CT 5550 Pumping stations andtransport pipelines

Guest lecture on waterhammer

Anton Heinsbroek Ph.D. / Ivo Pothofivo.pothof@deltares.nl

Learning goals

• Understand basic waterhammer phenomena• Key notions for preliminary risk assessment

• Pipe period – characteristic time• Wave speed• Joukowsky pressure

• Mitigating measures to reduce transient pressures

Waterhammer problems in practice

Pipe burst during commissioningtests of 150 km, 1.6 m Diam.Pipe.

Control valve closed too early

Waterhammer problems in practice

Check valve closure causedsevere pipe motion

Waterhammer problems in practice

Movie from Youtube –waterhammer on the highway

Waterhammer on the highway

Water hammer

Pressurised systemsExchange of kinetic and potential energy:

velocity changes pressure changes

Changes are propagated through the pipeline system as highspeed waves (pressure surges, water hammer)

The water hammer phenomenon

v v

v

H

The water hammer phenomenon

v

v v

The water hammer phenomenon

v

11

The water hammer phenomenon

Overpressure and negative pressure wavesHead and velocity are interrelatedPressure waves travel trough system

v

+ H

- H

Water hammer essentials

EquationsAssumptionsWave propagation speedcharacteristic timeJoukowsky pressure pulse

Water hammer equations

in w h ich a n dH s t v s t( , ) ( , )in w h ich a n dH s t v s t( , ) ( , )

g Hs A P

v v vt

vs

gc

Ht

cK A

d Ad p s

d sd p

80

0

1 1 1 1

2

2

/

w ith

g Hs A P

v v vt

vs

gc

Ht

cK A

d Ad p s

d sd p

80

0

1 1 1 1

2

2

/

w ith

Momentum:Momentum:

Continuity:Continuity:

Assumptions

Momentum• uniform velocity• velocity head is negligible•• quasi-steady friction applies

Continuity••

Wave speed• axial stress in pipe is zero => c1 = 1

v vx

d vd t

v vx

d vd t

ss

v st

ss

v st

v ps

pt

v ps

pt

15

Wave propagation speed

D

e

Pipe elasticity, Young’s modulus (E [Pa]), +liquid bulk modulus (K [Pa]), +density ( [kg/m3], -diameter - wall thickness ratio (D/e [-]), -

c = 1

C DeE

+ 1K

1

16

Wave propagation speed in water

steelcast iron

Ductile iron

concreteAsbestos cement

GRP (woven)

GRP (fibre)

perspex

PVCPVC (ductile)

HDPE

LDPE

17

Characteristic time

Travel time of a pressure wave to return to the source of thewave

2Lc

v

pomp klep

c + H

L

Water hammer first estimate

JoukowskiJoukowski:: H cg

v p c v or:H cg

v p c v or:

c

v v v v v- v v- v

H

H

L

2 L c2 L c

Water hammer first estimate

Reflections:Reflections:open reservoir (H)open reservoir (H)

closed end (Q)closed end (Q)

Water Hammer first estimate

Reflections on branches or diameter changes:Reflections on branches or diameter changes:

++

+

_A1

A2

A3

r A

Aii

n2 11

1

r A

Aii

n2 11

1

reflection:reflection:

s r 1s r 1transmission:transmission:

IfIf AA11 == AA22 == AA33::

r AA

23

1 13

r AA

23

1 13

s 13

1 23

s 13

1 23

Examples in WANDA

Valve closure (cases 1, 2)Diameter change (cases 8, 9)

Mitigation of waterhammerPrevention of unacceptable transient pressures

Reduce “c”Reduce rate of “ v”Limit local pressuresGeometrical modifications

H c vg

Reduce “c”

Other pipe material (E)

Increase “free gas” concentration (K) (tricky measure)Thinner pipe wall (e), not realistic

c = 11K

+ DeE

Reduce rate of “ v” - overview

Air vesselWater towersoft start/stop or frequency driven pumpsSlower valve manipulationsFlywheel on pumps

Air vesselsreduce rate of “ v”

Pro’s• Applicable at any pressure

discharge combination

Cons (depends on installation)• Air volume must be maintained (air

dissolves) with compressor, whichrequires maintenance

• Air vessels in side branches arevulnerable for biologicalcontamination

luchtuitlaatcompressor

"onbelucht"

Be- enontluchter

"belucht"

NOTE: check valverequirements

Fast closing check valve ordamped check valve is required

Sufficient distance between airvessel and suction level

Anchor forcesSee also presentation on check

valves

Effect air vessel (1)reduce rate of “ v”

G

I

A

D

J

V2

B4H: 0.00000 (m)

P2L: 100.000 (m)

B3H: 25.0000 (m)

E

V1

A1Windketel

B2H: 0.00000 (m)

P1L: 100.000 (m)

B1H: 25.0000 (m)

praktijkgeval - w indketel

Pressure H-node D Pressure H-node I Fluid level AIRVvn A1

Time (s)109876543210

Pres

sure

(bar

)

24

22

20

18

16

14

12

10

8

6

4

2

0

-2

Fluid level (m)

2

1.5

1

Effect air vessel (2)reduce rate of “ v”

Diverse windketels

Air vesselsreduce rate of “ v”

Water towerreduce rate of “ v”

Pompuitval

Dichtdraaien afsluiter

Pro• simple and reliable (no mechanical

components required)• Relatively large storage capacity (e.g. filling

up the water tower before the break of aworld cup final soccer)

Cons• Application is limited

> height of tower must exceed pump shut offhead

> esthetic objections against high tower• capacity of tower cannot be increased on an

increase of the water demand• odour problems (sewerage)• risk for water quality deterioration• maintenance is expensive

Diverse buffertorens

Water towerreduce rate of “ v”

By-pass linereduce rate of “ v”

Pro• No special requirements for pump check valves

Cons• ‘reservoir’ at sufficient level for effective by-pass• by-pass delivery starts only after the system pressure has dropped to

the suction level• Application is limited to rel. short systems lengths

Installatie by-pass leidingen

By-pass linereduce rate of “ v”

Soft-starters / FO pumpsreduce rate of “ v”

Pro• Beneficial during normal operation

Cons• After power failure these measures provide no protection

Slower valve manipulationreduce rate of “ v”

Pro• No expensive anti-surge devices required

Cons• Manipulations must be slower than several (> 5) pipe periods• Pipeline cannot be blocked or opened very quickly

Flywheelreduce rate of “ v”

c

werkdruk

Pompzondervliegwiel

Pompmetvliegwiel

werkdruk

c

Pro• Cheep construction• Gradual check valve closure• Limited maintenance

Cons• effect is limited to several km• Pump motor must be large enough to

start the flywheel• No effect if impeller blocks• Pump start costs more energy. Only

economically feasible for pumps that runcontinuously on fixed speed

Limit pressures - Overview

Local effect. Hence less effective than previous measuresSuitable if inadmissible pressure are local as well (e.g. high

points in cooling water system)

Safety valve / Pressure Relief Valve (PRV)Air valve / vent / vacuum breaker

Pressure relief valveLimit pressures

Veerbelastedrukbegrenzer

gasgevulde drukbegrenzer

gas onder overdruk

membraan

Pro• Pressure is limited locally

Cons• Periodic maintenance required• Relief lines required to dump ejected liquids• Risk of hammering PRV, if PRV capacity is not well sized

Installatie Drukontlastkleppen

Pressure relief valveLimit pressures

Damper/accumulator

Gas pocket separated by a membrane

Pro• No direct contact with liquid• Gas pocket does not dissolve• Set pressure provides flexibility

Cons• Volume limited• Activated only after set pressure is exceeded

Air valveLimit pressures

Pro• Limit pressure locally

Cons• All incoming air should be released afterwards• Correct installation and location are paramount for correct operation• Vulnerable for fouling, blocking. Hence periodic maintenance required

Installatie be/ontluchters

Feed tank

Pro• Simple construction• Self refilling

Cons• Limits negative pressure only• Risk of poor water quality in

feed tank

Geometrical modifications

Increase pipe diameterReduce average system pressure

• Minimise number of bends, etc.• Reduce downstream boundary head

Exercise 8

2.0 km

H=+20 m

H=+10 m

A

C = 500 m/s

L = 1000 m

D1 = 300 mm; D2 = 424 mm

frictionless pipe, conveying water

Draw time graphs of head at 0 km, 2.5 km and 5 km (first 22 s)

3.0 km

Fast valve opening

Exercise 9

Derive Joukowsky’s Law from Newton’s second law of motion. Youmay assume the wave speed equals c.