Lower Mode Response of Circular Cylinders in Cross-Flow

Abstract

Transverse amplitude responses of a circular cylinder in cross-flow were determined as a function of reduced velocities for a variety of spring constants and damping coefficients. Maxima were found at reduced velocities of 5 and 16, and were of comparable amplitude. The first resonance, designated the “fundamental mode,” was due to normal vortex street excitation of the spring-mass system. The second resonance, designated the “lower mode,” occurred when the natural frequency was approximately one-third of the normal vortex shedding frequency. By assuming that the driving force was sinusoidal, it was possible to evaluate the lift coefficients at resonance. Lift coefficients for the lower mode behaved similarly with amplitude ratio but were an order of magnitude lower than lift coefficients for the fundamental mode. A mechanism was used to oscillate the cylinder transversely at prescribed frequencies and amplitudes. Dominant wake frequencies were determined from a frequency analysis of the hot-wire signal for a range of velocities and a fixed frequency of oscillation. It was found that synchronization of the shedding frequency to the forcing frequency did not take place for the lower mode. The familiar “lock-in” region, or frequency synchronization over finite bandwidth, was observed for the fundamental mode only. Since the frequency associated with normal vortex shedding was not suppressed when oscillations took place in the lower mode, it would seem that a low frequency vortex street had not replaced the normal one. It is likely, then, that the spring-mounted cylinder responded subharmonically to the exciting force resulting from vortex shedding. In this regard, however, it was curious that subharmonic response was not found at a frequency ratio of 0.5 as it was at 0.33. A conceptual model, which incorporated features of both the low frequency vortex street and subharmonic response, was developed which accounted for lower mode response at a frequency ratio of 0.33 as well as the lack of response at 0.5.