Effects of endothermic chain-branching reaction on spherical flame initiation and propagation

A theoretical model is developed to describe the spherical flame initiation and propagation. It considers endothermic chain-branching reaction and exothermic recombination reaction. Based on this model, the effects of endothermic chain-branching reaction on spherical flame initiation and propagation are assessed. First, the analytical solutions for the distributions of fuel and radical mass fraction as well as temperature are obtained within the framework of large activation energy and quasi-steady assumption. Then, a correlation describing spherical flame initiation and propagation is derived. Based on this correlation, different factors affecting spherical flame propagation and initiation are examined. It is found that endothermicity of the chain-branching reaction suppresses radical accumulation at the flame front and thus reduces flame intensity. With the increase of endothermicity, the unstretched flame speed decreases while both flame ball radius and Markstein length increases. Endothermicity has a stronger effect on the stretched flame speed with larger fuel Lewis number. The Markstein length is found to increase monotonically with endothermicity. Furthermore, the endothermicity of the chain-branching reaction is shown to affect the transition among different flame regimes including ignition kernel, flame ball, propagating spherical flame, and planar flame. The critical ignition power radius increases with endothermicity, indicating that endothermicity inhibits the ignition process. The influence of endothermicity on ignition becomes relatively stronger at higher crossover temperature or higher fuel Lewis number. Moreover, one-dimensional transient simulations are conducted to validate the theoretical results. It is shown that the quasi-steady-state assumption used in theoretical analysis is reasonable and that the same conclusion on the effects of endothermic chain-branching reaction can be drawn from simulation and theoretical analysis.     

Detonation front structure and the competition for radicals

We examine the role of competition for radical species in determining detonation front structure for hydrogen and selected hydrocarbon fuels in air and oxygen. Numerical simulations and detailed reaction mechanisms are used to characterize the reaction zone length, shape, and sensitivity to temperature variation. We find that the effect of the competition for radicals on the energy release rate characteristics varies significantly for the chosen mixtures. Hydrogen exhibits a strong effect while in methane and ethane mixtures the effect is absent. Other hydrocarbons including acetylene, ethylene, and propane fall between these extreme cases. This competition is manifested by a peak in effective activation energy associated with a shift in the dominant reaction pathway in the initial portion of the reaction zone. The peak of the effective activation energy is centered on the extended second explosion limit. A five-step, four species reaction model of this competition process has been developed and calibrated against numerical simulations with detailed chemistry for hydrogen. The model includes a notional radical species and reactive intermediate in addition to reactants and products. The radical species undergoes chain-branching and there is a competing pathway through the reactive intermediate that is mediated by a three-body reaction followed by decomposition of the intermediate back to the radical species. We have used this model in two-dimensional unsteady simulations of detonation propagation to examine the qualitative differences in the cellular instability of detonation fronts corresponding to various degrees of competition between the chain-branching and reactive intermediate production. As the post-shock state approaches the region of competition between the radical and reactive intermediate, the detonation front becomes irregular and pockets of the reactive intermediate appear behind the front, but the detonation continues to propagate.     

Effect of thermal expansion on the linear stability of planar premixed flames for a simple chain-branching model: The high activation energy asymptotic limit

The linear stability of freely propagating, adiabatic, planar premixed flames is investigated in the context of a simple chain-branching chemistry model consisting of a chain-branching reaction step and a completion reaction step. The role of chain-branching is governed by a crossover temperature. Hydrodynamic effects, induced by thermal expansion, are taken into account and the results compared and contrasted with those from a previous purely thermal-diffusive constant density linear stability study. It is shown that when thermal expansion is properly accounted for, a region of stable flames predicted by the constant density model disappears, and instead the flame is unstable to a long-wavelength cellular instability. For a pulsating mode, however, thermal expansion is shown to have only a weak effect on the critical fuel Lewis number required for instability. These effects of thermal expansion on the two-step chain-branching flame are shown to be qualitatively similar to those on the standard one-step reaction model. Indeed, as found by constant density studies, in the limit that the chain-branching crossover temperature tends to the adiabatic flame temperature, the two-step model can be described to leading order by the one-step model with a suitably defined effective activation energy.     

Gas-phase spontaneous ignition of hydrocarbons

The ignition of hydrocarbons at low temperatures is experimentally studied in a rapid-mixture-injection static reactor. The ignition process was monitored using a high-speed color video camera. It was found that, at low temperatures, ignition starts in kernels, a feature also characteristic of methods for measuring the ignition delay time at high and medium temperatures (shock tube, rapid compression machine). Kernel-mode ignition is associated with gas-dynamic phenomena inherent in different techniques of heating the gas to the desired temperature. Ignition in the kernel is of chain-thermal nature. The emergence of a visible kernel can be considered the beginning of hot flame propagation. It is shown that, in the self-ignition mode, the propagation of the flame front from the initial kernel occurs by the induction mechanism, proposed by Ya.B. Zel’dovich, rather than by the diffusion-heat-conduction mechanism. Introduction of a platinum wire into the reactor produces a catalytic effect in the negative temperature coefficient region, while virtually unaffecting the ignition delay at lower temperatures.     

Ignition conditions and characteristics for high-porosity condensed materials subjected to local conductive heating

An experimental study of the ignition conditions (limiting heat source temperature) and characteristics (delay time) for high-porosity condensed materials under local conductive heating is reported. The study has been carried out on dry pine needles, a typical high-porosity combustible forest material. The dependence of the ignition delay for the material on the initial temperature of the heat source—a single cylindrical particle preheated to a high temperature—has been elucidated. A hypothesis concerning the mechanism of ignition of high-porosity condensed materials under local conductive heating has been formulated: the effect of high open porosity on the intensity of heat and mass transfer in the boundary layer of the material in the induction period has been substantiated.     

Temperature-dependent gas-surface chemical kinetic model for methane ignition catalyzed by in situ generated palladium nanoparticles

A temperature-dependent gas-surface kinetic model for methane oxidation over palladium is proposed. Thermodynamic data for the surface species (O, H, OH, H₂O, and CO) are derived from statistical mechanic analysis using literature heats of desorption and vibrational frequencies. The rate parameters in the model also satisfy thermo-kinetic constraints. The hydrogen oxidation submodel is validated against literature stagnation flow reactor experiments at 1300 K and 13 Pa. The current model is further tested against catalytic methane ignition in a laminar flow reactor at atmospheric pressure, and with time-resolved measurements of the size distribution of palladium nanoparticles generated in situ from an aerosol containing palladium acetate. The improved gas-surface model predicts closely the experimental data. The role of palladium nanoparticles in enhancing methane ignition is attributed to heat release due to catalytic methane oxidation over distributed nanoparticle surfaces, leading to a temperature rise and thus an accelerated gas-phase chain-branching process.     

Autoignition of surrogate fuels at elevated temperatures and pressures

Autoignition of Jet-A and mixtures of benzene, hexane, and decane in air has been studied using a heated shock tube at mean post-shock pressures of 8.5 ± 1 atm within the temperature range of 1000–1700 K with the objective of identifying surrogate fuels for aviation kerosene. The influence of each component on ignition delay time and on critical conditions required for strong ignition of the mixture has been deduced from experimental observations. Correlation equation for Jet-A ignition times has been derived from the measurements. It is found that within the scatter of experimental data dilution of n-decane with benzene and n-hexane leads to slight increase in ignition times at low temperatures and does not change critical temperatures required for direct initiation of detonations in comparison with pure n-decane/air mixtures. Ignition times in 20% hexane/80% decane (HD), 20% benzene/80% decane (BD) and 18.2% benzene/9.1% hexane/72.7% decane (BHD) mixtures at temperature range of T  1450–1750 K correlate well with induction time of Jet-A fuel suggesting that these mixtures could serve as surrogates for aviation kerosene. At the same time, HD, BD and BHD surrogate fuels demonstrate a stronger autoignition and peak velocities of reflected shock front in comparison with Jet-A and n-decane/air mixtures.     

Detonation structure under chain-branching kinetics with small initiation rate

The structure of ZND waves under simple three step chain-branching kinetics is analyzed, assuming a slow initiation rate but arbitrary chain-branching activation energy. The analysis allows for a complete solution for the ZND wave in all cases, inside or outside the chain-branching explosion region, or close to the explosion limit. Results show that even when the von Neumann point is inside the explosion region, chain-branching effectively stops and the chain-branching radical concentration reaches a small near-steady value before all the reactant is consumed. Beyond that point, chemistry proceeds slowly, at a rate of the order of the initiation rate. For a von Neumann point relatively close to the limit, the reactant concentration is still quite significant when chain-branching stops, but diminishes for von Neumann points deeper inside the explosion region. The assumption that initiation is much slower than chain-branching is often quite accurate, in which case the length required for complete burn is orders of magnitude longer than the chain-branching length, so that as a practical matter, combustion never completes. In contrast, numerical simulation shows that under the same conditions, the cellular wave results in a more complete burn.     

Application of an aerosol shock tube to the measurement of diesel ignition delay times

Shock tube ignition delay times were measured for DF-2 diesel/21% O₂/argon mixtures at pressures from 2.3 to 8.0 atm, equivalence ratios from 0.3 to 1.35, and temperatures from 900 to 1300 K using a new experimental flow facility, an aerosol shock tube. The aerosol shock tube combines conventional shock tube methodology with aerosol loading of fuel-oxidizer mixtures. Significant efforts have been made to ensure that the aerosol mixtures were spatially uniform, that the incident shock wave was well-behaved, and that the post-shock conditions and mixture fractions were accurately determined. The nebulizer-generated, narrow, micron-sized aerosol size distribution permitted rapid evaporation of the fuel mixture and enabled separation of the diesel fuel evaporation and diffusion processes that occurred behind the incident shock wave from the chemical ignition processes that occurred behind the higher temperature and pressure reflected shock wave. This rapid evaporation technique enables the study of a wide range of low-vapor-pressure practical fuels and fuel surrogates without the complication of fuel cracking that can occur with heated experimental facilities. These diesel ignition delay measurements extend the temperature and pressure range of earlier flow reactor studies, provide evidence for NTC behavior in diesel fuel ignition delay times at lower temperatures, and provide an accurate data base for the development and comparison of kinetic mechanisms for diesel fuel and surrogate mixtures. Representative comparisons with several single-component diesel surrogate models are also given.     

Large eddy simulation of the low temperature ignition and combustion processes on spray flame with the linear eddy model

Large eddy simulation coupled with the linear eddy model (LEM) is employed for the simulation of n-heptane spray flames to investigate the low temperature ignition and combustion process in a constant-volume combustion vessel under diesel-engine relevant conditions. Parametric studies are performed to give a comprehensive understanding of the ignition processes. The non-reacting case is firstly carried out to validate the present model by comparing the predicted results with the experimental data from the Engine Combustion Network (ECN). Good agreements are observed in terms of liquid and vapour penetration length, as well as the mixture fraction distributions at different times and different axial locations. For the reacting cases, the flame index was introduced to distinguish between the premixed and non-premixed combustion. A reaction region (RR) parameter is used to investigate the ignition and combustion characteristics, and to distinguish the different combustion stages. Results show that the two-stage combustion process can be identified in spray flames, and different ignition positions in the mixture fraction versus RR space are well described at low and high initial ambient temperatures. At an initial condition of 850 K, the first-stage ignition is initiated at the fuel-lean region, followed by the reactions in fuel-rich regions. Then high-temperature reaction occurs mainly at the places with mixture concentration around stoichiometric mixture fraction. While at an initial temperature of 1000 K, the first-stage ignition occurs at the fuel-rich region first, then it moves towards fuel-richer region. Afterwards, the high-temperature reactions move back to the stoichiometric mixture fraction region. For all of the initial temperatures considered, high-temperature ignition kernels are initiated at the regions richer than stoichiometric mixture fraction. By increasing the initial ambient temperature, the high-temperature ignition kernels move towards richer mixture regions. And after the spray flames gets quasi-steady, most heat is released at the stoichiometric mixture fraction regions. In addition, combustion mode analysis based on key intermediate species illustrates three-mode combustion processes in diesel spray flames.     

Effects of temperature and equivalence ratio on the ignition of n-heptane fuel spray in turbulent flow

Direct numerical simulations were performed to study the autoignition process of n-heptane fuel spray in a turbulent field. For the solution of the carrier gas fluid, the Eulerian method is employed, while for the fuel droplets, the Lagrangian method is used. Droplets are initialized at random locations in a two-dimensional isotropic turbulent field. A chemistry mechanism for n-heptane with 44 species and 112 reactions was adopted to describe the chemical reactions. Three cases with the same initial global equivalence ratio (0.5) and different initial gas phase temperatures (1100, 1200, and 1300 K) were simulated. In addition, two cases with initial global equivalence ratios of 1.0 and 1.5 and initial temperature 1300 K were simulated to examine the effect of equivalence ratio. Evolution of temperature, species mass fraction, reaction rate, and the joint PDF of temperature and equivalence ratio are presented. Effects of the initial gas temperature and equivalence ratio on vaporization and ignition are discussed. A correlation was derived relating ignition delay times to temperature and equivalence ratio. It was confirmed that with the increase of initial temperature, the autoignition occurs earlier. With the increase of the initial equivalence ratio, however, autoignition occurs later due to a larger decrease in gas phase temperature caused by fuel droplet evaporation. The results obtained in this study are expected to be constructive in understanding fuel spray combustion, such as that in homogeneous charge compression ignition systems.     

Simulation of the ignition of a liquid fuel with a hot particle

A two-dimensional gas-phase model of ignition of a flammable liquid by a single particle heated to a high temperature with consideration given to heat conduction, evaporation, diffusion, and convection of fuel vapor in an oxidizer medium was developed. Numerical simulations made it possible to determine the dependences of the ignition delay time for the liquid on the size and initial temperature of the particle. The minimum size and initial temperature of the particle at which ignition still occurs were estimated.     

镁颗粒群非稳态着火过程数值模拟

建立了镁颗粒群着火的一维非稳态有限影响体模型, 数值模拟颗粒群中镁颗粒的着火过程. 研究表明, 当镁颗粒表面反应加剧之后,颗粒相温度急剧上升, 迅速达到着火, 而其周围气相的温升速率却远小于颗粒的温升速率; 在着火过程中气相温度只在颗粒表面附近升高比较明显, 整体温度升高不大. 分析了颗粒群内部参数和环境参数对镁颗粒群着火的影响. 随颗粒浓度的增加, 颗 粒群变得易于着火, 其着火时间变短, 但颗粒浓度增大到一定程度后, 继续增大该值将对颗粒群的着火起消极作用. 环境压力对颗粒群着火的影响比较小,在1-5 atm范围内颗粒群的着火性能基本不变. 气相中氧气浓度对颗粒群的着火性能影响也不显著, 但当氧气浓度过小时, 对着火过程的影响将大大增强.颗粒粒径、气相/颗粒相初温、辐射源温度对颗粒 群着火的影响巨大,小粒径、高温度促使颗粒群快速着火.数值模拟与文献中试验 结果的变化趋势相一致.     

On the influence of singlet oxygen molecules on characteristics of HCCI combustion: A numerical study

Mechanisms of homogeneous charge compression ignition (HCCI) combustion enhancement are investigated numerically when excited O₂(a ¹Δ_g) molecules are produced at different points in the compression stroke. The analysis is conducted with the use of an extended kinetic model involving the submechanism of nitric oxide formation in the presence of singlet oxygen O₂(a ¹Δ_g) or O₂(b ¹Σ_g ⁺) molecules in the methane-air mixture. It is demonstrated that the abundance of excited O₂(a ¹Δ_g) molecules in the mixture even in a small amounts intensifies the ignition and combustion and allows one to control the ignition event in the HCCI engine. Such a method of energy supply in the HCCI engine is much more effective in advancement of combustion timing than mere heating of the mixture, because it leads to acceleration of the chain-branching mechanism. The excitation of O₂ molecules to the a ¹Δ_g electronic state makes it possible to organise the successful combustion in the cylinder at diminished initial temperature of the mixture and increase the effective energy released during HCCI combustion. The advance in the value of this energy is much higher than the energy needed for the excitation of oxygen molecules. Moreover, in this case, the output concentration of NO and CO can be reduced significantly.     

Detonation structure with pressure-dependent chain-branching kinetics

We study multi-dimensional stability and perform high resolution two-dimensional numerical simulations of detonations with a four-step chain-branching reaction model. The reaction model is designed to approximate hydrogen chemistry. It consists of a chain-initiation step and a chain-branching step, both temperature-dependent with Arrhenius kinetics, followed by two pressure-dependent termination steps. Increasing the chain-branching activation energy shortens the ZND reaction length and leads to more unstable detonations, according to the stability analysis. Computations with four values of the chain-branching activation energy are performed both in narrow and wide channels. In the wider channel, all cases studied show distinct keystone-shaped regions, associated with substantial differences in reactivity across the shear layer hence of the time and distance until chain-branching takes place. As the chain-branching activation energy increases, cells take a shorter time to form, and the ratio cell length over width decreases. The cell size is dominated by the longer unstable wavelength even when high frequency modes are more unstable, but cells appear earlier in narrow channels than in wider ones. Initially, the cellular structure looks weaker, and the cell size is dominated by the shorter, more unstable wavelength, but eventually, it adapts to the longest unstable wavelength still consistent with the domain width.     

Understanding cool flames and warm flames

Low-temperature flames such as cool flames, warm flames, double flames, and auto-ignition assisted flames play a critical role in the performance of advanced engines and fuel design. In this paper, an overview of the recent progresses in understanding low-temperature flames and dynamics as well as their impacts on combustion, advanced engines, and fuel development will be presented. Specifically, at first, a brief review of the history of cool flames is made. Then, the recent experimental studies and computational modeling of the flame structures, dynamics, and burning limits of non-premixed and premixed cool flames, warm flames, and double flames are presented. The flammability limit diagram and the temperature-dependent chain-branching reaction pathways, respectively, for hot, warm, and cool flames at elevated temperature and pressure will be discussed and analyzed. After that, the effect of low temperature auto-ignition of auto-igniting mixtures at high ignition Damköhler numbers at engine conditions on the propagation of cool flames, warm flames, and double flames as well as turbulent flames will be discussed. Finally, a new platform using low temperature flames for the development and validation of chemical kinetic models of alternative fuels will be presented. Discussions of future research of the dynamics and control of low temperature flames under engine conditions will be made.     

Simple model of inhibition of chain-branching combustion processes

A simple kinetic model has been suggested to describe the inhibition and extinction of flame propagation in reaction systems with chain-branching reactions typical for hydrocarbon systems. The model is based on the generalised model of the combustion process with chain-branching reaction combined with the one-stage reaction describing the thermal mode of flame propagation with the addition of inhibition reaction steps. Inhibitor addition suppresses the radical overshoot in flame and leads to the change of reaction mode from the chain-branching reaction to a thermal mode of flame propagation. With the increase of inhibitor the transition of chain-branching mode of reaction to the reaction with straight-chains (non-branching chain reaction) is observed. The inhibition part of the model includes a block of three reactions to describe the influence of the inhibitor. The heat losses are incorporated into the model via Newton cooling. The flame extinction is the result of the decreased heat release of inhibited reaction processes and the suppression of radical overshoot with the further decrease of the reaction rate due to the temperature decrease and mixture dilution. A comparison of the results of modelling laminar premixed methane/air flames inhibited by potassium bicarbonate (gas phase model, detailed kinetic model) with the results obtained using the suggested simple model is presented. The calculations with the detailed kinetic model demonstrate the following modes of combustion process: (1) flame propagation with chain-branching reaction (with radical overshoot, inhibitor addition decreases the radical overshoot down to the equilibrium level); (2) saturation of chemical influence of inhibitor, and (3) transition to thermal mode of flame propagation (non-branching chain mode of reaction). The suggested simple kinetic model qualitatively reproduces the modes of flame propagation with the addition of the inhibitor observed using detailed kinetic models.     

A numerical study of the autoignition of dimethyl ether with temperature inhomogeneities

The autoignition of dimethyl ether (DME) with temperature inhomogeneities is investigated by one-dimensional numerical simulations with detailed chemistry at high pressure and a constant volume. The primary purpose of the study is to provide an understanding of the autoignition of DME in a simplified configuration that is relevant to homogeneous charge compression ignition (HCCI) engines. The ignition structure and the negative temperature coefficient (NTC) behaviour are characterised in a homogeneous domain and one-dimensional domains with thermal stratification, at different initial mean temperatures and length scales. The thermal stratification is shown to strongly affect the spatial structure and temporal progress of ignition. The importance of diffusion and conduction on the ignition progress is assessed. It is shown that the effects of molecular diffusion decay relative to those of chemical reaction as the length-scale increases. This is to be expected, however the present study shows that these characteristics also depend on the mean temperature due to NTC behaviour. For the range of conditions studied here, which encompass a range of stratification length scales expected in HCCI engines, the effects of molecular transport are found to be small compared with chemical reaction effects for mean temperatures within the NTC regime. This is in contrast to previous work with fuels with single-stage ignition behaviour where practically realisable temperature gradients can lead to molecular transport effects becoming important. In addition, thermal stratification is demonstrated to result in significant reductions of the pressure-rise rate (PRR), even for the present fuel with two-stage ignition and NTC behaviour. The reduction of PRR is however strongly dependent on the mean initial temperature. The stratification length-scale is also shown to have an important influence on the pressure oscillations, with large-amplitude oscillations possible for larger length scales typical of integral scales in HCCI engines.     

Numerical simulation of solid-phase ignition of metallized condensed matter by a particle heated to a high temperature

Numerical simulation of the ignition of a composite propellant by a single “hot” particle of metal is carried out in the framework of the solid-phase model of ignition. The dependences of the ignition lag time for a metallized condensed matter on the initial temperature of a local energy source are determined. Close agreement of the obtained theoretical results with the known experimental data is found.     

Flame balls with thermally sensitive intermediate kinetics

Spherical flame balls are studied using a model for the chemical kinetics which involves a non-exothermic autocatalytic reaction, describing the chain-branching generation of a chemical radical and an exothermic completion reaction, the rate of which does not depend on temperature. When the chain-branching reaction has a large activation temperature, an asymptotic structure emerges in which the branching reaction generates radicals and consumes fuel at a thin flame interface, although heat is produced and radicals are consumed on a more distributed scale. Another model, based more simply, but less realistically, on the generation of radicals by decomposition of the fuel, provides exactly the same leading order matching conditions. These can be expressed in terms of jump conditions across a reaction sheet that are linear in the dependent variables and their normal gradients. Using these jump conditions, a reactive–diffusive model with linear heat loss then leads to analytical solutions that are multivalued for small enough levels of heat loss, having either a larger or a smaller radius of the interface where fuel is consumed. The same properties are found, numerically, to persist as the activation temperature of the branching reaction is reduced to values that seem to be typical for hydrocarbon chemistry. Part of the solution branch with larger radius is shown to become stable for low enough values of the Lewis number of the fuel.