Graham Dixon-Lewis

A computational model of the structure and extinction of strained, opposed flow, premixed methane-air flames

The application of laminar flamelet concepts to turbulent flame propagation requires a detailed understanding of strained laminar flames. Here we use numerical methods, including are-length continuation, to simulate the complex chemical kinetic behavior in premixed methane-air flames that are stabilized between two opposed-flow burners. We predict both the detailed structure and the extinction limits for these flames over a range of fuel-air mixtures. In addition to discussing the flame structure, a sensitivity analysis provides further insight on the chemical behavior near extinction. Finally, we discuss the comparison of the predictions with Laws experimental extinction data. An especially important aspect of this comparison is the recognition that fluid mechanical aspects of the traditional strained-flame analysis are deficient in representing experiments such as Laws. We develop and solve a new system of equations that is able to describe the experiments much more accurately.

Structure of laminar flames

The one-dimensional formulation of the opposed flow strained flame problem, starting from the cylindrical Navier-Stokes equations, is described and compared with the older, Hiemenz potential flow formulation. The eigenvalue in the newer formulation is shown to be a stress on the fluid, and it is shown that the Navier-Stokes equations reduce to expressions for (i) the pressure gradient profile normal to the flame, and (ii) the strain rate profile in the variable density system. The basic features of hydrogen and hydrocarbon flame chemistry are reviewed, and the importance of the temperature T i at which the system becomes effectively chain branching is demonstrated in the context of flame extinction. It is suggested that in a sense T i fulfils the function of an ignition temperature. The responses of flames to applied stresses are discussed for diffusion flames, and for premixed flames in both the symmetric back-to-back and the asymmetric unburnt-to-burnt configurations. It is shown that, in opposed flow systems of fixed geometry and finite dimensions, the behaviour of the symmetric back-to-back flames which are not too close to the inlet nozzles are for practical purposes characterized entirely by the applied stress. However, because of viscous effects, particularly near the nozzles, this applied stress cannot be measured directly with precision. Repercussions on extinction limit measurements, and on indirect determinations of one-dimensional burning velocities, are indicated. The use of measurements on expanding spherical flames for the determination of burning velocity is briefly discussed, as also are the effects of flow configuration on the stress and strain rate profiles at extinction.

The oxidation of graphite powder in flame reaction zones

The rate of burning of small concentrations of fine graphite powder has been measured in a flat, laminar weak methane-air flame at sub-atmospheric pressure. Measurements were obtained with a laser doppler system, that not only measured particle velocities, but also particle concentrations and size distributions through the flame. Particle temperatures were measured by the two colour method and gas temperatures with thermocouples. An appreciable increase in the oxidation rate was observed in the flame reaction zone, attributable to the reaction zone transient species, O, H, and OH. A computational study of the flame, with comprehensive chemical kinetics and detailed representation of the transport fluxes, yielded the concentrations of all species through the flame. The observed rates of graphite oxidation are kinetically explained in terms of rates of reaction of all species with graphite. The observed elevations of particle above gas temperature in the reaction zone are higher than would be expected if the heating were due only to reactions in which the carbon surface was attacked. Amongst other possible explanations there is that of heating by exothermic radical recombination on the carbon surface.

Laminar flame structure and burning velocities of premixed methanol-air

Burning velocities at an initial temperature of 323 K, over a range of equivalence ratios from 0.7 to 1.3 and a range of pressures from 0.089 to 0.25 atm, have been measured for flat, premixed, laminar, methanol-air adiabatic flames on a burner. Spatial profiles of gas temperature, velocity, and concentrations of CH{sub 3}OH, O{sub 2}, H{sub 2}, CO{sub 2}, and CO also were measured at equivalence ratios of 0.85, 1.0, and 1.25 at 0.089 atm and an initial temperature of 323K. These measurements are compared with the predictions of two chemical kinetic schemes. The first, Scheme A, involves the breakdown of CH{sub 3}OH to CH{sub 2}OH alone. The second, Scheme B, involves production of CH{sub 2}OH and CH{sub 3}O. Both models also yield values of laminar burning velocity over the wider pressure range of 0.1 to 10 atm and at equivalence ratios of 0.85, 1.0, and 1.25. This paper reports that comparisons of these values with those of experiment shows Scheme B to be superior and this extends also to the spatial concentration profiles of CO and CO{sub 2} measured on the burner.

Lean flammability limits and laminar burning velocities of CH4-air-graphite mixtures and fine coal dusts

Abstract Gas temperature, reactant concentrations, graphite burnup, and burning velocity have been measured close to the lean limit of CH 4 -air-graphite mixtures on a low-pressure, premixed laminar flame burner. The graphite dust was of about 4 μm diameter. These experiments suggest a gas temperature of 1550 K at the lean flammability limit. This is the basis of a chemical kinetic model for fine coal dust combustion that assumes CH 4 to be devolatilized from coal and gas phase reaction to be dominant. Computed relationships of the dependence of lean limit coal concentration on the proportion of volatile matter in the coal agree well with those of experiments. The model also yields values of laminar burning velocity over a wide range of coal concentrations and volatile contents.

Structure of laminar premixed carbonmethane-air flames and ultrafine coal combustion

Abstract Premixtures of graphite-methane-air have been burned in a flat laminar flame at a pressure of 0.16 atm. A fluidized bed was employed to entrain graphite particles of 4 μm diameter. The extended reaction zone enabled reliable measurements to be obtained of species concentrations, gas velocities, and temperatures. The measurements to a large degree validated the predictions of a one-dimensional mathematical model of the combustion. The model couples detailed carbon particle and gas-phase chemical kinetics, as well as radiative energy exchanges. Some limitations arise because the experimental flame is not truly one dimensional and also because of uncertainties in the chemical kinetics of the richer mixtures. Allowance for radiation improves the accuracy of the predictions, although its influence is not great. Earlier predictions that active radicals in the gas-phase catalyze the char oxidation are supported. The general validity of the model is the springboard for a related model for ultrafine coal combustion. This retains the coupled kinetics and radiation, but adds a coal devolatilization rate to the kinetic scheme and assumes the volatiles to consist entirely of methane, which mixes rapidly with the surrounding gas. Despite these restrictive assumptions, the model reveals important aspects of coal flame combustion and predicts a laminar burning velocity close to that measured.

Oxidation rates of carbon particles in methane-air flames

Abstract Small amounts of graphite were introduced into a laminar, flat, low-pressure, fuel-lean methane-air flame. The mean initial diameter of the particles was about 4 μm. The rate of oxidation of the particles was observed by optical means as they passed through the flame. In addition, measurements of particle and gas temperatures were used to estimate the heat released by the surface reaction. The results were found to be reasonably consistent with those found from more direct measurements of particle size. The study showed a very considerable enhancement (by a factor of up to 5) of the carbon oxidation rates in the main gaseous flame reaction zone as compared with the burned gas region, thus indicating the importance of the flame radicals O, OH, and H in controlling the oxidation. Consideration of the collision frequencies with the external surface area showed, however, that the bulk gas-phase concentrations of the radicals were insufficient for their direct diffusion and reaction to be able to account for the enhancement. At the same time consideration of the particle properties excludes porosity effects as a means of rate enhancement. An outline mechanism whereby the radicals catalyze attack by molecular oxygen is proposed. The CO arising from the char oxidation mechanism is simultaneously coupled with the other reactions involved in the CH 4 -air kinetic scheme. Numerical simulation shows the mechanism to be consistent with the observations if radical recombination at the particle surface is also included.

Laminar Premixed Flame Extinction Limits. I Combined Effects of Stretch and Upstream Heat Loss in the Twin-Flame Unburnt-to-Unburnt Opposed Flow Configuration

Numerical methods have been used to examine the combined effects of stretch and localized upstream heat loss on the properties of a stoichiometric laminar premixed methane-air flame. A symmetric unburnt-to-unburnt opposed flow configuration was investigated, in which fresh combustible premixture was discharged towards the stagnation plane from identical coaxial plug flow nozzles maintained at constant temperature, and separated by a fixed distance. A continuation method was used in tandem with Newton solutions for individual flame structures, in order to study the flame behaviour as the stretch rate (or nozzle inlet velocity) was varied. High- and low-stretch extinction limits were observed as positions of vertical tangency on the steady-state solution curves of flame property versus stretch rate. The complete series of solutions between these positions formed a set of isolae with both stable and unstable branches. The chemical behaviour at the limits and along both branches is discussed, with particular emphasis on the behaviour near the low-temperature low-stretch-rate limit. The importance of changes not only in the size of the radical pool, but also in the ratio of hydrocarbon (CH3) to non-hydrocarbon (H, O and OH) species therein, is demonstrated both near the limits and along the unstable solution branch. Attention is drawn to the significance of the conclusions in the context of flame extinguishment. The presentation and discussion of the flame behaviour is preceded by a full description of the computational approach.

Aspects of laminar premixed flame extinction limits

Numerical methods have been used to examine (1) the combined effects of stretch and upstream heatloss on the properties of a stoichiometric, laminar, pre-mixed methane-air flame, and (2) the combined effects of stretch and an extended, radiative heat loss on the properties of a fuel-lean methane-air flame, equivalence ratio Σ=0.57. Appropriate opposed flow configurations were investigated in both cases. In the first case, fresh gas was discharged towards the stagnation plane from identical, coaxial, plug flow nozzles maintained at constant temperature and separated by a fixed distance. Continuation methods were used in tandem with Newton solutions to study the flame behaviour as the stretch rate (or nozzle inlet velocity) was varied. High and low stretch extinction limits were observed as positions of vertical tangency on the steady-state solution curves of flame property vs stretch rate. The complete series of solutions between these positions formed a limit cycle with both stable and unstable branches. The chemical behaviour at the limits and along the unstable branch is discussed. The effect of radiative losses on the fuel-lean flame was studied in the unburnt-to-unburnt (UTU)configuration as above, but also in the unburnt-to-burnt (UTB) configuration where the ignited unburnt stream is opposed by a stream of its own equilibrium combustion products. If the flame is adiabatic, the product stream is input at the adiabatic equilibrium flame temperature. Such a system shows no abrupt extinction limits. On the other hand, if the radiative “sink” temperature is below some critical value, then, irrespective of the magnitude of the heat loss rate on a volumetric basis, the unburnt-to-burnt system will show abrupt extinctions if the stretch rate is increased sufficiently. Because of extremely slow numerical convergence, the numerical investigation of these limits for the methane-air system is not yet complete. However, such an investigation is in progress, and this combination of stretch and radiative loss effects is clearly of importance in relation to behaviour at composition limits of flammability.

Laminar premixed flame extinction limits. II Combined effects of stretch and radiative loss in the single flame unburnt-to-burnt and the twin-flame unburnt-to-unburnt opposed flow configurations

Numerical methods have been used to examine the effects of (a) stretch alone, and (b) a combination of stretch and radiative loss, on the properties and extinction limits of methane–air flames near the lean flammability limit. Two axisymmetric opposed flow configurations were examined: (i) a single flame, unburnt-to-burnt (UTB) system in which fresh reactant is opposed by a stream of its own combustion products at the unburnt temperature, and (ii) a symmetric unburnt-to-unburnt (UTU) configuration where twin flames are supported back to back, one on each side of the stagnation plane. The maximum temperatures achieved in the UTB system are always away from the stagnation plane. For a fixed sufficiently sub-adiabatic product stream temperature, increasing flame stretch or gaseous radiative emissivity, or a combination of both, will augment downstream conductive heat loss, leading to a reduction in Tmax and eventually to an abrupt extinction if the loss rate is sufficiently large. The UTU system is more complex, and offers the additional possibility of purely stretch-induced extinctions where the flames are forced together back-to-back so that radiative loss is restricted to upstream of the maximum temperature. Extinction in these cases occurs by straightforward truncation of the hot sides of the reaction zones. At sufficiently low stretch, near and at the standard flammability limit, radiative loss makes a major contribution to the overall extinction mechanism in both configurations. The detailed effects of flame stretch on extinction behaviour depend on the diffusion characteristics within the near-limit mixtures, in particular the Lewis number, Le, of the deficient component. The effect of high stretch is always to attenuate the composition range of flammability. However, for Le<1 this range is extended at low to moderate stretch, particularly in the UTU situations where downstream radiative loss is not present at extinction. Lewis number effects for a global methane–air chemistry, and with assumed Le≥1, are discussed in the light of numerical results previously presented by Ju et al. (Ju et al. 1998 Combust. Flame 113, 603–614).