Incorporation of turbulence in a nonlinear wake-oscillator model for the prediction of unsteady galloping response

The aeroelastic behavior of certain slender bluff bodies is known to be dominated in smooth flow by the interference of vortex-induced vibration and transverse galloping. In turbulent flow, wind tunnel experiments revealed a more complicated behavior, with some features that have not been fully understood yet. With the aim to explain the oscillation response observed for a sharp-edge rectangular cylinder with a side ratio of 1.5 and to make a step ahead in the simulation of the self-excited behavior of such bodies, a nonlinear wake-oscillator model that provided promising results in smooth flow is considered. The differential equations are randomized to account for the contribution of three-dimensional, partially-correlated, turbulent velocity fluctuations attacking the structure. Given the physical basis of the mathematical model, all the parameters but one are estimated based on wind tunnel tests on a stationary sectional model. In contrast, given the lack of wake measurements, one of the coupling coefficients in the equations is calibrated based on the cylinder response for a given value of the nondimensional mass-damping parameter (Scruton number). Then, the model is used to predict the vibrations recorded for very different values of the Scruton number, showing satisfactory accuracy. This fact highlights the key role played, even in turbulent flow, by vortex shedding and the importance of its nonlinear interaction with oncoming wind velocity fluctuations. The equations are also used to investigate the effect of turbulence intensity and integral length scale. In agreement with the experimental evidence, the response of the cylinder is found to be little sensitive to flow velocity fluctuations with small intensity (say, less than about 4%), but is remarkably affected by strong turbulence. The simulations also disclose a significant influence on the vibration amplitude of the integral length scale of turbulence. Finally, the proposed model might represent a useful engineering tool to estimate the unsteady galloping behavior of a slender structure immersed in a realistic large-scale turbulent flow, which seldom can be correctly reproduced in the wind tunnel.