Stabilization and onset of oscillation of an edge-flame in the near-wake of a fuel injector

The stabilization of an edge-flame in the near-wake of a fuel injector is discussed within the context of a diffusive-thermal model, but with a realistically computed flow. Although the boundary layer approximation can be used to describe the mixing process in the wake region, the velocity field in the immediate vicinity of the injector satisfies the full Navier-Stokes equations. The stabilization of the edge-flame and its dynamics are affected not only by diffusive-thermal effects, but also by the acceleration experienced by the fuel and oxidizer entrained into the mixing layer. The present calculations confirm an earlier prediction that edge-flame oscillations can be triggered by heat losses alone. Moreover, it is shown that when the intensity of the losses is excessive, oscillations can occur even when the Lewis numbers are less than one. New results are also obtained when examining the flame response to variations in Lewis numbers. For Lewis numbers that are not too large, there exists a minimum value of the Damkhler number D below which the edge-flame cannot be stabilized. The response curve, describing the standoff distance as a function of D is multi-valued and the turning point, which also coincides with the marginal stability state, identifies extinction or blowoff conditions. For D above this value, the edge-flame is steady and stable. For relatively large values of the Lewis number the response curve is monotonic. There is, however, a restricted range of states where the flame undergoes spontaneous oscillations with the edge-flame moving back and forth along the stoichiometric surface dragging behind it the trailing diffusion flame.     

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.     

Flame balls dynamics in divergent channel

A three-dimensional reaction-diffusion model for lean low-Lewis-number premixed flames with radiative heat losses propagating in divergent channel is studied numerically. Effects of inlet gas velocity and heat-loss intensity on flame structure at low Lewis numbers are investigated. It is found that continuous flame front exists at small heat losses and the separate flame balls settled within restricted domain inside the divergent channel at large heat losses. It is shown that the time averaged flame balls coordinate may be considered as important characteristic analogous to coordinate of continuous flame stabilized in divergent channel.     

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.     

Realizing microgravity flame spread characteristics at 1 g over a bed of nano-aluminum powder

Nanoscale aluminum (nAl) powders demonstrate relatively fast counter-flow flame spread rates compared to typical fuels such as Poly(methyl methacrylate) or cellulose at similar conditions. This allows for the dominant forward heat transfer mechanism to be through the solid fuel at higher applied oxidizer velocities, and flame structure characteristics typically observed in microgravity to be realized at 1 g conditions. Because of the porosity of the nAl powder, the gaseous oxidizer can diffuse into the bed and reactions within the solid phase become important. Using an energy balance applied to only the solid phase, an analytical model is developed which predicts the experiments for flame spread over a nAl bed. Moreover, an explanation for fingering phenomenon is established based on the effective Lewis and Damköhler numbers. This allows for an explanation of why flame spread over a bed of nAl will demonstrate this fingering instability in a quiescent, 1 g environment without a top plate to hinder buoyant flows.     

Dynamics of an edge-flame in the corner region of two mutually perpendicular streams

The stabilization and dynamics of an edge-flame in the corner region of two mutually perpendicular streams, one of fuel and the other of oxidizer, is studied within the context of a diffusive-thermal model, with an imposed flow satisfying the Navier-Stokes equations. The formulation allows for non-unity Lewis numbers and finite rate chemistry with an Arrhenius dependence on temperature. Two flow configurations, corresponding to inlet velocity profiles of uniform speed and of constant strain, have been examined. The results identify the dependence of the flame standoff distance on the flow as well as on the properties of the mixture, including the Damköhler D and Lewis numbers. For high flow rates, or small enough D, sufficient pre-mixing occurs in front of the edge-flame, which consequently takes on a tribrachial structure consisting of two premixed branches, one lean and one rich, with a trailing diffusion flame sheet. For large D, however, there is no enough premixing and the chemical reaction occurs in a small kernel very close to the corner, much like a local thermal explosion; further downstream the reaction occurs along a diffusion flame sheet that extends along the symmetry axis. The present results also predict the onset of spontaneous oscillations when the Lewis numbers are sufficiently large provided the flow rate is sufficiently high, or D reduced below a critical value. Oscillations are first sustained when D is reduced below criticality, but depending on the flow conditions, they are either damped leading to flame re-stabilization, or amplified leading to blow-off.     

Three-dimensional numerical simulations of cellular jet diffusion flames

Recent experimental investigations have demonstrated that the appearance of particular cellular states in circular non-premixed jet flames significantly depends on a number of parameters, including the initial mixture strength, reactant Lewis numbers, and proximity to the extinction limit (Damköhler number). For CO₂-diluted H₂/O₂ jet diffusion flames, these studies have shown that a variety of different cellular patterns or states can form. For given fuel and oxidizer compositions, several preferred states were found to co-exist, and the particular state realized was determined by the initial conditions. To elucidate the dynamics of cellular instabilities, circular non-premixed jet flames are modeled with a combination of three-dimensional numerical simulation and linear stability analysis (LSA). In both formulations, chemistry is described by a single-step, finite-rate reaction, and different reactant Lewis numbers and molecular weights are specified. The three-dimensional numerical simulations show that different cellular flames can be obtained close to extinction and that different states co-exist for the same parameter values. Similar to the experiments, the behavior of the cell structures is sensitive to (numerical) noise. During the transient blow-off process, the flame undergoes transitions to structures with different number of cells, while the flame edge close to the nozzle oscillates in the streamwise direction. For conditions similar to the experiments discussed, the LSA results reveal various cellular instabilities, typically with azimuthal wavenumber m = 1–6. Consistent with previous theoretical work, the propensity for the cellular instabilities is shown to increase with decreasing reactant Lewis number and Damköhler number.     

Oscillating edge-flames

It has been known for some years that when a near-limit flame spreads over a liquid pool of fuel, the edge of the flame can oscillate. It is also known that when a near-asphyxiated candle-flame burns in zero gravity, the edge of the (hemispherical) flame can oscillate violently prior to extinction. We propose that these oscillations are nothing more than a manifestation of the large Lewis number instability well known in chemical reactor studies and in combustion studies, one that is exacerbated by heat losses. As evidence of this we examine an edge-flame confined within a fuel-supply boundary and an oxygen-supply boundary, anchored by a discontinuity in data at the fuel-supply boundary. We show that when the Lewis number of the fuel is 2, and the Lewis number of the oxidizer is 1, oscillations of the edge occur when the Damköhler number is reduced below a critical value. During a single oscillation period there is a short premixed propagation stage and a long diffusion stage, behaviour that has been observed in flame spread experiments. Oscillations do not occur when both Lewis numbers are equal to 1.     

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.     

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.     

Experimental study of air dilution in oxy-liquid fuel flames

The influence of oxidizer dilution in oxy-liquid ethanol flames is experimentally investigated by using a coaxial air-assisted injector positioned in a vertical combustion chamber. This study accounts for the influence of a two-phase mode since two different injector geometries are used: for the first configuration, a vaporization mode is observed at nominal power in oxy conditions, while for the second one, a brush mode is observed. Dilution with air is applied by keeping oxidizer velocity constant. Flame structure is observed through CH emission: dilution leads to an increase in the flame diameter, and collective effects of two-phase combustion are encouraged. The effect of dilution on oxy flame stability is also studied: for a given oxygen mass fraction in the oxidizer, the oxidizer flow rate is increased until extinction occurs. Dilution leads to a less stable flame, which may be essentially explained by the decrease in laminar flame speed with dilution. For high oxidizer dilution levels, the change in flame structure might be another parameter to consider. Finally, species concentrations are measured using a standard gas sampling technique. NO and CO evolutions with dilution are different between both two-phase combustion regimes. An empirical approach based on thermal NO mechanism and CO oxidation reaction enables one to explain the evolutions for brush mode. For vaporization mode, the residence time in burned gases is also to be considered.     

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.     

Modes of particle combustion in iron dust flames

The so-called argon/helium test is proposed to identify the combustion mode of particles in iron dust flames. Iron powders of different particle sizes varying from 3 to 34 μm were dispersed in simulated air compositions where nitrogen was replaced by argon and helium. Due to the independence of the particle burning rate on the oxygen diffusivity in the kinetic mode, the ratio between the flame speeds in helium and argon mixtures is expected to be smaller if the particle burning rate is controlled by reaction kinetics rather than oxygen diffusion. Experiments were performed in a reduced-gravity environment on a parabolic flight aircraft to prevent particle settling and buoyancy-driven disruption of the flame. Uniform suspensions of the iron powders were produced inside glass tubes and a flame was initiated at the open end of the tube. Quenching plate assemblies of various channel widths were installed inside the tube and pass or quench events were used to measure the quenching distance. Flame propagation was recorded by a high-speed digital camera and spectral measurements were used to determine the temperature of the condensed emitters in the flame. The measured flame speeds and quenching distances were in good agreement with previously developed one-dimensional, dust flame model where the particles are assumed to burn in a diffusive mode and heat losses are described on a volumetric basis. However, a significant drop of the ratio of flame speeds in helium and argon mixtures was observed for finer 3 μm particles and was attributed to a transition from the combustion controlled by diffusion for larger particles to kinetically controlled burning of micron-size particles. In helium mixtures, the lower flame temperatures measured in suspensions of fine particles in comparison to larger particles reinforces this assumption.     

辐射传热对微重力环境下预混火焰传播特性的影响

1引言在火焰中，辐射过程是一种重要的传热方式。对该过程尽可能精确的计算，对于改进燃烧设备的设计、改善设备的运行性能十分有益。在正常重力环境下，与其它的释热现象相比，预混火焰中的辐射热损失十分微弱，因而，过去对预混火焰的分析中，往往忽略了辐射热损失的影响。近年来，对微重力（ug）环境下的预混火焰的研究结果表明，可燃极限与＃s最小点火能无关，自媳灭火焰（SEFs）发生时；其释放的能量比通常观察到的点火极限时的能量大几个数量级山，因此火焰伸张并不能解释“g环境下观察到的实验结果，辐射热损失可能是影响＃g火焰可…     

An experimental realization of an unstrained, planar diffusion flame

A unique burner was constructed to experimentally realize a one-dimensional unstrained planar non-premixed flame, previously considered only in idealized theoretical models. One reactant, the fuel mixture in the current experiments, is supplied through a porous plug at the bottom of the combustion chamber and flows vertically up towards the horizontal flame. The crux of the design is the introduction of the oxidizer from above in such a way that its diffusion against the upward product flow is essentially one-dimensional, i.e., uniform over the burner cross-section. This feature was implemented by introducing the oxidizer into the burner chamber from the top through an array of 625 closely spaced hypodermic needles, and allowing the hot products to escape vertically up through the space between the needles. Due to the injection of oxidizer through discrete tubes, a three-dimensional “injection layer” exists below the exit plane of the oxidizer supply tubes. Experimental evidence suggests that this layer is thin and that oxidizer is supplied to the flame by 1-D counterdiffusion, producing a nearly unstrained flame. To characterize the burner, flame position measurements were conducted for different compositions and flowrates of H₂–CO₂ and O₂–CO₂ mixtures. The measured flame locations are compared to an idealized one-dimensional model in which only diffusion of oxidizer against the product flow is considered. The potential of the new burner is demonstrated by a study of cellular structures forming near the extinction limit. Consistent with previous investigations, cellular instabilities are shown to become more prevalent as the initial mixture strength and/or the Damköhler number are decreased. As the extinction limit is approached, the number of cells was observed to decrease progressively.     

The role of unequal diffusivities in ignition and extinction fronts in strained mixing layers

We have studied flame propagation in a strained mixing layer formed between a fuel stream and an oxidizer stream, which can have different initial temperatures. Allowing the Lewis numbers to deviate from unity, the problem is first formulated within the framework of a thermo-diffusive model and a single irreversible reaction. A compact formulation is then derived in the limit of large activation energy, and solved analytically for high values of the Damköhler number. Simple expressions describing the flame shape and its propagation velocity are obtained. In particular, it is found that the Lewis numbers affect the propagation of the triple flame in a way similar to that obtained in the studies of stretched premixed flames. For example, the flame curvature determined by the transverse enthalpy gradients in the frozen mixing layer leads to flame-front velocities which grow with decreasing values of the Lewis numbers.

The analytical results are complemented by a numerical study which focuses on preferential-diffusion effects on triple flames. The results cover, for different values of the fuel Lewis number, a wide range of values of the Damköhler number leading to propagation speeds which vary from positive values down to large negative values     

Diffusive-thermal instabilities of diffusion flames: onset of cells and oscillations

A comprehensive stability analysis of planar diffusion flames is presented within the context of a constant-density model. The analysis provides a complete characterization of the possible patterns that are likely to be observed as a result of differential and preferential diffusion when a planar flame becomes unstable. A whole range of physical parameters is considered, including the Lewis numbers associated with the fuel and the oxidizer, the initial mixture fraction, and the flow conditions. The two main forms of instability are cellular flames, obtained primarily in fuel-lean systems when the Lewis numbers are generally less than one, and planar pulsations, obtained in fuel-rich systems when the Lewis numbers are generally larger than one. The cellular instability is predominantly characterized by stationary cells of characteristic dimension comparable to the diffusion length, but smaller cells that scale on the reaction zone thickness are also possible near extinction conditions. The pulsating instability is characterized by planar oscillations normal to the flame sheet with a well-defined frequency comparable to the reciprocal of the diffusion time; high-frequency modes are also possible just prior to extinction. The analysis also alludes to other possible patterns, such as oscillating cellular structures, which result from competing modes of instability of comparable and/or disparate scales. The expected pattern depends of course on the underlying physical parameters. Consequently, stability boundaries have been identified for the onset of one or another form of the instability. The conditions for the onset of cellular and pulsating flames, as well as the predicted cell size and the frequency of oscillations, compare well with the experimental record.     

Flame–wall interaction effects on the flame root stabilization mechanisms of a doubly-transcritical LO2/LCH4 cryogenic flame

High-fidelity numerical simulations are used to study flame root stabilization mechanisms of cryogenic flames, where both reactants (O₂ and CH₄) are injected in transcritical conditions in the geometry of the laboratory scale test rig Mascotte operated by ONERA (France). Simulations provide a detailed insight into flame root stabilization mechanisms for these diffusion flames: they show that the large wall heat losses at the lips of the coaxial injector are of primary importance, and require to solve for the fully coupled conjugate heat transfer problem. In order to account for flame–wall interaction (FWI) at the injector lip, detailed chemistry effects are also prevalent and a detailed kinetic mechanism for CH₄ oxycombustion at high pressure is derived and validated. This kinetic scheme is used in a real-gas fluid solver, coupled with a solid thermal solver in the splitter plate to calculate the unsteady temperature field in the lip. A simulation with adiabatic boundary conditions, an hypothesis that is often used in real-gas combustion, is also performed for comparison. It is found that adiabatic walls simulations lead to enhanced cryogenic reactants vaporization and mixing, and to a quasi-steady flame, which anchors within the oxidizer stream. On the other hand, FWI simulations produce self-sustained oscillations of both lip temperature and flame root location at similar frequencies: the flame root moves from the CH₄ to the O₂ streams at approximately 450 Hz, affecting the whole flame structure.     

Interactions of flame balls

Flame ball interactions are numerically investigated in a reaction–diffusion system characterized by single-step Arrhenius kinetics and radiative heat losses. It is found that the interactions of two neighbouring flame balls are characterized by two distinct regimes – a repulsion regime and an attraction regime, depending upon the separation distance. The two regimes join at a critical separation distance, which corresponds to an unstable equilibrium state. For supercritical separation distances, the two flame balls repel and drift apart from each other; whereas for sub-critical separation distances, they move towards each other and eventually merge into a single stationary flame ball. In this connection, flame ball interactions are found to exhibit a qualitatively reverse character in comparison with the well-known van der Waals curve which characterizes intermolecular forces.     

Flame spread and interactions in an array of thin solids in low-speed concurrent flows

Flame spread in an array of thin solids in low-speed concurrent flows was investigated and numerical solved. A previous steady, two-dimensional flame-spread model with flame radiation was employed and adapted in this work. The flame structures of spreading flames between parallel solids were demonstrated and some of the features were presented, including flow channelling effect and flame radiation interactions. The channelling effect is caused by flow confinement by the presence of the other solids; the flows through the hot combustion gases are accelerated downstream drastically. Radiation interactions between flames and solids contributed to a less heat-loss system, and radiation re-absorption by flames resulted in a larger flame with higher temperature, which increased the conductive heat fluxes to the solids and flame spread rate. Consequently, the extinction limit for the interacting flames is extended beyond the low-speed quenching limit for a single flame. The influence of the separation distance on the flame spread rate was also studied, which exhibits a non-monotonic behaviour. At larger separation distance, the flame spread rate increases with decreasing the separation distance owing to the channelling effect and radiation interactions. However, at very small separation distance, the flame spreading rate decreases with decreasing the distance because of the limited space for thermal expansion and flow résistance between solids.