The unstable behavior of cellular premixed flames induced by intrinsic instability

The unstable behavior of cellular premixed flames induced by intrinsic instability is studied by two-dimensional unsteady calculations of reactive flows. In the present numerical simulation, the compressible Navier–Stokes equation including a one-step irreversible chemical reaction is employed. We consider two basic types of phenomena to account for the intrinsic instability of premixed flames, i.e., hydrodynamic and diffusive-thermal effects. The hydrodynamic effect is caused by the thermal expansion through the flame front; the diffusive-thermal effect is caused by the preferential diffusion of mass versus heat. A disturbance with several wavelength components is superimposed on a planar flame, and the formation of a cellular flame induced by hydrodynamic and diffusive-thermal effects is numerically simulated. After the cellular-flame formation, the combination and division of cells are observed. The behavior of cellular-flame fronts becomes more unstable when the Lewis number is lower than unity, since the diffusive-thermal effect has a great influence on the unstable behavior. The cell size changes with time, and its average is greater than the critical wavelength and becomes smaller by decreasing the Lewis number. The flame velocity of cellular flames depends strongly on the length of computational domain in the direction tangential to the flame front. As the length of computational domain increases, the flame velocity becomes larger. This is because the long-wavelength components of disturbances play an important role in the shape of cellular flames, i.e., in the flame-surface area.     

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.     

Thermal expansion effect on the propagation of premixed flames in narrow channels of circular cross-section: Multiplicity of solutions,axisymmetry and non-axisymmetry

The present study examines, in presence of thermal expansion effects, the existence of the multiplicity of solutions previously reported within the context of diffusive-thermal modeling in [15], for lean premixed flames with low Lewis number (Le?<?1) propagating in narrow circular adiabatic channels subject to a Poiseuille flow. For this, direct numerical simulations have been carried out within the framework of variable-density Navier–Stokes equations and zero-Mach-number approximation. The simulations, conducted for both axisymmetric and three-dimensional cylindrical geometries, confirm the coexistence of multiple steady flame structures for a given flow rate. They show that axisymmetric flames concave towards the upstream are more unstable to three-dimensional perturbations than convex (toward the upstream) flames. This result evinces earlier findings obtained from stability analysis. The non-axisymmetry property of the flame is also found to push back the critical flashback limits at larger flow rate when compared to those predicted under the assumption of flame axisymmetry.     

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.     

Effect of thermo-hydrodynamic instability on structure and characteristics of filtration combustion wave of solid fuel

Numerical modelling of flame front stability for the inverse wave (with trailing combustion front) of filtration combustion of solid fuel is performed. The problem is treated in terms of dimensionless variables and parameters. It is found that propagation of a plane combustion front becomes unstable under certain conditions. In this case the front spontaneously inclines. The thermo-hydrodynamic mechanism is supposed to be responsible for instability developing. Anisotropic effective mass diffusivity (dispersion) is also taken into account. It turns out that anisotropic diffusivity affects structure and conversion distribution of the inclined combustion front. It is shown that the key parameters determining stability of combustion wave are dimensionless gas flow rate and width of reactor. The range of these parameters corresponding to the stable plane front is determined. It is shown that stability occurs either for small reactor widths (dimensionless values <1), or low gas flow rate (below 0.2). The optimised values of considered dimensionless parameters for maximal productivity are determined.     

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.     

Nonlinear equation for curved nonstationary flames and flame stability

A time-dependent nonlinear equation for a nonstationary curved flame front of an arbitrary expansion coefficient is derived under the assumptions of a small but finite flame thickness and weak nonlinearity. On the basis of the derived equation, stability of two-dimensional curved stationary flames propagating in tubes with ideally adiabatic and slip walls is studied. The stability analysis shows that curved stationary flames become unstable for sufficiently wide tubes. The obtained stability limits are in a good agreement with the results of numerical simulations of flame dynamics and with semiqualitative stability analysis of curved stationary flames. Possible outcomes of the obtained instability at the nonlinear stage are discussed. The instability may result in extra wrinkles at a flame front close to the stability limits and in self-turbulization of the flame far from the limits. The self-turbulization can also be interpreted as a fractal structure. The fractal dimension of a flame front and velocity of a self-turbulized flame are evaluated.     

Characteristic patterns of thermodiffusively unstable premixed lean hydrogen flames

Large-scale two-dimensional numerical simulations of thermodiffusively unstable, lean, premixed hydrogen flames have been performed using detailed finite rate chemistry to analyze flame intrinsic scales. The simulations feature a long integration time and large domain sizes to rule out effects of confinement on the dynamics of the flame front. For sufficiently large domain sizes, the total consumption speed of the flame is found to become independent of the domain size. An assessment of the characteristic scales of the flame front corrugation reveals the existence of a smallest and a largest flame intrinsic length scale. The smallest length manifests itself by local cusps, which lead to the formation of characteristic cells along the flame front. Their size is remarkably close to the most unstable wavelength predicted by a linear stability analysis of the flame front evolution in the linear regime. Independently of the domain size, a specific largest flame intrinsic structure, here referred to as flame finger, emerges from the interaction of multiple small-scale cusps. Thermodiffusively unstable flames are found to periodically form and destroy these flame fingers, but the formation of a global cusp that is known to emerge for purely hydrodynamically unstable flames is suppressed. The finite size of the largest scale fingers is explained by an instability in their movement. As they proceed towards the unburnt mixture, they tend to tilt and move laterally, thereby eventually being incorporated again by the rest of the flame. This behavior arises from the interaction of the flame fingers and the diverging velocity field ahead of them. Finally, the effect of equivalence ratio and unburnt gas temperature is investigated showing that flame fingers are found to develop only in case of a thermodiffusively unstable flame.     

Analysis of the flame dynamics in methane/hydrogen fuel blends at elevated pressures

We investigate the Flame Transfer Function (FTF) of a lean-premixed, laminar slit flame numerically. Based on the reference case at atmospheric pressure, we investigate four different scenarios: (i) varying the hydrogen content in the fuel at constant equivalence ratio (ER) (resulting in an increase of the laminar flame speed); (ii) varying the hydrogen content in the fuel at varying ER (resulting in a constant laminar flame speed); (iii) varying the operating pressures from 1 to 5 bar (resulting in a decrease of the laminar flame speed); and (iv) combining a hydrogen-enriched flame at an elevated pressure of 3 bar (resulting in the same flame speed as the reference case). We identify in this case that the laminar flame speed and the flame thickness impact the FTF independently. We show that the low-pass behavior of the flame is shifted towards higher frequencies when the operating pressure increases, and demonstrate that wrinkles along the flame front preserve in contrast to the atmospheric operating pressure configurations. These results are in line with past studies, that relate the dampening of flame front wrinkling to a decreasing Markstein length. We therefore conclude that a decreasing flame thickness, due to increasing operating pressure, causes a decreasing Markstein length and therefore less pronounced dampening of flame front wrinkles.     

Instability of a flame front propagating through a fuel-rich droplet–vapour–air cloud

A simple model of a flame front propagating through a fuel-rich droplet–vapour–air mixture is presented in which the fuel droplets are assumed to evaporate in a sharp front ahead of the reaction front. By performing a linear stability analysis neutral stability boundaries are determined. It is shown that the presence of the spray of droplets in the fresh mixture can have a profound effect by causing cellularization of the flame front. Specifically, we demonstrate that under certain circumstances a spray flame can be cellular when its equivalent non-spray flame is completely stable. Furthermore, it is shown that even when the non-spray flame is itself cellular the equivalent spray flame will have a finer cellular structure. These theoretical predictions verify qualitatively for the first time independent experimental observations from the literature. It is thus shown that the primary effect of the spray on the stability of these flames is due to heat loss from the absorption of heat by the droplets for vaporization. The influence of the initial liquid fuel loading and the latent heat of vaporization on the critical wavenumber associated with cellularity provide further evidence of the responsibility of the heat loss mechanism for these spray-related phenomena. Finally, the cellularity of the spray flames with their attendant increase in flame front area suggest a plausible rationale for the experimentally observed burning velocity enhancement induced by the use of a spray of fuel droplets.     

Simulation of hydrodynamic phenomena attendant on the flame front propagation in a tube behind a piston

The propagation of a propane-air flame in a model internal combustion chamber, a tube with one or two pistons, is studied experimentally. Situations are simulated in which the flame front moves in a semiopen flat or cylindrical tube between two pistons or between a piston and the closed end of the tube. The time dependence of the flame front position and acceleration is obtained for the case of the variable tube length and combustible mixture volume. Self-oscillation conditions for the flame front and piston are determined. A relation between their amplitude-frequency characteristics is found. It is established that the piston paradox motion effect, i.e., the motion of the piston toward the flame front, depends on the length of the tube. It is demonstrated that the piston effect is related to the formation of a “tulip” flame. An explanation to the observed hydrodynamic phenomena is given.     

Edge flames stabilized in a non-premixed microcombustor

The dynamics of an edge flame confined in a non-premixed microcombustor model is studied numerically within the context of a diffusive-thermal model. Fuel and oxidizer, separated upstream by a thin plate, flow through a channel with a prescribed velocity. At the tip of the plate, the fuel and oxidizer mix and, when ignited, an edge flame is sustained at some distance from the plate. The objective in this work is to consider the effects of confinement, differential diffusion, and heat loss on the dynamics of an edge flame in a narrow channel. We consider a wide range of channel widths and allow for changing Lewis numbers, and both adiabatic conditions and heat losses along the channel walls. The results illustrate how the flame shape and standoff distance are affected by the channel width, by mixture composition through variations in Lewis numbers and by heat losses. Conditions for flame stabilization, flame oscillations and flame extinction or blowoff are predicted.     

Structure and stability characteristics of turbulent planar flames with inhomogeneous jet in a concentric flow slot burner

Turbulent flames with compositionally inhomogeneous mixtures are common in many combustion systems. Turbulent jet flames with a circular nozzle burner were used earlier to study the impact of inhomogeneous mixtures, and these studies showed that the nozzle radius affects the flame stability. Accordingly, planar turbulent flames with inhomogeneous turbulent jet are created in a concentric flow slot burner (CFSB) to avoid this effect in the present study. The stability characteristics, the mixing field structure, and the flame front structure were measured, and the correlations between stability and the mixing field structure were investigated. The mixture fraction field was measured in non-reacting jets at the nozzle exit using highly resolved Rayleigh scattering technique, and the flame front was measured in some selected turbulent flames using high-speed Planar Laser-Induced Fluorescence (PLIF) of OH technique. The data show strong correlations between flame stability and the range of mixture fraction fluctuations. The flames are highly stabilized within a mixing field environment with the range of fluctuation in mixture fraction close to the range of the flammability limits. The mixing field structure is also illustrated and discussed using a mixing regime diagram and showed that the scatter of the data of the different cases is consistent with the classified mixing regimes. Lean flames are stabilized in the current slot burner. The flame front structure topology varies consistently from thin, small curvature at the low level of turbulence and higher equivalence ratio to more wrinkled, larger curvature, but a thicker structure at a higher level of turbulence and lower equivalence ratio.     

An Analytical Study of Hydrodynamic Instability in the Flame. 1. Viscous Gas in the Flame Zone

The problem of the hydrodynamic stability of slow combustion is analytically solved with consideration given to the viscosity of the gas in the flame zone, the temperature dependence of the viscosity, and the dependences of the flame speed on the front curvature according to the Markstein model and on the pressure. The viscous forces in the flame zone alone cannot ensure the stability of the flame at any values of the Reynolds number. These forces act only as amplifiers of the stabilizing factor according to the Markstein model or in the case of a negative dependence of the flame velocity on the pressure. This property of internal friction forces is the more pronounced, the stronger the viscosity increases with the temperature. Thermal expansion is not only a destabilizing factor, leading to an increase in viscosity and other transport coefficients, but also produces a stabilizing effect.     

Evaluation of models for flame stretch due to curvature in the thin reaction zones regime

Direct numerical simulation (DNS) was used to study modelling assumptions for the curvature-propagation component of flame stretch in the thin reaction zones regime of turbulent premixed combustion, a regime in which small eddies can penetrate the preheat zone but not the thinner fuel breakdown zone. Simulations of lean hydrogen–air and methane–air flames were conducted, and statistics of flame stretch due to curvature, henceforth referred to simply as stretch, were extracted from a species mass fraction iso-surface taken to represent the flame. The study focussed on investigating the modelling assumptions of Peters [J. Fluid Mech. 384 (1999) 107]. It was found that the mean stretch is dominated by stretch due to correlations of flame speed with curvature, and specifically the effects of tangential diffusion. The modelling suggestions of Peters were found to provide an improvement over the assumptions of a constant flame speed or a flame speed governed by the linear relationship with stretch at small and steady stretch. However for the conditions considered here, diffusive-thermal effects remain well into the thin reaction zones regime, and the suggestions of Peters generally over-predict the mean compressive stretch. An effective diffusivity for flame stretch was suggested and evaluated for the methane simulations. It was found that the effective diffusivity was comparable to the mass diffusivity for flames with a high ratio of flame time to eddy turnover time. The length scales contributing to stretch were investigated, and it was found that while most flame area has a radius of curvature greater than the laminar flame thickness, most stretch occurs in more tightly curved flame elements.     

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.     

Pattern formation in flame spread over thin solid fuels

The fingering char pattern emerging on the surface of thin cellulosic sheets burning against an oxidizing wind is discussed. Employing collocation-based averaging, the assumption of diffusive-thermal equilibrium, the strong temperature dependence of the reaction rate, and the strong disparity between the densities of the solid and gaseous phases, an elementary two-dimensional free-interface model for the flame spread is formulated. It is shown that the pattern-forming dynamics is functionally akin to the well-studied cellular instability occurring in low Lewis number premixed gas flames.     

微重力环境下V型层流预混火焰锋面不稳定性分析

本章试图寻求描述火焰锋面动态特性的方法，以解释微重力环境下出现的V型火焰锋面的涟漪现象。采用线性稳定性理论从经典的G方程中导出了描述火焰锋面动态结构的一阶偏微分方程。采用该方程计算了声波扰动后，不同时刻的V型火焰锋面的动态结构．对于谐波扰动，其频率与波数的关系是分析固有火焰锋面不稳定性的基础。因此，微重力环境下V型火焰锋面的不稳定性可能是声波与谐波相耦合的结果。     

Characterization of heat recirculation effects on the stabilization of edge flames in the near-wake of a mixing layer

A fundamental study aimed at investigating the stabilization characteristics of edge flames established in the near-wake of two merging streams, one containing fuel and the other oxidizer, is presented, with the main focus placed on the effects of the thermal interaction between the flame and the splitter plate. To this end, a diffusive-thermal model characterized by constant gas density and transport coefficients is used for conditions at which flame liftoff is likely to occur. It is assumed that the incoming streams are of equal strain rates, that the fuel and oxidizer are supplied in stoichiometric proportion, and that the mass diffusivities of the reactants are equal, such that the resulting combustion field is symmetric with respect to the centerline extending from the splitter plate. The results indicate that the plate has a negligible effect on the edge flame unless the tip of the plate intrudes into the preheat zone of the curved premixed flame segment forming the edge flame. In an overall adiabatic system, the heat conducted from the flame to the plate is completely recirculated back to the reactants via the lateral surfaces of the plate, thus supporting an excess enthalpy flame in the near-wake. The average output heat flux, defined as the total heat output through the lateral surfaces of the plate divided by the characteristic length associated with the temperature variation along the plate, is identified as an appropriate measure to characterize the heat recirculation efficiency.