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.
Issue Section:
Fluid-Structure Interaction
References
1.
Mandhane
, J. M.
, Gregory
, G. A.
, and Aziz
, K.
, 1974
, “A Flow Pattern Map for Gas-Liquid Flow in Horizontal Pipes
,” Int. J. Multiphase Flow
, 1
(4), pp. 537
–553
.10.1016/0301-9322(74)90006-82.
Dukler
, A. E.
, and Hubbard
, M. G.
, 1975
, “A Model for Gas-Liquid Slug Flow in Horizontal and Near Horizontal Tubes
,” Ind. Eng. Chem. Fundam.
, 14
(4), pp. 337
–347
.10.1021/i160056a0113.
Taitel
, Y.
, and Dukler
, A. E.
, 1977
, “A Model for Slug Frequency During Gas-Liquid Flow in Horizontal and Near Horizontal Pipes
,” Int. J. Multiphase Flow
, 3
(6), pp. 585
–596
.10.1016/0301-9322(77)90031-34.
Taitel
, Y.
, and Dukler
, A. E.
, 1976
, “A Model for Predicting Flow Regime Transitions in Horizontal and Near Horizontal Gas-Liquid Flow
,” AIChE J.
, 22
(1), pp. 47
–55
.10.1002/aic.6902201055.
Taitel
, Y.
, Barnea
, D.
, and Dukler
, A. E.
, 1980
, “Modelling Flow Pattern Transitions for Steady Upward Gas-Liquid Flow in Vertical Tubes
,” AIChE J.
, 26
(3), pp. 345
–354
.10.1002/aic.6902603046.
Dukler
, A. E.
, Maron
, D. M.
, and Brauner
, N.
, 1985
, “A Physical Model for Predicting the Minimum Stable Slug Length
,” Chem. Eng. Sci.
, 40
(8), pp. 1379
–1386
.10.1016/0009-2509(85)80077-47.
Fabre
, J.
, and Liné
, A.
, 1992
, “Modeling of Two-Phase Slug Flow
,” Annu. Rev. Fluid Mech.
, 24
, pp. 21
–46
.10.1146/annurev.fl.24.010192.0003218.
Sakaguchi
, T.
, Ozawa
, M.
, Hamaguchi
, H.
, Nishiwaki
, F.
, and Fujii
, E.
, 1987
, “Analysis of the Impact Force by a Transient Slug Flowing out of a Horizontal Pipe
,” Nucl. Eng. Des.
, 99
, pp. 63
–71
.10.1016/0029-5493(87)90108-79.
Zhang
, H. Q.
, Jayawardena
, S. S.
, Redus
, C. L.
, and Brill
, J. P.
, 2000
, “Slug Dynamics in Gas-Liquid Pipe Flow
,” J. Energy Res. Technol.
, 122
(1), pp. 14
–21
.10.1115/1.48315610.
Tay
, B. L.
, and Thorpe
, R. B.
, 2004
, “Effects of Liquid Physical Properties on the Forces Acting on a Pipe Bend in Gas-Liquid Slug Flow
,” Trans. IChemE, Part A, Chem. Eng. Res. Des.
, 82
(A3
), pp. 344
–356
.10.1205/02638760432287045311.
Das
, I. A. F.
, 2003
, “The Characteristics and Forces due to Slugs in an “S” Shaped Riser
,” Ph.D. thesis, Cranfield University, Cranfield, UK.12.
Owen
, I.
, and Hussein
, I. B.
, 1994
, “The Propulsion of an Isolated Slug Through a Pipe and the Forces Produced as it Impacts Upon an Orifice Plate
,” Int. J. Multiphase Flow
, 20
(3
), pp. 659
–666
.10.1016/0301-9322(94)90036-113.
Fenton
, R. M.
, and Griffith
, P.
, 1990
, “The Force at a Pipe Bend Due to the Clearing of Water Trapped Upstream
,” Transient Thermal Hydraulics and Resulting Loads on Vessel and Piping Systems, ASME, PVP190, pp. 59
–67
.14.
Bozkus
, Z.
, 1991
, “The Hydrodynamics of an Individual Transient Liquid Slug in a Voided Line
,” Ph.D. thesis, Michigan State University, East Lansing, MI.15.
Yang
, J.
, and Wiggert
, D. C.
, 1998
, “Analysis of Liquid Slug Motion in a Voided Line
,” ASME J. Pressure Vessel Technol.
, 120
(1), pp. 74
–80
.10.1115/1.284188916.
Bozkus
, Z.
, Baran
, Ö. U.
, and Ger
, M.
, 2004
, “Experimental and Numerical Analysis of Transient Liquid Slug Motion in a Voided Line
,” ASME J. Pressure Vessel Technol.
, 126
(2), pp. 241
–249
.10.1115/1.168878117.
Neumann
, A.
, 1991
, “The Forces Exerted on a Pipe Bend due to a Pipe Clearing Transient
,” M.Sc. thesis, MIT, Cambridge, MA.18.
Bozkus
, Z.
, and Wiggert
, D. C.
, 1997
, “Liquid Slug Motion in a Voided Line
,” J. Fluids Struct.
, 11
(8), pp. 947
–963
.10.1006/jfls.1997.011219.
Kayhan
, B. A.
, and Bozkus
, Z.
, 2011
, “A New Method for Prediction of the Transient Force Generated by a Liquid Slug Impact on an Elbow of an Initially Voided Line
,” ASME J. Pressure Vessel Technol.
, 133
(2), p. 021701
.10.1115/1.400262620.
De Martino
, G.
, Fontana
, N.
, and Giugni
, M.
, 2008
, “Transient Flow Caused by Air Expulsion Through an Orifice
,” J. Hydraul. Eng.
, 134
(9
), pp. 1395
–1399
.10.1061/(ASCE)0733-9429(2008)134:9(1395)21.
Kayhan
, B. A.
, 2009
, “Prediction of the Transient Force Subsequent to a Liquid Mass Impact on an Elbow of an Initially Voided Line
,” Ph.D. thesis, Middle East Technical University, Ankara, Turkey.22.
Streeter
, V. L.
, Wylie
, E. B.
, and Bedford
, K. W.
, 1998
, Fluid Mechanics
, 9th ed., McGraw-Hill
, Boston
.23.
Laanearu
, J.
, Annus
, I.
, Koppel
, T.
, Bergant
, A.
, Vučkovič
, S.
, Hou
, Q.
, Tijsseling
, A. S.
, Anderson
, A.
, and van't Westende
, J. M. C.
, 2012
, “Emptying of Large-Scale Pipeline by Pressurized Air
,” J. Hydraul. Eng.
, 138
(12), pp. 1090
–1100
.10.1061/(ASCE)HY.1943-7900.000063124.
Lichtarowicz
, A.
, and Markland
, E.
, 1963
, “Calculation of Potential Flow With Separation in a Right-Angled Elbow With Unequal Branches
,” J. Fluid Mech.
, 17
(4), pp. 596
–606
.10.1017/S002211206300153125.
Mankbadi
, R. R.
, and Zaki
, S. S.
, 1986
, “Computations of the Contraction Coefficient of Unsymmetrical Bends
,” AIAA J.
, 24
(8), pp. 1285
–1289
.10.2514/3.943326.
Chu
, S. S.
, 2003
, “Separated Flow in Bends of Arbitrary Turning Angles, Using the Hodograph Method and Kirchhoff's Free Streamline Theory
,” ASME J. Fluids Eng.
, 125
(3), pp. 438
–442
.10.1115/1.156731127.
Hou
, Q.
, Kruisbrink
, A. C. H.
, Pearce
, F. R.
, Tijsseling
, A. S.
, and Yue
, T.
, “Smoothed Particle Hydrodynamics Simulations of Flow Separation at Bends
,” Comput. Fluids.
, 90, pp. 138–146.28.
Monaghan
, J. J.
, 1992
, “Smoothed Particle Hydrodynamics
,” Annu. Rev. Astron. Astrophys.
, 30
, pp. 543
–574
.10.1146/annurev.aa.30.090192.00255129.
Rosswog
, S.
, 2009
, “Astrophysical Smooth Particle Hydrodynamics
,” New Astron. Rev.
, 53
(4-6), pp. 78
–104
.10.1016/j.newar.2009.08.00730.
Springel
, V.
, 2010
, “Smoothed Particle Hydrodynamics in Astrophysics
,” Annu. Rev. Astron. Astrophys.
, 48
, pp. 391
–430
.10.1146/annurev-astro-081309-13091431.
Libersky
, L. D.
, Petschek
, A. G.
, Carney
, T. C.
, Hipp
, J. R.
, and Allahdadi
, F. A.
, 1993
, “High strain Lagrangian hydrodynamics: A three-dimensional SPH code for dynamic material response,” J. Comput. Phys., 109(1), pp. 67–75.32.
Monaghan
, J. J.
, 1994
, “Simulating Free Surface Flows With SPH
,” J. Comput. Phys.
, 110
(2), pp. 399
–406
.10.1006/jcph.1994.103433.
Liu
, M. B.
, and Liu
, G. R.
, 2010
, “Smoothed Particle Hydrodynamics (SPH): An Overview and Recent Developments
,” Arch. Comput. Methods. Eng.
, 17
(1), pp. 25
–76
.10.1007/s11831-010-9040-734.
Monaghan
, J. J.
, 2012
, “Smoothed Particle Hydrodynamics and Its Diverse Applications
,” Annu. Rev. Fluid Mech.
, 44
, pp. 323
–346
.10.1146/annurev-fluid-120710-10122035.
Price
, D. J.
, 2012
, “Smoothed Particle Hydrodynamics and Magnetohydrodynamics
,” J. Comput. Phys.
, 231
(3), pp. 759
–794
.10.1016/j.jcp.2010.12.01136.
Lastiwka
, M.
, Basa
, M.
, and Quinlan
, N. J.
, 2009
, “Permeable and Non-Reflecting Boundary Conditions in SPH
,” Int. J. Numer. Meth. Fluids
, 61
(7), pp. 709
–724
.10.1002/fld.197137.
Hou
, Q.
, Kruisbrink
, A. C. H.
, Tijsseling
, A. S.
, and Keramat
, A.
, 2012
, “Simulating Transient Pipe Flow With Corrective Smoothed Particle Method
,” Proceedings of 11th International Conference on Pressure Surges
, BHR Group, Lisbon, Portugal, pp. 171
–188
.38.
Molteni
, D.
, and Colagrossi
, A.
, 2009
, “A Simple Procedure to Improve the Pressure Evaluation in Hydrodynamic Context Using the SPH
,” Comput. Phys. Commun.
, 180
(6), pp. 861
–872
.10.1016/j.cpc.2008.12.00439.
Hou
, Q.
, 2012
, “Simulating Unsteady Conduit Flows With Smoothed Particle Hydrodynamics
,” Ph.D. thesis, Eindhoven University of Technology, Eindhoven, The Netherlands. Available at:http://repository.tue.nl/73342040.
Hou
, Q.
, Zhang
, L. X.
, Tijsseling
, A. S.
, and Kruisbrink
, A. C. H.
, 2012
, “Rapid Filling of Pipelines With the SPH Particle Method
,” Procedia Eng.
, 31
, pp. 38
–43
.10.1016/j.proeng.2012.01.98741.
Crane
, 1985
, “Flow of Fluids Through Valves, Fittings, and Pipe
,” Technical Paper 410, Crane Co.42.
Garcia
, D.
, 2010
, “Robust Smoothing of Gridded Data in One and Higher Dimensions With Missing Values
,” Comput. Stat. Data Anal.
, 54
(4), pp. 1167
–1178
.10.1016/j.csda.2009.09.020Copyright © 2014 by ASME
You do not currently have access to this content.
