KINETICS PATHS TO RADICAL-INDUCED IGNITION OF METHANE/AIR MIXTURES

Combust. Sci. and Tech., 177: 2275 2298, 2005 Copyright Q Taylor & Francis LLC ISSN: 0010-2202 print/1563-521x online DOI: 10.1080/00102200500241065 KINETICS PATHS TO RADICAL-INDUCED IGNITION OF METHANE/AIR MIXTURES C. S. CAMPBELL* F. N. EGOLFOPOULOS Department of Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, California, USA Non-equilibrium plasmas may be used to dissociate reactants into radicals. In turn, these radicals react releasing energy and broadening the radical pool and thereby ignite or aid the ignition of a fuel=air mixture. Using methane as an archetypical fuel, this work studies the kinetic pathways that control homogeneous ignition in the presence of radicals, which were previously formed by external, non-chemical means. This type of ignition generally follows a well-defined fourstage chain sequence starting with reactions of the original radicals, followed by the reactions of their products, up to the point of ignition. The early chemical kinetic processes were found to be relatively insensitive to pressure, initial temperature, and=or stoichiometry of the mixture. Radical-induced ignition has two major advantages over thermal ignition. First, a major part of the ignition energy comes from exothermic reactions between the radicals and the oxidizer. As a result, radical-induced ignition can potentially require less energy than, for example, sparkplugs to which all the thermal energy must be supplied in the form of electricity. Second, radical ignition can reduce the ignition delay time by many orders of magnitude to values, under extreme conditions, of the order of few hundred nanoseconds, which are nearly 5 orders of magnitude lower than the tens of milliseconds ignition delays that are typical of thermal ignition. Received 30 November 2004; accepted 3 May 2005. This work was supported by AFOSR (Grant No. F49620-03-C-001). Address correspondence to campbell@usc.edu 2275

2276 C. S. CAMPBELL AND F. N. EGOLFOPOULOS Keywords: plasma-assisted ignition, ignition kinetics INTRODUCTION Ignition can be a limiting factor in air-breathing combustion at high speeds and=or at high altitude, such as SCRAMJETs and Unmanned Aerial Vehicles (UAVs). In high-flight Mach-number SCRAMJETs, ignition must occur within extremely short times. In UAV s, re-ignition must follow blowout at altitudes as high as 65,000 feet, where it is difficult, if not impossible, to ignite by standard techniques. Non-equilibrium plasma ignitors have been proposed as potential solutions. Fuel=air mixtures exposed to short duration electrical pulses form non-equilibrium plasmas, in which the electric field accelerates the free electrons to high energy without significantly raising the gas temperature (e.g., Bozhenkov et al., 2003; Liu et al., 2003; Starikovskaii, 2003). When the electrons collide with neutral gas molecules, they excite the vibrational energy modes. If the collisional energy is large enough, molecular bonds will break, generating radical species. These radicals readily react with the surrounding fuel and oxidizer molecules, releasing heat that in turn generates additional radicals, initiating thus a sequence that could eventually result in ignition. These reactions liberate more thermal energy than was required to generate the radicals so that, if the dissociation can be performed efficiently, less energy is required to ignite with radicals than to ignite thermally. Radical ignition can also dramatically reduce the ignition delay time (IDT). As thermal ignition starts with no radicals, (e.g., Egolfopoulos et al., 2002; Fotache et al., 1997), the initial presence of significant amounts of radicals in the mixture will shorten the IDT. For example, a typical IDT for thermal ignition is of the order of one-hundredth of a second (e.g., Fotache et al., 1997). As will be shown below, IDT s of radical-induced ignition can be as low as 200 nanoseconds, a reduction of 5 orders of magnitude. By varying the voltage on the ignitor electrodes, it is possible to have a degree of control over the energy of the electrons that dissociate fuel molecules into radicals and, thus, have a degree of control over which radicals are produced. This work is intended to better understand the chemical kinetic pathways that lead to ignition as a way of determining the optimum choice of the initial radical pool.

RADICAL-INDUCED IGNITION OF FUEL=AIR MIXTURES 2277 NUMERICAL APPROACH Numerous archetypical examples of the ignition of CH 4 =air mixtures in the presence of radicals were examined using the CHEMKIN-based (Kee et al., 1989), SENKIN (Lutz et al., 1988) code and the GRI 3.0 mechanism (Smith et al., 2000). As there are no designs of a practical non-equilibrium plasma ignitor to use as guidelines, the problem was reduced to its bare essentials using SENKIN to model the ideal situation of an isobaric, homogeneous, and adiabatic reactor, and, thus, limit the ignition problem purely to its chemical aspects. There could be some concerns in using GRI 3.0 for this type of study, as it has not been optimized for situations that involve large radical concentrations. Having said that and given that the mechanism is considered to be the most reliable one in predicting CH 4 oxidation, it is expected that even in the presence of large amounts of radicals in the initial reactant pool, it will satisfactorily describe to the first order the underlying chemical pathways that result to ignition. Thus, the basic conclusions reported in this work are expected to be largely valid. Additionally, the kinetics described by GRI 3.0 pertain to species at their ground states and the effects of possible excited states are not considered. It should be realized, however, that those excited states are short-lived and disappear within very few molecular collisions, having thus a minor effect on the results. Furthermore, many of the processes that will be discussed in the following, occur very rapidly on subnanosecond timescales. As such, oxidation mechanisms such as GRI 3.0 may underestimate the times required to complete these very short time processes because they do not account for vibrational relaxation of the molecules. However, while vibrational relaxation may increase the duration of nanosecond scale events, it will not affect the kinetic pathways that are the subject of this paper. In particular, except for the extreme case that will be reported in Figure 9, vibrational relaxation should have little or no effect on the Ignition Delay Times, simply because the IDT s are many orders of magnitude larger than the vibrational relaxation time. For the aforementioned problem of igniting after a high-altitude blowout, it can be shown that the pressure and temperature behind the compressor will be of the order of 1 atm and 300 K respectively, which will be used as starting conditions here. CH 4 ignition was investigated for two reasons. First, among all hydrocarbons, it is chemically the best

2278 C. S. CAMPBELL AND F. N. EGOLFOPOULOS Table 1. Threshold energies for the decomposition of methane to neutral radicals by electron interactions, from Janev and Reiter (2002) Reaction e þ CH 4! CH 3 þ H e þ CH 4! CH 2 þ H 2 e þ CH 4! CH þ H 2 þ H e þ CH 4! C þ 2H 2 Energy threshold 8.8 ev 9.4 ev 12.5 ev 14.0 ev characterized. Second, with an eye towards SCRAMJET s at high flight Mach numbers, i.e., 4 Mach 8, CH 4 can be produced in significant quantities when fuel is used to cool the fuselage and engine components (e.g., Edwards, 1996; Egolfopoulos and Dimotakis, 1998). In the process, the fuel will reach high enough temperatures to decompose mainly into CH 4 and C 2 H 4 (Egolfopoulos and Dimotakis, 1998). Given that, among hydrocarbons, CH 4 is difficult to ignite, improving its ignition response through radical addition could facilitate the overall ignition of any fuel blend. In these simulations it is assumed that the radicals are produced instantaneously by a pulse, so that at time t ¼ 0 a mixture of radicals co-exists with the fuel=air mixture. The dissociation is assumed to follow the prescriptions of Janev and Reiter (2002), shown in Table 1, for the decomposition to neutral radicals by interactions with plasma electrons. These prescriptions are used to determine the relative mix of CH radicals, H and H 2. Note that the CH 2 referenced throughout this report is the triplet form of CH 2. It was not possible to obtain information on the production of the singlet form CH 2 (S) by electron collisions. However, detailed analyses showed this to be unimportant as the dominant reaction involving CH 2 (S) is CH 2 (S) þ N 2! CH 2 þ N 2, which rapidly converts the singlet CH 2 (S) to triplet CH 2. RESULTS AND DISCUSSION The Kinetics of Radical-Induced Ignition Thermal ignition is achieved by gradually increasing the temperature of the mixture to produce radicals until the mixture undergoes a rapid temperature rise towards a vigorously burning state. This is not the case for radical-induced ignition where the ignition proceeds in stages, as first

RADICAL-INDUCED IGNITION OF FUEL=AIR MIXTURES 2279 the initial radicals react, followed by the reactions of their products. Each stage causes a temperature rise and generates more radicals until the system ignites. These processes are illustrated in Figure 1 for an atmospheric CH 4 =air mixture with at an equivalence ratio / ¼ 0.6 and an initial temperature of 300 K. Initially, it is assumed that the CH 4 fuel is decomposed into equal parts of CH 3,CH 2, CH, and C (so that the initial mole fractions of each are 0.074). This mixture is purely heuristic and is designed to clearly demonstrate the radical paths; an actual discharge would not generate an even mixture of radicals, but would most likely be heavy in CH 3 as this is the easiest radical to produce. Also, this formulation contains larger radical concentrations than is required for ignition of such a mixture. It is used in order to compare the results here with those induced by the individual radical species in Figures 3 6. To make the various cases comparable, the same dissociation energy is used in each case. As will be seen, CH 3 does not add much to the ignition process, and, as it will be shown in Figure 6, a large decomposition energy is required to generate enough CH 3 to induce ignition. As a result, larger than necessary radical decompositions must be used to make comparable, the easier-to-ignite cases in Figures 1 5. But recall that the goal of this study is to illustrate the kinetic paths to ignition by starting with various radical mixtures. It is not intended to test the feasibility or limits of radical ignition but only the kinetic pathways. To that end, tests show that the pathways are independent of the degree of initial decomposition (provided that enough radicals are produced to induce ignition). The temperature history shown in Figure 1 is representative of most radical-induced ignition processes studied herein, and occurs in three thermal steps that reflect four distinct chemical kinetic stages. In the first two thermal steps, kinetics processes raise the temperature to near 1000 K. Then after a time delay, a behavior that resembles thermal ignition is observed. However, the final ignition is not purely thermal, but is enhanced by the radical pool that results from the early stages. Note that the time scale of the figures begin at t ¼ 10 11 seconds as little happens between that time and the radical injection at t ¼ 0 s. The lower part of Figure 1 depicts the concentration histories of the most important radical species to demonstrate when the various species are being produced and=or consumed. For clarity, each sub-figure is scaled with the maximum concentration of the radical obtained in the computation and each has a different vertical scale. The quantitative values of the

2280 C. S. CAMPBELL AND F. N. EGOLFOPOULOS Figure 1. Time evolution of temperature and species (scaled) concentrations, in radicalinduced ignition. This case begins with atmospheric / ¼ 0.6 with CH 3,CH 2, CH, and C at initial mole fractions of 0.0075, and initial mixture temperature 300 K. Notice that the process proceeds in 3 distinct thermal steps. Note that time is plotted logarithmically. The time is given in seconds.

RADICAL-INDUCED IGNITION OF FUEL=AIR MIXTURES 2281 species concentrations are not important as the goal of this paper is to point out the dominant reactions whose effects are seen in the growth and reduction of the species concentration as they are produced and consumed quantitative concentrations give no insight into the reaction rates. (For example, if a species is being vigorously produced by one reaction, and vigorously consumed by another, its equilibrium concentration may be quite small, even though at the same instant, it is an active participant in the dominant reactions.) Also note that in all figures the units of the reported time are seconds. Reaction path analysis revealed the dominant kinetic paths. The first thermal step shown in Figure 1 contains two separate kinetics stages that will be referred to as Stages 1 and 1a. Stage 1 In Stage 1, the kinetics are dominated by reactions involving CH shown below in order of decreasing reaction rate: CH þ O 2! O þ HCO C þ O 2! O þ CO CH 3 þ H! CH 4 CH 2 þ H! CH þ H 2 CH þ H! C þ H 2 CH þ CH 4! H þ C 2 H 4 ð1þ ð2þ ð3þ ð4þ ð5þ ð6þ The most important products of this stage are HCO and to a lesser degree O, as these play a key role in the reactions controlling Stage 1a. They are produced mainly by (1), which involves CH whose kinetics dominate this first stage. Note that reactions (3) (5) only involve radicals that are provided with the initial pool, but in reactions (1), (2), and (6) CH and C react with undecomposed O 2 and CH 4 ; the latter set of reactions will thus recover more thermal energy than the energy initially used for decomposition. CH 2 also plays an important role because

2282 C. S. CAMPBELL AND F. N. EGOLFOPOULOS it reacts with H in reaction (4) to form additional CH. In that way CH 2 - production may be a relatively inexpensive (i.e., requiring less dissociation energy) way to produce the CH that is required for reactions (1), (5), and (6). As a result, an optimum ignitor might well be tuned to favor CH 2 production. Note that CH 3 mainly recombines with H in (3) to form CH 4. Even though this is the second most common reaction, it is relatively unimportant because it only recovers the original decomposition energy. Hence, CH 3 is not an important contributor and should be avoided in the choice of the initial radical pool. Reaction (6), CH þ CH 4! H þ C 2 H 4, becomes progressively more important for fuel-rich mixtures as it involves CH 4. It acts largely as a contributor of H radicals as the C 2 H 4 simply accumulates until final burning. Also H 2 is both a decomposition product (see Table 1) and a product of reactions (4) and (5). However, similarly to C 2 H 4,H 2 only accumulates until the system ignites. Note from the radical history that all of the initial CH 3,CH 2, and C have been consumed by 100 nanoseconds into the ignition process and the CH has all but disappeared in 10 nanoseconds. Their consumption is associated with the rise in the HCO concentration (from reaction 1) that leads to Stage 1a. Stage 1a This stage is dominated by the consumption of the HCO produced in Stage 1 by reaction (1). The dominant reactions ordered according to their rates are: HCO þ H! H 2 þ CO HCO þ O 2! HO 2 þ CO HCO þ O! OH þ CO HCO þ O! H þ CO 2 ð7þ ð8þ ð9þ ð10þ O 2 is consumed in (8) producing HO 2 that will be very important in Stage 2. Collectively, Stages 1 and 1a more than double the system temperature from 300 K to over 700 K. Note that all but one of the above reactions produce CO. As it can be seen in Figure 1, CO simply

RADICAL-INDUCED IGNITION OF FUEL=AIR MIXTURES 2283 accumulates through the pre-ignition stages. If the kinetics were frozen after Stage 1a, the mixture would thus contain significant quantities of CO at unusually low temperatures. Stage 2 This stage initiates at approximately one microsecond. The dominant reactions are: OH þ H 2! H þ H 2 O ð11þ H þ O 2! OH þ O OH þ CH 4! CH 3 þ H 2 O CH 3 þ H! CH 4 CH 4 þ H! CH 3 þ H 2 ð12þ ð13þ ð14þ ð15þ The most important radical in this stage is OH, which is consumed in (11) and (13). Reaction (12) produces OH but not in sufficient quantity to feed (11) and (13) that, collectively, have larger reaction rates. Additionally, none of the reactions of Stage 1 produce OH. The radical histories in Figure 1 indicate that OH accumulates during the interval between Stage 1a and Stage 2, due to the destruction of HO 2 through H þ HO 2! OH þ OH ð16þ and in Stage 1a through HCO þ O! OH þ CO (9); recall that HO 2 is produced in Stage 1a via HCO þ O 2! HO 2 þ CO (8), and to a lesser extent through the 3-body reaction H þ N 2 þ O 2! HO 2 þ N 2 ð17þ while HCO is produced in Stage 1 via CH þ O 2! O þ HCO (1). Consequently, Figure 1 depicts that the rise in OH coincides with a drop in HCO, O, and HO 2 concentrations. The accumulating OH via reactions (9) and (16) is responsible for the delay that is observed between Stages 1 and 2. In Stage 2 the temperature rises by 200 K. Then after a delay of about a millisecond, the final stage of ignition commences. Note in passing, that the concentration of OH appears to be small in Figure 1 during Stage 2, but this is an artifact of scaling the OH sub-figure to accommodate the maximum OH concentration, observed after ignition.

2284 C. S. CAMPBELL AND F. N. EGOLFOPOULOS Effect of Equivalence Ratio Figure 2 depicts the temperature histories for / ¼ 0.6 (also shown in Figure 1), 1.0, and 1.4. In all three cases, the same molar quantities of radicals were initially present, corresponding thus to the same decomposition energy. Decomposing the fuel into radicals adds enthalpy to the mixture, which can be recovered as thermal energy simply by recombining the radicals into the original fuel molecules. Keeping the initial decomposition energy fixed, allows for the isolation and study of the chemical effects of / on the ignition process. It can be seen that changing / has a minor effect on the kinetic paths. Notice that all three / s exhibit a very similar three-step temperature increase, and that Stages 1 and 2 occur at exactly the same times. But increasing / causes slightly lower temperatures during Stages 1 and 2. As / increases, the most notable change in the kinetics pathways is that the CH þ CH 4! H þ C 2 H 4 (6) in Stage 1 moves from the sixth largest reaction rate at / ¼ 0.6 to the second largest at / ¼ 1.4, due to the abundance of CH 4. This explains the lower temperatures seen at the larger /, as (6) competes with (1) for CH radicals; but while (1) generates the HCO Figure 2. Temperature profiles for / ¼ 0.6, 1.0, and 1.4 with an initial mixture temperature 300 K and p ¼ 1 atm. The initial extent of dissociation is the same as in Figure 1 so that the enthalpy added to the flow through dissociation is the same. The time is given in seconds.

RADICAL-INDUCED IGNITION OF FUEL=AIR MIXTURES 2285 that is critical to the ignition process as it fuels Stage 1a, (6) produces C 2 H 4 that remains unreacted until final ignition. Note also that the IDT increases significantly with /. For/ ¼ 1.4 it is roughly two orders of magnitude greater compared to / ¼ 0.6. Examining the early history for each / shows the presence of Stages 1, 1a, and 2 in all three temperature-histories, but also that the stages occur at exactly the same times and that each stage raises the temperature by approximately the same amount. Thus, the large difference in IDT s does not result from the early stages of radical-induced ignition. Partially, this is because lean methane mixtures are easier to ignite (e.g., Egolfopoulos et al., 2002; Fotache et al., 1997). But largely this is due to the competition for OH radicals between and CH 4 þ OH! CH 3 þ H 2 O ð18þ H 2 þ OH! H þ H 2 O ð19þ At low / s, there is little CH 4 available, and (19) is favored over (18) and in fact becomes the dominant reaction in the period just preceding the final ignition. This is beneficial mostly because it consumes the accumulated H 2 and provides H radicals that feed the main branching reaction: H þ O 2! OH þ O ð20þ At large / s and just before ignition, (19) falls to the seventh largest reaction rate while (18) rises to the second largest. As (18) produces inert H 2 O and the relatively unimportant CH 3, this kinetics chain tends to retard the ignition process. Ignition Pathways for Single Radical Species It is unlikely that the radical pool will be evenly distributed between the various species and may be dominated by a particular species. It is then instructive to examine the pathways that lead to ignition for each radical species alone, especially as these pathways might be masked in the evenly mixed case presented in Figure 1. The results are shown in Figures 3 6. In order to provide meaningful comparisons, all four cases were simulated under identical conditions to those shown in Figure 1. In particular, the same decomposition energy is used in all cases in order to assure that same the initial enthalpy is added to the system. As a result, the initial concentration

2286 C. S. CAMPBELL AND F. N. EGOLFOPOULOS Figure 3. Temperature and species (scaled) concentration histories for / ¼ 0.6 with initial mixture temperature 300 K and p ¼ 1 atm starting only with C radicals. The initial conditions are such that the decomposition energy is the same as the cases shown in Figures 1 and 2, and corresponds to an initial C mole fraction of 0.023. The time is given in seconds. of CH 3 in Figure 6 is larger than that of C in Figure 3 as less energy is required to decompose CH 4 to form CH 3 than is required to form C. Effect of C Addition: Figure 3 depicts the temperature and radical concentration histories for a / ¼ 0.6 mixture in which the initial radical pool consist solely of C and H 2 generated by e þ CH 4! C þ 2H 2.Asin

RADICAL-INDUCED IGNITION OF FUEL=AIR MIXTURES 2287 Figure 4. Temperature and species (scaled) concentration histories for / ¼ 0.6 with initial mixture temperature 300 K and p ¼ 1 atm starting only with CH radicals. The initial conditions are such that the decomposition energy is the same as the case shown in Figures 1 and 2, and corresponds to an initial CH mole fraction of 0.026. The time is given in seconds. Figure 1, this results in a three-step ignition. The initial temperature rise is due solely to the oxidation of C via C þ O 2! O þ CO ð2þ resulting in a large pool of CO and O radicals. HCO is not produced and, thus, there is no Stage 1a. In the first quiescent period OH accumulates through via reactions involving O radicals: O þ CH 4! CH 3 þ OH ð21þ

2288 C. S. CAMPBELL AND F. N. EGOLFOPOULOS Figure 5. Temperature and species (scaled) concentration histories for / ¼ 0.6 with initial mixture temperature 300 K and p ¼ 1 atm starting only with CH 2 radicals. The initial conditions are such that the decomposition energy is the same as the case shown in Figures 1 and 2, and corresponds to an initial CH 2 mole fraction of 0.038. The time is given in seconds. O þ H 2! H þ OH ð22þ Reaction (22) is responsible for the consumption of H 2 that results from the initial decomposition. The OH and O then initiate Stage 2 and the process proceeds as before. Note however, that the ignition delay is 3 10 3 seconds, roughly three times that in Figure 1, which indicates that pure C would not be the optimum radical choice.

RADICAL-INDUCED IGNITION OF FUEL=AIR MIXTURES 2289 Figure 6. Temperature and species (scaled) concentration histories for / ¼ 0.6 with initial mixture temperature 300 K and p ¼ 1 atm starting only with CH 3 radicals. The initial conditions are such that the decomposition energy is the same as the case shown in Figures 1 and 2, and corresponds to an initial CH 3 mole fraction of 0.048. The time is given in seconds. Effect of CH Addition: Figure 4 depicts the temperature and radical histories for a / ¼ 0.6 mixture in which the initial radical pool consists solely of CH. Recall that all primary reactions in Stage 1 that lead to Stage 1a involve CH. Interestingly, it was found that CH reacts via CH þ H! C þ H 2 ð5þ to produce C that subsequently reacts via

2290 C. S. CAMPBELL AND F. N. EGOLFOPOULOS C þ O 2! O þ CO ð2þ, (a Stage 1 reaction in both Figures 1 and 3, but because it must now wait for sufficient C to be generated, now occurs along with the Stage 1a reactions). Thus, it is not surprising that the temperature profile shown in Figure 4 is qualitatively similar to that of Figure 1, with a nearly identical three-step behavior. The most notable difference is that the IDT is shortened by nearly an order of magnitude to 100 microseconds as a result of an accelerated Stage 2 process. As the chain initiates with pure CH, more HCO and O are generated via CH þ O 2! O þ HCO ð1þ. This leads to both a more energetic consumption of the HCO in Stage 1a, which ends with 40 K larger temperature (compared the end of stage 1a in Figure 1) and to more OH production through O þ HCO! OH þ CO ð9þ. The larger OH concentration accelerates Stage 2, which in turn facilitates ignition. Effect of CH 2 Addition: Figure 5 depicts results for a / ¼ 0.6 mixture containing CH 2 as the only radical. The temperature history exhibits a more dramatic initial temperature rise and no apparent Stage 2; recall that CH 2 acts as a surrogate for CH as it decomposes to CH via CH 2 þ H! CH þ H 2 ð4þ. However, CH 2 forms by the plasma-ch 4 interaction e þ CH 4! CH 2 þ H 2, so that the initial mixture is devoid of the H radicals required for (4). Instead, the three primary reactions in the very early phases (t < 10 8 seconds) involve the oxidation of CH 2 via: CH 2 þ O 2! CH þ 2H CH 2 þ O 2! OH þ H þ CO CH 2 þ O 2! O þ CH 2 O ð23þ ð24þ ð25þ The first two reactions provide the H required for the consumption of CH 2 to CH, and the last two produce OH and O that are normally consumed in Stage 2 reactions. Thus, unlike the case shown in Figure 1, the system does not have to wait for OH to be produced through the relatively slow H þ HO 2! OH þ OH (16) reaction, and the Stage 2 reactions occur simultaneously with those of Stages 1 and 1a, resulting in the more noticable single-step temperature rise. Note that the ignition delay is roughly 4 10 4 seconds, which, while faster than the even mixture case shown in Figure 1, is about 4 times longer than the pure CH case shown in Figure 4. Thus, the initial radical mix should include some H radicals to feed reaction (4) and convert CH 2 to CH.

RADICAL-INDUCED IGNITION OF FUEL=AIR MIXTURES 2291 Effect of CH 3 Addition: Of the four radicals, CH 3 does the least to promote ignition. This may be noted from the long IDT of about 0.15 seconds shown in Figure 6, which is 2 orders of magnitude greater than the IDT realized in Figure 1. This is largely because the primary reaction involving CH 3 is the recombination reaction CH 3 þ H! CH 4 (3), which on one hand recovers the decomposition energy, but on the other does nothing else to enhance ignition. However, there apparently are additional kinetic mechanisms involved. Note that after the initial temperature rise the system goes through a long period at 714 K before igniting. A mixture of CH 4 with air cannot ignite at such a low temperature, so there must be some residual chemical activity that enhances ignition. While CH 3 is the least important radical, its kinetic contributions are some of the most complicated. In the early stages, CH 3 recombines to form C 2 H 6 through: CH 3 þ CH 3 þ M! C 2 H 6 þ M ð26þ The prominence of this reaction is due to the large amount of CH 3 present at the beginning of the simulation and its importance quickly diminishes as CH 3 is consumed, given the second-order dependence of this reaction on CH 3. But the reaction is of little importance as C 2 H 6 does not contribute to the pre-ignition chemistry and is only consumed upon ignition. The principal reaction chain for ignition begins with H left from the original decomposition ðe þ CH 4! CH 3 þ HÞ through the three-body H þ N 2 þ O 2! HO 2 þ N 2 reaction (17), and by subsequent reactions of HO 2. During the quiescent phase, HO 2 results in the production of CH 3 O and OH through: CH 3 þ HO 2! CH 3 O þ OH ð27þ Subsequently, the OH produced via (27) goes on to consume additional CH 4. Just before ignition occurs, CH 3 O becomes the principle source of H (e.g., Egolfopoulos et al., 2002), needed for the main branching reaction (20), both directly through: CH 3 O þ M 2! CH 2 O þ H þ M ð28þ and indirectly via a reaction sequence forming HCO from CH 2 O that initiates with either: OH þ CH 2 O! HCO þ H 2 O ð29þ

2292 C. S. CAMPBELL AND F. N. EGOLFOPOULOS or H þ CH 2 O! HCO þ H 2 ð30þ Subsequently, HCO leads to H production through: HCO þ M! H þ CO þ M ð31þ Reaction (18) also produces CO that is consumed upon ignition. Thus, CH 3 enhances ignition but not to the extent realized through the presence of C, CH, and CH 2 in the initial reactants. Effect of Pressure Figures 7 and 8 depict the effect of pressure on the ignition process, for 0.1 atm and 50 atm, respectively. The decomposition and other conditions are the same as for Figure 1 (at 1 atm) to which these may be compared. For the conditions considered here, increasing the pressure accelerates the ignition process. The most interesting feature of these figures is the effect of pressure on Stage 2. Figure 7 (0.1 atm) depicts that Stage 2 has been delayed until it runs up against the (final) ignition. Figure 8 (50 atm) depicts that Stage 2 has been accelerated to the point that it has merged with Stages 1 and 1a into what appears to be a single stage. By examining the dominant reactions and the radical history, it appears that there are no significant differences in the kinetic paths. This can be seen by following HO 2, which is key to the production of the OH radical that dominates Stage 2 through reaction (16). Note that at 0.1 atm (Figure 7) HO 2 reaches its peak concentration at about 5 10 7 seconds, at 1 atm (Figure 1) the HO 2 peak is reached a decade earlier at 5 10 8 seconds, and at 50 atm (Figure 8) HO 2 reaches its largest concentration at 8 10 10 seconds. The major difference appears to be the three-body reaction, H þ N 2 þ O 2! HO 2 þ N 2 ð17þ, which at 50 atm becomes the dominant supplier of HO 2 and yields HO 2 concentrations that are more than an order of magnitude larger than the maximum concentration seen at 1 atm. This accelerates the OH production through (16) bringing on an early appearance of Stage 2. Minimum Ignition Delay As one of the advantages of radical-induced ignition is the reduction in IDT, it is worth investigating the minimum IDT that could be potentially

RADICAL-INDUCED IGNITION OF FUEL=AIR MIXTURES 2293 Figure 7. Temperature and species (scaled) concentration history for p ¼ 0.1 atm, all other conditions are the same as in Figure 1. Note that the same three-stage ignition is still apparent although the start of Stage 2 is delayed so that it runs together with the final ignition. The time is given in seconds.

2294 C. S. CAMPBELL AND F. N. EGOLFOPOULOS Figure 8. Temperature and species (scaled) concentration history for p ¼ 50 atm, all other conditions are the same as in Figure 1. The time is given in seconds. The three-stage ignition is no longer apparent because Stage 2 has been accelerated so that it runs together with Stages 1 and 1a. Note that the time scale has been shifted one decade down from Figures 1 7 (beginning at 10 12 seconds and ending at 0.1 seconds) as the high pressure accelerates the overall ignition process.

RADICAL-INDUCED IGNITION OF FUEL=AIR MIXTURES 2295 achieved. After performing extensive simulations, it was determined that for / ¼ 1.0 the minimum IDT would be obtained by decomposing all the fuel at into C through e þ CH 4! C þ 2H 2. That case is shown in Figure 7. If one uses the initiation of CO oxidation as the point at which ignition occurs, the mixture ignites in 179 nanoseconds, 5 orders of magnitude faster than would be normal for thermal ignition and 4 orders of magnitude faster than the process shown in Figure 1; CO consumption is used as the ignition indicator given that is responsible for the main heat release in hydrocarbon oxidation (e.g., Glassman, 1996). It is a bit surprising that the optimum radical is C given that the results shown in Figures 3 6 suggest that CH results in the minimum IDT. However, the process shown in Figure 7 is different from any of the previous cases. In particular, there is enough enthalpy in the primary reaction C þ O 2! O þ CO ð2þ to raise the temperature to 1750 K, high enough for the CO to begin oxidizing primarily through CO þ OH! H þ CO 2. However, CO oxidation ends in approximately 10 5 seconds, at a temperature of about 2100 K. Somewhat surprisingly, the majority of the final temperature rise is due to the reactions involving O, OH, H, and HO 2, but following different reaction paths than in Stage 2 due to the larger temperature. This can be seen in Figure 7 by noting how O, OH, H, and HO 2 evolve during the large temperature rise between 10 5 and 10 4 seconds. The dominant reactions during this phase are: H þ OH þ M! H 2 O þ M O þ H 2! H þ OH ð32þ ð33þ H þ O 2 þ H 2 O! HO 2 þ H 2 O ð34þ H þ HO 2! 2OH ð35þ OH þ HO 2! O 2 þ H 2 O ð36þ In particular, HO 2 is now a vital player, being produced by (34) and consumed by (35) and (37), explaining, thus, the complex behavior of HO 2 during the final temperature rise. CONCLUDING REMARKS A non-equilibrium plasma ignitor dissociates the reactants into radicals without significantly raising the temperature of the mixture. Those radicals react, starting a kinetics sequence that eventually leads to ignition.

2296 C. S. CAMPBELL AND F. N. EGOLFOPOULOS Figure 9. Temperature and species (scaled) concentration histories for a / ¼ 1.0, CH 4 =air mixture, with all of the fuel decomposed into C. Note that the IDT, determined as the time at which CO begins to be consumed, is roughly 179 nanoseconds. The time is given in seconds. Detailed numerical simulations of a homogeneous, constant-pressure, adiabatic reactor, revealed the kinetic paths controlling the ignition of methane=air mixtures in the presence of various pools of radicals in the initial mixture. The ignition processes was found to proceed in a three-step thermal process that was divided into four distinct kinetics stages. The radical that is most important in initiating the chain is CH, which oxidizes to HCO,

RADICAL-INDUCED IGNITION OF FUEL=AIR MIXTURES 2297 the most important radical in Stage 1a. However, it is important to realize that CH 2 can act as a surrogate for CH as it reacts with H to produce CH. Furthermore, CH 2 is only marginally more expensive to produce than CH 3 and significantly less expensive than producing CH. Thus, an optimum ignitor will likely be tuned to accentuate CH 2 production, although the radical pool should be broader than CH 2 alone as it should contain an H producing reaction to feed the CH 2! CH decomposition through CH 2 þ H! CH þ H 2 (1.4). CH 3 was found to be relatively unimportant for ignition, as for the most part it recombines with H to form CH 4. There are two advantages to ignition by radicals. The first is that it greatly accelerates the ignition process. Given enough radicals, it is possible to achieve ignition in less than 200 nanoseconds even starting at 300 K 5 orders of magnitude lower than the 10 milliseconds ignition delay times typical of thermal ignition. The second advantage is a potentially reduced energy cost. Because the radicals liberate thermal energy when they react with the undecomposed fuel and oxidizer, the reaction process will add more thermal energy than is initially required to decompose the fuel into radicals. REFERENCES Bozhenkov, S.A., Starikovsjaia, S.M., and Starikovkmii, A.U. (2003) Nanosecond gas discharge ignition of H-2- and CH4-containing mixtures. Combust. Flame, 133, 133. Edwards, T. (1996) Fuels and Fuel System Area: Air Force Perspective, AFOSR=NASA Workshop on Supersonic Scramjet Combustion, 13 16 May 1996, Newport News, VA. Egolfopoulos, F.N. and Dimotakis, P.E. (1998) Non-premixed hydrocarbon ignition at high strain rates. Proc. Combust. Inst., 27, 641 648. Egolfopoulos, F.N., Campbell, C.S., and Andac, M.G. (2002) Hot particle ignition of methane flames. Proc. Combust. Inst., 29, 1605 1612. Fotache, C.G., Kreutz, T.G., and Law, C.K. (1997) Ignition of counterflowing methane versus heated air under reduced and elevated pressures. Combust. Flame, 108, 442. Glassman, I. (1996) Combustion, 3rd ed., Academic Press, San Diego. Janev, R.K. and Reiter, D. (2002) Collision processes of CH y and CH y þ hydrocarbons with plasma electrons and protons. Physics of Plasma, 9, 4071. Kee, R.J., Rupley, F.M., and Miller, J.A. (1989) Chemkin-II: A FORTRAN Chemical Kinetics Package for the Analysis of Gas-Phase Chemical Kinetics. Sandia Report SAND89-8009.

2298 C. S. CAMPBELL AND F. N. EGOLFOPOULOS Liu, J.B., Ronney, P.D., and Gunderson, M.A. (2003) Premixed flame ignition by transient plasma discharges, Proc Third Joint Meeting U.S. sections, Combust. Inst., Paper B25, 16 March 2003, Chicago, IL. Lutz, A.E., Kee, R.J., and Miller, J.A. (1988) SENKIN: A Fortran Program for Predicting Homogeneous Gas Phase Chemical Kinetics with Sensitivity Analysis, Sandia Report SAND87-8248. Smith, G.P., Golden, D.M., Frenklach, M., Moriarty, N.W., Eiteneer, B., Goldenberg, M., Bowman, C.T., Hanson, R.K., Song, S., Gardiner,, W.C. Jr., Lissianski, V., and Qin, Z. (2000) GRI-Mech 3.0, hhttp:==www.me. berkeley.edu=gri mech=i. Starikovskii, A.Y. (2003) Initiation of ignition by the action of a high-current pulsed discharge on a gas. Combustion, Explosion Shock Waves, 39, 619.