Free Oscillations of Spheroids on the Elastic Spring In a Viscous Fluid

Volume 2, Issue 1, February 2017     |     PP. 1-10      |     PDF (1066 K)    |     Pub. Date: February 28, 2017
DOI:    305 Downloads     18402 Views  

Author(s)

P.R. Andronov, Institute of mechanics, Moscow State University, Moscow, Russia
S.V. Guvernyuk, Institute of mechanics, Moscow State University, Moscow, Russia
G.Ya. Dynnikova, Institute of mechanics, Moscow State University, Moscow, Russia

Abstract
There is solved numerically the conjugate problem of the oscillations of the axisymmetric ellipsoids, fixed at the end of the elastic spring, in the space, filled with the incompressible and viscous fluid. There is used the non-grid method of the viscous vortex domains. There are shown the boundaries of usefulness for the simplified formulas for the calculation of the non-stationary drag force, taking into account the main stationary component, the influence of the attached mass and the influence of the history of the body motion. It is found that these formulas are more appropriate when the Reynolds numbers are of the order of 102 and the axisymmetric ellipsoids are more elongated.

Keywords
viscous fluid, spheroid, elastic spring, oscillations

Cite this paper
P.R. Andronov, S.V. Guvernyuk, G.Ya. Dynnikova, Free Oscillations of Spheroids on the Elastic Spring In a Viscous Fluid , SCIREA Journal of Mechanics. Volume 2, Issue 1, February 2017 | PP. 1-10.

References

[ 1 ] French A.P. Vibrations and Waves (New York: Norton & Company). 1971.
[ 2 ] Greiner W. Classical Mechanics. Point Particles and Relativity (New York: Springer). 2004.
[ 3 ] J. Mendoza-Arenas, E. L. D. Perico and F. Fajardo. Motion of a damped oscillating sphere as a function of the medium viscosity. European journal of physics. 31 (2010). Pp. 129–141.
[ 4 ] P.R. Andronov, M.Z. Dosaev, G.Ya. Dynnikova, Yu.D. Selyutskii, and S.D. Strekalov. Modeling of Oscillating Wind Turbine. Journal of Machinery Manufacture and Reliability, 2009, Vol. 38, No. 4, pp. 383–387.
[ 5 ] P. R. Andronov, D. A. Grigorenko, S. V. Guvernyuk, G. Ya. Dynnikova. Numerical simulation of plate autorotation in a viscous fluid flow. Fluid Dynamics, 42: 5, 719–731, 2007.
[ 6 ] G. Ya. Dynnikova. The Lagrangian approach to solving the time-dependent Navier-Stokes equations. Doklady Physics, 49: 11, 648–652, 2004.
[ 7 ] Andronov P.R., Guvernyuk S.V., Dynnikova G.Ya. Unsteady flow around and loads at a spheroid in a viscous incompressible medium. // Proceedings of the XVI All-Russian seminar on traffic control and navigation of aircraft. V. 1. Publ. SSC RAS Samara, 2013. Pp. 154-157 .