design of pelton turbines - ntnu

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Design of Pelton turbines

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Page 1: Design of Pelton turbines - NTNU

Design of Pelton turbines

Page 2: Design of Pelton turbines - NTNU

When to use a Pelton turbine

Page 3: Design of Pelton turbines - NTNU

Energy conversion in a Pelton turbine

Outlet Outlet of the runner

Inlet of the runner

Outlet of the needle

Inlet of the needle

2

2c

Page 4: Design of Pelton turbines - NTNU

Main dimensions for the Pelton runner

Page 5: Design of Pelton turbines - NTNU
Page 6: Design of Pelton turbines - NTNU

The ideal Pelton runnerAbsolute velocity from nozzle:

n1 Hg2c ⋅⋅= 1Hg2

ccn

11 =

⋅⋅=

Circumferential speed:

nu1

1 Hg221

2cu ⋅⋅⋅== 5.0u1 =

Euler`s turbine equation:

)cucu(2 u22u11h ⋅−⋅=η

1)05,00.15,0(2)(2 2211 =⋅−⋅⋅=⋅−⋅⋅= uuh cucuη

1c u1 = 0c 2u =

Page 7: Design of Pelton turbines - NTNU

The real Pelton runner• For a real Pelton runner there will always be lossWe will therefore set the hydraulic efficiency to:

96.0h =η

The absolute velocity from the nozzle will be:

995.0c99.0 u1 <≤

C1u can be set to 1,0 when dimensioning the turbine.This gives us:

)cucu(2 u22u11h ⋅−⋅=η

48,00,12

96,0c2

uu1

n1 =

⋅=

⋅η

=

Page 8: Design of Pelton turbines - NTNU

From continuity equation:

u1

2s c

4dzQ ⋅⋅π

⋅=

u1s cz

Q4d⋅π⋅⋅

=

Where:Z = number of nozzlesQ = flow rateC1u = nHg2 ⋅⋅

Page 9: Design of Pelton turbines - NTNU

The size of the bucket and number of nozzles

4.3dB1.3

s

≥>

Rules of thumb:B = 3,1 · ds 1 nozzleB = 3,2 · ds 2 nozzlesB = 3,3 · ds 4-5 nozzlesB > 3,3 · ds 6 nozzles

Page 10: Design of Pelton turbines - NTNU

Number of buckets

17≥z empirical

Page 11: Design of Pelton turbines - NTNU

Number of buckets

Page 12: Design of Pelton turbines - NTNU

Runner diameterRules of thumb:

D = 10 · ds Hn < 500 mD = 15 · ds Hn = 1300 m

D < 9,5 · ds must be avoided because waterwill be lost

D > 15 · ds is for very high head Pelton

Page 13: Design of Pelton turbines - NTNU

Speed number

zQ ⋅ω=Ω

5,0u0,1c

1

u1

==

4dc

4dQ

2s

u1

2s ⋅π

=⋅⋅π

=

D1

Hg2DHg2

Hg2Du2

Hg2 n

n

n

1

n

=⋅⋅⋅

⋅⋅=

⋅⋅⋅⋅

=⋅⋅

ω=ω

4z

Dds ⋅π

4zd

D1zQ

2s ⋅⋅π

⋅=⋅⋅ω=Ω

Page 14: Design of Pelton turbines - NTNU

For the diameter: D = 10 · dsand one nozzle: z = 1

09,041

101

4z

Dds =

⋅π=

⋅π=Ω

For the diameter: D = 10 · dsand six nozzle: z = 6

22,04

6101

4z

Dds =

⋅π=

⋅π=Ω

The maximum speed number for a Pelton turbine today is Ω = 0,22

The maximum speed number for a Pelton turbine with one nozzle is Ω = 0,09

Page 15: Design of Pelton turbines - NTNU

Dimensioning of a Pelton turbine

1. The flow rate and head are given*H = 1130 m*Q = 28,5 m3/s*P = 288 MW

2. Choose reduced valuesc1u = 1 ⇒ c1u = 149 m/su1 = 0,48 ⇒ u1 = 71 m/s

3. Choose the number of nozzlesz = 5

4. Calculate ds from continuity for one nozzle

m22,0cz

Q4du1

s =⋅π⋅⋅

=

Page 16: Design of Pelton turbines - NTNU

5. Choose the bucket widthB = 3,3 · ds= 0,73 m

Page 17: Design of Pelton turbines - NTNU

6. Find the diameter by interpolation

D/ds

Hn [m]

10

15

400 1400

m0,3d65,13D

65,138H005,0dD

s

ns

=⋅=⇓

=+⋅=

Page 18: Design of Pelton turbines - NTNU

7. Calculate the speed:

8. Choose the number of poles on the generator:

The speed of the runner is given by the generator and the net frequency:

where Zp=number of poles on the generator

The number of poles will be:

rpm452D60un

2D

60n2

2Du

1

1

=⋅Π⋅

=

⋅⋅Π⋅

=⋅ω=

]rpm[Z

3000np

=

764,6n

3000Zp ===

Page 19: Design of Pelton turbines - NTNU

]rpm[6,428Z

3000np

==

m16,3n60uD

2D

60n2

2Du 1

1 =⋅Π⋅

=⇒⋅⋅Π⋅

=⋅ω=

9. Recalculate the speed:

10. Recalculate the diameter:

11. Choose the number of buckets

z = 22

Page 20: Design of Pelton turbines - NTNU

12. Diameter of the turbine housing (for vertical turbines)

13. Calculate the height from the runner to the water level at the outlet (for vertical turbines)

m4,9BKDD gsinHou =⋅+=

K

z

8

9

1 64

m1,3DB5.3Height =≈⋅≈

Page 21: Design of Pelton turbines - NTNU

Given values:

*Q = 28,5 m3/s*H = 1130 m

Chosen values:

c1u = 1u1 = 0,48z = 5B = 0,73 mz = 22Zp = 7

Calculated values:

ds = 0,22 mn = 428,6 rpmD = 3, 16 mHeight = 3,1 mDhousing= 9,4 m*P = 288 MW

Page 22: Design of Pelton turbines - NTNU

GE Hydro

*Q = 28,5 m3/s*H = 1130 m*P = 288 MW

Jostedal, Sogn og Fjordane

Page 23: Design of Pelton turbines - NTNU

Jostedal, Sogn og FjordaneGE Hydro

*Q = 28,5 m3/s*H = 1130 m*P = 288 MW

Page 24: Design of Pelton turbines - NTNU

ExampleKhimti Power Plant

1. The flow rate and head are given*H = 660 m*Q = 2,15 m3/s*P = 12 MW

2. Choose reduced valuesc1u = 1 ⇒ c1u = 114 m/su1 = 0,48 ⇒ u1 = 54,6 m/s

3. Choose the number of nozzlesz = 1

Page 25: Design of Pelton turbines - NTNU

ExampleKhimti Power Plant

4. Calculate ds from continuity for one nozzle

5. Choose the bucket widthB = 3,2 · ds= 0, 5 m

mcz

Qdu

s 15,04

1

=⋅⋅⋅

Page 26: Design of Pelton turbines - NTNU

6. Find the diameter by interpolation

D/ds

Hn [m]

10

15

400 1400

mdD

HdD

s

ns

7,13,11

3,118005,0

=⋅=⇓

=+⋅=

Page 27: Design of Pelton turbines - NTNU

7. Calculate the speed:

8. Choose the number of poles on the generator:The speed of the runner is given by the generator and the net frequency:

where Zp=number of poles on the generator

The number of poles will be:

rpmD

un

DnDu

61360

2602

2

1

1

=⋅Π⋅

=

⋅⋅Π⋅

=⋅=ω

]rpm[Z

3000np

=

59,43000===

nZ p

Page 28: Design of Pelton turbines - NTNU

][6003000 rpmZ

np

==

mn

uDDnDu 74,160260

22

11 =

⋅Π⋅

=⇒⋅⋅Π⋅

=⋅=ω

9. Recalculate the speed:

10. Recalculate the diameter:

11. Choose the number of buckets

z = 22