Complete Secondary Flow Formulation for Thermohydrodynamic Analyses of Multiple Foil Bearings Lubricated With Non-Ideal Gases

Abstract Foil bearings are one of the candidates as oil-free bearing technology for small expandable turbojet engines or high-speed spool of small turbo fan engines below engine thrust below 22,500N (5000lb). Corrugated bump foils are the most popular underlying structure for the foil bearing providing stiffness and damping to the bearing. The bump foil flow resistance has been modeled using experimentally measured Darcy friction factors for the typical bump foil channels in the previous work. The flow resistance model of the bump foil bearings and flows around the bearings (leakage, leading edge groove flows, etc) were implemented to overall secondary flow network for a system incorporating multiple foil bearings. The secondary flow network model was proven very effective to find various cavity pressures along the secondary flows. For complete analysis of thermal behavior of foil bearings and the whole system, the flow network model developed in the previous work has to be combined with energy equations applied to the each secondary flow cavity to solve not only cavity pressures but also cavity temperatures. The energy balance equations for each cavity include not only enthalpy flux associated with all the secondary flows and bump channel flows and convective cooling of rotating surface exposed to the secondary flow paths. This paper presents complete mathematical formulations for the secondary flow temperatures compatible to the mass balance equations applied to the secondary flow cavities of typical turbojets and micro gas turbine rotors incorporating foil bearings. The formulations have been developed for general real gases, i.e., non-ideal gas with specific heat having strong dependency on both temperature and pressure.