Analytical Study of Hydrodynamic Instability in the Flame: 2. Account of the Viscosity of the Gas in the Cold and Hot Areas

Hydrodynamic instability is examined with consideration given to the viscosity of the fresh gas and combustion products, as well as to the dependences of the flame speed on the front curvature and of the transport coefficients on the temperature. For the perturbation frequency, an approximate second-order dispersion equation is derived. The flame is completely stable at very high viscosity or small dimensions. The greatest destabilizing role of the thermal expansion coefficient manifests itself at its relatively small values. As the expansion coefficient increases, the viscosity of the gas in the flame zone increases rapidly. In addition, the stabilizing effect according to the Markstein model is enhanced by thermal expansion.     

甲烷-煤尘爆炸物火焰传播特性

 在10 m³的爆炸罐中对体积分数为8%的甲烷和75 g/m³煤尘的混合物进行了系统的燃烧爆炸实验。分别利用光测方法和压力方法得到了爆炸物的层流燃烧速度、火焰传播速度、火焰厚度、马克斯坦长度以及爆炸特征值的变化规律。结果表明,在常温常压下,当点火能为40 J时：利用光测法得到的8%甲烷与75 g/m³煤尘混合物的燃烧速度为0.437 m/s,而根据压力-时间关系得到的混合物燃烧速度为0.459 m/s,两者符合较好;用火焰厚度与马克斯坦长度判定的火焰发展趋势相同,即向外传播的火焰趋于稳定;爆炸物的爆炸特征值最大值出现在0.5 m处,壁面的爆炸特征值偏小。     

乙烷含量对天然气、煤层气燃烧速率和火焰稳定性的影响

本文在定容燃烧弹中,研究了高温高压(0.75 MPa,450 K)下甲烷-乙烷-空气预混合气火焰传播规律,并系统分析了当量比、混合气中乙烷含量对混合气层流燃烧及火焰稳定性的影响.实验结果表明:随着混合气中乙烷含量的增加,不同当量比下无拉伸火焰燃烧速率均增大,马克斯坦长度增大,表明火焰稳定性增强.在实验范围内,无拉伸火焰...     

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.     

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.     

The stability of laminar explosion flames

The paper presents the results of a fundamental experimental and theoretical study of Darrieus–Landau, thermo-diffusive, instabilities in atmospheric explosions, and, on a smaller scale, in laboratory explosions in closed vessels. Pressure dependencies were sought to exploit the leading role of the Peclet number in the phenomena, so that similar Peclet numbers were achieved in both instances. However, in large atmospheric explosions large Peclet numbers were achieved by the size of the fireball, whereas in the closed vessel explosion it was achieved at a higher pressure by a much smaller flame, but because of the higher pressure, one endowed with a small laminar flame thickness. This study covers a much wider range of fuels and of pressures and the dependencies of the phenomena on both of these were carefully studied, although, for the atmospheric explosions, the data only covered propane and methane. The roles of both Markstein and Peclet numbers become clear and give rise to a more fundamental correlating parameter, a critical Karlovitz number, K_cl, for flame stability. This is based on the flame stretch rate, normalised by its multiplication by the chemical reaction time in a laminar flame. The experimentally measured dependencies of this key parameter on pressure and Markstein number are reported for the first time for so many different fuels. The critical Karlovitz number for flame stability decreases with increase in the strain rate Markstein number. As a result, it is possible to predict the extent of the unstable regime for laminar flames as a function of Ma_sr and pressure. Such data can be used to estimate the severity of large scale atmospheric explosions. As Ma_sr becomes highly negative, the regime of stability is markedly reduced.     

Flame stabilization with a tubular flame

A new technique to stabilize a flame in a high-velocity stream with use of a tubular flame has been proposed. To elucidate the validity of this technique, an experiment has been conducted by mounting a tubular flame burner on the nozzle. Flame stability limits and temperature distributions around the burner port have been determined, and experiments have been extended to the ducted combustion to measure pressure fluctuations and to analyze the burned gases. Results show that the tubular flame can successfully stabilize the main flame up to 130 m/s, which is the upper limit of the present supply facility. The main flame is well anchored at the exit of the nozzle, and the tubular flame efficiently supplies heat and radicals to the main flame. In the ducted combustion, the pressure fluctuations are reduced significantly. The exhaust gas analyses, however, indicate that an almost chemical equilibrium condition can be achieved at 50 m/s, but not at 90 and 130 m/s. Since the energy input relative to the main flame is just 6.1% at 130 m/s, the present tubular burner is not enough to burn all the unburned gas completely at high velocities, although the main flame can be anchored. The slit length and/or the slit width of the tubular flame burner should be larger to overcome this shortage. From the above results, it is concluded that the tubular flame has a potential for stabilizing a flame in a high-speed stream.     

双组分燃料的层流火焰速度模型

以往关于层流火焰速度的理论分析均只考虑单组分燃料,本文对双组分燃料的平面火焰进行了大活化能渐近理论分析。在理论分析中,将火焰结构分为预热区、化学反应区和平衡区,并在大活化能假设下对各个区域分别求解了关于温度与燃料质量分数的微分方程。根据每两个区域分界面上满足的结合条件,本文推导出了双组分燃料的层流火焰速度模型。该模型表明双组分燃料层流火焰速度的平方为各个单组分燃料层流火焰速度平方的加权平均。     

Analysis of the flame dynamics in methane/hydrogen fuel blends at elevated pressures

We investigate the Flame Transfer Function (FTF) of a lean-premixed, laminar slit flame numerically. Based on the reference case at atmospheric pressure, we investigate four different scenarios: (i) varying the hydrogen content in the fuel at constant equivalence ratio (ER) (resulting in an increase of the laminar flame speed); (ii) varying the hydrogen content in the fuel at varying ER (resulting in a constant laminar flame speed); (iii) varying the operating pressures from 1 to 5 bar (resulting in a decrease of the laminar flame speed); and (iv) combining a hydrogen-enriched flame at an elevated pressure of 3 bar (resulting in the same flame speed as the reference case). We identify in this case that the laminar flame speed and the flame thickness impact the FTF independently. We show that the low-pass behavior of the flame is shifted towards higher frequencies when the operating pressure increases, and demonstrate that wrinkles along the flame front preserve in contrast to the atmospheric operating pressure configurations. These results are in line with past studies, that relate the dampening of flame front wrinkling to a decreasing Markstein length. We therefore conclude that a decreasing flame thickness, due to increasing operating pressure, causes a decreasing Markstein length and therefore less pronounced dampening of flame front wrinkles.     

The asymptotic structure of weakly strained moderately rich methane—air flames

The asymptotic structure of weakly strained moderately rich premixed methane-air flames stabilized in stagnation-point flows is analysed. In the asymptotic analysis the influence of strain on the mass flux, on the temperature and on the concentration of chemical species in the flame is treated as a perturbation from their values in the corresponding unstrained flame. Perturbation analysis is carried out to the first order. The deviation of the mass burning rate in the strained flame from the mass burning rate in the corresponding unstrained flame is obtained in terms of the Markstein number. Chemical reactions taking place in the flame are described by a reduced chemical-kinetic mechanism made up of four global steps. The analysis gives a sufficient number of equations from which the Markstein numbers can be calculated. Numerical calculations are performed using a chemical-kinetic mechanism made up of elementary reactions. Markstein numbers are obtained and they are found to agree reasonably well with those calculated using the results of an asymptotic analysis. Markstein numbers are also found to agree reasonably well with those deduced from experiments. An interesting finding of the present study is that the Markstein number for moderately rich flames depends on the Lewis number of both fuel and oxygen.     

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.     

Stability of inclined planar flames as a local approximation of weakly curved flames

To evaluate the effect of vorticity usually generated by curved flames on the flame stability, laminar premixed planar flames inclined in the gravitational field is asymptotically examined. The flame structure is resolved by a large activation energy asymptotics and a long wave approximation. The coupling between hydrodynamics and diffusion processes is included and near-unity Lewis number is assumed. The results show that as the flame is more inclined from the horizontal plane it shows more unstable characteristics due to not only the decrease of the stabilizing effect of gravity but also the increase of the destabilizing effect of rotational flow. Unlike the planar flame propagating downward with the right angle to the upstream flow, the obtained dispersion relation involves the Prandtl number and shows the destabilizing effect of viscosity. The analysis predicts that the phase velocity of unstable wave depends on the Lewis number as well as the flame angle and, especially for unity Lewis number, it is the same with tangential velocity at the reaction zone. For relatively short wave disturbances, still much larger than flame thickness, the most unstable wavelength is nearly independent on the flame angle and the flame can be stabilized by gravity and diffusion mechanism.     

Studies of the dynamics of autoignition assisted outwardly propagating spherical cool and double flames under shock-tube conditions

The initiation, propagation, and transition of the autoignition assisted spherical cool flame and double flame are studied numerically and experimentally using n-heptane/air/He mixtures under shock-tube experimental conditions over a wide range of temperatures. The primary goal of the current study is to understand the effects of the ignition Damkohler number, ignition energy, flame curvature, and autoignition-induced flow compression on the propagation of spherical flames to ensure the proper interpretation of shock-tube flame speed measurements at engine-relevant conditions. The results show that at high ignition Damkohler number, there are three different flame regimes, cool flame, double flame, and hot flame. The cool flame speed accelerates dramatically with the increase of ignition Damkohler number. In addition, it is found that the change of flame regime, low-temperature autoignition, flame stretch, and autoignition-induced flow compression result in a complicated non-linear dependence of flame speed on stretch. The results also reveal that the spherical cool flame has much lower Markstein length compared to the hot flame at T > 600 K. Moreover, it is found that both the autoignition assisted cool flame and the trailing hot flame front in the double flame can propagate much faster that the hot flame alone at the same mixture conditions, leading to a nonlinear dependence of flame speed on the mixture initial temperature. The simulated flame trajectories and the flame speed dependence on temperature agree qualitatively well with the shock-tube experiments. A quantitative criterion to ensure the accurate speed measurement of the cool and hot flame is proposed. The present study provides important physical insight and guidance for the flame speed measurement using a shock-tube at engine relevant conditions.     

Effects of endothermic chain-branching reaction on spherical flame initiation and propagation

A theoretical model is developed to describe the spherical flame initiation and propagation. It considers endothermic chain-branching reaction and exothermic recombination reaction. Based on this model, the effects of endothermic chain-branching reaction on spherical flame initiation and propagation are assessed. First, the analytical solutions for the distributions of fuel and radical mass fraction as well as temperature are obtained within the framework of large activation energy and quasi-steady assumption. Then, a correlation describing spherical flame initiation and propagation is derived. Based on this correlation, different factors affecting spherical flame propagation and initiation are examined. It is found that endothermicity of the chain-branching reaction suppresses radical accumulation at the flame front and thus reduces flame intensity. With the increase of endothermicity, the unstretched flame speed decreases while both flame ball radius and Markstein length increases. Endothermicity has a stronger effect on the stretched flame speed with larger fuel Lewis number. The Markstein length is found to increase monotonically with endothermicity. Furthermore, the endothermicity of the chain-branching reaction is shown to affect the transition among different flame regimes including ignition kernel, flame ball, propagating spherical flame, and planar flame. The critical ignition power radius increases with endothermicity, indicating that endothermicity inhibits the ignition process. The influence of endothermicity on ignition becomes relatively stronger at higher crossover temperature or higher fuel Lewis number. Moreover, one-dimensional transient simulations are conducted to validate the theoretical results. It is shown that the quasi-steady-state assumption used in theoretical analysis is reasonable and that the same conclusion on the effects of endothermic chain-branching reaction can be drawn from simulation and theoretical analysis.     

稀甲烷/氢气预混湍流传播火焰实验研究

本文采用定容湍流燃烧弹获取了稀甲烷/氢气/空气在强湍流条件下的火焰发展历程,研究了湍流火焰在负马克斯坦数条件下的传播特性.结果表明,湍流火焰呈现自相似传播特性,即使在强湍流条件下,湍流传播火焰仍然会受到不稳定性的影响.并且随着马克斯坦数的减小,不稳定性对湍流传播火焰的影响增强。同时,本文获得一种新的湍流燃烧速度拟合公式,包含了负马克斯坦数条件下不稳定性对湍流燃烧速度的影响。     

Near Wall Dynamics of Premixed Flames

Highly-resolved numerical simulations employing detailed reaction kinetics and molecular transport have been applied to flame-wall interaction (FWI) of laminar premixed flames. A multiple plane-jet flame (2D) has been considered, which is operated with premixed methane/air mixtures at atmospheric conditions and with different equivalence ratios. Free flame (FF) and side-wall quenching (SWQ) conditions have been accomplished by defining one lateral boundary as either a symmetry plane for FF or a cold wall with fixed temperature for SWQ. An equidistant grid with a resolution of 20 µm is used to resolve the FWI zone. The GRI-3.0 mechanism is used for computing chemical reaction rates. The flame is tangentially compressed when approaching the cold wall, and elongated in the FF case, causing an inversion of the sign of the tangential strain rate Ka_s and a considerable decrease of the total stretch rate Ka_tot for the SWQ flame. The flame consumption speed S_L decreases with decreasing normal stretch due to curvature Ka_c while approaching the cold wall, but it increases with decreasing Ka_c for the FF case, leading to an inversion of the Markstein number Ma_tot based on Ka_tot from positive in FF to negative in the SWQ case. The results reveal a strong correlation of flame dynamics during transitions from FWI to freely propagating flames, which may bring a new perspective for modeling FWI phenomena by means of flame dynamics. To do this, the quenching effect of the wall may be reproduced by an inversion of the Markstein number from positive to negative in the FWI zone and applying the general linear Markstein correlation, leading to a decrease of the flame consumption speed. In addition, the quenching distance evaluated from S_L has been found to be almost equal to the unstretched laminar flame thickness, which compares quantitatively well with measured data from literature.     

A physical relationship between consumption and displacement speed for premixed flames with finite thickness

The characterization of premixed flames by a flame speed has been a subject that has occupied much interest in the literature in many systematic studies on combustion phenomena. Consumption and displacement speeds are two such flame speeds that are understood to describe the flame dynamics under the effect of flame curvature, flow non-uniformities, Lewis number and turbulence effects along with heat transfer with flame holders and cold walls. As such, much work has been done in the past where either one of these two speeds has been employed along with a linear sensitivity coefficient (Markstein length) for describing different sensitivities to stretch effects. However, despite recent attempts using the asymptotic theory, the relationship between these two quantities has only been clarified in a limited manner for flames of finite thickness. In this study, we use flame stretch theory that takes into account changes of stretch, curvature, heat transfer and Lewis number effects throughout the pre-heat zone and its integral effect on the flame reaction zone. A sound mathematical and physical basis is provided for understanding the two speeds that is valid for weak as well as strong stretch effects. Understanding from theory is further demonstrated by analysing several example 1D stretched flames along with a 2D bluff body flame near extinction.     

Flame propagation in narrow horizontal channels: Impact of the gravity field on the flame shape

In this paper, we study the effect of gravity, or buoyancy forces, on the structure of flames propagating in horizontal channels. It is shown that there are two mechanisms for the appearance of non-symmetric flames. The first, more obvious, is related to buoyancy, when a hotter gas of lower density tends to be located in the upper half of the channel. However, there is a second mechanism associated with the intrinsic flame instabilities, which also can cause the loss of flame symmetry. This mechanism can, at certain values of the parameters, act in the opposite direction, when hotter gases are enclosed in the lower part of the channel. In this case, two stable non-symmetric solutions may exist in the presence of gravitational forces and the establishment of one or another configuration depends on the initial conditions. The stability of these solutions is demonstrated by time-dependent computations.     

Extinction and flame bifurcations of stretched dimethyl ether premixed flames

Extinction limits and flame bifurcation of lean premixed dimethyl ether–air flames are numerically investigated using the counterflow flame with a reduced chemistry. Emphasis is paid to the combined effect of radiation and flame stretch on the extinction and flammability limits. A method based on the reaction front is presented to predict the Markstein length. The predicted positive Markstein length agrees well with the experimental data. The results show that flow stretch significantly reduces the flame speed and narrows the flammability limit of the stretched dimethyl ether–air flame. It is found that the combined effect of radiation and flow stretch results in a new flame bifurcation and multiple flame regimes. At an equivalence ratio slightly higher than the flammability limit of the planar flame, the distant flame regime appears at low stretch rates. With an increase in the equivalence ratio, in addition to the distant flame, a weak flame isola emerges at moderate stretch rates. With a further increase in the equivalence ratio, the distant flame and the weak flame branches merge together, resulting in the splitting of the weak flame branch into two weak flame branches, one at low stretch and the other at high stretch. Flame stability analysis demonstrates that the high stretch weak flame is also stable. Furthermore, a K-shaped flammability limit diagram showing various flame regimes and their extinction limits is obtained.     

Flame structure of HMX/GAP propellant at high pressure

The chemical and thermal structure of a HMX/GAP propellant flame was investigated at a pressure of 0.5 MPa using molecular beam mass spectrometry and a microthermocouple technique. The pressure dependence of the burning rate was measured in the pressure range of 0.5–2 MPa. The mass spectrometric probing technique developed for flames of energetic materials was updated to study the chemical structure of HMX/GAP flames at high pressures. Eleven species, including HMX vapor, were identified, and their concentrations were measured in a zone adjacent to the burning surface at pressures of 0.5 and 1 MPa. Temperature profiles in the propellant combustion wave were measured at pressures of 0.5 and 1 MPa. Species concentration profiles were measured at 0.5 MPa. Two main zones of chemical reactions in the flame were found. The data obtained can be used to develop and validate combustion models for HMX/GAP propellants.