Rotational Oscillations of a Cylinder with a Stabilizer in a Gas Flow

A mathematical model for describing the rotational oscillations of a cylinder with a stabilizer in an air flow is considered. The equation for the motion of a cylinder with a stabilizer contains moments of aerodynamic forces and suspension resistance. The Krylov–Bogolyubov method is used to reduce the equation to a system of two ordinary differential equations for a slowly varying oscillation amplitude and phase. Solutions are found that correspond to steady-state oscillations with a constant amplitude. The model predicts that the dependence of the squared oscillation amplitude is a linear function of the reciprocal velocity of the air flow. The Strouhal number of cylinder oscillations is a linear function of the squared amplitude and, hence, the dependence of the Strouhal number on the reciprocal velocity is also linear. In a wind tunnel, experiments are carried out to test the model predictions. The predictions of the mathematical model are compared with the results of the experiments carried out in the wind tunnel. In the experiments with the oscillating cylinder, a laser pointer is attached to the aft part of the cylinder, with its beam crossing the surface of the photodiode as the cylinder rotated. The photodiode signal is recorded by a Velleman PCS500A PC oscilloscope connected to a personal computer. Decoding the signal allows the period and amplitude of the oscillations to be determined. The experiments confirm the predictions of the mathematical model.