1. Draft Tube Flow

2. Swirl at the outlet from Francis runnersb2 c2 w2
c2u u2 c2 w2 u2 b2 c2
c2m w2
c2u u2 b2
c2m w2 c2

3. Phenomenon in the draft tube flow
Swirl flow
Flow in bend
Positive pressure gradient in the diffuser - separation

4. Swirl flow in draft tubes
Strong coupling between the flow field and the pressure gradients
Anisotropic turbulence
The turbulence is influenced by the geometry and the velocity
The draft tube flow is sensitive to the inlet conditions (velocity and pressure)
A vortex filament is present

5. Swirl flow

6. Swirl flow
Mean Axial Velocity

7. Vortex breakdown
Vortex breakdown is present when a negative axial velocity occurs in the center of the flow.
Vortex breakdown occurs when S > 1

8. Swirl flow
Rankine Vortex

9. Swirl flow

10. Swirl flow
Vortex filament at part load
Vortex filament at full load

11. Flow in bends
A - A A A

12. Flow in bends
Newton’s 2 law
From Bernoulli’s equation
Free Vortex

13. Positive pressure gradient in the diffuser

15. Results:
The hydraulic design of the draft tube gives secondary flow and therefore a reduced efficiency

16. The Navier Stokes equations in Cylindrical coordinates
r-direction:
q-direction:
z-direction:

17. Euler equations
r-direction:
q-direction:
z-direction:

18. r-direction Assume steady state solution Assume axis symmetry
Assume g-force to be neglectible

20. Pressure distribution at the inlet

21. 0,1 m
Pressure [Pa]

22. 0,1 m
Pressure [Pa]
Radius [m]

23. 400 mm

24. Pressure distribution at the inlet

25. 0,2 m
Pressure [Pa]

26. 0,2 m
Pressure [Pa]
Radius [m]

27. 0,4 m
Pressure [Pa]

28. 0,4 m
Pressure [Pa]
Radius [m]

29. Static Pressure at the inlet

30. Velocity at the inlet to the draft tube

31. Velocity