Stabilization and onset of oscillation of an edge-flame in the near-wake of a fuel injector

The stabilization of an edge-flame in the near-wake of a fuel injector is discussed within the context of a diffusive-thermal model, but with a realistically computed flow. Although the boundary layer approximation can be used to describe the mixing process in the wake region, the velocity field in the immediate vicinity of the injector satisfies the full Navier-Stokes equations. The stabilization of the edge-flame and its dynamics are affected not only by diffusive-thermal effects, but also by the acceleration experienced by the fuel and oxidizer entrained into the mixing layer. The present calculations confirm an earlier prediction that edge-flame oscillations can be triggered by heat losses alone. Moreover, it is shown that when the intensity of the losses is excessive, oscillations can occur even when the Lewis numbers are less than one. New results are also obtained when examining the flame response to variations in Lewis numbers. For Lewis numbers that are not too large, there exists a minimum value of the Damkhler number D below which the edge-flame cannot be stabilized. The response curve, describing the standoff distance as a function of D is multi-valued and the turning point, which also coincides with the marginal stability state, identifies extinction or blowoff conditions. For D above this value, the edge-flame is steady and stable. For relatively large values of the Lewis number the response curve is monotonic. There is, however, a restricted range of states where the flame undergoes spontaneous oscillations with the edge-flame moving back and forth along the stoichiometric surface dragging behind it the trailing diffusion flame.     

Oscillating edge-flames

It has been known for some years that when a near-limit flame spreads over a liquid pool of fuel, the edge of the flame can oscillate. It is also known that when a near-asphyxiated candle-flame burns in zero gravity, the edge of the (hemispherical) flame can oscillate violently prior to extinction. We propose that these oscillations are nothing more than a manifestation of the large Lewis number instability well known in chemical reactor studies and in combustion studies, one that is exacerbated by heat losses. As evidence of this we examine an edge-flame confined within a fuel-supply boundary and an oxygen-supply boundary, anchored by a discontinuity in data at the fuel-supply boundary. We show that when the Lewis number of the fuel is 2, and the Lewis number of the oxidizer is 1, oscillations of the edge occur when the Damköhler number is reduced below a critical value. During a single oscillation period there is a short premixed propagation stage and a long diffusion stage, behaviour that has been observed in flame spread experiments. Oscillations do not occur when both Lewis numbers are equal to 1.     

Flames in narrow circular tubes

We examine an axi-symmetric deflagration located in a tube with thermally active walls. It is noted that the flame-in-tube configuration defines a classical edge-flame, a flame in a shear flow for which there is a water-shed solution for a critical value of the Damköhler number (D), ignition front solutions for larger values of D, and failure wave solutions for smaller values. We examine semi-infinite tubes with a heat flux imposed at the tube wall ends, to simulate experiments reported in the 30th Symposium. We identify parameters for which stable solutions are obtained at certain flow rates, but unstable solutions are generated at higher flow rates, followed by stable solutions at still higher flow rates. These solutions are consistent with the experimental record. Instability leads either to regular oscillations or to a violent process characterized by quenching and re-ignition.     

Effects of fuel Lewis number on flame spread over solids

Using a detailed two-dimensional numerical model, a systematic investigation has been made to study the effect of fuel Lewis number (Le_F = α/D_F) and mass transfer on flame spread over thin solids. The fuel Lewis number affects the flame spread rates for both concurrent and opposed flames over thin fuels. The dependence of the flame spread rate on Le_F for these two spreading modes is, however, not the same. In opposed flame spreads (zero-gravity, self-propagation, and normal gravity downward propagation), the flame spread rate vs. Le_F curve is non-monotonic with a maximum value occurring at an intermediate value of Le_F = 0.5. In steady, concurrent spread in zero-gravity with low-speed flow and a constant flame length, the flame spread rate decreases with Le_F in a monotonic manner. By using the computational model as a tool, the effects of fuel mass diffusion perpendicular to and parallel with the solid surface are isolated to obtain more physical insight on the two-dimensional aspect of fuel mass transfer on flame spread. In addition, the model has also been used to decouple the solid evaporation process so that the fuel diffusion effect in the gas-phase can be isolated. Both of these theoretical exercises contribute to the understanding of mass transfer effects on the flame spreading phenomena over solids.     

Extinguishment of propane/air co-flowing diffusion flames by fine water droplets

In the present study, extinguishment of propane/air co-flowing diffusion flame by fine water droplets was investigated experimentally. Water droplets are generated by piezoelectric atomizers with the maximum droplets flow rate of 1500 ml/h. When the fuel injection velocity U_f is low, an attached laminar diffusion flame with a premixed flame at the base is stabilized. At some distance from the burner rim, a transition from laminar to turbulent diffusion flame occurs, and a turbulent diffusion flame is formed in the downstream region. When the fuel injector rim is thin (δ = 0.5 mm), the flame stability deteriorates with increase of the co-flowing air stream velocity U_a and the water droplets flow rate Q_m. The stability mechanism can be explained by the balance of the gas velocity and the burning velocity of premixed flame formed at the base. However, when the injector rim is thick (δ = 5 mm), a recirculation zone is produced downstream of the injector rim. The dependence of the quenching distance H_q on U_f and Q_m is relatively weak, and the stability diagram shows curious features. It was shown that U_a is crucially important since it determines flow residence time; if U_a < 0.4 m/s, water droplets can evaporate when they go by the recirculation zone, and the water vapor can diffuse into the recirculation zone. However, if U_a > 0.4 m/s, the water droplets should pass by the recirculation zone without sufficiently evaporated and are not so effective to extinguish the flame. The supply velocity of droplet-laden air should be low enough so that water droplets can evaporate and water vapor can diffuse into the premixed region at the base to obtain sufficient effectiveness of water droplets for fire suppression.     

On intrinsic oscillation in radiation-affected diffusion flames

A linear stability analysis is conducted to study the onset of near-limit flame oscillation with radiative heat loss in 1-D chambered planar flames using multi-scale activation-energy asymptotics. The oscillatory instability near the radiation-induced extinction limit at large Damköhler numbers is identified, in additional to the one near the kinetic limit at small Damköhler numbers. It is shown that radiative loss assumes a similar role as varying the thermal diffusivity of the reactants. Thus, flame oscillation near the radiative limit is still thermal-diffusive in nature although it may develop under unity Lewis numbers. The unstable range of Damköhler numbers near the radiative limit shows quite similar parametric dependence on the Lewis numbers of reactants, Le_F and Le_O, the stoichiometry, ?, and the radiative loss as that near the kinetic limit. They both increase monotonically with Le_O and ? and increase then decrease with Le_F. Increasing radiative loss extends the parameter range under which flame oscillations may develop. However, they show different dependence on the temperature difference between the supplying reactants. Unless radiative loss approaches its maximum value the system can sustain, flame oscillation near the radiative limit is only possible within a limited range of ΔT, whereas it is promoted monotonically with decreasing ΔT near the kinetic limit. Furthermore, while radiative loss shows small effect on the nondimensional oscillation frequency, the dimensional frequency of flame oscillations near the radiative limit can be substantially smaller than that near the kinetic limit.     

The thick flame asymptotic limit and Damköhler's hypothesis

We derive analytical expressions for the burning rate of a flame propagating in a prescribed steady parallel flow whose scale is much smaller than the laminar flame thickness.In this specific context, the asymptotic results can be viewed as an analytical test of Damköhler's hypothesis relating to the influence of the small scales in the flow on the flame; the increase in the effective diffusion processes is described. The results are not restricted to the adiabaticequidiffusional case, which is treated first, but address also the influence of non-unit Lewis numbers and volumetric heat losses. In particular, it is shown that non-unit Lewis numbereffects become insignificant in the asymptotic limit considered. It is also shown that the dependence of the effective propagation speed on the flow is the same as in the adiabatic equidiffusional case, provided it is scaled with the speed of the planar non-adiabatic flame.     

The differential diffusion effect of the intermediate species on the stability of premixed flames propagating in microchannels

The propagation of premixed flames in adiabatic and non-catalytic planar microchannels subject to an assisted or opposed Poiseuille flow is considered. The diffusive–thermal model and the well-known two-step chain-branching kinetics are used in order to investigate the role of the differential diffusion of the intermediate species on the spatial and temporal flame stability. This numerical study successfully compares steady-state and time-dependent computations to the linear stability analysis of the problem. Results show that for fuel Lewis numbers less than unity, Le_F < 1, and at sufficiently large values of the opposed Poiseuille flow rate, symmetry-breaking bifurcation arises. It is seen that small values of the radical Lewis number, Le_Z, stabilise the flame to symmetric shape solutions, but result in earlier flashback. For very lean flames, the effect of the radical on the flame stabilisation becomes less important due to the small radical concentration typically found in the reaction zone. Cellular flame structures were also identified in this regime. For Le_F > 1, flames propagating in adiabatic channels suffer from oscillatory instabilities. The Poiseuille flow stabilises the flame and the effect of Le_Z is opposite to that found for Le_F < 1. Small values of Le_Z further destabilise the flame to oscillating or pulsating instabilities.     

Response of non-premixed flames to bulk flow perturbations

This paper describes the dynamics of non-premixed flames responding to bulk velocity fluctuations, and compares the dynamics of the flame sheet position and spatially integrated heat release to that of a premixed flame. The space–time dynamics of the non-premixed flame sheet in the fast chemistry limit is described by the stoichiometric mixture fraction surface, extracted from the solution of the

-equation. This procedure has some analogies to premixed flames, where the premixed flame sheet location is extracted from the G = 0 surface of the solution of the G-equation. A key difference between the premixed and non-premixed flame dynamics, however, is the fact that the non-premixed flame sheet dynamics are a function of the disturbance field everywhere, and not just at the reaction sheet, as in the premixed flame problem. A second key difference is that the non-premixed flame does not propagate and so flame wrinkles are convected downstream at the axial flow velocity, while wrinkles in premixed flames convect downstream at a vector sum of the flame speed and axial velocity. With the exception of the flame wrinkle propagation speed, however, we show that that the solutions for the space–time dynamics of the premixed and non-premixed reaction sheets in high velocity axial flows are quite similar. In contrast, there are important differences in their spatially integrated unsteady heat release dynamics. Premixed flame heat release fluctuations are dominated by area fluctuations, while non-premixed flames are dominated by mass burning rate fluctuations. At low Strouhal numbers, the resultant sensitivity of both flames to flow disturbances is the same, but the non-premixed flame response rolls off slower with frequency. Hence, this analysis suggests that non-premixed flames are more sensitive to flow perturbations than premixed flames at O(1) Strouhal numbers.     

Diffusive-thermal instabilities of diffusion flames: onset of cells and oscillations

A comprehensive stability analysis of planar diffusion flames is presented within the context of a constant-density model. The analysis provides a complete characterization of the possible patterns that are likely to be observed as a result of differential and preferential diffusion when a planar flame becomes unstable. A whole range of physical parameters is considered, including the Lewis numbers associated with the fuel and the oxidizer, the initial mixture fraction, and the flow conditions. The two main forms of instability are cellular flames, obtained primarily in fuel-lean systems when the Lewis numbers are generally less than one, and planar pulsations, obtained in fuel-rich systems when the Lewis numbers are generally larger than one. The cellular instability is predominantly characterized by stationary cells of characteristic dimension comparable to the diffusion length, but smaller cells that scale on the reaction zone thickness are also possible near extinction conditions. The pulsating instability is characterized by planar oscillations normal to the flame sheet with a well-defined frequency comparable to the reciprocal of the diffusion time; high-frequency modes are also possible just prior to extinction. The analysis also alludes to other possible patterns, such as oscillating cellular structures, which result from competing modes of instability of comparable and/or disparate scales. The expected pattern depends of course on the underlying physical parameters. Consequently, stability boundaries have been identified for the onset of one or another form of the instability. The conditions for the onset of cellular and pulsating flames, as well as the predicted cell size and the frequency of oscillations, compare well with the experimental record.     

A LES-CMC formulation for premixed flames including differential diffusion

A finite volume large eddy simulation–conditional moment closure (LES-CMC) numerical framework for premixed combustion developed in a previous studyhas been extended to account for differential diffusion. The non-unity Lewis number CMC transport equation has an additional convective term in sample space proportional to the conditional diffusion of the progress variable, that in turn accounts for diffusion normal to the flame front and curvature-induced effects. Planar laminar simulations are first performed using a spatially homogeneous non-unity Lewis number CMC formulation and validated against physical-space fully resolved reference solutions. The same CMC formulation is subsequently used to numerically investigate the effects of curvature for laminar flames having different effective Lewis numbers: a lean methane–air flame with Le_eff = 0.99 and a lean hydrogen–air flame with Le_eff = 0.33. Results suggest that curvature does not affect the conditional heat release if the effective Lewis number tends to unity, so that curvature-induced transport may be neglected. Finally, the effect of turbulence on the flame structure is qualitatively analysed using LES-CMC simulations with and without differential diffusion for a turbulent premixed bluff body methane–air flame exhibiting local extinction behaviour. Overall, both the unity and the non-unity computations predict the characteristic M-shaped flame observed experimentally, although some minor differences are identified. The findings suggest that for the high Karlovitz number (from 1 to 10) flame considered, turbulent mixing within the flame weakens the differential transport contribution by reducing the conditional scalar dissipation rate and accordingly the conditional diffusion of the progress variable.     

A review of chemical diffusion: Criticism and limits of simplified methods for diffusion coefficient calculation

A review of the physics and modelling of mass diffusion involving different gaseous chemical species is firstly proposed. Both accurate and simplified models for mass diffusion involve the calculation of individual species diffusion coefficients. Since these are computationally expensive, in CFD they are commonly estimated by assuming constant Lewis or Schmidt numbers for each chemical species. The constant Lewis number assumption is particularly used. As a matter of fact, these assumptions have never been theoretically justified nor verified in practical flames. The only published information are the first observations by Smooke and Giovangigli about the Lewis number against temperature distributions in methane–air premixed and counterflow diffusion one-dimensional flames. The aim of this work is to verify these assumptions. Functional dependences of molecular properties appearing in these numbers are made explicit to show that while Sc _i depends only on composition, Le _i depends also on temperature and therefore it certainly cannot be assumed constant in a flame. Then, accurately calculating molecular properties, distributions of these characteristic numbers against temperature are obtained a posteriori from numerical simulations of different flames, premixed and non-premixed, and burning different fuels. For non-premixed flames, individual species Lewis number distributions are broad for most of the species considered in this article, whilst they are tight for premixed flames. Some attention is focused on the particular shape of Lewis distributions in non-premixed flames: they are characterized by four or five (when extinction is experienced) branches associated to precise regions in the flame (basically, lean, rich and stoichiometric combusting zones). Instead, the Schmidt distributions are always tighter, also when extinctions take place: for many species they can be approximatively assumed constant. Finally, a simplified procedure to estimate individual species diffusion coefficients is suggested, assuming the median of non-premixed flame Schmidt distributions has a constant value for each chemical species.     

Stability of inclined planar flames as a local approximation of weakly curved flames

To evaluate the effect of vorticity usually generated by curved flames on the flame stability, laminar premixed planar flames inclined in the gravitational field is asymptotically examined. The flame structure is resolved by a large activation energy asymptotics and a long wave approximation. The coupling between hydrodynamics and diffusion processes is included and near-unity Lewis number is assumed. The results show that as the flame is more inclined from the horizontal plane it shows more unstable characteristics due to not only the decrease of the stabilizing effect of gravity but also the increase of the destabilizing effect of rotational flow. Unlike the planar flame propagating downward with the right angle to the upstream flow, the obtained dispersion relation involves the Prandtl number and shows the destabilizing effect of viscosity. The analysis predicts that the phase velocity of unstable wave depends on the Lewis number as well as the flame angle and, especially for unity Lewis number, it is the same with tangential velocity at the reaction zone. For relatively short wave disturbances, still much larger than flame thickness, the most unstable wavelength is nearly independent on the flame angle and the flame can be stabilized by gravity and diffusion mechanism.     

Phenomenon of enhanced diffusion of lithium-ion in LiMn2O4 induced by electrochemical cycling

Lithium-ion diffusion in insertion-host materials is of significant interest because of its importance in improving the power density of lithium-ion batteries. In this study, the dependence of the chemical diffusion coefficient (D) of lithium-ion in spinel LiMn₂O₄ cathode material on electrochemical cycling has been investigated by the capacity intermittent titration technique (CITT). Results show that there are two minimum peaks in the curves of D∼E respectively at ∼3.95 and ∼4.12 V in the voltage range from 3.85 to 4.30 V. The curves of D∼E at different cycles show an interesting phenomenon that the values of D tend to increase with the cycling numbers. This phenomenon indicates an enhanced diffusion of lithium-ion in LiMn₂O₄ cathode material induced by the electrochemical cycling.     

Influence of radiation losses on the stability of premixed flames on a porous-plug burner

Analysis of the planar premixed flames on a porous plug was performed numerically for finite activation energy within the diffusive-thermal model. The paper is focused on the influence of radiation heat loses on the flame standoff distance and its linear stability. We show that the presence of volumetric heat losses limits the range of the mass flow range as well as it can promote the flame instabilities of different kinds, both oscillatory and cellular. The oscillatory instability, which for freely propagating flames can be usually observed for the Lewis number larger than one, in the porous-plug case occurs also for flames with unity and lower than unity Lewis number. For flames with Le < 1 both cellular and oscillatory instabilities can be observed simultaneously in a certain range of the mass flow rate.     

Counterflow diffusion flames: effects of thermal expansion and non-unity Lewis numbers

In this work we re-examine the counterflow diffusion flame problem focusing in particular on the flame–flow interactions due to thermal expansion and its influence on various flame properties such as flame location, flame temperature, reactant leakage and extinction conditions. The analysis follows two different procedures: an asymptotic approximation for large activation energy chemical reactions, and a direct numerical approach. The asymptotic treatment follows the general theory of Cheatham and Matalon, which consists of a free-boundary problem with jump conditions across the surface representing the reaction sheet, and is well suited for variable-density flows and for mixtures with non-unity and distinct Lewis numbers for the fuel and oxidiser. Due to density variations, the species and energy transport equations are coupled to the Navier–Stokes equations and the problem does not possess an analytical solution. We thus propose and implement a methodology for solving the free-boundary problem numerically. Results based on the asymptotic approximation are then verified against those obtained from the ‘exact’ numerical integration of the governing equations, comparing predictions of the various flame properties.     

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.     

Diffusion flame instabilities in a 0.75 mm non-premixed microburner

We examine the cellular instabilities of laminar non-premixed diffusion flames that arise in a polycrystalline alumina microburner with a channel wall gap of dimension 0.75 mm. Changes in the flame structure are observed as a function of the fuel type (H₂, CH₄, and C₃H₈) and diluent. The oxidizer is O₂/inert. In contrast to previous observations on laminar diffusion flame instabilities, the current instabilities occur in the direction of flow above the splitter plate, and only occur for the heavier fuel types. They are not observed in a H₂–O₂ mixture, which will only support a continuous laminar flame inside our burner, regardless of the initial mixture strength and whether or not the flame is in near-quenching conditions. The only exception is when helium is added to the H₂–O₂ mixture, raising the effective Lewis numbers of both components.