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Research Papers: Fluid-Structure Interaction

# Dynamic Force on an Elbow Caused by a Traveling Liquid Slug

[+] Author and Article Information
Darcy Q. Hou

State Key Laboratory of Hydraulic
Engineering Simulation and Safety, and
School of Computer Science and Technology,
Tianjin University,
Tianjin 300072, China
e-mail: darcy.hou@gmail.com

Arris S. Tijsseling

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

Zafer Bozkus

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

Contributed by the Pressure Vessel and Piping Division of ASME for publication in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received March 2, 2013; final manuscript received December 14, 2013; published online February 27, 2014. Assoc. Editor: Jong Chull Jo.

J. Pressure Vessel Technol 136(3), 031302 (Feb 27, 2014) (11 pages) Paper No: PVT-13-1043; doi: 10.1115/1.4026276 History: Received March 02, 2013; Revised December 14, 2013

## Abstract

The impact force on an elbow induced by traveling isolated liquid slugs in a horizontal pipeline is studied. A literature review reveals that the force on the elbow is mainly due to momentum transfer in changing the fluid flow direction around the elbow. Therefore, to accurately calculate the magnitude and duration of the impact force, the slug arrival velocity at the elbow needs to be well predicted. The hydrodynamic behavior of the slug passing through the elbow needs to be properly modeled too. A combination of 1D and 2D models is used in this paper to analyze this problem. The 1D model is used to predict the slug motion in the horizontal pipeline. With the obtained slug arrival velocity, slug length, and driving air pressure as initial conditions, the 2D Euler equations are solved by the smoothed particle hydrodynamics (SPH) method to analyze the slug dynamics at the elbow. The 2D SPH solution matches experimental data and clearly demonstrates the occurrence of flow separation at the elbow, which is a typical effect of high Reynolds flows. Using the obtained flow contraction coefficient, an improved 1D model with nonlinear elbow resistance is proposed and solved by SPH. The 1D SPH results show the best fit with experimental data obtained so far.

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## References

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## Figures

Fig. 4

Experimental setup of Owen and Hussein [12]

Fig. 3

Flow patterns of the slug motion in a voided line [14]

Fig. 2

Experimental setup used by Bozkus in Ref. [14]; SGP = slug generator pipe

Fig. 1

Experimental setup of Fenton and Griffith [13]

Fig. 5

Control volume moving with the liquid slug in an empty pipe adapted from Ref. [14]; β=A3/A2

Fig. 8

Pressure history after slug impact at the elbow for the case of L0 = 2.74 m and P0 = 138 kPa (20 psig)

Fig. 9

Flow separation at the elbow at two different times

Fig. 6

Control volume for the liquid slug after impact at the elbow and considering flow separation

Fig. 7

SPH setup of two-dimensional slug impact at elbow for the case of L0 = 2.74 m and P0 = 138 kPa (20 psig): (a) overview and (b) details at the elbow. The slug moves from right to left toward the elbow with a velocity of Vse = 22.4 m/s and Lse = 2.2 m.

Fig. 10

Pressure history at the elbow. Comparison between experiments [14] (solid line with circles) and numerical predictions by Bozkus and Wiggert [18] (solid line with squares), Yang and Wiggert [15] (solid line with diamonds) and present 1D SPH (solid line)

Fig. 11

Pressure history at the elbow. Comparison between experiments [14] (solid line with circles) and numerical predictions by Bozkus and Wiggert [18] (solid line with squares), Yang and Wiggert [15] (solid line with diamonds), Kayhan and Bozkus [19] (solid line with triangles) and present 1D SPH (solid line).

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