CT 5550 Pumping stations and transport pipelines · PDF fileCT 5550 Pumping stations and...
Transcript of CT 5550 Pumping stations and transport pipelines · PDF fileCT 5550 Pumping stations and...
CT 5550 Pumping stations andtransport pipelines
Guest lecture on waterhammer
Anton Heinsbroek Ph.D. / Ivo [email protected]
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.