Ellis,J. Pressure transients in water engineering, A guide to analysis and interpretation of behaviour

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acceptable. It is possible for the damping mechanism to have a two-

stage closure. For instance a relatively rapid closure may be adopted

between 100% open to 30% open in say 5 s and the remaining closure

from 30% open to shut taking 10 s. Reopening of the valve requires a

hydraulic actuator.

21.8 Nozzle valves

A second group of check valves involves axial movement of the valve

door rather than the rotational movement discussed hitherto. Three

examples are shown in Fig. 21.9. Many of these valves fall into the

category of nozzle valves. An axial spring mounted behind the door is

compressed by the forward ﬂow of water manifest as a differential hydro-

dynamic pressure force across the valve door. When ﬂow decelerates

the hydrodynamic force diminishes, allowing the spring to expand

422

(b) Nozzle check valve

. SOCLA type 402

(a) Demag type DRV-Z nozzle check valve

+ +

Open

Spring

Open

Shut

ShutLinear spring

Open Shut

Spring

Fig. 21.9. Valves with axial springs

Pressure transients in water engineering

and pushing the door on to its seat. The distance which the valve door

has to travel is generally small, allowing a relatively prompt closure to be

achieved.

Closure performance is governed by the equation:

axial forces ¼ 0

These pertinent forces are:

Hydrodynamic force ¼

p dA

Friction force ¼ R

Inertial force ¼ W

=g dv=dt

Buoyant weight ¼W

(þ sign in upwards ﬂow and  sign in down-

wards ﬂow)

Spring force ¼ x (where  is in N/mm and x is movement in mm)

Good closure performance can be achieved with a short stroke and a

small disk mass. An adjustable spring force gives ﬂexibility in applica-

tion of the valve.

As with other internal spring-assisted valves it is deemed inadvisable

to use this type of valve when the liquid carried contains material which

may become entangled with the spring and impede closure. Some of

these valves, such as the Demag nozzle type (Fig. 21.9a), have a stream-

lined body designed to maximise recovery of kinetic energy developed

as ﬂow passes through the throat of the valve. This streamlining

tends to produce a longer valve than other types which do not recover

the same amount of energy. There has to be a trade-off between energy

savings in the case of the more expensive longer-body type for which

increased space must be reserved within a pumping station and a

cheaper valve in which greater head loss occurs but which is shorter

and does not require the same amount of space. The globe-shaped

version is an example of a shorter body type (Fig. 21.9b), with a door

travel of about DN/4.

The Alstom Clasar wafer type illustrated in Fig. 21.9c, is a variation

on the axial movement valve. The valve door comprises a set of

concentric streamlined rings having a central shaft and axial spring.

When closed, these moving rings seal against a set of ﬁxed rings. On

opening, the spring is pulled into tension by the hydrodynamic force

acting on the set of moving rings. Travel of the moving rings is typically

<DN/10 and valve length is <DN/2. When a pump is tripped and ﬂow

423

Check valve characteristics

decelerates, the hydrodynamic force decreases allowing the spring to

pull the moving rings onto their seat. This valve has many advantages

including having a very good closure performance. Being a wafer-type

valve it is short, thus taking up minimal space. As with other valves,

having relatively constricted ﬂow passages and internal springs, the

valve is more suited to relatively clean liquids rather than sewage appli-

cations. Head drop through the valve when fully open is 2:2V

=ð2gÞ.

One other example of a valve employing a linear spring for closure is

the lift-disk shown in Fig. 21.10. The more complicated ﬂow passage

through the valve tends to yield a greater head loss than other patterns.

A very good closure performance is achieved, making this valve suitable

for applications such as in high-rise buildings.

There remain other patterns of check valve in which the closure

element is more unusual.

21.9 Moving ball

A further example of a free-acting type is the moving ball pattern in

which a spherical door is pushed along guides by ﬂow passing through

the valve, thus moving the door from its seat (Fig. 21.11). When

ﬂow ceases, the ball rolls back down the guides to seal the valve.

This valve is suited to sewage applications but does not have a good

closure performance. Its use should preferably be restricted to systems

424

+ Flow direction

SeatDisc

Guide bush

Spring

Cover

Body

Fig. 21.10. Lift-disk check valve

Pressure transients in water engineering

where ﬂow deceleration is relatively low at the valve, for instance solo

duty pump installations with modest static lift, so that the system-

imposed dV=dt is small. Advantages are that the ball is self-cleaning

with virtually no risk of blockage. This valve pattern ﬁnds application

in sewage systems and other areas such as mine drainage.

21.10 Sleeve or duckbill valve

Many of the free-acting valves considered, such as the swing check

valve, develop the necessary force to decelerate a reversed ﬂow by

mobilising the resistance offered by the valve and its surrounding

pipework and supports. Since these are generally relatively rigid, the

deceleration force is usually developed with only a small elastic defor-

mation of the valve and adjoining pipes. The reversed velocity is

reduced to zero in a very short time after the door meets its seat. The

sleeve valve represents a departure from this type of behaviour. Suitable

for both horizontal and vertical upward ﬂow, this valve contains no

obvious damping mechanism. A rubber sleeve is reinforced either

internally using fabric Nylon ply or possibly externally with longitudinal

stiff rubber strips. These additions act in the same manner as springs. At

design ﬂow the sleeve is opened to give a circular section and as ﬂow

decreases then these stiffening springs pull the rubber sleeve back to

a closed position (Fig. 21.12). The force required to resist and to

decelerate a reversed velocity is achieved by the subsequent deforma-

tion of the sleeve following closure. Up until the moment of initial

425

Valve open

Normal direction of flow Valve closed

Fig. 21.11. Moving ball check valve

Check valve characteristics

closure the valve acts much as a free-acting valve in that it does not

greatly affect the rate of ﬂow change. Subsequent to initial closure,

deformation of the sleeve over a signiﬁcant time produces a more

gradual ﬂow deceleration than say a swing-check valve, and this part

of the process is more akin to that of a damped valve.

This valve is suitable for lines conveying slurry, sludge, lime, chemical

slurries, paper plant waste and raw sewage, with the ﬂexibility of the

rubber sleeve allowing the valve to seal even in the presence of

gravel. When installed in appropriate conditions, the valve will produce

a quiet closure. If subject to excessive transient differential pressure

across the sleeve, the possibility of damage exists through the rubber

sleeve being pushed inside out or ‘inverted’. To prevent damage it is

essential to choose a valve having the ability to resist the maximum

differential pressure likely to be experienced across the valve. A range

426

(b) Flow reversed(a) Valve closed (c) Sleeve inverted

Cast iron or aluminium body

Neoprene, pure rubber, hypalon, EPT or Buna-N

sleeve reinforced with nylon fabric

Part open Fully openClosed

Direction of

reversed flow

Fig. 21.12. Sleeve or duckbill valve

Pressure transients in water engineering

of reinforcement options is available, from very soft where inversion will

occur at differential heads 6 mWG, to much stiffer forms with

maximum allowable differential pressure head 100 mWG. As far as

predicting behaviour of this type of valve is concerned, although the

valve is free-acting in the sense that it does not have any damping

mechanism, nonetheless the response of the valve during closure has

an inﬂuence upon the hydraulic transient event and thus upon the

maximum heads developed across the valve. The valve should ideally

be modelled as a part of the pipeline system.

The following represents an attempt to model the hydraulic transient

behaviour of a sleeve valve within a pipeline system.

With reference to Fig. 21.13, after the valve has initially closed, as

differential pressure changes so the deformed shape of the sleeve will

427

dVol

/dDH = rate of change of inlet volume

with differential head across valve

Piezometric line

u/s

d/s

Reversed flow

Valve body

V = velocity

Pipe area = A

Check sleeve

Inverted sleeve

Inlet volume = Vol

Vol

DH = H

d/s

– H

u/s

Fig. 21.13. Deﬁnition sketch for sleeve valve analysis

Check valve characteristics

alter and with it the volume of liquid on the inlet and outlet sides of the

sleeve. The total volume within the valve body remains constant — that

is, inlet volume þoutlet volume ¼constant. It is necessary to know the

relationship between inlet or outlet volume and differential head. This

information can be obtained from, for example, experimental measure-

ment or ﬁnite-element analysis of the sleeve under load. Given the

relationship between inlet volume and differential head and ignoring

inertial effects within the sleeve, then over a time increment of the

analysis:

VA ¼ dVol

=dt ¼ dVol

=d H  d H=dt ð21:1Þ

where Vol

is the inlet volume, H is the differential head ¼

d=s

 H

u=s

, V is the velocity and A is area of ﬂow. Digitising the

relationsh ip between inlet volume and differential head (Fig. 21.13),

and interpolating using initial values and averaging over the time

increment t then with dVol

=d H  Vol

=ðHÞ¼gradient of

Vol

=H curve and sufﬁx ‘o’ denoting conditions at the start of the

time increment:

ðV þ V

ÞA=2 ¼ gradient ½H

d=s

 H

u=s

ðH

d=so

 H

u=so

Þ=t

From the characteristic paths:

Jþ¼V þ g=aH

u=s

and J¼V  g=aH

d=s

 H

u=s

¼ a=g½2V ðJþþJÞ

Writing, constant ¼ 2a=g gradient=ðA tÞ and rearranging then:

V ¼ constant½JþþJþg=aðH

d=so

 H

u=so

Þ=ð2 constant  1ÞV

ð21:2Þ

Corresponding values of H

u=s

and H

d=s

are obtained by substituting the

value of V into the quasi-invariant equations.

Prior to initial sleeve closure and subsequent to any sleeve inversion,

the relationship between differential head and velocity should be

expressed in the form:

H ¼ K

=ð2gÞ

where K

is a loss coefﬁcient. The sleeve may become inverted if the

differential pressure exceeds a maximum permitted limit. Transient

analysis can be used to establish this limit for any system so that an

appropriate sleeve can be used.

428

Pressure transients in water engineering

A ﬂexible sleeve offering only a modest resistance will deform to a

greater extent under the inﬂuence of a reversed ﬂow and differential

pressure than will a sleeve of much higher stiffness. Two systems are

considered to illustrate behaviour of the valve.

The ﬁrst example concerns pumping failure within a short pipeline of

length 24 m and with a static head of 14 m. Pipe diameter was 400 mm.

A number of sleeve stiffnesses were considered, with the stiffness

deﬁned by the maximum allowable differential pressure head which if

exceeded would invert the sleeve.

Enclosed volume within the valve upstream of the sleeve varied

substantially for two stiffnesses represented by maximum allowable

differential pressure heads of 20 mWG and 50 mWG. For the smaller

stiffness the sleeve volume was reduced to around 15 litres from an

initial 58 litres, while the stiffer sleeve reduced in volume to around

41 litres. For the lower sleeve stiffness of 20 mWG, reversed velocity

reaches almost 1.4 m/s after about 1 s as shown in Fig. 21.14. For

the stiffer sleeve, maximum reversed velocity was about 0.8 m/s

after 0.88 s.

Concerning head variations, Fig. 21.15 shows head upstream of the

pump and at inlet and outlet of the sleeve valve for the sleeve with

maximum allowable head of 20 m. Since outlet head is largely deter-

mined by a constant downstream head for this short pipeline system

there is little variation in peak head. At the valve inlet, minimum

head is lower for the 20 m sleeve than for the 50 m head sleeve, because

429

0.001

0.121

0.240

0.359

0.478

0.597

0.716

0.835

0.954

1.073

1.192

1.311

1.430

1.549

1.668

1.788

1.907

2.026

2.145

2.264

2.383

2.502

2.621

2.740

2.859

2.978

3.097

3.216

3.336

3.455

3.574

Velocity (m/s)

Time (s)

Series 1

Series 2

Red valve h

max

= 20

2.5

1.5

0.5

–0.5

–1

–1.5

Fig. 21.14. Velocity at a sleeve valve after pump trip

Check valve characteristics

of the higher rate of deceleration for the much larger reversed velocity

achieved in the 20 m sleeve.

If the reversed velocity is too great, a sleeve may be deformed to an

extent that it becomes inverted. Under these conditions the valve may

no longer remain fully closed and could allow some reversed ﬂow to

continue. The rate of this continued reversed ﬂow will depend upon

the inverted shape and stiffness of the sleeve. To illustrate conditions,

a simple system was considered. A uniform pipeline of length 980 m was

chosen which rises continuously from invert level þ0.0 mAD down-

stream of a pumping station to an elevation þ30.0 mAD at chainage

980 m. Discharge level was set at þ40 mAD. Pipe diameter was

400 mm. Suction well level was 4.0 mAD.

Pump start produced an eventual steady velocity of 1.9 m/s. Alterna-

tive sleeve stiffnesses were examined, ranging from 60 m to 100 m.

After pump trip, velocity at the pump and in the pipeline decelerates

and reverses after about 4 s as shown in Fig. 21.16 for a 60 m sleeve. An

initial reversed velocity is developed, reaching around 0.3 m/s. As the

sleeve deforms in an endeavour to mobilise sufﬁcient strength to

decelerate the reversed ﬂow, it becomes inverted after around 6 s as

shown in Fig. 21.17.

Figure 21.18 shows the head variations predicted for this event. After

trip, head downstream of the pump falls to 10.0 mAD and thereafter

increases gradually. After around 4 s the sleeve becomes closed and ﬂow

430

Head (mAD)

Time (s)

Series 1

Series 2

Series 3

Red valve h

max

= 20

0.001

0.119

0.237

0.354

0.472

0.589

0.707

0.825

0.942

1.060

1.177

1.295

1.413

1.530

1.648

1.765

1.883

2.001

2.118

2.236

2.353

2.471

2.589

2.706

2.824

2.942

3.059

3.177

3.294

3.412

3.530

3.647

–2

Fig. 21.15. Head upstream and downst ream of a sleeve valve after pump trip

Pressure transients in water engineering

reverses, with head at the valve outlet rising steadily to a maximum

when the differential head across the valve reaches 60 m, at which

point the sleeve is considered to invert quite rapidly. Depending

upon the ﬁnal shape of the inverted sleeve, reversed ﬂow will continue

to proceed through the valve, producing a fall in valve outlet head.

Thereafter, conditions gradually approach a ﬁnal steady reversed ﬂow

condition within the system as a whole. The continuous reversed

431

Velocity (m/s)

Time (s)

Series 1

Series 2

Red valve – longer system h

max

= 60

0.005

0.353

0.701

1.049

1.396

1.744

2.092

2.440

2.788

3.136

3.484

3.832

4.180

4.526

4.875

5.223

5.571

5.919

6.267

6.615

6.963

7.311

7.659

8.007

8.354

8.702

9.050

9.398

9.746

10.094

10.442

2.5

1.5

0.5

–0.5

–1

Fig. 21.16. Velocity at failing sleeve valve

Volume (l)

Time

(

)

Series 1

Red valve – longer system: c

= 0.08, h

max

= 60.0

–10

–20

–30

4.091

4.170

4.248

4.327

4.405

4.483

4.562

4.640

4.719

4.797

4.875

4.954

5.032

5.111

5.189

5.267

5.346

5.424

5.503

5.581

5.659

5.738

5.816

5.895

5.973

6.051

6.130

6.208

6.287

6.365

6.443

6.522

Fig. 21.17. Downstream sleeve volume (computed)

Check valve characteristics