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.     

Visualization of multiple scalar and velocity fields in a lifted jet flame

The stabilization of lifted jet diffusion flames has long been a topic of interest to combustion researchers. The flame and flow morphology, the role of partial premixing, and the effects of large scale structures on the flame can be visualized through advanced optical imaging techniques. Many of the current explanations for flame stabilization can benefit from the flow and flame information provided by laser diagnostics. Additionally, the images acquired from laser diagnostic experiments reveal features invisible to the eye and line-of-sight techniques, thereby allowing a deeper insight into flame stabilization. This paper reports visualizations of flame and flow structures from Particle Image Velocimetry (PIV), Planar Laser-Induced Fluorescence (PLIF) and Rayleigh scattering. The techniques are surveyed and the success of visualization techniques in clarifying and furthering the understanding of lifted-jet flame stabilization is discussed.     

Dynamics of an edge-flame in the corner region of two mutually perpendicular streams

The stabilization and dynamics of an edge-flame in the corner region of two mutually perpendicular streams, one of fuel and the other of oxidizer, is studied within the context of a diffusive-thermal model, with an imposed flow satisfying the Navier-Stokes equations. The formulation allows for non-unity Lewis numbers and finite rate chemistry with an Arrhenius dependence on temperature. Two flow configurations, corresponding to inlet velocity profiles of uniform speed and of constant strain, have been examined. The results identify the dependence of the flame standoff distance on the flow as well as on the properties of the mixture, including the Damköhler D and Lewis numbers. For high flow rates, or small enough D, sufficient pre-mixing occurs in front of the edge-flame, which consequently takes on a tribrachial structure consisting of two premixed branches, one lean and one rich, with a trailing diffusion flame sheet. For large D, however, there is no enough premixing and the chemical reaction occurs in a small kernel very close to the corner, much like a local thermal explosion; further downstream the reaction occurs along a diffusion flame sheet that extends along the symmetry axis. The present results also predict the onset of spontaneous oscillations when the Lewis numbers are sufficiently large provided the flow rate is sufficiently high, or D reduced below a critical value. Oscillations are first sustained when D is reduced below criticality, but depending on the flow conditions, they are either damped leading to flame re-stabilization, or amplified leading to blow-off.     

Effects of imperfect premixing coupled with hydrodynamic instability on flame propagation

The problem of flame propagation in imperfectly premixed mixtures—mixtures of reactants with variable composition—is considered in this numerical study. We carry out two-dimensional direct numerical simulations of a flame propagating in a globally lean fuel-oxidizer mixture with imposed velocity and composition fluctuations of various intensities. The configuration adopted is that of a flame front interacting with spatially evolving fluctuations, and the characteristic scales of the domain and of the fluctuations imposed are significantly larger than the characteristic thickness of the flame, to account for important flame dynamics such as the hydrodynamic instability. One-step chemistry and Fick’s diffusion law are considered, along with unity Lewis number assumption for all the species. It is observed, in agreement with previous results, that relatively weak fluctuations in composition alone may lead to a large increase in flame length and burning rate. The hydrodynamic instability caused by gas expansion, catalyzed by the composition fluctuations interacting with the flame, is found to be responsible for the flame length enhancement. It is observed as well that the relative importance of this effect diminishes as the velocity fluctuations present become more intense, and that composition fluctuations have a small impact on flame length for these cases. It is additionally found that, with increasing intensity of composition fluctuations, there is eventually a reduction of burning rate per unit length of flame which leads, consequently, to a weak reduction of overall burning rate for the largest velocity fluctuation intensities covered by this study.     

Dynamics of flow–soot interaction in wrinkled non-premixed ethylene–air flames

A two-dimensional simulation of a non-premixed ethylene–air flame was conducted by employing a detailed gas-phase reaction mechanism considering polycyclic aromatic hydrocarbons, an aerosol-dynamics-based soot model using a method of moments with interpolative closure, and a grey gas and soot radiation model using the discrete transfer method. Interaction of the sooting flame with a prescribed decaying random velocity field was investigated, with a primary interest in the effects of velocity fluctuations on the flame structure and the associated soot formation process for a fuel-strip configuration and a composition with mature soot growth. The temporally evolving simulation revealed a multi-layered soot formation process within the flame, at a level of detail not properly described by previous studies based on simplified soot models utilizing acetylene or naphthalene precursors for initial soot inception. The overall effect of the flame topology on the soot formation was found to be consistent with previous experimental studies, while a unique behaviour of localised strong oxidation was also noted. The imposed velocity fluctuations led to an increase of the scalar dissipation rate in the sooting zone, causing a net suppression in the soot production rate. Considering the complex structure of the soot formation layer, the effects of the imposed fluctuations vary depending on the individual soot reactions. For the conditions under study, the soot oxidation reaction was identified as the most sensitive to the fluctuations and was mainly responsible for the local suppression of the net soot production.     

An analytical study of the flame dynamics of a transversely forced asymmetric two-dimensional Bunsen flame

Combustion instabilities in annular combustors are of great interest because of their industrial relevance. Azimuthal acoustic modes, which involve transverse acoustic forcing to flames, have become a key process related to annular combustor instabilities. Transverse mean flow may be a factor that affects azimuthal oscillations. This paper provides an analytical model for a transversely forced two-dimensional Bunsen flame under transverse mean flow. The model is established using a low-amplitude perturbation assumption applied to a G-equation formulation. Forced flame displacement and flame transfer functions (FTFs) are calculated. The results are verified based on numerical solutions of the G-equation. Effects of frequency, transverse mean flow velocity and vertical mean flow velocity on the FTFs are discussed. The symmetric flame without transverse mean flow has a vanishing response to transverse acoustic forcing, while asymmetric flames, which are formed with transverse mean flow, have a bandpass response to transverse forcing. The response at very low and high forcing frequencies is small, with higher transfer function gains only in a certain frequency range. This bandpass response, which is inherently linked to the asymmetry of the flame, is an important factor to account for when considering the flame dynamics related to transverse acoustic effects.     

Methane flames in a jet impinging onto a wall

Traditionally, research has focused on positive stretch in the stagnation flow and negative stretch along the Bunsen flame. Only a very limited amount of research has been devoted to studying the behavior of a conical Bunsen flame established in a stagnation flow, which is significantly affected by the combined effects of the curvature stretch and the aerodynamic straining. This investigation is aimed at studying the characteristics of laminar conical premixed flames in an impinging jet flow experimentally and theoretically. First, we analyze the transport processes of a nonreactive impinging jet flow numerically. For lower burner-to-plate distance, the potential core becomes concave at the top. Hence, a conical Bunsen flame established in such a flow field may suffer positive flow stretch. The predicted flame shapes using a simple model incorporated with the numerical results agree well with the experimental observations. Flame shapes exhibit double-solution characteristics in a certain range of methane concentrations. Experimentally, by following different paths of adjusting methane concentration (decreasing from rich to lean or increasing from lean to rich), two different flame configurations (planar or conical flame) may exist at the same flow conditions, namely burner-to-plate distance, inlet velocity, and methane concentration. At the higher (or lower) critical methane concentration, the transition from a flat flame to a conical flame (or from a conical flame to a flat flame) occurs. The calculation of stretch and measurement of flame temperature for the low inlet velocity, 0.8 m/s, show that the stretch of a conical flame established in a stagnation flow is negative (dominated by the flame curvature). However, it is important to emphasize that at high velocity, e.g., U_in = 1.6 m/s, a negatively stretched flame tip can suffer positive flow stretch. This significant finding has been verified in the experiment since the conical flame tip is higher than the positively stretched flat flame.     

Stabilized,flat iron flames on a hot counterflow burner

Metal powder combustion has traditionally been studied to mitigate the risk of industrial accidents and to determine the contributions of metals as additives to the performance of energetic materials. Recently, there has been growing interest in exploring the potential of metal powders as recyclable, zero-carbon energy carriers as an alternative to the hydrocarbons known to contribute to climate change. The present work introduces, for the first time, a stabilized flat iron flame. The counterflow burner used in this work is comprised of an inverted ceramic nozzle which sits above, and is aligned axially with, a lower nozzle producing a laminar flow of particles suspended in an oxidizing gas. A stabilized methane flame sits inside the top nozzle and the hot combustion products impinge upon the two-phase flow from the bottom nozzle, creating a stagnation plane. Spherical iron powder, with 90% of the particles less than 2.5 µm in size, is pre-loaded into a piston and dispersed using mixtures of 30% and 40% oxygen balanced in argon. Flame speeds are measured using particle image velocimetry (PIV), while flame temperatures are determined using multicolour pyrometry. It is found that flame speeds range between 30 cm/s and 45 cm/s for both oxidizing mixtures. Despite having fuel loadings below stoichiometric concentrations, the observed particle combustion temperatures are close to the adiabatic flame temperature of the stoichiometric mixture, indicating combustion in the diffusion-controlled regime for these small particles. Finally, the independence of the flame speeds with respect to oxygen concentration suggests flame propagation in the discrete regime.     

Measurements of local mixture fraction of reacting mixture in swirl-stabilised natural gas-fuelled burners

Local, time-dependent measurements of mixture fraction of the reacting mixture were obtained in a swirl-stabilised natural gas-fuelled, nominally non-premixed burner using the intensity of chemiluminescence from OH^∗ and CH^∗ radicals. The measurements quantified the mean, rms of fluctuations and probability density functions of local mixture fraction at the stabilisation region of the flame. In addition, the probability of flame presence and the degree of lean or rich versus stoichiometric reaction is reported. The burner was operated for three air flow Reynolds numbers (Re=18970, 29100 and 57600), at an overall equivalence ratio of 0.32, without and with imposed oscillations to the air flow of the burner at the resonance frequency of 350 Hz. Results show that combustion occurred in a partially premixed mode for all flow conditions, although fuel and air were injected separately in the reaction zone. The mean local mixture fraction was nearly stoichiometric at the base of the flame without imposed air oscillations, but with large fluctuations leading to around 80% of lean or rich reaction. The degree of non-stoichiometric reaction increased with axial distance from the burner exit and Reynolds number and lean reaction dominated. Imposed air oscillations led to lifted flames and increased the degree of non-stoichiometric reaction for Re=18970 and 29100, whereas the flame remained attached onto the injector for Re=57600 and little modification of the mixture fraction was observed.     

Geometrical study of spark ignition in two dimensions

Spark ignition, as the first step during the combustion in Otto engines, has a profound impact on the further development of the flame kernel. Over the last ten years growing concern for environment protection, including low emission of pollutants has increased the interest in the numerical simulation of ignition phenomena to guarantee successful flame kernel development even for lean mixtures.

However, the process of spark ignition in a combustible mixture is not yet fully understood. The use of detailed reaction mechanisms, combined with electrodynamical modelling of the spark, is necessary to optimize ignition of lean mixtures.

This work presents simulations of the coupling of flow, chemical reactions and transport with discharge processes in order to investigate the development of a stable flame kernel initiated by an electrical spark. A two-dimensional code to simulate the early stages of flame kernel formation, shortly after the breakdown discharge, has been developed. The model includes Joule heating. The spark plasma channel formed as a consequence of the breakdown is incorporated into the initial conditions. The computations include the initial phase (1–5 µs), which is governed by pressure wave formation, but also the transition to flame propagation. A thorough study of the influence of the electrodes' geometry, i.e. shape and size, and gap width, has been performed for air and a lean H₂–air mixture. Also a detailed methane-air mechanism was chosen as another example including combustion.

Due to the fast expansion of the plasma channel, together with the geometrical complexity of the electrodes, a complicated flow field develops after the emission of a pressure wave by the expanding channel. Special numerical methods, including artificial viscosity, are required to resolve the complicated flow field during these first 1–5 µs. The heat release through chemical reactions and transport processes is almost negligible during this short phase. The second phase, i.e. the development of a propagating flame and the flame kernel expansion, can last up to several milliseconds and is dominated by diffusive processes and chemical reactions. It has been found that the geometry greatly influences the developing flame kernel and the flow field. As soon as chemical reactions begin to contribute significantly to the heat release, the effect becomes smaller.     

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.     

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

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

An experimental study of partially premixed flame sound

The occurrence of oscillating combustion and combustion instability has led to resurgence of interest in the causes, mechanisms, suppression, and control of combustion noise. Noise generated by enclosed flames is of greater practical interest but is more complicated than that by open flames, which itself is not clearly understood. Studies have shown that different modes of combustion, premixed and non-premixed, differ in their sound generation characteristics. However, there is lack of understanding of the region bridging these two combustion modes. This study investigates sound generation by partially premixed flames. Starting from a non-premixed flame, air was gradually added to achieve partial premixing while maintaining the fuel flow rate constant. Methane, ethylene, and ethane partially premixed flames were studied with hydrogen added for flame stabilization. The sound pressure generated by methane partially premixed flames scales with M⁵ compared to M³ for turbulent non-premixed methane flames. Also, the sound pressure generated by partially premixed flames of ethane and ethylene scales as M^4.5. With progressive partial premixing, spectra level increases at all frequencies with a greater increase in the high-frequency region compared to the low-frequency region; flames develop a peak and later a constant level plateau in the low frequency region. The partially premixed flames of methane, ethylene, and ethane generate a similar SPL as a function of equivalence ratio when the fuel volume flow rate is matched. However, when fuel mass flow rate is matched, the ethane and ethylene flames produce a similar SPL, which is lower than that produced by the methane flame.     

Effects of electrodes and imposed flow on forced ignition in laminar premixed hydrogen/air mixtures with large Lewis number

Compared to quiescent premixed reactants, forced ignition of flowing/turbulent premixed reactants is expected to be more difficult because of increased dissipation of the deposited energy. However, the counterintuitive turbulence-facilitated ignition (TFI) has been observed in recent experiments for mixtures with large Lewis number, Le. The mechanisms behind TFI are still not well understood and this study aims to interpret a part of the TFI mechanisms through considering electrodes and imposed flow in the simulations of forced ignition in hydrogen/air mixtures. The imposed flow emulates the local turbulent effects around the electrodes which might blow the ignition kernel away from the electrodes. Since TFI occurs only for mixtures with large Le (e.g., lean hydrocarbon/air or rich H₂/air mixture), a fuel-rich (ϕ=5.1) H₂/air mixture with Le≈2.3 is investigated to reduce computational cost and consider more factors that may lead to TFI. Similar to TFI observed in experiments, the flow-facilitated ignition is observed for H₂/air with ϕ=5.1 and Le≈2.3 when the electrodes have a small gap distance. The detailed effects of including electrodes on forced ignition of quiescent and flowing mixtures are explored. It is found that the existence of electrodes not only induces heat loss but also affects the shape and global curvature/stretch of the ignition kernel. The heat loss to the electrodes is demonstrated to play an important role for the ignition of mixtures with large Le. Compared to quiescent mixtures, considering an imposed flow normal to the electrodes can blow the flame kernel away from the cold electrodes. Such movement of the ignition kernel can greatly reduce both the heat loss to the electrodes and flame curvature/stretch, and thereby promote the ignition in mixtures with large Le. These results help to understand the underlying mechanisms for the TFI observed in experiments.     

Fundamental limits of optical superresolution

Increasing the resolving power of optical systems beyond the limits imposed by diffraction, or superresolution, has considerable theoretical as well as practical interest. Several schemes have been proposed to achieve superresolution with reasonable success, but there are no criteria that enable one to determine what improvement can ultimately be attained for a certain level of resolution. We have determined fundamental limits imposed on the performance of any superresolution strategy. A brief analysis indicates that current optical-superresolution techniques can still have their performance considerably augmented.     

Formation of dynamic spatial flame structures for gas burning in microchannels with temperature gradients on walls

The thermal-diffusive model was applied to the problem of flame propagation in a microchannel with controlled temperature distribution in the walls; this demonstrated the possibility of formation of oscillating or rotating spatial flame structures, which were described previously in experimental works on microcombustion. Two cases were considered: combustion in a rectangular channel and in the clearance between two disks with radial feeding of premixture. In both cases, the typical across size of the channel was lower than the critical diameter determined with respect to the ambient temperature. The gas flow was assigned and described by the Poiseuille-flow velocity profile. Formation of oscillating flame in a rectangular channel and rotating patterns in a radial channel was observed for a certain range of gas flow rate. At low flow rates beyond this range, repetitive ignition/extinction of flame took place; at high flow rate we observed a steady flame mode. Formation of these special flame structures is related to heat transfer between gas and hot walls of the channel, as well as to velocity maldistribution in the microchannel.     

The effects of strain and curvature on the mass burning rate of premixed laminar flames

The Markstein number characterizes the effect that flame stretch has on the burning velocity. Different expressions for this number are deduced from integral analysis. According to a phenomenological law, the Markstein number can be separated into a part for the curvature of the flame and a part for the straining of the flow. This separation is analysed here. It appears that the Markstein number for curvature and the combined one for both curvature and strain are unique. It is, however, not possible to introduce a separate and unique Markstein number for the flow straining that can be used to describe its influence in different combustion situations. The theoretical and numerical analysis is applied to flat steady counterflow flames as well as to steady, imploding and expanding spherical flames.     

燃烧法合成碳纳米管的实验方案设计

碳纳米管是一种新型的碳材料,其合成方法多种多样。燃烧法是一种新兴的合成方法,燃烧过程提供用于碳纳米管生长的高温环境,同时也提供足够的烃原料。目前,用于合成碳纳米管的原料包括气体燃料和液体燃料,火焰类型主要有层流扩散火焰、逆流扩散火焰和预混火焰等。影响炭纳米管火焰合成的因素主要有气体成分,温度,催化剂,燃氧比和采样条件。我们采用甲烷扩散火焰用于实验研究炭纳米管的合成条件。实验系统包括扩散火焰喷嘴,混和段,质量流量计,取样探针和基板,气源。内径5 mm的喷嘴与内径100 mm的钢筒同轴。实验测得在气量为0．20 SLM时火焰高度为 3．5 cm。涂覆有催化剂的基板水平朝下置于火焰中采样,并将采集的样品进行电镜分析。本文还对燃烧法合成碳纳米管的机理进行了分析。     

On nonlinear model equations for the response of premixed flames to acoustic like accelerations

The response of a dynamical flame model to imposed acoustic accelerations is studied analytically and numerically. Through linear stability analyses, two analytical approximations for the primary and the parametric stability boundaries are found. The approximation for the primary instability boundary is accurate for any periodic accelerations, in the limit of large acoustic frequencies. The critical acoustic amplitude u _a for Landau–Darrieus instability suppression is identified and found to depend only on the density contrast and the shape of the periodic acoustic stimuli. The proposed model evolution equation is next integrated numerically with various imposed acoustic accelerations; the primary and parametric flame responses are identified. It is shown analytically and numerically that in the presence of a fully developed, yet weakened by acoustics, Landau–Darrieus (or primary) instability the wrinkle amplitude and the mean flame speed oscillate at the same frequency as the acoustic stimuli; the threshold for suppression of primary instability by acoustic forcing is determined exactly. Increasing the acoustic amplitude allows the flame to respond parametrically to the acoustics. This response is characterised by troughs and crests interchanging their roles while the mean flame speed again oscillates with the same frequency as the acoustic stimuli and at twice that of wrinkle amplitude oscillations.     

Strain rates,flow patterns and flame surface densities in hydrodynamically unstable,weakly turbulent premixed flames

Recent numerical and experimental studies have unveiled a potentially marked difference between the laminar as well as turbulent propagation of premixed flames exhibiting Darrieus–Landau (DL) (or hydrodynamic) instabilities from flames for which instabilities are inhibited. In this study we utilize two-dimensional numerical simulations of slot burner flames as well as experimental Propane–Air Bunsen flames to analyse differences in turbulent propagation, strain rate and induced flow patterns of hydrodynamically stable and unstable flames. We also investigate the effects of hydrodynamic instability on quantities which are directly related to reaction rate closure models, such as flame surface density and stretch factor. A clear enhancement of turbulent flame speed can be observed for unstable flames, generally mitigated at higher turbulence intensity, which is attributed to a flame area increase induced by the characteristic cusp-like DL-induced corrugation, absent in stable flames, which occurs concurrently and in synergy with turbulent wrinkling. Unstable flames also exhibit, both numerically and experimentally, a different correlation between strain rate and flame curvature and are observed to give rise to a channeling of the induced flow in the fresh mixture. Conditionally averaged flame surface density is also observed to attain smaller values in unstable flames, as a result of the thicker turbulent flame brush, indicating that closure models should incorporate instability-related parameters in addition to turbulence-related parameters.