A new approach to formulating the JFO cavitation model for hydrodynamic lubrication problems

Abstract The Jakobsson–Floberg–Olsson (JFO) cavitation models proposed by different authors have subtle differences in governing equations and unknowns, which often leads to confusion. To address this, this study introduces a general lubrication model to reformulate them. The general lubrication model was developed from the perspective of gas–liquid two-phase flow. Using this model, the Elrod, Payvar, and Ausas algorithms, along with their optimized variants, were re-derived. This re-derivation provides a consistent derivation process for the three cavitation algorithms with clear explanations and demonstrates that the Elrod and Payvar algorithms are based on the monotonic continuity condition, while the Ausas algorithm relies on if-else statements within loops. The equivalence, efficiency, and stability of the optimized Elrod, Payvar, and Ausas algorithms were numerically analyzed using cases of journal and thrust bearings. The results showed that the three algorithms provided almost consistent results; however, the Ausas algorithm exhibited higher efficiency and stability compared to the Elrod and Payvar algorithms. The difference in efficiency depended on the specific problem; for the current cases, it ranged from 1.0 to 1.9 for different relaxation factors. From a practical perspective, the three algorithms can be freely selected according to the user’s preferences because these differences become negligible in small-scale problems. In addition, the optimized algorithms are preferable to the original versions due to their improved stability and accuracy, as the decoupled velocity term offers additional benefits for numerical solutions.