Dynamics of a Cylinder Wake Under Controlled Excitation

This paper presents some results of experimental tests as well as a group theoretic analysis of a 2D cylinder wake under forced excitation. The response of the Karman wake (K mode) to external perturbations is studied. Reflection-symmetric (S mode) perturbations and asymmetric (K1 mode) perturbations are considered. The perturbations are generated by mechanically oscillating the test cylinder. Tests were done in a small wind tunnel. Depending on the excitation to Karman shedding frequency ratio, mode locked states, in the form of spatio-temporally fixed patterns, could be observed. Harmonic asymmetric (mode K1=K ) forcing at the Karman frequency strongly enhanced the Karman mode. Superharmonic forcing (with mode K1 ≠ K ) had little effect on the Karman mode K. However, a detuning effect was observed. On the other hand, subharmonic (1/2, 1/3) K1 mode forcing significantly affected the K mode, with strong response at K1 mode harmonics. Subharmonic S mode excitation had a damping effect on the K mode. On the other hand harmonic and superharmonic forcing triggered a period-doubling instability, destroying the original K mode. Using a group theoretic approach, the general amplitude equations governing the interaction of the S/K1 modes with the K mode have been derived. A qualitative analysis of the equations helps explains some of the experimental results. For K1/K mode interactions, the symmetrical ‘compatibility’, via common subgroups, explains the strong resonances observed experimentally for 1/1 and 1/3 frequency ratios. For a frequency ratio 1/2, it is shown that K1 and K mode symmetries are incompatible; the two modes do not have a common symmetry subgroup. Consequently, traveling wave solutions, induced by total symmetry breaking, rather than standard steady state modes are expected to be more likely to occur. For S/K mode interaction, an earlier result is reiterated; thus, the Karman mode is shown, theoretically, to be destroyed via a period-doubling instability. This effect occurs for S mode frequencies as high as 3 times the Karman frequency.Copyright © 2003 by ASME