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

Abstract

Gasexpanded lubricants (GELs) have the potential to increase bearing energy efficiency, longterm reliability, and provide for a degree of control over the rotordynamics of highspeed 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 timetransient behavior of a highspeed compressor was evaluated numerically to examine the effects of rapidly changing bearing dynamics on rotordynamic performance. Two cases were evaluated for an eightstage 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 highspeed 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 steadystate thermoelastohydrodynamic (TEHD) bearing model, which provided bearing stiffness and damping coefficients as inputs to a timetransient rotordynamic model using Timoshenko beam finite elements. The displacements and velocities of each node were solved for using a fourthorder 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 worstcase 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.