Numerical studies of a freely vibrating cylinder in a cross-flow

A numerical method with four different components is used to simulate the flow-induced vibration at the mid-span of a long slender cylinder, simply supported at both ends, and placed in a uniform cross-flow. The incompressible laminar flow, which is assumed to be two-dimensional, is calculated using a finite element method and the cylinder motion is analysed by a two-degree-of-freedom model (or a spring-damper-mass model). The fluid-cylinder interaction is resolved by an iterative time marching method and the calculated time series are analysed by the ARMA technique. The cases examined include stationary as well as freely vibrating cylinders in a cross-flow. In the vibrating cylinder case, resonance and off-resonance situations are considered. Comparisons are made with experimental measurements for stationary cylinders as well as for a freely vibrating cylinder at off-resonance. The reduced velocity examined varies from 3.6 to 9.2, corresponding to a Reynolds number (Re) range of 2000-5000. At least two different mass ratios and two different reduced damping parameters are investigated. The numerical method is capable of replicating the Strouhal number correctly in the Re range investigated. A comparison of the calculated cylinder dynamics with measurements tends to support the results obtained using the present approach. This is true for both stationary and freely vibrating cylinders over the range of parameters considered. Therefore, the present numerical approach can be used to analyse flow-induced vibration problems in the range of parameters investigated, in spite of the fact that the wake flow is three-dimensional and turbulent.