Continuous thermodynamics for droplet vaporization: Comparison between Gamma-PDF model and QMoM

Claire Laurent; Gérard Lavergne; Philippe Villedieu

doi:10.1016/j.crme.2009.06.004

Continuous thermodynamics for droplet vaporization: Comparison between Gamma-PDF model and QMoM
[Modélisation de l'évaporation des gouttes en thermodynamique continue : comparaison entre le modèle Gamma-PDF et la QMoM]

Claire Laurent ¹ ; Gérard Lavergne ¹ ; Philippe Villedieu ¹

¹ ONERA/DMAE, 2, avenue Edouard-Belin, BP 74025, 31055 Toulouse cedex 4, France

Comptes Rendus. Mécanique, Combustion for aerospace propulsion, Volume 337 (2009) no. 6-7, pp. 449-457.

Résumé
Abstract

La modélisation à Thermodynamique Continue (MTC) (Cotterman et al., 1985) est une méthode appropriée pour réduire les coûts de calcul associés à la modélisation de l'évaporation multi-composant. La composition des gouttes est modélisée par une fonction de distribution qui représente les dizaines d'espèces prises en compte par le modèle classique à Composants Discrets (MCD). Dans la première approche à Thermodynamique Continue développée pour cette application, la composition du mélange était décrite par une fonction de distribution de type fonction Γ (Hallett, 2000). Cependant, cette approche a été mise en défaut dès lors que de la vapeur se condensait à la surface de la goutte (Harstadt et al., 2003). La méthode proposée dans cet article, dite de Quadratrue des Moments, permet d'éviter toute hypothèse sur la forme de la fonction de distribution. A partir des travaux de Lage qui a appliqué cette méthode à l'équilibre thermodynamique des phases (Lage, 2007), ce papier élargit le domaine d'application de la QMoM à l'évaporation des gouttes multi-composant. Les différentes approches à Thermodynamique Continue sont décrites dans la première partie et les résultats obtenus dans un cas de condensation de vapeur sont ensuite comparés et analysés pour illusrer les améliorations apportées par la QMoM.

The Continuous Thermodynamics Model (CTM) (Cotterman et al., 1985) is a suitable method to reduce computational cost of multi-component vaporization models. The droplet composition is described by a probability density function (PDF) rather than tens of components in the classical Discrete Component Model (DCM). In the first CTM method developed for this application, the PDF was assumed to be a Γ-function (Hallett, 2000), but some problems had appeared in the case of vapor condensation at the droplet surface (Harstadt et al., 2003). The method put forward in this article, the Quadrature Method of Moments (QMoM), enables one to avoid any assumption on the PDF mathematical form. Following Lage who has developed this method for phase equilibria (Lage, 2007), this article widens the scope of QMoM to the modelling of multi-component droplet vaporization. The different CTM approaches are presented in the first part and the results obtained for a vapor condensation test case are then compared and analysed to illustrate improvements made by QMoM.

Publié le : 2009-06-01

DOI : 10.1016/j.crme.2009.06.004

Keywords: Combustion, Multi-component droplet, Vaporization, Continuous thermodynamics, Gamma-PDF model, Quadrature Method of Moments
Mots-clés : Combustion, Gouttelette multi-composant, Evaporation, Thermodynamique continue, Modèle Gamma-PDF, Méthode de Quadrature des Moments

Affiliations des auteurs :

Claire Laurent ¹ ; Gérard Lavergne ¹ ; Philippe Villedieu ¹

¹ ONERA/DMAE, 2, avenue Edouard-Belin, BP 74025, 31055 Toulouse cedex 4, France

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Claire Laurent; Gérard Lavergne; Philippe Villedieu. Continuous thermodynamics for droplet vaporization: Comparison between Gamma-PDF model and QMoM. Comptes Rendus. Mécanique, Combustion for aerospace propulsion, Volume 337 (2009) no. 6-7, pp. 449-457. doi : 10.1016/j.crme.2009.06.004. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2009.06.004/

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