Intrinsic transition mechanism to detonation of gaseous laminar flames in tubes

Paul Clavin

doi:10.5802/crmeca.232

Article de recherche

Intrinsic transition mechanism to detonation of gaseous laminar flames in tubes
[Mécanisme intrinsèque de la transition vers la détonation des flammes laminaires en phase gazeuse dans les tubes]

Paul Clavin ¹

¹ Aix Marseille Université, CNRS, Centrale Marseille, IRPHE, UMR7342, 49 rue Joliot Curie, BP 146, 13384 Marseille Cedex 13, France

Comptes Rendus. Mécanique, Volume 351 (2023), pp. 401-427.

Résumé
Abstract

La transition déflagration–détonation (DDT) sur le bout arrondi d’une flamme allongée (en forme de doigt) dans un tube est analysée dans la double limite d’une grande énergie d’activation et d’un petit nombre de Mach des flammes laminaires. L’analyse asymptotique met en évidence une transition spontanée de la flamme auto-accélérée sous l’effet d’une bifurcation noeud-col de l’écoulement gazeux à l’intérieur de la structure interne de la flamme laminaire. L’analyse prédit des conditions critiques d’emballement en temps fini de la pression qui sont en bon accord avec les données expérimentales de la DDT des flammes laminaires dans les tubes.

The deflagration-to-detonation transition (DDT) on the tip of an elongated flame in a tube is analyzed in the double limit of large activation energy and small Mach number of laminar flames. A spontaneous transition of a self-accelerated laminar flame taking the form of a dynamical saddle-node bifurcation of the flow inside the inner structure of the laminar flame is exhibited by the asymptotic analysis. The predicted critical conditions for the finite-time pressure runaway are in good agreement with the experimental data of the DDT onset in tubes.

Reçu le : 2023-08-29
Révisé le : 2023-10-09
Accepté le : 2023-10-09
Publié le : 2023-12-04

DOI : 10.5802/crmeca.232

Keywords: Deflagration-to-detonation transition, Asymptotic analysis, Finite time singularity, Dynamical saddle-node bifurcation
Mot clés : Transition déflagration détonation, Analyse asymptotique, Singularité en temps fini, Bifurcation dynamique noeud-col

Affiliations des auteurs :

Paul Clavin ¹

¹ Aix Marseille Université, CNRS, Centrale Marseille, IRPHE, UMR7342, 49 rue Joliot Curie, BP 146, 13384 Marseille Cedex 13, France

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     author = {Paul Clavin},
     title = {Intrinsic transition mechanism to detonation of gaseous laminar flames in tubes},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {401--427},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {351},
     year = {2023},
     doi = {10.5802/crmeca.232},
     language = {en},
}

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Paul Clavin. Intrinsic transition mechanism to detonation of gaseous laminar flames in tubes. Comptes Rendus. Mécanique, Volume 351 (2023), pp. 401-427. doi : 10.5802/crmeca.232. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.232/

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