pressure_pulsation_in_reciprocating_pump_part_2__Experimental_Investigation.pdf

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


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)



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)



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)



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



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)



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)



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)



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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