A stable numerical strategy for Reynolds-Rayleigh-Plesset coupling

TL;DR

This paper introduces a stable numerical method for coupling Reynolds and Rayleigh-Plesset equations, addressing stability issues in cavitation simulations of lubricated devices, and validates it on two physical scenarios.

Contribution

A new stable numerical strategy for Reynolds-Rayleigh-Plesset coupling that overcomes stability issues of previous staggered approaches.

Findings

The new method is stable in cavitation simulations.

It accurately models decompression wave propagation.

It compares favorably with the Elrod-Adams model in journal bearings.

Abstract

The coupling of Reynolds and Rayleigh-Plesset equations has been used in several works to simulate lubricated devices considering cavitation. The numerical strategies proposed so far are variants of a staggered strategy where Reynolds equation is solved considering the bubble dynamics frozen, and then the Rayleigh-Plesset equation is solved to update the bubble radius with the pressure frozen. We show that this strategy has severe stability issues and a stable methodology is proposed. The proposed methodology performance is assessed on two physical settings. The first one concerns the propagation of a decompression wave along a fracture considering the presence of cavitation nuclei. The second one is a typical journal bearing, in which the coupled model is compared with the Elrod-Adams model.