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.     

Piloted ignition of solid fuels at low ambient pressure and varying igniter location

In order to investigate the effects of ambient pressure and igniter location on piloted ignition of solid fuels, the ignition mass flux of PMMA was experimentally determined for locations of the igniter between 6 and 70 mm above the solid surface, under two external heat fluxes of 21.2 and 25.4 kW/m². The experimental results show that the ignition mass flux decreases as the igniter approached the solid surface until it reached a minimum, and then the ignition mass flux remains nearly constant followed by a slight increase with a further decrease of the igniter location. In addition, in another series of experiments the ignition mass flux for elm wood decreases by a factor 0.6 at reduced pressure 0.67 (Tibet 0.67 atm) compared to the ignition mass flux at normal pressure (Hefei, 1.0 atm). The results of this work are explained well by a numerical piloted ignition model which also explains recent observations on the ignition mass flux at reduced pressures in a forced-flow ignition and flame spread apparatus.     

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.     

Fast,non-diffusive ignition of a gaseous reacting mixture subject to a point energy source

The ignition of a gaseous reactive mixture subject to a localized energy source is analysed using large activation energy asymptotics. The energy released by the source results in a thermal non-uniformity in a small region of the gas. We distinguish two different regimes, non-diffusive and diffusive, depending on the dominant cooling mechanism during the ignition stage: expansion effects or heat conduction. We focus on the non-diffusive ignition, considering the energy source as instantaneous. We show the existence of a critical value of a Damköhler number, defined as the ratio of the characteristic times of the expansion waves and chemical reaction, such that ignition only occurs for supercritical values at a well-defined ignition time, which is calculated numerically. The ignition process for a non-instantaneous energy source is also described in terms of an initial inert heating stage and a shorter reactive stage ending in thermal runaway for supercritical values of the Damköhler number.     

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.     

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.     

Cinematographic imaging of hydroxyl radicals in turbulent flames by planar laser-induced fluorescence up to 5 kHz repetition rate

Temporally resolved measurements of transient phenomena in turbulent flames, such as extinction, ignition or flashback, require cinematographic sampling of two-dimensional scalar fields. Hereby, repetition rates must exceed typical flame-inherent frequencies. The high sensitivity planar laser-induced fluorescence (PLIF) has already proved to be a practical method for scalar imaging. The present study demonstrates the feasibility of generating tuneable narrowband radiation in the ultraviolet (UV) spectral range at repetition rates up to 5 kHz. Pulse energies were sufficiently high to electronically excite hydroxyl radicals (OH) produced in a partially-premixed turbulent opposed jet (TOJ) flame. Red-shifted fluorescence was detected two-dimensionally by means of an image-intensified CMOS camera. Sequences comprising up to 4000 frames per run were recorded. Besides statistically stationary conditions, extinction of a turbulent flame due to small Damköhler numbers is presented showing the potential of the technique.     

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.     

A computational study of syngas auto-ignition characteristics at high-pressure and low-temperature conditions with thermal inhomogeneities

A computational study was conducted to investigate the characteristics of auto-ignition in a syngas mixture at high-pressure and low-temperature conditions in the presence of thermal inhomogeneities. Highly resolved one-dimensional numerical simulations incorporating detailed chemistry and transport were performed. The temperature inhomogeneities were represented by a global sinusoidal temperature profile and a local Gaussian temperature spike (hot spot). Reaction front speed and front Damköhler number analyses were employed to characterise the propagating ignition front. In the presence of a global temperature gradient, the ignition behaviour shifted from spontaneous propagation (strong) to deflagrative (weak), as the initial mean temperature of the reactant mixture was lowered. A predictive Zel'dovich–Sankaran criterion to determine the transition from strong to weak ignition was validated for different parametric sets. At sufficiently low temperatures, the strong ignition regime was recovered due to faster passive scalar dissipation of the imposed thermal fluctuations relative to the reaction timescale, which was quantified by the mixing Damköhler number. In the presence of local hot spots, only deflagrative fronts were observed. However, the fraction of the reactant mixture consumed by the propagating front was found to increase as the initial mean temperature was lowered, thereby leading to more enhanced compression-heating of the end-gas. Passive scalar mixing was not found to be important for the hot spot cases considered. The parametric study confirmed that the relative magnitude of the Sankaran number translates accurately to the quantitative strength of the deflagration front in the overall ignition advancement.     

Theoretical and numerical studies of non-equilibrium slip effects on a catalytic surface

A new concentration slip model to describe the rarefied gas effect on the species transport in microscale chemical reactors was derived from the approximate solution of the Boltzmann equation. The present model is more general and recovers the existing models in the limiting cases. The analytical results showed that the concentration slip is dominated by two different mechanisms, the reaction induced concentration slip (RIC) and the temperature slip induced concentration slip (TIC). The magnitude of RIC slip is proportional to the product of the Damköhler number and Knudsen number. The impact of the velocity, concentration and temperature slips on the coupling between the surface catalytic reactions and the homogeneous gas phase reactions was examined using the detailed chemistry of hydrogen and methane within a wide range of accommodation coefficients in a two-dimensional microscale chemical reactor. The results showed that the impact of reaction induced concentration slip (RIC) effects on catalytic reactions strongly depends on the Damköhler number, the Knudsen number and the surface accommodation coefficient. It was found that the TIC slip had a strong effect on the fuel oxidation rates and the RIC slip dramatically changed the mass fraction distributions of radicals, especially when the mass accommodation coefficients were far less than unity.     

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.     

Homoclinic bifurcations in radiating diffusion flames

We analyse the dynamics of a model describing a planar diffusion flame with radiative heat losses incorporating a single step kinetic using timestepping techniques for Lewis number equal to one. We construct the full bifurcation diagram with respect to the Damköhler number including the branches of oscillating solutions. Based on this analysis we found, for the first time, homoclinic bifurcations that mark the abrupt disappearance of the nonlinear oscillations near extinction as reported in experiments.     

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.     

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.     

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.     

Effect of longitudinal heat conduction on the catalytic ignition of carbon monoxide in a boundary layer

The catalytic ignition of dry carbon monoxide and air in a boundary layer flow over a palladium plate is studied in this paper. The heterogeneous reaction mechanism is modelled with the dissociative adsorption of the molecular oxygen and the non-dissociative adsorption of CO, together with a surface reaction of the Langmuir-Hinshelwood type and the desorption reaction of the adsorbed product, CO₂(s). The critical condition for catalytic ignition, represented by the ignition Damköhler number, has been deduced using high activation energy asymptotics of the desorption kinetics of the most efficiently adsorbed reactant, CO(s). Longitudinal heat conduction along the plate has been considered and its influence on the ignition temperature has been evaluated. This influence is rather weak, indicating that the flat plate boundary layer flow configuration is a robust device to determine the critical conditions for catalytic ignition.     

Structure and dynamics of edge flames in the near wake of unequal merging shear flows

We examine in this study the structure and dynamic properties of an edge flame formed in the near-wake of two initially separated shear flows, one containing fuel and the other oxidiser. A comprehensive study is carried out within the diffusive-thermal framework where the flow field, computed a-priori, is used for the determination of the combustion field. Our focus is on the effects of three controlling parameters: the Damköhler number controlling the overall flow rate, the oxidiser-to-fuel strain rate ratio of the supply streams that determines the extent of oxidiser entrainment towards the mixing zone, and the Lewis number, assumed equal for the fuel and oxidiser, that depends on the mixture composition. Response curves, representing the edge flame standoff distance as a function of Damköhler number, exhibit two distinct shapes: C-shaped and U-shaped curves characterising the response of low and high Lewis number flames, respectively. Stability considerations show that the upper solution branch of the C-shaped response curve is unstable and hence corresponds to physically unrealistic states, but due to heat conduction toward the cold plate the lower solution branch is always stable. The states forming this solution branch correspond to flame attachment, where the edge flame remains practically attached to the tip of the plate until it is blown off by the flow when the velocity exceeds a critical value. The U-shaped response, on the other hand, consists of equilibrium states that are globally stable. Thus, high Lewis number flames can be always stabilised near the splitter plate, with the edge held stationary or undergoing a back and forth motion, or lifted and stabilised downstream by the flow. Insight into the distinct stabilisation characteristics, exhibited by the different Lewis number cases, is given by examining the relationship between the local flow velocity and the edge propagation speed.     

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.