Cool Flame Region Research Articles

On the Three-Stage Explosion Characteristics of Diethyl Ether-Oxygen Mixtures

ABSTRACT In this article, the three-stage explosion limits of diethyl ether (a typical alternative fuel with a high cetane number and high energy density) are taken as the research object. A comprehensive and in-depth analysis of the double negative temperature coefficient (NTC) behavior of the cool flame region and hot ignition region, through the detailed kinetic analysis, have been carried out. The results show that with the increase of the equivalence ratio, the double NTC phenomenon becomes more remarkable. In very lean conditions, such as the equivalence ratio of less than 0.5, the boundary between the first NTC region and the second NTC region becomes obscure, and a deeper single NTC phenomenon is formed as these two NTC regions merge. The whole explosion limit curve shifts to higher pressure conditions with the increase of the addition of inert gas. The NTC phenomenon in the moderate temperature region becomes more significant and the boundary between these two NTC regions is more obvious. In addition, the hot flame explosion limit also shows such two NTC response. The heat release rate (HRR) profile exhibits three-stage, two-stage, single-stage ignition, or non-ignition depending on the initial conditions. To elucidate the differences in the ignition process between the different explosion limit regimes, the sensitivity and reaction pathway analyses are performed. This study not only provides insight into the oxidation characteristics of ether fuels, but also provides theoretical support for high-performance engines.

Characterization of the oxymethylene ether fuels flame structure for ECN Spray A and Spray D nozzles

Synthetic fuels will play a major role on the reduction of pollutant emissions and carbon footprint of ICE engines. The use of renewable energy and CO2 for its production maps out a promising route to achieve ICE carbon neutrality. Among these fuels, oxymethylene ethers are also interesting for their potential to drastically reduce soot formation. However, a proper characterization of their properties and behaviour is mandatory to reach full implementation in commercial engines. For this reason, this work presents a detailed characterization of the flame structure of two types of oxymethylene ethers (OMEX and OME1) using high-speed chemiluminescence imaging and Planar Laser-Induced Fluorescence (PLIF). Test were performed in a constant-pressure combustion vessel, with the operating conditions and two different injector nozzles from the Engine Combustion Network (Spray A and Spray D). Regions associated with low-temperature chemical reactions are observed thanks to the formaldehyde PLIF while evolution of the high-temperature reactions has been analysed based on hydroxyl excited state (OH*) chemiluminescence and hydroxyl PLIF. On-resonant and off-resonant measurements were performed for OH PLIF with a dye laser in order to remove other radiation sources not linked to OH fluorescence, whilst 355 nm radiation from the third harmonic of a Nd:YAG laser are used to excite CH2O molecules. On the one hand, the results show that the combustion of OME1 with Spray A is characterized by a flame structure very different to that of a diffusion flame. It is characterized by large cool flame region followed by a short high-temperature zone. On the other hand, the combustion of OMEX with both nozzles and OME1 with Spray D show more similarities with a diffusion flame structure. The stoichiometry of the fuel and the equivalence ratio fields achieved strongly affect the structure and latter evolution of the flames.

Dynamics of FREI with/without cool flame interaction

The interactions between cool flames and flames with repetitive extinction and ignition (FREI) of stoichiometric n-heptane/air mixture were studied using a micro flow reactor with a controlled temperature profile from 373 to 1300 K. Two different flame dynamics with and without cool flames were observed in reactors with inner diameters dinner of 1 and 2 mm. Cool flames and FREI are spatially separated at dinner= 1 mm, whereas interactions between cool flames and FREI are observed at dinner= 2 mm. At dinner= 1 mm, the brightness intensity from cool flames depends on the inlet velocity (uinlet). Approximately above uinlet= 10 cm/s, the brightness intensity from cool flames decreases with increasing inlet velocity, despite a large amount of mixture input. This is because before low temperature ignition occurs under higher inlet velocity conditions, the mixture archives temperature where negative temperature coefficient is dominant. Reaction front propagation speed of FREI decreases monotonically due to heat loss because the extinction points of FREI are located in higher temperatures than the cool flame region. At dinner= 2 mm, the acceleration of the reaction front in the cool flame region is confirmed experimentally, as predicted in our previous two-dimensional numerical simulations. Additionally, the instantaneous reaction front speed after autoignition is analyzed at dinner= 1 mm. The instantaneous reaction front speed decreases as the time from extinction to ignition tex_ig becomes longer because a moderate mixing zone of reactants and products is formed.

A numerical investigation on the laminar flame speed of methane/air and iso-octane/air mixtures with ozone addition

A numerical study has been carried out to evaluate the influence of ozone addition on the laminar flame speed for both methane/air and isooctane/air mixtures under thermodynamic conditions typical of internal combustion engines. Ozone is a highly oxidising chemical species and modifies the fuel oxidation reaction pathways, mainly in the initial stages of combustion. In the case of alkanes, such as methane and isooctane, ozone enhances the laminar flame speed. This study aims to analyse similarities and differences of the flame structure of methane and isooctane for different values of ozone concentration and equivalence ratio and for a wide range of pressure and temperature conditions. A 1-D numerical model, validated against several experimental data taken from the scientific literature, has been employed and simulations have been carried out by using a chemical kinetic reaction mechanism for methane and three different mechanisms for isooctane. The results show that the laminar flame speed increases with ozone concentration in the range 0–7000 ppm. At 1 bar, the percentage enhancement in terms of LFS with the addition of 7000 ppm of ozone, compared to the case without ozone, is about 4% for both fuels, under stoichiometric conditions, as long as temperature is lower than about 540 K. On the other hand, at higher temperatures ozone addition enables the formation of a cool flame for isooctane/air mixtures, and the reactions follow a different path compared to the case with methane. This leads to a greater influence of ozone on the isooctane laminar flame speed. Besides, for isooctane/air stoichiometric mixtures, at 560 K with 7000 ppm ozone, LFS shows a non-monotonic behaviour with pressure, being higher at 20 bar than at 15 bar, which is somehow unexpected. If the reactants temperature increases, the non-monotonic trend appears at lower pressures and lower ozone concentrations and is due to the fast ozone decomposition, promoted by the pressure increase. Such a decomposition enables fuel oxidation reactions by OH radicals in the cool flame region. This phenomenon does not occur for the methane case.

The dependence of NTC behavior on the equivalence ratio and nitrogen fraction in cool flame region

Using propane (which issues a cool flame at low temperature oxidation) as the archetype of the higher alkanes, comprehensive computational research, with detailed mechanisms and theoretical analysis, was implemented to investigate the controlling points of the cool flame region and the negative temperature coefficient (NTC) behavior. It found that the temperatures of the two turnover points steadily decreased with the increase of equivalence ratio. The pressures of the upper turnover points decreased more when the equivalence ratios were less than 2.0, but the pressures of the lower turnover points showed no notable decrease. With an increase in the nitrogen fraction, the explosion limit curve shifted to the high-pressure region. However, the temperature variations of the turnover points were relatively small, and the dependence of the NTC degree on the equivalence ratio and the nitrogen molar fraction was derived. The slope of the NTC line showed a power law dependence on the equivalence ratio and was almost unrelated to the nitrogen ratio. To elucidate the key control mechanism, sensitivity analyses of the turnover points were performed.

Analysis of ECN spray A ignition in a Rapid Compression Machine using simultaneous OH* chemiluminescence and formaldehyde PLIF

The canonical diesel spray A is characterized in an optical Rapid Compression Machine (RCM) at high temperature and density conditions (900 K and 850 K, ρ = 23 kg/m3) using simultaneous high-speed OH* chemiluminescence and two-pulse 355 nm Planar Laser Induced Fluorescence (PLIF). The focus is on the time evolution and the repeatability of the early stages of both cool flame and hot ignition phenomena, and on the time evolution of the fluorescing formaldehyde region in between. In particular, time resolved data related to the cool flame are provided. They show the development of several separated kernels on the spray sides at the onset of formaldehyde appearance. Shortly after this phase, the cool flame region expands at high velocity around the kernels and further downstream towards the richer region at the spray head, reaching finally most of the vapor phase region. The position of the first high temperature kernels and their growth are then characterized, with emphasis on the statistics of their location. These time-resolved data are new and they provide further insights into the dynamics of the spray A ignition. They bring some elements on the underlying mechanisms, which will be useful for the validation and improvement of numerical models devoted to diesel spray ignition.

A numerical study on near-limit extinction dynamics of dimethyl ether spherical diffusion flame

The near-extinction oscillatory dynamics and underlying mechanism of the dimethyl ether (DME) spherical diffusion flames in the hot- and cool-flame conditions were studied by the numerical approach with detailed chemistry and transport models. It was found that the self-sustaining spherical cool diffusion flame could be readily obtained in a wide range of parameters, and additionally, the flammability limit could be considerably extended by the cool-flame chemistry. Strong oscillations that can trigger flame extinguishment prior to the steady-state extinction turning point were observed in either the hot or cool flame regime. The DME hot flame near extinction was governed by a single oscillatory mode with a fixed frequency (1 Hz) that was irrelevant with the ambient oxygen level. By contrast, the cool-flame extinction was controlled by dual oscillatory modes which had rather distinct frequencies, and the oscillatory period of the high-frequency mode increased significantly when approaching the extinguishment. Additionally, the transient dynamics of cool flame near extinction was much more complicated, due to the existence of strong coupling between the high-frequency and low-frequency oscillatory modes which was affected by the phase difference. The governing reactions that controlled the oscillatory extinction in hot- and cool-flame regions were revealed using a logarithmic sensitivity index. It was found that the hot-flame oscillatory extinction was controlled by the competition of high-temperature exothermic/endothermic reactions with the chain branching/termination reactions involving small molecules. The cool-flame oscillation was controlled by the low-temperature branching and termination competition in the negative temperature coefficient regime.

Cool flame characteristics of methane/oxygen mixtures

As one of the most important clean fuels, methane plays a significant role in the energy supply system, and its combustion characteristics directly affect the efficiency and emission. In order to avoid the production of a large number of nitrogen oxides, the low temperature combustion associated with cool flame is getting more and more attention. But until now the cool flame characteristics of methane is still unclear, even its existence is controversial. In this work, the property of premixed methane/oxygen cool flame has been experimentally studied in a cylindrical reactor and numerically analyzed using different mechanisms. The effects of pressure, temperature and equivalence ratio on methane cool flame have been investigated experimentally. The experimental results show that the cool flame can be obtained in the range of 0.2–4.8 equivalent ratio. The lower limit of pressure of the cool flame region decreases with the increasing initial temperature. The sensitivity and reaction path have been analyzed through the numerical simulation, which reveals that the bifurcation in CH3 oxidation process has remarkable effects on cool flame formation.

Nitric Oxide Circumstances in Nitrogen-Oxide Seeded Low-Temperature Powling-Burner Flames

<p>Flat low-temperature two-stage flames were established on a Powling burner using rich diethyl-ether/ air or n-heptane/air mixtures, and nitrogen monoxide NO was added into the fuel-air mixtures with a concentration of 240 ppm. The temperature development and chemical-species histories, especially of NO, nitrogen dioxide NO<sub>2</sub> and hydrogen cyanide HCN were examined associated with an emission-spectrum measurement from the low-temperature flames. Nitrogen monoxide was consumed in the cool-flame region, where NO was converted to the NO<sub>2</sub>. The NO<sub>2</sub> generated, however, fell suddenly in the cool-flame degenerate region, in which the HCN superseded. In the blue-flame region the NO came out again and developed accompanied with remained HCN in the post blue-flame region. The NO seeding into the mixture intensified the blue-flame luminescence probably due to the cyanide increase.</p>

Low temperature oxidation of n-hexane in a flow reactor

The risk of igniting a flammable mixture in fuel tank vapor space is a major concern in aviation safety. In order to analyze the hazards and develop mitigation strategies, it is necessary to characterize the explosive properties of kerosene vapor–air mixtures over wide ranges of initial conditions. n-Hexane has been extensively used in our laboratory as a single component surrogate of kerosene. In the present study, hexane oxidation by oxygen was studied in a flow reactor at equivalence ratios of 0.7, 1 and 1.5 for mixtures diluted at 90% with nitrogen. Residence time was set at 2s and the pressure at 100kPa. The evolution of the gas phase composition at the reactor exit was studied over the range 450–1000K. Laser-based diagnostics and gas chromatography analysis were used to characterize the exit mixture composition. The chemical species measurements revealed three distinct regimes of oxidation, namely (i) the cool flame region from 600 to 650K, (ii) the NTC region between 675 and 775K, and (iii) the high temperature oxidation regime from 800K. The modeling study demonstrated the capability of reproducing most of the trends observed experimentally.

Investigation of the intermediate oxidation regime of Diesel fuel

A very high temperature fuel–air mixture is necessary for the thermal partial oxidation process of hydrocarbon fuels in order to have a high reaction temperature which accelerate the reaction kinetics. For Diesel fuel and due to the ignition delay time behavior, different oxidation behavior can be realized at different preheating temperatures. In this work, the intermediate oxidation region of Diesel fuel is investigated. By making use of the ignition delay time behavior, an vaporizer like tube reactor is constructed in order to enable a very high preheating temperature without the risk of self-ignition in a time-independent experiment. The oxidation behavior of Diesel fuel in air is investigated numerically and experimentally. In the numerical part, the ignition delay time was estimated using CHEMIKIN tools for different air–fuel mixtures at different temperatures. The evaporation behavior of the Diesel fuel–air mixtures are investigated at relatively high air preheating temperatures ranging from 500 °C up to 680 °C. The amount of the process air was varied from an air ratio λ = 0.35 to λ = 0.6. The experiments are also performed with N 2 as an evaporation media and compared with those performed with air to detect any temperature increase in the case of Diesel–air mixtures. The amount of heat release in the low chemistry region as well as in the intermediate region is calculated for the case of Diesel/air mixtures. The experiments show that four different oxidation region of Diesel fuel can be distinguished depending on air inlet temperatures and on the air ratio. At a temperature lower than 723 K (450 °C), no chemical reaction takes place. The cool flame reactions start at temperatures above 723 K (450 °C). However, no stable cool flame can be achieved unless the air preheating temperature reached about 753 K (480 °C). The cool flame region is extended up to about 873 K (600 °C), at which the intermediate regime started. This regime stabilized to a short range up to about 923 K (650 °C) after which ignition takes place.

Kinetic modelling of a surrogate diesel fuel applied to 3D auto-ignition in HCCI engines

The prediction of auto-ignition delay times in HCCI engines has risen interest on detailed chemical models. This paper describes a validated kinetic mechanism for the oxidation of a model Diesel fuel (n-decane and α-methylnaphthalene). The 3D model for the description of low and high temperature auto-ignition in engines is presented. The behaviour of the model fuel is compared with that of n-heptane. Simulations show that the 3D model coupled with the kinetic mechanism can reproduce experimental HCCI and Diesel engine results and that the correct modelling of auto-ignition in the cool flame region is essential in HCCI conditions.

Sensitization of pentane-oxygen mixtures to DDT via cool flame oxidation

The effect of cool flame partial oxidation on the detonation sensitivity of a hydrocarbon fuel was investigated experimentally. The detonation sensitivity was quantified by measuring the run-up distance required for a deflagration to transit to a detonation wave (DDT) in a rough tube. Fuel rich pentane-oxygen mixtures at sub-atmospheric initial pressures were studied. Subsequent to the injection of the mixture into a heated detonation tube, the mixture underwent cool flame oxidation after a well-controlled delay time, dependent on the temperature of the tube. Typical delays ranged from 0.5 to 2 s (depending on temperature) and were reproducible to within one hundred milliseconds. This delay permitted the mixture in the detonation tube to be spark-ignited at various stages of the cool flame process using an igniter driven by a delay generator. The results show that increasing mixture temperature from room temperature to values below the cool flame region (below 250°C) resulted in an increase in run-up distance. However, as the mixture began to undergo cool flame oxidization, a significant reduction in the run-up distance was obtained (as large as 50%). The sensitization effect was found to occur only at the initial stage of the cool flame oxidation reaction. If the mixture was ignited at times long after the onset of cool flame, the mixture was found to be desensitized and the run-up distance increased. The sensitizing effect of the cool flame partial oxidation may be attributed to the presence of peroxides and free radicals associated with the initial cool flame process. However, these radical species are consumed as the cool flame reaction proceeds and the mixture becomes insensitive again.

Detailed spectral analysis of the process of HCCI combustion

The process of homogeneous charge compression ignition (HCCI) combustion was compared with stratified charge compression ignition (SCCI) and standard spark ignition (SI) using local spectrum analysis, with a transparent cylinder and piston. The engine was operated at 1000 rpm. The combustion characteristics were analyzed using the heat-release rate, burned-mass fraction, and time-series spectra. Local emission spectra were measured using Cassegrain optics, which have a measurement volume 0.1 mm in diameter and 0.8 mm in length. Regular gasoline was used for the SI engine and a 50:50 blend of iso-octane and n-heptane was used for the HCCI and SCCI engines. Detailed spectra were measured and compared to demonstrate the differences in the combustion process with time. The combustion characteristics of HCCI were distinguished from those of standard SI combustion using the emission spectrum, which measures the cool-flame region in front of the main hot flame. Cool-flame regions were found in both HCCI and SCCI. The cool-flame region in HCCI was about 12° crank angle in front of the main hot flame, while the two cool-flame regions in SCCI were 10 and 5° crank angle in front of the main flame. These cool flames have the spectral structure of formaldehyde bands regardless of combustion type. The characteristics of CO−O* emissions were well correlated with the ratio of heat release (ROHR), and chemiluminescence measurement was confirmed as a good method for analyzing engine combustion.

K-2004 反応抑制物質直接噴射による予混合圧縮着火機関の運転領域拡大(S23-1 火花点火機関と予混合圧縮着火機関)(S23 エンジンの燃料消費率と排気の同時低減に向けて)

The control of ignition and combustion behavior in a premixed charge compression ignition engine was investigated and ultra low NOx and smokeless combustion was achieved with direct in-cylinder injection of water or methanol as a reaction suppressor. The reaction suppressing effect increased with advancing injection timings of the suppressors, resulting from greater decreases in charge temperature as compression progressed. However, as the in-cylinder temperature is less than the water boiling point before 60° CA BTDC, water vaporization is delayed with too early injection timing and the suppressing effect decreased. Therefore, the optimum timing in terms of the suppressing effect was found at 60° CA BTDC thereabouts when the in-cylinder gas temperature reached the boiling point of water. Methanol showed the ignition suppression effect similar to water, and the water or methanol injection significantly reduced the heat release at cool flame region and also the rapid combustion after the hot flame, resulting from suppression of charge temperature increase.

The structure of cool flame fronts of pentane, iso-pentane and their mixture

An experimental study of the combustion of two isomers of n-pentane and iso-pentane in laminar cool flames has been carried out. Three flames were studied, one with n-pentane, the second with iso-pentane, and the third with an equimolar mixture of the two isomers. Particular attention has been given to the low temperature region ahead of the hot region of the flame and the cool flame chemistry occurring there. A unique experimental facility has been used to provide access to this cool flame region. Comparisons are made of the structures of the three flames, with particular attention on the different intermediate species produced and the correlations between the fuel molecule structure and the specific intermediates produced.

Modeling of the gas-phase oxidation of n-decane from 550 to 1600 K

To improve the performances of diesel engines and to reduce the emission of pollutants at their outlet, it is necessary to be able to model the combustion and the oxidation of higher alkanes. Up to now, only a few detailed kinetic mechanisms were written for modeling the combustion of alkanes higher than n -heptane and iso -octane and even fewer for modeling their oxidation at low temperature in the cool flame region or in the negative temperature coefficient (NTC) regime. This paper presents a modeling study of the oxidation and combustion of n -decane in a range of temperatures, from 550 to 1600 K, aiming at reproducing experiments performed in a jet-stirred reactor and in a premixed laminar flame. The study covered an important part of the wide range of temperatures that is observed in engines. It is worth noting that n -decane is actually present in diesel fuel. Detailed kinetic mechanisms have been automatically generated by using the computer package EXGAS developed in our laboratory. The predictions of the mechanisms were compared to the experimental results without any adjustment of kinetic data. The mechanism used for simulation at low temperature included 7920 reactions. A satisfactory agreement was obtained for the two kinds of experimental apparatus, both for the consumption of reactants and for the formation of most products. In the flame, the formation of pollutants, such as unsaturated compounds, was well reproduced. In the perfectly stirred reactor, a flow rate (flux) analysis at 650 K in the cool flame region showed a scheme of reaction close to that of n -heptane. Nevertheless, the higher reactivity of n -decane compared with that of lower linear alkanes such as n -heptane seems to be due not only to faster metathesis reactions favored by additional secondary abstractable atoms of hydrogen, but also to a lower relative flow rate of oxidations giving alkenes and the very unreactive HO 2 radicals. The long linear chain favors internal isomerizations and then reduces the relative flow rates of reactions competing with the addition of oxygen.

High Pressure Oxidation of Liquid Fuels from Low to High Temperature. 2. Mixtures of n-Heptane and iso-Octane

Abstract The oxidation of mixtures of n-heptane and iso-octane in a high-pressure jet-stirred reactor has been investigated experimentally in a wide range of conditions covering the low and high temperature oxidation regimes (550-1150K, 10 atm, o=1). The cool flame and negative temperature coefficient regimes were observed below 750K, Above 750 K, the normal high temperature oxidation of both fuels was observed. Reactants, intermediates and final products have been measured providing a useful picture of n-heptane-iso-octane mixtures oxidation. Cyclic ethers resulting from the low-temperature oxidation chemistry of n-heptane and iso-octane were identified. The evolution of their concentration as a function of RON have been measured. These results are interpreted in terms of reaction mechanism. Tentative correlations between RON and CO, CO2 and C2H4 in the cool flame region and for the high temperature oxidation (normal combustion) are presented.

Oscillatory ignitions and cool flames in the oxidation of butane in a jet-stirred reactor

The oxidation of butane ([C4H10] : [ O2] = 1.13:1.00) has been studied over the temperature and pressure ranges 371 ⩽T/K ⩽ 675, 226 ⩽P/Torr ⩽ 489 in a jet stirred reactor with a residence time of 9.4 s (1 Torr ≈ 133.3 Pa), The gas temperature and pressure were probed and phase diagrams constructed delineating regions of oscillatory ignitions and cool flames, and high- and low -temperature stationary states. On heating at an initial pressure of 400 Torr from 570 K sharp transitions were observed, first to an oscillatory ignition and then to an oscillatory cool flame region, followed by a smooth transition to a high-temperature stationary state via a supercritical Hopf bifurcation. On cooling from this high - temperature stationary state, oscillatory cool flames were observed with a sharp extinction at 542 K, without any entry to the oscillatory ignition region. The latter could be entered, however, by suddenly cooling the system from the oscillatory cool flame region by temporarily substituting nitrogen for oxygen in the gas streams. Complex waveforms, consisting of bursts of oscillatory cool flames interspersed with periods of monotonic cooling, were also observed at lower pressures. A Nd : YAG pumped dye laser was used to probe laser induced fluorescence from form aldehyde in the oscillatory ignition region. Variations in the internal surface of the reactor demonstrated the significance of surface reactions. An outline mechanism, based on detailed numerical simulations, is presented to account for the shape of the ignition profiles and the transition from multiple ignitions to oscillatory cool flames.

Numerical studies of a thermokinetic model for oscillatory cool flame and complex ignition phenomena in ethanal oxidation under well-stirred flowing conditions

A numerical study has been undertaken to predict quantitatively each of the non-isothermal reaction modes (stationary-state reaction, oscillatory cool flames and oscillatory two-stage and multiple-stage ignitions) associated with the oxidation of ethanal in a non-adiabatic well-stirred flow system (0.5 dm3) at a mean residence time of 3 s. The kinetic scheme comprises 28 species involved in 60 reactions and it is coupled to the thermal characteristics through enthalpy change in each step, heat capacities of the major components and a heat transfer coefficient appropriate to heat loss through the reaction vessel wall. Spatial uniformity of temperature and concentrations is assumed, matching the experimental conditions. Very satisfactory accord is obtained between the experimentally measured and predicted location of the different reaction modes in the (p-Ta) ignition diagram (wherepis pressure andTais temperature at ambient conditions), and the time-dependent patterns for oscillatory reaction agree with experimental measurements. The competition between degenerate branching and non-branching reaction modes is governed ultimately by the equilibrium CH3+O2⇌CH3O2. The predicted behaviour is found also to be especially sensitive to the rate of decomposition of the acetyl radical CH3CO + M → CH3+ CO + M. Corrections for its pressure dependence are essential if the predicted form of the oscillatory cool flame region in the (p-Ta) diagram is to match the experimental results. Variations of the rate of this reaction also give new kinetic insight into the origins of complex oscillatory wave-forms for cool flames that have been observed experimentally. Relationships between the results of the detailed kinetic computations and the predictions from a three-variable, thermokinetic model are examined. This model is the simplest of all reduced schemes that makes successful predictions of two-stage ignition phenomena.