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New oscillatory instability of a confined cylinder in a flow below the vortex shedding threshold

Published online by Cambridge University Press:  24 November 2011

B. Semin ,
A. Decoene ,
J.-P. Hulin ,
M. L. M. François  and
H. Auradou
B. Semin*
Affiliation:
Laboratoire FAST, Université Paris-Sud, Université Pierre et Marie Curie–Paris 6, CNRS, Bat. 502, Campus Univ., Orsay, F-91405, France
A. Decoene
Affiliation:
Department of Mathematics, Université Paris-Sud, Bat. 452, Campus Univ., Orsay, F-91405, France
J.-P. Hulin
Affiliation:
Laboratoire FAST, Université Paris-Sud, Université Pierre et Marie Curie–Paris 6, CNRS, Bat. 502, Campus Univ., Orsay, F-91405, France
M. L. M. François
Affiliation:
Laboratoire FAST, Université Paris-Sud, Université Pierre et Marie Curie–Paris 6, CNRS, Bat. 502, Campus Univ., Orsay, F-91405, France
H. Auradou
Affiliation:
Laboratoire FAST, Université Paris-Sud, Université Pierre et Marie Curie–Paris 6, CNRS, Bat. 502, Campus Univ., Orsay, F-91405, France
*
†Email address for correspondence: [email protected]
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Abstract

A new type of flow-induced oscillation is reported for a tethered cylinder confined inside a Hele-Shaw cell (ratio of cylinder diameter to cell aperture, ) with its main axis perpendicular to the flow. This instability is studied numerically and experimentally as a function of the Reynolds number and of the density of the cylinder. This confinement-induced vibration (CIV) occurs above a critical Reynolds number much lower than for Bénard–Von Kármán vortex shedding behind a fixed cylinder in the same configuration (). For low values, CIV persists up to the highest value investigated (). For denser cylinders, these oscillations end abruptly above a second value of larger than and vortex-induced vibrations (VIV) of lower amplitude appear for . Close to the first threshold , the oscillation amplitude variation as and the lack of hysteresis demonstrate that the process is a supercritical Hopf bifurcation. Using forced oscillations, the transverse position of the cylinder is shown to satisfy a Van der Pol equation. The physical meaning of the stiffness, amplification and total mass coefficients of this equation are discussed from the variations of the pressure field.

JFM classification

Instability: Instability Nonlinear Dynamical Systems: Low-dimensional models
Type
Papers
Information
Journal of Fluid Mechanics , Volume 690 , 10 January 2012 , pp. 345 - 365
Copyright
Copyright © Cambridge University Press 2011

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References

1. Anagnostopoulos, P. & Bearman, P. W. 1992 Response characteristics of a vortex-excited cylinder at low Reynolds number. J. Fluids Struct. 6, 39–50.CrossRefGoogle Scholar
2. Carberry, J., Sheridan, J. & Rockwell, D. 2005 Controlled oscillations of a cylinder: forces and wake modes. J. Fluid Mech. 538, 31–69.CrossRefGoogle Scholar
3. Chen, J.-H., Pritchard, W. G. & Tavener, S. J. 1995 Bifurcation for flow past a cylinder between parallel plates. J. Fluid Mech. 284, 23–41.CrossRefGoogle Scholar
4. Cossu, C. & Morino, L. 2000 On the instability of a spring-mounted circular cylinder in a viscous flow at low Reynolds numbers. J. Fluids Struct. 14, 183–196.Google Scholar
5. Facchinetti, M. L., de Langre, E. & Biolley, F. 2004 Coupling of structure and wake oscillators in vortex induced vibrations. J. Fluids Struct. 19, 123–140.CrossRefGoogle Scholar
6. Gabbai, R. D. & Benaroya, H. 2005 An overview of modelling and experiments of vortex-induced vibration of circular cylinders. J. Sound Vib. 282, 575–616.CrossRefGoogle Scholar
7. Govardhan, R. & Williamson, C. H. K. 2002 Resonance forever: existence of a critical mass and an infinite regime of resonance in vortex-induced vibration. J. Fluid Mech. 473, 147–166.CrossRefGoogle Scholar
8. Hecht, F., Pironneau, O., le Hyaric, A. & Ohtsuka, K. 2010 FreeFem++ manual.http://www.freefem.org/ff++/.Google Scholar
9. Hirt, C. W., Amsden, A. A. & Cook, J. L. 1974 An arbitrary Lagrangian–Eulerian computing method for all flow speeds. J. Comput. Phys. 14, 227–253.CrossRefGoogle Scholar
10. Horowitz, M. & Williamson, C. H. K. 2006 Dynamics of a rising and falling cylinder. J. Fluids Struct. 22, 837–843.Google Scholar
11. Janela, J., Lefebvre, A. & Maury, B. 2005 A penalty method for the simulation of fluid–rigid body interaction. ESAIM: Proc. 14, 115–123.CrossRefGoogle Scholar
12. Lazarkov, M. & Revstedt, J. 2008 Flow-induced motion of a short circular cylinder spanning a rectangular channel. J. Fluids Struct. 24, 449–466.Google Scholar
13. Lefebvre, A. 2007 Fluid–particle simulations with Freefem++. ESAIM: Proc. 18, 120–132.CrossRefGoogle Scholar
14. Leontini, J. S., Stewart, B. E., Thompson, M. C. & Kourigan, K. 2006 Wake state and energy transitions of an oscillating cylinder at low Reynolds number. Phys. Fluids 18, 067101.Google Scholar
15. Manneville, P. 2004 Instabilities, Chaos and Turbulence: an Introduction to Nonlinear Dynamics and Complex Systems. Imperial College Press.CrossRefGoogle Scholar
16. Maury, B. 1996 Characteristics ALE method for the unsteady 3D Navier–Stokes equations with a free surface. Comput. Fluid Dyn. 6, 175–188.CrossRefGoogle Scholar
17. Meis, M., Varas, F., Velàsquez, A. & Vega, J. M. 2010 Heat transfer enhancement in micro-channels caused by vortex promoters. Intl J. Heat Mass Transfer 53, 29–40.CrossRefGoogle Scholar
18. Mittal, S. & Singh, S. 2005 Vortex-induced vibrations at subcritical Re . J. Fluid Mech. 534, 185–194.CrossRefGoogle Scholar
19. Morse, T. L. & Williamson, C. H. K. 2009 Prediction of vortex-induced vibration response by employing controlled motion. J. Fluid Mech. 634, 5–39.CrossRefGoogle Scholar
20. Nayfeh, A. H. & Mook, D. T. 1995 Nonlinear Oscillations. John Wiley.CrossRefGoogle Scholar
21. Placzek, A., Sigrist, J.-P. & Hamdouni, A. 2009 Numerical simulation of an oscillating cylinder in a cross-flow at low Reynolds number: forced and free oscillations. Comput. Fluids 38, 80–100.CrossRefGoogle Scholar
22. Prasanth, T. K., Behara, S., Singh, S. P. & Mittal, S. 2006 Effect of blockage on vortex-induced vibrations at low Reynolds numbers. J. Fluids Struct. 22, 865–876.CrossRefGoogle Scholar
23. Rehimi, F., Alaoui, F., Nasrallah, S. B., Doubliez, L. & Legrand, J. 2008 Experimental investigation of a confined flow downstream of a circular cylinder centred between two parallel walls. J. Fluids Struct. 24, 855–882.CrossRefGoogle Scholar
24. Sánchez-Sanz, M., Fernandez, B. & Velazquez, A. 2009 Energy-harvesting microresonator based on the forces generated by the Kármán street around a rectangular prism. J. Microelectromech. Syst. 18, 449–457.CrossRefGoogle Scholar
25. Sánchez-Sanz, M. & Velazquez, A. 2009 Vortex-induced vibration of a prism in internal flow. J. Fluid Mech. 641, 431–440.CrossRefGoogle Scholar
26. Sarpkaya, T. 2004 A critical review of the intrinsic nature of vortex-induced vibrations. J. Fluids Struct. 19, 389–447.CrossRefGoogle Scholar
27. Semin, B., François, M. L. M. & Auradou, H. 2011 Accurate measurement of curvilinear shapes by virtual image correlation. Eur. Phys. J. Appl. Phys. 56, 10701.CrossRefGoogle Scholar
28. Semin, B., Hulin, J. P. & Auradou, H. 2009 Influence of flow confinement on the drag force on a static cylinder. Phys. Fluids 21 (10), 103604.CrossRefGoogle Scholar
29. Shair, F. H., Grove, A. S., Petersen, E. E. & Acrivos, A. 1963 The effect of confining walls on the stability of the steady wake behind a circular cylinder. J. Fluid Mech. 17, 546–550.CrossRefGoogle Scholar
30. Shiels, D., Leonard, A. & Roshko, A. 2001 Flow-induced vibration of a circular cylinder at limiting structural parameters. J. Fluids Struct. 15, 3–21.Google Scholar
31. Weast, R. C. & Astle, M. J. 1982 Handbook of Chemistry and Physics. CRC.Google Scholar
32. Williamson, C. H. K. & Govardhan, R. 2004 Vortex-induced vibrations. Annu. Rev. Fluid Mech. 36, 413–455.CrossRefGoogle Scholar
33. Williamson, C. H. K. & Govardhan, R. 2008 A brief review of recent results in vortex-induced vibrations. J. Wind Engng Ind. Aerodyn. 96, 713–735.CrossRefGoogle Scholar
34. Zovatto, L. & Pedrizetti, G. 2001 Flow about a circular cylinder between parallel walls. J. Fluid Mech. 440, 1305–1320.CrossRefGoogle Scholar