Determination of rotational derivatives of a cylinder with a coaxially mounted disk in an air stream

Abstract

The damped rotational oscillations of a cylinder whose length-to-diameter ratio is nine are considered. In the head part of the cylinder, a disc is mounted coaxially on the leg. The effect of the disk on damping oscillations is described by two parameters: the sum of the rotational derivatives mωz + mθz and the rotational derivative mθz. To determine these parameters in the aerodynamic tunnel of low speeds, an experiment is performed with the flow past a cylinder fixed on an elastic spring suspension. In the experiment, the diameter of the coaxial disk and the distance between the disk and the end of the cylinder varies. Deflected from the equilibrium position, the cylinder performs damping oscillations. The tension of one of the springs of suspension is measured using the strain gauge method. The signal is converted to digital form using the Velleman PCS500A PC oscilloscope and recorded to a file on the computer. Thus, the frequency of oscillations and the dependence of the amplitude of oscillations on time are determined. Disks whose diameter exceeds the diameter of the cylinder do not have a strong effect on the damping of oscillations of an elastically fixed cylinder. Disks of smaller diameter promote rapid damping of the oscillations. The presence of a large-diameter disk leads to a decrease in the coefficient mωz. A small-diameter disk acts in a opposite way.