Stability of freely propagating flames revisited

Lasseigne, D. G.; Jackson, T. L.; Jameson, Leland

doi:10.1088/1364-7830/3/4/301

Cited by 28 publications

(28 citation statements)

References 25 publications

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“…Upon linearization in , the jump conditions (8)- (10) to be applied at the reaction sheet (x = 0), become…”

Section: Jump Conditions At X =mentioning

confidence: 99%

“…Lasseigne et al [10] performed a numerical linear stability analysis of the one-step reaction CDM with finite activation energy (i.e. without invoking the high activation energy asymptotic limit).…”

Section: 22mentioning

confidence: 99%

“…These asymptotic one-step reaction studies also entail a near-equidiffusional flames (NEF) approximation, i.e they are valid for Lewis numbers asymptotically close to unity. Finite activation energy numerical linear stability studies, which do not invoke the asymptotic limit, have also been performed for the one-step reaction model, both in terms of the CDM [10] and the Reactive Navier-Stokes equations [11,12]. These studies show that, when the Lewis number is sufficiently far from unity, very high activation energies may be required for the asymptotic results to be quantitatively predic-tive.…”

Section: Introductionmentioning

confidence: 99%

“…However, these finite activation energy studies do not reveal any qualitatively different instabilities than those predicted by the asymptotic analyses, even when the activation energy is quite moderate. The main use of such finite activation energy calculations is hence to provide quantitative test problems for numerical codes designed to simulate the fully non-linear flame evolutions [10,13].…”

Section: Introductionmentioning

confidence: 99%

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Effect of thermal expansion on the linear stability of planar premixed flames for a simple chain-branching model: The high activation energy asymptotic limit

Sharpe

2008

Combustion Theory and Modelling

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Published paperThe linear stability of freely propagating, adiabatic, planar premixed flames is investigated in the context of a simple chain-branching chemistry model consisting of a chain-branching reaction step and a completion reaction step. The role of chain-branching is governed by a crossover temperature. Hydrodynamic effects, induced by thermal expansion, are taken into account and the results compared and contrasted with those from a previous purely thermal-diffusive constant density linear stability study. It is shown that when thermal expansion is properly accounted for, a region of stable flames predicted by the constant density model disappears, and instead the flame is unstable to a long-wavelength cellular instability. For a pulsating mode, however, thermal expansion is shown to have only a weak effect on the critical fuel Lewis number required for instability. These effects of thermal expansion on the two-step chain-branching flame are shown to be qualitatively similar to those on the standard one-step reaction model. Indeed, as found by constant density studies, in the limit that the chain-branching crossover temperature tends to the adiabatic flame temperature, the two-step model can be described to leading order by the one-step model with a suitably defined effective activation energy.

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“…Upon linearization in , the jump conditions (8)- (10) to be applied at the reaction sheet (x = 0), become…”

Section: Jump Conditions At X =mentioning

confidence: 99%

Section: 22mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Effect of thermal expansion on the linear stability of planar premixed flames for a simple chain-branching model: The high activation energy asymptotic limit

Sharpe

2008

Combustion Theory and Modelling

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“…This is the motivation for this paper, which should hence be viewed as the two-step analogue of the one-step CDM study in [5]. The purpose of the paper is twofold: first, to determine how well the HAEA analysis of [11] predicts the results of realistic, finite activation energy studies and to determine whether the HAEA results are even qualitatively correct for this problem; second, to provide a quantitative test of numerical methods for simulating the full nonlinear solutions of the two-step CDM, such as studies currently underway (L. Kagan, J. Dold, private communications).…”

Section: Introductionmentioning

confidence: 99%

Thermal-Diffusive Instability of Premixed Flames for a Simple Chain-Branching Chemistry Model with Finite Activation Energy

Sharpe¹

2009

SIAM J. Appl. Math.

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Article:Sharpe, G.J. (2009) Abstract.A linear stability of freely propagating, adiabatic premixed flames is investigated in the context of a thermal-diffusive or constant density model, together with a simple two-step chainbranching model of the chemistry. This study considers the case of realistic, finite activation energy of the chain-branching step, and emphasis is on comparing with previous high activation energy asymptotic results. It is found that for realistic activation energies, a pulsating instability is absent in regimes predicted to be unstable by the asymptotic analysis. For the cellular instability, however, the finite activation energy results are in qualitative agreement with the asymptotic results, in that the flame is unstable only below a critical Lewis number of the fuel and becomes more unstable as the Lewis number is decreased. However, it is shown that very high activation energies would be required for the asymptotic analysis to be quantitatively predictive. The flame is less unstable for finite activation energies than predicted by the asymptotic analysis, in that a lower fuel Lewis number is required for instability. It is also shown that the flame structure and stability can have nonmonotonic dependencies on the activation energy. 1. Introduction. A premixed flame is a subsonic combustion wave which propagates via diffusion of chemical species and conduction of heat between the hot burnt chemical products and the cold unburnt fuel. While, in theory, unconfined premixed flames can propagate steadily as planar waves, this may not be realized in practice due to cellular and pulsating instabilities induced by thermal-diffusive and/or hydrodynamic effects [1]. A linear stability analysis of the underlying planar wave is a first step towards understanding the origins of such instabilities and predicting the conditions under which they occur.The majority of flame stability developments have employed a standard one-step chemistry combustion model, with a single, exothermic reaction step F→P, where F denotes fuel and P products, together with an Arrhenius form of the reaction rate. In this context, Sivashinsky [2] used a constant density model (CDM) and employed a high activation energy asymptotic (HAEA) limit in order to investigate the linear stability of one-step chemistry flames. The CDM ignores hydrodynamic effects but has extensively been demonstrated to correctly capture thermal-diffusive effects on flame dynamics [3]. Sivashinsky [2] showed that below a critical Lewis number, Le (the ratio of temperature conductivity to molecular diffusivity), the flame is unstable to a cellular instability. This cellular mode corresponds to a positive real linear eigenvalue in the stability problem. This critical value of Le is less than one, but tends to unity from below as the activation energy of the reaction is increased. Sivashinsky further showed that, above a second critical Lewis number, the flame is unstable to a

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Large Matrices Arising in Traveling Wave Bifurcations

Šimon

2008

Large-Scale Scientific Computing

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Stability of freely propagating flames revisited

Cited by 28 publications

References 25 publications

Effect of thermal expansion on the linear stability of planar premixed flames for a simple chain-branching model: The high activation energy asymptotic limit

Effect of thermal expansion on the linear stability of planar premixed flames for a simple chain-branching model: The high activation energy asymptotic limit

Thermal-Diffusive Instability of Premixed Flames for a Simple Chain-Branching Chemistry Model with Finite Activation Energy

Large Matrices Arising in Traveling Wave Bifurcations

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