A finite-volume approach, based on the MUSCL-Hancock method, is presented and applied to liquid-column separation transients in pipelines. In the mathematical model, sudden closure of a valve on the downstream end of a pipeline initiates the hydraulic transient, while a head tank maintains constant upstream pressure. The two-phase fluid is treated as a homogeneous mixture, and changes in fluid pressure are assumed to occur at constant entropy. Effects of pipe elasticity on wave propagation speed are included in the model by coupling the circumferential stress-strain relation for the pipe wall to the local fluid pressure. In regions of the domain where the solution is smooth, second-order accuracy is achieved by means of data reconstruction based on sloping-difference formulas. Slope limiting prevents the development of spurious oscillations in the neighborhood of steep wave fronts. Data reconstruction leads to a piece-wise linear representation of the solution, which is discontinuous across cell boundaries. In order to advance the solution in time, a Riemann problem is solved on each cell junction to obtain mass and momentum flux contributions. A splitting technique, which separates flux terms from gravity and frictional effects, allows the compatibility equations for the Riemann problem to be expressed as total differentials of fluid velocity and an integral that depends only on the fluid pressure. Predictions for large-amplitude pressure pulses caused by liquid-column separation and rejoining are compared against experimental data available in the literature. Amplitude and timing of the predicted pressure response shows reasonably good agreement with experimental data even when as few as 20–40 computational cells are used to describe axial variations in fluid conditions along a pipeline of approximately 35m in length. An advantage of the current method is that it does not give rise to spurious oscillations when grid refinement is performed. The presence of nonphysical oscillations has been a drawback of a commonly used method based on discrete vapor cavities and characteristic treatment of wave propagation.

1.
Li
,
W. H.
, and
Walsh
,
J. P.
, 1964, “
Pressure Generated by Cavitation in a Pipe
,”
J. Engrg. Mech. Div.
0044-7951,
90
, pp.
113
133
.
2.
Safwat
,
H. H.
, 1972, “
Transients in Cooling Water Systems of Thermal Power Plants
,” D. Sci. dissertation, Delft University of Technology, Delft, The Netherlands.
3.
Arastu
,
A. H.
,
Chiu
,
C.
,
Griffith
,
P.
,
Rooney
,
J. W.
,
Sabin
,
J. W.
,
Safwat
,
H. H.
, and
Van Duyne
,
D. A.
, 1996, “
Water Hammer Handbook for Nuclear Plant Engineers and Operators
,” EPRI Report No. TR-106438,
Electric Power Research Institute
, Palo Alto, CA.
4.
Barbero
,
G.
, and
Ciaponi
,
C.
, 1991, “
Experimental Validation of a Discrete Free Gas Model for Numerical Simulation of Hydraulic Transients with Cavitation
,”
Proceedings of the Ninth Round Table of IAHR Group on Hydraulic Transients with Water Column Separation
,
Valencia
, Sept. 4–6, pp.
51
67
.
5.
Baltzer
,
R. A.
, 1967, “
Column Separation Accompanying Liquid Transients in Pipes
,”
ASME J. Basic Eng.
0021-9223,
89
, pp.
837
846
.
6.
Simpson
,
A.
, and
Wylie
,
E. B.
, 1987, “
Column Separation Experiments with Large Pressure Pulses
,” ASME Paper 87-PVP-18,
Pressure Vessel and Piping Conference
,
San Diego
, June 28–July 2.
7.
Simpson
,
A. R.
, and
Wylie
,
E. B.
, 1987, “
Recent Advances in the Understanding and Numerical Modelling of Column Separation in Pipelines
,”
Conference on Hydraulics in Civil Engineering
,
Melbourne
, October 12–14.
8.
Martin
,
C. S.
, 1983, “
Experimental Investigation of Column Separation with Rapid Closure of Downstream Valve
,”
Proceedings of the Fourth International Conference on Pressure Surges
, BHRA,
Bath, England
, September.
9.
Weyler
,
M. E.
,
Streeter
,
V. L.
, and
Larsen
,
P. S.
, 1971, “
An Investigation of the Effect of Cavitation Bubbles on the Momentum Loss in Transient Pipe Flow
,”
ASME J. Basic Eng.
0021-9223,
93
, pp.
1
10
.
10.
Bergant
,
A.
, and
Simpson
,
A. R.
, 1999, “
Pipeline Column Separation Flow Regimes
,”
J. Hydraul. Eng.
0733-9429,
125
, pp.
835
848
.
11.
Streeter
,
V. L.
, and
Wylie
,
E. B.
, 1967,
Hydraulic Transients
,
McGraw-Hill
,
New York
.
12.
Arastu
,
A. H.
,
Safwat
,
H. H.
, and
Husaini
,
S. M.
, 1992, “
Water Hammer Prevention, Mitigation, and Accommodation
,” Vol.
4
, Part 2, EPRI NP-6766, Electric Power Research Institute, Palo Alto, CA.
13.
Wylie
,
E. B.
, and
Streeter
,
V. L.
, 1993,
Fluid Transients in Systems
,
Prentice Hall
,
Upper Saddle River, NJ
.
14.
Bergant
,
A.
, and
Tijsseling
,
A.
, 2001, “
Parameters Affecting Water Hammer Wave Attenuation, Shape and Timing
,”
Proceedings of the Tenth International Meeting of IAHR Group on The Behaviour of Hydraulic Machinery Under Steady Oscillatory Conditions
,”
Trondheim, Norway
, June 26–28.
15.
Carlson
,
K. E.
,
Riemke
,
R. A.
,
Rouhani
,
S. Z.
,
Shumway
,
R. W.
, and
Weaver
,
W. L.
, 1995, “
RELAP5∕MOD3 Code Manual Vol. I: Code Structure, Systems Models, and Solution Methods
,” INEL-95∕0174, NUREG∕CR-5535, Idaho National Engineering Laboratory.
16.
Borkowski
,
J. A.
, and
Wade
,
N. L.
, (eds.), 1992, “
TRAC-BF1-MOD1: An Advanced Best-Estimate Computer Program for BWR Accident Analysis
,” EGG-2626, NUREG∕CR-4356, Idaho National Engineering Laboratory.
17.
Bilicki
,
Z.
,
Kardas
,
D.
, and
Michaelides
,
E. E.
, 1998, “
Relaxation Models for Wave Phenomena in Liquid-Vapor Bubble Flow in Channels
,”
ASME J. Fluids Eng.
0098-2202,
120
, pp.
369
377
.
18.
LeVeque
,
R. J.
, 2002,
Finite Volume Methods for Hyperbolic Problems
,
Cambridge University Press
,
Cambridge, UK
.
19.
Anderson
,
D. A.
,
Tannehill
,
J. C.
, and
Pletcher
,
R. H.
, 1984,
Computational Fluid Mechanics and Heat Transfer
,
Hemisphere
,
New York
, pp.
144
146
.
20.
Kranenburg
,
C.
, 1974, “
Gas Release during Transient Cavitation in Pipes
,”
J. Hydr. Div.
0044-796X,
100
, pp.
1383
1398
.
21.
Bergant
,
A.
, and
Simpson
,
A. R.
, 1995, “
Water Hammer and Column Separation Measurements in an Experimental Apparatus
,” Research Report No. R128, Department of Civil and Environmental Engineering, University of Adelaide.
22.
Crandall
,
S. H.
,
Dahl
,
N. C.
, and
Lardner
,
T. J.
, 1972,
An Introduction to the Mechanics of Solids
,
2nd ed.
,
McGraw-Hill
,
New York
, p.
94
.
23.
Perry
,
R. H.
, and
Chilton
,
C. H.
(eds.), 1973,
Chemical Engineers’ Handbook
,
5th ed.
,
McGraw-Hill
,
New York
, p.
23
-
48
.
24.
Lindeburg
,
M. R.
, 2001,
Mechanical Engineering Reference Manual
,
11th ed.
,
Professional Publications
,
Belmont, CA
.
25.
Bergant
,
A.
,
Simpson
,
A. R.
, and
Vítkovský
,
J.
, 2001, “
Developments in Unsteady Pipe Flow Friction Modelling
,”
J. Hydraul. Res.
0022-1686,
39
(
3
), pp.
249
257
.
26.
Brunone
,
B.
,
Golia
,
U. M.
, and
Greco
,
M.
, 1995, “
Effects of Two-dimensionality on Pipe Transients Modeling
,”
J. Hydraul. Eng.
0733-9429,
121
(
12
), pp.
906
912
.
27.
Vardy
,
A. E.
, and
Brown
,
J. M. B.
, 2003, “
Transient Turbulent Friction in Smooth Pipe Flows
,”
J. Sound Vib.
0022-460X,
259
(
5
), pp.
1011
1036
.
28.
Lahey
,
R. T.
, and
Moody
,
F. J.
, 1977,
The Thermal Hydraulics of a Boiling Water Nuclear Reactor
,
American Nuclear Society
,
La Grange Park, IL
, p.
228
.
29.
Igra
,
O.
,
Wu.
,
X.
,
Hu
,
G. Q.
, and
Falcovitz
,
J.
, 2002, “
Shock Wave Propagation Into a Dust-Gas Suspension Inside a Double-Bend Conduit
,”
ASME J. Fluids Eng.
0098-2202,
124
, pp.
483
491
.
30.
Igra
,
O.
,
Hu
,
G.
,
Falcovitz
,
J.
, and
Heilig
,
W.
, 2003, “
Blast Wave Reflection from Wedges
,”
ASME J. Fluids Eng.
0098-2202,
125
, pp.
510
519
.
31.
Strang
,
G.
, 1968, “
On the Construction and Comparison of Difference Schemes
,”
SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal.
0036-1429,
5
(
3
), pp.
506
517
.
32.
Ben-Artzi
,
M.
, and
Falcovitz
,
J.
, 2003,
Generalized Riemann Problems in Computational Fluid Dynamics
,
Cambridge University Press
,
Cambridge, UK
.
33.
Toro
,
E. F.
, 1999,
Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction
,
2nd ed.
,
Springer-Verlag
,
New York
.
34.
Thompson
,
P. A.
, 1988,
Compressible-Fluid Dynamics
,
Rensselaer Polytechnic Institute
, pp.
379
380
.
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