A circular cylinder, mounted on lightly damped springs, is allowed to vibrate in both in-line and cross-flow directions. Computations have been carried out for Reynolds number in the range 300-10^4. In most of the cases the trajectory of the cylinder corresponds to a Lissajou figure of 8. Lock-in is observed for a range of values of the structural frequency. Over a certain range of structural frequency (Fs), the vortex-shedding frequency of the oscillating cylinder does not match Fs exactly; there is a slight detuning. This phenomenon is referred to as soft-lock-in. In certain cases the oscillations of the cylinder result in a change in the vortex shedding mode and sometimes in a competition between the various modes. Figure 7 shows the flow field at a certain time instant for Re=1000, Fs=0.60.
Flow past a
pair of cylinders in tandem and staggered arrangements for Re=100 and 1000
reveal the effect of the unsteady wake on the downstream cylinder. Since
the spacing between the two cylinders is beyond the critical value for
proximity interference, it is expected that the upstream cylinder behaves
like an isolated single cylinder while the downstream one experiences wake-induced
flutter. The Re=100 flow leads to a very organized wake and large amplitude
motion is observed for the downstream cylinder. The wake looses its temporal
periodicity, beyond a few diameters downstream of the front cylinder, for
the Re=1000 flow. The upstream cylinder continues to respond as an isolated
single cylinder while the downstream one undergoes slightly more disorganized
motion. {\it Soft-lock-in} is observed in almost all the cases. Figure
7 shows the vorticity field for the two cylinder case that are initially
arranged in tandem and with the Fs of each cylinder equal to the vortex
shedding frequency of the stationary cylinders in the same arrangement
(=0.168). These studies form part of a project sponsored by DST.