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


• 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


• 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


• 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..


• 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


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


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


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

193783392 penstock surge consideration

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