Numerical Modelling of Gas Foil Journal Bearings

Abstract

In the pursuit of reducing the climate impact of aviation, there has been an increased interest in the adoption of renewable energy technologies. Examples of revolutionary technologies include hydrogen fuel cell systems and waste heat recovery using the organic Rankine cycle. The design of viable energy conversion systems for aviation poses unique challenges in terms of efficiency, weight and size. To this end, research on small-scale turbomachinery operating at high rotational speeds is increasingly pursued in the context of, for example, fuel cell air compressors or organic Rankine cycle turbines. Such machines typically call for oil-free operation to avoid contamination of the process fluid. Gas foil bearings can prove to be an enabling technology due to their reliability, oil-free operation and compatibility with high rotational speeds.

The use of gas foil bearings to support organic Rankine cycle turbines requires lubrication with complex working fluids at operating conditions near the saturated vapour line or thermodynamic critical point. Although there has been an increased interest in high-pressure gas lubrication in recent scientific literature, there is still a lack of understanding of the effects of non-ideal compressible flows on the performance of (gas foil) journal bearings. In order to further address this knowledge gap, this work focuses on the modelling of such bearings lubricated with dense fluids made by complex molecules like those adopted for waste heat recovery at high temperatures in aviation.

The compressible Reynolds equation governing the thin-film flow within the bearing is discretized using a finite difference method. The solution to the non-linear problem is obtained using a relaxation method in which a thermodynamic software program updates the non-ideal thermodynamic state properties after each iteration. The load-carrying capacity of the bearing is obtained by integrating the resulting steady-state pressure field around the rotor shaft. A perturbation method is applied to obtain the stiffness and damping coefficients used in a linearized rotor-dynamic analysis. The developed computational tool allows for the analysis of bearing performance under varying operating conditions.

The conclusions of this work emphasize the challenge of generating sufficient load-carrying capacity and rotor-dynamic stability associated with high-pressure gas lubrication in journal bearings. Bearings operating with compressible lubricants near the thermodynamic critical point are typically characterized by turbulent thin-film flows with non-negligible molecular interactions. Reduced peak pressures within the gas film are anticipated, resulting in a reduced load-carrying capacity as compared to ideal gas lubrication flows. It is shown that non-ideal thermodynamic effects have an impact on rotor-dynamic stability by affecting the steady-state attitude angle of the bearing.

The modelling of a gas foil journal bearing used to potentially support the turbine of the organic Rankine cycle hybrid integrated device (ORCHID) of the TU Delft has finally been considered. The results show the utility of a numerical model in assessing bearing performance and understanding the associated physics. This work can be used as a basis for future analysis and design of gas foil journal bearings lubricated with high-pressure process fluids.