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Research Papers: CFD and VIV

Hydrodynamic Forces and Flow Structures in Flow Past a Cylinder Forced to Vibrate Transversely and Inline to a Steady Flow

[+] Author and Article Information
S. Peppa

Department of Naval Architecture,
Technological Educational Institute of Athens,
Egaleo,
Athens 12210, Greece
e-mail: speppa@teiath.gr

L. Kaiktsis

Department of Naval Architecture and
Marine Engineering,
National Technical University of Athens,
P.O. Box 64033,
Zografos,
Athens 15710, Greece;
Department of Mechanical Engineering,
Khalifa University of Science,
Technology and Research,
P.O. Box 127788,
Abu Dhabi, UAE
e-mail: kaiktsis@naval.ntua.gr

G. S. Triantafyllou

Department of Naval Architecture and
Marine Engineering,
National Technical University of Athens,
P.O. Box 64033,
Zografos,
Athens 15710, Greece
e-mail: gtrian@deslab.ntua.gr

1Corresponding author.

Contributed by the Ocean, Offshore, and Arctic Engineering Division of ASME for publication in the JOURNAL OF OFFSHORE MECHANICS AND ARCTIC ENGINEERING. Manuscript received October 24, 2014; final manuscript received November 10, 2015; published online December 15, 2015. Editor: Solomon Yim.

J. Offshore Mech. Arct. Eng 138(1), 011803 (Dec 15, 2015) (11 pages) Paper No: OMAE-14-1134; doi: 10.1115/1.4032031 History: Received October 24, 2014; Revised November 10, 2015

This paper reports computational results of forces and wake structure in two-dimensional flow past a circular cylinder forced to vibrate both transversely and inline to a uniform stream, following a figure-eight trajectory. For a flow stream from left to right, we distinguish between a counterclockwise mode and a clockwise mode, if the upper part of the trajectory is traversed counterclockwise or clockwise, respectively. The present computations correspond to a range of transverse oscillation frequencies close to the natural frequency of the Kármán vortex street and several oscillation amplitudes, both for counterclockwise motion and clockwise motion. The nondimensional forces and nondimensional power transfer from the fluid to the body are calculated. The results demonstrate a strong dependence of the forces and power transfer on the direction in which the figure-eight is traversed. In general, counterclockwise motion maintains positive power transfer at higher oscillation amplitudes. Flow visualizations show that the wakes are characterized by the presence of two single (2S) vortex shedding mode at low oscillation amplitudes and can attain more complex structures at higher amplitudes.

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References

Bishop, R. E. D. , and Hassan, A. Y. , 1964, “ The Lift and Drag Forces on a Circular Cylinder Oscillating in a Flowing Fluid,” Proc. R. Soc. London, Ser. A, 277(1368), pp. 51–75. [CrossRef]
Williamson, C. H. K. , and Roshko, A. , 1988, “ Vortex Formation in the Wake of an Oscillating Cylinder,” J. Fluids Struct., 2(4), pp. 355–381. [CrossRef]
Gopalkrishnan, R. , 1993, “ Vortex-Induced Forces on Oscillating Bluff Cylinders,” Ph.D. thesis, MIT, Cambridge, MA.
Blackburn, H. M. , and Henderson, R. D. , 1999, “ A Study of Two-Dimensional Flow Past an Oscillating Cylinder,” J. Fluid Mech., 385, pp. 255–286. [CrossRef]
Anagnostopoulos, P. , 2000, “ Numerical Study of the Flow Past a Cylinder Excited Transversely to the Incident Stream. Part 1: Lock-in Zone, Hydrodynamic Forces and Wake Geometry,” J. Fluids Struct., 14(6), pp. 819–851. [CrossRef]
Willden, R. , McSherry, R. , and Graham, J. , 2008, “ Prescribed Cross-Stream Oscillations of a Circular Cylinder at Laminar and Early Turbulent Reynolds Numbers,” Fifth Bluff Bodies and Vortex-Induced Vibration Conference, pp. 7–10.
Jeon, D. , and Gharib, M. , 2001, “ On Circular Cylinders Undergoing Two-Degree-of-Freedom Forced Motions,” J. Fluids Struct., 15(3–4), pp. 533–541. [CrossRef]
Baranyi, L. , 2012, “ Simulation of a Low-Reynolds Number Flow Around a Cylinder Following a Figure-8-Path,” Int. Rev. Appl. Sci. Eng., 3(2), pp. 133–146. [CrossRef]
Kaiktsis, L. , Triantafyllou, G. S. , and Ozbas, M. , 2007, “ Excitation, Inertia, and Drag Forces on a Cylinder Vibrating Transversely to a Steady Flow,” J. Fluids Struct., 23(1), pp. 1–21. [CrossRef]
Peppa, S. , Kaiktsis, L. , and Triantafyllou, G. S. , 2010, “ The Effect of In-Line Oscillation on the Forces of a Cylinder Vibrating in a Steady Flow,” ASME Paper No. FEDSM-ICNMM2010-30054.
Karniadakis, G. E. , and Sherwin, S. J. , 2005, Spectral/hp Element Methods for Computational Fluid Dynamics, Oxford University Press, New York.
Karniadakis, G. E. , Israeli, M. , and Orszag, S. A. , 1991, “ High-Order Splitting Methods for the Incompressible Navier–Stokes Equations,” J. Comput. Phys., 97(2), pp. 414–443. [CrossRef]
Peppa, S. , 2012, “ Computational Study of Flow-Structure Interaction,” Ph.D. thesis, School of Naval Architecture and Marine Engineering, NTUA, Athens, Greece.

Figures

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Fig. 1

Spectral element grid for two-dimensional flow past a circular cylinder, including (a) the entire mesh and (b) a close-up view of the mesh around the cylinder

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Fig. 2

Nondimensional power transfer corresponding to y-motion, Py, and total power transfer, P, versus the reduced y-amplitude, for frequency ratio F = 1.0; here, the cases ε = 0 (transverse-only oscillation) and ε = 0.2 (clockwise and counterclockwise modes) are shown

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Fig. 3

Nondimensional power transfer corresponding to y-motion, Py, and total power transfer, P, versus the reduced y-amplitude, for frequency ratio F = 1.0; here, the cases ε = 0 (transverse-only oscillation) and ε = 0.4 (clockwise and counterclockwise modes) are shown

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Fig. 10

Nondimensional power transfer corresponding to y-motion, Py, and total power transfer, P, versus the reduced y-amplitude for frequency ratio F = 0.9; here, the cases ε = 0 (transverse-only oscillation) and ε = 0.2 (clockwise and counterclockwise modes) are shown

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Fig. 8

RMS fluctuation intensity of drag coefficient versus the reduced y-amplitude for frequency ratio F = 1.0; here, the cases ε = 0 (transverse-only oscillation) and ε = 0.2 (clockwise and counterclockwise modes) are shown

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Fig. 9

RMS fluctuation intensity of drag coefficient versus the reduced y-amplitude for frequency ratio F = 1.0; here, the cases ε = 0 (transverse-only oscillation) and ε = 0.4 (clockwise and counterclockwise modes) are shown

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Fig. 11

Nondimensional power transfer corresponding to y-motion, Py, and total power transfer, P, versus the reduced y-amplitude for frequency ratio F = 0.9; here, the cases ε = 0 (transverse-only oscillation) and ε = 0.4 (clockwise and counterclockwise modes) are shown

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Fig. 17

RMS fluctuation intensity of drag coefficient versus the reduced y-amplitude for frequency ratio F = 0.9; here, the cases ε = 0 (transverse-only oscillation) and ε = 0.4 (clockwise and counterclockwise modes) are shown

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Fig. 18

Nondimensional power transfer corresponding to y-motion, Py, and total power transfer, P, versus the reduced y-amplitude for frequency ratio F = 1.1; here, the cases ε = 0 (transverse-only oscillation) and ε = 0.2 (clockwise and counterclockwise modes) are shown

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Fig. 19

Nondimensional power transfer corresponding to y-motion, Py, and total power transfer, P, versus the reduced y-amplitude for frequency ratio F = 1.1; here, the cases ε = 0 (transverse-only oscillation) and ε = 0.4 (clockwise and counterclockwise modes) are shown

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Fig. 4

RMS fluctuation intensity of lift coefficient versus the reduced y-amplitude for frequency ratio F = 1.0; here, the cases ε = 0 (transverse-only oscillation) and ε = 0.2 (clockwise and counterclockwise modes) are shown

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Fig. 5

RMS fluctuation intensity of lift coefficient versus the reduced y-amplitude for frequency ratio F = 1.0; here, the cases ε = 0 (transverse-only oscillation) and ε = 0.4 (clockwise and counterclockwise modes) are shown

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Fig. 6

Time-averaged drag coefficient versus the reduced y-amplitude for frequency ratio F = 1.0; here, the cases ε = 0 (transverse-only oscillation) and ε = 0.2 (clockwise and counterclockwise modes) are shown

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Fig. 7

Time-averaged drag coefficient versus the reduced y-amplitude for frequency ratio F = 1.0; here, the cases ε = 0 (transverse-only oscillation) and ε = 0.4 (clockwise and counterclockwise modes) are shown

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Fig. 12

RMS fluctuation intensity of lift coefficient versus the reduced y-amplitude for frequency ratio F = 0.9; here, the cases ε = 0 (transverse-only oscillation) and ε = 0.2 (clockwise and counterclockwise modes) are shown

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Fig. 13

RMS fluctuation intensity of lift coefficient versus the reduced y-amplitude for frequency ratio F = 0.9; here, the cases ε = 0 (transverse-only oscillation) and ε = 0.4 (clockwise and counterclockwise modes) are shown

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Fig. 14

Time-averaged drag coefficient versus the reduced y-amplitude for frequency ratio F = 0.9; here, the cases ε = 0 (transverse-only oscillation) and ε = 0.2 (clockwise and counterclockwise modes) are shown

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Fig. 15

Time-averaged drag coefficient versus the reduced y-amplitude for frequency ratio F = 0.9; here, the cases ε = 0 (transverse-only oscillation) and ε = 0.4 (clockwise and counterclockwise modes) are shown

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Fig. 16

RMS fluctuation intensity of drag coefficient versus the reduced y-amplitude for frequency ratio F = 0.9; here, the cases ε = 0 (transverse-only oscillation) and ε = 0.2 (clockwise and counterclockwise modes) are shown

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Fig. 20

RMS fluctuation intensity of lift coefficient versus the reduced y-amplitude for frequency ratio F = 1.1; here, the cases ε = 0 (transverse-only oscillation) and ε = 0.2 (clockwise and counterclockwise modes) are shown

Grahic Jump Location
Fig. 21

RMS fluctuation intensity of lift coefficient versus the reduced y-amplitude for frequency ratio F = 1.1; here, the cases ε = 0 (transverse-only oscillation) and ε = 0.4 (clockwise and counterclockwise modes) are shown

Grahic Jump Location
Fig. 22

Time-averaged drag coefficient versus the reduced y-amplitude for frequency ratio F = 1.1; here, the cases ε = 0 (transverse-only oscillation) and ε = 0.2 (clockwise and counterclockwise modes) are shown

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Fig. 23

Time-averaged drag coefficient versus the reduced y-amplitude for frequency ratio F = 1.1; here, the cases ε = 0 (transverse-only oscillation) and ε = 0.4 (clockwise and counterclockwise modes) are shown

Grahic Jump Location
Fig. 24

RMS fluctuation intensity of drag coefficient versus the reduced y-amplitude for frequency ratio F = 1.1; here, the cases ε = 0 (transverse-only oscillation) and ε = 0.2 (clockwise and counterclockwise modes) are shown

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Fig. 25

RMS fluctuation intensity of drag coefficient versus the reduced y-amplitude for frequency ratio F = 1.1; here, the cases ε = 0 (transverse-only oscillation) and ε = 0.4 (clockwise and counterclockwise modes) are shown

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Fig. 26

Instantaneous vorticity isocontours of flow past a cylinder undergoing clockwise motion with F = 1.0, ε = 0.2, and transverse oscillation amplitude: (a) Ay/D = 0.20, (b) Ay/D = 0.25, (c) Ay/D = 0.30, (d) Ay/D = 0.45, and (e) Ay/D = 0.60

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Fig. 27

Instantaneous vorticity isocontours of flow past a cylinder undergoing counterclockwise motion with F = 1.0, ε = 0.2, and transverse oscillation amplitude: (a) Ay/D = 0.20, (b) Ay/D = 0.25, (c) Ay/D = 0.30, (d) Ay/D = 0.50, and (e) Ay/D = 0.60

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Fig. 28

Instantaneous vorticity isocontours of flow past a cylinder undergoing clockwise motion with F = 0.9, ε = 0.2, and transverse oscillation amplitude: (a) Ay/D = 0.05, (b) Ay/D = 0.20, (c) Ay/D = 0.25, (d) Ay/D = 0.50, and (e) Ay/D = 0.60

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Fig. 29

Instantaneous vorticity isocontours of flow past a cylinder undergoing counterclockwise motion with F = 0.9, ε = 0.2, and transverse oscillation amplitude: (a) Ay/D = 0.05, (b) Ay/D = 0.20, (c) Ay/D = 0.30, (d) Ay/D = 0.35, (e) Ay/D = 0.45, and (f) Ay/D = 0.60

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Fig. 30

Instantaneous vorticity isocontours of flow past a cylinder undergoing clockwise motion with F = 1.1, ε = 0.2, and transverse oscillation amplitude: (a) Ay/D = 0.05, (b) Ay/D = 0.25, (c) Ay/D = 0.40, (d) Ay/D = 0.45, and (e) Ay/D = 0.50

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Fig. 31

Instantaneous vorticity isocontours of flow past a cylinder undergoing counterclockwise motion with F = 1.1, ε = 0.2, and transverse oscillation amplitude: (a) Ay/D = 0.05, (b) Ay/D = 0.25, (c) Ay/D = 0.40, (d) Ay/D = 0.50, and (e) Ay/D = 0.60

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