Nonlinear cellular instabilities of planar premixed flames: numerical simulations of the Reactive Navier–Stokes equations

Sharpe, Gary J.; Falle, S. A. E. G.

doi:10.1080/13647830500472354

Cited by 26 publications

(14 citation statements)

References 35 publications

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“…The comparison with the high activation energy asymptotic expressions showed that for low Le the numerical dispersion relation differs from 332 C. Altantzis and others the theoretical expression. The long-time propagation was numerically simulated in domains with heights equal to approximately six and twelve times λ max , the wave length of the linearly most unstable mode, by Kadowaki, Suzuki & Kobayashi (2005), while Yuan, Ju & Law (2005) and Sharpe & Falle (2006) considered narrower domains (one to three λ max and one to two λ max , respectively). Larger domains of up to 10.6λ max were considered in (Yuan, Ju & Law 2007).…”

Section: Introductionmentioning

confidence: 99%

Hydrodynamic and thermodiffusive instability effects on the evolution of laminar planar lean premixed hydrogen flames

et al. 2012

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Numerical simulations with single-step chemistry and detailed transport are used to study premixed hydrogen/air flames in two-dimensional channel-like domains with periodic boundary conditions along the horizontal boundaries as a function of the domain height. Both unity Lewis number, where only hydrodynamic instability appears, and subunity Lewis number, where the flame propagation is strongly affected by the combined effect of hydrodynamic and thermodiffusive instabilities are considered. The simulations aim at studying the initial linear growth of perturbations superimposed on the planar flame front as well as the long-term nonlinear evolution. The dispersion relation between the growth rate and the wavelength of the perturbation characterizing the linear regime is extracted from the simulations and compared with linear stability theory. The dynamics observed during the nonlinear evolution depend strongly on the domain size and on the Lewis number. As predicted by the theory, unity Lewis number flames are found to form a single cusp structure which propagates unchanged with constant speed. The long-term dynamics of the subunity Lewis number flames include steady cell propagation, lateral flame movement, oscillations and regular as well as chaotic cell splitting and merging.

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Section: Introductionmentioning

confidence: 99%

Hydrodynamic and thermodiffusive instability effects on the evolution of laminar planar lean premixed hydrogen flames

et al. 2012

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“…However, calculations of the fully non-linear stages of the evolution, and studies of how these compare and contrast to the fully non-linear one-step model results, would perhaps be a more important next step. Direct numerical simulations using the two-step model, along the lines of the one-step computations in Sharpe and Falle [13], will be presented in a future article.…”

Section: Discussionmentioning

confidence: 99%

“…However, it should be noted that a linear analysis only gives information about stability boundaries, onset and initial growth stage of the instability. It is not relevant to the fully developed non-linear cells, which may be of a quite different characteristic wavelength to that predicted by the linear analysis [13].…”

Section: 11mentioning

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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“…However, calculations of the fully nonlinear stages of the evolution, and studies of how these compare and contrast to the fully nonlinear one-step model results, would perhaps be a more important next step. Direct numerical simulations using the two-step model, along the lines of the one-step computations in Sharpe and Falle [10], will be presented in a future article. Indeed, one purpose of the present work is to provide quantitative results against which simulations can be validated.…”

Section: T B Fixedmentioning

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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Nonlinear cellular instabilities of planar premixed flames: numerical simulations of the Reactive Navier–Stokes equations

Cited by 26 publications

References 35 publications

Hydrodynamic and thermodiffusive instability effects on the evolution of laminar planar lean premixed hydrogen flames

Hydrodynamic and thermodiffusive instability effects on the evolution of laminar planar lean premixed hydrogen flames

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

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