draft tube flow
DESCRIPTION
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 - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Draft Tube Flow](https://reader031.vdocument.in/reader031/viewer/2022020219/56815c85550346895dca99c1/html5/thumbnails/1.jpg)
Draft Tube Flow
![Page 2: Draft Tube Flow](https://reader031.vdocument.in/reader031/viewer/2022020219/56815c85550346895dca99c1/html5/thumbnails/2.jpg)
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
![Page 3: Draft Tube Flow](https://reader031.vdocument.in/reader031/viewer/2022020219/56815c85550346895dca99c1/html5/thumbnails/3.jpg)
Phenomenon in the draft tube flow
– Swirl flow– Flow in bend– Positive pressure gradient in the diffuser - separation
![Page 4: Draft Tube Flow](https://reader031.vdocument.in/reader031/viewer/2022020219/56815c85550346895dca99c1/html5/thumbnails/4.jpg)
• 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
![Page 5: Draft Tube Flow](https://reader031.vdocument.in/reader031/viewer/2022020219/56815c85550346895dca99c1/html5/thumbnails/5.jpg)
Swirl flow
R
z
R
zr
drUrR
drUUr
MomentumAxialMomentumAngularnumberSwirl
0
2
0
2
![Page 6: Draft Tube Flow](https://reader031.vdocument.in/reader031/viewer/2022020219/56815c85550346895dca99c1/html5/thumbnails/6.jpg)
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
![Page 7: Draft Tube Flow](https://reader031.vdocument.in/reader031/viewer/2022020219/56815c85550346895dca99c1/html5/thumbnails/7.jpg)
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
![Page 8: Draft Tube Flow](https://reader031.vdocument.in/reader031/viewer/2022020219/56815c85550346895dca99c1/html5/thumbnails/8.jpg)
Rankine Vortex
Swirl flow
![Page 9: Draft Tube Flow](https://reader031.vdocument.in/reader031/viewer/2022020219/56815c85550346895dca99c1/html5/thumbnails/9.jpg)
Swirl flow
![Page 10: Draft Tube Flow](https://reader031.vdocument.in/reader031/viewer/2022020219/56815c85550346895dca99c1/html5/thumbnails/10.jpg)
Swirl flow
Vortex filament at part load Vortex filament at full load
![Page 11: Draft Tube Flow](https://reader031.vdocument.in/reader031/viewer/2022020219/56815c85550346895dca99c1/html5/thumbnails/11.jpg)
Flow in bends
A
A
A - A
![Page 12: Draft Tube Flow](https://reader031.vdocument.in/reader031/viewer/2022020219/56815c85550346895dca99c1/html5/thumbnails/12.jpg)
StreamlineStreamline
Rcdbdsdndbdsdn
np 2
Flow in bends
0ncc
np1
.konstcR
Free Vortex
From Bernoulli’s equation
Newton’s 2 law
![Page 13: Draft Tube Flow](https://reader031.vdocument.in/reader031/viewer/2022020219/56815c85550346895dca99c1/html5/thumbnails/13.jpg)
Positive pressure gradient in the diffuser
![Page 14: Draft Tube Flow](https://reader031.vdocument.in/reader031/viewer/2022020219/56815c85550346895dca99c1/html5/thumbnails/14.jpg)
![Page 15: Draft Tube Flow](https://reader031.vdocument.in/reader031/viewer/2022020219/56815c85550346895dca99c1/html5/thumbnails/15.jpg)
Location of recirculation zones
Results:
The hydraulic design of the draft tube gives secondary flow and therefore a reduced efficiency
![Page 16: Draft Tube Flow](https://reader031.vdocument.in/reader031/viewer/2022020219/56815c85550346895dca99c1/html5/thumbnails/16.jpg)
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:
![Page 17: Draft Tube Flow](https://reader031.vdocument.in/reader031/viewer/2022020219/56815c85550346895dca99c1/html5/thumbnails/17.jpg)
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:
![Page 18: Draft Tube Flow](https://reader031.vdocument.in/reader031/viewer/2022020219/56815c85550346895dca99c1/html5/thumbnails/18.jpg)
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
![Page 19: Draft Tube Flow](https://reader031.vdocument.in/reader031/viewer/2022020219/56815c85550346895dca99c1/html5/thumbnails/19.jpg)
![Page 20: Draft Tube Flow](https://reader031.vdocument.in/reader031/viewer/2022020219/56815c85550346895dca99c1/html5/thumbnails/20.jpg)
Pressure distribution at the inlet
Low pressure zones
![Page 21: Draft Tube Flow](https://reader031.vdocument.in/reader031/viewer/2022020219/56815c85550346895dca99c1/html5/thumbnails/21.jpg)
Pre s
sure
[Pa ]
drdUU r
r rU 2
dzdUU r
z 0,
1 m
zUU
rU
rUU
rp r
zr
r
2
![Page 22: Draft Tube Flow](https://reader031.vdocument.in/reader031/viewer/2022020219/56815c85550346895dca99c1/html5/thumbnails/22.jpg)
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
![Page 23: Draft Tube Flow](https://reader031.vdocument.in/reader031/viewer/2022020219/56815c85550346895dca99c1/html5/thumbnails/23.jpg)
400
mm
![Page 24: Draft Tube Flow](https://reader031.vdocument.in/reader031/viewer/2022020219/56815c85550346895dca99c1/html5/thumbnails/24.jpg)
Pressure distribution at the inlet
![Page 25: Draft Tube Flow](https://reader031.vdocument.in/reader031/viewer/2022020219/56815c85550346895dca99c1/html5/thumbnails/25.jpg)
Pre s
sure
[Pa ]
drdUU r
r rU 2
dzdUU r
z 0,2
m
![Page 26: Draft Tube Flow](https://reader031.vdocument.in/reader031/viewer/2022020219/56815c85550346895dca99c1/html5/thumbnails/26.jpg)
Pre s
sure
[Pa ]
drdUU r
r rU 2
dzdUU r
z 0,2
m
Radius [m]
![Page 27: Draft Tube Flow](https://reader031.vdocument.in/reader031/viewer/2022020219/56815c85550346895dca99c1/html5/thumbnails/27.jpg)
drdUU r
r rU 2
dzdUU r
z
Pre s
sure
[Pa ]
0,4
m
![Page 28: Draft Tube Flow](https://reader031.vdocument.in/reader031/viewer/2022020219/56815c85550346895dca99c1/html5/thumbnails/28.jpg)
drdUU r
r rU 2
dzdUU r
z
Pre s
sure
[Pa ]
0,4
m
Radius [m]
![Page 29: Draft Tube Flow](https://reader031.vdocument.in/reader031/viewer/2022020219/56815c85550346895dca99c1/html5/thumbnails/29.jpg)
Static Pressure at the inlet
![Page 30: Draft Tube Flow](https://reader031.vdocument.in/reader031/viewer/2022020219/56815c85550346895dca99c1/html5/thumbnails/30.jpg)
Velocity at the inlet to the draft tube
![Page 31: Draft Tube Flow](https://reader031.vdocument.in/reader031/viewer/2022020219/56815c85550346895dca99c1/html5/thumbnails/31.jpg)
Velocity