Lewis Number Flames Research Articles

A PrioriAssessment of Algebraic Flame Surface Density Models in the Context of Large Eddy Simulation for Nonunity Lewis Number Flames in the Thin Reaction Zones Regime

The performance of algebraic flame surface density (FSD) models has been assessed for flames with nonunity Lewis number (Le) in the thin reaction zones regime, using a direct numerical simulation (DNS) database of freely propagating turbulent premixed flames with Le ranging from 0.34 to 1.2. The focus is on algebraic FSD models based on a power-law approach, and the effects of Lewis number on the fractal dimensionDand inner cut-off scaleηihave been studied in detail. It has been found thatDis strongly affected by Lewis number and increases significantly with decreasing Le. By contrast,ηiremains close to the laminar flame thermal thickness for all values of Le considered here. A parameterisation ofDis proposed such that the effects of Lewis number are explicitly accounted for. The new parameterisation is used to propose a new algebraic model for FSD. The performance of the new model is assessed with respect to results for the generalised FSD obtained from explicitly LES-filtered DNS data. It has been found that the performance of the most existing models deteriorates with decreasing Lewis number, while the newly proposed model is found to perform as well or better than the most existing algebraic models for FSD.

Effects of Lewis number on turbulent kinetic energy transport in premixed flames

The effects of global Lewis number on the statistical behaviour of turbulent kinetic energy transport in turbulent premixed flames are analysed using three-dimensional direct numerical simulation (DNS) data for freely propagating statistically planar flames with Lewis number ranging from 0.34 to 1.2. For flames with Lewis number significantly smaller than unity, it is observed that the turbulent kinetic energy is significantly augmented within the flame brush due to flame-generated turbulence. In these flames, it is demonstrated that effects of the mean pressure gradient and pressure dilatation are sufficient to overcome the effects of viscous dissipation. By contrast, for flames with Lewis number close to unity, it is found that the turbulent kinetic energy decays monotonically through the flame brush. In these flames, the effects of the mean pressure gradient and pressure dilatation terms are relatively much weaker than those of viscous dissipation. The modelling of the various unclosed terms of the turbulent kinetic energy transport equation has been analysed in detail. The predictions of existing models are compared with corresponding quantities extracted from DNS data. Based on this a-priori DNS assessment, either appropriate models are identified or new models are proposed where necessary. It is shown that the turbulent flux of turbulent kinetic energy exhibits counter-gradient transport for the low Lewis number flames where the turbulent scalar flux is also counter-gradient in nature. However, for flames with Lewis number close to unity, the turbulent flux of turbulent kinetic energy exhibits predominantly gradient type transport. A new model has been proposed for the flux of turbulent kinetic energy in premixed flames and is found to capture the qualitative and quantitative behaviour obtained from DNS data for all the different Lewis numbers considered.

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.

Statistics of Conditional Fluid Velocity in the Corrugated Flamelets Regime of Turbulent Premixed Combustion: A Direct Numerical Simulation Study

The statistics of mean fluid velocity components conditional in unburned reactants and fully burned products in the context of Reynolds Averaged Navier Stokes (RANS) simulations have been studied using a Direct Numerical Simulation database of statistically planar turbulent premixed flame representing the corrugated flamelets regime combustion. Expressions for conditional mean velocity and conditional velocity correlations which are derived based on a presumed bimodal probability density function of reaction progress variable for unity Lewis number flames are assessed in this study with respect to the corresponding quantities extracted from DNS data. In particular, conditional surface averaged velocities and the velocity correlations in the unburned reactants are demonstrated to be effectively modelled by the unconditional velocities and velocity correlations , respectively, for the major part of turbulent flame brush with the exception of the leading edge. By contrast, conditional surface averaged velocities and the velocity correlations in fully burned products are shown to be markedly different from the unconditional velocities and velocity correlations , respectively.

Comparison of 2D and 3D density-weighted displacement speed statistics and implications for laser based measurements of flame displacement speed using direct numerical simulation data

In a recent study, a light sheet imaging approach has been proposed (Hartung et al., J. Appl. Phys. B 96 (2009) 843–862) which permits measurement of a quantity S d ∗ 2 D , which is the two-dimensional projection of the actual density-weighted displacement speed S d ∗ for turbulent premixed flames. Here the statistics of S d ∗ and S d ∗ 2 D are compared using a direct numerical simulation database of statistically planar turbulent premixed flames. It is found that the probability density functions (pdfs) of S d ∗ 2 D approximate the pdfs of S d ∗ satisfactorily for small values of root-mean-square turbulent velocity fluctuation u′, though the S d ∗ 2 D pdfs are wider than the S d ∗ pdfs. Although the agreement between the pdfs and the standard-deviations of S d ∗ 2 D and S d ∗ deteriorate with increasing u′, the mean values of S d ∗ 2 D correspond closely with the mean values of S d ∗ for all cases considered here. The pdfs of two-dimensional curvature κ m 2 D and the two-dimensional tangential-diffusion component of density-weighted displacement speed S t ∗ 2 D are found to be narrower than their three-dimensional counterparts (i.e. κ m and S t ∗ respectively). It has been found that the pdfs, mean and standard-deviation of π / 2 × κ m 2 D and π / 2 × S t ∗ 2 D faithfully capture the pdfs, mean and standard-deviation of the corresponding three-dimensional counterparts, κ m and S t ∗ respectively. The combination of wider S d ∗ 2 D pdfs in comparison to S d ∗ pdfs, and narrower S t ∗ 2 D pdfs in comparison to S t ∗ pdfs, leads to wider S r ∗ + S n ∗ 2 D = S d ∗ 2 D - S t ∗ 2 D pdfs than the pdfs of combined reaction and normal-diffusion components of density-weighted displacement speed S r ∗ + S n ∗ . This is reflected in the higher value of standard-deviation of S r ∗ + S n ∗ 2 D , than that of its three-dimensional counterpart S r ∗ + S n ∗ . However, the mean values of S r ∗ + S n ∗ 2 D remain close to the mean values of S r ∗ + S n ∗ . The loss of perfect correlation between two and three-dimensional quantities leads to important qualitative differences between the S r ∗ + S n ∗ 2 D - κ m 2 D and S r ∗ + S n ∗ - κ m , and between the S d ∗ 2 D - κ m 2 D and S d ∗ - κ m correlations. For unity Lewis number flames, the S d ∗ - κ m correlation remains strongly negative, whereas a weak correlation is observed between S d ∗ 2 D and κ m 2 D . The study demonstrates the strengths and limitations of the predictive capabilities of the planar imaging techniques in the context of the measurement of density-weighted displacement speed, which are important for detailed model development or validation based on experimental data.

Lewis number effect on the propagation of premixed flames in narrow adiabatic channels: Symmetric and non-symmetric flames and their linear stability analysis

The propagation of premixed flames with different Lewis numbers in a planar channel subject to a Poiseuille flow is considered within the diffusive-thermal model for steady and time-dependent cases. It was found that, depending on the Lewis number and the flow rate, symmetric and non-symmetric flames are possible. The existence of multiple steady solutions in cases of the low Lewis number is demonstrated. The time-dependent simulations carried out for high Lewis number flames also showed the symmetric and non-symmetric oscillatory solutions. Linear stability analysis of two-dimensional steady-states was performed using a practical method developed in the paper and applied to calculate the main eigenvalue. It was shown that for symmetric flames with a low Lewis number the increase in the flow rate leads to a loss of stability with subsequent formation of non-symmetric solutions. For flames with a high Lewis number the Poiseuille flow produces a stabilization effect. The results of the stability analysis were successfully compared with the results of direct numerical simulations.

Effects of Lewis Number on Scalar Variance Transport in Premixed Flames

The influences of differential diffusion rates of heat and mass on the transport of the variances of Favre fluctuations of reaction progress variable and non-dimensional temperature have been studied using three-dimensional simplified chemistry based Direct Numerical Simulation (DNS) data of statistically planar turbulent premixed flames with global Lewis number ranging from Le = 0.34 to 1.2. The Lewis number effects on the statistical behaviours of the various terms of the transport equations of variances of Favre fluctuations of reaction progress variable and non-dimensional temperature have been analysed in the context of Reynolds Averaged Navier Stokes (RANS) simulations. It has been found that the turbulent fluxes of the progress variable and temperature variances exhibit counter-gradient transport for the flames with Lewis number significantly smaller than unity whereas the extent of this counter-gradient transport is found to decrease with increasing Lewis number. The Lewis number is also shown to have significant influences on the magnitudes of the chemical reaction and scalar dissipation rate contributions to the scalar variance transport. The modelling of the unclosed terms in the scalar variance equations for the non-unity Lewis number flames have been discussed in detail. The performances of the existing models for the unclosed terms are assessed based on a-priori analysis of DNS data. Based on the present analysis, new models for the unclosed terms of the active scalar variance transport equations are proposed, whenever necessary, which are shown to satisfactorily capture the behaviours of unclosed terms for all the flames considered in this study.

Characterization of low Lewis number flames

A recent numerical study of turbulence–flame interactions in lean premixed hydrogen, where the Lewis number was approximately 0.36, observed that flames at different equivalence ratios presented significantly different behavior despite having the same Karlovitz and Damköhler numbers. This differing behavior is due to the thermodiffusively-unstable nature of low Lewis number flames. In more than one dimension, differential diffusion focuses fuel into hot regions increasing the local burning rate, which was found to affect the leaner hydrogen flames more significantly. Ultimately, this difference between idealized flat flames and freely-propagating flames undermines the characterization of turbulent flames through Karlovitz and Damköhler numbers based on flat laminar quantities. This paper considers refining the definitions of these dimensionless numbers by replacing the flat laminar flame values with freely-propagating values. In particular, we perform three-dimensional simulations of freely-propagating flames over a range of equivalence ratios, and use data from those simulations to define modified Karlovitz and Damkölher numbers. This provides a framework to classify low Lewis number turbulent flames in the context of the premixed combustion regime diagram that eliminates anomalies with the traditional definitions for low Lewis number flames. We then perform a series of turbulent flame simulations that show that our new definitions effectively eliminate the dependence on fuel equivalence ratio.

DISTRIBUTED FLAMES IN TYPE Ia SUPERNOVAE

In the distributed burning regime, turbulence disrupts the internal structure of the flame, and so the idea of laminar burning propagated by conduction is no longer valid. The nature of the burning depends on the turbulent Damkohler number (Da), which steadily declines from much greater than one to less that one as the density decreases to a few 10^6 g/cc. Scaling arguments predict that the turbulent flame speed s, normalized by the turbulent intensity u, follows s/u=Da^1/2 for Da<1. The flame in this regime is a single turbulently-broadened structure that moves at a steady speed, and has a width larger than the integral scale of the turbulence. The scaling is predicted to break down at Da=1, and the flame burns as a turbulently-broadened effective unity Lewis number flame. We refer to this kind of flame as a lambda-flame. The burning becomes a collection of lambda-flames spread over a region approximately the size of the integral scale. While the total burning rate continues to have a well-defined average, s_{T} ~ u, the burning is unsteady. We present a theoretical framework, supported by both 1D and 3D numerical simulations, for the burning in these two regimes. Our results indicate that the average value of s can actually be roughly twice u for Da>1, and that localized excursions to as much as five times u can occur. The lambda-flame speed and width can be predicted based on the turbulence in the star and the turbulent nuclear burning time scale of the fuel. We propose a practical method for measuring these based on the scaling relations and small-scale computationally-inexpensive simulations. This suggests that a simple turbulent flame model can be easily constructed suitable for large-scale distributed supernovae flames.

Measurements of Laminar Burning Velocities and Markstein Lengths ofn-Butanol−Air Premixed Mixtures at Elevated Temperatures and Pressures

Measurements of laminar burning velocities and Markstein lengths of n-butanol−air premixed mixtures was made over a wide range of equivalence ratios at initial temperatures of 413, 443, and 473 K and initial pressures of 0.1 and 0.25 MPa using the high-speed schlieren photography and outwardly propagating flame. Effects of laminar flame thickness, thermal expansion ratio, and flame Lewis number on flame stability response were studied. Schlieren photos of flame propagation are recorded. The results show that laminar burning velocities of n-butanol−air premixed mixtures are increased with the increase of initial temperature, and they decrease with the increase of initial pressure. Markstein lengths are decreased with the increase of the equivalence ratio, and they decrease with the increase of initial temperature, and all these indicate that the flame instability is increased with the increase of equivalence ratio, the decrease of initial pressure, and the increase of initial temperature.

Physical Insight and Modelling for Lewis Number Effects on Turbulent Heat and Mass Transport in Turbulent Premixed Flames

The effects of global Lewis number on the behavior of Reynolds heat and mass fluxes in turbulent premixed flames are studied based on three-dimensional direct numerical simulation (DNS) of a number of statistically planar turbulent premixed flames with a global Lewis number ranging from Le = 0.34 to 1.2. For the same values of initial turbulent flow field parameters and duration of flame-turbulence interaction, it has been found that both Reynolds heat and mass fluxes may exhibit countergradient transport for flames with a Lewis number significantly smaller than unity; whereas predominantly gradient-type transport is obtained for flames with a Lewis number closer to unity. It is demonstrated that strong flame normal acceleration due to greater heat release in the low Lewis number flames acts to promote countergradient transport, and that the magnitude of the flame normal acceleration decreases with increasing Lewis number. Algebraic models for Reynolds heat and mass fluxes are proposed in which the effects of the Lewis number on flame normal acceleration are explicitly taken into account. The predictions of the new models are compared with DNS data, and the models are found to capture the influence of the Lewis number on turbulent scalar flux in a satisfactory manner for all the flames considered in this study.

Effects of Lewis number on scalar transport in turbulent premixed flames

The effects of global Lewis number on scalar transport in turbulent premixed flames are studied using direct numerical simulation. Under the same initial conditions of turbulent flow field, it is observed that flames with global Lewis numbers significantly smaller than unity tend to exhibit countergradient transport, whereas the extent of gradient transport is shown to increase with increasing global Lewis numbers. The velocity difference between reactants and products in the flame normal direction is shown to be significantly affected by the global Lewis number. The flame normal acceleration is shown to increase with decreasing Lewis number, leading to an increase in the magnitude of the mean pressure gradient in the mean direction of flame propagation. This effect is shown to be is responsible for promoting countergradient transport in low Lewis number flames. It is also shown that turbulent transport of flame surface density tends to exhibit countergradient behavior for the flames with Lewis number significantly smaller than unity.

Electrical control of the thermodiffusive instability in premixed propane–air flames

This work focuses upon the effects of DC electric fields on the stability of downward propagating atmospheric pressure premixed propane–air flames under experimental conditions that provide close coupling of the electric field to the flame. With the appropriate electrode geometry, modest applied voltages are shown to drive a stable conical flame first into a wrinkled-laminar flamelet geometry, and then further toward either a highly unstable distributed flamelet regime or a collective oscillation of the flame front. Applied potentials up through + 5 kV over a 40-mm gap encompassing the flame front have been used to force the above transition sequence in flames with equivalence ratios between 0.8 and 1.3 and flow velocities up to 1.7 m/s. Experiments are reported that characterize the field-induced changes in the geometry of the reaction zone and the structure of the resulting unstable flame. The former is quantified by combustion intensity enhancement estimates derived from high-speed two-dimensional direct and spectroscopic imaging of chemiluminescence signals. The flame fluid mechanical response to the applied field, brought about by forcing positive flame ions counter to the flow, drives the effective flame Lewis number to values suitable for the onset of the thermodiffusive instability, even near stoichiometric conditions. Possible field-driven flame ion recombination chemistry that would produce light reactants near the burner head and precipitate the onset of the thermodiffusive instability is proposed. Electrical measurements are also reported that establish that minimal electrical power input is required to produce the observed flame instabilities. Current continuity-based calculations allow estimates of the level of deficient light reactant necessary to cause the flame to become unstable. This applied-electric-field-induced modification of the thermodiffusive effect could serve as a potentially attractive means of controlling flame fluid-mechanical characteristics and validating combustion instability models over a wide range of equivalence ratios.

Coupled hydrodynamic and diffusional-thermal instabilities in flame propagation at subunity Lewis numbers

The dynamics of flame cell evolution due to the coupling between hydrodynamic and diffusional-thermal instabilities in subunity Lewis number flames was simulated using a sixth-order central difference scheme and newly developed nonreflective boundary conditions. Results show that the interaction between these two modes of instabilities yields distinct evolutions of cell splitting, merging, growth, local extinction, and lateral motion, leading to fluctuations of the flow and species concentrations as well as substantial increase in the flame speed. The study also demonstrates that small computational domains cannot correctly predict cell merging and transverse motion.

Electric-field-induced flame speed modification

The effects of pulsed and continuous DC electric fields on the reaction zones of premixed propane–air flames have been investigated using several types of experimental measurements. All observed effects on the flame are dependent on the applied voltage polarity, indicating that negatively charged flame species do not play a role in the perturbation of the reaction zone. Experiments designed to characterize the electric-field-induced modifications of the shape and size of the inner cone, and the concomitant changes in the temperature profiles of flames with equivalence ratios between 0.8 and 1.7, are also reported. High-speed two-dimensional imaging of the flame response to a pulsed DC voltage shows that the unperturbed conical flame front (laminar flow) is driven into a wrinkled laminar flamelet (cellular) geometry on a time scale of the order of 5 ms. Temperature distributions derived from thin filament pyrometry (TFP) measurements in flames perturbed by continuous DC fields show similar large changes in the reaction zone geometry, with no change in maximum flame temperature. All measurements are consistent with the observed flame perturbations being a fluid mechanical response to the applied field brought about by forcing positive flame ions counter to the flow. The resulting electric pressure decreases Lewis numbers of the ionic species and drives the effective flame Lewis number below unity. The observed increases in flame speed and the flame fronts trend toward turbulence can be described in terms of the flame front wrinkling and concomitant increase in reaction sheet area. This effect is a potentially attractive means of controlling flame fluid mechanical characteristics. The observed effects require minimal input electrical power (<1 W for a 1 kW burner) due to the much better electric field coupling achieved in the present experiments compared to the previous studies.

Flame extinction by spatially periodic shear flows

The previously studied model for nearly extinguished non-adiabatic flames propagating through a quiescent gas is extended to account for the effects due to the background flow-field. It is shown that for moderately strong large-scale periodic shear flows, their intensification results in flame speed enhancement. Yet for high Lewis number flames, there is a certain level of the flow intensity at which the flame speed reaches its maximum followed by the flame quenching. This paper is motivated by the experimentally known phenomenon of flame extinction by turbulence.

Dynamics of weakly stretched flames: quantitative description and extraction of global flame parameters

Generalized expressions for the flame response to weak stretch rate variations were derived based on an integral analysis. Together with values of the laminar flame speed, laminar flame thickness, and the one-step overall reaction order and activation energy determined from the computational results of the one-dimensional planar flame, these expressions for the stretched flames were then used to correlate the computational results of the spherical outwardly propagating, spherical inwardly propagating, and counterflow hydrogen/air and propane/air flames. These correlations yielded the laminar flame speeds through linear extrapolation to zero stretch rate, the Markstein lengths representing the sensitivity of the flame response to stretch rate, and the flame Lewis number. Furthermore, it is shown that the extracted Markstein lengths and Lewis numbers from the three flame configurations are largely the same for given equivalence ratio and system pressure, and that these Lewis numbers also agree well with those predicted from the two-reactant flame theory of Joulin and Mitani. The feasibility of a priori quantitative determination of stretch effects on laminar premixed flames is suggested.

The domain of influence of flame instabilities in turbulent premixed combustion

Although a number of experiments and numerical simulations indicate persistence of flame instability effects in turbulent premixed flames, the exact domain of influence of these instabilities remains unknown. In this study, a simple estimate of that domain is obtained by comparing a characteristic flame stretch due to flame instabilities, Ki, with a characteristic flame stretch due to turbulent eddies, Kt. The resulting criterion, (Kt/Ki)≤1, shows that instability effects are promoted by: small values of the ratio of turbulence intensity divided by the laminar flame speed (u′/sL): large values of the ratio of integral length scale divided by the laminar flame thickness (lt/lF) (given that (lt/lF)>10): large values of the heat release factor τ: large positive values of the flame Richardson number Ri (Ri measures buoyancy effects and is positive when the corresponding flow acceleration is directed from the fresh mixture to the burnt gas): small values (below one) of the flame Lewis number Le. Direct numerical simulations (DNS) are used to test the validity of the theoretical criterion. The numerical configuration corresponds to three-dimensional premixed flames propagating into a temporally decaying turbulent flow. The simulations are limited by DNS constraints to small length scale ratios, (lt/lF)≤10; they use Le=1 and correspond to different values of (u′/sL), τ and Ri. Due to the turbulence decay, all simulated flames with τ≠0 and Ri≥0 undergo a transition from turbulent to unstable flame surface dynamics. The DNS values of (Kt/Ki) at transition time are found to be of order one and are in good agreement with the theoretical predictions.

Radiation Modelling in Non-Luminous Nonpremixed Turbulent Flames

A finite-rate chemistry model for nonpremixed turbulent combustion, based on the stretched laminar flamelet (slf) approach, is extended to account for radiative heat transfer in non-luminous flames, in the optically thin limit. The model is applied to a methane/air flame, and results in greatly improved predictions of mean temperature, and of its probability density function. Mean carbon monoxide concentration predictions are instead shown to be somewhat deteriorated. The model is further tested to reproduce radiative heat flux levels; solutions obtained by determining the average heat flux divergence by full convolution with the pdT, and by the simpler but less fundamentally correct ‘mean-property’ method, are compared, and show a significant gap. A formulation to deal with non-unity Lewis number flames is proposed; the model holds potential for further extension.

Extinction mechanisms of near-limit premixed flames and extended limits of flammability

The response of near-flammability-limit, weakly burning, counterflow premixed flames as a function of stretch rate has been studied computationally with detailed chemistry and transport properties. The limit mechanisms and extinction phenomena are found to be strongly influenced by the combined effects of flame stretch, mixture non-equidiffusion, and radiative loss. For subunity Lewis number flames such as those of lean methane/air, the combined effects of mixture non-equidiffusion and positive stretch elevate the combustion intensity such that steady burning persists beyond the fundamental flammability limit defined for the one-dimensional planar flame. Furthermore, the flame response to stretch rate variations exhibits a dual-extinction, turning-point behavior in that flame extinction occurs not only for sufficiently large stretch rates and minimal radiative heat loss, but also for sufficiently small stretch rates and relatively substantial heat loss. Consequently, for a given mixture strength, steady combustion is possible only within a finite range of the stretch rate. This range steadily diminishes with decreasing mixture strength such that there exists a critical equivalence ratio, the extended flammability limit, beyond which steady burning for the stretch-enhanced flame also ceases to be possible. For lean propane/air flames, however, the mixture Lewis numbers are greater than unity such that the combined stretch and non-equidiffusion effects always diminish the burning intensity. Consequently, the transition from stretch-dominated extinction to loss-dominated extinction is monotonic in terms of the equivalence ratio, and the fundamental flammability limit is the proper flammability limit. The present results agree well with the recent experimental observations of near-limit, lean methane/air and propane/air flames, obtained under microgravity conditions needed to eliminate the influence of buoyancy, which could severely affect the response of these weakly burning flames. Implications of the present understanding on the experimental determination of flammability limits using the counterflow flame technique are also discussed.