13. Pressure distribution and
torque
0,24 · l Cord length, l
Suction side
Pressure side
Single profile
Cascade
The pressure at the outlet is lower for a cascade than
for a single profile. The cavitation performance will
therefore be reduced in a cascade.
14. Radial distribution of the
blade profile
CL =Lift coefficient for a cascade
CL1 =Lift coefficient for a single profile
The ratio t/l influences the lift coefficient in a
cascade. The cord length for a blade will therefore
increase when the radius becomes increase
16. Flow in the axial plane
The figure shows blades with two different design
of the blade in radial direction. This is because it
will influence the secondary flow in the radial
direction
18. Diameter of the runner
o
Ω = ω ⋅ Qn
1 .0
C m l = 0 . 1 2 + 0 .1 8 0 Ω (tiln æ rm e t)
0 .5
m l
C
0
1 .5 2 .0 2 .5 3 .0
0
Ω
Qn =
Π⋅ D −d
⋅ c1m
( 2 2
)
4
⇓
Qn ⋅ 4
D=
Π ⋅ c1m
19. Height of the guide vanes
and runner diameter
P
0 .7
ns = n ⋅ 54
0 .6
H n
d /D
d /D , B 0/D
0 .5
B 0/D
0 .4
0 .3
300 400 500 600 700 800 900
ns
20. Gap between hub and ring
and the runner blades
Gap between the
blade and ring
Gap between the
blade and hub
0 .9 0
V Efficiencyd
s = x 1 0 -3 d
ir k n in g s g ra
0 .8 5
0 .8 0
0 1 2 3 4 5 6
S p a l t e å pGap x = 1 0 0 0 s / D
n in g
21. Runaway speed
2 .6
RRunaway/ nspeedu r t a l l
ϕ2 ϕ1
2 .4
u s n in g s ta ll o r m a lt
ϕ3
ϕ4
2 .2
ϕ5
ϕ6
2
V o it h
0 0 .5 1 .0 2 .0 3 .0
Cavitation scoefficient t σ
k a v ita jo n s k o e ff is ie n
10 − H S
σ=
H
The figure shows different runaway speed at
different runner blade openings. The runaway speed
is dependent of the cavitation as shown in the figure
23. Example
• Find the dimensions D, d and Bo
• Given data: P = 16,8 MW
H = 16 m
Qn = 120 m3/s
n = 125 rpm
24. Speed number:
2 ⋅ g ⋅ H = 2 ⋅ 9,82 ⋅16 = 17,7 m s
n ⋅ 2 ⋅ Π 125 ⋅ 2 ⋅ Π
ω= = = 13,1 rad
60 60 s
ω 13,1 rad
ω= = s = 0,74 m −1
2 ⋅ g ⋅ H 17,7 m
s
120 m3
Q s = 6,78 m 2
Qn = =
2 ⋅ g ⋅ H 17,7 m
s
o
Ω = ω ⋅ Q n = 0,74 ⋅ 6,78 = 1,93
26. Diameter, d:
P 22826 Hp
ns = n ⋅ = 125rpm ⋅ = 590
Hn 4
5
16m 54
0 .7
0 .6
d /D
d /D , B 0/D
0 .5
B 0/D
0 .4
0 .3
300 400 500 600 700 800 900
n s
d
= 0,45 ⇒ d = D ⋅ 0,45 = 1,9 m
D
27. Height, B:
0 .7
0 .6
d /D
d /D , B 0/D
0 .5
B 0/D
0 .4
0 .3
300 400 500 600 700 800 900
n s
BO
= 0,41 ⇒ BO = D ⋅ 0,41 = 1,76 m
D