Cylindrical Flame Research Articles

A computational study on propagating spherical and cylindrical premixed flames

Perfectly spherical and cylindrical premixed methane/air flames are numerically investigated in orderto analyze the inner structure of the flame, the flame propagation, and stretch effects. Three kinds of flames are studied: steady, expanding, and imploding flames. To model the flames in detail, while minimalizing computational costs, a flamelet model is adapted to the spherical and cylindrical flames in combination with a skeletal reaction mechanism. The expression for the flame stretch rate follows directly from its mass-based definition and is shown to consist of two terms, one due to the propagation of the flame itself and the other one due to the variation of the flame thickness. This last term is usually ignored in literature. It is shown to be small compared with the other term, but important if one is interested in the dynamics of the flame itself. Parameters related to flame stretch such as the Karlovitz and Markstein numbers are obtained and analyzed. Furthermore, the flame propagation velocities of these expanding and imploding flames are shown to change only slightly throughout the flame. Both the gas and burning velocities, however, vary significantly when changing the position in the flame. The flame propagation velocity of the expanding spherical flame is in excellent agreement with experimental data.

Two-Dimensional Soot

Large soot aggregates (ca. 100 μm) in acetylene−air diffusion flames are physically flat and have a fractal dimension of D = 1.40 ± 0.04 consistent with simulations of two-dimensional diffusion-limited cluster aggregation. This occurs because the soot is constrained to a cylindrical annular flame front with a radial thickness that appears thin relative to the increasing dimensions of the soot aggregates, thus confining them to a two-dimensional space during aggregation.

Experiments on collapsing cylindrical flames

This article is concerned with the effect of curvature on laminar flame dynamics. This topic is of fundamental interest and it has practical implications in turbulent combustion. It is shown that highly curved premixed flames may be obtained by operating a standard axisymmetric burner in a specific pulsed mode. Collapsing cylindrical flames are observed by submitting the burner to suitably tuned plane pulsations of the flow velocity. The cylindrical flame pattern collapses in an essentially radial motion. In these circumstances the flame cylinder separates unburned inner gases from the burned outer flow. The temporal evolution of the flame may be monitored using schlieren images while the inner flow velocity is determined from particle image velocimetry (PIV). It is shown that these data yield the stretched laminar burning velocity up to very small radii. Models of the stretched laminar burning velocity as a function of curvature are compared to experimental data and Markstein lengths are deduced. These experiments indicate how laminar flames respond to large curvature values. The data gathered may be used to guide modeling efforts in the area of turbulent combustion.

Diffusional–thermal instability of cylindrical burner-stabilized premixed flames

Steady burning behavior and diffusional–thermal instability of cylindrical burner-stabilized premixed flames are studied via activation energy asymptotics. For the steadily burning flame, the analysis yields a solution of the flame temperature and standoff distance as functions of the mass flow rate supplied by the burner. The result shows that the flame may be stabilized by either heat loss to the burner or flow divergence, in agreement with an earlier investigation by Eng et al. In addition, the flame exhibits two dual flame behaviors; namely, there exist two flame speeds either for the same heat loss rate to the burner or at the same standoff distance, which is consistent with earlier investigations on the one-dimensional, planar burner-stabilized flame. The linear stability analysis reveals that there exists a critical wave number on both the angular and axial directions for which the flame is the most unstable, that the critical wave number on the angular direction increases with increasing flow supply rate from the burner, that the effect of flow divergence–induced flame curvature is to stabilize the flame so that the cylindrical burner-stabilized flame is more stable than its one-dimensional counterpart, that the stability boundaries of a cylindrical flame approach those of the adiabatic, freely propagating planar flame by continuously increasing the burner supply rate, and that a flame stabilized by a larger burner is less stable than that supported by a smaller burner.

Effects of exothermicity on unsteady diffusion flames

The effects of exothermicity on unsteady diffusion flames are analysed for one-dimensional geometries and homogeneous isobaric flow. The diffusive burning is described in terms of the mixture fraction by a non-linear integro-differential equation, depending on two parameters: the initial F O ratio and an exothermicity factor, which is function of the heat of reaction and the initial fuel concentration. The rates of fuel consumption with variable density increase significantly when compared to the fuel consumption rates with constant density for cylindrical and spherical flames. Their burning times are also significantly reduced, as a consequence of the stretching in flame area and smaller concentration gradients. Analytical expressions are obtained for flame position, flame sheet velocity, induced flow field, composition, temperatures, and consumption rates.

Combustion mechanism of flame propagation and extinction in a rotating cylindrical vessel

The effect of radial acceleration in a rotating vessel on flame propagation has been investigated experimentally. Methane–air mixture compositions between the lean flammability limit and stoichiometric were studied. The behavior of flame propagation and the extinction mechanism were examined in detail. The flame propagating in a rotating vessel is axisymmetric. Initially it propagates axially from the ignition point at one end of the cylindrical vessel to the opposite end. After touching the side wall of the cylindrical vessel the flame starts to propagate radially and is locally quenched at the contact surface with the walls. The axial propagation velocity of the flame under all conditions increases with the rotation rate. When local quenching occurs, the radial flame propagation velocity decreases and the extinction rate increases with increasing rotation rate. The extinction mechanism is a multistep process. The most probable stages in that mechanism are as follows. First, heat loss causes the cylindrical flame to extinguish locally near the walls. Once this happens, the combustion gases, which are in contact with the walls, are cooled and displaced radially under the action of centrifugal forces. They flow towards the region of the fresh mixture, which remains in contact with the previously extinguished flame. Differential buoyancy forces the cool gases to move ahead of the flame, which is then extinguished because it is now propagating into a partially diluted nonflammable mixture. The extinction wave propagates along the cylindrical surface of the flame to complete extinction.

Ignition and extinction fronts in counterflowing premixed reactive gases

We describe two-dimensional steady propagating flame fronts in the stagnation mixing layer between two opposed streams of the same reactive mixture, the propagation taking place in the direction perpendicular to the plane of strain. The front, which is curved by the nonuniform flow field, separates a chemically frozen region from a region with a twin-flame configuration. The front velocity is calculated in terms of the Lewis number, Le F , and the Damköhler number, Da. Da, equal to the inverse of the Karlovitz number, is defined as the ratio of the strain time to the transit time through the planar unstrained flame. For the cases corresponding to large Da, difficult to tackle numerically, analytical expressions are given, characterizing the flame shape, and the variation of the burning rate along the flame front from the nose up to the planar trailing branches. For moderately large and low values of Da, the study is carried out numerically, yielding, in particular, the propagation velocity in terms of Da, for different values of Le F . Different combustion regimes are thus described including flames propagating toward the unburnt mixture, or ignition fronts, standing flames and retreating flames, or extinction fronts. We also describe stationary cylindrical flames of finite-extent, or 2D burning spots. In particular, a critical Lewis number is found, below which negative propagation speeds do not exist while the 2D burning spots mentioned may be encountered. Typically, these exist only for sufficiently small Le F if the Da is within a range [ Da min , Da max ], depending on Le F . For Da < Da min , the 2D spots are quenched, whereas as Da is increased, they grow in size, tending to give birth to propagating (ignition) fronts; Da max is indeed found to be the smallest Da allowing for ignition fronts. We notice that the range of existence of the 2D spots, for a given Le F , can overlap with that of retreating (extinction) fronts, and possibly with that of 3D spots, or flame balls, in this flow. However, the 3D case is not addressed in this work.

Combined effects of radiation, flame curvature, and stretch on the extinction and bifurcations of cylindrical CH 4/air premixed flame

The combined effects of flame radiation, stretch, and curvature on the extinction and flame bifurcations of the cylindrical premixed CH 4/air flames are numerically investigated with a detailed chemistry. The interaction between radiation heat loss and flame curvature is emphasized. The results show that a mixture below the standard limit can burn in the cylindrical flame configuration by imposing a moderate stretch rate. This flame is quenched either by radiation heat loss at low stretch rate or by incomplete combustion with an excessive stretch. As the fuel concentration increases, it is found that two kinds of flames, normal flame and weak flame, can exist at the same boundary conditions. A G-shaped extinction curve showing the flammable regions of these two flame regimes is obtained. The relation between the flammability limit of the cylindrical flame and the standard limit is discussed. Furthermore, comparisons between the cylindrical flame and the counterflow flame are made. The results show that the interaction of flame curvature and radiation heat loss greatly affects the flame strength and extinction. It is shown that flame curvature extends the radiation extinction limit and accelerates the opening up of the sublimit flame branch. Comparisons between the predicted results with the experimental data show good agreements both in the extinction limit and in the extinction flame diameter.

Lewis Number Effects in Premixed Turbulent Combustion and Highly Perturbed Laminar Flames

Various perturbed laminar flames are numerically simulated by reducing combustion chemistry to a single reaction. The following flame configurations are addressed: expanding spherical, cylindrical, and symmetrical planar flames; converging spherical flame; expanding cylindrical and symmetrical planar flames affected by external steady or time-dependent strain rate; steady strained cylindrical and symmetrical planar flames. The results (1) show that a simple linear relation between the local consumption velocity and flame stretch rate is valid only for weakly perturbed laminar flames; (2) highlight the importance of transient effects; and (3) show that, in the case of a small Lewis number, the highest local combustion rate is reached in the expanding spherical flame ignited by the hot pocket of the critical radius. This highest local combustion rate is successfully used to describe the extensive Karpov's experimental data base on turbulent burning velocities for mixtures characterized by substantially different values of the Lewis number. Discussion of Karpov's experimental data showing the drastic effect of the Lewis number on turbulent burning velocity implies the important role played by highly perturbed flamelets in premixed turbulent combustion.

Studies on Effects of DC Electric Fields on Burning Velocity of Methane-Air Premixed Flame.

Effects of DC electric fields on burning velocity of methane-air premixed flame were investigated with a cylindrical flame burner with a earthed porous cylinder. The center electrode was mounted on the centerline of the porous cylinder, and the porous cylinder itself was used as the other electrode. The cylindrical flame was formed inside the porous cylinder, and the flame never deformed when electric fields were applied. Increase in flame radius was detected when the center electrode was over+7000V, and no change of the flame was detected when the center electrode was less than+7000V. When the center electrode was negative, no change of the flame was detected up to 9000V. Increase in flame radius with electric fields is considered to show increase in burning velocity because the flame radius at a fixed ejection velocity without electric field increases when the burning velocity of the premixed gas increases.

Extinction of turbulent diffusion flames by Kolmogorov microscale turbulence

The effects of turbulent straining on the structure and response of cylindrical diffusion flames were studied experimentally by using the counterflow flame configuration formed in the forward stagnation region of a porous cylinder from which propane or methane was ejected. From the shadowgraphs, it was found that the turbulence caused large-scale distortions with small amplitude on a diffusion flame which had a locally laminar structure. The time-averaged flame thickness was three times as large as the laminar flame. The turbulent flow field was measured in detail by a hot-wire anemometer. The temperature profiles were determined as functions of the applied strain rate by using a fine-wire thermocouple the thermal inertia of which was compensated electrically. The total strain rate applied to the flame was decomposed into the bulk strain rate induced by the mean flow velocity gradient and the turbulent strain rate which was modelled. In the present study, the latter was modelled by the reciprocal of the Kolmogorov time scale. The total strain rate at which the turbulent diffusion flame was extinguished coincided with the critical velocity gradient at which the extinction of a laminar flame occurred. With the increased of the total strain rate, the turbulent diffusion flame became thinner, and the maximum mean temperature gradually decreased due to the decrease of the maximum temperature within the laminar flamelet. On the other hand, the maximum rms fluctuating temperature was rather insensitive to the total strain rate over a wide range of total strain rates. However, close to extinction, nonreactive holes appeared intermittently in the flame along the stagnation line established in the forward stagnation region of the porous cylinder. These holes led to an abrupt increase in the maximum rms fluctuating temperature and, also, a decrease in the maximum mean temperature very close to the state of extinction.

Structure and dynamics of kink and cellular flames stabilized on a rotating burner

We describe the formation and evolution of spatiotemporal patterns in cylindrical premixed flames stabilized on a rotating cylindrical burner. We consider flames in the cellular regime, Le < 1, where the Lewis number Le is the ratio of thermal to mass diffusivity of a deficient component of the combustible mixture. For the parameter regime considered burner rotation tends to be stabilizing in that increasing the rotation rate generally promotes the development of traveling waves (TWs) from modulated traveling waves (MTWs). However, more complex dynamics occurs at the terminus of each of the TW branches. We find a number of unsteady, nonaxisymmetric modes of combustion, including (i) kink modes, where one or more kinks (characterized by a jump or discontinuity in the distance from the flame to the burner) rotate around the burner, (ii) cellular flames in which one or more cells rotate around the burner, (iii) Pacman modes, in which a rapidly rotating kink periodically overtakes and destroys more slowly rotating cells, with new cells created elsewhere, (iv) two front modes in which the flame, though governed by a 1-step reaction mechanism, exhibits two distinct regions of burning in a localized region of space, and (v) double fire rotating cellular flames (DF modes) which are MTWs where the modulation of each cell exhibits two maxima over each period such that one cell attains its first maximum simultaneously with the second maximum of its neighbor. Certain of the modes that we describe have not been previously observed for nonrotating burners either in experiment or in prior computation.

The baroclinic effect in combustion

The baroclinic effect is due to the nonalignment of pressure and density gradients, and its result is to induce vorticity production. Because of the steep density gradients and the almost universal presence of ambient pressure signals in combustion systems, the baroclinic effect is a crucial mechanism for the production of turbulence. In this paper, we provide a review of the results of numerical simulations of baroclinic interactions between planar pressure signals and cylindrical laminar flame fronts. In the first section, the evolution of a flame front affected by a single baroclinic impulse is considered. In the second section, we consider the effect of a double baroclinic impulse on a growing flame ball within a shock tube and examine the effect of viscosity on the evolution of the overall burning rate.

A nonlinear model for hydrodynamic instability of an expanding flame

Within the framework of a weakly nonlinear model that describes the front dynamics of a divergent cylindrical flame under the assumption of smallness of the gas-expansion coefficient, exact analytical solutions of the evolution equation for the disturbed-flame surface were constructed. These solutions are similar to those derived from the polar-decomposition method. Based on computer numerical simulation, a new approach for describing a self-accelerating expanding cylindrical flame is proposed.

An experimental realization of premixed methane/air cylindrical flames

The objectives of the present article are to report the development of an inward burning premixed cylindrical flame radiant tube and experimental verification of the similarity of the combustion species concentration and temperature fields. Methane and air were mixed with each other at the molecular level in a tee and in a long tube before entering the burner. Major conclusions of the present study are as follows: (1) The novel burner can stabilize steady state cylindrical flames at various radial positions within an annulus. (2) Measurements of concentrations of combusting species at different axial locations show that they are a function of radial distance only. Complete combustion was achieved without fuel leakage within the least count of the present instrument. Present experimental results support the existence of similarity in the flow field predicted by Takeno and Ishizuka. (3) Temperature measurements exhibit a self-similar radial profile for various axial distances. The self-similar temperature profiles and the large gradient in temperature near the outer wall indicate that the present configuration can result in a very high performance radiant tube.

Numerical Analysis on Instability of Cylindrical Flames

ABSTRACT Unsteady motions of 2-dimensional reactive flows have been simulated to investigate the hydrodynamic effect and the diffusive-thermal effect on the instability of freely expanding cylindrical flames. The numerical model includes compressibility, viscosity, heat conduction, molecular diffusion, one-step chemical reaction, and convection. We obtained the growth rates of disturbances superimposed on the cylindrical flames depending on their wave numbers. The results showed that the growth rates in the cylindrical flames are consistent with those in the plane flames for the case where the Lewis number is unity. Therefore, the hydrodynamic effect on the flame instability is independent of the mean curvature of the front. When the Lewis number is smaller/larger than unity, the growth rates in the cylindrical flames are lower/higher than those in the plane flames. It means that the instabilizing/stabilizing influence of the diffusive-thermal effect is less in the cylindrical flames than in the plane flames.

Extinction Characteristics of Stretched Premixed Flames of Methane-Propane Mixtures.

Concerning the stretched cylindrical premixed flames formed in a radial-flow nozzle burner, effects of fuel mixing between methane and propane were examined on the extinction characteristics, such as the velocity gradient (stretch rate) and flame diameter at the state of extinction and flame temperature variations with the velocity gradient. These fuels were used because they have been known to show different behavior to the extinction due to flame stretch. The results showed that the characteristics were not linearly related with the volume fraction of each component fuel, but inclined to be weighted with propane and that at the stoichiometric condition some mixed fuels had a stronger resistibility to flame extinction than the pure component fuel. To explain the results, theoretical analysis based on the flame sheet model was carried out for the investigation of the effects of stretch, fuel mixing, Lewis number and preferential diffusion on the flame temperature which is closely related to the extinction phenomena.

MODELING OF CONFINED AND UNCONFINED LAMINAR PREMIXED FLAMES ON SLIT AND TUBE BURNERS

ABSTRACT A model is presented for laminar premixed Bunsen flames on slit and cylindrical burners burning in a surrounding atmosphere. A comparison between modeling and experimental results shows that the model can reproduce the experimental results within 10% accuracy. The influence of a surrounding atmosphere and burner curvature on the flame shape, flow field and mass transport in 2D laminar premixed Bunsen flames is also investigated. It is found that flames on cylindrical burners confined between similar flames have a smaller flame length and flame tip curvature than flames on slit burners with comparable dimensions. These effects are caused by the larger available expansion space (in radial direction) for the cylindrical flames. Furthermore, it is shown that the flames in a surrounding atmosphere are less curved than flames confined between other flames; the curvature of the tip is also smaller. These effects are explained by the fact that the confining flames push the mass flow and the flame front t...

Structure and dynamics of Modulated Traveling Waves in cellular flames

We describe the formation and evolution of spatial and temporal patterns in cylindrical premixed flames. We consider the cellular regime, Le < 1, where the Lewis number Le is the ratio of thermal to mass diffusivity of a deficient component of the combustible mixture. A transition from stationary, axisymmetric flames to stationary cellular flames is predicted analytically if Le is decreased below a critical value. We present the results of numerical computations to show that as Le is further decreased, with all other parameters fixed, traveling waves (TWs) along the flame front arise via an infinite-period bifurcation which breaks the reflection symmetry of the cellular array. Upon further decreasing Le we find the development of different kinds of periodically modulated traveling waves (MTWs) as well as a branch of quasiperiodically modulated traveling waves (QPMTWs). These transitions are accompanied by the development of different spatial and temporal symmetries including period doublings and period halvings in appropriate coordinate systems. We also observe the apparently chaotic temporal behavior of a disordered cellular pattern involving creation and annihilation of cells. We analytically describe the stability of the TW solution near its onset using suitable phase-amplitude equations. Within this framework one of the MTWs can be identified as a localized wave traveling through an underlying stationary, spatially periodic structure.

Stretch effects extracted from inwardly and outwardly propagating spherical premixed flames

Unsteady propagation of spherical flames, both inward and outward, are studied numerically extensively for single-step reaction and for different Lewis numbers of fuel/oxidizer dependence of flame speed ratio ( s) and flame temperature ratio are obtained for a range of Lewis numbers and stretch ( κ ) values. These results of s versus κ show that the asymptotic theory by Frankel and Sivashinsky is reasonable for outward propagation. Other theories are unsatisfactory both quantitatively and qualitatively. The stretch effects are much higher for negative stretch than for positive stretch, as also seen in the theory of Frankel and Sivashinsky. The linearity of the flame speed ratio vs stretch relationship is restricted to nondimensional stretch of ±0.1. It is shown further that the results from cylindrical flames are identical to the spherical flame on flame speed ratio versus nondimensional stretch plot thus confirming the generality of the concept of stretch. The comparison of the variation of ( ds d κ ) κ = 0 with β( Lc − 1) show an offset between the computed and the asymptotic results of Matalon and Matkowsky. The departure of negative stretch results from this variation is significant. Several earlier experimental results are analysed and set out in the form of s versus κ plot. Comparison of the results with experiments seem reasonable for negative stretch. The results for positive stretch are satisfactory qualitatively for a few cases. For rich propaneair, there are qualitative differences pointing to the need for full chemistry calculations in the extraction of stretch effects.