Research Papers: Pipeline Systems

A New Method for Prediction of the Transient Force Generated by a Liquid Slug Impact on an Elbow of an Initially Voided Line

[+] Author and Article Information
Bülent A. Kayhan

 Konutkent Mahallesi, Pınar Apkan Sitesi, 2944 Sokak 8/10, Çayyolu, 06810 Ankara, Turkeybulentkayhan@hotmail.com

Zafer Bozkus

Department of Civil Engineering, Hydromechanics Laboratory, Middle East Technical University, 06531 Ankara, Turkeybozkus@metu.edu.tr

J. Pressure Vessel Technol 133(2), 021701 (Mar 14, 2011) (12 pages) doi:10.1115/1.4002626 History: Received July 03, 2009; Revised September 24, 2010; Published March 14, 2011; Online March 14, 2011

The aim of the present study is to predict the impact force applied by an individual transient liquid slug on an elbow at the end of a horizontal and initially empty pipeline. The liquid slug is driven by pressurized air in a tank located upstream of the pipeline. The time dependent pressure distribution along the elbow and a vertical extension segment after the elbow are solved with a 1D numerical approach along a curved line mesh. An assumed and calibrated axial turbulent velocity profile function with 3D skewed shape for the slug is also used in the solution. The impact pressures and the transient forces at the elbow are computed and also compared with those obtained experimentally and numerically from previous studies. Comparisons indicate that the new method developed in the present study predict the peak pressures and/or forces with higher accuracy than the previous method proposed by other researchers.

Copyright © 2011 by American Society of Mechanical Engineers
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Figure 1

System setup used by Bozkus (4)

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Figure 2

Control volume for the liquid slug selected by Bozkus (4) along the horizontal pipeline

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Figure 3

Velocity distribution in a curved pipe given by Prandtl (10-11) and Schlichting (12)

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Figure 4

Cross-sectional shape of the assumed turbulent velocity profile function

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Figure 5

Parameters of the axial velocity profile function

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Figure 6

(a) Complete physical setup for the system (4), (b) computational domains for the elbow and vertical extension segment, (c) cross section of the elbow, and (d) cross section of the vertical extension segment of the pipe

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Figure 7

Shape of the calibration function θc

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Figure 8

Computational domain with the nodal numbering along the s-coordinate

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Figure 9

General variation of the shape of the assumed axial velocity profile along the s-coordinate

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Figure 10

1D radial mesh at a cross section of the elbow

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Figure 11

Dynamic pressure distributions for Lin=2.13 m (7 ft), P0=68.91 kPa(10 psi (gauge)), t=0.942 s, and NELBW=90

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Figure 12

Normalized peak pressures versus Lp/Lin

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Figure 13

Pressure-time history plots at the elbow for Lin=1.22 m (4 ft) and P0=206.73 kPa(30 psi (gauge))

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Figure 14

Pressure-time history plots at the elbow for Lin=2.13 m (7 ft) and P0=137.82 kPa(20 psi (gauge))

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Figure 15

Pressure-time history plots at the elbow for Lin=3.35 m (11 ft) and P0=68.91 kPa(10 psi (gauge))

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Figure 16

Values of F∗ versus D∗

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Figure 17

Correlations between the dimensionless parameters



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