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Research Papers: CFD and VIV

Interference Between Two Stationary or Elastically Supported Rigid Circular Cylinders of Unequal Diameters in Tandem and Staggered Arrangements

[+] Author and Article Information
Shan Huang

Department of Naval Architecture and Marine Engineering,
University of Strathclyde,
100 Montrose Street,
Glasgow, G4 0LZ, UK
e-mail: shan.huang@strath.ac.uk

Andy Sworn

BP Exploration Operating Company Ltd.,
Chertsey Road, Sunbury on Thames,
Middlesex, TW16 7LN, UK

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 August 3, 2011; final manuscript received May 22, 2012; published online February 25, 2013. Assoc. Editor: Antonio C. Fernandes.

J. Offshore Mech. Arct. Eng 135(2), 021803 (Feb 25, 2013) (10 pages) Paper No: OMAE-11-1070; doi: 10.1115/1.4007053 History: Received August 03, 2011; Revised May 22, 2012

Analysis of model test results was carried out to investigate the hydrodynamic interaction between pairs of fixed or elastically supported rigid cylinders of dissimilar diameters in a water flume. The two cylinders are placed with one situated in the wake of the other. The spacing between the cylinders ranges from 1 to 15 times the larger cylinder diameter. The Reynolds numbers are within the subcritical range. For the vibrating cylinders which are free to oscillate in both the in-line and the cross-flow directions, the reduced velocity ranges from 1 to 13 and the low damping ratio of the test setup at 0.006 gives a combined mass-damping parameter of 0.02. For the fixed cylinders, the downstream cylinder experiences a drag reduction and it was found that this drag reduction also depends upon the diameter ratio. The lift on the fixed downstream cylinder has the frequency components derived from the upstream cylinder's vortex shedding as well as from its own vortex shedding, and the relative importance of the two sources is influenced by the spacing between the two cylinders. This is reflected in the downstream cylinder's vortex induced vibration (VIV) response which appears to be dependent upon the actual reduced velocities of both the cylinders.

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References

Figures

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Fig. 1

Schematic of the test setup

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Fig. 2

Mean drag coefficients of (a) upstream cylinder and (b) downstream cylinder. Tandem arrangement.

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Fig. 3

Mean drag of tandem smooth cylinders in comparison with the results of Igarashi [8]

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Fig. 4

Downstream cylinder drag coefficient versus transverse spacing Y for different diameter ratios

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Fig. 5

Mean lift coefficient of the downstream cylinder versus transverse spacing at X = 5 and U = 0.4 m/s. The lift points to the wake centerline.

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Fig. 6

Drag coefficients of upstream and downstream cylinders. Note the in-line spacing X is nondimensionalized by using the larger cylinder's diameter.

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Fig. 7

Amplitude spectrum density of lift coefficient on downstream cylinders as X and Y vary for U = 0.2, D1/D2 = 2 and 4, respectively

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Fig. 8

Strouhal number for D1/D2 = 2. St=f×D1/U.

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Fig. 10

Drag coefficient of downstream cylinder versus transverse spacing. Comparison between test results and that based upon Huse's wake model. The downstream cylinder is at X = 5 with Y varying.

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Fig. 9

Drag coefficient of downstream cylinder versus in-line spacing. Comparison between test results and that based upon Huse's wake model. The downstream cylinder is on the wake centerline.

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Fig. 11

VIV motion trajectories of both the upstream and downstream cylinders for the initial spacing X/D1 at 1.8, 2.0, 3.0, 4.0, 7.0, and 15, respectively (from left to right and top to bottom). In each graph, the trajectory on the left is for the upstream cylinder; the trajectory on the right is for the downstream cylinder.

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Fig. 12

Power spectral density of the cross-flow and the in-line motions of the two cylinders. The nominal reduced velocity Vr = 9. (a) X = 2; (b) X = 15. Note D1 = 2 × D2 in this case.

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Fig. 13

Power spectral density of the cross-flow and the in-line motions of the two cylinders. The nominal reduced velocity Vr = 5. (a) X = 2; (b) X = 15. Note D1 = 2 × D2 in this case.

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Fig. 14

Standard deviation of transverse motion of upstream cylinder. The horizontal axis is the nondimensional spacing between the two cylinders (nondimensionalized by using the upstream cylinder's diameter). Vr is the nominal reduced velocity.

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Fig. 15

Standard deviation of the transverse motion of downstream cylinder. The horizontal axis is the spacing between the two cylinders nondimensionalized by using the upstream cylinder's diameter.

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Fig. 16

Standard deviation of the transverse motion of the downstream cylinder versus the nominal reduced velocity at a variety of cylinder spacing

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Fig. 17

Standard deviation of the transverse motion of the downstream cylinder versus the modified reduced velocity. The cylinder spacing are indicated by X.

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Fig. 18

Mean wake velocity ucl along the wake centerline behind a fixed cylinder of diameter d, nondimensionalized by using the free stream velocity ui. Re = 1.4 × 105. Reproduced from Cantwell and Coles [13].

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