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CFD and VIV

Near-Bed Flow Mechanisms Around a Circular Marine Pipeline Close to a Flat Seabed in the Subcritical Flow Regime Using a k-ɛ Model

[+] Author and Article Information
Muk Chen Ong1

Department of Marine Technology,  Norwegian University of Science and Technology, NO-7491 Trondheim, Norwaymuk.c.ong@ntnu.no

Torbjørn Utnes

 SINTEF IKT Applied Mathematics, NO-7465 Trondheim, Norway

Lars Erik, Dag Myrhaug, Bjørnar Pettersen

Department of Marine Technology,  Norwegian University of Science and Technology, NO-7491 Trondheim, Norway

1

Corresponding author.

J. Offshore Mech. Arct. Eng 134(2), 021803 (Dec 05, 2011) (11 pages) doi:10.1115/1.4004631 History: Received January 25, 2010; Revised May 27, 2011; Published December 05, 2011; Online December 05, 2011

Flow mechanisms around a two-dimensional (2D) circular marine pipeline close to a flat seabed have been investigated using the 2D unsteady Reynolds-averaged Navier–Stokes (URANS) equations with a standard high Reynolds number k-ɛ model. The Reynolds number (based on the free stream velocity and cylinder diameter) ranges from 1 × 104 to 4.8 × 104 in the subcritical flow regime. The objective of the present study is to show a thorough documentation of the applicability of the k-ɛ model for engineering design within this flow regime by means of a careful comparison with available experimental data. The inflow boundary layer thickness and the Reynolds numbers in the present simulations are set according to published experimental data, with which the simulations are compared. Detailed comparisons with the experimental data for small gap ratios are provided and discussed. The effects of the gap to diameter ratio and the inflow boundary layer thickness have been studied. Although under-predictions of the essential hydrodynamic quantities (e.g., time-averaged drag coefficient, time-averaged lift coefficient, root-mean-square fluctuating lift coefficient, and mean pressure coefficient at the back of the pipeline) are observed due to the limitation of the turbulence model, the present approach is capable of providing good qualitative agreement with the published experimental data. The vortex shedding mechanisms have been investigated, and satisfactory predictions are obtained. The mean pressure coefficient and the mean friction velocity along the flat seabed are predicted reasonably well as compared with published experimental and numerical results. The mean seabed friction velocity at the gap is much larger for small gaps than for large gaps; thus, the bedload sediment transport is much larger for small gaps than for large gaps.

Copyright © 2012 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Definition sketch for flow around a circular cylinder close to a flat seabed. The origin of (x1 , x2 ) is at the center of the cylinder.

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Figure 2

Grid convergence study for CD and CL with respect to the number of elements in the computational domain at Re = 1.31 × 104 with δ/D = 0.48 and zw  = 1 × 10−6 m

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Figure 3

An example of the mesh (G/D = 0.4) with 20,480 elements and 20,816 nodes for the present simulations

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Figure 4

Time-averaged drag coefficient versus gap to diameter ratio

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Figure 5

Time-averaged lift coefficient versus gap to diameter ratio

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Figure 6

Strouhal number versus gap to diameter ratio

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Figure 7

Mean pressure coefficient around the cylinder for Re = 1.31 × 104 , δ/D = 0.48, and G/D = (0.1,0.4,0.8)

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Figure 8

Mean pressure coefficient around the cylinder for Re = 4.8 × 104 , δ/D = 0.8, and G/D = (0.1,0.4,0.8)

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Figure 9

Root mean square value of the fluctuating lift coefficient versus gap to diameter ratio

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Figure 10

Instantaneous nondimensional vorticity contours of flow around a marine pipeline for Re  = 1.31 × 104 and δ/D = 0.48 at the dimensionless time of 200D/U . Forty contour levels of ωD/U from −240 to 240 are plotted.

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Figure 11

Mean pressure coefficient along the flat seabed for Re = 4.8 × 104 , δ/D = 0.8, and G/D = (0.1,0.4,0.8)

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Figure 12

Mean friction velocity along the flat seabed for Re = 1 × 104 to 4.8 × 104 , δ/D = 0.14 to 0.8, and G/D = (0.1,0.4,0.6,0.8)

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Figure 13

Effect of the vortex shedding on the instantaneous friction velocity along the flat seabed for Re = 1.31 × 104 , δ/D = 0.48, zw  = 1 × 10−6 m, and G/D = (0.1,0.4,0.8)

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Figure 14

Instantaneous Shields parameter along the flat seabed for Re = 1.31 × 104 , δ/D = 0.48, zw  = 1 × 10−6 m, and G/D = 0.1

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Figure 15

Mean nondimensional bedload sediment transport along the flat seabed for Re = 1.31 × 104 , δ/D = 0.48, zw  = 1 × 10−6 m, and G/D = (0.1,0.4,0.8)

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