Propagation of a pulsating exothermic reaction front in the condensed phase

Шкадинский, К. Г.; Khaikin, B. I.; Мержанов, А. Г.

doi:10.1007/bf00748907

Cited by 209 publications

(116 citation statements)

References 2 publications

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“…The 2 A. C. Mclntosh, R. O. Weber and G. N. Mercer [2] later work of Metcalf et al [10] and Balmforth et al [1] has also shown that this is a general phenomenon that can occur at general Lewis numbers and with different reaction terms. For Arrhenius kinetics with infinite Lewis number (that is, solid fuels) there are indications (known experimentally [11] and confirmed numerically [4,6] that there is a possible period-doubling route to chaos. The paper by Weber et al [12] was able to confirm this with an accurate value determined for the minimum wave speed.…”

Section: Introductionmentioning

confidence: 91%

Non-adiabatic combustion waves for general Lewis numbers: wave speed and extinction conditions

McIntosh

Weber²,

Mercer³

2004

ANZIAM J.

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This paper addresses the effect of general Lewis number and heat losses on the calculation of combustion wave speeds using an asymptotic technique based on the ratio of activation energy to heat release being considered large. As heat loss is increased twin flame speeds emerge (as in the classical large activation energy analysis) with an extinction heat loss. Formulae for the non-adiabatic wave speed and extinction heat loss are found which apply over a wider range of activation energies (because of the nature of the asymptotics) and these are explored for moderate and large Lewis number cases-the latter representing the combustion wave progress in a solid. Some of the oscillatory instabilities are investigated numerically for the case of a reactive solid.

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Section: Introductionmentioning

confidence: 91%

Non-adiabatic combustion waves for general Lewis numbers: wave speed and extinction conditions

McIntosh

Weber²,

Mercer³

2004

ANZIAM J.

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“…Shkadinsky, Khaikin, and Merzhanov [18] predicted the simplest oscillatory regimes through numerical simulation on reaction-diffusion partial differential equations (PDEs). The system contains Arrhenius-kinetics terms that account for chemical conversion throughout the spatial domain.…”

Section: Introductionmentioning

confidence: 99%

“…They motivate it by noting that both the reaction-diffusion model as in [18] and the free-interface model in [14] assume a constant value of thermal diffusivity. However, some problems manifest a clear dependence of this parameter on degree of conversion.…”

Section: Introductionmentioning

confidence: 99%

Weakly Nonlinear and Numerical Analyses of Dynamics in a Solid Combustion Model

Gross

Yu²

2005

SIAM J. Appl. Math.

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Abstract. This paper contains qualitative and quantitative comparisons between a weakly nonlinear analysis and direct numerical simulations of a free-boundary problem. The former involves modulating the most linearly unstable mode, taking a small perturbation of the neutrally stable value νc of a parameter ν related to the activation energy. Analogously, we perform the direct numerical computations near the marginally unstable value, namely, ν = νc − 2 , where is rather small.We delineate the role of a different parameter σ (related to the Arrhenius kinetics) in the combustion dynamics when ν = νc − 2 . In particular, the numerics show that varying σ produces a period-doubling scenario when lies approximately between 0.08 and 0.12. We describe the σ intervals within which complex dynamics occur for various values of and for ν fixed at νc − 2 . When drops to approximately 0.06, the asymptotic and numerical solutions agree well for all physical values of σ.

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“…In numerical investigations of gasless solid combustion, Shkadinskii et al (1971) demonstrated that the pulsating regime of flame propagation existed in a model with single-step kinetics of the reaction. Based on numerical data, the phenomenological approximation of the neutral stability boundary was found and it was also shown that as the bifurcation parameter increased, the dynamics of pulsations became more and more complicated.…”

Section: Introductionmentioning

confidence: 99%

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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Propagation of a pulsating exothermic reaction front in the condensed phase

Cited by 209 publications

References 2 publications

Non-adiabatic combustion waves for general Lewis numbers: wave speed and extinction conditions

Non-adiabatic combustion waves for general Lewis numbers: wave speed and extinction conditions

Weakly Nonlinear and Numerical Analyses of Dynamics in a Solid Combustion Model

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

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