Uncertainties in interpretation of high pressure spherical flame propagation rates due to thermal radiation

It has been suggested that radiation heat loss may be a large source of experimental uncertainty in flame speed measurements using the outwardly propagating spherical flame method. Thermal radiation is usually not considered in interpretation of these experiments, yet it may contribute significantly to uncertainty especially for model-constraining conditions at low flame temperature and high pressure. In the present work, a conservative analytical estimate of the effects of radiation heat loss is derived and validated against detailed numerical simulations. A solver with a graphical interface is provided in the Supplemental material to allow implementation of these analytical results. The analytical estimate considers the radiation induced burned gas motion as well as the decreasing flame temperature due to conduction to the radiating burned gas and radiation loss from the flame zone. The results show that previous measurements of hydrogen flame speeds at low flame temperature by Burke et al. (2010) [3] are minimally affected by radiation, but flames with low flame speeds can be strongly inhibited by radiative loss. Future laminar spherical flame measurements and interpretation of existing determinations with low adiabatic flame speeds must include consideration of radiation effects to avoid large uncertainties.     

Effects of radiation and compression on propagating spherical flames of methane/air mixtures near the lean flammability limit

Large discrepancies between the laminar flame speeds and Markstein lengths measured in experiments and those predicted by simulations for ultra-lean methane/air mixtures bring a great concern for kinetic mechanism validation. In order to quantitatively explain these discrepancies, a computational study is performed for propagating spherical flames of lean methane/air mixtures in different spherical chambers using different radiation models. The emphasis is focused on the effects of radiation and compression. It is found that the spherical flame propagation speed is greatly reduced by the coupling between thermal effect (change of flame temperature or unburned gas temperature) and flow effect (inward flow of burned gas) induced by radiation and/or compression. As a result, for methane/air mixtures near the lean flammability limit, the radiation and compression cause large amounts of under-prediction of the laminar flame speeds and Markstein lengths extracted from propagating spherical flames. Since radiation and compression both exist in the experiments on ultra-lean methane/air mixtures reported in the literature, the measured laminar flame speeds and Markstein lengths are much lower than results from simulation and thus cannot be used for kinetic mechanism validation.     

Effects of hydrogen addition on the propagation of spherical methane/air flames: A computational study

A computational study is performed to investigate the effects of hydrogen addition on the fundamental characteristics of propagating spherical methane/air flames at different conditions. The emphasis is placed on the laminar flame speed and Markstein length of methane/hydrogen dual fuel. It is found that the laminar flame speed increases monotonically with hydrogen addition, while the Markstein length changes non-monotonically with hydrogen blending: it first decreases and then increases. Consequently, blending of hydrogen to methane/air and blending methane to hydrogen/air both destabilize the flame. Furthermore, the computed results are compared with measured data available in the literature. Comparison of the computed and measured laminar flame speeds shows good agreement. However, the measured Markstein length is shown to strongly depend on the flame radii range utilized for data processing and have very large uncertainty. It is found that the experimental results cannot correctly show the trend of Markstein length changing with the hydrogen blending level and pressure and hence are not reliable. Therefore, the computed Markstein length, which is accurate, should be used in combustion modeling to include the flame stretch effect on flame speed.     

高压乙烷火焰传播特性的试验研究

对乙烷气体在高压环境中的火焰传播特性进行了试验研究。试验压力从0．1MPa到1．5MPa，在相同的氧气／隋性气体比例下，通过调整氮气与氩气的比例，保持不同反应当量比时的理论绝热燃烧温度不变，得到了等绝热燃烧温度条件下的层流火焰形态及传播速度。试验表明：在相等的绝热燃烧温度条件下，火焰传播特性曲线与非等温条件下有明显的不同；高压环境下的火焰传播特性与常压条件下的火焰传播特性也有较大的不同。     

On the extraction of laminar flame speed and Markstein length from outwardly propagating spherical flames

Large discrepancies among the laminar flame speeds and Markstein lengths of methane/air mixtures measured by different researchers using the same constant-pressure spherical flame method are observed. As an effort to reduce these discrepancies, one linear model (LM, the stretched flame speed changes linearly with the stretch rate) and two non-linear models (NM I and NM II, the stretched flame speed changes non-linearly with the stretch rate) for extracting the laminar flame speed and Markstein length from propagating spherical flames are investigated. The accuracy and performance of the LM, NM I, and NM II are found to strongly depend on the Lewis number. It is demonstrated that NM I is the most accurate for mixtures with large Lewis number (positive Markstein length) while NM II is the most accurate for mixtures with small Lewis number (negative Markstein length). Therefore, in order to get accurate laminar flame speed and Markstein length from spherical flame experiments, different non-linear models should be used for different mixtures. The validity of the theoretical results is further demonstrated by numerical and experimental studies. The results of this study can be used directly in spherical flame experiments measuring the laminar flame speed and Markstein length.     

Measurement and correlation of laminar flame speeds of CO and C2 hydrocarbons with hydrogen addition at atmospheric and elevated pressures

The laminar flame speeds of mixtures of ethane, ethylene, acetylene, and carbon monoxide with small amount of hydrogen addition at atmospheric and elevated pressures were experimentally and computationally determined. It was found that the approximate linear correlation identified previously between the laminar flame speeds and an appropriate definition of the amount of hydrogen addition for methane, propane and n-butane at atmospheric pressure also largely applies to ethane, ethylene, and acetylene at atmospheric as well as elevated pressures. The linear correlation, however, does not hold for carbon monoxide, at all pressures, due to the strong catalytic effect of hydrogen on the oxidation of carbon monoxide. A mechanistic analysis shows that both the Arrhenius and diffusive contributions to the laminar flame speed are nearly linear functions of the hydrogen addition, which explains this overall approximate linear correlation.     

Nonlinear effects in the extraction of laminar flame speeds from expanding spherical flames

Various factors affecting the determination of laminar flames speeds from outwardly propagating spherical flames in a constant-pressure combustion chamber were considered, with emphasis on the nonlinear variation of the stretched flame speed to the flame stretch rate, and the associated need to nonlinearly extrapolate the stretched flame speed to yield an accurate determination of the laminar flame speed and Markstein length. Experiments were conducted for lean and rich n-butane/air flames at initial pressure, demonstrating the complex and nonlinear nature of the dynamics of flame evolution, and the strong influences of the ignition transient and chamber confinement during the initial and final periods of the flame propagation, respectively. These experimental data were analyzed using the nonlinear relation between the stretched flame speed and stretch rate, yielding laminar flame speeds that agree well with data determined from alternate flame configurations. It is further suggested that the fidelity in the extraction of the laminar flame speed from expanding spherical flames can be facilitated by using small ignition energy and a large combustion chamber.     

Effects of steam dilution on laminar flame speeds of H2/air/H2O mixtures at atmospheric and elevated pressures

The laminar flame speeds of H₂/air with steam dilution (up to 33 vol%) were measured over a wide range of equivalence ratio (0.9–3.0) at atmospheric and elevated pressures (up to 5 atm) by an improved Bunsen burner method. Burke, Sun, HP (High Pressure H₂/O₂ mechanism), and Davis mechanisms were employed to calculate the laminar flame speeds and analyze different effects of steam addition. Four studied mechanisms all underestimated the laminar flame speeds of H₂/air/H₂O mixtures at medium equivalence ratios while the Burke mechanism provided the best estimates. When the steam concentration was lower than 12%, increasing pressure first increased and then decreased the laminar flame speed, the inflection point appeared at 2.5 atm. When the steam concentration was greater than 12%, increasing the pressure monotonously decrease the laminar flame speed. The chemical effect was amplified by elevated pressure and it played an important role for the inhibiting effect of the pressure on laminar flame speed. The fluctuations of the chemical effect at 1 atm were mainly caused by three-body reactions, while the turn at 5 atm was mainly caused by the direct reaction effect. Elevated pressure and steam addition amplified the influences of uncertainties in the rate constants for elementary reactions, which might leaded to the disagreement between experimental and simulation results.     

Effect of cylindrical confinement on the determination of laminar flame speeds using outwardly propagating flames

The effect of nonspherical (i.e. cylindrical) bomb geometry on the evolution of outwardly propagating flames and the determination of laminar flame speeds using the conventional constant-pressure technique is investigated experimentally and theoretically. The cylindrical chamber boundary modifies the propagation rate through the interaction of the wall with the flow induced by thermal expansion across the flame (even with constant pressure), which leads to significant distortion of the flame surface for large flame radii. These departures from the unconfined case, especially the resulting nonzero burned gas velocities, can lead to significant errors in flame speeds calculated using the conventional assumptions, especially for large flame radii. For example, at a flame radius of 0.5 times the wall radius, the flame speed calculated neglecting confinement effects can be low by ∼15% (even with constant pressure).A methodology to estimate the effect of nonzero burned gas velocities on the measured flame speed in cylindrical chambers is presented. Modeling and experiments indicate that the effect of confinement can be neglected for flame radii less than 0.3 times the wall radius while still achieving acceptable accuracy (within 3%). The methodology is applied to correct the flame speed for nonzero burned gas speeds, in order to extend the range of flame radii useful for flame speed measurements. Under the proposed scaling, the burned gas speed can be well approximated as a function of only flame radius for a given chamber geometry - i.e. the correction function need only be determined once for an apparatus and then it can be used for any mixture. Results indicate that the flow correction can be used to extract flame speeds for flame radii up to 0.5 times the wall radius with somewhat larger, yet still acceptable uncertainties for the cases studied. Flow-corrected burning velocities are measured for hydrogen and syngas mixtures at atmospheric and elevated pressures. Flow-corrected flame speeds in the small cylindrical chamber used here agree well with previously reported flame speeds from large spherical chambers. Previous papers presenting burning velocities from cylindrical chambers report performing data analysis on flame radii less than 0.5 or 0.6 times the wall radius, where the flame speed calculated neglecting confinement effects may be low by ∼15 or 20%, respectively. For cylindrical chambers, data analysis should be restricted to flame radii less than 0.3 times the wall radius or a flow correction should be employed to account for the burned gas motions.With regard to the design of future vessels, larger vessels that minimize the flow aberrations for the same flame radius are preferred. Larger vessels maximize the relatively unaffected region of data allowing for a more straightforward approach to interpret the experimental data.     

Numerical investigation on the effects of reaction orders on the flame propagation dynamic behaviors for premixed gas in a closed tube

In this paper, the premixed flame propagation in a closed tube is surveyed using Computational Fluid Dynamics. The propagation characteristics of premixed flame are obtained coupling a single-step reaction mechanism with a laminar flame model. Three single-step reaction mechanisms are established with different reaction orders for hydrocarbon fuels. This study is to establish a wider range of reaction mechanisms and represent actual experimental conditions better. The numerical simulation results demonstrate that reaction orders can affect the tulip flame development. As the flame spreads, the tulip flame fronts become wrinkled. When the reaction order is 2, there are more wrinkles in the flame front and the degree of wrinkles is more obvious. Reaction orders also affect the flame tip velocity and the flame skirt velocity. The main reason is that laminar flame speeds are significantly different. When the reaction orders are 1.5 and 2, laminar flame speeds are mainly affected by temperature, which respectively increase by about 25% and 75%. When the reaction order is 1, the pressure is crucial for the variation of laminar flame speed. The laminar flame speed decreases by about 33%.     

甲醇-空气-氮气混合气预混球型火焰的试验研究

利用高速纹影摄像法在定容燃烧弹内研究了不同燃空当最比、初始压力、初始温度和气体稀释度下甲醇-空气-氮气混合气预混球型火焰的发展特性以及3种火焰锋面的不稳定性.获得了不同初始状态下的层流燃烧速度、质量燃烧流量和马克斯坦长度.高的初始压力时,火焰锋面生成的裂纹发展并形成细胞状结构.稀混合气时,浮力和电极的冷却作用对火焰的发展有重要影响.当量比在化学计量比附近时,随着初始温度的提高,流体动力学不稳定性被抑制.随着初始压力的增加,流体动力学不稳定性增强.稀释气的加入抑制了火焰锋面流体动力学的不稳定性.     

Experimental study on premixed combustion of spherically propagating methanol-air-nitrogen flames

The outward propagation and development of surface instability of the spark-ignited spherical premixed flames for methanol-air-nitrogen mixtures were experimentally studied by using a constant volume combustion chamber and a high-speed schlieren photography system. The laminar burning velocities, the mass burning fluxes, and the Markstein lengths were obtained at different equivalence ratios, dilution ratios, initial temperatures, and pressures. The laminar burning velocities and the mass burning fluxes give a similar curve versus the equivalence ratios. They increase with the increase of initial temperature and decrease with the increase of dilution ratio. The laminar burning velocity decreases with elevating the initial pressure, while the mass burning flux increases with the increase of the initial pressure. Markstein length decreases slightly with the increase of initial temperature for the rich mixtures. High initial pressure corresponds to low Markstein length. Markstein length increases with the increase of dilution ratio, which is more obvious when the mixture becomes leaner. Equivalence ratio has a slight impact on the development of the diffusive-thermal cellular structure at elevated initial pressures. The initial pressure has a significant influence on the occurrence of the flame front cellular structure. At the elevated pressures, the cracks on the flame surface branch and develop into the cell structure. These cells are bounded by cracks emitting a bright light, which may indicate soot formation. For very lean mixture combustion, the buoyancy effect and cooling effect from the spark electrodes have a significant impact on the flame propagation. The hydrodynamic instability, inhibited with the increase of initial temperature around the stoichiometric equivalence ratio, is enhanced with the increase of initial pressure and suppressed by mixture dilution.     

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.     

不同初始温度和水蒸气稀释比对乙醇/异辛烷层流火焰特性的影响

在101.3kPa的初始条件下,利用定容燃烧弹系统结合高速纹影摄像技术,研究不同水蒸气稀释比(0～10%)和不同初始温度(400～500K)下乙醇体积分数为10%的乙醇/异辛烷混合燃料(E10)的层流火焰特性。试验结果表明:E10/空气的层流火焰速度随着水蒸气稀释比的增加呈线性下降,随着初始温度的升高呈指数增加;无量纲层流火焰速度随着水蒸气稀释比的增加而下降,受当量比的影响不大。化学敏感性分析表明:链分支反应有利于提高E10/空气层流火焰速度,链终端反应则会降低层流火焰速度。水蒸气的稀释作用、热力学作用、直接反应作用和三体作用都会降低E10层流火焰速度,其中稀释作用的影响最大。     

Experimental study and proposed power correlation for laminar burning velocity of hydrogen-diluted methane with respect to pressure and temperature variation

The aim of the present work is to contribute to the better understanding of the combustion process and the laminar flame properties of methane/hydrogen-air flames at elevated temperatures and pressures. The heat flux method provides an accurate and direct measurement of laminar burning velocities (LBV) at elevated temperatures, while the constant volume chamber method provides measurements at elevated pressures. In the present work, a database of more than 250 experimental points for the range of temperature (298–373 K) and pressure conditions (1–5 bar) for mixtures up to 50% hydrogen in methane was generated using these two methods. Comparison with the sparse literature data shows quite good agreement. A power-law correlation for temperature and pressure is proposed for methane/hydrogen-air mixtures, which has a practical application in estimating the LBV of a natural gas/hydrogen mixture intended to replace pure natural gas in different processes. The power-law temperature exponent, α, and the pressure exponent, β, show inverse trends. The former decreases almost linearly and the latter increases approximately linearly when the hydrogen content is increased. The power-law exponents are highly affected by the mixture equivalence ratio, ?, showing a parabola like trend. However, for the pressure exponent this trend becomes almost linear for 50% H₂ in the mixture. The power-law correlation has been validated against experimental data for a wide range of temperature (up to 573 K), pressure (1–7.5 bar), equivalence ratios (? between 0.7 and 1.3) and H₂ contents up to 50%.     

Influence of CO2, CH4, and initial temperature on H2/CO laminar flame speed

The objective of this study is to investigate the impact of syngas composition by varying the H₂/CO ratio (1:3, 1:1, and 3:1 by volume), the CO₂ dilution (0%–40%), and methane addition (0%–40%) on laminar flame speed. Thus, laminar flame speeds of premixed syngas–air mixtures were measured for different equivalence ratios (0.8–2.2) and inlet temperatures (295–450 K) using the Bunsen-burner method. It was found that laminar flame speed increases with increasing H₂/CO ratio, while CO₂ dilution or CH₄ addition decreased it. The location of the maximum flame speed shifts to richer mixtures with decreasing H₂/CO ratio, while it shifts to leaner mixtures with the addition of CH₄ due to its inherent slower flame speed. The location of the maximum flame speed is also shifted towards leaner mixtures with the addition of CO₂ due to the preponderance of the reduction of the adiabatic flame temperature with increasing dilution. Comparison between experimental and numerical results shows a better agreement using a modified mechanism derived from GRI-Mech 3.0. A correlation, based on the experimental results, is proposed to calculate the laminar flame speed over a wide range of equivalence ratios, inlet temperatures, and fuel content.     

Flame propagation in stratified hydrogen–air mixtures: Spark placement effects

Two-dimensional laminar flame simulations of a forced-ignition event in an initially quiescent mixing layer of hydrogen and air have been carried out at atmospheric pressure using detailed chemistry and effective binary diffusion coefficients. Since control of the ignition location is known to be critical in direct-injection spark-ignition engines, this study primarily investigates the effect of initial spark placement within the flammability limits of hydrogen–air. Displacement and stabilization speeds of the propagating flame fronts have been computed along isocontours of water vapor representing 10% and 25% of the downstream equilibrium concentration. Following the period of spark energy addition the flame kernel is observed to develop into tribrachial flames that subsequently propagate along the stoichiometric line. For all cases of successful ignition, transient spark effects are observed to dissipate within 0.18 ms. Subsequent structure and propagation speed of the flame are not influenced by the transient development phase.     

Determination of laminar flame speeds using stagnation and spherically expanding flames: Molecular transport and radiation effects

The uncertainties associated with the extraction of laminar flame speeds through extrapolations from directly measured experimental data were assessed using one-dimensional direct numerical simulations with focus on the effects of molecular transport and thermal radiation loss. The simulations were carried out for counterflow and spherically expanding flames given that both configurations are used extensively for the determination of laminar flame speeds. The spherically expanding flames were modeled by performing high fidelity time integration of the mass, species, and energy conservation equations. The simulation results were treated as “data” for stretch rate ranges that are encountered in experiments and were used to perform extrapolations using formulas that have been derived based on asymptotic analyses. The extrapolation results were compared then against the known answers of the direct numerical simulations. The fuel diffusivity was varied in order to evaluate the flame response to stretch and to address reactant differential diffusion effects that cannot be captured based on Lewis number considerations. It was found that for large molecular weight hydrocarbons at fuel-rich conditions, the flame behavior is controlled by differential diffusion and that the extrapolation formulas can result in notable errors. Analysis of the computed flame structures revealed that differential diffusion modifies the fluxes of fuel and oxygen inside the flame and thus affect the reactivity as stretch increases. Radiation loss was found to affect notably the extracted laminar flame speed from spherically expanding flame experiments especially for slower flames, in agreement with recent similar studies. The effect of radiation could be eliminated however, by determining the displacement speed relative to the unburned gas. This can be achieved in experiments using high-speed particle image velocimetry to determine the flow velocity field within the few milliseconds duration of the experiment. In general, extrapolations were found to be unreliable under certain conditions, and it is proposed that the raw experimental data in either flame configurations are compared against results of direct numerical simulations in order to avoid potential falsifications of rate constants upon validation.     

Flammability limits and laminar flame speed of hydrogen–air mixtures at sub-atmospheric pressures

Hydrogen behavior at elevated pressures and temperatures was intensively studied by numerous investigators. Nevertheless, there is a lack of experimental data on hydrogen ignition and combustion at reduced sub-atmospheric pressures. Such conditions are related to the facilities operating under vacuum or sub-atmospheric conditions, for instance like ITER vacuum vessel. Main goal of current work was an experimental evaluation of such fundamental properties of hydrogen–air mixtures as flammability limits and laminar flame speed at sub-atmospheric pressures. A spherical explosion chamber with a volume of 8.2 dm³ was used in the experiments. A pressure method and high-speed camera combined with schlieren system for flame visualization were used in this work. Upper and lower flammability limits and laminar flame velocity have been experimentally evaluated in the range of 4–80% hydrogen in air at initial pressures 25–1000 mbar. An extraction of basic flame properties as Markstein length, overall reaction order and activation energy was done from experimental data on laminar burning velocity.     

Numerical study of laminar flame properties of diluted methane-hydrogen-air flames at high pressure and temperature using detailed chemistry

Technical limits of high pressure and temperature measurements as well as hydrodynamic and thermo-diffusive instabilities appearing in such conditions prevent the acquisition of reliable results in term of burning velocities, restraining the domain of validity of current laminar flame speed correlations to few bars and hundreds of Kelvin. These limits are even more important when the reactivity of the considered fuel is high. For example, the high-explosive nature of pure hydrogen makes measurements even more tricky and explains why only few correlations are available to describe the laminar flame velocity of high hydrogen blended fuels as CH₄-H₂ mixtures. The motivation of this study is thereby to complement experimental measurements, by extracting laminar flame speeds and thicknesses from complex chemistry one-dimensional simulations of premixed laminar flames. A wide number of conditions are investigated to cover the whole operating range of common practical combustion systems such as piston engines, gas turbines, industrial burners, etc. Equivalence ratio is then varied from 0.6 to 1.3, hydrogen content in the fuel from 0 to 100%, residual burned gas mass ratio from 0 to 30%, temperature of the fresh mixtures from 300 to 950 K, and pressure from 0.1 to 11.0 MPa. Many chemical kinetics mechanisms are available to describe premixed combustion of CH₄-H₂ blends and several of them are tested in this work against an extended database of laminar flame speed measurements from the literature. The GRI 3.0 scheme is finally chosen. New laminar flame speed and thickness correlations are proposed in order to extend the domain of validity of experimental correlations to high proportions of hydrogen in the fuel, high residual burned gas mass ratios as well as high pressures and temperatures. A study of the H₂ addition effect on combustion is also achieved to evaluate the main chemical processes governing the production of H atoms, a key contributor to the dumping of the laminar flame velocity.