Effect of the initial pressures on evolution of intrinsically unstable hydrogen/air premixed flame fronts

Laminar premixed flame front may be wrinkled due to the hydrodynamic and diffusive-thermal instabilities. This may lead to the occurrence of the cellular structure and the self-acceleration. The lean unstable hydrogen/air premixed flame at various initial pressures are studied to clarify the effect of the initial pressure on the evolution of the unstable laminar flame. Linear and nonlinear development stages of the unstable flame are simulated and investigated separately. In the linear stage, the initial sinusoidal wave disturbance on the flame front will still keep its initial configuration. The growth rate increases firstly and then decreases with the increase of the wavenumbers. The effect of the self-acceleration on the unstable flame front will be stronger in the linear stage at the higher initial pressure, since there are larger thermal expansion and constant Lewis number for hydrogen/air premixed flame at higher pressure. There are little discrepancies for the calculated growth rates with those predicted by the revised dispersion relation. The nonlinear stage of the unstable flame propagation could be divided into two stages, the transitional and the stable nonlinear stages. In the transitional stage, the flame front cells splits, merges and moves all the time and the initial wavenumber has a great influence on the cell evolution process. With the evolution of the cell on the flame front, the cellular structure on the flame front will not change greatly with the initial wavenumbers in the stable nonlinear stage. The effect of self-acceleration due to the wrinkling of the flame front at this stage is weakened with the increase of the initial pressure. At the higher pressure, more wrinkled structures with smaller mean curvature are distributed on the flame front. At last, results show that the flame front will propagate faster for the larger computation domain. Based on the fractal theory, the fractal dimension of lean hydrogen/air premixed flame with the equivalence ratio of 0.6 at 0.5 MPa in the 2D domain is obtained and around 1.26.     

Effects of the external turbulence on centrally-ignited spherical unstable Ch4/H2/air flames in the constant-volume combustion bomb

In the present study, we conducted experiments to investigate the effects of external turbulence on the development of spherical H₂/CH₄/air unstable flames developments at two different equivalence ratios associated with different turbulent intensities using a spherical constant-volume turbulent combustion bomb and high speed schlieren photography technology. Flame front morphology and acceleration process were recorded and different effects of weak external turbulent flow field and intrinsic flame instability on the unstable flame propagation were compared. Results showed the external turbulence has a great influence on the unstable flame propagation under rich fuel conditions. For fuel-lean premixed flames, however, the effects of external turbulence on the morphology of the cellular structure on the flame front was not that obvious. Critical radius decreased firstly and then kept almost unchanged with the augment of the turbulence intensity. This indicated the dominating inhibiting effect of flame stretch on the turbulent premixed flame at the initial stage of the flame front development. Beyond the critical radius, the acceleration exponent was found increasing with the enhancement of initial turbulence intensity for fuel-lean premixed flames. For fuel-rich conditions, however, the initial turbulence intensity had little effect on acceleration exponent. In order to evaluate the important impact of the intrinsic flame instability and external turbulent flow field for spherical propagating premixed flames, intrinsic flame instability scale and average diameter of vortex tube were calculated. Intrinsic flame instability scale decreased greatly and then stayed unchanged with the propagation of the flame front. The comparison between intrinsic flame instability scale and average diameter of vortex tube demonstrated that the external turbulent flow filed will be more important for the evolution of wrinkle structure in the final stage of the flame propagation, when the turbulence intensity was more than 0.404 m/s.     

高压下氢气-乙醇球形膨胀火焰的层流燃烧速度和火焰不稳定性研究

在初始温度为400 K、不同的初始压力（0.1 MPa、0.4 MPa）、氢气比例（70%、80%）和当量比（0.7 ~ 1.4）条件下进行氢气-乙醇预混燃烧实验,使用高速纹影技术记录火焰传播图像。对氢气-乙醇球形膨胀火焰中的层流燃烧速度（LBV）进行实验研究,发现LBV随着氢气比例的增加而增加,压力升高却有着负影响。对火焰发展不同阶段的火焰形貌进行了研究。当火焰表面的大裂纹分裂出现小裂纹并且导致新细胞再生时,火焰变得不稳定。通过热膨胀比、火焰厚度和刘易斯数等参数考察了流体动力学效应和热扩散效应对火焰固有不稳定性的影响。结果表明,流体动力不稳定性随着压力的增加而增加,热扩散不稳定性对压力变化的敏感性较低。此外,增加氢气比例或初始压力会导致火焰更早遭受不稳定。     

Explosion bomb measurements of ethanol-air laminar gaseous flame characteristics at pressures up to 1.4 MPa

The principal burning characteristics of a laminar flame comprise the fuel vapour pressure, the laminar burning velocity, ignition delay times, Markstein numbers for strain rate and curvature, the stretch rates for the onset of flame instabilities and of flame extinction for different mixtures. With the exception of ignition delay times, measurements of these are reported and discussed for ethanol-air mixtures. The measurements were in a spherical explosion bomb, with central ignition, in the regime of a developed stable, flame between that of an under or over-driven ignition and that of an unstable flame. Pressures ranged from 0.1 to 1.4 MPa, temperatures from 300 to 393 K, and equivalence ratios were between 0.7 and 1.5. It was important to ensure the relatively large volume of ethanol in rich mixtures at high pressures was fully evaporated. The maximum pressure for the measurements was the highest compatible with the maximum safe working pressure of the bomb. Many of the flames soon became unstable, due to Darrieus-Landau and thermo-diffusive instabilities. This effect increased with pressure and the flame wrinkling arising from the instabilities enhanced the flame speed. Both the critical Peclet number and the, more rational, associated critical Karlovitz stretch factor were evaluated at the onset of the instability. With increasing pressure, the onset of flame instability occurred earlier. The measured values of burning velocity are expressed in terms of their variations with temperature and pressure, and these are compared with those obtained by other researchers. Some comparisons are made with the corresponding properties for iso-octane-air mixtures.     

Inerting effect of carbon dioxide on confined hydrogen explosion

Taking maximum flame propagation velocity, maximum explosion pressure, maximum rate of pressure rise and time-average of rising pressure impulse as index, this paper is aimed at evaluating the inerting effects of carbon dioxide on confined hydrogen explosion by varying initial pressure, carbon dioxide addition and equivalence ratio. The results indicated that under enhancing hydrodynamic instability, the stronger flame destabilization occurs with the increase of initial pressure. At Φ = 0.8 and Φ = 1.0, the destabilization effect of thermodiffusive instability continues to increase with the increase of carbon dioxide addition. At all equivalence ratios, the destabilization effect of hydrodynamic instability decreases monotonously with the increase of carbon dioxide addition. All of maximum flame propagation velocity, maximum explosion pressure, maximum rate of pressure rise and time-average of rising pressure impulse reach the peak value at Φ = 1.5, and decrease significantly with increasing carbon dioxide addition. The inerting effect of carbon dioxide could be attributed to the reduction of thermal diffusivity, flame temperature and active radicals. The chemical effect of carbon dioxide reaches the peak value at Φ = 1.0. With the increase of carbon dioxide addition, the chemical effect continues to decrease at Φ = 0.8 and Φ = 1.0, and increase monotonously at Φ = 2.5.     

Laminar burning velocities and transition to unstable flames in H2/O2/N2 and C3H8/O2/N2 mixtures

Effects of positive flame stretch on laminar burning velocities, and conditions for transition to unstable flames, were studied experimentally for freely propagating spherical flames at both stable and unstable preferential-diffusion conditions. The data base involved new measurements for H₂/O₂/N₂ mixtures at values of flame stretch up to 7600 s⁻¹, and existing measurements for C₃H₈/O₂/N₂ mixtures at values of flame stretch up to 900 s⁻¹. Laminar burning velocities varied linearly with increasing Karlovitz numbers—either decreasing or increasing at stable or unstable preferential-diffusion conditions—yielding Markstein numbers that primarily varied with the fuel-equivalence ratio. Neutral preferential-diffusion conditions, however, were shifted toward the unstable side of the maximum laminar burning velocity condition that the simplest preferential-diffusion theories associate with neutral stability. All flames exhibited transition to unstable flames: unstable preferential-diffusion coditions yielded early transition to irregular flame surfaces, and stable preferential-diffusion conditions yielded delayed transition to cellular flames by hydrodynamic instability. Conditions for hydrodynamic instability transitions for H₂/O₂/N₂ mixtures were consistent with an earlier correlation due to Groff for propane/air flames, based on the predictions of Istratov and Librovich.     

乙醇预混火焰胞状不稳定性的数值模拟和理论研究

在一个恒定体积的密闭容器中开展了一系列圆柱形膨胀乙醇预混火焰胞状不稳定性的数值模拟研究,并通过临界贝克莱数、扰动对数增长率和临界火焰半径等理论分析研究了乙醇预混火焰胞状不稳定性。结果表明,在初始压力1MPa、初始温度358K、当量比0.8～1.6条件下,乙醇预混火焰胞状不稳定性非单调性增加,在当量比为1.2时不稳定性最为强烈。原因是热扩散(thermal diffusion,TD)不稳定性分子扩散影响明显,随着当量比的变化而急剧变化,当量比增加,扰动对数增长率先增大后减小;相反,流体动力学不稳定性对当量比并不敏感。此外,在当量比低于1.2时,几乎保持恒定的临界贝克莱数和急剧减小的火焰厚度导致临界火焰半径大幅下降,并在1.2处达到最小值。数值模拟和理论研究显示出一致的结果。     

Parameter extraction from spherically expanding flames propagated in hydrogen/air mixtures

The characteristics of hydrogen/air flame were studied by using the spherical expanding flame propagated in a constant volume chamber. The influence of ignition induced blast wave and the flame instability on flame propagation was investigated. The nonlinear evaluation method for laminar flame parameter evaluation was established. By using the nonlinear evaluation method and the experimental results of flame propagation, the laminar flame speed and Markstein length were extracted and the difference between the nonlinearly evaluated laminar flame speed and the linearly evaluated one was analyzed. The influence of initial pressure and equivalence ratio on laminar flame speed and flame thickness was investigated. The laminar flame speed varies with equivalence ratio and initial pressure. There exists an equivalence ratio at which the laminar flame speed gets its maximum value. And there also exists an initial pressure at which the laminar flame speed gets its maximum value. The critical radius, Markstein length and flame instability of hydrogen/air flame with different equivalence ratio at different initial pressure had been studied. In hydrogen/air flame the flame stability decreases with the increase of initial pressure, while it increases with the increase of equivalence ratio. The global stability of flame is determined by the combination of the stabilizing effect of stretch effect, thermodiffusive instability mechanism and hydrodynamic instability mechanism.     

Numerical simulation study and dimensional analysis of hydrogen explosion characteristics in a closed rectangular duct with obstacles

The influence of obstacles on hydrogen explosion is studied by numerical simulation and dimensional analysis. The numerical simulation is conducted based on the premixed model in a closed rectangular duct with rectangular obstacles, and ten variables that affect the flame propagation velocity are analyzed by dimensional analysis. Continuous acceleration of flame and collision annihilation of flame were successfully realized through triangular obstacles in simulation. The result shows that with the number of obstacles changes, the flame invariably converts to hemispherical flame, finger flame, tongue flame, quasi-plane flame, and mouth flame in turn. But the flame front is more twisted in two obstacles due to hydrodynamic instability and vortices. Through the comparative analysis of the flame and flow field in the duct during hydrogen explosion. It is found that the flame-obstacles-flow field coupling and its hydrodynamic phenomena determine the flame deformation and changes in propagation velocity. The result of the dimensional analysis shows that the drag coefficient can well depict the effects of the shape of the obstacles, and the dimensionless qualitative and quantitative model of flame propagation speed is given and verified.     

Experimental investigation on the onset of cellular instabilities and acceleration of expanding spherical flames

We experimentally investigated the cellular instabilities of expanding spherical propagation of hydrogen–air, methane–air, and propane–air flames. Using image-thresholding technique, the formations and developments of a cell on a flame surface were investigated. The size of the observed cell due to the hydrodynamic instability was larger than those generated by the diffusional–thermal instability. The critical flame radius and critical Peclet number for the onset of instability were evaluated. These critical values for hydrogen–air and methane–air flames increased with increasing concentration. The values decreased with increasing initial pressure because the flame thickness decreased with increasing initial pressure. The ratio of the increase in the burning velocity increased with increasing initial pressure, although that of the hydrogen–air flames only increased with decreasing concentration. The results demonstrated that acceleration of the flame speed is affected by the intensity of the diffusional–thermal and hydrodynamic instabilities.     

湍流预混火焰的分形特性

采用高速纹影摄影法获得了定容燃烧弹内预混湍流火焰的图像，分别用数盒子法和像素点覆盖法计算出了火焰图像的分形维数。湍流火焰的分形分析结果表明，定容燃烧弹内的预混湍流火焰结构具有分形特征，且属于非充分发展的湍流火焰。湍流火焰的分形维数反应了湍流脉动对火焰片的褶皱程度，湍流强度增大加剧湍流火焰前锋的褶皱，分形维数也随之增加。在相同湍流强度下，小尺度湍流对火焰前锋的褶皱作用更大。     

The effects of heat loss on the burning velocity of cellular premixed flames generated by hydrodynamic and diffusive-thermal instabilities

The effects of heat loss on the burning velocity of cellular premixed flames are investigated by two-dimensional unsteady calculations of reactive flows based on the compressible Navier-Stokes equation and on the diffusive-thermal model equation. Hydrodynamic and diffusive-thermal instabilities are taken into account as contributing to the intrinsic instability of premixed flames. A sufficiently small disturbance is superimposed on a planar flame to obtain the relation between the growth rate and the wavenumber, i.e., the dispersion relation. As the heat loss becomes larger, the growth rate decreases and the unstable range narrows. This is because hydrodynamic instability caused by thermal expansion weakens for nonadiabatic flames. To investigate the characteristics of cellular flames, the disturbance with the linearly most unstable wavenumber, i.e., the critical wavenumber, is superimposed. As the superimposed disturbance evolves, the cellular-flame front forms due to the intrinsic instability. The lateral movement of cellular flames is observed at low Lewis numbers, and the behavior of cellular-flame fronts becomes more unstable for nonadiabatic flames. As the heat-loss parameter increases, the burning velocity of a cellular flame normalized by that of a planar flame increases at Lewis numbers lower than unity. By contrast, when the Lewis number is not less than unity, the burning-velocity increment decreases by increasing the heat loss. Diffusive-thermal instability thus has a pronounced influence on the unstable behavior and burning velocity of nonadiabatic cellular flames.     

Investigation on unconfined hydrogen cloud explosion with external turbulence

Fully understanding the coupling mechanism between the enhancement of explosion overpressure and flame acceleration is a prerequisite for assessing hydrogen cloud explosion overpressure. In this research, unconfined fan-stirred hydrogen explosion experiments were performed to study the effects of flame instability and external turbulence on flame propagation and overpressure characteristics. The results showed that the combination of the external turbulence and the flame instability could result in great flame acceleration and explosion overpressure enhancement. For the intensity of external turbulence considered in this study, the combustion regimes were all in the flamelet zone. With the increase of the external turbulence intensity, the flame gradually got accelerated, and the explosion overpressure got enhanced. A theoretical prediction model for the upper and lower limit of the maximum overpressure was proposed, which fully accounted for flame instability, external turbulence, and flame-induced turbulence. It provides a conservative evaluation for hydrogen cloud explosion.     

Dynamic couplings of hydrogen/air flame morphology and explosion pressure evolution in the spherical chamber

This paper aims at exploring the dynamic couplings of flame morphology and explosion pressure evolution experimentally and theoretically. In the experiment, flame morphology and explosion pressure evolution under diffusional-thermal and hydrodynamic instability are recorded using high-speed schlieren photography and pressure transducer. In the theoretical calculation, the effects of cellular flame on the explosion pressure evolution are conducted using smooth flame, D = 2.0566, 2.1 and 7/3. The results demonstrate that the cellular flame formation of various equivalence ratios could be attributed to the fact Lewis number is less than unity on the lean side. The flame destabilization of Φ = 0.8 and 3.0 with increasing initial pressure is due to the decreasing flame thickness regardless of unchangeable thermal expansion ratio. Much smaller cells formation on the cellular flame surface as the explosion pressure rises could be attributed to the joint effect of the diffusional-thermal and hydrodynamic instability. Note that the explosion pressure evolution in spherical chamber is obviously underestimated assuming the flame surface is smooth during the hydrogen/air explosion. But the explosion overpressure is overpredicted significantly with D = 7/3. The theoretical overpressure with D = 2.1 is in satisfactory agreement with experimental results.     

A petascale direct numerical simulation study of the modelling of flame wrinkling for large-eddy simulations in intense turbulence

A new set of petascale direct numerical simulations (DNS) modelling lean hydrogen combustion with detailed chemistry in a temporally evolving slot-jet configuration is presented as a database for the development and validation of models for premixed turbulent combustion. The jet Reynolds number is 10,000, requiring grid numbers up to nearly seven billion, which was achieved by computation on 120,000 processor cores. In contrast to many prior DNS studies, a mean shear exists that drives strong turbulent mixing within the flame structure. Three cases are simulated with different Damköhler numbers, while Reynolds number is held fixed. Basic statistics are presented showing that integrated burning rates up to approximately six times the laminar burning rate are obtained. It is shown that increased flame surface area accounts for most of the enhanced burning while increases in the burning rate per unit area also play an important contribution.The database is then used to assess a new model of flame wrinkling intended for large-eddy simulations (LES). The approach draws on concepts from fractal geometry, requiring the modelling of an inner cut-off scale representing the smallest scale of flame wrinkling, and the fractal dimension controlling the resolution dependence of the unresolved flame surface area. In contrast to previous modelling, it is argued that the inner cut-off should be filter-size invariant in an inertial range. Then, dimensional and physical reasoning together with Damköhler’s limiting scaling laws for the turbulent flame speed are used to infer the cut-off and fractal dimension in limiting regimes. Two methods of determining the fractal dimension are proposed: a static, algebraic expression or a dynamic approach exploiting a Germano-type identity. Finally the model is compared against the DNS in a priori tests and is found to give excellent results, quantitatively capturing the trends with time, space, filter size and Damköhler number.     

Outward propagation velocity and acceleration characteristics in hydrogen-air deflagration

Propagation characteristics of hydrogen-air deflagration need to be understood for an accurate risk assessment. Especially, flame propagation velocity is one of the most important factors. Propagation velocity of outwardly propagating flame has been estimated from burning velocity of a flat flame considering influence of thermal expansion at a flame front; however, this conventional method is not enough to estimate an actual propagation velocity because flame propagation is accelerated owing to cellular flame front caused by intrinsic instability in hydrogen-air deflagration. Therefore, it is important to understand the dynamic propagation characteristics of hydrogen-air deflagration. We performed explosion tests in a closed chamber which has 300 mm diameter windows and observed flame propagation phenomena by using Schlieren photography. In the explosion experiments, hydrogen-air mixtures were ignited at atmospheric pressure and room temperature and in the range of equivalence ratio from 0.2 to 1.0. Analyzing the obtained Schlieren images, flame radius and flame propagation velocity were measured. As the result, cellular flame fronts formed and flame propagations of hydrogen–air mixture were accelerated at the all equivalence ratios. In the case of equivalent ratio φ = 0.2, a flame floated up and could not propagate downward because the influence of buoyancy exceeded a laminar burning velocity. Based upon these propagation characteristics, a favorable estimation method of flame propagation velocity including influence of flame acceleration was proposed. Moreover, the influence of intrinsic instability on propagation characteristics was elucidated.     

Experimental and simulation study of premixed syngas-air deflagration dynamics with elevated temperature and CO2 addition

Experimental and dynamic analyses of the deflagration characteristics of laminar premixed syngas-air at different preheating temperatures and with different CO₂ volume fractions were carried out in a rectangular half-open pipe. The effects of CO₂ concentration and different initial temperatures on the flame structure evolution, flame structure profile and reaction rate of critical radicals, flame propagation speed, overpressure dynamics and hydrodynamic instability of syngas-air mixture were studied. The FFCM-1 mechanism was used to predict the laminar burning velocity of syngas-air under relevant conditions. The results revealed that the addition of CO₂ inhibited the flame propagation and reduced the concentration of H, OH and O, thus reduced the laminar burning velocity. The increase in temperature promotes the chemical effect of CO₂, and the interaction between the flame front and the pressure wave is more pronounced, prolonging the duration of the " tulip " flame. Adding CO₂ reduces the flame front speed and overpressure, decreases the oscillation amplitude in late flame propagation, and inhibits the explosion intensity. Meanwhile, the temperature increase accelerates the flame propagation in the spherical and finger stages, and the maximum flame propagation speed and peak pressure appear earlier. In addition, as CO₂ content and temperature rise, flame hydrodynamic instability is difficult to ignore. However, there is a lack of data from studies of syngas deflagration dynamics at higher temperatures and with higher CO₂ additions. This suggests a focus on studies at higher temperatures as well as with higher CO₂ additions to enable the development of accurate kinetic models for wide range of syngas combustion. Also, the higher the initial temperature, the longer the time required for heating.     

A study of numerical hazard prediction method of gas explosion

A 3-dimensional computational fluid dynamics (CFD) simulation of a premixed hydrogen/air explosion in a large-scale domain is performed. The main feature of the numerical model is the solution of a transport equation for the reaction progress variable using a function for turbulent burning velocity that characterizes the turbulent regime of propagation of free flames derived by introducing the fractal theory. The model enables the calculation of premixed gaseous explosion without using fine mesh of the order of micrometer, which would be necessary to resolve the details of all instability mechanisms. The value of the empirical constant contained in the function for turbulent burning velocity is evaluated by analyzing the experimental data of hydrogen/air premixed explosion. The comparison of flame behavior between the experimental result and numerical simulation shows good agreement. The effect of mesh size on simulated flame propagation velocity is also tested, showing that the numerical result agrees reasonably well with experiment when the mesh size is less than about 20 cm.     

湍流预混火焰结构的测度分形研究

本文利用图像可视化技术，在小型火焰试验台上获得了Ｒｅｄ＝４３３５～１１１００范围内的燃气预混火焰的湍流热图像序列，并对２维湍流结构参数进行了测量。结合基于测度分析的分形理论，研究了湍流火焰的分维特性，结果表明：湍流火焰的２维形状结构具有分数维特性，且维数在２．０５～２．２６范围内。在此基础上，得到维数与Ｒｅｄ、热释放率及１次风流量等燃烧控制因子的依变关系，并讨论了湍流火焰分维结构的内在机理。     

Effect of nitrogen on deflagration characteristics of hydrogen / methane mixture

In order to study the influence of nitrogen on the deflagration characteristics of premixed hydrogen/methane, the explosion parameters of premixed hydrogen/methane within various volume ratios and different dilution ratios were studied by using a spherical flame method at room temperature and pressure. The results are as follows: The addition of nitrogen makes the upper limit of explosion of hydrogen/methane premixed gas drop, and the lower limit rises. For explosion hazard (F-number), hydrogen/methane premixed fuel with a hydrogen addition ratio of 10% has the lowest risk, and nitrogen has a greater impact on the dangerous degree of hydrogen and methane premixed gas whose hydrogen addition ratio does not exceed 30%. In terms of flame structure, the spherical flame was affected by buoyancy instability as the percentage of nitrogen dilution increased, but the buoyancy instability gradually decreased as the percentage of hydrogen addition increased. The addition of diluent gas reduces the spreading speed of the stretching flame and reduces the stretching rate in the initial stage of flame development. The laminar flame propagation velocity calculated by the experiment in this paper is consistent with the laminar flow velocity of the hydrogen/methane premixed gas calculated by GRI Mech 3.0. Considering the explosion parameters such as flammability limit, laminar combustion rate and deflagration index, when hydrogen is added to 70%, it is the turning point of hydrogen/methane premixed fuel.