Close
About
FAQ
Home
Collections
Login
USC Login
Register
0
Selected
Invert selection
Deselect all
Deselect all
Click here to refresh results
Click here to refresh results
USC
/
Digital Library
/
University of Southern California Dissertations and Theses
/
Experimental studies of high pressure combustion using spherically expanding flames
(USC Thesis Other)
Experimental studies of high pressure combustion using spherically expanding flames
PDF
Download
Share
Open document
Flip pages
Contact Us
Contact Us
Copy asset link
Request this asset
Transcript (if available)
Content
1 Experimental Studies of High Pressure Combustion Using Spherically Expanding Flames by Christodoulos Xiouris A Dissertation Presented to the Faculty of The Department of Aerospace and Mechanical Engineering Of the University of Southern California In Candidacy for the Degree of Doctor of Philosophy In the field of Mechanical Engineering December 2017 2 Acknowledgments This was a long trip of a lot of effort and struggling. The results presented in the current thesis would not be a reality without the collaboration of more than one person. So I would like to take this opportunity and thank everyone that supported me during this quest. I would like to thank my Professor Fokion N. Egolfopoulos for giving me the opportunity to do research in his lab and pursue my PhD in the combustion field. I would like to thank him for all our fruitful discussions and his support regarding research and non-research related issues. The same goes for all my colleagues with which I believe we grew together during these past years. More specifically I would like to thank Dr. Jagannath Jayachandran and Dr. Tailai Ye for their support in the research parts related to uncertainty quantification, experimental techniques, flame instabilities, and all the other numerous projects we worked together on. I would like to thank my college Hugo Burbano for our collaborative effort to examine flames of C 2 hydrocarbons and explain deficiencies in the state of the art foundational chemistry. My colleges Robert Lawson and Ashkan Movaghar for our collaboration in the flame instability related studies. Also I would like to thank Dr. Francesco Carbone for all his helpful advice on various subjects of my research. I would like to also thank Don Wiggins and Mike Cowan from the USC Viterbi/ Dornsife Machine Shop, because without their unbelievable work and the incredible suggestions I would have never been able to have the necessary facilities to perform such demanding experiments. Last but definitely not least I would like to thank my family. I would never have the opportunity to reach my current level if I it was not for them. They taught me how to accept the struggle and give my best self in everything I do. Also because they have been there for me no matter the occasion and shown me that I am never really away from home. 3 Table of Contents Experimental Studies of High Pressure Combustion Using Spherically Expanding Flames .......................... 1 Acknowledgments ......................................................................................................................................... 2 Abstract ......................................................................................................................................................... 5 Chapter 1 Introduction ................................................................................................................................. 6 1.1 Future energy consumption projections ............................................................................................ 6 1.2 Laminar combustion research ............................................................................................................ 7 1.3 Spherically expanding flames under constant pressure conditions ............................................. 10 1.4 Spherically expanding flames under constant volume conditions ................................................... 12 1.5 Instabilities in spherical expanding flames ....................................................................................... 13 Chapter 2 Experimental Approach .............................................................................................................. 15 2.1 Experimental facility ......................................................................................................................... 15 2.1.1 Cylindrical chamber facility ........................................................................................................ 15 2.1.2 Spherical chamber facility .......................................................................................................... 20 2.2 Experimental methodology............................................................................................................... 21 2.2.1 Constant pressure experiment .................................................................................................. 21 2.2.2 Constant volume experiment .................................................................................................... 24 Chapter 3 Modeling Approach .................................................................................................................... 27 3.1 Freely propagating flames ................................................................................................................ 27 3.2 Spherically expanding flames ............................................................................................................ 28 3.2.1 Direct numerical simulations ..................................................................................................... 28 3.2.2 Hybrid thermodynamic-radiation model ................................................................................... 29 Chapter 4 Results and Discussion ............................................................................................................... 31 4.1 DNS-assisted extrapolation for constant pressure experiments ...................................................... 31 4.2 Uncertainty quantification of spherically expanding laminar flame speeds .............................. 37 4.2.1 Mixture preparation................................................................................................................... 39 4.2.2 Data acquisition ......................................................................................................................... 42 4.2.3 Data processing .......................................................................................................................... 42 4.3 Studies of foundational fuel chemistry ............................................................................................. 53 4.3.1 Experimental approach .............................................................................................................. 54 4.3.2. Modeling approach ................................................................................................................... 56 4 4.3.3 Results and Discussion ............................................................................................................... 57 4.4 Flame acceleration due to flame instabilities ................................................................................... 68 4.3.1 Cylindrical chamber experiments .............................................................................................. 69 4.3.2 Spherical chamber experiments ................................................................................................ 72 Chapter 5 Summary and Future Recommendations .................................................................................. 85 5.1 Uncertainty quantification of spherically expanding laminar flame speeds .................................... 85 5.2 Studies of foundational fuel chemistry ............................................................................................. 85 5.3 Flame acceleration due to flame instabilities ................................................................................... 85 References .................................................................................................................................................. 86 5 Abstract Experiments involving laminar, premixed, spherically expanding flames were performed using two different experimental facilities. The first one involves experiments in a cylindrical constant volume chamber with optical access in which the flame is directly observed with high speed imaging using the shadowgraph technique. The second involves performing experiments in a totally spherical chamber with no optical access, for which the pressure evolution is the only observable and is used to derive flame speeds at much higher, engine relevant pressures and temperatures, taking advantage of the isentropic compression stage of the experiment. The first part of the study was aimed to define the uncertainty in data of laminar flame speed obtained from spherically expanding flames. A novel DNS (Direct Numerical Simulation) assisted extrapolation methodology was proposed in order to minimize systematic errors emerging from the use of theoretical linear and non-linear extrapolation equations to obtain the final value of the propagation speed at zero stretch rates. Moreover a complete, rigorous uncertainty quantification methodology was proposed, in order to calculate the errors from all the experimental aspects and then propagate and combine them to estimate the uncertainty in the final value of laminar flame speed. Such a study had never been performed in the past and is of high importance in order for the experimental targets to be meaningful for chemical scheme optimization of interest to the kinetic modeling community. Upon completion of the uncertainty quantification methodology, the second part of the study included a detailed investigation regarding our current knowledge of laminar flame speeds of C 2 hydrocarbons. Those fuels are of great significance as they comprise the foundational chemistry for the combustion of heavy hydrocarbons. Experiments of spherically expanding flames of CH 4 , C 2 H 6 , C 2 H 4 , C 2 H 2 mixtures were performed on an equal basis and the comparisons with kinetic model predictions revealed serious deficiency in predicting the propagation speed of rich acetylene flames. The importance of this evidence can also be supported by the fact that acetylene is one of main species involved in the reaction pathways that lead to soot production in combustion of hydrocarbon fuels under rich conditions. The third study in the current thesis revolves around flame acceleration due to instability formation on the flame surface during the compression stage of propagation. All studies currently existing in the literature have solely focused on describing the propagation characteristics of unstable flames during the initial, constant pressure stage of the flame propagation. In this study experiments were performed in both cylindrical and experimental configurations taking advantage of every capability. The onset of flame acceleration due to surface area growth caused from instabilities was promoted at various parts during propagation. The results obtained show an attenuating trend in the unstable flame acceleration, once the spherical flame enter the compression stage that is following the initial constant pressure and temperature propagation part. 6 Chapter 1 Introduction 1.1 Future energy consumption projections The ever increasing energy consumption trends impose the usage of fossil fuels as the only means of covering today’s energy needs. The high energy density of fossil fuels makes them a necessity for almost every-day applications and most importantly for transportation, aviation and space exploration. Renewable sources, though promising at first sight, will never be able to play the primary role. Many times, the costs involved for maintenance and operation of those sources/facilities, together with the pertinent efficiencies are not mentioned clearly and the trends followed or promises made are simply for the shake of investment and profit. Of course research involving renewables and nuclear sources should not cease, however combustion should remain the main focus of energy research. In its recent report [1] the U.S. Energy Information Administration (EIA) projects that the energy consumption worldwide will have an increase of about 50% between 2010 and 2040. The increase predicted to be ~300 quadrillion British units (Btu) and most of the growth will come from non-OECD countries, meaning countries outside the Organization for Economic Cooperation and Development. The map in Fig.1 better clarifies the current and following statements. Despite the relatively fast growth in renewable sources and nuclear energy, fossil fuels will still need to satisfy ~80% of the energy needs by 2040. 7 Fig. 1. Future energy consumption predictions. Being able to predict these future trends, energy research should continue focusing in fossil fuel combustion and in increasing the efficiency of the current devices and methodologies adopted. Moreover, explore ways of reducing the pollution emanating from combustion devices, as both factors are of equal significance. Stricter regulations are however needed, as no kind of research innovation is enough to control/satisfy the narrow-minded consuming tendencies of the population in “developed countries”. 1.2 Laminar combustion research Combustion research is an inter-disciplinary, multiscale topic, combining chemistry, fluid mechanics, and heat transfer and extending from quantum mechanics to large scale fluid flow modeling. Real life applications involve highly turbulent flows, which are almost impossible to analyze experimentally as the problem tackled is highly coupled. Depending on the specific conditions and the comparison of time scales between fluid mechanics and burning rate, simplifications can be made as not all pertinent disciplines are equally important for every 8 experiment. For certain cases even an oversimplified chemistry database/knowledge is more than enough, while the difficulty lies in the accurate modelling of energy cascade by eddies in the turbulent flow field. Halfway between combustion chemistry and complicated, reacting, turbulent flows there is a field which can contribute to both sides. This is the laminar combustion field. Laminar flames produced implementing canonical configurations with very well defined boundary conditions, can on one hand offer a very useful target for kinetic mechanism validation and at the same time provide very important scaling parameters necessary to the turbulent combustion community. When it comes to premixed flames the main validation target and scaling parameter needed is the flame propagation speed of the burning front, most commonly taken with respect to the unburnt mixture. The laminar flame speed, o u S , is defined as the propagation speed of a steady, laminar, one- dimensional, planar, stretch-free, and adiabatic flame, hereafter referred to as freely propagating flame. o u S is an important fundamental property of a combustible mixture being a measure of its reactivity, diffusivity, and exothermicity (e.g., [2][3]), an essential validation target for kinetic models, and a key scaling parameter in turbulent combustion. It has to be realized thus, that o u S needs to be considered as a “concept property” against which kinetic models are validated and/or optimized. There is extensive literature on the topic of laminar flame propagation and the interested reader can consult a number of review articles (e.g., [5][6][7][8][9][10][11]). The first measurements of flame propagation speeds have been reported 148 years ago in 1867 with the experiment of Bunsen [12]. Since then, a larger number of data has been reported in the literature derived from Bunsen flames (e.g., [13][14][15]), Spherically Expanding Flames (SEF) under constant pressure (e.g., [16][17][18][19][20]) and volume (e.g., [21][22][23][24][25][26][27]) conditions, Counter-Flow Flames (CFF) (e.g., [28][29][30]), and recently the heat flux method (e.g., [31][32][33]). Steady-state burner-type laminar flame experiments can be carried out up to pressures, P ≈ 10 atm or so to keep the Reynolds number below its transition value and avoid instabilities, while experiments at notably higher pressures can be carried out only using SEFs [11][34]. Figure 2 indicates the pressure range where each configuration is being operated at. A survey of 9 nearly 120 papers published in the major combustion journals on experimental determination of o u S , reveals that 65% of the measurements have been carried out at P = 1 atm, while only 8% for P < 1 atm and 27% for P > 1 atm. It is noted also, that the majority of the published o u S data, regardless of pressure, correspond to unburned mixture temperatures, T u , that are either ambient or slightly elevated. Furthermore, the number of flame propagation studies for gaseous fuels is notably higher than those corresponding to liquid fuels. With few exceptions, o u S data are scarce for conditions encountered in piston and jet engines, that is for liquid fuel flames at P = 20-50 atm and T u = 700-800 K, given that measurements can be rather challenging and highly uncertain. Fig. 2. Pressure capabilities of currently state of the art canonical configurations. Furthermore, at high pressures, o u S is the only measurable flame quantity, given that flame structures cannot be resolved due to the decreased flame thickness especially for premixed flames [11][34]. It is also of interest to note that the sensitivity of o u S to kinetics is similar to that of extinction strain rate, K ext , of premixed flames as well as non-premixed flames [30][35]. 10 1.3 Spherically expanding flames under constant pressure conditions Measurements of SEF’s date back in the early 1920s when Stevens [16] performed studies of flame propagation within soap bubbles propagating under nearly constant pressure conditions. Since then there has been a significant progress both experimentally and computationally, however significant scatter was apparent in the data from various groups. During the 1980’s the effect of stretch [3] on flame stretch was introduced and subsequently its subtraction from the measurements resulted in notable decrease in the experimental scatter. By combining the newly obtained information regarding stretch with the former analysis of Markstein [36] regarding the dependence of burning speed to fluid mechanics effects in laminar flames, Dowdy et. al. [17] performed measurements of laminar flame speeds using spherically expanding flames, under constant pressure conditions. Since then, more groups contributed on the pertinent physics and improvement in the knowledge of mixture dependence and stretch, pressure or temperature effects (e.g., [37][38][39] ). Experiments are typically performed in cylindrical system with full optical access from both sides. A high speed camera is recording the flame evolution and then the speed is derived from post-processing the radius vs. time data. It was shown that ignition effects are important at the very early stages of propagation [40] and the data involved should not be considered. Also, since the experiment is performed inside a closed vessel, confinement and compression effects [41][34] are responsible for flame distortion and deceleration correspondingly at the later stages of propagation. Thus, these data should be rejected as well. This leaves the experimentalist with a 1-3cm radius range where healthy data can be obtained. One of the major issues regarding obtaining the laminar flame speed, in both CFF and SEF configurations, is the fact that extrapolation needs to be performed to obtain the final value. More specifically, in SEFs under constant pressure conditions, the data set initially obtained comprises of the radius vs. time dependence of the propagating front. Using this information the propagation speed as a function of fluid mechanics/stretch is obtained, however the range does not extend all the way to zero stretch, which is where the flame speed “becomes” the true laminar flame speed. As expected the nonlinear nature of the data results in errors when various 11 methodologies are implemented for these extrapolations. This issue of data accuracy has been addressed in recent studies [44][45][46], in which the inadequacies of “standard” extrapolation methods used in CFF and SEF experiments were demonstrated by performing Direct Numerical Simulations (DNS) of the experiments and by performing extrapolations of the DNS data using formulas derived from theories (e.g., [47][48]) that invoke simplifying assumptions. It has been shown that in several instances such formulas fail to reproduce the known o u S value by as much as 60% [46]. An additional important result of those studies [44][45][46] is that using theories based on simplifying assumptions to interpret directly measured data and extract thus o u S , could diminish the value of the reported data and that instead DNS should be used, as first proposed by Wang et al. [49]. Two additional issues regarding SEF experiments are those of buoyancy and radiation heat losses. The most efficient way to tackle those issues is to choose mixtures which result in vigorously burning flames for which these effects are of low significance. For weakly burning flames the errors introduced can be significant and the corrections methodologies have their own uncertainties. It is also worth mentioning that a rigorous analysis regarding the uncertainty quantification in data obtained from SEFs did not exist currently in the literature and that task was undertaken as part of my research. The transient nature of the experiment along with the cost and effort involved in performing each experiment does not allow for extensive repetitions to obtain statistically significant number of data points. As a result a rigorous error propagation methodology is necessary in order for any type of comparisons to be meaningful. The analysis is presented in detail in the results section. Uncertainty quantification analysis was also performed for the constant volume experiment that is described in the results section. 12 1.4 Spherically expanding flames under constant volume conditions The need to measure o u S at engine-relevant conditions has been recognized long time ago. Lewis and von Elbe [21] were the first to propose that by using the pressure data during the isentropic compression stage (following the constant pressure stage) in SEF experiments, the flame propagation speed could be computed by invoking a number of assumptions and a detailed thermodynamic analysis. This proposition was a pioneering one as during the compression stage notably high pressures and T u can be achieved within 30 milliseconds or less, a time that is short enough to result in any measurable fuel decomposition and/or to compromise the integrity of the chamber for T u of the order of 600-800 K. Bradley and Mitcheson [23] and subsequently Metghalchi and Keck [24][25] adopted the approach of Lewis and von Elbe [21] and developed also a thermodynamic model that allowed for the measurement of o u S for flames of gaseous and liquid fuels. Following the previously described approximately constant pressure region, as the flame propagates outwards in the perfectly spherical vessel, the unburned gas starts being compressed isentropically and its pressure and temperature rises. Thus, the flame consumes a mixture that is at a different thermodynamic condition at each instant. Since introducing optical access causes deviation from sphericity, this time the pressure, P, is the only observable obtained from the experiment as the chamber needs to be perfectly spherical. However concerns have been raised about the potential formation of instabilities that could be unaccounted for in cases that optical access was not possible as well as about potential stretch effects. It is known that the formation of cells can lead to generation of flame surface area and as a result lead to increased burning rates. Metghalchi and co-workers [26][27] resolved the issue of cell formation, by performing measurements first in a cylindrical chamber with optical access and identify thus reactant compositions for which instabilities do not develop during the compression stage when the flame radius is large and the stretch effects are small. Then, identical initial conditions are established in a perfectly spherical chamber for which the assumptions of the thermodynamic model are applicable. Regarding stretch effects, Metghalchi 13 and co-workers [26][27] argued that they should be small at large flame radii and supported this argument by a series of carefully executed experiments. 1.5 Instabilities in spherical expanding flames Instabilities that lead to the formation of cells, and are relevant to SEF experiments, are the Darrieus-Landau, DL, and Thermal-Diffusive, TD, instabilities. The DL instability is caused by the density jump across the flame, represented by the ratio of densities of burned to unburned gas, σ; and the TD instability due to non-equidiffusion of thermal and chemical energy, identified by the Lewis number, Le. In the context of the TD instability, SEFs which are positively stretched are stable for Le > 1 and become unstable for Le < 1. For DL instabilities, stabilizing effects could result from stretch or non-equidiffusive effects present in a flame of Le > 1 mixtures. Even for mixtures with Le > 1, SEFs at high pressures could experience DL instabilities due to the notable decrease in the flame thickness. The studies of Darrieus [50] and Landau [51] treated a planar flame as a discontinuity, propagating at a constant speed and showed that it is inherently unstable. Subsequent studies indicated the importance of flame response to transport processes [52]. Significant work has been done regarding the prediction of the onset of cellularity in SEFs at constant pressure, both experimentally (e.g., [53][54][55][56]) and numerically (e.g., [57][58][59]). The formation of cells is observed as initial cracking of the flame, followed by the appearance of a coherent cellular structure which results in flame acceleration due to the increase in flame surface area. Further studies have demonstrated that the ever continuing cross-cracking can result in the acceleration becoming self-similar in nature (e.g., [60][61][62][63][64][65]), and can eventually lead to a fully turbulent flame. However no theoretical or experimental work currently exists in the literature regarding the onset of cells and the degree of flame acceleration during the compression stage of the constant volume SEF experiment; as denoted earlier this is the stage during which experimental data are collected, in order to derive S u . Thus, gaining knowledge of the physics of instability growth during this stage is invaluable from an experimental point of view. 14 The goal of this study is to investigate the extent to which the development of cells and the subsequent cell-induced flame area growth affect the propagation characteristics of SEFs during the compression stage of the constant volume experiment. To this end, experiments were first performed in a cylindrical chamber with optical access for flames that exhibited variable Markstein lengths, L b , in order to identity the thermodynamic conditions of the unburned gas corresponding to the onset of cellularity. Subsequently, measurements were performed for the same mixtures in a constant volume spherical chamber, and the burning rates obtained were compared against numerical results of smooth flames to provide insight in the effects of cellularity on the burning rate. 15 Chapter 2 Experimental Approach 2.1 Experimental facility 2.1.1 Cylindrical chamber facility Figure 3 depicts the schematic of the cylindrical chamber facility where the constant pressure data are obtained, while Fig. 4 is a picture of the facility itself. The chamber is constructed from 316-type stainless steel, measures 270 mm in length and 220 mm in diameter, and can operate up to 90 atm post-combustion pressure. It is fitted with 76 mm thick and 152 mm diameter fused quartz windows at both ends, which are sealed to the chamber with heavy duty O-rings. The initial pressure, P o , cannot exceed 8 atm in order to avoid failure of the quartz windows during the compression stage of the experiment. A modified Z-type shadowgraph system is implemented for the flame propagation imaging. The light from a high power LED source is initially focuses at a pinhole in order to obtain an “ideal” point source. The pinhole is placed at the focal length of the first concave mirror of 152.4 mm diameter and f10. This mirror produces the collimated band of light which, with the use of a flat mirror, is guided through the text section. Finally the parallel light passes through a second concave mirror identical to the one before, so that the light can be finally collected by the high speed camera. The propagating flame was imaged using a CMOS Phantom v710 monochrome high-speed camera, capable of achieving 25,000 fps in a 512x512 pixel window. A 601B1 Kistler dynamic pressure sensor was used to record the pressure trace during the experiment. Ignition and data acquisition were synchronized and controlled by a LabView program. The chamber is fitted with two opposing stainless steel electrodes that allow for central ignition. An ignition system has been designed to offer accurate control over the energy that is being discharged to the two 16 electrodes. Data are typically considered only for radii larger than ~8 mm in order to avoid effects from the ignition energy and smaller than approximately 30 mm (30% of our chamber radius) to avoid confinement and compression effects. Fig. 3. Schematic of the cylindrical chamber configuration. Fig. 4. Cylindrical chamber configuration. The filling of the chamber was done using the partial pressure method. The partial pressures were measured using high accuracy Omega PX409-A5V static pressure transducers with the 17 appropriate full-scale range to minimize uncertainties in the equivalence ratio, , defined as the ratio of fuel to air in the mixture scaled by the same ratio of a mixture having the same gas components but at stoichiometric proportions (i.e. complete combustion to get CO 2 and H 2 O). Transducers with 0-5psi, 0-15psi, 0-50psi, 0-150psi, and 0-500psi were typically used for the majority of the experiments mentioned in the current thesis. Once again it needs to be clarified that the cylindrical chamber configuration with optical access serves the purpose of collecting data only in the constant pressure region of flame propagation. Following that stage, the flame starts compressing the unburned gas and data in this domain can only be interpreted using the totally spherical with no optical access, chamber as it will be described later in this section. Figure 5 presents a typical pressure trace of a P o =3atm experiment. The regions of constant pressure and isentropic compression are denoted with “Con P” and “Con V” respectively. Fig. 5. Typical experimental pressure trace with denoted regions of data collection for the constant pressure and constant volume combustion cases. Figure 6a presents three snapshots of a typical smooth SEF, while Fig. 6b presents a flame transitioning from stable to unstable. Unstable flames are fundamentally not appropriate for the extraction of o u S . In order to avoid transition to unstable flames a common practice is the replacement of N 2 with He as the inert component, the reason being the following. As previously 18 defined, Le=α/D, with α the heat diffusivity of the mixture and D the mass diffusivity of the deficient reactant, is a measure of the flame energy loss via heat loss (not including radiation heat losses) over the energy gain through mass gain. If Le is smaller than unity then a SEF has a tendency towards TD instabilities. By utilizing He, which has higher heat diffusivity we can achieve higher Le numbers and suppress the TD instabilities. (a) (b) Fig. 6. Evolution of a) a stable laminar SEF and b) an SEF transitioning from stable to unstable. Another kind of instabilities in spherical expanding flames is hydrodynamic, which are caused due to the large density gradient between the burned and unburned gases across the flame. As the initial pressure is increased the flame becomes thinner and the gradient of the density, ρ, becomes steeper, which leads to DL instabilities. By replacing N 2 with He, flames with larger flame thickness are achieved and the density jump, being less abrupt, offers smooth flames even at much higher pressures. Finally at higher pressures the burning rate is increasing however the flame speed is reduced. As result buoyancy effects emerge, which does not allow for fundamental studies of flame propagation. Buoyancy effects are avoided with partial or total replacement of N 2 with Helium which results in an increase in the flame speed. On the other hand the amount of He that needs to be inserted in place of N 2 is increasing the mixture’s thermal diffusivity which causes serious ignition difficulties. Even if a significantly large amount of energy is used in order for a flame to start propagating the smoothness of the flame is going to be seriously damaged. This problem is especially important at lower pressures since the minimum ignition energy scales inversely with pressure. Figure 7 presents snapshots of failure to ignite due to this reason. 19 Fig. 7. Failure to ignite due to the mixture’s high thermal diffusivity. Considering all the above it is quite obvious that for many fuel cases, finding the correct region of equivalence ratios and diluent combination is a very challenging procedure experimentally and that many times a ‘’perfect recipe’’ does not really exist. A sophisticated ignition system was absolutely necessary, as in many cases the breakdown energy was not enough to lead to ignition. In order to deal with this difficulty an advanced ignition system was constructed, which was designed and tested in the past by Professor P.D. Ronney. The advantage of this ignition system is offering control over the energy that is being deposited between the two electrodes in order to ignite the mixture utilized each time. First 45kV are used to cause the necessary break-down between the electrodes and then a second system which can store up to 20 J of energy is dumping the excess of energy that is needed. The very sophisticated transistor configuration gives us the opportunity to accurately synchronize the two high voltage systems and also control the amount of energy we are using, by choosing the correct duration of each pulse. Following the description of this experimental setup and the utilized equipment the experimental procedure for a preparation of an experiment is presented so that the reader gets a better idea about the experiment. The experimental procedure leading to collecting data is the following: 1. Perfectly seal the chamber before starting any operation. 2. Use of vacuum pump and controller to achieve vacuum inside the chamber. Through a controller every possible leak can be detected and be dealt with. 20 3. Insert the first gas component by using the partial pressure method and measuring the pressure via the static pressure transducer. 4. Close the chamber inlet using a high pressure and temperature (severe duty) needle valve. 5. Vacuum the lines before inserting the next component and send everything to the central exhaust system. 6. Introduce the new gas whose pressure adds up to the previous ones. This procedure is repeated until the chamber is filled with all components. 7. The chamber is sealed and the Shadowgraph system is prepared. 8. The spark is initiated and the flame evolution is monitored using the high speed camera, while the dynamic pressure transducer is recording the pressure time evolution. 9. The combustion products are exhausted, and the chamber is vacuumed again for the next experiment. 2.1.2 Spherical chamber facility For some of the instability studies, which will be described in detail in a later section, the totally spherical chamber was implemented as the analysis was performed in the compression stage of the experiment. The schematic of the experiment is presented in Fig. 8. Fig. 8. Schematic of the spherical chamber configuration. 21 The entirely spherical chamber has an internal diameter of 203mm. The chamber is made of stainless steel and can withstand post-combustion pressures up to 200 atm. Mixture preparation and dynamic pressure measurements were performed using identical equipment and methodology as for the constant pressure experiments in the cylindrical chamber and were previously described. Since there is no optical access, the only observable is the pressure time history, which was then used to derive values for flame propagation speeds similarly to previous studies (e.g., [23][24][25][26][27]). 2.2 Experimental methodology 2.2.1 Constant pressure experiment As explained in the introduction, the spherically expanding flame configuration is the only one that allows for the measurement of stable/laminar flames at high pressures, P, i.e. greater than 5-7 atm. It is difficult to use the counterflow technique at higher pressures due to Reynolds number limitations. Shadowgraph and Schlieren techniques are used typically for monitoring the time evolution of the flame surface. The main assumptions are 1. That the burned gas is stationary, i.e. U b =0, which is shown theoretically and computationally to be true for the region that the pressure rise in the vessel is less than 2%. 2. That o ub o bu S S , where o S denotes the flame speeds at zero stretch, while subscripts “u” and “b” indicate unburned and burned equilibrium states. As a result, the notation o u S denotes the speed of an unstretched flame, with that speed taken with respect to the 22 unburned gas. It has to be pointed out that this equality holds only at the zero stretch limit and not for stretched flame speeds. The limitations of this experimental methodology are again buoyancy effects in the case of low-speed flames and the presence of DL and TD instabilities. Following ignition, the flame evolution is recorded with the high speed camera. Then for each image an edge detection algorithm is utilized which tracks the radial change in light intensity. Then a number of points are detected on the flame periphery, and a circle is fit. Having the flame radius, R f , at each time and accurately knowing the inter-frame time, the stretched burned flame speed f b dR S dt is calculated by numerical differentiation. Figure 9 depicts a schematic of the flame including all the velocity components involved. Fig. 9. Description of the propagation of a spherically expanding flame. U g is the velocity of the unburned gas ahead of the flame, S b the burned flame speed, and U b the inward velocity of the burned gas. The flame stretch rate is defined as 1 dA K A dt [3] where A is the area of an infinitely small element, and can be simplified in the case of outwardly propagating flames under constant pressure: 23 2 2 (4 ) 1 1 2 2 4 ff b ff d R dR dA KS A dt R dt Rf dt R (1) Thus, the variation of S b with K can be plotted and upon evaluation, data affected by ignition and compression at the two ends are removed. As mentioned in the introduction, some type of extrapolation is necessary finally, in order to obtain the burned flame speed at zero K. This extrapolation can be done assuming a, to the first order, linear relationship between S b and K [66]: o b b b S S L k (2) where L b is the Markstein length [36]. For situations of non-unity Lewis number and high K’s the flame response can deviate from the previous linear relation, imparting significant errors. To account for these second order effects various non-linear formulas were derived, all of them having as basis the formulation of Ronney and Sivashinsky [67]. One of the widely used versions is the one of Kelley et al. [68]: 22 ( ) ln( ) 2 b b b o o o b b b S S L K S S S (3) which results from the Ronney-Sivashinsky formulation by removing the unsteady term and assuming propagation in a quasi-steady manner. The same authors did further work on this subject [69] to explain the inadequacies of their extrapolation formula and suggest a new one by series expansion of again the [67] formulation. Of course problems regarding the extrapolation step are still evident (e.g. [45][46]). For mixtures close to stoichiometry and with Lewis number close to unity the observed discrepancies are reduced. 24 Finally, by applying the mass continuity equation the laminar flame speed can be calculated as: u b o b o u S S (4) The density ratio of burned to unburned gases at equilibrium is calculated using again the STANJAN algorithm [70] . Very recently a new approach was introduced for the calculation of o u S , based on the PIV (Particle Image Velocimetry) technique (e.g. [71]). In order to perform such a task a KHz speed camera and double-pulsed laser are necessary since the whole event is completed in ~50 msec. The main concept behind this idea is to first calculate the displacement velocity with respect to the unburned gas, U n =U g -S b , with U g the maximum velocity of the unburned mixture, just ahead of the flame. Silicon oil particles are implemented as seeding to infer the U g using PIV. To calculate S b this time, the R f is obtained from the disappearance of the silicon oil particles from the spherical flame. Us a result the U n for every R f is obtained and once again extrapolation to zero K is performed. Although promising due to certain advantages, this technique suffers from the fact that the subtraction of two large and noisy quantities results in a value with high percentage uncertainty. Moreover the cost involved in obtaining such diagnostic capabilities is prohibited for most labs. 2.2.2 Constant volume experiment This experiment takes advantage of the compression stage of the flame history. The spherical chamber allows for measurement of the pressure history solely. At the same time, if certain assumptions are satisfied the P vs R f relation can be obtained computationally implementing a simple thermodynamic model whose only input is the chamber dimensions, the initial thermodynamic conditions and the mixture composition. Having now the [P, t] data and [P,R f ] 25 thermodynamic prediction, the flame speed with respect to the unburned gas can be calculated via the formula [22] : 33 2 3 wf f u fu RR dR dP S dt R P dt (5) with u the heat capacity ratio of the unburned gas and R w the chamber radius. Since now compression effects are significant the inward velocity (Fig. 9), induced in the burned gas leaving the reaction zone, is not negligible (U b ≠0) which was the case in the constant pressure case described previously. The main assumptions involved are: I. The flame front is totally smooth and spherical. That imposes that the chamber needs to have a totally spherical geometry. II. The flame is infinitely thin. III. The unburned gas has uniform temperature and composition. IV. The pressure P is uniform throughout the vessel. V. The burned gas is in chemical equilibrium at any instant, thus accounting for dissociation at high temperatures attained during compression. VI. No chemical reactions occur in the unburned gas. 26 It has been shown ([34][72]) that stretch effects are insignificant when P/P o is more than ~2.5. This is of tremendous importance as in this case o uu SS and thus no extrapolation is needed to obtain the final value. Though at first sight it seems like the perfect approach to obtain data at engine relevant conditions, recent work [72] showed that this is not the entire story. In order for meaningful compression rates to be initiated the R f /R w ratio has to exceed a value of ~0.8. What that really means is that during data collection the flame ball has significant size and also significantly high temperatures, more than the initial adiabatic flame temperature, T ad , since the burned gas is also getting compressed during the flame propagation. As one can imagine the radiation heat losses are not minor anymore and a significant mismatch in the [P, R f ] occurs which can result in unphysical results. As a result the radiation effect has to be introduced to the previously mentioned thermodynamic modeling. Radiation theories however are still far from perfect. The accuracy of the results gets significantly improved, but still the only solution to this problem seems to be the measurement of the [R f , t] data along with the [P, t] data. 27 Chapter 3 Modeling Approach 3.1 Freely propagating flames In all the parts presented, o u S was computed using the PREMIX code [73][74], integrated with CHEMKIN [75] and the Sandia transport subroutine libraries [76]. The H and H 2 diffusion coefficients of several key pairs are based on the recently updated set [77]. The code has been modified to account for thermal radiation of CH 4 , CO, CO 2 , and H 2 O at the Optically Thin Limit (OTL) [78]. The computed o u S value constitutes the “known” answer of the speed of a freely propagating flame based on the kinetic and transport models used in DNS. These “baseline” values can be used then to quantify non-ideal effects like stretch, heat loss, etc., present in flames by analyzing deviations from the known o u S value. The simulations performed in the various studies of the thesis involved the kinetic models of Davis and co-workers [79], USC Mech II [80], JetSurf 2.0 [81], Dames et al. [82], and HP Mech [83] For certain cases involving DNS simulations of spherically expanding flames, utilized in extrapolation reasons, a reduced DRG [84] version of USC-Mech II consisting of 43 species and 319 reactions was created. However for all laminar flame speed calculations using the PREMIX code, the full schemes with the correct pressure coefficients were implemented. 28 3.2 Spherically expanding flames 3.2.1 Direct numerical simulations In order to model SEFs under constant pressure and constant volume conditions, a Transient One-dimensional Reacting flow Code (TORC) was employed. TORC was originally developed [44] to model the evolution of SEFs under constant pressure. The code has been modified subsequently in order to model the evolution of SEFs in a confined constant volume spherical domain thereby accounting for the compression stage during which pressure is assumed to vary in time but not in space, given the small Mach numbers associated with SEFs. Thus, the velocity field can be obtained using the mass conservation equation without having to solve the momentum conservation equation. The one-dimensional reacting flow conservation equations of mass, species and energy were integrated numerically in spherical coordinates [85] with the following Boundary Conditions (BC) for constant volume flame propagation: ( 𝑑𝑇 𝑑𝑅 ) 𝑅 =0 = 0, 𝑈 𝑅 =0 = 0, (𝑉 𝑘 ) 𝑅 =0 = 0 (BC1) ( 𝑑𝑇 𝑑𝑅 ) 𝑅 =𝑅 𝑤 = 0 or 𝑇 𝑅 =𝑅 𝑤 = 𝑇 𝑤𝑎𝑙𝑙 , 𝑈 𝑅 =𝑅 𝑤 = 0, (𝑉 𝐾 ) 𝑅 =𝑅 𝑤 = 0 (BC2) where T represents the temperature, R the spatial coordinate, U the gas velocity, R w the chamber radius, and V k the diffusion velocity of species k. Note that the chamber wall can be treated as either adiabatic or isothermal by specifying its temperature T wall . For the constant pressure results an outflow boundary condition was alternatively implemented, when compression effects were not of immediate interest. Second order upwind and central finite difference schemes, both derived for second order accuracy on a non-uniform grid, were used to discretize the convective and diffusive terms respectively. A Differential Algebraic Equation (DAE) system was obtained upon discretization of the spatial derivatives. High fidelity, fully implicit time integration of this DAE system was performed using the DASPK [86] solver. An adaptive grid algorithm was utilized to improve computational efficiency. The flame structure was resolved using at least 50 points at all times. This condition ensured grid 29 independent solutions. The code was integrated with the CHEMKIN and Sandia transport subroutine libraries and is also capable of performing calculations involving OTL-based radiation heat loss [78]. Details of the code relating to determination of a consistent initial condition, re-gridding algorithm, and BCs for constant pressure SEFs can be found in [44]. 3.2.2 Hybrid thermodynamic-radiation model The temporal variation of pressure, P, constitutes the only diagnostic in constant volume SEF experiments. The flame speed, S u , can be obtained using Eqn. 5 { 33 2 3 wf f u fu RR dR dP S dt R P dt } In all previous studies, [R f , P] was obtained using a thermodynamic model based on several assumptions (e.g., [23] [25]). A simplified Hybrid ThermoDynamic-Radiation (HTDR) [87] model was developed based on similar assumptions but is additionally capable of performing radiation heat loss calculations. The computational cost of HTDR is notably lower compared to TORC, and is the only viable way that radiation heat loss can be modeled with reasonable computational cost when interpreting experimental data, as will be discussed below. The HTDR model computes R f and the thermodynamic states of the burned and unburned gases as a function of P. All calculations, except for radiation heat loss, were based on equilibrium thermodynamics utilizing STANJAN-based subroutines [70]. The gas in the spherical vessel was treated as an assembly of a number of very thin spherical shells. The innermost shell was treated in the first step. Each computational step was associated with combustion of one shell, which involved three successive sub-steps: a. First, the reactants in a particular shell that undergoes combustion are allowed to attain chemical equilibrium under constraints of constant pressure and enthalpy, which results in an increase of its volume and temperature. All inner shells, which correspond to the burned gas, are also allowed to attain chemical equilibrium to account for the shifting in equilibrium during compression. 30 b. Second, each burned shell is allowed to lose heat through radiation at constant pressure, lowering its temperature and volume. c. Third, all shells are simultaneously compressed isentropically such that the total volume equals that of the spherical chamber, thus obtaining P and R f . The aforementioned three sub-step algorithm is repeated for the next outer shell until the reactants in all shells are consumed. The radiation heat flux was computed using two approaches involving RADCAL [88], a radiation subroutine with a narrow-band database for combustion gas properties. The first approach involves the adoption of the OTL assumption [89], which over-estimates the heat loss by not accounting for re-absorption. In the second approach, the radiation heat flux term is calculated more accurately by approximating the spectrally dependent re-absorption by using the Scaled Optically Thin Limit (SOTL) method, which is outlined in [72]. It should be noted that involving detailed narrow-band radiation models in SEF direct numerical simulations under constant pressure or constant volume conditions are computationally very expensive and thus impractical, given the large number of highly resolved in space and time flames that need to be computed. The approximations implemented in the computationally much cheaper HTDR are justified for the following two reasons. First, the temperature and species concentrations do not vary substantially inside the burned gas region. Second, the uncertainty in radiative properties of gases at such high temperatures is substantial. 31 Chapter 4 Results and Discussion 4.1 DNS-assisted extrapolation for constant pressure experiments Dowdy et al. [17] introduced the constant pressure approach with optical access in SEF experiments. Subsequently, Law, Ju and co-workers [19][20] adopted this approach and utilized a dual chamber configuration that allows for reaching pressures as high as 60 atm without compromising the integrity of the quartz windows. The main advantage of the optical access is that the flame radius can be measured directly. However, as mentioned already even the optical access does not eliminate uncertainties that are caused by extrapolations and other factors [11]. For example, in the study by Burke et al. [90], the overall uncertainties in the measured mass-burning rate are reported to be around 60% at P = 5 atm and about 40% at P = 10-20 atm for a = 2.5 H 2 /O 2 /Ar flame. As mentioned also in the Introduction, the study of Wu et al. [46] revealed that under certain conditions the extrapolations can result in errors in determining o u S by as much as 60%. Figure 10 is taken from [46] and indicates the inability of extrapolation formulas to predict accurately the unstretched values of S b. The correct extrapolation corresponds to the value 1 on the y-axis while the results are plotted as a function of the Karlovitz number, Ka, which is the ratio comparing the hydrodynamic and the combustion rates. On the other hand, it has been proposed that concerns related to extrapolations can be removed in the validation of kinetic models if the stretched flame speeds are compared against DNS results [49][44][45]. 32 Fig. 10. Inadequacy of various formulas to results in the correct value of the unstretched burned speed o b S for H 2 /air flames at various equivalence ratios [46]. Nonetheless, based on commonly used practices, o u S is essential for kinetic model validation and/or optimization [91], and accurate values need to be reported. Hence, an alternative method is introduced that utilizes DNS to obtain from experiments the stretch-free o b S and subsequently o u S using the continuity equation. The key hypothesis is that the shape of S b as a function of K, [S b, K], obtained from DNS is representative of that of experimental data. More specifically, it is assumed that the slope of the line connecting each experimental data point, [S b (K)] EXP , to the experimental [ o b S ] EXP that needs to be determined, is equal to its DNS counterpart, i.e., [ ( ) ] / [ ( ) ] / oo b b DNS b b EXP S K S K S K S K (6) 33 [S b (K)] DNS and [ o b S ] DNS are obtained from flame computations using TORC [44] and PREMIX [73][74] codes respectively. Note that since results from TORC computations are discrete in nature and [K] DNS values need not correspond to that of [K] EXP , interpolations are performed to obtain [S b (K)] DNS for the [K] EXP values, employing a polynomial fit to the entire [S b, K] DNS data set. This approach provides a mapping for each [S b (K)] EXP to obtain the corresponding [ o b S ] EXP value. Figure 11 depicts experimentally obtained [S b, K] values along with DNS results for a ϕ = 1.0 CH 4 /air flame at P o = 1 atm, T u,o = 298 K. An application of the DNS-based mapping technique to these measurements results in distributions of [ o b S ] EXP , and hence [ o u S ] EXP values obtained using mass continuity. Figure 12 depicts the distribution, along with a solid and a dashed line that indicate the mean and the median values respectively. The width of this distribution is a measure of the scatter of [S b (K)] EXP values about the mean experimental [S b, K] trend, and the difference in shape between the experimental and DNS [S b, K] curves. Fig. 11. Experimentally obtained S b as a function of K along with DNS results computed using the reduced USC Mech II model, for a CH 4 /air ϕ = 1.0 SEF at P o = 1 atm and T u,o = 298 K; symbols and lines represent the experimental and DNS results respectively. 34 Fig. 12. Distribution of experimental o b S and o u S values obtained post DNS-based mapping for a CH 4 /air, ϕ = 1.0 SEF at P o = 1 atm and T u,o = 298 K. The key hypothesis that the experimentally and numerically obtained [S b, K] slopes are equal (Eqn. 6), rests on the assumption that the chemical and transport models used as input to the DNS are able to capture the effect of stretch on flame propagation speed to sufficient accuracy. To assess the validity of this assumption, the kinetic model was modified artificially by increasing the pre-exponential factor of the main branching reaction H + O 2 → O + OH of the reduced USC Mech II model by 30%. This modified model was then used to compute [S b, K] behavior for a ϕ = 0.7 C 3 H 8 /air SEF and results obtained were compared against computations performed using the original model in Fig. 13; the choice of a lean C 3 H 8 /air mixture was made to enhance non-equidiffusion effects. The results indicate that even though the magnitude of S b changes significantly, the shape of the [S b, K] curve is rather insensitive to the notable change of the rate of the main branching reaction. The dependence of S b on K is largely through the Markstein length, L b , which is a function of the overall activation energy, Lewis number, and flame thickness. The corresponding differences in these quantities between the original and modified kinetic models are ~2%, 0% by definition, and ~10% respectively. Thus, the resulting change in L b and hence the [S b, K] behavior, is minor, a conclusion consistent with the DNS results of Fig. 13. 35 Fig. 13. S b variation with K for a ϕ = 0.7 C 3 H 8 /air SEF at P o =1 atm and T u,o = 298 K computed using the original reduced USC Mech II ( ─) and the modified kinetic model (- - -) that was obtained by increasing the pre-exponential factor of H + O 2 → O + OH by 30%. The modified kinetic model result has been translated (***) to illustrate the minor change in slope. The symbols (o) correspond to the experimental data, while at K=0 the resulting experimental mean o u S obtained using the DNS-assisted approach with the original model ( ─) and modified model (-- -) are denoted with (o) and (*) respectively. The propagation of hydrocarbon fuels is rather sensitive to the C 0 -C 4 kinetics, which is relatively well established [30]. Thus, o u S discrepancies between various models or between models and experiments are in most cases typically within 20-30%, and thus the usage of the DNS-based mapping procedure is justified. In principle though, this approach can be applied even in cases in which large discrepancies between experiments and predictions exist following an iterative procedure. First, interim o u S values are derived from the experimental [S b, K] data utilizing a kinetic model, using the aforementioned steps. The kinetic model is then optimized using the interim o u S values. Subsequently, the optimized model is used to derive new o u S values and so on. This iterative procedure is expected to converge within a few iterations. The 36 convergence can be monitored by analyzing the change in the width of the distribution of flame speed values (for example as shown in Fig. 12) obtained from the DNS-based mapping technique. As mentioned before, the width of the distribution is governed by the scatter of [S b (K)] EXP values about the mean experimental [S b, K] trend, and the difference in shape between the experimental and DNS [S b, K] curves. The iterative optimizations will improve the predictive capability of the model by reducing the discrepancy between the shape of experimental and numerical [S b, K]. As a result the converged model will result in a distribution that is solely dictated by the scatter of the experimental data. Note that a finite uncertainty is introduced in o u S no matter which method is utilized to subtract the effect of stretch, owing to the lack of knowledge of the actual [S b, K] behavior outside the experimental range. However, this uncertainty is minimized when the afore- mentioned DNS-based approach is used, as it constitutes the best possible theoretical model that accounts even for differential diffusion of the reactants into the reaction zone, which is overlooked in all asymptotically derived models and has been shown to result in substantial errors [44][46]. 37 4.2 Uncertainty quantification of spherically expanding laminar flame speeds For any experimental procedure, the quantification of all uncertainties is essential in model validation. It should be mentioned that while simple estimates of o u S sensitivity to certain parameters have been made in recent studies [92], no thorough studies of uncertainty quantification and propagation have been reported for SEF experiments. Although the transient nature of SEF experiments is prohibiting a statistical evaluation of the o u S uncertainties, tools are available to perform in-depth analysis. This is encouraged, contrary to performing a small number of repetitions which will result in incorrect statistical interpretation, since the sample is too small. The procedure can be split in three stages, namely mixture preparation, data acquisition, and data processing. First, the uncertainty of each stage will be evaluated separately, and subsequently will be combined to provide a realistic estimate of the total uncertainty in the reported o u S . During this investigation syngas, CH 4 , and C 3 H 8 flames at an initial temperature T u,o = 298 K are going be implemented. Experiments of CH 4 /air and C 3 H 8 /air flames at P o = 1 atm were also performed, since they are the typical validation targets among the various groups. Measurements at higher P o and T u were carried out using the four mixtures reported in Table 1 in which X i represents the mole fraction of species i and T ad the adiabatic flame temperature. Various combinations of O 2 , N 2 , and He were used as oxidizers, in order to suppress thermal- diffusive and hydrodynamic instabilities. Experiments were performed at various initial pressures (3 ≤ P o ≤ 7 atm range). 38 Mixture T ad (K) P o (atm) X H2 X CO X CH4 X C3H8 X O2 X N2 X HE 1 0.8 1600 3 to 7 0.0563 0.0563 0.0000 0.0000 0.0704 0.0000 0.8169 2 0.8 1800 3 to 7 0.0257 0.1028 0.0000 0.0000 0.0803 0.0000 0.7912 3 0.8 2100 3 to 7 0.0000 0.0000 0.0664 0.0000 0.1659 0.2303 0.5374 4 0.7 2000 3 to 7 0.0000 0.0000 0.0000 0.0266 0.1903 0.3916 0.3916 Table 1. Parameter space considered in the present investigation. The general equations [93][94][95] for uncertainty propagation from all parameters Q to the function F=F(Q 1 ,Q 2 , ...,Q M ), with M being the number of parameters involved, is: 2 22 1 1 1, M M M F i ij i i j j i i i j F F F a a a Q Q Q (7) with i a being the uncertainty of each parameter Q i , ij a the correlation coefficient between parameters Q i and Q j , and F a the final propagated uncertainty of F ; the notation a will be used henceforth to represent uncertainties. Most errors are by default normally distributed and it will be assumed for simplicity that a will be a representation of the 68% confidence interval. Equation 7 can be written also in matrix notation as: a F 2 =D T CD (8) with D being the column vector having as elements the partial derivatives of F, and C the covariance matrix, calculated as 1 () T AA , A being the weighted design matrix [93]. Equations 7 and 8 will be repeatedly used at the mixture preparation stage, and during the propagation of the uncertainty in R f to the propagation speed and stretch. In the case of uncorrelated parameters, Eqn. 7 can be simplified to: 39 2 22 1 M Fi i i F aa Q (9) It should be noted though, that the validity of the aforementioned formulas is limited only to small perturbations around the mean value. 4.2.1 Mixture preparation Experience shows that the sensitivity of o u S on ϕ could be significant. It is also expected that errors in the concentration of inert gases can also be of significance through its effect on T ad and thus kinetics. Information of all the species involved is necessary to define a mixture and thus evaluate the sensitivity on the propagation speed. Moreover there is an uncertainty in the reported values of initial temperature and pressure whose effect can also be of significance. Typically the mixture preparation is performed via successively inserting each mixture component following Dalton’s law of partial pressures, and measuring the static pressure at each step via transducers. For such transducers the uncertainty in the pressure indication is a certain percentage of the full range of the device. Thus, in order to improve accuracy the experimentalist needs to use a variety of transducers with different ranges and operate as close to full scale as possible. For combustible mixtures involving a single fuel component, the absolute pressure indications are chosen as independent variables, since they are non-correlated. Thus assuming that fuel and oxygen were the first two components inserted in the chamber, Eqn. 9 can be used with oxygen oxygen fuel 1 12 fuel oxygen fuel 2 1 ( , , ) v v st st nn p P P F P P P n p n P P (10) where (n oxygen /n fuel ) st represents the stoichiometric molar oxygen to fuel ratio, and p fuel and p oxygen the partial pressure of fuel and oxygen respectively; the pressure indications constitute the 40 parameters Q. P v is the initial vacuum pressure indication, and P 1 and P 2 the absolute pressure indications of each of the two successive steps. The case involving a single fuel component in air is the simplest one, but not the most common though in high-pressure SEF experiments, as helium is commonly used to assure flame stability. When oxygen and inert gases are introduced separately and/or multi-component fuels are investigated, the composition uncertainty cannot be expressed by ϕ alone. In this case, the ratios of partial pressures of the successively inserted species during the filling procedure are chosen as parameters: ( 1) 12 23 12 , ,..., N N S SS N S S S p pp R R R p p p (11) with i S p being the partial pressure of each component. First their uncertainties Ri a are calculated using Eqn. 9, and subsequently Eqn. 7 is implemented, with Q i = R i and F = o u S this time, to finally propagate their uncertainties to o u S . It should be noted that all ratios R i are coupled with each other due to the successive nature of the filling process. A calculation of the cross- correlation uncertainty terms ij a in Eqn. 7 is not a straightforward task. Using, however, the Schwarz inequality, ij i j a a a [95] the maximum possible uncertainty can be calculated without determining ij a , as follows: 2 22 1 1 1, M M M F i i j i i j j i i i j F F F a a a a Q Q Q (12) Simulations are necessary in order to obtain estimates for the partial derivatives needed in Eqns. 7-12. To that end, freely propagating flames were computed and brute-force variations of each Q i = R i parameter were performed while keeping the rest of the R j ratios constant. Similar approach was taken to evaluate the effects of T u,o and P o . In the present study all experiments were conducted at T u,o = 298 K, and ± 1 K uncertainty was chosen as a realistic estimate. Figure 14a depicts the computed Logarithmic Sensitivity Coefficients, (ln ) / (ln ) o u LSC d S d for C 3 H 8 /air mixtures at T u,o = 298 K and at different P o values. As 41 expected, off-stoichiometric mixtures exhibit larger LSC for all pressures. Figure 14b depicts the LSCs of o u S to T u,o , P o , and all the R i component ratios as earlier described, for the case of Mixture 4 at P o = 5 atm. The sensitivities on ϕ, N 2 /O 2 ratio, and initial temperature are high due to their effects on T ad while the sensitivity on He/N 2 ratio and pressure are minor. Fig. 14. Logarithmic sensitivity coefficients of o u S to: (a) ϕ for a C 3 H 8 /air mixtures with T u,o = 298 K at 1 (green), 5 (blue), and 10 atm (red), and (b) to all the pertinent parameters for a flame of Mixture 4 at T u,o = 298 K and P o = 5 atm. Finally using Eqn. 12, the uncertainties of all factors related to mixture preparation, , o u S MP a , that affect o u S can be now propagated as follows: , 2 22 2 2 2 2 , 1 1, , o i u o o u o o o o o MM u u u u u R Ri Rj T P S MP i j j i i i j u o o S S S S S a a a a a a R R R T P (13) 42 4.2.2 Data acquisition Prior to data collection, a shadowgraph/Schlieren system free of aberrations needs to be implemented; the reader should refer to [96] for a detailed description of the procedure. Image distortions caused by coma and astigmatism aberrations can introduce non-negligible errors (~1%) in the flame radius estimation, which in certain cases should be taken into account, as it will be described in the following section. In the configuration used in the present study this error is less than 0.4%. In previous studies by Metghalchi and co-workers [97] the correct procedure for flame location identification was outlined, when either shadowgraph or Schlieren is implemented. In the case of shadowgraph, implemented in the current study, the maximum absolute value of intensity gradient is defined as the marker of flame position and is located towards the unburned side of the flame. For that reason the 305 K isotherm was chosen as marker of the flame radius in the TORC simulation results. However, the results seem to be quite insensitive to this correction. 4.2.3 Data processing This is the final stage of the algorithm. It should be noted once more that the uncertainty calculated in this step is assumed to be uncorrelated to the uncertainty calculated at the mixture preparation stage. The data sample consists of a set of images recorded at a frequency of 13 kHz. The calibration factor, typically of the order of 3-10 pixel/mm, should be high enough with respect to the flame thickness, in order for high-speed imaging to be meaningful. In the current study, the calibration factor was 7.5 pixel/mm corresponding to a resolution of 2-7 pixels per flame thickness for the highly diluted flames considered in the present study. The typical procedure involves edge detection, and then using a certain number of points, a circle is fitted via the least squares method, to obtain the flame radius at each instant/image as shown in Fig. 15. 43 Fig. 15. Example of circle fitted on flame edge, detected using 32 points. An estimate of the uncertainty in the flame radius R f can be obtained using the following formula: 2 1 () 1 f k i fit i R rr a k (14) where i r is the distance of every edge point i from the fit-obtained circle center, and fit r is the fit-obtained circle radius, which henceforth is assumed to be the mean. Note that the number of points used to fit the circle can be of importance. By successively using 4, 8, 16, 32, and 64 equally spaced points it was observed that at least 16 to 32 points should be used in order to converge to a realistic estimate of the uncertainty in the radius, and an example is presented in Fig. 16. For all the cases in this study 32 points were used. In the case of a perfectly spherical flame, without distortions, the distribution of i r around fit r should be normal. Also the points used should be far from the electrode location in order for boundary layer effects to be avoided; only data that are unaffected by ignition and compression were considered (~1.2 – 3 cm). The microsecond-level exposure time of the camera allows for the error in time to be neglected. 44 Fig. 16. Convergence to the correct R f uncertainty value via use of higher number of points for the circle fit. The next step involves propagation of the radius error f R a in the derivative calculation, in order to obtain the uncertainty in the propagation speed / bf S dR dt , denoted as b S a , as well as the uncertainty in K (see Eqn. 1), K a . A local, weighted, least squares 2 nd -order polynomial fit, R f (t), was performed on the R f vs. t data in order to account for local curvature. The structure of the residuals is the proper indicator of the quality of the fit, and should be randomly distributed around zero, not showing any specific structure. Also, the uncertainty in the derivative, / f dR dt , is reduced with increasing number of points in the R f (t) fit. This would correspond to a larger domain of R f (t) for a given frame rate of camera. As a result, the choice of domain of fit was made to minimize uncertainty in / f dR dt while at the same time ensuring lack of structure in the residuals. Figures 16a and 16b illustrate an example of such a local fit and its corresponding residual distribution. The weighted design matrix is calculated for every fit performed and used for the calculation of the covariance matrix [93]. Thus, Eqn. 7 is implemented with ( ) / f F dR t dt and () 2 () f f dR t F R t dt respectively, and having as Q i ’s the coefficients of the fitted polynomial R f (t). 45 Figure 17c depicts uncertainty bars for the case of a ϕ = 1.0 CH 4 /air mixture, at P o = 1 atm and T u,o = 298 K. Note that bars shown in Fig. 16c represent the uncertainty that is based solely on the data processing step. It should be noted that if instead of least squares polynomial- fitting, finite difference schemes are implemented for the derivative calculation, the data noise is amplified notably. Using more degrees of freedom in the case of polynomial fitting, offers the advantage of averaging over the noise introduced from sampling and circle-fit; note that the data noise does not correspond to physics that is relevant to the combustion process. Fig. 17. (a) Local polynomial fit of R f vs. t data, (b) corresponding distribution of residuals, (c) S b vs. K data and their corresponding uncertainties during data processing for a ϕ = 1.0 CH 4 /air SEF at P o = 1 atm and T u,o = 298 K. Figure 18 shows comparisons of raw data from experiments and TORC simulations for SEFs of Mixture1 (50%H 2 -50%CO) and at various pressures. Once again the kinetic mechanism of Davis et al. was used in the current H 2 -CO simulations. 46 Fig. 18. a) Experimental S b vs. K data and their uncertainties for SEF’s of Mixture 1 at 3(o), 4(o), 5(o), 6(o), and 7(o) atm b) comparison of S b vs. K data with TORC results, at 3( ─) and 7( ─) atm for the same mixture, using Davis et al. mechanism. The final step of the post processing stage is the propagation of the uncertainties to the desired o b S through the previously suggested DNS-assisted mapping of each [S b (K)] EXP to [ o b S ] EXP (Eqn. 6). As mentioned earlier, the computed, using TORC, discrete S b values are fitted using a polynomial, so that they can be evaluated at each experimental K value. The uncertainty in the experimental K results in a corresponding uncertainty in the choice of computed S b to be used in Eqn. 6. This is determined by replacing K Ka as calculated previously. Having calculated the uncertainties in both the experimental and computed S b values, the uncertainty in the experimental o b S for each K is calculated from Eqn. 6. It should be noted that the percentage error in o u S is the same as in o b S , since the former is simply the multiplication of o b S by the density ratio. Thus, the uncertainty in o u S due to data acquisition and data post-processing, , o u S PP a are quantified. Finally, the combined uncertainty stemming from mixture preparation, and data acquisition and processing, can be calculated as [93]: 47 2 22 1 () oo step i uu SS i aa (11) On the other hand, if a kinetic model is validated against stretched flame speed data rather than the extrapolated o u S , the combined uncertainty in S b , resulting from mixture preparation and post-processing can be calculated using the sum of squared errors approach. The uncertainty in S b from mixture preparation can be considered to be approximately equal to that in o u S on a percentage basis. It is important to emphasize, that for all the steps of the uncertainty quantification procedure where an exact calculation was not possible or distributions were described based on limited data, the most conservative approach was chosen, calculating thus the upper and lower limits of the uncertainty. Table 2 depicts the o u S values for all constant pressure experiments performed for this study, along with the pertinent uncertainties. It is again indicated here that a is a representation of the 68% confidence interval of the parameter used as subscript. Note that all o u S s reported in Table 2 are greater than 20 cm/s, and hence effects of radiation and buoyancy can be neglected. Finally Figures 19 and 20 represent comparisons of CH 4 /Air and C 3 H 8 /Air flames at 1atm and 298 K, between various groups [98][99][100][101][102][103][104][105][106] . 48 Fig. 19. Comparison of current experimental data against that from literature for CH 4 /air mixtures at atmospheric conditions. Note that no radiation heat loss corrections have been made. Readers can refer to [107] for correction procedures. Fig. 20. Comparison of current experimental data against that from literature for C 3 H 8 /air mixtures at atmospheric conditions. Again, readers can refer to [107] for correction procedures. 49 Mixture#1 Mixture#2 P o (atm) 𝑆 𝑢 o (cm/s) a S u o ,MP (cm/s) , o u S PP a (cm/s) o u S a (cm/s) P o (atm) 𝑆 𝑢 o (cm/s) , o u S MP a (cm/s) , o u S PP a (cm/s) a S u o (cm/s) 3 31.8 1.0 0.7 1.2 3.0 30.8 0.6 0.4 0.7 4 28.1 1.5 0.6 1.7 4.0 28.6 0.7 0.6 1.0 5 25.8 1.2 0.6 1.4 5.0 26.7 0.7 0.5 0.9 6 23.6 1.0 0.7 1.2 6.0 25.3 0.7 0.7 1.0 7 21.6 1.0 0.8 1.3 7.0 24.2 0.7 0.7 1.0 Mixture#3 Mixture#4 P o (atm) 𝑆 𝑢 o (cm/s) , o u S MP a (cm/s) , o u S PP a (cm/s) o u S a (cm/s) P o (atm) 𝑆 𝑢 o (cm/s) , o u S MP a (cm/s) , o u S PP a (cm/s) a S u o (cm/s) 3 32.8 0.7 0.8 1.0 3.0 28.1 0.6 0.5 0.8 4 30.2 0.8 0.4 0.8 4.0 25.0 0.8 0.4 0.9 5 27.8 0.7 0.4 0.8 5.0 23.3 0.8 0.2 0.8 6 26.0 0.7 0.5 0.8 6.0 21.7 0.7 0.2 0.8 7 24.4 0.7 0.4 0.8 7.0 21.2 0.7 0.2 0.7 Table 2. Experimental o u S values and the attendant uncertainties. In Figures 21-24 the experimental data presented in Table 2 are being compared with predictions obtained using Davis et al., USC Mech II, Dames et al., HP Mech. 50 Fig. 21. Comparison of experimental data of Mixture 1 experiments, against predictions of various kinetic mechanisms. Fig. 22. Comparison of experimental data of Mixture 2 experiments, against predictions of various kinetic mechanisms. 51 Fig. 23. Comparison of experimental data of Mixture 3 experiments, against predictions of various kinetic mechanisms. Fig. 24. Comparison of experimental data of Mixture 4 experiments, against predictions of various kinetic mechanisms. 52 To conclude, a detailed error propagation methodology was developed, in order to quantify the uncertainty associated with the extraction of o u S from constant pressure SEF experiments. All the steps involved, from mixture preparation to data sampling and data post-processing were separately analyzed and finally the results were combined based on well documented error propagation formulas. More importantly, the error quantification at each step gives insight into the factors that mostly affect the accuracy of the results and help significantly improve the experimental procedure. More details can be found in [72]. Once more, uncertainty quantification is absolutely necessary in order for validation of reaction mechanisms to be meaningful. The same analysis was performed also for the constant volume SEF experiment case. The mixture preparation step is exactly identical, as the same equipment and filling procedure were implemented. Also all the numerical differentiations involved (see Eqn. 5), were performed based on the same methods and principles. What was of great interest was the analysis of uncertainties due to data collection and processing. The dynamic pressure transducers typically have a fixed measurement uncertainty ~0.5-1% of their full range. As a result the percentage error at higher pressures is lower. Moreover as the flame propagates and the unburned mixture is compressed the flame speed is ever increasing obtaining the highest values towards the end of data collection. As a result the percentage uncertainty at the last obtained value in the range is by far the lowest. However the main problem once more stems from the fact that the only measurable quantity is pressure, and the radius is derived based on it via the thermodynamic model. That combined with the highly coupled/nonlinear form of Eqn. 5 results in a large amplification of the final propagated uncertainty of o u S , as now the uncertainty from the P is nonlinearly translated to uncertainty in R f and all the involved derivatives. It is indicative that the uncertainty due to post- processing is approximately 5 times higher than the one introduced from mixture preparation. This is once more pointing towards the direction of finding ways to independently measure the pressure and radius evolutions in the constant volume experiment, by introducing optical access in a way that does not distort the sphericity of the vessel. 53 4.3 Studies of foundational fuel chemistry Following the rigorous uncertainty quantification approach, presented previously, the need to obtain high fidelity experimental data of basic fuel components is of great importance. Due to the hierarchical nature of the combustion chemistry of heavier hydrocarbons, the knowledge of chemical kinetics starts from the lighter foundational species to the heavier ones. The initial stages involving the breaking of the parent fuel molecule are typically fast/not rate controlling [30][108], thus resulting in a mixture of lower hydrocarbons that are described by the H 2 /C 1 -C 4 chemistry. Of course that is not to imply that the initial pathways of the parent-molecules- breaking are not affecting the end result, meaning the propagation speed. That is however the reason why various groups in the combustion community have been mostly focusing on producing high fidelity chemistry description for the reaction chemistry of basic fuel components, mainly alkanes, alkenes and alkynes molecules. Apart from the traditionally studied CH 4 and C 2 H 6 molecules, C 2 H 4 and C 2 H 2 chemistry is of high significance for the combustion of higher hydrocarbons as they are both major intermediates. More specifically C 2 H 2 is a key intermediate in rich hydrocarbon combustion and the main culprit for soot formation during high temperature oxidation under fuel rich conditions [109][110][111][112]. Thermodynamically, the formation of soot is due to the need to maximize entropy. It initiates with the formation of polycyclic aromatic hydrocarbons (PAHs), which are planar and have the tendency to coalesce with each other, forming thus larger, 3-dimensional structures, a step known as particle nucleation. Further coagulation takes place resulting in even larger/nanometer-size spherical particles in a mass growth stage. It has been shown[112], that mass growth of soot structures is largely caused through reactions of the soot surface with gas- pghase hydrocarbon species, most importantly C 2 H 2 . After a certain size has obtained the large now particles aggregate into fractal like structures. One of the most important species at the initial stages of aromatic ring formation is the propargyl radical C 3 H 3 • which is mainly produced from the reaction of CH 2 • with C 2 H 2 under fuel rich conditions. CH 2 • itself is produced from C 2 H 2 oxidation: C 2 H 2 +O•→CH 2 •+CO as part of the main flame chemistry. Then the following very important reactions include the reaction of C 3 H 3 • with itself and C 3 H 3 • [112]. Regarding data of laminar flames speed, the combustion community has heavily focused on the combustion of hydrogen and methane, neglecting the chemistry of C 2 flames. Moreover, as also mentioned in the introduction, most of those experiments were performed at ambient pressures and temperatures and most of the times lack the description of experimental uncertainty quantification. Laminar flame speeds of mixtures only up to 2atm have been reported using the counterflow configuration [113][114][115], while close to that pressure range or a slightly above, laminar flames speeds utilizing the spherically expanding flame configuration 54 were reported [116][105][117]. The only high pressure data reported recently for C 2 -hydrocarbon flames are those of [105][118][83]which all three studied spherically expanding flames. More specifically Satner et al. [118] only presented C 2 H 4 experiments ranging from 1-10atm and phi=0.85. Ju et al. [83] on the other hand present data of C 2 H 2 up to 20atm under both lean and rich conditions. He however did not study flames at the same conditions for the rest of the C 2 hydrocarbons. As it is evident, there currently exists no conclusive/comparative study of the propagation speeds of laminar flames resulting from all C 2 fuel components. Also most studies are performed on ambient condition, but regardless no common basis exists for the comparisons. Most of the authors do not also make any reference to the experimental uncertainty of the reported data, thus making a chemistry optimization process less meaningful. The following study presents such a comparative study, in an attempt to discover if there exist limitations in the state of the art chemical mechanisms. 4.3.1 Experimental approach Once again, the propagating flame was imaged using the CMOS Phantom v710 monochrome high-speed camera operated at ~50KHz this time and with a resolution of 7 pixel/mm. Upon vacuuming the chamber, the partial pressure method was implemented for filling the chamber with the appropriate gases. The partial pressures were measured using high accuracy Omega PX409-AV pressure transducers with the appropriate full-scale ranges (0-5, 0-15, 0-50, and 0- 150psi) to minimize any uncertainties in the equivalence ratio, . More details regarding the experimental system and the methods implemented can be found in the thesis Chapter 2 (Experimental Approach). Only stable flames were processed for the extraction of laminar flame speed data. Mixtures that resulted in flames with cellular morphology were disregarded. In order to achieve stable laminar flames Helium was as typically used as part of the mixture’s inert gases. This satisfies both the requirements for avoidance of instabilities. First, the increase of the mixtures effective Lewis number, Le eff , results in suppression of thermal-diffusive instabilities. Second, He offers increased flame thickness which increases the flame resistance against the inherent hydrodynamic instabilities. 55 Moreover it was made certain that no C 2 H 2 -polymerization effects polluted any of the presented data. The initial temperature of all experiments was only 298, very low compared to the typical high temperatures that cause polymerization effects [119]. Typically C 2 H 2 gas cylinders have internally a core filled with acetone which is used to keep acetylene stable and safe inside the cylinder. The experimental chamber was always slowly and carefully filled so that no high pressure differential could cause a leak of acetone in the lines. The lines were also carefully flushed prior to experiments. The constant pressure experiments involve the measurement of the flame radius, R f , as a function of time and subsequently the burned flame speed S b (dR f /dt) is derived (assuming the burned gas is stationary) with its stretch rate calculated as K (2/R f )(dR f /dt) [Williams]. The burned flame speed at zero stretch, S b o , was obtained through the DNS-assisted extrapolation technique [72] that was explained in Part 4.1 of Chapter 4.. This method compared to assymptotycally derived extrapolation equations avoids the need of calculating fitted parameters and takes into account the pertinent physics of the flame including Le number and species differential diffusion. Subsequently o u S is derived using the density ratio between the burned and unburned states at equilibrium. Only data unaffected by compression and ignition effects were processed for each case. Moreover mixtures that resulted in fast flames were chosen, avoiding thus issues of buoyancy and radiation. Laminar flame speeds of CH 4 , C 2 H 6 , C 2 H 4 , and C 2 H 2 flames with T u,o = 298 K and at various initial pressures were measured. The exact mixture compositions are reported in Table 1. X i represents the mole fraction of species i, and T ad the adiabatic flame temperature. As mentioned earlier, various combinations of O 2 , N 2 , and He were used as oxidizers, for the suppression of thermal-diffusive and hydrodynamic instabilities. For CH 4 and C 2 H 6 experiments the pressure data span the range 1 to 6 atm, offering a pressure ratio of 6. For the C 2 H 4 and C 2 H 2 cases however data were obtained down to as low as 0.5 atm, offering thus a range of data with pressure ratio 12 (0.5 to 6atm). The main difficulty was emanating from the attempt to keep the same N 2 /He ratio and T ad throughout the entire range of initial pressures and still get flames that are free of instabilities and propagate after ignition (problem of over-dilution). 56 Fuel φ T ad (K) P (atm) X Fuel X O2 X N2 X HE CH 4 0.8 2200 1-6 0.0723 0.1807 0.2241 0.5229 CH 4 1.3 2200 1-6 0.1082 0.1665 0.2176 0.5077 C 2 H 6 0.8 2100 1-6 0.0379 0.1659 0.2389 0.5573 C 2 H 6 1.3 2100 1-6 0.0567 0.1527 0.2372 0.5534 C 2 H 4 0.8 2100 0.5-6 0.0393 0.1475 0.2439 0.5692 C 2 H 4 1.3 2100 0.5-6 0.0563 0.1298 0.2442 0.5697 C 2 H 2 0.8 2100 0.5-6 0.0396 0.1237 0.2510 0.5857 C 2 H 2 1.3 2100 0.5-6 0.0531 0.1022 0.2534 0.5913 C 2 H 2 1.3 1900 3 0.0460 0.0885 0.2596 0.6058 C 2 H 2 1.3 2300 3 0.0605 0.1164 0.2469 0.5762 C 2 H 2 1 2100 3 0.0397 0.0993 0.2583 0.6026 C 2 H 2 1.5 2100 3 0.0632 0.1053 0.2495 0.5821 C 2 H 2 1.7 2100 3 0.0739 0.1086 0.2452 0.5722 Table 3. Parameter space considered in the present investigation 4.3.2. Modeling approach The o u S of freely propagating flames was again computed using the PREMIX code [73][74], integrated with CHEMKIN and the Sandia transport subroutine libraries as discussed in Chapter 3. For the DNS modeling of SEFs under constant pressure conditions the Transient One- dimensional Reacting flow Code (TORC) [44] was employed with outlet boundary condition since compression effects were not of immediate interest. Pressure is assumed to vary in time but not in space, given the small Mach numbers associated with SEFs. 57 Since TORC simulations are notably more expensive computationally, compared to the one- dimensional planar flame simulations using the PREMIX code, the choice was made to use a C 1 - C 3 version of USC Mech II having reactions involving C 4 and C 5 species removed. These simulations were performed to be implemented in the aforementioned DNS-assisted extrapolation technique [72]. The removal of those reactions seemed to have minimal effect for the cases of extrapolation. At this point it should be once again indicated that for all the laminar flame speed calculations, the computational values were obtained using the PREMIX code using the full version of every kinetic mechanism. 4.3.3 Results and Discussion As mentioned in the introduction, various laminar flame speed studies have been performed involving C 2 hydrocarbon fuels. Most of these studies however were only performed at atmospheric conditions. In addition most of these studies have not appropriately quantified experimental uncertainties. In order to perform chemical model optimization, experimental data with low, appropriately quantified uncertainties is necessary. This involves also systematic errors which mostly result from the extrapolation methodology used in order to obtain the stretch free S b o value. The purpose of this study is to obtain high fidelity laminar flame speed data for C 1 -C 2 hydrocarbon flames, for both lean and rich conditions, for which the kinetic pathways can be significantly different. Subsequently compare the level agreement between experiments and the corresponding modeling predictions. The approach taken for each case was to only vary pressure, while keeping ϕ, T ad , and N 2 /He ratio constant. The main challenge with this approach is to obtain smooth flames for all initial pressure conditions and at the same time avoid overly diluting the mixture to the extent that the initial kernel fails to propagate. Additionally, the equivalence ratios studied and the T ad chosen where kept the same for all the cases in order to obtain a more fair comparison. Figures 20 and 21 present the comparisons of experimental laminar flame speeds with simulations for both the lean and rich cases of CH 4 flames, and with P o ranging from 1 to 6atm. 58 Fig. 20. Comparison of experimental laminar flame speed of CH 4 mixtures with ϕ=0.8, T ad =2200K against simulation predictions. Fig. 21. Comparison of experimental laminar flame speed of CH 4 mixtures with ϕ=1.3, T ad =2200K against simulation predictions. 59 For ϕ=0.8 USC Mech II over predicts the experimental values by ~5%. For the ϕ=1.3 case it is the reverse, with an under prediction that increases with pressure from ~4% to -15%. In needs to be indicated once more that the TROE parameters for the C 2 H 4 +H(+M) = C 2 H 5 (+M) are the corrected ones, as indicated also in [82]. Dames et al. predictions consistently underestimate the experimental data both in the lean and rich sides with an excessive ~20% under prediction for the ϕ=1.3, 6atm case. In contrast, HP Mech predictions are the most consistent with a ~5% over prediction for both lean and rich sides. It needs to be indicated though that the experimental uncertainty for these cases is approximately ±8% with 95% confidence interval. That means that any discrepancy lower than that is totally reasonable. Figures 22 and 23 depict the same comparisons but for the C 2 H 6 cases. USC Mech II predictions are higher for the cases by ~9% and lower on the rich side by ~2%. Once more Dames et al. performs worse on the rich side, while HP Mech performs the best showing ~3% difference with the experimental results. Fig. 22. Comparison of experimental laminar flame speed of C 2 H 6 mixtures with ϕ=0.8, T ad =2100K against simulation predictions. 60 Fig. 23. Comparison of experimental laminar flame speed of C 2 H 6 mixtures with ϕ=1.3, T ad =2100K against simulation predictions. In Fig. 24 and 25 the results for C 2 H 4 are presented. For this case the P o range is 0.5-6 atm giving thus a total pressure ratio of 12. In the case of ethylene, USC Mech II performance seems better, with just ~5% discrepancy. HP Mech predictions on the contrary seem worse on the rich side. The experimental uncertainty for the C 2 H 4 cases is approximately ~ ±5% with 95% confidence interval. Fig. 24. Comparison of experimental laminar flame speed of C 2 H 4 mixtures with ϕ=0.8, T ad =2100K against simulation predictions. 61 Fig. 25. Comparison of experimental laminar flame speed of C 2 H 4 mixtures with ϕ=1.3, T ad =2100K against simulation predictions. For the first three fuel cases, i.e. CH 4 , C 2 H 6 , and C 2 H 4 , the model predictions are consistent and generally it could be described as low (~5%-10%). It always has to be kept in mind however that model predictions themselves have uncertainties which can be significant [91] and are not depicted in the figures, which are just comparing mean values. The comparisons for the lean C 2 H 2 cases are presented in Fig. 26 and 27. Once again, data with P o as low as 0.5 atm were obtained for this case. For ϕ=0.8 all 3 models perform well, with just USC Mech II discrepancies being slightly higher than the experimental uncertainty (~ ±4% with 95% confidence interval). For the C 2 H 2 ϕ=1.3 case however the discrepancies are significantly higher. The discrepancies when using USC Mech II range from 15% for the 0.5atm case to 23% for the 6atm case. Not only is the discrepancy significantly higher for the rich case, but also an increasing trend with pressure is evident. This is the case for all three kinetic models utilized. Dames et al. predictions show the lowest discrepancy from the experimental data still lying outside the experimental uncertainty range (~ ±4% with 95% confidence interval). 62 Fig. 26. Comparison of experimental laminar flame speed of C 2 H 2 mixtures with ϕ=0.8, T ad =2100K against simulation predictions. Fig. 27. Comparison of experimental laminar flame speed of C 2 H 2 mixtures with ϕ=1.3, T ad =2100K against simulation predictions. In order to examine the extend of disagreement on the rich side, Fig. 28 is depicting data taken, for flames at the same pressure P o =3atm and T ad =2100K, but for a range of equivalence ratios 0.8 < ϕ < 1.7. 63 Fig. 28. Comparison of experimental laminar flame speeds of C 2 H 2 mixtures at P o =3atm and T ad =2100K, with simulation predictions in the range ϕ=0.8-1.7. The results show an ever increasing trend in the discrepancy with increasing the equivalence ratio, reaching values as high as ~50% for the ϕ=1.7 case. This denotes a clear limitation in predicting values at very high equivalence ratios. Again Dames et al. mechanism seems to perform the best, however the same trend is observed. Soot production is not to blame for these discrepancies as T ad and C 2 H 2 /O 2 ratio are not high. Simulations performed using Jet Surf 2.0 [81] that includes soot related chemistry resulted in same LFS values as those obtained from USC Mech II, further supporting this argument. Another interesting aspect would be to examine the level of agreement for flames of different T ad , as the sensitivity of reactions to flame temperature is high. Figure 29 shows laminar flames speeds of C 2 H 2 flames with constant ϕ=1.3 and P o =3atm, and with a range of adiabatic flame temperatures 1900K < T ad < 2300K. A decreasing trend in the observed discrepancy between experiment and modeling is occurring as the adiabatic flame temperature is increased. For the 2300K case the difference is ~10% while for the 1900K gets as high as 30% using USC Mech II. Dames et al. discrepancies are once again the lowest out of the three kinetic models. 64 Fig. 29. Comparison of experimental laminar flame speeds and simulation predictions for flames of C 2 H 2 mixtures with ϕ=1.3, at P o =3atm and T ad =1900K, 2100K, and 2300K. From the aforementioned discussion it is evident that the current state of the art kinetic models fail to deliver satisfactory predictions for the case of rich acetylene flames. In an attempt to shed light into the reason of those discrepancies, the most important reactions and the species destruction paths are to be investigated. As expected both figures show, the highest sensitivity to be on the main branching reaction H+O 2 →O+OH with also the reactions involving HCCO being very important as HCCO is the main product of C 2 H 2 braking. Subsequently HCO radical is one of the key components. 65 Fig. 30. Ranked Logarithmic Sensitivity Coefficients (LSC) of laminar flame speed to kinetics for C 2 H 2 flamess with ϕ=1.3, at P o =3atm and T ad =2100K, using USC-Mech II and Dames et al. kinetic mechanisms. Fig. 31. Ranked Logarithmic Sensitivity Coefficients (LSC) of laminar flame speed to kinetics for C 2 H 2 flames with ϕ=1.7, at P o =3atm and T ad =2100K, using USC-Mech II and Dames et al. kinetic mechanisms. -0.1 0 0.1 0.2 0.3 0.4 0.5 H+O2<=>O+OH CO+OH<=>CO2+H HCO+M<=>CO+H+M HCCO+O2<=>OH+2CO CH2*+O2<=>H+OH+CO C2H2+O<=>HCCO+H CH3+H(+M)<=>CH4(+M) HCCO+H<=>CH2*+CO HCO+H<=>CO+H2 LSC USC-Mech II Dames et al. -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 H+O2<=>O+OH HCCO+O2<=>OH+2CO HCO+M<=>CO+H+M CH2+O2<=>HCO+OH C2H3+O2<=>CH2CHO+O CO+OH<=>CO2+H CH2*+O2<=>H+OH+CO C2H3+H<=>C2H2+H2 HCO+H<=>CO+H2 HCCO+H<=>CH2*+CO CH3+H(+M)<=>CH4(+M) LSC USCMII Dames et al. 66 The ϕ=1.7 case shown in Fig. 31 was chosen, as it was earlier (Fig. 28) shown that the highest discrepancies between experimental values and simulations was for this very mixture rich case.. Additionally, since the performance of Dames et al. is notably better, the LSC using both schemes is investigated. The LSC are very similar for cases however there is a difference for the CH 2 +O 2 →HCO+OH case which reaction seems to not be important for the case of Dames et al. This is not a surprise since in the corresponding paper [cite Enoch] it was clearly indicated that the CH 2 chemistry is one of the main modifications performed on JetSurf, USCMech. Species C 2 H 2 _1.7_3atm_2100K_USCMII % Species C 2 H 2 _1.7_3atm_2100K_Dames et al. % C 2 H 2 C 2 H 3 (+M) <->C 2 H 2 +H(+M) <5 C2H2 C 2 H 3 (+M) <->C 2 H 2 +H(+M) <5 C 2 H 2 +O<->CH 2 +CO 11.9 C 2 H 2 +O<->CH 2 +CO 12.3 C 2 H 2 +O<->HCCO+H 47.7 C 2 H 2 +O<->HCCO+H 49.2 C 2 H 2 +OH<->C 2 H+H 2 O 12.7 C 2 H 2 +OH<->C 2 H+H 2 O 11.7 C2H2+C2H<->C4H2+H 8.5 C 2 H 2 +C 2 H<->C 4 H 2 +H 7.7 CH 2 CH 2 +H<->CH+H 2 39.2 CH2 CH 2 +H<->CH+H 2 41.7 CH 2 +O 2 <->HCO+OH 31.5 CH 2 +O 2 <->OH+H+CO 10.3 CH 2 +O 2 <->CO 2 +2H 7.9 CH 2 +O 2 <->2H+CO 2 7.4 CH 3 +CH 2 <->C 2 H 4 +H 5.8 CH 2 +O 2 <->O+CH 2 O 5.8 C 2 H 2 +CH 2 <->C 3 H 3 +H 6 CH 2 +O 2 <->H 2 +CO 2 6.8 CH 3 +CH 2 <->C 2 H 4 +H 8.2 C 2 H 2 +CH 2 <->C 3 H 3 +H 7.4 HCCO HCCO+H<->CH 2 *+CO 53.3 HCCO HCCO+H<->CH 2 *+CO 43.2 HCCO+O<->H+2CO <5 HCCO+O<->H+2CO <5 HCCO+O2<->OH+2CO 18.9 HCCO+O 2 <->OH+2CO 19.4 HCCO+OH<->C 2 O+H 2 O 6.7 HCCO+OH<->C 2 O+H 2 O 5.1 CH 3 +HCCO<->C 2 H 4 +CO 10.7 CH 3 +HCCO<->C 2 H 4 +CO 12.4 CH 2 CO+H<->HCCO+H 2 13.7 HCO HCO+H<->CO+H2 6.9 HCO HCO+H<->CO+H 2 7 HCO+M<->CO+H+M 47.2 HCO+M<->CO+H+M 39.3 HCO+H 2 O<->CO+H+H 2 O 21.8 HCO+H 2 O<->CO+H+H 2 O 27.5 HCO+O 2 <->CO+HO 2 16.9 CH 2 CO+OH<->HCCO+H 2 O 6.7 Fig. 32. Integrated path analysis for C 2 H 2 flames with ϕ=1.7, at P o =3atm and T ad =2100K, using USC-Mech II and Dames et al. kinetic mechanisms. 67 To look deeper into the difference in chemical pathways between the two mechanisms, integrated path analysis was performed for the flame cases of interest. The integrated destruction of the species is being followed one at a time and a cut-off 5% lower limit is set. Figure 32 presents the most important information for the C 2 H 2 ϕ=1.7, at P o =3atm and T ad =2100K case in tabulated format for readability reasons. With yellow color are denoted the most important reaction pathways while with color purple the main differences between the two mechanisms. As also mentioned in the literature [cite Okjoo and Reference 36 of Okjoo] the C 2 H 2 +O→HCCO+H and C 2 H 2 +O→CH 2 +CO reactions are the dominant in terms of C 2 H 2 destruction with a branching ratio of 0.8:0.2. This is the case for both chemical mechanisms. Also as expected the CH2 pathways are completely different since this is one of the main differences between USC Mech II and Dames et al. As a result there is some subsequent difference in the following HCO reaction pathways. As mentioned also in the introduction those discrepancies need to be addresses by the chemical kinetics community as acetylene, apart from a very important part of the foundational chemistry of heavier hydrocarbons, is also the most important species with regards to soot formation. So as a first step this data should be used to investigate if some pathways are potentially wrong or if that is not the case, then this data should be used as optimization targets in order to improve the reaction rates that are causing those notable discrepancies. 68 4.4 Flame acceleration due to flame instabilities Implementing the spherically expanding flame method is the only viable approach for the measurement of laminar flame speeds at engine-relevant conditions, making it the reason for the technique’s recent popularity. Following the constant pressure regime, the expanding flame is compressing the unburned gas isentropically, offering thus data at high pressures and temperatures. Upon compression, flames become inherently unstable due to Darrieus–Landau instability, even for mixtures with Lewis number greater than unity as already mentioned. The goal of this study is to investigate the extent to which the development of cells and the subsequent cell-induced flame area growth affect the propagation characteristics of SEFs during the compression stage of the constant volume experiment. The onset of cellularity is methodically initiated in experiments at various stages of the compression by varying the ratio of He/Ar in the initial mixture composition, altering thus the flame thickness and the Lewis number, and the effect on the burning rate was analyzed. Experiments were first performed in the cylindrical chamber, with optical access, for flames that exhibited variable, L b , in order to identity the thermodynamic conditions of the unburned gas corresponding to the onset of cellularity. Subsequently, measurements were performed for the same mixtures in a constant volume spherical chamber, and the burning rates obtained were compared against numerical results of smooth flames to provide insight in the effects of cellularity on the burning rate. The contribution of the area wrinkling/growth on burning rate increase due to cellularity seems to be diminishing when the onset of cellularity occurs within the compression stage of propagation. This finding is of relevance in interpreting flame speed data obtained in constant volume spherically expanding flame experiments. For flames to remain stable for a large portion of flame propagation, meaning all the way within the compression stage, two conditions are necessary. First, the mixture needs to have Le greater than unity to suppress TD instabilities. Second, the flame thickness needs to be relatively large at high pressures in order to suppress hydrodynamic instabilities. Both of these requirements can be met using helium as diluent as also described in the experimental methodology section. 69 The first stage of this study was performing experiments of lean, = 0.8, T ad =1600K 50% H 2 -50% CO syngas mixtures at initial pressure P o = 3atm and initial unburned mixture temperature T u,o = 298 K. The inert was a mixture of He and Ar, ranging for each experiment from 100% He (0% Ar) to 100% Ar (0% He) in order to promote cellularity at different stages of propagation. The heat capacities of both inerts being the same resulted in all flames having an adiabatic flame temperature, T ad = 1600 K. This particular change in inert composition results in changes in flame thickness, l th , and L b , while it has a negligible effect on the flame structure and hence the controlling kinetic pathways. Subsequently the initial pressure of some of these mixtures was varied, in order to promote cellularity at different thermodynamic conditions, but for the same Le behavior. More specifically the main interest was to observe whether the flames of the same chemical mixture but with different initial pressure would present different acceleration characteristics depending on whether the flame was rendered unstable in the constant pressure or the compression stage. The time/pressure of instabilities was captured in the cylindrical chamber that offers optical access. Then the same experiments were performed in the blind totally spherical chamber and the flame speed was calculated. As has been shown [72] stretch effects become negligible inside the compression region so it is expected that the cellularity points would be reasonably close for flames of the same mixture in both chambers. Additionally flames of lean, = 0.8 C 2 H 2 /O 2 /N 2 mixtures were studied since they exhibit Le=1 behavior and can potentially clarify the behaviors observed, by keeping one more knob fixed. 4.3.1 Cylindrical chamber experiments Experiments were first performed in the cylindrical chamber that offers full optical access. The comparisons of experimental data against simulation results are presented in Fig. 33. The multi-component fuel nature of the mixture prohibits a trustworthy derivation of Le. It is evident that mixtures with 100% and 80% He in the inert He-Ar mixture, result in flames that exhibit negative dependence of S b on K and thus having positive L b . The trend observed is the opposite for the cases of mixtures with 60% He and 40% He. In the cases of 20 and 0% He, the flame is 70 rendered unstable at different points during the constant pressure stage propagation, leading to flame self-acceleration due to continuous flame surface growth. Also, note that the simulations (that correspond to smooth flames) are able to capture closely the variation of S b with K. The effect of flame acceleration due cellularity-induced surface area increase has been thoroughly studied for the constant pressure SEF case (e.g. [56][61][62][63][64][65]). The existing analysis in the literature predicts a radius increase described by a relation 1.5 f fonset R R t , with R fonset being approximately the radius of the appearance of the uniform cellular structure. Such trend is evident in the 0%He and 20%He case of Fig. 33. Fig. 33. Comparisons of experimental and computational S b vs. K for flames of mixtures with 100 (purple), 80 (blue), 60 (green), 40 (cyan), 20 (red), 0 (black) % He, at P o = 3 atm and T u,o = 298 K. Symbols and lines represent experimental and computational results respectively. For this study, the pressure at which cellularity occurs was determined by correlating the images to the pressure-time trace. Only the center region of the flame could be imaged since the diameter of the flame exceeded the diameter of the window once compression started. 71 Repetitions have revealed that the onset of cellularity-pressure correlation is quite consistent, always within the range of experimental uncertainty. The onset of cellularity observed for the 0, 20, 40, 60, 70 and 80% He, 3atm, T ad =1600K cases was 3.0, 3.2, 4.0, 8, 12, 14.5 atm respectively. For the additionally performed case, i.e. ( = 0.8, 50H 2 -50CO, 70%He, T ad =1600K, P o =5atm), ( = 0.8, 50H 2 -50CO, 70%He, T ad =2100K, P o =3atm), and ( = 0.8, 50H 2 -50CO, 20%He, T ad =1600K, P o =1atm) the points of cellularity onset were 14atm, 3.5atm, and 2.5atm correspondingly. Additionally, experiments were performed for = 0.8 C 2 H 2 /O 2 /N 2 flames at 1 and 2 atm for T ad =1800K and at 3 atm for T ad =2400K (Fig. 34). The purpose of these experiments was to prove that those flames are behaving equi-diffusionally. For the first two cases the temperature is decreased to 1800K in order for the hydrodynamic instabilities to initiate inside the compression stage of the experiment and not at the initially constant pressure propagation stage. Indeed for the 1 and 2atm cases it was observed that the cells formed at ~4atm for both cases. As expected, the 3atm, T ad =2400K case was performed in order to have instabilities initiating within the constant pressure region. The reason is to later observe the acceleration effects for the flames studied in the totally spherical chamber and examine if there are differences in the acceleration observed depending on which stage cellularity occurred. Fig. 34. S b vs. K data for flames of = 0.8, C 2 H 2 /O 2 /N 2 , obtained in the cylindrical chamber during constant pressure propagation. 0 100 200 300 400 500 600 700 800 900 1000 0 200 400 600 800 1000 1200 1400 S b (cm/s) K (1/s) C2H2_O2_N2_0.8_1atm_1800K C2H2_O2_N2_0.8_2atm_1800K C2H2_O2_N2_0.8_3atm_2400K 72 4.3.2 Spherical chamber experiments Experiments for the same mixture conditions were repeated in the perfectly spherical chamber and the pressure traces were recorded. The HTDR model was used to derive S u . Since in previous work [72] it has been demonstrated that the Karlovitz number, Ka, attains very low values for flames during the compression stage, the derived S u is equal to o S u if the flames are stable. However, for flames that have developed cells, the extracted S u represents a flame speed that has embedded in it the acceleration caused due to area increase, i.e. the percentage difference of S u from o S u is equal to the percentage increase of flame surface due to wrinkling. This is depicted in Figs. 35 and 36, which compare experimental and computational dP/dt and S u respectively, as a function of P, and for the two cases of 20% He and 80% He. It is observed that the trend, as well as the percentage difference between experimental and numerical values are similar for dP/dt and S u . It is interesting to note also that for the 80% He case, the numerical results over predict the experimental values, while for the case of 20% He the experimental values are significantly higher than the model prediction throughout the compression stage. This trend change cannot be attributed to kinetic effects. The actual reason is that the flame becomes already cellular during the constant pressure region, while the 1-D simulations model smooth flames. This also indicates that both dP/dt and S u are suitable markers of burning rate modifications. However, since dP/dt is affected by radiation heat loss, while S u is not [72], the latter is suggested for comparisons of such phenomena. 73 Fig. 35. Comparisons of experimental and TORC results of dP/dt vs. P, for flames of mixtures having = 0.8, 80 (blue) and 20% (red) He, at P o = 3 atm and T u,o = 298 K. Symbols and lines represent experimental and computational results respectively. Fig. 36. Comparisons of experimental and TORC results of S u vs. P, for flames of mixtures having = 0.8, 80 (blue) and 20% (red) He, at P o = 3 atm and T u,o = 298 K. Symbols and lines represent experimental and computational results respectively. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 7 8 9 10 11 12 13 dP/dt (atm/msec) P (atm) 20He_3atm_1600K_HTDR 80He_3atm_1600K_HTDR 20He_3atm_1600K_TORC 80He_3atm_1600K_TORC 0 10 20 30 40 50 60 7 8 9 10 11 12 13 S u o (cm/s) P (atm) 20He_3atm_1600K_HTDR 80He_3atm+1600K_HTDR 20He_3atm_1600K_TORC 80He_3atm_1600K_TORC 74 In this experiment, the majority of the isentropic compression is actually taking place at the later part of flame propagation and most of the data collection part is at the last fifth of the chamber radius, before the flame starts getting feedback from the wall. Figure 37 shows the P/P o vs R f /Rw for the same two experiments. As it is evident the majority of the pressure rise is taking place from 0.8 < R f /Rw < 1.0. Fig. 37. P/P o vs. R/R w , for flames of mixtures having = 0.8, 80 (blue) and 20% (red) He, at P o = 3 atm and T u,o = 298 K. Figures 38 and 39 present the change in the normalized flame thickness and the density ratio as a function of P/P o . As the flame propagates outwardly it compresses isentropically the unburned mixture, increasing thus the pressure, unburnt mixture temperature and as a result T ad increases as well. The flame thickness keeps decreasing during the evolution of the experiment, which is promoting further the transition to instabilities. The decrease is actually almost an order of magnitude. On the other hand, although T ad increases, the ratio of T ad /T u keeps decreasing which translates to a decrease in density jump across the flame of approximately 50%. This effect works against the transition to unstable flames. So the two effects are actually countering each other in terms of flame stability. 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 P/Po R f /R w 80He_3atm_1600K 20He_3atm_1600K 75 Fig. 38. Variation of flame thickness (lth) with increasing pressure and temperature vs. P/P o for flames of mixtures having = 0.8, 80 (blue) and 20% (red) He, at P o = 3 atm and T u,o = 298 K. Fig. 39. Density Ratio vs. P/P o for flames of mixtures having = 0.8, 80 (blue) and 20% (red) He, at P o = 3 atm and T u,o = 298 K. 0.0000 0.2000 0.4000 0.6000 0.8000 1.0000 1.2000 0.0 2.0 4.0 6.0 8.0 lth/lth o P/P o 80He_3atm_1600K 20He_3atm_1600K 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 0.0 2.0 4.0 6.0 8.0 σ/ σ o P/Po 80He_3atm_1600K 20He_3atm_1600K 76 Figure 40 shows the evolution of Peclet number Pe=R f /l th for the same two cases of (20%He, T ad =1600K, P o =3atm) and (80%He, T ad =1600K, P o =3atm). Pe is traditionally used in instabilities studies as the space coordinate since it measures the flame translation in number of flame thicknesses. As explained in Figure 38 though, in the case of a compressing spherical flame, the flame thickness constantly decreases. As a result, the Pe in this case is still a measure of flame translation but in terms of “ever-decreasing” flame thickness. Figure 40 shows a liner dependence of Pe to P/Po. Fig. 40. Pe vs. P/P o for flames of mixtures having = 0.8, 80 (blue) and 20% (red) He, at P o = 3 atm and T u,o = 298 K. Following the aforementioned arguments, the percentage deviation of the experimentally obtained S u values from the computed ones (using the PREMIX code) is considered an insightful quantity for comparison, and is presented as a function of P/P o in Fig. 41 for the = 0.8, P o = 3 atm, T u,o = 298 K, 50%H 2 -50%CO-O 2 -He-Ar cases. All the inert mixture cases that were considered in the present study are presented, and is worth mentioning again that a percentage deviation in S u is indicative of the percentage growth of area due to wrinkling, and thus of the mass burning rate compared to the smooth flame case. Also it needs to be indicated that the baseline percentage difference observed for the 100%He totally smooth flame were subtracted 0 200 400 600 800 1000 1200 1400 1600 1800 2000 0.0 2.0 4.0 6.0 8.0 Pe P/Po 80He_3atm_1600K 20He_3atm_1600K 77 from all cases in order to remove the effect of the difference due to the inherent discrepancies between experimental results and simulation predictions. The Davis et al. kinetic mechanism [79] was used for this study for all cases of 50H 2 -50CO. From Figure 36 it is evident that the laminar flame speed value is constantly increasing during the flame evolution. As a result, when using a systematic chemical mechanism with optimized/well defined reaction pathways, the percentage discrepancy is constantly decreasing. This baseline is actually an array as function of P/P o , ranging from approximately -23% to -18% for the range of P/Po that data is collected (before any wall heat loss effects). All three 100%He, 80%He, and 70%He, P o =3atm cases exhibited this -23% to -18% discrepancy trend. Fig. 41. Percentage difference of experimentally obtained S u from corresponding S u obtained using the PREMIX code and Davis et al. kinetic mechanism, as a function of P/P o , for flames of mixtures of = 0.8, 50%H 2 -50% and with various He% in the inert (He-Ar) composition. 78 As expected, the 70%, 80%, and 100% He remain at 0% since their discrepancy was used as the baseline. For the cases of 0%, 20%, and 40% He, flame acceleration was already initiated in the constant pressure region, and thus the percentage deviation is already high at the beginning of the compression stage, at ~70%, 50% and 25% correspondingly with respect to the baseline discrepancy. Based on published results of constant pressure flame propagation-acceleration due to cellularity [62][63][65] and something also observed in Figure 33, although an ever- increasing flame speed would be expected, the effect of flame acceleration seems to attenuate as the flame enters the compression stage. This is in contrast to the case of unstable flame propagation in the constant pressure stage of the experiment where the flame continuously accelerates in a self-similar manner. More interestingly for the cases with more than 40% He in the inert composition, and for which the onset of instability occurred well within the compression stage, the percentage increase is significantly lower (less than ~20%) and the increase rate once more attenuates, as depicted in Fig. 41. This observation indicates that maybe if the onset of cellularity is notably delayed it will result in significantly milder deviations compared to flames that develop a coherent cellular pattern at the very early stages of propagation, i.e. in the constant pressure region. This potentially means that the controlling mechanisms of instability phenomena in SEFs and the attendant effect on the burning rate can be significantly different depending on the stage of propagation, whether in the constant pressure or in the compression stage. As mentioned earlier in Figure 38 there is a significant decrease in flame thickness as the flame moves outwardly during the compression stage. As a result plotting in terms of Pe would be more confusing than helpful. Instead, it was chosen to indicate the approximate number of flame thicknesses propagated at each P/P o interval. This is indicated in all corresponding Figures 41-45 using numbers next to the curves (number of flame thicknesses). The way it was calculated was simply 11 ( )*2 / ( ) i i thi thi R R l l assuming an average flame thickness for each corresponding P/P o interval. 79 For all the comparisons presented up to this point, the only parameter modified was the ratio of He to Ar in the inert gas composition. The change in ratio results in a simultaneous change in both Le and l th , meaning that the results presented earlier correspond to unstable flames that are affected by both DL and TD instabilities. During an experiment if smooth flames are observed in the constant pressure stage, and cells start to form in compression stage, these flames are mostly affected by DL instabilities. This is because the Peclet number, Pe, has already attained large values thus indicating that DL effects are more important while Le remains unchanged. However, the onset of cellularity can as well start at the very early stages of propagation, due to TD instabilities. Also once cellular structures starts appearing on the flame surface, although globally the Ka number is very low, the local stretch due to local cell curvature becomes of significance and Le number effects can possible start being important once more. In order to examine separately the influence of l th and L b on the increase of burning rate due to onset of cellularity, three additional sub-studies were performed, that involve flame of mixtures exhibiting L b >0, L b <0, and L b =0 trend. Figure 42 depicts the percentage discrepancies (always with respect to the baseline) for mixtures that are exhibiting positive L b behavior. Despite the fact that in the cylindrical chamber experiments the initiation of cellular structure was observed at P=14.5atm for the P o =5atm case, both P o =5atm and P o =6atm flames show no sign of acceleration inside the compression region. In order to initiate the cellular structure even earlier, three additional experiments were performed for the same mixture and P o =3atm but having higher adiabatic flame temperatures (T ad =1800K, T ad =1900K and T ad =2100K) and thus lower flame thickness. It is evident form Figure 42 that although the % deviation for the 1900K & 2100K is already high due to acceleration in the constant pressure region, once the compression stage is attained the % discrepancy remains constant at ~20% and ~35% correspondingly. This is once more hinting towards the assumption that cell-induced flame acceleration is restricted once the flame enters the isentropic compression stage. For the 1800K case the flame started showing signs of acceleration at ~P/P o =2.5 but the increase attenuated at ~P/P o =4 to a value of approximately 20%. 80 Fig. 42. Percentage difference of experimentally obtained S u from corresponding S u obtained using the PREMIX code and Davis et al. kinetic mechanism, as a function of P/P o , for flames of mixtures of = 0.8, 50%H 2 -50%, 70%He in the inert (He-Ar) composition. Figure 43 depicts the percentage discrepancies (always with respect to the baseline) for mixtures that are exhibit negative L b behavior (Le<1). The initial mixture pressure P o was decreased in this case in order to increase the flame thickness and manage to retain smooth flames within the constant pressure propagation stage. This was obviously achieved as the P o =1atm does not show any signs of acceleration up until P/P o =3.5.What is of great interest once again is that the flame acceleration seems to attenuate to a constant value within the compression propagation stage , even though an ever increasing acceleration would be expected for mixtures exhibiting negative L b behavior. 81 Fig. 43. Percentage difference of experimentally obtained S u from corresponding S u obtained using the PREMIX code and Davis et al. kinetic mechanism, as a function of P/P o , for flames of mixtures of = 0.8, 50%H 2 -50%, 20%He in the inert (He-Ar) composition. In order to decouple the Le effect, the same C 2 H 2 experiments showed in Figure 34 were repeated in the spherical chamber. Figure 44 depicts the acceleration characteristics for those flames for which the acceleration (if any) initiates once more during different stages of propagation. Fig. 44. Percentage difference of experimentally obtained S u from corresponding S u obtained using the PREMIX code and Dames et al. kinetic mechanism, as a function of P/P o , for flames of mixtures of = 0.8, C 2 H 2 /O 2 /N 2 . 82 For the P o =1atm case no signs of flame acceleration are evident. For the P o =1.5atm and P o =2atm cases the flame seems to start accelerating at different stages within the compression regions, but this acceleration seems to once more attenuate and stay constant at ~20%. For the P o =3atm, T ad =2400K that has considerably smaller flame thickness, flame acceleration already initiates inside the constant pressure region and that is once more why the discrepancy is as high as ~ 45% at the early compression stages. However, throughout the healthy part of the compression region, the discrepancy increases by an additional ~7% only, supporting the argument of the previous cases in Figures 42 and 43. Despite the fact that the flame thickness is constantly decreasing during flame propagation inside the compression stage, it would still be worth plotting the results of Figure 44 in terms of Pe number and also indicate the number of flame thickness the flame has propagated between the same P/P o points as the once shown in Figure 44. These results are depicted in Figure 45. Fig. 45. Percentage difference of experimentally obtained S u from corresponding S u obtained using the PREMIX code and Dames et al. kinetic mechanism, as a function of Pe, for flames of mixtures of = 0.8, C 2 H 2 /O 2 /N 2 . The number of average flame thicknesses propagated during each interval are indicated with numbers next to each interval. As it can be noticed from Figure 45 the flame has propagated approximately ~100 “average” flame thicknesses during the compression region for which healthy data could be obtained. That number is enough to justify that the phenomena observed are not local noise of data processing or just a local effect in general. 83 From all the aforementioned results it can be reported with reasonable amount of certainty that an effect is taking place during the compression propagation stage that is actually attenuating the effect of cellular structure on the flame speed and thus on the flame’s burning rate. It is also worthwhile to point out that one of the main differences between the fluid flow in the constant pressure and constant volume SEF propagation is the compression induced inward flow [34]. This flow of burned gas towards the center of the chamber, in the constant volume case, causes a significant decrease in the rate of flame expansion (dR f /dt) and hence the stretch rate, as compared to the constant pressure case as is also presented in Fig. 46 [72]. This could potentially have a significant effect on the non-linear evolution of cells and could cause the relatively minor role of DL-induced instability on the measured burning rate. Fig. 46. Typical variation of the computed dR f /dt with R f using TORC; dashed line (---): constant pressure; solid line ( ─) constant volume [72]. It is to be expected that since the entire compression is taking place at the last 20% of the chamber radius (approximately 1.5cm in the case of the current setup), every cell/crest created is getting closer to the wall compared to the rest of the flame. As a result, it is in a sense forced to slow down due to the effect described in Fig. 46. Already existing theoretical stability studies of another combustion case ([120][121][122][123][124]), that of a flame propagating in a closed tube, can probably provide 84 some helpful insight. Those studies have shown that under confinement, the flame is once more compressing the unburnt gas as it propagates towards the end wall, producing again a negative velocity in the direction of the burned gas (with respect to the flame). The stability analysis results showed that contrary to an unconfined case, when wall boundary condition is imposed, the growth rate of instabilities of all wavelengths is initially delayed. Once again when mixtures of L b larger than a critical value are chosen, short-wavelength disturbances are can be stabilized even further. To conclude, in the case that cells start developing during the constant pressure stage, the effect on the burning rate is profound, as evident by notable deviations from results obtained in simulations that assume stable flames. On the other hand, when cells start developing during the compression stage, it was determined that the instability induced growth has a modest to minor effect on the burning rate as evident again from comparisons against one-dimensional simulation results. These findings are expected to be of direct relevance to the experimental determination of laminar flame speeds at engine-relevant conditions during the compression stage. 85 Chapter 5 Summary and Future Recommendations 5.1 Uncertainty quantification of spherically expanding laminar flame speeds Following the detailed uncertainty quantification methodology proposed, all groups should try to minimize the errors emerging from various stages during data collection. This uncertainty algorithm explains additionally which factors are not significantly contributing to the final uncertainty and thus no expenses should be made for those particular ones. Moreover, some data currently existing in the literature should probably be repeated so that more trustworthy targets exist for future chemistry optimization purposes. 5.2 Studies of foundational fuel chemistry The experimental results revealed clear deficiencies in current state of the art kinetic models to predict laminar flame speeds of rich acetylene mixtures at high pressures. The data presented in this work should serve as targets for chemistry optimization and/or modification in the near future. Additionally experiments closer to engine relevant conditions should probably be performed to extend our knowledge. 5.3 Flame acceleration due to flame instabilities The trends observed in the experiments presented in the current thesis are actually novel, in the sense that no group has performed similar studies in the past. Experimentalists should work closely with theoreticians and CFD scientists to tackle this serious issue. The nature of this experiment makes it very difficult to derive conclusive evidence of what is happening. As a result, simplified models and simulations are necessary to help decouple the problem and explain what is really the cause for this attenuation in the cellularity-induced flame acceleration. 86 References [1] U.S. Energy Information Administration. International Energy Outlook 2014 DOE/EIA- 0484(2014). [2] C.K. Law, Combustion physics, Cambridge University Press, 2008. [3] F.A. Williams, Combustion theory, Benjamin Cummins, Palo Alto, CA, 1985. [4] G.E. Andrews, D. Bradley, Determination of burning velocities: a critical review, Combust. Flame 18 (1972) 133-153. [5] J.W. Linnett, Methods of measuring burning velocities, Symp. (Int.) Combust. 4 (1953) 20-35. [6] E.F. Fiock, Physical measurements in gas dynamics and combustion, in high speed aerodynamics and jet propulsion (Part 1, R.W. Ladenburg, Ed.; Part 2, B. Lewis, R.N. Pease, H.S. Taylor, Eds.), Oxford University Press, London and New York (1955), Vol. 9, p. 409. [7] A.G. Gaydon, A.G., H.G. Wolfhard, Flames-their structure, radiation and temperature, 2nd Ed., Chapman & Hall, London (1960), pp. 56-88. [8] R.M. Fristrom, A.A. Westenberg, Flame structure, 1st Ed., McGraw-Hill, New York (1965), pp. 133-140. [9] C.J. Rallis, A.M. Garforth, The determination of laminar burning velocity, Prog. Energy Combust. Sci. 6 (1980) 303-329. [10] E. Ranzi, A. Frassoldati, R. Grana, A. Cuoci, T. Faravelli, A.P. Kelley, C.K. Law, Hierarchical and comparative kinetic modeling of laminar flame speeds of hydrocarbon and oxygenated fuels, Prog. Energy Combust. Sci. 38 (2012) 468-501. [11] F.N. Egolfopoulos, N. Hansen, Y. Ju, K. Kohse-Höinghaus, C.K. Law, F. Qi, Advances and challenges in laminar flame experiments and implications for combustion chemistry, Prog. Energy Combust. Sci. 43 (2014) 36-67. [12] R. Bunsen, On the temperature of flames of carbon monoxide and hydrogen, Pogg. Ann. Phys. u. Chem. 131 (1867) 161-179. [13] F.A. Smith, S.F. Pickering, Measurements of flame velocity by a modified burner method, Jour. Research Nat. Bur. Std. 17 (1936). 87 [14] N. Bouvet, C. Chauveau, I. Gökalp, S.-Y. Lee, R.J. Santoro, Characterization of syngas laminar flames using the Bunsen burner configuration, Int. J. of Hydrogen Energy 36 (2011) 992-1005. [15] J. Natarajan, T. Lieuwen, J. Seitzman, Laminar flame speeds of H 2 /CO mixtures: effect of CO 2 dilution, preheat temperature, and pressure, Combust. Flame 151 (2007) 104-119. [16] F.W. Stevens, The rate of flame propagation in gaseous explosive reactions, J. Am. Chem. Soc. 48 (1926) 1896-1906. [17] D.R. Dowdy, D.B. Smith, S.C. Taylor, The use of expanding spherical flames to determine burning velocities and stretch effects in hydrogen/air mixtures, Symp. (Int.) Combust. 23 (1991) 325-332. [18] S. Kwon, L.K. Tseng, G.M. Faeth, Laminar burning velocities and transition to unstable flames in H 2 /O 2 /N 2 and C 3 H 8 /O 2 /N 2 mixtures, Combust. Flame 90 (1992) 230-246. [19] S.D. Tse, D.L. Zhu, C.K. Law, Morphology and burning rates of expanding spherical flames in H 2 /O 2 /inert mixtures up to 60 atmospheres, Proc. Combust. Inst. 28 (2000) 1793-1800. [20] X. Qin, Y. Ju, Measurements of burning velocities of dimethyl ether and air premixed flames at elevated pressures, Proc. Combust. Inst. 30 (2005) 233-240. [21] B. Lewis, G. von Elbe, Determination of the speed of flames and the temperature distribution in a spherical bomb from time ‐pressure explosion records, J. Chem. Phys. 2 (1934) 283-290. [22] E.F. Fiock, C.F. Marvin (Jr), The measurement of flame speeds, Chem. Rev. 21 (1937) 367-387. [23] D. Bradley, A. Mitcheson, A., Mathematical solutions for explosions in spherical vessels, Combust. Flame 26 (1976) 201-217. [24] M. Metghalchi, J.C. Keck, Laminar burning velocity of propane-air mixtures at high temperature and pressure, Combust. Flame 38 (1980) 143-154. [25] M. Metghalchi, J.C. Keck, Burning velocities of mixtures of air with methanol, isooctane, and indolene at high pressure and temperature, Combust. Flame 48 (1982) 191-210. [26] K. Eisazadeh-Far, A. Moghaddas, J. Al-Mulki, H. Metghalchi, Laminar burning speeds of ethanol/air/diluent mixtures, Proc. Combust. Inst. 33 (2011) 1021-1027. 88 [27] A. Moghaddas, K. Eisazadeh-Far, H. Metghalchi, Laminar burning speed measurement of premixed n-decane/air mixtures using spherically expanding flames at high temperatures and pressures, Combust. Flame 159 (2012) 1437-1443. [28] C.K. Wu, C.K. Law, On the determination of laminar flame speeds from stretched flames, Symp. (Int.) Combust. 20 (1984) 1941–1949. [29] D.L. Zhu, F.N. Egolfopoulos, C.K. Law, Experimental and numerical determination of laminar flame speeds of methane/(Ar, N 2 , CO 2 )-air mixtures as function of stoichiometry, pressure, and flame temperature, Symp. (Int.) Combust. 22 (1988) 1537–1545. [30] C. Ji, E. Dames, Y.L. Wang, H. Wang, F.N. Egolfopoulos, Propagation and extinction of premixed C 5 -C 12 n-alkane flames, Combust. Flame 157 (2010) 277-287. [31] L.P.H. de Goey, A. van Maaren, R.M. Quax, Stabilization of adiabatic premixed laminar flames on a flat flame burner, Combust Sci Technol. 92 (1993) 201-207. [32] K.J. Bosschaart, L.P.H. de Goey, Detailed analysis of the heat flux method for measuring burning velocities, Combust. Flame 132 (2003) 170-180. [33] M. Goswami, S.C.R. Derks, K. Coumans, W.J. Slikker, M.H. de Andrade Oliveira, R.J.M. Bastiaans, C.C.M. Luijten, L.P.H. de Goey, A.A. Konnov, The effect of elevated pressures on the laminar burning velocity of methane+air mixtures, Combust. Flame 160 (2013) 1627-1635. [34] Z. Chen, M.P. Burke, Y. Ju, Effects of compression and stretch on the determination of laminar flame speeds using propagating spherical flames, Combust. Theor. Model. 13 (2009) 343-364. [35] C. Ji, Y.L. Wang, F.N. Egolfopoulos, Flame studies of conventional and alternative jet fuels, J. Propul. Power 27 (2011) 856–863. [36] G. H. Markstein, Non-steady flame propagation, Oxford: Pergamon 1964. [37] D. Bradley, P. H. Gaskell, X. J. Gu, Burning velocities, Markstein lengths, and Flame Quenching for Spherical Methane-Air Flames: A Computational Study, Combust. Flame 104 (1996) 176-198. [38] O. C. Kwon, G. M. Faeth, Flame/Stretch Interactions of Premixed Hydrogen-Fueled Flames: Measurements and Predictions, Combust. Flame 124 (2001) 590-610. 89 [39] G. Rozenchan, D. L. Zhu, C. K. Law, S. D. Tse, Outward propagation, Burning velocities and chemical effects of methane flames up to 60atm, Proc. Combust. Inst. 29 (2002) 1461-1469. [40] D. Bradley, R. A. Hicks, M. Lawes, C. G. W. Sheppard, and R. Wooley, The measurement of laminar burning velocities and Markstein Numbers for iso-octane-air and iso-octane-n-heptane-air mixtures at elevated temperatures and pressures in an explosion bomb, Combust. Flame 115 (1998) 126-144. [41] M. P. Burke, Z. Chen, Y. Ju, F. L. Dryer, Effects of cylindrical confinement on the determination of laminar flames speeds using outwardly propagating flames, Combust. Flame 156 (2009) 771-779. [42] K. Kumar, C.J. Sung, Laminar flame speeds and extinction limits of preheated n- decane/O 2 /N 2 and n-dodecane/O 2 /N 2 mixtures, Combust. Flame 151 (2007) 209-224. [43] A.P. Kelley, A.J. Smallbone, D.L. Zhu, C.K. Law, Laminar flame speeds of C 5 to C 8 n- alkanes at elevated pressures: experimental determination, fuel similarity, and stretch sensitivity, Proc. Combust. Inst. 33 (2011) 963-970. [44] J. Jayachandran, R. Zhao, Determination of laminar flame speeds using stagnation and spherically expanding flames: molecular transport and radiation effects, F.N. Egolfopoulos, Combust. Flame (2014) 2305-2316. [45] J. Jayachandran, A. Lefebvre, R. Zhao, F. Halter, B. Renou, A study of propagation of spherically expanding and counterflow laminar flames using direct measurements and numerical simulations, F.N. Egolfopoulos, Proc. Combust. Inst. 35 (2015) 695-702. [46] F. Wu, W. Liang, Z. Chen, Y. Ju, C.K. Law, Uncertainty in stretch extrapolation of laminar flame speed from expanding spherical flames, Proc. Combust. Inst. 35 (2015) 663–670. [47] J.H. Tien, M. Matalon, On the burning velocity of stretched flames, Combust. Flame 84 (1991) 238-248. [48] A.P. Kelley, C.K. Law, Nonlinear effects in the extraction of laminar flame speeds from expanding spherical flames, Combust. Flame 156 (2009) 1844-1851. [49] Y.L. Wang, A.T. Holley, C. Ji, F.N. Egolfopoulos, T.T. Tsotsis, H. Curran, Propagation and extinction of premixed dimethyl-ether/air flames, Proc. Combust. Inst. 32 (2009) 1035-1042. 90 [50] G. Darrieus 1938, Presented at 6 th Int Cong. Appl. Mech 1946, Paris. [51] L. D. Landau, E. M. Lifshitz, Fluid Mechanics, Pergamon, Oxford, 1987. [52] G. I. Shivashinsky, Instabilities, pattern formation, and turbulence in flames, Ann. Review Fluid Mech 15 (1983) 179-199. [53] E. G. Groff, The cellular nature of confined spherical propane-air flames, Combust. Flame 48 (1982) 51-62. [54] D. Bradley, C. G. W. Sheppard and R. Woolley, D. A. Greenhalgh, R. D. Lockett, The development and structure of flame instabilities and cellularity at low Markstein numbers in explosions, Combust. Flame 122 (2000) 195-209. [55] C. K. Law, G. Jomaas, J.K. Bechtold, Cellular instabilities of expanding hydrogen/propane spherical flames at elevated pressures:theory and experiment, Proceedings of the combustion Institute 30 (2005) 159-167. [56] C. K. Law, G. Jomaas, J. K. Bechtold, Cellular instabilities of expanding hydrogen/propane spherical flames at elevated pressures: theory and experiment, Proc. Combust. Inst. 30 (2005) 159-167. [57] A. G. Istratov, V. B. Librovich, On the stability of gasdynamic discontinuities associated with chemical reactions. The case of a spherical flame, Acta Astronautica 14 (1969) 453- 467. [58] M. L. Frankel, G. I. Sivashinsky, On the effects due to thermal expansion and Lewis number in spherical flame propagation, Combust. Sci. Technol. 31 (1983) 131-138. [59] J. K. Bechtold, M. Matalon, Hydrodynamic and diffusion effects on the stability of spherically expanding flames, Combust. Flame 67 (1987) 77-90. [60] Yu. A. Gostintsev, A. G. Istratov, Yu V. Shulenin, Self-similar propagation of a free turbulent flame in mixed gas mixtures Combust. Explos. Shock Waves 24 (1988) 563- 569. [61] D. Bradley, Instabilities and flame speeds in large-scale premixed gaseous explosions, Phil Trans R. Soc. Lond. A 357 (1999) 3567-3581. [62] O. C. Kwon, G. Rozenchan, C. K. Law, Cellular instabilities and self-acceleration of outwardly propagating spherical flames, Proc. Combust. Inst. 29 (2002) 1775-1783. [63] F. Wu, G. Jomaas, C. K. Law, An experimental investigation on self-acceleration of cellular spherical flames, Proceedings of the Combustion Institute 34 (2013) 937-945. 91 [64] Y. X. Xin, C. S. Yoo, J. H. Chen, C. K. Law, a DNS study of self-accelerating cylindrical hydrogen-air flames with detailed chemistry, Proceedings of the combustion Institute 35 (2015) 753-760. [65] S. Yang, A. Saha, F. Wu, C. K. Law, Morphology and self-acceleration of expanding laminar flames with flame-front cellular instabilities, Combustion and Flame 171 (2016) 112-118. [66] P. Clavin, Dynamic behavior of premixed flame fronts in laminar and turbulent flows, Prog. Energy Combust. Sci. 11 (1985) 1-59. [67] P. D. Ronney, G. I. Sivashinsky, A theoretical study of propagation and extinction of non-steady spherical flame fronts, SIAM J. Appl. Math 49 (4) (1989) 1029-1046. [68] A. P. Kelley, C. K. Law, Nonlinear effects in the extraction of laminar flame speeds from expanding spherical flames, 156 (2009) 1844-1851. [69] A. P. Kelley, J. K. Bechtold C. K. Law, Premixed flame propagation in a confining vessel with weak pressure rise, J. Fluid Mech. 691 (2012) 26-51. [70] A.E. Lutz, F.M. Rupley, R.J. Kee, W.C. Reynolds, E. Meeks, EQUIL: a CHEMKIN implementation of STANJAN for computing chemical equilibria. Sandia Technical Report, Sandia National Laboratories, 1998. [71] S. Balusamy, A. Cessou, B. Lecordier, Direct measurement of local instantaneous laminar burning velocity by a new PIV algorithm, Exp. Fluids 50 (2011) 1109-1121. [72] C. Xiouris, T. Ye, J. Jayachandran, F. N. Egolfopoulos, Laminar flame speeds under engine-relevant conditions: Uncertainty quantification and minimization in spherically expanding flame experiments, Combust. Flame 163 (2016) 270-283. [73] R.J. Kee, J.F. Grcar, M.D. Smooke, J.A. Miller, Premix: a FORTRAN program for modeling steady laminar one-dimensional premixed flames, Sandia Report, SAND85- 8240, Sandia National Laboratories, 1985. [74] J.F. Grcar, R.J. Kee, M.D. Smooke, J.A. Miller, A hybrid Newton/time-integration procedure for the solution of steady, laminar, one-dimensional, premixed flames, Symp. (Int.) Combust. 21 (1986) 1773–1782. [75] R.J. Kee, F.M. Rupley, J.A. Miller, Chemkin-II: a FORTRAN chemical kinetics package for the analysis of gas-Phase chemical kinetics, Sandia Report, SAND89-8009, Sandia National Laboratories, 1989. 92 [76] R.J. Kee, J. Warnatz, J.A. Miller, A FORTRAN computer code package for the evaluation of gas-phase viscosities, conductivities, and diffusion coefficients, Sandia Report, SAND83-8209, Sandia National Laboratories, 1983. [77] Y. Dong, A.T. Holley, M.G. Andac, F.N. Egolfopoulos, S.G. Davis, P. Middha, H. Wang, Extinction of premixed H 2 /air flames: chemical kinetics and molecular diffusion effects, Combust. Flame 142 (2005) 374–387. [78] F.N. Egolfopoulos, Geometric and radiation effects on steady and unsteady strained laminar flames, Symp. (Int.) Combust. 25 (1994) 1375–1381. [79] S.G. Davis, A. V. Joshi, H. Wang, F.N. Egolfopoulos, An optimized kinetic model of H 2 /CO combustion, Proc. Combust. Inst. 30 (2005) 1283-1292. [80] H. Wang, X. You, A. V. Joshi, Scott G. Davis, A. Laskin, F.N. Egolfopoulos C. K. Law, USC-Mech Version II. High-temperature combustion reaction model of H 2 /CO/C 1 -C 4 Compounds. http://ignis.usc.edu/USC_Mech_II.htm. [81] H. Wang, E. Dames, B. Sirjean, D.A. Sheen, R. Tangko, A. Violi, J.Y.W. Lai, F.N. Egolfopoulos, D.F. Davidson, R.K. Hanson, C.T. Bowman, C.K. Law, W. Tsang, N.P. Cernansky, D.L. Miller, R.P. Lindstedt, A High-Temperature Chemical Kinetic Model of n-Alkane (up to n-Dodecane), Cyclohexane, and Methyl-,Ethyl-, n-Propyl and n-Butyl- cyclohexane Oxidation at High Temperatures,JetSurF Version 2.0. <http://melchior.usc.edu/JetSurF/JetSurF2.0/Index.html>. [82] E. E. Dames, K.Lam, David F. Davidson, R. K. Hanson, An improved kinetic mechanism for 3-pentanone pyrolysis and oxidation developed using multispecies time histories in shock tubes, Combustion and Flame 161 (2014) 1135-1145. [83] X. Shen, X. Yang, J. Satner, J. Sun, Y. Ju, Experimental and kinetic studies of acetylene flames at elevated pressures, Proceedings of the Combustion Institute 35 (2015) 721-728. [84] T. Lu, C.K. Law, A directed relation graph method for mechanism reduction, Proc. Combust. Inst. 30 (2005) 1333-1341. [85] D. Bradley, P.H. Gaskell, X.J. Gu, Burning velocities, Markstein lengths, and flame quenching for spherical methane-air flames: a computational study, Combust. Flame 104 (1996) 176-198. [86] L.R. Petzold, A description of DASSL: a differential/algebraic system solver, in scientific computing, R.S. Stepleman et al. (Eds.), North-Holland, Amsterdam, 1983, pp. 65-68. 93 [87] T. Ye, Determination of Laminar flame speeds under engine relevant conditions, Thesis submitted in the University of Southern California, 2017. [88] W.L. Grosshandler, RADCAL: a narrow-band model for radiation. NIST Technical Note 1402, Calculations in a Combustion Environment, 1993. [89] H. Zhang, F.N. Egolfopoulos, Extinction of near-limit premixed flames in microgravity, Proc. Combust. Inst. 28 (2000) 1875-1882. [90] M. Burke, M. Chaos, F.L. Dryer, Y. Ju, Negative pressure dependence of mass burning rates of H 2 /CO/O 2 /diluent flames at low flame temperatures, Combust. Flame 157 (2010) 618-630. [91] D.A. Sheen, H. Wang, The method of uncertainty quantification and minimization using polynomial chaos expansions, Combust. Flame 158 (2011) 2358-2374. [92] Z. Chen, On the accuracy of laminar flame speed measure from outwardly propagating spherical flames: methane/air at normal temperature and pressure, Combust. Flame 162 (2015) 2442-2453. [93] I. Hughes, T. Hase, Measurements and their uncertainties: a practical guide to modern error analysis, Oxford University Press, 2010. [94] D. Sivia, Data analysis: a Bayesian tutorial, Oxford University Press, 1996. [95] J.R. Taylor, An introduction to error analysis: the study of uncertainties in physical measurements, University Science Books, Sausalito, U.S.A., 1997. [96] G.S. Settles, Schlieren and shadowgraph techniques: visualizing phenomena in transparent media, Springer Science and Business Media, 2012. [97] F. Parsinejad, J.C. Keck, H. Metghalchi, On the location of flame edge in shadowgraph pictures of spherical flames: a theoretical and experimental study, Exp. Fluids 43 (2007) 887-894. [98] X. J. Gu, M. Z. Haq, M.Lawes, and R. Wooley, Laminar burning velocity and Markstein lengths of methane-air mixtures, Combust. Flame 121 (2000) 41-58. [99] G. Rozenchan, D. L. Zhu, C. K. Law and S. D. Tse, Outward propagation, burning velocities and chemical effects of methane flames up to 60 atm, Proc. Combust. Inst. 29 (2002) 1461-1469. [100] Y. Dong, C. M. Vagelopoulos, G. R. Spedding and F. N. Egolfopoulos, Measurements of laminar flame speeds through digital particle image velocimetry: mixtures of methane 94 and ethane with hydrogen, oxygen, nitrogen, and helium, Proc. Combust. Inst. 29 (2002) 1419-1426. [101] X. Qin, Y. Ju, Measurements of burning velocities of dimethyl ether and air premixed flames at elevated pressures, Proc. Combust. Inst. 30 (2005) 233-240. [102] O. Park, P. S. Veloo, N. Liu, F. N. Egolfopoulos, Combustion characteristics of alternative gaseous fuels, Proc. Combust. Inst. 33 (2011) 887-894. [103] J. Beeckmann, L. Cai, H. Pitsch, Experimental investigation of the laminar burning velocities of methanol, ethanol, n-propanol, and n-butanol at high pressure, Fuel 117 (2014) 340-350. [104] C. M. Vagelopoulos and F. N. Egolfopoulos, Direct experimental determination of laminar flame speeds, Symp. (Int.) Combust. 27 (1998) 513-519. [105] G. Jomaas, X. L. Zheng, D. L. Zhu, C. K. Law, Experimental determination of counterflow ignition temperatures and laminar flame speeds of C2-C3 hydrocarbons at atmospheric and elevated pressures, Proc. Combust. Inst. 30 (2005) 193-200. [106] W. Lowry, J. de Vries, M. Krejci, E. Petersen, Z. Serinyel, W. Metcalfe, H. Curran, G. Bourque, Laminar flame speed measurements and modeling of pure Alkanes and alkane blends at elevated pressures, Journal of Engineering for Gas Turbines and Power, 133 (2011) 091501-1. [107] H. Yu, W. Han, J. Santner, X. Gou, C. H. Sohn, Y. Ju, Z. Chen, Radiation –induced uncertainty in laminar flame speed measured from propagating flames, Combust. Flame 161 (2014) 2815-2824. [108] X. You, F. N. Egolfopoulos, H. Wang, Detailed and simplified kinetic models of n- dodecane oxidation: The role of fuel cracking in aliphatic hydrocarbon combustion, Proc. Combust. Inst. 32 (2009) 403-410. [109] J. A. Miller, M. J. Pilling, J. Troe, Unravelling combustion mechanisms through a quantitative understanding of elementary reactions, Proceedings of the Combustion Institute 30 (2005) 43-88. [110] A. D. Abid, E. D. Tolmachoff, D. J. Phares, H. Wang, Y. Liu, A. Laskin, Size distribution and morphology of nanscent soot in premixed ethylene flames with and without benzene doping, Proceedings of the Combustion Institute 32 (2009) 681-688. 95 [111] A. D. Abid, J. Camacho, D. A. Sheen, H. Wang, Quantitative measurement of soot particle size distribution in premixed flames-The burner-stabilized stagnation flame approach, Combustion and Flame 156 (2009) 1862-1870. [112] H. Wang, Formation of nascent soot and other condensed-phase materials in flames, Proceedings of the Combustion Institute 33 (2011) 41-67. [113] F. N. Egolfopoulos, D. L. Zhu, C. K. Law, Experimental and numerical determination of laminar flame speeds: Mixtures of C2-hydrocarbons with oxygen and nitrogen, Proceedings of the 23d combustion Institute Symposium (1990) 471-478. [114] T. Hirasawa, C. J. Sung, A. Joshi, Z. Yang, H. Wang and C. K. Law, determination of laminar flame speeds using digital particle image velocimetry: Binary fuel blends of ethylene, n-butane, and toluene, Proceedings of the Combustion Institute, 29 (2002) 1427-1434. [115] O. Park, P. S. Veloo, F. N. Egolfopoulos, Flame studies of C 2 hydrocarbons, Proceedings of the Combustion Institute 34 (2013) 711-718. [116] M. I. Hassan, K. T. Aung, O. C. Kwon and G. M. Faeth, Properties of Laminar Premixed Hydrocarbn/Air Flames at Various Pressures, Journal of Propulsion and Power 14 (1998). [117] F. Wu, A. P. Kelley, C. T. D. Zhu, C. K. Law, Measurement and correlation of laminar flame speeds of CO and C2 hydrocarbons with hydrocarbons with hydrogen addition at atmospherica and elevated pressures, Int,. Journal of Hydrogen Energy 36 (2011) 13171- 13180. [118] J. Santner, F. L. Dryer, Y. Ju, The effects of water dilution on hydrogen, syngas, ethylene flames at elevated pressure, Proceedings of the Combustion Institute 34 (2013) 719-726. [119] Silcocks, C. G., The kinetics of the thermal polymerization of acetylene, Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences Vol. 242, issue 1231, pp. 411-429. [120] J. L. Mcgreevy, M. Matalon, Hydrodynamic Instability of a Premixed Flame Under Confinement, Combustion Science and Technology, 100 (1994) 75-94. [121] M. Matalon, J. L. Mcgreevy, The initial development of a Tulip Flame, Proceedings of the combustion Institute, 25 (1994) 1407-1413. [122] M. Matalon, P. Metzener, The propagation of premixed flames in closed tubes, J. Fluid Mech 336 (1997) 331-350. 96 [123] V. V. Bychkov, M. A. Liberman, Stability of a Flame in a closed Chamber, Physical Review Letters, 78 1997. [124] M. A. Liberman, V. V. Bychkov, S. M. Golberg, and L. E. Eriksson, Numerical study of Curved Flames under Confinement, Combustion science and Technology, 136 (1998) 221-251.
Abstract (if available)
Abstract
Experiments involving laminar, premixed, spherically expanding flames were performed using two different experimental facilities. The first one involves experiments in a cylindrical constant volume chamber with optical access in which the flame is directly observed with high speed imaging using the shadowgraph technique. The second involves performing experiments in a totally spherical chamber with no optical access, for which the pressure evolution is the only observable and is used to derive flame speeds at much higher, engine relevant pressures and temperatures, taking advantage of the isentropic compression stage of the experiment. ❧ The first part of the study was aimed to define the uncertainty in data of laminar flame speed obtained from spherically expanding flames. A novel DNS (Direct Numerical Simulation) assisted extrapolation methodology was proposed in order to minimize systematic errors emerging from the use of theoretical linear and non-linear extrapolation equations to obtain the final value of the propagation speed at zero stretch rates. Moreover a complete, rigorous uncertainty quantification methodology was proposed, in order to calculate the errors from all the experimental aspects and then propagate and combine them to estimate the uncertainty in the final value of laminar flame speed. Such a study had never been performed in the past and is of high importance in order for the experimental targets to be meaningful for chemical scheme optimization of interest to the kinetic modeling community. ❧ Upon completion of the uncertainty quantification methodology, the second part of the study included a detailed investigation regarding our current knowledge of laminar flame speeds of C₂ hydrocarbons. Those fuels are of great significance as they comprise the foundational chemistry for the combustion of heavy hydrocarbons. Experiments of spherically expanding flames of CH₄, C₂H₆, C₂H₄, C₂H₂ mixtures were performed on an equal basis and the comparisons with kinetic model predictions revealed serious deficiency in predicting the propagation speed of rich acetylene flames. The importance of this evidence can also be supported by the fact that acetylene is one of main species involved in the reaction pathways that lead to soot production in combustion of hydrocarbon fuels under rich conditions. ❧ The third study in the current thesis revolves around flame acceleration due to instability formation on the flame surface during the compression stage of propagation. All studies currently existing in the literature have solely focused on describing the propagation characteristics of unstable flames during the initial, constant pressure stage of the flame propagation. In this study experiments were performed in both cylindrical and experimental configurations taking advantage of every capability. The onset of flame acceleration due to surface area growth caused from instabilities was promoted at various parts during propagation. The results obtained show an attenuating trend in the unstable flame acceleration, once the spherical flame enter the compression stage that is following the initial constant pressure and temperature propagation part.
Linked assets
University of Southern California Dissertations and Theses
Conceptually similar
PDF
Determination of laminar flame speeds under engine relevant conditions
PDF
Modeling investigations of fundamental combustion phenomena in low-dimensional configurations
PDF
Experimental and kinetic modeling studies of flames of H₂, CO, and C₁-C₄ hydrocarbons
PDF
Pressure effects on C₁-C₂ hydrocarbon laminar flames
PDF
Studies of methane counterflow flames at low pressures
PDF
End-gas autoignition investigations using confined spherically expanding flames
PDF
Flame characteristics in quasi-2D channels: stability, rates and scaling
PDF
Accuracy and feasibility of combustion studies under engine relevant conditions
PDF
Investigations of fuel effects on turbulent premixed jet flames
PDF
Studies on the flame dynamics and kinetics of alcohols and liquid hydrocarbon fuels
PDF
Experimental investigation of the propagation and extinction of edge-flames
PDF
Studies of combustion characteristics of heavy hydrocarbons in simple and complex flows
PDF
Flame ignition studies of conventional and alternative jet fuels and surrogate components
PDF
CFD design of jet-stirred chambers for turbulent flame and chemical kinetics experiments
PDF
Re-assessing local structures of turbulent flames via vortex-flame interaction
PDF
Development of a novel heterogeneous flow reactor: soot formation and nanoparticle catalysis
PDF
An experimental study of shock wave attenuation
PDF
Nanomaterials under extreme environments: a study of structural and dynamic properties using reactive molecular dynamics simulations
Asset Metadata
Creator
Xiouris, Christodoulos
(author)
Core Title
Experimental studies of high pressure combustion using spherically expanding flames
School
Viterbi School of Engineering
Degree
Doctor of Philosophy
Degree Program
Mechanical Engineering
Publication Date
12/07/2017
Defense Date
10/18/2017
Publisher
University of Southern California
(original),
University of Southern California. Libraries
(digital)
Tag
C₂ hydrocarbon flames,extrapolation,flame instabilities,high pressure,laminar combustion,OAI-PMH Harvest,spherically expanding flames,uncertainty quantification
Language
English
Contributor
Electronically uploaded by the author
(provenance)
Advisor
Egolfopoulos, Fokion (
committee chair
), Ronney, Paul (
committee member
), Shing, Katherine (
committee member
)
Creator Email
xiouris.chr@gmail.com,xiouris@usc.edu
Permanent Link (DOI)
https://doi.org/10.25549/usctheses-c40-462012
Unique identifier
UC11268397
Identifier
etd-XiourisChr-5946.pdf (filename),usctheses-c40-462012 (legacy record id)
Legacy Identifier
etd-XiourisChr-5946.pdf
Dmrecord
462012
Document Type
Dissertation
Rights
Xiouris, Christodoulos
Type
texts
Source
University of Southern California
(contributing entity),
University of Southern California Dissertations and Theses
(collection)
Access Conditions
The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...
Repository Name
University of Southern California Digital Library
Repository Location
USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA
Tags
C₂ hydrocarbon flames
extrapolation
flame instabilities
high pressure
laminar combustion
spherically expanding flames
uncertainty quantification