Exploring fuel isomeric effects on laminar flame propagation of butylbenzenes at various pressures

This work reports an experimental and kinetic modeling investigation on the laminar flame propagation of three butylbenzene isomers (n-butylbenzene, iso-butylbenzene and tert-butylbenzene)/air mixtures. The experiments were performed in a high-pressure constant-volume cylindrical combustion vessel at the initial temperature of 423 K, initial pressures of 1–10 atm, and equivalence ratios (?) of 0.7–1.5. The laminar burning velocities of butylbenzene/O₂/He mixtures were also measured at 423 K, 10 atm and ? = 1.5 to provide additional experimental data under conditions that the butylbenzene/air experiments are susceptible of cellular instability. Comparison among the laminar burning velocities of butylbenzenes including both the three isomers investigated in this work and sec-butylbenzene investigated in our recent work [Combust. Flame 211 (2020) 18–31] shows remarkable fuel isomeric effects, that is, iso-butylbenzene has the slowest laminar burning velocities, followed by n-butylbenzene and tert-butylbenzene, while sec-butylbenzene has the fastest laminar burning velocities. A kinetic model for butylbenzene combustion was developed to simulate the laminar flame propagation of butylbenzenes. Sensitivity analysis was performed to reveal important reactions in laminar flame propagation of butylbenzenes, including both small species reactions and fuel-specific reactions. Kinetic effects are concluded to result in the different laminar burning velocities of four butylbenzene isomers. Small species reactions control the laminar flame propagation under lean conditions, which results in small differences of laminar burning velocities. Chain termination reactions, especially fuel-specific reactions, have important contributions to inhibit the laminar flame propagation under rich conditions. The structural features of butylbenzene isomers can significantly affect the formation of some crucial radicals such as methyl, cyclopentadienyl and benzyl radicals under rich conditions, which leads to remarkable fuel isomeric effects on their laminar burning velocities, especially at high pressures.     

Measurements of burning velocities of dimethyl ether and air premixed flames at elevated pressures

Laminar burning velocities of dimethyl ether (DME) and air premixed flames at elevated pressures up to 10 atm were measured by using a newly developed pressure-release type spherical bomb. The measurement system was validated using laminar burning velocities of methane–air flames. A comparison with the previous experimental data shows an excellent agreement and demonstrates the accuracy and reliability of the present experimental system. The measured flame speeds of DME–air flames were compared with the previous experimental data and the predictions using the full and reduced mechanisms. At atmospheric pressure, the measured laminar burning velocities of DME–air flames are in reasonable agreement with the previous data from spherical bomb method, but are much lower than both predictions and the experimental data of the PIV based counterflow flame measurements. The laminar burning velocities of DME–air flames at 2, 6, and 10 atm were also measured. It was found that flame speed decreases considerably with the increase of pressure. Moreover, the measured flame speeds are also lower than the predictions at high pressures. In addition, experiments showed that at high pressures the rich DME–air flames are strongly affected by the hydrodynamic and thermal-diffusive instabilities. Markstein lengths and the overall reaction order at different equivalence ratios were extracted from the flame speed data at elevated pressures. Sensitivity analysis showed that reactions involving methyl and formyl radicals play an important role in DME–air flame propagation and suggested that systematic modification of the reactions rates associated with methyl and formyl formations are necessary to reduce the discrepancies between predictions and measurements.     

Measurement of unstable burning velocities of iso-octane–air mixtures at high pressure and the derivation of laminar burning velocities

A new technique is reported for measuring burning velocities at high pressures in the final stages of two inwardly propagating flame kernels in an explosion bomb. The flames were initiated at diametrically opposite spark electrodes, close to the wall, in quiescent mixtures. Measurements of pressure and flame kernel propagation speeds by high-speed photography showed the burning velocities to be elevated above the corresponding laminar burning velocities as a result of the developing flame instabilities. The enhancement increased with increase in pressure and decreased with increase in Markstein number. When the Markstein number was negative, instabilities could be appreciable, as could the enhancement. For the iso-octane–air mixtures investigated, where the mixtures had well-characterised Markstein numbers or critical Peclet numbers at the relevant pressures and temperatures, it was possible to explain the enhancement quantitatively by the spherical explosion flame instability theory of Bechtold and Matalon, provided the critical Peclet number was that observed experimentally, and allowance was made for the changing pressure. With this theoretical procedure, it was possible to derive values of laminar burning velocity from the measured values of burning velocity over a wide range of equivalence ratios, pressures, and temperatures. The values became less reliable at the higher temperatures and pressures as the data on Markstein and critical Peclet numbers became less certain. It was found that with iso-octane as the fuel the laminar burning velocity decreased during isentropic compression.     

On laminar premixed flame propagating into autoigniting mixtures under engine-relevant conditions

Usually premixed flame propagation and laminar burning velocity are studied for mixtures at normal or elevated temperatures and pressures, under which the ignition delay time of the premixture is much larger than the flame resistance time. However, in spark-ignition engines and spark-assisted compression ignition engines, the end-gas in the front of premixed flame is at the state that autoignition might happen before the mixture is consumed by the premixed flame. In this study, laminar premixed flames propagating into an autoigniting dimethyl ether/air mixture are simulated considering detailed chemistry and transport. The emphasis is on the laminar burning velocity of autoigniting mixtures under engine-relevant conditions. Two types of premixed flames are considered: one is the premixed planar flame propagating into an autoigniting DME/air without confinement; and the other is premixed spherical flame propagating inside a closed chamber, for which four stages are identified. Due to the confinement, the unburned mixture is compressed to high temperature and pressure close to or under engine-relevant conditions. The laminar burning velocity is determined from the constant-volume propagating spherical flame method as well as PREMIX. The laminar burning velocities of autoigniting DME/air mixture at different temperatures, pressures, and autoignition progresses are obtained. It is shown that the first-stage and second-stage autoignition can significantly accelerate the flame propagation and thereby greatly increase the laminar burning velocity. When the first-stage autoignition occurs in the unburned mixture, the isentropic compression assumption does not hold and thereby the traditional method cannot be used to calculate the laminar burning velocity. A modified method without using the isentropic compression assumption is proposed. It is shown to work well for autoigniting mixtures. Besides, a power law correlation is obtained based on all the laminar burning velocity data. It works well for mixtures before autoignition while improvement is still needed for mixtures after autoignition.     

1-庚烯/空气的高压层流火焰传播研究

本文使用定容圆柱形燃烧弹,在初始温度373 K和初始压力1、2、5、10 atm的条件下,对当量比从0.7到1.5的1-庚烯/空气混合物的层流火焰传播进行了研究.利用记录的纹影图像处理得到层流火焰传播速度和马克斯坦长度.基于先前报道的1-己烯燃烧反应动力学模型,发展了1-庚烯的模型.该模型验证了本工作测量的1-庚烯层流火焰传播速度数据及文献中的1-庚烯着火延迟时间数据.通过开展敏感性分析和路径分析,帮助理解了1-庚烯在不同压力下的高温化学及其对层流火焰传播的影响.另外,比较了1-庚烯/空气和先前报道的正庚烷/空气的层流火焰传播.由于更强的放热性及反应活性,1-庚烯/空气的层流火焰传播速度在绝大多数条件下均快于正庚烷/空气的结果.     

A dynamical system approach for solving the steady structure of high speed deflagrations

High-speed deflagrations have burning velocities much higher than laminar ones, and compressible effects become important. In the present paper, we study the structure of such high speed deflagrations in the thickened flame limit for a one-step Arrhenius rate law, whereby the transport coefficients are increased to give rise to buring velocities of finite Mach number. We study their steady structure and compare with the laminar low-Mach classical structure. The singular nature of both the fresh and burned gases conditions in the compressible regime, i.e., for large values of flame propagation Mach number, which are both saddle points, precludes the application of simple shooting methods to obtain their structure. The steps leading to the flame structure borrow techniques used to treat mathematical features commonly found in the study of dynamical systems (phase portrait of the flame structure equations system, eigenvalue decomposition of its linearized version), that can also be used to further comment on the nature of high-speed flames. The method proposed permits to determine the structure of deflagrations propagating up to speeds of aproximately 0.95 of the CJ-deflagration burning velocity, for a wide range of gas parameters commonly found in the field of numerical simulation of accelerating flames and their transitions to detonations. We comment on how the increasing role of compressibility modifies the structure of the laminar flame.     

Characterizing the fuel-specific combustion chemistry of acetic acid and propanoic acid: Laminar flame propagation and kinetic modeling studies

In order to study the combustion chemistry of carboxyl functionality, the laminar burning velocity of acetic acid/air and propanoic acid/air mixtures was investigated in a high-pressure constant-volume cylindrical combustion vessel at 423 K, 1 atm and equivalence ratios of 0.7–1.4. Experimental results reveal that the flame propagation of propanoic acid flame is much faster than that of acetic acid flame, especially under rich conditions, and the laminar burning velocity of propanoic acid/air mixtures peaks at richer conditions than that of acetic acid. The present theoretical calculations for the isomerization and decomposition of propanoic acid radicals indicate that the primary radical products are HOCO, H and C₂H₅, while those in acetic acid flame are CH₃ and OH based on previous studies. A kinetic model of the two acids was developed mainly based on previous and the present theoretical calculation results. It could reasonably capture the measured laminar burning velocities of acetic acid/air and propanoic acid/air mixtures in this work, as well as the previous experimental data in literature. Based on the present model, CH₃- and ketene-related pathways play an important role in acetic acid flames. Under rich conditions, ketene is mostly converted to CH₃ via CH₂CO+HCH₃+CO, and the chain-termination reaction of CH₃+H(+M)=CH₄(+M) is enhanced, which strongly inhibits the propagation of rich acetic acid flames. In contrast, C₂H₅ and ethylene chemistry play an important role in propanoic acid flames. Rich conditions promote the decomposition of C₂H₅, yielding ethylene and H, which can facilitate the flame propagation. This can explain the shift of the peak laminar burning velocity of propanoic acid/air mixtures towards a slightly richer condition compared with that of acetic acid/air mixtures.     

Burning rates of turbulent iso-octane aerosol mixtures in spherical flame explosions

Experimental studies of aerosol combustion under quiescent and turbulence conditions have been conducted to quantify the differences in the flame structure and burning rates between aerosol and gaseous mixtures. Turbulence was generated by variable speed fans to yield rms turbulence velocities between 0.5 and 4.0 m/s and this was uniform and isotropic. Homogeneously distributed and near monodispersed iso-octane-air aerosol clouds were generated using a thermodynamic condensation method. Spherically expanding flames, following central ignition, at near atmospheric pressures were employed to quantify the flame structure and propagation rate. The effects of the diameter of fine fuel droplets on flame propagation were investigated. It is suggested that the inertia of fuel droplets is an important cause of flame enhancement during early flame development. During later stages, cellular flame instability and the effective, gaseous phase, equivalence ratio becomes important. The latter effect leads has increases the flame speed of rich mixtures, but decreases that of lean ones. Droplet enhancement of burning velocity can be significant at low turbulence but is negligible at high turbulence.     

Assessment of counterflow to measure laminar burning velocities using direct numerical simulations

The laminar burning velocity is a fundamental property that is extensively used in the study and modelling of premixed combustion processes. A counterflow flame configuration is commonly used to measure this quantity for different combustion systems. In this procedure, the burning velocities are typically measured at various low stretch conditions and the unstretched burning velocity is extrapolated from these measurements. This extrapolation is done assuming a theoretically one-dimensional system along the centre-line. We analyse the validity of this assumption by performing DNS studies with finite rate chemistry of the experimental counterflow configuration. The extrapolation process using one-dimensional computations is performed on the DNS data and the extrapolated value is compared to the computed laminar burning velocity for the chemical mechanism used. We show that the assumption works well if the nozzle exit velocity has a nearly top-hat profile. For non-uniform velocity profiles, it is shown that the temperature curvature at the centre-line becomes important. This effect cannot be captured by the one-dimensional formulation. Thus, experimental studies measuring laminar burning velocity need to ensure that the nozzle velocity profile is very close to uniform. The extrapolation to zero stretch using 1D counterflow simulations can be performed in different ways. Based on the results obtained in this paper, a simple and accurate extrapolation method is proposed.     

Estimation of laminar flame speeds using axisymmetric bunsen flames: Molecular transport effects

Intricacies associated with the estimation of laminar flame speed using the axisymmetric Bunsen flame technique were assessed, through parametric direct numerical simulations. The study involved methane-air mixtures at atmospheric pressure and temperature, and both the flame cone angle and flame surface area methods were utilized to estimate the laminar flame speeds based on conditions used in recent relevant experimental studies. The results provided insight into the details of the flame structure and allowed for the assessment of various non-idealities and the attendant uncertainties associated with the estimation of laminar flame speeds. Additionally, molecular transport effects were investigated by altering the fuel diffusivity, in order to evaluate its impact on the flame structure and propagation under the presence of negative stretch. The modification of fuel diffusivity was found to affect the burning rate as stretch varies. Under fuel rich conditions, decreasing the fuel diffusivity was found to have an opposite effect on the heat release and thus the burning rate, when compared to positively stretched flames that have been investigated recently in a similar manner. The reported results are expected to provide guidance in flame propagation experiments using the convenient Bunsen flame method at near-atmospheric or elevated pressures, as well as insight into the effects of negative stretch that has, compared to positive, attracted less attention in past studies.     

Role of large scale flow features on cycle-to-cycle variations of spark-ignited flame-initiation and its transition to turbulent combustion

This study investigates the influence of large-scale flow features, including flow structure and velocity magnitude, on the early-burn period variability in a homogenous-charge spark-ignited engine fueled with premixed propane-air mixture. Particle image velocimetry and in-cylinder pressure measurement data from a previous study - were processed to enable simultaneous flow characterization and flame-front tracking as well as apparent heat-release analysis. By combining probability analysis of flame development with conditional sampling of fast and slow early-burn cycles using 10% fuel mass fraction burned, it is shown that an undesirable flow structure produces an asymmetric flame development at the initial flame growth period. This asymmetric flame structure persists through the whole initial-to-turbulent transition period until the flame becomes fully turbulent. The undesirable flow condition is characterized by large-scale convective flows near spark plug rather than flows that lead to increased flame spread in multiple directions. The simultaneous flow and flame characterization enables the quantifications of flame-front propagation speed, unburned fuel-air mixture velocity ahead of flame front and local burning velocity at flame surface. Here the local burning velocity is referred to as laminar or turbulent flame speed. A simplified approach is introduced to derive integrated values for these quantities per crank-angle-degree, enabling the quantitative comparison of the trend-wise difference in these integrated metrics between fast and slow early-burn cycles. It is revealed that for the transition period, the CCV in the velocity magnitude of unburned fuel-air mixture ahead of the flame front accounts for nearly 50% to the variability of flame propagation speed. The burning velocity provides the remaining source of the flame propagation variability in this period. The flame propagation variations in the initial flame growth and fully turbulent periods are smaller than those in the transition period and are primarily dependent on the variability of large-scale flow features.     

Characterization of the effects of pressure and hydrogen concentration on laminar burning velocities of methane–hydrogen–air mixtures

The aim of the present work was to characterize both the effects of pressure and of hydrogen addition on methane/air premixed laminar flames. The experimental setup consists of a spherical combustion chamber coupled to a classical shadowgraphy system. Flame pictures are recorded by a high speed camera. Global equivalence ratios were varied from 0.7 to 1.2 for the initial pressure range from 0.1 to 0.5 MPa. The mole fraction of hydrogen in the methane + hydrogen mixture was varied from 0 to 0.2. Experimental results were compared to calculations using a detailed chemical kinetic scheme (GRIMECH 3.0). First, the results for atmospheric laminar CH₄/air flames were compared to the literature. Very good agreements were obtained both for laminar burning velocities and for burned gas Markstein length. Then, increasing the hydrogen content in the mixture was found to be responsible for an increase in the laminar burning velocity and for a reduction of the flame dependence on stretch. Transport effects, through the reduction of the fuel Lewis number, play a role in reducing the sensitivity of the fundamental flame velocity to the stretch. Finally, when the pressure was increased, the laminar burning velocity decreased for all mixtures. The pressure domain was limited to 0.5 MPa due to the onset of instabilities at pressures above this value.     

Effect of non-zero relative velocity on the flame speed of two-phase laminar flames

A numerical study of one-dimensional n-heptane/air spray flames is presented. The objective is to evaluate the flame propagation speed in the case where droplets evaporate inside the reaction zone with possibly non-zero relative velocity. A Direct Numerical Simulation approach for the gaseous phase is coupled to a discrete particle Lagrangian formalism for the dispersed phase. A global two-step n-heptane/air chemical mechanism is used. The effects of initial droplet diameter, overall equivalence ratio, liquid loading and relative velocity between gaseous and liquid phases on the laminar spray flame speed and structure are studied. For lean premixed cases, it is found that the laminar flame speed decreases with increasing initial droplet diameter and relative velocity. On the contrary, rich premixed cases show a range of diameters for which the flame speed is enhanced compared to the corresponding purely gaseous flame. Finally, spray flames controlled by evaporation always have lower flame speeds. To highlight the controlling parameters of spray flame speed, approximate analytical expressions are proposed, which give the correct trends of the spray flame propagation speed behavior for both lean and rich mixtures.     

Turbulent flame propagation limits of ammonia/methane/air premixed mixture in a constant volume vessel

Ammonia is one of promising energy carriers that can be directly used as carbon-neutral fuel for combustion applications. However, because of the low-burning velocity of ammonia, it is challenging to introduce ammonia to practical combustors those are designed for general hydrocarbon fuels. One of ways to enhance the combustibility of ammonia is by mixing it with other hydrocarbon fuels, such as methane, with a burning velocity is much higher than the burning velocity of ammonia. In this study, we conducted flame propagation experiments of ammonia/methane/air using a fan-stirred constant volume vessel to clarify the effect of methane addition to ammonia on the turbulent flame propagation limit. From experimental results, we constructed the flame propagation maps and clarified the flame propagation limits. The results show that the flame propagation limits were extended with an increase in mixing a fraction of methane to ammonia. Additionally, ammonia/methane/air mixtures with the equivalence ration of 0.9 can propagate at the highest turbulent intensity, even though the peak of the laminar burning velocity is the fuel-rich side because of the diffusional-thermal instability of the flame surface. Furthermore, the Markstein number of the mixture obtained in this research successfully expressed the strength of the diffusional-thermal instability effect on the flame propagation capability. The turbulence Karlovitz number at the flame propagation limit monotonically increases with the decreasing Markstein number.     

Framework for simulating stationary spherical flames

Understanding and quantifying the effects of flame stretch rate on the laminar flame speed and flame structure plays an important role from interpreting experimentally-measured laminar burning velocities to characterizing the impact of turbulence on premixed flames. Unfortunately, accounting for these effects often requires an unsteady reacting flow solver and may be computationally expensive. In this work, we propose a mathematical framework to perform simulations of stationary spherical flames. The objective is to maintain the flame at a constant radius (and hence a constant stretch rate) by performing a coordinate change. The governing equations in the new flame-attached frame of reference resemble the original equations for freely-propagating spherical flames. The only difference is the presence of additional source terms whose purpose is to drive the numerical solution to a steady state. These source terms involve one free parameter: the flame stretch rate, which may either be computed in real time or imposed by the user. This parameter controls ultimately the steady state flame radius and the steady state flame speed. That is why, at a given stretch rate, the results of the stationary spherical flame simulations match those of a freely-expanding spherical flame. As an illustration, the dependence of the laminar flame speed on the stretch rate is leveraged to extract Markstein lengths for hydrogen/air mixtures at different equivalence ratios, as well as for hydrocarbon/air mixtures (CH₄ and C₇H₁₆). Numerical predictions are in good agreement with experimental measurements (within experimental uncertainties). Finally, the proposed methodology is implemented in the chemical kinetic software FlameMaster. The use of a dedicated steady-state solver with a non-uniform optimized mesh leads to significant reductions in the computational cost, highlighting that the proposed methodology is ideally suited for other chemical kinetic software such as Chemkin/Premix and Cantera.     

Parameters influencing the burning rate of laminar flames propagating into a reacting mixture

The laminar flame speed is an important property of a reacting mixture and it is used extensively for the characterization of the combustion process in practical devices. However, under engine-relevant conditions, considerable reactivity may be present in the unburned mixture, introducing thus challenges due to couplings of auto-ignition and flame propagation phenomena. In this study, the propagation of transient, one-dimensional laminar flames into a reacting unburned mixture was investigated numerically in order to identify the parameters influencing the flame burning rate in the conduction-reaction controlled regime at constant pressure. It was found that the fuel chemical classification significantly influences the burning rate. More specifically, for hydrogen flames, the “evolution” of the burning rate does not depend on the initial unburned mixture temperature. On the other hand, for n-heptane flames that exhibit low temperature chemistry, the burning rate depends on the instantaneous temperature and composition of the unburned mixture in a coupled way. A new approach was developed allowing for the decoupling the flame chemistry from the ignition dynamics as well as for the decoupling of parameters influencing the burning rate, so that meaningful sensitivity analysis could be performed. It was determined that the burning rate is not directly affected by fuel specific reactions even in the presence of low temperature chemistry whose effect is indirect through the modification of the reactants composition entering the flame. The controlling parameters include but not limited to mixture conductivity, enthalpy, and the species composition evolution in the unburned mixture.     

Characteristics of laminar lifted flames in coflow jets with initial temperature variation

Characteristics of laminar lifted flames of propane highly diluted with nitrogen have been investigated by varying the initial temperature in coflow jets. The result showed that the lifted flame maintained the tribrachial structure up to the initial temperature of 900 K and the liftoff height decreased with initial temperature and dilution ratio. The overall behavior of liftoff heights correlated well with the jet velocity scaled by the stoichiometric laminar burning velocity, emphasizing the importance of the stoichiometric laminar burning velocity on the propagation speed of tribrachial flame. The exponent of the liftoff height with jet velocity in the relation of increased with initial fuel mole fraction, which has been attributed to the differential diffusion between propane and diluent nitrogen. Consequently, nitrogen concentration varied along the stoichiometric contour, which affected the propagation speed. Also, the exponent increased with initial temperature due to the sensitiveness of the propagation speed variation with nitrogen dilution on initial temperature. The liftoff conditions have been observed for the jet velocity even smaller than the stoichiometric laminar burning velocity at relatively low initial temperatures. This can be attributed to the effect of the buoyancy. Liftoff velocities accounting for the relative buoyancy effect were found to have a satisfactory correlation with regardless of initial temperatures and nitrogen dilution.     

Effects of Soret diffusion on the laminar flame speed and Markstein length of syngas/air mixtures

The effects of Soret diffusion on premixed syngas/air flames at normal and elevated temperatures and pressures are investigated numerically including detailed chemistry and transport. The emphasis is placed on assessing and interpreting the influence of Soret diffusion on the unstretched and stretched laminar flame speed and Markstein length of syngas/air mixtures. The laminar flame speed and Markstein length are obtained by simulating the unstretched planar flame and positively-stretched spherical flame, respectively. The results indicate that at atmospheric pressure the laminar flame speed of syngas/air is mainly reduced by Soret diffusion of H radical while the influence of H₂ Soret diffusion is negligible. This is due to the facts that the main reaction zone and the Soret diffusion for H radical (H₂) are strongly (weakly) coupled, and that Soret diffusion reduces the H concentration in the reaction zone. Because of the enhancement in the Soret diffusion flux of H radical, the influence of Soret diffusion on the laminar burning flux increases with the initial temperature and pressure. Unlike the results at atmospheric pressure, at elevated pressures the laminar flame speed is shown to be affected by the Soret diffusion of H₂ as well as H radical. For stretched spherical flame, it is shown that the Soret diffusion of both H and H₂ should be included so that the stretched flame speed can be accurately predicted. Similar to the laminar flame speed, the Markstein length is also reduced by Soret diffusion. However, the reduction is found to be mainly caused by Soret diffusion of H₂ rather than that of H radical. Moreover, the influence of Soret diffusion on the Markstein length is demonstrated to decrease with the initial temperature and pressure.     

Effect of velocity gradient on propagation speed of tribrachial flames in laminar coflow jets

The effect of velocity gradient on the propagation speed of tribrachial flame edge has been investigated experimentally in laminar coflow jets for propane fuel. It was observed that the propagation speed of tribrachial flame showed appreciable deviations at various jet velocities in high mixture fraction gradient regime. From the similarity solutions, it was demonstrated that the velocity gradient varied significantly during the flame propagation. To examine the effect of velocity gradient, detail structures of tribrachial flames were investigated from OH LIF images and Abel transformed images of flame luminosity. It was revealed that the tribrachial point was located on the slanted surface of the premixed wing, and this slanted angle was correlated with the velocity gradient along the stoichiometric contour. The temperature field was visualized qualitatively by the Rayleigh scattering image. The propagation speed of tribrachial flame was corrected by considering the direction of flame propagation with the slanted angle and effective heat conduction to upstream. The corrected propagation speed of tribrachial flame was correlated well. Thus, the mixture fraction gradient together with the velocity gradient affected the propagation speed.