Draft Tube Flow

Swirl at the outlet from Francis runners b2 c2 w2 c2u u2 c2 w2 u2 b2 c2 c2m w2 c2u u2 b2 c2m w2 c2

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

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

Swirl flow

Swirl flow Mean Axial Velocity

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

Swirl flow Rankine Vortex

Swirl flow

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

Flow in bends A - A A A

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

Positive pressure gradient in the diffuser

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

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

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

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

Pressure distribution at the inlet

0,1 m Pressure [Pa]

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

400 mm

Pressure distribution at the inlet

0,2 m Pressure [Pa]

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

0,4 m Pressure [Pa]

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

Static Pressure at the inlet

Velocity at the inlet to the draft tube

Velocity