Vortex-induced oscillations at low Reynolds numbers: Hysteresis and vortex-shedding modes

Abstract

Results are presented for the numerical simulation of vortex-induced vibrations (VIVs) of a cylinder at low Reynolds numbers (Re). A stabilized space–time finite-element formulation is utilized to solve the incompressible flow equations in primitive variables. The cylinder, of low nondimensional mass ( m * = 10 ), is free to vibrate in, both, the transverse and in-line directions. To investigate the effect of Re and reduced natural frequency, F n , two sets of computations are carried out. In the first set of computations the Reynolds number is fixed ( = 100 ) and the reduced velocity ( U * = 1 / F n ) is varied. Hysteresis, in the response of the cylinder, is observed at the low- as well as high-end of the range of reduced velocity for synchronization/lock-in. In the second set of computations, the effect of Reynolds number ( 50 ⩽ Re ⩽ 500 ) is investigated for a fixed reduced velocity ( U * = 4.92 ). The effect of the Reynolds number is found to be very significant for VIVs. While the vortex-shedding mode at low Re is 2S (two single vortices shed per cycle), at Re ∼ 300 and larger, the P + S mode of vortex shedding (a single vortex and one pair of counter-rotating vortices are released in each cycle of shedding) is observed. This is the first time that the P + S mode has been observed for a cylinder undergoing free vibrations. This change of vortex-shedding mode is hysteretic in nature and results in a very large increase in the amplitude of in-line oscillations. Since the flow ceases to remain two-dimensional beyond Re ∼ 200 , it remains to be seen whether the P + S mode of shedding can actually be observed in reality for free vibrations.