On the instantaneous formation of cavitation in hydrodynamic lubrication

Jesús Ildefonso Díaz; Sébastien Martin

doi:10.1016/j.crme.2006.08.003

On the instantaneous formation of cavitation in hydrodynamic lubrication
[Sur la formation instantanée de la cavitation en lubrification hydrodynamique]

Présenté par : Évariste Sanchez-Palencia

Jesús Ildefonso Díaz ¹ ; Sébastien Martin ^1,²

¹ Dept. de Matemática Aplicada, Fac. de Ciencias Matemáticas, Universidad Complutense Madrid, 28040 Madrid, Spain
² Institut Camille-Jordan CNRS-UMR 5208, INSA Lyon, bâtiment Léonard-de-Vinci, 69621 Villeurbanne cedex, France

Comptes Rendus. Mécanique, Volume 334 (2006) no. 11, pp. 645-650.

Résumé
Abstract

Nous considérons le modèle d'Elrod–Adams, qui permet d'étendre l'équation de Reynolds (classiquement utilisée en lubrification) à la prise en compte de la cavitation (formation de bulles de gaz). Nous montrons que le comportement de la pression et de la saturation du lubrifiant dépend, de manière cruciale, du comportement de la distance entre les deux surfaces $h (t, x, y)$ . En particulier, nous établissons deux formulations simples pour lesquelles nous établissons (rigoureusement) qu'une zone cavitée se forme instantanément (y compris à partir d'une situation initiale totalement saturée). Des résultats numériques sont également présentés.

We consider the Elrod–Adams model extending the classical lubrication Reynolds equation to the case of the possible presence of a cavitation region. We show that the behaviour of the pressure and saturation depends crucially on the behaviour of the separation $h (t, x, y)$ among the two surfaces. In particular, we exhibit some simple formulations for which we prove (rigorously) that a cavitation region is formed instantaneously (even for initially saturated flows). Some numerical experiences are also given.

Reçu le : 2006-08-14
Accepté le : 2006-08-25
Publié le : 2006-09-28

DOI : 10.1016/j.crme.2006.08.003

Keywords: Lubrication, Cavitation, Elrod–Adams model, Reynolds equation
Mot clés : Lubrification, Cavitation, Modèle d'Elrod–Adams, Équation de Reynolds

Affiliations des auteurs :

Jesús Ildefonso Díaz ¹ ; Sébastien Martin ^{1, 2}

¹ Dept. de Matemática Aplicada, Fac. de Ciencias Matemáticas, Universidad Complutense Madrid, 28040 Madrid, Spain
² Institut Camille-Jordan CNRS-UMR 5208, INSA Lyon, bâtiment Léonard-de-Vinci, 69621 Villeurbanne cedex, France

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     title = {On the instantaneous formation of cavitation in hydrodynamic lubrication},
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Jesús Ildefonso Díaz; Sébastien Martin. On the instantaneous formation of cavitation in hydrodynamic lubrication. Comptes Rendus. Mécanique, Volume 334 (2006) no. 11, pp. 645-650. doi : 10.1016/j.crme.2006.08.003. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2006.08.003/

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