Guide vanes in Francis turbines
El Cajon, HONDURAS
Revelstoke, CANADA
La Grande 3, Canada
P = 169 MW
H = 72 m
Q = 265 m3/S
D0 = 6,68 m
D1e = 5,71m
D1i = 2,35 m
B0 = 1,4 m
n = 112,5 rpm
La Grande 3, Canada
La Grande 3, Canada
Guide vane cascade, Francis
Guide Vane End Seals
•
•
•
High efficiency
Less erosion
Less leakage in closed pos.
Guide vanes
Main function:
Adjust the turbine load
The guide vanes consist of number of blades that can be adjusted
in order to increase or reduce the flow rate through the turbine.
The vanes are arranged between two parallel covers normal to
the turbine shaft.
Pressure distribution and torque
L
D
L
Torque
D
Arm
Guide vanes in closed position
π ⋅ D0
l=
Z
F0 = ρ ⋅ g ⋅ H ⋅ B0 ⋅ l
Torque = M 0 = F0 ⋅ a 0
Guide vanes in open position
Pressure distribution can be found
using Bernoulli’s equation:
c2
H=h+
+ losses
2⋅g
⇓
Contour of the guide vane
Trailing edge
Trailing edge
Pressure distribution along the contour of the guide vane:
 ξ ⋅ c2 
c2

h=H−
− ∑
⋅
2⋅g
2
g


Pressure distribution along the contour of the guide vane:
c2
2⋅ g
StagnationPoint at Leading Edge
Guide vane contour
Small flow rate
Large flow rate
Variation of the torque when the guide vane
opening changes:
2 ⋅ M ⋅ D0
Cm =
= f (α 0 )
2
ρ⋅Q
α0
2
3 1
4
Sin α0
Horsepower
ns = n ⋅
H5 4
cm1
c m1
Powerplant
ns
α0
Powerplant
ns
α0
Skjærka
66
12
Dynjafoss
208
27,5
Nedre Vinstra
69
12
Oltesvik
264
38,5
Hol I
72
13
Iverland
269
31,5
Mesna
78
13
Fiskumfoss
308
40,5
Røssåga
104
18
Fiskumfoss
308
36,5
Grønsdal
113
23
Gravfoss
346
37
Nore II
198
34
Solbergfoss
365
38
The guide vane maximum angle α0 at full load
Powerplant
ns
α0
1
Skjærka
66
12
2
Nedre
Vinstra
69
12
3
Hol I
72
13
4
Mesna
78
13
5
Røssåga
104
18
6
Grønsdal
113
23
7
Nore II
198
34
8
Dynjafoss
208
27,5
9
Oltesvik
264
38,5
10
Iverland
269
31,5
11
Fiskumfoss
308
40,5
12
Fiskumfoss
308
36,5
13
Gravfoss
346
37
14
Solbergfoss
365
38
NB: This is for Norwegian designed GE-turbines
Guide vane angle
Specific speed, ns
ns = n ⋅
Horsepower
H5 4
The servo’s work
The servo has to:
Take care of the torque from all guide vanes
for all guide vane angles
The torque consist of:
Hydraulic torque
Friction torque
Hydraulic torque
2 ⋅ Cm ⋅ D0
M=
2
ρ⋅Q
Cm = f (α 0 )
The hydraulic
torque can be
found from a
CFD-analysis
Friction torque
µ ⋅ d ⋅ H ⋅ BD ⋅ DD
M f = ±f f (Ω, α ) ⋅
Z
ff (Ω,α)= empirical value
µ
= friction factor
H
= Head
d
Opening
Friction
Stroke
Hy
d
Op
e
r au
lic
nin
g
High head Francis turbine
Measurements of the servo’s work
for
ces
Fully open
Force in 1000 kg
Cl
os
ing
Horse shoe vortex damage
Cavitation damage
Sand erosion in the guide vanes
Jhimruk Hydro Power Plant
Head cover
Head
cover
Head
cover
Guide kvane shaft
Bottom cover
The deflection of the head cover
Z
H = 435, P = 25 MW
1
2
Y
Reduction of clearance
Efficiency of repaired turbine
[MW]
H = 430 m
Design of the Guide Vane Inlet Angle
Cu inlet GuideVane ⋅ rinlet GuideVane = Cu inlet StayVane ⋅ rinlet StayVane
• The inlet angle can be
calculated by assuming a
free vortex from the flow
coming from the spiral
casing
Cm inlet GuideVane =
B
Q
π ⋅ Dinlet GuideVane ⋅ B
Dinlet Guide Vane
rinlet Stay Vane
Design of the Guide Vane Outlet Angle
• The outlet angle can be calculated by assuming a
free vortex from the flow in the gap between the
runner and the guide vanes
Cu 0 ⋅ ro = Cu1 ⋅ r1
Cmo
B0
Q
=
π ⋅ D0 ⋅ B0
r1
D0
Design of the Guide Vanes
How to choose the number of vanes
• The number of guide vanes has to be
different from the number of runner vanes.
zGuide Vanes
z Runner Vanes
≠ Integer
Design of the Guide Vanes
How to choose the number of vanes
• The number of guide vanes has to be
different from the number of runner vanes.
zGuide Vanes
z Runner Vanes
≠ Integer
Design of the Guide Vanes
How to choose the guide vane maximum
angle α0 at full load
α o = 4 ⋅ (− 4 ⋅ Ω 2 + 13 ⋅ Ω + 1)
α
Design of the Guide Vanes
Overlapping of the guide vanes
Design of the Guide Vanes
Number of guide vanes
Number of Guide Vanes
30
28
26
24
22
20
18
16
0,0
0,2
0,4
0,6
0,8
1,0
Speed Number
1,2
1,4
1,6
Design of the Guide Vanes
Diameter of guide vane shaft
1,7
Diameter Ratio D0/D1
D1
D0
= 0,29 ⋅ Ω + 1,07
D1
1,6
1,5
1,4
D2
1,3
1,2
1,1
1,0
0,0
0,2
0,4
0,6
0,8
Speed number
1,0
1,2
1,4
1,6
Statement of Problem
Givens
Net head…………..….201.5m
Flow rate…………...2.35m3/s
Turbine speed….1000rpm
Work out
Design of Runner, Guide vanes,
Stay vanes, Spiral casing andDraft tube
Compare
Design output with Jhimruk turbines
Design Considerations
Calculations - based on hydraulic principles only,
Thickness of runner blades - neglected,
Designs of components - done for the best efficiency point,
Other several assumptions - mentioned locally in calculations.
Design of Guide Vanes
Chosen:
Nos. of guide vanes z =20
1,7
Diameter of guide vane axis
D0 = D1 (0.29 Ω+1.07)
Ω = ω⋅ Q
−−
−−
2 ⋅π ⋅ n
ω=
60
.
ω
= 1.66
−−
Q = Q / 2 gH
Q = 0.037
Ω = ω⋅ Q
Ω = 0.319
−−
−−
D0 = 1.011m
D
D0
= 0,29⋅ Ω +1,07
D1
1
1,5
1,4
D
1,3
2
1,2
1,1
ω
= ω / 2 gH
−−
−−
Diameter Ratio D0/D1
1,6
−−
1,0
0,0
0,2
0,4
0,6
0,8
Speed number
1,0
1,2
1,4
1,6
Design of Guide Vanes
Tangential and meridional velocities
Assuming gap between runner and guide vanes
5% of the runner inlet diameter.
C u ( gvo ) =
C m ( gvo ) =
Cu 1
1 . 05
C u ( gvo ) = 39 . 64 m / s
Q
( z ∗ t gvo) 

[
∗
−
π
B1 
D gvo
Cos (α 1)

.
C m ( gvo ) = 8.58m / s
tan α(gvo) = Cm(gvo)/Cu(gvo)
α(gvo) = 12.210
Value of αgvo in full guide vane open position is selected 180
Design of Guide Vanes
L = 204
Velocities at outlet, axis and inlet of
guide vanes
(depending on varing values of α and t)
Outlet
Axis
Inlet
agvo=12.210 tgvo=5mm
Cm(gvo) = 8.582 m/sec
Cu(gvo) = 39.65 m/sec
Cgvo = 40.56 m/sec
agvc=28.040 tgvc=30mm
Cm(gvc) = 9.521m/sec
Cu(gvc) = 17.87 m/sec
Cgvc = 20.25 m/sec
agci=340 tgvi=15mm
Cm(gvi) = 7.864 m/sec
Cu(gvi) = 11.65 m/sec
Cgvi = 14.06 m/sec
.
Cgvi=14.06 m/sec
Cm(gvi)=7.86 m/sec
Cu(gvi)=11.65 m/sec
Cgvc=20.25 m/sec
Cm(gvc)=9.521 m/sec
Cu(gvc)=17.87 m/sec
Cgvo=40.56 m/sec
Cu(gvo)=39.65 m/sec
Cm(gvo)=8.58 m/sec
Design of Guide Vanes
.
Guide vane at Design
Position = 12.21°
Guide vane at Max. open
Position = 18°
Guide vane at closed position
Runner inlet
(Φ 0.870m)
Guide vane outlet for designα)
(Φ 0.913m)
Closed
Max.
Opening
Position
Guide vanes
Water
particle
Water from
spiral casing
R a d i a l
R guide
a d ivanes
a l
runner
runner guide vanes
v i e w
v i stay
e wvanes
and
and stay vanes