Skip to main content Accessibility help
×
Home

Oscillatory flow regimes for a circular cylinder near a plane boundary

  • Chengwang Xiong (a1) (a2), Liang Cheng (a1) (a3), Feifei Tong (a1) and Hongwei An (a1)

Abstract

Oscillatory flow around a circular cylinder close to a plane boundary is numerically investigated at low-to-intermediate Keulegan–Carpenter ( $KC$ ) and Stokes numbers ( $\unicode[STIX]{x1D6FD}$ ) for different gap-to-diameter ratios ( $e/D$ ). A set of unique flow regimes is observed and classified based on the established nomenclature in the ( $KC,\unicode[STIX]{x1D6FD}$ )-space. It is found that the flow is not only influenced by $e/D$ but also by the ratio of the thickness of the Stokes boundary layer ( $\unicode[STIX]{x1D6FF}$ ) to the gap size (e). At relatively large $\unicode[STIX]{x1D6FF}/e$ values, vortex shedding through the gap is suppressed and vortices are only shed from the top of the cylinder. At intermediate values of $\unicode[STIX]{x1D6FF}/e$ , flow through the gap is enhanced, resulting in horizontal gap vortex shedding. As $\unicode[STIX]{x1D6FF}/e$ is further reduced below a critical value, the influence of $\unicode[STIX]{x1D6FF}/e$ becomes negligible and the flow is largely dependent on $e/D$ . A hysteresis phenomenon is observed for the transitions in the flow regime. The physical mechanisms responsible for the hysteresis and the variation of marginal stability curves with $e/D$ are explored at $KC=6$ through specifically designed numerical simulations. The Stokes boundary layer over the plane boundary is found to be responsible for the relatively large hysteresis range over $0.25<e/D<1.0$ . Three mechanisms have been identified to the change of the marginal stability curve over $e/D$ , which are the blockage effect due to the geometry setting, the favourable pressure gradient over the gap and the location of the leading eigenmode relative to the cylinder.

Copyright

Corresponding author

Email address for correspondence: liang.cheng@uwa.edu.au

References

Hide All
An, H., Cheng, L. & Zhao, M. 2010 Steady streaming around a circular cylinder near a plane boundary due to oscillatory flow. J. Hydraul. Engng 137 (1), 2333.
Anagnostopoulos, P. & Minear, R. 2004 Blockage effect of oscillatory flow past a fixed cylinder. Appl. Ocean Res. 26 (3), 147153.
Barkley, D. & Henderson, R. D. 1996 Three-dimensional Floquet stability analysis of the wake of a circular cylinder. J. Fluid Mech. 322, 215241.
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, 337356.
Blackburn, H. M. & Henderson, R. D. 1999 A study of two-dimensional flow past an oscillating cylinder. J. Fluid Mech. 385, 255286.
Bolis, A.2013 Fourier spectral/ $hp$ element method: investigation of time-stepping and parallelisation strategies. PhD thesis.
Cantwell, C. D., Moxey, D., Comerford, A, Bolis, A., Rocco, G., Mengaldo, G., De Grazia, D., Yakovlev, S., Lombard, J-E, Ekelschot, D. et al. 2015 Nektar + +: An open-source spectral/hp element framework. Comput. Phys. Commun. 192, 205219.
Carstensen, S., Sumer, B. M. & Fredsøe, J. 2010 Coherent structures in wave boundary layers. Part 1. Oscillatory motion. J. Fluid Mech. 646, 169206.
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, 249271.
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, 359389.
Elston, J. R., Sheridan, J. & Blackburn, H. M. 2004 Two-dimensional Floquet stability analysis of the flow produced by an oscillating circular cylinder in quiescent fluid. Eur. J. Mech. (B/Fluids) 23 (1), 99106.
Henderson, R. D. & Barkley, D. 1996 Secondary instability in the wake of a circular cylinder. Phys. Fluids 8 (6), 16831685.
Hussain, A. F. 1986 Coherent structures and turbulence. J. Fluid Mech. 173, 303356.
Jacobsen, V., Bryndum, M. B., Fredsøe, J. et al. 1984 Determination of flow kinematics close to marine’ pipelines and their use in stability calculations. In Offshore Technology Conference, Offshore Technology Conference.
Justesen, P. 1991 A numerical study of oscillating flow around a circular cylinder. J. Fluid Mech. 222, 157196.
Kozakiewicz, A., Sumer, B. M. & Fredsøe, J. 1992 Spanwise correlation on a vibrating cylinder near a wall in oscillatory flows. J. Fluid Strcut. 6 (3), 371392.
Mouazé, D. & Bélorgey, M. 2003 Flow visualisation around a horizontal cylinder near a plane wall and subject to waves. Appl. Ocean Res. 25 (4), 195211.
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 numbers. J. Fluid Mech. 520, 157186.
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, 467494.
Rao, A., Stewart, B. E., Thompson, M. C., Leweke, T. & Hourigan, K. 2011 Flows past rotating cylinders next to a wall. J. Fluids Struct. 27 (5), 668679.
Rao, A., Thompson, M. C., Leweke, T. & Hourigan, K. 2013 The flow past a circular cylinder translating at different heights above a wall. J. Fluids Struct. 41, 921.
Rao, A., Thompson, M. C., Leweke, T. & Hourigan, K. 2015 Flow past a rotating cylinder translating at different gap heights along a wall. J. Fluids Struct. 57, 314330.
Sarpkaya, T. 1976 Forces on cylinders near a plane boundary. J. Fluids Engng 98 (3), 499.
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, 259290.
Shen, L. & Chan, E. 2013 Numerical simulation of oscillatory flows over a rippled bed by immersed boundary method. Appl. Ocean Res. 43, 2736.
Sumer, B. M. & Fredsøe, J. 1997 Hydrodynamics Around Cylindrical Structures. World Scientific.
Sumer, B. M., Jensen, B. L. & Fredsøe, J. 1991 Effect of a plane boundary on oscillatory flow around a circular cylinder. J. Fluid Mech. 225, 271300.
Tatsuno, M. & Bearman, P. W. 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, 157182.
Tong, F., Cheng, L., Xiong, C., Draper, S., An, H. & Lou, X. 2017 Flow regimes for a square cross-section cylinder in oscillatory flow. J. Fluid Mech. 813, 85109.
Tong, F., Cheng, L., Zhao, M. & An, H. 2015 Oscillatory flow regimes around four cylinders in a square arrangement under small KC and Re conditions. J. Fluid Mech. 769, 298336.
Williamson, C. H. K. 1985 Sinusoidal flow relative to circular cylinders. J. Fluid Mech. 155, 141174.
Zdravkovich, M. M. 1985 Forces on a circular cylinder near a plane wall. Appl. Ocean Res. 7 (4), 197201.
Zhao, M. & Cheng, L. 2014 Two-dimensional numerical study of vortex shedding regimes of oscillatory flow past two circular cylinders in side-by-side and tandem arrangements at low Reynolds numbers. J. Fluid Mech. 751, 137.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

JFM classification

Type Description Title
VIDEO
Movies

Xiong et al. supplementary movie 1
Animation of streakline in regime HA at (e/D, KC, β)=(0.25,10, 10).

 Video (5.6 MB)
5.6 MB
VIDEO
Movies

Xiong et al. supplementary movie 2
Animation of streakline in regime GVS at (e/D, KC, β)=(0.5, 6, 20).

 Video (3.3 MB)
3.3 MB
VIDEO
Movies

Xiong et al. supplementary movie 3
Animation of streakline in regime GVS-A at (e/D, KC, β)=(0.5, 6, 30).

 Video (3.2 MB)
3.2 MB
VIDEO
Movies

Xiong et al. supplementary movie 4
Animation of streakline in regime E at (e/D, KC, β)=(2, 6, 30).

 Video (3.3 MB)
3.3 MB
VIDEO
Movies

Xiong et al. supplementary movie 5
Animation of streakline in regime F' at (e/D, KC, β)=(0.25, 11, 20).

 Video (4.3 MB)
4.3 MB
VIDEO
Movies

Xiong et al. supplementary movie 6
Animation of streakline in regime F at (e/D, KC, β)=(2, 10, 20).

 Video (7.0 MB)
7.0 MB

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed