Rotational oscillations of a cylinder with the stabilizer in the gas flow

Authors

  • Nikolai A. Kiselev St. Petersburg State University, Universitetskaya nab., 7–9, St. Petersburg, 199034, Russian Federation
  • Anatoly N. Ryabinin St. Petersburg State University, Universitetskaya nab., 7–9, St. Petersburg, 199034, Russian Federation https://orcid.org/0000-0003-1237-5910

DOI:

https://doi.org/10.21638/11701/spbu01.2019.412

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.

Keywords:

wind tunnel, bluff body, unsteady forces, oscillations, mathematical simulation

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References

Литература

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References

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Ryabinin A.N., Kiselev N.A., “Rotational oscillation of a cylinder in air flow”, ARPN Journal of Engineering and Applied Sciences 12(23), 6803–6808 (2017).

Parkinson G.V., Brooks N.P., “On the aeroelastic instability of bluff cylinders”, Journal of Applied Mechanics 28, 252–258 (1961). https://doi.org/10.1115/1.3641663

Parkinson G.V., Smith J.D., “The square prism as an aeroelastic non-linear oscillator”, Quarterly Journal of Mechanics and Applied Mathematics 17, 225–239 (1964). https://doi.org/10.1093/qjmam/17.2.225

Novak M., “Aeroelastic galloping of prismatic bodies”, ASCE Journal of Engineering Mechanics Division 95, 115–142 (1969).

Alonso G., Meseguer J., Perez-Grande I., “Galloping instabilities of two-dimensional triangular cross-section bodies”, Experiments in Fluids 38, 789–795 (2005). https://doi.org/10.1007/s00348-005-0974-8

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Published

2019-11-28

How to Cite

Kiselev, N. A., & Ryabinin, A. N. (2019). Rotational oscillations of a cylinder with the stabilizer in the gas flow. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 6(4), 672–679. https://doi.org/10.21638/11701/spbu01.2019.412

Issue

Vol. 6 No. 4 (2019)

Section

Mechanics

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Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.

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