An approximate analytical model for the frequency response of evaporating droplets under a mixed feeding regime

Kwassi Anani; Roger Prud’homme; Mahouton N.  Hounkonnou

doi:10.5802/crmeca.146

An approximate analytical model for the frequency response of evaporating droplets under a mixed feeding regime
[Un modèle analytique approximatif pour la réponse en fréquence des gouttelettes d’évaporation sous un régime d’alimentation mixte]

Kwassi Anani ¹ ; Roger Prud’homme ² ; Mahouton N. Hounkonnou ³

¹ Laboratory of Mathematical Modelling and Applications, Department of Mathematics, University of Lomé, 02 BP 1515 Lomé, Togo
² Jean Le Rond d’Alembert Institute, UMR 7190 CNRS, Sorbonne University, 4 place Jussieu, 75252 Paris Cedex 05
³ University of Abomey-Calavi, International Chair in Mathematical Physics and Applications (ICMPA-UNESCO Chair) 072 B.P. 050 Cotonou, Republic of Benin

Comptes Rendus. Mécanique, Volume 351 (2023) no. S2, pp. 77-95.

Résumé
Abstract

Ce travail est l’une des approches analytiques pour évaluer la réponse en fréquence d’évaporation des gouttelettes injectées, en utilisant l’analogie de Heidmann i.e. d’une seule gouttelette alimentée en continu avec le même carburant liquide. Sur la base d’une analyse linéaire utilisant le critère de Rayleigh, un facteur de réponse sans dimension est déterminé. Les effets dus à la variation du coefficient de transfert de chaleur du processus d’alimentation, ainsi que ceux dus aux temps caractéristiques d’évaporation et au retard de phase sont analysés. Une augmentation brutale du facteur de réponse se produit, lorsqu’un coefficient thermodynamique du carburant injecté prend certaines valeurs spécifiques.

This work is one of the analytical approaches to evaluate the evaporation frequency response of injected droplets, using the Heidmann analogy of a single droplet that is continuously fed with the same liquid fuel. Based on a linear analysis using the Rayleigh criterion, a dimensionless response factor is determined. The effects due to the variation of the heat transfer coefficient of the feeding process, as well as those due to the characteristic evaporation times and phase delay are analyzed. An abrupt increase of the response factor occurs, when a thermodynamic coefficient of the injected fuel takes certain specific values.

Reçu le : 2022-06-13
Révisé le : 2022-09-08
Accepté le : 2022-10-26
Première publication : 2023-02-20
Publié le : 2023-11-10

DOI : 10.5802/crmeca.146

Keywords: Combustion instability, Injection regime, Evaporation, Double confluent Heun equation, Transfer function
Mot clés : instabilité de combustion, régime d’injection, évaporation, équation de Heun à double confluence, fonction de transfert

Affiliations des auteurs :

Kwassi Anani ¹ ; Roger Prud’homme ² ; Mahouton N. Hounkonnou ³

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     title = {An approximate analytical model for the frequency response of evaporating droplets under a mixed feeding regime},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {77--95},
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Kwassi Anani; Roger Prud’homme; Mahouton N.  Hounkonnou. An approximate analytical model for the frequency response of evaporating droplets under a mixed feeding regime. Comptes Rendus. Mécanique, Volume 351 (2023) no. S2, pp. 77-95. doi : 10.5802/crmeca.146. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.146/

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