Static and dynamic performances of refrigerant-lubricated bearings

For years now, gas bearings are successfully used over a large panel of turbo-machineries. Some of these systems are bound to be run in controlled environments such as refrigerating gas. In this work we present a theoretical and numerical model which takes into account the vapor/liquid lubricant transition, the laminar/turbulent flow transition and both temperature and viscosity 3D variations in the fluid and the solids for both static and dynamic situations. This model involves: the resolution of the generalized Reynolds equation for compressible fluids with 3D variable viscosity, the description of the turbulence effects by the phenomenological approach of Elrod, using a 3D eddy viscosity field, the resolution of a non-linear equation of state for the lubricant, able to describe the vapor/liquid transition and a local thermal approach to obtain a 3D estimation of the fluid temperature, thanks to the thin-film energy equation. The thermal effects in solids are also taken into account. In this study, we showed the importance of an accurate description of the film parameters, which variations largely influence the bearing behavior. Among the principal theories, there are: compressible lubricant, with an appropriate non-linear behavior when close to the vapor/liquid transition, vapor/liquid transition and calculation of the mixture equivalent parameters, turbulent flow for high-speed GFBs with a 3D eddy viscosity mode, a 3D behavior for viscosity, particularly the cross-film variations, (temperature dependent)and a 3D behavior for temperature, particularly in cross-film direction in order to be consistent with viscosity, but also in the axial direction in order to account for potential temperature gradient which considerably modifies the bearing 3D temperature profile. Both static and dynamic behaviors of GFBs are analyzed.