Multiple regimes of lock-in and hysteresis in free vibration of a rotating cylinder

Abstract

Flow-induced vibration of a rotating cylinder that is free to oscillate in the stream-wise and cross stream directions is studied in the laminar flow regime via linear stability analysis (LSA) and direct time integration (DTI). LSA reveals that the instability can arise from fluid-, elastic-, or coupled fluid-elastic modes depending on the rotation rate of the cylinder, α, and reduced speed, U*. Beyond α=2, the U*-range of lock-in increases exponentially with an increase in α. DTI brings out the multiple regimes of lock-in at various α. Each lock-in regime extends for a certain range of U* and is associated with a different mode of vortex shedding. The modes differ in terms of the number of pair of vortices shed during each cycle of cylinder oscillation. The amplitude of cylinder oscillation increases with an increase in the number of shed vortices. With an increase in Re, the number of vortex shedding modes increase. Vortices are generally shed during the upstream movement of cylinder, while the shear layer wraps around it resulting in large lift during the downstream motion. The flow as well as the oscillation amplitude is found to be sensitive to the initial condition for a certain range of α and U*. A flow regime is discovered where three distinct response states can be realized depending on the initial condition. Hysteresis in response to the cylinder and flow, with respect to increase and decrease in U*, occurs near the transition between lock-in and desynchronization and during the switch in the mode of vortex shedding.