https://orcid.org/0000-0002-9903-9719
Abstract
The wakes shed alternatively from two long stationary side-by-side cylinders have long been an issue in many engineering applications, such as wind energy harvesting schemes that utilize vortex-induced vibrations (VIVs). In this study, switching events of the wakes shed from two “short,” “flapping” side-by-side cylinders are investigated. To this end, the flow visualization and spectral analysis of the time-resolved data from hot-wire anemometers and the piezoelectric mount of flapping cylinders are carried out. Measurements are conducted with differing center-to-center spacing normalized by a single cylinder diameter (T/D)—gap ratio, and length-to-diameter ratio (L/D) in a Reynolds number range of 800 ≤ ReD ≤ 16,000. The results demonstrate the transition of wake shedding patterns, sequentially from a single bluff body wake, first bistable wakes, tristable wakes, second bistable wakes, and eventually to coupled wakes as the gap ratio is increased. Furthermore, the role of shortness and flapping of the two cylinders in determining the wake kinematics is elucidated, and the transitional sequences and switching of dominant shedding frequencies are detailed.
References
1.
Zdravkovich
, M. M.
, 1977
, “Review of Flow Interference Between Two Circular Cylinders in Various Arrangement
,” ASME J. Fluids Eng.
, 99
(4
), pp. 618
–633
.10.1115/1.34488712.
Sumner
, D.
, Wong
, S. S. T.
, Price
, S. J.
, and Paidoussis
, M. P.
, 1999
, “Fluid Behavior of Side-by-Side Circular Cylinders in Steady Cross-Flow
,” J. Fluids Struct.
, 13
(3
), pp. 309
–338
.10.1006/jfls.1999.02053.
Wang
, J.
, Fan
, D.
, and Lin
, K.
, 2020
, “A Review on Flow-Induced Vibration of Offshore Circular Cylinder
,” J. Hydrodyn.
, 32
(3
), pp. 415
–440
.10.1007/s42241-020-0032-24.
Lee
, Y. J.
, Qi
, Y.
, Zhou
, G.
, and Lua
, B. K.
, 2019
, “Vortex-Induced Vibration Wind Energy Harvesting by Piezoelectric MEMS Device in Formation
,” Sci. Rep.
, 9
, p. 20404
.10.1038/s41598-019-56786-05.
Brun
, C.
, Tenchine
, D.
, and Hopfinger
, E. J.
, 2004
, “Role of the Shear Layer Instability in the Near Wake Behavior of Two Side-by-Side Circular Cylinders
,” Exp. Fluids
, 36
(2
), pp. 334
–343
.10.1007/s00348-003-0726-66.
Atkins
, M. D.
, Dala
, L.
, and Kim
, T.
, 2016
, “Time-Averaged Behavior of Gap Flow Between Two Side-by-Side Circular Cylinders
,” AIAA J.
, 54
(9
), pp. 2742
–2754
.10.2514/1.J0546387.
Graham
, J. M. R.
, 1969
, “The Effect of End-Plates on the Two-Dimensionality of a Vortex Wake
,” Aeronaut. Q.
, 20
(3
), pp. 237
–247
.10.1017/S00019259000050598.
Okamoto
, T.
, and Yagita
, M.
, 1973
, “The Experimental Investigation on the Flow Past a Circular Cylinder of Finite Length Placed Normal to the Plane Surface in a Uniform Stream
,” Bull. JSME
, 16
(95
), pp. 805
–814
.10.1299/jsme1958.16.8059.
Chakroun
, W. M.
, Abdel Rahman
, A. A.
, and Quadri
, M. M. A.
, 1997
, “The Effect of Surface Roughness on Flow Around a Circular Cylinder
,” Wind Eng.
, 21
(1
), pp. 1
–12
.https://www.jstor.org/stable/4375023510.
Kim
, S.
, and Alam
, M. M.
, 2015
, “Characteristics and Suppression of Flow-Induced Vibrations of Two Side-by-Side Circular Cylinders
,” J. Fluids Struct.
, 54
, pp. 629
–642
.10.1016/j.jfluidstructs.2015.01.00411.
Wang
, X. Q.
, So
, R. M. C.
, Xie
, W.-C.
, and Zhu
, J.
, 2008
, “Free-Stream Turbulence Effects on Vortex-Induced Vibration of Two Side-by-Side Elastic Cylinders
,” J. Fluids Struct.
, 24
(5
), pp. 664
–679
.10.1016/j.jfluidstructs.2007.10.00712.
Xu
, S. J.
, Zhou
, Y.
, and So
, R. M. C.
, 2003
, “Reynolds Number Effects on the Flow Structure Behind Two Side-by-Side Cylinders
,” Phys. Fluids
, 15
(5
), pp. 1214
–1219
.10.1063/1.156161413.
Bearman
, P. W.
, and Wadcock
, A. J.
, 1973
, “The Interaction Between a Pair of Circular Cylinders Normal to a Stream
,” J. Fluid Mech.
, 61
(3
), pp. 499
–511
.10.1017/S002211207300083214.
Zdravkovich
, M. M.
, 1985
, “Flow Induced Oscillations of Two Interfering Circular Cylinders
,” J. Sound Vib.
, 101
(4
), pp. 511
–521
.10.1016/S0022-460X(85)80068-715.
Wang
, Z. J.
, and Zhou
, Y.
, 2005
, “Vortex Interaction in a Two Side-by-Side Cylinder Near-Wake
,” Int. J. Heat Fluid Flow
, 26
(3
), pp. 362
–377
.10.1016/j.ijheatfluidflow.2004.10.00616.
Alam
, M. M.
, and Zhou
, Y.
, 2007
, “Flow Around Two Side-by-Side Closely Spaced Circular Cylinders
,” J. Fluids Struct.
, 23
(5
), pp. 799
–805
.10.1016/j.jfluidstructs.2006.12.00217.
Sumner
, D.
, 2010
, “Two Circular Cylinders in Cross-Flow: A Review
,” J. Fluids Struct.
, 26
(6
), pp. 849
–899
.10.1016/j.jfluidstructs.2010.07.00118.
Chen
, W.
, Ji
, C.
, Alam
, M. M.
, and Yan
, Y.
, 2022
, “Three-Dimensional Flow Past Two Stationary Side-by-Side Circular Cylinders
,” Ocean Eng.
, 244
(15
), p. 110379
.10.1016/j.oceaneng.2021.11037919.
Alam
, M. M.
, Moriya
, M.
, and Sakamoto
, H.
, 2003
, “Aerodynamic Characteristics of Two Side-by-Side Circular Cylinders and Application of Wavelet Analysis on the Switching Phenomenon
,” J. Fluids Struct.
, 18
(3–4
), pp. 325
–346
.10.1016/j.jfluidstructs.2003.07.00520.
Spivack
, H. M.
, 1946
, “Vortex Frequency and Flow Pattern in the Wake of Two Parallel Cylinders at Varied Spacing Normal to an Air Stream
,” J. Aeronaut. Sci.
, 13
(6
), pp. 289
–301
.10.2514/8.1137521.
Afgan
, I.
, Kahil
, Y.
, Benhamadouche
, S.
, and Sagaut
, P.
, 2011
, “Large Eddy Simulation of the Flow Around Single and Two Side-by-Side Cylinders at Subcritical Reynolds Numbers
,” Phys. Fluids
, 23
(7
), p. 075101
.10.1063/1.359626722.
Zhou
, Y.
, Zhang
, H. J.
, and Yiu
, M. W.
, 2002
, “The Turbulent Wake of Two Side-by-Side Circular Cylinders
,” J. Fluid Mech.
, 458
, pp. 303
–332
.10.1017/S002211200200788723.
Kim
, H. J.
, and Durbin
, P. A.
, 1988
, “Investigation of the Flow Between a Pair of Circular Cylinders in the Flopping Regime
,” J. Fluid Mech.
, 196
, pp. 431
–448
.10.1017/S002211208800276924.
Williamson
, C. H. K.
, 1985
, “Evolution of a Single Wake Behind a Pair of Bluff Bodies
,” J. Fluid Mech.
, 159
, pp. 1
–18
.10.1017/S002211208500307X25.
Rooney
, D. M.
, Rodichok
, J.
, and Dolan
, K.
, 1995
, “Finite Aspect Ratio Effects on Vortex Shedding Behind Two Cylinders at Angles of Incidence
,” ASME J. Fluids Eng.
, 117
(2
), pp. 219
–226
.10.1115/1.281713326.
Sarpkaya
, T.
, 1979
, “Vortex-Induced Oscillations: A Selective Review
,” ASME J. Appl. Mech.
, 46
(2
), pp. 241
–258
.10.1115/1.342453727.
Irawan
, Y. H.
, Raza
, S. A.
, and Chern
, M.
, 2022
, “Numerical Predictions of Vibration Responses and Flow Energy Conversion Efficiency of Side-by-Side Cylinders at Moderate Reynolds Number
,” Appl. Ocean Res.
, 129
, p. 103392
.10.1016/j.apor.2022.10339228.
Dahl
, J. M.
, Hover
, F. S.
, Triantafyllou
, M. S.
, Dong
, S.
, and Karniadakis
, G. E.
, 2007
, “Resonant Vibrations of Bluff Bodies Cause Multivortex Shedding and High Frequency Forces
,” Phys. Rev. Lett.
, 99
(14
), p. 144503
.10.1103/PhysRevLett.99.14450329.
Bearman
, P. W.
, 2011
, “Circular Cylinder Wakes and Vortex-Induced Vibrations
,” J. Fluids Struct.
, 27
(5–6
), pp. 648
–658
.10.1016/j.jfluidstructs.2011.03.02130.
Sarpkaya
, T.
, 2004
, “A Critical Review of the Intrinsic Nature of Vortex-Induced Vibrations
,” J. Fluids Struct.
, 19
(4
), pp. 389
–447
.10.1016/j.jfluidstructs.2004.02.00531.
Williamson
, C. H. K.
, and Govardhan
, R.
, 2008
, “A Brief Review of Recent Results in Vortex-Induced Vibrations
,” J. Wind Eng. Ind. Aerodyn.
, 96
(6–7
), pp. 713
–735
.10.1016/j.jweia.2007.06.01932.
Dyrbye
, C.
, and Hansen
, S. O.
, 1997
, Wind Loads on Structures
, Wiley
, Hoboken, NJ
.33.
Feng
, C. C.
, 1968
, “The Measurement of Vortex Effects in Flow Past Stationary and Oscillating Circular and D-Section Cylinders
,” M.A.Sc. thesis
, University of British Columbia
, Vancouver, BC, Canada.10.14288/1.010404934.
Bearman
, P. W.
, 1984
, “Vortex Shedding From Oscillating Bluff Bodies
,” Annu. Rev. Fluid Mech.
, 16
(1
), pp. 195
–222
.10.1146/annurev.fl.16.010184.00121135.
Williamson
, C. H. K.
, and Govardhan
, R.
, 2004
, “Vortex Induced Vibrations
,” Annu. Rev. Fluid Mech.
, 36
(1
), pp. 413
–455
.10.1146/annurev.fluid.36.050802.12212836.
Parkinson
, G. V.
, 1974
, “Mathematical Models of Flow-Induced Vibrations of Bluff Bodies
,” Flow Induced Structural Vibrations
, E.
Naudascher
, ed., Springer
, Berlin, Germany
.37.
Quadflieg
, H.
, 1977
, “Vortex-Induced Forces on a Pair of Circular Cylinders in Incompressible High Reynolds Number Flow
,” Forsch. Ingenieurwes.
, 43
, pp. 9
–18
.10.1007/BF0256049638.
Zhou
, Y.
, Wang
, Z. J.
, So
, R. M. C.
, Xu
, S. J.
, and Jin
, W.
, 2001
, “Free Vibrations of Two Side-by-Side Cylinders in a Cross-Flow
,” J. Fluid Mech.
, 443
, pp. 197
–229
.10.1017/S002211200100517139.
King
, L. V.
, 1914
, “On the Convection of Heat From Small Cylinders in a Stream of Fluid: Determination of the Convective Constants of Small Platinum Wires With Applications to Hot Wire Anemometry
,” Proc. R. Soc. London A
, 90
(622
), pp. 563
–570
.10.1098/rsta.1914.002340.
Collis
, D. C.
, and Williams
, M. J.
, 1959
, “Two-Dimensional Convection From Heated Wires at Low Reynolds Numbers
,” J. Fluid Mech.
, 6
(3
), pp. 357
–384
.10.1017/S002211205900069641.
Coleman
, H. W.
, and Steele
, W. G.
, 2018
, Experimentation, Validation, and Uncertainty Analysis for Engineers
, 3
rd ed., Wiley
, Hoboken, NJ
.42.
Roshko
, A.
, 1953
, “On the Development of Turbulent Wakes From Vortex Streets
,” National Advisory Committee for Aeronautics
, Washington, DC, Report No. NACA-TN-2913
.https://ntrs.nasa.gov/api/citations/19930092207/downloads/19930092207.pdf43.
Farivar
, D.
, 1981
, “Turbulent Uniform Flow Around Cylinders of Finite Length
,” AIAA J.
, 19
(3
), pp. 275
–281
.10.2514/3.777144.
Sakamoto
, H.
, and Arie
, M.
, 1983
, “Vortex Shedding From a Rectangular Prism and a Circular Cylinder Placed Vertically in a Turbulent Boundary Layer
,” J. Fluid Mech.
, 126
, pp. 147
–165
.10.1017/S002211208300008745.
Williamson
, C. H. K.
, 1989
, “Oblique and Parallel Modes of Vortex Shedding in the Wake of a Circular Cylinder at Low Reynolds Numbers
,” J. Fluid Mech.
, 206
, pp. 579
–627
.10.1017/S002211208900242946.
Kamemoto
, K.
, 1976
, “Formation and Interaction of Two Parallel Vortex Streets
,” Bull. JSME
, 19
(129
), pp. 283
–290
.10.1299/jsme1958.19.28347.
Sun
, H.
, Kim
, E. S.
, Nowakowski
, G.
, Mauer
, E.
, and Bernitsas
, M. M.
, 2016
, “Effect of Mass-Ratio, Damping, and Stiffness on Optimal Hydrokinetic Energy Conversion of a Single, Rough Cylinder in Flow Induced Motions
,” Renewable Energy
, 99
, pp. 936
–959
.10.1016/j.renene.2016.07.02448.
Gao
, X.
, Shih
, W.-H.
, and Shih
, W. Y.
, 2013
, “Flow Energy Harvesting Using Piezoelectric Cantilevers With Cylindrical Extension
,” IEEE Trans. Ind. Electron.
, 60
(3
), pp. 1116
–1118
.10.1109/TIE.2012.218741349.
Looney
, S. W.
, and Hagan
, J. L.
, 2011
, “Statistical Methods for Assessing Biomarkers and Analyzing Biomarker Data
,” Handb. Stat.
, 27
, pp. 27
–65
.10.1016/S0169-7161(07)27004-X
