Ellis,J. Pressure transients in water engineering, A guide to analysis and interpretation of behaviour
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to permit flows from one group of pumps to pass into the alternative
system of mains in order to reach the reservoirs. Normally, around
50% of the pumps would be in use at any time, yielding about 20 Mld.
23.6.4 Pumpset inertia
The moment of inertia of the borehole pumpsets can often be quite
small. An equation for moment of inertia (MI) for a multi-stage
pump is of the form:
MI ¼ Motor inertia þ stage inertia number of stages ð23:4Þ
For the wellfield shown, pumpset inertia ranged from 0.0255 kg/m
2
to
0.0314 kg/m
2
. With such low inertia it may be expected that a very
rapid fall in head downstream of the wellhead will occur following a
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Collector
main loss
Borehole losses
Control valve loss
Initial water level
Cone of depression
Static water surface
after some time
Cone of depression
Minimum
pumping head
Pumping head
after some time
Bore hole
Aquifer
Wellhouse
Reservoi
r
Fig. 23.17. Head conditions at a well
Pressure transients in water engineering
pump trip and that the wellhead and other air valves may come into
operation.
23.6.5 Sequenced pump operation
Start-up of pumps is under operator control and to avoid excessive
demand upon the electrical supply network, sequential start of pumps
is desirable with a time delay between successive pump operation.
Considerable choice exists in the sequence used to start pumps. Opera-
tional circumstances may dictate that a certain set of pumps be used but
that may still leave the starting sequence in the operator’s hands. The
mode of pump starting can have an important effect upon the
maximum transient system pressure. For the system being considered,
some general guidelines can be established by considering a small
number of pump start sequences from the large number of possibilities.
Alternatives are illustrated using the pumps of GROUP I. Figure 23.18
shows the predicted piezometric head at well No. 1, located at the
upstream end of line No. 1 for a starting arrangement whereby pumps
of GROUP I were operated in sequence with a 1 s time delay between
operating successive pumps. Pumps were started at well No. 1 with the
final pumps to be started being those nearest to the reservoirs.
Maximum head predicted was below 380 mAD.
If the reverse sequence is used — that is, first starting those pumps
nearest to the reservoirs and finally the pumps around well No. 1 —
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380
370
360
350
340
330
320
310
0.00 0.25 0.5 0.75 1.00
Time
(
min
)
Elevation (mAOD)
Fig. 23.18. Head at well No. 1 for sequenced start commenc ing at well No. 1
Amplification of transient pressures
somewhat higher peak pressures were predicted. Figure 23.19 shows the
corresponding head variation at well No. 1. Maximum transient pres-
sure exceeded 420 mAD. Other starting arrangements also produced
higher starting pressures than those of Fig. 23.18 and it was concluded
that the optimum arrangement was to first start those pumps towards
the upstream end of the system and progress downstream towards the
reservoirs.
23.6.6 Pumping failure
Pumping failure has to consider the effect of an area power failure
affecting the entire wellfield. Instead of a pressure transient being
developed at a pumping station and spreading along its rising main,
in the case of the wellfield with a collector pipeline system, failure of
pumps distributed throughout the network means that piezometric
level starts to fall almost simultaneously at each wellhouse. With the
low moment of inertia of borehole pumps used in installations of this
kind, the rate of fall in piezometric level is rapid at any single wellhead.
The presence of an air valve having a good inflow capacity will usually
ensure that sub-atmospheric pressures local to the well remain modest.
As the downsurge spreads into the collector network there is oppor-
tunity for interaction between each of the rarefaction waves shown in
Fig. 23.20, with the potential for amplification of the head drop
produced at individual wellhouses.
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Time (min)
Elevation (mAOD)
420
400
380
360
340
320
0.00 0.50 1.00 1.50
Fig. 23.19. Head at well No. 1 for sequenced start ending with well No. 1
Pressure transients in water engineering
495
Vacuum pressure
(c)
(iii)
(iii)
(iii)
(iii)
(iv)
(iv)
(ii)
(ii)
(ii)
(ii)
(ii)
(ii)
2V
o
2V
o
2V
o
H
o
H
o
H
o
H
o
V
o
V
o
V
o
V
o
H
o
(b)
(a)
Collector main
Wellhouse
Riser
Pump
Branch
H
o
= steady pumping head
(i)
(i)
Fig. 23.20. Head variations due to area blackout
Amplification of transient pressures
Figure 23.20a shows the initial rarefaction waves (i) travelling from
each wellhead along the branch pipeline towards its connection with
the collector main.
In Fig. 23.20b the initial rarefaction waves have reached the
connection point with the collector. A partial reflection in the form
of a compression wave (iii) travels from the connection back towards
each wellhouse while rarefaction waves (ii) travel both upstream and
downstream along the collector from the connection points. These
rarefaction waves produce a fall in head within the collector main.
In Fig. 23.20c opposing rarefaction waves have met in the collector
main between the branch connections, leading to a doubling in ampli-
tude of head drop (iv). There is a strong possibility that severe vacuum
pressures will occur in the collector between adjacent wells.
Simulation of an area power failure affecting all GROUP I pumps
shows that such vacuum pressures develop along line No. 1 as shown
in Fig. 23.21. The profile of line No. 1 shows relatively low elevations
over the middle parts of the main with higher levels both towards
well No. 1, chainage 0 km, and also at the reservoir end of the pipeline,
chainage 6 km.
23.6.7 Air valve operation
Low pressure head is experienced throughout the network with air
valves operating at most wellheads. As time passes, flow towards the
496
km
mAOD
0 1 2 3 4 5 6
360
340
320
300
280
260
Fig. 23.21. Area blackout envelope curves along line No. 1 (initial stages)
Pressure transients in water engineering
reservoirs ceases and then reverses while positive flows continue from
the higher parts of the system around well No. 1. Air pockets at
these more elevated wellhead air valves will continue to grow while
air is expelled from the lower parts of the system. Air removal through
these lower air valves is facilitated by continued positive flows from the
higher parts of the system around well No. 1 and also by reversed flow
from the reservoirs.
As lower air valves close, compression waves are developed and a
general rise in head is developed over these lower central parts of the
network as shown in Fig. 23.21.
With reversed flow from the reservoirs increasing and air valves
closing, the compression wave propagating upstream travels into
progressively smaller pipes, being amplified until it finally enters the
DN 100 pipes around well No. 1. Closure of final air valves coupled
with the strength of the compression wave produces a maximum
transient head of over 440 mAD at well No. 1 (Fig. 23.22).
23.7 Potential for amplification
These examples serve to illustrate the particular problems associated
with complicated pipe networks where the pressure transients are
travelling into pipes of decreasing diameter and where looped arrange-
ments exist. The effect of pressure waves or the same type, either
compression or rarefaction, travelling in opposite directions carries
the risk of important amplification when these waves meet. Risk of
497
km
mAOD
0 1 2 3 4 5 6
440
420
400
380
360
340
320
300
280
260
Fig. 23.22. Area blackout envelope curves for line No. 1 (later stage)
Amplification of transient pressures
amplification is greater where the pressure transient is relatively
steep. Then there is only limited time for the effects of pressure wave
reflection to alleviate this effect. Use of pressure vessels can be very
beneficial in limiting rates of pressure change at the source of the
hydraulic transient, thus allowing the benefits of wave reflection to be
realised.
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Pressure transients in water engineering
24
Flow instabilities
In the large majority of water and sewerage systems, whenever a change
of flow state occurs, the action of pipeline resistance is sufficient to
cause the transient effects to be gradually dissipated thus allowing a
new steady flow state to be realised. On occasion, however, certain
features of a network may act to sustain an unsteady motion so that
a self-perpetuating oscillation is developed which does not decay over
time but may in some instances even increase in severity. Such a
condition of increasing amplitude of oscillation or resonance can be
very dangerous and must be avoided.
The phenomenon of resonance has been known for a considerable
time with experiments on the topic reported by Camichel et al.as
early as 1919 and with a presentation of the theory of resonance by
Jaeger in 1939. Not all instances of unstable behaviour result in
resonance but nevertheless can have undesirable consequences.
24.1 Types of oscillation
The theoretical period of elastic oscillation within a pipeline of length L is
4L=a and this is the fundamental period for a simple pipeline of uniform
characteristics. Harmonics can also develop having periods of oscillation
which are fractions of the fundamental period. In a pipeline consisting of
a series of pipes of differing properties such as diameter and wave speed,
partial reflections at junctions of different pipe types can cause the
oscillatory motion to have a different period called the apparent period.
For a dangerous resonant condition to develop there has to be an
energy input during each cycle of oscillation. As a simple illustration,
consider a child on a swing. At the optimum stage in the child’s
movement the parent gives the swing an additional push (energy
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input) as a consequence of which the child is able to swing to a higher
elevation with each successive cycle. This is an example of a forced
oscillation as an external agent is present. Ultimately, safety and
other considerations will curtail the height (amplitude) which the
swing reaches. Unfortunately, there are no such automatic constraints
on hydraulic systems.
A close investigation of boundary conditions led to the discovery of
self-exiting or self-induced oscillations in hydraulic systems. For
example, valve vibrations have been known to produce resonances in
pressure tunnels which have caused linings to become cracked. Pulsa-
tions have been observed in pipelines where the periodic movement
of turbine runner blades past fixed blades (guide vanes) has produced
pressure fluctuations. The period of these pulsations and resulting
resonance has often been eliminated by altering the number of
runner blades thus changing the relationship between the pipeline
period and the period of the pulsations.
Cyclical motion of a valve which allows a variable outflow to occur is
accompanied by pressure fluctuations which may become amplified if
the connected pipeline system responds to the same period of oscillation.
Resonance can only occur if there is an exciter present. This can be in the
form of a forcing function which excites the system at some period.
A second way in which resonance can occur is if say a valve responds to
oscillations occurring within the system, by self-excitation. In such cir-
cumstances the system controls the oscillation, and the operation of a
boundary condition such as a self-acting valve is influenced by the system.
Amplitude of a resonance may ultimately be limited if minimum head
during an oscillation falls to near the discharge head downstream of a
valve, so that energy conditions are not significantly influenced by
the valve response. When the head difference across a valve becomes
small it does not matter if the valve is fully opened or only partly
open as the flow rate through the valve will be small irrespective of
how much the valve is open. Resistance effects may act to some
extent to produce a peak amplitude <2H
o
where H
o
is the static
head upstream of the valve, as shown in Fig. 24.1.
While the resonant phenomenon has been well documented and
understood for many years, examples still continue to occur. Gordon
(2006b) recently described an instance of resonant behaviour at a
28 MW impulse turbine hydropower plant in the Andes. Rather than
installing the more usual cable connection from the turbine governor,
to control movement of the spear valve, it was decided to use a chain
of small ball bearings forming a flexible rod. It was hoped to avoid
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Pressure transients in water engineering
any stretching which might occur in a cable connection by using the ball
bearings. Unfortunately, a small amount of slack in the chain of ball
bearings was sufficient to confuse the governor about the precise
valve opening. This caused ‘hunting’ of the valve at a frequency
equalling the period of the penstock and produced a self-exiting
oscillation. Reverting to a cable connection eliminated the problem.
The impedance method of analysis can be used to predict the most
critical periods of oscillation in a pipeline network. It is not intended
to discuss this method but the interested reader can find a description
of the method in books, for example by Streeter and Wylie (1967) or by
Jaeger (1977).
To illustrate circumstances in which it is possible for flow within a
pipeline network to become unstable and fail to settle at a steady
operating condition, three examples have been included in this chapter.
The first illustration concerns a pumping installation and the second an
entirely gravity-driven system.
24.2 Pumping system — Glasgow East Main and Daer
network link
Figure 24.2 shows the plan arrangement of trunk mains serving south
and east parts of the city of Glasgow and its environs. Two systems
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Static head = H
o
Maximum amplitude = 2H
o
Self-actin
g
valve
Constant head
M
Fig. 24.1. Development of resonance
Flow instabilities