Effects Of Non-unity Lewis Numbers Research Articles

Effects of unburnt reaction progress on stretch flame dynamics under elevated temperatures

Flames in practical combustors and engines are inevitably subject to the effects of upstream chemical reaction progress and stretch, induced by elevated thermodynamic conditions and flow non-uniformities, respectively. Recent shock tube experiments and simulation studies on flame propagation have shown that flame speed under engine-relevant conditions can be enhanced with non-negligible upstream chemical reaction progress, especially when low-temperature heat release is involved in the unburnt mixture. On the other hand, depending on the mixture equivalence ratio and diluents, nonequidiffusion (including the non-unity Lewis number effect and the preferential diffusion effect) can couple with the flame stretch to fundamentally affect the flame propagation, which can manifest as either facilitation or suppression. Depending on the transport property of a reacting mixture, there hence can be either inhibition or promotion from unburnt reaction progress and stretch effects on flame propagation. In the current work, through one-dimensional numerical simulations of transient planar and spherical flames of n-heptane/air under elevated thermodynamic conditions, the combined effects of upstream chemical reaction progress and stretch on flame propagation are investigated. Results show that for both lean and rich n-heptane/air mixtures, flame speed can be substantially promoted with reaction progress, while the rich mixtures can exhibit opposite stretch dependence after first-stage ignition. Different definitions of effective Lewis number are adopted to explain the change in Markstein length for spherical flame in lean and rich mixtures reformed by the low temperature chemistry. This work fills an important gap in laminar premixed flame research relevant to practical combustion systems and can provide useful insight into local turbulent flame behaviors and phi-sensitivity in engine combustion.

Large eddy simulation of the Cambridge/Sandia stratified flame with flamelet-generated manifolds: Effects of non-unity Lewis numbers and stretch

The Cambridge/Sandia turbulent stratified flame (SwB5) is simulated with the LES and Flamelet-Generated Manifolds (FGM) combustion model. Three 3D FGM manifolds are adopted. With the purpose to examine the influence of transport properties, unity and non-unity Lewis numbers (Le) are included in the first two manifolds, respectively. The combined effects of non-unity Le and stretch are investigated in the third manifold. Heat loss to the wall is also modeled. Good agreement is found between the simulation and experiment. The equivalence ratio, temperature and mass fractions of CO and H2 are all well reproduced in contrast with previous simulations. It is found that using non-unity Le can even deteriorate the near-wall temperature modeling. Non-unity Le is proposed to be crucial for the CO prediction as well, besides H2. The equivalence ratio modeling is observed to be very important, which accounts for several non-unity Le effects. Flame stretch shows almost no impact on the velocity fields, whereas its effects on the species, equivalence ratio and temperature are identified, although to a limited extent for the Cambridge/Sandia flame.

A DNS study of the impact of gravity on spherically expanding laminar premixed flames

Determining laminar flame speeds from spherical flame experiments is difficult for low flame speeds, when the flame shapes quickly become non-spherical due to the influence of gravity. Direct Numerical Simulations (DNS) of spherically expanding laminar premixed flames whose motion is affected by buoyancy have been performed. A lean methane/air flame and a series of rich hydrogen/air flames diluted with molecular nitrogen are considered to investigate the effects of different fuels. All flames feature low flame speeds such that the gravitational force quickly leads to a strong deformation of the initially spherical shapes. To assess the effects of non-unity Lewis numbers in the hydrogen flames, an additional DNS of one hydrogen flame is conducted with unity Lewis numbers for all species. All DNS employ finite rate chemistry. The effect of buoyancy on the flame dynamics is found to be governed by the Richardson number, which describes the relative importance of buoyancy with respect to the flame expansion, unless significant variations of the flame propagation speed due to strain rate and curvature occur, as observed for the hydrogen/air flames with non-unity Lewis numbers. In contrast to spherical flames, the linear dependence of the flame’s displacement speed on stretch is not observed. Unless effects due to non-unity Lewis numbers prevail, the displacement speed is found to be proportional to strain rate and curvature, which vary independently along the flame front of a buoyant flame. Based on the DNS data, five techniques to determine the burning velocity of the unstretched premixed flame from data collected in buoyant flames are discussed. Among these techniques, a methodology based on flame volume, surface area, and surface-averaged curvature shows promising results with relative errors below 2% for flames where effects due to non-unity Lewis numbers are negligible.

Circulation-controlled firewhirls with differential diffusion

A flame-sheet theory for circulation-controlled firewhirls with differential diffusion is presented to investigate the effects of non-unity and unequal Lewis numbers on the flame shape and height of the firewhirls. Variable physical properties and a piecewise generalized power-law vortex model are implemented in the theory. For the fuel and oxidizer Lewis numbers being unequal but close to unity, the perturbation solutions of the Burke–Schumann-like transport equation for the Lewis-number-weighted coupling functions were obtained by using the Green's function method. The derived flame height expression not only confirms the previous discoveries, such as the Peclet number effect found by Chuah et al. (2011), the strong vortex effect by Klimenko and William (2013), and the variable density and mass diffusivity effects by Yu and Zhang (2017), but also demonstrates that the mass-diffusivity-ratio model correction newly proposed by Yu and Zhang (2017) is attributable to the leading-order non-unity Lewis number effect. The validity of the differential diffusion effects on the flame height was extended to arbitrary Lewis numbers and verified by means of the approximate far-field similarity solutions of the mixture fraction.

Flame thickness and conditional scalar dissipation rate in a premixed temporal turbulent reacting jet

The flame structure corresponding to lean hydrogen–air premixed flames in intense sheared turbulence in the thin reaction zone regime is quantified from flame thickness and conditional scalar dissipation rate statistics, obtained from recent direct numerical simulation data of premixed temporally-evolving turbulent slot jet flames [1]. It is found that, on average, these sheared turbulent flames are thinner than their corresponding planar laminar flames. Extensive analysis is performed to identify the reason for this counter-intuitive thinning effect. The factors controlling the flame thickness are analyzed through two different routes i.e., the kinematic route, and the transport and chemical kinetics route. The kinematic route is examined by comparing the statistics of the normal strain rate due to fluid motion with the statistics of the normal strain rate due to varying flame displacement speed or self-propagation. It is found that while the fluid normal straining is positive and tends to separate iso-scalar surfaces, the dominating normal strain rate due to self-propagation is negative and tends to bring the iso-scalar surfaces closer resulting in overall thinning of the flame. The transport and chemical kinetics route is examined by studying the non-unity Lewis number effect on the premixed flames. The effects from the kinematic route are found to couple with the transport and chemical kinetics route. In addition, the intermittency of the conditional scalar dissipation rate is also examined. It is found to exhibit a unique non-monotonicity of the exponent of the stretched exponential function, conventionally used to describe probability density function tails of such variables. The non-monotonicity is attributed to the detailed chemical structure of hydrogen-air flames in which heat release occurs close to the unburnt reactants at near free-stream temperatures.

The large-activation-energy analysis of extinction of counterflow diffusion flames with non-unity Lewis numbers of the fuel

Large-activation-energy asymptotic techniques are used to describe the effects of non-unity Lewis numbers of the fuel on strain-induced extinction of axisymmetric counterflow diffusion flames. The present work extends and clarifies previous investigations by accounting also for variable density and variable transport properties of the gas. In our asymptotic analysis the flame structure near extinction is, at leading order, given by the Burke–Schumann limit of infinitely fast reaction; i.e. two outer regions of equilibrium flow, with the fuel and the oxygen separated by an infinitesimally thin reaction layer where they arrive by diffusion in stoichiometric proportions. The leading-order description provides the basic flow structure, including the flame-sheet location, the fuel-consumption rate, the temperature gradients on both sides of the flame, and the peak value of the temperature, which plays a dominant role in flame extinction and differs significantly from the adiabatic-flame value for non-unity Lewis numbers. In the near-extinction regime small departures, due to finite rates, from the fast-reaction limit are enough to dominate the structure of the reaction layer, and must be taken into account in this thin layer and in the outer chemically frozen regions, where the corrections are associated with the reactants leaking, with small mass fractions, through the flame. The main effect of the differential diffusion in the near-extinction regime is due to the strong modification of the reaction rates resulting from the changes in the Burke–Schumann peak temperature, with only moderate corrections due to leakage of the reactants through the flame. For large values of the overall stoichiometric ratio S of the diffusion flame, defined as the mass of the air stream needed to burn to completion the unit mass of the fuel stream, the extinction conditions occur in a premixed-flame regime, in which the reaction layer is displaced towards the fuel side with respect to the Burke–Schumann flame sheet position and a fraction of the arriving fuel mass flux leaks through the reaction layer, while the mass fraction of the leaking oxygen decreases to negligibly small values. The asymptotic predictions are tested by comparison with numerical integrations of extinction curves based on continuation methods.

Effects of non-unity Lewis number of gas-phase species in turbulent nonpremixed sooting flames

Turbulence statistics from two three-dimensional direct numerical simulations of planar n-heptane/air turbulent jets are compared to assess the effect of the gas-phase species diffusion model on flame dynamics and soot formation. The Reynolds number based on the initial jet width and velocity is around 15, 000, corresponding to a Taylor scale Reynolds number in the range 100 ≤ Reλ ≤ 150. In one simulation, multicomponent transport based on a mixture-averaged approach is employed, while in the other the gas-phase species Lewis numbers are set equal to unity. The statistics of temperature and major species obtained with the mixture-averaged formulation are very similar to those in the unity Lewis number case. In both cases, the statistics of temperature are captured with remarkable accuracy by a laminar flamelet model with unity Lewis numbers. On the contrary, a flamelet with a mixture-averaged diffusion model, which corresponds to the model used in the multi-component diffusion three-dimensional DNS, produces significant differences with respect to the DNS results. The total mass of soot precursors decreases by 20–30% with the unity Lewis number approximation, and their distribution is more homogeneous in space and time. Due to the non-linearity of the soot growth rate with respect to the precursors’ concentration, the soot mass yield decreases by a factor of two. Being strongly affected by coagulation, soot number density is not altered significantly if the unity Lewis number model is used rather than the mixture-averaged diffusion. The dominant role of turbulent transport over differential diffusion effects is expected to become more pronounced for higher Reynolds numbers.

Modelling paradigms for MILD combustion

Three-dimensional Direct Numerical Simulation (DNS) data of methane-air MILD combustion is analysed to study the behaviour of MILD reaction zones and to identify a suitable modelling paradigm for MILD combustion. The combustion kinetics in the DNS was modelled using a skeletal mechanism including non-unity Lewis number effects. The reaction zones under MILD conditions are highly convoluted and contorted resulting in their frequent interactions. This leads to combustion occurring over a large portion of the computational volume and giving an appearance of distributed combustion. Three paradigms, standard flamelets, mild flame elements (MIFEs) and PSR, along with a presumed PDF model are explored to estimate the mean and filtered reaction rate in MILD combustion. A beta function is used to estimate the presumed PDF shape. The variations of species mass fractions and reaction rate with temperature computed using these models are compared to the DNS results. The PSR-based model is found to be appropriate, since the conditional averages obtained from the DNS agree well with those obtained using the PSR model. The flamelets model with MIFEs gives only a qualitative agreement because it does not include the effects of reaction zone interactions.

Scalar gradient behaviour in MILD combustion

The results of three-dimensional Direct Numerical Simulation (DNS) of Moderate, Intense Low-oxygen Dilution (MILD) and conventional premixed turbulent combustion conducted using a skeletal mechanism including the effects of non-unity Lewis numbers and temperature dependent transport properties are analysed to investigate combustion characteristics using scalar gradient information. The DNS data is also used to synthesise laser induced fluorescence (LIF) signals of OH, CH2O, and CHO. These signals are analysed to verify if they can be used to study turbulent MILD combustion and it has been observed that at least two (OH and CH2O) LIF signals are required since the OH increase across the reaction zone is smaller in MILD combustion compared to premixed combustion. The scalar gradient PDFs conditioned on the reaction rate obtained from the DNS data and synthesised LIF signals suggests a strong gradient in the direction normal to the MILD reaction zone with moderate reaction rate implying flamelet combustion. However, the PDF of the normal gradient is as broad as for the tangential gradient when the reaction rate is high. This suggests a non-flamelet behaviour, which is due to interaction of reaction zones. The analysis of the conditional PDFs for the premixed case confirms the expected behaviour of scalar gradient in flamelet combustion. It has been shown that the LIF signals synthesised using 2D slices of DNS data also provide very similar insights. These results demonstrate that the so-called flameless combustion is not an idealised homogeneous reactive mixture but has common features of conventional combustion while containing distinctive characteristics.

Direct numerical simulation of autoigniting mixing layers in MILD combustion

MILD combustion is a new combustion technology which promises an enhanced efficiency and reduced emission of pollutants. It is characterized by a high degree of preheating and dilution of the reactants. Since the temperature of the reactants is higher than that of autoignition, a complex interplay between turbulent mixing, molecular transport and chemical kinetics occurs. In order to reveal the fundamental reaction structures of MILD combustion, the process of a cold methane–hydrogen fuel jet issuing in a hot diluted coflow and the subsequent ignition process is modeled by direct numerical simulation of autoigniting mixing layers using detailed chemistry and transport models. Detailed analysis of one-dimensional laminar mixing layers shows that the ignition process is dominated by hydrogen chemistry and that non-unity Lewis number effects are of the utmost importance for modeling of autoignition. High scalar dissipation rates in mixing layers delay the autoignition time, but have a negligible effect on the chemical pathway followed during ignition. This supports the idea of using homogeneous reactor simulations for the construction of chemistry look-up tables. Simulations of two-dimensional turbulent mixing layers confirm the effect of scalar dissipation rate on autoignition time. The turbulence–chemistry interaction is limited under the investigated conditions, because the reaction layer lies at the edge of the mixing layer due to the very small value of the stoichiometric mixture fraction. When the oxidizer stream is more diluted, the autoignition time is delayed, allowing the developing turbulence to interact more with the ignition chemistry. The results of these direct numerical simulations employing a detailed reaction mechanism are expected to be used for the development of tabulated chemistry models and sub-grid scale models for large-eddy simulations of MILD combustion.

Understanding ignition processes in spray-guided gasoline engines using high-speed imaging and the extended spark-ignition model SparkCIMM: Part B: Importance of molecular fuel properties in early flame front propagation

Recent high-speed imaging of ignition processes in spray-guided gasoline engines has motivated the development of the physically-based spark channel ignition monitoring model SparkCIMM, which bridges the gap between a detailed spray and vaporization model and a model for fully developed turbulent combustion. Previously, both SparkCIMM and high-speed optical imaging data have shown that, in spray-guided engines, large variations in turbulence intensity, equivalence ratio, and enthalpy along the stretched and wrinkled spark plasma channel favor localized ignition spot formations in rich-mixture regions. In combination with strong local flow velocity, multiple successful ignition events along the re-striking spark lead to early non-spherical turbulent flame fronts. In this paper, SparkCIMM is enhanced by: (1) criteria to capture localized flame extinction phenomena, (2) a formulation of early flame kernel propagation based on the G-equation theory that includes effects of non-unity Lewis numbers, and (3) an extended equation to compute turbulent burning velocities of stretched flames in stratified mixtures. Localized rich ignition along the spark leads to early flames, whose propagation is, due to initially small turbulent Damköhler numbers, significantly influenced by molecular fuel properties. The analysis reveals that non-unity Lewis number curvature effects, intensified by heavy dilution by exhaust gas recirculation, strongly affect the early flame-kernel development in spray-guided gasoline engines. In particular, these effects significantly bias the flammability limit of flame kernels towards rich-mixtures while inhibiting their propagation in lean regions. Favorable initial conditions for combustion are found in rich-mixture regions, albeit in the presence of substantial equivalence ratio fluctuations and scalar dissipation rates. This paper demonstrates that the full complexity of the model equations developed here is required to reproduce the characteristic experimental features (spark channel stretching, multiple re-strikes, localized flame kernel formation, and early turbulent flame front corrugation) of spray-guided ignition phenomena.

The Effect of Preferential Diffusion on the Soot Initiation Process in Ethylene Diffusion Flames

The influence of differential diffusion of chemical species in the soot initiation process in turbulent flows is investigated through Direct Numerical Simulations coupled to a compact global chemical mechanisms for ethylene (C2H4) flame combustion (Lovas et al., Combust Sci Tech 182(11):1945–1960, 2010) featuring the important reaction steps for acetylene production. Our focus is on the formation of acetylene (C2H2) which is one of the most important species indicative of soot formation layers, especially in relation to the location of the H and H2 layers. The effect of preferential diffusion is assessed by comparison of results from unity and non-unity Lewis number simulations. The results indicate that under moderate turbulent conditions, where preferential diffusion effects become prominent, and with the global scheme used preferential diffusion greatly enhances the spread of the radical H whose peak value in mass fraction is reduced by a factor of about two; the spread of H2 is also enhanced though to a lesser extent. Importantly, the H and H2 spread into a range of mixture fraction Z between 0.2 and 0.3 which contains the soot formation range, supporting the hypothesis that soot formation is enhanced by preferential diffusion. Nevertheless, the acetylene formation layers themselves show little adjustment in the presence of non-unity Lewis numbers suggesting that the acetylene formation is dominated under the current conditions by the direct thermal decomposition of ethylene to acetylene in the global chemistry used. The specific Fi factors that appear in flamelet models are explicitly computed; only FH, FH2 and FCO show appreciable differences on the fuel lean range of mixture fraction due to non-unity Lewis numbers, suggesting that the effects of non-unity Lewis numbers could be incorporated by a selective inclusion of only a few of the Fi factors in order to save computational time.

Effects of Lewis number on flame surface density transport in turbulent premixed combustion

The transport of flame surface density (FSD) in turbulent premixed flames has been studied using a database obtained from Direct Numerical Simulation (DNS). Three-dimensional freely propagating developing statistically planar turbulent premixed flames have been examined over a range of global Lewis numbers from 0.6 to 1.2. Simplified chemistry has been used and the emphasis is on the effects of Lewis number on FSD transport in the context of Reynolds-averaged closure modelling. Under the same initial conditions of turbulence, flames with low Lewis numbers are found to exhibit counter-gradient transport of FSD, whereas flames with higher Lewis numbers tend to exhibit gradient transport of FSD. Stronger heat release effects for lower Lewis number flames are found to lead to an increase in the positive (negative) value of the dilatation rate (normal strain rate) term in the FSD transport equation with decreasing Lewis number. The contribution of flame curvature to FSD transport is found to be influenced significantly by the effects of Lewis number on the curvature dependence of the magnitude of the reaction progress variable gradient, and on the combined reaction and normal diffusion components of displacement speed. The modelling of the various terms of the FSD transport equation has been analysed in detail and the performance of existing models is assessed with respect to the terms assembled from corresponding quantities extracted from DNS data. Based on this assessment, suitable models are identified which are able to address the effects of non-unity Lewis number on FSD transport, and new or modified models are suggested wherever necessary.

Effects of Lewis Number on Scalar Dissipation Transport and Its Modeling in Turbulent Premixed Combustion

The effects of Lewis number (Le) on scalar dissipation rate transport of the reaction progress variable have been studied using 3-dimensional DNS data of freely propagating turbulent premixed flames with global Lewis number ranging from 0.34 to 1.2. It has been found that the effects of dilatation rate become increasingly strong with decreasing Le, and is particularly strong for the Le ≪ 1 flames because of greater rate of heat release. Moreover, increasingly strong flame normal acceleration in flames with decreasing Le gives rise to countergradient transport for the turbulent flux of the scalar dissipation rate, whereas this flux exhibits gradient transport for flames with Le ≥ 1. This turbulent flux is observed to correlate with the behavior of the turbulent scalar flux and this behavior is used to propose an algebraic closure for the turbulent flux of the scalar dissipation rate. The modeling of nonunity Le effects on the unclosed terms arising from the density change across the flame front, the turbulence–scalar interaction, the correlation between scalar gradient and the gradient of reaction rate and the molecular dissipation have been addressed. The extent of reaction progress variable gradient alignment with the most extensive (compressive) principal strain rate is found to increase (decrease) with decreasing Le. This alignment behavior gives rise to a sink contribution arising from the turbulence–scalar interaction in the Le ≪ 1 flames. By contrast, the turbulence–scalar interaction acts predominantly as a source term, although this contribution becomes a sink toward the burned gas side for the Le ≥ 1 flames. It has been demonstrated that existing models for the unclosed terms originating from the density change across the flame front and the turbulence–scalar interaction cannot account for strengthening (weakening) of heat release effects when Le < 1 (Le > 1). Suitable modifications to these models have been proposed to account for nonunity Lewis number effects, and validated using direct numerical simulation data. A simple algebraic expression is suggested that successfully relates the scalar dissipation rate of normalized temperature to the scalar dissipation rate of the reaction progress variable in nonunity Lewis number turbulent flames.

Effects of Lewis number on turbulent scalar transport and its modelling in turbulent premixed flames

The behaviour of the turbulent scalar flux in premixed flames has been studied using Direct Numerical Simulation (DNS) with emphasis on the effects of Lewis number in the context of Reynolds-averaged closure modelling. A database was obtained from DNS of three-dimensional freely propagating statistically planar turbulent premixed flames with simplified chemistry and a range of global Lewis numbers from 0.34 to 1.2. Under the same initial conditions of turbulence, flames with low Lewis numbers are found to exhibit counter-gradient transport, whereas flames with higher Lewis numbers tend to exhibit gradient transport. The Reynolds-averaged transport equation for the turbulent scalar flux is analysed in detail and the performance of existing models for the unclosed terms is assessed with respect to corresponding quantities extracted from DNS data. Based on this assessment, existing models which are able to address the effects of non-unity Lewis number on turbulent scalar flux transport are identified, and new or modified models are suggested wherever necessary. In this way, a complete set of closure models for the scalar flux transport equation is prescribed for use in Reynolds-Averaged Navier–Stokes simulations.

Response of spherical diffusion flames under rotation with general Lewis numbers

The structure and extinction of diffusion flames generated by a porous spherical burner or a fuel droplet in response to rotational motion were investigated through perturbation analysis, with emphasis on the effects of non-unity Lewis numbers (Le) for both fuel and oxidizer. The analysis shows that the rotational motion induces a secondary flow that distorts the otherwise spherical flame into a pancake shape. The flame temperature is also affected, such that the flame becomes more susceptible to extinction either at the poles or the equator, depending on the combined effects of Lewis numbers, flame stretch through local flow non-uniformity and ambient oxidizer concentration. The results reported here will help guide planned microgravity experiments.

Numerical Analysis of Jet Diffusion Flames Interacted with Large Scale Vortex

This paper describes a numerical study on the H2/N2 jet diffusion flame interacted with large scale vortices generated by oscillating the fuel velocity. Computations are made of transient diffusion flames. Attentions are paid to the dynamic behavior of the diffusion flames with the transient local extinction and to the flame structure in relation to the local flame parameters such as local flame stretch and preferential diffusion. The obtained results are as follows. (1) When the amplitude of fuel velocity is relatively small, flame extinction does not occur by interaction between flame and vortex, and the temperature characteristics depends on the effect of the preferential diffusion among species and the non-unity Lewis number effect. (2) When the amplitude of fuel velocity is large, the temperature decreases in the region where the stretch rate near the circumferential part of vortex is high. According to the procedure of non-equilibrium of chemical reaction, temperature and heat release rate begins to decrease at the region and the effect results in flame extinction. (3) The position of the local flame extinction does not always agree with that of higher stretch rate. During the procedure of the flame extinction, the position of higher stretch rate moves downstream from the position of extinction. (4) One of the edge flames constructed at the extinction propagates along the stoichiometric line around the vortex to the upstream region, and it is again connected with another edge flame.

Periodic motion of a Bunsen flame tip with burner rotation

Effects of burner rotation on the shapes and dynamics of premixed Bunsen flames have been investigated experimentally in normal gravity and in microgravity. Mixtures of CH 4-air and C 3H 8-air are issued from the burner tube with mean flow velocity U = 0.6 m/s. The burner tube is rotated up to 1400 rpm (swirl number S = 1.58). An oscillating flame with large amplitude is formed between a conical-shape flame and a plateau flame under the condition of Lewis number Le > 1 mixtures (rich CH 4-air and lean C 3H 8-air mixtures). In contrast, for Le ≤ 1 mixtures (lean CH 4-air and rich C 3H 8-air), asymmetric, eccentric flame or tilted flame is formed under the same swirl number range. Under microgravity condition, the oscillating flames are not formed, indicating that the oscillation is driven by buoyancy-induced instability associated with the unstable interface between the hot products and the ambient air. The flame tip flickering frequency ν is insensitive to burner rotation for S < 0.11. For S > 0.11, ν decreases linearly with increasing S. As S exceeds 0.11, a minimum value of axial mean velocity along the center line u j,m due to flow divergence is found and it has a linear relationship with ν. This result shows that u j,m has direct control of the oscillation frequency. When S approaches unity, the flame oscillation amplitude increases by a factor of 5, compared to the flickering amplitude of a conical-shape flame. This is accompanied by a hysteresis variation in the flame curvature from positive to negative and the thermo-diffusive zone thickness varying from small to large. With S > 1.3, the plateau flame has the same small flickering amplitudes as with S = 0. These results show that the competing centrifugal and buoyancy forces, and the non-unity Lewis number effect, play important roles in amplifying the flame-tip oscillation.

Opposed flow polydisperse spray diffusion flames: Steady state and extinction analysis

A new analysis of polydisperse opposed flow spray diffusion flames is presented. The model permits non-unity Lewis number effects for the gaseous components, as well as a finite rate of evaporation for the droplets. Combined effects of droplet loading and spray polydispersity on the characteristics of spray flames are investigated using outer region analytic solutions. Under the assumption that the droplets are in dynamic and thermal equilibrium with their surroundings it is demonstrated that spray polydispersity alone has a profound effect on flame location, temperature and the mode of combustion (homogeneous, or homogeneous and heterogeneous combustion). Conditions for flame extinction are also examined. Frequently, polydisperse sprays are described in a global fashion by relating to them as if they were comprised of single size droplets having some average diameter, such as the Sauter mean diameter or a mean diameter based on the total surface area of the spray. It is shown that this approach can be rather erroneous when flame extinction is under consideration. By comparing strain rates for extinguishment it is demonstrated that critical extinction conditions must be based on a true representation of the spray's polydispersity, otherwise errors of as much as almost 60% can ensue.

Numerical Analysis on Quenching of Premixed Flame at a Small Circular Hole Made in a Cooled Plate (Quenching Mechanism of Hydrogen-Air Premixed Flame)

In order to clarify the unsteady behavior and the quenching mechanism of the hydrogen-air premixed flame at a small circular hole made in the cooled plate put in the large container, the numerical calculation was carried out by using the detailed chemical kinetics. In this calculation, the stationary premixed gas is filled in the container at the start, and then the mixture is ignited at the end face and the flame propagates to the hole. At the hole, the flow is induced by the flame propagation and the heat is taken from the cooled wall, so that the flame front changes unsteadily and has the curvature. When the flame front has the curvature, the effects of non-unity Lewis number of the hydrogen fuel lean or rich mixtures appear in the quenching process. The relationship between the quenching diameter and the equivalence ratio are shown for the different thickness of the cooled plate. Moreover, the unsteady flame behavior and the critical quenching process are shown for the fuel lean and rich mixtures, and the quenching mechanism is examined so that the effects of the cooling and the Lewis number are charified.