Modification of response and suppression of vortex-shedding in vortex-induced vibrations of an elliptic cylinder

摘要

Numerical experiments are performed at a Reynolds number, Re of 100 to explore in two-dimensions, the un-damped, transverse-only vortex-induced vibrations of a rigid elliptic cylinder of aspect ratio 0.5. With major axis oriented parallel to the flow, the cylinder behaves as a streamlined object. The mass ratio of the oscillator is 10. Re is based on the length of the major axis. The reduced speed, U* is varied from 1 to 8. The lock-in initiates at U* = 3.5 and is soft in nature. The extent of lock-in gets severely truncated as compared to the one for a bluff oscillator; it spans just over an extremely narrow U* range of 3.5 to 4.2. The onset and closure of lock-in are marked with the oscillation frequency attaining its maximum and minimum, respectively. Streamlining of oscillator eliminates the whole of initial, quasi-periodic lower and desynchronization components of response. The response consists of a fragile periodic lower branch stretching over the range of lock-in and bracketed by a dominant pair of steady state regimes. The occurrence of peak response is noted at the onset of lock-in and the peak value is about 0.06 times the length of major axis. A closed standing wake characterizes the steady regimes while periodic vortex-shedding relates to the lower branch with weak vibrations. Interestingly, even in the steady regimes, the reduced speed is found to influence the surface pressure whereas global quantities like drag and lift forces remain invariant. In the lower branch, the mean surface pressure exhibits symmetry about base, thus mean lift disappears and wake mode is the basic anti-symmetric 2S. At the onset of lock-in, the instantaneous surface pressure is noticeably asymmetric along the upper and lower surfaces. Thus, vortex-shedding is strong and r.m.s. lift high. With rising U*, the strength of shedding decays, asymmetry of instantaneous pressure about the base weakens and consequently, r.m.s. lift falls. At U* = 4.3, the free shear layers turn straight, shedding gets suppressed and the regime of steady state recovers.