Premixed Flame Front Research Articles

Inner cutoff scale of flame surface wrinkling in turbulent premixed flames

The inner cutoff represents the smallest scale for the interaction of turbulent eddies with the premixed flame front. The nondimensional inner cutoff has been shown to scale with Karlovitz number, Ka β, where β is − 1 2 . Three experimental data sets, with available statistical information, strongly agree with this scaling. However, the five data sets, two without experimental error statistic, seem to favor β = − 1 3 , in accordance with the direct numerical simulation results. The inner cutoff expressions reported in literature, obtained through experimental data, numerical data, or physical reasoning, have been evaluated by comparing with five experimental data sets reported recently. It has been shown that the Gibson scale, which was proposed as the inner cutoff and asserts an inverse square dependence on Karlovitz number, does not show any agreement with the experimental data or direct numerical simulation results.

The Development of Pressure Induced Instabilities in Premixed Flames

Abstract The development of disturbances to a plane, premixed flame front under the action of an externally imposed pressure gradient, has been studied numerically in two spatial demensions. The flow has been modelled well into the non-linear regime in which a thin spike of unburnt gas penetrates into the burnt region. Even though the length scales of the applied pressure disturbances considered are very large compared to the flame width, the results show that the dominant mechanism in the early stages is the Rayleigh-Taylor effect. Variations of Lewis number are found to have very little effect on the progress of the interaction. Changes in the flame Mach number and disturbance wavelength are also investigated.

Transient pressure effects in the evolution equation for premixed flame fronts

A nonlinear evolution equation for a scalar field G(x, t) is derived, whose level surface G0=const. represents the interface of a thin premixed flame propagating in a flow field. The derivation is an extended version of an equation already proposed by Markstein [1]. It was reconsidered by Williams [2] as a basis for theoretical and numerical analysis and takes, in addition to flame curvature and flame stretch time variations of the bulk pressure, heat loss and nonconstant transport coefficients into account. The equation is an extension of earlier analyses where a flame evolution equation was derived for slightly wrinkled flames such that the front can be described by a single-valued function of a normal coordinate. That formulation excluded situations where the mean flame front has an arbitrary shape in space. Here the more general situation is analysed by using a two-length-scale asymptotic analysis. The leading-order solution of this analysis is equivalent to the equation originally derived by Markstein [1]. In addition to nonconstant properties and heat-loss effects, that had already been considered by Clavin and Nicoli [3], the influence of transient changes of the bulk pressure is analysed. All these effects are combined into a unified formulation which will serve as a basis for a new flamelet concept for premixed turbulent combustion.

Unsteady potential flows computation by cellular automata: The premixed flame instability

Abstract A cellular automaton leading to self-propagating fronts in a discrete fluid has been implemented. In spite of the stabilizing diffusive-convective mechanisms, planar propagation of these fronts becomes unstable due to a feed-back mechanism with the flow generated by the front itself. The stability properties have been analyzed in the continuum limit and compared with the discrete simulations as well as with the stability properties of premixed flame fronts.

Numerical simulations of Lewis number effects in turbulent premixed flames

The structure of a premixed flame front propagating in a region of two-dimensional turbulence is investigated using full numerical simulation including heat release, variable properties, and one-step Arrhenius chemistry. The influence of reactant Lewis number (Le = ratio of thermal to species diffusivity) is reported for Le = 0.8, Le = 1.0, and Le = 1.2 flames. Local flame behaviour is described by comparing the local instantaneous turbulent flame structure (local consumption rate of reactants) to the steady one-dimensional laminar flame structure for the same thermochemical parameters. Statistics of flame front strain rates and curvature are calculated and global quantities of interest in modelling (flame surface area, mean reactant consumption rate per unit area of flame, and turbulent flame speed) are reported. Principal findings are: that probability density functions (p.d.f.s) of flame curvature are nearly symmetric about a near-zero mean; that the flame tends to align preferentially with extensive tangential strain rates; that the local flame structure of the non-unity Lewis number flames correlates more strongly with local flame curvature than with tangential strain rate; that the mean consumption rate per unit area is relatively insensitive to curvature and is controlled by the mean tangential strain rate; and, that more flame area is generated for Le 1. Implications of the results for flamelet models of turbulent premixed combustion are discussed.

Curvature and Orientation Statistics of Turbulent Premixed Flame Fronts

Abstract The curvature of turbulent premixed flame fronts is an important spatial property that needs to be quantified over a range of turbulence conditions. In this study, measurements of flamelet curvature along with orientation statistics for u'/ SL = 1.42-5.71 are obtained from OH planar laser-induced fluorescence images of the flame boundary by applying a curve-tracing difference formula with interval length of the order of the inner cutoff scale. Use of this particular interval length is essential for accurate tracing of the flame boundary with implicit filtering of extraneous noise that can introduce significant errors in the curvature measurements. The distributions of flamelet curvature are found to be symmetric with respect to the zero mean, while the variance increases with increasing u'/SL. These distributions can be approximated by Gaussian distribution functions. The positive and negative mean curvatures show a nearly square-root dependence on u'/SL whereas the mean flamelet radius of curvat...

Acoustic Instability in Premixed Flames

Abstract This short paper presents an experimental description of the acoustic instability of a premixed flame front propagating in a tube. Four distinct types of behaviour are identified. Firstly a regime of acoustic stability in which the flame is cellular and non vibrating. Secondly a regime of primary acoustic instability in which the flame is quasi planar. Thirdly a regime of secondary acoustic instability, in which the oscillations can reach very high amplitudes, and where the flame front develops pulsating cellular structures. This latter regime breaks down into an incoherent auto-turbulent regime at sufficiently high acoustic amplitudes.

Numerical Analysis of Tulip Flame Formation in a Closed Vessel.

We have investigated the mechanism of tulip flame formation in a closed vessel by means of numerical analysis. We simulated the unsteady motions of two-dimensional reactive flows using the explicit MacCormack scheme. The numerical model contained compressibility, viscosity, heat conduction, molecular diffusion, reaction, and convection. It was shown in the simulation that the flame is initially convex toward the unburned gas and that a cusp forms at the center of the flame ; then the cusp grows and the tulip-shaped flame forms. The history of flame shapes was qualitatively consistent with the experimental results. It is essential to tulip flame formation that the heat release rate is decreased when the semi-elliptic flame reaches the side walls. The cusp on the flame is caused by this and the flame becomes tulip shaped. The growth of the cusp can be explained by the flame close to the wall running faster because of much consumption of the unburned gas and by the hydrodynamic instability of premixed flame fronts.

Simulation of free boundaries in flow systems by lattice-gas models

It has been recently proved that lattice-gas models with Boolean particles can provide a very powerful method to study viscous flows at moderate Reynolds and small Mach numbers (d'Humières, Pomeau & Lallemand 1985; Frisch, Hasslacher & Pomeau 1986; d'Humières & Lallemand 1986). We present here algorithms for an extension of these models to provide a simple and efficient way to simulate a large variety of flow problems with free boundaries. This is done by introducing two different types of particles that can react following a specific kinetic scheme based on autocatalytic reactions. In order to check the powerful character and the reliability of the method we also present preliminary results of two-dimensional computer simulations concerning problems ranging from the competition between molecular diffusion and turbulent mixing in flows presenting a Kelvin-Helmholtz instability to the spontaneous generation of turbulence in premixed flame fronts subject to the Darrieus-Landau instability. The dynamics of an interface developing a Rayleigh-Taylor instability is also considered as well as some typical problems of phase transition such as spinodal decomposition and the nucleation process.

Effect of variable heat loss intensities on the dynamics of a premixed flame front

The theoretical study concerning premixed flame fronts in nonuniform and unsteady flows was developed for an arbitrary gas expansion coefficient for small amplitudes of front corrugation and then extended to the finite amplitude case in the frame of an asymptotic analysis for large values of the Zeldovich number ..beta.. (..beta.. ..-->.. infinity) and in peturbation of the relative stretch flame intensity epsilon. As was anticipated by early semiphenomenological analyses, these theoretical studies point out that two effects, front curvature and flow inhomogeneities, influence the normal burning velocity U/sub n/. But to leading order in the power expansion in epsilon of the relative modification in normal burning velocity, these two effects appear through only one geometric scalar expressing the nondimensional flame stretch tau (d Insigma/dt) experienced by the curved fronts in a nonuniform flow.

Weakly Turbulent, Wrinkled Flames in Premixed Gases

Abstract The dynamic behaviour of an intrinsically stable premixed flame front, propagating downwards in a weakly turbulent incoming flow is investigated for an arbitrary gas expansion ratio. The complete hydrodynamic problem, in which the flame appears as a free boundary, is solved analytically in the linear approximation. In this case the mutual interaction between combustion and turbulence is fully described theoretically. The response of the flame is found as a function of both the frequency and wave number content of the incoming turbulence. In addition to the gas expansion ratio, only two other parameters appear in the theory, the Markstein number (characterizing the curved flame structure) and the Froude number (based on the flame speed and the flame thickness) Sensitivity of the turbulent flame speed to the characteristics of the incoming flow as well as to these numbers is considered. The theoretical results are illustrated by comparison with some recent laboratory experiments

Equation describing wrinkled flame fronts.

A one-parameter family of nonlinear integro-differential equations, which have been derived to model a wrinkled, premixed flame front, is investigated numerically. It is shown by computing positive Lyapunov exponents that these equations display a chaotic behavior. According to the value of the parameter, characterizing the equation, structures with a well-defined size may appear or not. We discuss this feature, and also the shape of the averaged energy spectrum.

Premixed flames in large scale and high intensity turbulent flow

The recent theory of Clavin and Williams [1] concerning the premixed flame fronts in non uniform as well as unsteady flows is extended to the case of large amplitudes of the front corrugation. The convective effects associated with the gas expansion are fully taken into account in the study of the flame structure. Only one scalar « the flame stretch » is shown to control the shape and the motion of the front This stretch can be split in two parts, one accounts for the geometry of the front (mean curvature) and the other for the non uniformity of the flow (rate of strain tensor).