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Draft Tube Flow

Draft Tube Flow. u 1. c 1. w 1. u 2. w 2. c 2. Swirl at the outlet from Francis runners. u 2. b 2. c 2. w 2. c 2u. u 2. b 2. c 2. c 2m. w 2. c 2u. u 2. b 2. c 2m. w 2. c 2. Phenomenon in the draft tube flow Swirl flow Flow in bend

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Draft Tube Flow

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  1. Draft Tube Flow

  2. u1 c1 w1 u2 w2 c2 Swirl at the outlet from Francis runners u2 b2 c2 w2 c2u 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. Mean Axial Velocity Swirl flow

  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. Rankine Vortex Swirl flow

  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

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

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

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

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

  18. Pressure distribution at the inlet

  19. 0,1 m Pressure [Pa]

  20. 0,1 m Pressure [Pa] Radius [m]

  21. 400 mm

  22. Pressure distribution at the inlet

  23. 0,2 m Pressure [Pa]

  24. 0,2 m Pressure [Pa] Radius [m]

  25. 0,4 m Pressure [Pa]

  26. 0,4 m Pressure [Pa] Radius [m]

  27. Static Pressure at the inlet

  28. Velocity at the inlet to the draft tube

  29. Velocity

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