Analysis of the Secondary Stationary Flow Around an Oscillating Circular Cylinder

This paper is devoted to the study of a viscous
incompressible flow around a circular cylinder performing harmonic
oscillations, especially the steady streaming phenomenon. The
research methodology is based on the asymptotic explanation method
combined with the computational bifurcation analysis. The research
approach develops Schlichting and Wang decomposition method.
Present studies allow to identify several regimes of the secondary
streaming with different flow structures. The results of the research
are in good agreement with experimental and numerical simulation
data.





References:
[1] G.G. Stokes, On the effect of the internal friction of fluids on the motion of pendulums. Trans. Camb. Phil. Soc., Vol. 9, pp. 8–106, 1851.
[2] T. Sarpkaya, M. Isaacson, Mechanics of wave forces on offshore
structures, Van Nostrand Reinhold, 1981.
[3] N. D. P. Barltrop, A. J. Adams, Dynamics of fixed marine structures
Butterworth-Heinemann, 1991.
[4] E. Naudascher, Flow-Induced Vibrations, An Engineering Guide,
Balkema, 1994.
[5] A. G. Yegorov, O. S. Zakharova, The energy-optimal motion of a
vibration- driven robot in a resistive medium, J. Appl. Math. Mech., Vol.74, pp. 443–451, 2010.
[6] A. G. Egorov, A. M. Kamalutdinov, A. N. Nuriev, V. N. Paimushin,
Theoretical-experimental method for determining the parameters of
damping based on the study of damped flexural vibrations of test
specimens. 2. Aerodynamic component of damping, Mechanics of Composite Materials Vol. 50, pp. 267–278, 2014.
[7] H. Schlichting, Berechnung ebener periodischer Grenzschichtstrmungen. Phys., Vol. 33, pp. 327–335, 1932.
[8] C.Y. Wang, On high-frequency oscillating viscous flows. J. Fluid Mech., Vol. 32, pp. 55–68, 1968.
[9] Y.A. Kuznetsov, Elements of Applied Bifurcation Theory, Springer, 1995.
[10] M. Tatsuno, P. W. Bearman, A visual study of the flow around an
oscillating circular cylinder at low Keulegan-Carpenter numbers and low Stokes numbers. J. Fluid Mech. Vol. 211, p. 157–182, 1990. [11] J. R Elston, The primary and secondary instabilities of flow generated by an oscillating circular cylinder.J. Fluid Mech. Vol. 550, pp. 359–389, 2006. [12] P. Justesen, A numerical study of oscillating flow around a circular cylinder. J. Fluid Mech. Vol. 222, pp. 157–196, 1991. [13] A. N. Nuriev, O. N. Zaitseva, Solution of the problem of oscillatory
motion of the circular cylinder in a viscous fluid in the OpenFOAM package. Herald of Kazan Technological University Vol. 8 pp. 116–123, 2013 (in Russian). [14] A. N. Nuriev, A. G. Egorov, Application of the bifurcation analysis for
the fluid mechanics problems. Herald of Kazan Technological University Vol. 4 pp. 104–109, 2013 (in Russian).