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.     

Homoclinic bifurcations in radiating diffusion flames

We analyse the dynamics of a model describing a planar diffusion flame with radiative heat losses incorporating a single step kinetic using timestepping techniques for Lewis number equal to one. We construct the full bifurcation diagram with respect to the Damköhler number including the branches of oscillating solutions. Based on this analysis we found, for the first time, homoclinic bifurcations that mark the abrupt disappearance of the nonlinear oscillations near extinction as reported in experiments.     

Effects of electrodes and imposed flow on forced ignition in laminar premixed hydrogen/air mixtures with large Lewis number

Compared to quiescent premixed reactants, forced ignition of flowing/turbulent premixed reactants is expected to be more difficult because of increased dissipation of the deposited energy. However, the counterintuitive turbulence-facilitated ignition (TFI) has been observed in recent experiments for mixtures with large Lewis number, Le. The mechanisms behind TFI are still not well understood and this study aims to interpret a part of the TFI mechanisms through considering electrodes and imposed flow in the simulations of forced ignition in hydrogen/air mixtures. The imposed flow emulates the local turbulent effects around the electrodes which might blow the ignition kernel away from the electrodes. Since TFI occurs only for mixtures with large Le (e.g., lean hydrocarbon/air or rich H₂/air mixture), a fuel-rich (ϕ=5.1) H₂/air mixture with Le≈2.3 is investigated to reduce computational cost and consider more factors that may lead to TFI. Similar to TFI observed in experiments, the flow-facilitated ignition is observed for H₂/air with ϕ=5.1 and Le≈2.3 when the electrodes have a small gap distance. The detailed effects of including electrodes on forced ignition of quiescent and flowing mixtures are explored. It is found that the existence of electrodes not only induces heat loss but also affects the shape and global curvature/stretch of the ignition kernel. The heat loss to the electrodes is demonstrated to play an important role for the ignition of mixtures with large Le. Compared to quiescent mixtures, considering an imposed flow normal to the electrodes can blow the flame kernel away from the cold electrodes. Such movement of the ignition kernel can greatly reduce both the heat loss to the electrodes and flame curvature/stretch, and thereby promote the ignition in mixtures with large Le. These results help to understand the underlying mechanisms for the TFI observed in experiments.     

On the stability of one-dimensional diffusion flames established between plane,parallel, porous walls

A one-dimensional, non-premixed flame stability analysis is undertaken.Oscillatory and cellular flame instabilities are identified by a careful studyof the numerically calculated eigenvalues of the linearized system of equations. The numerical investigation details the critical locations for changes in flame behaviour, as well as the critical values of variousparameters that affect flame stability. A critical Lewis number, greaterthan unity, is identified as the value where unstable oscillations maybegin to appear (Le?>?Le _c) and for which cellular flames can exist(Le?<?Le _c). Some prior discussions are clarified regarding theaforementioned critical values, as well as the role of convection inproducing flame instabilities. The methodology of the stability analysis isdiscussed in detail.     

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.     

Flames in narrow circular tubes

We examine an axi-symmetric deflagration located in a tube with thermally active walls. It is noted that the flame-in-tube configuration defines a classical edge-flame, a flame in a shear flow for which there is a water-shed solution for a critical value of the Damköhler number (D), ignition front solutions for larger values of D, and failure wave solutions for smaller values. We examine semi-infinite tubes with a heat flux imposed at the tube wall ends, to simulate experiments reported in the 30th Symposium. We identify parameters for which stable solutions are obtained at certain flow rates, but unstable solutions are generated at higher flow rates, followed by stable solutions at still higher flow rates. These solutions are consistent with the experimental record. Instability leads either to regular oscillations or to a violent process characterized by quenching and re-ignition.     

Structure and dynamic response of radiative diffusion flames

Nitrogen-diluted hydrogen burning in air is modeled numerically using a constant density and one-step reaction model in a plane two-dimensional counterflow configuration. An optically thin assumption is used to investigate the effects of radiation on the dynamics, structure, and extinction of diffusion flames. While there exist dual steady-state extinction limits for the 1D radiative flame response, it is found that as the 1D radiative extinction point is approached the 1D low-stretch diffusion flame exhibits oscillatory response, even with sub-unity Lewis number fuel. These radiation-induced limit cycle oscillations are found to have increasing amplitude and decreasing frequency as the stretch rate is reduced. Flame oscillation eventually leads to permanent extinction at the stretch rate which is larger than the steady-state radiative extinction value. Along the 1D radiative response curve, the transition from 1D flame to 2D structure and the differences in the resulting 2D flame patterns are also examined using a variety of initial profiles, with special emphasis on the comparison of using the initial profiles with and without a flame edge. Similar to the previous studies on the high-stretch adiabatic edge flames using the same configuration, the high-stretch radiative flames are found to resist 1D blow-off quenching through various 2D structures, including propagating front and steady cellular flames for initial profiles with and without flame edges. For all initial profiles studied, the low-stretch radiative flames are also found to exhibit different 2D flame phenomena near the 1D radiative extinction limit, such as transient cellular structures, steady cellular structures, and pulsating ignition fronts. Although the results demonstrate the presence of low-stretch and high-stretch 2D bifurcation branches close to the corresponding 1D extinction limits irrespective of the initial profile used, particular 2D flame structures in certain stretch rate range are initial profile dependent. The existence of two-dimensional flame structures beyond the 1D steady-state radiative extinction limit suggests that the flammable range is expanded as compared to that predicted by the 1D model. Hence, multi-dimensional flame patterns need to be accounted for when determining the flammability limits for a given system.     

The differential diffusion effect of the intermediate species on the stability of premixed flames propagating in microchannels

The propagation of premixed flames in adiabatic and non-catalytic planar microchannels subject to an assisted or opposed Poiseuille flow is considered. The diffusive–thermal model and the well-known two-step chain-branching kinetics are used in order to investigate the role of the differential diffusion of the intermediate species on the spatial and temporal flame stability. This numerical study successfully compares steady-state and time-dependent computations to the linear stability analysis of the problem. Results show that for fuel Lewis numbers less than unity, Le_F < 1, and at sufficiently large values of the opposed Poiseuille flow rate, symmetry-breaking bifurcation arises. It is seen that small values of the radical Lewis number, Le_Z, stabilise the flame to symmetric shape solutions, but result in earlier flashback. For very lean flames, the effect of the radical on the flame stabilisation becomes less important due to the small radical concentration typically found in the reaction zone. Cellular flame structures were also identified in this regime. For Le_F > 1, flames propagating in adiabatic channels suffer from oscillatory instabilities. The Poiseuille flow stabilises the flame and the effect of Le_Z is opposite to that found for Le_F < 1. Small values of Le_Z further destabilise the flame to oscillating or pulsating instabilities.     

Numerical analyses of deflagration initiation by a hot jet

Numerical simulations of axisymmetric reactive jets with one-step Arrhenius kinetics are used to investigate the problem of deflagration initiation in a premixed fuel–air mixture by the sudden discharge of a hot jet of its adiabatic reaction products. For the moderately large values of the jet Reynolds number considered in the computations, chemical reaction is seen to occur initially in the thin mixing layer that separates the hot products from the cold reactants. This mixing layer is wrapped around by the starting vortex, thereby enhancing mixing at the jet head, which is followed by an annular mixing layer that trails behind, connecting the leading vortex with the orifice rim. A successful deflagration is seen to develop for values of the orifice radius larger than a critical value a _c in the order of the flame thickness of the planar deflagration δ_L. Introduction of appropriate scales provides the dimensionless formulation of the problem, with flame initiation characterised in terms of a critical Damköhler number Δ_c=(a _c/δ_L)², whose parametric dependence is investigated. The numerical computations reveal that, while the jet Reynolds number exerts a limited influence on the criticality conditions, the effect of the reactant diffusivity on ignition is much more pronounced, with the value of Δ_c increasing significantly with increasing Lewis numbers . The reactant diffusivity affects also the way ignition takes place, so that for reactants with the flame develops as a result of ignition in the annular mixing layer surrounding the developing jet stem, whereas for highly diffusive reactants with Lewis numbers sufficiently smaller than unity combustion is initiated in the mixed core formed around the starting vortex. The analysis provides increased understanding of deflagration initiation processes, including the effects of differential diffusion, and points to the need for further investigations incorporating detailed chemistry models for specific fuel–air mixtures.     

Effect of Lewis number on premixed laminar lean-limit flames stabilized on a bluff body

In this paper, we present a study on the effect of Lewis number, Le, on the stabilization and blow-off of laminar lean limit premixed flames stabilized on a cylindrical bluff body. Numerical simulations and experiments are conducted for propane, methane and two blends of hydrogen with methane as fuel gases, containing 20% and 40% of hydrogen by volume, respectively. It is found that the Le?>?1 flame blows-off via convection from the base of the flame (without formation of a neck) when the conditions for flame anchoring are not fulfilled. Le?≤?1 flames exhibit a necking phenomenon just before lean blow-off. This necking of the flame front is a result of the local reduction in mass burning rates causing flame merging and quenching of the thin flame tube formed. The structure of these flames at the necking location is found to be similar to tubular flames. It is found that extinction stretch rates for tubular flames closely match values at the neck location of bluff-body flames of corresponding mixtures, suggesting that excessive flame stretch is directly responsible for blow-off of the studied Le?≤?1 flames. After quenching of the neck, the upstream part forms a steady and stable residual flame in the wake of the bluff body while the downstream part is convected away.     

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.     

Effects of fuel Lewis number on flame spread over solids

Using a detailed two-dimensional numerical model, a systematic investigation has been made to study the effect of fuel Lewis number (Le_F = α/D_F) and mass transfer on flame spread over thin solids. The fuel Lewis number affects the flame spread rates for both concurrent and opposed flames over thin fuels. The dependence of the flame spread rate on Le_F for these two spreading modes is, however, not the same. In opposed flame spreads (zero-gravity, self-propagation, and normal gravity downward propagation), the flame spread rate vs. Le_F curve is non-monotonic with a maximum value occurring at an intermediate value of Le_F = 0.5. In steady, concurrent spread in zero-gravity with low-speed flow and a constant flame length, the flame spread rate decreases with Le_F in a monotonic manner. By using the computational model as a tool, the effects of fuel mass diffusion perpendicular to and parallel with the solid surface are isolated to obtain more physical insight on the two-dimensional aspect of fuel mass transfer on flame spread. In addition, the model has also been used to decouple the solid evaporation process so that the fuel diffusion effect in the gas-phase can be isolated. Both of these theoretical exercises contribute to the understanding of mass transfer effects on the flame spreading phenomena over solids.     

Turbulent burning velocity and its related statistics of ammonia‐hydrogen‐air jet flames at high Karlovitz number: Effect of differential diffusion

To clarify the role of differential diffusion in highly turbulent premixed flames, a series of turbulent premixed ammonia/hydrogen/air flames were investigated using the NH-PLIF diagnostics. The investigated flames have almost the same laminar burning velocity, S_L, but are characterized by different Lewis number, Le, from 0.56 to 1.77. The Karlovitz number, Ka, of these flames ranges from 11 to 1052, and the turbulence intensity, u’/S_L, covers from 10 to 156. It is observed that the global consumption speed, S_T,GC/S_L, of sub-unity Le flames is much larger than that of super-unity Le flames at high Ka, indicating that the differential diffusion plays a significant role in highly turbulent flames. The flame surface density and the area ratio of turbulent flames with different Le are, however, similar under wide turbulent conditions. The stretch factor of sub-unity Le flames is estimated to be significantly larger than that of super-unity Le cases. The enhanced S_T,GC of sub-unity Le flames is suggested to be attributed to the promotion of local burning rates by the couple effect of differential diffusion and turbulent flame stretch within the flame brush, rather than the enlargement of flame surface area at high Ka. Furthermore, three correlations for the S_T,GC were developed based on Damkohler's second hypothesis with consideration of the Le effect. The correlation of S_T,GC/S_L ∼ (Re_T·Le^-2)^0.5 is further validated by using small-scale methane/air and large-scale ammonia/air flames at high Ka, where Re_T is turbulent Reynolds number. It suggests that the S_T,GC is roughly inversely proportional to the Le, and the differential diffusion effect should be included in the theoretical analysis and numerical simulation of highly turbulent flames.     

Effect of Le on criteria of transition to secondary acoustic instability of downward-propagating flame in a tube with controlled curvature induced by external laser

An experimental study is conducted to investigate the effect of Le on the transition to secondary acoustic instability when the curvature of the flame front in a tube is induced and controlled by using external laser irradiation. Once a downward-propagating flame in the primary acoustic instability region is exposed to a specific laser irradiation condition, the flame is transferred to the secondary acoustic instability region. The transition limit is decreased, that is, transition occurs is an easier manner, with increasing laser power input. While the flame propagates with increasing laser irradiation, the flame first exhibits a convex curvature owing to laser irradiation and then a concave structure is formed owing to buoyancy-induced flow. Two types of transition behavior caused by the concave structure and the convex structure are observed. The conflicting thermal-diffusive effect depending on Le leads to the differing transition behaviors. Based on an evaluation of the flame stretch effect attributed to the flame front curvature, it is confirmed that the Lewis number effect influences the transition criteria.     

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     

Lewis number effects on laminar and turbulent expanding flames of NH3/H2/air mixtures at elevated pressures

This study clarifies the effects of Lewis number (Le) on laminar and turbulent expanding flames of NH₃/H₂/air mixtures. The laminar burning velocity (S_L) and turbulent burning velocity (S_T) were measured using a medium-scale, fan-stirred combustion chamber with ammonia/hydrogen molar ratio (NH₃/H₂) of 50/50 and 80/20 under the maximum pressures of 5 atm. The lean laminar flame with NH₃/H₂ = 50/50 is significantly accelerated by the diffusional–thermal instability, which dominated the trend of S_T,c=0.1 with the equivalence ratio (ϕ). The lean normalized turbulent burning velocity (S_T/S_L) increases with the decrease of hydrogen content due to the weakening effects of S_L. However, the S_T/S_L reaches peak with hydrogen volumetric content less than 20% due to effects made by diffusional–thermal instability than S_L did. The turbulent flame of NH₃/H₂/air mixtures is characterized by self-similar acceleration propagation, and propagation with Le < 1 is faster. A modified correlation considering the effects of Le was proposed, as (d<r>/dt)/σS_L = 0.118(Re_T,flameLe⁻²)^0.57, which was able to predict not only the self-similar propagation of NH₃/H₂/air but also the previous syngas/air flames. The Kobayashi correlations modified by three kinds of Le power exponents were used to clarify the effects of Le by comparing their fitting parameters and predictive powers on experimental data and literature data. Similar pre-factors, power exponents and the goodness of fit (R²) were obtained with Le ranging from 0.58 to 1.62, which suggested that the determination of Le power exponent had no significant effect on the prediction accuracy of the S_T/S_L trend with data of Le near unity. This might be attributed to the fact that the variation ranges of the dimensionless number that characterizes the experimental conditions is much larger than that of the Le.     

Gravity effects on partially premixed flames: an experimental-numerical investigation

While premixed and nonpremixed microgravity flames have been extensively investigated, the corresponding literature regarding partially premixed flames (PPFs) is sparse. We report the first experimental investigation of burner-stabilized microgravity PPFs. Partially premixed flames with multiple reaction zones are established in microgravity on a Wolfhard–Parker slot burner in the 2.2 s drop tower at the NASA Glenn Research Center. Microgravity measurements include flame imaging, and thermocouple and radiometer data. Detailed simulations are also used to provide further insight into the steady and transient response of these flames to variations in g. The flame topology and interactions between the various reaction zones are strongly influenced by gravity. The flames widen substantially in microgravity. During the transition from normal to microgravity, the flame structure experiences a fast change and another relatively slower transient change. The fast response is due to the altered advection as the value of g is reduced, while the slow response is due to the changes in the diffusive fluxes. The radiative heat loss from the flames increases in microgravity. A scaling analysis based on a radiation Damköhler number is able to characterize the radiation heat loss.