Pressure pulsations in reciprocating pump pipingsystemsPart 2: experimental investigations and modelvalidation
K A Edge, O P Boston, S Xiao, M J Longvill and C R Burrows
Fluid Power Centre, School of Mechanical Engineering, University of Bath
Abstract: This paper reports on a series of laboratory tests on two reciprocating pump systems. Factors
affecting pressure and flow pulsation characteristics are discussed. Measured time-domain characteristics,
under non-cavitating and cavitating conditions, are compared with predictions from the computer model
developed in Part 1 of this paper. Generally, good agreement is achieved.
Keywords: reciprocating plunger pump, pipeline dynamics, pressure pulsations, cavitation, computer
model
1 INTRODUCTION
Despite their widespread use, problems can be encountered
in some plunger pump installations due to the pressure
pulsations which can occur in the delivery and suction
lines. These pulsations are created by interactions between
the unsteady flow drawn in and delivered by the pump and
the dynamic characteristics of the attached fluid lines. In
delivery lines, large-amplitude pipework vibration can be
created by the pressure pulsations which, in turn, can lead
to possible fatigue failure. Pipework vibration is also a
source of noise. Pressure pulsations in suction lines can
lead to cavitation, either in the line itself or in the cylinders
of the pump. If the cavitation is sufficiently severe,
pumping performance will deteriorate. Should cavities
collapse in the vicinity of surfaces, cavitation damage will
occur, potentially reducing the life of the pump. Moreover,
if cavities remain in a cylinder at the beginning of the
piston upstroke, shock loading of the piston and crank
assembly can occur on cavity collapse.
Part 1 of this paper (1) described the development of a
new distributed-parameter model of pipeline dynamics and
its integration within an existing model of pumping dyna-
mics, in order to model the complex interactions between
the pump and its suction and delivery lines. A new inlet
manifold model was also developed to account for the
possible presence of air pockets in the manifold. In order to
assess the effectiveness of the complete pump=pipeline
model, an extensive test programme has been undertaken
and in this part of the paper the results are compared with
computer predictions.
2 EXPERIMENTAL TEST RIGS
Two comprehensively instrumented test rigs were designed
and constructed in order to investigate pressure pulsations
in suction and delivery lines. Both test rigs were similar in
configuration but employed significantly different sizes of
pump. Figure 1 shows the general layout in schematic form
for both systems. Parametric information for rigs 1 and 2 is
239
The MS was received on 9 March 1996 and was accepted for publicationon 19 April 1997. Fig. 1 Schematic layout of test rigs
I01696 # IMechE 1997 Proc Instn Mech Engrs Vol 211 Part I
given in Tables 1 and 2 respectively. The pump employed
in test rig 1 was a triplex (three-cylinder) ceramic-plunger
unit with a maximum hydraulic power output of 9.8 kW.
This pump was driven by a variable-speed three-phase
electric motor, allowing the pump speed to be varied from
0 to 1000 r=min in steps of 6 r=min. The suction and
delivery lines, both of Tungum alloy, were horizontal and
straight, and clamped to minimize mechanical vibration.
The suction line diameter was deliberately undersized to
accentuate cavitation effects. A perspex reservoir was used
to allow visual assessment of the quality of the working
fluid, particularly in respect of the presence of entrained air
or vapour bubbles. To assist in the liberation of any gas
bubbles present in the return line, a baffle plate was
mounted inside the reservoir. A bell mouth was connected
to the entry of the suction line to minimize the effects of a
vena contracta, thereby reducing the possibility of local
cavitation at the higher flowrates. Although the pump
manufacturer recommended a minimum inlet pressure of
1.38 bar (g) for `optimum' performance, all tests were
conducted with the reservoir at atmospheric pressure. The
delivery line was terminated by a screw-down restrictor
valve which was used to control the mean delivery
pressure. Tests were performed using raw water, mineral oil
and water±white paraffin as the working fluid, although
only the results relating to water and oil are presented here.
Test rig 2 employed a triplex pump with a rated output of
45.9 kW. The general arrangement was very similar to test
rig 1 except that the pump was driven at a nominally
constant speed of 220 r=min with the speed reduction from
the 1500 r=min a.c. motor being achieved by means of a
belt drive. Both suction and delivery lines were horizontal
but incorporated smooth 908 bends (see Table 2) approxi-
mately 0.5 m from the manifold ports. The delivery line
was again terminated by a screw-down restrictor valve.
Only raw water tests were conducted with this system.
The same instrumentation was employed for both test
rigs. Pressure pulsations were measured at three locations
in both the suction and delivery lines, as shown in Fig. 1.
Initial tests on test rig 1 were conducted with piezoelectric
transducers, but these were found to give inconsistent
results at the low (subatmospheric) mean pressures in the
inlet line and were subsequently replaced with piezo-
resistive transducers. Piezoelectric pressure transducers
were used to record the pressure pulsations in the pump
delivery line with the mean pressure read from a pressure
gauge situated upstream of the loading valve. Flow ripple
was inferred from the pressure pulsations using a computer
software package; further details of this procedure are
given later.
Additional instrumentation, for studies not reported here,
included a strain-gauged connecting rod and a piezoelectric
pressure transducer installed in one cylinder. An optical
sensor provided a once-per-revolution trigger for the data
acquisition system. In the case of test rig 1 the leading edge
of the trigger pulse was arranged to occur when piston 3
(the cylinder closest to the delivery port) was at top dead
centre (TDC). In test rig 2, the trailing edge of the pulse
indicates piston 1 at TDC.
The amplified and conditioned transducer signals were
captured using a PC-based multichannel data acquisition
system. Each channel was sampled at 0.25 ms intervals
Table 1 Test rig 1 parametric data (line lengths are specified in figure titles)
Test pump Displacement 40.7 mL=revCrank length 15 mmCon-rod length 90 mmPiston diameter 2.4 3 10ÿ2 mUnswept volume at TDC 15 mLInlet manifold chamber volume (air±liquid ratio � 1 except for
Fig. 11)5.7 cm3
Suction line Internal diameter 15.8 mmEffective bulk modulus 6000 bar
Delivery line Internal diameter 10.2 mmEffective bulk modulus 9000 bar
Table 2 Test rig 2 parametric data
Test pump Displacement 0.782 mL=revCrank length 50.8 mmCon-rod length 308.9 mmPiston diameter 57.15 mmUnswept volume at TDC 0.655 L
Suction line Internal diameter 51.5 mmLength 3.72 mRatio of bend radius to internal pipe radius 17.5Effective bulk modulus 6000 bar
Delivery line Internal diameter 31.5 mmLength 3.39 mRatio of bend radius to internal pipe radius 11.1Effective bulk modulus 9000 bar
Proc Instn Mech Engrs Vol 211 Part I I01696 # IMechE 1997
240 K A EDGE, O P BOSTON, S XIAO, M J LONGVILL AND C R BURROWS
with, typically, 4000 samples=channel acquired at each test
condition.
3 FLOW FLUCTUATIONSÐTEST RIG 1
With a three-cylinder machine, at some points in the
pumping cycle one piston is pumping with the others on
their suction stroke. At other times, two pistons are
pumping, with one commencing delivery and the other
completing delivery. An illustrative example of the delivery
flow ripple that would occur with ideal timing (inlet and
delivery valves opening and closing exactly at piston top
and bottom dead centre positions) is shown, for one
revolution, in Fig. 2a. Points A1 to A3 correspond to each
of the three pistons commencing delivery in turn and points
B1 to B3 correspond to the end of delivery. In practice,
valve timing is affected by fluid compressibility effects, by
valve spring stiffnesses and, to a lesser extent, by inter-
actions with the attached pipelines. In essence, the delivery
valve will not open until the cylinder contents have been
compressed above the instantaneous delivery pressure; the
inlet valve will not open until the cylinder contents have
been decompressed to a level below the inlet pressure. The
effect of a delay in the start of delivery is that the double-
peak waveform of Fig. 2 is modified, with the initial
contribution of the cylinder flow to the pulse beginning at
point A no longer being present. An illustration of the
effect of different inlet valve closure periods on flow
pulsation characteristics is given in Fig. 2b.
Direct measurement of flow transients is both difficult
and expensive and as a consequence an indirect method
was employed, which requires the measurement of pressure
pulsations at three locations in the pipeline. From these,
and a knowledge of the wave propagation characteristics of
the line, it is possible to establish the `source' flow ripple
(2, 3). This method has been successfully applied to a wide
range of pumps of the fluid power type, but has not, to the
authors' knowledge, been used to study reciprocating
plunger pumps. The test is performed in two stages. The
first stage involves the determination of the impedance of
the pump discharge passage using a `secondary source' of
pressure pulsations. The second stage involves the meas-
urement of the pressure pulsations generated by the pump
alone. From these measurements and the previously cal-
culated pump impedance, the flow ripple is inferred. Full
details of the method are given in the ISO Standard (4).
The test method was applied to the delivery line using a
self-contained motor-driven rotary valve to act as the
secondary source. A typical pump impedance characteristic
is shown in Fig. 3. This is very similar in form to the
impedance of fluid power pumps. Below 1 kHz, the imped-
ance is capacitive in nature, corresponding to the com-
pliance of the fluid in the manifold. Above 1 kHz, fluid
inertia effects become dominant. The pressure pulsation
signal content above 1 kHz was extremely low and it was
difficult to make meaningful measurements much above
this frequency. As a consequence the impedance measure-
ments exhibit considerable scatter above 1.5 kHz. The
impedance characteristic did not vary significantly with
mean delivery pressure or speed, which is again in
Fig. 2 Idealized delivery flow ripple for test pump 1 at
200 r=min (for illustration purposes only) Fig. 3 Impedance of pump delivery passageway at 50 bar
I01696 # IMechE 1997 Proc Instn Mech Engrs Vol 211 Part I
PRESSURE PULSATIONS IN RECIPROCATING PUMP PIPING SYSTEMS. PART 2 241
agreement with results previously published for fluid power
pumps. Such an impedance can be modelled by a length of
pipe of constant cross-sectional area; this is consistent with
the assumption, made in Part 1 of this paper, that for
modelling purposes the delivery manifold can be included
as part of the delivery line.
A typical inferred flow corresponding to a pump speed
of 250 r=min and a delivery pressure of 50 bar is compared
with predicted behaviour in Fig. 4. At this speed, one
crankshaft revolution occurs in 0.24 s; within this period
six pulses are clearly exhibited.
The predictions (Fig. 4b) are based on a distributed
parameter model of the delivery line using 10 nodes. All
the principal features are captured in the predictions,
although there are some minor discrepancies. High-
frequency oscillations, superimposed upon the predicted
waveform and commencing at the opening of the delivery
valve (point A), are clearly visible. These arise because of
two effects: (a) the cylinder contents tend to be over-
compressed as the delivery valve takes a finite time to
open, leading to an initial `overshoot' followed by a
damped oscillation, and (b) the pressure forces acting on
the valve create a damped oscillatory motion which intro-
duces an oscillatory flowrate. The relative magnitude of
these effects depends on operating conditions and inter-
actions with the delivery line. The oscillations are also
present in the inferred flow ripple but are much less
pronounced. This is probably due to the difficulties in
accurately measuring the low-amplitude high-frequency
components of the pressure ripple signals from which the
flow ripple characteristics are inferred.
4 DELIVERY LINE PRESSURE PULSATIONSÐ
TEST RIG 1
The pressure pulsations at the pump outlet for a mean
delivery pressure of 40 bar and a speed of 200 r=min are
shown in Fig. 5a with the optical sensor trigger signal
superimposed. One revolution of the crankshaft occurs in
0.3 s and within this period six pulses occur as a direct
result of the unsteady flow produced by the pump. The
waveform is periodic over each revolution and, indeed, very
nearly periodic over each pumping cycle. The delivery
pulse associated with cylinder 2 (the `middle' cylinder of
the in-line configuration) occurs around 0.24 and 0.54 s,
and is only slightly diminished compared with the other
two cylinder pulses. As a result, intercylinder variations are
concluded to be negligibly small. The small-amplitude
high-frequency decaying oscillation which commences at
point A arises directly as a result of the high-frequency
flow pulsations discussed above. The flow pulsation inter-
acts with the fluid in the delivery line to create a pressure
pulsation which propagates into the pipeline at the local
acoustic velocity. Behaviour is also influenced by transmis-
sion line effects: a partial reflection can occur at the
loading valve which terminates the delivery line and the
pulsation propagates back to the pump where a further
reflection back into the line occurs (5). The consequent
multiple reflections (which gradually diminish due to the
loss of energy at the loading valve and to a lesser extent
due to effects of pipe friction) can affect both flow and
pressure pulsation characteristics.
Figures 5b and 5c show, for comparison with Fig. 5a,
predictions with a lumped parameter delivery line and
predictions with a distributed parameter delivery line using
10 nodes. Both lumped and distributed parameter models
capture the essential characteristics of the kinematically
induced pulsations and the peak-to-peak amplitudes are
close to those measured. However, the lumped parameter
model fails to predict the high-frequency oscillations
which, in this case, are primarily associated with the
motion of the delivery valve.
Figure 6 shows the simulated flow ripple generated by
the pump for the case of (a) the lumped parameter line
model and (b) the distributed parameter line model.
Clearly, for high-accuracy predictions, distributed para-
meter effects need to be included. This result also confirms
that it would be inadvisable to adopt the frequency-domain
approach to modelling which is commonly employed for
fluid power circuits (5). With such an approach, the pump
is represented as a flow ripple source, which, although
dependent on the mean delivery pressure, is taken to be
independent of pressure pulsations. This is evidently not
the case here. Singh and Madavan (6) recognized this
Fig. 4 Delivery flow ripple (250 r=min, 50 bar, water,
20 8C, line length 2.79 m)
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242 K A EDGE, O P BOSTON, S XIAO, M J LONGVILL AND C R BURROWS
problem and circumvented it by resorting to an iterative
method to accommodate the dependency of the flow
fluctuations on pressure pulsations.
This result also raises questions about the suitability of
ISO 10767-1 as a method of rating reciprocating pump
flow ripple, since the flow ripple itself is dependent on
wave propagation effects in the line and is consequently not
a unique rating for a given mean pressure and speed.
Computer simulation of the delivery pulsations was
undertaken over a range of speeds, pressures and pipe
lengths. It was found that the delivery behaviour was not
strongly coupled to inlet line conditions except when the
pump was cavitating. As a consequence, for cases where
only delivery line behaviour was of interest it was possible
to reduce computer simulation times by assuming that the
inlet manifold pressure was constant.
5 SUCTION LINE PRESSURE AND FLOW
PULSATIONSÐTEST RIG 1
As with the delivery line, the unsteady flow generated at
the pump inlet interacts with the suction line to create
pressure pulsations. Figure 7 shows the measured and
predicted pressure pulsations at the entry to the pump inlet
manifold at a pump speed of 200 r=min. For the predic-
tions, 10 nodal points on the inlet line were adopted. In the
experimental results (Fig. 7a) it is clear that there is a rather
greater variation between one cylinder and another than
was apparent in the delivery line. There is also a small
variation from one revolution to the next. This is probably
due to variations in the air pocket volume, with some air
being drawn from the pockets into the cylinders during
suction, only to accumulate again through the continuing
release of air in the inlet line. The numbering on the figure
corresponds to those cylinders communicating with the
manifold at any given time. For the predictions shown in
Fig. 7b, a single chamber upstream of the inlet valves was
assumed as described in Part 1 of this paper (1). Equal
volumes of air and water were assumed to be present in the
chamber (see Table 1). This gave results that correlated
well with the measurements, with both the levels and
general shape being successfully predicted. It is notable
that the peak-to-peak pressure pulsation magnitude is much
smaller than in the delivery manifold. This is because the
Fig. 5 Delivery pressure pulsations (200 r=min, 40 bar,
water, 20 8C, inlet line 2.38 m, delivery line
1.65 m)
Fig. 6 Predicted delivery flow ripple (200 r=min, 40 bar,
water, 20 8C, line length 1.65 m)
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PRESSURE PULSATIONS IN RECIPROCATING PUMP PIPING SYSTEMS. PART 2 243
presence of the air pocket means that there is considerable
local compliance and fluid inertia effects tend to be
dominant, unlike in the delivery line where compressibility
effects are more important. Without air pockets, the
predicted behaviour is totally unrealistic, as illustrated in
Fig. 7c. The model indicates severe cavitation with large
pressure spikes generated as cavities collapse in the cylin-
ders. Thus the air pocket model is essential for accurate
prediction of pulsation levels in this case.
The predicted inlet flow ripple assuming a constant inlet
pressure is shown in Fig. 8a. The unsteady flow drawn in
by the pump is broadly similar in character to that
generated at the delivery manifold. Differences occur as a
result of piston motion and valve timing. Because of the
crank mechanism, the piston motion is not sinusoidal, and
the rate of change of flow around the piston TDC is higher
than around BDC. This `distortion' of the motion is
accentuated for low con-rod±crank ratios, which are com-
monly used to achieve more compact pump designs. Also,
the volume of fluid in a cylinder prior to the commence-
ment of delivery is significantly higher than the volume
prior to the start of the suction stroke. As a consequence,
the compression phase takes longer than decompression
(which in turn influences valve timing). Figure 8b illus-
trates the predicted flow in the inlet manifold for the case
of a distributed parameter inlet line, with air pockets being
included in the simulation model. Clearly the flow ripple in
the manifold is substantially modified by the presence of
air. Cavitation is not occurring in the results shown in Fig.
8 but can have a profound influence on inlet flow and
pressure ripple, as will be shown later.
A closer agreement between predicted and measured
behaviour can be obtained by using the more detailed
manifold model proposed in Part 1(1). In this case,
individual restrictions and chambers are assumed to be
present upstream of each inlet valve. Intercylinder varia-
tions can be accounted for by selecting differing restrictions
upstream of each chamber and=or different volumes of air.
However, improved agreement could only be achieved by
trial-and-error adjustment of the unknown parameters,
thereby severely limiting the usefulness of this model.
Further work on manifold modelling will be necessary
Fig. 7 Inlet pressure pulsations (200 r=min, 40 bar, water,
20 8C, line length 2.38 m)
Fig. 8 Inlet flow ripple (200 r=min, 40 bar, water, 20 8C,
line length 2.38 m)
Proc Instn Mech Engrs Vol 211 Part I I01696 # IMechE 1997
244 K A EDGE, O P BOSTON, S XIAO, M J LONGVILL AND C R BURROWS
before the multiple-chamber model can be used for system
design; until such work is done, the simplified model is the
better choice. Even with this approach it is difficult to
judge the size of the air pocket(s) likely to be present,
although estimates can be made from manifold geometry.
To assess the sensitivity of results to the air±liquid ratio,
simulations were performed with different volumes of air
present. For the test conditions considered above, it was
found that a 10 per cent increase in the volume of air
present in the chamber at atmospheric pressure led to a 25
per cent reduction in the peak-to-peak amplitude of the
inlet pressure pulsation; a 10 per cent decrease in air
volume resulted in a 65 per cent increase in the peak-to-
peak amplitude.
Neither of the manifold models predicts the very short
duration `spikes', which are superimposed on the princi-
pal pressure waveform. These were present in all tests
conducted, with greatest prevalence around the times of
opening and closing of inlet valves. In a separate study
involving high-speed photography of in-cylinder cavita-
tion it was found that cavitation bubbles form in the
vicinity of the valve seat and are swept into the cylinder,
where they may collapse. It is feasible that the inlet
pressure `spikes' are associated with this process. This
argument is supported by the absence of such spikes on
the delivery line pressure waveform, where cavitation
would be suppressed because of the much higher mean
pressure.
An attempt was made to establish the inlet flow ripple
using the ISO Standard procedure (4). This is outside the
scope of the Standard, which is concerned solely with
delivery lines. Because of the low-pressure pulsation levels
present, it proved impossible to achieve consistent and
reliable results. However, pump impedance measurements,
shown in Fig. 9, do exhibit a strong inductive characteristic
even at low frequencies. This is consistent with a highly
compliant fluid mixture in the manifold and provides
supplementary evidence of an air pocket or pockets in the
inlet manifold.
6 SOME FACTORS AFFECTING PULSATION
LEVELS
6.1 Pump speed
Figure 10 shows measured and predicted pressure pulsa-
tions for both delivery and inlet for an increased pump
speed of 400 r=min. For the delivery line, good agreement
is obtained between measured and predicted behaviour
(Figs 10a and 10b respectively). The peak-to-peak level of
the predicted waveform is slightly less than that measured,
probably arising from the difficulty in selecting the correct
bulk modulus of elasticity of the water in the delivery line.
High-frequency oscillations superimposed upon the main
waveform are more prevalent than those obtained at
200 r=min. The prediction of this behaviour shows greater
damping than that obtained in experiment, but the
frequency of oscillation is close to that measured. Errors
arise here largely due to imperfect modelling of the forces
acting on the delivery valve during its opening phase. In
the case of the inlet line (Figs 10c and 10d), the general
features are adequately captured by the single-chamber
model, but once again neither the intercylinder variations
nor the short-duration spikes are predicted.
At much higher speeds, the pump cavitates and the
pressure ripple waveforms are significantly affected. It is
important to re-emphasize here that the suction line
diameter was deliberately undersized and the pump inlet
was not boosted (against the manufacturer's recommenda-
tions). Figure 11 shows the measured and predicted
behaviour at 1000 r=min. At the inlet (Fig. 11a), large-
magnitude pressure spikes were measured reaching nearly
7 bar. These spikes, labelled A, were found to occur when a
piston was at, or near, TDC and are associated with a
collapse of a vapour cavity in the cylinder, generating a
pressure pulse that propagates into the inlet manifold. The
subsequent oscillation is due to line dynamics. At points
labelled B, a cylinder commences suction and the pressure
falls to a near-constant level. It is notable that the waveform
Fig. 9 Impedance of pump inlet passageway
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PRESSURE PULSATIONS IN RECIPROCATING PUMP PIPING SYSTEMS. PART 2 245
is aperiodic. The predicted pulsation behaviour (Fig. 11b)
is broadly similar to that measured, although the waveform
remains periodic. The peak level of the sharp spikes is
lower than that measured and a very high frequency
oscillation occurs on cavity collapse. This is completely
damped at the point of inlet valve closure. The oscillations
due to line dynamics tend to be more heavily damped than
those observed experimentally, although in practice there is
considerable variation from cycle to cycle. The rapid fall in
pressure to a mean level of ÿ0.6 bar which occurs at the
start of suction is correctly predicted. To achieve this
agreement it was necessary to reduce the air pocket volume
to 10 per cent of that at the lower speeds. Without this
change, the model predicted well-damped oscillations sim-
ilar to those previously presented. This suggests that air
pockets form less readily at high pump speeds, probably
because the fluid velocity in the vicinity of each chamber is
sufficiently high to entrain the air and draw it into the
cylinder. In addition, less time is available between one
suction cycle and the next for air to accumulate in each
pocket.
In-cylinder cavitation is sufficiently strong to create a
significant delay in closure of the inlet valve. This leads to
larger delivery flow and pressure pulsation levels than at
lower speeds. The predictions underestimate this delay,
leading to pulsation levels lower than those measured (Figs
11c and 11d). The general characteristics of the waveform
are correctly predicted. At point C, where a cylinder
commences delivery, a very high frequency oscillation
occurs due to fluid inertia effects in the vicinity of the valve
seat. This was not observed experimentally.
It is inappropriate to run a pump under severely cav-
itating conditions. Other measurements have confirmed
that the cylinder pressure transients are closely reflected by
the force in the con-rod. It is conceivable that short-
duration high-amplitude pressure spikes in the cylinder
could lead, ultimately, to fatigue failure of the con-rod
and=or the bearings. The important issue here is not to
achieve high accuracy in the prediction of cavitating
behaviour but to be able to predict the onset of cavitation.
6.2 Fluid type
The results of tests using mineral oil as the working fluid
showed broadly similar behaviour to that obtained with
water. However, the increased viscous losses in the inlet
line led to a much lower mean inlet pressure, for a given
pump speed, compared to that obtained with water. A
typical result corresponding to a pump speed of 400 r=min
and 40 bar delivery is shown in Fig. 12.
The measured delivery pulsations (Fig. 12a) show a
significant variation from one pumping cycle to the next
although the waveform is periodic over each revolution.
One cylinder (that closest to the pipe connection port) is
Fig. 10 Pressure pulsations at 400 r=min (40 bar delivery, water, 20 8C, inlet line 2.38 m, delivery line
1.65 m)
Proc Instn Mech Engrs Vol 211 Part I I01696 # IMechE 1997
246 K A EDGE, O P BOSTON, S XIAO, M J LONGVILL AND C R BURROWS
cavitating, leading to late inlet valve closure and hence
delayed delivery. This greatly increases the peak-to-peak
pulsation level associated with this one cylinder. This
behaviour is not predicted (Fig. 12b) (although the model
is just on the limit of cavitation). Apart from this
discrepancy, the predicted behaviour captures the essential
features of the measured waveform.
At the inlet, the measured pressure (Fig. 12c) is also
periodic over each revolution with the pulsation level much
reduced compared with the results obtained with water at
the same test condition (Fig. 10d). This is directly a result
of the low effective fluid bulk modulus in the chambers,
corresponding to the low mean pressure. Predicted beha-
viour (Fig. 12d) shows a slightly lower mean inlet pressure
than that measured, indicating that the pipeline quasi-
steady friction loss is overestimated. The pulsations are
periodic over the pumping cycle and are of approximately
the correct magnitude, bearing in mind that the cycle-to-
cycle variation cannot be captured using the single-cham-
ber model.
7 PRESSURE PULSATIONSÐTEST RIG 2
Delivery pulsation behaviour in test rig 2 was found to be
very similar in character to that in test rig 1 and good
agreement was again achieved between predicted and
measured behaviour. A typical result, at a delivery pressure
of 60 bar, is shown in Fig. 13a, with the corresponding
prediction in Fig. 13b.
Suction line pulsation behaviour was significantly differ-
ent to that observed in test rig 1 except when the pump in
rig 1 was tested at high speed. An example of measured
behaviour is given in Fig. 13c. Pressure `spikes' occur in
the inlet line as a result of the collapse of cavities in the
Fig. 11 Pressure pulsations at 1000 r=min (40 bar delivery, water, 20 8C, inlet line 2.38 m, delivery
line 1.65 m)
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cylinders during and at the end of the suction stroke of each
piston. Spikes A1 and B1 are associated with cylinder 1.
Spikes A2 and B2 and spikes A3, B3 and C3 are associated
with cylinders 2 and 3 respectively. These spikes are
superimposed upon a pressure level close to the vapour
pressure. In the case of cylinder 1, cavities form in the early
part of the suction stroke. After the mid-stroke position is
passed, the piston velocity diminishes but the fluid con-
tinues to enter the cylinder at a sufficiently high rate to
collapse the cavities, creating the pressure spike A1.
Fig. 12 Pressure pulsations with mineral oil (400 r=min, 40 bar, delivery, 18 8C, inlet line 4.32 m,
delivery line 1.55 m)
Fig. 13 Pressure pulsations, test rig 2 (220 r=min, 60 bar delivery, water, 20 8C)
Proc Instn Mech Engrs Vol 211 Part I I01696 # IMechE 1997
248 K A EDGE, O P BOSTON, S XIAO, M J LONGVILL AND C R BURROWS
Further cavities subsequently form in the cylinder and these
remain until the piston commences its delivery stroke. The
resultant pressure rise creates spike B1, which assists in
closing the inlet valve thereby allowing the piston to
compress the cylinder contents. Behaviour in cylinder 2 is
virtually identical. In the case of cylinder 3 (closest to the
manifold port) cavity collapse occurs twice during the
suction stroke (spikes A3 and B3). Spike C3 occurs at the
end of suction. The overall inlet pressure waveform is
aperiodic and the magnitude of the spikes varies from cycle
to cycle. Clearly the interaction between the pump and its
inlet line is very complex.
In order to predict behaviour similar to that measured, it
was necessary to assume that the inlet valves commu-
nicated directly with the inlet manifold, without intermedi-
ate chambers being present. This is appropriate for this
design of pump which was configured such that the inlet
valves were located directly above the manifold. Any air
pockets that might form would be swept directly into the
cylinders during the suction stroke.
All the essential features of inlet pulsation behaviour are
captured by the computer model, including the aperiodicity,
as shown in Fig. 13d. The magnitude of the predicted
pressure spikes is very similar to that measured and the
time of their occurrence is approximately correct. Not all
of the measured spikes are predicted but in view of the
near-random behaviour, this should not be too surprising.
The predicted formation and collapse of cavities in one
cylinder is shown in Fig. 14. It is notable that size of these
cavities, expressed as a percentage of the instantaneous
cylinder volume, is quite small, but nonetheless sufficient
to create relatively large pressure spikes.
8 CONCLUSIONS
1. Experimental tests have been undertaken to establish the
pressure pulsation characteristics of reciprocating pump
suction and delivery lines over a wide range of operating
conditions. Emphasis has been placed on behaviour
under cavitating conditions. Two test rigs were used in
the study, employing pumps significantly different in
size and power rating. The computer model, developed
in Part 1 of this paper, has been found to be effective in
predicting the important characteristics of the delivery
pressure and flow pulsation waveforms in both systems.
There is potential to use the model to assist in the study
of pump=system interactions at the circuit design stage
and hence produce systems with lower pressure pulsa-
tion levels.
2. The delivery flow ripple is dependent upon the pressure
pulsation level as well as mean delivery pressure and
speed. This raises doubts about the suitability of ISO
10767-1 for rating the pressure and flow ripple charac-
teristics of reciprocating pumps. It also confirms the
importance of integrating the pump model with a
distributed parameter model of the delivery line.
3. It is hypothesized that, depending on the pump config-
uration and test conditions, air pockets can form in the
inlet manifold. This hypothesis is supported by compu-
ter simulation studies. These air pockets dampen inlet
pressure pulsation levels. In such circumstances, the
waveform is periodic over one revolution except at high
pump speeds. There is, however, some variation from
one pumping cycle to the next. Provided the air pocket
size can be estimated, good agreement between pre-
dicted and measured behaviour can be achieved.
4. Under strongly cavitating conditions, the inlet pressure
waveform is aperiodic, with short-duration pressure
spikes occurring as a result of the collapse of cavities in
the cylinders. The computer model predicts the beha-
viour with acceptable accuracy.
ACKNOWLEDGEMENTS
The work reported in this paper was undertaken as part of a
research programme funded by the Engineering and Phy-
sical Sciences Research Council (Grant GR=G56423). The
authors are grateful for the Council's support. They also
gratefully acknowledge the co-operation and support of ICI
Research and Technology Centre, Dawson Downie Lamont
Limited and CAT PUMPS (UK) Limited. Particular thanks
are extended to Mr Lez Warren of CAT PUMPS (UK)
Limited for his helpful remarks on the draft manuscript.
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250 K A EDGE, O P BOSTON, S XIAO, M J LONGVILL AND C R BURROWS