The motion of liquid filling a pipeline is impeded when the gas ahead of it cannot escape. Entrapped gas will lead to a significant pressure build-up in front of the liquid column, which slows down the column and eventually bounces it back. The pressure and temperature in the gas may become dangerously high, and for example, lead to fires and explosions caused by auto-ignition. This paper considers the case where the trapped gas can escape through a vent. One new element is that the pressure head of the liquid supply reservoir is fluctuating instead of staying constant. The obtained analytical and numerical solutions are utilized in parameter variation studies that give deeper insight in the system's behavior.

References

References
1.
Busch
,
N.-P. G.
, and
Grane
,
T.
,
2015
, “
Romeinen Vergruisden Spaanse Goudberg (Romans Milled Spanish Gold Mountain)
,”
Historia Jubileumuitgave
, Bonnier Publications International AS, Oslo, Norway, pp.
128
133
(in Dutch).
2.
Streeter
,
V. L.
, and
Wylie
,
E. B.
,
1967
,
Hydraulic Transients
,
McGraw-Hill
,
New York
.
3.
Kitagawa
,
A.
,
Urata
,
E.
, and
Takenaka
,
T.
,
1975
, “
On the Influence of Trapped Air on Transient Phenomena of Fluid Conduit
,”
Trans. Jpn. Hydraul. Pneumat. Soc.
,
6
(
2
), pp.
78
83
(in Japanese).
4.
Martin
,
C. S.
,
1976
, “
Entrapped Air in Pipelines
,”
Fluid Engineering, Second International Conference on Pressure Surges
,
London
, Sept., pp.
15
28
.
5.
Martin
,
C. S.
,
1996
, “
Experiences With Two-Phase Flow in Fluid Transients
,”
Seventh International Conference on Pressure Surges
,
Harrogate, UK
, Apr., pp.
65
75
.
6.
Lee
,
N. H.
, and
Martin
,
C. S.
,
1999
, “
Experimental and Analytical Investigation of Entrapped Air in a Horizontal Pipe
,”
ASME
Paper No. FEDSM99-6881.
7.
Martin
,
C. S.
, and
Lee
,
N. H.
,
2000
, “
Rapid Expulsion of Entrapped Air Through an Orifice
,”
Eighth International Conference on Pressure Surges
,
The Hague, The Netherlands
, Apr. 12–14, pp.
125
132
.
8.
Lee
,
N. H.
,
2005
, “
Effect of Pressurization and Expulsion of Entrapped Air in Pipelines
,”
Ph.D. thesis
, School of Civil and Environmental Engineering, Georgia Institute of Technology, Atlanta, GA.https://smartech.gatech.edu/handle/1853/11643
9.
Martin
,
C. S.
, and
Lee
,
N. H.
,
2012
, “
Measurement and Rigid Column Analysis of Expulsion of Entrapped Air From a Horizontal Pipe With an Exit Orifice
,”
11th International Conference on Pressure Surges
,
Lisbon, Portugal
, Oct., pp.
537
542
.
10.
Hashimoto
,
K.
,
Imaeda
,
M.
, and
Osayama
,
A.
,
1988
, “
Transients of Fluid Lines Containing an Air Pocket or Liquid Column
,”
J. Fluid Control
,
18
(
4
), pp.
38
54
.
11.
Abreu
,
J. M.
,
Cabrera
,
E.
,
García-Serra
,
J.
, and
Izquierdo
,
J.
,
1991
, “
Boundary Between Elastic and Inelastic Models in Hydraulic Transients Analysis With Entrapped Air Pockets
,”
IAHR, 9th Round Table on Hydraulic Transients With Water Column Separation
,
Valencia, Spain
, pp.
159
181
.
12.
Cabrera
,
E.
,
Abreu
,
J. M.
,
Pérez
,
R.
, and
Vela
,
A.
,
1992
, “
Influence of Liquid Length Variation in Hydraulic Transients
,”
ASCE J. Hydraul. Eng.
,
118
(
12
), pp.
1639
1650
.
13.
Izquierdo
,
J.
,
Fuertes
,
V. S.
,
Cabrera
,
E.
,
Iglesias
,
P. L.
, and
Garcia-Serra
,
J.
,
1999
, “
Peak Pressure Evaluation in Pipelines With Entrapped Air Pockets
,”
ASME
Paper No. FEDSM99-6882.
14.
Izquierdo
,
J.
,
Fuertes
,
V. S.
,
Cabrera
,
E.
,
Iglesias
,
P. L.
, and
Garcia-Serra
,
J.
,
1999
, “
Pipeline Start-Up With Entrapped Air
,”
IAHR J. Hydraul. Res.
,
37
(
5
), pp.
579
590
.
15.
Fuertes
,
V. S.
,
Arregui
,
F.
,
Cabrera
,
E.
, and
Iglesias
,
P. L.
,
2000
, “
Experimental Setup of Entrapped Air Pockets Model Validation
,”
Eighth International Conference on Pressure Surges
,
The Hague, The Netherlands
, Apr., pp.
133
145
.
16.
Bagnold
,
R. A.
,
1939
, “
Interim Report on Wave-Pressure Research
,”
J. Inst. Civ. Eng.
,
12
(7), pp.
201
226
.
17.
Brosset
,
L.
,
Ghidaglia
,
J. M.
,
Guilcher
,
P. M.
, and
Le Tarnec
,
L.
,
2013
, “
Generalized Bagnold Model
,”
23rd International Offshore and Polar Engineering Conference (ISOPE)
,
Anchorage, AK
, July, pp.
209
223
.
18.
Ramkema
,
C.
,
1978
, “
A Model Law for Wave Impacts on Coastal Structures
,”
16th Conference on Coastal Engineering
,
Hamburg, Germany
,
Aug. 27–Sept. 3
, pp.
2308
2327
.
19.
Abrahamsen
,
B. C.
, and
Faltinsen
,
O. M.
,
2011
, “
The Effect of Air Leakage and Heat Exchange on the Decay of Entrapped Air Pocket Slamming Oscillations
,”
Phys. Fluids
,
23
(
10
), p.
102107
.
20.
Abrahamsen
,
B. C.
, and
Faltinsen
,
O. M.
,
2012
, “
The Natural Frequency of the Pressure Oscillations Inside a Water-Wave Entrapped Air Pocket on a Rigid Wall
,”
J. Fluids Struct.
,
35
, pp.
200
212
.
21.
Liou
,
C. P.
, and
Hunt
,
W. A.
,
1996
, “
Filling of Pipelines With Undulating Elevation Profiles
,”
ASCE J. Hydraul. Eng.
,
122
(
10
), pp.
534
539
.
22.
De Martino
,
G.
,
Fontana
,
N.
, and
Giugni
,
M.
,
2008
, “
Transient Flow Caused by Air Expulsion Through an Orifice
,”
ASCE J. Hydraul. Eng.
,
134
(
9
), pp.
1395
1399
.
23.
Zhang
,
Y.
, and
Vairavarnoorthy
,
K.
,
2006
, “
Transient Flow in Rapidly Filling Air-Entrapped Pipelines With Moving Boundaries
,”
Tsinghua Sci. Technol.
,
11
(
3
), pp.
313
323
.
24.
Zhou
,
L.
,
Liu
,
D.
,
Karney
,
B.
, and
Zhang
,
Q.
,
2011
, “
Influence of Entrapped Air Pockets on Hydraulic Transients in Water Pipelines
,”
ASCE J. Hydraul. Eng.
,
137
(
12
), pp.
1686
1692
.
25.
Zhou
,
L.
, and
Liu
,
D.
,
2013
, “
Experimental Investigation of Entrapped Air Pocket in a Partially Full Water Pipe
,”
IAHR J. Hydraulic Res.
,
51
(
4
), pp.
469
474
.
26.
Zhou
,
L.
,
Liu
,
D.
, and
Karney
,
B.
,
2013
, “
Investigation of Hydraulic Transients of Two Entrapped Air Pockets in a Water Pipeline
,”
ASCE J. Hydraul. Eng.
,
139
(
9
), pp.
949
959
.
27.
Zhou
,
L.
,
Liu
,
D.
,
Karney
,
B.
, and
Wang
,
P.
,
2013
, “
Phenomenon of White Mist in Pipelines Rapidly Filling With Water With Entrapped Air Pockets
,”
ASCE J. Hydraul. Eng.
,
139
(
10
), pp.
1041
1051
.
28.
Trindade
,
B. C.
, and
Vasconcelos
,
J. G.
,
2013
, “
Modeling of Water Pipeline Filling Events Accounting for Air Phase Interactions
,”
ASCE J. Hydraul. Eng.
,
139
(
9
), pp.
921
934
.
29.
Tijsseling
,
A. S.
,
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
.
30.
Zhou
,
F.
,
Hicks
,
F. E.
, and
Steffler
,
P. M.
,
2002
, “
Transient Flow in a Rapidly Filling Horizontal Pipe Containing Trapped Air
,”
ASCE J. Hydraul. Eng.
,
128
(
6
), pp.
625
634
.
31.
Zhou
,
F.
,
Hicks
,
F.
, and
Steffler
,
P.
,
2004
, “
Analysis of Effects of Air Pocket on Hydraulic Failure of Urban Drainage Infrastructure
,”
Can. J. Civ. Eng.
,
31
(
1
), pp.
86
94
.
32.
Vasconcelos
,
J. G.
, and
Wright
,
J. W.
,
2009
, “
Investigation of Rapid Filling of Poorly Ventilated Stormwater Storage Tunnels
,”
IAHR J. Hydraul. Res.
,
47
(
5
), pp.
547
558
.
33.
Vasconcelos
,
J. G.
, and
Wright
,
J. W.
,
2011
, “
Geysering Generated by Large Air Pockets Released Through Water-Filled Ventilation Shafts
,”
ASCE J. Hydraul. Eng.
,
137
(
5
), pp.
543
555
.
34.
Pozos-Estrada
,
O.
,
Pothof
,
I.
,
Fuentes-Mariles
,
O. A.
,
Dominguez-Mora
,
R.
,
Pedrozo-Acuña
,
A.
,
Meli
,
R.
, and
Peña
,
F.
,
2015
, “
Failure of a Drainage Tunnel Caused by an Entrapped Air Pocket
,”
Urban Water J.
,
12
(
6
), pp.
446
454
.
35.
Guarga
,
R.
,
Acosta
,
A.
, and
Lorenzo
,
E.
,
1996
, “
Dynamic Compression of Entrapped Air Pockets by Elastic Water Columns
,”
IAHR, 18th Symposium on Hydraulic Machinery and Cavitation
,
Valencia, Spain
, Sept., pp.
710
719
.
36.
Chaiko
,
M. A.
, and
Brinckman
,
K. W.
,
2002
, “
Models for Analysis of Water Hammer in Piping With Entrapped Air
,”
ASME J. Fluids Eng.
,
124
(
1
), pp.
194
204
.
37.
Wang
,
K.-H.
,
Shen
,
Q.
, and
Zhang
,
B.
,
2003
, “
Modeling Propagation of Pressure Surges With the Formation of an Air Pocket in Pipelines
,”
Comput. Fluids
,
32
(
9
), pp.
1179
1194
.
38.
Lai
,
A.
,
Hau
,
K. F.
,
Noghrehkar
,
R.
, and
Swartz
,
R.
,
2000
, “
Investigation of Waterhammer in Piping Networks With Voids Containing Non-Condensable Gas
,”
Nucl. Eng. Des.
,
197
(
1–2
), pp.
61
74
.
39.
Epstein
,
M.
,
2008
, “
A Simple Approach to the Prediction of Waterhammer Transients in a Pipe Line With Entrapped Air
,”
Nucl. Eng. Des.
,
238
(
9
), pp.
2182
2188
.
40.
Barna
,
I. F.
,
Imre
,
A. R.
,
Baranyai
,
G.
, and
Ézsöl
,
G.
,
2010
, “
Experimental and Theoretical Study of Steam Condensation Induced Water Hammer Phenomena
,”
Nucl. Eng. Des.
,
240
(
1
), pp.
146
150
.
41.
Martin
,
C. S.
,
2013
, “
Waterhammer in a Horizontal Pipe Induced by Slug Formation and Rapid Condensation
,”
ASME
Paper No. PVP2013-97424.
42.
Vecchio
,
R. S.
,
Sinha
,
S. K.
,
Bruck
,
P. M.
,
Esselman
,
T. C.
,
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., pp.
7
17
.
43.
Thorley
,
A. R. D.
, and
Main
,
B. G.
,
1986
, “
Spontaneous Combustion in Vapour Cavities Subjected to Fluid Transients in Pipelines
,”
Fifth International Conference on Pressure Surges
,
Hannover, Germany
, Sept., pp.
139
147
.
44.
Thorley
,
A. R. D.
, and
Main
,
B. G.
,
1990
, “
Cavity Dynamics and the Risk of Explosive Combustion in Pipelines
,”
Sixth International Conference on Pressure Surges
,
Cambridge, UK
, Oct., pp.
357
370
.
45.
Richardson
,
S. M.
,
Saville
,
G.
, and
Griffiths
,
J. F.
,
1990
, “
Autoignition—Occurrence and Effects
,”
Trans. Inst. Chem. Eng., Part B
,
68
(
4
), pp.
239
244
.
46.
Leishear
,
R. A.
,
2017
, “
Nuclear Power Plant Fires and Explosions—Part I: Plant Designs and Hydrogen Ignition
,”
ASME
Paper No. PVP2017-66285.
47.
Leishear
,
R. A.
,
2017
, “
Nuclear Power Plant Fires and Explosions—Part II: Hydrogen Ignition Overview
,”
ASME
Paper No. PVP2017-66278.
48.
Leishear
,
R. A.
,
2017
, “
Nuclear Power Plant Fires and Explosions—Part III: Hamaoka Piping Explosion
,”
ASME
Paper No. PVP2017-66284.
49.
Leishear
,
R. A.
,
2017
, “
Nuclear Power Plant Fires and Explosions—Part IV: Water Hammer Explosion Mechanism
,”
ASME
Paper No. PVP2017-66279.
50.
Leishear
,
R. A.
,
2018
, “
Pump Start-Ups Ignite Nuclear Power Plants: History, Law, and Risk
,”
13th International Conference on Pressure Surges
,
Bordeaux, France
, Nov., pp.
13
28
.
51.
Bousso
,
S.
, and
Fuamba
,
M.
,
2014
, “
Numerical and Experimental Analysis of the Pressurized Wave Front in a Circular Pipe
,”
ASCE J. Hydraul. Eng.
,
140
(
3
), pp.
300
312
.
52.
Chosie
,
C. D.
,
Hatcher
,
T. M.
, and
Vasconcelos
,
J. G.
,
2014
, “
Experimental and Numerical Investigation on the Motion of Discrete Air Pockets in Pressurized Water Flows
,”
ASCE J. Hydraul. Eng.
,
140
(
8
), pp.
1
12
.
53.
Zhang
,
X.
,
Yu
,
B.
,
Wang
,
Y.
,
Xie
,
J.
,
Qiu
,
D.
, and
Sun
,
X.
,
2014
, “
Numerical Study on the Commissioning Charge-Up Process of Horizontal Pipeline With Entrapped Air Pockets
,”
Adv. Mech. Eng.
,
6
, p. 838926.
54.
Martins
,
S. C.
,
Ramos
,
H. M.
, and
Almeida
,
A. B.
,
2015
, “
Conceptual Analogy for Modelling Entrapped Air Action in Hydraulic Systems
,”
IAHR J. Hydraul. Res.
,
53
(
5
), pp.
678
686
.
55.
van Vuuren
,
S. J.
,
2015
, “
Effective De-Aeration of Pipelines and the Use of Captured Air to Mitigate Dynamic Pressures
,”
12th International Conference on Pressure Surges
, Dublin, Ireland, Nov., pp.
171
183
.http://www.ventomat.com.au/files/Effective%20deaeration%20and%20use%20the%20captured%20air%20to%20mitigate%20dynamic%20pressu....pdf
56.
Zhou
,
L.
,
Liu
,
D.
,
Karney
,
B.
,
Wang
,
H.
, and
Malekpour
,
A.
,
2015
, “
Rapid Filling of an Open-Ended Pipeline With Entrapped Air
,”
12th International Conference on Pressure Surges
,
Dublin, Ireland
, Nov., pp.
185
197
.
57.
Malekpour
,
A.
, and
Karney
,
B.
,
2015
, “
Exploring How Air Valves Change Transient Responses of Pipe Systems During Rapid Filling
,”
12th International Conference on Pressure Surges
,
Dublin, Ireland
, Nov., pp.
199
213
.
58.
Hou
,
Q.
,
Wang
,
S.
,
Kruisbrink
,
A. C. H.
, and
Tijsseling
,
A. S.
,
2015
, “
Lagrangian Modelling of Fluid Transients in Pipelines With Entrapped Air
,”
12th International Conference on Pressure Surges
, Dublin, Ireland, Nov., pp.
215
227
.https://www.researchgate.net/publication/292981119_Lagrangian_modelling_of_fluid_transients_in_pipelines_with_entrapped_air
59.
Martins
,
N. M. C.
,
Soares
,
A. K.
,
Ramos
,
H. M.
, and
Covas
,
D. I. C.
,
2015
, “
Entrapped Air Pocket Analysis Using CFD
,”
12th International Conference on Pressure Surges
, Dublin, Ireland, Nov., pp.
229
238
.https://www.researchgate.net/publication/299368816_Entrapped_air_pocket_analysis_using_CFD
60.
Apollonio
,
C.
,
Balacco
,
G.
,
Fontana
,
N.
,
Giugni
,
M.
,
Marini
,
G.
, and
Ferruccio Piccinni
,
A.
,
2016
, “
Hydraulic Transients Caused by Air Expulsion
,”
Water
,
8
(
1
), pp.
1
12
.
61.
Bergant
,
A.
,
Karadžić
,
U.
, and
Tijsseling
,
A. S.
,
2016
, “
Dynamic Water Behaviour Due to One Trapped Air Pocket in a Laboratory Pipeline Apparatus
,”
IOP Conf. Ser.: Earth Environ. Sci.
,
49
, p.
052007
.
62.
Zhou
,
L.
,
Wang
,
H.
,
Karney
,
B.
,
Liu
,
D.
,
Wang
,
P.
, and
Guo
,
S.
,
2018
, “
Dynamic Behavior of Entrapped Air Pocket in a Water Filling Pipeline
,”
ASCE J. Hydraul. Eng.
,
144
(
8
), p.
04018045
.
63.
Veilleux
,
J.-C.
, and
Shepherd
,
J. E.
,
2018
, “
Pressure and Stress Transients in Autoinjector Devices
,”
Drug Delivery Transl. Res.
,
8
(
5
), pp.
1238
1253
.
64.
Letelier
,
S. M. F.
, and
Leutheusser
,
H. J.
,
1983
, “
Unified Approach to the Solution of Problems of Unsteady Laminar Flow in Long Pipes
,”
ASME J. Appl. Mech.
,
50
(
1
), pp.
8
12
.
65.
Altstadt
,
E.
,
Carl
,
H.
,
Weis
,
R.
, and
Prasser
,
H. M.
,
2008
, “
Fluid-Structure Interaction During Artificially Induced Water Hammers in a Tube With a Bend—Experiments and Analyses
,”
Multiphase Sci. Technol.
,
20
(
3–4
), pp.
213
238
.
66.
Zhou
,
L.
,
Pan
,
T.
,
Wang
,
H.
,
Liu
,
D.
, and
Wang
,
P.
,
2018
, “
Rapid Air Expulsion Through an Orifice in a Vertical Water Pipe
,”
IAHR J. Hydraul. Res.
(epub).
67.
Li
,
L.
,
Zhu
,
D. Z.
, and
Huang
,
B.
,
2018
, “
Analysis of Pressure Transient Following Rapid Filling of a Vented Horizontal Pipe
,”
Water
,
10
(
11
), p.
1698
.
68.
Belfroid
,
S. P. C.
,
2017
, “
Acoustical Characteristics of Single and Two-Phase Horizontal Pipe Flow Through an Orifice
,”
ASME
Paper No. PVP2017-65732.
69.
Douglas
,
J. F.
,
Gasiorek
,
J. M.
,
Swaffield
,
J. A.
, and
Jack
,
L. B.
,
2011
,
Fluid Mechanics
,
6th ed.
,
Pearson Education
, Harlow, UK, Chap. 17.
70.
Potter
,
M. C.
,
Wiggert
,
D. C.
, and
Ramadan
,
B. H.
,
2017
,
Mechanics of Fluids
,
5th ed.
,
Cengage Learning
, Andover, NH, Chap. 9.
71.
Biasi
,
L.
,
Prosperetti
,
A.
, and
Tozzi
,
A.
,
1972
, “
Collapse of One-Dimensional Cavities in Compressible Liquids
,”
Phys. Fluids
,
15
(
10
), pp.
1848
1850
.
72.
Goyder
,
H.
,
2007
, “
Gas Waterhammer
,”
ASME
Paper No. PVP2007-26199.
73.
Bozkuş
,
Z.
, and
Wiggert
,
D. C.
,
1997
, “
Liquid Slug Motion in a Voided Line
,”
J. Fluids Struct.
,
11
(
8
), pp.
947
963
.
74.
Tijsseling
,
A. S.
,
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
.
75.
Tijsseling
,
A. S.
,
Hou
,
Q.
, and
Bozkuş
,
Z.
,
2015
, “
Analytical Expressions for Liquid-Column Velocities in Pipelines With Entrapped Gas
,”
ASME
Paper No. PVP2015-45184.
76.
Tijsseling
,
A. S.
,
Hou
,
Q.
, and
Bozkuş
,
Z.
,
2016
, “
Analytical and Numerical Solution for a Rigid Liquid-Column Moving in a Pipe With Fluctuating Reservoir-Head and Venting Entrapped-Gas
,”
ASME
Paper No. PVP2016-63193.
77.
Tijsseling
,
A. S.
,
Hou
,
Q.
, and
Bozkuş
,
Z.
,
2017
, “
Analytical Solutions for Liquid Slugs and Pigs Traveling in Pipelines With Entrapped Gas
,”
ASME
Paper No. PVP2017-65755.
78.
Tijsseling
,
A. S.
,
Hou
,
Q.
, and
Bozkuş
,
Z.
,
2018
, “
Moving Liquid Column With Entrapped Gas Pocket and Fluid-Structure Interaction at a Pipe's Dead End: A Nonlinear Spring-Mass System
,”
ASME
Paper No. PVP2018-84570.
79.
Bergant
,
A.
,
Simpson
,
A. R.
, and
Tijsseling
,
A. S.
,
2006
, “
Water Hammer With Column Separation: A Historical Review
,”
J. Fluids Struct.
,
22
(
2
), pp.
135
171
.
80.
Porca
,
P.
,
Lema
,
M.
,
Rambaud
,
P.
, and
Steelant
,
J.
,
2014
, “
Experimental and Numerical Multiphase-Front Fluid Hammer
,”
AIAA J. Propul. Power
,
30
(
2
), pp.
368
376
.
81.
Steelant
,
J.
,
2015
, “
Multi-Phase Fluid-Hammer in Aerospace Applications
,”
12th International Conference on Pressure Surges
, Dublin, Ireland, Nov., pp.
21
31
.https://www.researchgate.net/publication/284169896_Multi-Phase_Fluid-Hammer_in_Aerospace_Applications
You do not currently have access to this content.