Rotational oscillations of the cylinder with stabilizer in the gas flow

Abstract

A mathematical model for describing the rotational oscillations of a cylinder with a stabilizer in the air flow is considered. The equation of motion of a cylinder with a stabilizer contains moments of aerodynamic forces and suspension resistance. The Krylov - Bogolyubov method transforms the equation to a system of two ordinary differential equations for a slowly varying amplitude of oscillations and a phase. Solutions are found that correspond to steady-state oscillations with a constant amplitude. The model predicts that the dependence of the square of the oscillation amplitude is a linear function of the reverse velocity of the air flow. The Strouhal number of cylinder oscillations is a linear function of the square of the amplitude and, therefore, the dependence of the Strouhal number on the inverse velocity is also linear. In the wind tunnel, experiments were conducted that tested the model predictions. A comparison of the predictions of the mathematical model with the results of experiments conducted in a wind tunnel was made. In experiments with an oscillating cylinder, a laser pointer was attached to the aft part of the cylinder, the beam of which crossed the surface of the photodiode as the cylinder rotated. The photodiode signal was recorded by a Velleman PCS500A PC oscilloscope connected to a personal computer. Decoding the signal allowed us to determine the period and amplitude of oscillations. Experiments confirmed the predictions of the mathematical model.