Design of Pelton turbines

When to use a Pelton turbine

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

Main dimensions for the Pelton runner

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

1)05,00.15,0(2)(2 2211 uuh cucu

1c u1 0c 2u

The real Pelton runner     For a real Pelton runner there will always be losses.We will therefore set the hydraulic efficiency to:

96.0h

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

48,00,12

96,0c2

uu1

n1

From continuity equation:

u1

2s c

4dzQ

u1s cz

Q4d

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

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

Number of buckets

17z empirical

Number of buckets

Runner diameter Rules 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

Speed number

zQ

5,0u0,1c

1

u1

4dc

4dQ

2s

u1

2s

D1

Hg2DHg2

Hg2Du2

Hg2 n

n

n

1

n

4z

Dds

4zd

D1zQ

2s

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

09,04

1101

4z

Dds

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

22,04

6101

4z

Dds

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

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

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

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

6. Find the diameter by interpolation

D/ds

Hn [m]

10

15

400 1400

m0,3d65,13D

65,138H005,0dD

s

ns

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

]rpm[Z

3000np

764,6n

3000Zp

]rpm[6,428Z

3000np

m16,3n60uD

2D

60n2

2Du 1

1

9. Recalculate the speed:

10. Recalculate the diameter:

11. Choose the number of buckets

z = 22

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

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

GE Hydro

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

Jostedal, Sogn og Fjordane

Jostedal, Sogn og FjordaneGE Hydro

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

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

ExampleKhimti Power Plant

4. Calculate ds from continuity for one nozzle

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

mczQd

us 15,04

1

6. Find the diameter by interpolation

D/ds

Hn [m]

10

15

400 1400

mdD

HdD

s

ns

7,13,11

3,118005,0

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

]rpm[Z

3000np

59,43000

nZ p

][6003000 rpmZ

np

mn

uDDnDu 74,160260

22

11

9. Recalculate the speed:

10. Recalculate the diameter:

11. Choose the number of buckets

z = 22