Asymptotic Analysis of Laminar Flame Propagation for General Lewis Numbers

Bush, William B.; Fendell, Francis E.

doi:10.1080/00102206908952222

Cited by 233 publications

(74 citation statements)

References 3 publications

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“…In the special case of homogeneous combustion, e.g., combustion of gases in premixed flames (⑀ g ϭ 1), and for Le g ϭ 1 and ␣ i ϭ 0 (i.e., the gaseous key reactant is fully consumed) and the reaction order n being a natural number, the above solution reduces to that found by Zeldovich, Frank-Kamenetsky, and Semenov [4,18,19,22] and by Merzhanov [5]. The case ␣ i ϭ 0 can be easily obtained in premixed flames, by taking the reactant that is fully consumed as the gaseous key reactant y i .…”

Section: R Gort and J J H Brouwersmentioning

confidence: 86%

“…The limiting problem in which diffusion can be disregarded or is absent, i.e., only convective transport of the reactants is important, is considered numeri-2 R. GORT AND J. J. H. BROUWERS cally by Von Karman [4] and analytically by Merzhanov and Khaikin [5] and Gatica et al [7]. In contrast with a gas flame where the main concentration change occurs in the preheat zone due to diffusion of reactants and conduction of heat, the main change in concentration in a medium with no or very low diffusion occurs in the reaction zone.…”

Section: Introductionmentioning

confidence: 99%

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Theoretical analysis of the propagation of a reaction front in a packed bed

Gort

Brouwers

2001

Combustion and Flame

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The propagation of a reaction front through a packed bed is analyzed theoretically. The chemical reaction rate is represented by Arrhenius temperature kinetics with external transfer limitation and general power law dependency on both gaseous and solid reactant concentrations. Analogous to so-called "Activation Energy Asymptotics" developed for premixed laminar flames, the largeness of the activation energy of the chemical reaction is exploited to derive asymptotic solutions from the three governing differential equations pertaining to transport of heat, of solid reactant, and of gaseous reactant, making use of the method of matched asymptotic expansions. Two regions are distinguished, i.e., an outer region or preheat zone and an inner region or reaction zone. In the preheat zone, the reaction terms can be neglected as compared to the convective and diffusive terms. In the reaction zone, the diffusion of heat is dominating over the convective heat transport mechanism and balances the heat of reaction. In accordance with the magnitudes taken for the Lewis numbers, for solid and gaseous reactants convective transports are dominating and submitting diffusive transports in the reaction zone, respectively. Solutions in closed form are presented for governing variables including reaction front velocity whereby previously published results appear as special cases. The solutions provide direct insight into underlying physical processes and enable the effects of important parameters to be quantified analytically. © 2001 by The Combustion Institute

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Section: R Gort and J J H Brouwersmentioning

confidence: 86%

Section: Introductionmentioning

confidence: 99%

Theoretical analysis of the propagation of a reaction front in a packed bed

Gort

Brouwers

2001

Combustion and Flame

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“…For the Karlovitz number, we need a more accurate value of the velocity of the planar premixed flame than the first term, U L , of the asymptotic expansion given above. For large b, the ratio S L /U L is, according to [12], of the form…”

Section: Mathematical Formulationmentioning

confidence: 99%

Flame flashback and propagation of premixed flames near a wall

Kurdyumov

Fernandez

Liñán

2000

Proceedings of the Combustion Institute

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The flashback or propagation of premixed flames along the near-wall low-velocity region at the base of a laminar boundary layer of a reactive mixture has been studied numerically. The analysis, carried out using the constant density approximation for an Arrhenius overall reaction, accounts for the effects of the Lewis number of the fuel. The flow field, as seen by an observer moving with the front, includes the unknown flame front velocity U relative to the wall and the linear velocity gradient A at the base of the boundary layer. Due to this gradient, the flame front is curved with a radius of curvature l F ‫ס‬ S L /A, proportional to the planar flame velocity S L . The front velocity is changed from S L by a factor which depends on the Karlovitz number, or non-dimensional wall velocity gradient, defined as the ratio between the thickness of the planar flame and the front curvature l F . The front velocity has been calculated in the limiting cases of adiabatic and isothermal walls. The front velocity changes from negative to positive when the Karlovitz number decreases below a critical value, determining the onset of flashback. This critical value, which decreases when the Lewis number of the fuel increases, is smaller for isothermal than for adiabatic walls. In this second case, when the flame is not quenched close to the wall, flashback is prevented by flame stretch associated with flame curvature.

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“…The only mathematical tool devised so f a r for the r a t i o n a l solution of equations such as (1.1) is activation energy asymptotics , i.e. the construction of solutions in the limit 0 -T he pioneer ing work in premixed flames is the one-d imensional steady analysis of Bush and Fendell ( 1970) , and more recently Sivashinsky (1974aSivashinsky ( , 1974b and Bv~kma ster (1977) have obta ined results for both three-dimensional and uns teady flames. The structure of these flames is characterized by a flame-sheet of thickness to which all the reaction is confined , and -2-moreover , the analysis dema nds tha t the temperature in the reg ion beh ind the flame sheet (where V 0) differs by only an o(~-) amount from the adiabatic value (l-fT).…”

Section: Introductionmentioning

confidence: 99%

The quenching of two-dimensional premixed flames

Buckmaster

1979

Acta Astronautica

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Asymptotic Analysis of Laminar Flame Propagation for General Lewis Numbers

Cited by 233 publications

References 3 publications

Theoretical analysis of the propagation of a reaction front in a packed bed

Theoretical analysis of the propagation of a reaction front in a packed bed

Flame flashback and propagation of premixed flames near a wall

The quenching of two-dimensional premixed flames

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