estimates for the time-evolution of the rate constant for Reaction 5.1 throughout the fitting time. Since virtually all kinetic reactions in this study occur via Reaction 5.1, the fractional conversion of cyclohexene to ethylene is directly related to temperature variations via the adiabatic constraint, an appropriate gas-dynamic model of the shock tube, and accurate knowledge of the thermodynamic properties of the three major species present in the shock tube. Therefore kinetic simulations that are constrained to fit the measured ethylene time-histories accurately predict the corresponding temperature changes inside the shock tube. The uncertainty in the measured rate constant at high temperatures associated with the choice of gas-dynamic model was considered in detail, based on the discussion in Section on simulation of temperature changes behind reflected shock waves due to endothermic reactions. This uncertainty can be quantified by fitting the measured ethylene time-histories using both constant-pressure and constant-volume gas-dynamic models, which result in measured values of the rate constant for Reaction 5.1 that differ by no more than 2%. The uncertainty in the initial temperature behind the reflected shock wave, which is discussed in the following paragraph, for dilute experiments performed at high post-reflectedshock temperatures is ± 0.35%. Measurements were not performed at temperatures above 1300 K because the rapid formation of ethylene could not be measured accurately due the limited time resolution of the ethylene diagnostic, which is approximately 7 µs. 98

122 The uncertainty of the initial post-reflected-shock temperature is primarily dependent on the uncertainty in the extrapolated incident shock speed at the endwall of the shock tube. Incident shock speeds are calculated by monitoring the arrival times of the incident shock wave at a series of five pressure transducers near the endwall of the shock tube, which produce four measurements of the average incident shock speed between adjacent pairs of fast-response pressure transducers. Measured incident shock speeds show a linear attenuation rate of no more than 0.8 %/m. Incident shock speed measurements between a given pair of pressure transducers do not deviate from the linear fit used to extrapolate the measured incident shock speeds to the endwall by more than 0.17%. Therefore it is estimated that the incident shock speed at the endwall is known to within ± 0.13%, which contributes to an uncertainty in temperature behind the reflected shock wave of ± 0.26%. These estimates are consistent with the absolute measured timing error of the incident shock speed measurement system, which was characterized by mounting all five pressure transducers at the same axial location in the shock tube and monitoring the time response of the signal rise caused by the incident shock wave. It was observed that the signals in all five pressure transducers reached the trigger level of the shock speed counters within 1.1 µs of each other. Given that the typical time interval for an incident shock speed measurement between a pair pressure transducers at the conditions in this study is 500 µs, a 1.1 µs timing error corresponds to an overall 0.22% uncertainty in the incident shock velocity. This analysis is consistent with analysis of the uncertainty in the post-reflected-shock temperature performed by Herbon 50. Furthermore, it is consistent with laser-absorption measurements of temperature behind reflected shock waves performed in our laboratory by Farooq et al. 46, which indicate that the mean deviation between the measured and calculated temperature was less than 0.11%. It is noted that the uncertainties in the post-reflected-shock temperature reported here are primarily systematic and are significantly greater than those suggested by the scatter in the experimental data. The mean deviation in the rate constant measurements from the Arrhenius fit 99

123 in this study is 4.3%, which based on the temperature sensitivity of the measured rate constant suggests that the random uncertainty in the temperature is on the order of 0.15%. Due to the large number of vibration modes in cyclohexene, the post-reflected-shock temperature is also sensitive to the cyclohexene concentration in the shock tube, which is known to within ± 1.5% of the manometrically calculated value. In dilute experiments using 0.333% cyclohexene, the uncertainty in the initial cyclohexene mole fraction has a negligible effect on the uncertainty in the post-reflected-shock temperature. However, in experiments using 3% cyclohexene, the uncertainty in the cyclohexene concentration as well as its thermodynamic properties contributes approximately ± 0.2% to the uncertainty in the post-reflected-shock temperature. 5.4 Results A representative measurement and simulation of the ethylene mole fraction time-history is shown in Figure 5.1. The data exhibit low noise and simulations show excellent sensitivity to the target rate constant. The characteristic shape of ethylene formation as a function of time is in excellent agreement between measurements and simulations even at high temperatures, which indicates that simulations provide good estimates for the temperature time-history behind the reflected shock wave throughout the fitting time. 100

124 Ethylene Mole Fraction [%] Measurement k t = 0 = 1226 s k t = 0 0.9k t = time [ s] Figure 5.1: Representative measurement and simulation of ethylene mole fraction time-histories. Reaction rate constant for simulations specified at the post-reflected-shock temperature. Note that the rate constant changes slightly throughout the measurement time due to a small decrease in temperature. 1% cyclohexene diluted in argon. Post-reflected-shock conditions: T = 1192 K, P = 3.52 atm. Measurements of the rate constant for Reaction 5.1 at various temperatures are plotted in Figure 5.2, and tabulated in APPENDIX A. Data in the current study were acquired from atm and show no pressure dependence across the temperature range studied. Measurements are best-fit by the Arrhenius expression: k 5.1 = 4.84 x exp(-31900[k]/t) s -1 The maximum uncertainty in the rate constant measurements in the current work is approximately ± 36% at temperatures below 1000 K, ± 21% at temperatures from K, and ± 19% at temperatures above 1200 K. Due to the large temperature sensitivity of the rate constant for Reaction 5.1, the dominant contributor to the uncertainty in the measured rate constants is the 101

125 uncertainty in the post-reflected-shock temperature described in detail in the Section 5.3. Overall uncertainties were calculated by linearly adding the uncertainties due to the following factors (brackets indicate the contribution to the overall uncertainty in the rate constant for Reaction 5.1): temperature (± 26% low T, ± 9% high T), pressure (± 1.5% low T, ± 0.7% high T), initial cyclohexene mole fraction (± 1.5%), absorption cross-section of ethylene and 1,3-butadiene (± 2%), gas-dynamic model in simulations (± 1.5%, high T only), fitting uncertainty (± 2.0% nominally, ± 5% low T), effect of secondary reactions on kinetic modeling (+ 2.0%, high T only), effect of secondary reactions on measurement of ethylene (- 2.5%, high T only). 102

126 k [s -1 ] K 1111 K 1000 K k current study = 4.84 x exp( [K]/T) [s -1 ] /T [K -1 ] Current Study Arrhenius Fit Previous Work Lewis et al. Hidaka et al. Barnard et al. Kiefer et al. ( atm) Tsang (1965) Tsang (1970) Tsang (1973) Newman et al. Skinner et al. (3 atm) Kraus et al. Figure 5.2: Measurements of the rate constant for cyclohexene decomposition in the current study, as well as a comparison with measurements from the literature. Pressure range in the current study is atm. Pressure in past studies is indicated if measurements were performed at multiple pressures. Uncertainties in the current study are approximately equal to the height of the data points. Measurements in the current work exhibit lower scatter and uncertainty compared to previous studies. Uncertainties in the reaction rate constant measurements from past studies are generally on the order of ± a factor of Previous studies show good agreement with the current work at temperatures below 1250 K, and there exist greater discrepancies between studies at higher temperatures. Though past studies offer a variety of explanations for the observed discrepancies at high temperatures, they are not discussed in detail here because the focus of 103

127 discussion in the current work is at temperatures from K where Reaction 5.1 is typically used as a reference. In this temperature range, there is variable agreement between studies for this measured rate constant, as shown in Figure 5.3. It is noted that the Arrhenius rate constant expressions for some previous studies shown in Figure 5.3 have been extrapolated beyond the temperature range where measurements were performed. Figure 5.3 demonstrates that measurements by Barnard et al. 112 and Lewis et al. 91 are in good agreement with the current study. Lewis et al. 113 do not propose a new reaction rate constant expression for Reaction 5.1 and so it is not presented here. However, rate constant expressions for Reaction 5.1 by Tsang (1965) 108 and Tsang (1970) 109 are up to 38% and 64% lower, respectively, compared to measurements in the current study. Furthermore, rate constant expressions by Tsang (1973) 110, which are referred to as the best estimate among the studies by Tsang and are also the most commonly used in chemical thermometry and comparative rate studies 129,130, are up to 45% lower than the measurements in the current work. Nonetheless, it is noted that rate constant expressions from the current study and from the studies by Tsang likely lie within each other s combined uncertainties. Finally, measurements by Kraus et al. 118 are up to an order of magnitude lower compared to those in the current and other studies. It is noted that the lack of an observed pressure dependence of the rate constant for Reaction 5.1 between atm in the current work indicates that the discrepancies between the past studies discussed here are not caused by variations in experimental pressure. Analysis of the pressure dependence of Reaction 5.1 in previous work 112,114 confirms that all studies discussed above should not exhibit any significant pressure dependence at temperatures below 1200 K. 104

128 k [s -1 ] 1111 K 1053 K K 952 K /T [K -1 ] Current Study Arrhenius Fit Previous Work Tsang (1965) Tsang (1970) Tsang (1973) Kraus et al. Barnard et al. Arrhenius Fit Lewis et al. Figure 5.3: Subset of measurements of the rate constant for cyclohexene decomposition in the current study, as well as comparisons with measurements from the literature, in the temperature range where cyclohexene is commonly used as a reference. Pressure range in the current study is atm. The significance of the discrepancies in the recommended rate constant expressions for Reaction 5.1 can be quantified by examining the corresponding variations in the inferred temperature using the chemical thermometry method. As shown in Figure 5.4, the inferred temperature using the rate constant expression from the current work compared to using the rate constant expressions from studies by Tsang is up to 30 K lower at temperatures from K. Although these modest temperature discrepancies are not unexpected given the uncertainties in the individual rate constant measurements for cyclohexene decomposition, they 105

129 T [K] may have significant implications for other chemical kinetic studies. The temperature discrepancies reported here are in excellent agreement with a recent study by Heyne et al. 127, which indicates that temperature measurements from K in a flow reactor using a thermocouple are 17K lower compared to calculated values using cyclohexene as a chemical thermometer, when based on the rate constant for cyclohexene decomposition from Tsang (1973) 110. It is noted that errors in chemical thermometry or comparative rate methods associated with variations in the rate constant for Reaction 5.1 are primarily systematic. Therefore, rate constant measurements from previous studies can be corrected retroactively using the updated rate constant expression, if desired Tsang (1965) Tsang (1970) Tsang (1973) Barnard et al. Kraus et al T current study [K] Figure 5.4: Difference in the inferred temperature using chemical thermometry. ΔT = T previous work - T current work, where T current work is the inferred temperature using the rate constant expression for Reaction 1 from the current study, and T previous work is the inferred temperature using the rate constant for Reaction 5.1 from previous work. 106

130 5.5 Conclusions The rate constant for the reaction cyclohexene ethylene + 1,3-butadiene was measured between K and atm. No pressure dependence was observed at these conditions. Though measurements show fair agreement with previous studies, we believe this is the most accurate determination of the rate constant for the target reaction to date. Discrepancies with previous work in the measured rate constant for the target reaction correspond to variations in the inferred temperature using the chemical thermometry method of approximately 30 K. 107

131 6 CHAPTER 6: High-Temperature Acetylene Diagnostic 6.1 Introduction Acetylene is an important intermediate or product species during the combustion of many hydrocarbon fuels. It is also one of the primary precursors to soot 131. Improving the experimental tools available for performing kinetic studies of reacting systems involving acetylene is thus of significant interest to the combustion community. Due to their MHz time response and in-situ measurement capabilities, continuous wave (CW) laser absorption diagnostics have become an invaluable tool for studying chemical kinetics in shock tubes Though measurements of the acetylene mole fraction using scanned wavelength laser absorption, gas chromatography, and time-of-flight mass spectrometry have already been performed in kinetic studies , laser absorption diagnostics optimized for high-temperature, high-temporal resolution studies have not yet been demonstrated. In this work, a fixed wavelength direct absorption laser diagnostic for measurements of acetylene concentrations in shock tubes was developed. In addition, the utility of the proposed diagnostic for performing chemical kinetic studies was demonstrated by measuring acetylene species time-histories during the pyrolysis of propene and 1-butene. The IR spectrum of acetylene has been studied in great detail both theoretically and experimentally. Several of these studies have been used to develop the HITRAN 2012 spectroscopic database 138, which contains a comprehensive description of the acetylene spectrum in the 3300 cm -1 band that is of primary interest in this work. The acetylene spectrum near this wavelength is primarily composed of two cold bands, the ν 3 band and the ν 2 + (ν 4 + ν 5 ) 0 combination band, as well as at least 18 hot bands 139. Line positions and intensities for the two cold bands in the HITRAN 2012 database 138 were taken from work by Auwera et al. 140, and air- 108

132 and self-broadening coefficients were taken from work by Devi et al. 141 and Varanasi et al Details on the spectral parameters for the hot bands are described by Jacquemart et al Though significant effort has been made to include hot transitions in the HITRAN 2012 database 138, recently measured emission spectra by Moudens et al. 143 demonstrate that the database does not account for several hot-band transitions involving highly excited vibrational levels. Indeed, this is confirmed experimentally in this work and is discussed in the Section Experimental Methods The spectral location of the proposed acetylene diagnostic lies at the peak of the 3300 cm - 1 absorption band, as shown in Figure 1. Though acetylene exhibits stronger absorption near 700 cm -1, this wavelength is not easily accessible using current lasers. Furthermore, the 3300 cm -1 band offers stronger absorption compared to the 1300 cm -1 and 6500 cm -1 bands which were used to perform laser absorption measurements of acetylene in previous studies 136,137. Although simulations using the HITRAN 2012 database 138 do not fully agree with experimental measurements (see Section 6.4), the authors believe that the database is sufficiently accurate for selecting the optimal wavelength for the proposed diagnostic. 109

133 Absorption Coefficient [cm -1 atm -1 ] Proposed Diagnostic Wavenumber [cm -1 ] Figure 6.1: Absorption spectrum of acetylene at 1400 K, 1 atm calculated using HITRAN Primary plot shows the entire spectrum from cm -1, subplot shows spectrum in the 3300 cm -1 band. The absorption spectrum of acetylene was measured using scanned-wavelength direct absorption (DA) 144 at room temperature in a 79.9 cm pathlength cell, and at high temperatures behind reflected shock waves in the Stanford Kinetic Shock Tube. Measurements at room temperature and pressure were performed in order to characterize the performance of the laser (Nanoplus DFB laser, λ = ºC) and detector systems (Vigo Systems PVI-3TE-4), and to validate simulations using the HITRAN 2012 database 138 at these conditions. Scannedwavelength DA measurements were performed from cm -1 to cm -1 using a sawtooth signal scanned at 1 and 2.5 khz in the static cell and shock tube, respectively, with a peak-to-peak modulation current ranging from ma (di/dυ = -38 ma/cm -1 ). The ideal constant-volume (CV) test time in the shock tube was 1 ms, which allowed for at least 2 full scans of the acetylene spectrum per experiment. All shock tube measurements were performed using 2% acetylene/argon mixtures purchased from Praxxair (acetone free). 110

134 The absolute wavelength of the peak of the acetylene absorption feature at room temperature and pressure was measured using a Bristol 721 wavelength meter (ν uncertainty = ± cm -1 ). The relative wavelength in scanned-wavelength experiments was determined by measuring the transmission peak spacing of a solid germanium Fabry-Perot etalon (FSR = cm -1 ). The wavelength shift of the peak of the acetylene absorption feature relative to that at room temperature and pressure was determined by simultaneously measuring the laser intensity of a secondary beam that was pitched through a 2.5 cm reference cell filled with a 0.2% acetylene/argon mixture. Since knowledge of the absolute wavelength is not critical during the implementation of the diagnostic in kinetic studies, the authors recommend centering the laser at the peak of the acetylene absorption feature at the experimental conditions by adjusting the laser injection current/wavelength relative to the absorption peak of acetylene in the reference cell. This laser centering method requires accurate knowledge of the wavelength shift of the peak absorption coefficient at the experimental conditions relative to that at room temperature and pressure, as well a precise determination of the injection current-to-wavelength relationship for the laser device, both of which were measured accurately in this work. The uncertainty in the relative wavelength using this method is no greater than ± cm -1, which is significantly more accurate than absolute wavelength measurements using most commercial wavelength meters. The schematic for the proposed acetylene diagnostic for use in kinetic studies is shown in Figure 6.2. Due to the sub-0.15% low- and high-frequency noise of the laser/detector system, normalizing the measured transmitted laser intensity through the shock tube by the measured laser intensity at a reference detector upstream of the shock tube (common-mode-rejection) was not necessary. However, due to the relatively low power (~3mW) of the laser used in this work, measurements indicated that light emission due to acetylene or other hydrocarbons may affect laser absorption measurements. Therefore, as shown in Figure 6.2, an aperture and a narrow bandpass filter (CWL = 3332 cm -1, FWHM = 35 cm -1 ) were added downstream of the shock tube in order to eliminate this potential problem. 111

135 Figure 6.2: Schematic of the proposed acetylene diagnostic for kinetic studies in shock tubes (BP = Bandpass) 6.3 Interference Absorption Simulations using the HITRAN 2012 database 138 reveal that interference absorption due to the major combustion species such as CO, CO 2, C 2 H 2, CH 4, and H 2 O (below 4 atm) is negligible at the target wavelength for measuring acetylene concentrations. In addition, a broad survey of the absorption spectra of a variety of hydrocarbons using the HITRAN and PNNL 56 databases reveals that non-alkyne hydrocarbon species generally do not absorb light at the target wavelength, because their primary mid-ir absorption band occurs at lower wavenumbers near 3100 cm -1. However, the acetylene diagnostic proposed here will likely be deployed in reacting systems that contain larger alkynes that also absorb light at the target wavelength. In such experiments, interference absorption can be eliminated using a two-color technique described in Section It is important to note that although this method does not require accurate knowledge of the absolute absorption coefficient of the interfering species, it does assume that their absorption coefficients are wavelength independent at the two selected values. 112