On the orbital response of a rotating cylinder in a current

A new form of dynamic response has been observed in some simple experiments with a lightly damped rotating cylinder in a current. The response is orbital with a period several times the structural natural period and an amplitude ranging up to many diameters. It is mainly dependent on the ratio of current velocity to cylinder surface velocity, α, and the reduced velocity, V r (the ratio of current velocity to the product of natural frequency in water and diameter). Big orbital responses occur with 0.25 < α < 0.5 and V r > 5, and are accompanied by the expected large static response. To understand the flow mechanisms causing this response computational simulations have been made for two-dimensional laminar flow and the experimental response characteristics are qualitatively reproduced. Streamline and vorticity contour plots are output through a cycle and are related to instantaneous values of lift and drag coefficients and α (all based on flow relative to the cylinder). The movement of the stagnation point away from and towards the cylinder surface with intermittent wake formation in a cycle causes a large lift variation which is mainly responsible for the dynamic response. The variation of lift coefficient with α (as defined above) shows a generally negative gradient, and a pronounced hysteresis loop when substantial response occurs for α [gsim ] 0.25. The computations show that a small-amplitude, high-frequency response may also be superimposed on the high-amplitude, low-frequency response, most noticeably for α [lsim ] 0.25. This is consistent with a simple potential-flow idealization of the lift force. For α ∼ 0.2 a large dynamic response, not observed in the experiments, was produced in the computations due essentially to attached boundary-layer behaviour.