On the determination of laminar flame speed from low-pressure and super-adiabatic propagating spherical flames

The outwardly propagating spherical flame (OPF) method is popularly used to measure the laminar flame speed (LFS). Recently, great efforts have been devoted to improving the accuracy of the LFS measurement from OPF. In the OPF method, several assumptions are made. For examples, the burned gas is assumed to be static and in chemical equilibrium. However, these assumptions may not be satisfied under certain conditions. Here we consider low-pressure and super-adiabatic propagating spherical flames, for which chemical non-equilibrium exists and the burned gas may not be static. The objective is to assess the chemical non-equilibrium effects on the accuracy of LFS measurement from the OPF method. Numerical simulations considering detailed chemistry and transport are conducted. Stoichiometric methane/air flames at sub-atmospheric pressures and methane/oxygen flames at different equivalence ratios are considered. At low pressures, broad heat release zone is observed and the burned gas cannot quickly reach the adiabatic flame temperature, indicating the existence of chemical non-equilibrium of burned gas. Positive flow in the burned gas is identified and it is shown to become stronger at lower initial pressure. Consequently, the LFS measurement from OPF at low pressures is not accurate if the burned gas is assumed to be static and at chemical equilibrium. For super-adiabatic spherical flames, the burned gas speed is found to be negative due to the local temperature overshoot at the flame front. Such negative speed of burned gas can also reduce the accuracy of LFS measurement. It is recommended that the direct method measuring both flame propagation speed and flow speed of unburned gas should be used to determine the LFS at low pressures or for mixtures with super-adiabatic flame temperature.     

Effect of ignition energy on the uncertainty in the determination of laminar flame speed using outwardly propagating spherical flames

The initial propagation processes of expanding spherical flames of CH₄/N₂/O₂/He mixtures at different ignition energies were investigated experimentally and numerically to reduce the effect of ignition energy on the accurate determination of laminar flame speeds. The experiments were conducted in a constant-volume combustion bomb at initial pressures of 0.07???0.7?MPa, initial temperatures of 298???398?K, and equivalence ratios of 0.9???1.3 with various Lewis numbers. The A-SURF program was employed to simulate the corresponding flame propagation processes. The results show that elevating the ignition energy increases the initial flame propagation speed and expands the range of flame trajectory which is affected by ignition energy, but the increase rates of the speed and range decrease with the ignition energy. Based on the trend of the minimum flame propagation speed during the initial period with the ignition energy, the minimum reliable ignition energy (MRIE) is derived by considering the initial flame propagation speed and energy conservation. It is observed that MRIE first decreases and then increases with the increasing equivalence ratio and monotonously decreases with increasing initial pressure and temperature. As the Lewis number rises, MRIE increases. The results also suggest that during the data processing of the spherical flame experiment, the accuracy of determination of laminar flame speeds can be enhanced when taking the flame radius influenced by MRIE as the lower limit of the flame radius range. Then the flame radius influenced by MRIE was defined as RFR. It can also be found that there exist nonlinear relationships between RFR and the equivalence ratio and Lewis number, and the RFR decreases with increasing initial pressure and temperature.     

Effects of pressure rise rate on laminar flame speed under normal and engine-relevant conditions

Laminar flame speed (LFS) is one of the most important physicochemical properties of a combustible mixture. At normal and elevated temperatures and pressures, LFS can be measured using propagating spherical flames in a closed chamber. LFS is also used in certain turbulent premixed flame modelling for combustion in spark ignition engines. Inside the closed chamber or engine, transient pressure rise occurs during the premixed flame propagation. The effects of pressure rise rate (PRR) on LFS are examined numerically in this study. One-dimensional simulations are conducted for spherical flame propagation in a closed chamber. Detailed chemistry and transport are considered. Different values of PRR at the same temperature and pressure are achieved through changing the spherical chamber size. It is found that the effect of PRR on LFS is negligible under the normal and engine-relevant conditions considered in this study. This observation is then explained through the comparison between the unsteady and convection terms in the energy equation for a premixed flame.     

An investigation of flame zones and burning velocities of laminar unconfined methane-oxygen premixed flames

Numerical and experimental investigations of unconfined methane-oxygen laminar premixed flames are presented. In a lab-scale burner, premixed flame experiments have been conducted using pure methane and pure oxygen mixtures having different equivalence ratios. Digital photographs of the flames have been captured and the radial temperature profiles at different axial locations have been measured using a thermocouple. Numerical simulations have been carried out with a C2 chemical mechanism having 25 species and 121 reactions and with an optically thin radiation sub-model. The numerical results are validated against the experimental and numerical results for methane-air premixed flames reported in literature. Further, the numerical results are validated against the results from the present methane-oxygen flame experiments. Visible regions in digital flame photographs have been compared with OH isopleths predicted by the numerical model. Parametric studies have been carried out for a range of equivalence ratios, varying from 0.24 to 1.55. The contours of OH, temperature and mass fractions of product species such as CO, CO₂ and H₂O, are presented and discussed for various cases. By using the net methane consumption rate, an estimate of the laminar flame speed has been obtained as a function of equivalence ratio.     

Effect of Lewis number on premixed laminar lean-limit flames stabilized on a bluff body

In this paper, we present a study on the effect of Lewis number, Le, on the stabilization and blow-off of laminar lean limit premixed flames stabilized on a cylindrical bluff body. Numerical simulations and experiments are conducted for propane, methane and two blends of hydrogen with methane as fuel gases, containing 20% and 40% of hydrogen by volume, respectively. It is found that the Le?>?1 flame blows-off via convection from the base of the flame (without formation of a neck) when the conditions for flame anchoring are not fulfilled. Le?≤?1 flames exhibit a necking phenomenon just before lean blow-off. This necking of the flame front is a result of the local reduction in mass burning rates causing flame merging and quenching of the thin flame tube formed. The structure of these flames at the necking location is found to be similar to tubular flames. It is found that extinction stretch rates for tubular flames closely match values at the neck location of bluff-body flames of corresponding mixtures, suggesting that excessive flame stretch is directly responsible for blow-off of the studied Le?≤?1 flames. After quenching of the neck, the upstream part forms a steady and stable residual flame in the wake of the bluff body while the downstream part is convected away.     

Compressible turbulent flame speeds of highly turbulent standing flames

In this paper we present the first measurement of turbulent burning velocities of a highly turbulent compressible standing flame induced by shock-driven turbulence in a Turbulent Shock Tube. High-speed schlieren, chemiluminescence, PIV, and dynamic pressure measurements are made to quantify flame–turbulence interaction for high levels of turbulence at elevated temperatures and pressure. Distributions of turbulent velocities, vorticity and turbulent strain are provided for regions ahead and behind the standing flame. The turbulent flame speed is directly measured for the high-Mach standing turbulent flame. From measurements of the flame turbulent speed and turbulent Mach number, transition into a non-linear compressibility regime at turbulent Mach numbers above 0.4 is confirmed, and a possible mechanism for flame generated turbulence and deflagration-to-detonation transition is established.     

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.     

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.     

Effect of flame thickness variation on the mass burning rate of premixed counterflow flames with an oscillating strain rate

The mass-based stretch rate is used to study the response of premixed axisymmetric counterflow flames subject to an oscillating strain rate. Integral analysis is used to estimate the mass burning rate of the oscillating counterflow flames. From this study it can be concluded that the flame responds in a nonlinear manner. With an increase of the applied strain frequencies, it is found that unsteady stretch effects arising due to flame thickness variations become significant and the mass-based stretch rate is able to capture these nonlinear effects. The inclusion of these unsteady stretch effects in the mass-based stretch helps the integral analysis to predict the mass-burning rate of oscillating flames more accurately.     

Influence of micro-explosions on the stability of laminar premixed water-in-fuel emulsion spray flames

A model is presented for a one-dimensional laminar premixed flame, propagating into a rich, off-stoichiometric, fresh homogenous mixture of water-in-fuel emulsion spray, air and inert gas. Due to its relatively large latent heat of vaporisation, the water vapour acts to cool the flame that is sustained by the prior release of fuel vapour. To simplify the inherent complexity that characterises the analytic solution of multi-phase combustion processes, the analysis is restricted to fuel-rich laminar premixed water-in-fuel flames, and assumes a single-step global chemical reaction mechanism. The main purpose is to investigate the steady-state burning velocity and burnt temperature as functions of parameters such as initial water content in the emulsified droplet and total liquid droplet loading. In particular, the influence of micro-explosion of the spray’s droplets on the flame’s characteristics is highlighted for the first time. Steady-state analytical solutions are obtained and the sensitivity of the flame temperature and the flame propagating velocity to the initial water content of the micro-exploding emulsion droplets is established. A linear stability analysis is also performed and reveals the manner in which the micro-explosions influence the neutral stability boundaries of both cellular and pulsating instabilities.     

Experimental determination of counterflow ignition temperatures and laminar flame speeds of C2–C3 hydrocarbons at atmospheric and elevated pressures

Experimental data were acquired for: (1) the ignition temperatures of nitrogen–diluted ethylene and propylene by counterflowing heated air for various strain rates and system pressures up to 7 atm; (2) the laminar flame speeds of mixtures of air with acetylene, ethylene, ethane, propylene, and propane, deduced from an outwardly propagating spherical flame in a constant-pressure chamber, for extensive ranges of lean-to-rich equivalence ratio and system pressure up to 5 atm. These data, respectively, relevant for low- to intermediate-temperature ignition chemistry and high-temperature flame chemistry, were subsequently compared with calculated results using a literature C₁–C₃ mechanism and an ethylene mechanism. Noticeable differences were observed in the comparison for both mechanisms, and sensitivity analyses were conducted to identify the reactions of importance.     

Influence of pressure on near nozzle flow field and soot formation in laminar co-flow diffusion flames

Soot formation from combustion devices, which tend to operate at high pressure, is a health and environmental concern, thus investigating the effect of pressure on soot formation is important. While most fundamental studies have utilised the co-flow laminar diffusion flame configuration to study the effect of pressure on soot, there is a lack of investigations into the effect of pressure on the flow field of diffusion flames and the resultant influence on soot formation. A recent work has displayed that recirculation zones can form along the centreline of atmospheric pressure diffusion flames. This present work seeks to investigate whether these zones can form due to higher pressure as well, which has never been explored experimentally or numerically. The CoFlame code, which models co-flow laminar, sooting, diffusion flames, is validated for the prediction of recirculation zones using experimental flow field data for a set of atmospheric pressure flames. The code is subsequently utilised to model ethane-air diffusion flames from 2 to 33 atm. Above 10 atm, recirculation zones are predicted to form. The reason for the formation of the zones is determined to be due to increasing shear between the air and fuel steams, with the air stream having higher velocities in the vicinity of the fuel tube tip than the fuel stream. This increase in shear is shown to be the cause of the recirculation zones formed in previously investigated atmospheric flames as well. Finally, the recirculation zone is determined as a probable cause of the experimentally observed formation of a large mass of soot covering the entire fuel tube exit for an ethane diffusion flame at 36.5 atm. Previously, no adequate explanation for the formation of the large mass of soot existed.     

A computational study of soot formation and flame structure of coflow laminar methane/air diffusion flames under microgravity and normal gravity

A numerical study is conducted of methane–air coflow diffusion flames at microgravity (μg) and normal gravity (1g), and comparisons are made with experimental data in the literature. The model employed uses a detailed gas phase chemical kinetic mechanism that includes PAH formation and growth, and is coupled to a sectional soot particle dynamics model. The model is able to accurately predict the trends observed experimentally with reduction of gravity without any tuning of the model for different flames. The microgravity sooting flames were found to have lower temperatures and higher volume fraction than their normal gravity counterparts. In the absence of gravity, the flame radii increase due to elimination of buoyance forces and reduction of flow velocity, which is consistent with experimental observations. Soot formation along the wings is seen to be surface growth dominated, while PAH condensation plays a more major role on centreline soot formation. Surface growth and PAH growth increase in microgravity primarily due to increases in the residence time inside the flame. The rate of increase of surface growth is more significant compared to PAH growth, which causes soot distribution to shift from the centreline of the flame to the wings in microgravity.     

Flame propagation speed and Markstein length of spherically expanding flames: Assessment of extrapolation and measurement techniques

Laminar burning velocities are of great importance in many combustion models as well as for validation and improvement of chemical kinetic schemes. Determining laminar burning velocities with high accuracy is quite challenging and different approaches exist. Hence, a comparison of existing methods measuring and evaluating laminar burning velocities is of interest. Here, two optical diagnostics, high speed tomography and Schlieren cinematography, are simultaneously set up to investigate methods for evaluating laminar flame speed in a spherical flame configuration. The hypothesis to obtain the same flame propagation radii over time with the two different techniques is addressed. Another important aspect is the estimation of flame properties, such as the unstretched flame propagation speed and Markstein length in the burnt gas phase and if these are estimated satisfactorily by common experimental approaches. Thorough evaluation of the data with several extrapolation techniques is undertaken. A systematic extrapolation approach is presented to give more confidence into results generated experimentally. The significance of the linear extrapolation routine is highlighted in this context. Measurements of spherically expanding flames are carried out in two high-pressure, high-temperature, constant-volume vessels at RWTH in Aachen, Germany and at ICARE in Orleans, France. For the discussion of the systematic extrapolation approach, flame speed measurements of methane / air mixtures with mixture Lewis numbers moderately away from unity are used. Conditions were varied from lean to rich mixtures, at temperatures of 298–373 K, and pressures of 1 atm and 5 bar.     

Propagation of premixed laminar flames in 3D narrow open ducts using RBF-generated finite differences

Laminar flame propagation is an important problem in combustion modelling for which great advances have been achieved both in its theoretical understanding and in the numerical solution of the governing equations in 2D and 3D. Most of these numerical simulations use finite difference techniques on simple geometries (channels, ducts, ...) with equispaced nodes. The objective of this work is to explore the applicability of the radial basis function generated finite difference (RBF-FD) method to laminar flame propagation modelling. This method is specially well suited for the solution of problems with complex geometries and irregular boundaries. Another important advantage is that the method is independent of the dimension of the problem and, therefore, it is very easy to apply in 3D problems with complex geometries. In this work we use the RBF-FD method to compute 2D and 3D numerical results that simulate premixed laminar flames with different Lewis numbers propagating in open ducts.     

Effect of local variations of the laminar flame speed on the global finger-flame acceleration scenario

Numerous formulations describing the dynamics and morphology of corrugated flames, including the scenarios of flame acceleration, are based on a “geometrical consideration”, where the wrinkled-to-planar flame velocities ratio, S_w /S_L , is evaluated as the scaled flame surface area, while the entire combustion chemistry is immersed into the planar flame speed S_L , which is assumed to be constant. However, S_L may experience noticeable spatial/temporal variations in practice, in particular, due to pressure/temperature variations as well as non-uniform distribution of the equivalence ratio and/or that of combustible or inert dust impurities. The present work initiates the systematic study of the impact of the local S_L -variations on the global flame evolution scenario. The variations are assumed to be imposed externally, in a manner being a free functional of the formulation. Specifically, the linear, parabolic and hyperbolic spatial S_L -distributions are incorporated into the formulations of finger flame acceleration in pipes, and they are compared to the case of constant S_L . Both two-dimensional channels and cylindrical tubes are considered. The conditions promoting or moderating flame acceleration are identified, and the revisited equations for the flame shape, velocity and acceleration rate are obtained for various S_L -distributions. The theoretical findings are validated by the computational simulations of the reacting flow equations, with agreement between the theory and modelling demonstrated.     

A numerical study of the superadiabatic flame temperature phenomenon in HN3 flames

The phenomenon of superadiabatic flame temperature (SAFT) was discovered and investigated in a low-pressure HN₃/N₂ flame using numerical modelling. A previously developed mechanism of chemical reactions in the HN₃/N₂ flame at the pressure 50 Torr and the initial temperature T₀ = 296 K was revised. Rate constants of several important reactions involving HN₃ (HN₃ (+N₂) = N₂ + NH (+N₂), R1; HN₃ (+HN₃) = N₂ + NH (+HN₃), R2; HN₃ + H = N₂ + NH₂, R4; HN₃ + N = N₂ + NNH, R5; and HN₃ + NH₂ = NH₃ + N₃, R7) were calculated using quantum chemistry and reaction rate theories. Modified Arrhenius expressions for these reactions are provided for the 300–3500 K temperature range. Modelling of the flame structure and flame propagation velocity of the HN₃/N₂ flame at p = 50 Torr and T₀ = 296 K was performed using the revised mechanism. The results demonstrate the presence of the SAFT phenomenon in the HN₃/N₂ flame. Analysis of the flame structure and the kinetic mechanism indicates that the cause of SAFT is in the kinetic mechanism: exothermic reactions of radicals with hydrogen atoms occur in the post flame zone, which results in the formation of super equilibrium H₂ concentrations. The flame propagation velocity is largely determined by the second-order HN₃ decomposition reaction and not by the reaction of HN₃ with H, as was previously assumed. Calculation of the flame propagation velocity according to the Zeldovich-Frank-Kamenetsky theory with the decomposition reaction as a limiting stage yielded a value that agrees with that obtained in numerical modelling using the complete reaction mechanism.     

Effect of electric fields on reattachment and propagation speed of tribrachial flames in laminar coflow jets

The effects of electric fields on the reattachment of lifted flames have been investigated experimentally in laminar coflow jets with propane fuel by applying high voltages to the fuel nozzle. In case of AC, the frequency has also been varied. Results showed that reattachment occurred at higher jet velocity when applying the AC voltages, thus the stabilization limit of attached flames was extended by the AC electric field. Higher voltage and lower frequency of the AC were found to be more effective. On the contrary, the effect of DC was found to be minimal. To understand the early onset of the reattachment with the AC, occurring at higher jet velocity, the influence of AC electric fields on the propagation speed of tribrachial flame edge was investigated during the transient reattachment processes. The propagation speed increased reasonably linearly with the applied AC voltage and decreased inversely to the distance between the flame edge and the nozzle electrode. Consequently, the enhancement in the propagation speed of tribrachial flame edge was correlated well with the electric field intensity, defined as the applied AC voltage divided by the distance.     

High-pressure laminar flame speeds and kinetic modeling of carbon monoxide/hydrogen combustion

Laminar flame speeds were accurately measured for CO/H₂/air and CO/H₂/O₂/helium mixtures at different equivalence ratios and mixing ratios by the constant-pressure spherical flame technique for pressures up to 40 atmospheres. A kinetic mechanism based on recently published reaction rate constants is presented to model these measured laminar flame speeds as well as a limited set of other experimental data. The reaction rate constant of CO + HO₂ → CO₂ + OH was determined to be k = 1.15 × 10⁵T^2.278 exp(−17.55 kcal/RT) cm³ mol⁻¹ s⁻¹ at 300-2500 K by ab initio calculations. The kinetic model accurately predicts our measured flame speeds and the non-premixed counterflow ignition temperatures determined in our previous study, as well as homogeneous system data from literature, such as concentration profiles from flow reactor and ignition delay time from shock tube experiments.     

超声速层流/湍流压缩拐角流动结构的实验研究

在Ma=3.0的超声速风洞中, 分别对上游边界层为超声速层流和湍流, 压缩角度为25°和28°的压缩拐角流动进行了实验研究. 采用纳米粒子示踪平面激光散射(NPLS)技术获得了流场整体和局部区域的精细结构, 边界层、剪切层、分离激波、回流区和再附激波等典型结构清晰可见, 测量了超声速层流压缩拐角壁面的压力系数. 从时间平均的流场结构中测量出分离激波、再附激波的角度和再附后重新发展的边界层的增长情况, 通过分析时间相关的流场NPLS图像, 可以发现流场结构随时间的演化特性. 实验结果表明: 在25°的压缩角度下, 超声速层流压缩拐角流动发生了典型的分离, 边界层迅速增长失稳转捩, 并引起一道诱导激波, 流场中出现了K-H涡、剪切层和微弱压缩波结构, 而超声速湍流压缩拐角流动没有出现分离, 湍流边界层始终表现为附着状态; 在28° 的压缩角度下, 超声速层流压缩拐角流动进一步分离, 回流区范围明显扩大, 诱导激波、分离激波向上游移动, 再附激波向下游移动, 分离区流动结构复杂, 相比之下, 超声速湍流压缩拐角流动的回流区范围明显较小, 边界层增长缓慢, 流场中没有出现诱导激波、K-H涡和压缩波, 流动分离区域的结构也相对简单, 但分离激波的强度则明显更强. 关键词： 压缩拐角 层流 湍流 流动结构