design of stay vanes and spiral casing
DESCRIPTION
powerhouseTRANSCRIPT
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Design of stay vanes and spiral casing
Revelstoke, CANADA
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Guri-2, VENEZUELA
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Aguila, ARGENTINA
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Sauchelle-Huebra, SPAIN
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Sauchelle-Huebra, SPAIN
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Three Gorges Turbine, GE Hydro
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The spiral casing will distribute the water equally around the stay vanes
In order to achieve a uniform flow in to the runner, the flow has to be uniform in to the stay vanes.
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Flow in a curved channel
Streamline
-
StreamlineStreamline
The pressure normal to the streamline can be derived as:
dbdsdnn
pdbdsdnn
ppdbdspdFn
=
+=
-
Newton 2. Law gives:
StreamlineStreamline
Rc
n
p
adbdsdndbdsdnn
pn
21=
=
Rc
a2
n =
1
m
-
The Bernoulli equation gives:
.const2cp 2
=+
Derivation of the Bernoulli equation gives:
0n
cc
n
p1=
+
2
-
Equation 1 and 2 combined gives:
.constcR
0)Rc(d
0dRcdcR
Rc
n
c
=
=
=+
=
Free Vortex
Rc
n
p 21=
0n
cc
n
p1=
+
2
1
-
Inlet angle to the stay vanes
icm
cu
=
u
m
ic
ctana
-
Plate turbine
-
Find the meridonial velocity from continuity:
BR2Q
AQ
c
cAQ
0m
m
pi==
=
B
R0
-
Find the tangential velocity:
=
==
=
=
00y
u
0y
R
Ry
R
Ry
u
R
Ry
RRlnRB
Qc
RRln.constB
r
dr.constBQ
drr
.constBQ
drcBQ
0
0
0
By
R0 R
-
Example
By
Flow Rate Q = 1,0 m3/sVelocity C = 10 m/sHeight By = 0,2 mRadius R0 = 0,8 m
Find: L1, L2, L3 and L4
L1
C
L3
L2
L4
R0R
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Example
By
Flow Rate Q = 1,0 m3/sVelocity C = 10 m/sHeight By = 0,2 mRadius R0 = 0,8 m
L1
C
L3
L2
L4
R0R
sm
RRRB
QCy
u 9,12ln
00
=
=
mBC
QLy
5,01 =
=
-
Example
By
Flow Rate Q = 1,0 m3/sVelocity C = 10 m/sHeight By = 0,2 mRadius R0 = 0,8 m
We assume Cu to be constant along R0.
At =90o, Q is reduced by 25%
L1
C
L3
L2
L4
R0R
-
Example
By
Flow Rate Q = 0,75 m3/sVelocity Cu = 12,9 m/sHeight By = 0,2 mRadius R0 = 0,8 m
L1
C
L3
L2
L4
R0R
00
00
0
ln
ln.
RCBQ
uy
y
uyeRR
RRRCBQ
RR
constBQ
=
=
=
-
Example
By
Flow Rate Q = 0,75 m3/sVelocity Cu = 12,9 m/sHeight By = 0,2 mRadius R0 = 0,8 m
L1
C
L3
L2
L4
R0R
00
RCBQ
uyeRR =
L2 = 0,35 mL3 = 0,22 mL4 = 0,10 m
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Find the meridonial velocity from continuity:
10m
m
kBR2Q
AQ
c
cAQ
pi==
=R0B
k1 is a factor that reduce the inlet area due to the stay vanes
2yB
-
Find the tangential velocity:
Rc
c
.constcRc
Tu
Tu
=
==
=
=
+
pi
o
drRcrQ
dRcBQ
tT
u
rR
Ry
t
cos
sin2
2
2
0
R0B R0B
drdRrRR
rB
T
y
=
=
=
sincos
sin2
2yB
-
=
pi
d
cosrRsin
r2
Qc
T
22
T
o
R0B R0B
=
pi
d
cosrRsin
r2R
Qc
T
22
u
o
2yB
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Spiral casing design procedure1. We know the flow rate, Q. 2. Choose a velocity at the upstream section of the spiral
casing, C3. Calculate the cross section at the inlet of the spiral casing:
4. Calculate the velocity Cu at the radius Ro by using the equation:
pi=
CQ
r
=
pi
d
cosrRsin
r2R
Qc
T
22
u
o
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Spiral casing design procedure5. Move 20o downstream the spiral casing and calculate the
flow rate:
6. Calculate the new spiral casing radius, r by iteration with the equation:
totalo
o
new QQ = 36020
=
pi
o
drRcrQ tT cos
sin2
2
2
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Outlet angle from the stay vanes
cm
cu
=
u
m
c
ctana
.constRcu
=
kBR2Q
AQ
cmpi
==
-
Weight of the spiral casing
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Stay Vanes
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Number of stay vanes
16
18
20
22
24
26
28
30
0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6Speed Number
N
u
m
b
e
r
o
f
S
t
a
y
V
a
n
e
s
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Design of the stay vanes
The stay vanes have the main purpose of keeping the spiral casing together
Dimensions have to be given due to the stresses in the stay vane
The vanes are designed so that the flow is not disturbed by them
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Flow induced pressure oscillation
56.09.1
+=
t
cBf
Where f = frequency [Hz]B = relative frequency to the Von Karman oscillationc = velocity of the water [m/s]t = thickness of the stay vane [m]
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Where A = relative amplitude to the Von Karman oscillationB = relative frequency to the Von Karman oscillation