193783392 Penstock Surge Consideration
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Transcript of 193783392 Penstock Surge Consideration
Design principles
Surge Pressure
Examples
Penstock thickness sizing
• Surge consideration:
-As water is an incompressible fluid, any sudden blockage
of flow or rapid change in velocity in pipes causes
instantaneous increase in pressure known as surge.
-As it is cyclic, often referred to as “water hammer”.
-Thus penstock thickness should account for both static
head & surge head.
-In hydropower, surge is dependent on turbine type – as
various types of turbine have various flow obstruction
characteristics
Penstock thickness…
• Cross flow turbines:
– Sudden blockage of
flow not possible
– Nominal surge can
result if valve is closed
fast
Penstock thickness…
• Pelton turbines
– Sudden blockage
of flow possible
due to obstruction
at nozzle (e.g., by
gravels)
Penstock thickness - Pelton
nx
g
aVhsurge
1 n = no of nozzles
First calculate pressure wave velocity „a‟ as follows:
xtE
dxxa
9101.21
1440d = pipe dia in m
t = pipe thickness in mm
E = Young‟s modulus in
N/mm2
Then calculate surge head:
htotal = hgross + hsurge
Material properties:
Material Young’s
Modulus (E),
N/mm2
Coef. Of linear
expansion
(α)/oC
Ultimate Tensile
strength (S)
N/mm2
Ungraded mild
steel
2.0 x 105 12.5 x 10-6
320
Standard mild
steel (certified
e.g. IS 2062)
2.0 x 105
12.5 x 10-6
410
PVC 2750 (20 -60) x 10-6
35 -55
HDPE 1000 (140 –240)x 10-6
20 -35
Penstock thickness – Cross flow
• Calculate „a‟ as in the case of Pelton turbine
• Then calculate critical valve closure time Tc, l is the length of penstock in m.
• Now calculate parameter K, T is the min. valve closure time
a
lTc
2
2
xTgh
lVK
gross
Penstock thickness – Cross flow
• Calculate hsurge:
• If „K‟ is less than 0.01:
(closure time, T, is long)
Kxhh grosssurge
grosssurge hK
KK
h
42
2
Penstock thickness…
• Once surge head is known, for all type of turbines,
calculate effective thickness, teffective
– For mild steel (ms) divide „t‟ by 1.1 to allow for
welding defects
– ms: divide „t‟ by 1.2 to allow for rolling inaccuracy of
flat sheet
– ms: subtract 1 mm – 2 mm (10 – 20 yrs) for corrosion
allowance
– For HPDE t = teffective
Penstock thickness…
• Now check factor of safety,
– SF = Safety factor
– S = Ultimate tensile strength of material (see table)
– d = is pipe dia
– teffective & d should have the same units (m or mm)
dxxhx
SxtFS
total
effective
3105..
Penstock thickness…
• For mild steel:
If SF < 3.5 reject penstock option & repeat calculations with higher thickness. However SF > 2.5 OK if:
- Experienced site staff
- Slow closing valves incorporated
- Damage & safety risks are minimum
- Careful pressure testing at total head performed
- Refer to codes and mannuals, e.g., USBR
Penstock…
• Thickness calculations - Jhankre:
- Revisit data:
Length, l = 550 m, Gross head = 180 m
Diameter, d = 450 mm
Steel = IS-2062, UTS (S) = 400 x 106 N/m2,
E = 200 x 109 N/m2
Site welding decided
- Note: Pipe is long, so economical to decrease thickness with head.
Penstock…
• Start from the bottom
-Try thickness, t = 6 mm
Calculate wave velocity, a
sm
xx
xxxtE
dxxa /1077
1000
610200
450.0101.21
1440
101.21
1440
9
9
9
Penstock…
• Velocity,
• Surge head, n = 6, since six nozzles
smx
x
d
QV /83.2
)450.0(
450.04422
mxx
nx
g
aVhsurge 52
6
1
81.9
83.210771
Penstock…
• Total head :
mmmhhh surgegrosstotal 23252180
mmx
teffective 55.30.12.11.1
6
Selected thickness
Wleding Rolling
Corrosion
Penstock…
• Safety Factor:
S.F. = 2.72 > 2.5 OK, since:
- Experienced staff at site
- Slow closing valve
- Pipes were pressure tested
450.0102325
10400)100055.3(
105..
3
6
3 xxx
xx
dxxhx
SxtFS
total
effective
Penstock…
• At what static head can the thickness be decreased to 5 mm?
• V = 2.83 m/s (same Q & d)
sm
xx
xxxtE
dxxa /1033
1000
510200
450.0101.21
1440
101.21
1440
9
9
9
Penstock…
• Effective thickness
• Safety Factor (S.F.)
mmx
teffective 79.20.12.11.1
5
dxxxFS
Sxth
dxxhx
SxtFS
effective
total
total
effective
33 105..,
105..
mxxx
xxhOr total 182
450.010572.2
10400)100079.2(,
3
6
Why?
Penstock…
• Calculate surge head
mxx
nx
g
aVhsurge 50
6
1
81.9
83.210331
Penstock…
• Static head at which thickness can be
changed from 6 mm to 5 mm
• mmmhhh surgetotalstatic 13250182
C L turbine 6 mm Thk
F.S. = 2.72 Static head =180 m
5 mm Thk
F.S. = 2.72 Static head =132 m
Penstock
Penstock…
• Repeat process for change in pipe thickness
from 5 mm to 4 mm
& 4 mm to 3 mm
Penstock…
• Cross flow turbine case- Design Example
- Gross head = 40 m, Design flow = 185 l/s
dia = 300 mm, penstock length = 70 m,
welded from flat rolled steel
- S = 320 x 106 N/mm2
Select wall thickness.
Penstock…
• Calculate flow velocity in pipe
• Try thickness, t = 4 mm
smx
x
d
Q
A
QV /62.2
)300.0(
185.04422
sm
xx
xxxtE
dxxa /1047
1000
410200
300.0101.21
1400
101.21
1400
9
9
9
Penstock…
• Critical time:
• Try closure time T = 5 sec (practical)
ssm
mx
a
lTc 13.0
1047
7022
10087.054081.9
62.27022
xx
x
xTgh
lVK
gross
mSaymxKxhh grosssurge 4,7.30087.040
Penstock…
• 4 m surge for 40 m gross head is 10% surge
head, thus 20% rule is conservative
mmmhhh surgegrosstotal 44440
mmx
teffective 03.20.12.11.1
4
!!84.9300.010445
10320)100003.2
105..
3
6
3High
xxx
xx
dxxhx
SxtFS
total
effective
Penstock…
• Try 3 mm Thickness
sm
xx
xx
a /978
1000
310200
300.0101.21
1400
9
9
ssm
mx
a
lTc 14.0
978
7022
Penstock…
• Try closure time, T = 5 sec
10087.054081.9
62.27022
xx
x
xTgh
lVK
gross
mSaymxKxhh grosssurge 4,7.30087.040
mhtotal 44
mmx
teffective 27.10.12.11.1
3
Penstock…
• Note:
2 mm pipe would also be theoretically
OK,but it can buckle and get damaged
during transport. So use 3 mm!
!!16.6300.010445
10320)100027.1(
105..
3
6
3High
xxx
xx
dxxhx
SxtFS
total
effective