Wake oscillator modeling the combined instability of vortex induced vibration and galloping for a 2:1 rectangular cylinder

Reasonable success has been obtained in the literature using Tamura’s nonlinear wake-oscillator model to predict the combined instability arising from the interference of vortex induced vibration and galloping. However, the physical arguments concerning the near-wake behavior, which is a strong point of this model, have never been carefully examined for sharp-edged bluff bodies. This is tackled here, referring to a rectangular cylinder with a side ratio of two, which is known to be very prone to this type of instability, and for which new static and aeroelastic wind tunnel tests are carried out. Therefore, a few physically sound modifications of the equations are proposed and, based on flow measurements, the new version of the model is found to perform considerably better than previous formulations with respect to the local-effect equation, which links the Strouhal number and the characteristic length scales of the wake. Moreover, after a successful attempt to relate the near-wake geometric parameters of the model to specific and measurable wake length scales, a novel method is presented for a direct estimation from wake flow measurements of the key parameter f relating the unsteady force and the wake lamina rotation. This allows the derivation of all the aerodynamic parameters of the model from measurements on the stationary cylinder based on their physical meaning. Nevertheless, f is also calibrated through a set of aeroelastic tests for a high Scruton number. The two approaches provide consistent results, although the calibration procedure yields a somewhat larger value of f, slightly enhancing the prediction capabilities of the model, which are carefully assessed comparing the results with wind tunnel data for a wide range of Scruton numbers. This discrepancy can be explained based on some unconsidered effects in the wake-oscillator model, which are also discussed as a basis for a future development of Tamura’s model.