Predictions of fluctuating lift on a transversely oscillating square-section cylinder

Abstract

Two mathematical models are examined in an attempt to explain the behaviour of the fluctuating normal force induced by the transverse oscillation of a square-section cylinder in flow. When the cylinder is at rest, the approaching flow is normal to one of its faces. The models used are the quasi-steady theory of galloping due to Parkinson and unsteady aerofoil theory. The validity of both models is assessed by comparing predictions of the unsteady side force at the oscillation frequency and the phase angle between the side force and displacement with the authors' own experimental measurements. The quasi-steady theory is found to predict the experimental data well at high reduced velocity but, as expected, due to the influence of vortex shedding and fluid inertia forces, does not follow the data so well at intermediate to low reduced velocity. The unsteady aerofoil theory, on the other hand, by making some allowance for shed vorticity and fluid inertia forces, is found to model the flow over a larger range of the ratio of reduced velocity to dimensionless amplitude of oscillation, Ur/(A/D), with 26 being the approximate lower bound. Neither model is able to predict accurately conditions in the vortex lock-in regime.