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.     

Structure and dynamic response of radiative diffusion flames

Nitrogen-diluted hydrogen burning in air is modeled numerically using a constant density and one-step reaction model in a plane two-dimensional counterflow configuration. An optically thin assumption is used to investigate the effects of radiation on the dynamics, structure, and extinction of diffusion flames. While there exist dual steady-state extinction limits for the 1D radiative flame response, it is found that as the 1D radiative extinction point is approached the 1D low-stretch diffusion flame exhibits oscillatory response, even with sub-unity Lewis number fuel. These radiation-induced limit cycle oscillations are found to have increasing amplitude and decreasing frequency as the stretch rate is reduced. Flame oscillation eventually leads to permanent extinction at the stretch rate which is larger than the steady-state radiative extinction value. Along the 1D radiative response curve, the transition from 1D flame to 2D structure and the differences in the resulting 2D flame patterns are also examined using a variety of initial profiles, with special emphasis on the comparison of using the initial profiles with and without a flame edge. Similar to the previous studies on the high-stretch adiabatic edge flames using the same configuration, the high-stretch radiative flames are found to resist 1D blow-off quenching through various 2D structures, including propagating front and steady cellular flames for initial profiles with and without flame edges. For all initial profiles studied, the low-stretch radiative flames are also found to exhibit different 2D flame phenomena near the 1D radiative extinction limit, such as transient cellular structures, steady cellular structures, and pulsating ignition fronts. Although the results demonstrate the presence of low-stretch and high-stretch 2D bifurcation branches close to the corresponding 1D extinction limits irrespective of the initial profile used, particular 2D flame structures in certain stretch rate range are initial profile dependent. The existence of two-dimensional flame structures beyond the 1D steady-state radiative extinction limit suggests that the flammable range is expanded as compared to that predicted by the 1D model. Hence, multi-dimensional flame patterns need to be accounted for when determining the flammability limits for a given system.     

Stability of a spherical flame ball in a porous medium

Gaseous flame balls and their stability to symmetric disturbances are studied numerically and asymptotically, for large activation temperature, within a porous medium that serves only to exchange heat with the gas. Heat losses to a distant ambient environment, affecting only the gas, are taken to be radiative in nature and are represented using two alternative models. One of these treats the heat loss as being constant in the burnt gases and linearizes the radiative law in the unburnt gas (as has been studied elsewhere without the presence of a solid). The other does not distinguish between burnt and unburnt gas and is a continuous dimensionless form of Stefan's law, having a linear part that dominates close to ambient temperatures and a fourth power that dominates at higher temperatures.

Numerical results are found to require unusually large activation temperatures in order to approach the asymptotic results. The latter involve two branches of solution, a smaller and a larger flame ball, provided heat losses are not too high. The two radiative heat loss models give completely analogous steady asymptotic solutions, to leading order, that are also unaffected by the presence of the solid which therefore only influences their stability. For moderate values of the dimensionless heat-transfer time between the solid and gas all flame balls are unstable for Lewis numbers greater than unity. At Lewis numbers less than unity, part of the branch of larger flame balls becomes stable, solutions with the continuous radiative law being stable over a narrower range of parameters. In both cases, for moderate heat-transfer times, the stable region is increased by the heat capacity of the solid in a way that amounts, simply, to decreasing an effective Lewis number for determining stability, just as if the heat-transfer time was zero.     

Multiple speeds of flame edge propagation for Lewis numbers above one

Edges of diffusion flames in a counterflow burner are examined numerically for Lewis greater than unity. When the speed of propagation is plotted against Damköhler for a range of Lewis a fold bifurcation is observed. It is shown that there exist stable positively and negatively propagating edges for some Damköhler and Lewis number pairs. It is further shown that changed local conditions can lead to a transition from positive (advancing into the unburnt gasses) to negative (receding) propagation.     

Opposed-flow ignition and flame spread over melting polymers with Navier-Stokes gas flow

A numerical model is constructed to predict transient opposed-flow flame spread behaviour in a channel flow over a melting polymer. The transient flame is established by initially applying a high external radiation heat flux to the surface. This is followed by ignition, transition and finally steady opposed-flow flame spread. The physical phenomena under consideration include the following: gas phase: channel flow, thermal expansion and injection flow from the pyrolyzed fuel; condensed phase: heat conduction, melting, and discontinuous thermal properties (heat capacity and thermal conductivity) across the phase boundary; gas-condensed phase interface: radiation loss. There is no in-depth gas radiation absorption in the gas phase. It is necessary to solve the momentum, species, energy and continuity equations in the gas along with the energy equation(s) in the liquid and solid. Agreement is obtained between the numerical spread rate and a flame spread formula. The influence of the gas flow is explored by comparing the Navier-Stokes (NS) and Oseen (OS) models. An energy balance analysis describes the flame-spread mechanism in terms of participating heat transfer mechanisms.     

Direct numerical simulations of turbulent flame expansion in fine sprays

Direct Numerical Simulations of expanding flame kernels following localized ignition in decaying turbulence with the fuel in the form of a fine mist have been performed to identify the effects of the spray parameters on the possibility of self-sustained combustion. Simulations show that the flame kernel may quench due to fuel starvation in the gaseous phase if the droplets are large or if their number is insufficient to result in significant heat release to allow for self-sustained flame propagation for the given turbulent environment. The reaction proceeds in a large range of equivalence ratios due to the random location of the droplets relative to the igniter location that causes a wide range of mixture fractions to develop through pre-evaporation in the unreacted gas and through evaporation in the preheat zone of the propagating flame. The resulting flame exhibits both premixed and non-premixed characteristics.     

On the global structure and asymptotic stability of low-stretch diffusion flame: Forced convection

The present work analyzes cylindrical diffusion flames (Tsuji burner) under low stretch condition, considering fuel injection also from the backward region of the burner. To highlight the fundamental aspects of this flame, some assumptions are imposed, like constant thermodynamic and transport coefficients, unitary Lewis number and no radiative heat loss. It is also considered potential flow model and incompressible Navier–Stokes model. Despite the simplicity of the former model, results from both models show good agreement. Also, an asymptotic analysis describing the problem far from the burner is able to capture the most important mechanisms controlling the flame, then the flame shape is determined and the dependence of the characteristic length scales on Peclet number (based on the burner properties), free stream velocity and stoichiometry is revealed. The results show that the flame width is proportional to the mass stoichiometric coefficient and reciprocal to the Peclet number the 1/4 power and free stream velocity the 3/4 power, and that the flame height is proportional to the square of the mass stoichiometric coefficient and to the square root of the ratio of Peclet number to free stream velocity. In addition, an asymptotic stability analysis reveals low-stretch flame extinction to be caused by reduction in fuel and oxidizer concentrations, which provides the range of the stoichiometric coefficient for stable regime, and at the same time the range of heat released.     

Effect of Le on criteria of transition to secondary acoustic instability of downward-propagating flame in a tube with controlled curvature induced by external laser

An experimental study is conducted to investigate the effect of Le on the transition to secondary acoustic instability when the curvature of the flame front in a tube is induced and controlled by using external laser irradiation. Once a downward-propagating flame in the primary acoustic instability region is exposed to a specific laser irradiation condition, the flame is transferred to the secondary acoustic instability region. The transition limit is decreased, that is, transition occurs is an easier manner, with increasing laser power input. While the flame propagates with increasing laser irradiation, the flame first exhibits a convex curvature owing to laser irradiation and then a concave structure is formed owing to buoyancy-induced flow. Two types of transition behavior caused by the concave structure and the convex structure are observed. The conflicting thermal-diffusive effect depending on Le leads to the differing transition behaviors. Based on an evaluation of the flame stretch effect attributed to the flame front curvature, it is confirmed that the Lewis number effect influences the transition criteria.     

Flame structure and flame spread rate over a solid fuel in partially premixed atmospheres

We have investigated the downward flame spread over a thin solid fuel. Hydrogen, methane, or propane, included in the gaseous product of pyrolysis reaction, is added in the ambient air. The fuel concentration is kept below the lean flammability limit to observe the partially premixing effect. Both experimental and numerical studies have been conducted. Results show that, in partially premixed atmospheres, both blue flame and luminous flame regions are enlarged, and the flame spread rate is increased. Based on the flame index, a so-called triple flame is observed. The heat release rate ahead of the original diffusion flame is increased by adding the fuel, and its profile is moved upstream. Here, we focus on the heat input by adding the fuel in the opposed air, which could be a direct factor to intensify the combustion reaction. The dependence of the flame spread rate on the heat input is almost the same for methane and propane/air mixtures, but larger effect is observed for hydrogen/air mixture. Since the deficient reactant in lean mixture is fuel, the larger effect of hydrogen could be explained based on the Lewis number consideration. That is, the combustion is surely intensified for all cases, but this effect is larger for lean hydrogen/air mixture (Le < 1), because more fuel diffuses toward the lean premixed flame ahead of the original diffusion flame. Resultantly, the pyrolysis reaction is promoted to support the higher flame spread rate.     

LES/CMC modelling of ignition and flame propagation in a non-premixed methane jet

The Large Eddy Simulation (LES) / Conditional Moment Closure (CMC) model with detailed chemistry is used for modelling spark ignition and flame propagation in a turbulent methane jet in ambient air. Two centerline and one off-axis ignition locations are simulated. We focus on predicting the flame kernel formation, flame edge propagation and stabilization. The current LES/CMC computations capture the three stages reasonably well compared to available experimental data. Regarding the formation of flame kernel, it is found that the convection dominates the propagation of its downstream edge. The simulated initial downstream and radial flame propagation compare well with OH-PLIF images from the experiment. Additionally, when the spark is deposited at off-centerline locations, the flame first propagates downstream and then back upstream from the other side of the stoichiometric iso-surface. At the leading edge location, the chemical source term is larger than others in magnitude, indicating its role in the flame propagation. The time evolution of flame edge position and the final lift-off height are compared with measurements and generally good agreement is observed. The conditional quantities at the stabilization point reflect a balance between chemistry and micro-mixing. This investigation, which focused on model validation for various stages of spark ignition of a turbulent lifted jet flame through comparison with measurements, demonstrates that turbulent edge flame propagation in non-premixed systems can be reasonably well captured by LES/CMC.     

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.     

Measurements of the critical initiation radius and unsteady propagation of n-decane/air premixed flames

Unsteady flame propagation, the critical radius for flame initiation, and multiple flame regimes of n-decane/air mixtures are studied experimentally and computationally using outwardly propagating spherical flames at various equivalence ratios and pressures. The transient flame speeds, trajectories, and critical radius are measured. The experimental results are compared with direct numerical simulations using detailed high temperature kinetic models. Both experimental and numerical results show that there exist multiple flame regimes in the unsteady spherical flame initiation process. The transition between the flame regimes depends strongly on the mixture equivalence ratio (or Lewis number). It is found that there is a critical flame radius and that it increases dramatically as the mixture equivalence ratio and pressure decrease. The large increase of critical flame radius leads to a dramatic increase of the minimum ignition energy. Furthermore, the flame thickness and the radical pool concentration change significantly during the transition from the ignition flame regime to the self-sustained propagating flame regime. For the same steady state flame speeds, the predicted unsteady flame speeds and the critical flame radius differ significantly from the experimental results. Moreover, different chemical kinetic mechanisms predict different unsteady flame speeds. The existence of multiple flame regimes and the large critical radius of lean liquid fuel mixtures make the ignition of lean mixtures at low pressure and the development of a validated kinetic model more challenging. The unsteady flame regimes, speeds, and critical flame radius should be included as targets of future kinetic model development for turbulent combustion modeling.     

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.     

Propagation and extinction of an unsteady spherical spray flame front

Experimental evidence seems to indicate that the life of a laminar spherical flame front propagating through a fresh mixture of air and liquid fuel droplets can be roughly split into three stages: (1) ignition, (2) radial propagation with a smooth flame front and (3) propagation with flame front cellularization and/or pulsation. In this work, the second stage is analysed using the slowly varying flame approach, for a fuel rich flame. The droplets are presumed to vaporize in a sharp front ahead of the reaction front. Evolution equations for the flame and evaporation fronts are derived. For the former the combined effect of heat loss due to droplet vaporization and radiation plays a dominant explicit role. In addition, the structure of the evaporation front is deduced using asymptotics based on a large parameter associated with spray vaporization. Numerical calculations based on the analysis point to the way in which the spray modifies conditions for flame front extinction. Within the framework of the present simplified model the main relevant parameters turn out to be the initial liquid fuel load in the fresh mixture and/or the latent heat of vaporization of the fuel.     

Cellular and sporadic flame regimes of low-Lewis-number stretched premixed flames

3D structure and dynamical behavior of low-Lewis-number stretched premixed flames are numerically simulated within the framework of a thermo-diffusive model with one-step chemical reaction. The results are compared with microgravity experiments at qualitative level. The influence of Lewis number, equivalence ratio, and heat loss intensity on flame structure is investigated. It is experimentally and numerically found that lean counterflow flames can appear as a set of separate ball-like flames in a state of chaotic motion. It is shown that the time averaged flame balls coordinate may be considered as important characteristic similar to coordinate of continuous flame front. Numerical simulations reveal essential incompleteness of combustion at high level of heat losses. This incompleteness occurs in the process of lean mixtures combustion and is caused by fuel leakage through the gaps among ball-like flames.     

Laser spark ignition of a jet diffusion flame

In this work we report preliminary results on the laser ignition of a jet diffusion flame with jet flow rates ranging from 35 (Re=1086) to 103 cm³/s (Re=3197). The laser spark energy of about 4 mJ was used for all the tests. The relative amounts of fuel and air concentrations at the laser focus have been estimated using a variant of laser-induced breakdown spectroscopy. The ignition and the flame blow out times were measured using the time-resolved OH emission. Ignition times in the range from 3 to about 10 ms were observed depending on the experimental conditions and they increased towards the rich as well as the lean sides. The early time and late-time OH emissions indicate that chemical reactions during the initial stage of the blast wave expansion are not immediately responsible for the ignition. The ultimate fate of an ignition depends on the reactions at later times which determines whether the gas could undergo a transition from hot plasma to a propagating flame.     

Numerical study of the ignition behavior of a post-discharge kernel in a turbulent stratified crossflow

Ensuring robust ignition is critical for the operability of aeronautical gas-turbine combustors. For ignition to be successful, an important aspect is the ability of the hot gas generated by the spark discharge to initiate combustion reactions, leading to the formation of a self-sustained ignition kernel. This study focuses on this phenomena by performing simulations of kernel ignition in a crossflow configuration that was characterized experimentally. First, inert simulations are performed to identify numerical parameters correctly reproducing the kernel ejection from the ignition cavity, which is here modeled as a pulsed jet. In particular, the kernel diameter and the transit time of the kernel to the reacting mixture are matched with measurements. Considering stochastic perturbations of the ejection velocity of the ignition kernel, the variability of the kernel transit time is also reproduced by the simulations. Subsequently, simulations of a series of ignition sequences are performed with varying equivalence ratio of the fuel-air mixture in the crossflow. The numerical results are shown to reproduce the ignition failure that occurs for the leanest equivalence ratio ($?=0.6$). For higher equivalence ratios, the simulations are shown to capture the sensitivity of the ignition to the equivalence ratio, and the kernel successfully transitions into a propagating flame. Significant stochastic dispersion of the ignition strength is observed, which relates to the variability of the transit time of the kernel to the reactive mixture. An analysis of the structure of the ignition kernel also highlights the transition towards a self-propagating flame for successful ignition conditions.     

The role of radiative losses in self-extinguishing and self-wrinkling flames

We have developed a general theory of non-adiabatic premixed flames that is valid for flames of arbitrary shape that fully accounts for the hydrodynamic and diffusive-thermal processes, and incorporates the effects of volumetric heat losses. The model is used to describe aspects of experimentally observed phenomena of self-extinguishing (SEFs) and self-wrinkling flames (SWFs), in which radiative heat losses play an important role. SEFs are spherical flames that propagate considerable distances in sub-limit conditions before suddenly extinguishing. Our results capture many aspects of this phenomenon including an explicit determination of flame size and propagation speed at quenching. SWFs are hydrodynamically unstable flames in which cells spontaneously appear on the flame surface once the flame reaches a critical size. Our results yield expressions of the critical flame size at the onset of wrinkling and expected cell size beyond the stability threshold. The various possible burning regimes are mapped out in parameter space.     

Darrieus - Landau instability,growing cycloids and expanding flame acceleration

A premixed flame, propagating away from a point ignition source into an unlimited domain displays an increasing flame speed after the flame size has grown beyond a transition radius. Experiments by Gostintsev et al are described by the relation R = R₁ + At^3/2, where t is the time from ignition and, where S_L is the flame burning velocity and is the thermal diffusivity. The non-dimensional function a() is determined from the experimental results to be equal to 0.002², where is the density ratio across the flame.

In the present work, two-dimensional Lagrangian simulations of flame propagation also display a radial growth with a 3/2 power-law behaviour. This is a potential flow model - no vorticity is included. Hence, the Darrieus - Landau hydrodynamic instability by itself can generate flame acceleration. The numerical results are summarized by the relation R = R1+(2/40)L(SLt/L)3/2, where L is a reference length and is the volume production ratio, = - 1. Equating the zone of velocity jump in the numerical scheme with the temperature jump in hydrocarbon flames allows a definition of an effective thermal diffusivity in the numerical work as n = 0.0081SLL. With this relation, the radial growth is given as, in good agreement with the experimental result and the numerical results of Filyand et al.     

Bifurcation and extinction limit of stretched premixed flames with chain-branching intermediate kinetics and radiative loss

Premixed counterflow flames with thermally sensitive intermediate kinetics and radiation heat loss are analysed within the framework of large activation energy. Unlike previous studies considering one-step global reaction, two-step chemistry consisting of a chain branching reaction and a recombination reaction is considered here. The correlation between the flame front location and stretch rate is derived. Based on this correlation, the extinction limit and bifurcation characteristics of the strained premixed flame are studied, and the effects of fuel and radical Lewis numbers as well as radiation heat loss are examined. Different flame regimes and their extinction characteristics can be predicted by the present theory. It is found that fuel Lewis number affects the flame bifurcation qualitatively and quantitatively, whereas radical Lewis number only has a quantitative influence. Stretch rates at the stretch and radiation extinction limits respectively decrease and increase with fuel Lewis number before the flammability limit is reached, while the radical Lewis number shows the opposite tendency. In addition, the relation between the standard flammability limit and the limit derived from the strained near stagnation flame is affected by the fuel Lewis number, but not by the radical Lewis number. Meanwhile, the flammability limit increases with decreased fuel Lewis number, but with increased radical Lewis number. Radical behaviours at flame front corresponding to flame bifurcation and extinction are also analysed in this work. It is shown that radical concentration at the flame front, under extinction stretch rate condition, increases with radical Lewis number but decreases with fuel Lewis number. It decreases with increased radiation loss.