draft tube flow
Post on 10-Feb-2016
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Draft Tube Flow
Swirl at the outlet from Francis runners
c1 w1
u1
c2w2
u2
c2
w2
u2
2
c2
w2
u2
2
c2m
c2u
c2
w2
u2
2
c2m
c2u
Phenomenon in the draft tube flow
– Swirl flow– Flow in bend– Positive pressure gradient in the diffuser - separation
• Strong coupling between the flow field and the pressure gradients
rpF
zvv
rv
rv
rv
rvv r
rz
rrr
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
Swirl flow
R
z
R
zr
drUrR
drUUr
MomentumAxialMomentumAngularnumberSwirl
0
2
0
2
0,0
0,3
0,6
0,9
1,2
1,5
-1,0 -0,5 0,0 0,5 1,0
Radius [ - ]
Velo
city
[ -
]
S=0,1
S=0,4
S=0,7
S=0,95
Mean Axial Velocity
Swirl flow
Vortex breakdown
R
z
R
zr
drUrR
drUUr
MomentumAxialMomentumAngularnumberSwirl
0
2
0
2
Vortex breakdown is present when a negative axial velocity occurs 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 [ - ]
Velo
city
[ -
]
S=0,1
S=0,4
S=0,7
S=0,95
Rankine Vortex
Swirl flow
Swirl flow
Swirl flow
Vortex filament at part load Vortex filament at full load
Flow in bends
A
A
A - A
StreamlineStreamline
Rcdbdsdndbdsdn
np 2
Flow in bends
0ncc
np1
.konstcR
Free Vortex
From Bernoulli’s equation
Newton’s 2 law
Positive pressure gradient in the diffuser
Location of recirculation zones
Results:
The hydraulic design of the draft tube gives secondary flow and therefore a reduced efficiency
The Navier Stokes equations in Cylindrical coordinates
2
2
22
2
2
2 21111zUU
rU
rrU
rrrrpg
zUU
rUU
rU
rUU
tU rr
rrr
zrr
rr
2
2
22
2
2
2111zUU
rU
rrU
rrrpg
zUU
rUUU
rU
rUU
tU r
zr
r
2
2
2
2
2
111zUU
rrUr
rrzpg
zUUU
rU
rUU
tUz zzz
zz
zzz
r
r-direction:
z-direction:
-direction:
Euler equations
rpg
zUU
rUU
rU
rUU
tU
rr
zrr
rr
12
pgzUU
rUUU
rU
rUU
tU
zr
r1
zpg
zUUU
rU
rUU
tUz
zz
zzz
r
1
r-direction:
z-direction:
-direction:
r-direction
• Assume steady state solution 0tU r
• Assume axis symmetry 0 rU
rU
zUU
rU
rUU
rp r
zr
r
2
rpg
zUU
rUU
rU
rUU
tU
rr
zrr
rr
12
• Assume g-force to be neglectible 0 rg
Pressure distribution at the inlet
Low pressure zones
Pre s
sure
[Pa ]
drdUU r
r rU 2
dzdUU r
z 0,
1 m
zUU
rU
rUU
rp r
zr
r
2
Pre s
sure
[Pa ]
drdUU r
r rU 2
dzdUU r
z 0,
1 m
Radius [m]zUU
rU
rUU
rp r
zr
r
2
400
mm
Pressure distribution at the inlet
Pre s
sure
[Pa ]
drdUU r
r rU 2
dzdUU r
z 0,2
m
Pre s
sure
[Pa ]
drdUU r
r rU 2
dzdUU r
z 0,2
m
Radius [m]
drdUU r
r rU 2
dzdUU r
z
Pre s
sure
[Pa ]
0,4
m
drdUU r
r rU 2
dzdUU r
z
Pre s
sure
[Pa ]
0,4
m
Radius [m]
Static Pressure at the inlet
Velocity at the inlet to the draft tube
Velocity
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