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Research Papers: Fluid-Structure Interaction

Modeling Liquid Slugs Accelerating in Inclined Conduits

[+] Author and Article Information
Stan P. Korzilius

Department of Mathematics and
Computer Science,
Eindhoven University of Technology,
Eindhoven 5600 MB, The Netherlands
e-mail: s.p.korzilius@tue.nl

Arris S. Tijsseling

Department of Mathematics and
Computer Science,
Eindhoven University of Technology,
Eindhoven 5600 MB, The Netherlands
e-mail: a.s.tijsseling@tue.nl

Zafer Bozkuş

Hydromechanics Laboratory,
Department of Civil Engineering,
Middle East Technical University,
Ankara 06800, Turkey
e-mail: bozkus@metu.edu.tr

Martijn J. H. Anthonissen

Department of Mathematics and
Computer Science,
Eindhoven University of Technology,
Eindhoven 5600 MB, The Netherlands
e-mail: m.j.h.anthonissen@tue.nl

Wil H. A. Schilders

Department of Mathematics and
Computer Science,
Eindhoven University of Technology,
Eindhoven 5600 MB, The Netherlands
e-mail: w.h.a.schilders@tue.nl

Contributed by the Pressure Vessel and Piping Division of ASME for publication in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received March 9, 2017; final manuscript received August 9, 2017; published online September 27, 2017. Assoc. Editor: Tomomichi Nakamura.

J. Pressure Vessel Technol 139(6), 061301 (Sep 27, 2017) (10 pages) Paper No: PVT-17-1044; doi: 10.1115/1.4037716 History: Received March 09, 2017; Revised August 09, 2017

In this article, we simulate traveling liquid slugs in conduits, as they may occur in systems carrying high-pressure steam. We consider both horizontal and inclined pipes in which the slug is accelerated by a suddenly applied pressure gradient, while at the same time, gravity and friction work in the opposite direction. This causes a steep slug front and an extended slug tail. The shapes of front and tail are of interest since they determine the forces exerted on bends and other obstacles in the piping system. The study also aims at improving existing one-dimensional (1D) models. A hybrid model is proposed that enables us to leave out the larger inner part of the slug. It was found that the hybrid model speeds up the two-dimensional (2D) computations significantly, while having no adverse effects on the shapes of the slug's front and tail.

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References

Tijsseling, A. , Hou, Q. , Bozkuş, Z. , and Laanearu, J. , 2016, “ Improved One-Dimensional Models for Rapid Emptying and Filling of Pipelines,” ASME J. Pressure Vessel Technol., 138(3), p. 031301. [CrossRef]
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Carlson, M. , 2011, “ Condensation Induced Water Hammer and Steam Assisted Gravity Drainage in the Athabasca Oil Sands,” 14th International Topical Meeting on Nuclear Reactor Thermal Hydraulics, Toronto, ON, Canada, Sept. 25–30, Paper No. NURETH14-600.
Vecchio, R. , Sinha, S. , Bruck, P. , Esselman, T. , Zysk, G. , and Somrah, D. , 2015, “ The 2007 New York City Steam Explosion: Post-Accident Analysis,” 12th International Conference on Pressure Surges, Dublin, Ireland, Nov. 18–20, pp. 7–17.
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Prasser, H. , Ézsöl, G. , Baranyai, G. , and Sühnel, T. , 2008, “ Spontaneous Water Hammers in a Steam Line in the Case of Cold Water Ingress,” Multiphase Sci. Technol., 20(3–4), pp. 265–290. [CrossRef]
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Xing, L. , Yeung, H. , and Lo, S. , 2011, “ Investigation of Slug Flow Induced Forces on Pipe Bends Applying STAR-OLGA Coupling,” 15th International Conference on Multiphase Production Technology, Cannes, France, June 15, pp. 327–344.
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Hou, Q. , Tijsseling, A. , and Bozkuş, Z. , 2014, “ Dynamic Force on an Elbow Caused by a Traveling Liquid Slug,” ASME J. Pressure Vessel Technol., 136(3), p. 031302. [CrossRef]
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Tijsseling, A. , Hou, Q. , and Bozkuş, Z. , 2016, “ An Improved One-Dimensional Model for Liquid Slugs Traveling in Pipelines,” ASME J. Pressure Vessel Technol., 138(1), p. 011301. [CrossRef]
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Figures

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Fig. 1

A two-dimensional initial situation

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Fig. 2

Comparison of the tail of the slug at t = 0.25 s calculated with (a) the full simulation and (b) the hybrid model.

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Fig. 3

Comparison of the front of the slug at t = 0.25 s calculated with (a) the full simulation and (b) the hybrid model.

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Fig. 4

The slug's front velocity as a function of its position when (a) P = 105 Pa and (b) P = 106 Pa. Comparison between the SPH simulation and the one-dimensional models without (β = 0) and with holdup.

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Fig. 5

Illustration of the one-dimensional models with holdup, as in Ref. [20]

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Fig. 6

(a) the slug's length as a function of its front position for both P = 105 Pa and P = 106 Pa and (b) the values of β derived from the SPH simulation for P = 106 Pa, where the black line indicates β = 0.044

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Fig. 7

Setup of the numerical simulations. The tilted line is the horizontal and indicates the angle of inclination.

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Fig. 8

Simulation of a traveling liquid slug starting from rest in an inclined pipe, showing the pressure distribution in the slug. In Figures (e), (f) and (g) the slug is fully contained in the straight section of the pipe and the hybrid model is applied.

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Fig. 9

Representation of the observed slug flow pattern by Bozkuş and Wiggert [7]

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Fig. 10

Simulation of a traveling liquid slug in an inclined pipe.

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Fig. 11

Simulation of a liquid slug hitting and passing an elbow. The cross in (a) indicates the position of the monitor point.

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Fig. 12

The gauge pressure exerted by the liquid slug on the downstream bend in an inclined pipe when (a) L0 = 3 m and (b) L0 = 5 m. A comparison of our SPH simulation with the measurement of Bozkuş et al. [9]. Note: 100 psi ≈ 7 bar.

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Fig. 13

The front (right) and tail (left) of the slug are simulated with two-dimensional SPH. The middle part is replaced by a quasi two-dimensional model.

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