Flow-induced vibration of a trapezoidal cylinder at low Reynolds numbers

Abstract

This paper discusses the flow-induced vibration of a freely vibrating trapezoidal cylinder with a mass ratio of 10 at low Reynolds numbers (Re = 60–250). Over this range of the Reynolds number, we discuss the inflow and transverse amplitudes, frequency ratios, hydrodynamic forces, phase differences, and vortex modes. Comparing to square/circular cylinders with the same flow conditions, responses of the trapezoidal cylinder are much different. In both the vortex-induced vibration (VIV) and galloping regimes, double rise-up of the amplitudes and hydrodynamics forces is observed with respect to Re, as well as the two lock-ins for the frequency ratios. The phase differences and vortex modes in the wake are also found to be different from the square/circular cylinders. Thus, seven flow branches are identified, i.e., the initial branch, upper branch, lower branch, desynchronization region, initial galloping, upper galloping, and high galloping. Then, in order to interpret these branches, the evolutions of vortex formation and shedding in the wake are analyzed. It appears that the asymmetry of the trapezoidal cylinder to the inflow is the direct cause. In addition, a small degree of hysteresis is observed in the VIV regime and a larger degree is observed in the galloping regime.