Combustion waves in a model with chain branching reaction and their stability

Gubernov, Vladimir; Sidhu, Harvinder; Mercer, G. N.

doi:10.1080/13647830701716948

Cited by 22 publications

(24 citation statements)

References 23 publications

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“…The properties of the travelling combustion waves were investigated analytically by Dold (2007), Gubernov et al (2008a) and numerically by solving the set of equations (3.1) subject to boundary conditions (3.2) by Gubernov et al (2008aGubernov et al ( , 2009. It was found that varying the Lewis number for fuel, L A , has a substantial effect on the properties of the premixed flames, whereas the variation of Lewis number corresponding to the radicals, L B , affects only quantitative behaviour of the combustion waves.…”

Section: Properties Of the Travelling Wave Solutionmentioning

confidence: 99%

“…In the product region, the reaction must be completed; therefore, the branching term is less than the recombination term in the third equation of equation (2.1), that is r > s exp(−1/u b ). This condition was first derived in Gubernov et al (2008a) for the adiabatic case and defines the region in the parameter space, where the travelling combustion waves exist. Once this condition is violated the adiabatic combustion waves exhibit extinction.…”

Section: Properties Of the Travelling Wave Solutionmentioning

confidence: 99%

“…It is assumed that all the heat of the reaction is released during the recombination stage and the chain-branching stage does not produce or consume any heat. Following Gubernov et al (2008a), the governing equations for the non-dimensional temperature u, concentration of fuel v and radicals w, can be written in a non-dimensional form as…”

Section: Modelmentioning

confidence: 99%

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Period doubling and chaotic transient in a model of chain-branching combustion wave propagation

et al. 2010

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The propagation of planar combustion waves in an adiabatic model with two-step chain-branching reaction mechanism is investigated. The travelling combustion wave becomes unstable with respect to pulsating perturbations as the critical parameter values for the Hopf bifurcation are crossed in the parameter space. The Hopf bifurcation is demonstrated to be of a supercritical nature and it gives rise to periodic pulsating combustion waves as the neutral stability boundary is crossed. The increase of the ambient temperature is found to have a stabilizing effect on the propagation of the combustion waves. However, it does not qualitatively change the behaviour of the travelling combustion waves. Further increase of the bifurcation parameter leads to the period-doubling bifurcation cascade and a chaotic regime of combustion wave propagation. The chaotic regime has a transient nature and the combustion wave extinguishes when the bifurcation parameter becomes sufficiently large. For Lewis numbers of fuel close to unity, the parameter regions where pulsating solutions exist become very close to each other and this makes it difficult to experimentally observe the period-doubling. It is shown that the average velocity of pulsating waves is less than the speed of the travelling wave for the same parameter values.

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Section: Properties Of the Travelling Wave Solutionmentioning

confidence: 99%

Section: Properties Of the Travelling Wave Solutionmentioning

confidence: 99%

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Period doubling and chaotic transient in a model of chain-branching combustion wave propagation

et al. 2010

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“…Gubernov and coworkers [16,17,18,19] use another choice of scalings. The relationships between their dimensionless space and time scales (denoted by a "G" subscript) and those used here are…”

Section: Introductionmentioning

confidence: 99%

“…As for the one-step model, he found that the only qualitative difference from the CDM results is that the flame remains unstable to a long-wavelength hydrodynamic instability, even for Lewis numbers of the fuel above the critical value for purely thermal-diffusive induced instability. Gubernov and coworkers [16,17,18] then examined the linear stability of the two-step model for finite activation energies (i.e., without invoking the HAEA approximation) in the context of the CDM. They considered only one-dimensional perturbations corresponding to a purely longitudinal pulsating instability.…”

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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The effect of Lewis number variation on combustion waves in a model with chain-branching reaction

et al. 2008

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Combustion waves in a model with chain branching reaction and their stability

Cited by 22 publications

References 23 publications

Period doubling and chaotic transient in a model of chain-branching combustion wave propagation

Period doubling and chaotic transient in a model of chain-branching combustion wave propagation

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

The effect of Lewis number variation on combustion waves in a model with chain-branching reaction

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