Numerical investigation of laminar cross-flow non-premixed flames in the presence of a bluff-body

A knowledge of flame stability regimes in the presence of cylindrical bluff-bodies of various dimensions is essential to design non-premixed burners. The reacting flow field in such cases is reported to be three-dimensional and unsteady. In the literature, only a few experimental investigations with limited measurements are available. Therefore, in this work, a detailed numerical study of laminar cross-flow non-premixed methane–air flames in the presence of a square cylinder is presented. The flow, temperature, species and reaction fields have been predicted using a comprehensive transient three-dimensional reacting flow model with detailed chemical kinetics and variable thermo-physical properties, in order to get a good insight into the flame stabilisation phenomena. Further, analyses of quantities such as local equivalence ratio, cell Damköhler number, species velocity, net consumption rate of methane, which are not easily obtained through experiments even with detailed diagnostics, have been carried out. The influence of the flow field due to varying inlet velocity of the oxidiser, in the presence of the bluff-body, on flame anchoring location has been analysed in detail. Local equivalence ratio contours obtained from non-reacting flow calculations are seen to be quite useful in analysing the mixing process and in the prediction of flame anchoring locations when the flames are not separated. Cell Damköhler number has been calculated using cell size, species velocity of the fuel, which is a derived quantity, and the net reaction rate of the fuel. The flame zone, which is customarily inferred from the contours of temperature, CO and OH, is also shown to be predicted well by the contour line corresponding to a Damköhler number equal to unity. The net reaction rate of CH₄ and the net rates of two dominant reactions, which consume methane, show clearly the variation in the flame anchoring locations in these three cases. Further, the three-dimensionality of these flames are analysed by plotting the mean temperature contours in y–z planes. Finally, the unsteadiness in the separated flame case is analysed.     

On the sublimit solution branches of the stripe patterns formed in counterflow diffusion flames by diffusional–thermal instability

The nonlinear dynamics of striped diffusion flames, formed in a two-dimensional counterflow by diffusional–thermal instability with Lewis numbers sufficiently less than unity, is investigated numerically by examining various two-dimensional flame-structure solutions bifurcating from the one-dimensional steady solution. The Lewis numbers for fuel and oxidizer are identically set to be 0.3, and an overall single-step Arrhenius-type chemical reaction with a Zel'dovich number of 7 is employed as the chemistry model. Particular attention is focused on the flame-stripe solution branches in the sub-extinction regime and on the hysteresis encountered during the transition between different solution branches. In the numerical simulations, a nonlinear solution with eight stripes is first realized from the one-dimensional solution at a Damköhler number slightly greater than the extinction Damköhler number. The eight-stripe solution survives Damköhler numbers much smaller than the extinction Damköhler number until successive bifurcations, leading to the doubling of the pattern wavelength, occur at the subsequent forward-transition conditions. At the first forward-transition Damköhler number occurs the transition to a four-stripe solution, which in turn transits to a two-stripe solution at the second forward-transition Damköhler number, a value somewhat smaller than the first. However, further transition from a two-stripe solution to a one-stripe solution is not always possible even if a one-stripe solution can be accessed independently for particular initial conditions. The Damköhler-number ranges and shapes for the two-stripe and one-stripe solutions are found to be virtually identical, implying that each stripe could be an independent structure if the distance between stripes is sufficiently large. By increasing the Damköhler number, backward transitions can be observed. In comparison with the forward-transition Damköhler numbers, the corresponding backward-transition Damköhler numbers are always much greater, thereby indicating significant hysteresis between the stripe patterns of strained diffusion flames.     

The role of unequal diffusivities in ignition and extinction fronts in strained mixing layers

We have studied flame propagation in a strained mixing layer formed between a fuel stream and an oxidizer stream, which can have different initial temperatures. Allowing the Lewis numbers to deviate from unity, the problem is first formulated within the framework of a thermo-diffusive model and a single irreversible reaction. A compact formulation is then derived in the limit of large activation energy, and solved analytically for high values of the Damköhler number. Simple expressions describing the flame shape and its propagation velocity are obtained. In particular, it is found that the Lewis numbers affect the propagation of the triple flame in a way similar to that obtained in the studies of stretched premixed flames. For example, the flame curvature determined by the transverse enthalpy gradients in the frozen mixing layer leads to flame-front velocities which grow with decreasing values of the Lewis numbers.

The analytical results are complemented by a numerical study which focuses on preferential-diffusion effects on triple flames. The results cover, for different values of the fuel Lewis number, a wide range of values of the Damköhler number leading to propagation speeds which vary from positive values down to large negative values     

Transient convective burning of interactive fuel droplets in single-layer arrays

The transient convective burning of n-octane droplets interacting within single-layer arrays in a hot gas flow perpendicular to the layer is studied numerically, with considerations of droplet surface regression, deceleration due to the drag of the droplets, internal liquid motion, variable properties, non-uniform liquid temperature and surface tension. Infinite periodic arrays, semi-infinite periodic arrays with one row of droplets (linear array) or two rows of droplets, and finite arrays with nine droplets with centers in a plane are investigated. All arrays are aligned orthogonal to the free stream direction. This paper compares the behavior of semi-infinite periodic arrays and finite arrays with the behavior of previously studied infinite periodic arrays. Furthermore, it identifies the critical values of the initial Damköhler number for bifurcations in flame behavior at various initial droplet spacing for all these arrays. The initial flame shape is either an envelope flame or a wake flame as determined by the initial Damköhler number, the array configuration and the initial droplet spacing. The critical initial Damköhler number separating initial wake flames from initial envelope flames decreases with increasing interaction amongst droplets at intermediate droplet spacing (when the number of rows in the array increases or the initial droplet spacing decreases for a specific number of rows in the array). In the transient process, an initial wake flame has a tendency to develop from a wake flame to an envelope flame, with the moment of wake-to-envelope transition advanced for the increasing interaction amongst droplets at intermediate droplet spacing. For the array with nine droplets with centers in a plane, the droplets at different types of positions have different critical initial Damköhler number and different wake-to-envelope transition time for initial wake flame.     

Three-dimensional numerical simulations of cellular jet diffusion flames

Recent experimental investigations have demonstrated that the appearance of particular cellular states in circular non-premixed jet flames significantly depends on a number of parameters, including the initial mixture strength, reactant Lewis numbers, and proximity to the extinction limit (Damköhler number). For CO₂-diluted H₂/O₂ jet diffusion flames, these studies have shown that a variety of different cellular patterns or states can form. For given fuel and oxidizer compositions, several preferred states were found to co-exist, and the particular state realized was determined by the initial conditions. To elucidate the dynamics of cellular instabilities, circular non-premixed jet flames are modeled with a combination of three-dimensional numerical simulation and linear stability analysis (LSA). In both formulations, chemistry is described by a single-step, finite-rate reaction, and different reactant Lewis numbers and molecular weights are specified. The three-dimensional numerical simulations show that different cellular flames can be obtained close to extinction and that different states co-exist for the same parameter values. Similar to the experiments, the behavior of the cell structures is sensitive to (numerical) noise. During the transient blow-off process, the flame undergoes transitions to structures with different number of cells, while the flame edge close to the nozzle oscillates in the streamwise direction. For conditions similar to the experiments discussed, the LSA results reveal various cellular instabilities, typically with azimuthal wavenumber m = 1–6. Consistent with previous theoretical work, the propensity for the cellular instabilities is shown to increase with decreasing reactant Lewis number and Damköhler number.     

Multiple speeds of flame edge propagation for Lewis numbers above one

Edges of diffusion flames in a counterflow burner are examined numerically for Lewis greater than unity. When the speed of propagation is plotted against Damköhler for a range of Lewis a fold bifurcation is observed. It is shown that there exist stable positively and negatively propagating edges for some Damköhler and Lewis number pairs. It is further shown that changed local conditions can lead to a transition from positive (advancing into the unburnt gasses) to negative (receding) propagation.     

Oscillating edge-flames

It has been known for some years that when a near-limit flame spreads over a liquid pool of fuel, the edge of the flame can oscillate. It is also known that when a near-asphyxiated candle-flame burns in zero gravity, the edge of the (hemispherical) flame can oscillate violently prior to extinction. We propose that these oscillations are nothing more than a manifestation of the large Lewis number instability well known in chemical reactor studies and in combustion studies, one that is exacerbated by heat losses. As evidence of this we examine an edge-flame confined within a fuel-supply boundary and an oxygen-supply boundary, anchored by a discontinuity in data at the fuel-supply boundary. We show that when the Lewis number of the fuel is 2, and the Lewis number of the oxidizer is 1, oscillations of the edge occur when the Damköhler number is reduced below a critical value. During a single oscillation period there is a short premixed propagation stage and a long diffusion stage, behaviour that has been observed in flame spread experiments. Oscillations do not occur when both Lewis numbers are equal to 1.     

Edge flames stabilized in a non-premixed microcombustor

The dynamics of an edge flame confined in a non-premixed microcombustor model is studied numerically within the context of a diffusive-thermal model. Fuel and oxidizer, separated upstream by a thin plate, flow through a channel with a prescribed velocity. At the tip of the plate, the fuel and oxidizer mix and, when ignited, an edge flame is sustained at some distance from the plate. The objective in this work is to consider the effects of confinement, differential diffusion, and heat loss on the dynamics of an edge flame in a narrow channel. We consider a wide range of channel widths and allow for changing Lewis numbers, and both adiabatic conditions and heat losses along the channel walls. The results illustrate how the flame shape and standoff distance are affected by the channel width, by mixture composition through variations in Lewis numbers and by heat losses. Conditions for flame stabilization, flame oscillations and flame extinction or blowoff are predicted.     

Flame propagation in a small-scale parallel flow

We consider the propagation of laminar premixed flames in the presence of a parallel flow whose scale is smaller than the laminar flame thickness. The study addresses fundamental aspects with relevance to flame propagation in narrow channels, to the emerging micro-combustion technology, and to the understanding of the effect of small scales in a (turbulent) flow on the flame structure. In part, the study extends the results of a previous analytical study carried out in the thick flame asymptotic limit which has in particular addressed the validity of Damköhler's second hypothesis in the context of laminar steady parallel flows. Several new contributions are made here.

Analytical contributions include the derivation of an explicit formula for the effective speed of a premixed flame U _T in the presence of an oscillatory parallel flow whose scale ? (measured with the laminar flame thickness δ _L ) is small and amplitude A (measured with the laminar flame speed U _L ) is (1). The formula shows a quadratic dependence on both the amplitude and the scale of the flow. The validity of the formula is established analytically in two distinguished limits corresponding to (1) frequencies of oscillations (measured with the natural frequency of the flame U _L /δ _L ), and to higher frequencies of (A/?) (the natural frequency of the flow). The analytical study yields partial support of Damköhler's second hypothesis in that it shows that the flame behaves as a planar flame (to leading order) with an increased propagation speed which depends on both the scale and amplitude of the velocity fluctuation. However our formula for U _T contradicts the formula given by Damköhler in his original paper where U _T has a square root dependence on the scale and amplitude.

Numerical contributions include a significant set of two-dimensional calculations which determine the range of validity of the asymptotic findings. In particular, these account for volumetric heat loss and differential diffusion effects. Good agreement between the numerics and asymptotics is found in all cases, both for steady and oscillatory flows, at least in the expected range of validity of the asymptotics. The effect of the frequency of oscillation is also discussed. Additional related aspects such as the difference in the response of thin and thick flames to the combined effect of heat loss and fluid flow are also addressed. It is found for example that the sensitivity of thick flames to volumetric heat loss is negligibly affected by the parallel flow intensity, in marked contrast to the sensitivity of thin flames. Interestingly, and somewhat surprisingly, thin flames are found to be more resistant to heat loss when a flow is present, even for unit Lewis number; this ceases to be the case, however, when the Lewis number is large enough.     

Critical conditions at liftoff limit of a laminar n-butane-air jet diffusion flame

The stability mechanism of laminar coflow jet diffusion flames in normal gravity has been studied computationally and experimentally. N-butane, the heaviest alkane in a gaseous state at ambient temperature and pressure, is used as the fuel since the reaction mechanism is similar to that of higher (liquid) hydrocarbons. The critical mean n-butane jet and coflowing air velocities at flame stability limits are measured using a small fuel tube burner (0.8 mm inner diameter). The time-dependent, axisymmetric numerical code with a detailed reaction mechanism (58 species and 540 reactions), molecular diffusive transport, and a radiation model, reveals a flame structure. A fuel-lean peak reactivity spot (i.e., reaction kernel), possessing the hybrid nature of diffusion-premixed flame structure at a constant temperature of ≈1560 K, is formed at the flame base and controls the flame stability. In a near-quiescent environment, the flame base resides below the fuel tube exit plane and thereby premixing is limited. As the coflowing air velocity is increased incrementally under a fixed fuel jet velocity, the flame base moves slightly above (≈1 mm) the burner exit and vigorous premixed combustion becomes prevailing. The local heat-release rate at the reaction kernel nearly doubles due to the increased convective oxygen flux (i.e., a blowing effect). The local Damköhler number, newly defined as a ratio of the square root of the local heat-release rate and the local velocity, decreases gradually first and drops abruptly at a critical threshold value and the flame base lifts off from the burner rim. The calculated coflow air velocity at liftoff is ≈0.38 m/s at the fuel jet velocity of 2 m/s, which is consistent with an extrapolated measured value of 0.41 m/s. This work has determined the critical Damköhler number at the stability limit quantitatively, for the first time, for laminar jet diffusion flames.     

Bifurcation characteristics and flame dynamics of a ducted non-premixed flame with finite rate chemistry

The influence of system parameters such as the flame location, Peclet number and Damköhler number on the bifurcation characteristics and flame dynamics of a ducted non-premixed flame with finite rate chemistry is presented in this paper. In the bifurcation plot with flame location as the bifurcation parameter, subcritical Hopf bifurcation is found for lower values of flame location and supercritical Hopf bifurcation for higher values of flame location, for all the Damköhler numbers used in this study. The flame shapes are captured at eight different phases of a cycle of time series data of acoustic velocity at both the fold and Hopf points for bifurcation with flame location as the parameter. We find that the range of flame height variations at the Hopf point is more than the range of flame height variations obtained at the fold point. We also find that the flame oscillates in the same phase as pressure fluctuation but in a phase different from both velocity and heat release rate fluctuations in the region of hysteresis for bifurcation with flame location. The non-dimensional hysteresis width is plotted as a function of Damköhler number for variation of flame location in the subcritical region. An inverse power law relation is found between the non-dimensional hysteresis width and the Damköhler number. The bifurcation plot with Peclet number as parameter shows a subcritical Hopf bifurcation.     

Piloted ignition and extinction for solid fuels

Piloted ignition of solid fuels is investigated by simulating the transport and chemical reaction in a counter-flow arrangement where a known fuel (methane) is supplied through a porous burner and the power and the location of the igniter are varied. The porous burner arrangement simulates a pyrolyzing solid fuel at constant temperature by separating the gas phase from the solid conduction and pyrolysis phenomena. An Arrhenius one-step global reaction and a simplified transport model with Lewis number equal to one were used in the simulation. Only quasi-steady conditions are considered for the gas phase in this work because the response time for the solid phenomena is, in general, much larger than the response diffusion time for the gaseous phenomena. The relation of piloted ignition to extinction is also investigated. The effect of Damköhler number on ignition and extinction and the effect of the igniter on ignition are presented through a characteristic S curve obtained by plotting the evolving maximum temperature as a function of fuel mass flux. Based on the S-shaped curve (representing the maximum temperature in the system versus the mass flux of fuel), the relationship between the piloted ignition and extinction turning points and mass fluxes has been demonstrated in this paper. The piloted ignition turning point gradually approaches the extinction turning point with increasing Damköhler number and also with increasing power of the igniter. The ignition mass flux is found to depend basically on three parameters, Damköhler number, the location of the igniter and the power of the igniter all expressed in dimensionless forms.     

Chaotic oscillation in diffusion flame induced by radiative heat loss

We numerically investigate the dynamic behavior of flame front instability in a diffusion flame caused by radiative heat loss from the viewpoint of nonlinear dynamics. As the Damköhler number increases at a high activation temperature, the dynamic behavior of the flame front undergoes a significant transition from a steady-state to high-dimensional deterministic chaos through the period-doubling cascade process known as the Feigenbaum transition. The existence of high-dimensional chaos in flame dynamics is clearly demonstrated using a sophisticated nonlinear time series analysis technique based on chaos theory.     

A numerical study on extinction behaviour of laminar micro-diffusion flames

We conducted a numerical study on the fluid dynamic, thermal and chemical structures of laminar methane–air micro flames established under quiescent atmospheric conditions. The micro flame is defined as a flame on the order of one millimetre or less established at the exit of a vertically-aligned straight tube. The numerical model consists of convective–diffusive heat and mass transport with a one-step, irreversible, exothermic reaction with selected kinetics constants validated for near-extinction analyses. Calculations conducted under the burner rim temperature 300 K and the adiabatic burner wall showed that there is the minimum burner diameter for the micro flame to exist. The Damköhler number (the ratio of the diffusive transport time to the chemical time) was used to explain why a flame with a height of less than a few hundred microns is not able to exist under the adiabatic burner wall condition. We also conducted scaling analysis to explain the difference in extinction characteristics caused by different burner wall conditions. This study also discussed the difference in governing mechanisms between micro flames and microgravity flames, both of which exhibit similar spherical flame shape.     

Stabilization, propagation and instability of tribrachial triple flames

A tribrachial (or triple) flame is one kind of edge flame that can be encountered in nonpremixed mixing layers, consisting of a lean and a rich premixed flame wing together with a trailing diffusion flame all extending from a single point. The flame could play an important role on the characteristics of various flame behaviors including lifted flames in jets, flame propagation in two-dimensional mixing layers, and autoignition fronts. The structure of tribrachial flame suggests that the edge is located along the stoichiometric contour in a mixing layer due to the coexistence of all three different types of flames. Since the edge has a premixed nature, it has unique propagation characteristics. In this review, the propagation speed of tribrachial flames will be discussed for flames propagating in mixing layers, including the effects of concentration gradient, velocity gradient, and burnt gas expansion. Based on the tribrachial edge structure observed experimentally in laminar lifted flames in jets, the flame stabilization characteristics including liftoff height, reattachment, and blowout behaviors and their buoyancy-induced instability will be explained. Various effects on liftoff heights in both free and coflow jets including jet velocity, the Schmidt number of fuel, nozzle diameter, partial premixing of air to fuel, and inert dilution to fuel are discussed. Implications of edge flames in the modeling of turbulent nonpremixed flames and the stabilization of turbulent lifted flames in jets are covered.     

Turbulence/flame/wall interactions in non-premixed inclined slot-jet flames impinging at a wall using direct numerical simulation

In the present work, three-dimensional turbulent non-premixed oblique slot-jet flames impinging at a wall were investigated using direct numerical simulation (DNS). Two cases are considered with the Damköhler number (Da) of case A being twice that of case B. A 17 species and 73-step mechanism for methane combustion was employed in the simulations. It was found that flame extinction in case B is more prominent compared to case A. Reignition in the lower branch of combustion for case A occurs when the scalar dissipation rate relaxes, while no reignition occurs in the lower branch for case B due to excessive scalar dissipation rate. A method was proposed to identify the flame quenching edges of turbulent non-premixed flames in wall-bounded flows based on the intersections of mixture fraction and OH mass fraction iso-surfaces. The flame/wall interactions were examined in terms of the quenching distance and the wall heat flux along the quenching edges. There is essentially no flame/wall interaction in case B due to the extinction caused by excessive turbulent mixing. In contrast, significant interactions between flames and the wall are observed in case A. The quenching distance is found to be negatively correlated with wall heat flux as previously reported in turbulent premixed flames. The influence of chemical reactions and wall on flow topologies was identified. The FS/U and FC/U topologies are found near flame edges, and the NNN/U topology appears when reignition occurs. The vortex-dominant topologies, FC/U and FS/S, play an increasingly important role as the jet turbulence develops.     

Analytical predictions of shapes of laminar diffusion flames in microgravity and earth gravity

Flame shape is an important observed characteristic of flames that can be used to scale flame properties such as heat release rates and radiation. Flame shape is affected by fuel type, oxygen levels in the oxidiser, inverse burning and gravity. The objective of this study is to understand the effect of high oxygen concentrations, inverse burning, and gravity on the predictions of flame shapes. Flame shapes are obtained from recent analytical models and compared with experimental data for a number of inverse and normal ethane flame configurations with varying oxygen concentrations in the oxidiser and under earth gravity and microgravity conditions. The Roper flame shape model was extended to predict the complete flame shapes of laminar gas jet normal and inverse diffusion flames on round burners. The Spalding model was extended to inverse diffusion flames. The results show that the extended Roper model results in reasonable predictions for all microgravity and earth gravity flames except for enhanced oxygen normal diffusion flames under earth gravity conditions. The results also show trends towards cooler flames in microgravity that are in line with past experimental observations. Some key characteristics of the predicted flame shapes and parameters needed to describe the flame shape using the extended Roper model are discussed.     

Numerical description of axisymmetric blue whirls over liquid-fuel pools

This numerical investigation is focused on determining the structures of blue whirls, recently found to occur in laboratory investigations of fire whirls when the circulation becomes sufficiently large to produce a vortex breakdown that drastically shortens the fire whirl and correspondingly reduces residence times, so that the yellow flames turn blue. The computations address axisymmetric configurations for round pools of liquid fuels flush with and at the center of a larger solid horizontal disc, at the outer edge of which vanes of adjustable angles cause the entrained air to enter with a controllable azimuthal component of velocity. The nondimensionlized conservation equations employed include realistic Lewis numbers with temperature-dependent transport coefficients and a one-step chemical-kinetic approximation that correctly reproduces laminar burning velocities. Buoyancy and radiant energy transport from the flames to the liquid surface are both taken into account, the latter being found to be essential for the blue whirl. Along with the vaporization-equilibrium and energy-conservation boundary conditions at the fuel surface, inflow boundary conditions are provided by a recently developed solution for the boundary-layer flow over the solid disc, while zero-gradient outflow conditions are applied above the whirl. Controlling nondimensional parameters, besides Reynolds, Damköhler, and Froude numbers, are a ratio of radiant to convective energy flux and a ratio of azimuthal to inward radial flow velocity in the boundary layer at the edge of the disc. The computed conditions for the onset of the blue whirl, as well as the computed structure of the whirl itself, bear close resemblance to what was found experimentally.     

Stabilization mechanism of lifted flame edge in the near field of coflow jets for diluted methane

The stabilization mechanism of lifted flames in the near field of coflow jets has been investigated experimentally and numerically for methane fuel diluted with nitrogen. The lifted flames were observed only in the near field of coflow jets until blowout occurred in the normal gravity condition. To elucidate the stabilization mechanism for the stationary lifted flames of methane having the Schmidt number smaller than unity, the behavior of the flame in the buoyancy-free condition, and unsteady propagation characteristics after ignition were investigated numerically at various conditions of jet velocity. It has been found that buoyancy plays an important role for flame stabilization of lifted flames under normal gravity, such that the flame becomes attached to the nozzle in microgravity. The stabilization mechanism is found to be due to the variation of the propagation speed of the lifted flame edge with axial distance from the nozzle in the near field of the coflow as compared to the local flow velocity variation at the edge.     

Cell formation in non-premixed,axisymmetric jet flames near extinction

Systematic experiments with CO₂ diluted H₂–O₂ circular jet diffusion flames have been undertaken to study the formation of cellular flames, which occur for relatively low reactant Lewis numbers and near the extinction limit. The jet Reynolds number for all experiments was about 500, based on the centreline velocity, jet diameter and ambient fuel properties. The Lewis numbers, based on the initial mixture strength φ and ambient conditions of the investigated near-extinction mixtures, vary in the range 1.1–1.3 for oxygen and 0.25–0.29 for hydrogen (φ is defined here as the fuel-to-oxygen molar ratio normalized by the stoichiometric value). Various conditions near the extinction limit were investigated by fixing the fuel composition (H₂–CO₂ mixture), and systematically lowering the oxygen concentration in the co-flowing oxidizer stream past the point where cellular structures formed, until extinction occurred. The observed different instability states were correlated with the initial mixture strength and the proximity to the extinction limit.

The parameter space for cellularity was found to increase with decreasing initial mixture strength. For a given initial mixture strength, several cellular states were found to co-exist near the extinction limit, and the preferred number of cells (the azimuthal wave number) was observed to decrease with decreasing oxygen concentration (Damköhler number). These trends are consistent with previous theoretical work and our own stability analysis that will be reported elsewhere.