Adiabatic Flame Speeds and the Zeldovich-Li[nbar]án Model

Mikolaitis, David W.

doi:10.1080/00102208608923918

Cited by 14 publications

(10 citation statements)

References 6 publications

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“…Premixed combustion waves in models with chain-branching kinetic mechanism have drawn the interest of researchers for a long period of time [Chao & Law, 1994;Dold, 2007;Gubernov et al, 2006a;Gubernov et al, 2008a;Gubernov et al, 2008b;Joulin et al, 1985;Liñán, 1971;Mikolaitis, 1986]. These types of models can describe propagation of combustion waves in hydrocarbon-air mixtures, which is an issue of practical importance.…”

Section: Introductionmentioning

confidence: 99%

Pulsating Instabilities of Combustion Waves in a Chain-Branching Reaction Model

Gubernov

Kolobov

Полежаев

et al. 2009

Int. J. Bifurcation Chaos

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In this paper we investigate the properties and linear stability of traveling premixed combustion waves and the formation of pulsating combustion waves in a model with two-step chain-branching reaction mechanism. These calculations are undertaken in the adiabatic limit, in one spatial dimension and for the case of arbitrary Lewis numbers for fuel and radicals. It is shown that the Lewis number for fuel has a significant effect on the properties and stability of premixed flames, whereas varying the Lewis number for the radicals has only qualitative (but not qualitative) effect on the combustion waves. We demonstrate that when the Lewis number for fuel is less than unity, the flame speed is unique and is a monotonically decreasing function of the dimensionless activation energy. Moreover, in this case, the combustion wave is stable and exhibits extinction for finite values of activation energy as the flame speed decreases to zero. However, for the fuel Lewis number greater than unity, the flame speed is a C-shaped and double valued function. The linear stability of the traveling wave solution was determined using the Evans function method. The slow solution branch is shown to be unstable whereas the fast solution branch is stable or exhibits the onset of pulsating instabilities via a Hopf bifurcation. The critical parameter values for the Hopf bifurcation and extinction are found and the detailed map for the onset of pulsating instabilities is determined. We show that a Bogdanov—Takens bifurcation is responsible for both the change in the behavior of the traveling wave solution near the point of extinction from unique to double valued type as well as for the onset of pulsating instabilities. We investigate the properties of the Hopf bifurcation and the emerging pulsating combustion wave solutions. It is demonstrated that the Hopf bifurcation observed in our present study is of supercritical type. We show that the pulsating combustion wave propagates with the average speed smaller than the speed of the traveling combustion wave and at certain parameter values the pulsating wave exhibits a period doubling bifurcation.

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Section: Introductionmentioning

confidence: 99%

Pulsating Instabilities of Combustion Waves in a Chain-Branching Reaction Model

Gubernov

Kolobov

Полежаев

et al. 2009

Int. J. Bifurcation Chaos

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“…In the calculations, the Zel'dovich number was fixed at β = 5 as representative of combustion processes, which also corresponds to the value reported earlier for hydrogen chemistry [43]. The heat release parameter was kept fixed at γ = 0.7.…”

Section: Formulation Of the Problemmentioning

confidence: 99%

The differential diffusion effect of the intermediate species on the stability of premixed flames propagating in microchannels

Fernández-Galisteo

Jiménez

Sánchez–Sanz

et al. 2014

Combustion Theory and Modelling

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The propagation of premixed flames in adiabatic and non-catalytic planar microchannels subject to an assisted or opposed Poiseuille flow is considered. The diffusive-thermal model and the well-known two-step chain-branching kinetics are used in order to investigate the role of the differential diffusion of the intermediate species on the spatial and temporal flame stability. This numerical study successfully compares steady-state and time-dependent computations to the linear stability analysis of the problem. Results show that for fuel Lewis numbers less than unity, Le F < 1, and at sufficiently large values of the opposed Poiseuille flow rate, symmetry-breaking bifurcation arises. It is seen that small values of the radical Lewis number, Le Z , stabilise the flame to symmetric shape solutions, but result in earlier flashback. For very lean flames, the effect of the radical on the flame stabilisation becomes less important due to the small radical concentration typically found in the reaction zone. Cellular flame structures were also identified in this regime. For Le F > 1, flames propagating in adiabatic channels suffer from oscillatory instabilities. The Poiseuille flow stabilises the flame and the effect of Le Z is opposite to that found for Le F < 1. Small values of Le Z further destabilise the flame to oscillating or pulsating instabilities.

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“…With only a few exceptions (as found in [14][15][16][17][18][19]), analytical solutions describing laminar flames have been founded on the one-step model; flames have also been described using a variety of reduced-kinetic models for the chemistry [20][21][22], the rates of which are combinations of the rates of elementary hydrocarbon oxidation reactions, but these models are much more problematic to analyse in any general way. References for all the achievements of the one-step model are far too numerous to cite here; the reader can find many suitable citations in texts and review articles on combustion theory and in recent articles on the subject, e.g.…”

Section: Introductionmentioning

confidence: 99%