an improved hydrogen/oxygen mechanism based on …v abstract h2/o2 combustion chemistry is the core...

AN IMPROVED HYDROGEN/OXYGEN MECHANISM BASED ON SHOCK TUBE/LASER ABSORPTION MEASUREMENTS

A DISSERTATION

SUBMITTED TO THE DEPARTMENT OF MECHANICAL ENGINEERING

AND THE COMMITTEE ON GRADUATE STUDIES

OF STANFORD UNIVERSITY

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS

FOR THE DEGREE OF

DOCTOR OF PHILOSOPHY

Zekai Hong

November 2010

http://creativecommons.org/licenses/by-nc/3.0/us/

This dissertation is online at: http://purl.stanford.edu/dq332gy7321

© 2011 by Zekai Hong. 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.

ii



http://purl.stanford.edu/dq332gy7321

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

Ronald Hanson, Primary Adviser


Craig Bowman


David Davidson

Approved for the Stanford University Committee on Graduate Studies.

Patricia J. Gumport, Vice Provost Graduate Education

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

iii

v

ABSTRACT

H2/O2 combustion chemistry is the core of all hierarchical hydrocarbon combustion

mechanisms. Because of this, H2/O2 combustion chemistry has been the target of

extensive research and our understanding has been improved substantially over the years.

However, there still remains a critical need for improvements and the development of an

even higher fidelity H2/O2 mechanism. These improvements require the researcher to go

beyond existing methodologies and to adopt new approaches and better tools.

This thesis outlines the work carried out to produce such a high-fidelity mechanism. In

particular, a three-part strategy was implemented: 1) new shock tube/laser absorption

tools were developed, 2) rates constants of selected HO2/H2O2 reaction were measured,

and 3) a new mechanism was developed and validated.

1) Within the scope of this dissertation work, two major tools were developed: a

modified shock tube and a sensitive H2O diagnostic. A standard shock tube was

modified to eliminate gradual temperature or pressure rises behind reflected shock

waves due to non-ideal effects. Long and uniform test times were achieved with the

modified shock tube behind reflected shock waves, where kinetics experiments were

carried out. H2O time-histories behind reflected shock waves were recorded with an

H2O laser absorption diagnostic part of whose development was also included in this

study. Accurate knowledge of trace amounts of H2O in combustion systems provides

a unique new capability in studies of combustion chemistry. In addition, an OH laser

absorption diagnostic for OH that has been well-established in this laboratory was

used in combination with the H2O diagnostic for a more thorough understanding of

combustion kinetics.

2) The rate constants of four important reactions within the H2/O2 combustion system

were experimentally determined. By combining the modified shock tube technique

with the laser diagnostics for OH and H2O, various H2/O2 systems were studied to

vi

obtain more accurate rate constants for several important reactions at combustion

temperatures, including:

H + O2 = OH + O

H2O2 + M = 2 OH + M

OH + H2O2 = HO2 + H2O

O2 + H2O = OH + HO2

3) An improved H2/O2 reaction mechanism was compiled that incorporated the

aforementioned rate constant determinations, as well as recent studies from other

laboratories. The new mechanism was tested against OH and H2O species time-

histories in various H2/O2 systems, such as H2 oxidation, H2O2 decomposition, and

shock-heated H2O/O2 mixtures, and was found to be in very good agreement. In

addition, the current mechanism was validated against a wide range of more standard

H2/O2 kinetic targets, including ignition delay times, flow reactor species time-

histories, laminar flame speeds, and burner-stabilized flame structures.

vii

ACKNOWLEDGMENTS

First and foremost, I would like to express my immense gratitude to my advisor, Prof.

Hanson. He showed me the characteristics that are essential to an integrated scholar --

enthusiastic about unknowns, meticulous to details, hardworking, and humble despite

high achievements -- not by words, but by being a role model. I am also very grateful to

him for his mentorship and the opportunity that he offered me to work in a world-class

research laboratory.

I am very thankful to Prof. Bowman, for showing me how interesting a lecture can be,

even though the subjects are as serious as Physical Gas Dynamics or Combustion. He

also had enormous influence on me by offering insightful discussions. I am always

amazed by how knowledgeable Prof. Bowman is when we start research discussions. I

am very grateful to Prof. Mitchell who provided a lot of help during my years at Stanford.

I also want to thank Prof. Golden for offering numerous very helpful discussions.

Of course, my learning experience at Stanford would not have been this joyful without

Dr. Davidson. His encouragements guided me through the times of frustrations; and his

wisdom (e.g., destiny discussions) will continue to enlighten me in the future. Dr.

Jeffries’ unquestionable expertise in laser/optics is always a major source of help at times

of difficulties.

I am lucky in meeting a host of people more than willing to provide help in any way

possible: Ethan, Rob, Venky, Hejie, Zach, Sherry, Brian C., Jon Y, Megan, Sean, Dan

M., etc. I cannot forget the nights during my first year at Stanford working on homework

assignments with Jason, Dan H., Chen, and Zubin. I am also deeply indebted to Matt L.,

Genny and Leyen for spending enormous amount of time helping me to fix my writings. I

am very thankful to my fellow students who provided much-needed encouragements and

feedback when I was learning to teach: Vic, Ian, Matt C., Chris, Sijie, Ivo. The

viii

gym/dining hall crew certainly made the last year of my PhD life full of joys: Wei, Kai,

Brian L., Xing, Rito, Haocheng (Aerospace), and Yinan (Aerospace).

I want to express my deep appreciation to my parents and my family for their sacrifice

and unreserved support. At the same time, I feel extremely lucky to know some of the

most interesting Chinese students at Stanford and to be good friend with them. They are

like a family away from the home: Zongfu, Xinran, Yuerui, Qiqi, Jiang Li, Liangliang,

Ningdong, Pan Jun, Li Yuan, Zhuang, and many others.

Finally, I come to Danielle, my wife and my best friend, to whom I owe everything.

Without her, I surely would not be sitting at my desk on Stanford campus writing this

dissertation. It was through her love and support that I went through some of the most

dramatic setbacks in my life. It was through her love and support that I had the peace of

mind even at the times of difficulties. It is through her love and support that I have the

courage to take on most intimidating challenges. Words cannot express how much she

means to me, and how thankful I am for the time we have already had.

ix

…to Danielle

xi

TABLE OF CONTENTS

List of tables .......................................................................................................................xv

List of figures .................................................................................................................. xvii

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

1.1 Motivation ................................................................................................................1

1.2 Problem Formulation ...............................................................................................1

1.2.1 Modified shock tubes for better combustion kinetic studies .......................1

1.2.2 Sensitive H2O diagnostic to better understand combustion chemistry ........4

1.2.3 Improved rate constant of the reaction H + O2 → OH + O .........................5

1.2.4 Improved rate constants of reactions involving H2O2 and HO2 ...................6

1.2.5 High-fidelity H2/O2 mechanism ...................................................................8

1.3 Groundwork .............................................................................................................8

1.4 Scope and Orgnization ...........................................................................................10

Chapter 2: The Application of Driver Inserts to Improve Shock Tube Performance ........13

2.1 Introduction ............................................................................................................13

2.2 Standard Shock Tube .............................................................................................14

2.3 Model and Problem Solution .................................................................................15

2.3.1 Model Overview ........................................................................................15

2.3.2 First problem: determining the location of area change ............................16

2.3.3 Second problem: rate of area change calculation ......................................19

2.3.4 Final driver insert design ...........................................................................21

2.4 Modified Shock Tube Facility ...............................................................................22

2.5 Summary ................................................................................................................24

Chapter 3: Laser Diagnostics .............................................................................................25

3.1 Tunable Diode Laser Absorption of H2O near 2.55 μm ........................................25

3.2 Ring-Dye Laser Absorption of OH near 307 nm ...................................................32

Chapter 4: Rate Constant of Reaction H + O2 OH + O ................................................35

4.1 Previous Work .......................................................................................................35

xii

4.2 Experimental Details ..............................................................................................37

4.3 Results ....................................................................................................................37

4.4 Discussion ..............................................................................................................46

4.4.1 Sensitivity of k1 to k13 ...................................................................................46

4.4.2 Re-evaluation of the Masten et al. determination of k1 .................................47

4.4.3 Previous studies of k1 at temperatures below 1500 K ...................................48

4.4.4 Rate constant of the reverse reaction k-1 .......................................................50

4.5 Summary ................................................................................................................52

Chapter 5: Hydrogen Peroxide Thermal Decomposition...................................................53

5.1 Previous work ........................................................................................................53

5.2 H2O2 source and mixture preparation ....................................................................54

5.3 Results and Discussion ..........................................................................................57

5.3.1 Determination of H2O2 dissociation rate constant k3 ....................................57

5.3.2 Low-pressure limit and fall-off behavior in argon bath gas .........................58

5.3.3 Collider efficiencies ......................................................................................63

5.4 Summary ................................................................................................................65

Chapter 6: Rate Constant of Reaction OH + H2O2 H2O + HO2 ....................................67

6.1 Previous work ........................................................................................................67

6.2 Analyses .................................................................................................................69

6.2.1 Overview of approach ...................................................................................69

6.2.2 Analysis using detailed kinetics mechanism.................................................70

6.2.3 Test mixture non-uniformity considerations .................................................71

6.3 Results and Discussions .........................................................................................72

6.3.1 Lower temperature (1000 < T < 1200 K) example case ...............................72

6.3.2 Higher temperature (1200 K < T < 1460 K) example case ...........................78

6.3.3 Arrhenius plot of the reaction OH + H2O2 H2O + HO2 ............................82

6.3.4 Arrhenius plot of the reaction H2O2 + M 2 OH + M ................................85

6.3.5 Secondary reaction 2 OH H2O + O ..........................................................87

6.4 Summary ................................................................................................................89

Chapter 7: Experimental Study of the Rate of OH + HO2 H2O + O2 Using the

Reverse Reaction .........................................................................................................91

xiii

7.1 Previous Work .......................................................................................................91

7.2 Test Mixtures Preparation ......................................................................................92

7.3 Results and Discussion ..........................................................................................94

7.3.1 Determination of the rate of the reaction OH + HO2 H2O + O2 (k5) ........94

7.3.2 Uncertainty analysis ......................................................................................98

7.3.3 Arrhenius plot................................................................................................99

7.4 Summary ..............................................................................................................103

Chapter 8: Compilation of an Improved H2/O2 Mechanism ............................................105

8.1 Introduction ..........................................................................................................105

8.2 Overall Reaction Scheme .....................................................................................106

8.3 Reaction Rate Constants ......................................................................................110

8.3.1 H + O2 = OH + O (Rxn. 1) ..........................................................................110

8.3.2 H + O2 (+ M) = HO2 (+ M) (Rxn. 2) ..........................................................110

8.3.3 H2O2 (+ M) = 2 OH (+ M) (Rxn. 3) ............................................................113

8.3.4 OH + H2O2 = H2O + HO2 (Rxn. 4) .............................................................114

8.3.5 OH + HO2 = H2O + O2 (Rxn. 5) .................................................................114

8.3.6 H2O + M = H + OH + M (Rxn. 7) ..............................................................115

8.3.7 2 OH = H2O + O (Rxn. 8) ...........................................................................115

8.3.8 Other reactions ............................................................................................116

Chapter 9: Validation of the H2/O2 Mechanism ..............................................................119

9.1 Validations against Specialized Data ...................................................................119

9.1.1 H2 oxidation in extremely dilute mixtures ..................................................119

9.1.2 H2O2 thermal decomposition ......................................................................122

9.1.3 High-temperature H2O/O2 reaction .............................................................124

9.2 Validations against Conventional Combustion Data ...........................................125

9.2.1 Shock tube ignition delays ..........................................................................125

9.2.2 Species time-histories from flow reactors ...................................................126

9.2.3 Unstretched laminar flame speeds ..............................................................128

9.2.4 Burner-stabilized flame structure ................................................................131

9.3 Summary ..............................................................................................................133

Chapter 10: Conclusions and Future Work ......................................................................135

xiv

10.1 Summary of Results .......................................................................................135

10.2 Publications ....................................................................................................136

10.3 Future Work ...................................................................................................138

APPENDIX A: Driver Insert Design for Generalized Shock Tube Facilities and

Operating Conditions .................................................................................................141

A.1. Standard Shock TubeS with Tailored Driver Gases ..........................................141

A.2. Standard shock tubes with Helium Driver Gas ..................................................144

A.3. Convergent shock tubes .....................................................................................146

APPENDIX B: Additional H2O Time-Histories during H2 Oxidation ............................149

APPENDIX C: Additional Mechanism Validations ........................................................153

APPENDIX D: Mechanism Input Files in CHEMKIN Format.......................................163

D.1. Reaction Rate Constants ....................................................................................163

D.2. Thermodynamic Data .........................................................................................164

Bibliography ....................................................................................................................167

xv

LIST OF TABLES

Number Page Table 1. Test conditions and results for the H + O2 OH + O rate constant (k1). ...........45

Table 2. Low-temperature reaction rate coefficient k1 in the form k1 = ATnexp(−Θ/T). ...49

Table 3. Test conditions and results of H2O2 decomposition experiments in argon bath

gas. The H2O2 and H2O concentrations are initial values. ..............................62

Table 4. Test conditions and results of H2O2 decomposition experiments in nitrogen

bath gas. The H2O2 and H2O concentrations are initial values. ......................64

Table 5. Test conditions and results of H2O2 decomposition experiments in argon bath

gas. The H2O2 and H2O concentrations are initial values. ..............................84

Table 6. Test conditions and the experimentally determined rate constants of the

reaction OH + HO2 H2O + O2 (k5). ............................................................100

Table 7. Current H2/O2 Reaction Mechanism. k = ATn exp(Ea/RT) in units of [s-1],

[cm3mol-1s-1] or [cm6mol-2s-1]. .......................................................................108

xvii

LIST OF FIGURES

Number Page Figure 1-1. A non-ideal pressure rise of 2.2%/ms occurs for 7 ms in a pressure-driven,

15 cm inner-diameter shock tube, with constant area for both driver and

driven sections. T5 = 900 K, P5 = 4 atm, driver gas: 50% N2/ 50% He,

driven gas: Ar. ....................................................................................................2

Figure 1-2. Influence of dP5*/dt on measured and modeled ignition delay times for

hydrogen/oxygen/argon mixtures. Figure adapted from [16]. ..........................3

Figure 1-3. Representative experimental results for the rate constant of the reaction H

+ O2 → OH + O using a laser absorption OH diagnostic (Masten et al.

[19]) and the ARAS method (Pirraglia et al. [20]). ...........................................6

Figure 1-4. Previous studies of the rate constant of the reaction OH + H2O2 H2O +

HO2. The dashed line is the rate expression used by Ó Conaire et al. [5]

and Li et al. [4], the dotted line is the one adopted by GRI-Mech 3.0 [18]. ......7

Figure 1-5. Arrhenius plot of the rate constant of the reaction OH + HO2 H2O + O2.

Large scatter is seen in the measured reaction rate values. The dashed line

is the rate expression adopted by GRI-Mech 3.0 [18]; the solid line is the

one used by Li et al. [4] and Ó Conaire et al. [5]; the dotted line is the rate

expression used by Konnov mechanism [6]. .....................................................8

Figure 2-1. A schematic plot of a current driver-section insert modification in a shock

tube. A cone-shaped obstacle in the shock tube driver section can

effectively cancel the non-ideal pressure rise behind reflected shock

waves................................................................................................................14

Figure 2-2. The X-t wave diagram generated for the case where the incident shock

Mach Number Ms = 1.85 (corresponding to T5 = 900 K); driven gas is

argon; driver gas is 50% N2/50% He, all gases initially at 300 K. The

driven section length = 8.5 m results in a uniform reflected shock test time

of 10.8 ms. The location of the driver area change Xdist = −3.4 m. ..................18

xviii

Figure 2-3. Δt-Xdist curve calculated for the sample case where the incident shock

Mach number Ms = 1.85 (corresponding to T5 ≈ 900 K); the driven gas is

Ar, and the tailored driver gas mixture is 50% N2/50% He. Driven section

length L is 8.5 m. .............................................................................................18

Figure 2-4. The X-t wave diagram for the limiting case where the time interval Δt = 0.

The location of the driver area change Xdist = −0.9 m. .....................................19

Figure 2-5. Diagram of a divergent shock tube and the corresponding pressure regime

numbering scheme. ..........................................................................................20

Figure 2-6. ΔP5/P5 as a function of A4/A1 for the sample case shown in Figure 1-1.

Driven gas is argon and the driver gas is 50% N2/50% He. The initial

driver/driven pressure ratio P4/P1 is 11.9 and was used to achieve T5 ≈

900 K. ...............................................................................................................21

Figure 2-7. The relationship between A4/A1 and Xdist curve for the driver section. The

diaphragm location is at Xdist = 0 and the driver end wall is at Xdist = −3.4

m. .....................................................................................................................22

Figure 2-8. Test section pressure profile (2 cm from the end wall) for identical shock

wave experiments with and without a driver insert. Driver gas in both

experiments was 50% helium/50% nitrogen; the driven gas was argon.

The nominal initial reflected shock conditions were T5 = 900K, P5 = 4

atm....................................................................................................................23

Figure 2-9. The axial cross-section of the modified shock tube driver section. The

comparison is between the model prediction and the actual shape of the

driver insert that has the optimal performance experimentally. The inner

diameter of the driver section is 15 cm, diaphragm location is at X = 0 and

endwall is at X = −3.4 m. .................................................................................23

Figure 2-10. Highly uniform temperature profile obtained when pressure is precisely

maintained constant using a driver insert. Driver gas helium/nitrogen

(60%/40%), driven gas argon seeded with 2% CO2. Reflected shock

conditions: T5 = 952 K, P5 = 1.2 atm. The figure was adapted from

reference [49]. ..................................................................................................24

xix

Figure 3-1. Fundamental H2O bands offer nearly an order of magnitude increase in

peak line strengths over overtone bands. .........................................................26

Figure 3-2. Absorbance spectrum of isolated H2O vibrational line at 3920.09 cm-1. A

small neighboring line is seen near 3922 cm-1. ................................................27

Figure 3-3. By comparing an H2O absorbance time-history measured at 1383 K and

2.317 atm to the H2O time-history calculated H2O time-history calculated

using GRI-Mech 3.0, vβ at the center of the absorption feature was

evaluated to be 1.50 [cm-1atm-1]. By assuming a Voigt line-shape

function, Arγ was determined to be 1.29 × 10-2 [cm-1atm-1] at this

temperature. Test mixture: 2000 ppm H2/1000 ppm O2/Ar. ...........................30

Figure 3-4. The argon broadening coefficient experimentally determined in this work

can be expressed as ( )Ar Tγ = 0.0277×(296/T)0.50 [cm−1atm−1]. ......................31

Figure 3-5. A schematic of the H2O diagnostic for reflected shock experiments. .............32

Figure 3-6. Layout of the OH laser absorption diagnostic adapted from Ref. [37].

Labeled optics are: (f) Newport FSR-UG11 narrow bandpass filter; (l)

lens; (i) iris; (NDf) neutral-density filter; (b) 27% beamsplitter......................34

Figure 4-1. Previous experimental results for the rate constant of the reaction H + O2

OH + O (k1). ................................................................................................36

Figure 4-2. Typical pressure and laser transmission histories in reflected-shock

experiments: (a. upper) 0.1% O2, 0.9% H2, 99% Ar, 1472 K, 1.83 atm; (b.

lower) 0.1% O2, 2.9% H2, 97% Ar, 1100 K, 1.95 atm. ....................................38

Figure 4-3. H2O sensitivity plot at conditions of the corresponding panels of Figure

4-2. ...................................................................................................................40

Figure 4-4. Comparison of experimental and calculated H2O profiles using best-fit k1

with effect of ± 10% variation on k1 at conditions of the corresponding

panels of Figure 4-2. ........................................................................................41

Figure 4-5. Comparison of H2O time-histories calculated using constant and

temperature-dependent H2O absorption cross-sections at conditions of

Figure 4-2a. ......................................................................................................42

Figure 4-6. Sensitivity analyses for the maximum slope of the H2O profiles at the

conditions of the corresponding panels of Figure 4-2. ....................................43

xx

Figure 4-7. Arrhenius plot of experimentally determined k1 from this study and from

studies by Pirraglia et al. [20] and by Masten et al. [19]. k1 values used in

two recent kinetic mechanisms [5][6] are also shown. ....................................44

Figure 4-8. Percent residual difference between the Arrhenius fit and experimental

data from Masten et al. [19] and the current study. .........................................46

Figure 4-9. k1-k13 pairs that best-fit the experimental H2O profile at the conditions of

Figure 4-2b. The assigned error bar is the combined uncertainty from all

error sources except k13. ...................................................................................47

Figure 4-10. OH profile calculated with k1 suggested by Masten et al. [19] and the

updated OH enthalpy of formation can be rescaled to perfectly match their

experimental OH time-history. Conditions: T = 1980 K, P = 0.675 atm,

test mixture 5.0% H2/0.493% O2/Ar. ...............................................................48

Figure 4-11. Rate coefficient of the reverse reaction O + OH H + O2 (k-1)

determined from the forward rate coefficient k1 and the equilibrium

constant K1. ......................................................................................................51

Figure 5-1. A schematic of the experimental setup for generating H2O2/bath gas

mixtures............................................................................................................55

Figure 5-2. The dissociation rate of H2O2 is fitted to be 1.65 × 107 [cm3mol-1s-1] with

an estimated fitting error of ±10%. Test condition: 860 ppm H2O2/663

ppm H2O/332 ppm O2/Ar, 1.83 atm, 1057 K. ..................................................57

Figure 5-3. The formation of H2O is predominantly controlled by the dissociation rate

of H2O2. Conditions are those of Figure 5-2. ..................................................58

Figure 5-4. The decomposition rates of H2O2 (k3) in argon bath gas were measured at

various pressures and are compared to previous studies. ................................59

Figure 5-5. Fall-off behavior of H2O2 decomposition in argon bath gas. ..........................61

Figure 5-6. The comparison between the rate expressions used in two detailed

chemical kinetics mechanisms and the experimental data of this study

(long dashed line, GRI-Mech with ΔfHo(OH) updated; short dotted line, Ó

Conaire et al.; solid line, the limiting low-pressure rate fitted to the

experimental data at 0.9 and 1.7 atm of this study). ........................................63

xxi

Figure 5-7. The decomposition rates of H2O2 (k3) in nitrogen bath gas are compared

to the results obtained in argon at the same pressure. Solid lines are the

best fits. Dotted lines are calculated using kinetics mechanisms....................65

Figure 6-1. Previous studies of the rate constant of the reaction OH + H2O2 → H2O +

HO2 (+ - Wine et al. [112]; ■ - Sridharan et al. [118]; Δ - Kurylo et al.

[114]; ▼ - Keyser; ■ - Hippler et al. [26]; ● – Hippler et al. [25]). .............68

Figure 6-2. The dissociation rate of H2O2 (k3) is fitted to be 1.8 × 108 [cm3mol-1s-1]

with an estimated fitting error of ±10%. Initial test mixture: 2216 ppm

H2O2/1364 ppm H2O/682 ppm O2/Ar; initial reflected shock conditions:

1.95 atm, 1192 K. .............................................................................................73

Figure 6-3. The formation of H2O is predominantly controlled by the dissociation rate

of H2O2. Conditions are those of Figure 6-2. ..................................................73

Figure 6-4. The rate of the reaction OH + H2O2 H2O + HO2 (k4) is fitted to be 5.1

× 1012 [cm3mol-1s-1] with an estimated fitting error of ±3%. Special

attention was paid to match the peak in OH concentration. Conditions are

those of Figure 6-2. ..........................................................................................74

Figure 6-5. OH yield is predominantly controlled by the competition between the OH

formation reaction H2O2 + M 2 OH + M (k3) and the OH removal

reaction OH + H2O2 H2O + HO2 (k4). Conditions are those of Figure

6-2. ...................................................................................................................75

Figure 6-6. [OH]peak is controlled by k3 and k4. Other reactions show very minor or

no impact on [OH]peak. Conditions are those of Figure 6-2. ...........................75

Figure 6-7. OH profiles predicted by assuming a constant P-H process or a constant

U-V process behind the reflected shock wave. Identical k3 and k4 were

used in those calculations. The two models agree on the peak OH

concentration, while the constant U-V model predicts a slight hump

behavior after the OH spike. Conditions are those of Figure 6-2. ..................77

Figure 6-8. Comparison of pressure profiles: (1) 1134 K, 2900 ppm H2O2/816 ppm

H2O/Ar driven gas, with driver insert, dP/dt = 0%/ms; (2) 1100 K, 2444

ppm H2O2/1538 ppm H2O/Ar driven gas, without driver insert, dP/dt =

1.3%/ms. All pressure profiles have been rescaled to match the initial P5. ....78

xxii

Figure 6-9. At higher temperatures (T > 1200 K), the formation of H2O shows

significant sensitivity to OH + H2O2 H2O + HO2, whereas H2O2 + M

2 OH + M remains the most important one. Initial test mixture: 2540 ppm

H2O2/1234 ppm H2O/617 ppm O2/Ar; initial reflected shock conditions:

1.91 atm, 1398 K. .............................................................................................79

Figure 6-10. Similar to the example case at a lower temperature (Figure 6-5), OH

yield at an elevated temperature is controlled by the OH formation

reaction H2O2 + M 2 OH + M and the OH removal reaction OH + H2O2

H2O + HO2. Conditions are those of Figure 6-9. .......................................80

Figure 6-11. H2O time-history recorded at the conditions of Figure 6-9. The best-fit

H2O profile was achieved by setting k3 = 2.4 × 109 [cm3mol-1s-1] and k4 =

6.8 × 1012 [cm3mol-1s-1]. In comparison, the calculated curves with both k3

and k4 changed ±30% while keeping k3/k4 as determined from the

corresponding OH profile. ...............................................................................81

Figure 6-12. OH time-history recorded at the conditions of Figure 6-9. The best-fit

OH profile was achieved by the same pair of k3 and k4 values that best fits

the water profile in Figure 6-11. The calculated curves with k4 changed

±10% while keeping k3 at its overall optimal value. ........................................82

Figure 6-13. Arrhenius plot of the rate of the reaction OH + H2O2 H2O + HO2 (k4).

The solid line is the linear-fit to all the experimental data of the current

study. The dashed line is the rate expression used by Ó Conaire et al. [5]

and Li et al. [4], whereas the dotted line is the one adopted by GRI-Mech

3.0 [18]. ............................................................................................................83

Figure 6-14. The reaction rate of OH + H2O2 H2O + HO2 (k4), displays a non-

Arrhenius behavior over a wide temperature range. Experimental data are

well-represented by a sum of two Arrhenius expressions (solid line). ............86

Figure 6-15. Arrhenius plot of the second-order rate coefficient for H2O2 thermal

decomposition (k3). Excellent agreement was found between the current

study and the previous study [24]. The solid line is the linear-fit to the

experimental data of this study at 1.8 atm (bath gas: argon). ..........................86

xxiii

Figure 6-16. OH time-history recorded at the conditions of Figure 6-9. The optimal

rate of the reaction 2 OH H2O + O (k8) was determined by best-fitting

the OH time-history. The calculated curves with k8 changed ±30% while

retaining the values of all other parameters. ....................................................87

Figure 6-17. Arrhenius plot of the secondary reaction 2 OH H2O + O (k8). The

results obtained in the current study are within the estimated error bars of

Wooldridge et al. [57]. The solid line is the rate expression used by

Wooldridge et al. [57]. The dashed line is the rate expression reported by

Michael et al. [128] corrected for the updated OH heat of formation. ............89

Figure 7-1. Using the time-history of the laser absorbance near 2.5 μm, the steady-

state H2O concentration was determined to be 1.3%. The composition of

the test mixture can be calculated to be 1.3% H2O / 0.99% O2 / 97.71%

Ar. Initial reflected shock conditions: 1880 K, 1.74 atm. ...............................93

Figure 7-2. OH sensitivity plot at conditions of Figure 7-1. ..............................................95

Figure 7-3. Rate of production analysis (ROP) of OH at conditions of Figure 7-1. ..........96

Figure 7-4. Comparison of experimental and Senkin calculated OH profiles using

best-fit k-5 with the effect of ± 20% variation on k-5 at conditions of Figure

7-1. ...................................................................................................................97

Figure 7-5. Arrhenius plot of experimentally determined k-5 between 1600 and 2200

K. The best-fit to the measured k-5 values (solid line) can be expressed as

k-5 = 6.0 × 1014 exp(-35720 K/T) [cm3mol−1s−1]. .............................................99

Figure 7-6. Arrhenius plot of experimentally determined k5 between 1600 and 2200

K. The k5 expressions used in recent reaction mechanisms are also shown.

Dash: GRI-Mech 3.0 [18], dot: Konnov mechanism [6], solid: Li et al.

mechanism [4] and Ó Conaire et al. mechanism [5]. .....................................101

Figure 7-7. Arrhenius plots for k5 (★-this study; ◆- Srinivasan et al. [27]; ▼-

Hippler et al. [26]; ●- Kappel et al. [24]; ■- Keyser [137]; ▲- Cox et al.

[140] and Lii et al. [139]; ●- Schwab et al. [136]; ☆- Rozenshtein et al.

[141]; ×- Sridharan et al. [138]). k5 expressions adopted in some

commonly used reaction mechanisms [4]-[6][18] are also presented. The

ab initio calculation by Gonzalez et al. [148] can be scaled by 0.61 to well

xxiv

match the rate constant expression used in Li et al. [4] and Ó Conaire et al.

[5] kinetic mechanisms. .................................................................................102

Figure 8-1. Variation of the rate constant (k2) with pressure at 1100 K. Although the

rate constant expressions given in the three studies appear different, the

differences in the actual rate constants at pressures below 100 atm are

insignificant....................................................................................................112

Figure 8-2. Arrhenius plot for k2 at 10 atm. For typical combustion pressures (P <

100 atm), the rate constants are predominantly controlled by the low-

pressure limit rate constant of the reaction (k2,0). ..........................................112

Figure 8-3. Arrhenius plot for k13. Curves are k13 expressions proposed in some

previous mechanisms or reviews (red solid: Michael et al. [161]; black

solid: GRI-Mech 3.0 [18]; dash dot: Li et al. [4], also used by Ó Conaire et

al. [5]; dot: Tsang and Hampson [163]; short dash: Baulch et al. [80], also

used by Konnov [6]). .....................................................................................117

Figure 9-1. H2O time-history during the oxidation of H2 at 1472 K and 1.831 atm in a

fuel-rich H2/O2/Ar mixture (0.1% O2, 0.9% H2, balance Ar). Experimental

data (in blue) are from Section 4.3. A reference has indistinguishable

predicted species time-history as the one above it with a legend, if there is

no legend next to the reference (same thereafter). .........................................120

Figure 9-2. H2O time-history during the oxidation of H2 at 1100 K and 1.953 atm in a

fuel-rich H2/O2/Ar mixture (0.1% O2, 2.9% H2, balance Ar). Experimental

data (in blue) are from Section 4.3.................................................................121

Figure 9-3. OH time-history during the oxidation of H2 at 1980 K and 0.675 atm in a

fuel-rich H2/O2/Ar mixture (0.493% O2, 5% H2, balance Ar).

Experimental data (in blue) are from Masten et al. [19]. ...............................122

Figure 9-4. H2O time-history during the thermal decomposition of H2O2 at 1.95 atm,

1192 K. Test mixture: 2216 ppm H2O2/1364 ppm H2O/682 ppm O2/Ar.

Experimental data (in blue) are from Section 6.3. .........................................123

Figure 9-5. OH time-history during the thermal decomposition of H2O2 at conditions

of those of Figure 9-4. Experimental data (in blue) are from Section 6.3. ...123

xxv

Figure 9-6. OH time-history in a shock-heated 1.3% H2O/0.99% O2/97.71% Ar

mixture. Initial reflected shock conditions: 1880 K, 1.74 atm.

Experimental data (in blue) is from Section 7.3. ...........................................124

Figure 9-7. Ignition delay times predicted by the current mechanism, by assuming

either a constant U-V reactor (CHEMKIN) or a reactor with a pressure

rises at a rate of 2%/ms (CHEMSHOCK). The experimental data (in blue)

are from Pang et al. and are for mixtures of 4% H2, 2% O2, balance Ar at

3.5 atm [16] with an experimental facility-related pressure rise of 2%/ms. ..126

Figure 9-8. Species profiles from a flow reactor experiment [2]. The unburnt mixture

was at 880 K, 0.3 atm and comprised of 0.5% H2, 0.5% O2, with the

balance N2. The curves are calculated with the current mechanism using

an adiabatic approximation. All calculated curves are simultaneously

shifted forward by 0.071 s. ............................................................................127

Figure 9-9. H2 mole fractions recorded at 6.5 atm and at various initial temperatures

[2]. The unburnt mixtures were: (a) 1.29% H2/2.19% O2/N2, time shifted

forward by 0.30 s; (b) 1.30% H2/2.21% O2/N2, time shifted forward by

0.54 s; (c) 1.32% H2/2.19% O2/N2, time shifted forward by 0.40 s; (d)

1.36% H2/2.24% O2/N2, time shifted forward by 0.38 s; (e) 1.36%

H2/2.24% O2/N2, time shifted forward by 0.24 s. Curves are calculated

using the current mechanism and an adiabatic reactor. .................................128

Figure 9-10. Laminar flame speed for H2/O2 diluted in N2 and Ar at 1 atm. The mole

ratio between O2 and diluent (Ar, N2) is 1:3.76. Experimental data are

from references [184]-[188], the curves are the predictions using the

current mechanism. ........................................................................................129

Figure 9-11. Laminar flame speed in very diluted H2/O2/N2 mixtures (O2:N2=1:12)

with unburnt mixtures at standard temperature and pressure. Experimental

data are from references [190][191] and the curve is calculated using the

current mechanism. ........................................................................................130

Figure 9-12. Mass burning rates of H2/O2/Ar flames of equivalence ratio 2.5 at

various nominal flame temperatures ( fT ). The unburnt mixtures were: (a)

fT ~ 1800 K, 38.46% H2/7.69% O2/Ar; (b) fT ~ 1700 K, 35.21% H2/7.04%

xxvi

O2/Ar; (c) fT ~ 1600 K, 32.21% H2/6.44% O2/Ar; (d) fT ~ 1500 K,

29.41% H2/5.88% O2/Ar. Curves are calculated using the current

mechanism; data are from Burke et al. [155]. ................................................130

Figure 9-13. Species spatial profiles obtained from a burner-stabilized flame structure

study [192]. The species profiles were normalized using N2 mole fraction.

The unburnt mixture consisted of 18.83% H2 and 4.60% O2 (balance N2)

and was at 336 K and 1 atm. The temperature profile that is used for

simulation is taken from the same study [192]. Solid lines: simulations

using the current mechanism. ........................................................................132

Figure 9-14. The structure of a burner-stabilized flame studied using a mixture of

39.7% H2, 10.3% O2 and balance Ar (by mole) at 0.047 atm.

Experimental data are from the study by Vandooren & Bian [194]; the

curves are calculated using the current mechanism. ......................................132

1

CHAPTER 1: INTRODUCTION

1.1 MOTIVATION

Detailed kinetic mechanisms for the oxidation of hydrocarbons have the H2/O2 sub-

mechanism as a necessary starting point of their hierarchical structure [1]. This sub-

mechanism is critical because it contains many important elementary reactions involving

H, O, OH, HO2, H2O, and H2O2 that play significant roles in all stages of hydrocarbon

oxidation. Continued improvement of the H2/O2 sub-mechanism is thus necessary for the

continued development and refinement of high-fidelity hydrocarbon mechanisms.

Several detailed kinetic mechanisms dedicated to the H2/O2 system have been developed

recently [2]-[6]. In addition to these mechanisms, recently-refined H2/CO mechanisms

[7]-[10] also contain the corresponding H2/O2 sub-mechanisms. These mechanisms are

able to capture the behavior of chemical systems dominated by chain-branching reactions

(e.g., ignition delay times). However, systems dominated by the formation and

consumption of HO2 and H2O2 are still subject to relatively large uncertainties.

The goal of the present study is to make accurate rate constant measurements for some

important H2/O2 reactions, particularly these peroxide reactions with large uncertainties.

Using these newly determined rate constants, an H2/O2 mechanism will be compiled and

validated against various kinetic targets.

1.2 PROBLEM FORMULATION

1.2.1 Modified shock tubes for better combustion kinetic studies

High-temperature chemical kinetics experiments, such as measurements of ignition delay

times and species concentration time-histories, and determination of reaction rates, are

regularly performed behind reflected shock waves in ultra-clean shock tubes. Shock

tubes operated in this manner, often with the reactants diluted with an inert gas such as

2

argon, offer the potential advantages of near-ideal, constant volume reaction, with

instantaneous steps in temperature and pressure, and accurately known initial

temperature, pressure and mixture conditions.

The behavior behind reflected shock waves, however, can be compromised by non-

idealities found in real shock tubes. Non-ideal shock tube facility effects, such as

boundary layer growth [11][12], diaphragm-bursting mechanics [13]-[15], and other non-

ideal phenomena involved in shock tube experiments, can cause the pressure behind the

reflected shock wave near the endwall to gradually change, as illustrated by an example

pressure history in Figure 1-1.

0 5 10 150

1

2

3

4

5

Pre

ssur

e (a

tm)

Time (ms)

T5 = 912 K, Unmodified Shock Tube

dP5*/dt = 0.022/ms for 7 ms

Figure 1-1. A non-ideal pressure rise of 2.2%/ms occurs for 7 ms in a pressure-driven, 15 cm inner-diameter shock tube, with constant area for both driver and driven sections. T5 = 900 K, P5 = 4 atm, driver gas: 50% N2/ 50% He, driven gas: Ar.

By convention, T5 and P5 are used to denote the temperature and pressure, respectively,

behind the reflected shock; values of these parameters are calculated from the incident

shock speed, initial pressure, and initial temperature using standard normal shock

relations. The rate of pressure change behind the reflected shock, induced by non-ideal,

facility-dependent effects, is defined as dP5*/dt (= (dP5/dt)/P5). These changes in

pressure are accompanied by changes in temperature, which typically may be related to

pressure change through an assumption of isentropic compression. Because of the

Arrhenius behavior of many important chemical reactions having large activation

energies, even small changes in the temperature can significantly affect the reaction rate

of the chemical process being studied [12].

3

As an example, the influence of non-ideal pressure change can be seen in the analysis of

hydrogen/oxygen ignition delay time data [16]. Figure 1-2 presents measurements of

ignition delay time for hydrogen and two simulations: one using the conventional

constant volume/constant internal energy model, and one using CHEMSHOCK [17], a

model that uses the measured time-varying pressure as a constraint. Both simulations

utilize the same detailed reaction mechanism, known as GRI-Mech 3.0 [18]. The data

points [16] are plotted at the initial post-reflected shock temperature and are normalized

to a common initial pressure (3 - 5 atm) through use of the pressure dependence implicit

in the detailed chemical mechanism. As is evident in Figure 1-2, dP5*/dt changes as

small as 2%/ms for this chemical system can create variations in the ignition delay times

of over an order of magnitude at the low temperature end of the experiments. Values of

1−2%/ms adopted in this example are typical for one of the large diameter shock tubes in

this laboratory, while the rate can be much higher in smaller diameter shock tubes.

0.90 0.95 1.00 1.05 1.10 1.150.1

1

10

100

1000910 K

CHEMKIN: Constant U,V CHEMSHOCK: dP*/dt = 0.01/ms CHEMSHOCK: dP*/dt = 0.02/ms Experiment: dP*/dt = 0.01-0.02/ms

Igni

tion

Tim

e [

ms]

1000/T [1/K]

4% H2/2% O2/Ar3.5 atm

1110 K 1000 K

Figure 1-2. Influence of dP5*/dt on measured and modeled ignition delay times for hydrogen/oxygen/argon mixtures. Figure adapted from [16].

Though the influence of the facility-related temperature and pressure changes can be

included in the chemical kinetics modeling, a simpler but often still accurate modeling

constraint, such as a constant volume model, is normally used. Chemical modelers often

have to assume such a simple constraint when re-analyzing older shock tube data even

when it is not likely to be valid (such as at long test times), because of the absence of

published information about facility-related temporal changes in the conditions of the

4

experiments. Variations in dP5*/dt between shock tubes and laboratories make direct

comparisons between studies conducted in different laboratories more difficult.

Therefore, accurate kinetics measurements will require, at times, shock tube

modifications to minimize non-uniformity in the test conditions behind the reflected

shock wave. The first objective of this dissertation work is to develop a gas dynamic

model for these shock tube modifications. The model will allow a systematic approach to

design modifications to existing shock tube facilities in the form of driver inserts. Driver

inserts can compensate for non-ideal pressure/temperature rises behind reflected shock

waves.

1.2.2 Sensitive H2O diagnostic to better understand combustion chemistry

Stanford’s OH diagnostic has been a workhorse for combustion kinetic studies, not only

because of the key role OH-radicals play in combustion chemistry but also because OH-

radicals can be very sensitively detected using laser absorption diagnostic near 307 nm.

However, the OH diagnostic by itself does not provide sufficient information to fully

describe the combustion chemistry, even for the simplest H2/O2 system.

H2O is one of the final products of hydrocarbon combustion, and accurately knowing

H2O time-histories in reacting H2/O2 systems provides critical insights into these systems.

For example, accurate measurements of the rate constant for one of the most important

combustion reactions, H + O2 → OH + O, were in the past mainly carried out using OH

laser absorption (see discussions in Chapter 4). However, these OH diagnostics did not

produce high-accuracy data at temperatures below 1500 K because the OH yield is a

strong function of temperature and OH concentrations are too low for accurate detection

at these lower temperatures. Yields of H2O as the final product of H2 oxidation, on the

other hand, are not strongly affected by reaction temperature. In addition, by using

proper test mixtures, the H2O formation rate during H2 oxidation can be predominantly

controlled by the rate-limiting step H + O2 → OH + O. Therefore, a sensitive H2O

diagnostic has the potential to provide high-quality rate constant data for the key

combustion reaction H + O2 → OH + O at temperatures below the limit of the OH

diagnostic.

5

In addition to the aforementioned example where an H2O diagnostic provides direct

information of the target species (i.e. H2O), it also has the potential to provide indirect

information about other species. H2O2, for instance, cannot be easily and sensitively

detected by current optical diagnostic schemes. And to make the problem worse, H2O2 is

chemically unstable and undergoes fast surface decomposition. A sensitive H2O

diagnostic can be used to infer the H2O2 concentration by noting that one mole of H2O is

produced after one mole of H2O2 is completely decomposed. This strategy of inferring

H2O2 concentrations using an H2O diagnostic was successfully implemented for

determining the rate constant of H2O2 thermal decomposition (refer to Chapter 5 for more

details).

1.2.3 Improved rate constant of the reaction H + O2 → OH + O

The chain-branching reaction H + O2 OH + O is regarded as one of the most important

elementary reactions in combustion. At temperatures above 1500 K, the rate constant has

been experimentally determined with small uncertainty using an OH diagnostic, for

example, by Masten et al. [19]. However, at lower temperatures (T < 1500 K) the rate

constant was mainly determined using the ARAS (Atomic Resonance Absorption

Spectroscopy) method. Experimental results obtained using the ARAS method are

typically associated with larger scatter and larger uncertainty, for instance as seen with

data from Pirraglia et al. [20] in Figure 1-3.

For such an important reaction, a rate constant with a small uncertainty is desired at all

temperatures. Therefore, one objective of the current work is to reduce uncertainty for

the rate constant of reaction H + O2 → OH + O at temperatures below 1500 K. As

briefly mentioned in the above subsection, an H2O diagnostic holds the most promise to

achieve this goal.

6

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

1011

1012

1013

1429 K2x1013 3333 K

k 1 [cm

3 mol

-1se

c-1]

1000/T [1/K]

Pirraglia et al. (1989) Masten et al. (1990)

2000 K 1111 K

4x1010

Figure 1-3. Representative experimental results for the rate constant of the reaction H + O2 → OH + O using a laser absorption OH diagnostic (Masten et al. [19]) and the ARAS method (Pirraglia et al. [20]).

1.2.4 Improved rate constants of reactions involving H2O2 and HO2

Hydrocarbon ignition at intermediate temperatures (850 – 1200 K) is controlled by

hydrogen peroxide (H2O2) and hydroperoxyl radical (HO2) reactions, for example the

H2O2 thermal decomposition reaction, the reaction OH + H2O2 = HO2 + H2O, and the

reaction O2 + H2O = OH + HO2. In particular, the thermal decomposition of H2O2 has

been identified as the dominant chain-branching reaction that controls hydrocarbon

ignition in the intermediate temperature regime (850 K – 1200 K) [21].

However, reliable measurements of the rate constants for these reactions are not

available. Experimental challenges, such as the lack of a reliable H2O2 source and a

sensitive H2O2 diagnostic, have prevented accurate determination of the rate constant of

the H2O2 thermal decomposition reaction. In the temperature range between 1000 and

1200 K where intermediate temperature hydrocarbon ignition occurs, only a few studies

[22]-[24] have been carried out, and these were all performed in the same laboratory by

Troe and co-workers. The authors of those papers recognized the inherent difficulties in

their measurements, and have recommended independent studies by other groups.

Similarly, only a few studies of the reaction OH + H2O2 = HO2 + H2O have been

conducted at combustion temperatures [24]-[26], and these also were all performed in the

7

same laboratory. However, this reaction was only of secondary importance in these

previous studies and thus subject to large experimental uncertainties. An unusual up-turn

in the reaction rate at temperatures higher than 800 K was reported by Hippler et al. [26],

as shown in Figure 1-4. This dramatic change in the activation energy is difficult to

explain theoretically and needs to be experimentally verified. In addition, it might be

possible to significantly reduce the uncertainty associated with the rate constant

measurement by simultaneously measuring H2O and OH time-histories.

0.6 0.7 0.8 0.9 1.0 1.11012

1013

1014

k 4 [cm

3 mol

-1s-1

]

1000 K/T

Hippler et al. (1995) Hippler et al. (1992)

909 K1250 K1667 K

Figure 1-4. Previous studies of the rate constant of the reaction OH + H2O2 H2O + HO2. The dashed line is the rate expression used by Ó Conaire et al. [5] and Li et al. [4], the dotted line is the one adopted by GRI-Mech 3.0 [18].

The third reaction of interest is OH + HO2 H2O + O2. This reaction is a major HO2

termination path in lean combustion, and is responsible for the depletion of both OH and

HO2 radicals in burnt gases. Hippler et al. [26] reported a rate constant minimum near

1250 K. A more recent measurement by Kappel et al. [24] found the rate constant

minimum to be near 1000 K. However, no such strong temperature dependence was

observed by Srinivasan et al. [27], as can be seen from Figure 1-5 (refer to Chapter 7 for

more details). One goal of this study is to resolve this discrepancy using the modified

shock tube and the newly developed diagnostic scheme.

8

0.4 0.6 0.8 1.0

1013

10142500 K 1667 K 1250 K

k 5 [cm

3 mol

-1s-1

]

1000 K / T

Hippler et al. (1995) Kappel et al. (2002) Srinivasan et al. (2006) Goodings & Hayhurst (1988)3x1012

1000 K

Figure 1-5. Arrhenius plot of the rate constant of the reaction OH + HO2 H2O + O2. Large scatter is seen in the measured reaction rate values. The dashed line is the rate expression adopted by GRI-Mech 3.0 [18]; the solid line is the one used by Li et al. [4] and Ó Conaire et al. [5]; the dotted line is the rate expression used by Konnov mechanism [6].

1.2.5 High-fidelity H2/O2 mechanism

Our strategy for improving understanding of elementary reactions is to compile a high-

fidelity combustion mechanism that can more accurately predict the performance of

combustion applications. The last task of this dissertation is to incorporate the results of

the new rate constant measurements as proposed in this section into a new H2/O2

mechanism.

The mechanism will be extensively validated against a wide range of kinetics targets,

including species time-histories from shock tube experiments, ignition delay times,

species profiles from flow reactor experiments, flame speeds and mass burning rates, and

flame structures. The performance of the newly proposed H2/O2 mechanism will be

evaluated by comparing to previous mechanisms.

1.3 GROUNDWORK

The current work is made possible by three essential tools that are new to combustion

kinetic studies: 1) driver inserts that can be used to modify existing shock tubes, 2) urea-

9

H2O2 as a novel H2O2 source for combustion kinetic studies, and 3) a sensitive H2O

diagnostic scheme based on tunable diode laser absorption near 2.55 μm.

These tools have been used for other purposes prior to the current study. For instance,

the concept of using cone-shaped driver inserts to remove non-ideal facility-related

effects was proposed by Dumitrescu [28] in 1972. It was not until the current work,

however, that a detailed model for designing such driver inserts has been developed.

With the implementation of driver inserts, non-ideal pressure rises behind reflected shock

waves can be eliminated almost completely, thereby providing a near-ideal constant

energy-volume (constant U-V) homogenous environment for combustion kinetic studies.

Using shock tubes with properly designed driver inserts, higher-quality experiment data

can be obtained.

The H2O2 thermal decomposition system provides good isolation to separate important

peroxide reactions from interfering ones. However, this seemingly simple system is

greatly compromised by the unstable nature of H2O2; high-concentration H2O2 solutions

are extremely corrosive and explosive. A common practice of obtaining relatively pure

H2O2 was through multiple re-distillations from commercial products. Recently, urea-

H2O2 has appeared as a novel H2O2 source, which has been successfully applied in

combination with static cells to study chemical kinetics at low temperatures [29][30].

The reagent is available in the form of powder and can release relatively pure H2O2 vapor

upon gentle heating. This novel H2O2 precursor was extensively used over the course of

this dissertation work when H2O2 vapor was needed, completely replacing the need for

dangerous high-concentration H2O2 solutions.

H2O diagnostics based on tunable diode laser absorption spectroscopy have been

developed and extensively used at Stanford for various purposes. Previous studies

carried out in this laboratory have demonstrated numerous advantages of using solid-state

diode lasers [31][32]. Recent advances in laser technology enable ease of access to

fundamental H2O bands near 2.5 μm using DFB (Distributed Feedback) lasers. The

fundamental bands offer absorption lines that are at least an order of magnitude stronger

than those in overtones. Over the course of the present work, a H2O diagnostic scheme

10

based on a 2.55 μm DFB laser was developed, which provided unique opportunities for

improving the understanding of the H2/O2 system.

The new approaches discussed above were implemented in combination with other

powerful tools that have been widely used in previous combustion kinetic studies to get a

more comprehensive understanding of the H2/O2 system. In particular, Stanford’s OH

diagnostic has been extensively used by researchers to study combustion problems

ranging from ignition delay times [33], rate constants of elementary reactions [34],

species time-histories during fuel oxidation [35], to species heat of formation [36]. In the

current study, the OH laser diagnostic was used simultaneously with the H2O diagnostic

to provide more comprehensive understanding of H2/O2 reacting systems.

1.4 SCOPE AND ORGNIZATION

This thesis is divided into three parts. Chapters 2 and 3 form the first part of the present

work. The focus of this part is to develop new diagnostic schemes and to make

improvements to a standard shock tube, which is the major test facility used in the current

study.

The goal of the second part is to make accurate rate constant measurements for important

elementary reactions within the H2/O2 system using shock tube/laser absorption

techniques. This part consists of four chapters, Chapters 4–7, where each chapter

concerns one important elementary reaction within the H2/O2 system. One of the most

important combustion reactions, H + O2 OH + O, is discussed in Chapter 4; the H2O2

thermal decomposition reaction in Chapter 5; an important H2O2/HO2 reaction, OH +

H2O2 H2O + HO2, in Chapter 6; and the reaction between OH and HO2 (OH + HO2

H2O + O2) in Chapter 7.

The last part of the work aims at developing and validating an improved H2/O2

mechanism by incorporating this new understanding. The mechanism is compiled in

Chapter 8. The validation of the mechanism is discussed in Chapter 9, which includes

tests against OH and H2O concentration time-histories reported in the second part

(Chapters 4–7) of this thesis. In addition, the mechanism will be validated against a wide

11

range of standard H2/O2 kinetic targets, including ignition delay times, flow reactor

species time histories, laminar flame speeds, and burner-stabilized flame structures.

13

CHAPTER 2: THE APPLICATION OF DRIVER INSERTS TO IMPROVE SHOCK

TUBE PERFORMANCE

As introduced in Section 1.2, facility-related non-ideal effects, such as boundary layer

growth, can cause variations in the pressure histories seen in reflected shock wave

experiments. These variations can be reduced, and in some cases eliminated, by

modifying standard shock tube facilities using driver inserts. With the employment of

these driver inserts, near-ideal performance in reflected shock wave experiments can be

achieved, even at long test times. This near-ideal behavior simplifies the interpretation of

shock tube chemical kinetics experiments, particularly in experiments that are highly

sensitive to temperature and pressure changes.

2.1 INTRODUCTION

Dumitrescu was the first to propose compensating for the gradual change in P5, dP5*/dt,

by inserting a properly designed cone-shaped obstacle into the driver section of a shock

tube [28]. A schematic plot illustrating such a modification is shown in Figure 2-1.

Expansion waves reflected from the surface of the driver insert continuously propagate to

the far end of the driven section where the chemical kinetic studies are conducted. The

pressure decrease caused by the expansion wave that partially reflects from the driver

insert is superimposed on the pressure rise caused by boundary layer growth and incident

shock attenuation (as well as other non-ideal effects) to compensate for or cancel the rise

in P5.

Other methods could theoretically be used to counteract the non-ideal facility effects on

reflected shock properties, e.g., spatially varying driver gas composition, exotic test

section geometries, or boundary layer control, though none of these methods have been

extensively used. However the driver insert method is more easily adaptable to existing

shock tubes. Using this method, the driven section is kept free of any modification that

would limit optical access to the end section, and the driver insert can be easily installed

14

and modified to accommodate various test conditions. Expanding on Dumitrescu’s idea,

we have developed a simple direct method to design the shock tube driver inserts needed

to eliminate the non-ideal pressure rise that occurs behind reflected shock waves. With

this method, the need for highly uniform reflected-shock temperature/pressure time-

histories required by chemical kinetic studies can be accommodated.

Figure 2-1. A schematic plot of a current driver-section insert modification in a shock tube. A cone-shaped obstacle in the shock tube driver section can effectively cancel the non-ideal pressure rise behind reflected shock waves.

2.2 STANDARD SHOCK TUBE

The standard, high-purity shock tube to be modified was built of 304 stainless steel and

has an inner diameter of 14.13 cm. The driven section of the shock tube is 8.54 m long,

and the driver section is 3.35 m long. The driven section vacuum system consists of a

mechanical pump and a Varian V-250 turbomolecular pump to achieve ultimate pressures

of 10−7 Torr. An ultimate combined leak/outgassing rate of 10−6 Torr per minute can

typically be achieved with overnight pumping.

Reflected shock conditions are determined using standard normal shock relations. The

preshock initial mixture pressures P1 are measured using a high-accuracy Baratron

pressure transducer. Incident shock velocity measurements are made using five

piezoelectric pressure transducers (PCB) over the last 1.5 meters of the shock tube and

four interval counters (Fluke PM6666), and these velocity measurements are linearly

extrapolated to the endwall. Average incident shock speed attenuation rates are between

0.5−1.5%/meter. Uncertainty in the initial temperature behind the reflected shock wave,

T5, is ± 0.8% [37], resulting primarily from the uncertainty in the measured shock speed.

In addition to the five PCB pressure transducers for incident shock velocity

measurements, another sidewall piezoelectric pressure transducer (Kistler model 603B)

15

located 2 cm from the endwall is used to monitor pressure time-histories. Other details

about the facility can be found in Ref. [38].

To illustrate the non-ideal effects that are typical of standard shock tubes, an example

case is presented here. The driven gas is chosen to be argon, which is commonly used in

shock tube studies of high-temperature chemical kinetics. The target temperature T5 is

900 K, which corresponds to the reflected shock temperature produced by an incident

shock wave of Mach number Ms = 1.85 moving through the test gas at an initial

temperature of 300 K. The driver gas is a mixture of 50% N2 and 50% He, which is a

tailored driver gas [39]-[41] for this combination of driven gas and T5. To achieve the

desired shock strength, the initial driver/driven pressure ratio P4/P1 is determined to be

11.9 by normal shock theory, although larger values of P4/P1 are actually required to

compensate for various losses. The pressure rise behind the reflected shock in this

sample case was experimentally determined to vary almost linearly with time with a

value of dP5*/dt = 2.2%/ms for the duration of 7 ms, as shown in Figure 1-1. The

nonlinear pressure hump right after the linear pressure rise (i.e. from about 7 to about 11

ms) can be attributed to the interaction between the reflected shock wave and the

imperfect contact surface, which actually is a mixing zone between driver and driven gas

[43]. After 11 ms, the arrival of the expansion wave reflected from the driver endwall

lowers the pressure and temperature in the test section isentropically, thereby effectively

ending the nominal test time.

2.3 MODEL AND PROBLEM SOLUTION

2.3.1 Model Overview

The fundamental basis of this method of designing a shock tube driver modification is

that the driver insert partially reflects the expansion fan that originates at the diaphragm

location. The reflected expansion fan then produces a gradual pressure decrease in the

test section to compensate for the pressure rise due to the non-ideal effects. The critical

assumption made in this method is that the pressure rise due to non-ideal effects and the

pressure decrease caused by the expansion waves reflected from driver insert can be

16

superimposed linearly. To first-order, when the two opposite pressure changes are of the

same magnitude, the effects on temperature and pressure of the region behind reflected

shock waves by non-ideal facility effects are effectively eliminated.

The non-ideal rate of change in pressure dP5*/dt, is determined empirically, primarily due

to the fact that there is currently no simple, successful model to correlate the boundary

layer growth rate or incident shock wave attenuation rate to dP5*/dt in the region behind

the reflected shock. Difficulties of computing dP5*/dt either analytically or numerically

also stem from the lack of a suitable model for the coupled effects of boundary layer

growth and shock attenuation [11][44]-[46] with other non-ideal effects in a shock tube,

such as the finite opening time of the diaphragm and finite formation time of the incident

shock wave [13]-[15].

To design a driver obstacle that compensates for the non-ideal pressure rise at a particular

rate in the test section, it is essential to answer two questions: 1) how long does it take for

the information about the area change in the driver section to reach the test section by

means of the expansion waves reflected from the driver insert; and 2) how much does the

pressure at the test section vary with the area change in driver section. The exact solution

to the problem is complicated as these two phenomena are coupled. Fortunately, in a

first-order approximation, these two questions can apparently be answered separately

without introducing a large error, based on the following arguments. Introducing a

parameter termed the equivalence factor g, which relates the incident shock strength (and

hence the pressure at the test section) to the driver cross-sectional area, Alpher and White

[47] showed that this equivalence factor is only a weak function of area change in the

driver section. As the driver obstacle does not change the cross-section of the driver

dramatically, the decoupling of the two problems seems a reasonable simplification.

2.3.2 First problem: determining the location of area change

The time interval required for the expansion fan to reflect off the driver insert and reach

the test section can be determined using the method of characteristics. This will

determine the time delay before information about the pressure change due to a particular

area change in the driver section reaches the test section. We assume that the incident

17

shock propagation speed does not depend on the length of the driver section as long as

the expansion fan reflected from the driver endwall does not catch up with the incident

shock front. The reference point for time zero can then be defined by the instant that the

reflected shock wave passes the test section location, very near the end wall. The

reflected shock wave arrives at the test section at time t1 and the arrival of the reflected

expansion fan occurs at a later time t2, with a time interval between the two defined by

Δt = t2 − t1.

Existing computer codes can be used to predict wave propagation in shock tubes; one

example is the Riemann solver WiSTL [48] developed at the University of Wisconsin.

This published web-available code was developed for shock tubes with constant

driver/driven cross-sections and does not allow for area change in the driver section, but

the code can be used without modification to predict the time delay before the arrival of

expansion waves at the test section by assuming the driver section endwall (which is just

an extreme case of an area change) to be at different locations and calculating Δt. An

example X-t wave diagram calculated using the code is shown in Figure 2-2, also

showing a distance Xdist indicating the location of an area change relative to the

diaphragm. Xdist and Δt are −3.4 m and 10.8 ms, respectively, in this case.

In a similar fashion, Δt values can be computed for different Xdist locations. A calculated

curve which relates Δt with Xdist is shown in Figure 2-3. The figure shows that in order to

manipulate the pressure immediately after the arrival of the reflected shock at the test

section, i.e. with Δt = 0, the first area change, which is the start of the driver insert, should

be located at Xdist = −0.9 m. An X-t wave diagram is provided in Figure 2-4 for this

limiting case. It is clear that if an obstacle is placed at Xdist = −0.9 m, the expansion fan

arrives at the test section right after passage of the reflected shock wave. Please note that

the dashed lines in Figure 2-2 and Figure 2-4 are representative pressure contours and are

not complete. For example, in Figure 2-4 the contact surface continues to curve up near

15 ms due to expansion waves that are not explicitly displayed in the X-t diagram.

18

Figure 2-2. The X-t wave diagram generated for the case where the incident shock Mach Number Ms = 1.85 (corresponding to T5 = 900 K); driven gas is argon; driver gas is 50% N2/50% He, all gases initially at 300 K. The driven section length = 8.5 m results in a uniform reflected shock test time of 10.8 ms. The location of the driver area change Xdist = −3.4 m.

-3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.00

5

10

15

Tim

e D

elay

Δt [

ms]

Location of Area Change Xdist [m]

Figure 2-3. Δt-Xdist curve calculated for the sample case where the incident shock Mach

number Ms = 1.85 (corresponding to T5 ≈ 900 K); the driven gas is Ar, and the tailored

driver gas mixture is 50% N2/50% He. Driven section length L is 8.5 m.

The X-t wave diagrams used in the calculation are generated for ideal shocks, i.e.,

incident shock attenuation is neglected. The approximation is good when the shock

attenuation rate is small, say ~ 1% - 3%/m as typically observed in Stanford shock tubes.

However, for shock tubes with higher shock attenuation rates, this non-ideal effect may

also need to be accounted for. Although the shock attenuation effect essentially does not

change the expansion fan behavior, it bends the incident shock trajectory upwards in an

19

X-t diagram. In a kinetics experiment, the incident shock speed (slope of the incident

shock curve) near the endwall determines T5. Therefore, a stronger shock (smaller slope)

has to be produced at early times to obtain the final value needed for a target T5. This

being the case, t2 remains the same while t1 has to be corrected for the shock attenuation

effect to get t1' = t1 – L2A/2S, where L [m] is the shock tube driven section length, A [m-1]

is the measured shock attenuation rate, and S [m/s] is the incident shock speed measured

near the endwall. The resulting Δt therefore has to be increased by L2A/2S.

Figure 2-4. The X-t wave diagram for the limiting case where the time interval Δt = 0.

The location of the driver area change Xdist = −0.9 m.

2.3.3 Second problem: rate of area change calculation

To evaluate the correlation between the driver insert area change and the resulting

pressure variation in the test section, a divergent shock tube model is used. Alpher and

White’s theory [47] can be used to determine the pressure variation in P5 when the area

of the driver section differs from that of the driven section. Although the theory was

developed for a convergent shock tube (where the driver section has a larger cross-

section than that of the driven section), the analysis can be modified for present proposes

where the driver section has a smaller cross-section due to the driver insert.

In the divergent shock tube model, the shock tube is divided into three parts: driver

section of cross-section A4, driven section with cross-section A1, and a divergent “nozzle”

in between, as shown in Figure 2-5. Several constraints on the properties of the different

20

regions can be noted. The cold driver flow in region (3a) cannot exceed the speed of

sound. However, the motion of the gas can be either subsonic or supersonic in region (3)

depending on the shock strength. As a result, the shock strength has to be discussed

separately for both the subsonic and supersonic cases in region (3). Alpher and White’s

theory [47] can be directly applied in both cases with M3a = M3b' and P3a = P3b' to

compute the effect of area change on P5. In the subsonic case, M3b = M3 and P3b = P3.

However, in the supersonic case, another expansion fan appears downstream of the

nozzle zone (expansion fan II shown in Figure 2-5 which is not present in the subsonic

case). The presence of this second expansion fan complicates the problem, however, the

“choking” constraint at the throat (3b') gives M3a = M3b' = 1 and controls the pressure in

region (3) making the problem still solvable.

(3b)

Expansion fan II

DrivenSection

(1)(2)(3)

(3b')

DriverSection

(3a)(4)

pExpansion fan I Contact

surfaceIncident shock

Nozzle zone

Figure 2-5. Diagram of a divergent shock tube and the corresponding pressure regime numbering scheme.

With Alpher and White’s theory [47], we can calculate the deviation from P5 in a

constant cross-sectional area shock tube that is observed in the divergent shock tube. We

denote this perturbation by ΔP5, and we can then assess ΔP5/P5 as a function of A4/A1.

The ΔP5/P5 versus A4/A1 curve that is calculated for the sample case in this study is

shown in Figure 2-6.

21

0.0 0.5 1.0 1.5 2.0 2.5-40

-20

0

20

40

ΔP5/P

5 (%

)A4/A1

Figure 2-6. ΔP5/P5 as a function of A4/A1 for the sample case shown in Figure 1-1. Driven gas is argon and the driver gas is 50% N2/50% He. The initial driver/driven pressure ratio P4/P1 is 11.9 and was used to achieve T5 ≈ 900 K.

2.3.4 Final driver insert design

The final driver insert design is derived from the combination of the empirically observed

non-ideal pressure change rate dP5*/dt with the relationships between Δt and Xdist and

between ΔP5/P5 and A4/A1 which are calculated in the previous sections. Figure 2-7

shows the resulting A4/A1 as a function of Xdist required to eliminate the dP5*/dt of

2.2%/ms for 7 ms, for the sample case illustrated in Figure 1-1. The starting point and

the ending point of the area change generated by the insert are noted as Xdist(1) and Xdist

(2),

respectively. Here, Xdist(1) = −0.9 m is the location of the tip of the insert and corresponds

to the zero time delay in Figure 2-3, while Xdist(2)

is the location corresponding to a delay

time of 7 ms, where an area change in the insert is no longer needed, which from Figure

2-3 is −2.5 m. Notice that a linear correlation was approximated for the area change

between Xdist(1) and Xdist

(2), since both relationships between Δt and Xdist and between

ΔP5/P5 and A4/A1 occur in the nearly linear regions as can be seen from Figure 2-3 and

Figure 2-6.

22

-3 -2 -1 060

70

80

90

100

Xdist(2)

A4/A

1 [%

]

Location of Area Change Xdist [m]

Xdist(1)

Figure 2-7. The relationship between A4/A1 and Xdist curve for the driver section. The diaphragm location is at Xdist = 0 and the driver end wall is at Xdist = −3.4 m.

2.4 MODIFIED SHOCK TUBE FACILITY

Although the model predicts a continuous change in area, it is not practical to make a

smooth cone-shaped driver insert for each specific test condition. In addition, the

calculated relationship between A4/A1 and Xdist might require future adjustments owing to

the approximations made in the calculations as well due to the potential influence of the

other non-ideal effects mentioned previously. One solution is to make the driver insert

adjustable with discrete steps of area change.

Experiments showed that, with only minor adjustments, a discrete realization of the

predicted A4/A1 curve as a function of Xdist can eliminate non-ideal pressure rise almost

completely. For the sample case discussed in the previous sections, Figure 2-8 shows the

highly uniform pressure trace obtained using the driver insert technique compared to a

pressure trace recorded without pressure rise compensation. The pressure traces were

recorded using a Kistler 603B1 pressure gauge located 2 cm from the endwall. The exact

shape of the discrete driver insert used in the experiment is compared to the model

calculation in Figure 2-9. The good agreement between the modeled driver insert shape

and the optimal experimental shape shows the validity of the assumptions made in this

model.

23

0 5 10 150

1

2

3

4

5

Pre

ssur

e (a

tm)

Time (ms)

T5 = 897 K, w/ driver insert T5 = 912 K, w/o driver insert

dP*/dt = 0.022/ms

Figure 2-8. Test section pressure profile (2 cm from the end wall) for identical shock wave experiments with and without a driver insert. Driver gas in both experiments was 50% helium/50% nitrogen; the driven gas was argon. The nominal initial reflected shock conditions were T5 = 900K, P5 = 4 atm.

Assuming isentropic behavior of the test gas sample at the measurement station, uniform

pressure implies a uniform temperature profile. This temperature uniformity has been

confirmed with an in situ two-line thermometry diagnostic developed in this laboratory

using two distributed feedback (DFB) diode lasers near 2.7 μm [49]. The thermometry

has a resolution of 9 K. In these direct temperature measurements behind the reflected

shock, the argon test gas was seeded with 2% CO2, and therefore the test condition was

slightly different. However, the data clearly confirm that a uniform temperature profile is

obtained when pressure is also uniform, as can be seen in Figure 2-10.

-3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0-7.5-5.0-2.50.02.55.07.5

Model Actual Shape

Rad

ius

[cm

]

Axial Length X [m]

Figure 2-9. The axial cross-section of the modified shock tube driver section. The comparison is between the model prediction and the actual shape of the driver insert that has the optimal performance experimentally. The inner diameter of the driver section is 15 cm, diaphragm location is at X = 0 and endwall is at X = −3.4 m.

24

0 3 6 9 120

300

600

900

1200

0.0

0.6

1.2

1.8

2.4

T5 = 952 K, w/ driver insertTest gas: 2% CO2 / Ar

Time [ms]

Pre

ssur

e [a

tm]

Tem

pera

ture

[K]

Directly Measured Temperature

Pressure

Figure 2-10. Highly uniform temperature profile obtained when pressure is precisely maintained constant using a driver insert. Driver gas helium/nitrogen (60%/40%), driven gas argon seeded with 2% CO2. Reflected shock conditions: T5 = 952 K, P5 = 1.2 atm. The figure was adapted from reference [49].

The basic design can be extended to almost all shock tube configurations, including

convergent shock tubes. Generalized approaches for designing proper driver inserts are

included in Appendix A.

2.5 SUMMARY

A method for designing a shock tube free of non-ideal pressure rise behind the reflected

shock wave has been described. The method uses a two-step calculation for estimating

the geometry of the driver insert. The starting point of the method is to empirically

observe the non-ideal pressure rise rate dP5*/dt and the duration of this pressure rise. The

designed area change rate and position in driver’s cross-section is then calculated based

on this measured dP5*/dt.

Experiments show that driver inserts designed using this method effectively eliminate

dP5*/dt for fixed test times. By using the driver insert, highly uniform pressure traces

were obtained for both low temperature T5 = 900 K and high temperature T5 = 1700 K

cases, showing the robustness of the model. Experience with the driver insert also

suggested that the driver insert designed for a particular T5 can be used in a wider range

of temperatures (e.g., within ±100 K of the designed T5) with good pressure uniformity,

although the exact range depends on criteria, facility and test conditions.

25

CHAPTER 3: LASER DIAGNOSTICS

Using the method described in Chapter 2, the standard shock tube (Section 2.2) can be

modified to provide well-defined, near-ideal environments behind reflected shock waves

for conducting combustion kinetics experiments. For investigating transient combustion

reactions initiated by reflected shock waves, diagnostic schemes are desired that are non-

intrusive, offer large detection bandwidth, and have very high signal-to-noise ratio

(SNR). Laser diagnostics based on absorption spectroscopy possess all these desirable

features and are well-suited for combustion kinetics studies.

Two types of lasers were implemented in the current study for measuring time-resolved

OH and H2O concentrations. H2O time-histories were recorded using a DFB (distributed

feedback) tunable diode laser near 2.55 μm, whereas OH time-histories were recorded

using a ring-dye laser near 306 nm. Both lasers were operated at continuous wave (CW)

mode and the wavelengths were fixed at the center of the corresponding absorption

features. More details of each laser, including manufacturer, model, etc., are given below

in this chapter.

3.1 TUNABLE DIODE LASER ABSORPTION OF H2O NEAR 2.55 μm

As briefly discussed in Section 1.2, accurate H2O time-histories in reacting H2/O2

systems can provide critical insight into combustion kinetics, because H2/O2 combustion

chemistry is the core of all hierarchical hydrocarbon combustion mechanisms and H2O is

one of the final products of hydrocarbon combustion. Some preliminary analyses, as

presented in Section 1.2, show the potential of improving the fundamental understanding

of combustion kinetics by developing a sensitive H2O diagnostic.

An H2O laser absorption diagnostic based on diode lasers has been developed previously

for other applications, for example, internal-combustion engines [50][51], scramjets [52],

and combustion control [53]. These earlier applications utilized overtone H2O bands in

near-infrared (near 1.4 μm). However, fundamental H2O bands between 2.5 and 3.0 μm

26

offer nearly an order of magnitude increase in peak line strengths over the overtones, as

illustrated by Figure 3-1.

1.0 1.5 2.0 2.5 3.0

10-4

10-3

10-2

10-1

Wavelength [μm]

2v1

v1+v3

2v3

v1+v2v2+v3

v3v1

Li

nest

reng

th [c

m-2/a

tm]

H2O @ 1500 K

Figure 3-1. Fundamental H2O bands offer nearly an order of magnitude increase in peak line strengths over overtone bands.

Recent advances in laser technology allow some of the strongest absorption lines within

the fundamental H2O bands near 2.5 μm to be accessed by distributed feedback (DFB)

diode lasers. A recent static cell study [54] has demonstrated that, by taking advantage of

the newly available DFB lasers near 2.5 μm, H2O detectivity can be improved by almost

an order of magnitude over previous diagnostic schemes based on near-infrared diode

lasers.

This greatly improved H2O detectivity makes it possible to accurately measure trace

amounts of H2O (> 50 ppm) over a short pathlength, such as in a shock tube experiment.

The objective of this section is to describe the optimization of an H2O laser absorption

diagnostic for combustion kinetic studies behind reflected shock waves.

An H2O absorption feature at 2550.96 nm (3920.09 cm-1) within the v3 fundamental

vibrational band, as indicated by the green arrow in Figure 3-1, was chosen for the

current study, primarily because it has large line strength and is isolated from neighboring

lines. As can be seen in Figure 3-2, the closest water line has a negligibly small line

strength and is separated from the line center by 1.7 cm-1. Absorbance in the plot is

27

defined as the product of absorption coefficient per atmosphere of pressure vβ

[cm-1atm-1], the partial pressure of the absorbing species Pi [atm], and pathlength L [cm]

using Beer’s Law, )ln( ov v v iI I PLβ− = , where o

vI and vI are the incident and transmitted

laser intensities respectively.

3918 3919 3920 3921 39220.00

0.02

0.04

0.06

0.08

Abs

orba

nce

Wavenumber / cm-1

T =1100 KP = 2 atmL = 14.13 cm1000 ppm H2O / Ar

Figure 3-2. Absorbance spectrum of isolated H2O vibrational line at 3920.09 cm-1. A small neighboring line is seen near 3922 cm-1.

The absorption coefficient per atmosphere of pressure ( )v vS Tβ = Φ , where ( )S T is the

temperature-dependent line strength [cm-2atm-1] of the transition at temperature T [K] and

vΦ [cm] is the line-shape function. ( )S T can be expressed in terms of the line strength at

reference temperature 0( )S T as

10 0 0 00

0 0

( ) '' 1 1( ) ( ) exp[ ( )][1 exp( ][1 exp( )]( )

T Q T hcv hcvhcES T S TT Q T k T T kT kT

−− −= − − − −

where h [J·s] is Planck’s constant, c [cm·s-1] is the speed of light, k [J·K-1] is Boltzmann’s

constant, 0v [cm-1] is the line center frequency, ''E [cm-1] is the lower state energy of the

transition and ( )Q T is the partition function of the absorbing molecule. In the above

equation, the factor 0

0

( ) '' 1 1exp[ ( )]( )

Q T hcEQ T k T T

− − accounts for the equilibrium population

fraction of the absorbing molecule in the lower state; 10 0

0

[1 exp( ][1 exp( )]hcv hcvkT kT

−− −− −

28

for the induced emission; and 0TT

accounts for molecular number density as a function of

temperature. The partition function ( )Q T can be obtained from the following

polynomial:

2 3( )Q T a bT cT dT= + + +

where the coefficients of the polynomial a, b, c and d are given in HITRAN [55].

The line-shape function vΦ is approximated using a Voigt profile. The Voigt profile can

be characterized by the a parameter, which is defined as

ln 2 C

D

vavΔ=

Δ

where DvΔ and CvΔ are full width at half maximum (FWHM) due to Doppler and

pressure (collisional) broadening, respectively. CvΔ is often modeled as the product of

the system pressure and the sum of the mole fractions of each perturbing species A

multiplied by its process-dependent collision broadening coefficient 2 B Aγ − (FWHM)

2C A B AA

v P X γ −Δ = ∑

The collisional broadening coefficient γ (HWHM) can be calculated using the following

scaling relation with the temperature-dependent coefficient n:

00( ) ( )( )nTT T

Tγ γ= .

In the present study the parameters for the water feature at 3920.09 cm-1, such as 0( )S T ,

''E , and n, were taken from HITRAN [55], which have been verified previously in a

static cell [56]. In addition, 2 0( )N Tγ was approximated by 0( )air Tγ as provided in

HITRAN [55].

29

However, the collisional-broadening coefficient for argon ( )Ar Tγ is not available in

HITRAN whereas argon is a bath gas widely used in shock tube experiments. Since the

goal of the current work is to study combustion kinetics at high temperatures (T >

1000 K), we chose to determine ( )Ar Tγ behind reflected shock waves. The first step in

calibrating spectroscopic parameters is to prepare a mixture with its composition

precisely known. However, this has proven to be difficult for H2O, because H2O has a

very low vapor pressure at room temperatures and suffers from strong wall adsorption

effects.

Despite all the difficulties of precisely prepare an H2O/Ar mixture, H2O can be relatively

easily generated from H2 oxidation and the composition of an H2/O2/Ar mixture can

accurately controlled. In this study, we used a 2000 ppm H2/1000 O2/Ar mixture to

evaluate ( )Ar Tγ . The mixture was prepared by diluting a 4% H2/2% O2/Ar blend

supplied by Praxair Inc. to the desired concentration, with an estimated uncertainty of

±2% for each component.

The mixture was shock-heated to above 1100 K to initiate the oxidation process. After

ignition, H2O levels are predominately controlled by thermodynamic parameters and a

small set of well-established reactions (e.g. OH + OH → H2O + O [57]), and thus can be

precisely modeled by almost any modern kinetic mechanism, for example the Li et al.

mechanism [4] or GRI-Mech 3.0 [18]. In the current study, we used GRI-Mech 3.0 to

calculate H2O time-histories. By comparing an H2O absorbance time-history measured at

the center wavelength of the absorption feature (2550.96 nm) and the H2O time-history

calculated at the corresponding temperature and pressure, vβ at the center of the

absorption feature (defined earlier in this section) can be evaluated using the Beer’s Law,

since both the pathlength L and the partial pressure of the absorbing species Pi are

known. With line strength ( )S T taken from HITRAN, the argon broadening coefficient

( )Ar Tγ can be determined from the peak absorption cross-section assuming a Voigt line-

shape function vΦ .

30

Presented in Figure 3-3 is an example H2O time-history measured at 1383 K and

2.317 atm. Also shown in the same plot is a H2O profile calculated using GRI-Mech 3.0

in green. vβ at the center of the absorption feature at this temperature was determined to

be 1.50 [cm-1atm-1]. Therefore, Arγ at 1383 K was deduced to be 1.29×10-2 [cm-1atm-1]

using the Voigt function.

0 1 2 3

0

1000

2000

3000 Experimental data Calculated using GRI-Mech 3.0

Wat

er [p

pm]

Time [ms]

Figure 3-3. By comparing an H2O absorbance time-history measured at 1383 K and 2.317 atm to the H2O time-history calculated H2O time-history calculated using GRI-Mech 3.0, vβ at the center of the absorption feature was evaluated to be 1.50 [cm-1atm-1]. By assuming a Voigt line-shape function, Arγ was determined to be 1.29 × 10-2 [cm-1atm-1] at this temperature. Test mixture: 2000 ppm H2/1000 ppm O2/Ar.

By conducting similar tests at various temperatures, the argon broadening coefficient as a

function of temperature can be expressed as ( )Ar Tγ = 0.0277×(296/T)0.50 [cm−1atm−1], as

shown in Figure 3-4. Also presented in Figure 3-4 is the broadening coefficient for air

from HITRAN.

Due to the transient nature of reflected shock experiments and the fact that H2O

concentration varies with time, it is very difficult to get the argon broadening coefficient

by fitting to the complete line-shape function. However, Arγ determined using only vβ

at the center of the absorption feature provides sufficient accuracy for the current study.

This is because only vβ at the center of the absorption feature was used for converting

laser attenuation into H2O time-histories.

31

1000 1200 1400 16000.01

0.02

0.03

0.04γair(T)= 0.0660*(296/T)0.53

γ [c

m-1at

m-1]

Temperature [K]

HITRAN air Measured argon

γAr(T)= 0.0277*(296/T)0.5

Figure 3-4. The argon broadening coefficient experimentally determined in this work can be expressed as ( )Ar Tγ = 0.0277×(296/T)0.50 [cm−1atm−1].

At pressures of main interest in the current study (1 - 2 atm), the a parameter of Voigt

profiles is small, which indicates that Doppler broadening still plays a key role, and vβ at

the center of the absorption feature is not a strong function of the pressure broadening

coefficient. In addition, as will become evident later in this dissertation, the

determinations of reaction rate constant are insensitive to the absolute value of vβ , but

rather controlled by the relative slope of the H2O time-histories.

A schematic of the H2O diagnostic for reflected shock experiments is shown in Figure

3-5. A DFB diode laser near 2.55 μm from Nanoplus GmbH was used. The laser

wavelength and intensity were controlled by a combination of temperature and injection

current using commercial controllers (ILX Lightwave LDT-5910B and LDX-3620). The

laser wavelength was fixed at the center of the water absorption feature. Shortly before

taking data, the laser was scanned over the water line to ensure that it was located at line

center, as small wavelength drifts over time can occur. The typical operating condition

for the laser is 20.8 °C and 90 mA, with intensity noise 0.01% rms.

32

Figure 3-5. A schematic of the H2O diagnostic for reflected shock experiments.

The laser beam was collimated by a plano-convex lens, transmitted through the shock

tube, shielded by a Spectrogon narrow bandpass filter (center wavelength: 2585 ± 10 nm,

half width: 35 ± 5 nm), focused by a short-focal-length plano-convex lens to reduce

beam-steering effects, and detected by a liquid nitrogen-cooled InSb detector (IR

Associates IS-2.0, active area 2 × 2 mm, 1 MHz bandwidth). The diameter of the

collimated laser beam was 2 mm.

All optical measurements in this work were performed 2 cm from the end wall of the

shock tube using sapphire windows. The beam path outside the shock tube was purged

with pure N2 to minimize the laser attenuation due to ambient H2O.

3.2 RING-DYE LASER ABSORPTION OF OH NEAR 307 nm

An OH laser absorption diagnostic can provide critical insight into combustion kinetics,

because of the key role OH-radicals play in combustion chemistry. In the current study,

the OH diagnostic was mainly used in combination with the H2O diagnostic. The reason

for simultaneous measurements of H2O and OH is that each species shows a strong

sensitivity to reaction progress at different times, enabling the research to investigate and

refine both early-time reaction mechanism behavior (OH) and later-time behavior (H2O).

33

The laser beam path for the OH absorption diagnostic was in the same axial plane (but

rotated by 45o) as the H2O diagnostic (2 cm from the shock tube endwall), allowing for

simultaneous measurement of OH and H2O time-histories. A pair of fused-silica

windows was installed on the shock tube sidewalls to allow the transmission of the OH

laser.

OH-radicals can be very sensitively detected using the R1(5) line of the A2Σ+−X2Π (0,0)

band near 306.7 nm. This OH absorption feature, which has been well-characterized and

extensively utilized in chemical kinetics studies in the past [36][58][59], was chosen for

the current study. The absorption coefficient of the OH radical is well-established, and

measured OH concentrations are accurate to better than ±5% [36].

A schematic for the experimental setup that is adapted from Ref. [37] is presented in

Figure 3-6. A 5 W, 532 nm, cw beam produced by a Coherent Verdi laser pumps a

Spectra-Physics 380 ring-dye laser operating with Rhodamine R6G dye was used to

generate visible light at 613.4 nm. UV light (1-2 mW) at 306.7 nm was generated by

intra-cavity frequency doubling using a temperature-tuned AD*A crystal. Since the

wavelength and mode quality of the UV output is directly related to its fundamental light

at 613.4 nm, a part of the visible light was taken from the cavity for monitoring purposes.

Wavelength was determined using a Burleigh WA-1000 wavemeter and mode quality of

the visible light was examined by a scanning interferometer.

A part of the UV beam was split off as the reference beam; the remaining part was

transmitted through the shock tube for OH absorption. Both the reference and the

transmitted beams were monitored by Thorlabs PDA 36A detectors modified with large

area Hamamatsu S1722-02 photo diodes (with an effective active area of 13.2 mm2).

Both detectors were shielded by two identical spectral filters (Newport FSR-UG11,

center wavelength: 340 nm, half width: 70 nm) to reduce broadband interference. Further

details of the OH ring-dye laser absorption diagnostic may be found in Herbon et al.

[36][37].

34

Figure 3-6. Layout of the OH laser absorption diagnostic adapted from Ref. [37]. Labeled optics are: (f) Newport FSR-UG11 narrow bandpass filter; (l) lens; (i) iris; (NDf) neutral-density filter; (b) 27% beamsplitter.

Data

Acquisition

Powermeter

532nm pump laser

Tunable Dye Laser

Scanning interferometer

Si detector

Wavemeter

SHOCK TUBE

VIS 613.4nmUV 306.7nml f i b NDf

35

CHAPTER 4: RATE CONSTANT OF REACTION H + O2 OH + O

The chain branching reaction between atomic hydrogen and molecular oxygen H + O2

OH + O (Rxn. 1) is regarded as one of the most important elementary reactions in

combustion. Under typical combustion conditions, this reaction limits the rate at which

hydrogen is oxidized, which in turn controls the formation rate of the oxidation product

(H2O). Therefore, by carefully designing experiments, the rate constant of the reaction H

+ O2 OH + O may be precisely determined simply by studying H2O time-histories

during hydrogen oxidation. This chapter describes the measurement of this rate constant.

4.1 PREVIOUS WORK

H + O2 OH + O reaction has been the subject of many experimental studies and

reviews [60]-[70]. In 1973, Schott [61] inferred the rate coefficient of this reaction (k1)

from chemiluminescence measurements of O-CO recombination in shock-heated

H2/CO/O2/Ar mixtures at temperatures of 1250 to 2500 K. For many years Schott’s

approach appeared to be the most direct and his results were heavily weighted in the

subsequent review by Warnatz [71].

In the decade following publication of the early reviews, [71][72] more quantitative and

direct diagnostics methods were adopted to investigate k1. Atomic resonance absorption

spectroscopy (ARAS) was used to monitor the time-histories of atomic hydrogen

[20][63][65] or atomic oxygen concentrations [62][63] and other groups [19][66]-

[70][73] applied CW ring-dye laser absorption spectroscopy techniques to measure OH

radical time-history profiles and derived the rate coefficient of this reaction. Results from

previous studies are summarized in Figure 4-1.

At temperatures above 1500 K, k1 was mainly determined from OH time-histories in

shock-heated H2/O2/Ar mixtures. Despite similarities in the experiments, discrepancies

among the early studies [19][63][64][69] are as high as a factor of two at 2000 K.

Subsequent studies helped to resolve these discrepancies. Yu et al. [69] reanalyzed the

36

OH data from a previous study by Yuan et al. [66] and recovered results that supported

the measurements of Masten et al. [19]. Yang et al. [68] suspected that there were air

leaks in the shock tube in the previous k1 study from the same laboratory [64] and

reinvestigated the rate with another shock tube. Their new results again coincided with

the rate expression given Masten et al. [19]. Du and Hessler [67] extended the

measurements of k1 to temperatures as high as 5300 K and again confirmed the results by

Masten et al. [19]. The more recent study by Ryu et al. [70] and by Hwang et al. [73]

obtained almost identical k1 values of the previous researchers [19][67]-[69] over the

range 1500 to 2500 K using laser absorption spectroscopy of OH radical.

0.4 0.6 0.8 1.0

1011

1012

1013 1000 K1250 K1667 K

Hwang et al. (2005)

k 1 [cm

3 /mol

/sec

]

1000/T [1/K]

Frank & Just (1985)

Pirraglia et al. (1989)

Fujii & Shin (1988)

Pamidimukkala et al. (1981)

Schott (1973)Masten et al. (1990)

Shin & Michael (1991)

Ryu et al. (1995)

2500 K

Figure 4-1. Previous experimental results for the rate constant of the reaction H + O2 OH + O (k1).

At lower temperatures (T < 1500 K), however, disagreement still exists among the

reported values [20][62][65][70][73]. At 1100 K, k1 from Pamidimukkala et al. [62] is

approximately 65% of the rate constants recommended by other researchers [65][70].

The determinations of k1 at temperatures lower than 1500 K relied heavily on the ARAS

method [20][62][65], and these measurements typically resulted in relatively large scatter

(16% and 27% as reported in Refs. [20] and [65], respectively). In contrast,

measurements using OH laser absorption [70][73] yield much smaller scatter in the

inferred k1 values (e.g., 6% as reported in Ref. [70]). However, at lower temperatures, it

37

is difficult to accurately determine k1 from OH profiles due to complications discussed

later in the chapter. As pointed out by Hwang et al. [73], a factor of 1.3 discrepancy

exists between the two methods [20][70] at 1050 K. An alternative approach of

examining k1 with smaller scatter and better accuracy is desired at temperatures below

1500 K.

4.2 EXPERIMENTAL DETAILS

Both the test facility (the modified shock tube) and the diagnostic (H2O diagnostic) have

been discussed in Chapters 2 and 3 and are omitted in this section.

Test gas mixtures were prepared manometrically (with two MKS Baratron capacitance

manometers) in a stainless steel mixing tank equipped with a magnetic stirrer and

turbomolecular pump. Research-grade gases (99.999%) supplied by Praxair were used.

The Baratron has a precision better than 0.01 Torr for pressures under 100 Torr and 0.1

Torr for greater pressures. Using a double dilution procedure, two test gas mixtures were

prepared: 0.1% O2, 0.9% H2, balance Ar for tests at higher temperature (1250 – 1500 K),

and 0.1% O2, 2.9% H2, balance Ar for tests at lower temperatures (1100 – 1250 K). The

relative uncertainty in the test mixture compositions is less than 1% (i.e. 0.1% ± 0.001%

O2).

4.3 RESULTS

Typical reflected shock wave pressure and laser transmission profiles are shown in Figure

4-2. The data sets in the upper panel (Figure 4-2a) were obtained in a 0.1% O2/0.9%

H2/Ar mixture at initial conditions of 1472 K and 1.83 atm, close to the high-temperature

limit of the current data. The temporal profiles presented in the lower panel (Figure 4-2b)

were acquired using a 0.1% O2/2.9% H2/Ar mixture at 1100 K and 1.95 atm, which is

close to the low-temperature limit of the current study. The use of the larger H2

concentration at low temperatures reduced the ignition delay times but does not affect k1

determinations.

38

Figure 4-2 illustrates features common to all experiments in this study. After an initial

period when chain carrier radials (H, O, and OH) were being accumulated, light

absorption increased rapidly due to the formation of H2O until a chemical partial

equilibrium is achieved. Extremely uniform pressure profiles were obtained with the

driver inserts. Over the entire course of H2 oxidation, at 1100 K (Figure 4-2b)

approximately 7 ms, the pressure fluctuation was less than ±1.5%, and the estimated

long-time temperature variation is less than ± 0.6%, or ± 6.7 K. The initial temperature

was determined from the measured incident shock speed and the associated uncertainty

was estimated to be ± 7.7 K. The combined uncertainty in temperature for this low

temperature example is ± 10.2 K. For T = 1472 K (Figure 4-2a), the combined

temperature uncertainty is smaller (± 9.4 K), since the test time needed is shorter for

higher-temperature ignition.

0.90

0.95

1.00

0.85

0.90

0.95

1.00

0 2 4 6 8 100

1

2

3

Time [ms]

Pressure

Transmission

0 1 2 3 4 5 6 70

1

2

3

(b)

Pressure

Transmission

Pre

ssur

e [a

tm]

(a)

Tra

nsm

issi

on [I

/I o]

Figure 4-2. Typical pressure and laser transmission histories in reflected-shock experiments: (a. upper) 0.1% O2, 0.9% H2, 99% Ar, 1472 K, 1.83 atm; (b. lower) 0.1% O2, 2.9% H2, 97% Ar, 1100 K, 1.95 atm.

The mixtures were selected with the aid of computer simulations using a detailed

chemical kinetic mechanism and the Senkin [74] kinetics code, with the aim of

maximizing the sensitivity of the H2O growth to k1. An updated version of GRI-Mech

3.0 [18] was chosen to perform analyses in the current study. The updates to GRI-Mech

3.0 include the latest data for the OH heat of formation [36][75], the HO2 heat of

39

formation [76], the rate coefficients for the reactions OH + HO2 H2O + O2 [77] and

OH + H2O2 H2O + HO2 [78], and the rate constants of H2O2 thermal decomposition

[78][79]. The choice of the base mechanism for analyzing the experiment data only has

minor effects on the determination of k1, as will become evident in later analyses and

discussions.

Figure 4-3a shows the H2O sensitivity analysis for the conditions of Figure 4-2a. The

sensitivity coefficient α is the partial derivative of a species mole fraction with respect to

the rate constant parameter A of a reaction, normalized by the maximum species mole

fraction and the rate constant parameter A

)/)/(d/d()( maxiijjij AAXXt =α

where Xj is the mole fraction of species j and Ai is the pre-exponential factor of the

Arrhenius expression for the rate constant of reaction i, ( ) exp( / )nk T AT E RT= − . The

analysis indicates that formation of H2O is predominately controlled by the title reaction

of H + O2 OH + O. Only very small sensitivities are shown to the reactions OH + H2

H + H2O and O + H2 H + OH.

H2O concentration time-histories were calculated from the attenuated laser beam

transmissions (I/Io) using Beer’s law. Shown in Figure 4-4 are the H2O time histories

derived from the experimental observations in Figure 4-2. The plateau H2O level does

not depend on the reaction kinetics but is determined by a chemical partial equilibrium.

Typical discrepancies between the experimental observations and the numerical

simulations were less than 1%. The slight mismatch may be explained by error in initial

mixture composition, uncertainty in temperature, slight drift in laser center wavelength,

or wall condensation.

40

0 2 4 6 8

0

5

10

0.0 0.5 1.0 1.5

0

2

4

6

H+O2<=>O+OH H+O2(+M)<=>HO2(+M) H+HO2<=>2OH H+HO2<=>O2+H2

H

2O S

ensi

tivity

Coe

ffici

ent

Time [ms]

(b)

H+O2<=>O+OH O+H2<=>H+OH OH+H2<=>H+H2O

(a)

Figure 4-3. H2O sensitivity plot at conditions of the corresponding panels of Figure 4-2.

Also shown on Figure 4-4 are the best-fit H2O temporal profiles calculated using GRI-

Mech 3.0 and the Senkin kinetics code by varying k1 to match the maximum slope. Two

H2O profiles calculated using 110% and 90% of the best-fit k1 are presented for each test.

The fitting uncertainty of k1 is estimated to be ± 2%. More sample H2O time-histories are

shown in Appendix B.

To obtain the best-fit in Figure 4-4a, 0.35 ppm of H atom was artificially included in the

mixture used for the numerical simulation to match the onset of the rapid H2O formation.

The addition of H atom simulates the effects of residual contaminants in the shock tube

or the mixing tank. It should be noted, however, that the maximum slope of the H2O

profile, which is selected as the criteria for determining k1 in this study, is not affected by

the inclusion of this H atom addition, since the maximum slope is “determined at a point

in reaction progress where memory of the initial process is lost” [70]. Numerical

calculations confirmed this assumption. The levels of H atoms artificially included for

Senkin calculations were found to decrease almost exponentially as the test temperature

drops. The H atom concentration needed to match the onset of the H2O profile in Figure

4-4b (1100 K) was only 0.0012 ppm.

41

2 3 4 5 6 70

500

1000

1500

2000

25000.0 0.2 0.4 0.6 0.8 1.00

500

1000

1500

2000

2500

Wat

er C

once

ntra

tion

[ppm

]

Time [ms]

Best fit k1

Best fit k1 x 1.1 Best fit k1 x 0.9 Experiment

(b)

Best fit k1

Best fit k1 x 1.1 Best fit k1 x 0.9 Experiment

(a)

Figure 4-4. Comparison of experimental and calculated H2O profiles using best-fit k1 with effect of ± 10% variation on k1 at conditions of the corresponding panels of Figure 4-2.

Here, all H2O profiles have been rescaled so that the plateau H2O concentrations match

with the calculated equilibrium levels. Small rescaling does not affect the determination

of k1. Since very dilute mixtures (0.1% O2) were used in the study, the temperature rise

due to exothermicity of the reaction was typically less than 15 K. For instance, the

temperature rise was approximately 9 K when the H2O plateau was reached for T =

1472 K (Figure 4-2a). The change in H2O absorption cross-section due to a 9 K

temperature rise is approximately 1.3% at this temperature. The difference between H2O

time-histories calculated using constant and temperature-dependent H2O absorption

cross-sections is negligible, as evident in Figure 4-5. Therefore, H2O absorption cross-

sections were treated as constants within each measurement. The aforementioned fitting

uncertainty includes the effects of rescaling and the simplified treatment of the constant

H2O absorption cross-sections.

H2O sensitivity analyses in Figure 4-3 provide rough estimates of the relative significance

of the interfering reactions to the target reaction H + O2 OH + O. To quantitatively

evaluate the uncertainty of k1 introduced by all error sources, sensitivity analyses of the

selected criteria, i.e., the maximum slope of H2O profile, were conducted. Each error

source was disturbed by its estimated uncertainty, and k1 subsequently adjusted to regain

42

the best-fit to experimental data. The percentage change of k1 is the uncertainty

associated with that error term. The maximum slope sensitivities for the conditions of

Figure 4-2 are demonstrated in Figure 4-6, with the estimated uncertainty associated with

each error source shown in parentheses.

0.0 0.2 0.4 0.6 0.8 1.00

500

1000

1500

2000

2500H

2O C

once

ntra

tion

[ppm

]

Time[ms]

T-dependent absorption cross-section Constant absoprtion cross-section

Figure 4-5. Comparison of H2O time-histories calculated using constant and temperature-dependent H2O absorption cross-sections at conditions of Figure 4-2a.

The estimated uncertainties of the rate coefficients for the interfering reactions are taken

from the latest review by Baulch et al. [80]. In 2009, a study [81] found that recent H2/O2

mechanisms use substantially different values for the rate constant of one of the

interfering reactions, O + H2 H + OH, at the temperature of their interest (1045 K). At

temperatures where the reaction O + H2 H + OH becomes a significant interfering

reaction in the current work (e.g., 1472 K, Figure 4-6a), the discrepancy among the rate

constant expressions for this reaction is not significant and can be well-contained in the

uncertainty bar assigned by Baulch et al. [80]. For instance, the percentage difference

between two alternative expressions [80][82] is only 6% at 1472 K.

Figure 4-6a indicates that at high temperature (1472 K), the approach taken by the

present study successfully constrains the uncertainties introduced by interfering reactions.

The determination of the reflected shock temperature was found to be the single largest

source of uncertainty, at ±3.4%, highlighting the importance of improving the

temperature uniformity in the shock tube using the driver insert technique discussed in

43

Section 2.4. The combined root-sum-square (RSS) of the estimated uncertainties of all

sources for k1 is approximately ±4.6%.

-0.25 0.00 0.25 0.50 0.75 1.00 1.25

Maximum Slope Sensitivity

0.3% 2.0% 3.4% 0.3% 0.2% 1.7% 1.5% 1

Uncertainty in Mixture (0.3% )

Fitting Uncertainty (2.0% )

Temperature Uncertainty (9.4 K )

H+HO2<=>2OH (40% )

H+O2+M<=>HO2+M (50% )

O+H2<=>H+OH (60% )

OH+H2<=>H+H2O (60% )

H+O2<=>O+OH

(a) Combined uncertainty: 4.6%

-0.25 0.00 0.25 0.50 0.75 1.00 1.25

0.6% 2.0% 6.2% 0.6% 0.3% 0.1%-5.5% 2.1% 0.0% 1

Uncertainty in Mixture (0.6% )

Fitting Uncertainty (2.0% )

Temperature Uncertainty (10.2K )

H+HO2<=>O+H2O (200% )

O+H2<=>H+OH (60% )OH+H2<=>H+H2O (60% )H+HO2<=>O2+H2 (100% )H+HO2<=>2OH (40% )

H+O2+M<=>HO2+M (50% )

H+O2<=>O+OH

(b) Combined uncertainty: 8.8%

Figure 4-6. Sensitivity analyses for the maximum slope of the H2O profiles at the conditions of the corresponding panels of Figure 4-2.

The maximum slope sensitivity analysis of the low temperature experiment (Figure 4-6b)

indicates that the combined uncertainty of the inferred k1 is 8.8%. The uncertainty in

temperature is again the largest source of error. In addition, at the lower temperatures,

some errors are now introduced by interfering reactions, in particular HO2 reactions. For

example, the estimated factor of two uncertainty [80] of the rate constant of reaction H +

HO2 O2 + H2 (k13) results in a k1 uncertainty of 5.5%. The uncertainty associated with

k13 is discussed in Section 4.4. Although H2O formation shows pronounced sensitivity to

reaction H + O2 + M HO2 + M (k2) at low temperature (Figure 4-3b), the determination

of k1 is immune to the uncertainty in k2 by taking the “maximum slope” approach. The

quoted k2 uncertainty in Figure 4-6b is taken from Baulch et al. review [80] and takes into

44

account fall-off and third body effects. The selection of k2 only changes the onset of H2O

formation, which is a similar effect to that of adding small quantities of H-atoms.

The experimental k1 values are summarized both in Table 1 and Figure 4-7. A least-

squares fit to the current data over the temperature range 1100 K to 1527 K gives k1 =

(1.12 ± 0.08) × 1014 exp(-7805 ± 90 K/T) [cm3mol-1s-1]. Presented on the same figure are

two sets of experimental data reported by previous researchers [19][20]. Excellent

agreement is found between the present study and the study by Masten et al. [19] at the

overlapping temperatures. In addition, the current data from this study fall completely

within the data reported by Pirraglia et al. [20], but with much smaller scatter and a

slightly different activation energy.

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

1011

1012

1013

1429 K2x1013 3333 K

k 1 [cm

3 mol

-1se

c-1]

1000/T [1/K]

Pirraglia et al. (1989) Masten et al. (1990) This study O Conaire et al. (2004) Konnov (2008) Best-fit (this study+Masten et al.)

2000 K 1111 K

4x1010

Figure 4-7. Arrhenius plot of experimentally determined k1 from this study and from studies by Pirraglia et al. [20] and by Masten et al. [19]. k1 values used in two recent kinetic mechanisms [5][6] are also shown.

Also shown in Figure 4-7 are k1 expressions used in two recent H2 combustion

mechanisms [5][6]. The rate coefficient k1 used by Ó Conaire et al. mechanism [5] has a

slightly larger activation energy, because the expression was based on the Pirraglia et al.

[20] work. Konnov [6] adopted Baulch et al.’s recommendation for k1 [80], which agrees

very well with the experimental data at high temperatures [19] but shows increasing

discrepancy with our data at low temperatures. Other recent combustion mechanisms,

such as the Li et al. H2 mechanism [4], the Saxena and Williams H2/CO mechanism [9],

45

and GRI-Mech [18]/JetSurF [83], have similar k1 values to our least-square fit over the

entire temperature range between 1100 and 3370 K.

Table 1. Test conditions and results for the H + O2 OH + O rate constant (k1).

P [atm]

T [K] Test mixture k1

[cm3mole-1s-1] Artificially added H-atom to simulate impurity [ppm]

1.97 1091 2.9%H2/0.1% O2/Ar 8.40E+10 0.0015

1.95 1100 2.9%H2/0.1% O2/Ar 9.30E+10 0.0011

1.94 1112 2.9%H2/0.1% O2/Ar 9.40E+10 0.0027

1.93 1126 2.9%H2/0.1% O2/Ar 1.11E+11 0.0012

1.86 1132 2.9%H2/0.1% O2/Ar 1.17E+11 0.0013

1.88 1166 2.9%H2/0.1% O2/Ar 1.41E+11 0.00165

1.84 1197 2.9%H2/0.1% O2/Ar 1.71E+11 0.0022

2.06 1230 2.9%H2/0.1% O2/Ar 1.97E+11 0.0042

2.01 1256 2.9%H2/0.1% O2/Ar 2.29E+11 0.0045

2.03 1267 0.9% H2/0.1% O2/Ar 2.39E+11 0.03

1.59 1277 0.9% H2/0.1% O2/Ar 2.51E+11 0.039

2.00 1285 0.9% H2/0.1% O2/Ar 2.49E+11 0.043

1.99 1310 0.9% H2/0.1% O2/Ar 3.07E+11 0.031

1.91 1317 0.9% H2/0.1% O2/Ar 2.92E+11 0.055

1.76 1352 0.9% H2/0.1% O2/Ar 3.54E+11 0.068

1.93 1376 0.9% H2/0.1% O2/Ar 3.83E+11 0.135

1.89 1410 0.9% H2/0.1% O2/Ar 4.47E+11 0.155

1.85 1448 0.9% H2/0.1% O2/Ar 5.15E+11 0.23

1.83 1472 0.9% H2/0.1% O2/Ar 5.55E+11 0.35

2.67 1527 0.9% H2/0.1% O2/Ar 6.40E+11 0.4

Combining the Masten et al. data with the results from the present study, we obtain an

expression k1 = (1.04 ± 0.03) × 1014 exp(-7705 ± 40 K/T) [cm3mol-1s-1] that is suitable

over the temperature range from 1100 to 3370 K, as presented in Figure 4-7. A plot of

46

the percent residual differences between the Arrhenius fit and experimental data from

Masten et al. [19] and the current study is presented in Figure 4-8. The standard

deviation of all the experimental data is less than 5%. In the same plot, the percent

differences between this fit and the expressions used in some representative H2/O2

mechanisms [4]-[6][18] are also presented.

0.3 0.4 0.5 0.6 0.7 0.8 0.9-30

-20

-10

0

10

20

30 1111 K1429 K2000 K

Masten et al. (1990) Hong et al. (2010)

Res

idua

l Diff

eren

ce (%

)

1000 K/T

Li et al. (2004) O Conaire et al. (2004) Konnov (2008) GRI-Mech 3.0

3333 K

Figure 4-8. Percent residual difference between the Arrhenius fit and experimental data from Masten et al. [19] and the current study.

4.4 DISCUSSION

4.4.1 Sensitivity of k1 to k13

Near the low temperature end of the present study (T = 1100K), the determination of k1

shows a stronger sensitivity to the rate constant of H + HO2 O2 + H2 (k13). This rate

constant, in fact, introduces the second largest uncertainty in k1 (next to the temperature

uncertainty). This is partly a result of the limited knowledge of k13; we have used a factor

of two for the uncertainty in the rate constant as assigned in the review by Baulch et al.

[80]. Discrepancies of the same order exist among the values of k13 used in several

combustion mechanisms [4]-[6][18][83]. Once a better understanding of k13 becomes

available, the accuracy of k1 could be improved further.

47

Figure 4-9 shows the correlation between k1 and k13 at T = 1100 K, which is obtained by

varying k13 in GRI-Mech 3.0 [18] and subsequently adjusting k1 to regain the best-fit to

the experimental observation. The slope of the line dk1/dk13 = 0.055 suggests that the

best fit k1 would increase by 5.5% if k13 was doubled. The GRI-Mech 3.0 [18] uses k13 =

2.75 × 1013 [cm3mol-1s-1] at T = 1100 K, while other mechanisms use k13 values ranging

from 1.14 × 1013 [cm3mol-1s-1] [4][5][9] to 4.11 × 1013 [cm3mol-1s-1] [6] at the same

temperature.

0 1 2 3 4 5 66

7

8

9

10

11

12k 1 [

x 10

10 c

m3 m

ol-1s-1

]

k13 [x1013 cm3mol-1s-1]

Figure 4-9. k1-k13 pairs that best-fit the experimental H2O profile at the conditions of Figure 4-2b. The assigned error bar is the combined uncertainty from all error sources except k13.

At higher temperatures the sensitivity of our k1 determination to k13 decreases rapidly. At

temperatures above 1350 K, dk1/dk13 is less 1% and can be safely neglected. The analysis

also revealed that two different initial H2 concentrations used in this study do not have an

impact on the behavior of dk1/dk13.

4.4.2 Re-evaluation of the Masten et al. determination of k1

The Masten et al. (and other high temperature studies [19][66]-[70]) determination of k1

relied on OH laser absorption experiments. However, ∆fHo298(OH) was recently revised

from 9.40 kcal/mol to 8.91 kcal/mol [36][75], and this change may affect the original k1

determination.

48

Masten et al. [19] saw modest differences between the measured and calculated OH

plateau values and attributed these to several factors including uncertainty in OH

absorption cross-section, and uncertainty in the mixture composition. To avoid these

differences they treated the OH profiles as self-calibrating, and always rescaled the

experimentally observed OH plateaus to the calculated levels.

Representative data at 1980 and 2898 K from Masten et al. [19] were reanalyzed using

the revised OH heat of formation. Although the calculated OH plateau level is different

from the experimental data, it can be rescaled as was done by Masten et al. For the

1980 K data, the rescaled OH profile matches well with their experimental data (Figure

4-10), suggesting that the inferred k1 was not affected by the update in ∆fHo298(OH). At

2898 K, a similar analysis shows that k1 only needs to be increased by 1%, well within

the uncertainty of the measurement. Therefore, k1 values from Masten et al. [19] can be

retained.

50 100 150 200 2500

100

200

300

Experimental data Masten et al. (1990)

Calculation

OH

Con

cent

ratio

n [p

pm]

Time [μs]

Figure 4-10. OH profile calculated with k1 suggested by Masten et al. [19] and the updated OH enthalpy of formation can be rescaled to perfectly match their experimental OH time-history. Conditions: T = 1980 K, P = 0.675 atm, test mixture 5.0% H2/0.493% O2/Ar.

4.4.3 Previous studies of k1 at temperatures below 1500 K

Table 2 summarizes the low-temperature recommendations for k1 from selected previous

studies along with the result from the present study. Two major approaches were taken in

the efforts to determine k1 at temperature below 1500 K: 1) the H-ARAS approach by

49

Pirraglia et al. [20] and by Shin and Michael [65]; and 2) the OH laser absorption

approach by Ryu et al. [70] and by Hwang et al. [73]. Discrepancies exist among these

studies.

Table 2. Low-temperature reaction rate coefficient k1 in the form k1 = ATnexp(−Θ/T).

A [cm3mole-1s-1K-n]

n Θ [K]

T range [K]

Reference

1.2 × 1014 8101 1000-2500 Pamidimukkala et al. [62] (1.68 ± 0.19) × 1014 8119 ± 139 960-1710 Pirraglia et al. [20] (6.93 ± 0.96) × 1013 6917 ± 193 1103-2055 Shin & Michael [65] 1.59 × 1017 -0.927 8493 1050-2700 Yuan et al. [66] (7.13 ± 0.31) × 1013 7065 ± 140 1050-2500 Ryu et al. [70] 6.73 × 1015 -0.50 8390 950-3100 Hwang et al. [73] (1.12 ± 0.08) × 1014 7805 ± 90 1100-1527 This study (1.04 ± 0.03) × 1014 7705 ± 40 1100-3370 This study + Masten et al. [19]

In the analysis of the low concentration ARAS studies, the reaction H + O2 + M HO2 +

M (k2), which can be responsible for H atom decay, was neglected in both H-ARAS

studies. Recent study has greatly improved the understanding of this competing reaction

[84]. k1 values inferred from H-ARAS studies can be reevaluated to account for the error

of neglecting k2. The error associated with neglecting k2 was estimated to be

approximately 7% at one representative test condition reported by Pirraglia et al. (T =

1098 K, P = 0.25 atm, 1.85% O2/0.074% NH3/Ar), which helps to account for the

difference between the present study and Pirraglia et al. at 1100 K.

However, the difference between Pirraglia et al. and this study is 21% at T = 1500 K,

where the influence of k2 becomes insignificant and can be safely neglected. In addition,

we noticed that the discrepancy between both H-ARAS studies [20][65] is significant

(about 20% at 1100 K). This substantial discrepancy, as well as the large scatter seen in

the H-ARAS studies, may be attributed to photolytes used to generate H radicals.

Pirraglia et al. found that k1 values using an H2O photolyte were consistently larger (by

60%) than the results using NH3 as the photolyte. They also observed unusually low

initial H atom concentrations and large errors associated with the H2O photolyte [20], and

therefore excluded the H2O photolyte data in the final expression of k1. Shin and Michael

50

[65] also observed that the H2O photolyte resulted in higher k1 values over the entire

experimental temperature range by 20%. However, they decided to include the H2O-

photolyte data in their final expression since the possible systematic difference (20%)

was smaller than the experimental scatter (27%).

Ryu et al. [70] extended the measurements of k1 to temperatures as low as 1050 K using

OH laser absorption. Test mixtures of high concentration (4% H2/1% O2/Ar) had to be

employed to compensate for the low OH yield at low temperatures. Calculation with the

GRI-Mech 3.0 [18] shows that the temperature rise is approximately 180 K when the OH

peak concentration is reached, or 370 K when oxidation is completed with the

concentration stated in the reference. Other factors, such as the temperature dependence

of the OH absorption coefficient, and more pronounced impacts from interfering

reactions, may contribute to the difference between the H-ARAS [20] and the OH [70]

approaches. To reconcile the discrepancy, Hwang et al. [73] used the OH diagnostic to

reinvestigate the reaction. Although mixtures with high H2 and O2 concentrations were

used in their study to evaluate k1 at low temperatures, temperature profiles were

continuously updated using experimentally recorded pressure profiles during the course

of reaction, and the corrected OH time-histories were fitted using comprehensive

computer simulations. The low-temperature (T < 1500 K) results of Hwang et al. [73]

support the previous H-ARAS study [20] and are in excellent agreement with the current

study (within 6% at 1100 K).

4.4.4 Rate constant of the reverse reaction k-1

The rate constant of the reverse reaction

O + OH H + O2 (Rxn. -1)

has received much theoretical study, since the O + OH reaction occurs on an potential-

energy surface that is almost barrierless, and therefore k-1 has only a weak temperature

dependence. The measured k1 values in the present study can be transformed to k-1 via

the correlation K1 = k1/k-1, where K1 is the equilibrium constant from thermodynamic

calculations. Using the data from the JANAF tables [85] with the updates for OH

51

[36][75], K1 can be expressed as K1 = 14.50 exp(-7956 K/T) over the temperature range

from 1000 K to 1500 K.

Combining with the k1 expression given previously in Section 4.3 over the similar

temperature region, k-1 can be expressed as: k-1 = 7.71 × 1012 exp(152 K/T)

[cm3mole-1s-1], as plotted in Figure 4-11. The slightly negative temperature dependence

has been confirmed by the experiments of Howard and Smith [86] and of Lewis and

Waston [87]. These measurements do not contradict the rationale that no energy barrier

for the reverse reaction as these can be explained by the re-dissociation of HO2* back to

O + OH [88] (see Figure 4-11). In the same figure, several other theoretical calculations

[89]-[91] are also shown. The measurements of this study show the best agreement with

the predictions by Varadas et al. [90], within 15% over the entire temperature range from

1000 to 1500 K.

0 500 1000 15000

1x1013

2x1013

3x1013

4x1013

k -1 [c

m3 m

ol-1s-1

]

T [K]

Calculations: Troe (1988) Lin et al. (2008) Germann & Miller (1997) Varandas et al. (1992)

Measurements: Howard & Smith (1981) Lewis & Waston (1980) This study

Figure 4-11. Rate coefficient of the reverse reaction O + OH H + O2 (k-1) determined from the forward rate coefficient k1 and the equilibrium constant K1.

Miller et al. [92] proposed a rate expression for k1 (1.98 × 1014 (T/1000 K)-0.591

exp(-8152 K/T) [cm3mol-1s-1]) by combining the equilibrium constant of the reaction and

the reverse rate constant from theoretical studies. Their expression utilizes an activation

energy identical to 00HΔ of the reaction. Using the same approach and best-fitting our

current data and those of Masten et al. [19], we obtained a 3-parameter expression k1 =

1.58 × 1014 (T/1000 K)-0.262 exp(-8152 K/T) [cm3mol-1s-1] over the temperature range

from 1100 to 3370 K. The standard deviation for ln(k1) of this 3-parameter fit is 0.04,

52

which is identical to that of the 2-parameter expression proposed in Section 4.3, and

therefore can be used as an alternative for combustion modeling.

4.5 SUMMARY

Very dilute fuel-rich H2/O2 mixtures were shock-heated to temperatures between 1100 K

and 1532 K to study the rate coefficient of the branching reaction H + O2 OH + O (k1).

Using tunable diode laser absorption of H2O near 2.5 μm, H2O time-histories were

recorded. The rate coefficients of the reaction were determined by varying k1 in GRI-

Mech 3.0 to generate H2O profiles that best-fit the experimental observations. The

results are well-fit by k1 = (1.12 ± 0.08) × 1014 exp(-7805 ± 90 K/T)[cm3mol-1s-1], with

estimated uncertainties of 4.6% at 1500 K and 8.8% at 1100 K.

The determinations of k1 from previous OH laser absorption studies were reevaluated

using the updated OH enthalpy of formation and the results in the literature were found to

be unaffected. Excellent agreement between this study and that of Masten et al. [19] was

found at the overlapping temperatures. By combining the results of the two studies, we

recommend the expression k1 = (1.04 ± 0.03) × 1014 exp(-7705 ± 40 K/T) [cm3mol-1s-1]

over the temperature range from 1100 to 3370 K. At temperatures below 1500 K, good

agreement was found between the present study and that by Pirraglia et al. [20]. In

addition, excellent agreement (within 6% over 1100 – 1500 K) was found between the

present study and the recent OH measurements by Hwang et al. [73].

53

CHAPTER 5: HYDROGEN PEROXIDE THERMAL DECOMPOSITION

Hydrocarbon ignition at intermediate temperatures (850 – 1200 K) is controlled by

hydrogen peroxide (H2O2) and hydroperoxyl radical (HO2) reactions. For instance, the

thermal decomposition of hydrogen peroxide (H2O2)

H2O2 + M OH + OH + M (Rxn. 3)

has been identified as the dominant chain-branching reaction that controls hydrocarbon

ignition in the intermediate temperature regime (850 K – 1200 K). In fact, to quote

Westbrook [21], the decomposition of hydrogen peroxide is “the central kinetic feature in

engine knock in spark ignition engines, in ignition in liquid-fueled diesel engines, and in

the operation of homogeneous charge, compression ignition (HCCI) engines.” A

significant amount of H2O2 is accumulated at lower temperatures in the reactive mixture

before ignition, followed by the rapid decomposition of H2O2 during ignition at

temperatures near 1050-1100 K that produces two highly reactive hydroxyl (OH)

radicals.

This chapter discusses the experimental investigation of the rate constant of H2O2 thermal

decomposition (k3) using the experimental setup described in Chapters 2 and 3 (the

modified shock tube and the H2O diagnostic).

5.1 PREVIOUS WORK

The decomposition reaction of H2O2 (Rxn. 3) has been studied in the temperature range

between 700 and 900 K in static cells and flow systems by several research groups [93]-

[97]. However, in the temperature range between 850 and 1200 K where intermediate

temperature hydrocarbon ignition occurs, only a few shock tube studies [22]-[24] have

been carried out, and these were all performed in the same laboratory by Troe and co-

workers. In their investigations, the thermal decomposition of H2O2 was measured

behind reflected shock waves using UV absorption spectroscopy at 215 nm and 290 nm.

54

These deep UV measurements are influenced by both strongly varying absorption cross-

sections and interfering species. At 215 nm, HO2 absorbs much more strongly than H2O2

[98][99], and therefore the HO2 concentration and HO2 reactions, as well as the

decomposition of H2O2, have to be accounted for to fully interpret the absorbance at

215 nm. At 290 nm HO2 absorption is negligible, but the poor detection sensitivity of

H2O2 limits measurement accuracy. The authors of those papers recognized the inherent

difficulties in their measurements and have recommended independent studies by other

groups.

Attempts have also been made to measure the reverse recombination reaction (Rxn. –3)

[100]-[103]. A common approach to study the recombination reaction is to record OH

decay after the initial photolysis of OH precursors. However, the recombination reaction

(Rxn. –3) on the singlet H2O2 potential energy surface competes with the reaction

(Rxn. 8) on the triplet surface.

OH + OH + M H2O2 + M (Rxn. −3)

OH + OH H2O + O (Rxn. 8)

The recombination reaction (Rxn. –3) is pressure dependent while reaction (Rxn. 8) is

not. Theoretically, the rates for reactions (Rxn. –3) and (Rxn. 8) can be distinguished by

varying pressure. However, distinguishing the two reaction rates is difficult and a factor

of three discrepancy exists in the literature for room temperature measurements of both of

these reactions [100][101]. The interpretation of OH decay profiles in the recombination

experiments is further complicated by reactions between OH and interfering species from

OH precursors, for example, NO [103].

5.2 H2O2 SOURCE AND MIXTURE PREPARATION

High-temperature gas-phase measurements of the hydroperoxy reaction system are

complicated by the highly reactive nature of high-purity H2O2 and the lack of a simple

H2O2 precursor. Commercially available water/H2O2 solutions are difficult to use

because the vapor pressure of water is significantly higher than that of H2O2 [104].

55

Almost all previous researchers used high-concentration H2O2 solutions (99%) purified

by re-distillation. Concentrated H2O2 is highly volatile and corrosive, and hence a

different method to produce H2O2 is desired.

An alternative precursor for H2O2 is available commercially. The urea-hydrogen

peroxide adduct (carbamide peroxide, formula: (NH2)2CO·H2O2) is sold as a solid, is easy

to handle and releases relatively pure hydrogen peroxide gas upon gentle heating

(typically to 45 °C). Successful use of this material as a gas-phase H2O2 source was

demonstrated recently by Ludwig et al. [29][30].

Urea-hydrogen peroxide adduct (powder, 15−17% active oxygen basis) was provided by

Sigma−Aldrich. Approximately 10 gram of urea-hydrogen peroxide powder was mixed

with roughly an equivalent amount of sand (SiO2, Sigma−Aldrich) in a polycarbonate

flask. The flask was sealed with a platinum-cured silicone stopper and placed in a water

bath maintained at 45 °C. The purpose of mixing with sand is to prevent urea-hydrogen

peroxide powder from agglomerating upon heating. Research grade argon or nitrogen

(99.999%) was passed through the flask at a flow rate of 0.4−0.5 SLPM (standard liters

per minute) to get a typical H2O2 concentration of about 800 ppm. A stable supply of

H2O2 at this rate can be generated for approximately 3−4 hours. The H2O2/carrier gas

mixture was then directed into the driven section of the shock tube from a filling port

near the endwall. A schematic is shown in Figure 5-1.

Figure 5-1. A schematic of the experimental setup for generating H2O2/bath gas mixtures.

To reduce H2O2 decomposition on surfaces, the tube and valves downstream of the flask

were chosen to have surfaces of either stainless steel (grade 316) or Teflon. H2O2

decomposes at accelerated rates when hydrocarbons are also present even in trace

56

amounts, therefore it was important to remove the residual impurities in the shock tube

by passing H2O2/carrier gas flow through the length of the driven section of the tube for

approximately 20−30 minutes before taking data.

Despite all of the precautions being taken, H2O2 decomposition was still observed in the

shock tube with a time constant of the order of 15 minutes. Previous work [30] has

shown that less than 10% of initially generated H2O2 decomposes in the flask at 45 °C.

Furthermore, the rate of homogeneous thermal decomposition of H2O2 is known to be

small. This suggests that the observed H2O2 decomposition predominantly takes place on

the shock tube wall surfaces. To reduce the decomposition of H2O2, it is thus important

to minimize the contact time between H2O2 vapor and shock tube walls. However, to

achieve the desired T5 and P5, the corresponding preshock pressure P1 was as high as 160

Torr. Given the relatively large volume of the driven section (134 L), a regular filling

procedure at a flow rate of 0.4−0.5 SLPM required up to an hour. As a result, an

alternative filling strategy was developed to significantly reduce the waiting time: first,

the entire shock tube was filled with the H2O2/bath gas mixture to about 10-14 Torr (3−4

minutes); next, the shock tube was brought to the target P1 with pure bath gas using a

filling port near the diaphragm location, thereby compressing the initial H2O2 mixture

into a smaller volume in the test section adjacent to the endwall. We refer to this

procedure as staged filling. As the measurement location (2 cm from endwall) is

separated by at least one meter from the approximate contact region between the initially-

filled test mixture and the pure argon, we have not observed any irregularities or lack of

reproducibility in our data with this filling procedure.

Initial H2O2 loadings were determined by taking the difference between the initial and

final H2O concentrations. O2 was also present in the initial mixtures as the other

decomposition product of H2O2. The initial O2 concentrations were assumed to be half of

the initial H2O concentrations. Numerical simulations using GRI-Mech 3.0 [18] suggest

that the presence of H2O and O2 in the test gas mixture only affects average collider

efficiency. Although the third-body efficiency of H2O is perhaps ten times larger than

that of N2, 500 ppm of H2O (and 250 ppm O2) introduces less than 1% uncertainty in the

determination of the H2O2 decomposition rate in an argon diluent.

57

5.3 RESULTS AND DISCUSSION

5.3.1 Determination of H2O2 dissociation rate constant k3

In the present study, the dissociation rate constant k3 is defined as the second-order rate of

reaction (Rxn. 3). Time-histories of water absorbance at the line center were converted

into water concentrations using spectroscopy data discussed in Section 3.1. Figure 5-2

shows an example water concentration profile recorded at 1057 K, 1.83 atm, in an argon

bath gas. Water concentrations at time zero and in the plateau region at late times are

663 ppm and 1523 ppm, respectively, corresponding to a water yield of 860 ppm.

Considering the overall reaction of H2O2 decomposition can be described by

2 2 2 2H O = H O + 1 2 O

the initial H2O2 loading is inferred to be 860 ppm.

0 2 4 6400

800

1200

1600

[H2O

] / p

pm

Time [ms]

Experimental Best fit (k3=1.65 x 107 [cm3mol-1s-1]) Best fit +/- 20%

Figure 5-2. The dissociation rate of H2O2 is fitted to be 1.65 × 107 [cm3mol-1s-1] with an estimated fitting error of ±10%. Test condition: 860 ppm H2O2/663 ppm H2O/332 ppm O2/Ar, 1.83 atm, 1057 K.

Using a detailed chemical kinetics mechanism, GRI-Mech 3.0 [18], water sensitivity

coefficients were calculated with the Senkin [74] kinetics code package. The definition

of sensitivity coefficient is discussed in Section 4.3. Figure 5-3 is the water sensitivity

plot for conditions of Figure 5-2, showing that H2O formation is predominantly

controlled by k3. No other reactions show sensitivity at a noticeable level using GRI-

Mech 3.0. Therefore, k3 can be determined simply by changing this rate in the

58

mechanism to best fit experimental water time-histories. The best-fit dissociation rate for

the example case is 1.65 × 107 [cm3mol-1s-1] with an estimated fitting error of less than

±10% (Figure 5-2).

In addition to the fitting uncertainty, uncertainty in temperature is the other major source

of error. As discussed in Section 2.2, the initial temperature T5 immediately behind the

reflected shock wave is determined from the measured incident shock speed and the

uncertainty is estimated to be ± 8 K. The long-time temperature variation is evaluated to

be less than ± 0.8%, or ± 8 K. The combined uncertainty in temperature is estimated to

be ± 11 K, resulting in an associated uncertainty in the measured reaction rate of ± 21%.

The decomposition rate of H2O2 is inferred essentially from the relative slope of H2O

formation profile. Therefore uncertainty in the H2O absorption cross-section does not

significantly affect the accuracy of this measurement. Combining the uncertainties in

fitting and temperature, we estimate the overall uncertainty in k3 to be ± 23%.

0 3 6 9

0.0

0.1

0.2

0.3

H2O

Sen

sitiv

ity C

oeffi

cien

t

Time [ms]

H2O2+M<=>2OH+M OH+H2O2<=>HO2+H2O OH+HO2<=>O2+H2O

Figure 5-3. The formation of H2O is predominantly controlled by the dissociation rate of H2O2. Conditions are those of Figure 5-2.

5.3.2 Low-pressure limit and fall-off behavior in argon bath gas

Experimentally measured k3 data in argon bath gas at 0.9, 1.7 and 3.2 atm are provided in

Table 3. Best fits of experimental determinations of k3 at various pressures yield the

following expressions:

59

16.12 0.09 3 -1 -13

15.92 0.13 3 -1 -13

15.75 0.15 3 -1 -13

(M Ar, 0.9 atm) 10 exp( -21650 230 K ) [cm mol s ]



k T

k T

k T

±

±

±

= = ±

= = ±

= = ±

The results also are summarized in an Arrhenius plot; see Figure 5-4. Good agreement is

seen between this study and that of Kappel et al. [24].

The reduced experimental scatter in the present study, relative to past studies, enables an

evaluation of the pressure dependence of k3. Comparison of the measurements at 0.9 and

1.7 atm does not show deviation from second-order behavior, suggesting that the

dissociation reaction of H2O2 is close to its low-pressure limit at pressures below 1.7 atm.

A best fit to all the data obtained at 0.9 and 1.7 atm yields the low-pressure limit in argon

to be k3,0 = 1015.97±0.10 exp(−21220 ± 250 K/T) [cm3mol-1s-1] over the temperature range

1000 to 1200 K.

0.8 0.9 1.0

107

108

109

1111K

Current Study k3(0.9 atm) k3(1.7 atm) k3(3.2 atm)

k3(1 atm), Kappel et al. (2002) k3(4 atm), Kappel et al. (2002) k3, 0, Sellevag et al. (2009)

k 3 [c

m3 /m

ol/s

]

1000/T [1/K]

1250K 1000K

Bath gas: argon

Figure 5-4. The decomposition rates of H2O2 (k3) in argon bath gas were measured at various pressures and are compared to previous studies.

Recently, Sellevåg et al. [105] calculated the high-pressure limit rate of H2O2

decomposition using variable reaction coordinate transition-state theory, classical

trajectory simulations, and a two-transition-state model. They also analyzed the

experimental data by Kappel et al. [24] to obtain the energy transfer parameter ΔEd with

argon as the bath gas. Using a two-dimensional master equation (2D-ME), the

60

low-pressure limit of the reaction was calculated. Their result is compared to the

experimental data in Figure 5-4. The limiting low-pressure rate recommended by

Sellevåg et al. over the temperature range of 1000 to 1200 K can be approximated by a

two-parameter Arrhenius formula k3,0 = 1016.01 exp(−21230 K/T) [cm3mol-1s-1], in

excellent agreement with the experimental measurements of the present work. At

3.2 atm, a small reduction (approximately 10%) in k3 from the proposed low-pressure

limit rate k3,0 was observed. However, the experimental uncertainty of 23% prevents a

more definite conclusion on pressure fall-off to be drawn. Experiments conducted at

much higher pressures are needed to evaluate the fall-off curve since there are no existing

direct measurements of the H2O2 dissociation rate near the high-pressure limit.

Sellevåg et al. [105] also calculated the fall-off curves for the decomposition of H2O2 in

argon near its low-pressure limit, as plotted in Figure 5-5. Although Sellevåg et al.

extracted ΔEd from the study by Kappel et al. [24], they found that “the experimental data

seem to systematically fall-off faster from the low-pressure limit than can be explained

by (their) 2D-ME calculations.” Using the best fits to experimental results at 0.9, 1.7,

and 3.2 atm from this study, the fall-off behavior at various temperatures can be

estimated at corresponding pressures. The comparison between the experimental data

and the theoretical curves shows excellent agreement, confirming the observed second-

order reaction behavior.

The fall-off curves in argon have also been estimated by Kappel et al. [24] based on their

measurements made at 1, 4, and 15 atm. The authors acknowledged the uncertainties

inherent in their fall-off curves, predominantly due to the lack of data near the high-

pressure limit and to their experimental scatter. Their fall-off curves suggest that the

departure from the low-pressure limit occurs at much lower pressures. The extrapolated

k3,∞ from the Kappel et al. fall-off curves fall about a factor of 10 below the recent

theoretical predictions by Troe and Ushakov [106]. That theoretical calculation of k3,∞

[106] is supported by the only existing set of high-pressure (150 bar) recombination

measurements [102]; the agreement is within a factor of two. The high-pressure rates

were obtained in hydroxyl recombination experiments conducted at room temperature.

Although the dissociation rates k3 inferred from recombination experiments are less

61

accurate due to the competition from the interference reaction (Rxn. 8), they confirm our

observation that there is only small departure from the low pressure limit at 3.2 atm.

10-5 10-4 10-3 10-2100

101

102

103

104

1051250 K

1150 K

1050 K

Falloff curve, Sellevag et al. (2009) Falloff curve, Kappel et al. (2002) Experiment, this study Experiment, Kappel et al. (2002)

k 3 x [A

r] [s

-1]

[Ar] / mol cm-3

950 K

Figure 5-5. Fall-off behavior of H2O2 decomposition in argon bath gas.

The measured H2O2 decomposition rates are also compared with the predictions of two

detailed kinetic mechanisms in Figure 5-6. The decomposition rate of H2O2 used in the

Ó Conaire et al. mechanism [5] is based on Baulch et al.’s review of k3 [60] and the

theoretical study by Brouwer et al. [108]. In GRI-Mech 3.0 [18], the rate is given in the

reverse direction (k−3), based on the Baulch et al. review of k−3 [80] and a hydroxyl

recombination experiment by Zellner et al. [101]. From k−3, the corresponding k1 can be

inferred from the relationship through the equilibrium constant K3 = k3/k−3 using a heat of

formation of H2O2 of ∆fHo298(H2O2) = −32.49 ± 0.04 kcal/mol [109]. ∆fHo

298(OH) has

been updated from 9.40 kcal/mol to 8.91 kcal/mol by Herbon et al. [36] and Ruscic et al.

[75]. K3 can be expressed as K3 = 106.44 exp(−24685 K/T) [cm-3mol] in the temperature

range of 1000 – 1200 K. The comparisons suggest that the rate expressions used in both

kinetics mechanisms (GRI-Mech 3.0 [18] and Ó Conaire et al. [5]) are larger than the

current results and would therefore overpredict the rate of H2O2 thermal decomposition,

while the recent calculations by Sellevåg et al. [105] show much better agreement (Figure

5-5).

62

Table 3. Test conditions and results of H2O2 decomposition experiments in argon bath gas. The H2O2 and H2O concentrations are initial values.

T K

P atm

[H2O] ppm

[H2O2] ppm

k3 cm3mol-1s-1

1077 1.776 560 850 2.50E+07 1020 1.698 498 512 9.50E+06 1085 1.845 346 280 2.90E+07 1067 1.813 363 261 2.30E+07 1100 1.757 561 748 4.15E+07 1120 1.738 410 874 5.50E+07 1124 1.717 434 796 6.40E+07 1139 1.708 438 505 8.00E+07 1157 1.705 453 613 1.05E+08 1167 1.676 390 551 1.20E+08 1169 1.626 394 436 1.30E+08 1065 1.811 522 900 1.90E+07 1190 1.663 432 753 1.80E+08 1204 1.64 315 367 2.10E+08 1029 1.667 1530 480 1.10E+07 1057 1.831 663 860 1.60E+07 1047 1.857 639 838 1.50E+07 1009 1.776 447 853 8.20E+06 1054 1.663 473 851 1.70E+07 1132 1.721 373 605 6.80E+07 1095 1.78 303 574 3.27E+07 1170 1.656 403 775 1.20E+08

1100 3.133 471 710 3.50E+07 1115 3.089 435 772 4.50E+07 1129 2.997 440 717 5.70E+07 1154 2.964 454 769 8.30E+07 1182 2.935 411 713 1.43E+08 1075 3.186 670 860 2.30E+07 1057 3.262 658 745 1.70E+07 1036 3.309 400 773 1.05E+07 1016 3.352 437 1058 8.00E+06

1101 0.901 372 625 4.10E+07 1123 0.877 356 840 5.70E+07 1163 0.867 191 744 1.05E+08 1183 0.856 370 1422 1.49E+08 1216 0.85 440 1459 2.50E+08 1081 0.934 500 1160 2.60E+07 1065 0.974 372 1116 1.89E+07 1030 0.977 431 932 1.00E+07 1038 0.98 424 1094 1.16E+07

63

0.8 0.9 1.0

107

108

109

1111K

k3(0.9 atm), this study k3(1.7 atm), this study k3(3.2 atm), this study

k3(1.7 atm), GRI-Mech [ΔfHo(OH) updated]

k3(1.7 atm), O'Conaire et al. (2004)

Bath gas: argon

k 3 [cm

3 mol

-1s-1

]

1000 K / T

1250K 1000K

Figure 5-6. The comparison between the rate expressions used in two detailed chemical kinetics mechanisms and the experimental data of this study (long dashed line, GRI-Mech with ΔfHo(OH) updated; short dotted line, Ó Conaire et al.; solid line, the limiting low-pressure rate fitted to the experimental data at 0.9 and 1.7 atm of this study).

5.3.3 Collider efficiencies

For most practical combustion studies, nitrogen is the most significant collision partner.

The difference in collider efficiency between argon and nitrogen was therefore examined.

Similar H2O2 decomposition experiments were conducted in nitrogen bath gas at

pressures near 1.7 atm.

Accurate determinations of the temperatures in shock tube experiments with nitrogen are

more complicated, however, owing to vibrational relaxation processes. Nitrogen

molecules undergo vibrational relaxation [110] behind shock waves to re-establish the

equilibrium between vibrational and translational/rotational modes. The process can be

characterized by two limiting temperatures: 1) frozen temperature: the temperature of

translational/rotational modes before any vibrational relaxation has taken place, and 2)

equilibrium temperature: the temperature when the molecule is fully vibrationally

relaxed. To decide which temperature most accurately describes the chemical kinetics

processes, the characteristic times of vibrational relaxation τV-T were compared to the

corresponding characteristic times of H2O2 decomposition τdecomp.

64

The characteristic times of vibrational relaxation τV-T for the test mixtures in the present

study can be estimated using the relation

2 2 2 2

2 2 2 2 2 2 2

N H O H O

V T N -N N -H O N -H O

1τ τ τ τ−

Φ Φ Φ= + +

as suggested by Millikan and White [110], where XΦ is the mole fraction of the collision

partner X and 2N -Xτ is the characteristic time of vibrational relaxation of N2 by X.

2 2N -Nτ

and 2 2ON -Hτ can be evaluated at corresponding test conditions using the correlations given

in the references [110][111]. However, no data were found for 22 2N -H Oτ and it was

approximated by 2 2ON -Hτ due to the similarities in molecular structure and composition.

The estimated τV-T values, along with the corresponding τdecomp, are listed in Table 4.

Table 4. Test conditions and results of H2O2 decomposition experiments in nitrogen bath gas. The H2O2 and H2O concentrations are initial values.

Tfrozen K

Tequilbrium K

P atm

[H2O] ppm

[H2O2]ppm

τV-T milliseconds

τdecomp milliseconds τV-T / τdecomp

k3 cm3mol-1s-1

1147 1089 1.485 531 1474 0.626 0.306 2.05 1.29E+08 1185 1122 1.448 416 1800 0.567 0.177 3.20 2.33E+08 1230 1154 1.413 390 1675 0.600 0.101 5.94 4.49E+08

However, the two characteristic times are comparable except for tests conducted near the

high-temperature extreme of the present study, where the decomposition of H2O2 is

significantly faster than the vibrational relaxation of N2 (τV-T/τdecomp > 2). Therefore, the

temperatures at which these tests were evaluated are best approximated by the

vibrationally frozen temperature and are shown in the Arrhenius plot in Figure 5-7. The

collider efficiency of argon relative to nitrogen was found to 0.67. Previous low

temperature (< 850 K) flow reactor experiments [93] reported a relative efficiency of 0.67

for argon bath gas, in excellent agreement with the findings of this study.

65

0.80 0.85 0.90 0.95 1.00

107

108

109 1111 K1250 K

This study, Ar bath This study, N2 bath

GRI-Mech [ΔfHo(OH) updated], Ar bath

GRI-Mech [ΔfHo(OH) updated], N2 bath

k 3 [c

m3 m

ol-1s-1

]1000 K / T

Pressure: 1.7 atm1000 K

Figure 5-7. The decomposition rates of H2O2 (k3) in nitrogen bath gas are compared to the results obtained in argon at the same pressure. Solid lines are the best fits. Dotted lines are calculated using kinetics mechanisms.

5.4 SUMMARY

The decomposition rate of H2O2 was studied behind reflected shock waves over the

temperature range between 1000 and 1200 K using laser absorption spectroscopy of

water at 2550.96 nm. The decomposition rates of H2O2 were determined by fitting the

measured water profiles, and were not significantly influenced by competing reactions.

Agreement with previous studies by Troe and co-workers is very good. No pressure

dependence of the decomposition rate constant was resolved between 0.9 and 1.7 atm in

argon. At 3.2 atm, an approximate 10% deviation from these lower pressure

measurements was observed. The low-pressure reaction rate constant was inferred from

these measurements and found to be k3,0 = 1015.97±0.10 exp(−21220 ± 250 K/T)

[cm3mol-1s-1] (1000-1200 K). The collider efficiency of argon relative to nitrogen was

experimentally determined to be 0.67, in excellent agreement with low temperature

experiments conducted in a flow reactor [93].

67

CHAPTER 6: RATE CONSTANT OF REACTION OH + H2O2 H2O + HO2

Hydrogen peroxide kinetics play an important role in the larger problem of peroxy-

radical (RO2) chemistry important in the intermediate temperature oxidation of

hydrocarbons. The H2O2 thermal decomposition system provides a unique opportunity to

isolate and study H2O2 and HO2 reactions at combustion temperatures. In addition to the

H2O2 thermal decomposition reaction studied in the last chapter (Rxn. 3), another

important reaction involving H2O2 and HO2 that can be studied is OH + H2O2 H2O +

HO2 (Rxn. 4).

In addition, a reliable, clean HO2 precursor is desirable to study HO2 reactions with alkyl

radicals. The H2O2 decomposition system is a possible way to fulfill this need, since HO2

is produced by a simple two-step process:

H2O2 + M OH + OH + M (Rxn. 3)

OH + H2O2 H2O + HO2 (Rxn. 4)

The goal of this chapter is to measure the rate constant of Rxn. 4 (k4) by adding the OH

diagnostic (Section 3.2) to H2O2 thermal decomposition experiments for k3

determinations described in Chapter 5.

6.1 PREVIOUS WORK

Reaction OH + H2O2 H2O + HO2 (Rxn. 4) has received considerable attention near

room temperature [112]-[122] because OH and HO2 catalyze the destruction of ozone

(O3), and H2O2 is an important reservoir for both radicals. The low temperature

experimental data for the rate constant of the reaction OH + H2O2 H2O + HO2 (k4)

show good consistency, ranging from 9.3 × 1011 to 1.20 × 1012 [cm3mol-1s-1] at 298 K.

However, some researchers reported a small positive temperature dependence of the rate

constant [112]-[116][118] while others found a negative temperature dependence

[117][119] over their measured temperature ranges, as shown in Figure 6-1. Atkinson et

68

al. [122] reviewed the available low temperature data and proposed an evaluated rate

expression of k4 = 1.75 × 1012 exp(−160 K / T) [cm3mol-1s-1] with a value of 1.02 × 1012

[cm3mol-1s-1] at room temperature.

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

1012

1013

1014

5x1011

k 4 [cm

3 mol

-1s-1

]

1000 K/T

Wine et al. (1981) Sridharan et al. (1980) Kurylo et al. (1982) Keyser (1980) Hippler et al. (1995) Hippler et al. (1992)

250 K400 K1000 K5x1014

Figure 6-1. Previous studies of the rate constant of the reaction OH + H2O2 → H2O + HO2 (+ - Wine et al. [112]; ■ - Sridharan et al. [118]; Δ - Kurylo et al. [114]; ▼ - Keyser; ■ - Hippler et al. [26]; ● – Hippler et al. [25]).

As opposed to the extensive studies at low temperatures, only very few studies of Rxn. 4

were conducted at combustion temperatures [24]-[26] and these were all performed in the

same laboratory. The limited availability of experimental data for k4 is due to

experimental difficulties and the unstable nature of H2O2 at high temperatures and the

lack of sensitive diagnostics for H2O2. One of the earlier studies [25] essentially inferred

the ratio of the rates for the two reactions, OH + H2O2 H2O + HO2 and OH + HO2

H2O + O2. The expression for k4 from the most recent Hippler et al. study [26] is widely

used in chemical kinetics mechanisms for combustion [4]-[6][18] and accepted in the

latest evaluation by Baulch et al. [80]. An unusual up-turn in the reaction rate at

temperatures higher than 800 K was reported by Hippler et al. [26], as can be seen in

Figure 6-1.

69

6.2 ANALYSES

6.2.1 Overview of approach

Four reactions dominate the thermal decomposition of H2O2. The two reactions

mentioned at the beginning of the chapter (Rxn. 3 and Rxn. 4) yield OH and HO2

radicals, while two others consume the radicals:

OH + HO2 H2O + O2 (Rxn. 5)

HO2 + HO2 H2O2 + O2 (Rxn. 6)

OH radicals are primarily formed by Rxn. 3 and removed by Rxn. 4 and Rxn. 5.

Therefore, the time evolution of OH can be described by:

3 2 2 4 2 2 5 2[OH] 2 [H O ][M] [OH][H O ] [OH][HO ]d k k kdt

= − − (Eqn. 1)

Initially OH builds up following the decomposition of H2O2, and is gradually depleted

due to Rxn. 4 and Rxn. 5. When OH concentration peaks, the above equation can be

rewritten as:

24 3 5

peak 2 2

[HO ][M]2[OH] [H O ]

k k k= − (Eqn. 2)

Considering that Rxn. 4 is the major HO2 formation channel, only a small amount of HO2

is present when the OH concentration is at its peak. Therefore, the second term on the

right can be dropped, and to first order, the rate constant of the title reaction can be

related to k3 and [OH]peak by:

4 3peak

[M]2[OH]

k k≈ (Eqn. 3)

70

6.2.2 Analysis using detailed kinetics mechanism

Data analysis and simulations were performed using an updated version of the chemical

kinetics mechanism, GRI-Mech 3.0 [18]. The mechanism has been updated to

incorporate the latest data for the OH heat of formation [36][75], the HO2 heat of

formation [76], the rate constant for the reaction OH + HO2 H2O + O2 (k5 = 4.28 ×

1013 (T/300 K)−0.21 exp(113 K/T) [cm3mol−1s−1]) [77], and the thermal decomposition rate

of H2O2 [79]. Using this mechanism a sensitivity analysis (see Section 5.3 for the

definition) for OH was performed with the Senkin [74] kinetics code package. The

results of the sensitivity analysis coincide with our expectation that two reactions control

the time evolution of OH: H2O2 + M 2 OH + M, which shows predominantly positive

sensitivity, and OH + H2O2 H2O + HO2, which shows predominantly negative

sensitivity. Sensitivity analysis plots are presented later in this chapter.

As will become evident from these sensitivity analyses, the kinetics that control OH and

H2O formation in the H2O2 thermal decomposition system can be well-described by a

small set of reactions, which consists of two major reactions (Rxn. 3 and Rxn 4) and three

minor reactions (Rxn. 5, Rxn. 6, Rxn. 8). Rxns. 3 – 6 have been mentioned earlier in the

chapter, and Rxn. 8 is:

OH + OH H2O + O (Rxn. 8)

The limited number of reaction rate constants that do show a significant effect on the

modeling of the experimental measurements are called active parameters [123][124]. Of

the five identified active parameters, the rate constants of Rxns. 3, 4, and 8 will be

determined experimentally in the current study. The coefficient for Rxn. 5 is updated

from our recent study [77], and the rate constant expression for Rxn. 6 is that used in

almost all other recent mechanisms [4]-[6] and is based on the Kappel et al. study [24].

Because of the limited number of important reaction rate constants, the results of this

study are nearly immune to the choice of the base kinetic mechanism. With this

expectation, we tested two representative mechanisms, the modified GRI-Mech 3.0 as

previously described and the Li et al. mechanism [4]. If identical k3 and k4 expressions

are used, the two mechanisms predict effectively indistinguishable H2O time-histories

71

and near-identical OH time-histories. The small difference in the predicted OH

concentrations stems from the different rate expressions used for k8, as GRI-Mech 3.0

uses Wooldridge et al. data [57] and the Li et al. mechanism [4] uses results from the

work by Sutherland et al. [125]. However, this small difference does not affect our

determination of k3 and k4, as will become evident in Section 6.3. In this study, we use

the modified GRI-Mech 3.0 as the base kinetics mechanism.

6.2.3 Test mixture non-uniformity considerations

It is possible that the stratified filling procedure used may introduce some small axial

non-uniformity in the test mixtures, but this should not significantly affect incident shock

speed. As mentioned above, we have used the in-situ H2O diagnostic described in

Section 3.1 to accurately determine the mixture composition at the test location. Because

extremely dilute test mixtures were used in this study, small axial variations in mixture

composition will have very small influence on the incident shock speed and reflected

shock temperatures. Comparisons between the 4000 ppm H2O2/H2O mixtures used in

this study and pure Ar shock wave experiments indicate that at most, a maximum of only

6 K difference may be expected in reflected shock temperatures.

It may be possible that radial H2O2 concentration gradients could exist if H2O2 undergoes

significant surface decomposition on the sidewall of the shock tube. However, while

some reaction of H2O2 may occur at the shock tube wall, such effects are limited by the

slow H2O2 diffusion rate to the wall. A rearrangement of Eqn. 2 in Section 6.2 shows

that the measured [OH]peak is not a strong function of H2O2 concentration, and thus the k4

rate coefficient determination is also not a strong function of H2O2 concentration or its

(possible) varying radial distribution. In fact, simulations using variable amounts of

H2O2 have indicated that the entire OH profile is not a strong function of the initial H2O2

concentration.

72

6.3 RESULTS AND DISCUSSIONS

6.3.1 Lower temperature (1000 < T < 1200 K) example case

It has been demonstrated in the previous chapter that in the temperature range from 1000

to 1200 K, H2O formation during the decomposition of H2O2 is predominantly controlled

by k3. No other reaction shows significant sensitivity at temperatures ranging from 1000

to 1200 K.

From the analyses in Section 6.2, it is natural to select the OH diagnostic for the

determination of k4. We chose to also implement the simultaneous H2O diagnostic for

two reasons: 1) with initial H2O2 concentrations accurately measured using the H2O

diagnostic, comprehensive kinetics analyses can be performed for OH time-histories; 2)

with real-time k3 determinations using the H2O diagnostic, the temperature uncertainty in

k3 does not propagate to k4.

Considering that the overall reaction of H2O2 decomposition is described by

H2O2 H2O + ½ O2

and noting the mole-for-mole conversion between H2O2 and H2O, initial H2O2 loadings

can be inferred from H2O concentration profiles by taking the difference between the

initial and final H2O concentrations, as described in Section 5.3.

Figure 6-2 shows an example H2O time-history obtained at 1192 K, 1.95 atm, in an argon

bath gas. H2O concentrations at time zero and in the plateau region at later times are

1364 ppm and 3580 ppm, respectively, corresponding to an initial H2O2 loading of 2216

ppm. Using GRI-Mech 3.0 [18] with the modifications described in Section 6.2, water

sensitivity coefficients were calculated with the Senkin [74] kinetics code package.

Figure 6-3 is the H2O sensitivity plot for conditions of Figure 6-2, with the sensitivity

coefficient defined in Section 4.3.

73

0.0 0.2 0.4 0.6 0.8 1.00

1000

2000

3000

4000

Experimental Best-fit

H2O

[ppm

]Time [ms]

Figure 6-2. The dissociation rate of H2O2 (k3) is fitted to be 1.8 × 108 [cm3mol-1s-1] with an estimated fitting error of ±10%. Initial test mixture: 2216 ppm H2O2/1364 ppm H2O/682 ppm O2/Ar; initial reflected shock conditions: 1.95 atm, 1192 K.

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.1

0.2

0.3

H2O

Sen

sitiv

ity C

oeffi

cien

t

Time [ms]


Figure 6-3. The formation of H2O is predominantly controlled by the dissociation rate of H2O2. Conditions are those of Figure 6-2.

The rate constant of the reaction H2O2 + M 2 OH + M (k3) was determined by

changing k3 in the chemical kinetics mechanism to best-fit the experimental H2O time-

histories, as described in Section 5.3. The value of k3 for the example case is

1.8 × 108 [cm3mol-1s-1] with an estimated fitting error of ±10% (see Section 5.3). The

relatively high activation energy of the reaction H2O2 + M 2 OH + M (42 kcal/mol)

renders the rate k3 very temperature sensitive. The uncertainty in k3 associated with the

temperature uncertainty was estimated to be 21% (see Section 5.3). However, when the

chemical kinetics mechanism was updated with the experimental k3 values for the

purpose of determining k4, the temperature uncertainty in k3 does not propagate to k4

74

since both k3 and k4 were evaluated simultaneously and were at exactly the same

temperature. Only a 10% fitting uncertainty in k3 propagates to k4.

With the initial H2O2 concentration and k3 determined from the H2O diagnostic, the rate

of the reaction OH + H2O2 H2O + HO2 (k4) can be derived from the OH time-history,

as OH yield is predominantly controlled by the competition between k3 and k4. Figure

6-4 shows the OH concentration time-history from the same test as Figure 6-2 and Figure

6-3. The corresponding OH sensitivity plot is presented in Figure 6-5. The OH

sensitivity coefficients were calculated using GRI-Mech 3.0 [18] with k3 and k4 values

updated to the experimentally determined values.

0.0 0.2 0.4 0.6 0.8 1.00

20

40

60

80 Experimental Best fit k4

Best fit k4 +/- 20%

[OH

] / p

pm

Time [ms]

Figure 6-4. The rate of the reaction OH + H2O2 H2O + HO2 (k4) is fitted to be 5.1 × 1012 [cm3mol-1s-1] with an estimated fitting error of ±3%. Special attention was paid to match the peak in OH concentration. Conditions are those of Figure 6-2.

By changing k4 in the chemical kinetics mechanism, the calculated OH profile matches

measurement in the peak OH concentration, as shown in Figure 6-4. The associated

fitting uncertainty is estimated to be ±3%. The other two reactions that the OH yield

shows sensitivity to at early times are OH + HO2 H2O + O2 (k5) and HO2 + HO2

H2O2 + O2 (k6). HO2 concentration is still low when OH concentration peaks. Therefore,

the calculated [OH] maximum is not significantly affected by the choice of a k5 value.

Figure 6-6 illustrates that even a factor of two uncertainty in k3 results in only a ±3%

uncertainty in the inferred k4, and this is a much larger uncertainty in k3 than assigned

75

(±27%) in our recent study [32]. The rate of the reaction HO2 + HO2 H2O2 + O2 does

not affect the peak OH concentration, as can be seen in Figure 6-6.

0.0 0.2 0.4 0.6 0.8 1.0-1.0

-0.5

0.0

0.5

1.0 H2O2+M<=>2OH+M OH+H2O2<=>HO2+H2O OH+HO2<=>O2+H2O 2OH<=>O+H2O 2HO2<=>O2+H2O2

OH

Sen

sitiv

ity C

oeffi

cien

t

Time [ms]

Figure 6-5. OH yield is predominantly controlled by the competition between the OH formation reaction H2O2 + M 2 OH + M (k3) and the OH removal reaction OH + H2O2

H2O + HO2 (k4). Conditions are those of Figure 6-2.

0.0 0.2 0.4 0.6 0.8 1.00

20

40

60

80

0.00 0.01 0.02 0.0350

55

60

65

70

[OH

] / p

pm

Time [ms]

Experimental Best fit Factor 2 uncertainty k6

Factor 2 uncertainty k5

[OH

] / p

pm

Time [ms]

Figure 6-6. [OH]peak is controlled by k3 and k4. Other reactions show very minor or no impact on [OH]peak. Conditions are those of Figure 6-2.

Uncertainties in k4 come from various error sources, noticeably uncertainties in k3, OH

concentration, temperature, secondary reactions, and fitting procedures. As discussed

previously, the uncertainty in k3 that propagates to k4 is estimated to be ±10%.

Secondary reactions and fitting procedures introduce uncertainties of ±3% and ±5%,

respectively. The OH line strength has an estimated maximum uncertainty of ±5% [36].

76

At the same time, a 0.02 cm-1 uncertainty in UV light wavelength introduces additional

±1.5% uncertainty. The combined temperature uncertainty was evaluated to be 11K [79]

and the associated uncertainty in k4 is estimated to be ±2%. Therefore, the overall

uncertainty of the example case at 1192 K can be estimated to be ±13%.

OH time-histories were calculated assuming test mixtures were at constant pressure and

enthalpy (constant P-H) behind reflected shock waves in the current study, as opposed to

a usually assumed constant volume and internal energy (constant U-V). Shown in Figure

6-7 is a comparison of OH profiles calculated assuming constant P-H and constant U-V

reactors with the identical k3 and k4 values. The k3 value was determined from the H2O

time-history (Figure 6-2), where the two reactor models result in almost identical H2O

profiles. The k4 value was inferred from the OH peak concentration (Figure 6-4), where

the two models agree very well, as can been seen from the comparison in Figure 6-7.

However, the two models start to diverge after the early-time OH spike. The constant U-

V reactor model predicts a hump behavior, which was not observed in the experiment.

No discussion on this issue was found in the work by Hippler et al. [26] as their

experimental data were only compared to model calculations at early times before this

discrepancy could appear.

We initially attempted to resolve the discrepancy from a chemical kinetics perspective.

The rates of the other two reactions that also show OH sensitivities, OH + HO2 H2O +

O2 (k3) and HO2 + HO2 H2O2 + O2 (k4), were both adjusted by a factor of two while

retaining the constant P-H assumption (Figure 6-6). None of those adjusted OH profiles

show a similar hump behavior, suggesting that the discrepancy could not be explained by

chemical kinetics parameters.

It is significant that k3 is a strong function of temperature, with an activation energy of

42.1 kcal/mol (see Section 5.4). In contrast, k4 only weakly depends on temperature with

an activation energy of only 5.2 kcal/mol, as will be discussed later in the paper.

Therefore, a temperature rise favors k3 and shifts the balance towards higher OH

concentrations. For an exothermic system, such as the decomposition of H2O2,

temperature rises higher in a constant U-V reactor than at constant P-H, which apparently

77

explains the discrepancy between the two models. At late times (> 0.6 ms in Figure 6-7),

H2O2 is close to depletion and temperature effects on k3 diminish; as a result, the OH

profiles calculated with both the models converge again.

0.0 0.2 0.4 0.6 0.8 1.0

0

20

40

60

80

OH

[ppm

]

Time [ms]

Constant P-H Constant U-V

Figure 6-7. OH profiles predicted by assuming a constant P-H process or a constant U-V process behind the reflected shock wave. Identical k3 and k4 were used in those calculations. The two models agree on the peak OH concentration, while the constant U-V model predicts a slight hump behavior after the OH spike. Conditions are those of Figure 6-2.

The mixtures used in this study were very dilute so that increases in temperature due to

the exothermicity of H2O2 decomposition were minimized. For the example case

discussed here, GRI-Mech 3.0 [18] predicts final temperature rises of 20 K and 11 K by

the constant U-V reactor model and the constant P-H reactor model, respectively. It may

be possible in the future to distinguish these two reactor models by taking advantage of a

highly sensitive diagnostic recently developed for shock tube temperature measurements

[49].

To ensure that the observed departure in the experimental OH profile from the commonly

adopted constant U-V reactor model is not a result of using the driver insert, a test was

conducted without the driver insert. Pressure profiles for these experiments are shown in

Figure 6-8.

Neither pressure profile in Figure 6-8 shows any evidence of reaction-induced pressure

change, as the energy release due to chemical reaction is so small that it cannot be

resolved by the pressure measurements. (The linear rise in pressure seen in profile 2 is

78

due to facility effects such as boundary layer growth.) The measured OH time-history for

the experiment without driver insert (not shown here) was very similar to the profile

observed with driver insert (i.e. similar to the measured OH profile in Figure 6-7) and

does not show the hump feature that appears in the constant U-V model in Figure 6-7.

Thus the departure from the constant U-V reactor model was not caused by using the

driver insert.

0 1 2 3 40

1

2

3

1

Pre

ssur

e [a

tm]

Time [ms]

2

Figure 6-8. Comparison of pressure profiles: (1) 1134 K, 2900 ppm H2O2/816 ppm H2O/Ar driven gas, with driver insert, dP/dt = 0%/ms; (2) 1100 K, 2444 ppm H2O2/1538 ppm H2O/Ar driven gas, without driver insert, dP/dt = 1.3%/ms. All pressure profiles have been rescaled to match the initial P5.

6.3.2 Higher temperature (1200 K < T < 1460 K) example case

As temperature rises above 1200 K, H2O formation starts to show increasingly

pronounced sensitivity to the reaction OH + H2O2 H2O + HO2, as can be seen from

Figure 6-9 at 1398 K. The apparent reason is that H2O2 is mainly consumed by its

thermal decomposition at lower temperatures (1000 < T < 1200 K). However, at elevated

temperatures, OH concentration increases dramatically such that the reaction OH + H2O2

H2O + HO2 becomes an important channel in the removal of H2O2. Radical-radical

reactions that lead to final products (H2O and O2) are typically very fast and the

consumption of H2O2 is the rate-limiting step, either through H2O2 + M 2 OH + M or

OH + H2O2 H2O + HO2. Therefore, at elevated temperatures, k3 could not be solely

determined from H2O concentration time-histories.

79

0.00 0.02 0.04 0.06 0.08 0.10-0.05

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

H2O

Sen

sitiv

ity C

oeffi

cien

t

Time [ms]


Figure 6-9. At higher temperatures (T > 1200 K), the formation of H2O shows significant sensitivity to OH + H2O2 H2O + HO2, whereas H2O2 + M 2 OH + M remains the most important one. Initial test mixture: 2540 ppm H2O2/1234 ppm H2O/617 ppm O2/Ar; initial reflected shock conditions: 1.91 atm, 1398 K.

Fortunately, the OH sensitivity coefficient plot in Figure 6-10 shows that both the

reaction rates (k3 and k4) that control H2O formation also control OH yields. With two

constraints (H2O and OH), it is possible to determine two independent unknowns (k3 and

k4). In addition, the problem is well posed because k3 and k4 sensitivities to H2O are

similar, whereas the OH sensitivities have opposite signs. In the current study, H2O and

OH time-histories of all the tests performed at higher temperatures (1200 < T < 1460 K)

were analyzed at the same time to infer both k3 and k4 with small uncertainties.

Example H2O and OH profiles of the test conditions of Figure 6-9 are presented in Figure

6-11 and Figure 6-12, respectively. We used a search algorithm to evaluate k3 and k4.

Specifically, the best-fit k3 and k4 were determined iteratively between the profiles of the

two species, beginning by adjusting k3 and k4 together to match H2O time-histories with

k3/k4 ratios fixed at the values estimated from [OH]peak. k4 values were then fine-tuned to

match OH time-histories while keeping k3 unchanged to get updated k3/k4 ratios. The

process continued until good fits had been achieved for both species time-histories. The

sensitivity coefficient plots in Figure 6-9 and Figure 6-10 were generated using GRI-

Mech 3.0 [18] with experimentally evaluated k3 and k4.

80

0.00 0.02 0.04 0.06 0.08 0.10-1.0

-0.5

0.0

0.5

1.0

OH

Sen

sitiv

ity C

oeffi

cien

t

Time [ms]

H2O2+M<=>2OH+M OH+H2O2<=>HO2+H2O 2OH<=>O+H2O OH+HO2<=>O2+H2O 2HO2<=>O2+H2O2

Figure 6-10. Similar to the example case at a lower temperature (Figure 6-5), OH yield at an elevated temperature is controlled by the OH formation reaction H2O2 + M 2 OH + M and the OH removal reaction OH + H2O2 H2O + HO2. Conditions are those of Figure 6-9.

Recall that at lower temperatures (1000 < T < 1200 K), the initial H2O2 loading was

determined by taking the difference between the initial and the final plateau H2O levels

without corrections (see Section 5.3). The accuracy of the approach is satisfactory at

lower temperatures since near-complete (> 99%) conversions to final products (H2O and

O2) following the decomposition of H2O2 can be assumed. Chemical kinetics

calculations show that H2O2 and HO2 are depleted when a H2O plateau is reached. A

small fraction of the initial H2O2 is converted to and remains as OH, but this represents

typically less than 0.5% of the initial water concentration.

At high temperatures, initial H2O2 concentration must be related to both the final H2O

and OH concentrations. For the example case at 1398 K, there is a residual OH

concentration of approximately 130 ppm at 0.1 ms (Figure 6-12) when the apparent H2O

plateau was achieved (Figure 6-11). The initial H2O2 concentration must thus be

increased by 65 ppm to correct for the residual OH. Similar adjustments were made for

all the tests conducted at temperatures higher than 1200 K. Good agreement was found

between chemical kinetics calculations using corrected H2O2 initial concentrations and

experimental observations.

k3 and k4 errors stem from uncertainties in fitting, uncertainty in temperature, and

uncertainties in interfering reactions. The fitting uncertainties of k3 and k4 were estimated

81

jointly. By setting a constant k3/k4 ratio, k3 and k4 can both be determined within ±15%

accuracy by fitting the H2O profile, as illustrated in Figure 6-11. In addition, the k3/k4

ratio has an estimated fitting error of ±4% as derived from the OH profile (Figure 6-12).

The overall fitting uncertainty for both k3 and k4 are bounded by ±16%, which is the root-

sum-square (RSS) of the two separate fitting uncertainties. The uncertainty in k3

associated with temperature uncertainty was estimated to be ±21% (see Section 5.3). By

contrast, the uncertainties in k4 resulting from temperature uncertainty and OH absorption

cross-section uncertainty were evaluated to be ±2% and ±5% as discussed earlier in this

chapter. Uncertainty from interfering reactions was estimated to be less than ±3% for

both k3 and k4. Therefore, the overall uncertainties for k3 and k4 are less than ±27% and

±17%, respectively, for the example case at T = 1398 K.

0.00 0.02 0.04 0.06 0.08 0.100

1000

2000

3000

4000

Experimental Best fit Best fit k3 +/- 30% (k3/k4 unchanged)

[H2O

] / p

pm

Time [ms]

Figure 6-11. H2O time-history recorded at the conditions of Figure 6-9. The best-fit H2O profile was achieved by setting k3 = 2.4 × 109 [cm3mol-1s-1] and k4 = 6.8 × 1012 [cm3mol-1s-1]. In comparison, the calculated curves with both k3 and k4 changed ±30% while keeping k3/k4 as determined from the corresponding OH profile.

We also found that the difference between OH profiles calculated using the constant U-V

and the constant P-H reactor models diminishes as temperature increases. The trend

coincides with our expectation, because the decomposition of H2O2 is greatly enhanced at

elevated temperatures and the OH formation rate via H2O2 thermal decomposition

becomes comparable to the OH removal rate via the reaction OH + H2O2 H2O + HO2.

As the temperature-sensitive H2O2 decomposition reaction losses its dominance in the

H2O2 decomposition system, OH profiles show less sensitivity to temperatures. This

observation may in turn justify the constant P-H reactor model we adopted to address the

82

discrepancies between experimentally observed OH profiles and calculations based on

the constant U-V reactor model.

0.00 0.02 0.04 0.06 0.08 0.100

100

200

300

400

500

[OH

] / p

pm

Time [ms]

Experimental Best fit Best fit k4 +/- 10% (k3 unchanged)

Figure 6-12. OH time-history recorded at the conditions of Figure 6-9. The best-fit OH profile was achieved by the same pair of k3 and k4 values that best fits the water profile in Figure 6-11. The calculated curves with k4 changed ±10% while keeping k3 at its overall optimal value.

6.3.3 Arrhenius plot of the reaction OH + H2O2 H2O + HO2

Using the approaches described in earlier in this section, the rate constant of the reaction

OH + H2O2 H2O + HO2 was determined at 1.8 atm over the entire temperature range

from 1000 to 1460 K. Experimental data were summarized in Table 5 and in Figure 6-13

as an Arrhenius plot, and compared to the results reported by Hippler et al. [25][26]. The

current study shows reasonable agreement with the previous studies at lower

temperatures (T < 1300 K). However, at temperatures higher than 1300 K, the study by

Hippler et al. [26] reported a dramatic increase in the reaction rate. Since the

measurements made by Hippler et al. [25][26] were the only available experimental data,

their values were widely used in combustion mechanisms [4]-[6][18], as represented by

the dotted line and the dashed line in Figure 6-13.

We also carried out rate measurements at 1 atm. As the total pressure decreased from 1.8

to 1 atm, the OH formation rate is reduced almost by half, since the major OH formation

channel H2O2 + M 2 OH + M is pressure dependent, whereas the OH removal channel

OH + H2O2 H2O + HO2 is not [26][126]. Measured OH yields at 1 atm were expected

83

to be approximately half of those at 1.8 atm to recover a pressure-independent k4. As

demonstrated in Figure 6-13, the data obtained from 1 and 1.8 atm experiments show

remarkable consistency, suggesting a low likelihood for systematic error. A linear-fit to

all the data (1 and 1.8 atm) yields an expression

k4 = 1013.66 exp(−2630 K/T) [cm3mol-1s-1] ( 1020 < T < 1460 K)

0.6 0.7 0.8 0.9 1.0 1.11012

1013

1014

k 4 [cm

3 mol

-1s-1

]

1000 K/T

This study (1.8 atm) This study (1.0 atm) Hippler et al. (1995) Hippler et al. (1992)

909 K1250 K1667 K

Figure 6-13. Arrhenius plot of the rate of the reaction OH + H2O2 H2O + HO2 (k4). The solid line is the linear-fit to all the experimental data of the current study. The dashed line is the rate expression used by Ó Conaire et al. [5] and Li et al. [4], whereas the dotted line is the one adopted by GRI-Mech 3.0 [18].

We performed a simple Arrhenius fit to all of the Hippler et al. data [26] to yield an

A-coefficient of 4.6 × 1016 [cm3mol-1s-1] and an activation energy of 19.7 kcal/mol. The

ab initio calculations by Ginovska et al. [126] reveal that the barrier heights on the

ground state pathways is only 7.3 or 7.8 kcal/mol [126] above the precursor complex

(H3O3), whereas the precursor complex is 6.2 kcal/mol lower in energy than the separated

H2O2 and OH species. The activation energy from this study is 5.2 kcal/mol, in better

agreement with the theoretical calculations. As well, the effective A-coefficient from

Hippler et al. [26] is unusually large. By comparison, the A-coefficient resulting from

the current study, 4.6 × 1013 [cm3mol-1s-1], is a more reasonable value.

84

Table 5. Test conditions and results of H2O2 decomposition experiments in argon bath gas. The H2O2 and H2O concentrations are initial values.

T K

P atm

[H2O] ppm

[H2O2] ppm

k3 (M = Ar) cm3mol-1s-1

k4 cm3mol-1s-1

k8 cm3mol-1s-1

1221 1.921 1793 2827 3.0E+08 5.5E+12 1192 1.949 1364 2216 1.8E+08 5.1E+12 1160 2.008 480 1500 9.8E+07 4.7E+12 1133 2.070 842 1291 6.4E+07 4.4E+12 1106 2.126 1043 378 3.9E+07 4.0E+12 1045 2.066 1235 1670 1.6E+07 4.2E+12 1039 2.192 2196 3632 1.1E+07 4.0E+12 1020 2.192 1218 3360 1.0E+07 3.6E+12 1089 2.239 725 1678 2.9E+07 4.2E+12 1277 2.031 324 2200 6.2E+08 6.0E+12 1052 1.966 826 2204 1.7E+07 3.8E+12 1100 1.947 1538 2444 3.6E+07 4.0E+12 1128 1.884 1042 3210 6.2E+07 4.3E+12 1176 1.810 988 3256 1.3E+08 4.7E+12 1.7E+12 1233 1.746 514 2228 3.1E+08 5.2E+12 1.9E+12 1344 1.974 608 2836 1.3E+09 6.8E+12 2.0E+12 1277 2.020 1038 3011 5.6E+08 6.2E+12 2.0E+12 1317 2.011 1166 2729 9.3E+08 6.5E+12 2.1E+12 1374 1.945 1062 2684 1.8E+09 7.9E+12 2.2E+12 1398 1.909 1234 2540 2.4E+09 6.8E+12 2.3E+12 1424 1.868 1357 3148 3.0E+09 6.5E+12 2.2E+12 1461 1.834 1346 2837 4.7E+09 8.2E+12 1134 1.874 816 2900 6.9E+07 4.5E+12

1430 1.039 1154 3367 3.2E+09 7.4E+12 1313 1.057 1170 3250 9.7E+08 6.5E+12 1249 1.113 1218 3806 3.8E+08 5.1E+12 1190 1.152 786 3650 1.7E+08 4.7E+12 1147 1.224 775 3157 8.0E+07 4.3E+12

To account for the discrepancy between the current study and that of Hippler et al. [26],

experimental procedures of the previous study were carefully reviewed. The thermal

decomposition rate of H2O2 (k3) utilized in their study was k1 = 5.8 × 1031 T -4.55

exp(-25580 K/T) with argon as the third body, which was approximately 40% larger than

determined in the current study and translated to an approximate 40% difference in k4.

Their first example (Figure 1 of reference [26], T = 1152 K) yields a new k4 = 4.2

[cm3mol-1s-1], in good agreement with our current study, if their data are reevaluated with

our H2O2 thermal decomposition rate.

85

However, at elevated temperatures, the large discrepancy in k4 (more than a factor of 3)

cannot be explained by utilizing different values for k3. Unfortunately, absolute OH

yields for a high temperature example case (Figure 3 of Ref. [26], T = 1566 K) were not

provided. However, by examining the experimental conditions included in the paper

(Table 3 of Ref. [26]), we found a dramatic decrease in [H2O2] of the test mixtures,

dropping from 1220 ppm at 931 K to 54 ppm at 1678 K. Given that a sensitive H2O2

diagnostic was not available when the work [26] was accomplished, the authors had to

derive [H2O2] from the early rises in OH time-histories and the thermal decomposition

rate of H2O2 determined in separate studies [98][127]. Without providing an explanation

for such dramatic reduction in [H2O2], we conjecture that the measured OH yields were

only fractions of the true values. This may in turn explain their rate of the OH removal

reaction OH + H2O2 H2O + HO2 (k4) being too large at high temperatures. We also

noticed that Hippler et al. [26] conducted their experiments at pressures near 0.4 atm.

The OH absorption feature is narrow at those low pressures as the pressure broadening

[36] is less pronounced, resulting in a higher uncertainty in OH absorption cross-section.

Most previous studies of k4 were carried out near room temperature. The studies by Wine

et al. [112], Sridharan et al. [118], Kurylo et al. [114], and Keyser [115] show remarkable

consistency and are plotted in Figure 6-14 along with the results of this study (both at 1

and 1.8 atm). A strong non-Arrhenius behavior is apparent. All the experimental data

can be well represented by a sum of two Arrhenius expressions:

k4 = 1012.24 exp(-160 K/ T) + 1013.88 exp(-3660 K/ T) [cm3mol-1s-1] (280 < T < 1640 K)

6.3.4 Arrhenius plot of the reaction H2O2 + M 2 OH + M

By combining the H2O and OH diagnostics, the measurements of H2O2 decomposition

rate have been extended beyond the higher limit of the temperature range of our previous

study (1200 K, see Chapter 5) to 1460 K. Results of this study (both discussed in this

chapter and in Chapter 5) and a previous study [24] are shown in Figure 6-15.

86

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

1012

1013

k 4 [cm

3 mol

-1s-1

]

1000 K/T

This study Wine et al. (1981) Sridharan et al. (1980) Kurylo et al. (1982) Keyser (1980)

250 K400 K1000 K

Figure 6-14. The reaction rate of OH + H2O2 H2O + HO2 (k4), displays a non-Arrhenius behavior over a wide temperature range. Experimental data are well-represented by a sum of two Arrhenius expressions (solid line).

0.7 0.8 0.9 1.0106

107

108

109

1010

4.0 atm, Kappel et al. (2002) 1.0 atm, Kappel et al. (2002)

1111 K

1.8 atm, This chapter 1.0 atm, This chapter 1.7 atm, Chapter 5 0.9 atm, Chapter 5

k 3 [cm

3 mol

-1s-1

]

1000 K / T

1250 K 1000 K1428 K

Figure 6-15. Arrhenius plot of the second-order rate coefficient for H2O2 thermal decomposition (k3). Excellent agreement was found between the current study and the previous study [24]. The solid line is the linear-fit to the experimental data of this study at 1.8 atm (bath gas: argon).

Excellent agreement was found between the separate measurements of the current study

over the entire overlapped temperature range from 1000 to 1200 K, as discussed in

Chapter 5 and this chapter, respectively. It was also confirmed that the pressure

dependence of k3 is negligible at pressures lower than 2 atm, as reported in the previous

study. The linear-fit to the data obtained at 1.8 atm of this study thus yields a

determination of the low-pressure limit of H2O2 decomposition rate in argon:

87

k3 = 1015.98 exp(−21250 K/T) [cm3mol-1s-1] (1020 < T < 1460 K)

By comparison, the low-pressure limit in argon reported in Chapter 5 can be represented

by the expression k3 = 1015.97 exp(−21220 K/T) [cm3mol-1s-1] for temperatures between

1000 and 1200 K, showing extraordinary consistency.

6.3.5 Secondary reaction 2 OH H2O + O

The OH sensitivity coefficient plot for the example case at the elevated temperature

(Figure 6-10) reveals that the reaction 2 OH H2O + O becomes an important OH

removal channel after the OH peak. The rates of the two other reactions that show

substantial sensitivities during the OH decay, H2O2 + M 2 OH + M and OH + H2O2

H2O + HO2, have been determined relatively accurately in the present study. Therefore, a

good estimation can be obtained for the rate of the secondary reaction 2 OH H2O + O

(k8) by varying its value in the chemical kinetics mechanism to capture the trend of OH

decay. For the example case at 1398 K of this study, the best-fit OH profile is presented

in Figure 6-16, in comparison with the ones calculated with k8’s 30% above or below its

optimal value.

0.00 0.02 0.04 0.06 0.08 0.100

100

200

300

400

500

[OH

] / p

pm

Time [ms]

Experimental Best fit Best fit k8 +/- 30%

Figure 6-16. OH time-history recorded at the conditions of Figure 6-9. The optimal rate of the reaction 2 OH H2O + O (k8) was determined by best-fitting the OH time-history. The calculated curves with k8 changed ±30% while retaining the values of all other parameters.

88

Recalling the discussion earlier in this section regarding the difference between using a

constant U-V and a constant P-H model, the question arises, are the k8 values inferred

from the decay of OH susceptible to the choice of these two models. The issue is found

to be minor by a careful examination of Figure 6-5 and Figure 6-7, because the

predictions by the two models converge when the reaction 2 OH H2O + O becomes an

important OH removal channel.

Major error sources of k8 include uncertainty in fitting, uncertainties in k3 and k4, and

uncertainty in temperature. The fitting uncertainty was estimated to be ±15%. The

temperature uncertainty in k3 and k4 does not propagate to k8. The uncertainty inherited

from k3 and k4 is primarily from their fitting errors (±16%) and was evaluated to be ±17%

by varying k8 to best-fit the OH time-history while k3 and k4 were at the limits of their

fitting uncertainties. The uncertainty in k8 associated with temperature uncertainty was

estimated to be ±5%. Therefore, the overall uncertainty of k8 is ±24%.

Similar best-fit procedures were carried out for the tests at temperatures higher than

1176 K. For the tests conducted at temperatures lower than 1176 K, OH yields were so

low that 2 OH H2O + O is a minor channel for OH decay. All of the inferred k8 values

are plotted in Figure 6-17. k8 has been measured by Wooldridge et al. [57] with

estimated uncertainties of -16% to +11% at T > 2100 K and -22% to +25% at T =

1050 K. The k8 values determined in the present study are in good agreement with those

of the Wooldridge et al. [57].

In addition, the reverse reaction O + H2O 2 OH has been experimentally investigated

[125][129] and an expression for k8 has been derived from these two studies using

equilibrium constants [128]. Correcting for the updated OH heat of formation [36][75],

k8 is well represented by 4.34 × 103 T2.7exp(951 K/T) [cm3mol-1s-1] (dashed curve in

Figure 6-17), in good agreement with the expression k8 = 3.57 × 104 T2.40exp(1063 K/T)

[cm3mol-1s-1] recommended by Wooldridge et al. [57].

89

0.4 0.5 0.6 0.7 0.8 0.9 1.0

2x1012

4x1012

6x1012

8x10121013

k 8 [cm

3 mol

-1s-1

]

1000 K / T

Wooldridge et al. (1994) This study

1000 K2500 K 1429 K

1012

Figure 6-17. Arrhenius plot of the secondary reaction 2 OH H2O + O (k8). The results obtained in the current study are within the estimated error bars of Wooldridge et al. [57]. The solid line is the rate expression used by Wooldridge et al. [57]. The dashed line is the rate expression reported by Michael et al. [128] corrected for the updated OH heat of formation.

6.4 SUMMARY

The H2O2 thermal decomposition system was studied behind reflected shock waves over

the temperature range between 1020 and 1460 K using laser absorption diagnostics for

both H2O and OH. Good detectivity for H2O was achieved using tunable diode laser

absorption of water at 2550.96 nm within its v3 fundamental band. The initial

compositions of the reactant mixtures were determined using the sensitive H2O

diagnostic. OH absorption was measured using the well-characterized R1(5) line of the

OH A2Σ+−X2Π (0,0) band near 306.7 nm.

The determinations of the thermal decomposition rate of H2O2 (k3) were extended to

1460 K by jointly interpreting H2O and OH time-histories. The low-pressure reaction

rate constant was found to be k3 = 1015.98 exp(−21250 K/T) [cm3mol-1s-1], in excellent

agreement with that was reported previously in Chapter 5. The estimated uncertainties of

k3 were ±27% for temperatures higher than 1200 K and ±23% for temperatures between

1000 and 1200 K.

The rate of the reaction OH + H2O2 H2O + HO2 (k4) was evaluated at pressures of 1

and 2 atm, over the entire temperature range between 1020 and 1460 K by analyzing the

90

time-histories of H2O and OH. No pressure dependence of the reaction rate was found.

The measurements can be represented by the Arrhenius expression k4 =

1013.66 exp(−2630 K/T) [cm3mol-1s-1] over the measured temperature range with an

overall uncertainty ranging from ±13% at low temperatures to ±17% at high

temperatures. Non-Arrhenius behavior was found by comparing the results of the current

study to the previous measurements near room temperature [112][114][115][118]. Over

a wide temperature range from 280 to 1640 K, the behavior can be described by a sum of

two Arrhenius expressions: k4 = 1012.24 exp(-160 K/T) + 1013.88exp(-3660 K/T)

[cm3mol-1s-1].

The rate of a secondary reaction 2 OH H2O + O (k8) was evaluated by examining the

decay of OH at elevated temperatures (T > 1176 K). The results were well within the

estimated uncertainty limits of the work of Wooldridge et al. [57]. Their rate constant

expression k8 = 104.55T2.40exp(1063 K/ T) [cm3mol-1s-1] (298 < 2380 K) is supported by

the present study.

91

CHAPTER 7: EXPERIMENTAL STUDY OF THE RATE OF OH + HO2 H2O + O2

USING THE REVERSE REACTION

The reaction

OH + HO2 H2O + O2 (Rxn. 5)

plays an important role in combustion chemistry. It is a major HO2 termination path in

lean combustion [130][131], and it is responsible for the depletion of both OH and HO2

radicals in burnt gases [132]. The reaction has a very strong influence on the lift-off

height of turbulent methane-air flames even at atmospheric pressure [133]. In addition,

recent studies have shown that hydrocarbon ignition times at high pressures show a very

strong negative sensitivity to this reaction [134][135]. The reaction also plays an

important role in atmospheric chemistry as it is regarded as a dominant chain termination

for OH and HO2 radicals, both of which catalyze ozone destruction in the upper

atmosphere [136]-[141]. Despite its importance, only a handful of experimental studies

of this reaction have been conducted at elevated temperatures [24]-[27][132][142].

Note that the products of the target reaction OH + HO2 H2O + O2 are H2O and O2.

H2O and O2 mix to form another stable H2/O2 system at room temperatures other than the

H2/O2 oxidation systems and the H2O2 decomposition systems discussed in Chapters 4-6.

The aim of this chapter is to experimentally investigate the rate constant of the reaction

OH + HO2 H2O + O2 (k5) by beginning with H2O/O2 mixtures and using the reverse

reaction.

7.1 PREVIOUS WORK

An Arrhenius plot of previous measurements of k5 conducted at high temperatures is

shown in Figure 1-5. In the early work by Goodings and Hayhurst [132], k5 values were

estimated from temperature measurements of burner flames. More quantitative

measurements of k5 were later carried out using laser absorption of OH or HO2. Hippler

92

et al. [26] reported a k5 minimum near 1250 K in a study of the H2O2 decomposition

system. A more recent measurement by Kappel et al. [24], again in the H2O2

decomposition system, found the rate minimum to be near 1000 K. Thus, it is possible

that a rapid increase in k5 over the small temperature range from 970 to 1220 K, may be

responsible for the large spread of data seen by Kappel et al. [24] shown in Figure 1-5. In

these two studies, OH and HO2 radicals were intermediate species of H2O2

decomposition. However, no such strong temperature dependence of k5 was observed by

Srinivasan et al. [27] in a reaction system containing NO2 and C2H5I. When heated by

reflected shock waves, C2H5I rapidly decomposes into C2H5 and I radicals, with C2H5

subsequently decomposing to form H and C2H4. These H radicals initiate reactions by

attacking NO2 to yield OH; the generated OH radicals in turn react with NO2 to form

HO2. With the co-existence of OH and HO2 in the system, Srinivasan et al. [27] were

able to study the reaction OH + HO2 H2O + O2. An average value for k5 = (4.0 ± 1.6)

× 1013 [cm3mol−1s−1] was reported between 1200 and 1700 K.

Almost all the previous studies of the reaction OH + HO2 H2O + O2 involved OH and

HO2 as the reactants. To the author’s knowledge, this reaction has not been studied in its

reverse direction using H2O and O2 as reactants, although the reaction scheme should be

much simpler and more direct. Computer simulations using a detailed chemical kinetics

mechanism, GRI-Mech 3.0 [18], indicate that the formation of OH radicals in

instantaneously-heated H2O/O2 mixtures is predominantly controlled by the kinetics of

the reaction. Here, we apply this reverse-reaction strategy in a shock tube using UV laser

absorption of OH.

7.2 TEST MIXTURES PREPARATION

Test mixtures were prepared by passing a stream of premixed 1% O2/Ar (Praxair)

through a flask filled with degassed pure water. The apparatus was adapted from the one

developed in Chapter 5 for generating H2O2 vapor (see Figure 5-1) simply by replacing

urea hydrogen peroxide powder in the flask with pure water. The flask was kept in an

ice-water bath to maintain a low water vapor pressure. The flow rate of the carrier gas

(premixed O2/Ar) was adjusted to achieve a water concentration near 1.5% in the test

93

mixtures, thereby avoiding condensation in the shock tube. The test mixture was directed

into the driven section of the shock tube from a filling port near the endwall. Total filling

pressures in the driven section (P1) were between 0.04 – 0.12 atm.

Actual H2O mole fractions in the test mixtures were determined using the H2O diagnostic

described in Section 3.1. Figure 7-1 shows a sample time-history of the H2O laser

absorbance obtained at 1880 K and 1.74 atm, which exhibits features common to all tests.

Laser absorbance A is defined in the Beer-Lambert Law as ln( / )ov vA I I= − , where o

vI

and vI are the incident and transmitted laser intensities, respectively. Detailed

discussions on laser absorbance can be found in Section 3.1.

0.0 0.2 0.4 0.6 0.8 1.00.0

0.5

1.0

Abs

orba

nce

Time [ms]

Experimental data Steady State

Figure 7-1. Using the time-history of the laser absorbance near 2.5 μm, the steady-state H2O concentration was determined to be 1.3%. The composition of the test mixture can be calculated to be 1.3% H2O / 0.99% O2 / 97.71% Ar. Initial reflected shock conditions: 1880 K, 1.74 atm.

The apparent overshoot in H2O laser absorption that occurs within a few microseconds

near time zero is a result of the vibrational relaxation of H2O. The equilibrium

temperature upstream of the reflected shock wave is 984 K in this example case. After

the passage of the reflected shock wave, the H2O vibrational mode eventually reaches

equilibrium with the translational and rotational modes, and a thermal equilibrium is

reestablished at 1880 K. Because the fraction of H2O molecules in the lower energy state

of the absorption transition peaks around 400 K [56], the H2O absorbance decreases

dramatically from 984 to 1880 K. A vibrational relaxation study of H2O in argon bath

94

gas by Kung and Center [143] suggests that the characteristic time of the process is

approximately 0.5 μs, consistent with the rapid fall in absorbance near time zero that

defines the passage of the reflected shock.

Following the initial sharp decline in laser absorption, the temperature continues to

decline over the next 100 μs to a final steady-state value because of the slower vibrational

relaxation time scale for O2 in this mixture.

Little fluctuation in H2O concentration is seen after 0.1 ms. The estimated overall

uncertainty in the H2O concentration is ±10%, which also includes the uncertainty in the

absorption cross-section. The steady-state H2O concentration, which is the mean value

between 0.1 – 1 ms, was used to calculate test mixture composition. By putting emphasis

on the OH temporal profile after 0.1 ms, error in k5 due to this simplification can be

minimized.

Although the temperatures of core flow behind reflected shock waves were between 1600

– 2200 K in the current study, the walls of the shock tube were still at room temperature.

Condensation on room temperature walls was avoided by using mixtures with water

vapor partial pressure (behind reflected shock) less than the saturation pressure of water

vapor at room temperature (0.032 atm).

7.3 RESULTS AND DISCUSSION

7.3.1 Determination of the rate of the reaction OH + HO2 H2O + O2 (k5)

Using a kinetics mechanism, the OH sensitivity coefficient can be calculated with the

Senkin kinetics suite [74]. The sensitivity coefficient has been defined in Section 4.3.

Figure 7-2 is the corresponding OH sensitivity plot for the conditions of Figure 7-1. The

sensitivity coefficient was calculated using an updated version of GRI-Mech 3.0 [18].

The parameters updated in the mechanism are: (1) the OH heat of formation [36][75], (2)

the HO2 heat of formation [76], and (3) the rate constant for the reaction H + O2 O +

OH [144]. In addition, the rate expression for the reaction OH + HO2 H2O + O2 was

replaced by its reverse counterpart.

95

OH formation shows the largest sensitivity to the rate of the reverse reaction H2O + O2

OH + HO2 (k-5). Therefore, k-5 can be accurately evaluated by changing this rate in the

chemical kinetics mechanism to best fit experimental OH time-histories. k-5 can then be

readily converted to k5 through the equilibrium constant: K5 = k5/k-5. Once a k-5 value

was experimentally determined, the sensitivity coefficient was recalculated with the

updated k-5. The sensitivity plot in Figure 7-2 was calculated using the experimentally

determined k-5.

0.0 0.2 0.4 0.6 0.8 1.0-0.2

0.0

0.2

0.4

0.6

0.8

1.0

OH

Sen

sitiv

ity C

oeffi

cien

t

Time [ms]

O2+H2O<=>OH+HO2 H+O2<=>O+OH OH+H2<=>H+H2O 2OH<=>O+H2O

Figure 7-2. OH sensitivity plot at conditions of Figure 7-1.

It is also evident from the sensitivity analysis that only a few reactions control the

kinetics of a simple reaction system such as the one under investigation. Among these

controlling reactions, the dominant one (O2 + H2O OH + HO2) is the target of this

study. The rate expressions for the reaction OH + H2 H + H2O are essentially identical

for all commonly used mechanisms [4]-[6][18], and are based on the study by Michael et

al. [145]. However, for the reaction 2 OH H2O + O, the Li et al. [4] and the Ó Conaire

et al. [5] mechanisms use the rate expression from an early study [125], whereas GRI-

Mech 3.0 [18] uses the one recommended by a more recent study [57]. In addition, GRI-

Mech 3.0 was updated with the rate constant for the reaction H + O2 O + OH from a

very recent study [144]. The updated GRI-Mech 3.0 thus reflects recent improvements in

the H2/O2 mechanism and was selected as the base mechanism to analyze experimental

data in the present study. It should also be noted that the selection of the base mechanism

96

only has very minor effects on the determination of k5, as OH formation is predominantly

controlled by the kinetics of the target reaction.

The rate of production analysis (ROP) was carried out as well for the conditions of Figure

7-1, as presented in Figure 7-3. Although there are three other major channels to produce

OH besides the target reaction in its reverse direction H2O + O2 OH + HO2, this

reaction is the initiation and rate-limiting step for OH formation. Near time zero, OH is

produced almost exclusively via H2O + O2 OH + HO2. Shortly after the initial radical

pool is established, OH production through other reaction channels rapidly accelerates,

each ROP contribution achieving plateau levels within ~ 100 μs. This is a clear

indication that H2O + O2 OH + HO2 is the rate-limiting step, and explains why OH

shows dominant sensitivity to this reaction.

0.0 0.2 0.4 0.6 0.8 1.0

0

2

4

6

8

10

OH

RO

P [1

x10-8

mol

e/cm

3 -sec

]

Time [ms]

O+H2O<=>2OH O2+H2O<=>OH+HO2 H+O2<=>O+OH H+H2O<=>OH+H2

Figure 7-3. Rate of production analysis (ROP) of OH at conditions of Figure 7-1.

Using the Beer-Lambert law, laser attenuation at 306.7 nm due to the absorption of OH

radicals can be converted to OH temporal profiles. Shown in Figure 7-4 is the OH time-

history obtained from the same experiment as the H2O laser absorbance in Figure 7-1.

The experimental data are compared with the best-fit profile calculated using a k-5 value

of 3.1 × 106 [cm3mol-1s-1]. Two OH profiles calculated using 120% and 80% of the best-

fit k-5 are presented on the same plot. The fitting uncertainty of k-5 is conservatively

estimated to be ± 10%.

97

0.0 0.2 0.4 0.6 0.8 1.00

10

20

OH

Con

cent

ratio

n [p

pm]

Time [ms]

Experimental Best fit k-5

Best fit k-5 +/- 20%

Figure 7-4. Comparison of experimental and Senkin calculated OH profiles using best-fit k-5 with the effect of ± 20% variation on k-5 at conditions of Figure 7-1.

A near-linear increase in OH concentration was observed over 1 ms without showing an

apparent sign of fall-off to gradually reach a plateau, suggesting that the equilibrium OH

level might be much higher than the experimental observation at 1 ms. A thermodynamic

calculation using the latest heats of formation for OH [36][75] and HO2 [76] indicates

that the equilibrium OH concentration is 173 ppm for this example. In addition, a

kinetics calculation using GRI-Mech 3.0 [18] predicts that it takes approximately 50 ms

to achieve the equilibrium OH level.

However, a small non-linear rise was observed between 0 – 0.1 ms. This behavior can be

attributed to residual impurities in the shock tube, despite efforts to keep the shock tube

very clean and evacuated between shock wave experiments to pressures ~10−7 Torr. An

experiment was conducted at similar conditions but excluding H2O from the test mixture.

We still observed a very similar small rapid rise in OH concentration at early times,

confirming that the target reaction is not responsible for this brief non-linear OH rise.

The residual impurity issue has been encountered repeatedly in previous studies

[36][144]. At temperatures of interest in this study, trace amounts of hydrocarbon

impurities are converted into OH radicals almost instantly by the vastly abundant O2. In

practice, the impurity effects are modeled by artificially including H- atoms in the initial

mixture used for the numerical simulation. For the example case shown, 0.7 ppm of H

98

atom was included in calculating the OH profiles in Figure 7-4 and the OH sensitivity

coefficients in Figure 7-2.

7.3.2 Uncertainty analysis

It is seen from Figure 7-2 that OH formation shows some sensitivity to three reactions

other than the target reaction of this study. 1) The uncertainty associated with the

reaction rate of H + O2 O + OH is less than ±5% [144] over the entire temperature

range of the interest of this work. The resulting uncertainty in k-5 is less than ±2%, and

can be neglected here. 2) OH formation shows sensitivity only to the reaction 2 OH O

+ H2O between 0 – 0.1 ms. As was discussed in the previous section, we rely heavily on

the OH time-history after 0.1 ms for the assessment of k-5. Here again, the error

introduced by uncertainty in the rate of the reaction 2 OH O + H2O can be eliminated

by not including the experimental data obtained between 0 – 0.1 ms. 3) The reaction OH

+ H2 H2O + H has negative sensitivity to OH formation over the entire test time and

needs to be carefully evaluated for uncertainty in its reaction rate. The review by Baulch

et al. [80] assigns a factor of two uncertainty to the reaction rate of OH + H2 H2O + H.

Our analysis reveals that k-5 is subject to only about ±4% uncertainty because of this

interference reaction.

As briefly mentioned in Chapter 3, uncertainties in H2O and OH absorption cross-

sections were estimated to be ±10% and ±5%, respectively, resulting in a k-5 uncertainty

of ±12%. In addition, the temperature uncertainty has been assessed to be ±23 K in this

temperature range, which introduces approximately ±22% uncertainty in inferred k-5

values. Combining uncertainties from all error sources – such as the best-fitting

procedure (±10%), absorption cross-sections of OH and HO2 (±12%), interfering

reactions (±4%), and temperature (±22%) – the overall uncertainty for k-5 is ±27% at T =

1880 K. At lower temperatures, OH yields decrease significantly and the fitting

uncertainty becomes larger. For instance, the fitting uncertainty was estimated to be

±20% at T = 1591 K, which leaded to an overall uncertainty for k-5 ±32% at this

temperature.

99

7.3.3 Arrhenius plot

Experiments were conducted over a wide temperature range from 1600 to 2200 K.

Figure 7-5 summarizes all experimental k-5 values. The best-fit to all the data points

yields an expression for k-5: 6.0 × 1014 exp(-35720 K/T) [cm3mol−1s−1]. The equilibrium

constant of the reaction can be calculated using the current thermochemical data,

[36][75][76][109] yielding K5 = 0.0642 exp(35420 K/T) between 1600 and 2200 K. The

entropy change for the reaction OH + HO2 O2 + H2O is small, and therefore, the

exponential part of the equilibrium constant is predominantly the difference in formation

enthalpies. Note that the activation energy for the reverse reaction O2 + H2O OH +

HO2 is almost identical to the difference in formation enthalpies. This suggests that there

is no or only a small energy barrier on the reaction path of the forward reaction.

0.45 0.50 0.55 0.60 0.65105

106

107

This study Best-fit

2222 K 1818 K

k -5

[cm

3 mol

-1s-1

]

1000 K / T

1538 K

Figure 7-5. Arrhenius plot of experimentally determined k-5 between 1600 and 2200 K. The best-fit to the measured k-5 values (solid line) can be expressed as k-5 = 6.0 × 1014 exp(-35720 K/T) [cm3mol−1s−1].

The measured k-5 values are converted into k5 using the equilibrium constant, and are

summarized in Table 6 and Figure 7-6. No apparent temperature dependence of k5 was

found between 1600 and 2200 K. The solid line in the figure represents the average of k5

= (3.3 ± 0.9) × 1013 [cm3mol−1s−1] from this study, in good agreement with k5 = (4.0 ±

1.6) × 1013 [cm3mol−1s−1] between 1237 and 1554 K as reported by Srinivasan et al. [27].

100

Table 6. Test conditions and the experimentally determined rate constants of the reaction OH + HO2 H2O + O2 (k5).

T [K]

P [atm]

k-5 [cm3mol-1s-1]

K5

k5 [cm3mol-1s-1]

1591 1.93 1.14E+05 2.98E+08 3.40E+13 1698 1.84 3.95E+05 7.35E+07 2.90E+13 1658 1.90 2.72E+05 1.21E+08 3.30E+13 1764 1.80 9.80E+05 3.37E+07 3.30E+13 1798 1.76 1.43E+06 2.30E+07 3.29E+13 1880 1.74 3.07E+06 9.76E+06 3.00E+13 1915 1.70 4.63E+06 6.92E+06 3.20E+13 1939 1.65 5.82E+06 5.50E+06 3.20E+13 2018 1.61 1.30E+07 2.69E+06 3.50E+13 2070 1.58 1.85E+07 1.73E+06 3.20E+13 2117 1.52 3.04E+07 1.18E+06 3.60E+13

For comparison, the expressions for k5 used in commonly employed mechanisms [4]-

[6][18] are also plotted in Figure 7-6. The rate constant expression adopted in the

mechanisms by Li et al. [4] and Ó Conaire et al. [5] is based on the early reviews by

Baulch et al. [146][147]. On the other hand, GRI-Mech 3.0 [18] and the Konnov

mechanism [6] estimate the rate constant of the reaction OH + HO2 H2O + O2 based on

low temperature studies [136]-[139] and the high temperature study by Hippler et al.

[26]. The two latter kinetic mechanisms assign relatively large positive activation

energies (>17 kcal/mol) to k5 at high temperatures. As temperature rises, the agreement

between this study and the Konnov mechanism/GRI-Mech 3.0 degrades.

It should be noted that although the k5 expression used by Li et al. [4] and Ó Conaire et

al. [5] well represents the results of the current study, the study by Srinivasan et al. [27],

and those at low temperatures [136][137][139][140], caution should be exercised when

extending the expression beyond the experimentally confirmed regions, particularly,

between 400 and 1200 K. This is because a deep and narrow rate constant minimum may

exist close to 1250 K [26] or 1000 K [24] as a result of “the formation of intermediate

complexes” [26].

Calculating the ab initio surfaces are difficult for the reaction of OH + HO2 H2O + O2

[148]-[152]. It is therefore difficult to theoretically confirm the anomalous temperature

101

dependency observed by Hippler et al. [26] and Kappel et al. [24]. A calculation that

uses collision theory to estimate a rough upper bound for the reaction OH + HO2 on the

triplet energy surface has been carried out [27]. The calculation assumes that the reaction

is barrier-free and leads to a conclusion that the rate constant k5 is expected to level off at

high temperatures, even if the narrow minimum may exist near 1000 K. Therefore, the

lack of strong temperature dependence at high temperatures as found in the current study

does not completely rule out the possibility of a minimum k5 near 1000 K. Independent

study in the temperature range of 900 – 1200 K is needed to confirm this unusually deep

and narrow rate constant minimum.

0.45 0.50 0.55 0.60 0.65

1014

Li et al. (2004) & O Conaire et al. (2004)

2x1013

2222 K 1818 K

k 5 [cm

3 mol

-1s-1

]

1000 K/ T

This study GRI-Mech 3.0 Konnov (2008)

1538 K3x1014

Figure 7-6. Arrhenius plot of experimentally determined k5 between 1600 and 2200 K. The k5 expressions used in recent reaction mechanisms are also shown. Dash: GRI-Mech 3.0 [18], dot: Konnov mechanism [6], solid: Li et al. mechanism [4] and Ó Conaire et al. mechanism [5].

Gonzalez et al. carried out thorough ab initio calculations on the reaction between OH

and HO2 on the singlet [149] and triplet [148] potential energy surfaces, respectively. On

the singlet potential energy surface, the reaction proceeds via a 3A hydrogen-bonded

complex HO⋅⋅⋅HO2, and leads to the formation of triplet oxygen; whereas on the singlet

potential energy surface singlet oxygen ( 1gΔ ) is formed through an hydrogen trioxide

(HOOOH) intermediate, which has a 1A electronic state. They concluded that the

reaction on the singlet energy surface is unimportant for pressures up to a few

atmospheres and for temperatures below 2500 K.

102

The reaction proceeds predominantly on the triplet energy surface as an H-abstraction

reaction. Gonzalez et al. [148] found that the hydrogen-bond in the complex HO⋅⋅⋅HO2 is

too weak to produce a significant pressure dependence. Their ab initio calculations

reveal that the rate of the target reaction is not controlled by the transition state on the

triplet energy surface. Therefore, the reaction rate is essentially the rate of formation of

the hydrogen-bonded complex, which is referred to as the capture rate and is controlled

by the long-range interaction between OH and HO2. The capture rate constant was

calculated using vibrationally/rotationally adiabatic theory and found to be k5 = 7.05 ×

1013 (T/300 K)−0.21 exp(113 K/T) [cm3mol−1s−1] [148], as illustrated by the dash-dot curve

in Figure 7-7. The negative temperature dependence is mainly explained by the fact that

the electronic partition function of one of the reactants, the OH radical, increases at

elevated temperatures due to a low-lying energy state 2Π1/2, which is only 0.41 kcal/mol

[153] above the ground state 2Π3/2.

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

1013

1014

5x1014 Calculation, Gonzalez et al. (1992) Li et al. (2004) and O Conaire (2004) GRI-Mech 3.0 Konnov (2008)

250 K333 K500 K

k 5 [cm

3 mol

-1s-1

]

1000 K / T

1000 K4000 K

5x1012

0.4 0.6 0.8 1.0 1.2 1.4

1013

1014

714K5x1014 1000K

k 5 [cm

3 mol

-1s-1

]

1000 K / T

1667K

5x1012

Figure 7-7. Arrhenius plots for k5 (★-this study; ◆- Srinivasan et al. [27]; ▼- Hippler et al. [26]; ●- Kappel et al. [24]; ■- Keyser [137]; ▲- Cox et al. [140] and Lii et al. [139]; ●- Schwab et al. [136]; ☆- Rozenshtein et al. [141]; ×- Sridharan et al. [138]). k5 expressions adopted in some commonly used reaction mechanisms [4]-[6][18] are also presented. The ab initio calculation by Gonzalez et al. [148] can be scaled by 0.61 to well match the rate constant expression used in Li et al. [4] and Ó Conaire et al. [5] kinetic mechanisms.

Although the vibrationally/rotationally adiabatic theory calculations by Gonzalez et al.

[148] capture the negative temperature dependence of k5 accurately, the predicted values

are consistently higher than experimental data. Gonzalez et al. [148] scaled down their

103

calculation results to match the low temperature experimental data by Keyser [137] to

yield a new expression k5 = 4.28 × 1013 (T/300)−0.21 exp(113 K/T) [cm3mol−1s−1]. The

rescaling leads to k5 values (not shown in Figure 7-7) very close to those calculated using

the expression recommended by early Baulch reviews [146][147] between 200 and

2000 K.

7.4 SUMMARY

Small amounts of H2O vapor were blended with premixed 1% O2/Ar bath gas to form

H2O/O2/Ar mixtures. Using tunable diode laser absorption of H2O near 2.5 μm, the test

mixture compositions were evaluated directly. These mixtures were shock-heated to

temperatures between 1600 and 2200 K to study OH time-histories using laser absorption

at 306.7 nm.

OH formation is predominantly controlled by the reverse reaction H2O + O2 OH +

HO2 (k-5). Because k5 is directly proportional to k-5 through the equilibrium constant: K5

= k5/k-5, the values of k5 were determined by varying them in a modified version of GRI-

Mech 3.0 to generate OH profiles that best-fit the experimental observations. k5 was

found to be (3.3 ± 0.9) × 1013 [cm3mol-1s-1] between 1600 and 2200 K. Srinivasan et al.

[27] reported an average k5 value of (4.0 ± 1.6) × 1013 [cm3mol−1s−1] between 1237 and

1554 K, in good agreement with the current study. The combination of the two studies

suggests only a weak temperature dependence of k5 above 1200 K.

The k5 expression recommended by Baulch et al. [146][147], k5 = 2.89 × 1013

exp(252 K/T) [cm3mol−1s−1], accurately represents the measurements of the current study,

the study by Srinivasan et al. [27], and those at low temperatures [136][137][139][140].

However, as noted above, there is still some uncertainty about the behavior of this

reaction rate constant in the temperature range of 400 – 1200 K. An independent study of

k5 in the temperature range of 900 – 1200 K would help to resolve this uncertainty.

105

CHAPTER 8: COMPILATION OF AN IMPROVED H2/O2 MECHANISM

Detailed kinetic mechanisms for the oxidation of hydrocarbons have the H2/O2 sub-

mechanism as a necessary starting point of their hierarchical structure [1]. This sub-

mechanism is critical because it contains many important elementary reactions involving

H, O, OH, HO2, H2O, and H2O2 that play a role in all stages of hydrocarbon oxidation.

Continued improvement of the H2/O2 sub-mechanism is thus necessary for the continued

development and refinement of high-fidelity hydrocarbon mechanisms.

8.1 INTRODUCTION

Several detailed kinetic mechanisms dedicated to the H2/O2 system have been developed

recently [2]-[6]. In addition to these mechanisms, recent H2/CO mechanisms [7]-[10]

also contain the corresponding H2/O2 sub-mechanisms. While these mechanisms are able

to capture the behavior of chemical systems dominated by chain-branching reactions (i.e.

ignition delay times), systems dominated by the formation and consumption of HO2 and

H2O2 are still subject to relatively large uncertainties.

However, work in this area is continuing, even in the short time since publication of an

updated H2/O2 mechanism by Konnov [6] in 2008. As discussed in Chapters 4-7,

experimental studies using shock tube/laser absorption techniques of this work have

resulted in improved high-temperature rate constants for the following reactions:

H + O2 = OH + O (Rxn. 1, see Chapter 4)

H2O2 + M = 2 OH + M (Rxn. 3, see Chapter 5)

OH + H2O2 = HO2 + H2O (Rxn. 4, see Chapter 6)

O2 + H2O = OH + HO2 (Rxn. 5, see Chapter 7)

The goal of this chapter is to compile an improved H2/O2 mechanism that takes advantage

of these reaction rate determinations and the results of other recent rate coefficient

106

studies, and incorporates the most current thermochemical data for OH and HO2. The

overall reaction scheme is first discussed. This is followed by discussions of several

individual reaction rates.

8.2 OVERALL REACTION SCHEME

Before the evaluation of individual reaction rate constants, an overall reaction scheme

needs to be chosen. The H2/O2 sub-mechanism in GRI-Mech 3.0 [18] has 20 reversible

elementary reactions. Later H2/CO mechanisms by Davis et al. [8] and Sun et al. [10] use

the same 20-reaction scheme for H2 chemistry.

The mechanisms by Li et al. [4], Ó Conaire et al. [5], and the H2/O2 sub-mechanism by

Sun et al. [10] were premised on the 19-reaction scheme of Mueller et al. [2]. The

reaction H + HO2 = H2O + O was not included in these three mechanisms, as the authors

argued that this reaction is kinetically similar to the reaction H + HO2 = OH + OH.

However, the work by Konnov [6] showed that these two reactions, although not

important in slow hydrogen oxidation processes, have opposite signs in laminar flame

sensitivities. Hence we have retained the reaction H + HO2 = H2O + O in this H2/O2

mechanism.

A 21-reaction scheme was adopted in the Konnov mechanism [6]. The additional

reaction is the chain-initiation step H2 + O2 = OH + OH. As calculations of potential

energy surfaces [154] showed that this reaction is highly unlikely, it has not been

included in the current H2/O2 mechanism. For similar reasons the recent H2/O2 chemistry

by Williams and co-workers [9] does not include this reaction, though it was included in

an earlier mechanism from that group [3].

The reaction O + OH (+ M) = HO2 (+ M) is not included in most H2/O2 sub-mechanisms,

[2][4]-[6][8][10] with the exception of two sub-mechanisms by Williams and co-workers

[3][9]. A recent study [155] demonstrated that this reaction may impact predictions in

lean high-pressure flames. However, given the level of uncertainty in its rate constant

(ranging from 1015 [156] to 1.2 × 1017 [cm6mol-2s-1] [157]), this reaction is also not

107

included in the current mechanism. The reaction may be included in future versions of

the mechanism once more accurate experimental data become available.

In summary, the current mechanism consists of 20 reactions in a form identical to that

found in GRI-Mech 3.0. The improved mechanism (labeled “current mechanism”

throughout this thesis) is presented in Table 7, where five of the reaction rate constants

that are inherited directly from the GRI-Mech 3.0 mechanism (Rxns. 6, 8, 10, 15, and 16)

are denoted by asterisks. Uncertainties for the current rate constants and temperature

ranges over which experimental validation exists can be also found in the table. The

proposed mechanism and thermochemical data in CHEMKIN format are included in

Appendix D.

In Table 7, a pressure-dependent reaction is indicated by a species enclosed in

parenthesis. For example, Rxns. 2a - 2d represent the recombination reaction H + O2 →

HO2. A “(+M)” symbol in Rxn. 2d indicates that any species can act as a third body for

this pressure-dependent reaction, where “M” stands for an arbitrary third body. The

parameters describing the high-pressure limit (k∞) for such reactions are listed in the same

line as the chemical formula, whereas those of the low-pressure limit (k0) are provided in

the line following the chemical formula. For a reaction containing the “(+M)” symbol,

species can be specified to have an enhanced collider efficiency (or third-body

efficiency). A unity collider efficiency is assigned to a species if no collider efficiency is

explicitly specified. The effective concentration of the third body is the sum of the

concentration of each species multiplied by the corresponding collider efficiency.

A special case is that the rate constant of a pressure-dependent reaction due to a third

body cannot be expressed by the general form with the “(+M)” symbol. The CHEMKIN

convention is to use a separate expression to account for the collider efficiency of this

third body. For example, “(+Ar)” in Rxn. 2a indicates that Ar can act as the third body

for the recombination reaction H + O2 → HO2. Because the third body effect of Ar for

this reaction has been accounted by Rxn. 2a, the collider efficiency for Ar in Rxn. 2d is

set to be zero to prevent double-counting.

108

Table 7. Current H2/O2 Reaction Mechanism. k = ATn exp(Ea/RT) in units of [s-1],

[cm3mol-1s-1] or [cm6mol-2s-1].

No. Reaction A n Ea [cal/mol]

Ref. Uncertainty (±%)

T rangee [K]

1 H+O2=OH+O 1.04E+14 15286 [144] 10 1100-3370

2a H+O2(+Ar)=HO2(+Ar)b 5.59E+13 0.2 0 [159] 18-35 1050-1250

Low-pressure limit 6.81E+18 -1.2 0 [159] - -

2b H+O2(+H2O)=HO2(+H2O)c 5.59E+13 0.2 0 [159] - -


2c H+O2(+O2)=HO2(+O2)b 5.59E+13 0.2 0 [159] - -


2d H+O2(+M)=HO2(+M)b 5.59E+13 0.2 0 [159] - -


Collider efficiency (N2=1): H2=1.5, Ar =0, H2O = 0, O2 = 0 [160] - -

3 H2O2(+M)=2OH(+M)d 8.59E+14 48560 [105] 21 1000-1200

Low-pressure limit 9.55E+15 42203 [79][78] - -

Collider efficiency (Ar=1): N2=1.5, H2O=9 [79][101][102]

- -

4 OH+H2O2=H2O+HO2 1.74E+12 318 [78] 27 1020-1460

OH+H2O2=H2O+HO2 7.59E+13 7269 [78] - -

5 OH+HO2=H2O+O2 2.89E+13 -500 [77] 27 1600-2200

6* HO2+HO2=H2O2+O2 1.50E+11 -1603 [24]

HO2+HO2=H2O2+O2 4.20E+14 11980 [24]

7a H2O+M=H+OH+M 6.06E+27 -3.31 120770 [162]

Collider efficiency (Ar=1): H2O=0, H2=3, N2=2, O2=1.5 [162]

7b H2O+H2O=OH+H+H2O 1.00E+26 -2.44 120160 [162]

8* OH+OH=H2O+O 3.57E+04 2.4 -2111 [57] 15-25 1050-2380

9 O+H2=H+OH 3.82E+12 7948 [80]

O+H2=H+OH 8.79E+14 19170 [80]

10* H2+OH=H2O+H 2.17E+08 1.52 3457 [80]

11 H+HO2=OH+OH 7.08E+13 300 [4]

109

12 H+HO2=H2O+O 1.45E+12 0 [80]

13 H+HO2=H2+O2 3.66E+06 2.087 -1450 [161]

14 O+HO2=OH+O2 1.63E+13 -445 [80]

15* H2O2+H=HO2+H2 1.21E+07 2.0 5200 [84]

16* H2O2+H=H2O+OH 1.02E+13 3577 [80]

17 H2O2+O=OH+HO2 8.43E+11 3970 [80]

18a H2+M=H+H+M 5.84E+18 -1.1 104380 [4]

Collider efficiency (Ar=1): H2O=14.4, Ar=0, H2=0, N2=0, O2=0 [4][10]

18b H2+H2=H+H+H2 9.03E+14 0 96070 [80]

18c H2+N2=H+H+N2 4.58E+19 -1.4 104380 [4]

18d H2+O2=H+H+O2 4.58E+19 -1.4 104380 [4]

19a O+O+M=O2+M 6.16E+15 -0.5 0 [163]

Collider efficiency (N2=1): H2=2.5, H2O=12, Ar=0 [163]

19b O+O+Ar=O2+Ar 1.89E+13 0 -1788 [163]

20 O+H+M=OH+M 4.71E+18 -1.0 0 [163]

Collider efficiency (N2=1): H2=2.5, H2O=12, Ar=0.75 [163]

a: The input files for reaction rate constants and thermodynamic data in CHEMKIN format are included in Appendix D.

b: Fcent = 0.7 [158]; c: Fcent = 0.8 [158]; d: Fcent = 1

d: The T range [K] corresponds to the published temperature range of the experimental validation for that reaction rate constant.

*: Reaction rate constants inherited from GRI-Mech 3.0.

110

A Reaction with a “+M” symbol (without parenthesis) is very similar to a “(+M)”

reactions, for example Rxn. 7a in Table 7. The difference is that the fall-off behavior and

the high-pressure limit of a pressure-dependent reaction denoted by “+M” are omitted.

Therefore, the parameters next to the chemical formula are for the low-pressure limit.

Such simplifications are made to reactions with negligible fall-off behavior even at

elevated pressures (< 100 atm) and of secondary importance in typical combustion

environment.

The thermodynamic data used for the current mechanism are all consistent with the latest

database of Burcat [109]. These data include updates to the enthalpy of formation of OH

[36][75] and HO2 [76]. Transport data are not within the scope of the current paper, but

can be adapted from JetSurF 1.1 [158], which is the latest version of a detailed chemical

reaction mechanism for large hydrocarbon fuels.

8.3 REACTION RATE CONSTANTS

8.3.1 H + O2 = OH + O (Rxn. 1)

The rate constant for the chain branching reaction H + O2 = OH + O has been discussed

in detailed in Chapter 4. The rate constant expression recommended in Section 4.5 is

listed in Table 7. It should be noted however, as discussed in Section 4.4, that a major

source of uncertainty in k1 is due to the uncertainty in the rate constant of the reaction H

+ HO2 = H2 + O2 (k13). Minor adjustments may need to be made to k1 as more accurate

data for k13 become available.

8.3.2 H + O2 (+ M) = HO2 (+ M) (Rxn. 2)

The chain-terminating reaction H + O2 (+ M) = HO2 (+ M) competes with the major

chain-branching reaction H + O2 = OH + O for H radicals. The low-pressure limit (k2,0)

of the three-body reaction has been studied in recent years by several groups including

Bates et al. (2001) [159], Michael et al. (2002) [160], and Hwang et al. (2005) [73]. A

complete review of experimental studies near the low-pressure limit before 2005 can be

found in Baulch et al. [80]. The study by Hwang et al. [73] (Ar bath gas) was published

111

after the Baulch review [80], but their data are well within the quoted uncertainty limits

in the Baulch 2005 review.

For a pressure-dependent reaction, it is also important to specify the high-pressure

limiting rate constant and fall-off behavior. An early experimental investigation by

Cobos et al. [164] studied the rate constant up to 200 atm at room temperature (M = Ar,

N2). However, until recently, only a few high-pressure experimental studies have been

reported at elevated temperatures. Hahn et al. [165] studied the rate constant with Ar as

the third body at temperatures up to 700 K and pressures up to 900 atm. In 2008,

Fernandes et al. [84] extended the Hahn et al. study to three bath gases (Ar, N2, and He),

higher temperatures (up to 900 K), and slightly higher pressures (up to 950 atm). By

combining the theoretical high-pressure limiting rate constant (k2,∞ determined from

classical trajectory calculations [166]) and low-pressure limiting rate constants (k2,0 from

the literature [80][160][167][168]) the fall-off behavior was then evaluated. At about the

same time, Sellevåg et al. [169] conducted a separate theoretical study for the high-

pressure limit and fall-off behavior of the reaction. At higher temperatures, the only

direct measurement in the fall-off region was reported by Bates et al. [159], a few indirect

evaluations based on shock tube ignition delay times exist, for example, by Pang et al.

[16] and by Mertens et al. [170].

The three recent high-pressure studies (Fernandes et al. [84], Sellevåg et al. [169], and

Bates et al. [159]) reported significantly different high-pressure limiting rate constants

(k2,∞) and center broadening factors (Fcent). However, the differences among the three

expressions in the actual rate constant are insignificant below 100 atm, as evidenced by

Figure 8-1. Miller et al. [92] have pointed out that the deviation from third-order

behavior of the reaction under typical combustion conditions is not significant [92] with

the exception of supercritical water oxidation. Therefore, the predictive capability of an

H2/O2 mechanism for typical combustion simulations relies more on the accuracy of k2,0

than that of k2,∞ and Fcent.

As illustrated by Figure 8-2, the discrepancies among k2 values from different studies

basically stem from the differences in k2,0 at typical combustion conditions. Because

112

Bates et al. [159] conducted the only direct experimental measurements at high

temperature (1050 – 1250 K), their k2 expressions, including k2,0, k2,∞, and Fcent, are

adopted in the current mechanisms for M = Ar, N2, and H2O. For M = O2 and H2, the

expressions for the low-pressure limit rate constants are taken from the work by Michael

et al. [160].

1 10 100 10001010

1011

1012

1013

M = Ar

k 2 [cm

3 mol

-1s-1

]

P [atm]

Fernandes et al. (2008) Sellevag et al. (2008) Bates et al. (2001)

H + O2 (+ M) = HO2 (+ M)T = 1100 K

M = N2

Figure 8-1. Variation of the rate constant (k2) with pressure at 1100 K. Although the rate constant expressions given in the three studies appear different, the differences in the actual rate constants at pressures below 100 atm are insignificant.

300 700 1100 1500

1011

1012

M = Ar

M = N2

H + O2 (+ M) = HO2 (+ M)P = 10 atm

5x1011

5x1012

k 2 [

cm3 m

ol-1s-1

]

T [K]

Fernandes et al. (2008) Sellevag et al. (2008) Bates et al. (2001)

Figure 8-2. Arrhenius plot for k2 at 10 atm. For typical combustion pressures (P < 100 atm), the rate constants are predominantly controlled by the low-pressure limit rate constant of the reaction (k2,0).

113

8.3.3 H2O2 (+ M) = 2 OH (+ M) (Rxn. 3)

The low-pressure limiting rate constant of the reaction in Ar bath gas has been discussed

in Chapters 5 and 6, and can be specified by k3,0 (Ar) = 9.55 × 1015 exp(−21250 K/T)

[cm3mol-1s-1]. The collider efficiency of N2 relative to Ar was estimated to be 1.5.

However, collider efficiencies for other bath gas species were rarely determined by

experiments. This could lead to large uncertainty when species other than Ar and N2 are

present in large concentrations. In the current mechanism, the O2 collider efficiency is

set equal to that of N2. Suggested values for the collider efficiencies of H2O relative to

N2 have been estimated to be 6 or 9 relative to Ar based on early room-temperature

studies by Zellner et al. [101] and Forster et al. [102].

Due to the lack of experimental data at high pressures, the current mechanism relies on

theoretical studies [105][106] for the high-pressure limiting rate constant (k3,∞). Both

theoretical calculations resulted in much larger k3,∞ values than the one recommended by

Kappel et al. [24]. The larger k3,∞ values from these two theoretical studies [105][106]

are supported by high-pressure studies at room temperature [101][103], which is in good

agreement with the recommendation by a very recent review paper [107]. Please note

that there are a few typos in the reference. For example, to be consistent with the rest of

the paper [107], Eqn. 5.4 should read k1,∞ ≈ 1.04 × 1015 (T/1000 K)n exp(-24534 K/T)

[s-1] instead of k1,∞ ≈ 1.04 × 1013 (T/1000 K)n exp(-24534 K/T) [s-1]. Accordingly, part

(b) of Table 2 in the same reference [107] should read k1,∞ = 1.0 × 1015 (T/1000 K)0.9

exp(-E0/RT) [s-1].

Although the uncertainty in k3,∞ is relatively large as a result of the lack of high-pressure

experimental data, it should be noted that, for most combustion applications, the

predictive power of a mechanism is determined mostly by the accuracy of k3,0. The

reason is that the deviation from the low-pressure limiting behavior of the H2O2 thermal

decomposition reaction is insignificant under typical combustion conditions (up to

50 atm), similar to the argument presented for the chain-terminating reaction H + O2

(+M) = HO2 (+M).

114

8.3.4 OH + H2O2 = H2O + HO2 (Rxn. 4)

The current mechanism uses a k4 rate constant recommended in Section 6.4 that is the

sum of two Arrhenius expressions that they derived by combining their high-temperature

data with previous studies at low to intermediate temperatures. It should be noted that

currently, to the knowledge of the authors, no experimental data exist between 500 –

1000 K, where some groups have suggested that a significant change in the activation

energy could exist. Further experimental data are needed to confirm this possible

transition in activation energy.

8.3.5 OH + HO2 = H2O + O2 (Rxn. 5)

The rate constant of the reaction OH + HO2 = H2O + O2 (k5) probably has the largest

uncertainty (of the 20 reaction rate constants) among the comparative mechanisms, as

evidenced by Figure 7-7. This is because of the unusual behavior reported by two

previous studies [24][26], see Section 7.3. Both studies suggest that the reaction rate

constant has a strong temperature dependence at high temperatures.

Srinivasan et al. [27] experimentally studied k5 and reported an average value for k5 =

(4.0 ± 1.6) × 1013 [cm3mol−1s−1] between 1237 and 1554 K. However, the experimental

scatter prevented these authors from drawing a strong conclusion about the temperature

dependence of the reaction rate constant. Our experimental investigation (see Chapter 7)

clearly shows that the strong temperature dependency of k5 assumed in some mechanisms

[6][8][18] does not exist between 1600 and 2200 K, and that k5 can be well-represented

by (3.3 ± 0.9) × 1013 [cm3mol−1s−1]. This latest study is in good agreement with the

Srinivasan study [27].

These two recent studies, together with studies at low temperatures [136]-[140] support

the expression that was recommended in early Baulch et al. reviews [146][147] and is

used in the current mechanism. As pointed out in Section 7.3, caution should be

exercised when using the above k5 expression between 400 and 1200 K, because a rate

constant minimum may possibly exist near 1250 K [26] or 1000 K [24].

115

8.3.6 H2O + M = H + OH + M (Rxn. 7)

In most previous mechanisms [3]-[5][7]-[10][18], this reaction was expressed in the

recombination direction. Recently, Srinivasan and Michael [162] studied the thermal

decomposition of H2O between 2196 and 2792 K and reported a rate constant for the

decomposition direction. Their new expression is adopted in the current mechanism and

the mechanism by Konnov [6]. The uncertainty of the Srinivasan and Michael study was

estimated by the authors to be ±18%. However, as pointed out by Konnov, there also

exist data [171][172] that are systematically lower than other literature values by a factor

of 4-5. As a result, the uncertainty of the reaction rate constant was estimated to be a

factor of 2 by Konnov.

It is also noticed that the description of the fall-off behavior of the reaction H2O + M = H

+ OH + M was purposely omitted in previous mechanisms, for the reason that the

deviation from the low-pressure limiting rate is insignificant under typical combustion

conditions (i.e. pressures up to 50 atm). A theoretical study has been recently carried out

to investigate the reaction’s pressure dependence and its high-pressure limiting rate [169].

Using k7,∞, and Fcent given in the literature [169], it appears that the second-order rate

constant expression is satisfactorily accurate in describing the kinetics of this reaction

under typical combustion conditions. In light of the level of uncertainty that exists in k7,0,

use of a second-order rate constant for H2O thermal decomposition is deemed sufficient

and is thus retained in the current mechanism.

8.3.7 2 OH = H2O + O (Rxn. 8)

The rate constant of the reaction 2 OH = H2O + O (k8) was measured by Wooldridge et

al. [57] in our laboratory with estimated uncertainties of -16% to +11% at T > 2100 K

and -22% to +25% at T = 1050 K. The reaction has also been studied in the reverse

direct O + H2O 2 OH (k-8) by the Brookhaven group in 1991 [125][129]. Using the

updated OH heat of formation [36][75], k-8 can be converted to k8 = 4.34 × 103 T2.7

exp(951 K/T) [cm3mol-1s-1], in good agreement with the Wooldridge expression k8 = 3.57

× 104 T2.40exp(1063 K/T) [cm3mol-1s-1] [57]. A reevaluation of k8 in Section 6.3 is in

116

excellent agreement with the two aforementioned expressions. The rate expression of

Wooldridge et al. [57] is used in the current mechanism.

8.3.8 Other reactions

Other rate constants are identical to those suggested by GRI-Mech 3.0 [18] (Rxns. 6, 8,

10, 15, and 16) or from the review by Baulch et al. [80] (Rxns. 9, 10, 12, 14, 16, and 17).

As discussed in the introduction section, Konnov [6] has pointed out that it may be

necessary to include all three product channels of the reaction between H and HO2 (H +

HO2 = 2 OH; H + HO2 = H2O + O; and H + HO2 = H2 + O2).

In particular, reactions H + HO2 = 2 OH (Rxn. 11) and H + HO2 = H2 + O2 (Rxn. 13)

have been demonstrated [4][5] to be important in capturing species time-histories from

flow reactor studies and laminar flame speeds. However, knowledge of these two rate

constants is very limited. The only known set of near-direct experiments of the reaction

H + HO2 = H2 + O2 at combustion temperatures was performed by Michael et al. [161] by

studying the reverse initiation reaction H2 + O2 = H + HO2 between 1662 and 2097 K.

Using the equilibrium constant, forward rate constants (k13) can be calculated from data

reported by Michael et al. [161] in the reverse direction (k-13) and are plotted in Figure

8-3. In the same plot, a k13 value at 773 K inferred from an early flame study by Baldwin

and Walker [173] is also presented. For simplicity, experimental results near room

temperature [174]-[177] are not shown in the same figure. Michael et al. [161]

recommended an expression for k-13 based on their experimental and theoretical studies,

which leads to k13 = 3.66 × 106 T2.087 exp(730 K/T) [cm3mol-1s-1] if the equilibrium

constant given in the same study [161] is utilized for the conversion. This k13 expression

is adopted in the current mechanism; see the red curve in Figure 8-3.

We have used the same expression for the rate constant of the reaction H + HO2 = 2 OH

as that in the Li et al. [4] mechanism, as that mechanism shows good agreement with

currently available data from flow reactor studies and laminar flame speed measurements.

The rate constants for the third product channel H + HO2 = H2O + O are taken directly

from the evaluation by Baulch et al. [80].

117

0.4 0.6 0.8 1.0 1.2 1.41012

1013

1014833 K1250 K

Michael et al. (2000) Baldwin and Walker (1974)

k 13 [c

m3 m

ol-1s-1

]1000 K/ T

Michael et al. (2000) GRI-Mech 3.0 Li et al. (2004)

O Conaire et al. (2004) Tsang and Hampson (1986) Baulch et al. (2005)

Konnov (2008)

2500 K

Figure 8-3. Arrhenius plot for k13. Curves are k13 expressions proposed in some previous mechanisms or reviews (red solid: Michael et al. [161]; black solid: GRI-Mech 3.0 [18]; dash dot: Li et al. [4], also used by Ó Conaire et al. [5]; dot: Tsang and Hampson [163]; short dash: Baulch et al. [80], also used by Konnov [6]).

The rate constant of the reaction O + H2 H + OH (k9) has been discussed in Section 4.3

briefly. The recommendation for k9 from the Baulch et al. review [80] was adopted in the

current mechanism. However, because alternative expressions for k9 can differ

substantially at certainty temperatures, as pointed out by Gkagkas and Lindstedt [81], one

should be aware of these alternatives, for example, reference [82].

119

CHAPTER 9: VALIDATION OF THE H2/O2 MECHANISM

The mechanism compiled in Chapter 8 is tested (and its performance compared to that of

other H2/O2 mechanisms) against recently reported OH and H2O concentration time-

histories in various H2/O2 systems, such as H2 oxidation, H2O2 decomposition, and

shock-heated H2O/O2 mixtures. In addition, the mechanism is validated against a wide

range of standard H2/O2 kinetic targets, including ignition delay times, flow reactor

species time-histories, laminar flame speeds, and burner-stabilized flame structures. This

validation indicates that the updated mechanism should perform reliably over a wide

range of reactant concentrations, stoichiometries, pressures, and temperatures from 950 to

greater than 3000 K.

9.1 VALIDATIONS AGAINST SPECIALIZED DATA

The goal of this section is to validate the current mechanism at conditions where

“‘controversial’ reactions are manifested” [6] or important reactions are isolated. To

achieve this goal, some specialized conditions have to be exploited, for instance, the

study of H2 oxidation in extremely diluted mixtures. In addition to investigations of H2

ignition (oxidation), other combinations of species containing only H and/or O elements,

for example, H2O2 and H2O, provide unique opportunities to test and validate the H2/O2

mechanism. In the following examples, comparisons will be made with simulations

based on the current mechanism and those of Li et al. (2004) [4], Ó Conaire et al. (2004)

[5], Konnov et al. (2008) [6], and GRI-Mech 3.0 (1999) [18].

9.1.1 H2 oxidation in extremely dilute mixtures

Both H2O and OH time-histories have been reported during H2 oxidation in extremely

dilute mixtures [19][144]. H2 ignition delay times are strongly susceptible to impurities

[144], whereas the rapid rise of the slope of both the H2O and OH profiles at ignition is

not significantly affected by impurities. Therefore, the relative shapes of these profiles,

120

instead of the absolute time scales, are valuable kinetic targets for validating the H2/O2

sub-mechanisms.

In Figure 9-1 and Figure 9-2, experimental H2O time-histories (Section 4.3) recorded at

1472 K and 1100 K, respectively, are compared to mechanism predictions. Trace

amounts of H-atoms (at sub-ppm levels) are included as reactants in the CHEMKIN

inputs to simulate impurity effects, and thus allow the ignition delay times to be matched

very accurately. Alternatively, the simulations can be shifted in time to match the

ignition delay times.

0.2 0.4 0.6 0.8 1.0 1.20

400

800

1200

1600

2000

2400

Current Mechanism Konnov (2008) Li et al. (2004) GRI-Mech 3.0

O Conaire et al. (2004)

H2O

Con

cent

ratio

n [p

pm]

Time [ms]

Figure 9-1. H2O time-history during the oxidation of H2 at 1472 K and 1.831 atm in a fuel-rich H2/O2/Ar mixture (0.1% O2, 0.9% H2, balance Ar). Experimental data (in blue) are from Section 4.3. A reference has indistinguishable predicted species time-history as the one above it with a legend, if there is no legend next to the reference (same thereafter).

At 1472 K, the Ó Conaire et al. mechanism [5] overpredicts the H2O formation rate at

ignition, which can be explained by the fact that the rate constant for the reaction H + O2

= OH + O (k1) used in their mechanism is too large at temperatures near 1500 K (see

Figure 4-6), since H + O2 = OH + O is the rate-limiting step during fuel-rich H2 oxidation

and directly controls the H2O formation rate. At 1100 K, the present mechanism and

GRI-Mech 3.0 [18] accurately simulate the H2O time-histories, whereas other

mechanisms are not as successful. Similarly, this discrepancy can be attributed to the fact

that the k1 values used in the Li et al. [4], the Ó Conaire et al. [5], and the Konnov [6]

mechanisms are too large at temperatures near 1100 K.

121

2 3 4 5 6

0

900

1800

Current Mechanism GRI-Mech 3.0

O Conaire et al. (2004) Li et al. (2004) Konnov (2008)

H2O

Con

cent

ratio

n [p

pm]

Time [ms]

Figure 9-2. H2O time-history during the oxidation of H2 at 1100 K and 1.953 atm in a fuel-rich H2/O2/Ar mixture (0.1% O2, 2.9% H2, balance Ar). Experimental data (in blue) are from Section 4.3.

At higher temperatures, OH time-histories have been reported [19] and are used to

validate the current mechanism. Figure 9-3 compares data and simulations of OH time-

history during the oxidation of H2 at 1980 K and 0.675 atm in a fuel-rich H2/O2/Ar

mixture (0.493% O2, 5% H2, balance Ar). Experimental data (in blue) are from Masten et

al. [19]. Due to small uncertainties in the OH absorption cross-section and the mixture

compositions, the OH profiles were treated as self-calibrating by matching the plateau

values in the original work of Masten et al. [19]. We took the same approach by re-

scaling calculated OH profiles to match the experimental OH plateau. Only the current

mechanism and the latest Konnov mechanism [6] closely match these experimental data.

The difference among the predicted OH profiles can be primarily explained by the

different k1 values used in the mechanisms tested. Because H + O2 = OH + O is the rate-

limiting reaction of the three-step chain-branching during fuel-rich H2 oxidation, the

increase in OH radical concentration is predominantly controlled by the kinetics of this

reaction. For instance, the Ó Conaire et al. mechanism overpredicts the OH formation

rate (Figure 9-3) because the k1 values used in the mechanism are too large near 1980 K.

122

50 100 150 2000

100

200

300

Current Mechanism Konnov (2008)

Li et al. (2004) GRI-Mech 3.0 O Conaire et al. (2004)

OH

Con

cent

ratio

n [p

pm]

Time [μs]

Figure 9-3. OH time-history during the oxidation of H2 at 1980 K and 0.675 atm in a fuel-rich H2/O2/Ar mixture (0.493% O2, 5% H2, balance Ar). Experimental data (in blue) are from Masten et al. [19].

9.1.2 H2O2 thermal decomposition

The thermal decomposition of H2O2 provides a unique opportunity to test and validate

rate constant values for isolated H2O2/HO2 reactions. Both H2O and OH time-histories

have been previously reported (Section 6.3). In Figure 9-4 and Figure 9-5, experimental

data recorded at initial reflected shock conditions of 1192 K, 1.95 atm with 2216 ppm

initial H2O2 are compared to mechanism predictions. The H2O profiles predicted by Li et

al. [4], Ó Conaire et al. [5], and GRI-Mech 3.0 [18] are almost indistinguishable and are

represented by one single curve in Figure 9-4. The current mechanism has the best

performance among all the mechanisms tested.

The difference in the predicted H2O formation rates is primarily from the rate constants

used in these mechanisms for the H2O2 decomposition reaction (k3), because at the

conditions of Figure 9-4 the rate-limiting step from the reactant H2O2 to the products

(H2O and O2) is the H2O2 decomposition reaction. For instance, the k3 value used in the

Konnov mechanism [6] is approximately 4 times of that in the current mechanism.

The OH time-history presented in Figure 9-5 was measured simultaneously with the H2O

profile shown in Figure 9-4. Again, the best agreement is seen with the current

mechanism. The Konnov mechanism [6] overpredicts OH concentrations, primarily

because it over-estimates the rate constant of H2O2 decomposition (k3). Other

123

mechanisms (Li et al. [4], Ó Conaire et al. [5], and GRI-Mech 3.0 [18]), although they

overpredict the rate of H2O2 thermal decomposition (Figure 9-4), underpredict the peak

OH values. This opposite effect is attributed to the larger rate constant (than that

recommended here) used in these mechanisms [4][5][18] for Rxn. 4 OH + H2O2 = H2O +

HO2.

0.0 0.2 0.4 0.6 0.8 1.01000

2000

3000

4000

Current Mechanism Konnov (2008) Li et al. (2004)

O Conaire (2004) GRI-Mech 3.0

H2O

[ppm

]

Time [ms]

Figure 9-4. H2O time-history during the thermal decomposition of H2O2 at 1.95 atm, 1192 K. Test mixture: 2216 ppm H2O2/1364 ppm H2O/682 ppm O2/Ar. Experimental data (in blue) are from Section 6.3.

0.0 0.4 0.8

0

50

100

150

Current Mechanism Konnov (2008) Li et al. (2004)

O Conaire et al. (2004) GRI-Mech 3.0

OH

Con

cent

ratio

n [p

pm]

Time [ms]

Figure 9-5. OH time-history during the thermal decomposition of H2O2 at conditions of those of Figure 9-4. Experimental data (in blue) are from Section 6.3.

Comparisons between experimental H2O/OH time-histories and mechanism predictions

are also made at a much higher temperature (1498 K). These comparisons lead to results

similar to those of the 1192 K case discussed above (see Appendix C).

124

9.1.3 High-temperature H2O/O2 reaction

Another environment that provides opportunities for improving the understanding of

H2/O2 reactions is the high-temperature H2O/O2 system. Representative OH time-

histories have been reported in shock-heated H2O/O2/Ar mixtures (Section 7.3). A

sample OH profile is shown in Figure 9-6 for a reflected shock wave experiment with a

mixture consisting of 1.3% H2O, 0.99% O2, balance Ar at 1880 K and 1.74 atm. The

current mechanism and the Li et al. [4] and Ó Conaire et al. [5] mechanisms all reproduce

the experimental OH time-history with good accuracy and are indistinguishable in Figure

9-6.

0.0 0.2 0.4 0.6 0.8 1.00

10

20

30

40

50

OH

Con

cent

ratio

n [p

pm]

Time [ms]

Current Mechanism Li et al. (2004) O Conaire et al. (2004)

Konnov (2008) GRI-Mech 3.0

Figure 9-6. OH time-history in a shock-heated 1.3% H2O/0.99% O2/97.71% Ar mixture. Initial reflected shock conditions: 1880 K, 1.74 atm. Experimental data (in blue) is from Section 7.3. The discrepancy among the mechanisms [4]-[6][18] can be mainly attributed to the

different rate constants used for the reaction OH + HO2 = H2O + O2 (k5). This is the case

because the reaction OH + HO2 = H2O + O2 is the initiation and rate-limiting step for OH

formation in instantaneously heated H2O/O2 mixtures, as discussed in detail in Section

7.3. For example, the k5 value at 1880 K used in the Konnov mechanism is

approximately 3.5 times of that in the current mechanism, as evidenced by Figure 7-6.

125

9.2 VALIDATIONS AGAINST CONVENTIONAL COMBUSTION DATA

In addition to validating the current mechanism at specialized reaction conditions, the

mechanism is also validated against experimental data obtained under more conventional

combustion conditions. These include ignition delay times in shock tubes, species time-

histories in flow reactors, unstretched laminar flame speeds, and burner-stabilized flame

structures.

These more conventional data have been studied extensively in the development of

previous mechanisms [2][4]-[6][8]. Almost all these mechanisms have achieved good

agreement with these experimental data, and for simplicity, these comparisons are not

included in these discussions.

9.2.1 Shock tube ignition delays

Shock tube ignition delay times are widely used for the calibration of combustion

mechanisms at intermediate to high temperatures (T > 1000 K). H2 ignition delay

behavior has been extensively studied by previous researchers, for example see

references [16][178]-[183]. The recent shock tube study of H2 ignition delay times by

Pang et al. [16] provides a unique opportunity for the validation of the current

mechanism, because the Pang et al. [16] study reported the facility-related non-ideal

pressure rise as a function of time. This enables a more accurate simulation of ignition

behavior.

Li et al. [17] have developed a method, CHEMSHOCK, to account for the effects of non-

ideal pressure rise behind reflected shock waves by using the experimentally-measured

pressure time-history (up to the time of ignition) as a constraint on the calculation. Using

this method, the ignition delays times from Pang et al. [16] are compared to the

predictions made by the current mechanism in Figure 9-7 using dP*/dt = 2%/ms (P* =

P/P0, where P0 is the initial post-reflected-shock pressure).

The comparison shows excellent agreement over the entire temperature range studied by

Pang et al. [16]. Ignition delay predictions made with a constant energy-volume (U-V)

approximation, also using the current mechanism, are contrasted in the same plot. The

126

discrepancy between the two approaches (constant U-V and time-varying pressure)

becomes significant at long ignition delay times (τ > 1 ms).

0.9 1.0 1.110-1

100

101

102

Pang et al. (2009) Current Mechanism (dP*/dt = 2%/ms) Current Mechanism (constant U,V)

Igni

tion

time

τ [m

s]

1000 K / T

1111 K 1000 K 909 K

Figure 9-7. Ignition delay times predicted by the current mechanism, by assuming either a constant U-V reactor (CHEMKIN) or a reactor with a pressure rises at a rate of 2%/ms (CHEMSHOCK). The experimental data (in blue) are from Pang et al. and are for mixtures of 4% H2, 2% O2, balance Ar at 3.5 atm [16] with an experimental facility-related pressure rise of 2%/ms.

In addition to the experimental investigation discussed above, ignition delay times were

also studied at elevated pressures, at different equivalence ratios (φ), and with various

bath gases, such as N2 and H2O [178]-[183]. The predictions using the current

mechanism consistently enjoy good agreement with these experimental data.

Comparisons with these data are presented in Appendix C.

9.2.2 Species time-histories from flow reactors

Flow reactors enable combustion to be studied at intermediate temperatures (typically

below 1200 K), where hydrogen peroxide and hydroperoxyl reactions can be important.

Although our experimental studies (Chapters 4-7) have improved the understanding of

these reactions, the rate constants of some of the reactions still lack the support of

consistent experimental data. For example, the reactions H + HO2 = 2 OH and H + HO2

= H2 + O2 are subject to large uncertainties as evidenced by the recent review of Baulch

et al. [80]. Due to the uncertainties in the rate constants of these reactions, flow reactor

127

experiments at intermediate temperatures provide some of the most valuable data for

hydrogen mechanism validation [6].

A common approach for converting experimental profiles as a function of axial distance

into time profiles is to shift the calculated time histories to match the points where 50%

of a major reactant is consumed [2]. This approach is used in the present study to make

comparisons between experimental data and simulations using the current mechanism. In

addition, an adiabatic process is usually assumed to model combustion in flow reactors,

although heat losses cannot be completely eliminated. As shown in Figure 9-8, the

adiabatically calculated exhaust gas temperature is slightly higher (~5 K) than

measurements. Previous studies have shown that differences in species time-histories are

minor if the experimentally measured temperature profile is used instead of the

adiabatically calculated one [2][6]. For simplicity, species time-histories are calculated

with the adiabatic assumption (shown as curves) in the current study and compared to

experimental data.

0.00 0.02 0.04

0.0

0.1

0.2

0.3

0.4

0.5

0.00 0.02 0.04

870

880

890

900

910

920

T

H2O

H2Spe

cies

Mol

e Fr

actio

n (%

)

Time [s]

O2

Tem

pera

ture

[K]

Figure 9-8. Species profiles from a flow reactor experiment [2]. The unburnt mixture was at 880 K, 0.3 atm and comprised of 0.5% H2, 0.5% O2, with the balance N2. The curves are calculated with the current mechanism using an adiabatic approximation. All calculated curves are simultaneously shifted forward by 0.071 s.

The experimental data presented in Figure 9-8 were taken at 880 K, 0.3 atm, with 0.5%

H2 and 0.5% O2 diluted in N2 by Mueller et al. [2]. After shifting all calculated curves

(species time-history and temperature) forward by 0.071 s, the simulations compare

128

favorably with the experimental data. The mechanism is also validated against flow

reactor data over a range of equivalence ratios φ, temperatures, and pressures. For

instance, H2 mole fraction profiles were experimentally measured at φ ≈ 0.5, 6.5 atm,

and over a temperature range of 884 – 934 K [2], as shown in Figure 9-9. The

comparisons at all temperatures show excellent agreement. Further mechanism

validations against flow reactor data can be found in Appendix C.

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

(e) 934 K (d) 914 K

(c) 906 K

(a) 884 K

H2 M

ole

Frac

tion

(%)

Time [s]

(b) 889 K

Figure 9-9. H2 mole fractions recorded at 6.5 atm and at various initial temperatures [2]. The unburnt mixtures were: (a) 1.29% H2/2.19% O2/N2, time shifted forward by 0.30 s; (b) 1.30% H2/2.21% O2/N2, time shifted forward by 0.54 s; (c) 1.32% H2/2.19% O2/N2, time shifted forward by 0.40 s; (d) 1.36% H2/2.24% O2/N2, time shifted forward by 0.38 s; (e) 1.36% H2/2.24% O2/N2, time shifted forward by 0.24 s. Curves are calculated using the current mechanism and an adiabatic reactor.

9.2.3 Unstretched laminar flame speeds

The speed of freely propagating flames can be studied as a function of equivalence ratio,

temperature, pressure, and dilution. Using the concept first suggested by Wu and Law,

[184] experimentally-measured flame speeds, either in counter-flow burners or in

constant-volume bombs, must be corrected for flame stretch effects. Figure 9-10

provides measured and simulated results for the unstretched laminar flame speed at

standard initial temperature and ambient pressure, as a function of equivalence ratio of

mixtures with N2 and Ar as diluents. The mole ratio between O2 and diluents was fixed

at 1:3.76. In the case of N2 diluent, the O2/N2 mixture is essentially that of air.

129

The data in Figure 9-10 are taken from various literature sources [184]-[188]. The curves

are the predictions made with the current mechanism using the “Flame Speed Calculator”

model of CHEMKIN-PRO [189]. The flame speed calculations are repeated until the

temperature and species slopes at the boundaries are close to zero and both gradient and

curvature controls are less than 0.1.

0 1 2 3 4 50

200

400

Wu & Law (1984) Kwon & Faeth (2001) Dowdy et al. (1990) Tse et al. (2000) Vagelopoulos et al. (1994)U

nstre

tche

d Fl

ame

Spee

d [c

m/s

]

Equivalence Ratio (Φ)

N2

Ar

Figure 9-10. Laminar flame speed for H2/O2 diluted in N2 and Ar at 1 atm. The mole ratio between O2 and diluent (Ar, N2) is 1:3.76. Experimental data are from references [184]-[188], the curves are the predictions using the current mechanism.

As evident in Figure 9-10, the agreement between experimental data and mechanism

predictions are very good for both diluents at a moderate dilution ratio (O2:diluent =

1:3.76), standard temperature (unburnt mixtures), and ambient pressure. Experimental

studies have also been reported when a more diluted oxidizer mixture (O2:N2 = 1:12) was

used at the standard temperature and pressure [190][191]. At these conditions, the

current mechanism predicts unstretched flame speeds that agree with experimental data

[190][191], as presented in Figure 9-11.

Recently, Burke et al. [155] studied the mass burning rate ( of ) of H2 flames at pressures

up to 25 atm, where of is defined as the product of the unburnt gas density ( uρ ) and

unstretched laminar flame speed ( ous ). Negative pressure dependence of mass burning

rates was found for H2/O2/Ar flames of equivalence ratio 2.5 [155], whereas all

mechanisms tested in the Burke et al. study [155] either could not fully capture the

negative pressure dependence [4]-[6][8][9] or under-predict mass burning rates [10][36].

130

0.5 1.0 1.5 2.0 2.5 3.0 3.50

10

20

30

40

50

Hermanns et al. (2007) Egolfopoulos & Law (1990) U

nstre

tche

d Fl

ame

Spe

ed [c

m/s

]

Equivalence Ratio (Φ)

Figure 9-11. Laminar flame speed in very diluted H2/O2/N2 mixtures (O2:N2=1:12) with unburnt mixtures at standard temperature and pressure. Experimental data are from references [190][191] and the curve is calculated using the current mechanism.

0 5 10 15 20 250.0

0.5

1.0

1.5

2.0

(b) Tf ~ 1700 K

(c) Tf ~ 1600 K

(d) Tf ~ 1500 KMas

s B

urni

ng R

ate

[g c

m-2s-1

]

Pressure [atm]

(a) Tf ~ 1800 K

Figure 9-12. Mass burning rates of H2/O2/Ar flames of equivalence ratio 2.5 at various nominal flame temperatures ( fT ). The unburnt mixtures were: (a) fT ~ 1800 K, 38.46% H2/7.69% O2/Ar; (b) fT ~ 1700 K, 35.21% H2/7.04% O2/Ar; (c) fT ~ 1600 K, 32.21% H2/6.44% O2/Ar; (d) fT ~ 1500 K, 29.41% H2/5.88% O2/Ar. Curves are calculated using the current mechanism; data are from Burke et al. [155].

As presented in Figure 9-12, the current mechanism accurately captures the negative

pressure dependence of mass burning rates at various nominal flame temperatures ( fT ).

In addition, the overall agreement between the current mechanism predictions (curves)

and experimental data (scatters and error bars) is good. Further improvements of the

131

mechanism may require a better understanding of reactions involving HO2, such as H +

O2 (+M) = HO2 (+M), H + HO2 = H2 + O2, and H + HO2 = 2 OH [155].

9.2.4 Burner-stabilized flame structure

Burner-stabilized flame structures reported in the literature can also be used to validate

the current mechanism. The “Premixed Burner” model of CHEMKIN-PRO [189] is used

in the present study to carry out calculations. A set of experimental data that is widely

used for the validation of H2 mechanisms is from the work by Dixon-Lewis et al. [193]

(Figure 9-13). The study used a fuel-rich H2/O2/N2 mixture (mole fraction: 18.83% H2,

4.60% O2, balance N2). The unburnt gas was at 336 K and 1 atm, with the calculated

adiabatic flame temperature of 1078 K. The experimentally measured burning velocity

was 9.2 ± 0.2 [cm/s] referring to unburnt gas at 291 K. To account for heat losses in the

burner flame, the temperature profile is specified using the experimental data reported in

the same work [193]. In Figure 9-13, the comparisons are made between species profiles

as functions of distance above the burner surface. Note that the species mole fractions

are normalized by N2 mole fraction, as presented in the original work [193]. Very good

agreement between the mechanism predictions and experimental data are found.

A more recent study conducted using a low pressure (0.047 atm) burner was reported by

Vandooren and Bian [194] using molecular beam sampling and mass spectrometry

(MBMS). The reactant mixture was composed of 39.7% H2, 10.3% O2 and balance Ar

(by mole). Both the experimental data and simulations using the current mechanism are

shown in Figure 9-14, and are in reasonable agreement with each other. Similar to what

has been reported by Ó Conaire et al. [5], there is some discrepancy between

experimental data and mechanism predictions in the close vicinity of the burner surface.

More accurate simulations of species profiles will likely require that radical quenching on

the burner surface be properly included [5].

In addition to the flame structures obtained at ambient or lower pressures, burner-

stabilized flame structure has also been studied at an elevated pressure (10 atm) by

Paletskii et al. [195]. The comparison between these experimental data and the

mechanism predictions yields reasonable good agreement (presented in the supplemental

132

materials). However, at this elevated pressure, the flame front thickness is only 0.7 mm,

whereas the claimed spatial resolution of the probe was approximately 0.1 mm. As

pointed out by Konnov [6], the more gradual changes in the experimental profiles may be

a result of the spatial averaging effects by the probe.

-2 0 2 4 6 8

0.00

0.05

0.10

0.15

0.20

0.25

0.30

H2

H2O x 2S

peci

es m

ole

Frac

tion/

N2 m

ole

fract

ion

Distance [mm]

O2 x 2

Figure 9-13. Species spatial profiles obtained from a burner-stabilized flame structure study [192]. The species profiles were normalized using N2 mole fraction. The unburnt mixture consisted of 18.83% H2 and 4.60% O2 (balance N2) and was at 336 K and 1 atm. The temperature profile that is used for simulation is taken from the same study [192]. Solid lines: simulations using the current mechanism.

0.0 0.5 1.0 1.5 2.0 2.5 3.0-0.05

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

O2

H2O

Spe

cies

mol

e fra

ctio

n

Distance [cm]

H2

Figure 9-14. The structure of a burner-stabilized flame studied using a mixture of 39.7% H2, 10.3% O2 and balance Ar (by mole) at 0.047 atm. Experimental data are from the study by Vandooren & Bian [194]; the curves are calculated using the current mechanism.

133

9.3 SUMMARY

The H2/O2 mechanism presented in Table 7 was tested against recently reported OH and

H2O concentration time-histories in various H2/O2 systems, such as H2 oxidation, H2O2

decomposition, and shock-heated H2O/O2 mixtures. In comparison with other recent

H2/O2 mechanisms [4]-[6][18], the current one has better performance under these

specialized conditions.

In addition, the mechanism was validated against a wide range of standard H2/O2 kinetic

targets, including ignition delay times, flow reactor species time-histories, laminar flame

speeds, and burner-stabilized flame structures. The performance of the current

mechanism is comparable to other recently published H2/O2 mechanisms [4]-[6][18].

This validation indicates that the updated mechanism should perform reliably over a wide

range of reactant concentrations, stoichiometries, pressures, and temperatures from 950 to

greater than 3000 K.

135

CHAPTER 10: CONCLUSIONS AND FUTURE WORK

10.1 SUMMARY OF RESULTS

Although modern H2/O2 mechanisms [2][4]-[6][8][10][18] can successfully capture the

behavior of combustion systems dominated by chain-branching reactions (i.e. ignition

delay times), systems dominated by the formation and consumption of HO2 and H2O2 are

still subject to relatively large uncertainties. These large uncertainties are due to many

technical difficulties in making accurate measurements of the rate constants for these

reactions. The goal of this dissertation is to improve the understanding of several key

elementary reactions within the H2/O2 system.

In view of challenges associated with studying HO2 and H2O2 reactions, new

experimental techniques were required, with improved control of the test environment. A

semi-analytical model was developed to guide the modification of standard shock tubes

by installing driver inserts. With properly shaped driver inserts, gradual temperature or

pressure rises behind reflected shock waves due to non-ideal effects can be alleviated or

be completely eliminated. A shock tube modified with driver inserts was used

throughout this study to provide long test times that were highly uniform both in

temperature and pressure.

In addition to the efforts to obtain a precisely controlled test environment, diagnostic

methods have to be carefully selected or developed to obtain better sensitivity to the

kinetics of our target reactions. H2O and OH were chosen as two probed species. The

laser diagnostic for OH had been well-established for combustion kinetic studies in this

laboratory prior to the current work and was directly implemented without modifications.

In addition, this study introduced use of an H2O diagnostic, for the first time, as a

powerful tool for investigating combustion kinetics.

By combining the modified shock tube technique with the laser diagnostics for OH and

H2O, various H2/O2 systems were experimentally studied, such as H2 oxidation, H2O2

136

decomposition, and shock-heated H2O/O2 mixtures. These shock tube/laser absorption

measurements offered more accurate rate constants for several important reactions at high

temperatures, such as:

H + O2 = OH + O (Rxn. 1, see Chapter 4)

H2O2 + M = 2 OH + M (Rxn. 3, see Chapter 5)

OH + H2O2 = HO2 + H2O (Rxn. 4, see Chapter 6)

O2 + H2O = OH + HO2 (Rxn. 5, see Chapter 7)

An improved H2/O2 reaction mechanism was compiled that incorporated the

aforementioned rate constant determinations, as well as recent studies from other

laboratories. The new mechanism was tested against OH and H2O species time-histories

in various H2/O2 systems, such as H2 oxidation, H2O2 decomposition, and shock-heated

H2O/O2 mixtures, and was found to be in very good agreement. In addition, the current

mechanism was validated against a wide range of more standard H2/O2 kinetic targets,

including ignition delay times, flow reactor species time-histories, laminar flame speeds,

and burner-stabilized flame structures.

10.2 PUBLICATIONS

The work detailed in this dissertation has been published in the following papers:

• Z. Hong, D.F. Davidson, and R.K. Hanson, “An Improved H2/O2 Mechanism

based on Recent Shock Tube/Laser Absorption Measurements,” Combust. Flame

(2010), doi: 10.1016/j.combustflame.2010.10.002.

• Z. Hong, D.F. Davidson, E.A. Barbour, and R.K. Hanson, “H + O2 → OH + O

Rate over the Temperature Range of 1100-1530 K: A Shock Tube Study Using

Tunable Diode Laser Absorption of H2O near 2.5 μm,” Proc. Combust. Inst.

(2010), doi: 10.1016/j.proci.2010.05.101.

• Z. Hong, R.D. Cook, D.F. Davidson, and R.K. Hanson, “A New Shock Tube

Study of the Reactions OH + H2O2 → H2O + HO2 and H2O2 +M → 2 OH +M

137

using Simultaneous Laser Absorption of H2O and OH,” J. Phys. Chem. A, 114,

5718-5727 (2010).

• Z. Hong, S.S. Vasu, D.F. Davidson, and R.K. Hanson, “Experimental Study of

the Rate of OH + HO2 → H2O + O2 at High Temperatures Using the Reverse

Reaction,” J. Phys. Chem. A, 114, 5520-5525 (2010).

• Z. Hong, A. Farooq, E.A. Barbour, D.F. Davidson, and R.K. Hanson, “Hydrogen

Peroxide Decomposition Rate: A Shock Tube Study using Tunable Laser

Absorption of Water near 2.5 μm,” J. Phys. Chem. A 113, 12919-12925 (2009).

• Z. Hong, G.A. Pang, S.S. Vasu, D.F. Davidson, and R.K. Hanson, “The Use of

Driver Inserts to Reduce Non-ideal Pressure Variations Behind Reflected Shock

Waves,” Shock Waves 19, 113-123 (2009).

Additional work that is not discussed within the scope of this dissertation has been

reported in following papers:

• Z. Hong, K.-Y. Lam, D. F. Davidson, and Ronald K. Hanson, “A Comparative

Study of the Oxidation Characteristics of Cyclohexane, Methylcyclohexane, and

n-Butylcyclohexane at High Temperatures,” submitted to Combust. Flame.

• Z. Hong, D.F. Davidson, and R.K. Hanson, “Contact Surface Tailoring Condition

for Shock Tubes with Different Driver and Driver Section Diameters,” Shock

Waves 19, 331-336 (2009).

• Z. Hong, D.F. Davidson, S.S. Vasu, and R.K. Hanson, “The Effect of Oxygenates

on Soot Formation in Rich Heptane Mixtures: A Shock Tube Study,” Fuel 88,

1901-1906 (2009).

• S.S. Vasu, Z. Hong, D.F. Davidson, and R.K. Hanson, “Shock Tube/Laser

Absorption Measurements of the Reaction Rates of OH with Ethylene and

Propene,” J. Phys. Chem. A 114, 11529–11537 (2010).

138

• K.-Y. Lam, Z. Hong, D.F. Davidson, R.K. Hanson, “Shock Tube Ignition Delay

Time Measurements of Propane/O2/Argon Mixtures at Near-Constant-Volume

Conditions,” Proc. Combust. Inst. (2010), doi:10.1016/j.proci.2010.06.131.

• D.F. Davidson, Z. Hong, G.L. Pilla, A. Farooq, R.D. Cook, and R.K. Hanson,

“Multi-Species Time-History Measurements During n-Dodecane Oxidation

Behind Reflected Shock Waves,” Proc. Combust. Inst. (2010), doi:

10.1016/j.proci.2010.05.104.

• D.F. Davidson, Z. Hong, G.L. Pilla, A. Farooq, R.D. Cook, and R.K. Hanson,

“Multi-Species Time-History Measurements During n-Heptane Oxidation Behind

Reflected Shock Waves,” Combust. Flame 157 (2010) 1899-1905.

• S.S. Vasu, D.F. Davidson, Z. Hong, V. Vasudevan and R.K. Hanson, “n-

Dodecane Oxidation at High Pressures: Measurements of Ignition Delay Times

and OH Concentration Time Histories,” Proc. Combust. Inst. 32 (2009) 173-180.

• S.S. Vasu, D.F. Davidson, Z. Hong and R.K. Hanson, “A Shock Tube Study of

Methyl-cyclohexane Ignition over a Wide Range of Pressure and Temperature,”

Energy Fuels 23 (2009) 175-185.

• D.F. Davidson, S.C. Ranganath, K.Y. Lam, M. Liaw, Z. Hong, and R.K. Hanson,

“Ignition Delay Time Measurements of Normal Alkanes and Simple

Oxygenates,” J. Prop. Power 26 (2010) 280-287.

10.3 FUTURE WORK

It is evident from this study that continued work on some elements of the H2/O2 sub-

mechanism is still needed. In particular, accurate measurements of reaction rate

coefficients are needed for several HO2 reactions (H+HO2 in particular), as well as for

rate constant measurements and collisional efficiencies at high temperature and high

pressure for HO2 and H2O2 decomposition reactions. It is likely that as the commercial

139

use of high-pressure reactors increases, the need for this information will become even

more critical.

In addition, more species diagnostics can be added to the current experimental setups to

acquire additional information about H2/O2 chemistry. For example, a sensitive

diagnostic scheme for HO2 could be very useful when applied to study the H2O2 thermal

decomposition system to yield information about the kinetics of the reaction HO2 + HO2

= H2O2 + O2 (Rxn. 6).

Furthermore, the general strategies that were developed within the scope of H2/O2

combustion chemistry can be extended to larger combustion systems. For instance, a key

combustion reaction CH3 + HO2 → products may be studied by taking advantage of our

successful experience with the H2O2 system.

141

APPENDIX A: DRIVER INSERT DESIGN FOR GENERALIZED SHOCK TUBE

FACILITIES AND OPERATING CONDITIONS

Following the approach outlined in Chapter 2, the basic design of driver inserts can be

extended to almost all shock tube configurations, including convergent shock tubes.

Generalized approaches for designing proper driver inserts are discussed in three

categories: 1) standard shock tubes operated with tailored driver gases, 2) standard shock

tubes operated with helium driver gas, and 3) convergent shock tubes. A standard shock

tube has identical diameters for both the driver and driven sections, whereas a convergent

shock tube has a larger inner diameter in the driver section than that in the driven section.

A.1. STANDARD SHOCK TUBES WITH TAILORED DRIVER GASES

An operation chart has been summarized in Figure A- 1 to facilitate driver insert design

for various T5 and driven section length combinations in argon test gas. The charts were

calculated assuming tailored driver gases are used, the composition of which can be

found in the panel A. The purpose of using tailored driver gas in this study is to achieve

long test times.

The design of the appropriate driver insert depends heavily on the test temperature

desired (i.e. T5), and there are four variables that are all functions of the desired T5. The

composition of the tailored driver gas to be used can be determined from the chart in

panel A. The location of the tip of the driver insert (i.e. Xdist(1) in Figure 2-7) depends on

the driver section length, and can be determined using the chart in panel B.

The length of the required area change is related to the test time desired, and the chart in

panel C shows the required area change length. The distance between the starting and

ending locations of the area change ([Xdist(1) − Xdist

(2)] in Figure 2-7) can be determined by

multiplying the time-normalized [Xdist(1) − Xdist

(2)] in panel C by the desired uniform test

time, where the time-normalized [Xdist(1) − Xdist

(2)] is defined as the increment of the

distance between Xdist(1) and Xdist

(2) for each unit of test time that needs to be compensated

142

for non-ideal pressure rise. It is not surprising to find that the time-normalized distance

[Xdist(1) − Xdist

(2)] is independent of driven section length under our first-order

approximations. This is because the timing difference caused by the variations in driven

section length is compensated by the corresponding starting point of area change Xdist(1).

900 1200 1500 1800

6

8

10

12

900 1200 1500 180040

50

60

70

80

90

100

900 1200 1500 1800-1.4

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

900 1200 1500 18000.1

0.2

0.3

0.4

0.5

0.6

0.7Area change slope between Xdist

(1)

and Xdist(2) per unit dP*

5/dt (0.01/ms)

N

orm

aliz

ed S

lope

[%/m

]

T5 [K]

D

XHe in tailored driver gas Balance N2

X He

[%]

T5 [K]

A

Driven L = 5.5 m Driven L = 7 m Driven L = 8.5 m Driven L = 10 m

Xdi

st(1

) [m]

T5 [K]

B

[Xdist(1) - Xdist

(2)] per unit test time

(1 ms) to be compensated

T5 [K]

Nor

mal

ized

[Xdi

st(1

) - X di

st(2

) ] [m

/ms]

C

Figure A- 1. Charts calculated for determining the relationship between A4/A1 and Xdist for constant area shock tubes operated with argon driven gas and tailored driver gas. Panel C and panel D are independent of driven section length.

Lastly, the rate of the approximately linear area change between locations Xdist(1) and

Xdist(2) can be accessed as a product of the pressure-normalized slope found in the chart in

panel D and the non-dimensional pressure rise rate for the experimentally observed

dP5*/dt. We have defined 1%/ms as one unit of non-dimensional pressure rise rate and

the normalized slope is the rate of area change between Xdist(1) and Xdist

(2) for each unit of

non-dimensional pressure rise rate. This normalized area change slope is again

independent of driven section length due to the first order approximations made in the

calculation.

143

To clearly illustrate the method, we outline the procedure here for the previous example

case:

Decide on the desired test conditions: driven gas argon, T5 = 900 K, and P5 = 4 atm;

Choose the tailoring driver gas by referring to panel A in Figure A- 1: 50% N2 in

balance He for T5 = 900 K;

Empirically determine the non-ideal pressure rise rate from the experimental data:

dP5*/dt = 2.2%/ms (Figure 1-1);

Refer to panel B in Figure A- 1 to determine the location of the start of the area change

using the shock tube driven section length as a parameter (L = 8.5 m in the sample case):

Xdist(1) = −0.9 m;

Establish the duration over which the pressure rise is to be compensated: 7 ms from

Figure 1-1;

Calculate the distance between the starting location and the ending location of the area

change [Xdist(1) − Xdist

(2)] by multiplying the normalized distance (0.23 m/ms from panel C

in Figure A- 1) with the desired test time length (7 ms) to get [Xdist(1) − Xdist

(2)] = 1.6 m, so

hence the ending point of the area change is at Xdist(2) = −2.5 m;

Determine the slope between Xdist(1) and Xdist

(2) by multiplying the normalized slope

(8.5%/m from panel D in Figure A- 1) with the experimentally observed pressure rise rate

(dP5*/dt = 2.2%/ms) to get a slope of 18.7%/m;

Generate the A4/A1 curve as a function of Xdist (Figure 2-7);

Build the driver insert as shown in Figure 2-9 and test it.

Similar calculations were performed with nitrogen as the test gas. These are shown in

Figure A- 2. As can be seen from Panel A in Figure A- 2, the highest T5 can be achieved

in nitrogen using 100% helium tailoring is 1717 K (T1 = 300 K).

144

600 900 1200 1500 18004

6

8

600 900 1200 1500 180060

70

80

90

100

600 900 1200 1500 1800-1.5

-1.0

-0.5

0.0

600 900 1200 1500 18000.3

0.4

0.5

0.6Area change slope between Xdist

(1)

and Xdist(2) per unit dP*

5/dt (0.01/ms)

Nor

mal

ized

Slo

pe [%

/m]

T5 [K]

D

XHe in tailored driver gas

X He

[%]

T5 [K]

A


X dist

(1) [m

]

T5 [K]

B

[Xdist(1) - Xdist

(2)] per unit test time

(1 ms) to be compensated

T5 [K]

Nor

mal

ized

[Xdi

st(1

) -Xdi

st(2

) ] [m

/ms]

C

Figure A- 2. Charts calculated for determining the relationship between A4/A1 and Xdist for constant area shock tubes operated with nitrogen driven gas and tailored driver gas. Panel C and panel D are again independent of driven section length.

It has been demonstrated that a fixed driver insert designed for a particular T5 gives

relatively good performance (90% of the initial non-ideal pressure rise is removed) for

temperatures within ±100 K of the designed T5. However, this temperature range is

dependent on facility and test conditions and cannot be quantified precisely. The current

design algorithm for the driver insert does not depend on pressure as long as other

parameters are held constant. In reality, the scaling in pressure does have impact on the

driver insert design through the empirically observed dP5*/dt rate.

A.2. STANDARD SHOCK TUBES WITH HELIUM DRIVER GAS

In some cases, long test time is not essential and helium driver gas is commonly used,

since it is the most efficient inert driver gas that can be used to achieve strong shocks

with relatively low P4/P1 ratio.

145

For shock wave experiments with argon driven gas and pure helium driver gas, the charts

in Figure A- 1 are not appropriate but the general procedures described in the previous

subsection are still valid if applied with the following new parameters. The location of

the tip of the driver insert (i.e. Xdist(1) in Figure 2-7), again depends on the driven section

length and designed T5, and can be determined by referring to Figure A- 3 if argon is used

as the driven gas. In contrast to the tailored driver gas case discussed in Section A.1, the

calculation shows that for the helium driver case, both the time-normalized [Xdist(1) −

Xdist(2)] as in Figure A- 1 Panel C, and the normalized slope, as in Figure A- 1 Panel D,

are almost independent of T5 (±5%) ranging from 900 – 1800 K. The calculated values

are 0.62m/ms and 2.9%/m for time-normalized [Xdist(1) − Xdist

(2)] and normalized slope

respectively.

900 1200 1500 1800-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

Xdi

st(1

) [m]

T5 [K]


Figure A- 3. Calculated chart for determining the relationship between Xdist(1) and T5 for

argon driven gas and helium driver gas.

For shock wave experiments with nitrogen (N2) driven gas and pure helium driver gas,

Xdist(1) can be determined using Figure A- 4. Time-normalized [Xdist

(1) − Xdist(2)] and

normalized slope are also almost independent of T5, and have values of 0.50m/ms and

4%/m respectively in this case.

146

900 1200 1500 1800-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

Xdi

st(1

) [m]

T5 [K]


Figure A- 4. Calculated chart for determining the relationship between Xdist(1) and T5 for

nitrogen driven gas and helium driver gas.

A.3. CONVERGENT SHOCK TUBES

This general method can be applied to the other category of shock tube facilities –

convergent shock tubes. To design driver inserts for a convergent shock tube, it is better

to consider an imaginary conventional shock tube that has the driven cross-section

enlarged to match the driver cross-section in the corresponding convergent shock tube

while keeping all other geometric dimensions equal. If the incident shock Mach number

in the imaginary conventional shock tube can be matched to that in the convergent shock

tube by applying a higher initial driver gas pressure P4, to first order, a driver insert

designed for that test condition in the imaginary conventional shock tube works also for

the convergent shock tube under the corresponding test condition. The accuracy of this

estimation is very good for all convergent shock tube with moderate cross-section area

ratios.

To see how the approximation can be justified, we performed our analysis on the High

Pressure Shock Tube (HPST) at Stanford, which was designed for pressures to 1000 atm

[12]. The HPST has a driven section of 5 cm inner diameter, 5 m long, and driver section

of 7.5 cm inner diameter, 3 m long. The cross-section area ratio of this convergent shock

tube is therefore 2.25. A calculation shows that to match the incident shock Mach

number, P4 in the imaginary conventional shock tube is about 40% higher than that in

HPST. One can also refer to the equivalence factor g in [47] for the amplitude of the

147

difference in P4 in two shock tubes. Assuming isentropic expansion, a 40% difference in

the initial driver pressure only leads to about a 5 − 7% difference in the speed of sound in

the fully expanded driver gas, depending on the specific heat ratio of the driver gas.

Additionally, the speed of sound is identical in the unexpanded driver gas since it is only

a function of temperature. Therefore the characteristic curves in the driver section are not

sensitive to the area change at the diaphragm location. On the other hand, since the

incident shock Mach number is matched, the characteristic curves are almost identical in

the driven section in two shock tubes.

When helium is used as the driver gas and argon as the driven gas in a convergent shock

tube, the location of the tip of the driver insert can be estimated using Figure A- 3. In

addition, the time-normalized [Xdist(1) − Xdist

(2)] can be approximated with 0.62 m/ms,

which is also the value for the conventional uniform-bore shock tubes. However, the

normalized slope for convergent shock tubes is different from that for conventional shock

tubes and is A4/A1 ratio dependent. In a separate calculation, we found that for A4/A1 =

2.25, the normalized slope is about 4.0%/m (area percentage change refers to the real

driver cross-section area A4). Note that due to the nonlinearity of ΔP5/P5 when A4/A1 > 1

(e.g., Figure 2-6), the linear area change approximation leads to increasingly large errors

if the approach is adopted to compensate for large pressure rises.

As an example, the driver insert technique has been successfully applied to HPST. In an

effort to understand soot formation in diesel engine, soot formation experiments were

conducted in the HPST for T5 near 1700 K and P5 = 18 atm. Under such conditions, non-

ideal pressure rise rates as high as 7.5%/ms were observed when strong shocks were

produced in argon using helium as the driver gas. The soot formation process is

relatively slow; test times of 2 ms or longer are needed. As a result, the 15% pressure

rise that occurs over 2 ms in the unmodified shock tube is a serious departure from the

constant U-V reactor model. A driver insert designed using the method described in this

paper eliminated the non-ideal pressure rise and a pressure uniformity of ±2.4% was

achieved for 2 ms, as can be seen in Figure A- 5. The exact shape of the discrete driver

insert is compared to the model prediction in Figure A- 6.

148

0 1 2 3

0

5

10

15

20

25

30

Pre

ssur

e [a

tm]

Time (ms)

Pressure w/ driver insert Pressure w/o driver insert

dP*/dt = 0.075/ms

2 milliseconds of uniform test time

Figure A- 5. Comparison of pressure traces obtained with and without HPST driver insert. Pressure rise without driver insert (over 2 ms) is 15%, compared to ±2.4% pressure variation with driver insert. Driver gas is helium and driven gas is argon in these examples. Reflected shock conditions are T5 = 1698 K and P5 = 18 atm.

-3 -2 -1 0

-3-2-10123 Model

Actual Shape

Rad

ius

[cm

]

Axial Length X [m]

Diaphragm

Figure A- 6. The axial cross-section of the HPST driver insert section. The comparison is between the model prediction and the actual shape of the driver insert that has the optimal performance experimentally. The inner diameters of the driver section and the driven section are 7.5 cm and 5 cm respectively. Diaphragm location is at X = 0 and endwall is at X = −3 m.

149

APPENDIX B: ADDITIONAL H2O TIME-HISTORIES DURING H2 OXIDATION

0 1 2 3 4 5 6 70

500

1000

1500

2000

2500

Wat

er [p

pm]

Time [ms]

Figure B- 1. H2O time-history recorded at 1100 K, 1.95 atm. Test mixture 2.9% H2/0.1% O2/Ar. 0.0011 ppm of H atom was artificially included in the mixture used for the numerical simulation to match the ignition delay.

-0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00

500

1000

1500

2000

2500

Wat

er [p

pm]

Time [ms]


150

-0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.00

500

1000

1500

2000

2500

Wat

er [p

pm]

Time [ms]


0 1 2 3

0

500

1000

1500

2000

2500

Wat

er [p

pm]

Time [ms]


151

-0.5 0.0 0.5 1.0 1.5 2.00

500

1000

1500

2000

2500

Wat

er [p

pm]

Time [ms]


-0.5 0.0 0.5 1.0 1.50

500

1000

1500

2000

2500

Wat

er [p

pm]

Time [ms]


153

APPENDIX C: ADDITIONAL MECHANISM VALIDATIONS

0.00 0.02 0.04 0.06 0.08 0.10500

1000

1500

2000

2500

3000

3500

4000

Current Mechanism Konnov (2008) GRI-Mech 3.0 Li et al. (2004) O Conaire et al. (2004)H

2O C

once

ntra

tion

[ppm

]

Time [ms]

Figure C- 1. H2O time-history during the thermal decomposition of H2O2 at 1.91 atm, 1498 K. Test mixture: 2540 ppm H2O2/1234 ppm H2O/617 ppm O2/Ar. Data are experimental data from Section 6.3.

0.00 0.02 0.04 0.06 0.08 0.10

0

200

400

600

800

OH

Con

cent

ratio

n [p

pm]

Time [ms]

Current Mechanism Konnov (2008) GRI-Mech 3.0 Li et al. (2004)

O Conaire et al. (2004)

Figure C- 2. OH time-history during the thermal decomposition of H2O2 at conditions of those of Figure C- 1. Data are experimental data from Section 6.3.

154

0.80 0.85 0.90 0.95 1.00 1.0510

100

1000

Igni

tion

Del

ay T

ime

[μs]

1000/T [1/K]

Figure C- 3. Comparison between experimental data (Slack [178]) and the prediction of the current mechanism in a stoichiometric H2/air mixture at 2 atm.

0.75 0.80 0.85 0.90 0.95 1.00

10

100

1000

Igni

tion

Del

ay T

imes

[μs]

1000/T [1/K]

Figure C- 4. Comparison between experimental data (Bhaskaran et al. [179]) and the prediction of the current mechanism in a mixture consisting of 22.59% H2, 14.79% O2, balance N2 at 2.5 atm.

0.92 0.94 0.96 0.98 1.00 1.02 1.040.1

1

10

τ [O

2] mol

-μs/

dm3

1000 / T [1/K]

155

Figure C- 5. Comparison between experimental data (Skinner & Ringrose [180]) and the prediction of the current mechanism in a mixture consisting of 8% H2, 2% O2, balance Ar at 5 atm.

0.5 0.6 0.7 0.8 0.9 1.010-3

10-2

10-1

100

τ

[O2] m

ol-μ

s/dm

3

1000/T [1/K]

Figure C- 6. Comparison between experimental data (Schott & Kinsey [181]) and the prediction of the current mechanism in a mixture consisting of 1% H2, 2% O2, balance Ar at 1 atm.

0.4 0.5 0.6 0.7 0.810-4

10-3

10-2

10-1

τ

[O2] m

ol-μ

s/dm

3

1000/T [1/K]

Figure C- 7. Comparison between experimental data (Schott & Kinsey [181]) and the prediction of the current mechanism in a mixture consisting of 4% H2, 2% O2, balance Ar at 1 atm.

156

0.50 0.55 0.60 0.65 0.70 0.75101

102

Igni

tion

Del

ay T

ime

[μs]

1000/T [1/K]

Figure C- 8. Experimental data are from Petersen et al. [182]. Test mixture consisted of 0.1% H2, 0.05% O2, and balance Ar at 64 atm. Ignition time defined as the point where d(OH)/dt is maximum.

0.76 0.77 0.78 0.79 0.80 0.81 0.82 0.83 0.84 0.85101

102

103

Igni

tion

dela

y Ti

me

[μs]

1000/T [1/K]

Figure C- 9. Experimental data are from Petersen et al. [182]. Test mixture consisted of 2% H2, 1% O2, and balance Ar at 33 atm. Ignition time defined as the point where d(OH)/dt is maximum.

157

0.78 0.80 0.82 0.84 0.86 0.88 0.90 0.92 0.94 0.96101

102

103

Igni

tion

Del

ay T

ime

[μs]

1000/T [1/K]

Figure C- 10. Experimental data are from Wang et al. [183]. Test mixture consisted of 11.25% H2, 63.75% air, 25% H2O, at 4-5 atm. Ignition time defined as the onset of OH emission.

0.78 0.80 0.82 0.84 0.86 0.88 0.90 0.92

102

103

Igni

tion

Del

ay T

ime

[μs]

1000/T [1/K]


158

0.82 0.84 0.86 0.88 0.90 0.92 0.94 0.96102

103

Igni

tion

Del

ay T

ime

[μs]

1000/T [1/K]


0.0 0.1 0.2 0.3 0.40.00

0.25

0.50

0.75

1.000.0 0.1 0.2 0.3 0.4

930

950

970

990

1010

H2O

O2

Spec

ies

Mol

e Fr

actio

n (%

)

Time [s]

H2 T

Tem

pera

ture

[K]

Figure C- 13. Species profiles from a flow reactor experiment (scatters) [2]. Unburnt mixture was at 934 K, 3.02 atm and consisting of 0.95% H2, 0.49% O2, and N2 balance gas. The curves are calculated with the current mechanism by using adiabatic approximation and are shifted forward simultaneously by 0.22 s. The calculated adiabatic temperature profile is also compared with experimental values.

159

0.0 0.1 0.2 0.3 0.40.0

0.2

0.4

0.6

0.8

1.0

O2

H2O

Spec

ies

Mol

e Fr

actio

n (%

)Time [s]

H2

Figure C- 14. Species profiles from a flow reactor experiment (scatters) [2]. Unburnt mixture was at 933 K, 3.4 atm and consisting of 1.01% H2, 0.52% O2, and N2 balance gas. The curves are calculated with the current mechanism by using adiabatic approximation and are shifted forward simultaneously by 0.35 s.

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.70.0

0.2

0.4

0.6

0.8

1.0

O2

H2

Spe

cies

Mol

e Fr

actio

n (%

)

Time [s]

H2O

Figure C- 15. Species profiles from a flow reactor experiment (scatters) [2]. Unburnt mixture was at 934 K, 6.0 atm and consisting of 1.01% H2, 0.52% O2, and N2 balance gas. The curves are calculated with the current mechanism by using adiabatic approximation and are shifted forward by 0.34 s.

160

0.00 0.01 0.02 0.030.0

0.2

0.4

0.6

870

880

890

900

910

920

O2

H2

Spec

ies

Mol

e Fr

actio

n (%

)

Time [s]

T

H2O

Tem

pera

ture

[K]

Figure C- 16. Species profiles from a flow reactor experiment (scatters) [2]. Unburnt mixture was at 880 K, 0.32 atm and consisting of 0.5% H2, 0.5% O2, and N2 balance gas. The curves are calculated with the presented mechanism by using adiabatic approximation and are shifted forward by 0.069 s. The calculated adiabatic temperature profile is also compared with experimental values.

0 5 10 15 20 25 30 350.0

0.2

0.4

0.6

(b)H2 M

ole

fract

ion

(%)

Time [ms]

(a)

Figure C- 17. H2 mole fraction profiles from a flow reactor experiment (scatters) [2]. (a): 897 K, 0.60 atm, 0.50% H2/0.34% O2/N2, φ = 0.75, time shift =75 ms; (b) 896 K, 0.60 atm, 0.50% H2/0.76% O2/N2, φ = 0.33, time shift = 48 ms.

161

0.00 0.04 0.08 0.12 0.16 0.200.0

0.2

0.4

0.6

0.8

1.0

H2 M

ole

Frac

tion

(%)

Time [s]

Figure C- 18. H2 mole fraction profile from a flow reactor experiment (scatters) [2]. Unburnt mixture was at 943 K, 2.5 atm and consisting of 1% H2, 1.5% O2, and N2 balance gas. The H2 time-history was shifted forward by 0.23 s in time.

0.00 0.25 0.50 0.75 1.00 1.25 1.500.0

0.4

0.8

1.2

(b)H2 M

ole

Frac

tion

(%)

Time [s]

(a)

Figure C- 19. H2 mole fraction profiles from a flow reactor experiment (scatters) [2]. (a): 914 K, 15.7 atm, 1.18% H2/0.61% O2/N2, φ = 1, time shift = 0.27 s; (b) 914 K, 15.7 atm, 1.18% H2/2.21% O2/N2, φ = 0.27, time shift = 0.31 s.

162

-0.2 0.0 0.2 0.4 0.6 0.8 1.0-0.02

0.00

0.02

0.04

0.06

0.08

0.10

0.12

O2

Spec

ies

Mol

e Fr

actio

n (%

)

Distance [mm]

H2

H2O

Figure C- 20. The structure of a burner-stabilized flame studied using a mixture of 10% H2, 5% O2 and balance Ar (by mole) at 10 atm and 363 K. Data are from the study by Paletskii et al. [195]; and the curves are calculated using the current mechanism.

163

APPENDIX D: MECHANISM INPUT FILES IN CHEMKIN FORMAT

D.1. REACTION RATE CONSTANTS

ELEMENTS O H N AR END SPECIES H2 H O O2 OH H2O HO2 H2O2 N2 AR END REACTIONS !----------- R 1 ----------- H+O2<=>O+OH 1.040E+14 .000 15286.00 !----------- R 2 ----------- H+O2(+M)=HO2(+M) 5.590E+13 0.200 0.00 LOW / 2.650E+19 -1.300 0.0/ TROE /0.70 1.0E-30 1.0E+30 1.0E+30/ H2/2.5/ H2O/0.00/ H2O2/12.0/ AR/0.00/ O2/0.00/ H+O2(+AR)=HO2(+AR) 5.590E+13 .200 0.00 LOW / 6.810E+18 -1.200 0.0/ TROE /0.70 1.0E-30 1.0E+30 1.0E+30/ H+O2(+O2)=HO2(+O2) 5.590E+13 .200 0.00 LOW / 5.690E+18 -1.100 0.0/ TROE /0.70 1.0E-30 1.0E+30 1.0E+30/ H+O2(+H2O)=HO2(+H2O) 5.590E+13 .200 0.00 LOW / 3.700E+19 -1.000 0.0/ TROE /0.80 1.0E-30 1.0E+30 1.0E+30/ ! Bates et al. / Baulch review !----------- R 3 ----------- H2O2(+M)<=>2OH(+M) 8.590E+14 .000 48560.00 LOW / 9.550E+15 .000 42203. / TROE /1.0 1e-10 1e10 1e10/ !collider efficiency relative to Ar H2/2.5/ H2O/ 15.0/ H2O2/ 15.0/ N2/1.50/ AR/1.00/ ! high-pressure limit uses Sellevag's value !----------- R 4 ----------- OH+H2O2<=>HO2+H2O 7.586E+13 .000 7269.00 DUPLICATE OH+H2O2<=>HO2+H2O 1.738E+12 .000 318.00 DUPLICATE !----------- R 5 ----------- OH+HO2<=>H2O+O2 2.890E+13 .000 -500.00 !----------- R 6 ----------- 2HO2<=>O2+H2O2 1.300E+11 .000 -1603.00 DUPLICATE 2HO2<=>O2+H2O2 4.200E+14 .000 11980.00 DUPLICATE !----------- R 7 ----------- H2O+M<=>H+OH+M 6.060E+27 -3.310 120770.00 !relative to AR O2/ 1.50/ H2O/ 0.00/ N2/ 2.00/ H2/ 3.00/ H2O+H2O<=>OH+H+H2O 1.000E+26 -2.440 120160.00 !----------- R 8 ----------- OH+OH<=>H2O+O 3.570E+04 2.400 -2111.00 ! Wooldridge et al. / Sutherland et al. / Hong et al. !----------- R 9 ----------- O+H2<=>H+OH 3.820E+12 .000 7948.00 DUPLICATE O+H2<=>H+OH 8.790E+14 0.000 19170.00 DUPLICATE

164

!----------- R10 ----------- OH+H2<=>H+H2O 2.170E+08 1.520 3457.00 !----------- R11 ----------- !Li et al./O Conaire et al. H+HO2<=>OH+OH 7.080E+13 .000 300.00 !----------- R12 ----------- H+HO2<=>H2O+O 1.450E+12 .000 .00 !----------- R13 ----------- !J.V. Michael et al. H+HO2<=>H2+O2 3.660E+06 2.087 -1450.00 !----------- R14 ----------- O+HO2<=>OH+O2 1.630E+13 .000 -445.00 !----------- R15 ----------- H2O2+H<=>HO2+H2 1.210E+07 2.000 5200.00 !----------- R16 ----------- H2O2+H<=>H2O+OH 1.020E+13 .000 3577.00 !----------- R17 ----------- H2O2+O<=>OH+HO2 8.430E+11 .000 3970.00 !----------- R18 ----------- H2+M<=>H+H+M 5.840E+18 -1.100 104380.00 H2/0.00/ H2O/14.4/ H2O2/14.4/ AR/ 1.0/ O2/0.00/ N2/0.00/ H2+H2<=>H+H+H2 9.030E+14 .000 96070.00 H2+N2<=>H+H+N2 4.580E+19 -1.400 104380.00 H2+O2<=>H+H+O2 4.580E+19 -1.400 104380.00 !----------- R19 ----------- O+O+M<=>O2+M 6.160E+15 -0.500 .00 H2/ 2.5/ H2O/12.0/ H2O2/12.0/ AR/ 0.0/ O+O+AR<=>O2+AR 1.890E+13 .000 -1788.00 !----------- R20 ----------- O+H+M<=>OH+M 4.710E+18 -1.000 .00 H2/ 2.5/ H2O/12.0/ H2O2/12.0/ AR/ 0.75/ END

D.2. THERMODYNAMIC DATA

THERMO 300.000 1000.000 5000.000 O L 1/90O 1 00 00 00G 200.000 3500.000 1000.000 1 2.56942078E+00-8.59741137E-05 4.19484589E-08-1.00177799E-11 1.22833691E-15 2 2.92175791E+04 4.78433864E+00 3.16826710E+00-3.27931884E-03 6.64306396E-06 3 -6.12806624E-09 2.11265971E-12 2.91222592E+04 2.05193346E+00 4 O2 TPIS89O 2 00 00 00G 200.000 3500.000 1000.000 1 3.28253784E+00 1.48308754E-03-7.57966669E-07 2.09470555E-10-2.16717794E-14 2 -1.08845772E+03 5.45323129E+00 3.78245636E+00-2.99673416E-03 9.84730201E-06 3 -9.68129509E-09 3.24372837E-12-1.06394356E+03 3.65767573E+00 4 H L 7/88H 1 00 00 00G 200.000 3500.000 1000.000 1 2.50000001E+00-2.30842973E-11 1.61561948E-14-4.73515235E-18 4.98197357E-22 2 2.54736599E+04-4.46682914E-01 2.50000000E+00 7.05332819E-13-1.99591964E-15 3 2.30081632E-18-9.27732332E-22 2.54736599E+04-4.46682853E-01 4 H2 TPIS78H 2 00 00 00G 200.000 3500.000 1000.000 1 3.33727920E+00-4.94024731E-05 4.99456778E-07-1.79566394E-10 2.00255376E-14 2 -9.50158922E+02-3.20502331E+00 2.34433112E+00 7.98052075E-03-1.94781510E-05 3 2.01572094E-08-7.37611761E-12-9.17935173E+02 6.83010238E-01 4 OH RUS 78O 1H 1 00 00G 200.000 3500.000 1000.000 1 3.09288767E+00 5.48429716E-04 1.26505228E-07-8.79461556E-11 1.17412376E-14 2 3.61585000E+03 4.47669610E+00 3.99201543E+00-2.40131752E-03 4.61793841E-06 3 -3.88113333E-09 1.36411470E-12 3.37227356E+03-1.03925458E-01 4 H2O L 8/89H 2O 1 00 00G 200.000 3500.000 1000.000 1 3.03399249E+00 2.17691804E-03-1.64072518E-07-9.70419870E-11 1.68200992E-14 2 -3.00042971E+04 4.96677010E+00 4.19864056E+00-2.03643410E-03 6.52040211E-06 3 -5.48797062E-09 1.77197817E-12-3.02937267E+04-8.49032208E-01 4 HO2 T 1/09H 1.O 2. 0. 0.G 200.000 5000.000 1000. 1 4.17228741E+00 1.88117627E-03-3.46277286E-07 1.94657549E-11 1.76256905E-16 2 3.10206839E+01 2.95767672E+00 4.30179807E+00-4.74912097E-03 2.11582905E-05 3 -2.42763914E-08 9.29225225E-12 2.64018485E+02 3.71666220E+00 1.47886045E+03 4 H2O2 L 7/88H 2O 2 00 00G 200.000 3500.000 1000.000 1 4.16500285E+00 4.90831694E-03-1.90139225E-06 3.71185986E-10-2.87908305E-14 2 -1.78617877E+04 2.91615662E+00 4.27611269E+00-5.42822417E-04 1.67335701E-05 3

165

-2.15770813E-08 8.62454363E-12-1.77025821E+04 3.43505074E+00 4 N2 121286N 2 G 300.000 5000.000 1000.000 1 0.02926640E+02 0.14879768E-02-0.05684760E-05 0.10097038E-09-0.06753351E-13 2 -0.09227977E+04 0.05980528E+02 0.03298677E+02 0.14082404E-02-0.03963222E-04 3 0.05641515E-07-0.02444854E-10-0.10208999E+04 0.03950372E+02 4 AR 120186AR 1 G 300.000 5000.000 1000.000 1 0.02500000E+02 0.00000000E+00 0.00000000E+00 0.00000000E+00 0.00000000E+00 2 -0.07453750E+04 0.04366000E+02 0.02500000E+02 0.00000000E+00 0.00000000E+00 3 0.00000000E+00 0.00000000E+00-0.07453750E+04 0.04366000E+02 4 END

167

BIBLIOGRAPHY

[1] C.K. Westbrook, F.L. Dryer, Prog. Energy Combust. Sci. 10 (1984) 1–57.

[2] M.A. Mueller, T.J. Kim, R.A. Yetter, F.L. Dryer, Int. J. Chem. Kinet. 31 (1999)

113–125.

[3] G. Del Álamo, F.A. Williams, A.L. Sánchez, Combust. Sci. Tech. 176 (2004) 1599–

1626.

[4] J. Li, Z. Zhao, A. Kazakov, F.L. Dryer, Int. J. Chem. Kinet. 36 (2004) 566–575.

[5] M. Ó Conaire, H.J. Curran, J.M. Simmie, W.J. Pitz, C.K. Westbrook, Int. J. Chem.

Kinet. 36 (2004) 603–622.

[6] A.A. Konnov, Combust. Flame 152 (2008) 507–528.

[7] I.Gy. Zsély, J. Zádor, T. Turányi, Proc. Combust. Inst. 30 (2005) 1273–1281.

[8] S.G. Davis, A.V. Joshi, H. Wang, F. Egolfopoulos, Proc. Combust. Inst. 30 (2005)

1283–1292.

[9] P. Saxena, F.A. Williams, Combust. Flame 145 (2006) 316–323.

[10] H. Sun, S.I. Yang, G. Jomaas, C.K. Law, Proc. Combust. Inst. 31 (2007) 439–446.

[11] H. Mirels, Proceedings of the Eighth International Shock Tube Symposium, edited

by J.L. Stollery, A.G. Gaydon, P.R. Owen, Chapman and Hall, London, 6/2-6/30

(1972).

[12] E.L. Petersen, R.K. Hanson, Shock Waves 10 (2001) 405–420.

[13] D.R. White, J. Fluid Mechanics 4 (1958) 585–599.

[14] R.S. Hickman, L.C. Farrar, Phys. Fluids 18 (1975) 1249–1252.

168

[15] E.L. Petersen, A shock tube and diagnostics for chemistry measurements at elevated

pressures with application to methane ignition. Ph.D. Thesis, Department of

Mechanical Engineering, Stanford University (1998).

[16] G.A. Pang, D.F. Davidson, R.K. Hanson, Proc. Combust. Inst. 32 (2009) 181–188.

[17] H. Li, Z. Owens, D.F. Davidson, R.K. Hanson, Int. J. Chem. Kinet. 40 (2008) 189–

198.

[18] G.P. Smith, D.M. Golden, M. Frenklach, N.W. Moriarty, B. Eitneer, M.

Goldenberg, C.T. Bowman, R.K. Hanson, S. Song, W.C. Gardiner, V.V. Lissianski,

Z. Qin, available at: http://www.me.berkeley.edu/gri-mech, accessed July 10, 2010.

[19] D.A. Masten, R.K. Hanson, C.T. Bowman, J. Phys. Chem. 94 (1990) 7119-7128.

[20] A.N. Pirraglia, J.V. Michael, J.W. Sutherland, R.B. Klemm, J. Phys. Chem. 93

(1989) 282-291.

[21] C. Westbrook, Proc. Combust. Institute 28 (2000) 1563 – 1577.

[22] E. Meyer, H.A. Olschewski, J. Troe, H. Gg. Wagner, Proc. Combust. Inst. 12

(1969) 345−355.

[23] H. Kijewski, J. Troe, Int. J. Chem. Kinet. 3 (1971) 223−235.

[24] Ch. Kappel, K. Luther, J. Troe, Phys. Chem. Chem. Phys. 4 (2002) 4392−4398.

[25] H. Hippler, J. Troe, Chem. Phys. Lett. 192 (1992) 333 – 337.

[26] H. Hippler, H. Neunaber, J. Troe, J. Chem. Phys. 103 (1995) 3510 – 3516.

[27] N.K. Srinivasan, M.-C. Su, J.W. Sutherland, J.V. Michael, B. Ruscic, J. Phys.

Chem. A 110 (2006) 6602–6607.

[28] L.Z. Dumitrescu, Physics of Fluids 15 (1972) 207–209.

169

[29] W. Ludwig, B. Brandt, G. Friedrichs, F. Temps, J. Phys. Chem. A 110 (2006)

3330−3337.

[30] W. Ludwig, Kinetics of the Reaction C2H5+HO2 by Time-Resolved Mass

Spectrometry. Ph.D. Dissertation, Institut für Physikalische Chemie, Christian-

Albrechts-Universität zu Kiel, Kiel, Germany, 2004.

[31] A. Farooq, J.B. Jeffries, R.K. Hanson, Meas. Sci. Technol. 19 (2008) 1–11

[32] H. Li, A. Farooq, J.B. Jeffries, R.K. Hanson, App. Physics B 89 (2007) 407–416.

[33] V. Venkatesh, D.F. Davidson, R.K. Hanson, Proc. Comb. Inst. 30 (2005) 1155–

1163.

[34] V. Vasudevan, D.F. Davidson, R.K. Hanson, J. Phys. Chem. A 109 (2005) 3352–

3359.

[35] D.F. Davidson, Z. Hong, G.L. Pilla, A. Farooq, R.D. Cook, R.K. Hanson,

Combustion and Flame, in press (doi: doi:10.1016/j.combustflame.2010.01.004).

[36] J.T. Herbon, R.K. Hanson, D.M. Golden, C.T. Bowman, Proc. Combust. Inst. 29

(2003) 1201–1208.

[37] J.T. Herbon, Shock Tube Measurements of CH3+O2 Kinetics and the Heat of

Formation of the OH Radical. Ph.D. Dissertation, Stanford University, Stanford,

CA, 2004. http://thermosciences.stanford.edu/pdf/TSD-153.pdf, accessed July 10,

2010.

[38] M.A. Oehlschlaeger, D.F. Davidson, R.K. Hanson, J. Physical Chemistry A 108

(2004) 4247–4253.

[39] R.L. Petrov, J. Engineering Physics 31 (1976) 1106–1110.

[40] A.R. Amadio, M.W. Crofton, E.L. Petersen, Shock Waves 16 (2006) 157–165.

[41] Z. Hong, D.F. Davidson, R.K. Hanson, Shock Waves 19 (2009) 331–336.

170

[42] M. Nishida, Shock Tubes. In: Handbook of Shock Waves, Vol. 1, pp. 553-585,

Academic, New York (2001).

[43] W.J. Hooker, Physics of Fluids 4 (1961) 1451–1463.

[44] R.J. Emrich, C.W. Curtis, J. Applied Physics 24 (1953) 360–363.

[45] K.J. Badcock, Int. J. Numerical Methods in Fluids 14 (1992) 1151–1171.

[46] E.L. Petersen, R.K. Hanson, AIAA J. 41 (2003) 1314–1322.

[47] R.A. Alpher, D.R. White, J. Fluid Mechanics 3 (1958) 457–470.

[48] http://silver.neep.wisc.edu/~shock/tools/xt.html, accessed 3 February 2009.

[49] A. Farooq, J.B. Jeffries, R.K. Hanson, Applied Physics B 96 (2009) 161–173.

[50] G.B. Rieker, H. Li, X. Liu, J.T.C. Liu, J.B. Jeffries, R.K. Hanson, Proc. Combust.

Inst., 31 (2007) 3041-3049.

[51] D.W. Mattison, J.B. Jeffries, J.B. R.K. Hanson, R.R. Steeper, Proc. Combust. Inst.

31 (2007) 791-798.

[52] G.B. Rieker, J.B. Jeffries, R.K. Hanson, T. Mathur, M.R. Gruber, C.D. Carter, Proc.

Combust. Inst. 32 (2009) 831 – 838.

[53] N. Docquier, S. Candel, Prog. Energy Combust. Sci. 28 (2002) 107 – 150.

[54] A. Farooq, J.B. Jeffries, R.K. Hanson, Meas. Sci. Technol. 19 (2008) 075604.

[55] A. Goldman, R.R. Gamache, A. Perrin, J.M. Flaud, C.P. Rinsland, L.S. Rothman, J.

Quant. Spectrosc. Radiat. Transfer 66 (2000) 455–486.

[56] E.A. Barbour, Modeling and Laser-Based Sensing of Pulsed Detonation Engines.

Ph.D. Dissertation, Stanford University, Stanford, CA, 2009.

http://thermosciences.stanford.edu/pdf/TSD-177.pdf (accessed August 26, 2010).

171

[57] M.S. Wooldridge, R.K. Hanson, C.T. Bowman, Int. J. Chem. Kin. 26 (1994) 389–

401.

[58] V. Vasudevan, D.F. Davidson, R.K. Hanson, J. Phys. Chem. A 109 (2005) 3352–

3359.

[59] D.F. Davidson, M.A. Oehlschlaeger, J.T. Herbon, R.K. Hanson, Proc. Combust.

Inst. 29 (2002) 1295 – 1301.

[60] D.L. Baulch, D.D. Drysdale, D.G. Horne, A.C. Lloyd, Evaluated Kinetic Data for

High Temperature Reactions, vol. 1. Butterworths, London, 1972.

[61] G. L. Schott, Combust. Flame 21 (1973) 357-370.

[62] K.A. Pamidimukkala, G.B. Skinner, Thirteenth International Symposium on Shock

Waves and Shock Tubes, SUNY, Albany, 1981, p. 585-592.

[63] P. Frank, Th. Just, Ber. Bunsenges. Phys. Chem. 89 (1985) 181-187.

[64] N. Fujii, K. S. Shin, Chem. Phys. Lett. 151 (1988) 461-465.

[65] K.S. Shin, J.V. Michael, J. Chem. Phys. 95 (1991) 262-273.

[66] T. Yuan, C. Wang, C.-L. Yu, M. Frenklach, M. J. Rabinowitz, J. Phys. Chem. 95

(1991) 1258-1265.

[67] H. Du, J. P. Hessler, J. Chem. Phys. 96 (1991) 1077-1092.

[68] H. Yang, W. C. Gardiner, K. S. Shin, N. Fujii, Chem. Phys. Lett. 231 (1994) 449-

453.

[69] C.-L. Yu, M. Frenklach, D. A. Masten, R. K. Hanson, C. T. Bowman, J. Phys.

Chem. 98 (1994) 4770-4771.

[70] S. Ryu, S. M. Hwang, M. J. Rabinowitz, J. Phys. Chem. 99 (1995) 13984-13991.

172

[71] J. Warnatz, in: W. C. Gardiner (Ed.), Combustion Chemistry, Springer-Verlag, New

York, 1984.

[72] N. Cohen, K. R. Westberg, J. Phys. Chem. Ref. Data 12 (1983) 531-590.

[73] S. M. Hwang, Si-Ok Ryu, K.J. De Witt, M.J. Rabinowitz, Chem. Phys. Lett. 408

(2005) 107-111.

[74] A.E. Lutz, R.J. Kee, J.A. Miller, Senkin: A FORTRAN Program for Predicting

Homogeneous Gas Phase Chemical Kinetics with Sensitivity Analysis, Report No.

SAND87-8248, Sandia National Laboratory, 1988.

[75] B. Ruscic, A.F. Wagner, L.B. Harding, R.L. Asher, D. Feller, D.A. Dixon, K.A.

Peterson, Y. Song, X.M. Qian, C.Y. Ng, J.B. Liu, W.W. Chen, J. Phys. Chem. A

106 (2002) 2727–2747.

[76] B. Ruscic, R.E. Pinzon, M.E. Morton, N.K. Srinivasan, M.-C. Su, J.W. Sutherland,

J.V. Michael, J. Phys. Chem. A 110 (2006) 6592-6601.

[77] Z. Hong, S.S. Vasu, D.F. Davidson, R.K. Hanson, J. Phys. Chem. A 114 (2010)

5520-5525.

[78] Z. Hong, R.D. Cook, D.F. Davidson, R.K. Hanson, J. Phys. Chem. A 114 (2010)

5718-5727.

[79] Z. Hong, A. Farooq, E. A. Barbour, D. F. Davidson, R. K. Hanson, J. Phys. Chem.

A.113 (2009) 12919-12925.

[80] D.L. Baulch, C.T. Bowman, C.J. Cobos, R.A. Cox, Th. Just, J.A. Kerr, M.J. Pilling,

D. Stocker, J. Troe, W. Tsang, R.W. Walker and J. Warnatz, J. Phys. Chem. Ref.

Data 34 (2005) 757-1397.

[81] K. Gkagkas and R.P.Lindstedt, Combust. Theory Modelling 13 (2009) 607-643.

[82] C.T. Bowman, personal communication (November 23, 2010). “The rate constant

of the reaction O + H2 H + OH can be expressed by 8.97 × 103 T2.90 exp(-3180/T)

173

[cm3mol-1s-1] over the range 297 - 3500 K. Reliability of this expression is Δlog k =

± 0.03 over the same temperature range”.

[83] B. Sirjean, E. Dames, D.A. Sheen, X.-Q. You, C. Sung, A.T. Holley, F.N.

Egolfopoulos, H. Wang, S.S. Vasu, D.F. Davidson, R.K. Hanson, H. Pitsch, C.T.

Bowman, A. Kelley, C.K. Law, W. Tsang, N.P. Cernansky, D.L. Miller, A. Violi,

R.P. Lindstedt, available at http://melchior.usc.edu/JetSurF/Version0_2/Index.html.

[84] R.X. Fernandes, K. Luther, J. Troe, V.G. Ushakov, Phys. Chem. Chem. Phys. 10

(2008) 4313-4321.

[85] M.W. Chase Jr., J.R. Curnutt, J.R. Downey Jr., R.A. McDonald, A.N. Syverud,

E.A. Valenzuela, J. Phys. Chem. Ref. Data 11 (1982) 695-940.

[86] M.J. Howard, I.W. Smith, J. Chem. Soc., Faraday Trans. 2 77 (1981) 977-1008.

[87] R.S. Lewis, R.T. Waston, J. Phys. Chem. 84 (1980) 3495-3503.

[88] J. Troe, Proc. Combust. Inst. 22 (1988) 843- 862.

[89] S. Lin, H. Guo, P. Honvault, C. Xu, D. Xie, J. Chem. Phys. 128 (2008) 014303.

[90] A.J.C. Varandas, J. Brandão, M.R. Pastrana, J. Chem. Phys. 96 (1992) 5137-5150.

[91] T.C. Germann, W.H. Miller, J. Phys. Chem. A 101 (1997) 6358-6367.

[92] J.A. Miller, M.J. Pilling, J. Troe, Proc. Combust. Inst. 30 (2005) 43-88.

[93] R.R. Baldwin, D. Brattan, Proc. Combust. Inst. 8 (1991) 110−119.

[94] C.K. McLane, J. Chem. Phys. 17 (1949) 379−385.

[95] C.N. Satterfield, T.W. Stein, J. Phys. Chem. 61 (1957) 537−540.

[96] W. Forst, Can. J. Chem. 36 (1958) 1308−1319.

[97] D.E. Hoare, J.B. Protheroe, A.D. Walsh, Trans. Faraday Soc. 55 (1959) 548–557.

174

[98] H. Kijewski, J. Troe, Helv. Chim. Acta 55 (1972) 205−213.

[99] O.J. Nielsen, M.S. Johnson, T.J. Wallington, L.K. Christensen, J. Platz, Int. J.

Chem. Kinet. 34 (2002) 283−291.

[100] D.W. Trainor, C.W. von Rosenberg Jr., J. Chem. Phys. 61 (1974) 1010−1015.

[101] R. Zellner, F. Ewig, R. Paschke, G. Wagner, J. Phys. Chem. 92 (1988) 4184−4190.

[102] R. Forster, M. Frost, D. Fulle, H.F. Hamann, H. Hippler, A. Schlepegrell, J. Troe, J.

Chem. Phys. 103 (1995) 2949−2958.

[103] D. Fulle, H.F. Hamann, H. Hippler, J. Troe, J. Chem. Phys. 105 (1996) 1001−1006.

[104] J.J.Van Laar, Z. Physik. Chem. 72 (1910) 723−751.

[105] S.R. Sellevåg, Y. Georgievskii, J.A. Miller, J. Phy. Chem. A 113 (2009) 4457-4467.

[106] J. Troe, V.G. Ushakov, Phys. Chem. Chem. Phys. 10 (2008) 3915-3924.

[107] J. Troe, Combust. Flame (2010), doi: 10.1016/j.combustflame.2010.08.013.

[108] L. Bouwer, C.J. Cobos, J. Troe, H.-R. Dübal, F.F. Crim, J. Chem. Phys. 86 (1987)

6171−6182.

[109] A. Burcat, B. Ruscic, Third Millennium Ideal Gas and Condensed Phase:

Thermochemical Database for Combustion; Joint Argonne National Laboratories

report ANL-05/20 and a Technion Aerospace Report TAE 960; Argonne, Illinois,

2005.

[110] R.C. Millikan, D.R. White, J. Chem. Phys. 39 (1963) 3209−3213.

[111] R.E. Center, J.F. Newton, J. Chem. Phys. 68 (1978) 3327−3333.

[112] P.H. Wine, D.H. Semmes, A.R. Ravishankara, J. Chem. Phys. 75 (1981) 4390 –

4395.

175

[113] G.L. Vaghjiani, A.R. Ravishankara, N. Cohen, J. Chem. Phys. 93 (1989) 7833 –

7837.

[114] M. Kurylo, J.L. Murphy, G.S. Haller, K.D. Cornett, Int. J. Chem. Kin. 14 (1982)

1149 – 1161.

[115] L.F. Keyser, J. Phys. Chem. 84 (1980) 1659 – 1663.

[116] E. Jiménez, T. Gierczak, H. Stark, J.B. Burkholder, A.R. Ravishankara. J. Phys.

Chem. A 108 (2004) 1139–1149.

[117] J.J. Lamb, L.T. Molina, C.A. Smith, M.J. Molina, J. Phys. Chem. 87 (1980) 4467–

4470.

[118] U.C. Sridharan, B. Reimann, F. Kaufman, J. Chem. Phys. 73 (1980) 1286 – 1293.

[119] A.B. Vakhtin, D.C. McCabe, A.R. Ravishankara, S.R. Leone, J. Phys. Chem. A 107

(2003) 10642 – 10647.

[120] A. Mellouki, S. Teton, G. Laverdet, A. Quilgars, G. Le Bras, J. Chim. Phys. 91

(1994) 473 – 487.

[121] S.P. Sander, R.R. Friedl, A.R. Ravishankara, D.M. Golden, C.E. Kolb, M.J. Kurylo,

M.J. Molina, G.K. Moortgat, B.J. Finlayson-Pitts, P.H. Wine, R.E. Huie, V.L.

Orkin, Chemical Kinetics and Photochemical Data for Use in Atmospheric Studies

Evaluation Number 15, Jet Propulsion Laboratory, California Institute of

Technology, Pasadena, CA, 2006. http://jpldataeval.jpl.nasa.gov/ (accessed

September 24, 2009).

[122] R. Atkinson, D.L. Baulch, R.A. Cox, J.N. Crowley, R.F. Hampson, R.G. Hynes,

M.E. Jenkin, M.J. Rossi, J. Troe, Atmos. Chem. Phys. 4 (2004) 1461 – 1738.

[123] G. Box, R.D. Meyer, J. Res. Nat. Bur. Stand. 90 (1985) 495 – 500.

[124] M. Frenklach, H. Wang, M.J. Rabinowitz, Prog. Energy Combust. Sci. 18 (1992)

47–73.

176

[125] J.W. Sutherland, P.M. Patterson, R.B. Klemm, Proc. Combust. Inst. 23 (1991) 51–

57.

[126] B. Ginovska, D.M. Camaioni, M. Dupuis, J. Chem. Phys. 127 (2007) 084309.

[127] J. Troe, Ber. Bunsen-Ges. 73 (1969) 946–952.

[128] J.V. Michael, Prog. Energy Combust. Sci. 18 (1992) 327 – 347.

[129] A. Lifshitz, J.V. Michael, Proc. Combust. Inst. 23 (1991) 59–67.

[130] J. Peeters, G. Mahnew, Proc. Combust. Inst. 14 (1973) 133–146.

[131] E.L. Petersen, D.F. Davidson, R.K. Hanson, Combust. Flame 117 (1999) 272–290.

[132] J.M. Goodings, A.N. Hayhurst, J. Chem. Soc. Faraday Trans. 2 84 (1988) 745–762.

[133] K. Gkagkas, R.P. Lindstedt, Proc. Combust. Inst. 31 (2007) 1559–1566.

[134] S.S. Vasu, D.F. Davidson, R.K. Hanson, Comb. Flame 156 (2009) 736–749.

[135] E.L. Petersen, M. Röhrig, D.F. Davidson, R.K. Hanson, C.T. Bowman, Proc.

Combust. Inst. 26 (1996) 799–806.

[136] J.J. Schwab, W.H. Brune, J.G. Anderson, J. Phys. Chem. 93 (1989) 1030–1035.

[137] L.F. Keyser, J. Phys. Chem. 92 (1988) 1193–1200.

[138] U.C. Sridharan, L.X. Qiu, F. Kaufman, J. Phys. Chem. 88 (1984) 1281–1282.

[139] R.-R. Lii, R.A. Gorse Jr., M.C. Sauer Jr., S. Gordon, J. Phys. Chem. 84 (1980) 819–

821.

[140] R.A. Cox, J.P. Burrows, T.J. Wallington, Chem. Phys. Letters 84 (1981) 217–221.

[141] V.B. Rozenshtein, Yu.M. Gershenzon, S.D. Il’in, O.P. Kishkovitch, Chem. Phys.

Letter 112 (1984) 473–478.

177

[142] H. Hippler, J. Troe, J. Willner, J. Chem. Phys. 93 (1990) 1755–1760.

[143] R.T.V. Kung, R.E. Center, J. Chem. Phys. 62 (1975) 2187–2194.

[144] Z. Hong, D.F. Davidson, E.A. Barbour, R.K. Hanson, Proc. Combust. Inst. 33

(2010), in press (doi: 10.1016/j.proci.2010.05.101).

[145] J.V. Michael, J.W. Sutherland, J. Phys. Chem. 92 (1988) 3853–3857.

[146] D.L. Baulch, C.J. Cobos, R.A. Cox, C. Esser, P. Frank, Th. Just, J.A. Kerr, M.J.

Pilling, J. Troe, R.W. Walker, J. Warnatz, J. Phys. Chem. Ref. Data 21 (1992) 411.

[147] D.L. Baulch, C.J. Cobos, R.A. Cox, P. Frank, G. Hayman, Th. Just, J.A. Kerr, T.

Murrells, M.J. Pilling, J. Troe, R.W. Walker, J. Warnatz, J. Phys. Chem. Ref. Data

23 (1994) 847–1033.

[148] C. Gonzalez, J. Theisen, L. Zhu, B. Schlegel, W.L. Hase, E.W. Kaiser, J. Phys.

Chem. 96 (1992) 1767–1774.

[149] C. Gonzalez, J. Theisen, L. Zhu, B. Schlegel, W.L. Hase, E.W. Kaiser, J. Phys.

Chem. 95 (1991) 6784 – 6792.

[150] C.F. Jackels, D.H. Phillips, J. Chem. Phys. 84 (1986) 5013–5024.

[151] D.W. Toohey, J.G. Anderson, J. Phys. Chem. 93 (1989) 1049–1058.

[152] D. Cremer, J. Chem. Phys. 69 (1978) 4456–4471.

[153] D.C. Clary, H.J. Werner, Chem. Phys. Lett. 112 (1984) 346 – 350.

[154] J.V. Michael, J.W. Sutherland, L.B. Harding, A.F. Wagner, Proc. Combust. Inst. 28

(2000) 1471–1478.

[155] M.P. Burke, M. Chaos, F.L. Dryer, Y. Ju, Combust. Flame 157 (2010) 618–631.

[156] T.C. Germann, W.H. Willer, J. Phys. Chem. A 101 (1997) 6358–6367.

178

[157] C.B. Kretschmer, Investigation of Atomic Oxygen Recombination Rates, Aerojet-

General Corporation Report 1611 (AFOSR-TR-59-62), AD 217008, May 1959.

[158] B. Sirjean, E. Dames, D.A. Sheen, F.N. Egolfopoulos, H. Wang, D.F. Davidson,

R.K. Hanson, H. Pitsch, C.T. Bowman, C.K. Law, W. Tsang, N.P. Cernansky, D.L.

Miller, A. Violi, R.P. Lindstedt, A high-temperature chemical kinetic model of n-

alkane, cyclohexane, and methyl-, ethyl-, n-propyl and n-butyl-cyclohexane

oxidation at high temperatures, http://melchior.usc.edu/JetSurF/JetSurF1.1,

accessed June 2010.

[159] R.W. Bates, D.M. Golden, R.K. Hanson, C.T. Bowman, Phys. Chem. Chem. Phys.

3 (2001) 2337–2342.

[160] J.V. Michael, M.-C. Su, J.W. Sutherland, J.J. Carroll, A.F. Wagner, J. Phys. Chem.

A 106 (2002) 5297–5313.

[161] J.V. Michael, J.W. Sutherland, L.B. Harding, A.F. Wagner, Proc. Combust. Inst. 28

(2000) 1471–1478.

[162] N.K. Srinivasan, J.V. Michael, Int. J. Chem. Kinet. 38 (2006) 211–219.

[163] W. Tsang, R.F. Hampson, J. Phys. Chem. Ref. Data 15 (1986) 1087–1279.

[164] C.J. Cobos, H. Hippler, J. Troe, J. Phys. Chem. 89 (1985) 342–349.

[165] J. Hahn, L. Kransnoperov, K. Luther, J. Troe, Phys. Chem. Chem. Phys. 6 (2004)

1997–1999.

[166] L.B. Harding, J. Troe, V.G. Ushakov, Phys. Chem. Chem. Phys. 2 (2000) 631–642.

[167] R. Atkinson, D.L. Baulch, R.A. Cox, J.N. Crowley, R.F. Hampson, R.G. Hynes,

M.E. Jenkins, M.J. Rossi, J. Troe, Atoms. Chem. Phys. 4 (2004) 1461–1738.

[168] S.P. Sander, R.R. Friedl, D.M. Golden, M.J. Kurylo, R.E. Huie, V.L. Orkin, G.K.

Moortgat, A.R. Ravishankara, C.E. Kolb, M.J. Molina, B.J. Finlayson-Pitts, JPL

Publ. 02-25, 2003 (NASA-JPL, 2003).

179

[169] S.R. Sellevåg, Y. Georgievskii, J.A. Miller, J. Phys. Chem. A 112 (2008) 5085–

5095.

[170] J.D. Mertens, D.M. Kalitan, A.B. Barrett, E.L. Petersen, Proc. Combust. Inst. 32

(2009) 295–303.

[171] V. Naudet, S. Javoy, C.E. Paillard, Combust. Sci. Tech. 164 (2001) 113–128.

[172] S. Javoy, V. Naudet, S. Abid, C.E. Paillard, Exp. Therm. Fluid Sci. 27 (2003) 371–

377.

[173] R.R. Baldwin, R.W. Walker, J. Chem. Soc. Faraday Trans. 1 75 (1979) 140–154.

[174] W. Hack, A.W. Preuss, H.Gg. Wagner, K. Hoyermann, Ber. Bunsen-Ges. Phys.

Chem. 83 (1979) 212–217.

[175] B.A. Thrush, J.P.T. Wilkinson, Chem. Phys. Lett. 84 (1981) 17–19.

[176] U.C. Sridharan, L.X. Qiu, F. Kaufman, J. Phys. Chem. 86 (1982) 4569–4574.

[177] L.F. Keyser, J. Phys. Chem. 90 (1986) 2994–3003.

[178] M.W. Slack, Combust. Flame 28 (1977) 241–249.

[179] K.A. Bhaskaran, M.C. Gupta, Th. Just, Combust. Flame 21 (1973) 45–48.

[180] G.B. Skinner, G.H. Ringrose, J. Chem. Phys. 42 (1965) 2190–2192.

[181] G.L. Schott, J.L. Kinsey, J. Chem. Phys. 29 (1958) 1177–1182.

[182] E.L. Petersen, D.F. Davidson, M. Röhrig, R.K. Hanson, in: B. Sturtevant, J.E.

Shepherd, H.G. Hornung (Eds.), Proceedings of the twentieth International

Symposium on Shock Waves, Pasadena, California, 1995, p. 941–946.

[183] B.L. Wang, H. Olivier, H. Grönig, Combust. Flame 133 (2003) 93–106.

[184] C.K. Wu, C.K. Law, Proc. Combust. Inst. 20 (1984) 1941–1949.

180

[185] O.C. Kwon, G.M. Faeth, Combust. Flame 124 (2001) 590–610.

[186] C.M. Vagelopoulos, F.N. Egolfopoulos, C.K. Law, Proc. Combust. Inst. 25 (1994)

1341–1347.

[187] D.R. Dowdy, D.B. Smith, S.C. Taylor, A. Williams, Proc. Combust. Inst. 23 (1990)

1341–1347.

[188] S.D. Tse, D.L. Zhu, C.K. Law, Proc. Combust. Inst. 28 (2000) 1793–1800.

[189] CHEMKIN-PRO, (Reaction Design, San Diego, California, USA, 2008)

<http://www.reactiondesign.com>.

[190] F.N. Egolfopoulos, C.K. Law, Proc. Combust. Inst. 23 (1990) 333–340.

[191] R.T.E. Hermanns, A.A. Konnov, R.J.M. Bastiaans, L.P.H. de Goey, Energy Fuels

21 (2007) 1977–1981.

[192] F.N. Egolfopoulos, C.K. Law, Combust. Flame 80 (1990) 7–16.

[193] G. Dixon-Lewis, M.M. Sutton, A. Williams, Proc. Roy. Soc. Lond. A. 317 (1970)

227–234.

[194] J. Vandooren, J. Bian, Proc. Combust. Inst. 23 (1990) 341–346.

[195] A.A. Paletskii, L.V. Kuibida, T.A. Bolshova, O.P. Korobeinichev, R.M. Fristrom,

Combustion, Explosion, and Shock Waves 32 (1996) 245–250.

an improved hydrogen/oxygen mechanism based on …v abstract h2/o2 combustion chemistry is the core...

Documents