Wake modes behind a streamwisely-oscillating cylinder at constant and ramping frequencies

Abstract

studied at Reynolds number Re = 360–460 which are observed by laser-induced fluorescence flow visualization technique. The forcing frequency fe ranges from 0 to 6.85 fs , where fs is the vortex shedding frequency behind a stationary cylinder, and the forcing amplitude A=d ¼ 0:2; 0:5; 1:0, where d is the cylinder diameter. Both time-invariant and linearly ramping fe are investigated. Following our previous modal notation, the following conclusions can be drawn: firstly, three rarely reported modes in numerical studies, C-I, C-II and S-III, are now confirmed in experiments (though with differentiable appearance in their far wake behaviour) at higher A and/or fe ranges and the envelope lines of S modes and C modes, yielded from a vortex circulation model, are shown to be dependent on the peak relative velocity of the free stream to the cylinder surface. So is the occurrence of the S-II mode. Secondly, near the demarcation of A modes and S-I mode, wake mode undergoes constant transition in a stochastic manner at fixed Re, A and fe. Thirdly, a typical hysteretic effect can be observed when the oscillation frequency of the cylinder ramps up and down in a linear way, and the extent of delay is dependent on the ramping rate k. Finally, mode switching during frequency ramping obeys a unidirectional order. During k\0 (ramp-down), when S-I (Type-II) mode switches to A-IV mode, or A-IV to A-III, the flow structure downstream is affected by the upstream and the entire wake flow eventually switched, which is classified as slow switches. In contrast, during k[0 (ramp-up), a clear and abrupt switch can be observed in the wake when A-IV or A-III switch to S-I (Type-II) modes, which are jump switches.