Comparison of Modelling Approaches for Bump-Type Foil Thrust Bearings Operating With CO₂

Different forms of Reynolds equation are widely used to predict the performances of foil thrust bearings for air cycle machines. When analyzing bearings operating with highly dense CO₂, computational fluid dynamics yields more accurate results, particularly at the high rotational speed. In addition, the structural deformation of the top and bump foils are also considered. For some applications, the high temperature increase caused by the viscous heating effect are also modelled in literature. The multi-physics effects within foil bearings, including the fluid flow, structural deformation and viscous heating create challenges and modelling complexity to accurately predict its performances. The aim of this paper is to review and compare different modelling approaches for foil thrust bearings with CO₂ at a range of operating conditions, including loads and rotational speed. For steady state performances, results from turbulent Reynolds equation and computational fluid dynamics are in close agreement for foil thrust bearings operating with low load (large rotor to top foil separations). However, considerable differences exist between turbulent Reynolds equation and computational fluid dynamics method at high loads (small rotor to top foil separation). Here the computational fluid dynamics method must be employed, as the centrifugal inertia effect becomes significant. The top foil deflection need to be considered as the corresponding deformation is significant compared to the initial separation between the rotor and the top foil. At the rotational speed larger than 30000 rpm, the results from the fully fluid-structure-thermal simulations differ from other modelling approaches. The additional deformation caused by temperature increase largely alters the separation between the rotor and top foil. For dynamic performance, the top foil deflection again must be considered as the equivalent stiffness and damping are influenced by bump foil structures. This work provides recommendations for the selection of the suitable modelling approaches for bump-type foil thrust bearings operating with supercritical CO₂.