Reactant Lewis Numbers Research Articles

Diffusive-thermal instabilities of a planar premixed flame aligned with a shear flow

The stability of a thick planar premixed flame, propagating steadily in a direction transverse to that of unidirectional shear flow, is studied. A linear stability analysis is carried out in the asymptotic limit of infinitely large activation energy, yielding a dispersion relation. The relation characterises the coupling between Taylor dispersion (or shear-enhanced diffusion) and the flame thermo-diffusive instabilities, in terms of two main parameters, namely, the reactant Lewis number L e and the flow Peclet number P e . The implications of the dispersion relation are discussed and various flame instabilities are identified and classified in the L e - P e plane. An important original finding is the demonstration that for values of the Peclet number exceeding a critical value, the classical cellular instability, commonly found for L e < 1 , exists now for L e > 1 but is absent when L e < 1 . In fact, the cellular instability identified for L e > 1 is shown to occur either through a finite-wavelength stationary bifurcation (also known as type-I s ) or through a longwave stationary bifurcation (also known as type-II s ). The latter type-II s bifurcation leads in the weakly nonlinear regime to a Kuramoto-Sivashinsky equation, which is determined. As for the oscillatory instability, usually encountered in the absence of Taylor dispersion in L e > 1 mixtures, it is found to be absent if the Peclet number is large enough. The stability findings, which follow from the dispersion relation derived analytically, are complemented and examined numerically for a finite value of the Zeldovich number. The numerical study involves both computations of the eigenvalues of a linear stability boundary-value problem and numerical simulations of the time-dependent governing partial differential equations. The computations are found to be in good qualitative agreement with the analytical predictions.

Mathematical modeling of the production of magnetic nanoparticles through counter-flow non-premixed combustion for biomedical applications

PurposeThe widespread usage of magnetic nanoparticles (MNPs) requires their efficient synthesis during combustion process. This study aims to present a mathematical model for the oxidation of MNPs in a counter-flow non-premixed combustion system to produce MNPs, where the key sub-processes during the oxidation reaction are involved.Design/methodology/approachTo accurately describe structure of flame and determine distributions of temperature and mass fractions of both reactants and products, equations of energy and mass conservations were solved based on the prevailing assumptions that three regions, i.e. preheating, reaction and oxidizer zones exist.FindingsThe numerical simulation was first validated against experimental data and characteristics of the combustion process are discussed. Eventually, the influences of crucial parameters such as reactant Lewis numbers, strain rate ratio, particle size, inert gas and thermophoretic force on structure of flame and combustion behavior were examined. The results show that maximum flame temperature can achieve 2,205 K. Replacing nitrogen with argon and helium as carrier gases can increase flame temperature by about 27% and 34%, respectively. Additionally, maximum absolute thermophoretic force was found at approximately 9.6 × 10–8 N.Originality/valueTo the best of authors’ knowledge, this is the first time to numerically model the preparation of MNPs in a counter-flow non-premixed combustion configuration, which can guide large-scale experimental work in a more effective way.

Transition to detonation of an expanding spherical flame

With a freely expanding unwrinkled spherical flame as an example, it is shown that deflagration-to-detonation transition in unconfined gaseous systems is possible, provided the flame is close to its propagability threshold and the deficient reactant Lewis number is not too small. The transition is triggered by the thermal runaway induced by positive feedback between the accelerating flame and the flame-driven pressure build-up. A possible way to account for the impact of wrinkling is discussed.

Effects of syngas addition on flame propagation and stability in outwardly propagating spherical dimethyl ether-air premixed flames

Experiments in outwardly propagating spherical flame were carried out to investigate unstretched laminar burning velocity and flame instability by adding 25%, 50%, and 75% syngas to DME-air mixtures at room temperature and elevated pressures up to 0.3 MPa. The measured unstretched laminar burning velocities were compared to numerical predictions using PREMIX code with Zhao reaction mechanism and good agreement was found between them. Flame instability was also investigated through evaluating Markstein length and cellular instability. Behavior of the Markstein lengths was described well by the deficient reactant Lewis number and highly affected by the amount of syngas addition to the DME-air mixtures. Effects of syngas addition and increased initial pressure on cell formation on the flame surface were also examined through evaluating the Lewis number, flame thickness, and thermal expansion ratio. Regardless of syngas addition, the cellular instability was enhanced mainly by the hydrodynamic instability due to decreased flame thickness while diffusional-thermal instability was minor.

Important role of chemical interaction on flame extinction in downstream interaction between stretched premixed H2-air and CO-air flames

Important role of chemical interaction in flame extinction is numerically investigated in downstream interaction among lean (rich) and lean (rich) premixed as well as partially premixed H2- and CO-air flames. The strain rate varies from 30 to 5917 s−1 until interacting flames cannot be sustained anymore. Flame stability diagrams mapping lower and upper limit fuel concentrations for flame extinction as a function of strain rate are presented. Highly stretched interacting flames are survived only within two islands in the flame stability map where partially premixed mixture consists of rich H2-air flame, extremely lean CO-air flame, and a diffusion flame. Further increase in strain rate finally converges to two points. It is found that hydrogen penetrated from H2-air flame (even at lean flame condition) participates in CO oxidation vigorously due to the high diffusivity such that it modifies the slow main reaction route CO + O2 → CO2 + O into the fast cyclic reaction route involving CO + OH → CO2 + H. These chemical interactions force even rich extinction boundaries with deficient reactant Lewis numbers larger than unity to be slanted at high strain rate. Appreciable amount of hydrogen in the side of lean H2-air flame also oxidizes the CO penetrated from CO-air flame, and this reduces flame speed of the H2-air flame, leading to flame extinction. At extremely high strain rates, interacting flames are survived only by a partially premixed flame such that it consists of a very rich H2-air flame, an extremely lean CO-air flame, and a diffusion flame. In such a situation, both the weaker H2- and CO-air flames are parasite on the stronger diffusion flame such that it can lead to flame extinction in the situation of weakening the stronger diffusion flame. Important role of chemical interaction in flame extinction is discussed in detail.

Thermal-diffusive instabilities in unstretched, planar diffusion flames

The recent development of a novel research burner at EPFL has opened the way for experimental investigations of essentially unstretched planar diffusion flames. In particular, it has become feasible to experimentally validate theoretical models for thermal-diffusive instabilities in idealized one-dimensional diffusion flames. In this paper, the instabilities observed close to the lean extinction limit are mapped in parameter space, notably as function of the two reactant Lewis numbers. Cellular and pulsating instabilities are found at low and high Lewis numbers, respectively, as predicted by linear stability analyses. The detailed investigation of these two types of instabilities reveals the dependence of cell size and pulsation frequency on the transport properties of the reactants and on flow conditions. The experimental scaling of the cell size is found in good agreement with linear stability. The comparison between experimental and theoretical pulsation frequencies, on the other hand, was hampered by the impossibility of experimentally reproducing the parameters of the stability calculations. Hence, a heuristic correlation between pulsation frequency and flow parameters, transport properties, in particular the Damköhler number, and oscillation amplitude has been developed and awaits theoretical interpretation.

Effect of flame stretch in downstream Interaction between premixed syngas-air flames

The effect of strain rate in downstream interactions between lean (rich) and lean (rich) premixed syngas flames with the fuel composition of 50% H 2 and 50% CO is numerically investigated by varying the strain rate in the range of 5∼500 s −1. The flame stability maps for several strain rates are presented and main concerns are focused on the downstream interactions on the lean and rich extinction boundaries. The fuel composition of 50% H 2 and 50% CO with effective Lewis numbers larger than unity for both lean and rich extinction boundaries is chosen for grasping the important role of hydrogen with the deficient reactant Lewis numbers much smaller than unity. The results show that the lean extinction boundaries have the slanted shape, thereby leading to strong interactions; meanwhile the rich extinction boundaries at appropriately low strain rates are of square, indicating weak interactions. However, at highly strained interacting rich flames, the rich extinction boundaries show a slanted shape, thereby leading to strong interactions even for Lewis numbers much larger than unity. In such situations, thermal and chemical interactions are explained in detail. It is found that, in interacting flames, the excessive heat loss of the stronger flame partly to the weaker flame and mostly to the ambience is the mechanism of flame extinction.

Thermo-diffusive instabilities in axisymmetric, non-premixed jet flames

A general linear stability model, including hydrodynamic effects, has been developed for non-premixed axisymmetric jet flames. This stability model can be employed to investigate several types of instabilities which form in reacting jet flows, including (i) the Kelvin–Helmholtz modes which typically dominate at relatively high Damköhler numbers, and (ii) the thermo-diffusive modes which occur for relatively low Damköhler numbers near the extinction limit—the focus of the current study. The linear stability model developed for the reacting jet allows for variation of several important hydrodynamic and combustion parameters, including the velocity and density ratios of the fuel-to-oxidizer streams, the jet Reynolds number Re, and the ratio of the jet radius to the momentum thickness of the mixing layer, Damköhler number, and the initial mixture strength parameter. The jet flame was modelled using a one-step reaction with finite activation energy, and different Lewis numbers, ratios between the thermal and mass diffusivities, could be specified for the reactants. For jet flames at low Damköhler numbers near the extinction limit, investigations concentrated on the various absolutely unstable thermo-diffusive modes that form. Parameters were chosen that were representative of previous experimental jet flame studies. Consistent with previous experimental work, computations reveal that an axisymmetric pulsation is the dominate instability at relatively large reactant Lewis numbers, and cellular modes (single-cell or multi-cell flames) are dominate at relatively low Lewis numbers. The propensity for the cellular instabilities was shown to increase with decreasing reactant Lewis number, initial mixture strength and Damköhler number near the extinction limit. For relatively high initial mixture strength, computations also show that an azimuthal wavenumber m=1 mode can be dominate at intermediate fuel Lewis number values near the extinction limit.

Scaling of cell size in cellular instabilities of nonpremixed jet flames

Systematic experiments have been undertaken to study the parameter dependence of cellular instability and in particular the scaling of the resulting cell size in CO 2-diluted H 2–O 2 jet diffusion flames. Cellular flames are known to arise near the extinction limit when reactant Lewis numbers are relatively low. The Lewis numbers of the investigated near-extinction mixtures, based on the initial mixture strength ϕ m and ambient conditions, varied in the ranges [1.1–1.3] for oxygen and [0.25–0.29] for hydrogen ( ϕ m is defined here as the fuel-to-oxygen mass ratio, normalized by the stoichiometric ratio). The experiments were carried out both in an axisymmetric jet (AJ) burner and in a two-dimensional slot burner known as a Wolfhard–Parker (WP) burner with an oxidizer co-flow (mostly 100% O 2) of fixed low velocity. First, the region of cellular flames adjacent to the extinction limit was characterized in terms of initial H 2 concentration and fuel jet velocity, with all other parameters fixed. Then, the wavelength of the cellular instability, i.e., the cell size, was determined as a function of the fuel jet velocity and the initial mixture strength ϕ m . For conditions not too close to extinction, this wavelength is found to increase with the square root of the vorticity thickness of the jet shear layer and roughly the 1/5 power of ϕ m . Very close to extinction, this scaling breaks down and will likely switch to a scaling with the flame thickness, i.e., involving the Damköhler number.

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 CO 2-diluted H 2/O 2 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.

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.

A general asymptotic theory of diffusion flames with application to cellular instability

A general asymptotic formulation is presented for diffusion flames of large-activation-energy chemical reactions. In this limit chemical reaction is confined to a thin zone which, when viewed from the much larger diffusion scale, is a moving two-dimensional sheet. The formulation is not restricted to any particular configuration, and applies to conditions extending from complete combustion to extinction. The detailed structure of the reaction zone yields jump conditions that permit full determination of the combustion field on both sides of the reaction zone, as well as the instantaneous shape of the reaction sheet itself. The simplified system is subsequently used to study the intrinsic stability properties of diffusion flames and, in particular, the onset of cellular flames. We show that cellular diffusion flames form under near-extinction conditions when the reactant in the feed stream is the more completely consumed reactant, and the corresponding reactant Lewis number is below some critical value. Cell sizes at the onset of instability are on the order of the diffusion length. Predicted cell sizes and conditions for instability are therefore both comparable with experimental observations. Finally, we provide stability curves in the fuel and oxidant Lewis number parameter plane, showing where instability is expected for different values of both the initial mixture strength and the Damköhler number.

Non-premixed jet flame pulsations near extinction

A systematic experimental study was aimed at elucidating the conditions for which regular axisymmetric pulsations of the anchoring base of diluted propane and methane jet diffusion flames are observed. These self-excited oscillations result in the periodic streamwise contraction and extension of the flame length. The key experimental parameters governing this type of instability, which was only found near the extinction limit, are identified as the reactant stream Lewis numbers, the oxidizer-to-fuel-stream velocity ratio, and the initial mixture strength. For the diluted propane and methane flames studied, the tendency for pulsations increases with decreasing initial mixture strength, increasing reactant Lewis numbers (effective Lewis number typically >1), and decreasing oxidizer stream velocity (for fixed fuel velocity). Finally, possible connections between these experimental findings and combustion instabilities predicted by recent theoretical analyses are briefly discussed.

Numerical simulations of Lewis number effects in turbulent premixed flames

The structure of a premixed flame front propagating in a region of two-dimensional turbulence is investigated using full numerical simulation including heat release, variable properties, and one-step Arrhenius chemistry. The influence of reactant Lewis number (Le = ratio of thermal to species diffusivity) is reported for Le = 0.8, Le = 1.0, and Le = 1.2 flames. Local flame behaviour is described by comparing the local instantaneous turbulent flame structure (local consumption rate of reactants) to the steady one-dimensional laminar flame structure for the same thermochemical parameters. Statistics of flame front strain rates and curvature are calculated and global quantities of interest in modelling (flame surface area, mean reactant consumption rate per unit area of flame, and turbulent flame speed) are reported. Principal findings are: that probability density functions (p.d.f.s) of flame curvature are nearly symmetric about a near-zero mean; that the flame tends to align preferentially with extensive tangential strain rates; that the local flame structure of the non-unity Lewis number flames correlates more strongly with local flame curvature than with tangential strain rate; that the mean consumption rate per unit area is relatively insensitive to curvature and is controlled by the mean tangential strain rate; and, that more flame area is generated for Le 1. Implications of the results for flamelet models of turbulent premixed combustion are discussed.