Calculation of the flow around an oscillating cylinder with a coaxial disk in the head at low Reynolds numbers

The hypothesis of curved models is used to calculate the flow around a cylinder performing damped rotational oscillations in the air flow. The influence of a disk coaxially fixed in the head of the cylinder on the oscillations is studied. The elongation of the cylinder (the ratio of the length of the cylinder to its diameter) is nine. The diameter of the disk is equal to 0.6 of the diameter of the cylinder. It is assumed that the only reason for the damping of on the oscillations is aerodynamic force. The parameters characterizing the attenuation of rotational on the oscillations of the cylinder occurring in the air flow at the Reynolds number $\mathrm{Re}$ = 750 are determined. It turned out that the presence of a coaxial disk in the head leads to a faster attenuation of on the oscillations. This fact is in qualitative agreement with the results of an experiment to determine rotational derivatives in a wind tunnel at large Reynolds numbers. The hypothesis of quasi-stationary is applied in the calculation of translation vibrations of the cylinder. The parameter characterizing the damping of vibrations of a cylinder with a disk in absolute magnitude slightly exceeds the same parameter for a cylinder without a disk, which corresponds to the results of the experiment.