8/23/2019 Nazakat

1/31

Draft Tube Flow

8/23/2019 Nazakat

2/31

Swirl at the outlet from Francis

runners

c1 w1

u1

c2w2

u2

c2

w2

u22

c2w2

u22

c2m

c2u

c2

w2

u22

c2m

c2u

8/23/2019 Nazakat

3/31

Phenomenon in the draft tube flow

Swirl flow

Flow in bend

Positive pressure gradient in the diffuser - separation

8/23/2019 Nazakat

4/31

Strong coupling between the flow field and the

pressure gradients

rpF

zvv

rv

rv

rv

rvv rrzrrr =++

2

Swirl flow in draft tubes

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

8/23/2019 Nazakat

5/31

Swirl flow

==

R

z

R

zr

drUrR

drUUr

MomentumAxialMomentumAngularnumberSwirl

0

2

0

2

8/23/2019 Nazakat

6/31

0,0

0,3

0,6

0,9

1,2

1,5

-1,0 -0,5 0,0 0,5 1,0

Radius [ - ]

Velocity

[-]

S=0,1

S=0,4

S=0,7S=0,95

Mean Axial Velocity

Swirl flow

8/23/2019 Nazakat

7/31

Vortex breakdown

==

R

z

R

zr

drUrR

drUUr

MomentumAxial

MomentumAngularnumberSwirl

0

2

0

2

Vortex breakdown is present when a negative axial velocityoccurs in the center of the flow.

Vortex breakdown occurs when S > 1

0,0

0,3

0,6

0,9

1,2

1,5

-1,0 -0,5 0,0 0,5 1,0

Radius [ - ]

Velocity

[-

S=0,1

S=0,4

S=0,7

S=0,95

8/23/2019 Nazakat

8/31

Rankine Vortex

Swirl flow

8/23/2019 Nazakat

9/31

Swirl flow

8/23/2019 Nazakat

10/31

Swirl flow

Vortex filament at part load Vortex filament at full load

8/23/2019 Nazakat

11/31

Flow in bends

A

A

A - A

8/23/2019 Nazakat

12/31

StreamlineStreamline

R

cdbdsdndbdsdn

n

p 2=

Flow in bends

0n

cc

n

p1 =

+

.konstcR

=

Free Vortex

From Bernoullis equation

Newtons 2 law

8/23/2019 Nazakat

13/31

Positive pressure gradient in the

diffuser

8/23/2019 Nazakat

14/31

8/23/2019 Nazakat

15/31

Location ofrecirculation zones

Results:

The hydraulic design of the draft tube gives secondary

flow and therefore a reduced efficiency

8/23/2019 Nazakat

16/31

The Navier Stokes equations in

Cylindrical coordinates

[ ]

++

+=+++2

2

22

2

2

2 21111

z

UU

r

U

r

rU

rrrr

pg

z

UU

r

UU

r

U

r

UU

t

U rrrr

rz

rrr

r

[ ]

+++

+=+++

2

2

22

2

2

2111

z

UU

r

U

rrU

rrr

pg

z

UU

r

UUU

r

U

r

UU

t

Ur

zr

r

++

+=+++

2

2

2

2

2

111

z

UU

rr

Ur

rrz

pg

z

UU

U

r

U

r

UU

t

Uz zzzz

zz

zzr

r-direction:

z-direction:

-direction:

8/23/2019 Nazakat

17/31

Euler equations

r

p

gz

U

Ur

UU

r

U

r

U

Ut

Ur

r

z

rr

r

r

12

=+++

pgz

UU

r

UUU

r

U

r

UU

t

Uz

rr

1=+++

z

pg

z

UU

U

r

U

r

UU

t

Uzz

zz

zzr

1=+++

r-direction:

z-direction:

-direction:

8/23/2019 Nazakat

18/31

r-direction

Assume steady state solution 0=t

Ur

Assume axis symmetry 0=

rU

r

U

z

UU

r

U

r

UU

r

p rz

rr

+=2

r

pgz

UUr

UU

r

U

r

UUt

Ur

rz

rrr

r

12

=+++

Assume g-force to be neglectible 0= rg

8/23/2019 Nazakat

19/31

8/23/2019 Nazakat

20/31

Pressure distribution at the inlet

Low pressure zones

8/23/2019 Nazakat

21/31

Pressu

re[Pa]

dr

dUU rr

r

U2+dz

dUU rz

0,1m

zUU

rU

rUU

rp rzrr

+=

2

8/23/2019 Nazakat

22/31

Pre

ssu

re[

Pa

]

dr

dUU rr

r

U2+dz

dUU rz

0,1m

Radius [m]

zUU

rU

rUU

rp rzrr

+=

2

8/23/2019 Nazakat

23/31

400m

m

Pressure distribution at the

8/23/2019 Nazakat

24/31

Pressure distribution at the

inlet

8/23/2019 Nazakat

25/31

Pre

ssure

[Pa

]

dr

dUU rr

r

U2+dz

dUU rz

0,2m

8/23/2019 Nazakat

26/31

Pre

ssure

[Pa ]

dr

dUU rr

r

U2+dz

dUU rz

0,2m

Radius [m]

8/23/2019 Nazakat

27/31

dr

dUU rr

r

U2+dz

dUU rz

Pre

ssure

[Pa

]

0,4m

8/23/2019 Nazakat

28/31

dr

dUU rr

r

U2+dz

dUU rz

Pressu

re[Pa]

0,4m

Radius [m]

8/23/2019 Nazakat

29/31

Static Pressure at the inlet

8/23/2019 Nazakat

30/31

Velocity at the inlet to the draft tube

8/23/2019 Nazakat

31/31

Velocity