1. Design of stay vanes and spiral casing
Revelstoke, CANADA

2. Guri-2, VENEZUELA

3. Aguila, ARGENTINA

4. Sauchelle-Huebra, SPAIN

5. Sauchelle-Huebra, SPAIN

6. Three Gorges Turbine, GE Hydro

7. The spiral casing will distribute the water equally around the stay vanes
In order to achieve a uniform flow in to the runner, the flow has to be uniform in to the stay vanes.

8. Flow in a curved channel
Streamline

9. The pressure normal to the streamline can be derived as:

10. Newton 2. Law gives: m 1

11. The Bernoulli equation gives:
Derivation of the Bernoulli equation gives: 2

12. Equation 1 and 2 combined gives:
Free Vortex

13. Inlet angle to the stay vanescm ai cu

14. Plate turbine

15. Find the meridonial velocity from continuity:B

16. Find the tangential velocity:R0 R By

17. Example C L4 Flow Rate Q = 1,0 m3/s Velocity C = 10 m/s
Height By = 0,2 m
Radius R0 = 0,8 m
Find: L1, L2, L3 and L4 L1 q L3 R0 R L2 By

18. Example C L4 Flow Rate Q = 1,0 m3/s Velocity C = 10 m/s
Height By = 0,2 m
Radius R0 = 0,8 m L1 q L3 R0 R L2 By

19. Example C L4 Flow Rate Q = 1,0 m3/s Velocity C = 10 m/s
Height By = 0,2 m
Radius R0 = 0,8 m
We assume Cu to be constant along R0.
At q=90o, Q is reduced by 25% L1 q L3 R0 R L2 By

20. Example C L4 Flow Rate Q = 0,75 m3/s Velocity Cu = 12,9 m/s
Height By = 0,2 m
Radius R0 = 0,8 m L1 q L3 R0 R L2 By

21. Example C L4 Flow Rate Q = 0,75 m3/s Velocity Cu = 12,9 m/s
Height By = 0,2 m
Radius R0 = 0,8 m L1 q L3 R0 R L2
L2 = 0,35 m
L3 = 0,22 m
L4 = 0,10 m By

22. Find the meridonial velocity from continuity:B
k1 is a factor that reduce the inlet area due to the stay vanes

23. Find the tangential velocity:

25. Spiral casing design procedure
We know the flow rate, Q.
Choose a velocity at the upstream section of the spiral casing, C
Calculate the cross section at the inlet of the spiral casing:
Calculate the velocity Cu at the radius Ro by using the equation:

26. Spiral casing design procedure
Move 20o downstream the spiral casing and calculate the flow rate:
Calculate the new spiral casing radius, r by iteration with the equation:

27. Outlet angle from the stay vanescm a cu

28. Weight of the spiral casing

29. Stay Vanes

30. Number of stay vanes

31. Design of the stay vanes
The stay vanes have the main purpose of keeping the spiral casing together
Dimensions have to be given due to the stresses in the stay vane
The vanes are designed so that the flow is not disturbed by them

32. Flow induced pressure oscillation
Where
f = frequency [Hz]
B = relative frequency to the Von Karman oscillation
c = velocity of the water [m/s]
t = thickness of the stay vane [m]

33. Where
A = relative amplitude to the Von Karman oscillation
B = relative frequency to the Von Karman oscillation