In the paper, the selected aspects concerning description of viscoelastic behavior of pipe walls during unsteady flow are analyzed. The alternative convolution expression of the viscoelastic term is presented and compared with the corresponding term referring to unsteady friction. Both approaches indicate similarities in the forms of impulse response functions and the parameter properties. The flow memory was introduced into convolution and its impact on the solution was analyzed. To reduce the influence of the numerical errors, implicit Preissmann scheme was applied. The calculation results were verified based on laboratory tests. The study indicated that the flow memory is related to pipe material properties and significantly influences the calculation results. It also showed the role of retardation time in calculations and its relation to flow memory. The proposed approach enabled more detailed analysis of viscoelasticity impact on the pressure characteristics.

References

1.
Wylie
,
E. B.
, and
Streeter
,
V. L.
,
1978
,
Fluid Transients
,
McGraw-Hill Inc.
,
New York
.
2.
Chaudhry
,
M. H.
,
1987
,
Applied Hydraulic Transients
,
Van Nostrand Reinhold
,
New York
.
3.
Ghidaoui
,
M. S.
,
Zhao
,
M.
,
McInnis
,
D. A.
, and
Axworthy
,
D. H.
,
2005
, “
A Review of Water Hammer Theory and Practice
,”
ASME Appl. Mech. Rev.
,
58
(
1
), pp.
49
76
.10.1115/1.1828050
4.
Duan
,
Z.
,
Yovanovich
,
M. M.
, and
Muzychka
,
Y. S.
,
2012
, “
Pressure Drop for Fully Developed Turbulent Flow in Circular and Noncircular Ducts
,”
ASME J. Fluids Eng.
,
134
(
6
), p.
061201
.10.1115/1.4006861
5.
Schmandt
,
B.
, and
Herwig
,
H.
,
2013
, “
Loss Coefficients for Periodically Unsteady Flows in Conduit Components: Illustrated for Laminar Flow in a Circular Duct and a 90 Degree Bend
,”
ASME J. Fluids Eng.
,
135
(
3
), p.
031204
.10.1115/1.4023196
6.
Zielke
,
W.
,
1968
, “
Frequency Dependent Friction in Transient Pipe Flow
,”
ASME J. Basic Eng.
,
90
(
1
), pp.
109
115
.10.1115/1.3605049
7.
Suzuki
,
K.
,
Taketomi
,
T.
, and
Sato
,
S.
,
1991
, “
Improving Zielke's Method of Simulating Frequency-Dependent Friction in Laminar Liquid Pipe Flow
,”
ASME J. Fluids Eng.
,
113
(
4
), pp.
569
573
.10.1115/1.2926516
8.
Brunone
,
B.
,
Golia
,
U. M.
, and
Greco
,
M.
,
1995
, “
Effects of Two-Dimensionality on Pipe Transients Modeling
,”
J. Hydraul. Eng.
,
121
(
12
), pp.
906
912
.10.1061/(ASCE)0733-9429(1995)121:12(906)
9.
Vardy
,
A. E.
, and
Brown
,
J. M. B.
,
2004
, “
Efficient Approximation of Unsteady Friction Weighting Functions
,”
ASCE J. Hydraul. Eng.
,
130
(
11
), pp.
1097
1107
.10.1061/(ASCE)0733-9429(2004)130:11(1097)
10.
Vardy
,
A. E.
, and
Brown
,
J. M. B.
,
2003
, “
Transient Turbulent Friction in Smooth Pipe Flows
,”
J. Sound Vib.
,
259
(
5
), pp.
1011
1036
.10.1006/jsvi.2002.5160
11.
Meniconi
,
S.
,
Duan
,
H. F.
,
Brunone
,
B.
,
Ghidaoui
,
M. S.
,
Lee
,
P. J.
, and
Ferrante
,
M.
,
2014
, “
Further Developments in Rapidly Decelerating Turbulent Pipe Flow Modeling
,”
J. Hydraul. Eng.
,
140
(
7
), p.
04014028
.10.1061/(ASCE)HY.1943-7900.0000880
12.
Szymkiewicz
,
R.
, and
Mitosek
,
M.
,
2014
, “
Alternative Convolution Approach to Friction in Unsteady Pipe Flow
,”
ASME J. Fluids Eng.
,
136
(
1
), p.
011202
.10.1115/1.4025509
13.
Brunone
,
B.
,
Karney
,
B. W.
,
Mecarelli
,
M.
, and
Ferrante
,
M.
,
2000
, “
Velocity Profiles and Unsteady Pipe Friction in Transient Flow
,”
J. Water Resour. Plann. Manag.
,
126
(
4
), pp.
236
244
.10.1061/(ASCE)0733-9496(2000)126:4(236)
14.
Bergant
,
A.
,
Simpson
,
A. R.
, and
Vitkovsky
,
J.
,
2001
, “
Developments in Unsteady Pipe Flow Friction Modeling
,”
J. Hydraul. Res.
,
39
(
3
), pp.
249
257
.10.1080/00221680109499828
15.
Silva-Araya
,
W. F.
, and
Chaudhry
,
H.
,
2001
, “
Unsteady Friction in Rough Pipes
,”
ASCE J. Hydraul. Eng.
,
127
(
7
), pp.
607
618
.10.1061/(ASCE)0733-9429(2001)127:7(607)
16.
Ramos
,
H.
,
Covas
,
D.
,
Borga
,
A.
, and
Loureiro
,
D.
,
2004
, “
Surge Damping Analysis in Pipe Systems: Modeling and Experiments
,”
J. Hydraul. Res.
,
42
(
4
), pp.
413
425
.10.1080/00221686.2004.9728407
17.
Vitkovsky
,
J. P.
,
Bergant
,
A.
,
Simpson
,
A. R.
, and
Lambert
,
M. F.
,
2006
, “
Systematic Evaluation of One-Dimensional Unsteady Friction Models in Simple Pipelines
,”
J. Hydraul. Eng.
,
132
(
7
), pp.
696
708
.10.1061/(ASCE)0733-9429(2006)132:7(696)
18.
Pezzinga
,
G.
,
2009
, “
Local Balance Unsteady Friction Model
,”
J. Hydraul. Eng.
,
135
(
1
), pp.
45
56
.10.1061/(ASCE)0733-9429(2009)135:1(45)
19.
Storli
,
P.-T.
, and
Nielsen
,
T. K.
,
2011
, “
Transient Friction in Pressurized Pipes. II: Two-Coefficient Instantaneous Acceleration-Based Model
,”
J. Hydraul. Eng.
,
137
(
6
), pp.
679
695
.10.1061/(ASCE)HY.1943-7900.0000358
20.
Vardy
,
A. E.
, and
Hwang
,
K.-L.
,
1991
, “
A Characteristics Model of Transient Friction in Pipes
,”
J. Hydraul. Res.
,
29
(
5
), pp.
669
684
.10.1080/00221689109498983
21.
Pezzinga
,
G.
,
1999
, “
Quasi-2D Model for Unsteady Flow in Pipe Networks
,”
J. Hydraul. Eng.
,
125
(
7
), pp.
676
685
.10.1061/(ASCE)0733-9429(1999)125:7(676)
22.
Pezzinga
,
G.
,
Brunone
,
B.
,
Cannizzaro
,
D.
,
Ferrante
,
M.
,
Meniconi
,
S.
, and
Berni
,
A.
,
2014
, “
Two-Dimensional Features of Viscoelastic Models of Pipe Transients
,”
J.Hydraul. Eng.
,
140
(
8
), p.
0401403
.10.1061/(ASCE)HY.1943-7900.0000891
23.
Brunone
,
B.
, and
Berni
,
A.
,
2010
, “
Wall Shear Stress in Transient Turbulent Pipe Flow by Local Velocity Measurement
,”
J. Hydraul. Eng.
,
136
(
10
), pp.
716
726
.10.1061/(ASCE)HY.1943-7900.0000234
24.
Duan
,
H.-F.
,
Ghidaoui
,
M.
,
Lee
,
P. J.
, and
Tung
,
Y.-K.
,
2010
, “
Unsteady Friction and Visco-Elasticity in Pipe Fluid Transients
,”
J. Hydraul. Res.
,
48
(
3
), pp.
354
362
.10.1080/00221681003726247
25.
Duan
,
H.-F.
,
Ghidaoui
,
M.
,
Lee
,
P. J.
, and
Tung
,
Y.-K.
,
2012
, “
Relevance of Unsteady Friction to Pipe Size and Length in Pipe Fluid Transients
,”
J. Hydraul. Eng.
,
138
(
2
), pp.
154
166
.10.1061/(ASCE)HY.1943-7900.0000497
26.
Covas
,
D.
,
Stoianov
,
I.
,
Ramos
,
H.
,
Graham
,
N.
, and
Maksimovic
,
C.
,
2005
, “
The Dynamic Effect of Pipe-Wall Viscoelasticity in Hydraulic Transients. Part II—Model Development, Calibration and Verification
,”
J. Hydraul. Res.
,
43
(
1
), pp.
56
70
.10.1080/00221680509500111
27.
Keramat
,
A.
,
Tijsseling
,
A. S.
,
Hou
,
Q.
, and
Ahmadi
,
A.
,
2011
, “
Fluid-Structure Interaction With Pipe-Wall Viscoelasticity During Water Hammer
,”
J. Fluids Struct.
,
28
, pp.
434
455
.10.1016/j.jfluidstructs.2011.11.001
28.
Keramat
,
A.
,
Kolahi
,
A. G.
, and
Ahmadi
,
A.
,
2013
, “
Waterhammer Modeling of Viscoelastic Pipes With a Time-Dependent Poisson's Ratio
,”
J. Fluids Struct.
,
43
, pp.
164
178
.10.1016/j.jfluidstructs.2013.08.013
29.
Soares
,
A. K.
,
Covas
,
D.
, and
Reis
,
L. F.
,
2008
, “
Analysis of PVC Pipe-Wall Viscoelasticity During Water Hammer
,”
J. Hydraul. Eng.
,
134
(
9
), pp.
1389
1394
.10.1061/(ASCE)0733-9429(2008)134:9(1389)
30.
Ferry
,
J. D.
,
1980
,
Viscoelastic Properties of Polymers
,
Wiley
,
New York
.
31.
Aklonis
,
J. J.
,
MacKnight
,
W. J.
, and
Shen
,
M.
,
1972
,
Introduction to Polymer Viscoelasticity
,
Wiley
,
New York.
32.
Williams
,
M. L.
,
1964
, “
Structural Analysis of Viscoelastic Materials
,”
AIAA J.
,
2
(
5
), pp.
785
798
.10.2514/3.2447
33.
Covas
,
D.
,
Stoianov
,
I.
,
Ramos
,
H.
,
Graham
,
N.
, and
Maksimovic
,
C.
,
2004
, “
The Dynamic Effect of Pipe-Wall Viscoelasticity in Hydraulic Transients. Part I—Experimental Analysis and Creep Characterization
,”
J. Hydraul. Res.
,
42
(
5
), pp.
516
530
.10.1080/00221686.2004.9641221
34.
Kłosowski
,
P.
,
Komar
,
W.
, and
Woźnica
,
K.
,
2009
, “
Finite Element Description of Nonlinear Viscoelastic Behaviour of Technical Fabric
,”
Constr. Build. Mater.
,
23
(
2
), pp.
1133
1140
.10.1016/j.conbuildmat.2008.06.002
35.
Ghilardi
,
P.
, and
Paoletti
,
A.
,
1986
, “
Additional Viscoelastic Pipes as Pressure Surges Suppressors
,”
5th International Conference on Pressure Surges
,
M.
Papworth
, ed.,
BHRA
,
Hannover, Germany
, pp.
113
121
.
36.
Pezzinga
,
G.
, and
Scandura
,
P.
,
1995
, “
Unsteady Flow in Installations With Polymeric Additional Pipe
,”
ASCE J. Hydraul. Eng.
,
121
(
11
), pp.
802
811
.10.1061/(ASCE)0733-9429(1995)121:11(802)
37.
Bergant
,
A.
,
Tijsseling
,
A.
,
Vitkovsky
,
J.
,
Covas
,
D.
,
Simpson
,
A.
, and
Lambert
,
M.
,
2003
, “
Further Investigation on Parameters Affecting Water Hammer Wave Attenuation, Shape and Timing. Part 1: Mathematical Tools
,”
International Meeting of the Working Group on the Behaviour of Hydraulic Machinery Under Steady Oscillatory Conditions
,
IAHR
,
Stuttgard
.
38.
Meniconi
,
S.
,
Brunone
,
B.
, and
Ferrante
,
M.
,
2012
, “
Water-Hammer Pressure Waves Interaction at Cross-Section Changes in Series in Viscoelastic Pipes
,”
J. Fluids Struct.
,
33
, pp.
44
58
.10.1016/j.jfluidstructs.2012.05.007
39.
Meniconi
,
S.
,
Brunone
,
B.
,
Ferrante
,
M.
, and
Massari
,
C.
,
2014
, “
Energy Dissipation and Pressure Decay During Transients in Viscoelastic Pipes With an In-Line Valve
,”
J. Fluids Struct.
,
45
, pp.
235
249
.10.1016/j.jfluidstructs.2013.12.013
40.
Soares
,
A. K.
,
Covas
,
D.
, and
Reis
,
L. F.
,
2011
, “
Leak Detection by Inverse Transient Analysis in an Experimental PVC Pipe System
,”
J. Hydroinf.
,
13
(
2
), pp.
153
166
.10.2166/hydro.2010.012
41.
Chow
,
V. T.
,
1964
,
Handbook of Applied Hydrology
,
McGraw-Hill
,
New York
.
42.
Zarzycki
,
Z.
,
Kudźma
,
S.
, and
Urbanowicz
,
K.
,
2011
, “
Improved Method for Simulating Transients of Turbulent Pipe Flow
,”
J. Theor. Appl. Mech.
,
49
(
1
), pp.
135
158
.
43.
Vardy
,
A. E.
, and
Brown
,
J. M. B.
,
2004
, “
Transient Turbulent Friction in Fully Rough Pipe Flows
,”
J. Sound Vib.
,
270
(
1–2
), pp.
233
257
.10.1016/S0022-460X(03)00492-9
44.
Kodura
,
A.
, and
Weinerowska
,
K.
,
2007
, “
The Influence of the Local Pipeline Leak on Water Hammer Properties
,”
Proceedings of the 2nd National Congress of Environmental Engineering
,
Pawlowski
et al., eds., Lublin, Poland, Sept. 4–8,
Taylor and Francis Group
,
London
, pp.
239
244
.
45.
Cunge
,
J. A.
,
Holly
,
F. M.
, Jr.
, and
Verwey
,
A.
,
1980
,
Practical Aspects of Computational River Hydraulics
, Vol.
3
,
Pitman Publishing Limited
,
London
.
46.
Johnston
,
N.
,
Pan
,
M.
,
Kudzma
,
S.
, and
Wang
,
P.
,
2014
, “
Use of Pipeline Wave Propagation Model for Measuring Unsteady Flow Rate
,”
ASME J. Fluids Eng.
,
136
(
3
), p.
031203
.10.1115/1.4026106
47.
Szymkiewicz
,
R.
,
2010
,
Numerical Modeling in Open Channel Hydraulics
,
Springer
,
New York
.10.1007/978-90-481-3674-2
48.
Weinerowska-Bords
,
K.
,
2007
, “
Accuracy and Parameter Estimation of Elastic and Viscoelastic Model of Water Hammer
,”
Task Quaterly
,
11
(
4
), pp.
383
395
.
49.
Price
,
W. L.
,
1978
, “
Controlled Random Search Procedure for Global Optimization
,”
Toward Global Optimization 2
,
L. C. W.
Dixon
, and
G. P.
Szegö
, eds.,
North-Holland Publishing Company
,
Amsterdam
, pp.
71
84
.
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