Flow-Mediated Interaction Between a Forced-Oscillating Cylinder and an Elastically-Mounted Cylinder in Less Regular Regimes

Flow-mediated interaction between two immersed cylinders is relevant to various natural phenomena and engineering applications. Here, we study the interaction between an actively oscillating cylinder and an elastically- mounted passive cylinder. Both cylinders are rigid, of the same diameter and constrained to move along the two cylinders' centre line. This problem is simulated by an in-house finite-element solver. Six non-dimensional groups are chosen as input: the active cylinder's frequency 0.05 - 3.2 and amplitude 0.159 - 1.432, the passive cylinder's damping ratio 0 - 0.02 and mass ratio 2, the Reynolds number 35 - 315 and the gap distance 2.5. The resulting Keulegan-Carpenter number and the Stokes number are KC = 1 - 9 and β = 35, corresponding to the single-cylinder oscillating flow regimes A, C, E, F and G. In total, 2,176 combinations are studied. An increase in KC leads to higher irregularity and larger vibration amplitude of the passive cylinder. In regime C, the passive cylinder vibrates in a pulse-beating pattern due to the periodic switching of the streaming direction. In regime E, the passive cylinder responds with intermittent irregularity. In regime F, the flow structure switches intermittently among unrecognizable irregularities and 3 regular patterns resembling those observed in regimes C and E. In regime G, the flow is highly irregular and circular, where vortices shed from consecutive cycles can merge, forming a much larger one.