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.     

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.     

Premixed flames modelled with thermally sensitive intermediate branching kinetics

The foundations of a relatively simple two-step kinetic scheme for flame chemistry are outlined, involving a model chain branching process that should adopt the activation temperature of a rate-limiting branching reaction in order to offer a broad approximation for hydrocarbon flames. A model energetic intermediate reactant then acts as a buffer between fuel consumption and the release of heat, as the intermediate is converted into products through a completion reaction step. By taking the rate of the latter reaction to be linear in the concentration of the intermediate, which is consistent with the final state being an equilibrium in a broader chemical system, a form of the model is arrived at which admits asymptotic solutions in a thermodiffusive context with constant coefficients. These are developed to second order for large values of the activation energy of the branching reaction and are found to involve the same trends that are seen for lean methane and hydrogen flames calculated using detailed chemical and transport models. Linear stability analysis identifies the ranges of Lewis numbers in which cellular or oscillatory instability can arise, with the latter form of instability disappearing above a threshold heat of reaction. These and the underlying flame solutions themselves depend on the heat of reaction and the degree of heat loss but not on the activation temperature of the branching reaction, to leading order. Near the limit of flammability a direct parallel arises with one-step kinetic models for premixed flames.     

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.     

Effects of heat conduction and radical quenching on premixed stagnation flame stabilised by a wall

The premixed stagnation flame stabilised by a wall is analysed theoretically considering thermally sensitive intermediate kinetics. We consider the limit case of infinitely large activation energy of the chain-branching reaction, in which the radical is produced infinitely fast once the cross-over temperature is reached. Under the assumptions of potential flow field and constant density, the correlation for flame position and stretch rate of the premixed stagnation flame is derived. Based on this correlation, the effects of heat conduction and radical quenching on the wall surface are examined. The wall temperature is shown to have great impact on flame bifurcation and extinction, especially when the flame is close to the wall. Different flame structures are observed for near-wall normal flame, weak flame, and critically quenched flame. The fuel and radical Lewis numbers are found to have opposite effects on the extinction stretch rate. Moreover, it is also demonstrated that only when the flame is close to the wall does the radical quenching strongly influence the flame bifurcation and extinction. The extinction stretch rate is shown to decrease with the amount of radical quenching for different fuel and radical Lewis numbers. Besides, the coupling between the wall heat conduction and radical quenching is found to greatly influence the bifurcation and extinction of the premixed stagnation flame.     

对流速度对燃料液滴火焰形态及燃烧的影响

考虑气相非稳态及液滴内部环流,建立运动液滴非稳态蒸发燃烧模型.模型采用动网格方法精确追踪液滴表面位置,采用守恒方程组更新液滴表面边界条件.根据单步全局化学反应机理,仿真研究正庚烷燃料液滴在不同对流速度下的火焰形态及燃烧.结果表明:运动液滴内部环流使液滴内部低温区向环流中心移动.当液滴运动速度大于某临界值后,火焰形态由包覆火焰转变为尾迹火焰.包覆火焰的富燃区范围、高温区范围及燃烧速率明显较尾迹火焰大;包覆火焰的液滴表面温度及表面蒸发流率分布也明显不同于尾迹火焰.     

A comparative study of H2-air premixed flame in micro combustors with different physical and boundary conditions

A numerical study of H₂-air premixed combustion in the micro channels with a detailed chemical reaction mechanism is performed by solving the two-dimensional fully elliptic governing equations of continuity, momentum, energy and species, coupled with the energy equation in the solid wall. A reference case is defined as the combustion in a cylindrical tube with 0.8 mm inner diameter and 8 mm length with a non-slip wall and a uniform velocity profile at the inlet plane. Different physical and boundary conditions have been applied in order to investigate their respective effects on the flame temperature. The conditions studied in the current paper include the combustor size and geometry, inlet velocity profile, axial heat conduction in the solid wall and slip-wall and temperature jump at the gas–solid interface. It is noted that effects of Knudsen number (slip-wall and temperature jump) on the thermal and fluid field are not very significant in a d = 0.4 mm micro combustor. Furthermore, the qualitative effects of Knudsen number on the flame temperature are analysed. The results of this paper indicate that these various boundary and physical conditions have effects on the flame temperature to different extent and should be carefully monitored when applied for different applications.     

Counterflow diffusion flames: effects of thermal expansion and non-unity Lewis numbers

In this work we re-examine the counterflow diffusion flame problem focusing in particular on the flame–flow interactions due to thermal expansion and its influence on various flame properties such as flame location, flame temperature, reactant leakage and extinction conditions. The analysis follows two different procedures: an asymptotic approximation for large activation energy chemical reactions, and a direct numerical approach. The asymptotic treatment follows the general theory of Cheatham and Matalon, which consists of a free-boundary problem with jump conditions across the surface representing the reaction sheet, and is well suited for variable-density flows and for mixtures with non-unity and distinct Lewis numbers for the fuel and oxidiser. Due to density variations, the species and energy transport equations are coupled to the Navier–Stokes equations and the problem does not possess an analytical solution. We thus propose and implement a methodology for solving the free-boundary problem numerically. Results based on the asymptotic approximation are then verified against those obtained from the ‘exact’ numerical integration of the governing equations, comparing predictions of the various flame properties.     

双组分燃料的层流火焰速度模型

以往关于层流火焰速度的理论分析均只考虑单组分燃料,本文对双组分燃料的平面火焰进行了大活化能渐近理论分析。在理论分析中,将火焰结构分为预热区、化学反应区和平衡区,并在大活化能假设下对各个区域分别求解了关于温度与燃料质量分数的微分方程。根据每两个区域分界面上满足的结合条件,本文推导出了双组分燃料的层流火焰速度模型。该模型表明双组分燃料层流火焰速度的平方为各个单组分燃料层流火焰速度平方的加权平均。     

Bifurcation and extinction limit of stretched premixed flames with chain-branching intermediate kinetics and radiative loss

Premixed counterflow flames with thermally sensitive intermediate kinetics and radiation heat loss are analysed within the framework of large activation energy. Unlike previous studies considering one-step global reaction, two-step chemistry consisting of a chain branching reaction and a recombination reaction is considered here. The correlation between the flame front location and stretch rate is derived. Based on this correlation, the extinction limit and bifurcation characteristics of the strained premixed flame are studied, and the effects of fuel and radical Lewis numbers as well as radiation heat loss are examined. Different flame regimes and their extinction characteristics can be predicted by the present theory. It is found that fuel Lewis number affects the flame bifurcation qualitatively and quantitatively, whereas radical Lewis number only has a quantitative influence. Stretch rates at the stretch and radiation extinction limits respectively decrease and increase with fuel Lewis number before the flammability limit is reached, while the radical Lewis number shows the opposite tendency. In addition, the relation between the standard flammability limit and the limit derived from the strained near stagnation flame is affected by the fuel Lewis number, but not by the radical Lewis number. Meanwhile, the flammability limit increases with decreased fuel Lewis number, but with increased radical Lewis number. Radical behaviours at flame front corresponding to flame bifurcation and extinction are also analysed in this work. It is shown that radical concentration at the flame front, under extinction stretch rate condition, increases with radical Lewis number but decreases with fuel Lewis number. It decreases with increased radiation loss.     

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.     

Combustion waves in a model with chain branching reaction and their stability

In this paper the travelling wave solutions in the adiabatic model with the two-step chain branching reaction mechanism are investigated both numerically and analytically in the limit of equal diffusivity of reactant, radicals and heat. The properties of these solutions and their stability are investigated in detail. The behaviour of combustion waves are demonstrated to have similarities with the properties of non-adiabatic one-step combustion waves in that there is a residual amount of fuel left behind the travelling waves and the solutions can exhibit extinction. The difference between the non-adiabatic one-step and adiabatic two-step models is found in the behaviour of the combustion waves near the extinction condition. It is shown that the flame velocity drops down to zero as the extinction condition is reached. Prospects of further work are also discussed.     

On the existence of steady-state gaseous microgravity spherical diffusion flames in the presence of radiation heat loss

Whether steady-state gaseous microgravity spherical diffusion exist in the presence of radiation heat loss is an important fundamental question and has important implications for spacecraft fire safety. In this work, experiments aboard the International Space Station and a transient numerical model are used to investigate the existence of steady-state microgravity spherical diffusion flames. Gaseous spherical diffusion flames stabilized on a porous spherical burner are employed in normal (i.e., fuel flowing into an ambient oxidizer) and inverse (i.e., oxidizer flowing into an ambient fuel) flame configurations. The fuel is ethylene and the oxidizer oxygen, both diluted with nitrogen. The flow rate of the reactant gas from the burner is held constant. It is found that steady-state gaseous microgravity spherical diffusion flames can exist in the presence of radiation heat loss, provided that the steady-state flame size is less than the flame size for radiative extinction, and the flame develops fast enough that radiation heat loss does not drop the flame temperature below the critical temperature for radiative extinction (1130 K). A simple model is provided that allows for the identification of initial conditions that can lead to steady-state spherical diffusion flames. In the spherical, infinite domain configuration, the characteristic time for the diffusion-controlled system to effectively reach steady-state is found to be on the order of 100,000 s. Despite a narrow range of attainable conditions, flames that exhibit steady-state behavior are observed aboard the ISS for up to 870 s, even with the constraint of a finite boundary. Steady-state flames are simulated using the numerical model for over 100,000 s.     

Oscillatory cool flame combustion behavior of submillimeter sized n-alkane droplet under near limit conditions

This paper reports simulation results of oscillatory cool flame burning of an isolated, submillimeter sized n-heptane (n-C₇H₁₆) droplet in a selectively ozone (O₃) seeded nitrogen-oxygen (N₂-O₂) environments at atmospheric pressure. An evolutionary one-dimensional droplet combustion code encompassing relevant physics and detailed chemistry was employed to explore the roles of low-temperature chemistry, O₃ seeding, and dynamic flame structure on burning behaviors. For X_O2= 21% and a range of selective ozone seeding, near-quasi-steady cool flame burning is achieved directly (without requiring hot flame initiation and radiative extinction). Under low oxygen index conditions, but with significant O₃ seeding (X_O3 = 5%), a nearly quasi-steady cool flame is initially established that then transitions to a dynamically oscillating cool flame burning mode which continues until the droplet is completely consumed. It is found that the oscillation occurs as result of a initial depletion of fuel vapor-oxidizer layer evolving near the droplet surface and its dynamic re-establishment through liquid vaporization and vapor/oxidizer transport. A kinetic analysis indicates that the dynamic competition between the reaction classes- (a) degenerate chain branching and (b) chain termination/propagation - along with continuous fuel and oxygen leakage through the flame location contributes to an oscillatory burning phenomena of ever-increasing amplitude. Analysis based on single full-cycle of oscillatory burning shows that the reaction progression matrices (evolution of heat and species) for QOOH➔chain propagation/termination reactions (here, Q = C₇H₁₄-) directly scales with the gas phase temperature field. On the contrary, the QOOH➔degenerate branching reactions undergoes three distinct stages within the same oscillatory cycle. The coupled flame dynamics and kinetics suggest that in the oscillatory burning mode, kinetic processes dynamically cross through conditions characterizing the negative temperature coefficient (NTC) turnover temperature, separating low temperature and NTC kinetic regimes. In addition, a parametric study is conducted to determine the role of O₃ seeding level on the observed oscillation phenomena.     

Flame structure and flame spread rate over a solid fuel in partially premixed atmospheres

We have investigated the downward flame spread over a thin solid fuel. Hydrogen, methane, or propane, included in the gaseous product of pyrolysis reaction, is added in the ambient air. The fuel concentration is kept below the lean flammability limit to observe the partially premixing effect. Both experimental and numerical studies have been conducted. Results show that, in partially premixed atmospheres, both blue flame and luminous flame regions are enlarged, and the flame spread rate is increased. Based on the flame index, a so-called triple flame is observed. The heat release rate ahead of the original diffusion flame is increased by adding the fuel, and its profile is moved upstream. Here, we focus on the heat input by adding the fuel in the opposed air, which could be a direct factor to intensify the combustion reaction. The dependence of the flame spread rate on the heat input is almost the same for methane and propane/air mixtures, but larger effect is observed for hydrogen/air mixture. Since the deficient reactant in lean mixture is fuel, the larger effect of hydrogen could be explained based on the Lewis number consideration. That is, the combustion is surely intensified for all cases, but this effect is larger for lean hydrogen/air mixture (Le < 1), because more fuel diffuses toward the lean premixed flame ahead of the original diffusion flame. Resultantly, the pyrolysis reaction is promoted to support the higher flame spread rate.     

Phenomenological model of chain-branching premixed flames

In this work, we introduce a global kinetic model that includes fuel, oxygen, products and two radical species involved in the reversible chain-branching, chain-propagation and chain-termination reactions. The model naturally extends the Zeldovich–Liñán and Zeldovich–Barenblatt–Dold models and can be used to describe both premixed and diffusion flames. Here it is applied to the problem of the deflagration wave propagation in the hydrocarbon fuel/air mixture with arbitrary equivalence ratio under the simplifying thermal-diffusive approximation. The conservation equations are solved numerically in order to obtain the velocity and structure of the combustion wave. It is demonstrated that the peak values of the adiabatic flame temperature and deflagration velocity are shifted towards the rich mixture composition if the reverse reactions of product decomposition are taken into account. The dependence of the flame speed and temperature on parameters of the system is analysed. The prospects of further investigation are discussed.     

A spray flamelet/progress variable approach combined with a transported joint PDF model for turbulent spray flames

A spray flamelet/progress variable approach is developed for use in spray combustion with partly pre-vaporised liquid fuel, where a laminar spray flamelet library accounts for evaporation within the laminar flame structures. For this purpose, the standard spray flamelet formulation for pure evaporating liquid fuel and oxidiser is extended by a chemical reaction progress variable in both the turbulent spray flame model and the laminar spray flame structures, in order to account for the effect of pre-vaporised liquid fuel for instance through use of a pilot flame. This new approach is combined with a transported joint probability density function (PDF) method for the simulation of a turbulent piloted ethanol/air spray flame, and the extension requires the formulation of a joint three-variate PDF depending on the gas phase mixture fraction, the chemical reaction progress variable, and gas enthalpy. The molecular mixing is modelled with the extended interaction-by-exchange-with-the-mean (IEM) model, where source terms account for spray evaporation and heat exchange due to evaporation as well as the chemical reaction rate for the chemical reaction progress variable. This is the first formulation using a spray flamelet model considering both evaporation and partly pre-vaporised liquid fuel within the laminar spray flamelets. Results with this new formulation show good agreement with the experimental data provided by A.R. Masri, Sydney, Australia. The analysis of the Lagrangian statistics of the gas temperature and the OH mass fraction indicates that partially premixed combustion prevails near the nozzle exit of the spray, whereas further downstream, the non-premixed flame is promoted towards the inner rich-side of the spray jet since the pilot flame heats up the premixed inner spray zone. In summary, the simulation with the new formulation considering the reaction progress variable shows good performance, greatly improving the standard formulation, and it provides new insight into the local structure of this complex spray flame.     

Oscillatory thermal-diffusive instability of combustion waves in a model with chain-branching reaction and heat loss

In this paper we investigate the properties and the linear stability of premixed combustion waves in a non-adiabatic thermal-diffusive model with a two-step chain-branching reaction mechanism. Here we focus only on the emergence of the pulsating instabilities, and the stability analysis is carried out for Lewis numbers for fuel greater than one, and various values of Lewis number for radicals. We consider the problem in two spatial dimensions to allow perturbations of a multidimensional nature. It is demonstrated that the flame speed as a function of the parameters is a double-valued C-shaped function, i.e. for a given set of parameter values there are either two solutions, fast and slow solution branches, propagating with different speed, or the combustion wave does not exist. The extinction of combustion waves occurs at finite values of the parameters and non-zero flame speed. The flame structure demonstrates a slow recombination regime behaviour with negligible fuel leakage for the fast solution branch away from the extinction condition. For parameter values close to the extinction condition and on the slow solution branch, the fuel leakage is significant and a fast recombination regime is observed. It is demonstrated that two types of instabilities emerge in the model: the uniform planar and the travelling instability. The slow solution branch is always unstable due to the uniform perturbations. The fast solution branch is either stable or loses stability due to the travelling or uniform perturbations. The switching between the onset of various regimes of instability is due to the bifurcation of co-dimension two. In the adiabatic limit this bifurcation is found for Lewis number for fuel equal to one, whereas in the non-adiabatic case it moves towards values above unity. The properties of the travelling instability are studied in detail.     

二甲醚HCCI燃烧高温反应动力学分析

应用单区燃烧模型对二甲醚均质压燃燃烧的化学反应动力学过程进行了数值模拟研究。通过分析在内燃机压燃燃烧边界条件下二甲醚高温氧化反应过程中的关键基元反应速度、关键中间产物以及自由基的浓度随曲轴转角的变化,得到了二甲醚燃烧氧化的高温反应途经。结果表明,二甲醚均质压燃燃烧具有明显的两阶段放热特性,即低温反应放热和高温反应放热。高温反应阶段又可分为蓝焰反应阶段和热焰反应阶段,其中蓝焰反应阶段是甲醛氧化成CO的过程,热焰反应主要是CO氧化成CO2的过程。二甲醚氧化产物之一甲酸(HOCHO)在蓝焰反应阶段分解生成CO2。     

燃料敏感性对内燃机部分预混燃烧(PPC)光谱特性的影响研究

在一台光学发动机上,利用火焰高速成像技术和自发光光谱分析法,研究了燃料敏感性(S)为0和6时对发动机缸内火焰发展和燃烧发光光谱的影响。试验过程中,通过改变喷油时刻(SOI=-25,-15和-5°CA ATDC)使燃烧模式从部分预混燃烧过渡到传统柴油燃烧模式。通过使用正庚烷、异辛烷、乙醇混合燃料来改变燃料敏感性。结果表明,在PPC模式下(-25°CA ATDC),火焰发展过程是从近壁面区域开始着火,而后向燃烧室中心发展,即存在类似火焰传播过程,同时在燃烧室下部未燃区域也形成新的着火自燃点。敏感性对燃烧相位影响较大,对缸内燃烧火焰发展历程影响较小;高敏感性燃料OH和CH带状光谱出现的时刻推迟,表明高敏感性燃料高温反应过程推迟,且光谱强度更低,表明碳烟辐射强度减弱。在PPC到CDC之间的过渡区域(-15°CA ATDC),燃烧火焰发光更亮,燃烧反应速率比-25°CA ATDC时刻的反应速率更快。高、低敏感性燃料对缸压放热率的影响规律与-25°CA ATDC相近,此时的燃烧反应更剧烈,放热率更高,碳烟出现时刻更早。该喷油时刻下的光谱强度高于PPC模式下的光谱强度,说明此时的CO氧化反应与碳烟辐...