Structure and dynamics of edge flames in the near wake of unequal merging shear flows

We examine in this study the structure and dynamic properties of an edge flame formed in the near-wake of two initially separated shear flows, one containing fuel and the other oxidiser. A comprehensive study is carried out within the diffusive-thermal framework where the flow field, computed a-priori, is used for the determination of the combustion field. Our focus is on the effects of three controlling parameters: the Damköhler number controlling the overall flow rate, the oxidiser-to-fuel strain rate ratio of the supply streams that determines the extent of oxidiser entrainment towards the mixing zone, and the Lewis number, assumed equal for the fuel and oxidiser, that depends on the mixture composition. Response curves, representing the edge flame standoff distance as a function of Damköhler number, exhibit two distinct shapes: C-shaped and U-shaped curves characterising the response of low and high Lewis number flames, respectively. Stability considerations show that the upper solution branch of the C-shaped response curve is unstable and hence corresponds to physically unrealistic states, but due to heat conduction toward the cold plate the lower solution branch is always stable. The states forming this solution branch correspond to flame attachment, where the edge flame remains practically attached to the tip of the plate until it is blown off by the flow when the velocity exceeds a critical value. The U-shaped response, on the other hand, consists of equilibrium states that are globally stable. Thus, high Lewis number flames can be always stabilised near the splitter plate, with the edge held stationary or undergoing a back and forth motion, or lifted and stabilised downstream by the flow. Insight into the distinct stabilisation characteristics, exhibited by the different Lewis number cases, is given by examining the relationship between the local flow velocity and the edge propagation speed.     

The role of spontaneous waves in the deflagration-to-detonation transition in submillimetre channels

Flame acceleration and transition to detonation in submillimetre two-dimensional planar and three-dimensional square channels were simulated by solving the compressible reactive Navier–Stokes equations. A simplified chemical–diffusive model was used to describe the diffusive transport and chemical reaction of a highly reactive mixture, such as stoichiometric ethylene and oxygen in 2D and 3D channels. The walls of the channels were modelled as no-slip and adiabatic. The initial flame acceleration and precursor shock formation were consistent with earlier results. Viscous dissipation in the boundary layer heats the reactants, which have been compressed by the precursor shock. The strength of the precursor shock and the amount of viscous dissipation increase until the temperature of the boundary layer is high enough to ignite the reactants. This produces a spontaneous wave, which, in most of the cases considered, initiates the detonation. The spontaneous wave first forms where the flame attaches to the wall in the planar channels, and forms at the corner where two walls meet in the square channels. In a separate study, the boundary layer also ignited in a computation for a circular tube containing a mixture hydrogen and oxygen represented by a detailed chemical reaction mechanism. The formation of spontaneous waves to the extent studied appears to be robust, and is relatively insensitive to channel geometry, fuel and oxidiser mixture, and the level of detail in the chemical–diffusive models used.     

A LES-CMC formulation for premixed flames including differential diffusion

A finite volume large eddy simulation–conditional moment closure (LES-CMC) numerical framework for premixed combustion developed in a previous studyhas been extended to account for differential diffusion. The non-unity Lewis number CMC transport equation has an additional convective term in sample space proportional to the conditional diffusion of the progress variable, that in turn accounts for diffusion normal to the flame front and curvature-induced effects. Planar laminar simulations are first performed using a spatially homogeneous non-unity Lewis number CMC formulation and validated against physical-space fully resolved reference solutions. The same CMC formulation is subsequently used to numerically investigate the effects of curvature for laminar flames having different effective Lewis numbers: a lean methane–air flame with Le_eff = 0.99 and a lean hydrogen–air flame with Le_eff = 0.33. Results suggest that curvature does not affect the conditional heat release if the effective Lewis number tends to unity, so that curvature-induced transport may be neglected. Finally, the effect of turbulence on the flame structure is qualitatively analysed using LES-CMC simulations with and without differential diffusion for a turbulent premixed bluff body methane–air flame exhibiting local extinction behaviour. Overall, both the unity and the non-unity computations predict the characteristic M-shaped flame observed experimentally, although some minor differences are identified. The findings suggest that for the high Karlovitz number (from 1 to 10) flame considered, turbulent mixing within the flame weakens the differential transport contribution by reducing the conditional scalar dissipation rate and accordingly the conditional diffusion of the progress variable.     

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.     

Kinetics and extinction of non-premixed cool and warm flames of dimethyl ether at elevated pressure

The growing demand of clean and efficient propulsion and energy systems has sparked an interest in understanding low-temperature combustion at high pressure. Cool flame transition and extinction limits as well as oxygen concentration dependence at elevated pressures provide insights of the low-temperature and high-pressure fuel reactivity. A new experimental high-pressure counterflow burner platform was designed and developed to achieve the studies of high-pressure cool flames. Dimethyl ether (DME) was chosen to study its non-premixed cool flame in high-pressure counterflow burner at pressure up to 5 atm, perhaps for the first time. This paper investigates the effects of pressure on cool flame structure, extinction and transition limits, and oxygen concentration dependence as well as ozone assisted warm flames of DME in experiments and numerical simulations. The results show that the reignition transition from cool flame to hot flame occurs either with the decrease of the strain rate at a given fuel concentration and pressure or with the increase of fuel mole fraction or pressure at a given strain rate. Furthermore, it is shown that the higher pressure shifts the cool flame to higher strain rates and results in higher cool flame extinction strain rates. However, the existing kinetic model of DME fails in predicting the cool flame extinction limit at elevated pressures. Besides, the cool flame extinction limits are proportional to nth power of the oxygen concentration, [O₂]ⁿ, and the increase of pressure leads to stronger extinction limit dependence (larger n) on oxygen concentration. The present experiment and detailed kinetic analysis show clearly that increasing pressure promotes the low-temperature chemistry including the oxygen addition reactions. In addition, stable warm flame was first experimentally observed by using DME at elevated pressure with ozone sensitization.     

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.     

Influences of stoichiometry on steadily propagating triple flames in counterflows

Most studies of triple flames in counterflowing streams of fuel and oxidizer have been focused on the symmetric problem in which the stoichiometric mixture fraction is 1/2. There then exist lean and rich premixed flames of roughly equal strengths, with a diffusion flame trailing behind from the stoichiometric point at which they meet. In the majority of realistic situations, however, the stoichiometric mixture fraction departs appreciably from unity, typically being quite small. With the objective of clarifying the influences of stoichiometry, attention is focused on one of the simplest possible models, addressed here mainly by numerical integration. When the stoichiometric mixture fraction departs appreciably from 1/2, one of the premixed wings is found to be dominant to such an extent that the diffusion flame and the other premixed flame are very weak by comparison. These curved, partially premixed flames are expected to be relevant in realistic configurations. In addition, a simple kinematic balance is shown to predict the shape of the front and the propagation velocity reasonably well in the limit of low stretch and low curvature.     

Cell formation in non-premixed,axisymmetric jet flames near extinction

Systematic experiments with CO₂ diluted H₂–O₂ circular jet diffusion flames have been undertaken to study the formation of cellular flames, which occur for relatively low reactant Lewis numbers and near the extinction limit. The jet Reynolds number for all experiments was about 500, based on the centreline velocity, jet diameter and ambient fuel properties. The Lewis numbers, based on the initial mixture strength φ and ambient conditions of the investigated near-extinction mixtures, vary in the range 1.1–1.3 for oxygen and 0.25–0.29 for hydrogen (φ is defined here as the fuel-to-oxygen molar ratio normalized by the stoichiometric value). Various conditions near the extinction limit were investigated by fixing the fuel composition (H₂–CO₂ mixture), and systematically lowering the oxygen concentration in the co-flowing oxidizer stream past the point where cellular structures formed, until extinction occurred. The observed different instability states were correlated with the initial mixture strength and the proximity to the extinction limit.

The parameter space for cellularity was found to increase with decreasing initial mixture strength. For a given initial mixture strength, several cellular states were found to co-exist near the extinction limit, and the preferred number of cells (the azimuthal wave number) was observed to decrease with decreasing oxygen concentration (Damköhler number). These trends are consistent with previous theoretical work and our own stability analysis that will be reported elsewhere.     

Experimental and computational investigation of extinction and autoignition of propane and n-heptane in nonpremixed flows

An experimental and computational investigation is carried out to characterize the influence of reactants on critical conditions for extinction and for autoignition of propane and n-heptane in nonpremixed counterflow configurations. Propane or vaporized n-heptane mixed with nitrogen is transported in one stream while the other stream is made up of air mixed with nitrogen. Measurements of the oxidizer stream temperature needed for autoignition are made at fixed values of the strain rate, either with the fuel mass fraction varied at a fixed oxygen mass fraction or with the oxygen mass fraction varied at a fixed fuel mass fraction. Extinction strain rates for propane are measured as a function of the oxygen mass fraction with room-temperature feed streams and the fuel mass fraction fixed and for n-heptane as a function of the fuel mass fraction with the oxygen mass fraction and feed-stream temperatures fixed. Predictions of critical conditions for extinction and autoignition are made employing detailed kinetic mechanisms. Predictions of critical conditions for extinction are in reasonable agreement with measurements, but there are significant discrepancies for autoignition. Measurements show that increasing the mass fraction of either fuel or oxygen increases the overall reactivity thereby reducing the autoignition temperature. The kinetic models predict the increase in reactivity of the mixing layer with increasing mass fraction of fuel but predict very little change in reactivity of the mixing layer with increasing mass fraction of oxygen, thus failing to predict the influence of oxygen on autoignition. It is concluded that there may exist kinetic pathways responsible for this disagreement that are yet to be discovered, and paths that fail to explain the results are identified.     

Scaling relations for the length of coaxial oxy-flames with and without swirl

An extensive experimental study is carried out to analyze scaling laws for the length of methane oxy-flames stabilized on a coaxial injector. The central methane fuel stream is diluted with N₂, CO₂ or He. The annular air stream is enriched with oxygen and can be impregnated with swirl. Former studies have shown that the stoichiometric mixing length of relatively short flames is controlled by the mixing process taking place in the vicinity of the injector outlet. This property has been used to derive scaling laws at large values of the stoichiometric mixture fraction. It is shown here that the same relation can be extended to methane oxy-flames characterized by small values of the stoichiometric mixture fraction. Flame lengths are determined with OH* chemiluminescence measurements over more than 1000 combinations of momentum ratio, annular swirl level and composition of the inner and outer streams of the coaxial injector. It is found that the lengths of all the flames investigated without swirl collapse on a single line, whose coefficients correspond to within 15% of flame lengths obtained for fuel and oxidizer streams at much larger stoichiometric mixture fractions. This relation is then extended to the case of swirling flames by including the contribution of the tangential velocity in the flow entrainment rate and is found to well reproduce the mixing degree of the two co-axial streams as long as the flow does not exhibit a vortex breakdown bubble. At higher swirl levels, when the flow features a central recirculation region, the flame length is found to also directly depend on the oxygen enrichment in the oxidizer stream.     

Critical temperature and reactant mass flux for radiative extinction of ethylene microgravity spherical diffusion flames at 1 bar

In microgravity combustion, where buoyancy is not present to accelerate the flow field and strain the flame, radiative extinction is of fundamental importance, and has implications for spacecraft fire safety. In this work, the critical point for radiative extinction is identified for normal and inverse ethylene spherical diffusion flames via atmospheric pressure experiments conducted aboard the International Space Station, as well as with a transient numerical model. The fuel is ethylene with nitrogen diluent, and the oxidizer is an oxygen/nitrogen mixture. The burner is a porous stainless-steel sphere. All experiments are conducted at constant reactant flow rate. For normal flames, the ambient oxygen mole fraction was varied from 0.2 to 0.38, burner supply fuel mole fraction from 0.13 to 1, total mass flow rate, ṁ_total, from 0.6 to 12.2 mg/s, and adiabatic flame temperature, T_ad, from 2000 to 2800 K. For inverse flames, the ambient fuel mole fraction was varied from 0.08 to 0.12, burner supply oxygen mole fraction from 0.4 to 0.85, ṁ_total from 2.3 to 11.3 mg/s, and T_ad from 2080 to 2590 K. Despite this broad range of conditions, all flames extinguish at a critical extinction temperature of 1130 K, and a fuel-based mass flux of 0.2 g/m²-s for normal flames, and an oxygen-based mass flux of 0.68 g/m²-s for inverse flames. With this information, a simple equation is developed to estimate the flame size (i.e., location of peak temperature) at extinction for any atmospheric-pressure ethylene spherical diffusion flame given only the reactant mass flow rate. Flame growth, which ultimately leads to radiative extinction if the critical extinction point is reached, is attributed to the natural development of the diffusion-limited system as it approaches steady state and the reduction in the transport properties as the flame temperature drops due to increasing flame radiation with time (radiation-induced growth.)     

拉伸流扩散火焰面结构及熄火的研究

对拉伸层流扩散火焰面进行了数值模拟,考察了在以往湍流燃烧的火焰面模型中,假定Lewis数等于1的可靠性,研究了不同分子扩散和火焰辐射对火焰面结构、氮氧化物排放和熄火临界的影响.计算结果表明,Lewis数等于1的假定在火焰面结构的计算中存在很大的近似性,火焰辐射可以引起低拉伸条件下的熄火临界.     

An a priori study of different tabulation methods for turbulent pulverised coal combustion

In many practical pulverised coal combustion systems, different oxidiser streams exist, e.g. the primary- and secondary-air streams in the power plant boilers, which makes the modelling of these systems challenging. In this work, three tabulation methods for modelling pulverised coal combustion are evaluated through an a priori study. Pulverised coal flames stabilised in a three-dimensional turbulent counterflow, consisting of different oxidiser streams, are simulated with detailed chemistry first. Then, the thermo-chemical quantities calculated with different tabulation methods are compared to those from detailed chemistry solutions. The comparison shows that the conventional two-stream flamelet model with a fixed oxidiser temperature cannot predict the flame temperature correctly. The conventional two-stream flamelet model is then modified to set the oxidiser temperature equal to the fuel temperature, both of which are varied in the flamelets. By this means, the variations of oxidiser temperature can be considered. It is found that this modified tabulation method performs very well on prediction of the flame temperature. The third tabulation method is an extended three-stream flamelet model that was initially proposed for gaseous combustion. The results show that the reference gaseous temperature profile can be overall reproduced by the extended three-stream flamelet model. Interestingly, it is found that the predictions of major species mass fractions are not sensitive to the oxidiser temperature boundary conditions for the flamelet equations in the a priori analyses.     

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.     

Effect of the reversibility of the chemical reaction on triple flames

We examine a new aspect of triple flames, namely the effect of the reversibility of the chemical reaction on flame propagation. The study is carried out in the configuration of the two-dimensional strained mixing layer formed between two opposing streams of fuel and oxidiser. The chemical reaction is modelled as a single reversible reaction following an Arrhenius law in the forward and backward directions. The problem is formulated within the constant-density (thermo-diffusive) approximation, the main non-dimensional parameters relevant to this study being a reversibility parameter R (equal to zero in the irreversible case), a non-dimensional measure of the strain rate ? and a stoichiometric parameter S. We provide analytical (asymptotic) expressions for the local burning speed of the triple flame in terms of ?, S, and R. In particular we describe how the propagation speed of the front is decreased by an increase in R and how the location of its leading edge is affected by reversibility. For example, it is found that the leading edge shifts towards the fuel stream for S > 1 and towards the oxidiser if S < 1, as R is increased. A detailed numerical study is conducted covering all propagation regimes ranging from weakly stretched positively propagating (ignition) fronts to thick negatively propagating (extinction) fronts. In the weakly stretched cases we show that the numerics are in good agreement with the asymptotic findings. Furthermore, the results allow the determination of the domains of the distinct propagation regimes, mainly in the terms of R and ?. In line with our physical intuition, it is found that reversibility reduces the domain of ignition fronts and promotes extinction. The results provide a systematic investigation which can be considered as a first step when considering a more realistic chemistry, or poorly explored aspects (such as the existence of a temperature gradient in the unburnt mixture), when analyzing triple flames.     

The influence of water on extinction and ignition of hydrogen and methane flames

The influence of water vapor on critical conditions of extinction and autoignition of premixed and nonpremixed flames is investigated. The fuels tested are hydrogen (H₂) and methane (CH₄). Studies on premixed systems are carried out by injecting a premixed reactant stream made up of fuel, oxygen (O₂), and nitrogen (N₂) from one duct, and an inert-gas stream of N₂ from the other duct. Critical conditions of extinction are measured for various amounts of water vapor added to the premixed reactant stream. The ratio of fuel to oxygen is maintained at a constant value, and the amounts of water vapor and nitrogen are so chosen that the adiabatic temperature remains the same. This ensures that the physical influence of water is the same for all cases. Therefore, changes in values for the critical conditions of extinction are attributed to the chemical influence of water vapor. Studies on nonpremixed systems are carried out by injecting a fuel stream made up of fuel and N₂ from one duct ,and an oxidizer stream made up of O₂ and N₂ from the other duct. Critical conditions of extinction are measured with water vapor added to the oxidizer stream. The concentrations of reactants are so chosen that the adiabatic temperature and the flame position stay the same for all cases. Critical conditions of autoignition are measured by preheating the oxidizer stream of the nonpremixed system. Water vapor is added to the oxidizer stream. Numerical calculations are performed using a detailed chemical-kinetic mechanism and compared with measurements. Experimental and numerical studies show that addition of water makes the premixed and nonpremixed flames easier to extinguish and harder to ignite. The chemical influence of water is attributed to its enhanced chaperon efficiency in three body reactions.     

Characterization of heat recirculation effects on the stabilization of edge flames in the near-wake of a mixing layer

A fundamental study aimed at investigating the stabilization characteristics of edge flames established in the near-wake of two merging streams, one containing fuel and the other oxidizer, is presented, with the main focus placed on the effects of the thermal interaction between the flame and the splitter plate. To this end, a diffusive-thermal model characterized by constant gas density and transport coefficients is used for conditions at which flame liftoff is likely to occur. It is assumed that the incoming streams are of equal strain rates, that the fuel and oxidizer are supplied in stoichiometric proportion, and that the mass diffusivities of the reactants are equal, such that the resulting combustion field is symmetric with respect to the centerline extending from the splitter plate. The results indicate that the plate has a negligible effect on the edge flame unless the tip of the plate intrudes into the preheat zone of the curved premixed flame segment forming the edge flame. In an overall adiabatic system, the heat conducted from the flame to the plate is completely recirculated back to the reactants via the lateral surfaces of the plate, thus supporting an excess enthalpy flame in the near-wake. The average output heat flux, defined as the total heat output through the lateral surfaces of the plate divided by the characteristic length associated with the temperature variation along the plate, is identified as an appropriate measure to characterize the heat recirculation efficiency.     

On the global structure and asymptotic stability of low-stretch diffusion flame: Forced convection

The present work analyzes cylindrical diffusion flames (Tsuji burner) under low stretch condition, considering fuel injection also from the backward region of the burner. To highlight the fundamental aspects of this flame, some assumptions are imposed, like constant thermodynamic and transport coefficients, unitary Lewis number and no radiative heat loss. It is also considered potential flow model and incompressible Navier–Stokes model. Despite the simplicity of the former model, results from both models show good agreement. Also, an asymptotic analysis describing the problem far from the burner is able to capture the most important mechanisms controlling the flame, then the flame shape is determined and the dependence of the characteristic length scales on Peclet number (based on the burner properties), free stream velocity and stoichiometry is revealed. The results show that the flame width is proportional to the mass stoichiometric coefficient and reciprocal to the Peclet number the 1/4 power and free stream velocity the 3/4 power, and that the flame height is proportional to the square of the mass stoichiometric coefficient and to the square root of the ratio of Peclet number to free stream velocity. In addition, an asymptotic stability analysis reveals low-stretch flame extinction to be caused by reduction in fuel and oxidizer concentrations, which provides the range of the stoichiometric coefficient for stable regime, and at the same time the range of heat released.