A new cavitation model in lubrication: The case of two-zone cavitation
Résumé
A generalization of the Elrod-Adams model of cavitation in lubricated devices is proposed, such that the translation velocity V for the saturation field θ can be given any value between S/2 and S, with S being the relative speed of the surfaces. The lack of uniqueness of the classical model when V≠S/2 is explained and a suitable supplementary condition is proposed to fix this issue. The new model is rigorously analyzed, though in the simplified mathematical setting of a one-dimensional problem with a single pressurized region. The main result states the existence of a unique solution globally in time, unless of course the cavitation boundary leaves the domain or disappears. A few preliminary numerical examples are included to illustrate the model.