Large eddy simulations and global stability analyses of an annular and cylindrical rotor/stator cavity limit cycles

Abstract

Although rotating cavity flows are essential components of industrial applications, their dynamics is still largely misunderstood. From computer hard-drives to turbopumps of space launchers, designed devices often produce flow oscillations that can destroy the component prematurely, or produce disturbing noise or undesired operating modes of the system. The fundamentals of encountered static and rotating flow boundary layers have evidenced, a long time ago now, the presence of specific boundary layer instabilities and structures for low Reynolds numbers. For higher Reynolds numbers and fully enclosed systems, features are, however, more complex with the apparition of multifrequency oscillations populating the entire cavity limit cycle. For these flows, Large Eddy Simulation (LES) has illustrated the capacity of reproducing features and limit cycles. However, identifying the origin and region within these flows that are responsible for mode selections remains difficult if not impossible using such computational fluid dynamics tools. The present contribution evaluates a LES and a global stability analysis framework to identify the mechanisms responsible for the observed limit-cycles of two types of rotor-stator cavities. In particular, the presence of a central body or shaft and its impact on the instability selection is of interest here, i.e., the identification of the regions of mode activation for a cylindrical as well as an annular cavity is detailed. Results issued by the conjunct use of dynamical mode decomposition and Global Linear Stability Analysis (GLSA) confirm the observed LES dynamics. Most importantly, GLSA gives access to the triggering mechanisms at the root of the limit-cycles expression as well as hints on the mode selection. In that respect, a cylindrical cavity is shown to sustain more complex features than an annular cavity because of an enhanced flow curvature near the central shaft.