Non-adiabatic Flame Research Articles

The structure and stability of nonadiabatic flame balls

Recent experiments in microgravity suggest the possibility of stationary spherical premixed flames (flame balls) in which the only fluxes are diffusional. We construct stationary solutions of this nature, starting with simple model equations and using activation energy asymptotics. Sufficiently large volumetric heat losses quench the flame, and for heat losses less than the quenching value there are two possible solutions, a small flame, and a large flame. For vanishing heat loss the small solution is identical to one constructed by Zeldovich, and is known to be unstable, whereas the large solution is characterized by a flame of infinite radius. We examine the linear stability of these stationary solutions, and show that all small flames are unstable to one-dimensional (radial) perturbations. Large flames are unstable to three-dimensional perturbations, but only if they have a radius greater than some critical value. Thus there is a band of large flames, lying between the quenching point and unstable flames, that are stable.

Analysis of a nonadiabatic flame propagating through gradients of fuel or temperature

Using the analytic techniques of large activation energy asymptotics applied to a slowly-varying flame, an equation is derived that describes the burning rate of an unsteady nonadiabatic flame traveling through shallow gradients in fuel concentration or temperature. Solutions of this equation show that (1) the transient burning rate responds more slowly to these gradients than does the local steady-state burning rate, (2) an unsteady flame in an inhomogeneous mixture propagates into a region where the mixture is outside of the homogeneous flammability limits predicted by the steady theory, and (3) the burning rate of the unsteady flame approaches zero at a finite position in the gradient, even with a single-step Arrhenius reaction mechanism. This behavior arises from the accumulation, of enthalpy in the preheat zone, which in turn arises from the differing rates of heat conduction and mass diffusion.

Theory of nonadiabatic flame propagation in dissociation equilibrium

Effects of dissociation equilibrium and heat loss on the structure and propagation of the one-dimensional laminar flame in the doubly-infinite domain have been studied using matched asymptotic analysis in the limit of large activation energy. Analytical solutions have been obtained with an explicit, expression for the burning rate eigenvalue as function of the dissociation and heat loss parameters. Results show that dissociation alone cannot cause extinction of an adiabatic flame. Extinction, however, is facilitated in the simultaneous presence of heat loss. Salient features of the structure of both the adiabatic and nonadiabatic flames are identified.

Interaction of Pulsating and Spinning Waves in Nonadiabatic Flame Propagation

We consider nonadiabatic premixed flame propagation in a long cylindrical channel. A steadily propagating planar flame exists for heat losses below a critical value. It is stable provided that the Lewis number and the volumetric heat loss coefficient are sufficiently small. At critical values of these parameters, bifurcated states, corresponding to time-periodic pulsating cellular flames, emanate from the steadily propagating solution. We analyze the problem in a neighborhood of a multiple primary bifurcation point. By varying the radius of the channel, we split the multiple bifurcation point and show that various types of stable periodic and quasi-periodic pulsating flames can arise as secondary, tertiary, and quaternary bifurcations. Our analysis describes several types of spinning and pulsating flame propagation which have been experimentally observed in nonadiabatic flames, and also describes additional quasi-periodic modes of burning which have yet to be documented experimentally.

The Extinction of Slowly-Varying Nonadiabatic Flames

Abstract Using the techniques of large activation energy asymptotics, we observe that a slowly-varying planar nonadiabatic flame will extinguish (1) as the burning rate approaches zero, rather than at finite burning rate as predicted by the steady theory, and (2) at a finite position, when subjected to a wide class of external stimuli. An example is given in which the external stimuli arises from either fuel or concentration variations ahead of the flame.

Shapes, Velocities and Propagation Limits of a Non-Adiabatic Cellular Flame

Abstract We study a non-linear evolution equation which describes a non-adiabatic flame near the propagation limit due to heat losses, and takes into account the cellular instability of thermal and diffusional origin: Using numerical integration and shooting methods, we show that: i) Heat loss induced regime multiplicity also exists for cellular fronts, even when the cell size is prescribed. ii) Extinction by heat losses still occurs when cells are present, but is shifted; the new limit changes with the cell size. iii) Cellularity widens the propagation range, the shift being larger for lighter fuels. iv) For a fixed lateral flame dimension, many steady cellular patterns coexist for the same heat loss intensity, each one having its own velocity and propagation limit.

Measurements of the structure of sooting laminar diffusion flames at elevated pressures

Measurements of the structure of sooting two-dimensional laminar ethylene-air diffusion flames have been made in the pressure range from 1.0 to 2.5 atmospheres. The effect of elevated pressure on soot formation was investigated through the use of light-scattering techniques to determine the soot volume fraction, particle size, and particle number density. At a fixed vertical location in the flame, maximum and integrated soot volume fractions increased approximately as the pressure raised to a power of 1.7±0.3, and the soot yield (mass of soot/mass of fuel) increased approximately as the pressure to a power of 0.7±0.3 This pressure dependence is larger than can be accounted for by variation in the stoichiometric adiabatic flame temperature with pressure, and is in the opposite direction from what would be predicted on the basis of the measured decrease in peak temperature with pressure in this non-adiabatic flame. Both the size and the number density of soot particles increased with pressure.

Influences of Upstream Versus Downstream Heat Loss/Gain on Stability of Premixed Flames

Abstract Influences of upstream versus downstream volumetric heat loss/gain on the linear stability of laminar premixed flames are investigated. A single-step irreversible reaction governed by Arrhenius-type rate law is considered within the framework of a diffusional-thermal stability model. The resulting dispersion relations show that while both upstream and downstream losses enhance the tendency towards instability, downstream loss is more effective in promoting instability. The characteristics of cellular as well as the travelling-wave type instabilities in the presence of heat loss/gain from either the downstream or upstream side of the flame have been determined. Also, the impact of these various modes of heat loss/gain on the rate of growth of the characteristic cell size of cellular flames is assessed. The dispersion relation describing the stability of non-adiabatic flames with a two-reactant chemical model is determined as being similar to that corresponding to the single-reactant model. The pra...

On the Stability of Nonadiabatic Flames

A linear stability analysis is carried out for the cellular instability of a nonadiabatic downward-propagating premixed flame. It is shown that if the molecular weight of the deficient reactant is sufficiently small, then an increase in heat loss may lead to destabilization of an adiabatically stable flame (i.e., a flame which is stable in the absence of heat losses).

Elongation of a nonadiabatic flame during combustion of mixed gases and volatile explosives

Elongation of a nonadiabatic flame during combustion of mixed gases and volatile explosives

Asymptotic analysis of non-adiabatic flames: Heat losses towards small inert particles

We study the propagation of a flame front into a heterogeneous mixture of dilute premixed reactive gas and small heat-conducting inert particles. Arrhenius kinetics are assumed for the reaction rate. The analysis is performed within the framework of a thermal-diffusional model for large values of the activation temperature of the reaction rate. First, steady propagations are studied. We show that: o (i) particles of small size (or heat capacity) act almost as a gaseous diluent: a monotonous flame speed versus particle concentration curve is obtained. (ii) with particle sizes exceeding well-defined critical values, up to three regimes are possible for the same fresh mixture. (iii) for particles with large thermal inertia, we again encounter the phenomenon of quenching by conductive losses towards isothermal bodies. In a second step, a linear stability analysis is performed by the normal modes method. We obtain the dispersion relation in terms of the Lewis number of the reactant, the activation temperature and the size and concentration of the particles, and show that: (iv) In case of multiple regimes, the intermediate ones are always unstable. (v) with a sufficiently high initial concentration of particles in the fresh mixture, the flame front always exhibits cellular instability. (vi) heavy particles promote the appearance of travelling waves, while light ones tend to suppress them.

Toward a second-law taxonomy of combustion processes

Combustion is the source of heat—or sensible enthalpy—in a vast range of processes. Efforts directed at making the use of energy as effective as possible must include the attempt to match the quality of energy supplied to the quality of energy required. The extent to which that match is achieved is reflected in the second-law performance of the process. The thermodynamic function exergy offers a convenient means of quantifying that performance. The second-law performance of several combustion processes has been analyzed in terms of the exergy subsidy which they require. Sample calculations have been carried out for methane burning in stoichiometric proportions with air. To facilitate the computation of the exergies, the reference potentials have been tabulated in terms of the ambient partial pressures of CO 2, H 2O, and O 2, and the K p 's of formation. The adiabatic flame of CH 4-air with dissociation requires an exergy subsidy of 286 MJ/kmol of CH 4 for an effectiveness of 0.68. When dissociation of combustion products is neglected, the reference potentials cancel in the calculation of exergy subsidies. This simplified model is applicable to stoichiometric and lean mixtures. The non-dissociating adiabatic flame has an effectiveness of 0.718. Non-dissociating non-adiabatic flames require an exergy subsidy ranging from 235 MJ/kmol in the limit of zero heat release at 2325 °K to 809 when heat is supplied at 298 °K. The flame in a well stirred reactor at 1764 °K requires an exergy subsidy of 294 MJ per kmol of CH 4 burned in it. The open diffusion flame uses up all the fuel exergy and has zero effectiveness. The thermodynamic benefits of replacing a pure fuel with “low-Btu gas” are minor unless the gas is flared or otherwise vented. The effect of increasing the heat transfer coefficient between the combustion stream and the process stream in an isothermal furnace is always to improve the effectiveness.

Linear stability analysis of nonadiabatic flames: Diffusional-thermal model

The method of matched asymptotic expansions, in terms of a suitably reduced activation energy, is applied to investigate the effects of heat losses on linear stability of a planar flame, which is governed by a one-step irreversible Arrhenius reaction. The density change associated with the heat release is neglected in order to eliminate the Landau hydrodynamic instability. Attention is focused on diffusional-thermal instability mechanisms. The dispersion relation is obtained in terms of the diffusive properties of the limiting reactant and of the heat-loss intensity. For a given loss intensity-less than the critical value leading to extinction-the two steady planar regimes have different stability properties: (1) the “slow” regimes (which do not reduce to the adiabatic one when the heat-loss intensity goes to zero) are shown to be always unstable; and (2) for the “fast” regimes (which include and generalize the adiabatic one) cellular structures are predicted to occur when the limiting component is sufficiently light. If the limiting component is moderately light, the “fast” regimes are stable and unstructured in nearly adiabatic conditions; however, they are destabilized by an increase of heat losses and must exhibit cells before the extinction limit is reached. Similarly, for mixtures involving a realistically heavy limiting component, our analysis predicts the appearance of transverse travelling waves near the extinction limit.

Stability of combustion of powder in a phenomenological model with nonadiabatic flame

A stability criterion for combustion of powder is obtained, taking into account the effect of the processes in the gas phase. It is shown that consideration of the effects of a nonadiabatic flame leads to the stability reserve of combustion being reduced and the natural frequency of vibrations being lowered. The effects thus found are physically explained by the radiation of a part of energy from the combustion zone with thermal and acoustic waves.

Boundary conditions of the downstream singularity in non-adiabatic flames

Boundary conditions of the downstream singularity in non-adiabatic flames

Flame Propagation in Free-Radical-Containing Solids at Low Temperatures

A nonadiabatic theory of flames is formulated which describes the features of flame propagation in free radical containing cryogenic solids. This ``cryogenic flame'' theory is an extension of nonadiabatic flame theory associated with gaseous flames. The general features of cryogenic flames prescribed by the theory include: the characteristic propagation velocity of the reaction wave, the spatial structure of the composition and temperature fields, and the extinction limits associated with flame existence-nonexistence. Application of the formulation is illustrated for the case of flame propagation in N-atom-containing solid N2.

Burning velocity and reaction rates in constant temperature non-adiabatic flames

Flames with different fuel/oxygen ratios can be burnt at constant final temperatures on cooled porous burners, the constant temperature being maintained by changing burning velocity so that more heat is abstracted from the flames of greater calorific value. It is not obvious whether the required change of burning velocity is also associated with a change in the rate of fuel consumption, and this question has been investigated. In some lean hydrogen or hydrocarbon flames, the rate of fuel consumption has been found to be almost constant in constant temperature flames despite large changes in burning velocity with mixture ratio; and for such flames, the change in burning velocity is accounted for merely by the necessary change in heat abstraction. In fuel-rich hydrogen flames, however, the increased burning velocity of progressively richer mixtures is also associated with a faster reaction rate. In the course of the work, it was noted that the maximum rate of fuel consumption did not occur at a constant fraction of the final temperature or of the temperature rise, and this casts doubt on an assumption sometimes made to deduce ‘activation energies’ of flame reactions.

Burning velocity and the structure of flames near extinction limits

Burning velocities and structure of flames are calculated near various extinction limits according to a non-adiabatic flame theory. The theory prescribes burning velocity structure, extinction limits and includes adiabatic theory as a special case. Numerical results are obtained through the use of analogue computers as illustrated.