Mixture Fraction Gradient Research Articles

A direct numerical simulation of cool-flame affected autoignition in diesel engine-relevant conditions

In diesel engines, combustion is initiated by a two-staged autoignition that includes both low- and high-temperature chemistry. The location and timing of both stages of autoignition are important parameters that influence the development and stabilisation of the flame. In this study, a two-dimensional direct numerical simulation (DNS) is conducted to provide a fully resolved description of ignition at diesel engine-relevant conditions. The DNS is performed at a pressure of 40 atmospheres and at an ambient temperature of 900 K using dimethyl ether (DME) as the fuel, with a 30 species reduced chemical mechanism. At these conditions, similar to diesel fuel, DME exhibits two-stage ignition. The focus of this study is on the behaviour of the low-temperature chemistry (LTC) and the way in which it influences the high-temperature ignition. The results show that the LTC develops as a “spotty” first-stage autoignition in lean regions which transitions to a diffusively supported cool-flame and then propagates up the local mixture fraction gradient towards richer regions. The cool-flame speed is much faster than can be attributed to spatial gradients in first-stage ignition delay time in homogeneous reactors. The cool-flame causes a shortening of the second-stage ignition delay times compared to a homogeneous reactor and the shortening becomes more pronounced at richer mixtures. Multiple high-temperature ignition kernels are observed over a range of rich mixtures that are much richer than the homogeneous most reactive mixture and most kernels form much earlier than suggested by the homogeneous ignition delay time of the corresponding local mixture. Overall, the results suggest that LTC can strongly influence both the timing and location in composition space of the high-temperature ignition.

Statistical Analysis of the Reaction Progress Variable and Mixture Fraction Gradients in Flames Propagating into Droplet Mist: A Direct Numerical Simulation Analysis

ABSTRACTThe statistics of reaction progress variable, , and mixture fraction, , and their gradients (i.e., and ) in flames propagating in droplet mist, where the fuel was supplied in the form of monodisperse droplets, have been analyzed for different values of turbulent velocity fluctuations (), droplet equivalence ratios (, and droplet diameters ( based on three-dimensional direct numerical simulations (DNS) in a canonical configuration under decaying turbulence. The combustion process in the gaseous phase has been found to take place predominantly in fuel-lean mode, even for . The probability of finding fuel-lean mixture increases with increasing initial droplet diameter due to slower evaporation of larger droplets. It has been shown that the joint probability density function (i.e., joint PDF) of and (i.e., ), cannot be approximated in terms of discrete delta functions throughout the flame brush for the cases considered here. Furthermore, the magnitude of cannot be adequately approximated by the product of marginal PDFs of , and variable, (i.e., ). The statistical properties of the Favre probability density functions (Favre-PDFs) of the mixture fraction, , and oxidizer-based reaction progress variable, , have been analyzed at several locations across the flame brush and a -function distribution has been found to capture the Favre-PDFs of and obtained from the DNS data. Furthermore, a log-normal distribution has been shown to capture the qualitative behaviors of the PDFs of the gradient of the mixture fraction and the gradient of the reaction progress variable, and , respectively, but discrepancies between the log-normal distribution and the DNS data were observed at the tails of PDFs. In addition, the interrelation between and was examined in terms of the PDFs of the cosine of the angle between them (i.e., and it was observed that most droplet cases exhibited much greater likelihood of positive values of than negative values. Finally, the joint PDF of and , , has been compared with that of P( (i.e., assuming statistical independence of and ) and a good level of agreement has been obtained. The bivariate log-normal distribution has been considered both assuming correlation between and and assuming no correlation for the purpose of modeling , and the variant with no correlation has been found to be more successful in capturing qualitative behavior of although quantitative discrepancies have been observed due to inaccuracies involved in parameterizing P( and P(by log-normal distributions.

Analysis of the filtered non-premixed turbulent flame

Results related to the filtered non-premixed turbulent flame statistics are presented. Considering non-premixed turbulent combustion modeling in the framework of large eddy simulations (LES), a turbulent flamelet equation is derived based on the filtered governing equations. Using a direct numerical simulation (DNS) data set, the statistical properties of two important parameters, the scalar dissipation and chemical source term, are analyzed in details. Numerical results show that for the scalar dissipation term, the probability density function (PDF) of the magnitude of the mixture fraction gradient changes is strongly dependent on the filter scale, whereas the PDF of the turbulent diffusivity is almost invariant. Theoretically from the scalar structure function a scaling law can be expected for the conditional mean of the difference between the filtered and nonfiltered scalars with respect to the filter scale, which is important for estimating the chemical source in the subgrid scale models.

Effect of axial diffusion on the response of diffusion flames to axial flow perturbations

This paper elucidates the behavior and dynamics of non-premixed flames responding to bulk fluctuations in flow velocity. It expands previous work on this problem by consistently incorporating finite Peclet number (▪) effects, and differentiating inflow boundary and dynamical effects on the flame dynamics. For analytical tractability, prior treatments of this problem generally prescribe the inflow boundary conditions into the domain. This paper shows, however, that prescribed inflow conditions, such as a step or constant local diffusive flux boundary condition, neglect axial diffusion effects in the region where their effects are most important; i.e., in the near-burner exit region where high transverse gradients and mass burning rates control the heat release dynamics. As the burning rate of non-premixed flames are controlled by mixture fraction gradients, the influence of axial diffusion substantively influences several burning rate characteristics of the flame. In addition, these effects cause the leading edge position of the flame front to oscillate, even for infinitely fast chemistry. Even in Pe≫1 flames, axial diffusion introduces several fundamentally new features to the problem, resulting in exponentially decaying, dispersive flame wrinkle propagation with downstream distance. Also investigated here are asymptotic results for the heat release dynamics. It is shown that axial diffusion introduces a triple-zone asymptotic structure into the unsteady heat release characteristics, resulting in O(1) flame transfer function trends for St≪1 (to which an n–τ model is developed), O(1/St1/2) for intermediate Strouhal numbers, and O(1/St) for high Strouhal numbers. Finally, it is shown that the phase of the heat release response is approximately half that of a premixed flame with the same length, due to the concentration of unsteady heat release near the burner outlet, where transverse gradients are largest.

Stabilization of laminar nonpremixed DME/air coflow flames at elevated temperatures and pressures

The structure and stabilization mechanism of laminar nonpremixed autoignitive DME/air coflow flames was investigated at elevated temperatures and pressures. Computations with detailed chemistry were performed for DME and heated coflow air at 30 atm with uniform inlet velocities (2.4, 3.2, and 8.0 m/s) imposed for both streams. The heat release rate profiles are first examined for each case to demonstrate a multibrachial thermal structure. Species concentrations and temperature were sampled along mixture fraction iso-contours, and Chemical Explosive Mode Analysis (CEMA) was performed to identify the controlling chemistry at representative points. One-dimensional Lagrangian Flamelet Analysis (LFA) was also performed and compared with the two-dimensional computations to elucidate the relative importance of diffusion processes parallel and normal to the mixture fraction gradient. Various coflow temperatures with different inlet velocities are examined to elucidate their influences on the multibrachial structure as well as the stabilization mechanism. NTC (negative temperature coefficient)-affected inhomogeneous autoignition and the coupled effects with premixed flame propagation on stabilization are further studied. It is found that, at high coflow boundary temperatures or low inlet velocities, the classical tribrachial flame structure is achieved, and autoignition contributes less to the stabilization due to reduced heat and radical accumulation. The kinematic balance between the local flow speed and flame propagation speed is the dominant stabilization mechanism. On the contrary, kinetic stabilization is achieved at lower coflow temperatures or higher inlet velocities as autoignition becomes dominant. Due to the transition of the dominant chemical pathways during autoignition, the kinetically stabilized structure is usually multibrachial. The transition of different stabilization mechanisms can be made by changing either the boundary velocity or temperature of the coflow. Based on these results and previous work (Deng et al., 2015) [12], a regime diagram is constructed that identifies the possible stabilization regimes: blow out, kinetically stabilized, autoignition-propagation-coupled stabilized, kinematically stabilized, and burner stabilized.

Enhanced Power Output from a Gaseous Fuel Burner Involving Pulsed Spark Discharge

The thermal output of a burner comprising concentric methane/air mixtures was increased upon using a modulated frequency, pulsed electric discharge via spark plugs. The computations predicted that the density/velocity gradients introduced by the spark pulsating temperature field increased the local peak acceleration to 251 m/s2. At 40 Hz, a velocity difference as high as 3.5 times the mixture local velocity was provided ahead of the flame lift-off position. By displacing the two electrodes along the combustor centerline, the favorable turbulence effects on combustion were maximized at 120 Hz. The burner firing capacity with inner fuel-rich and outer fuel-lean mixtures was thus extended to 14.9 m/s, where 0.28% of the burner output was required for the dielectric breakdown of gases across a 2-mm gap between the two electrodes thus providing plasma-assisted combustion. Although the peak temperature around the spark increased at least by 1200 K, the correspondingly reduced residence time across the flame zones by 93.3% reduced the NOx specific emissions by 76%. While the flame was shifted downstream from the burner face along the first half of the combustor, the HC and CO emissions, respectively, reached magnitudes as low as 0.09% and 730 ppm. As the mixture fraction gradient was reduced to 0.01 cm−1 with inner fuel-lean and outer fuel-rich mixtures, there was a flame speed increase of 16.4 m/s, which provided a maximum firing intensity of 28.6 MW/m3, while the heat flux increased with the flame stabilization height. As the peak rate of radiation heat transfer preceded the convection one, the combustor efficiency as a heater was maintained above 29%. Increasing the mixtures’ velocity difference to 3.0 m/s increased the turbulent kinetic energy to a maximum of 9.8 m2/s2 such that enlarging the gap distance to 4 mm increased the temperature fluctuations at least by 32%.

Stabilization and structure of n-heptane tribrachial flames in axisymmetric laminar jets

A set of tribrachial flames of n-heptane/air is simulated with finite rate chemistry and detailed transport in a realistic laminar jet configuration for which experimental data are available. The flames differ by the temperature of the unburnt mixture and stabilization height, which controls the mixture fraction gradient ahead of the flame front. The simulations reproduce the lift-off heights in the experiments, showing that the flame stabilizes further downstream as the unburnt temperature decreases. For the lowest unburnt temperature, resulting in a weak mixture fraction gradient at the tribrachial point, positive stretch along the rich premixed wing leads to an increase in the rate of chemical reaction in the whole flame. The tribrachial flame burning velocity exceeds that in the unstretched, one-dimensional flame. For the highest temperature, the flame stabilizes closest to the nozzle. Large flame tilt, large mixture fraction gradient, and small radius of curvature lead to a reduction in the heat release rate and the flame propagates slower than its one-dimensional counterpart. The observed behavior is explained with a detailed analysis of the flame geometry, differential diffusion effects, flame stretch, and transport of heat and mass from the burnt gases to the flame front.

Droplet/ligament modulation of local small-scale turbulence and scalar mixing in a dense fuel spray

In this study, the modulation of turbulence and scalar mixing by finite-size droplets/ligaments in a dense fuel spray is investigated using a DNS (Direct Numerical Simulation) dataset. Ejected from a spray nozzle with a high speed, a liquid-fuel jet deforms and the fuel spray is atomized into many ligaments and droplets. During these processes, the gas flow becomes turbulent due to droplet/ligament dynamics. At the same time, droplet evaporation and mixing with ambient air are affected by the small-scale gas turbulence. An understanding of the mixing characteristics in the dense spray zone is important for modeling spray combustion. In a region where the droplet number density is relatively low, a universal feature of isotropic turbulence was found, although the alignments of strain eigenvectors with vorticity and the mixture fraction gradient are slightly modulated by the presence of droplets, which is a characteristic of particle-laden flows. In gas-phase regions close to droplet surfaces, where the dissipation rate of turbulent kinetic energy is strongly increased, the alignments are more modulated, especially those of the scalar gradient with strain eigenvectors. This can also be seen in the topology similarity among energy dissipation, enstrophy and scalar dissipation in the near field of droplet/ligament surfaces. For the first time, it is found that droplets whose size is comparable to turbulence scales do affect the mixing characteristics in a realistic turbulent spray. This finding has shed new light upon the modeling of flow turbulence and scalar mixing in an evaporating and atomizing fuel spray.

Triple flame: Inherent asymmetries and pentasectional character

A two-dimensional triple-flame numerical model of a laminar combustion process reflects flame asymmetric structural features that other analytical models do not generate. It reveals the pentasectional character of the triple flame, composed of the central pure diffusion-flame branch and the fuel-rich and fuel-lean branches, each of which is divided into two sections: a near-stoichiometric section and a previously unreported near-flammability-limits section with combined diffusion and premixed character. Results include propagation velocity, fuel and oxidiser mass fractions, temperature and reaction rates. Realistic stoichiometric ratios and reaction orders match experimental planar flame characteristics. Constant density, a one-step reaction, and a mixture fraction gradient at the inlet as the simulation parameter are imposed. The upstream equivalence ratio or the upstream reactant mass fractions are linear or hyperbolic functions of the transverse coordinate. The use here of experimental kinetics data differs from previous analytical works and results in flame asymmetry and different flammability limits. Upstream mixture composition gradient affects propagation velocity, flame curvature, diffusion flame reaction rate, and flammability limits. Flammability limits extend beyond those of a planar flame due to transverse heat and mass diffusion causing the pentasectional character.

Pulverized coal combustion with opposing/cross-flow methane/air mixtures

Pulverized coal co-firing with opposing premixed methane/air flames in a cross-flow arrangement was found to extend the coal burning limits and reduce its NOx emissions by creating a high temperature NOx-reducing zone between the resulting multiple flame envelopes. By using a primary air stream, the stability limit reached a peak value of 25.1 m/s while the exhaust NOx mole fraction got values as low as 1.2 × 10–4 due to HCN reaction with NOx generated from both the coal primary flame envelope and the premixed flames. The NOx exhaust emissions were reduced to values below 60 ppm as the gas/coal heat input ratio increased to 1.5, where a nonunity Lewis number predicted the peak NOx concentrations across the annular region surrounding the flame. The effectiveness of NOx reduction increased by employing triple flames in place of the primary air since each NOx peak generated from methane combustion was followed by a region of NOx reduction upon consuming a significant amount of the HCN released from coal. Extending the coal flame stability limit to 32.3 m/s contributed to NOx reduction via decreasing the residence time for NOx formation across the combustor exit section. Decreasing the triple flame mixture fraction gradient and keeping a higher overall equivalence ratio reduced the NOx exhaust concentrations to 50 ppm and increased the percent of heat transfer by radiation to reach a peak of 48.8%. Decreasing the particle size to 135 µm and increasing the number of opposing jets to 16 pronounced favorable aerodynamic effects by minimizing the HC and NOx emissions, respectively, to values below 0.16% and 65 ppm. Increasing the opposing jets’ diameter to separation reduced the flame length by 26.7%, while maximizing the staging height kept the NOx emissions below 40 ppm at a strain rate of 2050 s–1.

Statistics of Reaction Progress Variable and Mixture Fraction Gradients from DNS of Turbulent Partially Premixed Flames

Statistically planar turbulent partially premixed flames for different initial intensities of decaying turbulence have been simulated for global equivalence ratios <φ> = 0.7 and <φ> = 1.0 using three-dimensional, simplified chemistry–based direct numerical simulations (DNS). The simulation parameters are chosen such that the flames represent the thin reaction zones regime combustion. A random bimodal distribution of equivalence ratio φ is introduced in the unburned gas ahead of the flame to account for the mixture inhomogeneity. The results suggest that the probability density functions (PDFs) of the mixture fraction gradient magnitude |∇ξ| (i.e., P(|∇ξ|)) can be reasonably approximated using a log-normal distribution. However, this presumed PDF distribution captures only the qualitative nature of the PDF of the reaction progress variable gradient magnitude |∇c| (i.e., P(|∇c|)). It has been found that a bivariate log-normal distribution does not sufficiently capture the quantitative behavior of the joint PDF of |∇ξ| and |∇c| (i.e., P(|∇ξ|, |∇c|)), and the agreement with the DNS data has been found to be poor in certain regions of the flame brush, particularly toward the burned gas side of the flame brush. Moreover, the variables |∇ξ| and |∇c| show appreciable correlation toward the burned gas side of the flame brush. These findings are corroborated further using a DNS data of a lifted jet flame to study the flame geometry dependence of these statistics.

On the Relationship Between the Statistics of the Resolved and True Rate of Dissipation of Mixture Fraction

The relationship between the one-point probability-density-function (PDF) of the dissipation rate of mixture fraction fluctuations and the corresponding resolved quantity available in large eddy simulation (LES) is analyzed. The investigation pursues two fronts: an a priori study using direct numerical simulation (DNS), and an analytic development that, using common turbulence physics simplifications, relates the one-point statistics of the resolved and true scalar dissipations. Particularly, the analysis reveals the connection between the multi-point correlations of the mixture fraction gradient and the one-point PDF of the resolved scalar dissipation. A DNS of a temporally evolving shear layer with and without heat release is used to quantify the accuracy of the analytical result. It is verified, both by filtering the DNS and from the theory, that increasing the filter cutoff width reduces the magnitude of the resolved scalar dissipation fluctuations, as expected and observed experimentally. Comparison with DNS indicates that the analytical relationship predicts the behavior of the resolved scalar dissipation PDF well at the center planes of the shear layer, where turbulence is locally more isotropic and homogeneous. Large-scale anisotropy and inhomogeneities in the DNS degrade the accuracy of the approximate analytical result close to the edges of the shear layer. These results may be improved with future investigations to account fully for the missing statistics in LES, which have the potential to allow a more accurate quantification of finite-rate chemistry effects in reacting flows.

Multi-kHz mixture fraction imaging in turbulent jets using planar Rayleigh scattering

In this study, we describe the development of two-dimensional, high repetition-rate (10-kHz) Rayleigh scattering imaging as applied to turbulent flows. In particular, we report what we believe to be the first sets of high-speed 2D Rayleigh scattering images in turbulent non-reacting jets, yielding temporally correlated image sequences of the instantaneous mixture fraction field. Results are presented for turbulent jets of propane issuing into a low-speed co-flow of air at jet-exit Reynolds numbers of 10,000, 15,000, and 30,000 at various axial positions downstream of the jet exit. The quantitative high-speed mixture fraction measurements are facilitated by the use of a calibrated, un-intensified, high-resolution CMOS camera in conjunction with a unique high-energy, high-repetition rate pulse-burst laser system (PBLS) at Ohio State, which yields output energies of ∼200 mJ/pulse at 532 nm with 100-μs laser pulse spacing. The quality, accuracy, and resolution of the imaging system and the resulting image sets are assessed by (1) comparing the mean mixture fraction results to known scaling laws for turbulent jets, (2) comparing instantaneous images/mixture fraction profiles acquired simultaneously with the high-speed CMOS camera and a well-characterized, high-quantum efficiency CCD camera, and (3) comparing statistical quantities such as the probability density function of the mixture fraction results using the high-speed CMOS camera and the CCD camera. Results indicate accurate mixture fraction measurements and a high potential for accurately measuring mixture fraction gradients in both time and space.

Exploratory studies of modeling approaches for hydrogen triple flames

A review of triple flame modeling is first presented, which demonstrates the need for additional work in this area. Building on previous methods described in the literature, a hybrid model that uses a weighted average of one-dimensional premixed and diffusion flamelet reaction rates has been proposed and evaluated for a hydrogen triple flame. Results indicated that some type of progress variable is needed for application of the diffusion flamelet contribution. Weighting the premixed flamelet reaction rate contribution at 100%, it is shown that peak temperatures between the model and a case employing detailed chemistry vary 7.5%, while heat release rate, flame speed, and mass fraction contours agree well. A second model, based on a library of reaction rates built from numerical studies which directly resolve the propagating triple flame has also been tested. Computational time for the baseline case is shown to be reduced by a factor of 3 ½ in comparison to use of detailed chemistry. The role of scalar dissipation rate as a necessary independent variable to the library has also been investigated using simulations with variable mixing layer thicknesses. Overall, it is found that large changes in local mixture fraction gradient cause rather small changes in propagation speed and total heat release rate of the hydrogen triple flame. This implies that such a model may be useful for CFD simulations that do not employ spatial resolution capable of resolving the triple flame itself.

화염 곡률과 스칼라 소산율에 따른 층류부상화염의 화염전파속도에 관한 연구

삼지화염의 화염안정화 메커니즘 중 중요한 한 가지는 화염전파속도이다. 화염전파속도의 정량적인 규명을 위해 Bilger는 층류 유동이론에 근거하여 혼합분율 기울기에 비선형적으로 연관된 삼지화염전파속도를 제시하였다. 그러나 지금까지의 연구에서는 화염의 곡률 반경과 스칼라소산율 및 삼지화염의 화염전파속도에 관한 직접적인 관계에 관하여 제시된 바가 없었다. 본 논문은 실험과 수치해석에 따른 수치해석 결과를 검증하고, 수치해석을 통해 스칼라소산율에 따른 화염전파속도를 확인하였다. 그리고 화염스트레치 분석을 통하여 화염전파속도의 곡률반경 및 스칼라소산율에 따른 의존도를 명확히 하였다. Flame propagation velocity is the one ofmainmechanismof the stabilization of triple flame. To quantify the triple flame propagation velocity, Bilger presents the triple flame propagation velocity depending on the mixture fraction gradient, based on the laminar jet flow theory. However, in spite of these many analyses, there was not presented any relation of these variables, triple flame propagation velocity, radius of flame curvature and scalar dissipation rate indirectly. In the present research, we have checked the results of numerical simulation with experiment and numerical analysis and verified the flame propagation velocity with a scalar dissipation rate proposed by Bilger through the numerical simulation. Also we have clarified that flame propagation velocity was depended on the radius of flame curvature and scalar dissipation rate.

Alignment statistics of active and passive scalar gradients in turbulent stratified flames

The scalar gradient alignment statistics for active and passive scalar gradients (e.g., fuel mass fraction gradient and mixture fraction gradient) are presented here for turbulent stratified flames. It has been shown that, under some conditions, the active scalar gradient may align with the most extensive principal strain rate in contrast to the passive scalar gradient that remains aligned with the most compressive principal strain rate even when the active scalar gradient aligns preferentially with the most extensive principal strain rate. Physical explanations are provided for the observed behaviors.

The effects of laser-sheet thickness on dissipation measurements in turbulent non-reacting jets and jet flames

The effects of laser-sheet thickness on planar laser measurements of scalar gradients in turbulent flows are studied. Experiments are performed in the near field of a turbulent, non-premixed, axisymmetric jet flame and in the near field of a non-reacting, isothermal turbulent jet. Laser Rayleigh scattering provides two-dimensional measurements of the instantaneous temperature and mixture fraction fields in the flame and non-reacting jet, respectively. The effect of spatial resolution on measurements of the mean dissipation and the power spectral density of axial temperature and mixture-fraction gradients is examined. The effect of varying the laser-sheet thickness is compared to that of spatial filtering within the image plane. Measurements of the mean dissipation and power spectral density are significantly less sensitive to resolution degradation in the non-differentiated dimensions than in the differentiated dimension. For example, on the jet flame centreline, the dissipation-cut-off microscale, which is determined from the measured power spectral density, is overestimated by 9% when the beam-waist thickness is increased from a 1/e-squared width of 160 µm to 624 µm. In contrast, spatial filtering along the direction of differentiation with a smoothing kernel of 624 µm width produces a bias of 76% in the cut-off microscale. These results experimentally confirm the theoretical analysis of previous studies. A simple spatial model illustrates the origin of this difference and approximately predicts its magnitude for both planar and line measurements. A criterion for matching in-plane and out-of-plane resolution is established. For many planar gradient measurements, considerably less out-of-plane resolution is needed than in-plane resolution. The combined effects of noise and spatial averaging on the dissipation measurements are also briefly examined.

Effects of compositional fluctuations on premixed flames

Fully compressible direct numerical simulation (DNS) is used to study the behaviour of a stratified turbulent premixed flame in the wrinkled flamelet regime (ReΛ = 38, u′/S L = 0.7, Da = 2.3) with reduced multi-step chemistry. A laminar premixed flame in an initially quiescent domain propagates into a turbulent flow so that the scalar and velocity fields are correctly coupled. Comparison of a stratified scenario (0.4 < φ < 1.2) with an otherwise identical homogeneous case indicates that in this regime the turbulent flame speed is increased by enhanced flame front wrinkling as a result of differential propagation speeds. The preferential propagation into more combustible mixture results in a correlation between the mixture fraction and progress variable, particularly at the leading edge of the flame brush. In front of the flame, the composition gradient preferentially aligns with the most compressive strain. Within the flame front, the progress variable gradient preferentially aligns with the most extensive turbulent strain, and in the latter portion of the flame the alignment between the mixture fraction gradient and the most compressive principal strain deteriorates. Despite this, the convenient approximation of the joint pdf by assuming statistical independence of the mixture fraction and progress variable does not introduce a significant error in the approximation of the reaction rates.

Effects of Fuel Lewis Number on Localised Forced Ignition of Turbulent Mixing Layers

The influences of fuel Lewis number Le F on localised forced ignition of inhomogeneous mixtures are analysed using three-dimensional compressible Direct Numerical Simulations (DNS) of turbulent mixing layers for Le F = 0.8, 1.0 and 1.2 and a range of different root-mean-square turbulent velocity fluctuation u′ values. For all Le F cases a tribrachial flame has been observed in case of successful ignition. However, the lean premixed branch tends to merge with the diffusion flame on the stoichiometric mixture fraction isosurface at later stages of the flame evolution. It has been observed that the maximum values of temperature and reaction rate increase with decreasing Le F during the period of external energy addition. Moreover, Le F is found to have a significant effect on the behaviours of mean temperature and fuel reaction rate magnitude conditional on mixture fraction values. It is also found that reaction rate and mixture fraction gradient magnitude $\vert \nabla \xi \vert $ are negatively correlated at the most reactive region for all values of Le F explored. The probability of finding high values of $\vert \nabla \xi \vert $ increases with increasing Le F . For a given value of u′, the extent of burning decreases with increasing Le F . A moderate increase in u′ gives rise to an increase in the extent of burning for Le F = 0.8 and 1.0, which starts to decrease with further increases in u′. For Le F = 1.2, the extent of burning decreases monotonically with increasing u′. The extent of edge flame propagation on the stoichiometric mixture fraction ξ = ξ st isosurface is characterised by the probability of finding burned gas on this isosurface, which decreases with increasing u′ and Le F . It has been found that it is easier to obtain self-sustained combustion following localised forced ignition in case of inhomogeneous mixtures than that in the case of homogeneous mixtures with the same energy input, energy deposition duration when the ignition centre is placed at the stoichiometric mixture. The difficultly to sustain combustion unaided by external energy addition in homogeneous mixture is particularly prevalent in the case of Le F = 1.2.

Extinction of laminar jet diffusion microflames

This paper presents a theory to predict the extinction limit of laminar jet diffusion microflames, defined as flames established on submillimeter-diameter burners. The classical Burke–Schumann (BS) theory is first extended to include the effect of one-step, finite-rate chemistry. Then, a theory of diffusion-flame extinction is applied using activation-energy asymptotics to predict the extinction limit. The present theory correctly reproduces experimental observations, i.e., u L ∼ d −2, where u L is the fuel jet velocity at the extinction limit (lower limit) and d the burner diameter. According to the BS theory, the gradient of mixture fraction at the flame-sheet location is infinite at the burner rim, and it decreases with increasing axial distance to the minimal value at the flame tip. Therefore, local extinction initiates at the burner rim, and extinction occurs when the mixture-fraction gradient at the flame tip is greater than a critical value. This view of microflame extinction is supported by the results of experiments and numerical simulations. It is found that the present theory can be applied for various types of fuels, those are, methane, propane, and butane.