Two tandem cylinders of different diameters in cross-flow: flow-induced vibration

Abstract

This paper presents a systematic study of the cross-flow-induced vibration on a spring-supported circular cylinder of diameter $D$ placed in the wake of a fixed cylinder of smaller diameter $d$. The ratios $d/D$ and $L/d$ are varied from 0.2 to 1.0 and from 1.0 to 5.5, respectively, where $L$ is the distance between the centre of the upstream cylinder to the forward stagnation point of the downstream cylinder. Extensive measurements are conducted to capture the cylinder vibration and frequency responses, surface pressure, shedding frequencies and flow fields using laser vibrometer, hot-wire, pressure scanner and particle image velocimetry techniques. Six distinct flow regimes are identified. It has been found that a violent vibration may erupt for the spring-supported cylinder, and its dependence on $d/D$ and $L/d$ is documented. A careful examination and analysis of the flow structure, along with the simultaneously captured pressure distribution around and vibration of the downstream cylinder, cast light upon the mechanisms behind this vibration and its sustainability. The roles of added mass, flow-induced damping and physical aspects in the process of initiating the vibration are discussed in detail.