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Ocean Engineering

Friction Factor Estimation for Turbulent Flows in Corrugated Pipes with Rough Walls

[+] Author and Article Information
Maxim Pisarenco1

Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlandsm.pisarenco@tue.nl

Bas van der Linden, Arris Tijsseling

Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands

Emmanuel Ory

Single Buoy Moorings Inc., P.O. Box 199, MC 98007 Monaco Cedex, Monaco

Jacques Dam

Stork Inoteq, P.O. Box 379, 1000 AJ Amsterdam, The Netherlands

1

Corresponding author.

J. Offshore Mech. Arct. Eng 133(1), 011101 (Nov 03, 2010) (9 pages) doi:10.1115/1.4001439 History: Received September 07, 2009; Revised January 20, 2010; Published November 03, 2010; Online November 03, 2010

Abstract

The motivation of the investigation is the critical pressure loss in cryogenic flexible hoses used for LNG transport in offshore installations. Our main goal is to estimate the friction factor for the turbulent flow in this type of pipes. For this purpose, two-equation turbulence models ($k−ϵ$ and $k−ω$) are used in the computations. First, the fully developed turbulent flow in a conventional pipe is considered. Simulations are performed to validate the chosen models, boundary conditions, and computational grids. Then a new boundary condition is implemented based on the “combined” law of the wall. It enables us to model the effects of roughness (and maintain the right flow behavior for moderate Reynolds numbers). The implemented boundary condition is validated by comparison with experimental data. Next, the turbulent flow in periodically corrugated (flexible) pipes is considered. New flow phenomena (such as flow separation) caused by the corrugation are pointed out and the essence of periodically fully developed flow is explained. The friction factor for different values of relative roughness of the fabric is estimated by performing a set of simulations. Finally, the main conclusion is presented: The friction factor in a flexible corrugated pipe is mostly determined by the shape and size of the steel spiral, and not by the type of the fabric, which is wrapped around the spiral.

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Figures

Figure 1

Typical flexible pipe

Figure 2

Schematic representation of the mesh for a wall function and a near-wall model approach

Figure 3

Dependence of the friction factor f on the thickness yp+ of the near-wall region at Reynolds numbers of order 106. Solid line – computed values, dashed line – experimental values (from the Moody diagram). The k−ϵ model is used.

Figure 4

Computational domain and the fine mesh used for the last step of the computations

Figure 5

Computed and measured friction factors for smooth pipes (e/D=0)

Figure 6

Computed and measured friction factors for smooth pipes (e/D=0) zoomed around Re∼106

Figure 7

Computed (dashed lines) and measured (solid lines) friction factors for flow in pipes with rough walls. The k−ϵ model is used.

Figure 8

Computed (dashed lines) and measured (solid lines) friction factors for flow with rough walls using a combined law of the wall; Eqs. 13,14,16. The k−ϵ model is used.

Figure 9

Computational domain with the adapted mesh (generated from an initial mesh by an adaptive solver). Distances are in meters.

Figure 10

Numerical error versus total iteration number. Each curve corresponds to a mesh and has its local origin at the end of the previous curve.

Figure 11

A typical solution. Colored surface — pressure, arrows — velocity field, and green lines — streamlines. This computation was performed for ΔP=3×104 Pa, ρ=500 kg/m3, and η=0.01 Pa s.

Figure 12

Pressure profile along the radial direction at x=0

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