This document describes the design process for a Pelton turbine. It begins with the key dimensions and equations for Pelton turbines. It then provides an example of dimensioning a Pelton turbine with the given parameters of flow rate, head, and power output. The process involves choosing values for variables like number of nozzles and buckets, then calculating dimensions like jet diameter, runner diameter, and speed based on the design equations.

1. Design of Pelton
turbines

2. When to use a Pelton
turbine

3. Energy conversion in a
Pelton turbine
Outlet Outlet of Inlet of Outlet of Inlet of
the runner the runner the needle the needle
c2
2

4. Main dimensions for the
Pelton runner

6. The ideal Pelton runner
Absolute velocity from nozzle:
c1
c1 = 2 ⋅ g ⋅ H n c1 = =1
2 ⋅ g ⋅ Hn
Circumferential speed:
c1u 1
u1 = = ⋅ 2 ⋅ g ⋅ Hn u1 = 0.5
2 2
Euler`s turbine equation:
ηh = 2(u1 ⋅ c1u − u 2 ⋅ c 2 u )
c1u = 1 cu 2 = 0
η h = 2 ⋅ (u1 ⋅ c1u − u 2 ⋅ c 2u ) = 2 ⋅ (0,5 ⋅1.0 − 0,5 ⋅ 0) = 1

7. The real Pelton runner
• For a real Pelton runner there will always be losses
We will therefore set the hydraulic efficiency to:
ηh = 0.96
The absolute velocity from the nozzle will be:
0.99 ≤ c1u < 0.995
C1u can be set to 1,0 when dimensioning the turbine.
This gives us:
ηh = 2(u1 ⋅ c1u − u 2 ⋅ c 2 u )
⇓
ηn 0,96
u1 = = = 0,48
2 ⋅ c1u 2 ⋅1,0

8. From continuity equation:
π⋅d 2
Q = z⋅ ⋅ c1u
s
4
⇓
4⋅Q
ds =
z ⋅ π ⋅ c1u
Where:
Z = number of nozzles
Q = flow rate
C1u = 2 ⋅ g ⋅ Hn

9. The size of the bucket
and number of nozzles
B
3.1 > ≥ 3.4
ds
Rules of thumb:
B = 3,1 · ds 1 nozzle
B = 3,2 · ds 2 nozzles
B = 3,3 · ds 4-5 nozzles
B > 3,3 · ds 6 nozzles

10. Number of buckets
z ≥ 17 empirical

11. Number of buckets

12. Runner diameter
Rules of thumb:
D = 10 · ds Hn < 500 m
D = 15 · ds Hn = 1300 m
D < 9,5 · ds must be avoided because water
will be lost
D > 15 · ds is for very high head Pelton

13. Speed number
Ω = ω Q⋅z
c1u = 1,0
π ⋅ ds
2
π ⋅ ds
2
Q= ⋅ c1u = u1 = 0,5
4 4
ω 2 ⋅ u1 2 ⋅ g ⋅ Hn 1
ω= = = =
2 ⋅ g ⋅ Hn D ⋅ 2 ⋅ g ⋅ Hn D ⋅ 2 ⋅ g ⋅ Hn D
1 π ⋅ ds ⋅ z
2
Ω = ω⋅ Q ⋅ z = ⋅
D 4
ds π⋅z
Ω=
D 4

14. For the diameter: D = 10 · ds
and one nozzle: z=1
ds π ⋅ z 1 π ⋅1
Ω= = = 0,09
D 4 10 4
The maximum speed number for a Pelton
turbine with one nozzle is Ω = 0,09
For the diameter: D = 10 · ds
and six nozzle: z=6
ds π⋅z 1 π⋅6
Ω= = = 0,22
D 4 10 4
The maximum speed number for a Pelton
turbine today is Ω = 0,22

15. 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 values
c1u = 1 ⇒ c1u = 149 m/s
u1 = 0,48 ⇒ u1 = 71 m/s
3. Choose the number of nozzles
z=5
4. Calculate ds from continuity for one nozzle
4⋅Q
ds = = 0,22 m
z ⋅ π ⋅ c1u

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

17. 6. Find the diameter by interpolation
D
= 0,005 ⋅ H n + 8 = 13,65
ds
⇓
D = 13,65 ⋅ d s = 3,0 m
D/ds
15
10
400 1400 Hn [m]

18. 7. Calculate the speed:
D 2⋅Π ⋅n D
u1 = ω ⋅ = ⋅
2 60 2
⇓
u ⋅ 60
n= 1 = 452 rpm
Π⋅D
8. Choose the number of poles on the generator:
The speed of the runner is given by the generator and
the net frequency:
3000
n= [rpm]
Zp
where Zp=number of poles on the generator
The number of poles will be:
3000
Zp = = 6,64 = 7
n

19. 9. Recalculate the speed:
3000
n= = 428,6 [rpm]
Zp
10. Recalculate the diameter:
D 2⋅Π ⋅n D u ⋅ 60
u1 = ω ⋅ = ⋅ ⇒ D= 1 = 3,16 m
2 60 2 Π⋅n
11. Choose the number of buckets
z = 22

20. 12. Diameter of the turbine housing (for vertical turbines)
D Hou sin g = D + K ⋅ B = 9,4 m
K
9
8
1 4 6 z
13. Calculate the height from the runner to the water level
at the outlet (for vertical turbines)
Height ≈ 3.5 ⋅ B ≈ D = 3,1 m

21. Given values: Chosen values: Calculated values:
*Q = 28,5 m3/s c1u = 1 ds = 0,22 m
*H = 1130 m u1 = 0,48 n = 428,6 rpm
z=5 D = 3, 16 m
B = 0,73 m Height = 3,1 m
z = 22 Dhousing= 9,4 m
Zp = 7 *P = 288 MW

22. *Q = 28,5 m3/s
*H = 1130 m
*P = 288 MW
GE Hydro
Jostedal, Sogn og Fjordane

23. *Q = 28,5 m3/s
*H = 1130 m
*P = 288 MW
GE Hydro
Jostedal, Sogn og Fjordane

24. Example
Khimti Power Plant
1. The flow rate and head are given
*H = 660 m
*Q = 2,15 m3/s
*P = 12 MW
2. Choose reduced values
c1u = 1 ⇒ c1u = 114 m/s
u1 = 0,48 ⇒ u1 = 54,6 m/s
3. Choose the number of nozzles
z=1

25. Example
Khimti Power Plant
4. Calculate ds from continuity for
one nozzle
4⋅Q
ds = = 0,15 m
z ⋅ π ⋅ c1u
5. Choose the bucket width
B = 3,2 · ds= 0, 5 m

26. 6. Find the diameter by interpolation
D
= 0,005 ⋅ H n + 8 = 11,3
ds
⇓
D = 11,3 ⋅ d s = 1,7 m
D/ds
15
10
400 1400 Hn [m]

27. 7. Calculate the speed:
D 2⋅Π ⋅n D
u1 = ω ⋅ = ⋅
2 60 2
⇓
u1 ⋅ 60
n= = 613 rpm
Π⋅D
8. Choose the number of poles on the
generator:
The speed of the runner is given by
the generator and the net frequency:
3000
n= [rpm]
Zp
where Zp=number of poles on the
generator
The number of poles will be:
3000
Zp = = 4,9 = 5
n

28. 9. Recalculate the speed:
3000
n= = 600 [rpm]
Zp
10. Recalculate the diameter:
D 2⋅Π ⋅n D u1 ⋅ 60
u1 = ω ⋅ = ⋅ ⇒ D= = 1,74 m
2 60 2 Π⋅n
11. Choose the number of buckets
z = 22