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.     

Experimental comparison of opposed and concurrent flame spread in a forced convective microgravity environment

Flame spread experiments in both concurrent and opposed flow have been carried out in a 5.18-s drop tower with a thin cellulose fuel. Flame spread rate and flame length have been measured over a range of 0–30 cm/s forced flow (in both directions), 3.6–14.7 psia, and oxygen mole fractions 0.24–0.85 in nitrogen. Results are presented for each of the three variables independently to elucidate their individual effects, with special emphasis on pressure/oxygen combinations that result in earth-equivalent oxygen partial pressures (normoxic conditions). Correlations using all three variables combined into a single parameter to predict flame spread rate are presented. The correlations are used to demonstrate that opposed flow flames in typical spacecraft ventilation flows (5–20 cm/s) spread faster than concurrent flow flames under otherwise similar conditions (pressure, oxygen concentration) in nearly all spacecraft atmospheres. This indicates that in the event of an actual fire aboard a spacecraft, the fire is likely to grow most quickly in the opposed mode as the upstream flame spreads faster and the downstream flame is inhibited by the vitiated atmosphere produced by the upstream flame. Additionally, an interesting phenomenon was observed at intermediate values of concurrent forced flow velocity where flow/flame interactions produced a recirculation downstream of the flame, which allowed an opposed flow leading edge to form there.     

Stabilization, propagation and instability of tribrachial triple flames

A tribrachial (or triple) flame is one kind of edge flame that can be encountered in nonpremixed mixing layers, consisting of a lean and a rich premixed flame wing together with a trailing diffusion flame all extending from a single point. The flame could play an important role on the characteristics of various flame behaviors including lifted flames in jets, flame propagation in two-dimensional mixing layers, and autoignition fronts. The structure of tribrachial flame suggests that the edge is located along the stoichiometric contour in a mixing layer due to the coexistence of all three different types of flames. Since the edge has a premixed nature, it has unique propagation characteristics. In this review, the propagation speed of tribrachial flames will be discussed for flames propagating in mixing layers, including the effects of concentration gradient, velocity gradient, and burnt gas expansion. Based on the tribrachial edge structure observed experimentally in laminar lifted flames in jets, the flame stabilization characteristics including liftoff height, reattachment, and blowout behaviors and their buoyancy-induced instability will be explained. Various effects on liftoff heights in both free and coflow jets including jet velocity, the Schmidt number of fuel, nozzle diameter, partial premixing of air to fuel, and inert dilution to fuel are discussed. Implications of edge flames in the modeling of turbulent nonpremixed flames and the stabilization of turbulent lifted flames in jets are covered.     

Opposed flame spread over folded PMMA plate with various internal angles

The effect of the internal angle on downward flame spread over a thick folded plate is experimentally investigated in this study. The lateral side of a thermoplastic plate is cut at desired angles and two of these plates are welded to form a single folded sample. All the faces other than the front and two 5-mm areas of the front face from each side were coated to inhibit the combustion. Experiments are conducted for various folded plates of different angles, 60°, 90°, 120°, and 180°. Following ignition at the upper edge of the sample, the opposed flame spread on the front face is observed and the flame spread rate at various positions is quantified by image analysis. The flame spreads more rapidly at the folding edge, while the other parts then accelerate to catch up with the corner spread and, eventually, all the parts across the width achieve the same flame spread rate as the folding edge. This result indicates that the flame spread rate at the folding edge is the characteristic value which represents the steady-state of the system of interest. A simple model is developed considering change of heated volume against the flame and change of the induced flow velocity due to the geometry. The former effect is formulated from geometrical consideration in the vicinity of the edge, while the latter is formulated based on an experimental fact that the flame height is inversely proportional to the internal angle. A prediction formula of the flame spread rate at the folding edge is established by modifying the conventional one for the flat plate. The calculated flame spread rate shows reasonably good agreement with the experimental data. This study helps fundamental understanding of the flame spread behavior of practical combustibles such as pillars or rods with various cross-sectional shapes.     

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.     

Effect of velocity gradient on propagation speed of tribrachial flames in laminar coflow jets

The effect of velocity gradient on the propagation speed of tribrachial flame edge has been investigated experimentally in laminar coflow jets for propane fuel. It was observed that the propagation speed of tribrachial flame showed appreciable deviations at various jet velocities in high mixture fraction gradient regime. From the similarity solutions, it was demonstrated that the velocity gradient varied significantly during the flame propagation. To examine the effect of velocity gradient, detail structures of tribrachial flames were investigated from OH LIF images and Abel transformed images of flame luminosity. It was revealed that the tribrachial point was located on the slanted surface of the premixed wing, and this slanted angle was correlated with the velocity gradient along the stoichiometric contour. The temperature field was visualized qualitatively by the Rayleigh scattering image. The propagation speed of tribrachial flame was corrected by considering the direction of flame propagation with the slanted angle and effective heat conduction to upstream. The corrected propagation speed of tribrachial flame was correlated well. Thus, the mixture fraction gradient together with the velocity gradient affected the propagation speed.     

Flame spread across surfaces of PBX 9501

There is little flame spread data for homogeneous energetic materials and no data for nitramines. We report the results of flame spread experiments of PBX 9501 (HMX (cyclotetramethylenetetranitramine) based explosive). The horizontal flame spread rate, S_f, is of the same order of magnitude as normal deflagration and varies nearly as the square root of pressure, as our scaling analysis presented here predicts. In the vertical orientation, the flame propagation downward was observed to be slightly faster than horizontal flame spread, presumably because of the melt layer flowing downward on the sample. In an accident scenario, a charge may be fractured or the surface roughened. Consequently, we also examined the effect of roughness. Minor roughness created by explosives machining was found to have a negligible affect on flame spread. However, more significant roughness can increase the rate between two and three times over normal flame spread for the conditions considered here. In addition we examine the effect of sample edges and configuration. Corners result in more favorable heat loss and therefore affect flame spread rate. We argue that the increased spread rate on edges and rough surfaces is because of favorable heat transfer convergence.     

Structure of propagating edge diffusion flames in hydrocarbon fuel jets

Direct numerical simulations with a C₃-chemistry model have been performed to investigate the transient behavior and internal structure of flames propagating in an axisymmetric fuel jet of methane, ethane, ethylene, acetylene, or propane in normal earth gravity (1g) and zero gravity (0g). The fuel issued from a 3-mm-i.d. tube into quasi-quiescent air for a fixed mixing time of 0.3 s before it was ignited along the centerline where the fuel–air mixture was at stoichiometry. The edge of the flame formed a vigorously burning peak reactivity spot, i.e., reaction kernel, and propagated through a flammable mixture layer, leaving behind a trailing diffusion flame. The reaction kernel broadened laterally across the flammable mixture layer and possessed characteristics of premixed flames in the direction of propagation and unique flame structure in the transverse direction. The reaction kernel grew wings on both fuel and air sides to form a triple-flame-like structure, particularly for ethylene and acetylene, whereas for alkanes, the fuel-rich wing tended to merge with the main diffusion flame zone, particularly methane. The topology of edge diffusion flames depend on the properties of fuels, particularly the rich flammability limit, and the mechanistic oxidation pathways. The transit velocity of edge diffusion flames, determined from a time series of calculated temperature field, equaled to the measured laminar flame speed of the stoichiometric fuel–air mixtures, available in the literature, independent of the gravity level.     

Numerical studies of curved stationary flames in wide tubes

The nonlinear problem of the propagation of curved stationary flames in tubes of different widths is studied by means of direct numerical simulation of the complete system of hydrodynamic equations including thermal conduction, viscosity, fuel diffusion and chemical kinetics. While only a planar flame can propagate in a narrow tube of width smaller than half of the cut–off wavelength determined by the linear theory of the hydrodynamic instability of a flame front, in wider tubes stationary curved flames propagate with velocities considerably larger than the corresponding velocity of a planar flame. It is shown that only simple ‘single-hump’ slanted stationary flames are possible in wide tubes, and ‘multi–hump’ flames are possible in wide tubes only as a nonstationary mode of flame propagation. The stability limits of curved stationary flames in wider tubes and the secondary Landau–Darrieus instability are investigated. The dependence of the velocity of the stationary flame on the tube width is studied. The analytical theory describes the flame reasonably well when the tube width does not exceed some critical value. The dynamics of the flame in wider tubes is shown to be governed by a large–scale stability mechanism resulting in a highly slanted flame front. In wide tubes, the skirt of the slanted flame remains smooth with the length of the skirt and the flame velocity increasing progressively with the increase of the tube width above the second critical value. Results of the analytical theory and numerical simulations are discussed and compared with the experimental data for laminar flames in wide tubes.     

Stabilization mechanism of lifted flame edge in the near field of coflow jets for diluted methane

The stabilization mechanism of lifted flames in the near field of coflow jets has been investigated experimentally and numerically for methane fuel diluted with nitrogen. The lifted flames were observed only in the near field of coflow jets until blowout occurred in the normal gravity condition. To elucidate the stabilization mechanism for the stationary lifted flames of methane having the Schmidt number smaller than unity, the behavior of the flame in the buoyancy-free condition, and unsteady propagation characteristics after ignition were investigated numerically at various conditions of jet velocity. It has been found that buoyancy plays an important role for flame stabilization of lifted flames under normal gravity, such that the flame becomes attached to the nozzle in microgravity. The stabilization mechanism is found to be due to the variation of the propagation speed of the lifted flame edge with axial distance from the nozzle in the near field of the coflow as compared to the local flow velocity variation at the edge.     

Spherical turbulent flame propagation of pulverized coal particle clouds in an O2/N2 atmosphere

The present study aims to clarify the effects of turbulence intensity and coal concentration on the spherical turbulent flame propagation of a pulverized coal particle cloud. A unique experimental apparatus was developed in which coal particles can be dispersed homogeneously in a turbulent flow field generated by two fans. Experiments on spherical turbulent flame propagation of pulverized coal particle clouds in a constant volume spherical chamber in various turbulence intensities and coal concentrations were conducted. A common bituminous coal was used in the present study. The flame propagation velocity was obtained from an analysis of flame propagation images taken using a high-speed camera. It was found that the flame propagation velocity increased with increasing flame radius. The flame propagation velocity increases as the turbulence intensity increases. Similar trends were observed in spherical flames using gaseous fuel. The coal concentration has a weak effect on the flame propagation velocity, which is unique to pulverized coal combustions in a turbulent field. These are the first reports of experimental results for the spherical turbulent flame propagation behavior of pulverized coal particle clouds. The results obtained in the present study are obviously different from those of previous pulverized coal combustion studies and any other results of gaseous fuel combustion research.     

Estimation of laminar flame speeds using axisymmetric bunsen flames: Molecular transport effects

Intricacies associated with the estimation of laminar flame speed using the axisymmetric Bunsen flame technique were assessed, through parametric direct numerical simulations. The study involved methane-air mixtures at atmospheric pressure and temperature, and both the flame cone angle and flame surface area methods were utilized to estimate the laminar flame speeds based on conditions used in recent relevant experimental studies. The results provided insight into the details of the flame structure and allowed for the assessment of various non-idealities and the attendant uncertainties associated with the estimation of laminar flame speeds. Additionally, molecular transport effects were investigated by altering the fuel diffusivity, in order to evaluate its impact on the flame structure and propagation under the presence of negative stretch. The modification of fuel diffusivity was found to affect the burning rate as stretch varies. Under fuel rich conditions, decreasing the fuel diffusivity was found to have an opposite effect on the heat release and thus the burning rate, when compared to positively stretched flames that have been investigated recently in a similar manner. The reported results are expected to provide guidance in flame propagation experiments using the convenient Bunsen flame method at near-atmospheric or elevated pressures, as well as insight into the effects of negative stretch that has, compared to positive, attracted less attention in past studies.     

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.     

Modelling of lifted turbulent diffusion flames in a channel mixing layer by the flame hole dynamics

The partial quenching structure of turbulent diffusion flames in a turbulent mixing layer is investigated by the method of flame hole dynamics as an effort to develop a prediction model for the turbulent flame lift off. The essence of the flame hole dynamics is derivation of the random walk mapping, from the flame-edge theory, which governs expansion or contraction of the quenching holes initially created by the local quenching events. The numerical simulation for the flame hole dynamics is carried out in two stages. First, a direct numerical simulation is performed for a constant-density fuel–air channel mixing layer to obtain the background turbulent flow and mixing fields, from which a time series of two-dimensional scalar-dissipation-rate array is extracted. Subsequently, a Lagrangian simulation of the flame hole random walk mapping, projected to the scalar dissipation rate array, yields a temporally evolving turbulent extinction process and its statistics on partial quenching characteristics. In particular, the probability of encountering the reacting state, while conditioned with the instantaneous scalar dissipation rate, is examined to reveal that the conditional probability has a sharp transition across the crossover scalar dissipation rate, at which the flame edge changes its direction of propagation. This statistical characteristic implies that the flame edge propagation instead of the local quenching event is the main mechanism controlling the partial quenching events in turbulent flames. In addition, the conditional probability can be approximated by a heavyside function across the crossover scalar dissipation rate.     

An investigation of oscillating instabilities in deflagrations with edges

We examine the Lewis-number-greater-than-1 stability of a deflagration sitting on a porous-plug burner with an inert coflow. The flame edges generated by the coflow influence the stability, and this influence is examined. Very wide flames display the same stability characteristics as unbounded flames (flames sans edges), but for moderately wide flames the instability is suppressed. A new two-dimensional instability can occur for narrow flames. There is a range of mass fluxes for which a monotonic decrease in burner (flame) width generates a transition from unstable flames to stable flames, to unstable flames, to quenching. The insertion of a cold probe into the combustion field can stabilize an unstable flame or destabilize a stable flame, depending on the point of insertion.     

On the role of radiation and dimensionality in predicting flow opposed flame spread over thin fuels

In this work a flame-spread model is formulated in three dimensions to simulate opposed flow flame spread over thin solid fuels. The flame-spread model is coupled to a three-dimensional gas radiation model. The experiments [1] on downward spread and zero gravity quiescent spread over finite width thin fuel are simulated by flame-spread models in both two and three dimensions to assess the role of radiation and effect of dimensionality on the prediction of the flame-spread phenomena. It is observed that while radiation plays only a minor role in normal gravity downward spread, in zero gravity quiescent spread surface radiation loss holds the key to correct prediction of low oxygen flame spread rate and quenching limit. The present three-dimensional simulations show that even in zero gravity gas radiation affects flame spread rate only moderately (as much as 20% at 100% oxygen) as the heat feedback effect exceeds the radiation loss effect only moderately. However, the two-dimensional model with the gas radiation model badly over-predicts the zero gravity flame spread rate due to under estimation of gas radiation loss to the ambient surrounding. The two-dimensional model was also found to be inadequate for predicting the zero gravity flame attributes, like the flame length and the flame width, correctly. The need for a three-dimensional model was found to be indispensable for consistently describing the zero gravity flame-spread experiments [1] (including flame spread rate and flame size) especially at high oxygen levels (>30%). On the other hand it was observed that for the normal gravity downward flame spread for oxygen levels up to 60%, the two-dimensional model was sufficient to predict flame spread rate and flame size reasonably well. Gas radiation is seen to increase the three-dimensional effect especially at elevated oxygen levels (>30% for zero gravity and >60% for normal gravity flames).     

Numerical study of sporadic combustion waves in straight channels of different diameters

The dynamics of flames propagating in straight channels filled with a stationary low-Lewis-number premixed gas mixture is studied numerically. A method for determining the propagation velocity of a sporadic combustion wave consisted of separate flame spots is proposed. Dependencies of the sporadic combustion wave propagation velocity, the residual fuel concentration and the number of flame spots on the channel size and the value of radiation heat losses are obtained. Analysis of numerical results show that for the channels of diameter exceeding some value the number of separate cup-like fragments constituting sporadic combustion wave is proportional to the channel cross-sectional area. At smaller diameters, the number of flame spots changes insignificantly and is one or two. It is shown that one of the universal characteristics of the sporadic combustion wave depending only on mixture properties but independent on system geometry is the area necessary to accommodate one reacting spot. Flame velocity which is another fundamental combustion characteristic is found to be almost independent on channel size starting from some critical diameter. This diameter, however, depends on mixture properties or radiative heat loss intensity and corresponds to the sporadic flame containing from several to ten reacting spots. Thus, the main properties of sporadic combustion waves in wide channels can be determined by numerical modeling of the flame propagation in the relatively narrow channels in which the flame consists of 1–10 cup-like fragments.     

Opposed-flow flame spread in microgravity-theoretical prediction of spread rate and flammability map

The spread rate formulas of de Ris in the thermal regime of opposed-flow flame spread are inarguably the most well-known formulas in the flame spread literature. Similar easy-to-use formulas are lacking in all other regimes of flame spread. This paper presents a simplified analysis leading to the development of closed-form expressions for spread rate for both thin and thick fuels in the microgravity regime of opposed-flow flame spread. The resulting formulas, expressed in terms of the thermal limit of spread rate and a radiation number that can be evaluated from the known parameters of the problem, are shown to reproduce the experimentally and numerically observed trends quite well at both limits of fuel thickness. These formulas are utilized to develop quantitative criterion to delineate thin and thick fuels in the microgravity and thermal regimes. The transition between the microgravity and thermal regimes is also explored. The flammability maps, derived from the spread rate expressions, are the first of their kind, establishing fuel thickness as one of the critical parameters.