On quasi-steadiness of transverse galloping of rectangular cylinders at Reynolds numbers below 10,000

Abstract

Forced transverse oscillations are used to investigate the quasi-steady behavior of a rectangular cylinder with a side ratio of 2 at Reynolds numbers less than 10,000 (based on cylinder thickness). To this end, phase-averaged measurements of the transverse force acting on the oscillating cylinder at different phases of motion are compared to the mean force acting on the static cylinder at different angles of attack. The force data are complemented with boundary-layer-resolved measurements of the streamwise velocity using single-component molecular tagging velocimetry. The experiments are conducted for two Reynolds numbers of 2,500 and 7,500, two oscillation amplitudes of 20 % and 50 % of the cylinder thickness, and reduced velocities in the approximate range of 2–30 times the reduced velocity corresponding to the vortex shedding frequency. The results show that the reduced velocity threshold required to attain quasi-steady behavior is strongly dependent on Reynolds number in the investigated range. The effect is such that the lower the Reynolds number, the higher the threshold. This behavior is linked to viscous effects which render the shear layer too slow to adapt to the cylinder motion with decreasing Reynolds number. A most pronounced effect is observed at the lowest reduced velocity and Reynolds number, where the shear layer reattaches on the side of the cylinder during the cycle at an angle of attack less than half that exhibited for the static cylinder. Overall, the study shows that in addition to the time scale associated with vortex shedding, when the Reynolds number is sufficiently low, a viscous time scale characteristic of the shear layer dynamic response should be included in determining the validity of quasi-steadiness.