Non-adiabatic Flame Research Articles

Heat recirculation effects on flame propagation and flame structure in a mesoscale tube

Heat recirculation effects on flame propagation and flame structure are theoretically and experimentally examined in a mesoscale tube as the simplest model of heat-recirculating burners. Solutions for steady propagation are obtained using a one-dimensional two-temperature approximation. The results show that the low heat diffusivities of common solid materials permit significant heat recirculation through the wall only for a slowly-propagating condition, otherwise the flame behaves almost like a freely-propagating nonadiabatic flame. This limited heat recirculation sharply pinches and stretches two well-known branches of the freely-propagating nonadiabatic flame, resulting in the appearance of two slow-propagation branches. On the upper slow-propagation branch flames can reach superadiabatic temperatures and on the lower one, which is stretched from the classical unstable lower branch, flames can be stable. As the tube inner diameter decreases, another burning regime appears where flames are barely sustained by the heat recirculation. Further reduction of the tube inner diameter makes no flame exist. It is also revealed that a flame in a mesoscale tube has two length scales, i.e. the conventional flame thickness and a convective preheat zone thickness, and that the latter should be much larger than the former for significant heat recirculation. It is theoretically predicted that a heat-recirculating, even superadiabatic, flame with positive propagation velocity against the gas flow can exist in a mesoscale tube. It is also found that a flame transition from one branch to another in a given tube is well described by only one dimensionless parameter. Finally, these theoretical results show good qualitative agreements with experiments, especially for the transition behaviours.

Strained premixed flames: Effect of heat-loss, preferential diffusion and reversibility of the reaction

We provide an analytical description of the effect of preferential diffusion and volumetric heat-loss on strained premixed flames within a reversible chemistry model. The model comprises a single reversible reaction of the form F⇌P whose forward and backward rates follow an Arrhenius law. An asymptotic analysis of the problem is carried out in the limit of infinitely large activation energy of the forward reaction. The study allows for non-unit Lewis numbers for the fuel F and the product P. Two main contributions are made. The first contribution consists in identifying the fundamental differences in the asymptotic description of the non-adiabatic flame between the reversible and irreversible cases, and resolving the difficulties by a suitable generalization of the so-called near-equidiffusion flame approximation to the reversible case, including the derivation of appropriate jump conditions at the reaction sheet. This is used to demonstrate that the one-step reversible chemistry model is reducible to the classical irreversible chemistry model, provided that an effective reduced Lewis number and an effective heat-loss parameter are used. The second contribution is the determination of the domain of the solutions and their multiplicity, for selected values of , in the -ε plane, where ε is a non-dimensional measure of the strain rate. For , the diagrams are found to consist of four regions with one, two, three, and four solutions respectively, including the frozen solution. For , an additional region with three solutions is identified. For larger values of , the two regions with three solutions merge, and the region with four solutions is of insignificant size. Our diagrams are found to be in good agreement with, and complementary to, numerically determined diagrams in flammability limit studies based on one-step and detailed chemistry models. They are also a valuable component in studying non-adiabatic premixed edge-flames.

The analytical investigation of premixed combustion in cylindrical micro-combustor

In this study, an analytical model for heat recirculation in cylindrical micro-combustors is presented, including the effects of heat transfer from the product gas stream in the reaction zone and post-flame region to the reactant in the preheat zone, structural heat conduction through the combustor walls and heat loss to ambient. Eventually, the explicit expression for the flame speed in non-adiabatic condition and the implicit expression for adiabatic condition are obtained in this research. In addition, comparison is made between adiabatic and non-adiabatic flame speeds. It is demonstrated that the streamwise heat conduction through the structure of combustor plays an important role in the flame broadening in both adiabatic and non-adiabatic conditions. Moreover, it is shown that reducing the size of the combustor to a submillimetre scale extremely increases the surface-to-volume ratio, leading to the decrease in the flame speed and flame quenching.

The effects of radiation on the dynamic behavior of cellular premixed flames generated by intrinsic instability

Two-dimensional unsteady calculations of reactive flow on the basis of the compressible Navier–Stokes equation were performed to elucidate the effects of radiation on the dynamic behavior of cellular premixed flames generated by intrinsic instability. The disturbance superimposed on a planar flame evolved owing to hydrodynamic and diffusive-thermal effects, and then the cellular flame front formed. The dynamic behavior of cellular flames appeared at low Lewis numbers, and it became stronger as radiative heat loss increased. The island of the unburned gas surrounded by the burned gas was observed in non-adiabatic flames with low Lewis numbers. The average cell size of the non-adiabatic flame was slightly small compared with the adiabatic flame, even though the critical wavelength of the former flame was larger than that of the latter flame. This indicates that the radiation has a pronounced influence on the dynamics of premixed flames with low Lewis numbers. Owing to the dynamic behavior, the burning velocity of cellular flames changed drastically with time, which was due principally to the combination and division of cells. The average burning velocity of the non-adiabatic cellular flame was somewhat small compared with the adiabatic cellular flame. This is because that the burning velocity of planar flames decreases owing to radiation and that the dynamic behavior of cellular flames becomes stronger. In addition, the average burning velocity became larger monotonically as the length of computational domain increased. The reason is that the long wavelength components of disturbances play a significant role in the front shape of cellular flames.

Theoretical investigation of flame propagation through compositionally stratified methane–air mixtures

Flame propagation speeds in compositionally stratified methane–air mixtures were theoretically calculated as a function of the equivalence ratio distribution in the unburnt mixture and compared with experimental results. A solution of non-adiabatic flame propagation under a quasi-steady approximation was able qualitatively to describe the experimentally observed characteristics of flame speeds in stratified mixtures, which were flame speed increase in the vicinity of the flammability limits as well as for high equivalence ratio gradients. However, this analysis failed to provide quantitative agreement with the experimental results. In order to address this, the cumulative heat support effects on flame temperature, depending on the history of flame propagation, had to be accounted for. Quantitative agreement with the experiments was achieved, especially for propagation in lean mixtures.

A combined experimental/computational investigation of stratified combustion in methane–air mixtures

Although the importance of stratified combustion was early realized, there are still not enough data to fully characterize it mainly due to experimental difficulties of setting up mixture stratification in a controllable manner. As a contribution toward this shortage, controllable stratification was achieved with a technique based on convective-diffusive balance in a novel chamber. The measured flame speeds in the chamber showed that there were significant deviations from quasi-homogeneous flame speeds especially for flames that experienced higher concentration gradients. The experimental results were rationalized theoretically, using appropriate flame asymptotics. The emphasis lies on the establishment of the lean flammability extension, which can lead to significant fuel economy in practical systems and to the increase in flame speeds because of the non-adiabatic flames established in stratified media.

On the Route to Extinction in Nonadiabatic Solid Flames

We consider nonadiabatic gasless solid fuel combustion employing a reaction sheet model. We derive an integrodifferential equation for the location of the interface separating the fresh fuel from the burned products. There are two parameters in our model, the Zeldovich number Z, related to the activation energy of the exothermic chemical reaction, and the heat loss parameter $\Gamma$. For any value of Z there is an extinction limit $\Gamma_{m}$, so that if $\Gamma > \Gamma_{m}$, the combustion wave cannot be sustained. For all values of Z and $\Gamma < \Gamma_{m}$ the model admits a uniformly propagating combustion wave. This solution is subject to a pulsating instability for Z sufficiently large. The effect of heat losses is destabilizing in the sense that pulsations occur for smaller values of Z when heat loss is considered.We consider the dynamics of the combustion wave as $\Gamma$ increases, thus, describing the dynamics of the model on the route to extinction. We consider values of Z below the adiaba...

Adaptive numerical simulation of pulsating planar flames for large Lewis and Zeldovich ranges

We study numerically the behaviour of pulsating planar flames in the thermo-diffusive approximation. The numerical scheme is based on a finite volume discretization with an adaptive multi-resolution technique for automatic grid adaption. This allows an accurate and efficient computation of pulsating flames even for very large activation energies. Depending on the Lewis number and the Zeldovich number, we observe different behaviours, like stable or pulsating flames, the latter being either damped, periodic, or a-periodic. A bifurcation diagram in the Lewis–Zeldovich plane is computed and our results are compared with previous computations [Rogg B. The effect of Lewis number greater than unity on an unsteady propagating flame with one-step chemistry. In: Peters N, Warnatz J, editors, Numerical methods in laminar flame propagation, Notes on numerical fluid mechanics, vol. 6. Vieweg; 1982. p. 38–48.] and theoretical predictions [Joulin G, Clavin P. Linear stability analysis of nonadiabatic flames: diffusional-thermal model. Combust Flame 1979;35:139–53]. For Lewis numbers larger than 6 we find that the stability limit is again increasing towards larger Zeldovich numbers and not monotonically decreasing as predicted by the asymptotic theory. A study of the flame velocities for different Zeldovich numbers shows that the amplitude of the pulsations strongly varies with the Lewis number. A Fourier analysis yields information on their frequency.

The effects of heat loss on the burning velocity of cellular premixed flames generated by hydrodynamic and diffusive-thermal instabilities

The effects of heat loss on the burning velocity of cellular premixed flames are investigated by two-dimensional unsteady calculations of reactive flows based on the compressible Navier–Stokes equation and on the diffusive-thermal model equation. Hydrodynamic and diffusive-thermal instabilities are taken into account as contributing to the intrinsic instability of premixed flames. A sufficiently small disturbance is superimposed on a planar flame to obtain the relation between the growth rate and the wavenumber, i.e., the dispersion relation. As the heat loss becomes larger, the growth rate decreases and the unstable range narrows. This is because hydrodynamic instability caused by thermal expansion weakens for nonadiabatic flames. To investigate the characteristics of cellular flames, the disturbance with the linearly most unstable wavenumber, i.e., the critical wavenumber, is superimposed. As the superimposed disturbance evolves, the cellular-flame front forms due to the intrinsic instability. The lateral movement of cellular flames is observed at low Lewis numbers, and the behavior of cellular-flame fronts becomes more unstable for nonadiabatic flames. As the heat-loss parameter increases, the burning velocity of a cellular flame normalized by that of a planar flame increases at Lewis numbers lower than unity. By contrast, when the Lewis number is not less than unity, the burning-velocity increment decreases by increasing the heat loss. Diffusive-thermal instability thus has a pronounced influence on the unstable behavior and burning velocity of nonadiabatic cellular flames.

The Effect of Heat Loss on the Unstable Behavior of Cellular Premixed Flames

The effect of heat loss on the unstable behavior of cellular premixed flames is investigated by two-dimensional unsteady calculations of reactive flows, based on the diffusive-thermal model equation. To obtain the relation between the growth rate and the wave number, i.e., the dispersion relation, a sufficiently small disturbance is superimposed on a planar flame. The superimposed disturbance grows exponentially with time, which is consistent with the prediction of linear analyses. As the heat loss becomes larger, the growth rate increases at small wave numbers and decreases at large wave numbers. To investigate the unstable behavior of cellular flames, the disturbance with the linearly most unstable wave number, i.e., the critical wave number, is superimposed. The superimposed disturbance evolves, and the cellular-flame front is formed, owing to intrinsic instability. The larger the heat loss, the deeper the cell and the greater the burning velocity. When the heat loss is taken into account, the lateral movement of cellular flames is more likely to be observed, which is observed only at sufficiently low Lewis numbers for adiabatic flames. In addition, the chaotic behavior of cellular-flame fronts is observed in non-adiabatic flames with low Lewis numbers.

予混合火炎の不安定性に及ぼす熱損失効果

The effect of heat loss on the instability of premixed flames is studied by two-dimensional unsteady calculations of reactive flows, based on the compressible Navier-Stokes equation. We take account of hydrodynamic and diffusive-thermal effects as to the intrinsic instability of premixed flames. A sufficiently small disturbance is superimposed on a planar flame to obtain the relation between the growth rate and the wave number. As the heat loss becomes larger, the growth rate decreases and the unstable range narrows. This is because that the hydrodynamic instability generated by thermal expansion becomes weaker. To study the unstable behavior of cellular flames, the disturbance with the linearly most unstable wave number, i.e., the critical wave number, is superimposed. The superimposed disturbance evolves, and the cellular-flame front is formed, owing to intrinsic instability. The lateral movement of cellular flames is observed at low Lewis numbers, and the behavior of cellular-flame fronts becomes more unstable for non-adiabatic flames. With an increase in the heat loss, the burning velocity of a cellular flame normalized by that of a planar flame increases at Lewis numbers lower than unity. When the Lewis number is not less than unity, on the other hand, the flame-velocity increment decreases by increasing the heat loss.

Evans function analysis of the stability of non-adiabatic flames

The steady propagation of a planar laminar premixed flame, with a one-step exothermic reaction and linear heat loss, is studied. The corresponding travelling wave equations are solved numerically, and the temporal stability to longitudinal perturbations of any resulting flames is investigated using the Evans function. The dependence of the flame velocity on the heat loss parameter is determined for different values of the Lewis number. These curves have a turning point, as obtained previously by asymptotic expansions for large activation energy. For Lewis numbers close to unity the upper branch of the curve gives stable flames, the lower branch unstable flames, and the turning point is a saddle-node bifurcation point. For larger values of the Lewis number there is a Hopf-bifurcation point on the upper branch of the curve, dividing it into stable and unstable sections. The saddle-node and Hopf-bifurcation curves are also determined. The two curves have a common, Takens–Bogdanov, bifurcation point.

High order effects in one step reaction sheet jump conditions for premixed flames

The differences need to be understood between the leading order jump conditions, often assumed at a flame sheet in combustion theory, and the actual effect of a one step chemical reaction governed by Arrhenius kinetics. These differences are higher order in terms of a large activation temperature analysis and can be estimated using an asymptotic approach. This paper derives one order of asymptotic correction to the leading order jump conditions that are normally used for describing premixed laminar combustion, providing additional contributions that are due to curvature, flow through the flame sheet and the temperature gradient into the burnt gas. As well as offering more accurate asymptotic results, these can be used to estimate the errors that are inherent in adopting only the leading order version and they can point towards major qualitative changes that can occur at finite activation temperatures in some cases. Applied to steady non-adiabatic flame balls it is found that the effect of a non-zero temperature gradient in the burnt gas provokes the most serious deficiency in the asymptotic approach.

An Asymptotic Model of Nonadiabatic Catalytic Flames in Stagnation-Point Flow

A formal asymptotic model is derived for a nonadiabatic catalytic flame in stagnation-point flow. In the present context, the premixed reaction in the bulk gas is augmented by a surface catalytic reaction on the stagnation plane, where conductive heat losses are allowed to occur. In addition, the thermal effects of a finite-volume combustor are accounted for by allowing for volumetric heat losses from the bulk gas. The analysis exploits the near-equidiffusional limit corresponding to near-unity Lewis numbers, and yields a general nonsteady nonplanar model for the reactionless outer flow subject to boundary conditions that reflect both surface catalysis and distributed chemical reaction in a thin boundary layer. For the case of steady planar combustion, the surface-temperature response indicates the possibility of multiple solution branches, which are shown to be linearly stable, and a corresponding extension of the extinction limit that demonstrates how the presence of a surface catalyst can counterbalance the extinguishing effects of heat loss and stretch in nonadiabatic strained flames. The present model is particularly relevant for small-volume combustors, where the increased surface-to-volume ratio can lead to extinction of the nonadiabatic flame in the absence of a catalyst.

Flame extinction by spatially periodic shear flows

The previously studied model for nearly extinguished non-adiabatic flames propagating through a quiescent gas is extended to account for the effects due to the background flow-field. It is shown that for moderately strong large-scale periodic shear flows, their intensification results in flame speed enhancement. Yet for high Lewis number flames, there is a certain level of the flow intensity at which the flame speed reaches its maximum followed by the flame quenching. This paper is motivated by the experimentally known phenomenon of flame extinction by turbulence.

Extinction limits of nonadiabatic, catalyst-assisted flames in stagnation-point flow

An idealized geometry corresponding to a premixed flame in stagnation-point flow is used to investigate the effects of catalysis on extending the extinction limits of nonadiabatic stretched flames. Specifically, a surface catalytic reaction is assumed to occur on the stagnation plane, thereby augmenting combustion in the bulk gas with an exothermic surface reaction characterized by a reduced activation energy. Assuming the activation energies remain large, an asymptotic analysis of the resulting flame structure yields a formula for the extinction limit as a function of various parameters. In particular, it is demonstrated that the presence of a surface catalyst can extend the burning regime, thus counterbalancing the effects of heat loss and flame stretch that tend to shrink it. The analysis is relevant to small-volume combustors, where the increased surface-to-volume ratio can lead to extinction of the nonadiabatic flame in the absence of a catalyst.

The thick flame asymptotic limit and Damköhler's hypothesis

We derive analytical expressions for the burning rate of a flame propagating in a prescribed steady parallel flow whose scale is much smaller than the laminar flame thickness.In this specific context, the asymptotic results can be viewed as an analytical test of Damköhler's hypothesis relating to the influence of the small scales in the flow on the flame; the increase in the effective diffusion processes is described. The results are not restricted to the adiabaticequidiffusional case, which is treated first, but address also the influence of non-unit Lewis numbers and volumetric heat losses. In particular, it is shown that non-unit Lewis numbereffects become insignificant in the asymptotic limit considered. It is also shown that the dependence of the effective propagation speed on the flow is the same as in the adiabatic equidiffusional case, provided it is scaled with the speed of the planar non-adiabatic flame.

Collective effects and dynamics of non-adiabatic flame balls

The dynamics of a homogeneous, polydisperse collection of non-adiabatic flame balls (FBs) is investigated by analytical/numerical means. A strongly temperature-dependent Arrhenius reaction rate is assumed, along with a light enough reactant characterized by a markedly less than unity Lewis number (Le). Combining activation-energy asymptotics with a mean-field type of treatment, the analysis yields a nonlinear integro-differential evolution equation (EE) for the FB population. The EE accounts for heat losses inside each FB and unsteadiness around it, as well as for its interactions with the entire FB population, namely mutual heating and faster (Le < 1) consumption of the reactant pool. The initial FB number density and size distribution enter the EE explicitly. The latter is studied analytically at early times, then for small total FB number densities; it is subsequently solved numerically, yielding the whole population evolution and its lifetime. Generalizations and open questions relating to ‘spotty’ turbulent combustion are finally evoked.

PSR-based microstructural modeling for turbulent combustion processes and pollutant formation in double swirler combustors

The present study numerically investigates the fuel-air mixing characteristics, flame structure, and pollutant emission inside a double-swirler combustor. A PSR (Perfectly Stirred Reactor) based microstructural model is employed to account for the effects of finite rate chemistry on the flame structure and NO formation. The turbulent combustion model is extended to nonadiabatic flame condition with radiation by introducing an enthalpy variable, and the radiative heat loss is calculated by a local, geometry-independent model. The effects of turbulent fluctuation are taken into account by the joint assumed PDFs. Numerical model is based on the non-orthogonal body-fitted coordinate system and the pressure/velocity coupling is handled by PISO algorithm in context with the finite volume formulation. The present PSR-based turbulent combustion model has been applied to analyze the highly intense turbulent nonpremixed flame field in the double swirler combustor. The detailed discussions were made for the flow structure, combustion effects on flow structure, flame structure, and emmission characteristics in the highly intense turbulent swirling flame of the double swirler burner.

Numerical modeling for the H2/CO bluff-body stabilized flames

This study investigates the nonpreximed H2/CO-air turbulent flames numerically. The turbulent combustion process is represented by a reaction progress variables model coupled with the presumed joint probability function. In the present study, the turbulent combustion model is applied to analyze the nonadiabatic flames by introducing additional variable in the transport equation of enthalpy and the radiative heat loss is calculated using a local, geometry independent model. Calculation are compared with experimental data in terms of temperature, and mass fraction of major species, radical, and NO. Numerical results indicate that the lower and higher fuel-jet velocity flames have the distinctly different flame structures and NO formation characteristics in the proximity of the outer core vortex zone. The present model correctly predicts the essential features of flame structure and the characteristics of NO formation in the bluff-body stabilized flames. The effects of nonequilibrium chemistry and radiative heat loss on the thermal NO formation are discussed in detail.