Validation of a Three-dimensional CFD Analysis of Foil Bearings with Supercritical CO2

Foil bearings are an integral part of oil-free turbomachines which have been selected as a potential technology to enable cost efficient Supercritical Carbon Dioxide Brayton cycle for solar power application. Using high pressure CO2 as the operating fluid means that within the film Reynolds numbers in the highly turbulent regime are observed, therefore, using traditional simulation tools, such as two-dimensional Reynolds equation, derived for simulating bearing operating with laminar flow is not appropriate. The resulting turbulence enhances hydrodynamic load capacity and increases frictional losses. In this study, some improvements such as moving wall and periodic boundary conditions to the UQ in-house CFD code Eilmer are presented. These are verified using Taylor-Couette flow, and axisymmetric and wavy Taylor vortices are simulated under different Taylor number. A hydrostatic air thrust bearing with steady-state behaviour is also studied, which shows good agreement with the results from modified Reynolds equation. Finally, a preliminary Three-Dimensional Computational Fluid Dynamic simulation of a foil bearings is presented. A rigid foil bearing is studied with ambient air and high pressure CO2 as operating fluid, respectively and the lift force and power loss are compared with the results from Reynolds equation. Introduction The supercritical CO2 (sCO2) closed Brayton cycle, which uses high pressure CO2 as its working fluid, is an alternative to conventional steam turbines, offering the potential for better overall economics due to a higher electrical conversion efficiency and lower capital cost. Dostal et al. [1] showed that the sCO2 cycle has a higher efficiency than the superheated steam cycle at temperatures above 470◦C, which makes it suitable for nuclear power applications. sCO2 cycle for solar thermal application has also been proposed [2, 3]. Before realizing sCO2 cycles, a number of challenges need to be overcome, making this an active area of research. The key components of this cycles (turbine, compressor, stators, bearings, seal) need to be re-studied due to the new working fluid and especially the non-linear behaviour exhibited by sCO2 [4, 5, 6]. Kuz et al. [4] studied one-dimensional design methodology for supercritical CO2 compressor and turbine. Pecnik et al. [5] presented a three-dimensional CFD study of the impeller of a centrifugal compressor operating with sCO2 in the thermodynamic region slightly above the vapor-liquid critical point. Kim et al. [6] provided CFD investigation of a centrifugal compressor with supercritical CO2 as working fluid, the steady-state numerical predictions using the k−ω SST model were found to return satisfactory results in the case of sCO2 operating condition, but the gas conditions were quite far from the critical point. However, besides these key components, sCO2 bearings design cannot be neglected. Many of early tests of sCO2 cycle at Sandia used ball bearings to allow for testing. However, the ball bearings were expected to have a limited lifetime that varies from 20 hours to 2000 hours depending on the thrust load that was assumed [7], and then the design also included the option to operate with gas foil bearings. Conboy [8] presented a preliminary study of foil bearing with high pressure CO2 as operating fluid, the Reynolds equation considering turbulence effect was solved, but the analysis of gas foil bearings was largely based on data reported by NASA Glenn Research Centre by DellaCorte and Bruckner [9], these correlations were developed for gases at low pressure and not for high pressure CO2. High pressure CO2 is far denser than air, less viscous compared to oil, and highly non-ideal, these factors present unique challenges in predictive modelling as compared to more conventional lubricants and applications, including the potential for turbulence in lubrication films. In order to better understand the fluid behaviour in bearing chamber, a three-dimensional Computational Fluid Dynamic analysis method should be developed and validated. This paper demonstrates the suitability of Eilmer [10] for bearings simulation by verifying and validating it against analytical or experimental results. Taylor-Couette flow is used to verify the Moving wall and periodic boundary conditions. Hydrostatic air thrust bearing is employed to study the suitability of Eilmer in simulating the centrifugal inertia effect. Wavy thrust bearins is then used to test the suitability of Eilmer in simulating the performance of bearings with a typical geometry.