Transient Analysis of Gas-Expanded Lubrication and Rotordynamic Performance in a Centrifugal Compressor

Abstract

Gas-expanded lubricants (GELs) have the potential to increase bearing energy efficiency, long-term reliability, and provide for a degree of control over the rotordynamics of high-speed rotating machines. Previous work has shown that these tunable mixtures of synthetic oil and dissolved carbon dioxide could be used to maximize the stability margin of a machine during startup by controlling bearing stiffness and damping. This allows the user to then modify the fluid properties after reaching a steady operating speed to minimize bearing power loss and reduce operating temperatures. However, it is unknown how a typical machine would respond to rapid changes in bearing stiffness and damping due to changes in the fluid properties once the machine has completed startup. In this work, the time-transient behavior of a high-speed compressor was evaluated numerically to examine the effects of rapidly changing bearing dynamics on rotordynamic performance. Two cases were evaluated for an eight-stage centrifugal compressor: an assessment under stable operating conditions as well as a study of the instability threshold. These case studies presented two contrasting sets of transient operating conditions to evaluate, the first being critical to the viability of using GELs in high-speed rotating machinery. The fluid transitions studied for machine performance were between that of a polyol ester (POE) synthetic lubricant and a GEL with a 20% carbon dioxide content. The performance simulations were carried out using a steady-state thermoelastohydrodynamic (TEHD) bearing model, which provided bearing stiffness and damping coefficients as inputs to a time-transient rotordynamic model using Timoshenko beam finite elements. The displacements and velocities of each node were solved for using a fourth-order Runge–Kutta method and provided information on the response of the rotating machine due to rapid changes in bearing stiffness and damping coefficients. These changes were assumed to be rapid due to (1) the short lubricant residence times calculated for the bearings and (2) rapid mixing due to high shear rates in the machine bearings causing sudden changes in the fluid properties. This operating condition was also considered to be a worst-case scenario as an abrupt change in the bearing dynamics would likely solicit a more extreme rotordynamic response than a more gradual change, making this analysis quite important. The results of this study provide critical insight into the nature of operating a rotating machine and controlling its behavior using GELs, which will be vital to the implementation of this technology.