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Research Papers: Ocean Engineering

# Investigation of the Dynamic Loads on a Vertically Oscillating Circular Cylinder Close to the Sea Bed: The Role of Viscosity

[+] Author and Article Information
Alessio Pierro

Techfem S.p.a.,
Fano 61032, Italy
e-mail: a.pierro@techfem.it

Enrico Tinti

SPS Fano S.r.l.,
Fano 61032, Italy
e-mail: enrico.tinti@spsfano.it

Stefano Lenci

Polytechnic University of Marche,
Ancona 60121, Italy
e-mail: s.lenci@univpm.it

Maurizio Brocchini

Polytechnic University of Marche,
Ancona 60121, Italy
e-mail: m.brocchini@univpm.it

Giuseppina Colicchio

Marine Technology Research Institute,
CNR Insean,
Rome 00128, Italy
e-mail: giuseppina.colicchio@cnr.it

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 November 25, 2016; final manuscript received June 5, 2017; published online August 16, 2017. Assoc. Editor: Xi-Ying Zhang.

J. Offshore Mech. Arct. Eng 139(6), 061101 (Aug 16, 2017) (12 pages) Paper No: OMAE-16-1151; doi: 10.1115/1.4037247 History: Received November 25, 2016; Revised June 05, 2017

## Abstract

The flow around an oscillating cylinder close to a horizontal solid boundary is studied to gather information about the load acting on pipelines, while they are laid on the sea bottom. The problem is simplified assuming that the pipeline section is rigid and oscillates harmonically only in the normal-to-seabed direction so that the problem can be tackled in two dimensions. A computational fluid dynamics (CFD) solver is used to take into account viscous effects in the hypothesis of laminar flow conditions. This best suits the conditions of pipeline layering when the Reynolds number, $Re=Um·D/ν$, ranges in order of 450–120,000, while the Keulegan–Carpenter number, $KC=Um·D/T$, ranges in order of 0.45–2. Nonetheless, boundary layer separation and vortex shedding are considered. Focus is on the determination of the lift force for which a novel analytical approximate expression is proposed. Such an analytical result can provide useful support to the studies related with the structural analysis of the pipe laying.

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## References

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## Figures

Fig. 1

Problem scheme and parameters definition

Fig. 2

Coordinates and variable in the complex plane

Fig. 3

Added mass, Ca (left), and drag coefficients, CD (right) from the Wilde solution

Fig. 4

Added mass (left) and drag (right) coefficients from the Stokes–Wang solution

Fig. 5

The chosen domain for the CFD runs

Fig. 6

Mesh domain: (a) overall grid view and (b) mesh detail around the cylinder

Fig. 8

Drag coefficient as function of ζ(t) at fixed β for different values of KC (left) and as function of ζ(t) at fixed KC for different values of β (right)

Fig. 7

Added mass coefficient in the function of ζ(t) for different values of β

Fig. 14

Dimensionless lift force detail at θ=3π/2 for different β at KC=0.45

Fig. 10

Lift force comparison with new computed force (15) with KC=0.45 and β= 10,000 (left) and with KC=1.25 and β=66,667 (right). The black line gives the theoretical force by Wilde, the green line the new force computed with Eq.(15), and the red one that computed by the OpenFOAM solver.

Fig. 17

Model validation far from the bottom for different pairs of KC and β (increasing from top-left)

Fig. 18

Different levels of mesh refinement: medium (up) and coarse (down)

Fig. 19

Vertical force for different grid refinements with KC = 0.45 and β = 1000

Fig. 11

(a) Vorticity magnitude around the cylinder, (b) velocity magnitude around the cylinder, (c) pressure field around the cylinder, and (d) pressure distribution around the circle, far from the bottom (red) and near the bottom (black) at t=0+nT

Fig. 12

Dimensionless lift force for various KC at β=1000

Fig. 13

Dimensionless lift force for various β at KC=0.45

Fig. 15

θ=3π/2: (a) vorticity magnitude and pressure contour for KC=0.45 and β=1000, (b) vorticity magnitude and pressure contour for KC=0.45 and β=30,000, and (c) vertical velocity in the midsection of the cylinder for the two values of β

Fig. 16

Vertical force comparison between simulated and computed (17) for different flow regimes. The green line the force computed with Eq. (17) and the red one that computed by the OpenFOAM solver.

Fig. 9

Comparison between computed and simulated lift force with KC=0.45 and β= 10,000 (left) and with KC=1.25 and β=66,667 (right). The black line gives the theoretical force by Wilde, the green line the force computed with Eq. (14), and the red one that computed by the OpenFOAM solver.

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