Quantification of ignition time uncertainty based on the classical ignition theory and Fourier analysis

Aymeric Lamorlette

doi:10.1016/j.crme.2014.06.002

Quantification of ignition time uncertainty based on the classical ignition theory and Fourier analysis

Aymeric Lamorlette ¹

¹ Aix-Marseille Université, CNRS, Centrale Marseille, M2P2 UMR 7340, 13451 Marseille cedex 20, France

Comptes Rendus. Mécanique, Volume 342 (2014) no. 8, pp. 459-465.

Abstract
Résumé

This study aims at modeling the effect of incoming heat flux fluctuations, on solid material ignition. In order to propose a general methodology based on the classical ignition theory that can be applied to any kind of solid target, kernels accounting for the target temperature response regarding an incoming heat flux are considered for thermally thick and thin solids with low or high thermal inertia. A Fourier decomposition of the incoming heat flux is then used to calculate the target response to harmonic heat fluxes. Finally, effects of harmonic fluctuations on ignition are discussed based on the previous analytical results, allowing us to discriminate situations where ignition time is expected to be rather predictable from situations where ignition time is expected to be less predictable thanks to an uncertainty quantification of the ignition time.

Cette étude a pour but la modélisation des effets des fluctuations du flux de chaleur impactant un matériau solide sur l'ignition de ce dernier. Afin de proposer une méthodologie générale, fondée sur la théorie classique de l'ignition, qui pourra être appliquée à n'importe quel type de cible, des noyaux rendant compte de la réponse en température à une sollicitation thermique sont considérés pour des solides thermiquement épais et fins, et pour de basses et hautes inerties thermiques. Une décomposition en séries de Fourier de la sollicitation est alors utilisée pour calculer la réponse de la cible aux flux harmoniques. Finalement, les effets de ces fluctuations sont discutés à partir des résultats analytiques précédents, permettant de discriminer des situations où le temps d'ignition devrait être plutôt prédictible de situations où il risque d'être moins prédictible, et ce grâce à une quantification de l'incertitude du temps d'ignition.

Received: 2014-01-14
Accepted: 2014-06-02
Published online: 2014-06-20

DOI: 10.1016/j.crme.2014.06.002

Keywords: Heat transfer, Piloted ignition, Ignition uncertainty
Mots-clés : Transfert thermique, Ignition pilotée, Incertitude de l'ignition

Author's affiliations:

Aymeric Lamorlette ¹

¹ Aix-Marseille Université, CNRS, Centrale Marseille, M2P2 UMR 7340, 13451 Marseille cedex 20, France

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     author = {Aymeric Lamorlette},
     title = {Quantification of ignition time uncertainty based on the classical ignition theory and {Fourier} analysis},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {459--465},
     publisher = {Elsevier},
     volume = {342},
     number = {8},
     year = {2014},
     doi = {10.1016/j.crme.2014.06.002},
     language = {en},
}

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Aymeric Lamorlette. Quantification of ignition time uncertainty based on the classical ignition theory and Fourier analysis. Comptes Rendus. Mécanique, Volume 342 (2014) no. 8, pp. 459-465. doi : 10.1016/j.crme.2014.06.002. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2014.06.002/

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