Forman A. Williams

The asymptotic structure of stoichiometric methaneair flames

A C1-chain mechanism for methane flames is systematically reduced through steady-state and partial-equilibrium assumptions to the three-step mechanism I CH4+O2→CO+H2+H2O , II CO+H2O⇄CO2+H2 , III O2+2H2→2H2O , with rates that still contain the kinetic information of the elementary mechanism. A basic asymptotic structure for premixed stoichiometric methane flames is derived from this mechanism for pressures and temperatures sufficiently large that the Damkohler numbers of the second and third reactions are expected to be large. It turns out that the first reaction occurs in a thin fuel-consumption layer embedded between a chemically inert upstream layer and a broader (but still asymptotically thin) downstream layer where H2 and CO are oxidized. At the leading edge of the oxidation layer there is a nonequilibrium layer of the second reaction which tends to equilibrium downstream. The fuel-consumption layer is thin because the ratio of the rate coefficients of the reactions O2+H→klOH+O , CH4+H→kllCH3+H2 (which describe the competition of oxygen and fuel for the H atom) is small. The small parameter δ = k1[O2]o(k11[CH4]u) scales the fuel concentration within this layer; the subscripts o and u on the concentrations identify conditions at the layer and in the unburnt mixture, respectively. Since reaction 11 is fast, the fuel depletes the radicals, causing the upstream layer to be radical-free and therefore chemically inert. By using the basic structure to provide the orders of magnitude of concentrations of all intermediates, the influences of additional reactions are estimated and added to the kinetic scheme. Numerical calculations of flame velocities at various pressures and preheat temperatures are performed, and the range of validity of the assumptions is discussed. The asymptotic structure identified here relies entirely on competition between rate coefficients; the relevant activation energies are not large. Nevertheless, effective overall activation energies can be identified from the results. These activation energies are calculated and employed in exploring the relationship between the present asymptotic structure and activation-energy asymptotics.

Strained Premixed Laminar Flames Under Nonadiabatic Conditions

Abstract The method of activation energy asymptotics is used to describe the behavior and characteristics of nonadiabatic flamelets involving counterflowing reactants and products under the assumption of a unity Lewis number. For moderate and low rates of strain the results are analogous to those obtained in earlier applications of the method, namely reaction zones which are maintained in a first approximation by a diffusive-reactive balance. Indeed for low rates of strain many features of flamelet behavior are independent of the extent of the nonadiabaticity since the reaction zone is insulated from the stream of altered enthalpy by a diffusive-convective zone near the stagnation point. Two limiting processes are considered. One pertains to nearly adiabatic flamelets and exposes the principal qualitative results of this study. The second pertains to the full, nonadiabatic case. Flamelets with product streams having elevated enthalpies are shown to possess essentially the same features as the adiabatic fl...

A DISCUSSION OF TURBULENT FLAME STRUCTURE IN PREMIXED CHARGES

Propagation of turbulent flames in spark-ignition engines is considered from the viewpoint of the different possible regimes of premixed turbulent combustion. Nondimensional parameters defining known combustion regimes are reviewed, and numerical values of these parameters are estimated for both research and production engines. The reaction-sheet regime is inferred to apply at least for some operating conditions, and therefore literature on turbulent flame propagation in the reaction-sheet regime is reviewed. Implications of these results on interpretations of existing experimental observations of combustion in engine cylinders and on modeling of turbulent flame propagation in engines are discussed.

A simplified model of flame spread in an opposed flow along a flat surface of a semi-infinite solid

Abstract A flame-spread model is analyzed in which heat release occurs at the planar interface of two media, each of which moves with a different but constant velocity. The steady-state, two-dimensional equations for conservation of energy in each medium are solved subject to a prescribed temperature distribution on the downstream half of the interface and continuity of the normal heat flux on the upstream half. Differing thermal conductivities in normal and streamwise directions are allowed in each medium. The approach involves introduction of Fourier transforms in the streamwise coordinate and use of the Wiener-Hopf technique. The model is shown to be equivalent to that of de Ris with radiant transfer neglected and also may be interpreted in terms of distributed electrical or radiant heating without combustion. Parametric results are obtained for various heat fluxes and for spread rates. The study helps to improve understanding of mechanisms of flame spread under conditions controlled by heat transfer.

Effects of Oxygen on Soot Formation in Methane Diffusion Flames

Abstract The effect of small additions of oxygen to the fuel on formation of soot in methane-air diffusion flames was studied over a range of flow rates and of burner diameters. The flames studied were shorter than those of previous studies, purely blue or blue and yellow without soot escape. Heights of various distinctive features were measured, and composition and temperature profiles were obtained; the distinctive features include.onset and termination of visible emission of radiation and deposition of material on a quartz filament inserted into the flame. The results indicate negligible influences of oxygen addition and thereby suggest that ions from the primary mechanism CH+Orarr;CHO++e- are unimportant in soot formation in these flames. A simplified one-step kinetic model accounting for buoyancy and momentum was developed and employed to obtain estimates of overall rate parameters for flame attributes related to soot formation.

Observations on the combustion of boron slurry droplets in air

Abstract Single fiber-supported slurry droplets composed of boron in JP-10 were ignited and burned in room-temperature air. Initial droplet diameters ranged from 1.2 to 3.0 mm and initial boron weight fractions f from 0 to 0.7. It was observed that although the liquid fuel apparently burns completely the boron does not ignite under these experimental conditions. For the pure liquid the combustion is smooth with a measured burning-rate constant of 0.43 mm2/s. At low f there is periodic swelling of the droplet with mildly disruptive emission of gas from the interior; the severity of this irregularity is greatest for f ≈ 0.1 and negligible for f ≳ 0.2. For f ≲ 0.4 a reduction in droplet diameter, according to a d2 law, is observed for a period of time, followed by a burning period of essentially constant diameter. For f ≳ 0.5, the droplet diameter remains practically constant during combustion, although the measured burning time conforms to a d2 law. These observations are compared quantitatively with theoretical predictions and are found to agree within accuracies ranging from 10% to 25%.

Influences of two-phase flow in the deflagration of homogeneous solids

Theoretical analyses are developed for the deflagration of solids such as nitramines that experience exothermic reactions in liquid layers at their surfaces. Relative motion of gas and liquid in a two-phase region at the surface is considered, with influences of pressure gradients and of surface-tension gradients taken into account for the drops and bubbles. It is shown that these influences tend to produce gas velocities in excess of liquid velocities. Burning-rate expressions are derived by activation-energy asymptotics, with special attention paid to the role of interphase heat transfer.

Diffusional/Thermal Coupling and Intrinsic Instability of Solid Propellant Combustion

Abstract Intrinsic instability in the steady, planar deflagration of a homogeneous solid propellant is considered through an asymptotic analysis for large values of nondimensional overall activation energies for the surface pyrolysis and gas-phase combustion processes. It is shown that the previously known pulsating instability is essentially connected with condensed-phase pyrolysis, and that new instability phenomena, which are associated with intrinsic gas-flame instability and which are sensitive to the value of the gas-phase Lewis number and to the distance of the gas flame from the propellant surface, arise. These results are obtained by relaxing the usual assumptions of quasi-steadiness and quasi-planarity for the gas phase, so that the coupling of intrinsic diffusional/thermal instabilities in the gas and solid phases becomes an integral feature of the model. The steady, planar deflagration thus may be unstable not only to pulsating disturbances, but also to (time-independent, nonplanar) cellular p...

Some Implications of Recent Theoretical Studies in Turbulent Combustion

Nomenclature = coefficients in assumed probability density function, Eq. (14) = molecular diffusion coefficient = interior distribution for the probability density function of £ = enthalpy = step function = intermittency functions = extinction parameter, cf. Eq. (31) = length scale characterizing large eddies = probability density functions, single and multivariate = = turbulence Reynolds number, l/2(puZut/p) 1/2t/v0 - parameter for ordering reaction rates, cf.Eq. (17) = temperature = Cartesian velocity components = mass rate of production per unit volume of the /th species contribution to the production of the /th trace species from trace species, cf. Eqs. (21) and (22) = Cartesian coordinate = mass fraction of the /th species = mass fraction of the /th element = delta function = mass density = mixture variable, cf. Eq. (1) = dissipation terms = kinematic viscosity = viscosity coefficient

Premixed combustion in a vortex

An asymptotic analysis for large Peclet numbers has been performed in order to describe the roll-up of a premixed flame by a single vortex. In this limit the process consists of two steps: o 1) The fast-time inviscid roll-up of the flame surface as a passive surface into a spiral around the vortex. 2) The slow-time flame propagation between the spirals. Since the spirals are closer to each other towards the center of the vortex, the latter process leads to the development of a reacted core, similar to that found by Marble for diffusion flames. The growth rate of the reacted core is derived first in terms of a more global order-of-magnitude estimate, then a detailed mathematical analysis is performed to test the estimate. Its essential parts are a transformation to Lagrangian coordinates and an asymptotic analysis of the resulting equation. The flame propagation between the spirals is assumed to be quasi-stationary. The flames are stretched by the convective motion and may extinguish for Lewis numbers larger than unity. Finally, under an approximation of radial symmetry, the radial mass flow rate produced by gas expansion is calculated.