MASTER'S THESIS

Reduced Kinetic Mechanism of Methane Oxidation for Rocket Applications

Alan Kong 2015

Master of Science (120 credits) Space Engineering - Space Master

Luleå University of Technology Department of Computer Science, Electrical and Space Engineering Reduced Kinetic Mechanism of Methane Oxidation for Rocket Applications

Author: External Supervisor: Fa Quan Alan Kong Dr. Victor Zhukov Examiner: Dr. Victoria Barabash

A thesis submitted in the partial fulfilment of the requirements for the Joint European Master in Space Science and Technology

Lule˚aUniversity of Technology Universit´ePaul Sabatier Toulouse III Department of Computer Science, Facult´edes Sciences et d’Ing´enierie Electrical and Space Engineering D´epartement de Physique Division of Space Technology October 2015 Abstract

Methane, which has properties intermediate between hydrogen and kerosene, is a fuel of several developed and designed rocket engines. Detailed kinetic mechanisms of methane oxidation consist of around 200 or more reactions and about 40-50 species. At the current moment CFD simulations with the use of detailed methane mechanisms can be performed only on supercomputers. However, detailed kinetic mechanisms can be reduced, taking the specifics of rocket combustion chambers. The aim of the present project is to develop a reduced kinetic mechanism of methane oxidation suitable for CFD simulations for rocket applications. The main objective of this thesis work will be a skeletal kinetic mechanism of methane oxidation which is optimized for rocket application. A full detailed methane kinetic mechanism was chosen and reduced to form a skeletal mechanism for rocket application. The resultant skeletal mechanism contains 23 species and 49 reactions and were validated with two separate set of experimental data of ignition delay time at pressure of 50 atm. It is also verified with ignition delay time and counterflow flame temperature profile at rocket condition with pressure of 60 bar. The resultant skeletal mechanism was created through the elimination of species and reactions that are not important to the prediction of ignition delay time and temperature in counterflow non-premixed flame. Reaction path analysis and sensitivity analysis were used to reduced the full mechanism. C3,C4 species were found to be insignificant for methane combustion in rocket condition. C2 species and sub-mechanism were considered important to describe fuel rich methane combustion. The skeletal mechanism had a performance increase in computation time of up to 10 times as compared to computation time of the full mechanism. The ignition delay time and temperature profile predicted by the skeletal mechanism are within 5% difference with values predicted by the full mechanism. The resultant skeletal mechanism is attached as Appendix A in this thesis in CHEMKIN format. Acknowledgements

This master thesis work was conducted at the Deutsches Zentrum f¨urLuft- und Raumfahrt (DLR), Institute of Space Propulsion, Lampoldshausen, Germany. The master thesis was carried out in fulfillment of the requirements for the Joint European Master in Space Science and Technology (SpaceMaster) program. This work was done under the supervision of Dr. Victor Zhukov from the Raketenantriebe (Rocket Engine Development) Department. I would like to thank my supervisor and DLR for giving me the opportunity to conduct my master thesis at DLR Lampoldshausen. Special thanks goes to Dr. Zhukov for providing me guidance, feedback and time to answer my questions on the topic of chemical kinetics.

I would like to thank my LTU examinar, Dr Victoria Barabash who is always helpful in answering questions on the bureaucratic and administrative matter regarding the master thesis and also for giving tips on how to go about completing the master thesis. I would also like to thank Anette Brandstrom and Maria Winneb¨ack, the two lovely and extremely helpful administrative staff at LTU Kiruna Rymdcampus who were always attending our questions and taking good care of me and my fellow SpaceMaster students in Kiruna. I would also like to thank Sven Mollin for the discussion on the SpaceMaster program, its history and what the future holds for this program. I was also very grateful for his help in providing the contact for my internship in the Satellite Research Center at the Nanyang Technological University in Singapore.

I would also like to thank my colleagues in the Raketenantriebe Department as well as the M¨ockm¨uhlWohnheimers for making my time in DLR Lampoldshausen really enjoyable with all the parties, schnitzel challenges, DLR Cup and Motorman Run. Special thanks also goes to Lionel, Scott, Bombardieri, Sam, Jeremy Wang and Chan, Sebastian, Baskar and Sukruth for the wonderful atmosphere living at Wohnheim.

I would like to also thank all my fellow SpaceMaster friends, Ferran, Nick, Steffen, Jeremy, Toby, Garima, Manisha, Martin, Chuck, Yo, Sam, Tommy and many more who had made these two years one of the best years of my life. The auroras, epic skiing and snowboarding trips, large dinner parties we have and the sauna session were some of the fond memories that I will cherish and carry with me wherever I go. I would also like to thank all my LTU peers from Ringv¨agen,Oscar, Emil, Joakim, Pappis for making my second semester in Kiruna just as enjoyable as the first with the house party, the celebration for Santa Lucia and the awesome pool session every Friday at the Kiruna Bad House. Last but not least, I would like to thank my family for their support in giving me the opportunity to participate in this master program.

ii Contents

Abstract i

Acknowledgements ii

Contents iii

List of Figuresv

List of Tables vi

Nomenclature vii

1 Introduction1 1.1 Methane: An Alternative Choice For Rocket Propellant...... 1 1.2 A Brief Introduction to Chemical Liquid Propellant Rocket Engine...... 2 1.2.1 LPRE Combustion Chamber...... 3 1.2.2 Determining the Performance of LPRE...... 4 1.2.3 Operating Condition in Rocket Combustion Chamber...... 5 1.3 Problem definition...... 7 1.3.1 Combustion Modelling in Rocket Engine...... 7 1.3.2 Challenges of Combustion Modelling in Rocket Engine...... 7 1.4 Thesis Motivations...... 8

2 Literature Review 10 2.1 Focus of Literature Review...... 10 2.2 Chemical Kinetics...... 10 2.3 Thermodynamics Properties...... 13 2.4 Transport Properties...... 13 2.4.1 Mixture-Averaged Transport Properties...... 16 2.5 Choice of kinetic mechanism for reductions...... 17

3 Reduction Methods 18 3.1 Choice of Simulations and Initial Condition...... 18 3.2 PSR and Batch Reactor...... 18 3.3 Counterflow Non-Premixed Laminar Flame...... 22 3.4 Reductions Techniques...... 26 3.4.1 Reaction Path Analysis...... 26 3.4.2 Sensitivity Analysis...... 27

iii Contents iv

3.5 Cantera, An Objected Oriented Software for Chemical Kinetics, Thermodynamics and Transport Problems...... 28 3.6 Summary of the Reduction Procedure...... 29

4 Simulation and Analysis 31 4.1 Reaction Path Analysis...... 31 4.1.1 0D Reaction Path Analysis...... 31 4.1.2 1D Reaction Path Analysis...... 33 4.1.3 Conclusion of Reaction Path Analysis...... 37 4.2 Sensitivity Analysis...... 38 4.2.1 0D Sensitivity Analysis...... 39 4.2.2 1D Sensitivity Analysis...... 40 4.2.3 Conclusion of Sensitivity Analysis...... 42 4.3 Final Skeletal Kinetic Mechanism...... 42

5 Validation, Verification and Performance 44 5.1 Validation With Ignition Delay Time...... 44 5.1.1 Validation With Past Experiments...... 44 5.1.2 Verification With Rocket Condition...... 45 5.2 Verification against Temperature Profile From Counterflow Flame Simulation 46 5.3 Performance Of Final Skeletal Mechanism...... 47

6 Summary, Conclusions and Future Work 48 6.1 Conclusions...... 48 6.2 Future Work and Outlook...... 48

Bibliography 50

A Final Skeletal Mechanism, CHEMKIN Format 54

B Major Species Profiles 57 List of Figures

1.1 Theoretical Vacuum Isp of Various Propellant [12]...... 1 1.2 Schematics of a Gas Generator Rocket Engine [35]...... 3 1.3 Typical Stress Load and Temperature Profile Near Chamber Wall [35]....4 1.4 Parameters In A Rocket Combustion Chamber [35]...... 4 1.5 Methane Rocket Engine Demonstrator Unit by Aerojet [16]...... 6

3.1 PSR with H radical ignitor...... 20 3.2 Major Species Mole Fractions for PSR...... 20 3.3 Batch Reactor at Constant Pressure of 60 bar...... 21 3.4 Experimental imaging of gaseous hydrogen and liquid oxygen in single coaxial fuel oxidizer injector (TOP) and the idealized counterflow flame problem in 1D (BOTTOM) by Juniper et al [17]...... 24 3.5 1D Counterflow Flame Structure...... 25 3.6 Temperature and heat release profile of counterflow flame with fuel/oxidizer inlet T = 300K, a = 9400s−1 and p = 60 atm. normal line: T profile, dashed line: Q profile, dots: positions where Sr are calculated...... 28 3.7 Reduction Procedures...... 29

4.1 Reaction path diagram at T = 800K, t = 0.57s ...... 31 4.2 Reaction path diagram at T = 2100K, t = 0.58s ...... 32 4.3 Reaction path diagram at T = 3086K, t = 0.58s ...... 34 4.4 Reaction path diagram at z = 0.0497mm ...... 35 4.5 Reaction path diagram at z = 0.0533mm ...... 36

4.6 C3 Submechanism...... 37 4.7 Sensitivity Analysis for PSR Simulations...... 39 4.8 Sensitivity Analysis for Counterflow Flame Simulations...... 41

5.1 Validation with experimental data in [28, 43]...... 44 5.2 Comparision of different mechanisms at rocket combustion conditions.... 45 5.3 Verification with 1D counterflow flames...... 46

v List of Tables

1.1 Typical Rocket Engine Operating Condition [2, 22, 23, 35]...... 5

3.1 Chemical Equilibrium Condition for CH4/O2 mixture in PSR for φ = 1... 19

4.1 Species Elimination, red: species not shown in all reaction path diagram, green: species with net element flux of less than 0.05 and appear in the temperature range of T = 2500K − 3000K, orange: species with insignificant effect on the calculated ignition delay time and temperature profile in counterflow flame, blue: species with low net element flux of less than 0.07 but more than 0.05...... 38

5.1 Simulation times for 0D autoignition and 1D counterflow flame simulations. 47

vi Nomenclature

Abbreviations LOX Liquid Oxygen LPRE Liquid Propellant Rocket Engine DLR Deutsches Zentrum f¨urLuft- und Raumfahrt CFD Computational Fluid Dynamics GRI MECH Gas Research Institute Mechanism RAMEC Ram Accelerator Mechanism by Eric Petersen REDRAM Reduced Ram Accelerator Mechanism by Eric Petersen PSR Perfectly Stirred Reactor fwhm Full width half maximum 0D Zero dimensional 1D One dimensional 2D Two dimensional 3D Three dimensional XML Extensible Markup Language CTML XML-based format file for Cantera QSS Quasi Steady-State max Maximum min Minimum standard condition Temperature: 298.15K, Pressure: 1.0 bar

vii Nomenclature viii

Symbols

C1 Species with 1 Carbon Atom

C2 Species with 2 Carbon Atom

C3 Species with 3 Carbon Atom

C4 Species with 4 Carbon Atom

C5 Species with 5 Carbon Atom

C7 Species with 7 Carbon Atom

Isp Specific Impulse

m˙ f Mass flow rate of fuel

m˙ o Mass flow rate of oxidizer

m˙ ign Mass flow rate of ignitor T Temperature

Ti Initial temperature

Tad Adiabatic temperature at chemical equilibrium p Pressure ρ Density m Mass t Time

tign Ignition delay time R Universal gas constant

g0 Gravitational constant

kB Boltzmann constant ¯0 Cp Heat capacity at constant pressure in molar units, standard condition ¯0 Cv Heat capacity at constant volume in molar units, standard condition S¯0 Entropy in molar units, standard condition H¯ 0 Enthalpy in molar units, standard condition Q Total heat release from all reactions

C˙ rjk Carbon atom element flux from species j to species k in reaction r

Sr Sensitivity coefficient Nomenclature ix

Units s seconds ms 10−3 seconds kg kilogram m metre mm 10−3 metre µm 10−6 metre mol mole kmol kilo-mole bar 100 000 Pa atm 101 325 Pa, standard atmosphere K kelvin P a pascals Chapter 1

Introduction

1.1 Methane: An Alternative Choice For Rocket Propellant

In the past decade, there have been increasing interests on fuel propellants for in-space and launcher rocket propulsion that reduce the operation cost of launching and improve rocket operating efficiency and performance. According to Figure 1.1, hydrogen provides the best performance in terms of specific impulse, Isp at a high cost while kerosene provides a cost optimized option for rocket propellants. In order to obtain the best performance at the lowest cost, both methane and kerosene [2] have since stood out as the most promising options for reusable boosters [2], main stage [38] and upper stage rocket engine [26]. Figure 1.1 illustrates the theoretical Isp achievable in vacuum for various propellants at different mixture ratio where the mixture ratio is determine bym ˙ o/m˙ f .

4500 LOX-LH2 4300

] 4100

·s/kg [N 3900 vac

I LOX-Propane LOX-Kerosene 3700

Impulse 3500 LOX-Ethanol LOX-Methane

LOX-Methanol

Vacuum 3300

c 90%-H2O2-Kerosene 3100 90%-H2O2-Ethanol Specifi

2900 Ideal N2O4-MMH Ideal Specific Vacuum 2700 Impulse

pc = 100 bar, Ae/At = 45, CET93 2500 0 1 2 3 4 5 6 7 8 9 Propellant Mixture Ratio O/F [-]

Figure 3: Ideal specific impulse of various propellant combinations Figure 1.1: Theoretical Vacuum Isp of Various Propellant [12]

1 Chapter 1. Introduction 2

It is clear that both methane and kerosene offer comparable performance at much cheaper operating cost then hydrogen with methane providing a slightly higher Isp over kerosene. Other benefits of methane over kerosene include low production of soot and less coking, cheaper cost in production and storage and better cooling properties compatible with liquid oxygen due to similar thermodynamic properties [2, 11]. Methane is also a green propellant with low pollution to the environment and is safe to handle and store [11]. Rocket fuel tank size can be reduced due to the high density of methane as compared to hydrogen and a less complicated cooling system can be designed, thus providing more payload mass in return [2]. Therefore, methane is an excellent choice for upper stage and main stage engine. With the increasing interest for Mars return missions, the motivation to use methane becomes prevalent. Studies [40] have suggested that methane is abundant on Mars atmosphere and possibly under the surface crust. This implies that methane could be synthesis on Mars into rocket fuel to be used for a return mission from Mars and in the future, facilities a manned mission to Mars. For this thesis, the rocket operating condition of both upper stage and main stage rocket engines were considered. In the next section, a brief introduction to liquid propellant rocket engine is provided with reference from [35].

1.2 A Brief Introduction to Chemical Liquid Propellant Rocket Engine

A chemical rocket engine utilizes the chemical energy release from combustion reactions to create high pressure, high mass flow rate in a combustion chamber and in turns generate thrust to propel the rocket forward. A liquid propellant rocket engine (LPRE) uses propellants stored in liquid form and the propellants are systematically feed into the combustion chamber via a complicated piping system. Propellants can come in the form of monopropellant and bipropellant [35]. A monopropellant contains fuel and oxidizer that are mixed into a single fluid before it is injected into the combustion chamber, catalyzed and burned. A bipropellant separates the fuel and oxidizer propellants before injection, mixing and combustion take place in the combustion chamber. Such combustion processes for bipropellant can be classified as a non-premixed combustion and it is of primary interest for this thesis [39]. Figure 1.2 shows a simple example of a type of LPRE consisting of a gas generator engine cycle. In this engine cycle, a small part of the fuel propellant is burned to power a gas generator that will in turns drive the turbopumps to deliver the fuel and oxidizer to the combustion chamber [14]. Other types of engine cycle include the pressure feed cycle, expander cycle and the staged combustion cycle. From Figure 1.2, several key components of a LPRE can be identified. A typical LPRE is consisted of propellant tanks, feed system made up of valves and pipelines, combustion chamber, nozzle and a complex cooling system [35]. For this thesis, the focus will be on the operating condition in a combustion chamber where the chemical processes of methane oxidation take place for combustion as the oxygen oxidizes the methane fuel during burning. It is also at the combustion chamber where extensive Computational Fluid Dynamics (CFD) simulations had been done in an effort to predict the performance and assist in the designing of rocket engine without the need for expensive experimental testing [5]. CFD is also used to predict and better understand ignition and transient behavior during rocket engine start-up and other combustion processes that cannot be analyzed experimentally due to the limitation of current measuring instruments [35]. In Chapter 1. Introduction 3 section 1.3, some of the challenges in using CFD for combustion modelling is discussed and served as the basis for the thesis motivation. A short description of a combustion chamber and the major design parameters are given below.

Figure 1.2: Schematics of a Gas Generator Rocket Engine [35]

1.2.1 LPRE Combustion Chamber

A rocket combustion chamber is consist of the injector, the combustion chamber where the fuel and oxidizer react with each other, de Laval nozzle for supersonic gas expansion, cooling system, an ignition system and connections to coolant pipes and propellant tanks [14]. The combustion chamber is a complex structure that requires all components to be able to withstand the high temperature (T > 3000K) and stress load generated during rocket operation [35]. Cooling had to be adequate along the chamber walls to prevent melting of its structure. Figure 1.3a shows a typical stress load applied to the chamber wall during combustion. Figure 1.3b shows an example of how the temperature changes along the radial direction of the combustion chamber with a film cooled wall, a type of cooling method for rocket combustion chamber [14, 35]. It is trivial from Figure 1.3 that the design of rocket combustion chamber requires two important parameters, namely the temperature of hot gases in the combustion chamber and the wall heat flux at the chamber walls. These parameters determine the materials needed to construct the chamber structure and the cooling requirement for chamber walls. The chamber size and geometry are designed according to the thrust level required and had to be large enough for the fuel and oxidizer to be fully atomized, mixed, evaporated and to ensure full combustion before exit to nozzle [35]. Another important parameter is the composition of gas at nozzle which determines the performance of the engine and this is elaborated in section 1.2.2. Other design parameters include the nozzle area ratio, the types of feed system to use and chamber pressure. These Chapter 1. Introduction 4 design parameters are mainly dependent on the performance requirement for each individual rocket engine but would not be discussed as it is not within the scope of this thesis.

(a) Stress Load on Chamber Walls (b) Temperature Profile Near Film Cooled Walls

Figure 1.3: Typical Stress Load and Temperature Profile Near Chamber Wall [35]

1.2.2 Determining the Performance of LPRE

Figure 1.4 shows an ideal rocket combustion chamber and the variables involved in the calculation for the performance of a LPRE. In the figure, subscript 1 represent the combustion chamber, subscript 2 represent the nozzle exit, subscript 3 represent the ambient environment and subscript t represent nozzle throat. These simple equations can give adequate design guidelines for real engine.

Figure 1.4: Parameters In A Rocket Combustion Chamber [35]

A simple steady state rocket thrust equation is given by [35]:

F =mv ˙ 2 + (p2 − p3)A2 (1.1a)

ve = v2 + (p2 − p3)A2/m˙ (1.1b) Chapter 1. Introduction 5 where F is the rocket thrust andm ˙ is the mass flow rate at the nozzle. v, p and A are the velocity, pressure and area at the location as depicted in Figure 1.4. ve is the effective exhaust velocity at the nozzle and it is not similar to v2 due to the pressure difference between the nozzle and the ambient atmosphere in the case for a main stage engine [35]. For an upper stage engine, p3 is negligible and addition thrust is provided via the product of p2 and A2. Isp is commonly used as a measure of performance for rocket engine and is given by [35]:

ve F Isp = = (1.2) g0 mg˙ 0

In order to prevent the undesirable effect of p3 > p2 and a consequent reduction in thrust, nozzles are usually designed such that the pressure at nozzle is equal or greater then the pressure at ambient [14, 35]. Thus, with p3 = p2, the effective exhaust velocity ve is equal to the velocity at nozzle, v2. The velocity at nozzle can be determined by equation (1.3),

v u 0 " # u 2k R T1 p2 (k−1)/k v2 = t 1 − [35] (1.3) k − 1 M p1

where k is the ratio of specific heat given by k = cp/cv. cp and cv is the heat capacity of gas mixture within the combustion chamber at constant pressure and volume respectively. 0 R T1/M = RT1 due to the fact that the gas constant R is inversely proportional to the average molecular mass of the gas mixture in the combustion chamber, M [35]. Therefore, there is a direct relationship between the average molecular mass of gas mixture, the temperature of the hot gas mixture within the combustion chamber and the Isp as seen from equations (1.2) and (1.3). Consequently, it is crucial to accurately predict the composition of gases in a rocket combustion chamber through CFD.

1.2.3 Operating Condition in Rocket Combustion Chamber

For this thesis, the operating condition selected for the current study is defined in Table 1.1.

Methane Rocket Operating Condition Chamber Pressure 40 - 100 Bar Chamber Operating Temperature 3600K Chamber Injection Temperature Fuel: 300K - 500K Oxidizer: 100K - 300K

Mixture Ratio for Maximum Isp 3.4

Gas Composition Pure CH4 and O2

Table 1.1: Typical Rocket Engine Operating Condition [2, 22, 23, 35]

Due to the variety of rocket engines available, it is important to confine the problem and set the operating condition for one type of engine. It is difficult to define the appropriate rocket condition as most methane rocket engines are currently under development [16]. Thus, a general overview of possible methane rocket operating condition was given in Table 1.1 Chapter 1. Introduction 6 and used as a guideline for this thesis. In rocket combustion, both the methane fuel and oxygen oxidizer do not contain any diluents and thus, the simple 1 step chemical reaction for methane combustion is given by reaction (1.4) where methane and oxygen reacts to form carbon dioxide and water.

CH4 + 2 O2 )−−−−* CO2 + 2 H2O (1.4)

The above equation shows the stoichiometric mixture ratio for methane and oxygen where all reactants are reacted to form the products with no excess of either methane or oxygen

[39]. For 16kg of CH4, 64kg of O2 are required for stoichiometric reaction and thus the stoichiometric mixture ratio, given by the ratio of the mass of O2 and CH4, is 4.0. If there are more CH4 present, the mixture ratio is less than 4.0 and the engine is said to run fuel rich and likewise if there are more O2 present, the mixture ratio is larger then 4.0 and the engine runs oxidizer rich [35]. For a upper stage rocket engine, a high Isp is desired and therefore, the rocket engine usually operates under fuel rich condition that served to increase the Isp by decreasing the average molecular mass of the hot gas according to equation (1.3) with the introduction of lighter CH4 into the resultant gas mixture after reaction. From [2, 22, 23] and Figure 1.1, an optimum mixture ratio of 3.4 is predicted theoretically to produce the highest

Isp for methane and this is chosen for the current study. A rocket fuel is usually stored at a cooler temperature and therefore it is commonly used to cool the combustion chamber before injection [14, 35]. The injection temperature is shown in Table 1.1. It is difficult to specify the injection temperature for the fuel as different types of rocket engine uses different cooling methods which result in different fuel temperature during injection. Therefore, the injection temperature for fuel and oxidizer are assumed to be 300K for this thesis as the interest is only on gas phase interaction. The operating condition defined in Table 1.1 serve as a guideline for the initial condition of the simulations carried out for mechanism reduction and will be elaborated in later Chapters. Below shows the firing of a subscale demonstrator methane rocket engine from Aerojet.

Figure 1.5: Methane Rocket Engine Demonstrator Unit by Aerojet [16] Chapter 1. Introduction 7

1.3 Problem definition

1.3.1 Combustion Modelling in Rocket Engine

Rocket combustion modelling strive to predict the following parameters for designing rocket engine and analysis of rocket performance [14, 35].

• Temperature of hot gases in combustion chamber • Chamber wall heat flux • Composition of gases in combustion chamber and at the chamber nozzle

These parameters determine the geometry, material and the performance of the rocket engine [14]. With the increase in computation power and capability, CFD have been widely used as a design tool for rocket combustion chamber where flames in the chamber are described as a fluid flow. A CFD model uses several numerical techniques and sophisticated algorithms to solve the Navier Stokes equations, the governing equations for fluid flow [12]. In the case of combustion, the flow problem becomes extended, multi-physical and multi-phase which includes several branch of science such as fluid mechanics, thermodynamics, chemical kinetics and transport theory [5]. Furthermore, most of the flow problems in rocket combustion are turbulent and this increases the complexity in the problem to solve. Coupling of fluid mechanics and chemical kinetics seek to incorporate the chemistry in a reacting combustion flow. Although current CFD are capable of solving several fluid problems, the inclusion of chemical kinetics severely increases the amount of computation resource required and this is discussed in the next section.

1.3.2 Challenges of Combustion Modelling in Rocket Engine

To accurately predict the required parameters for rocket combustion, detailed chemistry of reactions in the form of a full chemical kinetic mechanism needs to be incorporated with a CFD model [18, 39]. A chemical kinetic mechanism is a list of elementary reactions that describe in detail, with intermediate species, how the products is formed from the reactants [39]. It includes most of the possible reactions pathway for the reactants in Arrenhius form and it is used to determine the reaction rate and heat released from each reactions. The topic of chemical kinetic and kinetic mechanism will be elaborated further in Chapter 2. In the case of methane combustion, detailed kinetic mechanisms had already been developed extensively and widely available for industrial and academic purposes. These mechanisms include the GRI MECH [10, 24], RAMEC [27] and several more mentioned in [34]. However, most of these mechanisms are very large, containing 35 to 50 species and as much as 300 reactions within the mechanism. When the mechanisms are included in the CFD model, it becomes computationally expensive and excessive with the need of large memory for storing the data, high processor speed to solve and computer clusters to run the simulations in parallel. Furthermore, combustion problem are also mathematically stiff with time scales spanning several order of magnitudes and to resolve the solution requires excessive computational time and data that may masked important data of interest and makes analysis much more complicated and difficult [18, 20, 39]. The coupling effect between Chapter 1. Introduction 8 the chemistry and fluid flow also create an issue in the accuracy of the computation whereby an error in the reaction rate predicted by the kinetic mechanism may result in large error in the final CFD solutions [18]. All these problems can be exemplified by looking at the computation time needed for the simplest and most well known H2−O2 mechanism in [42]. For a test problem of flame propagation with 400 cells, a mechanism with 13 reactions took 19 hours to complete a simulation of 1ms while a 29 reactions mechanism took 36 hours to complete the same simulations, indicating that as the number of reactions and species in the mechanism increases, the computation time increases as well and it becomes harder to find a converged solution [42]. Accuracy of the 13 reactions mechanism was also lower than that of the 29 reactions mechanism. Extending this to methane combustion which contains detailed mechanism up to 10 times the size of H2−O2 mechanism, it is therefore imperative to find a compromised between the required accuracy and computation resources available.

1.4 Thesis Motivations

The solution to the above mentioned problems come in the form of kinetic mechanism reduction where the size of the mechanism is decreased by elimination of unimportant species and reactions while retaining the main properties of the detailed mechanism according to some selected criteria predefined by the goal of the CFD simulation [18, 20, 29, 39]. This provides a trade off between computation times, accuracy and computation resources available. Thus, the main goal of this thesis is to develop a skeletal chemical kinetic mechanism of methane oxidation according to operating condition within the rocket combustion chamber in an effort to incorporate methane oxidation chemistry and reduce computation time and resources needed. The developed skeletal mechanism would be tailored to the need for rocket combustion chamber design and allow for rapid prototyping with potentially high cost saving on testing of development rocket units. The reduction of a full mechanism to a skeletal one is the first step towards the creation of a reduced kinetic mechanism for methane rocket engine. The definition of different types of mechanism will be discussed in Chapter 2.

The developed skeletal mechanism should achieved the following for rocket operating condition:

Main Objectives

• The size of the skeletal mechanism should be below 50 reactions. • The skeletal mechanism should produced results within 5% error from the full mechanism.

Secondary Objective

• Check the importance of C3,C4 species for methane combustion under no dilution of oxidizer

The validation criteria for the performance of the developed skeletal mechanism are set according to the important parameters mentioned in section 1.3.1. The main criteria selected Chapter 1. Introduction 9 for this thesis is the ability to accurately predict the temperature of hot gases in the combustion chamber. With an accurate prediction of temperature, the wall heat flux and composition of gas can be determined accordingly [35]. Subsequently, the temperature profile and ignition delay times served as 2 possible validation and verification parameters which will be used in this thesis. Validation and verification are done in rocket condition according to Table 1.1. Chapter 2

Literature Review

2.1 Focus of Literature Review

The focus of this literature review is to give a general background on the topic of chemical kinetics and the required knowledge to use the software Cantera [8] by David Goodwin from Caltech. A description of the software is done in Chapter 3. All of the background materials in this Chapter are taken from Combustion: Physical and Chemical Fundamentals, Modeling and Simulation, Experiments, Pollutant Formation by J¨urgenWarnatz, Ulrich Maas and Robert Dibble [39], Combustion Physics by Chung K. Law [20] and Chemically Reacting Flow: Theory and Practice by Robert Kee, Michael Coltrin and Peter Glarborg [18].

2.2 Chemical Kinetics

Chemical kinetics is the description of the rate of chemical reactions and how molecules collide to form products from reactants. The study of chemical kinetics is required to adequately describe the combustion processes in a chemical rocket engine where much of the energy comes from the reactions between the methane fuel, CH4 and the oxidizer made up of pure oxygen, O2. For a general chemical reaction given by:

kf A + B + C + ... )−−−−* D + E + F + ... (2.1) kb

The resultant change in concentration of species A, [A] is given by:

d[A] = −k [A]a[B]b[C]c... (2.2) dt f where a, b, c are the reaction orders for species A, B, C. kf represents the forward reaction rate from reactant species A, B, C to product species D, E, F. For the reverse or backward reaction rate kb, it is given in a similar form by:

d[A] = k [D]d[E]e[F]f ... (2.3) dt b 10 Chapter 2. Literature Review 11

At chemical equilibrium, there is no change in concentration for each species and therefore, the relationship between the forward and backward reaction rate is given by:

d e f kf [D] [E] [F] ... = a b c = Kc (2.4) kb [A] [B] [C] ... where Kc is the equilibrium constant of the reaction in concentration units. Kp, an useful quantity used to determine the value Kc, is the equilibrium constant of the reaction in pressure units. Both of these expressions can be determined from the Gibbs free Energy, G¯0 and Helmholtz free energy, A¯0 by the equations:

0 Kp = exp(−∆RG¯ /RT ) (2.5a) 0 Kc = exp(−∆RA¯ /RT ) (2.5b)

0 ∆RG¯ is the change in Gibbs free energy for each reactions or the standard Gibbs free energy of reaction. The bar denote molar values for the Gibbs free energy and 000 represent standard 0 condition of T = 298.15K and p = 1.0 bar. These descriptions apply to ∆RA¯ for Helmholtz 0 0 free energy. Both ∆RG¯ and ∆RA¯ can be determined from the thermodynamic properties in section 2.3. An elementary reaction is a reaction occurring at the molecular scale exactly the way as described by the reaction equation [39]. The reaction order a, b, c are always constant and follows the molecularity of the elementary reaction which is equivalent to the stoichiometric coefficient in the reaction equation. A reaction mechanism is made up of these elementary reactions which describe in detail how CH4 and O2 are reacted to form CO2 and H2O through several intermediate reaction steps made up of intermediate species. There are 3 types of molecularity of reactions given by:

A −−→ products (Unimolecular) A + B −−→ products (Bimolecular) A + B + C −−→ products (Trimolecular)

A unimolecular reaction is first order, bimolecular is second order and trimolecular is third order, giving the reaction order values of 1,2 and 3 respectively. For a elementary reactions, the molecularity of the reaction is equal to the order of the reactions and thus, the change in concentration of a species is given by:

R S ∂[Ci] X (p) (re) Y (re) = k (ν − ν ) [C ]νrs (2.7) ∂t r ri ri s r s where [Ci] is the concentration of species i, k is the forward reaction rate of reaction r, and ν is the stoichiometric coefficient for the elementary reaction. (p) and (re) represent the product species and reactant species respectively. The subscript of r, s and i represent the reaction index, species index other then i and the species i within the reaction mechanism containing a total of R reactions and S species. [Cs] is the concentration of all reactant species in the reaction r other then species i. νri is the stoichiometric coefficient for species i in reaction r and likewise, νrs is the stoichiometric coefficient of species other then i within the reaction. Chapter 2. Literature Review 12

Arrenhius Equation The Arrenhius equation describes the temperature dependence of forward reaction rate of each reaction step r. This is given by:

b kf = AT exp(−Ea/RT ) (2.8) where A is the pre-exponential factor, b is the value that determines the temperature dependence of the pre-exponential factor and Ea is the activation energy needed for the bonds in the molecules to break and initiate the reaction. The Arrenhius equation is an important expression used to build up the reaction kinetic mechanism input files as shown in AppendixA where the entire mechanism is consists of these Arrenhius parameters.

Pressure Dependence of Reactions Rate The pressure dependence of reaction rate is given by the Lindemann model in the expression below as defined for a trimolecular reaction.

k0[M] kf = [21] (2.9) 1 + k0[M] k∞ where k∞ is the high pressure rate coefficient, k0 is the low pressure rate coefficient and [M] is the concentration of the third body collision body, M and is given by taking into account the collision efficiency of all possible third body partners with [Cj] as the concentration of the third body partners and αj as the collision efficiency of each possible collision partner. At low pressure limit, [M] → 0 and at high pressure limit, [M] → ∞, giving the corresponding low pressure limit reaction rate of k0[M] and high pressure limit reaction rate of k∞. Low pressure reaction rates are specified in the kinetic mechanism input file. X [M] = αj[Cj][29] (2.10) j

For pressure in between these pressure limits, the Troe formulation was used to introduce a correction factor in equation (2.9) given below where P = k0[M] : r k∞   Pr kf = k∞ F (2.11) 1 + Pr

The factor F is determine by:

"  2#−1 ln Pr + c ln F = ln Fcent 1 + (2.12) n − d · (ln Pr + c) where c = −0.4 − 0.67 ln Fcent, n = 0.75 − 1.27 ln Fcent, d = 0.14 and Fcent given by:

 T   T   T  F = a · exp − + exp − + (1 − a) · exp − (2.13) cent T ∗ T ∗∗ T ∗∗∗

The Troe parameters are labeled in the kinetic mechanism file and are specified in the order of a, T ∗∗∗,T ∗,T ∗∗. Sometimes, there is a possibility for the same reaction to proceed with two reaction pathway of different reaction rates and these reactions are labeled duplicate reactions in the reaction mechanism. To calculate the reaction rates for duplicate reactions, Chapter 2. Literature Review 13 these are given below where n represent the number of duplicate reactions

X bn kf = AnT exp(−(Ea)n/RT )[8] (2.14) n

The fuel equivalence ratio φ gives comparison of fuel-oxidizer ratio with the same ratio for stoichiometric composition. It is given by:

x /x φ = f o (2.15) xf,stoich/xo,stoich where xf represent fuel mole fraction in the mixture and xo represent oxidizer mole fraction in the mixture. xf,stoich and xo,stoich represent the fuel and oxidizer mole fraction at stoichiometry respectively, In the case of methane with pure oxygen, xf,stoich/xo,stoich = 0.5. A fuel rich composition has φ > 1 and a fuel lean composition has φ < 1. For φ = 1, the composition is considered stoichiometric and the highest combustion temperature occur at regions containing this mixture composition.

2.3 Thermodynamics Properties

¯0 ¯0 ¯ 0 For the thermodynamics properties, quantities such as Cp , S , H and all reference thermodynamic values for each species at standard condition (standard T = 298.15K and ¯0 ¯0 ¯0 standard p = 1.0 bar) are needed to determine values such as ∆RG , ∆RA , Kc, Kp and Cv . ¯0 ¯0 ¯ 0 Thus, a common way is to store the values of Cp , S , H in polynomial form by expressing these values in NASA 14 coefficient format given by [25]:

C0 p = a + a T + a T 2 + a T 3 + a T 4 (2.16a) R 1 2 3 4 5 H0 a a a a = a T + 2 T 2 + 3 T 3 + 4 T 4 + 5 T 5 + a (2.16b) R 1 2 3 4 5 6 S0 a a a = a ln T + a T + 3 T 2 + 4 T 3 + 5 T 4 + a (2.16c) R 1 2 2 3 4 7

Two sets of 7 coefficient of a1 to a7 for high temperature range (T > 1000K) and low temperature range (T < 1000K) were provided in the thermodynamic data input files. The low temperature range usually starts from T = 300K for most species. The first 7 coefficient of the NASA 14 coefficient are the high temperature range and the next 7 0 0 0 coefficient are the low temperature range. From the calculated Cp , H and S , the other remaining thermodynamic quantities can be inferred and used in flame simulations.

2.4 Transport Properties

A brief explanation of the quantities used in the transport input file for Cantera [8] are provided in this section. The formulations transport properties are taken from [18]. The transport input was used only for counterflow flame simulations. Since the choice of transport model used is not within the scope of this thesis, a simple mixture-averaged transport model Chapter 2. Literature Review 14 was used to determine the transport properties of viscosity, diffusion and heat conduction. The corresponding heat flux, diffusion flux of species concentration and the momentum flux can be determined and used to solve the governing differential equations for counterflow flames in section 3.3. The effect of thermal diffusion (Soret effect) and the effect of energy transport due to concentration gradient (Dufour effect) were neglected since the contribution of these effects are small and negligible for combustion problems [39]. Furthermore, to include the Soret effect, a multi-component transport model needs to be selected in Cantera which increases the computation time. This was not needed for the current simulation setup of just pure methane and oxygen and therefore, were not considered for this thesis. The transport input file contains 6 Lennard-Jones parameters used to determine the three transport properties of viscosity, diffusion coefficient and thermal conductivity. The transport file contains 7 columns and the data in each column corresponds to species name, geometry,

ε/kB, σ,µ ¯,α ¯ and Zrot. Geometry contains the index that represent the geometrical configuration of each species molecule. 000 denotes a single atom, 010 denotes a linear molecule 0 0 and 2 denotes a nonlinear molecule. ε/kB represent the Lennard-Jones potential well depth, σ represent the collision diameter,µ ¯ represent the dipole moment of species and α¯ represent the polarizability of species. These quantities are used to evaluate the collision (2,2)∗ (1,1)∗ integral Ω and Ω which are used to determine the transport properties. Zrot is the rotational relaxation collision number used to determine the rotational contribution to thermal conductivity.

Viscosity

The pure species viscosity, µk for each species k is given by [18]: √ 5 πm k T µ = k B (2.17) k 2 (2,2)∗ 16 πσkΩ mk is the mass and σk is the collision diameter of species k, T is the temperature of mixture (2,2)∗ and kB is the Boltzmann constant. The collision integral Ω is determine by empirically ∗ fitting the collision integral to a function of reduced temperature T = T/(εk/kB) and ∗ 2 3 reduced dipole moment δk = 0.5µ ¯k/(εkσk) where εk/kB is the potential well depth andµ ¯k is the dipole moment of species k

Diffusion

The binary diffusion coefficient Djk of species j and k is given by [18]: q 3 3 3 2πkBT /mjk D = (2.18) jk 2 (1,1)∗ 16 pπσjkΩ where p is the pressure, mjk is the reduced molecular mass given by mjk = (mjmk)/(mj + (1,1)∗ mk). The collision integral Ω is given by fitting the collision integral to a function of ∗ ∗ 2 3 reduced temperature Tjk = T/(εjk/kB) and reduced dipole moment δjk = 0.5µ ¯jk/(εjkσjk). These reduced quantities requires the evaluation of εjk, σjk andµ ¯jk which are dependent on the type of collision partners involved. 2 cases are identified and the evaluation of εjk, σjk andµ ¯jk are given below:

√ 2 Case 1 : εjk = εjεk, σjk = 0.5(σj + σk), µ¯jk =µ ¯jµ¯k (2.19a) 2√ −1/6 2 Case 2 : εjk = ξ εjεk, σjk = 0.5(σj + σk)ξ , µ¯jk = 0 (2.19b) Chapter 2. Literature Review 15 where 1 q q ξ = 1 + α¯∗µ¯∗ ε /ε , α¯∗ =α ¯ /σ3, µ¯∗ =µ ¯ / ε σ3 (2.20) 4 j k k j j j j k k k k Case 1 is used when either both collision partners are polar or both partners are non-polar. Case 2 is used when one collision partner is polar and the other partner is non-polar. In Case 2, the species j is considered as the non-polar species and species k is considered as the ∗ ∗ polar species.α ¯j is therefore the reduced polarizability of the non-polar species j andµ ¯k is the reduced dipole moment of the polar species k. The self-diffusion coefficient Dkk used for the determination of thermal conductivity, λk for species k is given by [18]: q 3 3 3 2πkBT /mkk D = (2.21) kk 2 (1,1)∗ 16 pπσkkΩ where mkk = mk/2 and σkk = σk according to (2.19a).

Thermal Conductivity

The pure species thermal conductivity, λk for each species k is given by [18]:   µk λk = ftrans Cv,trans + frot Cv,rot + fvib Cv,vib (2.22) Wk where     5 2 Cv,rot A ρDkk 2 A ρDkk ftrans = 1 − , frot = 1 + , fvib = (2.23a) 2 π Cv,trans B µk π B µk   5 ρDkk 2 5 Cv,rot ρDkk A = − ,B = Zrot + + (2.23b) 2 µk π 3 R µk where Wk is the molecular weigh of species k and Cv,trans, Cv,rot, Cv,vib are the translational, rotational and vibrational contribution to the heat capacity Cv respectively. Dkk is determined according to (2.21) and ρ is the density of species in mixture given by the ideal gas equation of state, ρ = (pWk)/(RT ). The vibrational contribution to heat capacity, Cv,vib is readily calculated from Cv as determined from thermodynamic database and is given by:

Cv,vib = Cv − Cv,trans − Cv,rot (2.24)

Depending on the geometry of the species molecule, both Cv,trans and Cv,rot can be determined according to the expression given below:

3 linear : C = R,C = R (2.25a) v,trans 2 v,rot 3 3 non − linear : C = R,C = R (2.25b) v,trans 2 v,rot 2 3 single atom : C = R,C = 0 (2.25c) v,trans 2 v,rot where R is the universal gas constant and Cv is the heat capacity of species at constant volume. For the special case of single atom, there are no rotational and vibration contribution to Cv and therefore, both Cv,rot, Cv,vib are equal to zero and ftrans = 5/2, giving the thermal conductivity as:   µk 5 λk = Cv,trans (2.26) Wk 2 Chapter 2. Literature Review 16

The quantity Zrot used in (2.23b) has a temperature dependence given by:

F (298) Z (T ) = Z (298) (2.27) rot rot F (T )

The value Zrot(298) is the rotational relaxation collision number at T = 298K and is provided in the transport data input files. This value represent the number of collision required to F (298) remove the energy from a rotationally excited species. F (T ) is the correction factor for Zrot(298) with a dependence in temperature and F (T ) is given by:

π3/2 ε/k 1/2 π2 ε/k  ε/k 3/2 F (T ) = 1 + B + + 2 B + π3/2 B (2.28) 2 T 4 T T

2.4.1 Mixture-Averaged Transport Properties

The mixture-averaged transport properties of a mixture are determined from the pure species viscosity, thermal conductivity and binary diffusion coefficients. The mixture-averaged viscosity is provided from [18] where µk is given by (2.17):

X Xkµk µ = P (2.29a) XjΦkj k j  −1/2  1/2 1/4!2 1 Wk µk Wj and Φkj = √ 1 + 1 + (2.29b) 8 Wj µj Wk

The mixture-averaged thermal conductivity is provided below where λk is determined by (2.22): 1 X 1  λ = Xkλk + P (2.30) 2 Xk/λk k k

Xk is the mole fraction of species k in the mixture and likewise, Wk is the molecular weight of species k in the mixture. The mixture-averaged diffusion coefficient is provided below where

Djk is determined by (2.18): 1 − Yk Dkm = P (2.31) j6=k Xj/Djk where Yk is the mass fraction of each species k and Dkm is the diffusion coefficient for species k diffusing into the mixture m made up of all species other then k. The three transport properties discussed here are used to determine the diffusion flux of species ji and heat flux jq in section 3.2 and 3.3. Chapter 2. Literature Review 17

2.5 Choice of kinetic mechanism for reductions

There are several different types of mechanism available to address the user requirement and focus in research. Full mechanism are detailed mechanism that contains all elementary reactions required to accurately predict experimental shock tube data. Skeletal mechanism are obtained from the full mechanism by elimination of unimportant elementary reactions and species [42]. A reduced mechanism is generally obtained by assumption of quasi-steady state species and partial equilibrium where reactions are lumped together to form non-elementary reactions [33]. The focus of this thesis is the development of a skeletal mechanism for rocket application. A good starting point was to choose an appropriate full mechanism that was validated against the required temperature and pressure range. Two mechanisms were considered for the skeletal reduction. This includes the full mechanism from Petersen et al, RAMEC [27] and the full mechanism from Zhukov et al [41] with C5 to C7 species truncated from the mechanism. RAMEC is a detailed mechanism consisting of 38 species and 190 reactions. It was validated for temperature range of 1040K to 1500K, pressure range of 40 bar to 260 bar and for φ = 0.4, 3.0, 6.0. The detailed mechanism from Zhukov et al is consisted of 207 species and 2329 reactions. It was validated for temperature range of 850K to 1700K, pressure range from 1 bar to 530 bar and φ = 0.5. Considering the higher temperature and pressure range validated as well as the inclusion of larger hydrocarbon species up to C4, the mechanism from Zhukov et al was chosen as the target full mechanism for reduction and formation of the new skeletal mechanism. This was also chosen to fulfill the secondary objective of the thesis. From here on, full mechanism refers to the full mechanism from [41]. Chapter 3

Reduction Methods

3.1 Choice of Simulations and Initial Condition

A homogeneous Prefectly Stirred Reactor (PSR), a constant pressure batch reactor with adiabatic walls and a counterflow laminar flame simulation were selected as test conditions for the analysis of the full mechanism [18]. The PSR was used to generate the reaction path diagrams, the constant pressure batch reactor was used to determine the ignition delay time of pure CH4 and pure O2 mixture and the counterflow laminar flame simulation was used to investigate the chemistry in non-premixed flame. Rocket combustion are in general non-premixed and therefore the closest condition achievable was in counterflow laminar flame where the fuel and oxidizer are separated before combustion [17, 35]. In this thesis, the focus is on simulating the operating conditions in the rocket combustion chamber and developed a skeletal mechanism according to these conditions.

3.2 PSR and Batch Reactor

PSR

Following the guideline from Table 1.1, a chamber pressure of 60 bar was chosen as the test case for the PSR simulation with adiabatic walls. A equivalence ratio of φ = 1 was chosen with stoichiometric mixture of CH4 fuel and O2 oxidizer. The equivalence ratio was selected as it produced the highest adiabatic temperature in chemical equilibrium when combustion takes place. An inlet temperature of 300K was used for both methane and oxygen in the PSR to represent the injection temperature. This was used since most of the thermodynamic data included has a temperature range starting from 300K [41]. A stoichiometric mixture of CH4 and O2 with a starting temperature of 300K was used to filled up the PSR initially before the simulation. Since CH4 is not hypergolic with O2 and does not autoignite at 300K in the PSR case, an ignitor inlet of gaussian mass flow of H radical was included to start the ignition. The mass flow rate for ignitor inlet,m ˙ ign was set as [8]:

−(t − t )2  m˙ = a · exp 0 (3.1) ign 2b2

18 Chapter 3. Reduction Methods 19

√ where b = fwhm/(2 2 ln 2). a is the magnitude of the ignition pulse, t0 is the time at which the ignition pulse becomes maximum, t is the time of the simulation and fwhm is the full width half maximum of the pulse. The values used were a = 35.0, t0 = 0.4 and fwhm = 0.2. fwhm was chosen such that the ignition pulse width was small enough to limit the H radical contribution to the over chemistry of the methane combustion. a was chosen such that an ignition can be successful induced as indicated by the sharp raise in temperature within a small time scale. An exhaust outlet was introduced for the PSR case to complete the problem and represent the rocket nozzle throat area or the exit area of the combustion chamber. The exhaust outlet is consisted of the composition of initial mixture in the PSR at chemical equilibrium which represent the burnt gases in the exhaust. The pressure in the exhaust outlet is 5 bar lower then the PSR with a valve included to regulate the pressure of the PSR and the exhaust at the same level. The PSR simulation was carried out with constant pressure and ideal gas to mimic the operating condition in a rocket engine [35]. The ideal gas assumption is valid for the chosen pressure and temperature range. The chemical equilibrium composition of the mixture in PSR is shown in Table 3.1.

T T Pressure X X X X X X i ad CH4 O2 CO2 H2O OH CO 300 K 3608.8K 60 bar 3.3198E-11 0.0703 0.1404 0.4541 0.0922 0.1429

Table 3.1: Chemical Equilibrium Condition for CH4/O2 mixture in PSR for φ = 1

Ti is the initial temperature before chemical equilibrium, Tad is the adiabatic temperature achieved at chemical equilibrium, X is the mole fraction of CH and likewise for the CH4 4 other species. A plot of the time evolution of temperature and major species mole fraction in the PSR simulation was shown in Figure 3.1 and 3.2. The autoignition temperature of methane at T = 873K [32] was also drawn in Figure 3.1. This was to show that the ignition source needs to increase the temperature of the methane and oxygen mixture above 873K for methane to ignite and the sharp raise in temperature from 873K to Tad represent ignition of methane. A constant pressure and enthaply was used for PSR simulation as rocket engines usually maintain the pressure within the combustion chamber [35]. PSR simulation is also analogous to the ignition zone in the combustion chamber usually found after the spray zone from the injector where methane and oxygen are well mixed and ready to ignite [14]. Thus, major chemical reaction pathway of methane oxidation could be determined from PSR simulation and this allows the description of the ignition behavior in the rocket combustion chamber. Therefore, this was the reason why PSR simulation was used to in generating the reaction path diagram for the reaction path analysis. Chapter 3. Reduction Methods 20

4000

3500

3000

2500 T 2000 Autoignition T dT dt max 1500 Temperature [K] 1000

500

0 0.0 0.2 0.4 0.6 0.8 1.0 Time [s]

Figure 3.1: PSR with H radical ignitor

0.35 0.7 0.16 0.30 0.6 0.14 0.25 0.5 0.12 0.10 4 2

0.20 2 0.4 O H O C C 0.08 X X X 0.15 0.3 0.06 0.10 0.2 0.04 0.05 0.1 0.02 0.00 0.0 0.00 0.0 0.5 1.0 0.0 0.5 1.0 0.0 0.5 1.0 Time [s] Time [s] Time [s]

0.5 0.10 0.25

0.4 0.08 0.20

0.3 0.06 0.15 O O H 2 C O H X X X 0.2 0.04 0.10

0.1 0.02 0.05

0.0 0.00 0.00 0.0 0.5 1.0 0.0 0.5 1.0 0.0 0.5 1.0 Time [s] Time [s] Time [s]

Figure 3.2: Major Species Mole Fractions for PSR

Batch Reactor

A constant pressure batch reactor with adiabatic walls was used to determine the ignition delay time of pure methane combustion with pure oxygen. The ignition delay time will be used as a form of validation for the developed skeletal mechanism in Chapter 5. Ignition delay time is an important measure for ignition behavior and it is usually used to determine reaction time scale for the Damk¨ohlernumbers which is used to simulate turbulence flame and the determine the regime of combustion modelling [18, 39]. The Damk¨ohlernumbers is given by the ratio of fluid flow time scale over chemical time scale and gives an idea of whether the diffusion rates (driven by mixing) or reactions (driven by chemical kinetics) is dominant in the combustion chamber of rocket engine. It can be inferred that combustion in rocket engine contains a wide range of time scale that needs to be resolve to accurately describe the combustion behavior in the rocket combustion chamber and further emphasized on the difficulty in resolving these time scale with current computation resources [39]. Several definition of ignition delay time are available in literature and the time taken to reach Chapter 3. Reduction Methods 21 the point of maximum temperature gradient was used as the definition for ignition delay time although there are only subtle difference in the value of tign calculated between the dT methods [41]. For this thesis, the ignition delay time is defined as the time where dt is maximum. Figure 3.3a shows how tign is determined and Figure 3.3b shows the large change in temperature within a small time scales where there is a temperature increase of 1600K within a short time interval of 0.2µs.

4000 4000

3500 3500 3000 tign

2500 3000

2000

Temperature [K] Temperature [K] 2500 1500

1000 T T dT 2000 dT dt max dt max 500 0.000 0.001 0.002 0.003 0.004 1.9897 1.9898 1.9899 1.9900 1.9901 Time [s] Time [ms]

(a) Autoignition, Ti = 1000K (b) Expanded Plot of (A)

Figure 3.3: Batch Reactor at Constant Pressure of 60 bar

The batch reactor is similar to the PSR but does not include any inlet and outlet from the reactor [18]. It represent the autoignition of methane and oxygen where the ignition is solely due to chemical kinetic. The pressure and composition selected are identical to those used in PSR of 60 bar and stoichiometric composition of CH4 and O2. The initial temperature for the batch reactor simulation needs to be high and near the autoignition temperature of methane to give realistic results for ignition delay time. Thus, any initial temperature that gives an ignition delay time of more then 5s were considered unrealistic and excluded from the batch simulations as this allows enough time for heat loss through the reactor walls and the adiabatic walls assumption becomes invalid [8, 18, 39]. A range of initial temperature starting from T = 700K to T = 2500K was used to determine the ignition delay time at each temperature and this is shown further in Chapter 5. Spatial homogeneity of pressure, temperature and species compositions were assumed for both PSR and batch reactor. No transport properties were included in these simulations.

Governing Equations of PSR and Batch Reactor

Since rocket combustion is characterized by turbulent fast mixing of fuel and oxidizer, the chamber content was considered well mixed and spatially homogeneous [14, 35, 39]. Since there are no spatial gradient in PSR and Batch Reactor, the conservation equation for momentum is not need for these simulations. The governing equations of a Batch Reactor with adiabatic walls (no heat loss through walls) are given below and taken from [18].

Conservation of Mass dm k =ω ˙ W V (3.2) dt k k Chapter 3. Reduction Methods 22

dmk where dt is the change in mass of species k in the batch reactor, t is time,ω ˙ k is the molar production rate of species k, Wk is the molecular weight of species k and V is the volume of the reactor.

Conservation of Species dY ω˙ W k = k k (3.3) dt ρ where ρ is the density of mixture in the batch reactor given by the ideal gas equation of state P and ρ = p/(RT k Yk/Wk). Yk is the mass fraction of species k given by Yk = mk/m where m is the total mass of the mixture in the batch reactor.

For a constant pressure batch reactor, the conservation of energy is given by:

Conservation of Energy

dT X hA¯ ρc = − h ω˙ W + (T − T ) (3.4) p dt k k k V ∞ k where cp is the specific heat capacity at constant pressure, hk is the specific enthalpy for species k, h¯ is the heat transfer coefficent at the walls, A is the walls area of the batch reactor and T∞ is the environment temperature surrounding the batch reactor. For a batch reactor with adiabatic walls, the second term in (3.4) can be neglected.

The governing equations for a PSR with adiabatic walls are given below without taking into account surface reactions at the walls and the expressions are taken from [8, 18]

dm X X = m˙ − m˙ (3.5a) dt in out in out dYk X m˙ in ω˙ kWk = (Y − Y ) + (3.5b) dt ρV k,in k ρ in dT X hkω˙ kWk X m˙ in X c = − + (h − h Y ) (3.5c) p dt ρ ρV in k k,in k in k m˙ in is the mass flow rate at inlets andm ˙ out is the mass flow rate at outlets. Yk,in is the mass fraction of each species k at the inlets and Yk represent the mass fractions of species k in the PSR. hin is the specific enthaply of the inlet composition. The next section will describe the counterflow flame simulation conducted for methane oxidation.

3.3 Counterflow Non-Premixed Laminar Flame

A counterflow laminar flame is used to simulate the non-premixed nature of rocket combustion. The formulations of this counterflow configuration follows that of [36] by Tsuji and reduces the combustion problem to 1D. The governing equations for a counterflow laminar flame is shown below and taken from [39]: Chapter 3. Reduction Methods 23

∂ρ ∂ρν + 2ρG + z = 0 (3.6) ∂t ∂z ∂G J 1 ∂  ∂G ∂G + + G2 − µ + ν = 0 (3.7) ∂t ρ ρ ∂z ∂z z ∂z ∂ν 1 ∂p 4 ∂ 2µ ∂G 4 ∂  ∂ν  ∂ν z + + (µG) − − µ z + ν z = 0 (3.8) ∂t ρ ∂z 3ρ ∂z ρ ∂z 3ρ ∂z ∂z z ∂z ∂T 1 ∂p ∂T 1 ∂  ∂T  1 X ∂T 1 X − + ν − λ + c j + h r = 0 (3.9) ∂t ρ ∂t z ∂z ρc ∂z ∂z ρc p,i i,z ∂z ρc i i p p i p i ∂w ∂w 1 ∂ r i + ν i + j = i (3.10) ∂t z ∂z ρ ∂z i,z ρ where T is the temperature, ρ is the density of mixture, p is the pressure, µ is the viscosity, cp,i is the specific heat capacity at constant pressure for species i, cp is the heat capacity of the gas mixture at constant pressure, λ is the heat conductivity, ji,z is the diffusion flux of species i in axial direction, z, along the facing oxidizer and fuel inlets. G is the tangential velocity gradient normal to the z direction and J is the pressure gradient normal to the z direction. hi is the specific enthaply of species i and jq is the heat flux determine by ∂T Fourier’s law jq = −λ ∂z . The diffusion flux ji,z can be determine via Fick’s law given by DT j = −DM ρ wi ∂xi − i ∂T where DM is the diffusion coefficient for species i into the other i,z i xi ∂z T ∂z i T species and Di is the thermal diffusion coefficient. xi is the mole fraction of species i and wi is the mass fraction of species i. ri is the mass rate of production for species i and νz is M the velocity of gas along the axial direaction, z. The transport properties of µ, λ and Di T are determined according to section 2.4 and Di is neglected as mentioned in section 2.4. By introducing suitable boundary condition similar to rocket operating condition, the counterflow flame solution could be solve. Figure 3.4 shows an illustration of a idealized counterflow flame problem and its representation in a experimental single coaxial injector for a rocket combustion chamber [17]. The top colored simulation show experimental imaging results of a cryogenic fuel injector with the oxidizer in the middle inlet represented in gray scale and the fuel on the outer inlet represented by the color scale. The zoom in portion represent the bottom left hand diagram of the flame. The bottom left hand diagram resembles the well-known counterflow flame problem as depicted on the bottom right hand diagram with hydrogen from the top coming in contact with oxygen from the bottom. For this thesis, the counterflow flame simulation will be using methane fuel coming from the left side and oxygen from the right side as depicted in Figure 3.5. For the simulation, the fuel and oxidizer are injected at supercritical condition with fuel and oxidizer inlet temperatures of 300K and pressure of 60 atm. These conditions are representative of the rocket combustion chamber such as the VINCI engine [19]. As long as pure CH4 and O2 were used for the simulation, the general flame structure is not affected. A high strain rate of a = 9400s−1 was chosen to represent the turbulent mass flow of methane and oxygen as the injection mass flow rates are usually high in rocket engine. The mixture ratio ofm ˙o/m˙f was kept at 3.4. Chapter 3. Reduction Methods 24

Figure 3.4: Experimental imaging of gaseous hydrogen and liquid oxygen in single coaxial fuel oxidizer injector (TOP) and the idealized counterflow flame problem in 1D (BOTTOM) by Juniper et al [17].

A scaling law for counterflow flame simulation by Fiala et al [6] was used to facilitate a better convergent of the 1D solution at elevated pressure up to 60 atm. Only steady state solution of the 1D simulation was considered for this thesis. The batch simulation starts 2 2 from a known converged 1D solution with p = 1 bar,m ˙f = 1.0 kg/m /s ,m ˙o = 3.4 kg/m /s and a grid size of 30mm with 162 adaptively inserted grid points along the domain. Each time a converged solution was found, the grid was refined by inserting more sampling points where there was a large gradient in the solution profile and sampling points were removed when there were no large change. The pressure was subsequently increased in a logarithmic manner up to the desired high pressure of 60 atm while keeping the strain rate constant and solving the problem with the scaled grid and solution profiles at every pressure steps up to 60 atm. According to [6], parameters such as temperature profile, grid size and mass flow rate for fuel and oxidizer were scaled according to the relative change in pressure and strain rate. Once the desired pressure was achieved, the strain rate could be scaled accordingly to a desired lower or higher value [6]. The resultant final simulated solution had a grid size of 0.18mm and 186 grid points with a strain rate of a = 9400s−1. The grid starts from the fuel inlet on the left with 0.0mm and end at the oxidizer inlet on the right at 0.18mm. This was illustrated in Figure 3.5. A high strain rate is indicated by a high mass flow rate of −1 2 fuel and oxidizer. For a = 9400s , the resultant mass flow rate ism ˙f = 24 kg/m /s and 2 m˙o = 82 kg/m /s. There are several definition for strain rate a, in a counterflow condition and the mean strain rate given by equation (3.11) was used [8]. Chapter 3. Reduction Methods 25

∆ν a = z (3.11) mean ∆z

A mixture average diffusion transport model was used for the simulation. Although more complicated transport models exist, these were not considered as it was outside the scope of the thesis. Figure 3.5 shows a typical solution and flame structure of a counteflow non-premixed laminar flame. It also shows the major and minor radical mole fraction profiles present in the flame structure.

4000 4000 0.030

1.00 3500 3500 0.025 3000 3000 0.80 T T 0.020 2500 CH4 2500 H O2 0.60 O 2000 CO2 2000 C2H2 0.015 H2O C2H4 1500 1500 CO 0.40 Mole Fraction C2H6 Mole Fraction

Temperature [K] Temperature [K] 0.010 OH C3H3 1000 1000 0.20 0.005 500 500

0 0.00 0 0.000 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 Distance [mm] Distance [mm]

(a) Product, Reactants and Major Radicals (b) C2 Radicals, C3H3 and O,H Radicals

Figure 3.5: 1D Counterflow Flame Structure

The peak temperature is located at 0.064mm from the left. A flame thickness of about 50µm was determined and this can give an indication on the mesh size to be used in a CFD simulation of the flame. The region towards the left of the peak temperature is defined as the fuel rich region where there is excess of methane than oxygen and likewise, the region on the right side of the peak temperature is defined as fuel lean side where there is an excess of oxidizer [18, 39]. This corresponds to the 0D case where the fuel rich region in 1D represents a region with equivalence ratio of φ > 1 and fuel lean represent a region of φ < 1. Towards the fuel inlet, φ → ∞ and towards the oxidizer inlet, φ → 0. It is clear that the highest amount of water and carbon dioxide are formed at the stoichiometric region of φ = 1 corresponding to the peak temperature and stoichiometric combustion and it is this point that separates the fuel rich and fuel lean region. The peak amount of OH radical also coincide with the peak temperature and the peak amount of CO coincide with the maximum dT heat release and the location where dz is maximum. Figure 3.5b shows the minor radicals produced such as O, H, C3H3 and C2H2 radicals. C2H2 and C3H3 radicals are stable at high temperature [1] at T > 2500K and are considered for the developed skeletal mechanism although further investigation would be needed via reaction path analysis and sensitivity analysis to determine if these radicals play a major role in methane oxidation under rocket condition. These reduction techniques are described in the next chapter. Chapter 3. Reduction Methods 26

3.4 Reductions Techniques

There are several reductions techniques available in [37] for eliminating species and reactions in a kinetic mechanism that do not contribute significantly to the prediction of certain properties such as laminar flame speed, ignition delay time tign and temperature profile of a counterflow or free propagating flame. For this thesis, the reaction path analysis and the sensitivity analysis had been utilized in the reduction process. Petersen et al [27, 29] and Frouzakis [7] had successfully implemented these two techniques to obtain skeletal mechanism according to criteria such as ignition delay time and final heat release.

Reaction path analysis allows the identification of slow reactions and species with low net production rate are considered to be unimportant and can be safely eliminated from the full mechanism [39]. Sensitivity analysis identifies rate limiting reactions according to certain criteria chosen as the reduction guideline [39]. Rate limiting reactions are defined by low net element flux and are the slowest reactions that control the overall reaction time for methane oxidation. These criteria can be in the form of the tign, final temperature or the concentration of certain species such as OH radical which are commonly used as heat release marker in rocket combustion chamber experiments [22]. Reactions that are not rate limiting can then be systematically removed from the kinetic mechanism to reduced the size of the overall mechanism since these reactions do not have a directly influence on the criteria selected. Both techniques are implemented for the PSR and counterflow flame simulations. The two reductions techniques will be briefly explained in the following sections.

3.4.1 Reaction Path Analysis

Reaction path analysis is conducted to construct a reaction path diagram that describes the net element flux between species at an instance in time during the evolution of the chemistry in the a PSR. The formula for calculating the conserved properties of element moles and the element flux in reaction r is given by Revel et al [31] and shown in equation (3.12).

kr nC,j nC,k C˙ rjk = (3.12a) NC,r R X C˙ jk(t) = C˙ rjk(t) (3.12b) r

C˙ rjk represents the element flux of C atom from species j to species k in reaction r at an instance in time t. kr is the reaction rate from species j to k for reaction r, nC,j and nC,k are the number of C atoms in species j and k respectively and NC,r is the total number of C atoms in reaction r for both products and reactants. By summing all element flux of C atom from species j to k as illustrated in equation 3.12b, the total element flux C˙ jk from species j to k is obtained. By summing all-flowing and out-flowing total element fluxes for each species in the kinetic mechanism, the net element fluxes are calculated and a reaction path diagram is constructed with nodes representing species and interconnecting arrows representing the net element flux [31]. An outward pointing arrow from a node signifies a net out-flow element flux from one species to another and likewise for a inward pointing arrow. The thickness of the arrow is an indication of the magnitude of carbon element flux. In this way, the major Chapter 3. Reduction Methods 27 reaction pathway from methane oxidation can be determined and used to highlight important species. By setting a threshold on the value of net element flux, only those with significantly large amount were included in the reaction path diagram [8]. This will be discussed in more details in Chapter4 where the simulation results are shown. In the PSR simulations, the reaction path diagram illustrates important species and reaction pathway during ignition and the reaction path diagram for the counterflow flame simulations provide an insight on key reaction pathway for non-premixed steady state combustion in a rocket engine.

3.4.2 Sensitivity Analysis

Sensitivity analysis [37] was used to determine the rate limiting reaction steps of the full kinetic mechanisms. Through the analysis, the influence of input parameters of a system on the output solutions can be determined. In the case of combustion, the input parameters are the reaction rates for each steps and output solution variables such as temperature, enthalpy or the mole/mass fractions of a species can be selected [39]. For this thesis, only temperature is used. For the PSR, a system of partial differential equations to solve the following initial value problem can be obtained in equation (3.13)[37]:

dT = f(T, k),T (t ) = T (3.13) dt 0 0 where the system of equations f is describe in equations (quote eariler). k represents the input parameter vector containing all the reaction rates for each steps in a kinetic mechanism. The effect of a change in the reaction rates on the final temperature can be described in equation (3.14). R X ∂T T (t, k + ∆k) = T (t, k) + ∆k + ... (3.14) ∂k r r r This change can be quantify by the local sensitivity coefficients defined by the partial derivative ∂T [37]. A normalized sensitivity coefficient S given by equation (3.15) is used in ∂kr r this thesis to compare the influence of each reaction steps on the final temperature calculated.

Sr is a measure of percentage change in temperature for a 1% change in reaction rate for reaction step r. A larger Sr indicates a rate limiting reactions. Threshold value of Sr can be set to give a cutoff between important and redundant reactions for the simulated condition.

Sr is also calculated for one instance in time during the a PSR simulation.

kr ∂T Sr = (3.15) T ∂kr

For counterflow flame simulations, Sr is calculated in the same form as (3.15) with T output dT dT solution variables replaced by Tmax, Qmax, dt max or dt min. The locations of these points are shown in Figure 3.6. For the counterflow flame case, a reference initial solution is obtained before the reaction rate parameters is perturbed by a small amount ∆kr. The counterflow flame problem is solved again using the new perturbed reaction rates and the same spatial grid points [8]. A finite difference approximation is performed using the initial and new solutions to calculate Sr. Tmax is used as the primary reductions criteria and the other three are considered as a guideline to ensure that the counterflow flame temperature profile retained its shape. Chapter 3. Reduction Methods 28

4000 1e128 Tmax Temperature 3500 Total heat release, Q 6 Qmax 3000 dT/dt max 4 2500

2000 2

1500 dT/dtmin

Temperature [K] 0 1000 2

500 Total Heat Release Rate, Q [W/m3]

0 4 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 Distance [mm]

Figure 3.6: Temperature and heat release profile of counterflow flame with fuel/oxidizer inlet T = 300K, a = 9400s−1 and p = 60 atm. normal line: T profile, dashed line: Q profile, dots: positions where Sr are calculated.

3.5 Cantera, An Objected Oriented Software for Chemical Kinetics, Thermodynamics and Transport Problems

Several software tools are available for the analysis of chemical mechanism, mechanism reduction, 0D homogeneous reactor and 1D laminar flame simulations. Such software tools include CHEMKIN [3], Cantera [8], Cosilab [4] and FlameMaster [30]. These softwares were able to perform both sensitivity analysis and reaction path analysis. Both CHEMKIN and Cosilab require the purchase of a user license. FlameMaster is available upon request and uses a format different from the widely used CHEMKIN format for input files. Cantera was chosen as the most suitable option due to its open source nature, excellent online support, extensive documentation, free to use and available interface to multiple programming platform such as Python, MATLAB, Fortran and C++. For this thesis, Cantera was used with Python for easy scripting and plotting was done using Matplotlib [13]. Reaction path diagrams generated can be opened using the Graphviz [9] program. Simulations are done by creating objects representing the phases of matter, interfaces of the phases, reactor netowrks and flames for 1D case. In this thesis, the IdealGasConstPressureReactor module was used for the 0D simulation and the CounterflowDiffusionFlame module was used for the 1D simulation.

Input Files: Cantera primarily works with a .cti file which is preprocessed from CHEMKIN formatted input files using the Python scripts ck2cti.py and ctml writer.py that comes with the installation. The file converter ck2cti.py takes in the conventional CHEMKIN input files for kinetic mechanism, thermodynamic and transport data and merge them to form a single .cti file which is then converted to a XML-based, CTML format when the phase is imported to Cantera. Further information on input files can be found in [8]. Chapter 3. Reduction Methods 29

3.6 Summary of the Reduction Procedure

0D 1D 0D 1D

Figure 3.7: Reduction Procedures

Figure 3.7 illustrates the reduction procedure to obtain the final skeletal mechanism. The reduction procedure can be briefly categorized into 3 main steps:

• Reaction path analysis and reduction

• Sensitivity analysis and reduction

• Refinement reduction

Reaction path analysis was carried out using Cantera for PSR and counterflow flame simulations. Reaction path diagrams were generated at 100K temperature interval from Ti to Tad for PSR and at every grid points on the 1D spatial domain for counterflow flame. The diagram generated were instantaneous reaction path diagram at a specific point of time and temperature for the PSR case. For the counterflow flame simulations, a local reaction path diagram was generated at the desired grid points for the steady state solution. The diagrams were analyzed and species not shown in the reaction path diagram were eliminated. Species with low element flux or terminating species were also systematically eliminated since they did not represent a major reaction pathway for methane combustion and the net production rate of these species were negligible. C atom was the conserved properties within this closed system and all reaction path diagrams were generated to track the C atom flux from CH4 to CO2 [8, 31]. Although reaction path diagram for O atom and H atom could be generated, these diagrams often involved too much species and were hard to analyze. Therefore, these were not included in this thesis. After minor species were eliminated along with reactions containing these species, an initial skeletal mechanism, ReduceRXN, was obtained. This mechanism was validated and verified according to the three criteria as depicted in Figure 3.6 and will be elaborated in Chapter5.

Sensitivity analysis was subsequently performed on ReduceRXN for PSR and counterflow flame simulations. Due to the stiffness of the problem, sensitivity analysis of the full mechanism could take up to 2 days for PSR and 4 hours for counterflow flame simulation. 1D sensitivity analysis took a shorter computation time since it uses saved solutions loaded from previously successful simulations. Furthermore, 0D sensitivity analysis took small time step to resolve the sensitivity of all the reactions in the full mechanism. If sensitivity analysis was done on the full mechanism, most data generated would contain excessive Chapter 3. Reduction Methods 30 and unimportant values that would take up too much memory space and masked the useful data with it, making analysis more difficult. Thus, sensitivity analysis was only performed with the smaller ReduceRXN mechanism to reduced the required computation times, memory for calculation and improved on the analysis of the mechanism. For PSR, sensitivity coefficients were obtained at temperature of 800K and 2100K to represent low temperature and high temperature chemistry for methane combustion [39]. For counterflow flame, sensitivity coefficients were obtained at the position marked in Figure 3.6. Reactions with sensitivity coefficient lower then a threshold could be considered non-rate limiting and thus could be eliminated from ReduceRXN. As a result, after the validation and verification steps, ReduceSens was obtained.

The mechanism size of ReduceSens could be further reduced through the refinement process of manually selecting reactions based on the absolute magnitude of the sensitivity coefficients, removing them one by one in the order from smallest to largest and running simulations to determine if there were major changes in tign and the temperature profile in 1D. A key point was that the resultant mechanism after each reaction removal must satisfy all three validation and verification criteria otherwise, the reactions had to be retained. It was not trivial that a reaction important for the 0D case was also important for the 1D case and hence, this refinement process was repeated until error exceeds 5% from the full mechanism or the experimental values and thereafter no more reactions were removed. The final refined ReduceSens skeletal mechanism was thus generated. Chapter 4

Simulation and Analysis

4.1 Reaction Path Analysis

4.1.1 0D Reaction Path Analysis

0.883 CH4 CH3O2 CH3O2H

1 0.935 0.0263 0.885

0.0446 0.0316 CH3 CH3O CH3OH

0.958

0.652 0.634 CH2O HCO CO

0.018 0.00723

0.0172 0.0172 0.0169 HCO3 HCO3H HCO2 CO2

Scale = 0.59 Reaction path diagram following C at 800.0K

Figure 4.1: Reaction path diagram at T = 800K, t = 0.57s

Figure 4.1 shows the reaction path diagram generated for a PSR under constant pressure at a time instance when T = 800K for initial condition of p = 60 bar, Ti = 300K and stoichiometric gas composition of CH4 and O2 with addition of H radical as ignition agent. The values on the arrow represent the net element flux of C atom as described in section 3.4.1. The values shown were normalized against the maximum net element flux in the diagram and the scaling of the normalization were provided in the figure. The unit for the net element flux is in kmol/m3/s [8]. A threshold value of 0.005 or 0.5% of the maximum net element flux was chosen as a initial conservative guess and only species with values greater than this threshold were included in the diagram. This value was chosen to allow the inclusion of

C3 and C4 species into the reaction path diagram. The thickness of the arrows were scaled according to the values of the net element fluxes. For the PSR case, net element flux of values greater than 0.2 or 20% of the maximum net element flux were highlighted in red and were

31 Chapter 4. Simulation and Analysis 32 identified as major pathway. Minor pathway were highlighted in green with net element flux value between 0.05 to 0.2. For the PSR simulation, two temperature regime were identified with low temperature regime at T < 1000K and high temperature regime at T > 1000K [20]. The first two reaction path diagram shown represent these two temperature regime. The main pathways during pre-ignition at T = 800K was described in (4.1).

CH4 −−→ CH3 −−→ CH3O2 −−→ CH3O2H −−→ CH3O −−→ CH2O −−→ HCO −−→ CO (4.1)

There were no significant minor pathways as the net flux values were below 0.05. At low combustion temperature regime of T < 1000K, it was clear that CH3O2 and CH3O2H played a vital role in initiating the combustion of methane. The other species in (4.1) were important for the majority of the combustion when the temperature climb from T = 1000K to T = Tad and this was shown with Figure 4.2 and 4.3. From [27, 34, 44], it was shown that CH3O2, together with HO2 and H2O2 were produced in a great amount during preignition as the pressure was elevated up to 100 bar. This, together with Figure 4.1, suggested the significance of CH3O2 in low temperature methane oxidation. This point was further reinforced with sensitivity analysis in section 4.2. Although CH3O2H was shown in this diagram, it was not included in the final skeletal mechanism due to the fact that it had little influence on the ignition delay time tign and almost played no important role in the non-premixed counterflow flame.

CH4 C3H8

1 0.00941 0.00506

CH3 NC3H7 IC3H7

0.0771 0.265 0.347 0.03 0.0115 0.00964

CH2(S) 0.0134 0.0659 C2H6 C3H6

0.0215 0.0252 0.397 CH3O 0.0156 CH3OH 0.00567 0.00553

CH2 C2H5 0.0336 C3H5-A C3H5-T

0.101 0.412 0.00728 0.0313 CH2OH

C2H4 0.00747 C2H5CO C2H5O 0.349

0.224 0.00517 0.0109 0.0382

0.0363 0.0483 C2H3 CH2CHO 0.0083 C2H5CHO 0.0156

0.0628 0.0789 0.0198

0.0789 C2H2 CH2O

0.588

HCO

0.734

CO

0.131

CO2

Scale = 1.1e+005 Reaction path diagram following C at 2100.0K

Figure 4.2: Reaction path diagram at T = 2100K, t = 0.58s Chapter 4. Simulation and Analysis 33

Figure 4.2 shows the reaction path diagram at T = 2100K. This reaction path diagram was representative of the major pathway for T = 1000K up to T = 3000K [20]. The major pathways were as follows:

CH4 −−→ CH3 −−→ CH3O −−→ CH2O −−→ HCO −−→ CO −−→ CO2 (4.2a)

CH4 −−→ CH3 −−→ C2H6 −−→ C2H5 −−→ C2H4 −−→ C2H3 (4.2b)

The diagram shows the importance of C2 mechanism as the alternative reaction pathway for CH4 although the significance of C2 mechanism was more pronounced for the non-premixed counterflow flame. Minor pathway leading to CH2(s) were present which would grow into a major pathway as shown in Figure 4.3. The reactions with methanol, CH3OH and ethanol CH2OH leading up to formaldehyde, CH2O, were in low net element flux and indicated a low production rate of these species during combustion. CH2O, methyl oxide, CH3O and HCO were important intermediate species for methane combustion and were included in the

final skeletal mechanism. On the right of Figure 4.2, it showed the existence of a minor C3 reaction mechanism which occurred in low values of net element flux of less then 0.05. The C3 mechanism did not have an arrow connecting to the main reaction path diagram due to the fact that the net element flux from the C3 species were lower then the threshold of 0.005. It suggested that C3 mechanism might not play a major role for the PSR case in determining the ignition delay time. Figure 4.3 shows the reaction path diagram at T = 3086K where there was the greatest amount of change in temperature with respect to time. It was important to note that there was a change in the major pathway from (4.2) as described below:

CH4 −−→ CH3 −−→ CH2O −−→ HCO −−→ CO −−→ CO2 (4.3a)

CH4 −−→ CH3 −−→ CH2(s) (4.3b)

The main pathway from (4.2) differed from (4.3) such that CH2O was formed directly from methyl radical, CH3 instead of going through CH3O. The reaction pathway towards CH2(s) became more prevalent. This occurred at the operating temperature of rocket engine. There was also no sign of C3 mechanism in the reaction path diagram. C2 mechanism became less significant due to the reduced amount of CH3 available to form ethane, C2H6 as the CH4 fuel was been consumed towards the end of the global reaction (1.4). Species such as HCCO and C2H were only present at T > 2500K and in small quantity, thus these species were eliminated from the final skeletal mechanism. Reactions with methanol and ethanol were also in low net element fluxes and therefore, will not be included in the developed kinetic mechanism. At this point of time, the heat release rate was the greatest which gave raise to the highest increase in temperature and correspondingly, the largest net element flux from

CO −−→ CO2, demonstrating the occurrence of complete combustion. This gave an indication of CO mole fraction as another important measure of temperature.

4.1.2 1D Reaction Path Analysis

The 1D reaction path analysis were carried out on each grid point of the counterflow flame simulations results to examine the chemistry at each region of the counterflow flame, providing an insight into the chemistry for a wide range of φ values for methane combustion. Only reaction path diagram from the fuel rich side were included in this section as the oxidizer Chapter 4. Simulation and Analysis 34

CH4

0.577

CH3

0.0065 0.134 0.0322

0.00768 0.0131 C2H6 CH2 0.0488 CH3OH

0.011 0.0136 0.14 0.0123

C2H5 0.0225 CH CH3O

0.0231 0.00768 0.0151

C2H4 0.0456

0.157 0.0075 0.0153 C 0.229

0.00648 C2H3 0.00575 0.0056 0.105 0.0282

0.137 0.367 0.031

C2H2 0.00662 0.0263

0.0108 0.0968 0.119 0.0292 0.0621

CH2CO HCCO 0.08

0.00884 0.0222 0.0103

0.0771 0.0222 0.0133 CH2(S)

0.00756

0.049 0.00889 0.0123 0.0154 CH2OH

0.00871 0.0392 0.0677

0.00948 C2H CH2O 0.0997

0.0326 0.711

0.0335 HCO 0.00854

1

CO

0.261

CO2

Scale = 8.8e+005 Reaction path diagram following C at 3086.0K

Figure 4.3: Reaction path diagram at T = 3086K, t = 0.58s rich side only depicted complete combustion for steady state solution since there were excess oxygen to complete the combustion processes and the major pathway was consisted only of

CO −−→ CO2. Furthermore, this reaction pathway dominates the other reaction pathways during steady state combustion as all other net element flux were below the threshold of 0.005 and thus not shown in the reaction path diagram. This was evident in all grid points toward the right of the peak temperature representing the fuel lean side of the counterflow flame. Furthermore, the reaction path diagrams from the fuel rich side contained vital information on the involvement of larger hydrocarbon species for counterflow flame and could be used to access the importance of C3 and C4 species in counterflow flame. Figure 4.4 shows the reaction path diagram at grid point 0.0467mm from the fuel side. This point corresponded to a location with temperature of T = 2300K and was found at the fuel rich side of the counterflow flame simulation. Chapter 4. Simulation and Analysis 35

CH4

1

CH3

0.0273 0.429

0.0249 CH2(S) 0.381 C2H6

0.011 0.0202 0.448

CH3OH 0.0412 CH2 C2H5

0.0238 0.0267 0.796

CH2OH CH3O CH C2H4

0.0327 0.484 0.0116

CH2O IC3H7 NC3H7

0.107 0.0571 C2H3 0.0183 0.0147

CO2 HCO 0.482 C3H6

0.112 0.0189 0.0142

CO C2H2 C3H5-S C3H5-T C3H5-A

0.0127 0.0111 0.0109 0.0145 0.017

0.0456 CH2CO C3H4-P C3H4-A

C2H 0.0332 0.0372

0.0541

C3H3

Scale = 1.4e+004 1D Reaction path diagram at position 0.0497mm

Figure 4.4: Reaction path diagram at z = 0.0497mm

For fuel rich combustion, the major reaction pathway was via the C2 mechanism following (4.4). It had similarity with the alternative major reaction pathway of (4.2) in the PSR case.

It also showed the existence of a C3 sub-mechanism with low net element flux and there were no minor reaction pathway of consideration at this location. It could be inferred that the C2 sub-mechanism was important for methane oxidation in the non-premixed condition where region of combustion were fuel rich and C2 sub-mechanism was needed to be taken into account for accurate prediction of temperature in the non-premixed case. C3 mechanism played a very minor role in methane combustion as the formation of C3 species were strongly dependent on C2 species as shown in the diagram where the only pathways to any C3 species were from C2H4 and C2H2. Only a small portion of C1 species were converted into C2 species and in turns these small pool of C2 species transformed into C3 species, giving the low net element flux towards C3 species from C2. All C2H5 goes into C2H4 and later C2H2 as shown in the major pathways in Figure 4.4. This could explain the reason behind the low net element flux from C2H4,C2H2 to C3 species as most of the C2 species were converted to C2H2 according the the major pathway in (4.4). Furthermore, the net element flux towards C3 species were low (< 0.05) and indicated that the species were produced in low concentration and therefore could be eliminated from the full mechanism.

CH4 −−→ CH3 −−→ C2H6 −−→ C2H5 −−→ C2H4 −−→ C2H3 −−→ C2H2 (4.4) Chapter 4. Simulation and Analysis 36

dT Figure 4.5 shows the reaction path diagram where dz was the maximum on the fuel rich side, located at the grid position of 0.0533mm. At this point, the condition were leaning towards φ = 1 as the flame region became stoichiometric in composition. The major pathway dT resembled that of Figure 4.3 where dt was at maximum in the PSR case and also produced the same transition to CH2O pathway from CH3O as the temperature increased. Importantly, the diagram retained the major pathway of the C2 submechanism from the fuel rich side in Figure 4.4. Thus, to incorporate fuel rich combustion in the counterflow flame case, C2 sub-mechanism was required. At this stage, C3 sub-mechanism were becoming less important as the net element flux from C2 species fell below the threshold 0.05. Minor pathway included the reaction pathways via CH3OH and CH2OH as well as towards CH2(s). Also, formation of C3H3 became increasingly important, albeit in low concentration and low net element flux as compared to the major reaction pathway.

CH4

1

CH3

0.0654 0.0547

0.0213 C2H6 0.165 CH2

0.0773 0.0859 0.0709

C2H5 0.0891 CH

0.211 0.0213

C2H4 0.0261

0.479

C2H3 0.0474 0.0153 0.124

0.473 0.0308 0.0512 0.0614

C3H6 C2H2 0.0379

0.0763 0.0196 0.233

C3H5-A C3H5-T C2H 0.0611 0.0162

0.0137 0.0805 HCCOH 0.0452

C3H4-A C3H4-P 0.0561 0.0157 HCCO

0.019 0.0295

C3H3 CH2CO CH2(S)

0.0132

0.0327 0.0172 CH3OH

0.0148 0.0441 0.061 0.0128

0.0161 0.0288 CH2OH CH3O

0.0329 0.117 0.0162

CH2O

0.47

HCO CO2 0.0113

0.498 0.0982

CO

Scale = 3.8e+004 1D Reaction path diagram at position 0.0533mm

Figure 4.5: Reaction path diagram at z = 0.0533mm Chapter 4. Simulation and Analysis 37

4.1.3 Conclusion of Reaction Path Analysis

A summary and conclusion from the reaction path analysis was provided in this section. The important reaction pathway and the resultant important species identified were given in (4.1), (4.2), (4.3) and (4.4). There existed a C3 sub-mechanism, as shown in Figure 4.6, present in the counterflow flame combustion, found at region where temperature was lower then the methane autoignition temperature of 873K [32]. This was also observed in PSR simulation. There also exist some traces of C4 species in the 1D reaction path diagram although this was not observed in the PSR case. These higher C3,C4 hydrocarbon had net element flux diminishes as the temperature increases and are very dependent on the production of the predecessor C2,C3 species which were produced in small amount. Hence, the concentration of these C3,C4 species were low throughout the combustion process. The value of the net element flux for this species were also below 0.05 of the max net element flux of the species and therefore, had little influences on the overall reaction pathway from methane to carbon dioxide. Both C3H3 and C2H2 were stable at high temperature above 2500K [1] but due to the low net element flux and hence, low production rate, these species were eliminated from the full mechanism. C2H2 was kept as it was part of the major reaction pathway for fuel rich combustion and was part of the C2 mechanism fuel rich major reaction pathway. It was thus concluded that C3 and C4 sub-mechanism could be eliminated from the full kinetic mechanism for rocket condition without any effect on the overall properties of the full mechanism.

IC3H7 C3H5-A C3H4-A C3H8 C3H6 C3H3 IC3H7 C3H5-T C3H4-P

C3 Submechanism

Figure 4.6: C3 Submechanism

Table 4.1 shows all species up to C2 in the full mechanism. Those species not highlighted by any color were included in the mechanism after reaction path analysis. C1,C2 species with net element flux of less than 0.05 were removed from the full mechanism. The red highlighted species were C2 species that did not appear in any reaction path diagram and were removed from the mechanism. Species highlighted in green were species with very low net element flux of less than 0.05 and only appeared at a narrow range of temperature from 2500K to 3000K and thus, could be taken out from the mechanism. Species highlighted in orange were species that appeared in reaction path diagram but had insignificant influence on the prediction of ignition delay time and temperature profile in counterflow simulation and were subsequently eliminated from the full mechanism. Although both CH3OH and CH2OH were found in minor reaction pathway, they were low in net element flux of less than 0.07 for the whole simulated duration in PSR and in all grid position in counterflow flame and thus, were eliminated from the fuel mechanism. Hence, these species could be taken out of the mechanism. The entire H2−O2 sub-mechanism was retained. This was because the most active radicals in combustion were O, H and OH and these species’ concentration were highly sensitive to other species in the H2−O2 sub-mechanism and the removal of these radicals would result in a big change to the other species within this sub-mechanism [20, 39]. Production of heat Chapter 4. Simulation and Analysis 38 release during combustion were also strongly dependent on the reactions with these radicals. Furthermore, it was the accumulation of these highly reactive radicals that characterized the ignition and combustion behavior in rocket engine and thus, any reduced and skeletal mechanism for methane combustion should contain the H2−O2 sub-mechanism [39]. These radicals react readily to break down CH4 and O2 into intermediate species and recombine to form the products CO2 and H2O. CH3O2 is vital for the accurate prediction of ignition delay time at region of low temperature and high pressure [27] and thus was included in the skeletal mechanism to account for ignition at elevated pressure in rocket combustion chamber. A final 26 species, 165 reactions was obtained after elimination of the species according to Table 4.1 and reactions that contained these unimportant species to form the ReduceRXN mechanism. ReduceRXN was validated and verified before sensitive analysis was conducted on this mechanism. Validation and verification results were shown in Chapter 5.

H,O Mechanism C1 Mechanism C2 Mechanism H CH C2H2 C2H3O1-2 H2 CH2 C2H3 C2H4O1-2 H2O CH2(s) C2H4 C2H4O2H H2O2 CH2O C2H5 C2H5O2 HO2 CH3 C2H6 C2H5O2H O CH3O C2H C2H5OH O2 CH3O2 C2H5O CH2O2HCHO OH CH4 HCCO CH3CHO CO HCCOH CH3CO CO2 CH2CHO CH3CO2 HCO CH2CO CH3CO3 C CH3CO3H CH3O2H O2C2H4O2H CH2OH O2C2H4OH CH3OH PC2H4OH HCO2 SC2H4OH HCO3 HCO3H

Table 4.1: Species Elimination, red: species not shown in all reaction path diagram, green: species with net element flux of less than 0.05 and appear in the temperature range of T = 2500K − 3000K, orange: species with insignificant effect on the calculated ignition delay time and temperature profile in counterflow flame, blue: species with low net element flux of less than 0.07 but more than 0.05

4.2 Sensitivity Analysis

Sensitivity analysis were conducted on the reduced ReduceRXN mechanism consisting of 165 reactions and 26 species. The main objective of this sensitivity analysis was to reduced further the number of reactions such that it is of an appropriate size for CFD computation as well as to facilitate the forming of a reduced mechanism with the assumption of QSS species and species at partial equilibrium [33]. The initial round of reduction with sensitivity analysis was to decrease the size of ReduceRXN by half so that the mechanism becomes more manageable for the refinement process. This was done via selecting 80 reactions from ReduceRXN with the highest absolute magnitude of sensitivity coefficient, Sr for 0D sensitivity analysis and combining it with 40 reactions from the 1D sensitivity analysis with the largest magnitude Chapter 4. Simulation and Analysis 39

of Sr for Tmax. Sensitivity analysis from the other three selected criteria were used as a guideline and the 10 reactions with the highest Sr for these criteria were included for the first round of reduction via sensitivity analysis. There were several overlapping of important reactions between the 0D and 1D case and similar reactions were consequently taken out of the resultant mechanism while retaining the number of species involved. After the first round of reductions, a smaller ReduceSens skeletal mechanism was formed with 82 reactions and 26 species. This skeletal mechanism undergoes a refinement process as illustrated in Figure 3.7. This refinement process involved taking out one reaction at a time manually and going through the validation and verification process to determine if the reaction is important for the final skeletal mechanisms. One major criteria was that the resultant mechanism needed to be able to predict ignition delay time and the temperature profile accurately within 5% error of the full mechanism and experimental value. The developed skeletal mechanism should not introduce large changes in temperature. The validation and verification were set up as such so that the resultant mechanism could be used for a wide range of application including estimating the ignition behavior and start-up of rocket engine combustion over a large temperature range and mixture composition, φ. The refinement process stopped when there were no more reactions that could be taken out of the mechanism without introducing more than 5% error in the prediction according to the main objective of this thesis in section 1.4.

4.2.1 0D Sensitivity Analysis

CH3+H2O2<=>HO2+CH4 2OH(+M)<=>H2O2(+M) 2OH(+M)<=>H2O2(+M) CH3+H2O2<=>HO2+CH4 CH3+O2<=>OH+CH2O HO2+CH2O<=>HCO+H2O2 2HO2<=>O2+H2O2 2HO2<=>O2+H2O2 HO2+CH3<=>O2+CH4 CH3+O2<=>OH+CH2O 2HO2<=>O2+H2O2 2HO2<=>O2+H2O2 HO2+CH2O<=>HCO+H2O2 O2+CH2O<=>HO2+HCO CH3O2+CH3<=>CH3O+CH3O CH3O2+CH3<=>CH3O+CH3O O2+CH2O<=>HO2+HCO HO2+CH3<=>O2+CH4 HO2+CH3<=>OH+CH3O HO2+CH3<=>OH+CH3O CH3O2+HO2 => CH3O+OH+O2 CH3O2+HO2=>CH3O+OH+O2 CH3O2+CH3O2 = O2+CH3O+CH3O OH+CH4<=>CH3+H2O CH3+O2<=>O+CH3O OH+CH2O<=>HCO+H2O

0.4 0.2 0.0 0.2 0.4 0.6 0.8 1.0 0.4 0.2 0.0 0.2 0.4 0.6 0.8 1.0

Normalized Sr , T = 800K Normalized Sr , T = 2100K

(a) 800K, 60 bar (b) 2100K, 60 bar

Figure 4.7: Sensitivity Analysis for PSR Simulations

Figure 4.7 shows the 13 reactions with the largest absolute sensitivity coefficient for a PSR simulations at T = 800K and T = 2100K. The values were taken at the same temperature as with the 0D reaction path analysis since these temperature were representative of the major reaction path for the low temperature (T < 1000K) and high temperature (T > 1000K) combustion regime [20]. The reactions were arranged in the order of smallest to largest absolute value of Sr with a positive sensitivity coefficient increasing the temperature predicted and a negative sensitivity coefficient decreasing the temperature predicted [37]. Indirectly, removing a reaction of positive Sr decreases the ignition delay time predicted and the opposite effect occurs for removal of a reaction with negative Sr. The sensitivity coefficient were Chapter 4. Simulation and Analysis 40

normalized with the maximum value of Sr obtained. From Figure 4.7, it was observed that for methane combustion at elevated pressure, the temperature was highly sensitive to reaction involving hydrogen peroxide, HO2 and H2O2. This was due to the fact that HO2 formation rate increases ten times more than the formation of radicals OH and O, the main oxidizing agents during combustion [43]. The ignition promoter at low and high combustion was given by reactions (4.5a) and (4.5b), with (4.5c) for T = 800K and (4.5d) for T = 2100K.

CH3 + H2O2 )−−−−* HO2 + CH4 (4.5a)

OH + OH + M )−−−−* H2O2 + M (4.5b)

CH3 + O2 )−−−−* OH + CH2O (4.5c)

HO2 + CH2O )−−−−* HCO + H2O2 (4.5d)

These reactions were characterized by the formation of radicals such as OH as well as the formation of HO2 and H2O2 which would facilitate the formation of highly reactive OH radicals through the reactions (4.6a) and (4.5b) [20, 27, 39]. Reactions (4.6a) and (4.6b) shows the main ignition inhibitor for both temperature regime. Here, it showed the importance of CH3O2 in forming the reactive radical CH3O for combustion pathway leading to CH2O which will readily form HCO via (4.5d) and ultimately towards CO and CO2.

HO2 + HO2 )−−−−* O2 + H2O2 (4.6a)

CH3O2 + CH3 )−−−−* CH3O + CH3O (4.6b)

Most of the reactions shown here were included in the final refined version with the exception of reactions (4.7a) and (4.7b) which were found to have no significant influence on the ignition delay time predicted for both experimental and rocket condition.

CH3O2 + HO2 )−−−−* CH3O + OH + O2 (4.7a)

CH3O2 + CH3O2 )−−−−* O2 + CH3O + CH3O (4.7b)

4.2.2 1D Sensitivity Analysis

Figure 4.8 shows the 13 reactions with the highest Sr for counterflow flame at position dT dT of Tmax, Qmax, dt max and dt min. The important reactions from 1D sensitivity analysis were vastly different from the 0D sensitivity analysis. Reactions (4.8) show the reactions most sensitive to Tmax. A change in the reaction rate of these reactions would increase the temperature predicted in the 1D simulation with the exception of reaction (4.8e) which decreases the temperature in the profile. For Qmax, similar important reactions were shown.

CH3 + OH )−−−−* CH2O + H2 (4.8a)

H + OH + M )−−−−* H2O + M (4.8b)

C2H2 + O )−−−−* CH2 + CO (4.8c)

CO + O + M )−−−−* CO2 + M (4.8d)

CH3 + CH3 )−−−−* C2H5 + H (4.8e) Chapter 4. Simulation and Analysis 41

CH3+OH<=>CH2O+H2 C2H2+O<=>CH2+CO H+OH+M<=>H2O+M CH3+OH<=>CH2O+H2 C2H2+O<=>CH2+CO H+OH+M<=>H2O+M CO+O+M<=>CO2+M 2CH3<=>C2H5+H 2CH3<=>C2H5+H CO+O+M<=>CO2+M H+HO2<=>2OH H+HCO(+M)<=>CH2O(+M) H+H2O+O2<=>H2O+HO2 CH2+H(+M)<=>CH3(+M) H+O2<=>O+OH H2O+HCO<=>CO+H+H2O CH2+OH<=>CH2O+H CH2+OH<=>CH2O+H CH2+CH3<=>C2H4+H CH2O+OH<=>H2O+HCO H2+O<=>H+OH H+HCO<=>CO+H2 CO+OH<=>CO2+H C2H4+H(+M)<=>C2H5(+M) CH3+H(+M)<=>CH4(+M) CH2O+H<=>H2+HCO

0.4 0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.0 0.5 0.0 0.5 1.0

Normalized Sr , Tmax Normalized Sr , Qmax

(a) Tmax (b) Qmax

2CH3<=>C2H5+H CH3+OH<=>CH2O+H2 CH3+H(+M)<=>CH4(+M) C2H2+O<=>CH2+CO C2H2+O<=>CH2+CO 2CH3<=>C2H5+H H+HCO(+M)<=>CH2O(+M) CH2+OH<=>CH2O+H CH3+OH<=>CH2O+H2 C2H4+H(+M)<=>C2H5(+M) CH4+H<=>CH3+H2 CH2+CH3<=>C2H4+H H+O2<=>O+OH C2H6+H<=>C2H5+H2 H2O+HCO<=>CO+H+H2O 2CH3(+M)<=>C2H6(+M) H+OH+M<=>H2O+M C2H2+H(+M)<=>C2H3(+M) CH2+OH<=>CH2O+H H2+O<=>H+OH CH2+H(+M)<=>CH3(+M) CH3+O<=>CH2O+H CH2O+H<=>H2+HCO H2+OH<=>H+H2O C2H6+H<=>C2H5+H2 C2H4+OH=>CH2O+CH3

1.0 0.5 0.0 0.5 1.0 1.0 0.5 0.0 0.5 1.0 S dT S dT Normalized r , dt max, Fuel Side Normalized r , dt min, Oxidizer Side

dT dT (c) dt max (d) dt min Figure 4.8: Sensitivity Analysis for Counterflow Flame Simulations

For the fuel rich side the important reactions were reactions (4.8e), (4.9a), (4.8c), (4.9b) and (4.8a).

CH3 + H + M )−−−−* CH4 + M (4.9a)

H + HCO + M )−−−−* CH2O + M (4.9b)

For oxidizer rich side, the important reactions were (4.8a), (4.8c), (4.8e), (4.10a) and (4.10b)

CH2 + OH )−−−−* CH2O + H (4.10a)

C2H4 + H + M )−−−−* C2H5 + M (4.10b)

Overall, there were increasing importance of C2 reactions in the formation of important C2 species from C2H6 to C2H3 [20, 39]. Reactions such as (4.8c) and (4.8e) were found not to have significant impact on the prediction of ignition delay time and counterflow flame temperature profile during the refinement process and were subsequently eliminated from ReduceSens. Chapter 4. Simulation and Analysis 42

4.2.3 Conclusion of Sensitivity Analysis

For the first round of reduction with sensitivity analysis, an initial mechanism of 26 species and 82 reactions were obtained via the combination of the sensitivity analysis results from 0D and 1D case. On the refinement process, it was found that even though sensitive analysis gave valuable information on which reaction had a great impact on the selected validation and verification criteria, the effect of removal of reactions were not obvious. Hencefore, with the refinement process, up to 33 reactions along with 3 species were found to contribute little effect on the ignition delay time and temperature profile in counterflow flames. The species eliminated were C2H2, CH2(s) and CH. Much of the reactions removed were from the 0D sensitivity analysis and it showed that a minimum set of important reactions from sensitivity analysis was required for the accurate prediction of ignition delay time. Reactions such as (4.6b) and (4.5b) were extremely important for describing the behavior of low temperature methane chemistry during preigniton [27, 34]. For 1D calculation, a minimum set of reactions pertaining to the description of fuel rich methane combustion are included in ReduceSens for better agreement with the peak temperature of non-premixed counterflow flame. Important reactions for the fuel lean side were shown to be similar to important reaction from the 0D sensitivity analysis. Ignition of methane usually begin with the process of H abstraction from CH4 molecules to form methyl radical, CH3 and subsequently leading to the formation of CH3O2 through the reaction of the enhanced amount of O2 molecule present in rocket combustion chamber [34, 41]. The presence of more formation of CH3O2 leaded to more CH3O providing a direct reaction pathway to complete combustion to form CO2. Reactions consisting of HO2 and H2O2 were also important and vital in the formation of OH radicals which was key to the description of combustion behavior as shown from the comparison made with experiments using OH radical as heat markers in testing of sub-scaled rocket combustion chamber [22, 23].

4.3 Final Skeletal Kinetic Mechanism

A final refined version of ReduceSens was obtained after the entire reduction procedure for rocket condition and a CHEMKIN format mechanism input file was generated and could be found in AppendixA, showing all the reactions included in the developed skeletal mechanism. The final skeletal mechanism is consisted of 23 species and 49 elementary reactions. All included reactions are reversible. The mechanism also contains two duplicate reactions related to the important species of HO2 and H2O2 and the calculation of their reaction rate were described in Chapter 2. All forward and reverse reaction rate can be determined likewise as described in Chapter 2. Reactions important for counterflow flame were included in the kinetic mechanism and were indicated in the mechanism file. The threshold values for reaction path analysis and sensitivity analysis used were conservative guesses as these values vary from different simulation conditions and were not found in literature. It was also not clear how the elimination of species and reactions would affect the temperature profile and ignition delay time directly and therefore, to prevent the risk of taking away possible important species and reactions, these conservative values were used. After the initial reduction by sensitivity analysis, a compact mechanism of 82 reactions and 26 species was small enough for the refinement process where each reactions was systematically taken Chapter 4. Simulation and Analysis 43 out one by one and checked for large deviation with the temperature profile in counterflow flame and the ignition delay time for both experimental and rocket condition. Those reactions that introduced a large deviation from the full mechanism as well as ReduceRXN were kept in the final skeletal mechanism during the refinement process and reactions with no significant effects on the predicted ignition delay time and temperature profile were eliminated. These deviation had to be larger than the difference between experimental results from literature and the prediction made using the full mechanism in the case of batch reactor simulation at experimental conditions. For rocket conditions, the deviation needs to be larger then 5% error between the results predicted by the new mechanism and the full mechanism, normalized against the full mechanism value. For the temperature profile of counterflow flame, the peak temperature was used and the deviation in peak temperature obtained with the new mechanism needs to be larger than 5% of the peak temperature predicted by the full mechanism before it was determined to be important for the final skeletal mechanism. Thus, in this way, the mechanism of 23 species and 49 reactions was obtained. In the next Chapter, the results from the validation and verification processes were shown and discussed. Chapter 5

Validation, Verification and Performance

5.1 Validation With Ignition Delay Time

In this Chapter, the resultant skeletal mechanism after reduction were validated and verified with experiments and simulation results from full mechanism in rocket conditions. Validation was used when describing the comparison with experimental data and verification was used when the comparison was done with simulation results using the full mechanism.

5.1.1 Validation With Past Experiments

Ignition Delay Times, 50 atm 1000 (µs)

𝑛𝑛 100 𝑔𝑔 𝑖𝑖 Full Mechanism _ 𝜏𝜏 GRI 3.0 ReduceSens ReduceRXN Zhukov et al, 2003 Petersen et al, 1999 10 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 1000/T(K-1)

Figure 5.1: Validation with experimental data in [28, 43]

44 Chapter 5. Validation, Verification and Performance 45

Two mechanism, one from the reduction by reaction path analysis, ReduceRXN, and the final developed skeletal mechanism, ReduceSens, were validated against two set of experimental data at 50 atm. The experimental data comes from shock tube experiment done by Petersen et al [28] and Zhukov et al [43] and consisted of ignition delay times measured at highly elevated pressure of more than 40 bar. Petersen et al [28] investigated the ignition delay times for CH4/O2/diluent at φ = 0.4, 3.0, 6.0 using either N2, Ar or He as diluent gas. Zhukov et al [43] investigated the ignition delay time for methane-air mixtures at φ = 0.5 and at pressure up to 450 atm. These two experiments were chosen for validation as the pressure level were similar to rocket operating condition as described in Table 1.1. Figure 5.1 showed that both ReduceSens and ReduceRXN were in good agreement with the full mechanisms and experimental data, with ReduceSens having a better fit to experimental data. As a comparison, the most widely used GRI MECH 3.0 [10] was plotted. It was shown that GRI MECH 3.0 could not be used at pressure of 50 atm due to the fact that it did not contained species such as CH3O2 that were important for low temperature and high pressure condition. This pressure was also out of the validity range of GRI MECH 3.0 and thus, could not predicted well the ignition delay time at 50 atm. These statements were valid for all pressure above 10 bar as the mechanism was not validated beyond this pressure level [10] and thus, GRI MECH 3.0 should not be used for rocket application as rocket engine usually operates at pressure above 40 bar. The maximum allowable error for the developed skeletal mechanism was the difference in ignition delay time between full mechanism and the experimental values. Both ReduceSens and ReduceRXN were therefore, within the allowable error range.

5.1.2 Verification With Rocket Condition

Rocket Condition, 60 Bar, φ = 1.0

1000

100 (µs) 𝑛𝑛 𝑔𝑔 𝑖𝑖

_ 10 𝜏𝜏

Full Mechanism REDRAM 1 GRI 3.0 ReduceSens ReduceRXN 0.1 0.45 0.55 0.65 0.75 0.85 0.95 1.05 1000/T(K-1)

Figure 5.2: Comparision of different mechanisms at rocket combustion conditions Chapter 5. Validation, Verification and Performance 46

Figure 5.2 showed the calculated ignition delay time for rocket condition as depicted in Chapter 3 where p = 60 bar, φ = 1 and using only pure methane and oxygen without diluents. The results from using REDRAM kinetic mechanism [29], the skeletal mechanism developed from RAMEC [27] were also plotted to test the capability of the mechanism at rocket condition. GRI MECH 3.0 was plotted for comparison. Presently, there are no data available in literature from shock tube experiments at condition similarly to rocket condition as most of the experiments were done with either air as oxidizer or with an oxygen mixture diluted with inert gas such as nitrogen or argon. The result skeletal mechanism should have ignition delay time within 5% error from the full mechanism. From Figure 5.2, REDRAM, ReduceSens and ReduceRXN had comparable accuracy in the prediction of ignition delay as compared to the full mechanism. GRI MECH 3.0 failed to predict the ignition delay time for T < 1200K and it was shown that with the decreased in diluents, the accuracy of GRI MECH 3.0 severely diminished.

5.2 Verification against Temperature Profile From Counterflow Flame Simulation

4000 Full Mechanism 3500 REDRAM Jones-Lindstedt ReduceRXN 3000 ReduceSens

2500

2000

1500 Temperature [K]

1000

500

0 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 Distance [mm]

Figure 5.3: Verification with 1D counterflow flames

The developed mechanism was also verified with the temperature profile for counterflow flame simulation. As a comparison, results obtained using REDRAM was plotted. Results obtained from Jones–Lindstedt mechanism [15] was also included to compare the performance between a skeletal mechanism of 49 reactions and a reduced mechanism of 4 reactions. Jones–Lindstedt was selected as it is widely available in many CFD software such as ANSYS CFX, ANSYS Fluent and OpenFoam and is commonly used for CFD simulation in methane combustion. The allowable error for the temperature profile wss 5% difference from the full mechanism and the reduced or skeletal mechanism should have a temperature profile that fits the profile obtained using the full mechanism. Maximum temperature was used Chapter 5. Validation, Verification and Performance 47 as a verification criteria to make comparison between mechanism. Both REDRAM and Jones–Lindstedt mechanism performed poorly in the case of non-premixed combustion for rocket engine. Peak temperature were under predicted with error value up to 1500K. Jones–Lindstedt mechanism [15] do not contain OH, O, H radicals and thus, less heat release was accounted for in the formation and recombination of such radicals. The predicted peak temperature was thus much lower. For REDRAM, the skeletal mechanism was reduced using ignition delay time as criteria and simulations were only performed for 0D [29]. Hence, the resultant mechanism contains less reactions to account for fuel rich combustion and the predicted peak temperature was lower by 500K. This stressed the importance of correctly identifying the appropriate simulation condition that represented the desired application environment for reduction as it would greatly influence which reactions to be eliminated and which to keep. From the figure, both ReduceSens and ReduceRXN were in good agreement with the full mechanisms. No validation was done for the counterflow flame as there was no available experiment data at pressure above 10 atm. This suggested that more work needs to be done to obtain validation data for the developed kinetic mechanism. As a secondary verification, the comparison with species profile of CH4,O2, CO2,H2O, CO and OH were included in Appendix B. The same observation could be made with the accuracy of Jones–Lindstedt and REDRAM mechanism for predicting these species’ mole fraction. Both ReduceSens and ReduceRXN performed well in predicting the species profile within 5% error of the full mechanism with larger error seen in the prediction of CO and OH radicals.

5.3 Performance Of Final Skeletal Mechanism

The computation performance of the final skeletal mechanism were compared with the full mechanisms and ReduceRXN for the 0D autoignition and 1D counterflow flame simulations. The resulting computation times were shown in Table 5.1. With full mechanism, the computation times are significantly longer for 0D and 1D simulations.

Types of Simulations 0D Autoignition 1D Counterflow Flame Reactions Species Full Mechanism 304.28s 2869.12s 2329 207 ReduceRXN 22.95s 33.38s 165 26 ReduceSens 21.88s 22.36s 49 23

Table 5.1: Simulation times for 0D autoignition and 1D counterflow flame simulations

By reducing the size of the full mechanisms by more then 10 times, the computation time was reduced by a similar amount. The benefit of the reduction was more pronounced for the counterflow flame simulation where the computation time was reduced by 2 orders of magnitude. The final skeletal mechanism produced the shortest computation time for both cases. Although the difference in computation was only around 10s in the 1D case, if the use of the mechanism was extended to 2D and 3D simulations with hundreds of grid cells to solve, the advantage of having a smaller size mechanism quickly becomes obvious [41]. The computation spends the most time in resolving the chemistry of the problem [18] which contain highly non-linear differential equations with stiff time scale and with the coupling of more complicated transport model to better describe the transport properties of the flow, the computation speed up from having a smaller size kinetic mechanism would be much more trivial. Chapter 6

Summary, Conclusions and Future Work

6.1 Conclusions

A final skeletal mechanism of 26 species and 49 reactions was developed from the full mechanism of Zhukov et al [41] which consists of 2329 reactions and 207 species. The mechanism was obtained by the use of reaction path analysis and sensitive analysis and the mechanism was shown to perform well in rocket condition in the prediction of ignition delay time and temperature profile for counterflow flame simulations. The predicted values were within 5% error from the full mechanism and also within the maximum allowable error range with experimental data. All thesis objective were achieved. C3,C4 species were found to be not significant in methane oxidation under rocket operating condition. Species such as CH3OH and CH2OH were found not sensitive to ignition delay times and temperature profile of counterflow flame. C2 sub-mechanism consisting of C2H6 to C2H3 were considered important for fuel rich combustion of methane. The performance of the developed skeletal mechanism was validated with shock tube experiments and verified for ignition delay time and temperature profile of counterflow flame in rocket condition for pure methane and pure oxygen gas mixture.

6.2 Future Work and Outlook

There are room for further reduction of the current skeletal mechanism. One of the immediate work available is to reduce the mechanism further by incorporating quasi steady state and partial equilibrium assumption to eliminate more species from the skeletal reaction by lumping reaction together to form non-elementary reactions within the kinetic mechanism. A more compact reduced mechanism could be developed that can be used directly for CFD application. For the current thesis, there were severely limited experimental data available at the desired rocket condition and thus, more experiments can be planned to gather data for high pressure above 50 bar. In particular interest would be counterflow flame experiments at elevated pressure above 50 bar as the non-premixed nature of counterflow

48 Chapter 6. Summary, Conclusions and Future Work 49

flame gives a directly correlation between the experiments and combustion processes in a rocket combustion chamber. Since the condition in a rocket combustion chamber are strongly non-uniform, it is preferable to carry out experiments in a wide range of equivalence ratio φ. Furthermore, the counterflow flame experiments allow the investigation of a wide range of equivalence ratio and pressure range and thus, provides extremely valuable information on the chemical kinetics in the rocket combustion chamber. Work done in laminar counterflow flame can also be extended to turbulence flow within the combustion chamber found in every rocket engine. A multi-component transport model could be use for the counterflow flame simulation to get a more accurate description and fitting to experimental data. Most of the Arrenhius parameters used were backdated and old and effort should be put into determining these parameters accurately since the Arrenhius parameters formed the basis of the kinetic mechanism input files used for the simulations. A further validation steps for the kinetic mechanism was to compared the flow velocity and species profile of OH radical with experimental results obtained from laser based measuring techniques for a counterflow flame configuration. Another important model validation for 0D case is the comparison of laminar flame speed with experiments in plug flow reactor and simulation of free propagating premixed flames. The laminar flame speed is an important quantity that determine the velocity flow generated in the nozzle and nozzle throat. It is also used to determine the performance of rocket engine. Another useful quantity for turbulence studies is the extinction strain rate which characterizes the counterflow flame simulations in rocket condition. This quantity can be determine to examine the extinction behavior of methane flames under elevated temperature. Bibliography

[1] G Blanquart, P Pepiot-Desjardins, and H Pitsch. Chemical mechanism for high temperature combustion of engine relevant fuels with emphasis on soot precursors. Combustion and Flame, 156(3):588–607, 2009.

[2] H. Burkhardt, A. Herbertz, J. Klevanski, and M. Sippel. Kerosene vs. Methane: A Propellant Tradeoff for Reusable Liquid Booster Stages. Journal of Spacecraft and Rockets, 41(5):762–769, September 2004. doi: 10.2514/1.2672.

[3] CHEMKIN. Version 10131, Reaction Design: San Diego, 2013. http://www. reactiondesign.com/.

[4] Cosilab. Rotexo, 2015. http://www.rotexo.com/.

[5] Luigi Cutrone, Francesco Battista, Giuliano Ranuzzi, Salvatore Bonifacio, and Johan Steelant. A cfd method for simulation of mixing and combustion in high-pressure lox/methane rocket engines. AIAA Paper, 949:2008, 2008.

[6] Fiala, Thomas and Sattelmayer, Thomas. Nonpremixed counterflow flames: Scaling rules for batch simulations. Journal of Combustion, 2014:7, 2014. doi: 10.1155/2014/ 484372. Article ID 484372.

[7] Frouzakis G, E and Boulouchos K. Analysis and reduction of the CH4-air mechanism at lean conditions. Combustion Science and Technology, 159:281–303, 2000.

[8] Goodwin David G. and Moffat Harry K.and Speth Raymond L. Cantera: An Object-oriented Software Toolkit for Chemical Kinetics, Thermodynamics, and Transport Processes. http://www.cantera.org, 2015. Version 2.2.0.

[9] Gansner, Emden R. and North, Stephen C. An open graph visualization system and its applications to software engineering. Software - Practice And Experience, 30(11): 1203–1233, 2000.

[10] Gregory P. Smith, David M. Golden, Michael Frenklach, Nigel W. Moriarty, Boris Eiteneer, Mikhail Goldenberg, C. Thomas Bowman, Ronald K. Hanson, Soonho Song, William C. Gardiner, Jr., Vitali V. Lissianski, and Zhiwei Qin. GRI-MECH 3.0. http://www.me.berkeley.edu/gri_mech/.

[11] D Haeseler, V Bombelli, P Vuillermoz, R Lo, T Mar´ee, and F Caramelli. Green propellant propulsion concepts for space transportation and technology development needs. In ESA Special Publication, volume 557, page 4, 2004.

50 Bibliography 51

[12] O.J. Haidn. Advanced Rocket Engines. Advances on Propulsion Technology for High-Speed Aircraft, pages 6–1 – 6–40, 2008. Educational Notes RTO-EN-AVT-150, Paper 6. Neuilly-sur-Seine, France: RTO.

[13] Hunter, J. D. Matplotlib: A 2D graphics environment. Computing In Science & Engineering, 9(3):90–95, 2007.

[14] Huzel, D.K. and Huang, D.H. Modern Engineering for Design of Liquid-Propellant Rocket Engines. Progress in astronautics and aeronautics. American Institute of Aeronautics & Astronautics, 1992.

[15] Jones, WP and Lindstedt, RP. Global reaction schemes for hydrocarbon combustion. Combustion and flame, 73(3):233–249, 1988.

[16] Donald Judd, S Buccella, M Alkema, R Hewitt, B McLaughlin, G Hart, and E Veith. Development testing of a lox/methane engine for in-space propulsion. AIAA, 5079:9–12, 2006.

[17] Matthew Juniper, Nasser Darabiha, and S´ebastienCandel. The extinction limits of a hydrogen counterflow diffusion flame above liquid oxygen. Combustion and flame, 135 (1):87–96, 2003.

[18] Robert J. Kee, Michael E. Coltrin, and Peter Glarborg. Chemically Reacting Flow: Theory and Practice. John Wiley & Sons, Inc., March 2003.

[19] W. Kitsche. Operation of a Cryogenic Rocket Engine: An Outline with Down-to-Earth and Up-to-Space Remarks. Springer Aerospace Technology. Springer Berlin Heidelberg, 2010. ISBN 9783642105654.

[20] Chung K. Law. Combustion Physics. Cambridge University Press, 2006.

[21] Lindemann, F. A. and Arrhenius, Svante and Langmuir, Irving and Dhar, N. R. and Perrin, J. and McC. Lewis, W. C. Discussion on the radiation theory of chemical action. Trans. Faraday Soc., 17:598–606, 1922. doi: 10.1039/TF9221700598.

[22] Lux, Johannes and Haidn, Oskar. Flame Stabilization in High-Pressure Liquid Oxygen/Methane Rocket Engine Combustion. Journal of Propulsion and Power, 25 (1):15–23, JAN-FEB 2009. ISSN 0748-4658. doi: 10.2514/1.36852.

[23] Lux, Johannes and Suslov, Dmitry and Bechle, Martin and Oschwald, Michael and Haidn, Oskar. Investigation of sub-and supercritical LOX/methane injection using optical diagnostics. volume 5077, page 2006. American Institute of Aeronautics and Astronautics, 2006. doi: 10.2514/6.2006-5077. Joint Propulsion Conferences.

[24] M. Frenklach, H. Wang, C. L. Yu, M. Goldenberg, C.T. Bowman, R.K. Hanson, D.F. Davidson, E.J. Chang, G.P. Smith, D.M. Golden, W.C. Gardiner and V. Lissianski. GRI-MECH 1.2. http://www.me.berkeley.edu/gri_mech/.

[25] McBride, B.J. NASA Glenn Coefficients for Calculating Thermodynamic Properties of Individual Species. NASA technical paper. National Aeronautics and Space Administration, John H. Glenn Research Center at Lewis Field, 2002. NASA/TP-2002-211556. Bibliography 52

[26] G Ordonneau, O Haidn, S Soller, M Onofri, and Gunter Grund. Oxygen-methane combustion studies in in space propulsion programme. In 4th European Conference For Aerospace Sciences,(Eucass), St Petersburg, Russia, 2011.

[27] Petersen, E.L. and Davidson, D.F. and Hanson, R.K. Kinetics modeling of shock-induced ignition in low dilution CH4/O2 mixtures at high pressures and intermediate temperatures. Combustion and Flame, 117(1–2):272–290, 1999. ISSN 0010-2180.

[28] Petersen, E.L. and Davidson, D.F. and Hanson, R.K. Ignition delay times of ram accelerator CH4/O2/diluent mixtures. Journal of Propulsion and Power, 15(1):82–91, January 1999. ISSN 0748-4658. doi: 10.2514/2.5394.

[29] Petersen, E.L. and Hanson, R.K. Reduced kinetics mechanisms for ram accelerator combustion. Journal of Propulsion and Power, 15(4):591–600, July 1999. ISSN 0748-4658. doi: 10.2514/2.5468.

[30] Pitsch, H. FlameMaster v3.3.10: A C++ Computer Program for 0D Combustion and 1D Laminar Flame Calculations. http://www.itv.rwth-aachen.de/downloads/ flamemaster/, 2007.

[31] Revel, J. and Boettner, J.C. and Cathonnet, M. and Bachman, J.S. Derivation Of A Global Chemical Kinetic Mechanism For Methane Ignition and Combustion. Journal De Chimie Physique Et De Physico-Chimie Biologique, 91(4):365–382, April 1994. ISSN 0021-7689.

[32] Robinson, C. and Smith, D.B. The auto-ignition temperature of methane. Journal of Hazardous Materials, 8(3):199 – 203, 1984. ISSN 0304-3894. doi: 10.1016/0304-3894(84) 85001-3.

[33] R.W. Bilger and S.H. St˚arnerand R.J. Kee. On reduced mechanisms for methane-air combustion in nonpremixed flames. Combustion and Flame, 80(2):135 – 149, 1990. ISSN 0010-2180. doi: 10.1016/0010-2180(90)90122-8.

[34] Simmie, John M. Detailed chemical kinetic models for the combustion of hydrocarbon fuels. Progress in Energy and Combustion Science, 29(6):599 – 634, 2003. ISSN 0360-1285. doi: 10.1016/S0360-1285(03)00060-1.

[35] Sutton, G.P. and Biblarz, O. Rocket Propulsion Elements. John Wiley & Sons, Inc., 8th edition, 2011.

[36] Tsuji, Hiroshi. Counterflow diffusion flames. Progress in Energy and Combustion Science, 8(2):93 – 119, 1982. ISSN 0360-1285. doi: http://dx.doi.org/10.1016/ 0360-1285(82)90015-6.

[37] Turanyi, T. and Tomlin, A.S. Analysis of Kinetic Reaction Mechanisms. Springer Berlin Heidelberg, 2014.

[38] Hilda Vernin and Pascal Pempie. Lox/ch4 and lox/lh2 heavy launch vehicle comparison. In 45th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, page 5133, 2009. Bibliography 53

[39] Maas U. Warnatz J. and Dibble R.W. Combustion: Physical and Chemical Fundamentals, Modeling and Simulation, Experiments, Pollutant Formation. Springer Berlin Heidelberg, 2006. ISBN 978.

[40] Webster, C.R. et al. Mars methane detection and variability at Gale crater. Science, 347(6220):415–417, 2015. doi: 10.1126/science.1261713.

[41] Zhukov, Victor P. Kinetic model of alkane oxidation at high pressure from methane to n-heptane. Combustion Theory and Modelling, 13(3):427–442, 2009. doi: 10.1080/ 13647830902767302.

[42] Zhukov, Victor P. Verification, validation, and testing of kinetic mechanisms of hydrogen combustion in fluid-dynamic computations. ISRN Mechanical Engineering, 2012, 2012.

[43] Zhukov, V.P. and Sechenov, V.A. and Starikovskii, A.Yu. Spontaneous ignition of methane–air mixtures in a wide range of pressures. Combustion, Explosion and Shock Waves, 39(5):487–495, 2003. ISSN 0010-5082. doi: 10.1023/A:1026186231905.

[44] Zhukov, V.P. and Sechenov, V.A. and Starikovskii, A.Yu. Autoignition of a lean propane-air mixture at high pressures. Kinetics and Catalysis, 46(3):319–327, 2005. ISSN 0023-1584. doi: 10.1007/s10975-005-0079-7. Appendix A

Final Skeletal Mechanism, CHEMKIN Format

3 Units for the Arrenhius expression are in cal, mol, cm , s and activation energy Ea is in cal/mol. Three-body reactions are specified with a collision partner M with default collision efficiency of 1.0. Troe and Lindemann parameters for falloff, trimolecular reactions are included. Duplicate reactions are treated as describe in Chapter 2. Reactions important for 1D chemistry are indicated in the mechanism file. All reactions are reversible and denoted by <=>.

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ! Full Mechanism: V.P. Zhukov, V.A. Sechenov, A.Yu. Starikovskii, "Autoignition ! of a Lean Propane{Air Mixture at High Pressures", Kinetics and Catalysis, ! Vol. 46, No. 3, 2005, pp. 319{327. ! doi:10.1007/s10975-005-0079-7 ! http://dx.doi.org/10.1007/s10975-005-0079-7 ! Truncated mechanism (C1-C4), Release 08.12.2014 ! obtained by cutting off C5-C7 reactions ! 207 species; 2329 reactions !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ! Modified by Alan Kong, 14.08.2015 ! Generated mechanism after Reaction Path Analysis and Sensitivity Analysis. ! Final Skeletal Mechanism after Refinement Process ! 23 species; 49 reactions !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ELEMENTS H C O N AR END SPECIES H2 H O O2 OH H2O HO2 H2O2 CH2 CH3 CH4 CO CO2 HCO CH2O CH3O C2H3 C2H4 C2H5 C2H6 CH3O2 N2 AR END

54 Appendix A. Skeletal Mechanism, CHEMKIN Format 55

REACTIONS CAL/MOLE O2+CH2O<=>HO2+HCO 1.000E+14 0.000 40000.00 H+O2+M<=>HO2+M 2.800E+18 -0.860 0.00 O2/0.00/ H2O/0.00/ CO/0.75/ CO2/1.50/ C2H6/1.50/ N2/0.00/ AR/0.00/ H+2O2<=>HO2+O2 3.000E+20 -1.720 0.00 H+CH2O(+M)<=>CH3O(+M) 5.400E+11 0.454 2600.00 LOW / 2.200E+30 -4.800 5560.00/ TROE/ 0.7580 94.00 1555.00 4200.00 / H2/2.00/ H2O/6.00/ CH4/2.00/ CO/1.50/ CO2/2.00/ C2H6/3.00/ 2OH(+M)<=>H2O2(+M) 7.400E+13 -0.370 0.00 LOW / 2.300E+18 -0.900 -1700.00/ TROE/ 0.7346 94.00 1756.00 5182.00 / H2/2.00/ H2O/6.00/ CH4/2.00/ CO/1.50/ CO2/2.00/ C2H6/3.00/ AR/0.70/ OH+HO2<=>O2+H2O 2.900E+13 0.000 -500.00 OH+H2O2<=>HO2+H2O 1.750E+12 0.000 320.00 DUPLICATE OH+H2O2<=>HO2+H2O 5.800E+14 0.000 9560.00 DUPLICATE OH+CH4<=>CH3+H2O 1.000E+08 1.600 3120.00 2HO2<=>O2+H2O2 1.300E+11 0.000 -1630.00 DUPLICATE 2HO2<=>O2+H2O2 4.200E+14 0.000 12000.00 DUPLICATE HO2+CH3<=>O2+CH4 1.000E+12 0.000 0.00 HO2+CH3<=>OH+CH3O 2.000E+13 0.000 0.00 HO2+CO<=>OH+CO2 1.500E+14 0.000 23600.00 HO2+CH2O<=>HCO+H2O2 1.000E+12 0.000 8000.00 CH3+O2<=>O+CH3O 2.675E+13 0.000 28800.00 CH3+O2<=>OH+CH2O 3.600E+10 0.000 8940.00 CH3+H2O2<=>HO2+CH4 2.450E+04 2.470 5180.00 CH3+CH2O<=>HCO+CH4 3.320E+03 2.810 5860.00 CH3O+HO2<=>CH2O+H2O2 1.200E+13 0.000 0.00 CH3O2+CH3<=>CH3O+CH3O 3.000E+13 0.000 -1200.00 CH3O+O2<=>HO2+CH2O 4.280E-13 7.600 -3530.00 CH3+O2<=>CH3O2 1.700E+60 -15.100 18785.00 CH3O+CH3<=>CH2O+CH4 2.410E+13 0.000 0.00 O+CH4<=>OH+CH3 1.020E+09 1.500 8600.00 ! !!!!!!!!!!!!!!!!!!!!!!!!!!!1D_Important_Reactions!!!!!!!!!!!!!!!!!!!!!!!!!!!! ! H+O2<=>O+OH 8.300E+13 0.000 14413.00 H+O2+H2O<=>HO2+H2O 9.380E+18 -0.760 0.00 O+H2<=>H+OH 5.000E+04 2.670 6290.00 O+CH3<=>H+CH2O 8.430E+13 0.000 0.00 O+CO+M<=>CO2+M 6.020E+14 0.000 3000.00 H2/2.00/ O2/6.00/ H2O/6.00/ CH4/2.00/ CO/1.50/ CO2/3.50/ C2H6/3.00/ AR/0.50/ H+OH+M<=>H2O+M 2.200E+22 -2.000 0.00 Appendix A. Skeletal Mechanism, CHEMKIN Format 56

H2/0.73/ H2O/3.65/ CH4/2.00/ C2H6/3.00/ AR/0.38/ H+CH3(+M)<=>CH4(+M) 1.270E+16 -0.630 383.00 LOW / 2.477E+33 -4.760 2440.00/ TROE/ 0.7830 74.00 2941.00 6964.00 / H2/2.00/ H2O/6.00/ CH4/2.00/ CO/1.50/ CO2/2.00/ C2H6/3.00/ AR/0.70/ H+HCO(+M)<=>CH2O(+M) 1.090E+12 0.480 -260.00 LOW / 1.350E+24 -2.570 1425.00/ TROE/ 0.7824 271.00 2755.00 6570.00 / H2/2.00/ H2O/6.00/ CH4/2.00/ CO/1.50/ CO2/2.00/ C2H6/3.00/ AR/0.70/ H+C2H4(+M)<=>C2H5(+M) 1.080E+12 0.454 1820.00 LOW / 1.200E+42 -7.620 6970.00/ TROE/ 0.9753 210.00 984.00 4374.00 / H2/2.00/ H2O/6.00/ CH4/2.00/ CO/1.50/ CO2/2.00/ C2H6/3.00/ AR/0.70/ H+C2H4<=>C2H3+H2 1.325E+06 2.530 12240.00 H+C2H6<=>C2H5+H2 1.150E+08 1.900 7530.00 OH+H2<=>H+H2O 2.160E+08 1.510 3430.00 OH+CH2<=>H+CH2O 2.000E+13 0.000 0.00 OH+C2H6<=>C2H5+H2O 3.540E+06 2.120 870.00 HCO+O2<=>HO2+CO 7.600E+12 0.000 400.00 HCO+M<=>H+CO+M 1.870E+17 -1.000 17000.00 H2/2.00/ H2O/0.00/ CH4/2.00/ CO/1.50/ CO2/2.00/ C2H6/3.00/ CH3+OH<=>CH2O+H2 8.000E+12 0.000 0.00 CH2+CH3<=>H+C2H4 4.000E+13 0.000 0.00 O2+CO<=>O+CO2 2.500E+12 0.000 47800.00 OH+CO<=>H+CO2 4.760E+07 1.228 70.00 OH+CH2O<=>HCO+H2O 3.430E+09 1.180 -447.00 H+CH2O<=>HCO+H2 2.300E+10 1.050 3275.00 H+CH4<=>CH3+H2 6.600E+08 1.620 10840.00 2CH3(+M)<=>C2H6(+M) 2.120E+16 -0.970 620.00 LOW / 1.770E+50 -9.670 6220.00/ TROE/ 0.5325 151.00 1038.00 4970.00 / H2/2.00/ H2O/6.00/ CH4/2.00/ CO/1.50/ CO2/2.00/ C2H6/3.00/ AR/0.70/ END Appendix B

Major Species Profiles

Mole fraction profiles of CH4,O2,H2O, CO2, OH and CO. Note that Jones–Lindstedt mechanism does not contain OH radical.

1.0 1.0 Full Mechanism Full Mechanism REDRAM REDRAM Jones-Lindstedt Jones-Lindstedt 0.8 0.8 ReduceRXN ReduceRXN ReduceSens ReduceSens

0.6 0.6

0.4 0.4 O2 Mole Fractions CH4 Mole Fractions

0.2 0.2

0.0 0.0 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 Distance [mm] Distance [mm]

0.18 0.6 Full Mechanism Full Mechanism 0.16 REDRAM REDRAM Jones-Lindstedt 0.5 Jones-Lindstedt 0.14 ReduceRXN ReduceRXN ReduceSens ReduceSens 0.12 0.4

0.10 0.3 0.08 CO2 Mole Fractions 0.06 H2O Mole Fractions 0.2

0.04 0.1 0.02

0.00 0.0 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 Distance [mm] Distance [mm]

0.10 0.30 Full Mechanism Full Mechanism REDRAM REDRAM ReduceRXN 0.25 Jones-Lindstedt 0.08 ReduceSens ReduceRXN ReduceSens 0.20

0.06

0.15

0.04 CO Mole Fractions OH Mole Fractions 0.10

0.02 0.05

0.00 0.00 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 Distance [mm] Distance [mm]

57