Unsteady fluid dynamic forces acting on a single row of cylinders vibrating in a cross flow

Abstract

This paper examines the vibrational characteristics of a single row of three circular cylinders, of small aspect ratio (1-93), subjected to a water cross flow, and clarifies the unsteady fluid force acting on the cylinders. The cylinder system, having a pitch-to-diameter ratio of 1.33 and mass-damping parameter of about 0-5, exhibits two kinds of instability, i.e., an out-of-phase mode instability and an in-phase mode instability, occurring at the low, reduced velocity of 2.9 and the high, reduced velocity of 12.6, respectively. An unsteady fluid force, measured by forcing the central cylinder to oscillate sinusoidally in water at the natural frequency of the two nearby cylinders which are free to vibrate, reveals a phase-lead of the force with respect to displacement. This phase-lead reaches about 30 degrees, for an oscillation amplitude of 10% of the cylinder diameter. Wake flow patterns show an oscillation of the flow separation points with a phase-lead to the cylinder motion; this may be considered as a major reason for the phase-lead of the unsteady force to displacement, generating, in turn, a negative damping in the cylinder system.