A three-dimensional numerical investigation of vortex induced vibration of a step cylinder

Abstract

The vortex-induced vibration of a step cylinder comprising two coaxially arranged cylinders of different diameters with a step between them is simulated numerically. The purpose is to investigate the impact of the interaction between the two cylinders on the vibration and the wake mode of the step cylinder. In this study, the Reynolds number, diameter ratio, and mass ratio are fixed at 150, 0.5, and 2, respectively. Two distinct lock-in regimes are observed, which are named larger cylinder (LC) lock-in regime and smaller cylinder (SC) lock-in regime. In the SC lock-in regime (for reduced velocities between 2.25 and 2.75), the vortex shedding of the SC synchronizes with the vibration, while the vortex shedding of the LC does not. The lift coefficient of the LC has dual frequency components, a lower-frequency and smaller-amplitude component and a higher-frequency and larger-amplitude component associated with vortex shedding and vibration, respectively. In the LC lock-in regime (for reduced velocities between 4 and 7), the vortex shedding of the LC synchronizes with the vibration, while the vortex shedding frequency of the SC increases with increasing reduced velocity, with reduced velocities of 4 and 5 being exceptions, at which the vortex shedding of both the LC and the SC locks in with the vibration frequency. The dual lock-in at reduced velocities of 4 and 5 results in a periodic chainlike wake behind the step where all the vortices from the LC are linked together by N-N loops. At the reduced velocity of 7, a very small difference between the vortex shedding frequency of the SC and twice the vibration frequency causes a low-frequency beating of the lift coefficient. The wake is in the indirect mode with an N-cell in the SC lock-in regime but changes to the direct mode without an N-cell in the LC lock-in regime. It is confirmed that in either of the lock-in regimes, the lock-in cylinder excites the vibration, whereas the non-lock-in cylinder damps the vibration. The damping effect of the non-lock-in cylinder results in a vibration amplitude lower than that in the lock-in regime of a uniform lock-in cylinder.