Stability and control of an annular rotor/stator cavity limit cycle

Abstract

Rotating cavity flows have been widely studied for years because of many implications that these have on industrial applications. These flows can indeed generate, under specific conditions, self-sustained oscillations that can be noisy or even dangerous for the integrity of a system. The coherent structures or flow modes composing this unsteady phenomenon usually called “pressure band phenomenon” are misunderstood and therefore difficult to control. In the present study, the dynamics of an annular rotor/stator cavity is investigated to shed some light on the flow organization and identify control strategies based on reliable theory and analysis to stabilize the observed undesired flow modes. No specific tool is known today to control a multi-frequency phenomenon. To address this first issue, the mode dominance and interactions appearing in this multi-frequency problem are investigated, thanks to dynamic mode tracking and control [M. Queguineur et al., “Dynamic mode tracking and control with a relaxation method,” Phys. Fluids 31, 034101 (2019)]. The benefit of this method is to be able to follow in time several modes while controlling them one by one and observe mode dominance and interactions. This purely numerical controller shows that, here, the dominant mode of the annular cavity is at the source of another low frequency mode. Based on this information and to develop a physically relevant control strategy, the global linear stability framework previously used by Queguineur et al. [“Large eddy simulations and global stability analyses of an annular and cylindrical rotor/stator cavity limit cycles,” Phys. Fluids 31, 104109 (2019)] is further developed to make use of the sensitivity to a base flow modification theory. This specific analysis indeed enables us to point out the exact location where the base flow should be modified to shift the dominant mode frequency and/or growth rate. In this context, passive controller positioning is identified for the studied annular cavity flow. Such strategies are then validated through new large eddy simulations of a controlled cavity using low amplitude injection/suction demonstrating the adequacy of the analysis and control strategy.