Experimental study of wake-induced vibration response in a flexibly mounted tandem cylinder system with a prescribed dynamically oscillating upstream cylinder

The wake-induced vibration (WIV) of a flexibly mounted circular cylinder, positioned in tandem with an upstream circular cylinder, is investigated through experimental analysis. The upstream cylinder undergoes forced oscillations with a peak-to-peak amplitude of 0.5 times the cylinder’s diameter ($D$) and frequencies ranging from 0.5 to 2 times the natural frequency of the downstream cylinder. By imposing a prescribed motion on the upstream cylinder, this study diverges from conventional investigations of WIV in tandem cylinder arrangements. In our approach, the downstream cylinder responds to a wake characterized by independently controlled dynamics – such as wake width and shedding frequency – distinct from the geometry and inherent characteristics of the source cylinder. This study examines oscillation amplitudes, frequencies, and flow forces in a reduced velocity range of $U^{\ast }$ = 2.9 – 18.0, corresponding to Reynolds numbers of 650 to 3500, across various center-to-center spacings of $S/D$ = 4, 6, 8. Qualitative and quantitative flow field assessments are conducted using hydrogen bubble imaging and a volumetric Particle Tracking Velocimetry (PTV) technique, respectively.

The dynamic response shows that the downstream cylinder experiences WIV for each forcing frequency ratio. Due to the distinct wake dynamics created in each case, the downstream cylinder experiences continuous large-amplitude oscillations persisting to the highest reduced velocity tested at a frequency ratio of 1. At a frequency ratio of 2, the onset of oscillations is delayed to higher reduced velocities. The frequency contents of the observed oscillations directly correspond to the prescribed upstream motion, indicating the detection of the incoming wake. The wake structure developed downstream shows a strong dependence on the dynamic characteristics of the upstream cylinder. A Q-criterion analysis reveals the dominant structures prevailing downstream of the tandem pair and their three-dimensional nature. Additionally, a spatiotemporal mode analysis using the proper orthogonal decomposition technique elucidates the coherent vortical structures responsible for the various downstream cylinder responses observed in each upstream condition.