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Transient Movement in a Single Looped Water Distribution Network.
Pressure Simulation and Experimental Measurement
ANCA CONSTANTIN, MĂDĂLINA STĂNESCU, CLAUDIU ŞTEFAN NIłESCU
Hydraulic Engineering Department, Faculty of Civil Engineering
“Ovidius” University
Constanta, 22B Unirii Str.
ROMANIA
aconstantina@univ-ovidius.ro, http://www.univ-ovidius.ro/faculties/civil_eng
Abstract: - Transient movement results as a hydraulic system response to sudden valve manoeuvres in a water
supply network. Investigation on pressure variation was carried out on a representative loop of a pipe network.
Both numerical simulation and experimental laboratory measurements were developed in order to validate the
software Hammer for looped networks. Theoretical and experimental results reveal the same extreme pressure
values, but the recorded oscillations have a lower frequency and an increased damping ratio than the simulated
ones.
Key-Words: - Hydraulics, Water Distribution Network, Water Hammer, Pressure
1 Introduction
Looped pipe configuration is preferred in urban
water distribution networks for its reliability [6].
Consumers, placed in the nodes of the network have
no regular demand pattern. Any manoeuvre of a
valve on the network may be a source of
disturbance, generating transient movement along
the pipes. Pressure variation might be considerable
as the manoeuvres are fast. Valves operation pattern
might influence the extreme pressure values reached
during a hydraulic shock.
The identification of the most vulnerable
consumers, in terms of pressure variation, as early
as the engineering design phase, is of great interest
for the hydraulic engineers. Numerical simulation is
a useful tool for pointing out the extreme pressure
variation over time in a specified section of a pipe.
Our goal was to investigate if Hammer, an automate
programme special conceived for hydraulic shock
simulation, is reliable in the case of looped
networks.
2 Transient Movement Analysis in a
Looped Network
Investigations on pressure variation over time, in the
nodes of a looped network were performed both by:
numerical simulation;
experimental measurement.
The pressure oscillation graphs are analyzed in
order to find out if the extreme values resulted by
numerical simulation cover the ones registered by
the transducers; the damping ratio and oscillation
frequency are compared, aiming to see how accurate
the automate programme is.
Fig.1 Geometry of the studied single loop network
The single loop network used for simulation and
subjected to laboratory experimental measurements
is represented in Fig.1. The considered loop is
similar from hydraulic view point to a real single
loop network. The system is supplied by a reservoir
with constant water level of 2m. Each node is
equipped with a ball valve that can be opened at
different opening angles. The source is placed in
node 1. The valves in nodes 2, 3 and 4 are the water
consumers. The looped network lies in the same
Recent Researches in Computational Techniques, Non-Linear Systems and Control
ISBN: 978-1-61804-011-4
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horizontal plane. All the four sides of the loop are
HDPE pipes.
In Table 1 there are given the values of the flow
rate in the nodes and through the pipes of the loop,
in the case of steady state water movement.
Table 1. Flow rate values in steady state water
movement, [l/s]
Nodes
1 2 3 4
0.449 0.235 0.182 0.0321
Pipes
1-2 2-3 3-4 1-4
0.255 0.020 0.162 0.194
It is investigated the dynamic response of the
hydraulic system to the following operation
scenario: all the three valves in the consumers nodes
2, 3 and 4 are completely open. Previous calibration
of the network showed that the steady state
movement is reached after only 2 seconds from the
valve opening. After 5 seconds of operation, the
valves in node 2 is suddenly closed and after other 5
seconds valves in nodes 3 and 4 are simultaneously
and sudden closed. It is only one among the
numerous scenarios that could be taken into account
with respect to the possibility of operation and
consumption in nodes.
2.1 Pressure Variation Numerical
Simulation
Hammer programme was developed for solving
hydraulic shock problems in water branched pipe
networks. The programme was adapted to looped
networks by the use of fictive nodes that turn a
linear system into a looped network.
The mathematical model of the water hammer
phenomenon is composed of two main equations:
momentum and mass balance equations. They may
be transformed and written in finite differences [5],
as the velocity (1) and the head (2) equations:
(1)
(2)
where: index i accounts for time, index j accounts
for node, v-velocity, [m/s]; H-head, [m]; c-celerity,
[m/s]; -step of time, [s]; -pipe’s diameter, ;
-Darcy’s coefficient; g-gravity acceleration.
The programme uses the method of
characteristics for solving water hammer problems,
considering one dimension movement of water [4].
The wave celerity is constant along the pipes.
The initial pressure and velocity conditions
correspond to the steady state movement of water in
the loop. The boundary conditions are implemented
according to the above mentioned operation
scenario.
Pressure as a time dependant function is
graphically represented for each node of the loop.
2.2 Pressure Variation Experimental
Measurement
The laboratory stand allows accurate and real-time
display (graphical and / or tabular) of physical
quantities collected from transducers mounted in the
network nodes. Each node of the loop is equipped
with a MBS 33 pressure transducer that provides a
reliable pressure measurement.
The flexible sensor covers an output signal in the
range of 4 ÷ 20 mA and a gap measuring pressure
from 0 ÷ 1 bar to 0 ÷ 600 bar at operating
temperatures of -40 ÷ +85o C. The pressure
transducer MBS 33 has a very good vibration
stability and a robust construction. Collected data
are processed in LabVIEW programming
environment;
The valves in the looped network are operated in
accordance with the pre-established scenario. Once
again, pressure as a time dependant function is
graphically represented for each node of the loop.
3 Results
The collected data allows us to represent, on the
same diagram, pressure variation over time in each
node, in both cases: numerical simulation and
experimental measurement. This superposition
makes it easier to compare the two evolutions of
pressure in the hydraulic system.
Recent Researches in Computational Techniques, Non-Linear Systems and Control
ISBN: 978-1-61804-011-4
239
Fig.2.Pressure variation in node 2
In Fig.2 there is represented the pressure
variation in the node 2, the closest to the input node
1, and also the node with the greatest withdrawal.
Hammer programme indicates extreme pressure
values that cover the extreme pressure values
recorded by the measure system. But, we may notice
that the absolute value of minimal pressure indicated
by the numerical simulation is about 30% greater
than the measured one.
Fig.3.Pressure variation in node 3
Fig.4.Pressure variation in node 4
The graphs in Fig. 3 and Fig.4 indicate that the
extreme pressure values in the nodes 3 and 4 are
very well estimated by the automate programme.
The Hammer programme shows the under
damped oscillation of pressure in the hydraulic
system and calculates with good accuracy the
amplitude of the first oscillation. But the pattern of
decaying oscillation differs. The envelope of the
wave form is represented as a function of time in
Fig.5,6 and 7, for the three consumer nodes. In each
node, the envelope of the simulated oscillation is of
exponential form, but the envelope of the measured
one is better approximated by a polynomial of order
3. The real oscillation proves to be amplitude
modulated.
The logarithmic decrement, , is given by the
relationship:
1max
max
ln
+
=
i
i
p
p
D
(3)
where maximal pressures at two
consecutive oscillations, at the moments .
Fig.5.Oscillation envelope, in node 2
Fig.6. Oscillation envelope, in node 3
Recent Researches in Computational Techniques, Non-Linear Systems and Control
ISBN: 978-1-61804-011-4
240
Fig.7. Oscillation envelope, in node 4
In the case of under damped oscillation, the
damping ratio is related to the logarithmic
decrement by the relationship:
22
4π+
=δ
D
D
(4)
Fig.8.Damping ratio variation in node 2
Fig.9.Damping ratio variation in node 3
Fig.10.Damping ratio variation in node 4
The graphical representation of the damping
ratio, in each node, is given in Fig.8, 9 and 10. The
damping ratio is and it takes small values,
revealing a slow damping of the oscillation [2].
This is a main consequence of the small friction
coefficient of the HDPE pipes [7]. Simulated
oscillation exhibits even a smaller damping ratio
than the real one.
The natural frequency of pressure simulated
oscillation is 5.12 Hz, instead the real one of 3.125
Hz.
4 Conclusion
Hammer programme calculates with accuracy the
maximal amplitude of pressure variation in the
hydraulic system that means the amplitude of the
first oscillation. Taking into account that extreme
pressure values dictate the pipes size, we may say
that this programme is an useful tool in the
engineering design.
The simulation reveals the most vulnerable
consumer, the one exposed to the extreme pressures
in the network.
The disadvantage consists of a poor evaluation of
the damping ratio. The real oscillation decays faster
than the simulated one. Furthermore, being derived
from a variant dedicated to branched networks, the
programme doesn’t take into account the waves
reflected in the nodes. This may be the cause for the
amplitude modulated shape of the real oscillation.
References:
[1] Cabrera, E., Vela, A. F., Improving Efficiency
and reliability in Water Distribution Systems,
Kluwer Academic Publishers, Dordrecht,
Nederlands, 1995.
Recent Researches in Computational Techniques, Non-Linear Systems and Control
ISBN: 978-1-61804-011-4
241
[2] Luca, D., Stan, C, Oscillation and waves,
http://newton.phys.uaic.ro/notemain.html,
2007.
[3] Obradovic, D., Lonsdale, P., Public Water
Supply. Models, Data and Operational
Management, E &FN SPON, Routledge,
London, 1998.
[4] Popescu, M., Arsenie, D.I., Vlase, P., Applied
Hydraulic Transients for Hydropower Plants
and Pumping Stations, Balkema Publishers,
Lisse, Abington, Tokyo, 2003, 2004.
[5] Streeter, V.L., Wylie, B. E., Hydraulic
transients, McGraw – Hill Book Company,
New York, 1987
[6] Swamee, P. K., Sharma A. K., Design of Water
Supply Pipe Networks, John Wiley & Sons,
Inc., Hoboken New Jersey, 2008.
[7] * * * Manual of Water Supply Practices. PE-
Design and Installation, American Water
Works Association, Denver, 2005.
Recent Researches in Computational Techniques, Non-Linear Systems and Control
ISBN: 978-1-61804-011-4
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