Development and application of multiphysics simulation tools for foil thrust bearings operating with carbon dioxide

Abstract

Foil bearings can enable different turbomachinery architecture. The use of the cycle’s working fluid within the bearings results in an oil-free and compact turbomachinery system. Using CO2 as the operating fluid for a foil bearing creates new operating and new modelling challenges. These include turbulent flow within the film, non-negligible inertia forces, high windage losses, non-ideal gas behaviour and reduced rotordynamic damping. Since the flow phenomena within foil bearings are complex, involving fluid flow, structural deformation and heat transfer, use of the conventional Reynolds equation is not proven to be suitable for foil bearings with CO2 as the operating fluid. To address these modelling issues, a multi-physics multi-timescale simulation tool including fluid, structure and thermal solvers was developed to predict the performance of foil bearings and to create insight on their operations with CO2. New flow physics and operation challenges for foil thrust bearings with CO2 were built and described in details next.To model the fluid flow within foil bearings, the modifications of the in-house computational fluid dynamics solver are first presented to enable laminar simulations within foil bearings. To reduce the computational cost for turbulent simulations, a compressible wall function is implemented. The checker-boarding effect, due to the high aspect ratio cell is eliminated by a fourth-order artificial dissipation term, while maintaining the second order spatial accuracy. These modifications result in a fast and stable solver for turbulent simulations of CO2 foil thrust bearings without contaminating the flow field. For the fluid-structure simulation, the in-house computational fluid dynamics solver is modified by implementing a moving grid capability. This capability is validated with inviscid, viscous and turbulent flow cases. A separate bespoke finite difference code based on the Kirchhoff plate equation for the circular thin plate is developed in Python to solve the structural deformation within foil thrust bearings. A fluid-structure coupling strategy and the corresponding mapping algorithm are employed for steady state and time-accurate transient simulations.Using the developed fluid-structure simulation tool, the steady state performances of foil thrust bearings with CO2 are investigated. The centrifugal inertia effects are found to be significant for foil thrust bearings with CO2. In the ramp region, they generate an additional inflow close to the rotor inner edge, resulting in a higher peak pressure. Contrary in the flat region, the inertia force creates a rapid mass loss through the bearing outer edge, which reduces pressure in this region. These different flow fields alter bearing performance compared to conventional air foil bearings. Conventional Reynolds equation cannot account for the irregular radial velocity profiles that are driven by strong inertial effects. In addition, the turbulence effects increase load capacity and power loss simultaneously. The steady state simulations indicate that both load and power loss increase linearly with the decreasing rotor to top foil separations and the increasing rotational speeds. A slower rate is observed for power loss. The rotational speed has a larger effect on power loss compared than the rotor to top foil separations.Finally, a heat conduction solver is added to the fluid-structure simulation tool. This results in a multi-physics multi-timescale tool for the fluid-structure-thermal simulation. The coupling strategy is then proposed and validated with different test cases. The heat transfer models of the solid structures within foil thrust bearings are discussed. Numerical simulations of foil thrust bearings with air and CO2 are performed at the same load condition. It is found that foil thrust bearings with CO2 significantly benefit from increased convective cooling on the rear surface of the rotor, if the rotor operates in a high pressure CO2 environment. The centrifugal pumping that naturally occurs in CO2 bearings due to the high fluid density provides a new and effective cooling mechanism for the CO2 bearing. The fluid-structure modelling approach is found to applicable at the rotational speed less than 30 000 rpm. However, the thermal solver has to be included when foil bearings are operating at higher rotational speeds. This is due to the large deflection caused by thermal stresses.This project is the first work of its kind to use the high fidelity multi-physics multi-timescale simulation tool to simulate foil thrust bearings with CO2. The results reveal new flow physics, steady state performances of foil bearings at different operating conditions.