A Mass-Conserving Complementarity Formulation to Study Fluid Film Lubrication in the Presence of Cavitation for Non-Newtonian and Compressible Fluids

A mass-conserving formulation of the Reynolds equation has been recently developed using the concept of complementarity [1]. The mathematical derivation of the Linear Complementarity Problem (LCP) implemented in the solver favoured in [1] overcomes the drawbacks previously associated with the use of such complementarity formulations for the solution of cavitation problems in which reformation of the liquid film occurs. In the present paper, the proposed methodology, already successfully applied to solve textured bearing and squeeze problems in the presence of cavitation in a one dimensional domain and for incompressible fluids [1], has been extend to a two dimensional domain and the fluid compressibility has been included in the formulation. The evolution of the cavitated region and the contact pressure distribution are studied for a number of different configurations. Some of the results obtained with the proposed scheme are critically analysed and compared with the predictions obtained using alternative formulations (including full CFD calculations). The stability of the proposed algorithm and its flexibility in terms of the implementation of different compressibility laws is highlighted.