An apparatus-independent extinction strain rate in counterflow flames

Resistance to extinction by stretch is a key property of any flame, and recent work has shown that this property controls the overall structure of several important types of turbulent flames. Multiple definitions of the critical strain rate at extinction (ESR) have been presented in the literature. However, even if the same definition is used, different experiments report different extinction strain rates for flames burning the same fuel-air mixture at very similar temperatures using similarly constructed opposed-flow instruments. Here we show that at extinction, all these flames are essentially identical, so one would expect that each would be assigned the same value of a parameter representing its intrinsic resistance-to-stretch-induced-extinction, regardless of the specifics of the experimental apparatus. A similar situation arises in laminar flame speed measurements since different apparatuses could result in different strain rate distributions. In that instance, the community has agreed to report the unstretched laminar flame speed, and methods have been developed to translate the experimental (stretched) flame speed into a universal unstretched laminar flame speed. We propose an analogous method for translating experimental measurements for stretch-induced extinction into an unambiguous and apparatus-independent quantity (ESR_∞) by extrapolating to infinite opposing burner separation distance. The uniqueness of the flame at extinction is shown numerically and supported experimentally for twin premixed, single premixed, and diffusion flames at Lewis numbers greater than and less than one. A method for deriving ESR_∞ from finite-boundary experimental studies is proposed and demonstrated for methane and propane experimental diffusion and premixed single flame data. The two values agree within the range of ESR differences typically observed between experimental measurements and simulation results for the traditional ESR definition.     

Analytical predictions of shapes of laminar diffusion flames in microgravity and earth gravity

Flame shape is an important observed characteristic of flames that can be used to scale flame properties such as heat release rates and radiation. Flame shape is affected by fuel type, oxygen levels in the oxidiser, inverse burning and gravity. The objective of this study is to understand the effect of high oxygen concentrations, inverse burning, and gravity on the predictions of flame shapes. Flame shapes are obtained from recent analytical models and compared with experimental data for a number of inverse and normal ethane flame configurations with varying oxygen concentrations in the oxidiser and under earth gravity and microgravity conditions. The Roper flame shape model was extended to predict the complete flame shapes of laminar gas jet normal and inverse diffusion flames on round burners. The Spalding model was extended to inverse diffusion flames. The results show that the extended Roper model results in reasonable predictions for all microgravity and earth gravity flames except for enhanced oxygen normal diffusion flames under earth gravity conditions. The results also show trends towards cooler flames in microgravity that are in line with past experimental observations. Some key characteristics of the predicted flame shapes and parameters needed to describe the flame shape using the extended Roper model are discussed.     

Experimental measurements of two-dimensional planar propagating edge flames

The study of edge flames has received increased attention in recent years. This work reports the results of a recent study into two-dimensional, planar, propagating edge flames that are remote from solid surfaces (called here, “free-layer” flames, as opposed to layered flames along floors or ceilings). They represent an ideal case of a flame propagating down a flammable plume, or through a flammable layer in microgravity. The results were generated using a new apparatus in which a thin stream of gaseous fuel is injected into a low-speed laminar wind tunnel thereby forming a flammable layer along the centerline. An airfoil-shaped fuel dispenser downstream of the duct inlet issues ethane from a slot in the trailing edge. The air and ethane mix due to mass diffusion while flowing up towards the duct exit, forming a flammable layer with a steep lateral fuel concentration gradient and smaller axial fuel concentration gradient. We characterized the flow and fuel concentration fields in the duct using hot wire anemometer scans, flow visualization using smoke traces, and non-reacting, numerical modeling using COSMOSFloWorks. In the experiment, a hot wire near the exit ignites the ethane-air layer, with the flame propagating downwards towards the fuel source. Reported here are tests with the air inlet velocity of 25 cm/s and ethane flows of 967-1299 sccm, which gave conditions ranging from lean to rich along the centerline. In these conditions the flame spreads at a constant rate faster than the laminar burning rate for a premixed ethane-air mixture. The flame spread rate increases with increasing transverse fuel gradient (obtained by increasing the fuel flow rate), but appears to reach a maximum. The flow field shows little effect due to the flame approach near the igniter, but shows significant effect, including flow reversal, well ahead of the flame as it approaches the airfoil fuel source.     

The rate of expansion of spherical flames

In this paper we investigate the acceleration of the expansion of premixed spherical flames and evolution of the cellular patterns on their surfaces. An asymptotic model is used for the simulations and a spectral numerical algorithm is employed to study flames over large time intervals. Numerous numerical experiments indicate that for large enough time the acceleration of a two-dimensional expanding flame slows down but the expansion rate is still able to reach values significantly exceeding the burning rate of an exactly circular flame. The importance of the effect of forcing was also confirmed and the validity of simulations of sectors of circular flame fronts was studied in order to justify prospective use of the Fourier spectral model for three-dimensional spherical flames.     

A computational study of soot formation and flame structure of coflow laminar methane/air diffusion flames under microgravity and normal gravity

A numerical study is conducted of methane–air coflow diffusion flames at microgravity (μg) and normal gravity (1g), and comparisons are made with experimental data in the literature. The model employed uses a detailed gas phase chemical kinetic mechanism that includes PAH formation and growth, and is coupled to a sectional soot particle dynamics model. The model is able to accurately predict the trends observed experimentally with reduction of gravity without any tuning of the model for different flames. The microgravity sooting flames were found to have lower temperatures and higher volume fraction than their normal gravity counterparts. In the absence of gravity, the flame radii increase due to elimination of buoyance forces and reduction of flow velocity, which is consistent with experimental observations. Soot formation along the wings is seen to be surface growth dominated, while PAH condensation plays a more major role on centreline soot formation. Surface growth and PAH growth increase in microgravity primarily due to increases in the residence time inside the flame. The rate of increase of surface growth is more significant compared to PAH growth, which causes soot distribution to shift from the centreline of the flame to the wings in microgravity.     

Effect of flame thickness variation on the mass burning rate of premixed counterflow flames with an oscillating strain rate

The mass-based stretch rate is used to study the response of premixed axisymmetric counterflow flames subject to an oscillating strain rate. Integral analysis is used to estimate the mass burning rate of the oscillating counterflow flames. From this study it can be concluded that the flame responds in a nonlinear manner. With an increase of the applied strain frequencies, it is found that unsteady stretch effects arising due to flame thickness variations become significant and the mass-based stretch rate is able to capture these nonlinear effects. The inclusion of these unsteady stretch effects in the mass-based stretch helps the integral analysis to predict the mass-burning rate of oscillating flames more accurately.     

Simulations of normal and inverse laminar diffusion flames under oxygen enhancement and gravity variation

Steady-state global chemistry calculations for 20 different flames were carried out using an axisymmetric Computational Fluid Dynamics (CFD) code. Computational results for 16 flames were compared with flame images obtained at the NASA Glenn Research Center. The experimental flame data for these 16 flames were taken from Sunderland et al. [4 Sunderland, P. B., Krishnan, S. S and Gore, J. P. 2004. Effects of oxygen enhancement and gravity on normal and inverse laminar jet diffusion flames. Combust. Flame, 136: 254–256. [Crossref], [Web of Science ®] , [Google Scholar]] which included normal and inverse diffusion flames of ethane with varying oxidiser compositions (21, 30, 50, 100% O₂ mole fraction in N₂) stabilised on a 5.5 mm diameter burner. The test conditions of this reference resulted in highly convective inverse diffusion flames (Froude numbers of the order of 10) and buoyant normal diffusion flames (Froude numbers ～0.1). Additionally, six flames were simulated to study the effect of oxygen enhancement on normal diffusion flames. The enhancement in oxygen resulted in increased flame temperatures and the presence of gravity led to increased gas velocities. The effect of gravity-variation and oxygen enhancement on flame shape and size of normal diffusion flames was far more pronounced than for inverse diffusion flames. For normal-diffusion flames, their flame-lengths decreased (1 to 2 times) and flames-widths increased (2 to 3 times) when going from earth-gravity to microgravity, and flame height decreased by five times when going from air to a pure oxygen environment.     

The importance of thermal radiation transfer in laminar diffusion flames at normal and microgravity

The importance of radiation heat loss in laminar and turbulent diffusion flames at normal gravity has been relatively well recognized in recent years. There is currently lack of quantitative understanding on the importance of radiation heat loss in relatively small scale laminar diffusion flames at microgravity. The effects of radiation heat transfer and radiation absorption on the structure and soot formation characteristics of a coflow laminar ethylene/air diffusion flame at normal- and microgravity were numerically investigated. Numerical calculations were conducted using GRI-Mech 3.0 combustion chemistry without the NO_x mechanism and complex thermal and transport properties, an acetylene based soot formation model, and a statistical narrow-band correlated-k non-grey gas radiation model. Radiation heat transfer and radiation absorption in the microgravity flame were found to be much more important than their counterparts at normal gravity. It is important to calculate thermal radiation transfer accurately in diffusion flame modelling under microgravity conditions.     

Influence of advective heat flux on extinction scalar dissipation rate and velocity in negative edge flames

A counterflow flame geometry, which has previously been experimentally shown to produce stable negative edge flames, was studied using numerical simulations. In this geometry, the flame edge is formed off the counterflow centreline owing to a local increase in scalar dissipation rate. Hot products from the stable nonpremixed flame on the centreline flow through the edge at velocities of ～ 1–5 m/s. The size of the counterflow burner and the gas flowrates are varied in the simulations to alter the flame strength and velocity at the flame edge. The advection of products through the edge is shown to extend the flame extinction to higher scalar dissipation rates than required for centreline extinction. For high velocities, the scalar dissipation rate required for flame extinction can be related to the centreline extinction value by considering only the effect of energy addition to the flame edge via advection. However, for lower edge flame velocities, the effects of increased thermal and species diffusion through the edge must also be included. Since the advection at the edge is a product of both the local velocity and temperature gradient, a single correlation between the scalar dissipation rate and the negative edge flame velocity does not exist.     

Conditional moment closure and transient flamelet modelling for detailed structure and NO x formation characteristics of turbulent nonpremixed jet and recirculating flames

This study has been mainly motivated to assess computationally and theoretically the conditional moment closure (CMC) model and the transient flamelet model for the simulation of turbulent nonpremixed flames. These two turbulent combustion models are implemented into the unstructured grid finite volume method that efficiently handles physically and geometrically complex turbulent reacting flows. Moreover, the parallel algorithm has been implemented to improve computational efficiency as well as to reduce the memory load of the CMC procedure. Example cases include two turbulent CO/H₂/N₂ jet flames having different flow timescales and the turbulent nonpremixed H₂/CO flame stabilized on an axisymmetric bluff-body burner. The Lagrangian flamelet model and the simplified CMC formulation are applied to the strongly parabolic jet flame calculation. On the other hand, the Eulerian particle flamelet model and full conservative CMC formulation are employed for the bluff-body flame with flow recirculation. Based on the numerical results, a detailed discussion is given for the comparative performances of the two combustion models in terms of the flame structure and NO _x formation characteristics.     

The role of radiative losses in self-extinguishing and self-wrinkling flames

We have developed a general theory of non-adiabatic premixed flames that is valid for flames of arbitrary shape that fully accounts for the hydrodynamic and diffusive-thermal processes, and incorporates the effects of volumetric heat losses. The model is used to describe aspects of experimentally observed phenomena of self-extinguishing (SEFs) and self-wrinkling flames (SWFs), in which radiative heat losses play an important role. SEFs are spherical flames that propagate considerable distances in sub-limit conditions before suddenly extinguishing. Our results capture many aspects of this phenomenon including an explicit determination of flame size and propagation speed at quenching. SWFs are hydrodynamically unstable flames in which cells spontaneously appear on the flame surface once the flame reaches a critical size. Our results yield expressions of the critical flame size at the onset of wrinkling and expected cell size beyond the stability threshold. The various possible burning regimes are mapped out in parameter space.     

Pressure and temperature dependence of soot in highly controlled counterflow ethylene diffusion flames

Soot volume fraction and dispersion index were measured by pyrometry in a series of highly controlled counterflow diffusion flames, with peak temperatures, T_max, spanning a few hundred degrees and pressure covering the 0.1–0.8 MPa range. An unprecedented level of control was implemented by selecting flames with a self-similar structure to ensure that the normalized temperature-time history experienced by the reactants was the same, regardless of pressure. The self-similarity was verified by suitably rescaling the transverse coordinate with respect to a characteristic diffusion length. At constant T_max, the soot volume fraction increases approximately by two orders of magnitude as the pressure is raised from 1 atm to 4 atm, and by one to two additional orders of magnitude with an additional doubling of the pressure to 8 atm. At constant pressure, the soot load spans two to three orders of magnitude and soot formation exhibits increased sensitivity to temperature as the pressure is raised. Soot inception occurs near the flame, with an increase in soot concentration that becomes steeper at higher T_max. The increase is accompanied by a decrease in the dispersion exponent that is suggestive of dehydrogenation and aging of the particles and is sharper at higher T_max. Soot experiences continuous growth in a monotonically decreasing temperature field until it is convected away radially at the stagnation plane, with essentially no opportunity for oxidation. Evidence of two distinct mechanisms for soot formation was found: the classic high temperature, high activation energy process affecting soot formed in the vicinity of the flame and followed by dehydrogenation; and a relatively low-temperature, zero activation energy process, associated with the increase in volume fraction at low-temperatures in proximity of the stagnation plane. The latter is tentatively attributed to dimerization of aromatics, as revealed by the concurrent increase in the dispersion index corresponding to an increase in the particle hydrogen content.     

Ignition and extinction of low molecular weight esters in nonpremixed flows

An experimental and kinetic modeling study is carried out to characterize combustion of low molecular weight esters in nonpremixed, nonuniform flows. An improved understanding of the combustion characteristics of low molecular weight esters will provide insights on combustion of high molecular weight esters and biodiesel. The fuels tested are methyl butanoate, methyl crotonate, ethyl propionate, biodiesel, and diesel. Two types of configuration – the condensed fuel configuration and the prevaporized fuel configuration – are employed. The condensed fuel configuration is particularly useful for studies on those liquid fuels that have high boiling points, for example biodiesel and diesel, where prevaporization, without thermal breakdown of the fuel, is difficult to achieve. In the condensed fuel configuration, an oxidizer, made up of a mixture of oxygen and nitrogen, flows over the vaporizing surface of a pool of liquid fuel. A stagnation-point boundary layer flow is established over the surface of the liquid pool. The flame is stabilized in the boundary layer. In the prevaporized fuel configuration, the flame is established in the mixing layer formed between two streams. One stream is a mixture of oxygen and nitrogen and the other is a mixture of prevaporized fuel and nitrogen. Critical conditions of extinction and ignition are measured. The results show that the critical conditions of extinction of diesel and biodiesel are nearly the same. Experimental data show that in general flames burning the esters are more difficult to extinguish in comparison to those for biodiesel. At the same value of a characteristic flow time, the ignition temperature for biodiesel is lower than that for diesel. The ignition temperatures for biodiesel are lower than those for the methyl esters tested here. Critical conditions of extinction and ignition for methyl butanoate were calculated using a detailed chemical kinetic mechanism. The results agreed well with the experimental data. The asymptotic structure of a methyl butanoate flame is found to be similar to that for many hydrocarbon flames. This will facilitate analytical modeling, of structures of ester flames, using rate-ratio asymptotic techniques, developed previously for hydrocarbon flames.     

Investigation of soot sensitivity to strain rate in ethylene counterflow soot formation oxidation flames

Soot sensitivity to strain rate is mainly responsible for soot formation intermittence in practical combustion devices. This work provides a fundamental study on soot formation in Soot Formation Oxidation (SFO) counterflow flames at varying strain rates. While the problem has been extensively studied in Soot Formation (SF) configurations, where the dominant process is nucleation, investigations remain scarce in the corresponding SFO cases. In the latter, the high temperatures and strong oxidative environments make the surface reactions prevail over nucleation. The work provides a new dataset for ethylene SFO flames in a wide range of strain rates and sheds light on the main processes concurring in determining soot strain rate sensitivity in such conditions. In particular, the peak of soot volume fraction (SVF) is primarily controlled by surface growth and oxidation. The latter becomes progressively more dominant on the side of the SVF distribution toward the oxidizer nozzle, where the presence of oxidizing agents is significant. The soot mechanism adopted predicts a SVF distribution and sensitivity to strain rate in agreement with experimental data. The latter is found similar to corresponding SF cases, although soot loads in the two configurations differ by almost an order magnitude, and the SVF sensitivity is known to be more accentuated for lower soot loads. A deeper investigation revealed that the nucleation process through dimerizations primarily controls the SVF sensitivity, providing the onset of soot necessary for further growth. Then, the latter tends to reduce SVF sensitivity depending on its impact. PAH sensitivities mostly agree with theoretical observation even though further validations on the kinetic mechanism are needed to improve its predictions in lean conditions. The simplistic yet effective model based on the hybrid method of moments and the employment of a reduced kinetic mechanism makes the approach amenable for turbulent computational fluid dynamic (CFD) simulations.     

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.     

Analysis of steady state polydisperse counterflow spray diffusion flames in the large Stokes number limit

A new mathematical analysis is presented of certain aspects of the behavior of opposed flow polydisperse spray diffusion flames within the framework of a model in which large slip is permitted between the droplets and their host surroundings. The sectional approach is used to model the polydisperse spray. Operating conditions are identified under which the inverses of sectional Stokes numbers are small spray-related parameters to be used in a perturbation analysis of the liquid phase governing equations. The steady state equations and their solutions are similar in form to the equivalent equations considered in previous work of the authors in which dynamical equilibrium of the droplets with the carrier phase was assumed. However, here there is much more mathematical complexity involved in the spray equations solution. A hybrid Eulerian–Lagrangian approach is also suggested to get an insight into the phenomenon of reversal in the motion of the droplets that has been reported in independent experimental and computational research. Computed results based on the analytical solutions up to the 1st order of approximation reveal the influence of large droplet slip on the droplets velocity field and on the spray diffusion flame’s thermal field, for which appreciable heterogeneous combustion can occur under the operating conditions considered.     

Prediction of NO in turbulent diffusion flames using Eulerian particle flamelet model

The combustion characteristics for the turbulent diffusion flames using the unsteady flamelet concept have been numerically investigated. The Favre-averaged Navier–Stokes equations are solved by a finite volume method of SIMPLE type that incorporates the laminar flamelet concept with a modified k ? ε turbulence model. The NO formation is estimated by solving the Eulerian particle transport equations in a postprocessing mode. Two test problems are considered: CH₄/H₂/N₂ jet flame and CH₄/H₂ stabilised bluff body flame. The temperature and species profiles are well captured by the flamelet model. Two different chemical mechanisms (GRI 2.11 and 3.0) give nearly identical results for temperature and species except NO. The GRI 3.0 gives significantly higher NO levels compared to the GRI 2.11. This is mainly attributed to the difference in NO formation by the prompt mechanism. The NO formation is sensitive to the number of flamelet particles. The NO levels for two test flames do not change when the flamelet particle number exceeds six.     

Application of the Lagrangian CMC method in elliptic bluff body and swirl flames

The Lagrangian CMC method was implemented in the open source programme OpenFOAM and applied to turbulent nonpremixed bluff body and swirl flames. Lagrangian CMC is more efficient than Eulerian CMC with the number of Lagrangian flame groups much less than the number of computational cells for Eulerian CMC equations in general. It is based on the conditional flame structure depending on the residence time of the fuel of fixed Lagrangian identity from the nozzle. According to sensitivity study the injected fuel was divided into ten flame groups according to the injection sequence with the resulting conditional profiles between those by ISR and Eulerian CMC. Minor deviation from Eulerian CMC was attributed to the flame structure that is difficult to be characterised by the residence time only in elliptic recirculating flows of the bluff body and swirl flames. The Eulerian and Lagrangian CMC showed the same trend of deviation from measurements for conditional temperature, H₂O, OH, CO and H₂ mass fractions. The significant deviation of H₂ was due to uncertainty in the reaction chemistry, as observed in the previous works based on other reaction mechanisms for methane and methanol.     

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.     

Computational and experimental study of JP-8, a surrogate, and its components in counterflow diffusion flames

Non-sooting counterflow diffusion flames have been studied both computationally and experimentally, using either JP-8, or a six-component JP-8 surrogate mixture, or its individual components. The computational study employs a counterflow diffusion flame model, the solution of which is coupled with arc length continuation to examine a wide variety of inlet conditions and to calculate extinction limits. The surrogate model includes a semi-detailed kinetic mechanism composed of 221 gaseous species participating in 5032 reactions. Experimentally, counterflow diffusion flames are established, in which multicomponent fuel vaporization is achieved through the use of an ultrasonic nebulizer that introduces small fuel droplets into a heated nitrogen stream, fostering complete vaporization without fractional distillation. Temperature profiles and extinction limits are measured in all flames and compared with predictions using the semi-detailed mechanism. These measurements show good agreement with predictions in single-component n-dodecane, methylcyclohexane, and iso-octane flames. Good agreement also exists between predicted and measured variables in flames of the surrogate, and the agreement is even better between the experimental JP-8 flames and the surrogate predictions.