Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-28T13:52:03.696Z Has data issue: false hasContentIssue false
  • English
  • Français

Vortex-induced vibration of a prism in internal flow

Published online by Cambridge University Press:  13 November 2009

M. SÁNCHEZ-SANZ  and
A. VELAZQUEZ
M. SÁNCHEZ-SANZ*
Affiliation:
Aerospace Propulsion and Fluid Mechanics Department, School of Aeronautics, Universidad Politécnica de Madrid, Plaza Cardenal Cisneros 3, 28040 Madrid, Spain
A. VELAZQUEZ
Affiliation:
Aerospace Propulsion and Fluid Mechanics Department, School of Aeronautics, Universidad Politécnica de Madrid, Plaza Cardenal Cisneros 3, 28040 Madrid, Spain
*
†Email address for correspondence: mario.sanchez@upm.es
Get access Rights & Permissions [Opens in a new window]

Abstract

In this article, we study the influence of solid-to-fluid density ratio m on the type of vortex-induced oscillation of a square section prism placed inside a two-dimensional channel. We assume that the solid body has neither structural damping nor spring restoring force. Accordingly, the prism equation of motion contains only inertia and aerodynamics forces. The problem is considered in the range of Reynolds numbers Re ∈ [50 200] (based on the prism cross-section height h) and channel widths H = H′/h ∈ [2.5 10]. We found that, for each Re and H, there is a critical mass ratio mc that separates two different oscillation regimes. For m > mc, the prism oscillation is periodical and contains a single harmonic. For m < mc, the prism oscillation changes completely and assumes an irregular pattern that is characterized by multiple harmonics that appear to belong to a uniform spectrum. The change from one regime to the other is abrupt and we were not able to observe a transitional regime in which the number of response harmonics grew by finite steps. The value of the critical mass ratio grows along with the Reynolds number and the channel width.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 641 , 25 December 2009 , pp. 431 - 440
Copyright
Copyright © Cambridge University Press 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Chorin, A. J. 1967 A numerical method for solving incompressible viscous flow problems. J. Comput. Phys. 2, 12–26CrossRefGoogle Scholar
Govardham, R. & Williamson, C. H. K. 2002 Resonance forever: existence of a critical mass an infinite regime of resonance in vortex-induced vibration. J. Fluid Mech. 473, 147–166.CrossRefGoogle Scholar
Kelkar, K. M. & Patankar, S. V. 1992 Numerical prediction of vortex shedding behind a square cylinder. Intl J. Numer. Methods Fluids 14, 327–341.CrossRefGoogle Scholar
Mendez, B. & Velazquez, A. 2004 Finite point solver for the simulation of two-dimensional laminar, incompressible, unsteady flows. Comput. Methods Appl. Mech. Engng 193, 825–848.CrossRefGoogle Scholar
Mittal, S. & Singh, S. 2005 Vortex-induced vibrations at subcritical Re. J. Fluid Mech 534, 185–194.CrossRefGoogle Scholar
Okajima, A. 1982 Strouhal numbers of rectangular cylinders. J. Fluid Mech. 123, 379–398.CrossRefGoogle Scholar
Okajima, A., Yi, D., Sakuda, A. & Nakano, T. 1997 Numerical study of blockage effects on aerodynamics characteristics of an oscillating rectangular cylinder. J. Wind Engng Ind. Aerodyn 67–68, 91–102.CrossRefGoogle Scholar
Robichaux, J., Balachandar, S. & Vanka, S. P. 1999 Three-dimensional Floquet instability of the wake of square cylinder. Phys. Fluids 11, 560–578.CrossRefGoogle Scholar
Rogers, S. E., Kwak, D. & Kiris, C. 1991 Numerical solution of the incompressible Navier–Stokes equations for steady-state and time-dependent problems. AIAA J. 29 (4), 603–610.CrossRefGoogle Scholar
Ryan, K., Thompson, M. C. & Hourigan, K. 2005 Variation in the critical mass ratio of a freely oscillating cylinder as a function of Reynolds number. Phys. Fluids 17, 038106.CrossRefGoogle Scholar
Sanchez-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
Sarpkaya, T. 2004 A critical review of the intrinsic nature of vortex-induced vibrations. J. Fluids Struct. 19, 389–447.CrossRefGoogle Scholar
Shiels, D., Leonard, A. & Roshko, A. 2001 Flow induced vibration of a circular cylinder at limiting structural parameters. J. Fluids Struct. 15, 3–21.CrossRefGoogle Scholar
Velazquez, A., Arias, J. R. & Mendez, B. 2008 Laminar heat transfer enhancement downstream of a backward facing step by using a pulsating flow. Intl J. Heat Mass Transfer 51, 2075–2089.CrossRefGoogle Scholar
Williamson, C. H. K. & Govardhan, R. 2004 Vortex induced vibrations. Annu. Rev. Fluid Mech. 36, 413–455.CrossRefGoogle Scholar
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