Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-04T01:07:39.176Z Has data issue: false hasContentIssue false
  • English
  • Français

Direct numerical simulation of oscillatory flow around a circular cylinder at low Keulegan–Carpenter number

Published online by Cambridge University Press:  27 September 2010

HONGWEI AN ,
LIANG CHENG  and
MING ZHAO
HONGWEI AN*
Affiliation:
School of Civil and Resource Engineering, University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia
LIANG CHENG
Affiliation:
School of Civil and Resource Engineering, University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia
MING ZHAO
Affiliation:
School of Civil and Resource Engineering, University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The Honji instability is studied using direct numerical simulations of sinusoidal oscillatory flow around a circular cylinder. The three-dimensional Navier–Stokes equations are solved by a finite element method at a relatively small value of the Keulegan–Carpenter number KC. The generation and subsequent development of Honji vortices are discussed over a range of frequency parameters by means of flow visualization. It is found that the spacing between Honji vortices is only weakly dependent on the frequency of oscillation, but is strongly correlated to KC because it is the terms within the governing equation containing KC that dominate the three-dimensional features of the flow. An empirical relationship between KC and the spacing between neighbouring vortices is proposed. The three-dimensional steady streaming structure within the vortices is identified and it is found that at high frequencies the steady streaming is two-dimensional although the instantaneous flow structure is itself fully three-dimensional.

JFM classification

Boundary Layers: Boundary layer separation Instability: Instability
Type
Papers
Information
Journal of Fluid Mechanics , Volume 666 , 10 January 2011 , pp. 77 - 103
Copyright
Copyright © Cambridge University Press 2010

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

Barkley, D. & Henderson, R. D. 1996 Three-dimensional Floquet stability analysis of the wake of a circular cylinder. J. Fluid Mech. 322, 215–241.CrossRefGoogle Scholar
Bearman, P. W., Downie, M. J., Graham, J. M. R. & Obasaju, E. D. 1985 Forces on cylinders in viscous oscillatory flow at low Keulegan–Carpenter numbers. J. Fluid Mech. 154, 337–356.CrossRefGoogle Scholar
Bearman, P. W. & Mackwood, P. R. 1992 Measurements of the hydrodynamic damping of oscillating cylinders. In Proceedings of 6th International Conference on the Behaviour of Offshore Structures (BOSS '92), pp. 405–414. London.Google Scholar
Brooks, A. N. & Hughes, T. J. R. 1982 Streaming upwind/Petrov–Galerkin formulations for convection dominated flow with particular emphasis on the incompressible Navier–Stokes equations. Comput. Meth. Appl. Mech. Engng 32, 199–259.CrossRefGoogle Scholar
Choi, J. I., Oberoi, R. C., Edwards, J. R. & Rosati, J. A. 2007 An immersed boundary method for complex incompressible flows. J. Comput. Phys. 224, 757–784.CrossRefGoogle Scholar
Dütsch, H., Durst, F., Becker, S. & Lienhart, H. 1998 Low-Reynolds-number flow around an oscillating circular cylinder at low Keulegan–Carpenter numbers. J. Fluid Mech. 360, 249–271.CrossRefGoogle Scholar
Elston, J. R., Blackburn, H. M. & Sheridan, J. 2006 The primary and secondary instabilities of flow generated by an oscillating circular cylinder. J. Fluid Mech. 550, 359–389.CrossRefGoogle Scholar
Guilmineau, E. & Queutey, P. 2002 A numerical simulation of vortex shedding from an oscillating circular cylinder. J. Fluids Struct. 16, 773–794.CrossRefGoogle Scholar
Hall, P. 1984 On the stability of the unsteady boundary layer on a cylinder oscillating transversely in a viscous fluid. J. Fluid Mech. 146, 347–367.CrossRefGoogle Scholar
Holtsmark, J., Johnsen, I., Sikkeland, T. & Skavlem, S. 1954 Boundary layer flow near a cylindrical obstacle in an oscillating incompressible fluid. J. Acoust. Soc. Am. 26, 26–39.CrossRefGoogle Scholar
Honji, H. 1981 Streaked flow around an oscillating circular cylinder. J. Fluid Mech. 107, 507–520.CrossRefGoogle Scholar
Iliadis, G. & Anagnostopoulos, P. 1998 Viscous oscillatory flow around a circular cylinder at low Keulegan–Carpenter numbers and frequency parameters. Intl J. Numer. Meth. Fluids 26, 403–442.3.0.CO;2-V>CrossRefGoogle Scholar
Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 69–74.CrossRefGoogle Scholar
Jester, W. & Kallinderis, Y. 2003 Numerical study of incompressible flow about fixed cylinder pairs. J. Fluids Struct. 17, 561–577.CrossRefGoogle Scholar
Justesen, P. 1991 A numerical study of oscillating flow around a circular cylinder. J. Fluid Mech. 222, 157–196.CrossRefGoogle Scholar
Kondo, N. 1994 Third-order upwind finite element solutions of high-Reynolds-number flows. Comput. Meth. Appl. Mech. Engng 112, 227–251.Google Scholar
Lin, X. W., Bearman, P. W. & Graham, J. M. R. 1996 A numerical study of oscillatory flow about a circular cylinder for low values of beta parameter. J. Fluids Struct. 10, 501–526.CrossRefGoogle Scholar
Maull, D. J. & Milliner, M. G. 1978 Sinusoidal flow past a circular cylinder. Coastal Engng 2, 149–168.CrossRefGoogle Scholar
Morison, J. R., O'Brien, M. P., Johnson, J. W. & Schaaf, S. A. 1950 The force exerted by surface waves on piles. Petrol. Trans. 189, 149–157.Google Scholar
Nehari, D., Armenio, V. & Ballio, F. 2004 Three-dimensional analysis of the unidirectional oscillatory flow around a circular cylinder at low Keulegan–Carpenter and β-number. J. Fluid Mech. 520, 157–186.CrossRefGoogle Scholar
Obasaju, E. D., Bearman, P. W. & Graham, J. M. R. 1988 A study of forces, circulation and vortex patterns around a circular cylinder in oscillating flow. J. Fluid Mech. 196, 467–494.CrossRefGoogle Scholar
Riley, N. 2001 Steady streaming. Annu. Rev. Fluid Mech. 33, 43–65.CrossRefGoogle Scholar
Saghafian, M., Stansby, P. K., Saidi, M. S. & Apsley, D. D. 2003 Simulation of turbulent flows around a circular cylinder using nonlinear eddy-viscosity modelling: steady and oscillatory flows. J. Fluids Struct. 17, 1213–1236.CrossRefGoogle Scholar
Sarpkaya, T. 1977 In-line and transverse forces on cylinders in oscillatory flow at high Reynolds numbers. J. Ship Res. 21, 200–216.CrossRefGoogle Scholar
Sarpkaya, T. 1986 Force on a circular cylinder in viscous oscillatory flow at low Keulegan–Carpenter numbers. J. Fluid Mech. 165, 61–71.CrossRefGoogle Scholar
Sarpkaya, T. 2002 Experiments on the stability of sinusoidal flow over a circular cylinder. J. Fluid Mech. 457, 157–180.CrossRefGoogle Scholar
Sarpkaya, T. 2005 On the parameter β = Re/KC = D 2/νT. J. Fluids Struct. 21, 435–440.CrossRefGoogle Scholar
Sarpkaya, T. 2006 Structures of separation on a circular cylinder in periodic flow. J. Fluid Mech. 567, 281–297.CrossRefGoogle Scholar
Sarpkaya, T. & Butterworth, W. 1992 Separation points on a cylinder in oscillating flow. Trans. ASME J. Offshore Mech. Arctic Engng 114, 28–35.CrossRefGoogle Scholar
Scandura, P., Armenio, V. & Foti, E. 2009 Numerical investigation of the oscillatory flow around a circular cylinder close to a wall at moderate Keulegan–Carpenter and low Reynolds numbers. J. Fluid Mech. 627, 259–290.CrossRefGoogle Scholar
Stokes, G. G. 1851 On the effect of the internal friction of fluids on the motion of pendulums. Trans. Camb. Phil. Soc. 9, 8–106.Google Scholar
Stuart, J. T. 1966 Double boundary layers in oscillatory viscous flow. J. Fluid Mech. 24, 673–687.CrossRefGoogle Scholar
Sumer, B. M. & Fredsøe, J. 1997 Hydrodynamics Around Cylindrical Structures. World Scientific.CrossRefGoogle Scholar
Tatsuno, M. & Bearman, P. 1990 A visual study of the flow around an oscillating circular cylinder at low Keulegan–Carpenter numbers and low Stokes numbers. J. Fluid Mech. 211, 157–182.CrossRefGoogle Scholar
Uzunoglu, B., Tan, M. & Price, W. G. 2001 Low-Reynolds-number flow around an oscillating circular cylinder using a cell viscous boundary element method. Intl J. Numer. Meth. Engng 50, 2317–2338.CrossRefGoogle Scholar
Wang, C. Y. 1968 On high-frequency oscillatory viscous flows. J. Fluid Mech. 32, 55–68.CrossRefGoogle Scholar
Williamson, C. H. K. 1985 Sinusoidal flow relative to circular cylinders. J. Fluid Mech. 155, 141–174.CrossRefGoogle Scholar
Wu, J. Z., Lu, X. Y. & Zhuang, L. X. 2007 Integral force acting on a body due to local flow structures. J. Fluid Mech. 576, 265–286.CrossRefGoogle Scholar
Zhang, J. & Dalton, C. 1999 The onset of three-dimensionality in an oscillatory flow past a fixed circular cylinder. Intl J. Numer. Meth. Fluids 30, 19–42.3.0.CO;2-#>CrossRefGoogle Scholar
Zhao, M., Cheng, L. & Zhou, T. 2009 Direct numerical simulation of three-dimensional flow past a yawed circular cylinder of infinite length. J. Fluids Struct. 25, 831–847.CrossRefGoogle Scholar