Openfoam Simulation of the Flow in the Hoelleforsen Draft Tube Model
Draft Tube Flow
description
Transcript of Draft Tube Flow
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