A second-order in time and space model to solve the coupled Reynolds–Rayleigh–Plesset equations for the dynamics of cavitated hydrodynamic journal bearings

Abstract

Cavitation in hydrodynamic bearings is a fundamental factor in the behavior of the fluid film and in the equilibrium position the journal will have after the application of external loads. The calculation of these parameters by robust tools is an active research topic even though accuracy, stability and conservativeness are not so often discussed. This work shows the results obtained through the implementation of a novel model developed from first principles that allows characterizing the pressure field of a liquid–gas lubricant mixture avoiding the reported instabilities with the time derivative of the mixture density. The formulation also relies on a coupled transport equation describing the evolution of the liquid fraction, ensuring mass conservation. This model is applied to study cases with gaseous, vaporous or pseudo-cavitation through the use of the Rayleigh–Plesset equation to characterize the physical behavior of the bubbles formed taking into account the characteristic time of each phenomenon. High resolution schemes are used for the spatial treatment of the advection and a temporal discretization based on the Strang splitting method which allows for a second order convergence in space and time. The numerical results obtained are contrasted and discussed with experimental data found for static and dynamic bearings for the three types of cavitation mentioned, obtaining a very good agreement.