Content uploaded by J.P. Ferreira
Author content
All content in this area was uploaded by J.P. Ferreira on Jul 05, 2019
Content may be subject to copyright.
Pressure wave behaviour due to entrapped air in
hydraulic transient events
J P Ferreira 1, E Ghezzi 2, M Ferrante 2, D I C Covas 1
1 CERIS, Instituto Superior Técnico, Universidade de Lisboa, Portugal
2 Dipartimento di Ingegneria Civile ed Ambientale, University of Perugia, Italy
ABSTRACT
The aim of the current paper is to analyse the effect of an air pocket on the transient
pressure wave signal using physical data. Transient pressure data were collected from an
experimental laboratory facility assembled at Instituto Superior Técnico. The pipe
system has a reservoir-pipe-valve configuration and the pipe is made of copper, is 15 m
long and has a 20 mm inner diameter. The simulated entrapped air pocket is located in
the middle of the pipe. Each test was repeated several times (ca. 20 times for non air
pocket tests and 5 times for air pocket tests) for each flow rate in order to obtain mean
and standard deviation values in time of the pressure signal. Transient pressures were
collected at 40 kHz acquisition frequency to illustrate the signal post-processing
procedure. Mean pressure signal values and down-sampled values were calculated and
used in the subsequent analysis. Collected data have shown that maximum overpressures
can be higher than the Joukowsky maximum pressure pulse depending on the air pocket
initial volume and initial Reynolds number. A reflected pressure wave is generated
associated to the entrapped air contraction and expansion. A clear pressure wave delay
and damping is observed for the air pocket tests.
Keywords: Hydraulic transients, air pocket, damping, joukowsky pulse.
NOTATION
a = pressure wave speed (ms1);
D = pipe inner diameter (m);
e = pipe-wall thickness (m);
f = frequency (Hz);
g = gravity acceleration (ms2);
H = piezometric head (m);
L = pipe length (m);
Q = discharge (m3s1);
S = pipe cross-sectional area (m2);
Re = Reynolds number (-);
t = time (s);
U = fluid mean velocity (ms1);
'H = transient pressure variation (m)
Q = kinematic viscosity (-);
T = standard deviation.
Underscripts
J = Joukowsky overpressure;
0 = initial conditions.
© BHR Group 2018 Pressure Sur
g
es 13 105
1 INTRODUCTION
Air is often accumulated in pressurized water pipe systems as a result of the inadequate
air valve sizing, installation or operation, the inadequate design of pump suction lines,
the liquid contact with pressurised air, the occurrence of transient pressures or the fast
water pipe filling after a disruption (Martin, 1976, Liou and Hunt, 1997, Izquierdo et al.,
1999, Pozos et al., 2010). Air can appear in three different forms: dissolved in the liquid,
entrained as small bubbles mixed with water and entrapped in air pockets. Dissolved air
has as a maximum saturation rate as a function of the air components (e.g. oxygen,
hydrogen) and the mixture during transient events behaves as a single-phase fluid.
Entrained air creates a compressible two-phase mixture (gas-liquid) that propagates
transient pressure waves with a significantly lower and time-dependent celerity. This
entrained air tends to release and to accumulate in higher pipe sections along time (Liou,
2000, Bergant et al., 2006). Finally, entrapped pockets are formed in pipe systems at
higher elevation sites or in pipe locations with installed valves and fittings (e.g. service
connections and dead ends), as localized entrapped air, or along large extensions of
quasi-horizontal pipes, as distributed or very large air pockets located at the upper pipe
section (Pozos et al., 2010).
The presence of air pockets causes several operational problems in pipe systems, such as
local head losses during normal operation (reducing the flowrate when air cavities
become large) and the increase of hydraulic transient pressures due to the liquid-gas
interaction (Liu and Zhou, 2009). Experience has shown that maximum transient
pressures may be significantly higher than those expected due to the presence of massive
air cavities in pipes, compromising the safety of the system. These maximum transient
pressures strongly depend on air pocket volumes and on flow regime (Zhou et al., 2011,
Martins et al., 2015, Martins et al., 2017). In the presence of air pockets, the pressure
wave may have a different behaviour than that in common transient events as pressure
may locally drop and increase (Covas et al., 2006), amplify and compromise the pipe
maximum resistance loads leading to pipe failure (Pozos et al., 2012).
The aim of the present paper is to analyse the effect of the air pockets on the transient
pressure signal using collected pressure data from an experimental facility at Instituto
Superior Técnico. Transient pressures were measured with an acquisition frequency of
40 kHz. Each test was repeated several times. Mean values and down-sampled values of
the pressure signals were calculated for reducing data noise. Analysis of collected data
has shown that maximum overpressures are higher than the Joukowsky pulse, depending
on the air volume and initial flow rate. A reflected pressure wave is generated by the
entrapped air contraction and expansion. A clear pressure wave delay and damping are
observed for the air pockets tests.
2 DATA COLLECTION
The experimental tests were carried out in an existing experimental pipe facility at the
Laboratory of Hydraulics and Environment (LHE) of Instituto Superior Técnico (IST),
Portugal. The system was composed of a straight copper pipe of 15 m length, L, with an
inner diameter, D, of 2 mm and a thickness, e, of 1 mm. A centrifugal pump was
installed at the upstream end of the pipe with a nominal head and discharge of 46 m and
3.6 m3/h, respectively. A hydropneumatic vessel with a total capacity of 60 litres was
installed (in derivation) after the pump to stabilize the pressure in the system and to
simulate a constant-head reservoir.
106 © BHR Group 2018 Pressure Sur
g
es 13
Two spherical valves with the same inner diameter (20 mm) were installed at the
downstream end of the pipe system. The first was an automatically operated valve (V1),
connected to a pneumatically actuated solenoid valve to generate fast hydraulic transient
events in the pipe system (Ferreira et al., 2018). The second was a manual valve (V2)
used to control the steady-state discharge before each test. After both valves, there was a
polyethylene-returning pipe with a higher diameter and with ca. 20 m length that closes
the hydraulic circuit.
Figure 1 – Schematic of the experimental facility
An acrylic tube with a drilled small orifice was installed in derivation with the copper
pipe to simulate the air pocket. This device had a 5 mm diameter orifice, an inside total
length of 45 mm and a lateral entrance to supply/release air used to change the initial air
pocket size. This device is depicted in Figure 2.
The data acquisition system (DAS) was composed of a
desktop computer, an oscilloscope, a trigger-
synchronizer, an electromagnetic flowmeter (with a
0.4% accuracy) and two strain-gauge type pressure
transducers (25 bars nominal pressure and span
accuracy of ±0.25% of the nominal pressure). The first
transducer (PT1) was located upstream of the valve V1
and the second (PT2) at the pipe mid-length,
immediately downstream of the air pocket simulation
device. Different closures times were tested for each
initial discharge by changing the air pressure introduced
in the hydropneumatic operating system of valve V1.
Previous studies (Ferràs et al., 2016, Martins et al., 2016) have shown that estimated
pressure wave speed of the copper pipe, a, was 1,250 m/s, having been based on the
traveling time of the transient pressure waves between two consecutive transducers (PT1
and PT2). All tests were carried out for totally developed initial discharges and with an
acquisition frequency of 40 kHz, despite the maximum pressure transducers response
being lower than 1 kHz.
The air pocket was simulated in the system by means of the referred acrylic piece with a
½’ valve attached at 2.5 cm from the bottom of the device to control the air inlet/outlet
between each test. Two air pockets were tested to assess the transient pressure variation
Figure 2 – Acrylic device
to simulate air pocket
© BHR Group 2018 Pressure Sur
g
es 13 107
associated to each air pocket volume: the first (AP1) with a volume of air of 60 mm3 and
the second (AP2) with 230 mm3 which correspond to 0.0013 and 0.0049 % of the water
volume of the pipe, respectively.
Transient tests were carried out in the pipe with no air pockets for four initial steady-
state conditions presented in Table 1. Despite having closure times between 0.04 and
0.07 s , corresponding to slow manoeuvres (2L/a = 0.024 s), the effective closure times
of the downstream ball valve were significantly lower (ca. 4-10% of the total closure
time), varying between 0.28 and 0.50 × 102 s (Ferreira et al., 2018).
Table 1 – Set of transient tests
Description Q0
(l/h)
Q0
(×10-3 m3/s) Re0 Number of
repetitions
No air Pocket
59.5 0.017 1052 18
220.0 0.061 3890 20
396.0 0.110 7003 20
457.0 0.127 8082 38
Air pocket 1
(AP1)
59.5 0.017 1052 5
220.0 0.061 3890 5
396.0 0.110 7003 5
457.0 0.127 8082 5
Air pocket 2
(AP2)
59.5 0.017 1052 5
220.0 0.061 3890 5
396.0 0.110 7003 5
457.0 0.127 8082 5
Examples of transient pressures collected at transducers PT1 and PT2 are presented in
Figure 3 and those collect for the two air pockets are presented in Figures 4 and 5.
(a)
(b)
Figure 3 – Transient pressure data without the air pocket collected at
(a) PT1 and (b) PT2
108 © BHR Group 2018 Pressure Sur
g
es 13
(a)
(b)
Figure 4 – Transient pressure data for air pocket AP1collected at
(a) PT1 and (b) PT2
(a)
(b)
Figure 5 – Transient pressure data for air pocket AP2 collected at
(a) PT1 and (b) PT2
Collected data has significant noise generated by electric radiations and pipe vibrations,
and should, therefore, be processed in order to compare the effects of the air pockets on
the pressure signals. This issue will be treated in next section.
3 DATA PROCESSING
Transient pressure data processing is a three-step procedure. The first step consists of the
synchronization of the beginning of the manoeuvre in all pressure signals carried out for
the same conditions (corresponding to the repetition of the test). The second involves to
the calculation of mean and standard deviation values at each time step for the given
acquisition frequency (in this case 40 kHz). The third step corresponds to the down-
sampling of the signal in order to reduce the noise preserving the existing features. Codes
for mean values calculation and down-sampling have been implemented in Matlab and
used herein to process the signal.
© BHR Group 2018 Pressure Sur
g
es 13 109
An example of the signal at PT1 obtained by the elaboration of 38 tests is presented in
Figure 6, for tests with no air pockets, referring to the same conditions with Q0 = 396 L/h
and duration of 0.28×102 s. This test-type is used herein to analyse the acquisition
frequency and the noise associated to pressure signal. Despite the pressure transducers
response time being lower than 1 ms (according to the manufacturer), the chosen
acquisition frequency was 40 kHz, in order to illustrate the analysis of the mean
calculation and the down-sampling of the signals.
Figure 6 – Experimental tests (38 total) with no air pocket for Q = 396 l/h
(manoeuvre duration of 0.28×10
2 s). Raw data with 40 kHz
The arrival time of the pressure wave fronts has been synchronised and the data have
been adjusted in time accordingly. The mean and standard deviation, T, values have
been evaluated at each time step for the available 38 data samples. The obtained mean
pressure signal is shown in Figure 7a) along with the interval corresponding to +/2V.
In Figure 7b) the residuals obtained comparing one of the 38 tests with the mean values
of Figure 7a) are shown in a normal probability plot. The residuals for all tests cannot be
considered as normally distributed with a significance level of 10%. The mean value of
the standard deviation is 0.63 m, while the accuracy of the transducer is 0.64 m.
Figure 7 – (a) Mean values in time of the 38 pressure signals (solid line) and
intervals corresponding to +/
2 T (dashed lines). (b) Residuals for one of the
38 tests with respect to the mean values, in normal probability plot
110 © BHR Group 2018 Pressure Sur
g
es 13
In Figure 8, the Fourier transform of the pressure signal for one of the 38 tests (dotted
line) is compared with the Fourier transform of the mean of the 38 pressure signals (solid
line) shown in Figure 7 in the time domain. The noise level reduction is evident
especially for frequencies f >500 Hz, where the single pressure signal is mostly due to
noise. As a result, once the mean signal in time is obtained, it is down-sampled at 1 kHz
for further analyses, to reduce the computational burden without a significant loss of
information content. Figure 9 shows the comparison of the mean signal (dotted line) with
a single signal down-sampled at 1 kHz (solid line). The latter shows some variations with
respect to the former, probably due to noises, with an amplitude of about two standard
deviations (dashed lines).
Figure 8 – Comparison of a signal from one of the 38 tests (dotted line) with the
mean of the 38 signals (solid line) in the frequency domain, for two different
frequency ranges
Figure 9 – Detail of the comparison of the mean signal (dotted line) and of its
intervals corresponding to +/
2 T (dashed lines) with a single signal down-sampled
at 1 kHz (solid line)
4 DATA ANALYSIS AND DISCUSSION
Different initial discharges were tested for two initial air volumes and the corresponding
extreme transient pressures are analysed and discussed herein. Three different features
are observed in transient pressure signals (see Figures 10 and 11).
© BHR Group 2018 Pressure Sur
g
es 13 111
The first feature is a sequence of reflected pressure waves created by the air pocket. The
first wave takes the form of a sudden pressure drop in the first transient wave, followed
by a pressure increase, created by the entrapped air contraction and, subsequent,
expansion. In the second pressure wave, the drop is hardly noticeable but there is a
massive pressure increase, significantly higher than the Joukowsky overpressure,
'HJ=aQ/gS. This is due to the superposition of reflected waves and the effect of the air
pocket successive volume variation.
(a)
(b)
(c)
(d)
Figure 10 – Processed transient pressure data with and without two air pockets
for two flow rates. Down-sampled mean values for 1 kHz. (a)-(b) Q0=457 l/h;
(c)-(d) Q0=59.7 l/h
When the transient event is generated, the air pocket compresses, accumulating potential
energy, until a maximum compression is reached, and then the pocket dramatically
expands. This abrupt expansion generates a pressure peak, converting the potential
energy into an additional pressure in the liquid during the air expansion, as observed by
other researchers (Covas et al., 2003, Martins et al., 2017). Another effect that increases
these overpressures is the occurrence of localized cavitation during the transient event in
certain sections of the pipe, as the minimum pressure reaches the water vapour pressure
for some flow rates (e.g. 457 l/h). This extreme overpressure clearly increases with the
initial flow rate in the pipe (compare Figure 10a-d), occurring higher values in the third
pressure wave for the highest flow rate, and seems to decrease with the air pocket size
(as discussed below).
112 © BHR Group 2018 Pressure Sur
g
es 13
The second feature is a generalized delay the pressure wave propagation in time when
compared to the no-air pocket tests. This phenomenon was experimentally observed by
Covas et al. (2003) and by Bergant et al. (2016) when comparing with numerical results.
This delay increases with the size of the air pocket due to the effect of the successive air
compression/expansion that introduces a retarded response on the wave propagation.
This delay decreases with the decrease of initial flow rate (see Figure 12) since lower
flows generate lower pressure variations that decrease the interaction between the gas
and the liquid and the consequent reflected waves. As the Reynolds number decreases,
the pressures waves with two air pockets tend to overlap with those of the intact pipe.
For higher Reynolds numbers, the pressure wave shift tends to be much higher.
The third feature concerns the pressure wave amplitude. The presence of the air pocket
introduces an additional damping in the transient pressure wave. This is due to the
dissipation of transient pressures in the compression and expansion of the air pocket.
This damping hardly varies with the initial flow rate (see Figure 11), because the
dissipative effect of the air compression/expansion is much more relevant than the
dissipative effect of unsteady friction (Bergant et al., 2008).
(a)
(b)
(c)
(d)
Figure 11 – Processed transient pressure data in terms of (H-H0)/
'
HJ for four flow
rates. Down-sampled mean values for 1 kHz. (a)-(b) Air pocket 1;
(c)-(d) Air pocket 2
© BHR Group 2018 Pressure Sur
g
es 13 113
As referred, the maximum observed overpressures are higher than the theoretical
Joukowsky pressure-head variation for the two air pockets sizes. These maximum
pressures tend to increase with the flow rate. Maximum and minimum pressure
variations have been analysed and results are plotted in Figure 12 in a dimensionless
form in terms of (HmaxH0)/'HJ and (HminH0)/'HJ and of Reynolds number, Re=UD/Q.
Results show that:
(i) the maximum transient pressures observed with the air pocket is 10 to 50%
higher than the Joukowsky pulse and increases with Re;
(ii) the maximum value of 50% is justified by the occurrence of transient
cavitation for the smallest air pocket AP1 and for the highest Re;
(iii) the minimum pressures observed with the air pockets are between 0 and 18%
lower than Joukowsky pulse, being limited by the vapour pressure.
These pressure variations require further tests to be carried out in order to analyse the
dependence of the extreme pressures on the air pocket size and initial flow rate and to
obtain prediction regression laws to be used in the pipe systems design and diagnosis.
(a)
(b)
Figure 12 – (a) Maximum dimensionless piezometric head variation as a function of
the Reynolds number. (b) Minimum dimensionless piezometric head variation as a
function of the Reynolds number
5 FINAL REMARKS
Transient tests were carried out in an experimental pipe facility for several initial flow
rates and for two entrapped air volumes. Collected data with 40 kHz frequency was
postprocessed: mean values were calculated and further down-sampled at a proper
frequency to filter the noise preserving the existing pressure signal features.
Processed data were analysed in terms of wave reflections, time delay and damping.
Observed overpressures were higher than the Joukowsky pulse depending on the
entrapped air volume and on the initial flow rate. A clear pressure wave frequency
decrease is observed with the air volume increase. A reflected pressure wave is identified
associated to the entrapped air contraction and expansion. Further experimental test with
different air pocket sizes and for different initial Reynolds numbers are necessary for a
better understanding of the phenomenon.
114 © BHR Group 2018 Pressure Sur
g
es 13
6 REFERENCES
Bergant, A., Karadžiü, U. and Tijsseling, A. (2016). "Dynamic water behaviour due to
one trapped air pocket in a laboratory pipeline apparatus." IOP Conference Series:
Earth and Environmental Science, 49 (5), 052007.
Bergant, A., Simpson, A. R. and Tijsseling, A. S. (2006). "Water hammer with column
separation: A historical review." Journal of Fluids and Structures, 22 (2), 135-171.
Bergant, A., Tijsseling, A. S., Vitkovsky, J. P., Covas, D. I. C., Simpson, A. R. and
Lambert, M. F. (2008). "Parameters affecting water-hammer wave attenuation, shape
and timing - Part 1: Mathematical tools." Journal of Hydraulic Research, 46 (3),
373-381.
Covas, D., Ramos, H., Lopes, N. and Almeida, A. B. (2006). "Water Pipe System
Diagnosis by Transient Pressure Signals". in Water Distribution Systems Analysis
Symposium 2006, Cincinnati, Ohio.
Covas, D., Stoianov, I., Ramos, H., Graham, N. and Maksimovic, C. (2003).
"Dissipation of Pressure Surges in Water Pipeline Systems". in First Joint
Conference IAHR-IWA on Pumps, Electromechanical Devices and Systems - PEDS
2003, Valência, Espanha.
Ferràs, D., Manso, P. A., Schleiss, A. J. and Covas, D. I. C. (2016). "Experimental
distinction of damping mechanisms during hydraulic transients in pipe flow."
Journal of Fluids and Structures, 66 424-446.
Ferreira, J. P. B. C. C., Martins Nuno, M. C. and Covas Dídia, I. C. (2018). "Ball Valve
Behavior under Steady and Unsteady Conditions." Journal of Hydraulic
Engineering, 144 (4), 04018005.
Izquierdo, J., Fuertes, V. S., Cabrera, E., Iglesias, P. L. and Garcia-Serra, J. (1999).
"Pipeline start-up with entrapped air." Journal of Hydraulic Research, 37 (5), 579-
590.
Liou, C. P. and Hunt, W. A. (1997). "Filling of pipelines with undulating elevation
profiles." Journal of Hydraulic Engineering-Asce, 122 (10), 534-539.
Liou, J. C. P. (2000). "Numerical Properties of the Discrete Gas Cavity Model for
Transients." Journal of Fluids Engineering, 122 (3), 636-639.
Liu, D. and Zhou, L. (2009). "Numerical Simulation of Transient Flow in Pressurized
Water Pipeline with Trapped Air Mass." 2009 Asia-Pacific Power and Energy
Engineering Conference, 1-4.
Martin, C. S. (1976). "Entrapped air in pipelines." Second International Conference on
Pressure Surges, London, England, 15-28.
Martins, N. M. C., Delgado, J. N., Ramos, H. M. and Covas, D. I. C. (2017). "Maximum
transient pressures in a rapidly filling pipeline with entrapped air using a CFD
model." Journal of Hydraulic Research, 55 (4), 506-519.
Martins, N. M. C., Soares, A. K., Ramos, H. M. and Covas, D. I. C. (2016). "CFD
modeling of transient flow in pressurized pipes." Computers & Fluids, 126 129-140.
Martins, S. C., Ramos, H. M. and Almeida, A. B. (2015). "Conceptual analogy for
modelling entrapped air action in hydraulic systems." Journal of Hydraulic
Research, 53 (5), 678-686.
Pozos, O. E., Fuentes, O. A. M. and Pozos, A. (2012). "Gas pockets in a wastewater
rising main: a case study." Water Science and Technology, 66 (10), 2265.
Pozos, O. E., Gonzalez, C. A., Giesecke, J., Marx, W. and Rodal, E. A. (2010). "Air
entrapped in gravity pipeline systems." Journal of Hydraulic Research, 48 (3), 338-
347.
Zhou, L., Liu, D.-y. and Ou, C.-q. (2011). "Simulation of Flow Transients in a Water
Filling Pipe Containing Entrapped Air Pocket with VOF Model." Engineering
Applications of Computational Fluid Mechanics, 5 (1), 127-140.
© BHR Group 2018 Pressure Sur
g
es 13 115
