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Curved and stretched flames: the two Markstein numbers

Published online by Cambridge University Press:  28 September 2011

Paul Clavin  and
José C. Graña-Otero
Paul Clavin*
Affiliation:
Institut de Recherche sur les Phénomènes Hors Equilibre, Universités d’Aix Marseille et CNRS, 49 rue Joliot Curie, BP 146, 13384 Marseille CEDEX 13, France
José C. Graña-Otero
Affiliation:
ETSI Aeronáuticos, Universidad Politécnica de Madrid, Pl. Cardenal Cisneros 3, Madrid 28040, Spain
*
†Email address for correspondence: [email protected]
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Abstract

The analytical result concerning the Markstein number of adiabatic flames was obtained in 1982 with the one-step Arrhenius model in the limit of a large activation energy. This result is not relevant for real flames. The form of the law expressing the flame velocity in terms of the total stretch rate of the flame front through a single Markstein length is not conserved when the location of the front (surface of zero thickness) changes within the flame thickness. It is shown in this paper that two different Markstein numbers characterize usual wrinkled flames sustained by a multiple-step chemical network, for the modification of the flame velocity due to the curvature of the front and for the effect of the flow strain rate. In contrast to , depends on the location of the flame surface within the flame thickness, in such a way that the final result for the flame dynamics is not depending on this choice. The first part of the paper is devoted to present a general method of solution, valid for any multiple-step chemical network. The two Markstein numbers for two-step chain-branching models representing rich hydrogen–air flames and lean hydrocarbon–air flames are then computed analytically in the second part.

JFM classification

Reacting Flows: Flames
Type
Papers
Information
Journal of Fluid Mechanics , Volume 686 , 10 November 2011 , pp. 187 - 217
Copyright
Copyright © Cambridge University Press 2011

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